Modern Problems in Construction: Selected Papers from MPC 2021 (Lecture Notes in Civil Engineering, 287) 3031127021, 9783031127021

Table of contents :
Contents
The Mathematical Model of a Multilayer Wall of a Plate Heat Exchanger
1 Introduction
2 Materials and Methods
3 Results
4 Discussion
5 Conclusion
References
Comparing Embedded Technologies for Aerial Geomatics Using Unmanned Aerial Systems
1 Introduction
2 Methods
3 Results
3.1 LiDAR vs Photogrammetry
3.2 Difference Between RTK and PPK Drones
4 Conclusions
References
Bulldozer Sensing Technique for the Purpose of Automation for Bulldozer’s Workflow
1 Introduction
2 Method
3 Results
3.1 Mathematical Model to Estimating the Position of Blade Cutting Edge
3.2 System Configuration for the Purpose of Automation for bulldozer's Workflow
4 Conclusions
References
The Study of the Stability of a Statically Indeterminate Double-Span Frame Made of Timber, Considering the Degrading Conditions of Support
1 Introduction
2 Methods
3 Results and Discussion
4 Conclusion
References
Variant of the Formula for the Design Resistance of the Soil for Slab Foundations
1 Introduction
2 Methods
2.1 Methods for Assigning the Design Resistance of the Base of Slab Foundations
2.2 Variant of the Design Resistance of the Base of Slab Foundations
3 Results
4 Conclusions
References
A New Method of Checking the Stability of the Frame Structural System in the Event of an Emergency Situation Associated with the Draft of One of the Columns
1 Introduction
2 Methods
2.1 Testing
3 Results and Discussion
4 Conclusion
References
Aging and Long-Term Mechanical Impact in the Durability of Wood Composites
1 Introduction
2 Methods
3 Results and Discussion
3.1 Example
4 Conclusions
References
Analysis of the Implemented Project for the Construction of a High-Rise Building Between Two Low-Rise Buildings in the Zone of Maximum Mutual Influence of Their Foundations
1 Introduction
1.1 Survey
1.2 Engineering and Geological Situation in the Construction Area.
2 Methods
3 Results and Discussion
4 Conclusions
References
The Effect of Reinforced Concrete for Crack Resistance and Rigidity Based on Mechanics of Fracture Under Bending with Torsion
1 Introduction
2 Methods
3 Results
4 Conclusions
References
Numerical Modeling of Steel Joints
1 Introduction
2 Method
3 Results and Discussion
4 Conclusions
References
Component Compositions of Mixtures of Cement-Wood Heat-Insulating Material
1 Introduction
2 Methods
3 Results and Discussion
4 Conclusions
References
Experimental Establishment of the Required Number of Experiments Per Point in Determining the Thermal Fluctuation Constants of the Generalized Zhurkov for the Method of Direct Temperature and Control Point
1 Introduction
2 Methodology
3 Results
4 Conclusion
References
Effects of Basalt Fibre on the Strength of Concrete
1 Introduction
2 Methods
3 Results and Discussion
4 Conclusions
References
Experimental Studies of the Effect of Reinforcement on the Bearing Capacity of a Sandy Base Under Static and Cyclic Loading
1 Introduction
2 Materials and Methods
3 Results and Discussion
4 Conclusions
References
The Effect of Long-Term Storage on the Compressive Strength Along the Grain of Pine Timber
1 Introduction
2 Materials and Methods
3 Results and Discussion
4 Conclusion
References
Fast-Hardening Slag-Alkaline Heat-Resistant Aerated Concrete of Increased Heat Resistance with Additives of Fly Ash of Novocherkassk SDPP
1 Introduction
2 Materials and Methods
2.1 Materials
2.2 Methods
3 Results and Discussion
4 Conclusions
References
The Temperature Control Methods for the Heat Supply System of Buildings and Structures
1 Introduction
2 Experimental
3 Results
4 Discussion
5 Conclusion
References
The Mathematical Model of Automated Control of Heat Flows in the Supply and Exhaust Ventilation System
1 Introduction
2 Materials and Methods
3 Results
4 Conclusion
References
Prognostic Approach to Sustainable Development in Urban Planning Analysis of Green Areas
1 Introduction
2 Materials and Methods
3 Evaluation
4 Conclusions
References
The Construction Technique Employed in the Erection of the Masonry Dome of the Mosta Rotunda, Malta
1 Introduction
2 The Mosta Rotunda
2.1 Background
2.2 The Building Team
2.3 Construction of the Dome
3 The Mġarr Church as a Case Study
3.1 Background
3.2 Relevance
4 Final Comments
References
Optimization of the Routing of Heating Networks
1 Introduction
2 Methods
3 Results and Discussion
4 Conclusions
References
Hydrodynamics of the Flow of an Ideal Liquid When It Flows Out of the Bottom Hole of a Parabolic Tank
1 Introduction
2 Methods
3 Results and Discussion
4 Conclusions
References
Experimental Study of Deformation of Flexible Timber Compressed Elements Under Environmental Loading
1 Introduction
2 Methods of Experimental Research. Designs of Experimental Frames
2.1 Stability of the Compressed Elements of the Experimental Frames During Subsidence of the Base of the Middle Rack
2.2 Investigation of the Influence of the Negative Properties of the Heaving Soil on the Stability of the Compressed Elements of the Experimental Frames
3 Conclusions
References
Hardening Mode and Foam Concrete Properties
1 Introduction
2 Materials and Methods
3 Results and Discission
4 Conclusions
References
Two-Dimensional Temperature Fields of Variants Design of a Double-Skin Facade Structure
1 Introduction
2 Methods
2.1 Heat Engineering Calculation of Option 1. Gas Silicate Masonry (400 mm)
2.2 Thermal Engineering Calculation 2 Options. Double Facade, Buffer Zone Width 200 mm
2.3 Heat Engineering Calculation 3 Options. Double Facade, Buffer Zone Width 400 mm
2.4 Heat Engineering Calculation 4 Options. Double Facade, Buffer Zone Width 600 mm
2.5 Heat Engineering Calculation of the 5th Option. Double Facade, Buffer Zone Width 800 mm
2.6 Heat Engineering Calculation of the 6th Option—Double Facade, Buffer Zone Width 1000 mm
3 Results and Discussion
4 Conclusions
References
Using Linear Equations in Calculating the Heat Capacities of Gases
1 Introduction
2 Materials and Methods
3 Results
4 Conclusions
References
Method for Analysis of Hierarchies for Development of Gas Industry Enterprises
1 Introduction
2 Methods
3 Results and Discussion
4 Conclusions
References
Improving the Reliability of Gas Distribution Networks
1 Introduction
2 Methods
3 Results and Discission
4 Conclusions
References
Determination of Homogeneous Foundation’s Settlement Based on the Integral Estimation Method
1 Introduction
2 Methods
3 Results
4 Conclusions
References
The Use of Ash and Slag Waste in the Production of Building Materials
1 Introduction
2 Methods
3 Results and Discussion
4 Conclusions
References
Thermofluctuation Constants of Built-Up Section Wooden Beams Without Special Ties
1 Introduction
2 Methodology
3 Results and Discussion
4 Conclusion
References

Citation preview

Lecture Notes in Civil Engineering

Nikolai Vatin Ekaterina Gennadyevna Pakhomova Danijel Kukaras   Editors

Modern Problems in Construction Selected Papers from MPC 2021

Lecture Notes in Civil Engineering Volume 287

Series Editors Marco di Prisco, Politecnico di Milano, Milano, Italy Sheng-Hong Chen, School of Water Resources and Hydropower Engineering, Wuhan University, Wuhan, China Ioannis Vayas, Institute of Steel Structures, National Technical University of Athens, Athens, Greece Sanjay Kumar Shukla, School of Engineering, Edith Cowan University, Joondalup, WA, Australia Anuj Sharma, Iowa State University, Ames, IA, USA Nagesh Kumar, Department of Civil Engineering, Indian Institute of Science Bangalore, Bengaluru, Karnataka, India Chien Ming Wang, School of Civil Engineering, The University of Queensland, Brisbane, QLD, Australia

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Nikolai Vatin · Ekaterina Gennadyevna Pakhomova · Danijel Kukaras Editors

Modern Problems in Construction Selected Papers from MPC 2021

Editors Nikolai Vatin Peter the Great St. Petersburg Polytechnic University Saint-Petersburg, Russia

Ekaterina Gennadyevna Pakhomova Faculty of Construction and Architecture Southwest State University Kursk, Russia

Danijel Kukaras Faculty of Civil Engineering University of Novi Sad Subotica, Serbia

ISSN 2366-2557 ISSN 2366-2565 (electronic) Lecture Notes in Civil Engineering ISBN 978-3-031-12702-1 ISBN 978-3-031-12703-8 (eBook) https://doi.org/10.1007/978-3-031-12703-8 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Contents

The Mathematical Model of a Multilayer Wall of a Plate Heat Exchanger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vladimir Yezhov, Natalia Semicheva, Aleksey Burtsev, and Nikita Perepelitsa

1

Comparing Embedded Technologies for Aerial Geomatics Using Unmanned Aerial Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alexey Bulgakov, Daher Sayfeddine, Wen-der Yu, and Natalia Buzalo

13

Bulldozer Sensing Technique for the Purpose of Automation for Bulldozer’s Workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alexey Bulgakov, Georgii Tokmakov, and Wen-der Yu

21

The Study of the Stability of a Statically Indeterminate Double-Span Frame Made of Timber, Considering the Degrading Conditions of Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alexey Bulgakov, Ksenia Dubrakova, Dmitrii Mishin, and Klaus Holschemacher

31

Variant of the Formula for the Design Resistance of the Soil for Slab Foundations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alexey Bulgakov, Jens Otto, Iuliia Matvienko, and Oksana Osipova

39

A New Method of Checking the Stability of the Frame Structural System in the Event of an Emergency Situation Associated with the Draft of One of the Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alexey Bulgakov, Klaus Holschemacher, Ksenia Dubrakova, and Pavel Maltsev

49

Aging and Long-Term Mechanical Impact in the Durability of Wood Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Semyon Mamontov, Aleksandr Mamontov, Pavel Monastyrev, Sergey Emelianov, and Ekaterina Pahomova

57

v

vi

Contents

Analysis of the Implemented Project for the Construction of a High-Rise Building Between Two Low-Rise Buildings in the Zone of Maximum Mutual Influence of Their Foundations . . . . . . Ali Al−Bukhaiti, Vektor Ledenev, Yaroslav Savinov, and Olga Umnova The Effect of Reinforced Concrete for Crack Resistance and Rigidity Based on Mechanics of Fracture Under Bending with Torsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vladimir Kolchunov Numerical Modeling of Steel Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Anastasia Alekseeva, Nina Buzalo, Jens Otto, and Alexey Bulgakov

67

79 97

Component Compositions of Mixtures of Cement-Wood Heat-Insulating Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 N. V. Kuznetsova and A. D. Seleznev Experimental Establishment of the Required Number of Experiments Per Point in Determining the Thermal Fluctuation Constants of the Generalized Zhurkov for the Method of Direct Temperature and Control Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 A. V. Erofeev and T. I. Gorokhov Effects of Basalt Fibre on the Strength of Concrete . . . . . . . . . . . . . . . . . . . 123 Alexey Bulgakov, Klaus Holschemacher, Iuliia Davidenko, and Vladimir Bredikhin Experimental Studies of the Effect of Reinforcement on the Bearing Capacity of a Sandy Base Under Static and Cyclic Loading . . . . . . . . . . . . 129 Vasiliy M. Antonov, Ibtehal Abdulmonem Al-Naqdi, Pavel V. Monastyrev, Sergey Emelianov, and Ekaterina Pakhomova The Effect of Long-Term Storage on the Compressive Strength Along the Grain of Pine Timber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Alexander Masalov and Viktoriia Solodilova Fast-Hardening Slag-Alkaline Heat-Resistant Aerated Concrete of Increased Heat Resistance with Additives of Fly Ash of Novocherkassk SDPP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 Sergey Emelianov, Alexey Bulgakov, Jens Otto, Arsen Avakyan, Kirill Protsenko, Gennadiy Skibin, and Alexander Mikheev The Temperature Control Methods for the Heat Supply System of Buildings and Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Dmitry Tyutyunov, Aleksey Pihtin, and Aleksey Borodin

Contents

vii

The Mathematical Model of Automated Control of Heat Flows in the Supply and Exhaust Ventilation System . . . . . . . . . . . . . . . . . . . . . . . . 177 Dmitry Tyutyunov, Alexey Burtsev, Nikita Perepelitsa, and Alexander Burtsev Prognostic Approach to Sustainable Development in Urban Planning Analysis of Green Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 Yana Zolotukhina, Ekaterina Prokshits, Semyon Podvalny, and Yulia Pashchenko The Construction Technique Employed in the Erection of the Masonry Dome of the Mosta Rotunda, Malta . . . . . . . . . . . . . . . . . . . 201 Lino Bianco Optimization of the Routing of Heating Networks . . . . . . . . . . . . . . . . . . . . 215 Ekaterina Kopytina, Evgeny Umerenkov, Anastasia Chuikina, Natalya Petrikeeva, and Dmitry Chudinov Hydrodynamics of the Flow of an Ideal Liquid When It Flows Out of the Bottom Hole of a Parabolic Tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 Boris Kumitskiy, Svetlana Tul’skaya, Viktor Morozov, Egor Aralov, and Victor Budnikov Experimental Study of Deformation of Flexible Timber Compressed Elements Under Environmental Loading . . . . . . . . . . . . . . . . 233 Alexey Bulgakov, Jens Otto, Sergei Dubrakov, and Denis Shvartcer Hardening Mode and Foam Concrete Properties . . . . . . . . . . . . . . . . . . . . . 247 Mikhail Novikov, Andrey Goykalov, Elvira Semenova, and Vladislav Pakhomov Two-Dimensional Temperature Fields of Variants Design of a Double-Skin Facade Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 Angelina Tkachuk, Elina Umerenkova, Andrey Goikalov, and Mikhail Novikov Using Linear Equations in Calculating the Heat Capacities of Gases . . . . 271 Dmitry Kitaev, Svetlana Tulskaya, and Vitaly Zhmakin Method for Analysis of Hierarchies for Development of Gas Industry Enterprises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 Galina Martynenko, Vitaly Zhmakin, Vera Ukhlova, Vladimir Lukyanenko, and Maria Popova Improving the Reliability of Gas Distribution Networks . . . . . . . . . . . . . . . 291 Kuznetsov Sergey, Kolosov Aleaxander, and Kuznetsova Galina

viii

Contents

Determination of Homogeneous Foundation’s Settlement Based on the Integral Estimation Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 Ksenia Dubrakova, Alexey Bulgakov, and Thomas Bock The Use of Ash and Slag Waste in the Production of Building Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 Olga Sotnikova, Elena Zhidko, and Sergei Tenyachkin Thermofluctuation Constants of Built-Up Section Wooden Beams Without Special Ties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 A. V. Erofeev and P. V. Monastyrev

The Mathematical Model of a Multilayer Wall of a Plate Heat Exchanger Vladimir Yezhov , Natalia Semicheva , Aleksey Burtsev , and Nikita Perepelitsa

Abstract The aim of the research is a mathematical simulation of an experimental installation of a complex multilayer plate heat exchanger with deep heat recovery from waste gases and ventilation emissions with simultaneous heating of the supply air and generation of thermoelectricity. The methods of computer simulation in the Solidworks software environment with the Flow simulation package is considered. Applying mathematical tools, the study presents a method for intensifying the heat transfer coefficient by turbulators installed on a ribbed flat wall. As a result of the study, an optimal mathematical and computer model of a complex multilayer plate heat exchanger was obtained. Keywords Heat exchanger · Heat · Heat transfer · Thermal conductivity · Turbulence · Thermoelectricity · Effectiveness

1 Introduction The process of development of the fuel and energy and housing and utilities sectors of the Russian Federation is associated with the problems of energy conservation and environmental safety. The basics of calculating heat transfer through a layer of substances are presented in [1–3]. The solutions of the problems of heat transfer through multilayer plates, through the layers of substances bounded by walls with heat release in the layer are presented and analyzed. The cases of cylindrical and spherical layers are considered. The authors substantiated the use of cleaning and disposal systems as well as the use of devices and complexes of heat exchange equipment in [3]; the study allows reducing the temperature of waste gases and ventilation emissions, improving environmental safety of the territory adjacent to the installation site of such equipment by treatment of harmful impurities of nitrogen, carbon oxides, sulfur, ash, etc.

V. Yezhov (B) · N. Semicheva · A. Burtsev · N. Perepelitsa Southwest State University, 94, 50 Let Oktyabrya ul., Kursk 305040, Russia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_1

1

2

V. Yezhov et al.

As described in [4, 5], the use of filter-absorber allows cleaning flue gases and ventilation emissions from harmful impurities of nitrogen and carbon oxides, sulfur, and the use of a thermoelectric generator provides cooling of gases entering the atmosphere and generating electricity. The implementation of the solutions proposed in [6–8] makes it possible to increase the efficiency of heat production units, as a result, to ensure a steady increase in the efficiency of obtaining and distributing heat energy from the source to the final consumer. The economic growth of the country, the improvement of the ecological situation and the safety of the population’s lives are closely related to this. The authors considered the basic provisions of the theory of heat transfer, the main types of heat transfer: heat conduction, convection, thermal radiation; highlighted the processes of combined heat transfer; showed their role in the operation of power and heat technological devices and installations in [9, 10]; the authors provided general information about the processes of heat transfer in chemical equipment; considered the mechanisms of heat transfer by heat conduction, radiation and convection as well as with complex heat transfer in [11–13]. In order to increase the effectiveness of ventilation units, this study proposes to use a complex plate heat exchanger which allows reducing hazardous substances emissions and low-grade heat in order to protect the environment and improve environmental safety of the area adjacent to the building [14–16].

2 Materials and Methods To achieve the above objectives, an experimental setup (Fig. 1a) consisting of two blocks was developed; the blocks are a complex multilayer plate heat exchanger (MPHE) and an absorber. The MPHE block (Fig. 1b) is made in the form of ribbed heat-conducting sections (Fig. 2a), into which semiconductor Peltier thermoelectric elements are mounted (Fig. 2b). To intensify the heat transfer process, cylindrical turbulators were installed on the ribs.

3 Results Air heated in the heater was used as a heat carrier. Air taken by a fan from the laboratory room was used as a working medium. Experiments on the study of heat transfer with counterflow in the thermoelectric section were carried out for the modes consisting of a number of fixed velocities and air flow rates using the experimental setup. A number of experimental studies were carried out using the MPHE installation, shown in Tables 1, 2 and 3.

The Mathematical Model of a Multilayer Wall …

3

2

1 3

7 5 4

6 (а)

(b)

Fig. 1 Experimental setup: a – general view; b – channels of hot air flow; 1 – heat exchanger body; 2 – filter absorber; 3 – air heater; 4 – fan; 5 – cooling radiator; 6 – turbulators; 7 – conductive tracks

2 1 1

2

3

4

5

(а)

(b)

Fig. 2 A section of the experimental setup: a – a view of the cold side; b – a view of the hot side; 1 – a cooling radiator; 2 – turbulators; 3 – conductive tracks; 4 – a thermal gasket; 5 – Peltier element Table 1 Experiments without installed turbulators and thermal gaskets Operation mode

Hot air inlet temperature

Hot air outlet temperature

Cold air inlet temperature

Cold air outlet temperature

Section 1 voltage, mV

Total voltage, mV

Section 1 current, mA

Total current, mA

Hot flow rate, m/s

Cold flow rate m/s

1

50

47

20

21

10.8

24

0.96

0.96

2.4

1.9

2

70

65

20

21

25.2

60

2.76

2.76

2.7

1.9

3

90

87

20

21

57.6

142.8

5.52

5.52

3.0

1.9

4

V. Yezhov et al.

Table 2 Experiments without installed turbulators but with installed thermal gaskets Operation mode

Hot air inlet temperature

Hot air outlet temperature

Cold air inlet temperature

Cold air outlet temperature

Section 1 voltage, mV

Total voltage, mV

Section 1 current, mA

Total current, mA

Hot flow rate, m/s

Cold flow rate m/s

1

50

42

20

21

27

60

2.4

2.4

2.4

1.9

2

70

58

20

21

63

150

6.9

6.9

2.7

1.9

3

90

75

20

22

144

357

13.8

13.8

3.0

1.9

Section 1 voltage, mV

Total voltage, mV

Section 1 current, mA

Total current, mA

Hot flow rate, m/s

Cold flow rate m/s

Table 3 Experiments with installed turbulators Operation mode

Hot air inlet temperature

Hot air outlet temperature

Cold air inlet temperature

Cold air outlet temperature

1

50

29

20

23

90

200

8

8

1.9

1.2

2

70

41

20

23

210

500

23

23

2.4

1.2

3

90

60

20

24

480

1,020

46

46

2.7

1.2

In experiment No. 3 (Table 3), turbulators with a pitch of 40 mm along the length, made in the form of cylindrical surfaces, with a diameter of 8 mm and a length of 15 mm, were installed on aluminum radiators. As can be seen from these experiments, the installation of turbulators significantly intensified the heat transfer process by increasing the temperature difference between the cold and hot sides from 28 to 30.5 °C (+ 8.93%) from 3.55 to 4.11 W/m2 ·°C (+ 13.4%); simultaneously, there is an increase in electricity generation both per unit of thermoelectric element and the installation as a whole. For example, the total voltage of the installation without turbulators and thermal gaskets was 24 mW; after the installation of gaskets voltage increased by 2.5 times up to 60 mV; installed turbulators contributed to its increase up to 200 mV. The installation of thermal gaskets improves the contact between the semiconductor Peltier elements and the cooling radiators, which made it possible to increase temperature difference and, as a result, electricity generation. In addition, the hot air temperatures at the outlet of the heat exchanger decreased significantly from 47 to 29 °C, and as a result, the temperatures of cold air entering the laboratory room increased from 21 to 24 °C. At the same time, a decrease in the hot flow rate from 2.4 to 1.9 m/s is noted, which takes place due to the increased aerodynamic resistance. In order to simulate the flows inside the MPHE experimental installation, a computer model shown in Figs. 3a and 3b was developed. We used the Solidworks software with the Flow simulation package version 2018. The purpose of the simulation was to determine the areas of turbulence and vorticity of flows along the direction of hot and cold air movement.

The Mathematical Model of a Multilayer Wall …

5

Fig. 3 Computer model of the experimental setup

The following boundary conditions obtained in the course of experimental studies were adopted: – Mass air flow at the inlet is G1 = 2.4 kg/s; at the outlet, it is G2 = 1.9 kg/s; – Hot air temperature at the inlet is 80 °C; at the outlet, it is 60 °C; – Cold air temperature at the inlet is 20 °C; at the outlet, it is 23 °C. The simulation results are shown in Figs. 4, 5 and 6. Turbulence zones are highlighted in yellow. Vorticity areas of cold flow are marked in blue. Figure 6 shows vorticity areas of the cold flow.

Fig. 4 Flows turbulization simulation: a – cold air flow; b – hot air flow

6

V. Yezhov et al. 2

1

2 1

2

1

1 2

2

1

1

Fig. 5 Turbulence zones simulation: 1 – cold flow turbulence zone; 2 – hot flow turbulence zone 0.001

Turbulence scale [m]

0.00088 0.00076 0.00064 0.00052 0.0004

0

0.05

0.1

0.15 Length [m]

0.2

0.25

0.3

Fig. 6 The diagram of the scale of turbulence

4 Discussion As a result of simulation, the following dependencies were obtained: – The curves of the scale of turbulence (Fig. 6) which characterizes the effective size of the moving gas volumes, in which at a given time interval all the particles have the same movement velocities shown in blue; in this case some volumes of gas, in addition to the average velocity, have disordered, rapidly changing additional velocities – pulsation velocities shown in red.

The Mathematical Model of a Multilayer Wall …

7

For a turbulent boundary layer, under the previously adopted restrictions, the 2 2 ∂ x +  y ∂ yy = ν ∂∂ y2x and equations of energy x ∂∂tx +  y ∂∂ty = a ∂∂yt2 , motion x ∂ ∂x continuity

∂x ∂x

+

∂ y ∂y

= 0 can be written as follows:

     ∂t ∂  ∂t ∂t + y = λ + λg ρcρ x ∂x ∂y ∂y ∂y      ∂x ∂  ∂x ∂x ρ x + y = μ + μg ∂x ∂y ∂y ∂y

(1) (2)

∂ y ∂x + =0 ∂x ∂y

(3)

– Turbulent viscosity coefficient (Fig. 7) which characterizes the superposition of the pulsating motion, shown in red, on the averaged motion, shown in blue, due to the increase in resistance to flow (increase in viscosity) – the averaged viscosity motion. Streamlines of averaged motion are permeable to pulsating motion. This transfer determines the turbulent friction between the layers in the averaged motion. The turbulent viscosity arising in the near-wall regions of the turbulent flow decreases as it approaches the wall due to the effect of the turbulence scale. According to Prandtl: l = χy

(4)

Turbulent viscosity coefficient [Pa*s]

0.01

0.008

0.006

0.004

0.002

0

0

0.05

0.1

0.15 Length [m]

Fig. 7 The diagram of the turbulent viscosity coefficient

0.2

0.25

0.3

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For turbulent (pulsating) heat transfer, it can be written: qt = ρcρ  y [t(y1 ) − t(y2 )] = −ρcρ  y l 

dt dy

(5)

Turbulent transfer in terms of the quantity of motion can be described as follows: st = −ρ y [x (y1 ) − x (y2 )] = ρ y l 

dx dy

(6)

Substituting expression (4) into Eq. (5), we obtain:   qt = −ρcρ l  dy

2  dx

  dt   dy

(7)

Based on (6), the turbulent transfer with the inclusion of the proportionality coefficient will be as follows:  st = ρl 2

dx dy

2 (8)

where l is the length of the mixing path – the distance from the layer of the initial volume to the mixing layer, in this case enthalpy transfer is carried out along with the mass of the liquid. – The diagram of the kinetic energy of the turbulent flow (Fig. 8) characterizes the average kinetic energy per unit mass of the flow associated with vorticity in the turbulent flow, i.e. characterized by a change in the RMS velocity pulsations: E=

1 2 x +  y2 + z2 2

(9)

As well as by the degree of turbulence:  Tu =

2E = 302



1 2 +  2 +  2  x y z 3 0

(10)

– the diagram of turbulence dissipation (Fig. 9) characterizes the transition of part of the flow energy (kinetic energy) into the energy of disordered processes – heat. To take into account the process of energy dissipation, a function that can be derived

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9

Turbulent energy [J/kg]

200 160 120 80 40 0

0

0.05

0.1

0.15 Length [m]

0.2

0.25

0.3

Fig. 8 The diagram of turbulence energy

from the Navier–Stokes equations using the Reynolds averaging procedure is introduced: εε = −2ν 2

∂ 2 u i ∂ 2ui ∂ xk ∂ xm ∂ xk ∂ xm

(11)

As can be seen from Fig. 9, the system can be called dissipative, because the energy of ordered motion decreases over time due to the transition to heat as a result of thermal conductivity.

turbulence energy dissipation [W/kg]

500000 400000 300000 200000 100000 0

0

0.05

0.1

Fig. 9 The diagram of turbulence dissipation

0.15 Length [m]

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Further, the obtained dependences (1)–(11) are used in the equations of the heat flow through a ribbed flat wall: Q = qh = Fh

t 1 − t2 1 Fh α1 F1

+

δ  Fh λ F1

+

1 α2

= kh (t1 − t2 )

(12)

and the equations of heat flow through a cylindrical rod: qh = α(t1 − t2 ) =

qυ r υ qυ r υ → Q = qh Fh = 2πr0 l = qυ πr02 l 2 2

(13)

The obtained computer simulation data, the diagrams of the scale of turbulence (Fig. 6) and the turbulent viscosity coefficient (Fig. 7) in particular indicate that in the process of movement, part of the flow has the same velocities, while some volumes of gas have disordered, rapidly changing additional velocities, the so-called pulsating nature of the flow, due to the increase in resistance to flow (increase in viscosity) – the viscosity of the averaged movement due to the use of turbulators in the form of cylindrical surfaces. The diagram of the kinetic energy of the turbulent flow (Fig. 8), which characterizes the average kinetic energy due to the change in the RMS velocity fluctuations indicates a gradual dissipation of turbulence (Fig. 9) as a result of the transition of the flow energy into heat due to thermal conductivity.

5 Conclusion As a result of the study, mathematical equations for the dependence of turbulent heat transfer to the quantity of motion were obtained, which will subsequently serve in solving differential equations of convective heat transfer and determining the optimal method for intensifying the coefficient of heat transfer through a ribbed wall with cylindrical swirlers installed on it.

References 1. Metallidou CK, Psannis KE, Egyptiadou EA (2020) Energy efficiency in smart buildings: IoT approaches. IEEE Access 8:63679–63699. https://doi.org/10.1109/ACCESS.2020.2984461 2. Sadeghi HM, Babayan M, Chamkha A (2020) Investigation of using multi-layer PCMs in the tubular heat exchanger with periodic heat transfer boundary condition. Int J Heat Mass Transf 147:118970. https://doi.org/10.1016/J.IJHEATMASSTRANSFER.2019.118970 3. Arasteh H, Mashayekhi R, Ghaneifar M, Toghraie D, Afrand M (2020) Heat transfer enhancement in a counter-flow sinusoidal parallel-plate heat exchanger partially filled with porous media using metal foam in the channels’ divergent sections. J Therm Anal Calorim 141(5):1669–1685. https://doi.org/10.1007/S10973-019-08870-W

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4. Fu Z, Liang X, Li Y, Li L, Zhu Q (2021) Performance improvement of a PVT system using a multilayer structural heat exchanger with PCMs. Renew Energy 169:308–317. https://doi.org/ 10.1016/J.RENENE.2020.12.108 5. Siavashi M, Talesh Bahrami HR, Aminian E (2018) Optimization of heat transfer enhancement and pumping power of a heat exchanger tube using nanofluid with gradient and multilayered porous foams. Appl Therm Eng 138:465–474. https://doi.org/10.1016/J.APPLTHERM ALENG.2018.04.066 6. Neagu AA, Koncsag CI, Barbulescu A, Botez E (2016) Estimation of pressure drop in gasket plate heat exchangers. Ovidius Univ Ann Chem 27(1):62–72. https://doi.org/10.1515/AUOC2016-0011 7. Duan L, Cao Z, Yao G, Ling X, Peng H (2017) Visual experimental study on residence time of particle in plate rotary heat exchanger. Appl Therm Eng 111:213–222. https://doi.org/10. 1016/J.APPLTHERMALENG.2016.09.087 8. Vafajoo L, Moradifar K, Hosseini SM, Salman BH (2016) Mathematical modelling of turbulent flow for flue gas-air Chevron type plate heat exchangers. Int J Heat Mass Transf 97:596–602. https://doi.org/10.1016/J.IJHEATMASSTRANSFER.2016.02.035 9. Zhu X, Haglind F (2020) Relationship between inclination angle and friction factor of chevrontype plate heat exchangers. Int J Heat Mass Transf 162:120370. https://doi.org/10.1016/J.IJH EATMASSTRANSFER.2020.120370 10. Gusew S, Stuke R (2019) Pressure drop in plate heat exchangers for single-phase convection in turbulent flow regime: experiment and theory. Int J Chem Eng. https://doi.org/10.1155/2019/ 3693657 11. Kapustenko P, Klemeš JJ, Arsenyeva O, Fedorenko O, Kusakov S, Bukhkalo S (2020) The utilisation of waste heat from exhaust gases after drying process in plate heat exchanger. Chem Eng Trans 81:589–594. https://doi.org/10.3303/CET2081099 12. Matsegora O, Arsenyeva O, Kapustenko P, Zorenko V, Solovey L (2018) A generalized mathematical model of the fouling formation on the heat transfer surface in non-dimensional view and its application for plate heat exchangers design. Bull Natl Tech Univ “KhPI” Ser: Innov Res Students’ Sci Work 0(40):28–32. https://doi.org/10.20998/2220-4784.2018.40.05 13. Tovazhnyanskyy L, Arsenyeva O, Perevertaylenko O, Kusakov S, Vasilenko A, Arsenyev P, Yuzbashyan A (2019) Investigation of heat transfer and pressure drop in waved-form channels of panel-plate heat exchangers. Bull Natl Tech Univ “KhPI” Ser: Innov Res Students’ Sci Work 0(21):10–14. https://doi.org/10.20998/2220-4784.2019.21.02 14. Ezhov V, Semicheva N, Tyutyunov D, Burtsev A, Perepelitsa N (2021) Version of a mathematical model of purge ventilation system with a complex recuperative heat exchanger. J Appl Eng Sci 19(1):246–251. https://doi.org/10.5937/JAES0-30068 15. Yezhov VS, Semicheva NE, Tyutyunov DN, Burtsev AP, Perepelitsa NS, Burtsev AP (2021) Mathematical model for automated heat flow control of an energyefficient ventilation system. Proc Southwest State Univ 25(1):38–52. https://doi.org/10.21869/2223-1560-2021-25-1-38-52 16. Yezhov V, Semicheva N, Burtsev A, Perepelitsa N (2021) Experimental calculation of the main characteristics of thermoelectric EMF source for the cathodic protection station of heat supply system pipelines. In: Advances in intelligent systems and computing, AISC, vol 1259, pp 225–237. https://doi.org/10.1007/978-3-030-57453-6_19

Comparing Embedded Technologies for Aerial Geomatics Using Unmanned Aerial Systems Alexey Bulgakov , Daher Sayfeddine , Wen-der Yu , and Natalia Buzalo

Abstract Two widely used technologies for remote sensing and aerial geomatics missions, LiDAR and photogrammetry, have been analyzed. The deployed drones have been also classified into two major groups: real-time and post processing kinematic. The post-processing kinematic is less error and risk-prone due to the less mandatory communication lines between the satellite, the drone and its station and the Continuously Operating Reference Stations. It has been shown that the challenge of the vulnerability of drones to the GPS signal loss can be overcome by visual odometry. The obtained results can be used for various flight mission tasks in many industry branches. Keywords Optical odometry · Photogrammetry · Geomatics · Unmanned aerial systems · LiDAR · Real-time kinematic · Post-processing kinematic · Remote sensing

1 Introduction The applications of geomatics within the engineering as well as in academic works have increased rapidly over the last decades. The exploration of the geomatics and its swift expansion have also introduced additional problems to look at in terms of standardization, quality assurance and proper correlation with impacted scientific fields. Spatial analysis has proven to be important in all disciplines. We can clearly see that the modern world is depending on the geomatics at least in five major A. Bulgakov (B) Southwest State University, 50 let Oktyabrya St. 94, 305040 Kursk, Russia e-mail: [email protected] D. Sayfeddine · N. Buzalo South-Russian State Polytechnic University, Prosveshcheniya St. 132, 346428 Novocherkassk, Russia e-mail: [email protected] W. Yu Chaoyang University of Technology, Jifeng East Road 168, 41349 Taichung, Taiwan e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_2

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fields: advanced smart farming, mining sector surveys, smart cities planning, supreme contribution for autonomous driving research sector and visualization of our everchanging surrounding environment [1]. Geomatics has directly and positively impacted precision agriculture. The use of the navigation systems allows to increase the production and improve the yield per field as seeding, harvesting and fertilization are carried out much more efficiently [2]. More advanced technologies in the agriculture field are being deployed such as the hyperspectral imaging [3]. In mining, the importance of the surveys dates as back as the third century BCE since the use of the diopter, an astronomical and surveying instrument. The dial, an inaccurate compass was used by the Romans to explore the Rio Tinto copper mines in Spain. By the middle of the nineteenth century, more sophisticated devices were being produced. Theodolites were equipped with telescopes, spirit levels and vertical quadrants, enabling the measurement of vertical angles. Theodolites made surveying more accurate by measuring fixed points in the mine, so it became no longer necessary to rely on the compass. The development in sensor technologies has lifted the mine surveys to another level. Today, mine surveying is an exact science using modern theodolites (total stations) [4–6], laser terrestrial scanners, aerial photogrammetry and satellite imagery. In construction field, aerial surveys are used extensively either for planning, monitoring or detection tasks [7]. The data collected by the remotely piloted aircraft systems applied for geomatics are grouped as follows: aerial high-definition images, telemetry and remote sensing, measurements related to the visible and invisible wavelengths analysis of the electromagnetic spectrum such as infrared, gamma and ultraviolet radiation and multi-echo laser scanning with LiDAR.

2 Methods To start, we will devise how each of these technologies works. LiDAR is a technology based on emission of a laser beam that will be reflected to the source allowing to determine the distance to a certain object. The working principle is similar to a Doppler radar allowing to describe the LiDAR as an active sensor as it emits energy rather than detecting is. In contrast, photogrammetry is considered passive [6]. The main operating principle consist of acquiring measurements using parallax, the effect whereby the position or direction of an object appears to differ when viewed from different positions, e.g., through the viewfinder and the lens of a camera. Hence, this technology is based on a very demanding modeling process of image geometry and its acquisition.

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3 Results 3.1 LiDAR vs Photogrammetry From results perspective, the ultimate result by applying a LiDAR technology is 3D point cloud consisting of a set of data point with determined coordinates representing a reflection of an object [5]. Its density depends on the characteristics of the sensor (scanning frequency and repetition rate), as well as the flight parameters. Assuming that the scanner pulses and oscillates at a fixed rate, the density of the scatter plot will depend on the flight altitude and the speed of the vector. As such, it highly depends on the flight control system accuracy and very sensitive to the choice of the drone itself (fixed-wing, rotorcraft). The 3D point cloud shape is monochrome, as the LiDAR only captures colorless dots. This implies additional challenges on the identification and recognition of the captured object and mandate a post-processing step to overlay coloring layer based on the reflectivity or elevations. An example of 3D point cloud results before and after colorization is depicted in Fig. 1. As for the photogrammetry, the ultimate results are various depending on the assigned task. However, we can differentiate the following: – Raw capture images. This is a straightforward task consisting of storing the captured image from the camera without any post-processing activities. – Orthoimage. This is a corrected image acquired by the aerial asset (drone, satellite). The correction is required to fit a uniform scale across the image. Such process is called orthorectification. – Digital elevation model specifically the digital surface model (DSM). This is a 3D computer graphic model representing the elevation data of a terrain, widely used in GIS applications and especially for landscaping. – Colored 3D point clouds.

Fig. 1 Computer simulation of monochrome 3D point cloud

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By analyzing the aforementioned, we can quickly reach to a conclusion that photogrammetry is a better approach. However, this fact is very superficial as more in-depth analysis is required from application point of view. Since LiDAR uses laser beam, it is possible to penetrate layers such as vegetation, in contrast to the photogrammetry, making LiDAR very ideal for terrain surface modeling unlike photogrammetry which is ideal for the surface modeling. As a consequence, LiDAR is in-facto technology to acquire and model fine objects especially modeling the power lines, telecommunication towers. Since the result is monochrome and it is based on emission-reflection scheme, operating the LiDAR does not require light and can be deployed any time during day of night. In contrast, the surface model allows for better visualization and can be used primarily for inspection tasks, however, it cannot be used to detect fine objects. It should be stated that the 3D point cloud generated by the photogrammetric procedure differentiate from the one achieved by the LiDAR as the first is more suitable for objects with lower level of geometric details but where visualization is essential (due to the advantage of RGB colored 3D point cloud versus monochrome point cloud). This comparison leads us to reflect about the precision of the results. As per definition, precision in topography has two components: the relative and absolute. The first characterizes the position of the objects with reference to each other’s while the latter studies the obtained position of the object with reference to its real position on Earth-bod axis. Based on what we stated earlier about the dependency of the LiDAR point cloud model accuracy on the flight stability, this sensor is always used in combination with inertial unit and Global Navigation Satellite System or GNSS receiver. This allows to pair the point cloud model with information about the position, rotation and motion of the scanned object. Ideally, this combination achieves a relative precision between 1–3 cm. The absolute precision is achieved by using a minimum of 2 Ground Control Points GCP and other points for verification purposes [8–17]. If the required accuracy is not satisfied by the GNSS, advanced real-time kinematic/post-process kinematic (RTK/ PPK) positioning systems can be deployed. RTK/PPK drones will be discussed in the following paragraphs. Pertaining to the photogrammetry, the accuracy level is comparable with the LiDAR 1–3 cm, however, setting up the stage to allow obtaining the needed results requires significant experience in selecting the equipment, planning the flight mission and processing the data. This is explained by the image overlap percentage needed for the photogrammetry 60–90% compared to 20–30% for the LiDAR. Photogrammetry can make use of GCPs and RTK/PPK systems as well. For post-processing time, it should be noted that the acquiring of LiDAR point cloud is very fast and can consume several minutes compared to highly demanding computing power and time resources for the photogrammetry, which analyzes many more gigabytes of images and theoretically the processing time is 5 to 10 times the time consumed for data acquisition. On the other hand, the LiDAR point cloud require additional classification (since the dots does not offer visualization) hence the need of expensive post-processing software.

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3.2 Difference Between RTK and PPK Drones Post-processed and real-time kinematic are not new technologies. They have been used widely in surveys for many years in order to enhance the accuracy of the data acquired vide satellite systems. With the recent increase in drones’ deployments in surveying tasks, these technologies are used to correct the drone mapping data discarding the need to have Ground Control points, hence, improving the independence of the drone from ground operators. It should be noted that both technologies are used to improve the absolute precision of the data sets. The differentiating factors in deploying and selecting any of these technologies depend on the environmental conditions at first place. In fact, factoring in the differences leads to optimal results in terms of time and money. A RTK drone is an aerial robot equipped with GNSS RTK receiver that gathers data from satellites and stationary emitters on ground so the correct the image locations in real-time regime while flying. This technology is strictly related to global trajectory planning, when the pose of the UAV is identified while flying minimizing the dependence from the ground operators. The challenges faced by the RTK drone is due to the satellite data itself, playing the assisting role, as this data is error prone due to tropospheric delays. Later, the data from the ground emitter is taken into consideration to correct the errors of the satellite improving the accuracy data set corrected by the satellite from 1 m to few centimeters range. This leads us to consider the need to have extremely reliable connection between the three components of the RTK System. In fact, RTK system require 4 constant communication line to achieve a result, as shown in Fig. 2. In Fig. 2, line (1) represents the connection between the satellite and the drone, line (2) between the satellite and the GNSS ground station or the Continuously Operating Reference Stations (CORS) network, line (3) between and GNSS or CORS and the drone control station and finally between the drone and its station. As such, the reliability of the signals and the presence of obstacles (lead lining, faraday frequency

Fig. 2 RTK Real time kinematic [18]

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cages) can present a huge challenge to RTK system that should be considered prior to deployment of the drone. In contrast, the PPK drone is equipped with GNSS PPK receiver that gathers data from satellites and logs it for retrieval after the flight. At first glance, the error from the satellite data sets exists same as in the RTK variant and corrected by the GNSS station. However, in the PPK variant the connection between the GNSS to the drone station nor the latter to the correction data communication are required as all data are logged in later on. The only needed reliable connections are between the satellites and GNSS/CORS network, and the line between the satellites and drone (not to forget between the drone and its controlling station) allowing to decrease the needed communication line as shown in Fig. 3. That leaves us to the following pros and cons comparison between RTK and PPK is shown in Table 1.

Fig. 3 PPK Post-processed kinematic [18]

Table 1 RTK vs PPK RTK

PPK

PROS

Immediate correction Real time high-accuracy repositioning No GPS is needed

Less connection lines are needed Allows virtual reference station instead (VRS) of CORS Simpler setups in comparison with RTK Mission beyond telemetry is applicable ost flight corrections are allowed

CONS

Mission success depends of several technologies which makes the system error-prone Short-term signal loss implies heavy abortive works Mission beyond telemetry range is not achievable No post flight correction is available

Does not support real-time high accuracy positioning

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On the other hand, the stereo-visual odometry is more accurate, it uses additional camera pair to incrementally correct the pose of the drone. The algorithm is divided into five steps: – Rectification of the images. This step removes distortion from the images. – Feature extraction. By detecting local features in each image using well known algorithms such as Harris, SURF and SIFT. – Stereo feature matching. By matching features of the same object taken from left and right angles. – Temporal video matching. By correctly identifying the left and right image pertaining to a certain object with interval [t; t−1]. – Incremental pose recovery. This is achieved by triangulating the studied features in the previous points. The stereo-visual odometry is challenged by very crowded scenes, making feature extraction and temporal matching very demanding task.

4 Conclusions To summarize, two widely used technologies for remote sensing and aerial geomatic missions: LiDAR and photogrammetry. Each of these technologies has its inherent advantages and challenges. The success of the flight mission depends strictly on the certain expertise to study the terrain and flight circumstances. While LiDAR can detect fine objects and swiftly generate point cloud set points, its output is monochrome and difficult to visualize, however, it is perfect for terrain surface model missions. The photogrammetry is more sophisticated, generate 2D and 3D models in RGB format, but cannot identify fine objects such us power and telecommunication lines. It requires additional setting up expertise as well. Both the methods as expensive in some part of their algorithms considering the computational power, generating and correcting software. LiDAR uses lasers to perform measurements, while photogrammetry is based on analysis of captured images. These two technologies can of course be combined to allow even more precise measurements. The deployed drones have been also classified into two major groups: real-time and post processing kinematic. We have come to a conclusion that post-processing kinematic is less error and risk-prone due to the less mandatory communication lines between the satellite, the drone and its station and the CORS station. We have also studied the vulnerability of both the drones to the GPS signal loss and indicated that this challenge can be overcome by visual odometry and identified two special types of the odometry: monocular and stereo-visual, analyzed their pros and cons.

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References 1. Geiger A, Lenz P, Urtasun R (2012) Are we ready for autonomous driving? the kitty vision benchmark suite. In: Proceedings of the conference. IEEE, pp 3354–3361 2. Van Wagen W (2017) Advancing smart farming thanks to geospatial technologies. https://www.gim-international.com/content/arti-cle/advancing-smart-farming-thanks-togeospatial-technologies 3. Hagen N, Kudenov M (2013) Review of snapshot spectral imaging technologies. Opt Eng 52(9):24 4. Rick J (2018) Total station. In: Varela S.L.L (ed) The encyclopedia of archaeological sciences. John Wiley & Sons, Inc, Hoboken 5. Boulch A, Le Saux B, Audebert N (2017) Unstructured point cloud semantic labeling using deep segmentation networks. 3DOR 2:7 6. Remondino F (2011) Heritage recording and 3d modeling with photogrammetry and 3D scanning. Remote Sens 3(6):1104–1138 7. Bulgakov A, Emelianov S, Sayfeddine D (2015) Aerial inspection of buildings facades using quadrotor. Procedia Eng 85:140–146 8. Bulgakov A, Bock T, Sayfeddine D, Fares A (2020) Generation of orthomosaic model for construction site using unmanned aerial vehicle. In: Proceedings of the ISARC 2020, pp 900– 904 9. Bertram T, Bock T, Bulgakov A, Evgenov A (2014) Generation the 3D model building by using the quadcopter. In: Proceedings of the 31st international symposium on automation and robotics in construction and mining, 9–11 July 2014. University of Technology, Australia, pp 778–783 10. Bulgakov A, Evgenov A, Weller C (2015) Automating high-rise structures inspection using quadrotor. Procedia Eng 123:101–109 11. Eker R, Alkan E, Aydin A (2021) Accuracy comparison of UAV-RTK and UAV-PPK methods in mapping different surface types. Eur J Forest Eng 7(1):12–25. https://doi.org/10.33904/ejfe. 938067 12. Fernández-Hernandez J, González-Aguilera D, Rodríguez-Gonzálvez P, Mancera-aboada J (2015) Image-based modelling from Unmanned Aerial Vehicle (UAV) photogrammetry: an effective, low-cost tool for archaeological applications. Archaeometry 57:128–145 13. Giordan D, Manconi A, Remondino F, Nex F (2017) Use of unmanned aerial vehicles in monitoring application and management of natural hazards. Geomat Nat Haz Risk 8:1–4 14. Gomez C, Purdie H (2016) UAV- based photogrammetry and geocomputing for hazards and disaster risk monitoring – a review. Geoenviron Disast 3:23 15. Zhang H, Aldana-Jague E, Clapuyt F, Wilken F, Vanacker V, Van Oost K (2019) Evaluating the potential of post-processing kinematic (PPK) georeferencing for UAV-based struture-frommotion (SfM) photogrammetry and surface change detection. Earth Surf Dyn 7:807–827 16. Cledat E, Jospin LV, Cucci DA, Skaloud J (2020) Mapping quality prediction for RTK/PPKequipped micro-drones operating in complex natural environment. J Photogram Remote Sens 167:24–38 17. Tushev S, Sukhovilov B (2017) Photogrammetric system accuracy estimation by simulation modelling. In: 2017 International conference on industrial engineering, applications and manufacturing (ICIEAM), pp 1–6. https://doi.org/10.1109/ICIEAM.2017.8076464 18. https://wingtra.com/ppk-drones-vs-rtk-drones

Bulldozer Sensing Technique for the Purpose of Automation for Bulldozer’s Workflow Alexey Bulgakov , Georgii Tokmakov , and Wen-der Yu

Abstract A new configuration of the system is proposed to automate the bulldozer workflow without the use of a laser. A mathematical model has been developed to assess the position of the cutting edge of the blade. A method for collecting data on the parameters of the working process in dynamics for identifying the working process of a bulldozer, assessing the statistical characteristics of disturbing influences and confirming the mathematical models of the working processes of the bulldozer is demonstrated. The advantages of this method are the high accuracy in assessing the parameters of the working process and the ability to use the information obtained in the bulldozer automation system. The approach can potentially be used to automatically control various types of construction machines for earthworks without the use of laser sensors. Keywords Mechatronic system · Bulldozer blade · Leveling control · Sensing system

1 Introduction There is a very common laser control system (Fig. 1) is a high-tech earthmoving installation that allows you to perform work without the usual use of building poles and leveling rods. The use of laser technology, components of the used machinery, and a remote laser transmitter allows the machine control system to obtain accurate A. Bulgakov (B) Southwest State University, 50 let Oktyabrya St. 94, 305040 Kursk, Russia e-mail: [email protected] G. Tokmakov South-Russian State Polytechnic University, Prosveshcheniya St. 132, 346428 Novocherkassk, Russia e-mail: [email protected] W. Yu Chaoyang University of Technology, Jifeng East Road 168, 41349 Taichung, Taiwan e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_3

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Fig. 1 Laser inspection system for construction equipment

Fig. 2 Possible relief

information about the terrain, displaying it on the display located in the cab, and, ultimately, setting the blade in the desired position. Laser inspection systems are designed for use in a wide range of ground handling construction jobs where stringent requirements are put forward for technological tolerances and increased labor productivity. Laser control systems allow you to perfectly fit into the work of leveling the ground on objects with a flat surface and slopes - which is often found in industrial facilities, during the construction of business buildings, and in residential construction (Fig. 2). A laser transmitter located outside the cab on a tripod emits a thin beam of light that rotates 360° to create a slope calculation above the construction site. The cutting edge, located above the surface to be graded, is controlled by a signal sent from an electrically driven tripod that automatically locates the laser receiver within 1.5 mm of the center of the laser beam [1].

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The display located in the cab of the bulldozer shows information about the position of the knife blade relative to the ground, at the same time showing where the construction site should be excavated, and where - dumping. The automatic control of the position of the blade allows precise adjustment of the cutting edge. Depending on the content of the correcting signals, the hydraulic double control valve automatically raises or lowers the blade edge, constantly holding it in the desired position, which ensures precise work execution and guarantees an optimal level of labor productivity [2]. The advancement of GLONASS/GPS technology and its use in construction helps to reduce labor requirements and helps heavy equipment operators to complete the work order under the design solution, through careful excavation and filling of soil, it can achieve material cost savings [3]. Such a control system is a high-tech machine control system and a dialogue control system that allows you to reach the proper level of earthwork without elevation marks and leveling rails. Digital design inputs, manuals, and instructions in the dozer’s automatic blade position control system help you achieve the desired result faster, more efficiently, and economically, with lower operating costs. The system can be applied in a wide range of construction earthworks - from excavation and filling of soil with high labor productivity to finishing planning with narrow tolerances. General design, backfilling of the planes of one or two slopes, the formation of construction bedding, base plate, parking lot, road and highway construction planning can be carried out on the onboard computer using the system [4].

2 Method When carrying out the research, the method of analytical and simulation modeling of the technological process of soil profiling by a bulldozer was applied. Decomposition of the bulldozer workflow model; for those sub-processes where analytical modeling is possible based on knowledge of the relationships between the parameters of the bulldozer, analytical dependencies are obtained. Modeling goals: – highlighting the main subsystems in the structure of the bulldozer and the connections between them; – development of analytical and simulation models of workflow elements, their inclusion in the general structure of the model;

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The general structure of the model of the process of soil grading by a bulldozer has been developed, due to the goals of managing work processes.

3 Results 3.1 Mathematical Model to Estimating the Position of Blade Cutting Edge Observations [5] show that quite often while designing a face its roughness is progressing, reaching a size at which the control over the workflow is lost. In this case, the operator has to align the face deliberately, trying to ensure its “tranquil” profile that allows doing excavation works smoothly, without frequent control system switching and reducing the dozer’s operating speed that causes a slowdown and shows inferiorities of the blade control system. Obviously, if the control system operates in the antiphase towards deviations of the tractor frame with sufficient accuracy, the initial face roughness will not evolve and will be gradually cut. One of the most likely causes of the opposite phenomenon observed in practice, is the disparity between the velocity of the dozer Vp and actual conveying speed of the working body Vot required in certain areas Si of the digging operating cycle, where i – is the number of the speed change Vot . Speed ratio depends on the dozer’s geometrical dimensions (Fig. 3) and its control system. Mathematical model of the dozer’s movement on a straight line tracking (frame alignment) is built using the Lagrange equations of the 2nd kind, under the assumption that the contribution to the dynamics of the drive gears and a track is small, compared with the contribution of the remaining parts of the dozer. S1

Fig. 3 Dozer’s geometrical dimensions

+Vot

S1

S2 G C2

Vot= 0 S2

Bulldozer Sensing Technique for the Purpose of Automation …







d ∂T − dt ∂ x˙  d ∂T − dt ∂ ϕ˙

∂T ∂x ∂T ∂ϕ

= Qx , = Qϕ ,

25

(1)

Mathematical model of the dozer’s movement on a straight line tracking frame. where kinetic energy:   1  ˙ 2 lc2 ϕsin(ϕ) ˙ 2 + 2xl ˙ + 2 Jc2 ϕ˙ 2 + 21 σhx x˙ 2 T = 21 m1 x˙ 2 + 21 m2 x˙ 2 + (l2 lc2 ϕ) ˙ 2 ϕsin(ϕ) ˙ + (l2 ϕ) ˙ 2 + 2xl + 21 σ hxi2z ϕ˙ 2 ;

(2)

generalized forces acting on a dozer: Qx = −σhgl2 sin0 + FT − Fs , Qϕ = −(m2 lc2 + sxh)gl2 cosϕ + M;

(3)

m1 – tractor mass; m2 – blade frame mass; σ – soil surface density; FT machine pulling power; Fs ground cutting resistance; h – depth of the soil cutting; lc2 – center of the blade mass; iz - gyration radius of the dumping soil. ˙ ˙ ¨ + m2 l2 lc2 ϕ˙ 2 cosϕ + σhx˙ 2 + σhx¨ m1 x¨ + m2 x¨ + m2 l2 lc2 ϕsinϕ  x2+ σh2 xl22 ϕsinϕ 1 1 1 2 2 2 2 (4) ¨ + σhxl2 ϕsinϕ  + σhxl2 ϕ˙ cosϕ − 2 σhx˙ − 2 σhiz ϕ˙ − 2 σh x˙ + l2 ϕ˙ ˙ 2 ϕsinϕ + 2xl ˙ = −σhgl2 sinϕ + FT − Fcopp . 2 ¨ 2 lc2 sinϕ + m2 xl ˙ 2 lc2 cosϕϕ˙ + Jc2 ϕ¨ + σhx˙ l 22 ϕ˙ + σhxl22 ϕ¨ ϕ¨ + m2 xl m2 l22 lc2 ˙ 2 sin0 + σhxl2 cosϕϕ˙ + σhxi ˙ 2z ϕ˙ + σhxi2z ϕ¨ − m2 xl ˙ 2 lc2 ϕcosϕ + σhxl ˙ ˙ 2 ϕcosϕ ˙ = −(m2 lc2 + σxh)gl2 cosϕ − (m2 lc2 + σxh)gl2 cosϕ + M. − σhxxl

(5)

The system (1) solution allows getting the differential Eqs. (4) and (5) that describe the dozer’s movement on a straight line track, and determining control actions through the parameters of the machine in areas Si of the digging operating cycle as the coefficients ai in the dependence Vot = ai Vp . Such a dependence is typical for dozers with a single-motor drive with a hard pump hydraulic drive connection to the motor shaft. At the beginning of digging (Fig. 3), the frame of the tractor makes a strictly forward movement over a distance of S1 + S2 without hesitation relatively its mass center. The blade cutting edge in the area S1 dives into the soil to a depth equal to a predetermined cutting thickness h. Thus, the control action a1 may be determined by the formula: a1 =

30itr m l2 pr k Fz ipr C5 n

(6)

where itr , ipr - tractor transmission and hydraulic pump ratios; n - number of hydraulic cylinders; m - fluid mass in the hydraulic cylinders;

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Fig. 4 The movement the dozer “dives” in the drawn buttonhole

-Vot

G

S3

In the area S2 the movement is made with a2 = 0 until the mass center of the tractor won’t move to the buttonhole edge. On further movement the dozer “dives” in the drawn buttonhole (Fig. 4), so in the area S3 it is necessary to lift the blade at a rate of Vot , determined by the coefficient a3 :

  aV t aC1 C1 +V t a3 = tgb e −1 . (7) 1+ C1 + V t The area S3 ends after the dozer’s back gear hits the edge of the face and reverse alignment of tractor frame starts. Length of the alignment area is S4 ≈ S1 . Obviously, during this period it is necessary to start dropping the blade. The a4 determines the rate of dropping the blade in the given area: a4 =

3 S1

(C4 + S3 + Vt)2

.

(8)

To implement control actions ai = f (Si , t, h) the dozer must be equipped with a vertical blade control system.

3.2 System Configuration for the Purpose of Automation for bulldozer’s Workflow The purpose of the experimental studies was to compare the performance of a bulldozer equipped with modernized and serial working equipment. The main goal of the experiment is to collect the data needed to identify the bulldozer’s workflow [5, 6]. The sensors connection scheme is shown in Fig. 5. As a result of measurements, signals P(t), v(t) and digging depth l(t) were obtained, used to identify the working process of the bulldozer.

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27

Fig. 5 Connection scheme of sensors

To collect experimental information on the parameters of the working process of the bulldozer in dynamics, laboratory studies of the process of cutting the soil with a flat knife during movement were carried out. The automated collection of the values, of the speed v and the resistance force movement P was carried out. Experimental signals are used to identify the workflow using neural network mathematical models. Experimental data loaded simulation model. Simulation tasks: – to single out the main sub-systems in bulldozer’s structure and interrelations b tween the sub-systems; – to develop analytic and simulation models for workflow elements and to include them into the general structure of the model. The structure meets the goals of workflow control. When moving soil by the bulldozer, it is necessary to utilize bulldozer’s traction capacity in full keeping the nominal traction value; when surfacing, the altitudes of the right and left side of the blade are to correspond the design marks. The key element at the scheme (Fig. 6) shows the choice for the first or the second operational mode. At developing the models, we use mathematical apparatus of the random processes theory, transfer functions, table interpolation, numerical solution of algebraic equations and ordinary differential equations in the Cauchy form. Random changes in the coordinates of untreated soil surface, as well as normalized fluctuations in the resistance forces on the working organ, caused by the heterogeneity of the soil are highlighted among the disturbing effects on the working organ of the bulldozer from soil conditions. Disturbance cause unwanted vertical movement of the working organ

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Fig. 6 Verification system modeling surface

that affects both the coordinates and the change in the digging depth. Dependence of the blade position and dig depth from disturbances reflects the intricate relationship between the geometric parameters of the bulldozer in space. Loading conditions on the working organ are due to random variation in the dig depth and heterogeneity of soil properties. Soil digging process with bulldozer working organ is studied on the base of the finite element model of the soil mass, a mathematical model of random forces of resistance on the working organ being developed. The actual bulldozer velocity depends on the strength and the properties of the mover, transmission and the power unit. In its turn, disturbance parameters, movement of the working organ and the formation of stress depend on the velocity. Bulldozer drive model and mover interaction with the soil include engine model, mechanical and hydro mechanical transmission, as well as slipping. Control system regulator depending on the objectives, control algorithm and the incoming data from the bulldozer as a control object produces electrical signals to the electro- hydraulic distributors being part of the working organ hydro drive. Lifting or burying the blade is done to control either the pulling power, or the blade coordinates. After training the model, load the data into the on-board complex of the bulldozer to check the adequacy of the model. To evaluate the proposed system, two experiments were carried out: – Operator controlled without using an automatic system (Fig. 6a). – When controlling the operator using the developed system (Fig. 6b). After that, the results were compared. Thus, it can be noted that the system allows you to simulate a bulldozer digging surface with a deviation not exceeding 2 cm.

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29

4 Conclusions Input model signal, used for training, simulation and verification is presented in Fig. 7a. Adaptive learning for the model is stopped at time t = 9.5 s. Receiving at this moment a neural network model parameter values, modeled digging resistance force and bulldozer current velocity (Fig. 7b, 7c) are accomplished, as well as the forecast for another 0.5 s is developed [7–10]. Figure 7d shows the output of neural network models- pulling power of the bulldozer. In modeling and prediction of the neural network output is close to the experimental data only in the time interval of 7–10 s. This is due to a change in unmeasurable chip thickness, as well as the rapidly changing conditions of the mover clutch with the ground. Therefore, the parameters of the adaptive neural network model must be adjusted in real time. The accuracy of prediction of pulling power N(t) has been estimated; the average relative error being 14.7% on an interval from 7 to 10 s [7]. Identification Technique of bulldozer workflows and models obtained on its basis, are designed for use in the development of adaptive systems of automatic workflow management of bulldozer [11, 12]. For the formation of the control actions influencing the bulldozer, particularly electrical signals actuating control valves of hydraulic cylinders lifting and lowering

90

P(t) 80

m

P, кН kN

70 60 50

P(t)

40 30

0

1

2

3

4

a)

6

7

8

9

10

b)

v(t)

1,5

N(t)

100

1

kW N, кВт

v, м/с m/s

5

150

2

50

0,5

N(t)

v(t) 0

t, сs

0

1

2

3

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t, sс

5

6

7

8

9

10

0

0

1

2

3

4

t, сs

5

6

7

8

9

10

c) Fig. 7 Comparison of Bulldozer operational parameters obtained with the Model and actual operational parameters: a - Deepening Dozer Blade; b - Digging Resistance Force; c - Bulldozer Current Velocity; d - Bulldozer Pulling Power

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the working organ, the structure and algorithms of adaptive neural network controller have been designed.

References 1. Trimble Corporation. Civil Engineering and Construction, Grade Control for Dozers. On-line https://construction.trimble.com/products-and-solutions/grade-control-dozers, Accessed 2019 2. Komatsu Corporation. Intelligent Machine Control. On-line https://www.komatsu.eu/en/Kom atsu-Intelligent-Machine-Control, Accessed 2019 3. Roberts GW, Dodson AH, Ashkenazi V (1999) Global positioning system aided autonomous construction plant control and guidance. Autom Constr 8(5):589–595 4. Bulgakov A, Vakolyuk A, Glebov N, Bienkowski N (2017) A laser system for the control of the complex for the construction of mini tunnels. J Appl Eng Sci 4(15):467–470. https://doi. org/10.5937/jaes15-15457, http://aseestant.ceon.rs/index.php/jaes/article/view/15457 5. Krapivin DM, Nefedov VV, Tokmakov GE (2010) Mathematical model for the movement of mechatronischen devices for the intelligent building site. Mechatronik, Lik, Novocherkassk, pp 50–54 6. Bock T, Bulgakov A (2016) Planning of movements of building robots with speed optimization. J Rob Mechatron 2(28):158–161 7. Bulgakov A, Bock T, Tokmakov G (2015) Adaptive control of bulldozer’s workflows. In: 5th international construction specialty conference, Vancouver, 7–10 June 2015, pp 434–442 8. ROBO Industries Autonomous Machine Control System On-line http://www.aee.us.com/pagevideo.html. Accessed 2019 9. Yin G, He F, Li Z, Ling J (2020) Workspace description and simulation of a backhoe device for hydraulic excavators. Autom Constr 119:103325 10. Lee Y-S, Kim S-H, Seo J, Han J, Han C-S (2020) Blade control in Cartesian space for leveling work by bulldozer. Autom Constr 118:10326 11. Rutkovskij L, Pilinskij M (2004) Neural networks, genetic algorithms and fuzzy systems. Gorzachaza Liniza Telekom 12. Georgy ME, Chang LM, Zhang L (2005) Prediction of engineering performance: a neurofuzzy approach. J Constr Eng Manag 131(5):548–557

The Study of the Stability of a Statically Indeterminate Double-Span Frame Made of Timber, Considering the Degrading Conditions of Support Alexey Bulgakov , Ksenia Dubrakova , Dmitrii Mishin , and Klaus Holschemacher Abstract The object is to study the operability of the frame-rod system in case of sudden loss of stability of one of the racks. As a subject, a frame-rod structure made of timber is considered, when loaded, a degrading destruction of the middle rack occurs. A special place in this area is occupied by the problems of studying the stability of the equilibrium of objects, since very often the process of loss of stability develops almost at lightning speed and makes it impossible to evacuate people and take measures to prevent destruction. A critical analysis of the current state of the problem of stability of core structures made of timber is carried out, the criteria for the stability of statically indeterminate structural systems made of timber are determined. An experimental plan was developed, the framework under study was designed and tested. Based on the experimental data obtained, graphs of clock-type sensor readings were constructed, showing the dependence of the deformations of the frame racks on the load applied to the frame, as well as the behavior of deformations during the destruction of the support at a load close to critical. The analysis of experimental data with the determination of the value of dynamic load coefficients is carried out. A calculation algorithm was derived to determine the nature of the destruction of structural system elements and to evaluate the operation of the structure in extreme conditions. The stability criteria can show the condition of the building depending on the indicator of the coefficients of dynamic loads. Keywords Stability of timber systems · Dynamic loading coefficient · Bifurcation · Critical force · Deformations · CTS - Clock type sensors

A. Bulgakov (B) · K. Dubrakova · D. Mishin Southwest State University, 50 let Oktyabrya St. 94, 305040 Kursk, Russia e-mail: [email protected] D. Mishin e-mail: [email protected] K. Holschemacher Leipzig University of Applied Sciences, Karl-Liebknecht-St. 132, 04277 Leipzig, Germany e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_4

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1 Introduction Often, the factor of loss of stability of the entire structural system is one element or a small group of them. Therefore, a particularly important issue in solving the problems of stability of structural systems is the identification of the most dangerous elements or parts of the structure with low resistance to loss of stability. And if the features of deformation of rods and structural systems under short-term force loading are sufficiently investigated, then the features of bifurcation of timber structures under prolonged force loading remain practically unexplored. Meanwhile, such studies are important not only for studying the features of deformation of loaded elements of timber structures, solving traditional safety problems of structural systems, but also for assessing the residual life and protection of operated structural systems from progressive destruction caused by the loss of stability of core structures made of timber under force loading. In this regard, it is impossible not to mention such famous scientists as F.W. Zok [1], K.O. Dubrakova [2], K.A. Varenik, A.S. Varenik [3, 4], V.I. Travush [5], V.V. Galishnikova [6], P. Marti [7], D.A. Nethercot [8], C.L. Dos Santos [9], B. R. Ellingwood [10], M. Amini [11], D. V. Rosowsky [12], Y. Suzuki [13], A. J. M. Jorissen [14], John W. van de Lindt [15], D. Zonta [16], HB Xiong [17], J.P. Judd [18]. Issues related to the search for ways to improve the safety of buildings and structures will be relevant as long as a person builds. A special place in this area is occupied by the problems of studying the stability of the equilibrium of objects, since very often the process of loss of stability develops almost at lightning speed and makes it impossible to evacuate people and take measures to prevent destruction. The main purpose of the work is to develop stability criteria, as well as an algorithm for calculating a two-span frame of a frame type when changing the support scheme of one of the racks during operation. The stability criteria can show the condition of the building depending on the indicator of the coefficients of dynamic loads. In connection with the above research, a promising direction is to improve the algorithm for determining the critical parameters of the stability of structural systems made of timber, considering the deterioration of operating conditions under design and beyond-design impacts, the development of which contributes to reducing the number of operational accidents. A large number of researchers have been and are engaged in the issues of stability of rods and rod systems.

2 Methods The physical sign of stability of the equilibrium form is the behavior of the loaded structure when it deviates from the equilibrium position by a certain small amount, therefore, the compressive load at which the stability of the structure is lost is determined - the critical force of the Rcr , the coefficients of dynamic overloads are determined.

The Study of the Stability of a Statically Indeterminate Double-Span …

33

At the first stage, the type of bifurcation and the critical force for the pillars of the frame under study are determined. The calculation is performed according to the well-known rules of construction mechanics. The coefficients of the secular stability equation v are determined:  νi = li ×

Pi , (EI)i

(1)

where, l is the length of the rack; P is the critical force; E is the modulus of elasticity; I is the moment of inertia of the section of the racks. The coefficients of the free length of the racks μ are found by the following formula: μi =

π , νi

(2)

The critical force of the Rcr is determined by the formula: Pκ p =

ν2i × EI , 2 l0i

(3)

where, vi 2 is the coefficient of the secular equation; l2 0 i is the free length of the racks; E is the modulus of elasticity; I is the moment of inertia of the section of the racks. The work of the racks A is found according to the formula (4) and the type of bifurcation of the racks of the frame under study is determined. 1 Ai = (Mi × Zi ), 2

(4)

where, M is the bending moment; Z is the displacement. The minimum moment of inertia of the Imin racks is determined by formulas (5), (6). Ix =

b × h3 , 12

(5)

Iy =

h × b3 , 12

(6)

where, b, h are the dimensions of the cross-section of the rack. The coefficients of dynamic Kd reloads are calculated according to the formula: Kdi =

Mafterthedestruction Mbeforethedestruction

(7)

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3 Results and Discussion For the analysis of practical data, the installation of a frame-rod structural system was designed considering the change in the support scheme of one of the racks (Fig. 1). Clock-type sensors were used to analyze the measured deformations. Using these calculations, a stability criterion and algorithm for calculating frametype structures were obtained when changing the support scheme of one of the racks during operation, which allows determining the nature of the destruction of structural system elements and evaluating the work of the structure in extreme conditions. In the course of the study of the stability of statically indeterminate frame-rod structural systems made of timber, considering the degrading conditions of support, the following calculation algorithm was derived. At the first stage, we select the computational scheme of the investigated system, construct the basic system of the displacement method and the equivalent system of the displacement method, determine the degree of kinematic uncertainty n, calculate the coefficients of the secular stability equation vi, write the system of canonical equations and the determinant of the system of canonical equations, construct characteristic plots Mi, determine the coefficients rij . Next, we calculate the determinant of the system of canonical equations and the coefficient of the secular equation, in which the determinant of the system of canonical equations is closest to 0, we determine the coefficients of the free length of the racks μi and the free length of the racks l0 i , with the available values we find the critical force of the Rcr in general, we determine the displacement Zi , we construct the total plot M + Mf as the sum of the total diagram M and the cargo diagram Mf ; we determine the work of the racks Ai as a criterion of stability, we determine the type of bi-furcation and the value of the critical force of Rcr (Fig. 2). Using the proposed algorithm, a two-span frame was calculated considering the degrading conditions of support. For a frame with a rigid pinching of the supports, the critical force was determined for the extreme racks Rcr = 15.6EI = 421.2 kg., for the middle rack Rcr = 31.1EI = 839.85 kg.

Fig. 1 The scheme of redistribution of efforts

The Study of the Stability of a Statically Indeterminate Double-Span …

35

Fig. 2 Experimental frame

4 Conclusion For a frame with a hinge pinching of the middle support, the critical force was determined for the extreme pillars of the Rcr = 6.65EI = 179.5 kg., for the middle pillar of the Rcr = 15.04EI = 406.08 kg (Figs. 3 and 4). Calculate the critical force, determine the coefficients of dynamic loading for each node; Kd1 = 2.23, Kd2 = 1.83, Kd3 = 0.42, Kd4 = 0.31, Kd5 = 0.19. The practical coefficients of dynamic loading for each node are determined; Kd1 = 1, Kd2 = 1.11, Kd3 = 1.008, Kd4 = 1.15, Kd5 = 1.083. When the conditions of support of one of the frame-rod structure pillars degrade, its elements can move from passive bifurcation to active or vice versa, changing the critical parameters of the stability of the system in the whole.

Fig. 3 The main system of the displacement method

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Fig. 4 The main system of the displacement method

A calculation algorithm was derived that allows determining the nature of the destruction of structural system elements and evaluating the operation of the structure in extreme states. The results obtained can be useful in further design, and are considered to ensure greater stability of building structures when changing the support scheme of one of the racks during operation. The experimental data of this work will be used to study the stability of statically indeterminate rod systems made of timber under dynamic influences and to consider rod systems with a greater degree of kinematic or static in determinability. Changing the support scheme of one of the pillars of the frame-rod structural system does not affect the type of loss of stability of the compressed-curved rods, but affects the value of the critical force for such rods, reducing it. These changes are associated with an increase in the influence of the work of the transverse forces and moments (Fig. 5). The coefficients of dynamic reloading show the condition of the building; 0–1 normative technical condition, 1–1, 15 operable; 1–2 limited operable; more than 2 emergency condition of the building, operation is unacceptable. The scientific novelty of the research is; e, mm 200 100 0 -100

0

500

1000

P, Kg 2000

1500

-200 -300 -400 -500 -600

CTS1

CTS2

Fig. 5 Graph of clock-type sensor readings

CTS3

CTS4

CTS5

The Study of the Stability of a Statically Indeterminate Double-Span …

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1. A method for experimentally determining the coefficients of dynamic loading of a two-span timber statically indeterminate frame made of timber when changing the support scheme of one of the racks. 2. Stability criterion. 3. The algorithm of computational analysis and the results of a numerical study of the stability of a two-span timber statically indeterminate frame when changing the support scheme of one of the racks during operation.

References 1. Zok FW, Latture RM, Begley MR (2016) Periodic truss structures. J. Mech Phys Solids 96:184– 203. https://doi.org/10.1016/j.jmps.2016.07.007 2. Dubrakova KO, Dubrakov SV, Altuhov FV et al (2019) The buckling of the physically nonlinear frame-rod structural systems. IOP Conf Ser Mater Sci Engg. 698(2):022007. https://doi.org/ 10.1088/1757-899X/698/2/022007 3. Varenik KA, Varenik AS, Sanzharovskij RS (2018) Boltzmann principle of superposition in the theory of wood creep for deformations in time. IOP Conf Ser Mater Sci Eng 441(1):012057. https://doi.org/10.1088/1757-899X/441/1/012057 4. Varenik AS, Varenik KA (2014) Regarding creep of wood. Modern Prob Sci Educ 2:88. http:// www.science-education.ru/pdf/2014/2/429.pdf 5. Pyatikrestovsky KP, Travush VI, Pogoreltsev AA et al (2018) Development of structures from solid wood for objects of infrastructure. Int J Comput Civ Struct Eng 14(1):145–154. https:// doi.org/10.22337/2587-9618-2018-14-1-145-154 6. Galishnikova VV, Ignatiev VA (2006) Regular rod systems. In: Theory and methods of calculation. Volograd, VolgGASU. ISBN:5–98276–125–7 7. Marti P (2013) Theory of structures: fundamentals, framed structures, plates and shells. https:// doi.org/10.1002/9783433602638 8. Nethercot DA (2000) Frame structures: global performance, static and stability behaviour: general report. J Constr Steel Res 55(1–3):109–124. https://doi.org/10.1016/s0143-974 x(99)00080-2 9. Dos Santos CL, Morais JJL, de Jesus AMP (2015) Mechanical behaviour of wood T-joints. Experimental and numerical investigation. Frattura ed Integrità Strutturale, 9(31):23–37. https://doi.org/10.3221/IGF-ESIS.31.03 10. Ellingwood BR, Rosowsky DV (2004) Fragility assessment of structural systems in lightframe residential construction subjected to natural hazards. Structures 130:1921–1930. https:// doi.org/10.1061/40700(2004)119 11. Amini M, van de Lindt J (2013) Quantitative insight into rational tornado design wind speeds for residential wood-frame structures using fragility approach. J Struct Eng 140(7):04014033. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000914 12. Rosowsky DV, Ellingwood BR (2002) Performance based engineering of wood frame housing: fragility analysis methodology. J Struct Eng 128:32–38. https://doi.org/10.1061/(ASCE)07339445(2002)128:1(32) 13. Suzuki Y, Maeno M (2006) Structural mechanism of traditional wooden frames by dynamic and static tests. Struct Control Health Monit 13(1):508–522. https://doi.org/10.1002/stc.153 14. Jorissen AJM, Dorlijn J, Snijder HH (2016) Strength and stability of traditional timber frames. In Proceedings of the world conference on timber engineering, Vienna, Austria, pp 1–8. https:// pure.tue.nl/ws/files/52485118/jorisstr2016.pdf 15. van de Lindt JW, Pei S, Pryor SE, Shimizu H, Isoda H (2010) Experimental seismic response of a full-scale six-story light-frame wood building J Struct Eng 136(10):1262–1272. https:// doi.org/10.1061/(ASCE)ST.1943-541X.0000222

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16. Zonta D, Loss C, Piazza M, Zanon P (2011) Direct displacement-based design of glulam timber frame buildings. J Earthq Eng 15(3):491–510. https://doi.org/10.1080/13632469.2010.495184 17. Xiong HB, Liu YY (2016) Experimental study of the lateral resistance of bolted glulam timber post and beam structural systems. J Struct Eng 142(4):E4014002. https://doi.org/10.1061/(asc e)st.1943-541x.0001205 18. Judd JP, Fonseca FS, Walker CR, Thorley PR (2012) Tensile strength of varied-angle mortise and tenon connections in timber frames. J Struct Eng 138(5):636–644. https://doi.org/10.1061/ (ASCE)ST.1943-541X.0000468

Variant of the Formula for the Design Resistance of the Soil for Slab Foundations Alexey Bulgakov , Jens Otto , Iuliia Matvienko , and Oksana Osipova

Abstract The normative formula for calculating the design soil resistance for slab foundations linearly depends on the width of the foundation. With an increase in width, a moment may come when the design resistance exceeds the ultimate load on the base, which shows the incorrect application of the normative formula for slab foundations. In the new formula, the depth of the foundation is taken as the length characteristic. According to the research results, the new formula gives a more accurate value of the design resistance for a slab foundation, which does not exceed the ultimate pressure. Keywords Design soil resistance · Depth of foundation · Slab foundation · Strength condition

1 Introduction The stress components from the linear elasticity solution for a strip load with surcharge are substituted into the Mohr–Coulomb strength condition. At low intensities of the strip load P, the strength condition is not fulfilled (the yield function f < 0) and the soil medium is considered as if elastic (it is clear that not every prelimiting state is elastic). As the band load increases P to the load at which plastic deformations originate P1 , points appear under the edges of the load strip at which f = 0. The load P1 is called the Puzyrevsky load [5]. With a further increase in P, regions appear under the edges of the load strip, at the boundaries of these regions f A. Bulgakov (B) Southwest State University, 50 let Oktyabrya Street 94, 305040 Kursk, Russia e-mail: [email protected] J. Otto Technical University of Dresden, Mommsen Street 10, 01069 Dresden, Germany e-mail: [email protected] I. Matvienko · O. Osipova South-Russian State Polytechnic University, Prosveshcheniya Street 132, 346428 Novocherkassk, Russia © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_5

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= 0, and inside these regions f > 0, i.e. there are statically inadmissible stress fields inside the regions. These fantastic areas are called areas of destruction or “plastic” areas. The intensity of the strip load, corresponding to the penetration of “plastic” regions into the base to a depth of a quarter of the width of the load strip, is called the design resistance of the foundation soils R. R=

π (0, 25bγ + γ h + c · ctgφ) + γh ctgφ + φ − π2

(1)

The value of R and is proposed by the building rules 22.13330.2016 as the limit of loads at which the settlement of the foundation is allowed to be calculated by the method of layer-by-layer summation. Moreover, the non-exceeding of the average pressures Pav under the base of the foundation, the value of R began to be considered as a condition for calculating the bearing capacity. The issues of the adequacy of formula (1) were considered in [2], from which it is clear that the modernization of the formula is necessary. In the scientific literature, there is an opinion that the use of formula (1) for assigingthe design resistance of soil foundations of slab foundations is of little use. For example, A.V. Pilyagin and A.G. Safina in [3, 4] write that when applying formula (1) to large slab foundations, the value of the design resistance is greatly exaggerated. This conclusion is quite obvious, since according to formula (1), the value of R linearly depends on the width of the foundation b, increasing indefinitely with the growth of b. This is also evidenced by the research of D.M. Shapiro [1, 4] and Dyby V.P. [6, 17, 22]. Similarly, A.I. Osokin writes [7] that the calculation of the resistance according to the formula from the joint venture leads to an overestimation of the permissible load values and, as a consequence, the foundation works in the plastic deformation zone to a greater extent than is commonly believed. There are studies where, to clarify the value of the calculated soil resistance, the multilayer base [8] and the deformation anisotropy of soils [9] are taken into account. It should be noted that the concept of design soil resistance is Russian and is not used in other countries. But foreign works by Chen F.H. [10], Bhattacharya P., Kumar J. [11], Oh W.T., Vanapalli S.K. [12], Bolton M.D. [13], Vesic A.S. [14], Michalowski R.L. [15], Van Baars S. [18, 19], Michalowski R.L. [20], Zhu M. [21], Merifielda, R.S. [23], Lau C. K. [24], Nguyen D.L. [25] in which the development of “plastic” areas under the bottom of the foundation is investigated when it is loaded. Despite numerous studies, the problem of determining the design soil resistance for slab foundations has not yet been solved. Therefore, it is necessary to develop a method that makes it possible to obtain the design soil resistance applicable for slab foundations, which is consistent with experimental studies.

Variant of the Formula for the Design Resistance …

41

2 Methods 2.1 Methods for Assigning the Design Resistance of the Base of Slab Foundations The problem of determining the design resistance of the foundations of slab foundations does not have one solution. There can be both engineering proposals (as in A.G. Safina [16], and formulas derived on the basis of some hybrid soil foundation model. It is also possible to use the statistics of average pressures under slab foundations in realized projects to create a “practical” formula. If for the foundation under the column the restriction on R guarantees the stability of the foundation, then, apparently, for the slab foundation by limiting the load, the phenomenon of soil extrusion along the edge of the foundation should be prevented (Fig. 1). The extrusion pressure is determined by Prandtl’s formula (3), generalized in [17] for the strength condition (plasticity condition) in the form: σ3 = −C + Aσ1 P = Ae

π( A−1) √ 2 A

 q+

C A−1

(2)

 −

C A−1

(3)

Since formula (3) was obtained for a weightless soil, then (3) is the lower estimate of the unknown ultimate load. The possible design resistance of the base of slab foundations looks like this P = k Ae

π( A−1) √ 2 A

 q+

C A−1

 −

C A−1

where the coefficient k, less than one, is selected from the required safety factor.

Fig. 1 Extruding soil from under the slab foundation

(4)

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Fig. 2 Elastic half-space loaded with semi-infinite loads

2.2 Variant of the Design Resistance of the Base of Slab Foundations Let the main idea of the derivation of the design pressure be to limit the depth of penetration of the “limiting zones” into the base. We will follow the proven method of deriving formula (1), which is as follows. The solution of the linear theory of elasticity for a half-space loaded with a strip load with surcharge is substituted into the strength condition (2). The equation of the curve is obtained, at the points of which the condition f = 0 is fulfilled. Then the dependence between the intensity of the strip load P and the coordinate zmax of the deepest point of the curve is found. At zmax = 0, the Puzyrevsky load is obtained, and at zmax = 0.25b it from formula (1). In the described technique, we will make the following changes. We will not consider the width b. As a characteristic of the length, we will choose the depth of the foundation h (Fig. 2). We replace the solution for the strip load with the well-known solution for semi-infinite loads (5). In a weightless linearly elastic foundation under semi-infinite loads, a stress field arises: − 2θ + sin θ ) σr = −P + P−q 2π (π − 2θ − sin θ) σθ = −P + P−q (π 2π P−q τr θ = −P + 2π (1 + cos 2θ)

(5)

Note that the following rule is used in formulas (5) and in the following: compressive stresses are negative. Using the well-known formulas, we pass from the main stresses to the main stresses π  − θ + cos θ σ1 = −P + P−q π 2  (6) π − θ − cos θ σ3 = −P + P−q π 2

Variant of the Formula for the Design Resistance …

43

We add to the stresses (6) hydrostatic stresses from the own weight of the soil γ (h + z) and substitute them into the condition of the limiting state (2):   σ3 − γ (h + z) = −C + A σ1 − γ (h + z)

(7)

Let us express from Eq. (7) the quantity z z=

1 (−C − σ3 + Aσ1 ) − h (A − 1)γ

(8)

We will consider (8) as the equation of the boundary of the “destruction zone”. From the equation P −q P −q 1+ A dz =− + · sin θ = 0 dθ πγ πγ 1− A find θ = arcsin

1− A 1+ A

(9)

Substituting (9) in (6) and (7), we obtain the relationship between zmax and the intensity of the load P. P P − hγ 1 z (A − 1)γ γ π γ



√ π 1− A 2 A − arcsin − 2 1+ A 1− A

(10)

max

Solving Eq. (10) with respect to P, we find the expression for the critical loads Rπ =

−hγ K − π



C A−1

+ γ h + z max γ

π−K

 ,

(11)

where h is the depth of the foundation, γ is the specific gravity of the soil, zmax is the depth of penetration of the “limiting zones” into the base, A, C are the coefficients for the Mohr–Coulomb strength condition, K is the coefficient equal to: √ 1− A 2 A π − K = − arcsin 2 1+ A 1− A

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3 Results To determine the scope of the developed formula, consider an example. Example. Let us calculate the design soil resistance for a foundation with a variable base width b, a depth of h = 2 m, an angle of internal friction ϕ = 23°, specific adhesion c = 24 kPa, specific gravity of soil γ = 18.3 kN/m3 . We calculate the coefficients for the strength condition of the Coulomb-Mohr: A=

1+Sinφ 1−Sinφ

= 2.283 C =

2·c·Cosφ 1−Sinφ

= 72.52

We set the depth of penetration of “limiting zones” into the base (Fig. 3): z max = 0.5h = 1m We determine the calculated soil resistance by the proposed method: √ π 1− A 2 A − arcsin − = 4.328 2 1+ A 1− A  C  −hγ K − π A−1 + γ h + z max γ Rπ = π−K

K =

We calculate the calculated soil resistance for similar initial data according to formula (1), recommended by building rules 22.13330.2016 for a foundation with a changing base width from 1 to 40 m and summarize the calculation results in Table 1. For similar initial data, we calculate the limiting pressure according to the generalized Prandtl formula (3), which is equal to Pprandtl = 750.1 kPa. From Table 1, it can be seen that with a foundation width of 39 m, R > Prandtl, which shows the incorrect application of formula (1) for calculating slab foundations. If for the calculated example we build a graph of the dependence of the calculated soil resistance on the width of the foundation (Fig. 4), then it is possible to highlight the areas of

Fig. 3 Penetration scheme of the “limit zone” at the edge of the foundation

Variant of the Formula for the Design Resistance …

45

Table 1 Design soil resistance calculated by the normative method Foundation width, m

1

2

3

4

5

6

7

8

9

10

Design resistance of 295.3 307.5 319.6 331.7 343.8 355.9 368.0 380.1 392.2 404.4 soil R, kPa Foundation width, m

11

12

15

20

25

30

35

38

39

40

Design resistance of 416.5 428.6 464.9 525.5 586.1 646.6 707.2 743.5 755.6 767.8 soil R, kPa

Fig. 4 Dependence of the design resistance on the width of the foundation

application of the normative and proposed calculation method R. For the initial data from the example, the calculated soil resistance can be calculated using formula (1) to the width the soles of the foundation equal to 12 m, after which it is advisable to calculate according to the new formula (11), which does not depend on the width of the foundation.

4 Conclusions According to the research results, it can be concluded that the calculated soil resistance calculated for slab foundations according to formula (1) from building rules 22.13330.2016 has an overestimated value, in some cases approaching the ultimate pressure on the foundation, and sometimes even exceeding it. The derived formula (11) gives a more accurate value of the design soil resistance for slab foundations, since does not depend on the width of the foundation sole. When calculating according to the new formula, the value of the calculated soil resistance cannot exceed the limiting pressure calculated according to the generalized Prandtl formula. To calculate foundations with a small base width, you can use formula (1), and with an increase in the width of the foundations, when R according to building rules

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22.13330.2016 exceeds Rslab according to the derived formula, you can use formula (11), thus it is advisable to divide the scope of both formulas.

References 1. Shapiro DM (2015) Analytical and numerical linear calculations of shallow foundations bases. Vestnik PNRPU Constr Arch 4:5–18. https://doi.org/10.15593/2224-9826/2015.4.01 2. Bogomolov AN, Bogomolova OA, Ushakov AN (2021) Two approaches for determining areas of plastic deformation in a homogeneous base foundation. Constr Geotech 3(12):105–116. https://doi.org/10.15593/2224-9826/2021.3.11 3. Pilyagin AV (2007) On the question of determining the design resistance of anisotropic soils of foundations. In Pilyagin AV, Safina AG (eds) Russian Geotechnics - a step into the xxi century: works of the anniversary conference, dedicated to the 50th anniversary of romggif 2007, Moscow, vol II, pp 141–144 4. Pilyagin AV (2004) On the issue of determining the design resistance of foundations for various loading schemes. Izvestia KGASA 1(2):43–44 5. Shapiro DM, Gotman YA (2013) Elastoplastic design of beds for shallow foundations. Soil Mech Found Eng 4(50):158–163. https://doi.org/10.1007/s11204-013-9228-6 6. Osipova ON, Dyba VP, Skibin GM, Matvienko MP, Udychak MV (2019) Stressed deformed condition of base foundation in the model of hard-linear-deformable soil ground. https://doi. org/10.2991/isees-19.2019.90 7. Osokin AI, Skvortsov KD (2020) Optimization of the formula for design soil resistance. Bull Civil Eng 5(82):117–122 8. Bogomolov AN, Bogomolova OA, Vaingolts AI, Ermakov OV (2014) Comparison of the results of calculating the bearing capacity of a two-layer foundation of a buried strip foundation in different ways. PNRPU Bulletin Build Arch 2:106–116 9. Nuzhdin LV, Korobova OA, Nuzhdin ML (2014) A practical method for calculating the settlement of foundations taking into account the deformation anisotropy of foundations. PNRPU Bull Constr Arch 4:245–263 10. Chen FH (1988) Foundations on expansive soil. Amsterdam 463 11. Bhattacharya P, Kumar J (2007) Bearing capacity of foundations on soft clays with granular column and trench. Soils Found 57:488–495 12. Oh WT, Vanapalli SK (2018) Modeling the stress versus settlement behavior of shallow foundations in unsaturated cohesive soils extending the modified total stress approach. Soils Found 58:382–397 13. Bolton MD (1986) The strength and dilatancy of sands. Geotechnique 36(1):65–78 14. Vesic AS (1973) Analysis of ultimate loads of shallow foundation. J Soil Mech Found Div 99(1):45–73 15. Michalowski RL (2001) Upper-bound load estimates on square and rectangular footings. Géotechnique 51(9):787–798 16. Safina AG (2011) Ways to improve the reliability of the forecast of the stress-strain state of the foundations of slab foundations: dissertation ... Cand. tech. sciences. Yoshkar-Ola, 143 17. Dyba VP (2008) Estimates of the bearing capacity of foundations. South-Russian State Technical University, SRSTU (NPI), 202 18. Van Baars S (2014) The inclination and shape factors for the bearing capacity of footings. Soils Found 54(5):985–992 19. Van Baars S (2015) The bearing capacity of footings on cohesionless soils. Electron J Geotech Eng 20:25–27 20. Michalowski RL (1997) An estimate of the influence of soil weigh ton bearing capacity using limit analysis. Soils Found 37(4):57–64

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21. Zhu M, Michalowski RL (2005) Shape factors for limit loads on square and rectangular footings. J Geotech Geoenviron Eng 131(2):223–231 22. Osipova ON, Dyba VP, Skibin GM, Matvienko MP, Udychak MV (2019) Stressed deformed condition of base foundation in the model of hard-linear-deformable soil ground. In: Atlantis highlights in material sciences and technology (1). Engineering and earth sciences: applied and fundamental research: proceedings of the International Symposium, dedicated to the 85th anniversary of H.I. Ibragimov (ISEES 2019), 28–29 February, pp 461–464 23. Merifielda RS, Lyaminb AV, Sloanb SW (2006) Limit analysis solutions for the bearing capacity of rock masses using the generalised Hoek-Brown criterion. Int J Rock Mech Min Sci 43(9):920–937 24. Lau CK, Bolton MD (2011) The bearing capacity of footings on granular soils. II: experimental evidence. Geotechnique 61(8):639–650. https://doi.org/10.1680/geot.7.00207 25. Nguyen DL et al (2016) Discussion on size effect of footing in ultimate bearing capacity of sandy soil using rigid plastic finite element method. Soils Found 56:93–103

A New Method of Checking the Stability of the Frame Structural System in the Event of an Emergency Situation Associated with the Draft of One of the Columns Alexey Bulgakov , Klaus Holschemacher , Ksenia Dubrakova , and Pavel Maltsev Abstract The article is devoted to the study of ensuring the stability of the frame structural system at the time of an emergency situation associated with the settlement of the base from one of the columns in the frame of an industrial building. A technique for assessing the stability of frame systems in the event of an emergency situation associated with subsidence/heaving of one of the building supports has been developed. The results of experimental studies of the critical parameters of the stability of the system are obtained. Keywords Stability · Construction system · Bifurcation · Subsidence Soils

1 Introduction Nowadays, the growing challenges of natural and man-made nature and the noticeable state of the country’s fixed assets, it is necessary to closely monitor the maintenance of the normal functioning of buildings and structures, associated, first of all, with the protection of the life and health of citizens [1]. Buildings and structures must meet the structural and functional requirements for the perception of the expected force and environmental impacts obtained during design calculations, as well as possible beyond design basis impacts on the facility. The causes of accidents can be both computer or human “miscalculations” in the design, construction or operation of a building, as well as emergency impacts of a natural or man-made nature (carts failures, earthquakes, floods, hurricanes, subsidence of the foundation, man-made accidents at work, etc.) [2, 3]. Situations also occur when, as a result of a relatively small impact on individual elements, the design scheme of the frame changes, which leads to the collapse of the entire building [4]. Incredibly, such localized damage is A. Bulgakov (B) · K. Dubrakova · P. Maltsev Southwest State University, 50 let Oktyabrya Street 94, 305040 Kursk, Russia e-mail: [email protected] K. Holschemacher Leipzig University of Applied Sciences, Karl-Liebknecht-Street 132, 04277 Leipzig, Germany e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_6

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often more dangerous than a uniform large overload of the entire construction system [5]. Object of study – one-story frame industrial building. Purpose of work: conduct a study in the direction of ensuring the stability of the frame structural system at the time of an emergency situation associated with the settlement of the base from one of the columns in the frame of an industrial building. To achieve this purpose, the following tasks were formulated and solved: 1) Consider the available methods and the basis of the theory applied at the moment when design of frame buildings and analyze it. 2) Using the software package, simulate the frame of a one-story industrial building, calculate the model to determine the permissible and critical settlement of structural elements in the design calculation. 3) Carry out numerical studies of the stability of the frame structural system in the moment of an emergency related to the settlement of the base of one of the supports. 4) Analyze the features of the building structure during the settlement of the base one of the columns of a one-story industrial building.

2 Methods In the SCAD program [6], a model of the frame of an industrial building was designed with the following dimensions: plan 12 × 6 m (Fig. 1). The building has 2 spans of 6 m each, the step is 6 m. Reinforced concrete of class B25 was adopted as a material for production.

Fig. 1 Model of the frame of an industrial building in the PC “SCAD”. Demonstration of the function used and the consolidation of links

A New Method of Checking the Stability of the Frame Structural System …

51

The calculation is made in 2 steps using the numerical method [7, 8] in the software-building complex SCAD++ 21.1.1.1. to study the state of the reinforced concrete frame of an industrial building at the time of upsetting and heaving of the central column with a step of 1 cm. The range of column movement from the design position is from 0 to −8/+8 cm [9]. On the lower side of the column there is a fixed hinge that establishes ties in the X Y Z directions (rigid pinching in the foundation of the column), on the upper side there is also a fixed hinge that establishes ties in the X Y Z directions (rigid conjugation of the column and the beam) [10]. Loading the frame is done as follows [11]: 1. The action of the self-weight of the structure. Distributed load. 2. The action of a constant payload. Nodal load. For each of the 6 knots - 40 kN. 3. The action of the step-by-step upsetting of the central column of the first row with a step of 1 cm, ranging from −1 to −8 cm (function of a given displacement).

2.1 Testing Let’s calculate the minimum radius of gyration for the specified column, the section of which is 200 * 200 mm (Fig. 2) [12].  i min =

I = A



 a4 12 A

=

204 = 5.774 centimeters, 12 ∗ 20 ∗ 20

(1)

where i_min is the minimum radius of gyration; I (Ix, Iy) - axial moments of inertia, since the column, in our case, has a square section, then Ix = Iy = I; A - is the cross-sectional area of the column. We also determine the flexibility for this column [13]. λ = μl / i_min = (0.5 ∗ 300) /5.774 = 26,

(2)

where λ is the flexibility of the rod; μ is the coefficient of the calculated length, in our case, with rigid pinching of the column from above and below, is 0.5. l is the length of the column; i_min - minimum radius of gyration. Fig. 2 The size of the sections of structural elements used

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We determine the parameter, according to the numerical data of which we will subsequently build a graph and draw a conclusion on it. ξ=

l0 , l

(3)

where ξ is the investigated parameter introduced; l0 - free length of the column, obtained from the results of software calculation in the PC “SCAD”.

3 Results and Discussion As a result, studies of the graph of the dependence of ξ (the ratio of the free length of the column l0 to its length l) on the displacement of the column were obtained [14]. When the settlement of column 2 is from −1 to −8 cm, the parameter ξ increases for all columns to −4 cm, from −4 to −5 cm the graph value sharply changes to a decreasing one and then again increases upward, the direction of the graph changes to a decreasing one to −5 cm (Fig. 3). When column 2 heaves from +1 to +8 cm the graphs behave closely to linear graphs for columns 1, 3, 4, 5, 6 increase, for column 2 is decrease (Fig. 4). Graphs of the dependence of the critical force of the Pcr on the movement of the column were also obtained. With the settlement of column 2 the value of Pcr decreases when moving from −2 to −4 cm. From −4 to −5 cm the direction of the graph changes sharply to increasing one and then gradually decreases (Fig. 5). With heaving the graphs of the dependence of the critical force on the displacement of the column are close to linear, for columns 1,3,4,5,6 the values of the force Pcr decrease and only for column 2 increase (Fig. 6). 3. Also, based on the analysis of the forces (Mi , Qi ) in the elements of the spatial structure in the SCAD software package, the types of bifurcation for the columns of the structure were determined: Fig. 3 The graph of dependence ξ (the ratio of the free length of the column l0 to its length l) on the value of the settlement of the column 2

A New Method of Checking the Stability of the Frame Structural System … Fig. 4 The graph of dependence ξ (the Ratio of the free length of the column l0 to its length l) on the value of the heaving of the column 2

Fig. 5 The graph of the dependence of the critical force of the Pcr on the amount of column settlement

Fig. 6 The graph of the dependence of the critical force of the Pcr on the amount of column heaving

53

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1) When the base of the central column settles before reaching the displacement mark of −4 cm, the nature of the bifurcation changes from the active stage for columns 1, 2, 3, 5 to the passive and for columns 4, 6 from the passive to the active [15]. 2) With the heaving of the base of the central column, the nature of the bifurcation does not change during the experiment, for columns 1, 2, 3, 5 the nature of the bifurcation is passive, for columns 4, 6 it is active [16, 17].

4 Conclusion 1. Considered the available methods and foundations of the theory currently used in the design of frame buildings. 2. Using the SCAD program to model the frame of a one-story industrial building, calculate the model and formulate another possible way to determine the type of bifurcation and its point. 3. Having analyzed the existing theory of frame-rod structures, at the time of studying this issue, one of the methods was proposed for determining the stability of the frame structural system at the time of an emergency situation associated with the settlement of the foundation of one of the columns. The developed method for assessing the stability of frame systems in the event of an emergency situation associated with subsidence/heaving of one of the building supports proves, that there are criteria according to which it is possible to assess the stability of a building and structure, as well as permissible deformations, and there is also a dependence of the nature of bifurcation on the value moving the base.

References 1. Federal Law of December 30, 2009 N 384-FZ (2009) Technical regulations on the safety of buildings and structures. (in Russian) 2. Airapetov GA, Ivanov VT, Petrov KS, Sidorov Mya (2004) Building materials. In: Airapetov GA, Nesvetaeva GV (Eds) Phoenix, Rostov-on-Don, p 608. ISBN 987-6385-76-0. (in Russian) 3. Alexandrov AV (2001) The role of individual elements of the rod system in buckling. MIIT Bull Sci Tech J 5:46 (in Russian) 4. Aleksandrov AV, Matveev AV (2009) Criteria for identifying the most dangerous elements and their use in problems of structural stability. In: 4th scientific-practical conference. (in Russian) 5. Perelmuter AV, Slivker VI (2001) Design models of structures and the possibility of their analysis. Runway “Compass”, Kiev, pp 364–369. (in Russian) 6. Bulanov VE, Mazov AA (2010) Certificate of state. registration of computer programs 2010617702. Calculation of deformations of eccentrically compressed rods. Copyright holder Tamb. state tech. un-t .; application 09.21.10; registered 11/19/10 in the register of computer programs. (in Russian) 7. Dubrakova KO (2018) Issues of stability of statically indeterminate systems made of wood. BST Bull constr technol. (in Russian)

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8. Kuznetsov GV, Polovnikov VYu (2015) Processes of heat and mass transfer in structures and zones of placement of underground heating networks. In: Skuratov AP (ed) Publishing House of SB RAS, - Novosibirsk, p 280. ISBN 978–5–7692–1637–4. (in Russian) 9. Aistov NN (1938) Testing by static load of building structures, their elements and models. Moscow-Leningrad, People’s Commissariat of the RSFSR, p 240 10. Alexandrov AV, Potapov VD (2000) Strength of materials. Moscow, Higher School, p 560. (in Russian) 11. Aleksandrov AV (2002) About the calculation of rod structures for stability. Ind Civil Constr 3:16 (2002). (in Russian) 12. Belsky GE, Belsky GE (1961) Stability of centrally compressed rods and frames in the elastoplastic stage. Calc Struct Work Elastoplast Stage Coll Articles (7):239–267. (in Russian) 13. Iakovenko I, Kolchunov V (2017) The development of fracture mechanics hypotheses applicable to the calculation of reinforced concret structures for the second group of limit states. J Appl Eng Sci 15(3):366–375. https://doi.org/10.5937/jaes15-14662. (in Russian) 14. Bulanov VE (2008) On the stress-strain state of eccentrically compressed elements. In: Bulanov VE, Mazov AA (eds) Scientific research and their practical application. Current state and development paths, 2008: Sat scientific works on the materials of International. Scientific and practical conference T. 3. Technical sciences. Chernomorye, Odessa, pp 14–18 15. Zarubina LP (2017) Protection of territories and construction sites from flooding by groundwater Moscow –Vologda. Infra-Engineering 213. http://biblioclub.ru/index.php?page=book& id=466499, Accessed 01 Oct 2019. (in Russian) 16. Kadushkin YuV (2015) Fundamentals of technology for the construction of buildings and structures: Guidelines for independent work on the topic “Technological map for the installation of building structures of an industrial building Agro-industrial complex “for students studying in the direction of preparation [08.03.01” Construction “(bachelor’s level)]. In: Kadushkin YuV, Belentsov YuA, Zakharenko EA (eds) Ministry of Agriculture of the Russian Federation, St. Petersburg State Agrarian University, Department of Construction of Buildings and Structures. St. Petersburg: SPbGAU, p 108. http://biblioclub.ru/index.php?page=book&id=445942. (in Russian) 17. Verzhbovskiy GB, Veselev YuA, Lagutin VV, Lukashevich EB (2021) Reference book of a modern designer. In: Mayilyana LR (ed) 7th ed. Phoenix, Rostov-on-Don, p 544 https://biblio club.ru/index.php?page=book&id=271604, Accessed 29 Oct 2021. ISBN 978-5-222-17699–3. (in Russian)

Aging and Long-Term Mechanical Impact in the Durability of Wood Composites Semyon Mamontov , Aleksandr Mamontov , Pavel Monastyrev , Sergey Emelianov , and Ekaterina Pahomova

Abstract The object of research is wood composites. The aim of the work is to develop a reliable method for predicting the durability of wood composites operating under mechanical loading and climatic aging. The research methodology is based on the provisions of the thermo-fluctuation theory of fracture of a solid. The strength is evaluated by long-term mechanical transverse bending tests before and after aging. Climatic aging is simulated in thermal and UV chambers. The change in the value of the thermal fluctuation constants after aging as a result of the destruction of composites has been established. Empirical equations are obtained for predicting the durability of wood composites by the duration of accelerated aging. A graphic-analytical method for determining the coefficients of new equations is described. A method for calculating a correction that takes into account the change in the value of thermal fluctuation constants after aging is shown. The correction is introduced into the well-known equations of the thermofluctuation theory to predict the durability. A method has been developed for predicting the durability of wood composites taking into account their aging. Approbation of the technique on the example of accelerated aging of plywood showed a high convergence of the results with experimental data on aging. Keywords Wood composites · Aging · Prediction method · Durability

1 Introduction The successful use of wood composites in certain operating conditions depends on their ability to maintain their properties, that is, on their durability.

S. Mamontov (B) · A. Mamontov · P. Monastyrev Tambov State Technical University, Sovetskaya street, 106, 392000 Tambov, Russia e-mail: [email protected] S. Emelianov · E. Pahomova Southwest State University, 50 Let Oktyabrya street, 94, 305040 Kursk, Russia © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_7

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For a reasonable determination of the service life of a composite material, it is necessary to have information about its behavior under the intended operating conditions. Such information can be obtained either by prolonged climatic exposures or by accelerated artificial aging tests of materials [1–15]. In this case, it is necessary to have simple and reliable relationships between the kinetic parameters of physicochemical processes and the macro-properties of the material. However, it is not always possible to obtain such ratios, let alone describe them from a mathematical point of view, which reduces the quality of predicting the service life. Moreover, most methods for predicting durability do not take into account long-term mechanical stress on the material. The authors made an attempt to develop a universal and reliable method for predicting the service life of wood composites, the absence of which is an urgent problem.

2 Methods The proposed methodology for predicting the durability of wood composites operating under climatic aging is based on the equations of the thermofluctuation theory of solid fracture [16–19] and an extrapolation method for predicting durability based on the results of accelerated aging [20–22].

3 Results and Discussion The general scheme of the technique is presented in Fig. 1. Let’s consider a more detailed description of the main stages of the developed technique. 1. For a material not subject to aging, thermal activation laws of destruction are constructed and the values of thermal fluctuation constants are determined. Given the voltage and operating temperature, the theoretical durability is calculated using the generalized Zhurkov equation and its modifications, which does not take into account the effect of aging factors [16, 17]. As the operating temperature, you can take the equivalent temperature T eqv characterizing the non-stationarity of the temperature effect in a certain climatic region and calculated according to the Goikhman-Smekhunova formula, or adopted in accordance with Russian State Standard GOST 9.707–81. To be able to take into account the aging factors acting on the material during operation in a specific climatic region, it is necessary to carry out accelerated laboratory aging, energetically equivalent in its effect to the real climatic one. To do this, it is necessary to determine the duration of laboratory aging τ accel using Eq. (1), in which τ expl it is necessary to take equal theoretical life from clause 2.

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Fig. 1 General scheme of the methodology for predicting the durability of wood composites, taking into account aging and mechanical stress

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 τaccel = τex pl ex p

E R



1 Taccel

−

1



Teqv

(1)

where is τ accel , h – the duration of accelerated laboratory aging at a temperature T accel ; τ expl, h - duration of operation (storage) at an equivalent temperature T eqv , K; E, J/mol is the apparent activation energy of the aging process, corresponding to T eqv ; R = 8.31 J/mol • K - universal gas constant. The value of the apparent activation energy E can be determined using nomograms, given by T eqv and the climatic region. In addition, the value of the activation energy E can be calculated from the kinetic curves of the change in the ultimate strength of the material at different temperatures of accelerated laboratory aging. The calculation method is described in detail in Russian State Standard GOST 9.707–81. It is important to note that the same standard allows using the effective activation energy of thermooxidative destruction obtained from the results of thermogravimetric analysis as E. Thus, knowing E and T eqv , and also T tvor , the duration of accelerated thermal aging at a given temperature T accel is determined. It is assumed that the T accel should be 10 K higher than the normal operating temperature of the material and 10 K lower than the maximum (critical) temperature, which causes changes in the material uncharacteristic for the operating period. 2. Tests are carried out according to a given accelerated mode in laboratory conditions. 3. In the process of accelerated aging, it is recommended to remove samples and determine their ultimate strength at regular intervals of aging, the number of which should be at least 5. Thus, a kinetic curve of strength change is constructed. 4. After accelerated aging, it is necessary to plot the dependence of the time to failure on stress in coordinates lgτ −σ. To be able to use interpolation and extrapolation methods, it is recommended to build several dependencies for different durations of artificial aging. 5. Using the values of the coefficient K (Table 1) and the values of the short-term strength of the material for different duration of aging, the correction is calculated Δ = K•Δi k (where is Δi k – a correction at initial values of the thermal fluctuation constants, determined from the values of short-term strength before and after aging) to the durability of the material not subject to aging, allowing to take into account the effect of aging factors. Correction Δi k , taking into account the change in short-term strength during aging, is calculated using formulas 2–4. The choice of the formula is determined by the form of graphs of the dependences of time to failure on stress in the coordinates lgτ -σ, obtained at different temperatures: a. In a case of the straight bundle ik

  T γ 1− =− (σ0 − σi ) 2.3RT Tm

(2)

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Table 1 Values of the K coefficient for plywood Type of impact

Duration of impact, hours

The dependence of durability on stress after aging for a given time, hours 50

150

300

Thermal aging at 80 °C

50

−0,012 σ + 1,20

−0,016 σ + 2,28

0,043 σ−4,33

150

0,017 σ−1,79

0,024 σ−3,42

−0,064 σ + 6,47

300

0,011 σ−1,14

0,015 σ−2,18

−0,041 σ + 4,13

UV irradiation

50

0,024 σ−2,40

−0,002 σ−1,5

0,19 σ−24,18

150

−0,009 σ + 0,92

0,001 σ + 0,57

−0,071 σ + 9,26

300

−0,0025σ + 0,26

0,0002 σ + 0,16

−0,02 σ + 2,57

b. In a case of the backward bundle ik

γ/ =− 2.3RT



 / Tm − 1 (σ0 − σi ) T

(3)

c. In a case of the parallel lines ik = −β(σ0 − σi )

(4)

where is γ , γ  , β, T m , T m – thermo-fluctuation constants of the non-aging composite; T is the operating temperature, K; σ 0 , σ i - ultimate strength of the composite before and after aging, MPa. 6. If the duration of accelerated aging calculated according to formula (1) turns out to be significant (700 h or more), then the following actions must be performed: a. According to the kinetic dependences of the change in the indicator responsible for the performance (for example, residual strength), built at different temperatures, choose the duration from which the indicator changes monotonically (for example, 100 h), which indicates the stabilization of the material structure; b. It is need to carry out artificial aging during chosen time (100 h) and build a graph of the dependence of the time to failure on stress in the coordinates lgτ-σ. 7. Using the graphoanalytical method of processing straight lines (Figs. 2, 3) and Eqs. (5) and (6), determine the durability for the duration of accelerated aging, established in paragraph 3 of the method. For Fig. 2 lgτ = A + 0, 435(B0 − dσ )(tst.h − C) − (U0 −γ σ )(1/T0 − 1/Ti )/2, 3R

(5)

For Fig. 3  l gτ = A + 0, 435 · B0 · tst·h − dσ − U (1/T0 − /Ti ) 2, 3R

(6)

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Fig. 2 Scheme for determining coefficients for Eq. 5

Fig. 3 Scheme for determining coefficients for Eq. 6

where is a - A, B0 , d and C – coefficients determined by the graphoanalytical method; U, U 0 , γ - thermal fluctuation constants of the material not subject to aging; t st.h - hour is the duration of accelerated laboratory aging, h; T 0 is the temperature of obtaining direct durability for non-aging material, K; T i - operating temperature, K; σ - stress, MPa; R = 8.31 J/molK - universal gas constant.

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3.1 Example Let’s consider an example of calculating the durability of a plywood sheet taking into account the effect of aging factors on it. The values of the thermal fluctuation constants are known. Determine the theoretical durability of plywood that is not subject to aging at σ = 50 MPa and T = 293 K.

0 −γ σ 1 − TTm = 5.14 + (−101.87+1.27·50)·1000 lgτtheor = lgτm + U2.3RT 2.3·8.31·293  1 − 293 = 7.89 209 Determine the duration of accelerated heat aging at 80 °C

3.1.1

Prediction of Durability by Graphic-Analytical Method

Based on the results of mechanical tests, we construct the dependence lgτ - σ for plywood after 50 h of thermal aging (Fig. 4). To predict the durability of plywood after 150 h of heat aging, we use Eq. (6). The coefficients of the equation were preliminarily found by the graphical analytical method: A = 11,69; B = −0,0293; d = 0,076. lgτ  1 = 11.69 − 0.435 · 0.0293 · 150 − 0.076 · 50 + 1 = 5.98 − 293 293

101.87·1000 2.3

Fig. 4 Dependence of the logarithm of the time to failure of stress for plywood before and after 50 h of heat aging

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Fig. 5 Comparison of experimental results and calculation of durability for plywood after 150 h of heat aging

We check the obtained forecast by the value of the thermal fluctuation constants obtained experimentally for plywood after 150 h of heat aging: lgτ m = 0,23 s; T m = 268 K; U 0 = -562,6; = γ −4,3. lgτ = 0.23 +

  293 (−562.6 + 4.3 · 50) · 1000 1− = 6.02 2.3 · 8.31 · 293 268

We build an experimental dependence of the durability on stresses for plywood after 150 h of thermal aging and apply the calculated prediction points (Fig. 5). It can be seen that the prediction points fit fairly well the experimental dependence, which indicates a high convergence of the calculated values with the experimental ones.

3.1.2

Predicting Longevity by Introducing an Amendment

Let us determine the durability of plywood subjected to 150 h of heat aging using the correction  = K · ik . The value of the coefficient K is taken according to Table 1 at a given stress value of 50 MPa. K = −0, 016 σ + 2, 28 = −0, 016 · 50 + 2, 28 = 1, 48 γ 1− k50 = − 2.3RT

T Tm



 1− (σ0 − σ50 ) = − −1.27·1000 2.3·8.3·293

293 209



(142.37 − 156.11) = 1.25  = 1, 48 · 1, 25 = 1, 85   293 (−101.87 + 1.27 · 50) · 1000 1− − 1.85 = 6.04 lgτ = 5.14 + 2.3 · 8.31 · 293 209

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The durability values obtained by different methods indicate a fairly high convergence. The scatter of results does not exceed 2%.

4 Conclusions 1. Analysis of the existing methods for predicting the durability of composite materials revealed the absence of methods that allow taking into account the interdependent influence of long-term mechanical stress and factors of natural aging on durability, which reduces the quality of its prediction. 2. The study of the process of destruction of wood composites from the standpoint of the thermal fluctuation theory showed that aging causes a change in the value of thermal fluctuation constants due to degradation of the structure, which can be taken into account when predicting the durability by introducing correction factors. 3. A graphoanalytical method has been proposed that makes it possible to predict the change in the durability of wood composites in the process of accelerated aging using empirical equations. 4. The proposed method for predicting the durability of materials, taking into account the interdependent effect of aging factors and long-term mechanical stress, makes it possible to determine the life of a material during natural aging based on the results of accelerated aging, which significantly reduces (is about 3 times) the time spent in comparison with existing methods. 5. The example given in the work on assessing the durability of plywood after heat aging showed a fairly high convergence of the results of calculation and experiment. The scatter of results does not exceed 2%.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

Verzhbovskiy GB (2016) Procedia Eng 150:1831–1836 Friedrich D, Luible A (2016) Constr Build Mater 124:1142–1152 Butylina S, Hyvärinen M, Kärki T (2012) Polym Degrad Stab 97(3):337–345 Belec L, Nguyen TH, Nguyen DL, Chailan JF (2015) Compos A Appl Sci Manuf 68:235–241 Yadav SKJ, Vedrtnam A, Gunwant D (2020) Constr Build Mater 262:120785 Friedrich D (2019) J Build Eng 23:68–76 Qin J, Jiang J, Tao Y, Zhao S, Zeng W, Shi Y, Lu T, Guo L, Wang S, Zhang X, Jie G, Wang J, Xiao M (2021) Polym Test 93:106940 Celina MC (2013) Polym Degrad Stab 98(12):2419–2429 Matkoviˇc S, Pogaˇcnik A, Kalin M (2021) Wear 480–481:203944 Tocháˇcek J, Vrátníˇcková Z (2014) Polym Test 36:82–87 Laycock B, Nikoli´c M, Colwell JM, Gauthier E, Halley P, Bottle S, George G (2017) Prog Polym Sci 71:144–189 Ratanawilai T, Srivabut C (2022) Case Stud Constr Mater 16:e00791

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13. Kychkin AK, Startsev OV, Lebedev MP, Polyakov VV (2020) Procedia Struct Integrity 30:71– 75 14. Ratanawilai T, Taneerat K (2018) Constr Build Mater 172:349–357 15. Mayandi K, Rajini N, Ayrilmis N, Devi MPI, Siengchin S, Mohammad F, Al-Lohedan HA (2020) J Mark Res 9(6):15962–15988 16. Brandman GS, Shamov IV, Tarakanov OG (1982) Polym Sci U.S.S.R. 24(5):1042–1046 17. Boyda˘g FS, ¸ Özcanlı YL, Alekberov VA, Hikmet I (2005) Compos Part B Eng 37(2–3):249–254 18. Byessonov MI, Volodin VP, Kenunen IV (1990) Polym Sci U.S.S.R. 32(4):626–633 19. Bronnikov SV, Vettergren’ VI, Korzhavin LN, Frenkel’ SYa (1989) Polym Sci U.S.S.R. 31(6):1386–1393 20. Moon B, Kim K, Park K, Park S, Seok CS (2020) Mech Mater 147:103405 21. Xue W, Li Y, Kai F, Xiang H, Li Y (2020) Constr Build Mater 237:117632 22. Le Saux V, Le Gac PY, Marco Y, Calloch S (2014) Polym Degrad Stab 99:254–261

Analysis of the Implemented Project for the Construction of a High-Rise Building Between Two Low-Rise Buildings in the Zone of Maximum Mutual Influence of Their Foundations Ali Al−Bukhaiti , Vektor Ledenev , Yaroslav Savinov , and Olga Umnova Abstract The implemented project of construction of a seven-storey building between the four-storey and five-storey buildings at a distance of “wall to wall” is investigated. The building was built in 1999th at the address: Russian Federation, Tambov city, St. Sovetskaya, no. 156. In 2003rd and 2021st, a visual and instrumental examination of the technical condition of the walls, both of the building itself and of the adjacent buildings, was carried out. In this project, an action has been implemented to reduce the effect of additional load from the foundation of a highrise building on shallow strip foundations by using bored piles with widening in the lower parts. To analyze the stress–strain state of the foundation soils, modeling was carried out using the Plaxis3D program. The results of the survey and computer modeling showed the high efficiency of the chosen constructive solution for the foundations of the attached building. No cracks associated with the mutual influence of the foundations were found on the facades of old buildings adjacent to the new one. Computer simulations showed that the pile foundation divided the zones of compressible soil beneath adjacent buildings to different depths. And he transferred the load from the heaviest 7-storey building to a depth of 12 m, where alluvial sands with a modulus of deformation 3.2 times higher than that of surface clay soils occur. Thanks to the use of bored piles under the new building, followed by their reinforcement and concreting, dynamic effects on neighboring buildings were excluded. Keywords Building · Structure · Mutual influence · Damage · Finite element method · Engineering-geological element · Subsidence soils · Additional settlement · Technical inspection · Stress–strain state

A. Al−Bukhaiti (B) · V. Ledenev · O. Umnova Tambov State Technical University, Tambov, Russia e-mail: [email protected] Y. Savinov LLC JV “Mostostroy”, Tambov, Russia © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_8

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1 Introduction The construction of a high-rise building in a dense urban development in the immediate vicinity of previously constructed buildings is always a difficult engineering task, because the previously constructed building is in the zone of influence of the settlement of the new foundations on the deformation of the base and the structure of the existing one [4, 5, 7, 14, 15]. The attached building partially rests on the compacted soil of the base of previously constructed buildings, which provokes uneven settlement of the entire group of buildings located in the zone of the sedimentary funnel formed along the perimeter of the attached building. The size of the zone of influence is calculated during the design process [1, 9, 11]. Also, the dynamic impact on the foundation of an existing building when piling or sheet piling during the construction of a new building often negatively affects previously constructed buildings. The purpose of our research is to assess the effectiveness of engineering measures used in the construction of a high-rise building, built in a zone of mutual influence with old buildings. For this, the authors solved the following tasks: survey of a group of interacting buildings, analysis of engineering and geological data for the construction site [8, 10, 17], applied a modern method of computer modeling by the finite element method in the Plaxis3D program to calculate with high accuracy the width of the outer zone of compressible soil along the perimeter each building participating in the process of mutual influence, there can be several such buildings at the same time. Today there are several methods for determining the width of the IW zone [2, 3, 6, 18], including the method of computer simulation.

1.1 Survey A group of three buildings located at: Russian Federation, Tambov city, Sovetskaya st., d. 156, 158 and the seven-story building built between them, belonging to house number 158, were surveyed by the authors in 2005th and 2021st (Fig. 1). These buildings are located in zones of mutual influence, because their walls are tightly adjacent to each other. The first building was built in 1958th, at st. Sovetskaya, 156 (see Table 1). This is a 4-storey “stalinka” with strip rubble foundations, walls made of ceramic bricks 800 mm thick, wooden floors, plastered. At the time of construction of the second building, it already had wall damage in the form of inclined cracks. The second building “Khrushchev” was added after 5th years outside the zone of mutual influence, because it is located 12 m from the first. According to the residents, it began to deform immediately after construction, and characteristic subsidence cracks began to appear on the facades, especially the southern section of the house, bounded by the second expansion joint (Fig. 3).

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Fig. 1 Situational plan of buildings at the address: st. Sovetskaya, d. 156; 158: a main facades; b photo, top view; c a diagram of the zones of mutual influence of buildings 1, 2, 3 stages of construction

Table 1 Characteristics of the group of buildings under consideration Build queue

Address

Build date

Number of storeys

Wall material

Foundations material

Floor material

1

Sovetskaya street, 156

1958

4

Ceramic brick, plastered

Foundation of Wooden from shallow laying, logs keram. brick

2

Sovetskaya street, 158

1963

5

Silicate brick

Foundation of shallow laying, Prefabricated concrete foundations

Reinforced concrete hollow core slabs

3

Sovetskaya street, 156 (outbuilding)

1999

7

Plastered silicate brick

Bored piles with widening

Reinforced concrete hollow core slabs

In 1994th, between two previously constructed buildings, construction began on the third one, designed by “TAMBOVGRAZHDANPROEKT” LLC, with a height of 7 floors. It was a challenging engineering task because the new house fell into the

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Fig. 2 An example of a pile foundation “bored yew piles” applied on an attached high-rise building of the third stage

zones of mutual influence of both buildings, which, moreover, had already damaged the load-bearing walls. To solve this problem, the following decisions were made: 1. It was decided to strengthen the building of the first stage of construction from the side of the attached house with tie belts. 2. To separate the levels of bearing mutually influencing soils of the foundation, the foundation of the new building is deeply laid - pile, 10 m deep, with a pile diameter of 800 mm, with broadening in the lower part up to 1200 mm (Fig. 2). 3. In order to exclude dynamic impacts, drilling piles with broadening are accepted. The strip foundations of the building of the second stage were built of FBS concrete blocks, laid on a sand preparation with a thickness of 20 cm. Let’s consider the influence of an extension of a new higher (heavy) 7-storey building to the existing 5-storey one. In 2004 and 2018, the building of the first stage was redecorated from the facades (plastering, whitewashing, painting). At the time of the survey in 2005th, according to the residents as well, because of a visual inspection, the condition of the buildings was established. – House No. 158 new crack opening is not observed. The facades have only old, non-progressive cracks. – The seven-storey extension between houses No. 158 and 156 is currently cracked and evicted work is underway to strengthen the load-bearing structures. – House No. 156, there is the formation of new cracks and the opening of old ones, destruction of the plastered layer, soaking of the walls (Fig. 3).

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Fig. 3 Scheme of cracks in the walls of buildings on the Sovetskaya Street, houses №158 (a) and №156

All buildings of the group under consideration have damage in the form of cracks on their facades, however, these damage are not related to mutual influence. So, buildings of the 1st and 2nd stages of construction have cracks associated with uneven subsidence, which were already at the time of construction of the building of the 3rd stage. And the attached high-rise building itself has cracks caused by design errors, namely, the insufficient section of the columns, which are currently reinforced with steel frames.

1.2 Engineering and Geological Situation in the Construction Area. All buildings of the group under consideration have damage in the form of cracks on their facades, however, these damage are not related to mutual influence. So,

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Fig. 4 Lithological column II of the above-floodplain terrace (2t)

buildings of construction stages 1 and 2 have deformations associated with uneven subsidence. According to the scheme of engineering-geological zoning of the territory of the Tambov city [17], the group of buildings under consideration is located on the second above-floodplain terrace of the river. Tsna in the area in the region III-G1-A1, with a groundwater level deeper than 10 m, on the north side of the river. Student. The thickness of subsiding soils ranges from 2 to 3 m (Fig. 4). This area contains site III-G1-A1-21 (Fig. 5, a), where subsidence deluvial loess-like loams Ld (2t) III are widespread. The modulus of deformation of self-compacting soils for 80 years fluctuates within 4–6 MPa, while the underlying layer of alluvial Upper Quaternary loams with a modulus of deformation of 4 … 10 MPa. The consistency of clayey soils varies from hard to semi-hard and tough plastic. The data obtained on the basis of research [12, 13, 15–17] are given in Table 2, and are used by the authors of this article when calculating the VAT of soils of the foundations of the buildings under study. IGE No. 1 - soil and vegetation soil and technogenic deposits are not taken into account, since the foundations of the buildings under consideration are based on IGE No. 2 and below. At the time of the re-examination of this group of buildings in 2021st, no new deformations associated with mutual influence were found. The building of the first stage is now plastered and no new cracks have appeared.

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a)

c) b)

Fig. 5 Engineering-geological zoning of the central part of Tambov: a Fragment of the microzoning scheme; b a fragment of the deformation modulus zoning scheme; c the plan of the group of buildings under consideration

2 Methods 3D modeling of the stress state of the “foundation-foundation-building” system was carried out in the calculation program “Plaxis 3D” (Fig. 6). As a result of calculations, pictures of the distribution of displacement and stress fields in base soils (FBS) were obtained (Fig. 7). During the modeling, separate finite element models of buildings on soils were built with the characteristics indicated in Table 2.

3 Results and Discussion The widest zone of soil, subjected to vertical displacements uz = 16 … 36 mm, is located along the perimeter of the building of the first stage of construction. Modeling in “Plaxis 3D” showed that its width is about, 8 m along the perimeter of the building of the first stage, 1.2 m along the perimeter of the building of the second stage, and 0.5 m - of the third stage of construction (Fig. 7a). Figure 6b illustrates the transfer of total vertical stresses σzz from the pile foundation of the building of the third stage of construction to the lower, more durable IGE No. 2 and 3 sandy soil a (2t) III, this reduces the vertical displacement under it. Accordingly, the influence from a heavier building on neighboring less heavy ones has been reduced. Compressive vertical stresses, as it were, spread over the boundaries of the soil layers, almost not connecting with each other. The pile foundation divided the zones of compressible soil beneath adjacent buildings to different depths. And he transferred the horizontal load Ux from the heaviest 7-storey building to a greater depth (Fig. 7e).

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Table 2 Characteristics of base soils Physical and mechanical characteristics of soil

Engineering-geological elements (EGE) EGE №1

EGE №2

EGE №3

EGE №4

Soil type

Soil and vegetable soil + technogenic

Subsidence loess-like deluvial loams LdIII(2t)

Alluvial loams a (2t) III and La (2t) II

Sandy soils a (2t) III

Average layer thickness (m)

1,5–2

2–3

1,5–2

1,5–2

Bulk density  γb =  CM3

1,61

1,89

1,91

1,48

Dry density  γd =  CM3

1,37

1,56

1,56

1,5

Natural moisture (Wc%)

3

2,2

2,2

1,8

Internal friction angle ϕ,

The data do not participate in the calculations, since the IGE is not the foundation soil

19,1

22,13

33

0,27

0,34

0,08

0,35 — 0,37

0,35 — 0,37

0,30 — 0,35

Shift factor fs = tgϕ

0,34

0,4

0,64

Deformation modulus E, kN/m2

9200

8000

28,000

Specific adhesion c, kPa Poisson’s ratio, ν

Fig. 6 Building a 3D model in the program “Plaxis 3D”

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Fig. 7 The results of calculating the stress–strain state of soils of the foundations of the program “Plaxis 3D”: a top view of the zone of mutual influence vertical displacements Uz; b 3D fields of distribution of vertical stresses σzz over IGE layers; c vertical displacement Uz view from the side of the Lev Tolstoy square; d vertical displacement Uz view from the side of Soviet st.; e horizontal stresses Ux view from the side f the Lev Tolstoy square

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4 Conclusions 1. The scheme of engineering-geological zoning (Fig. 5) shows the effectiveness of the considered engineering solution in conditions of high variability of the deformative characteristics of base soils. 2. Surveys showed that damage to buildings of the 1st and 2nd stages was caused by uneven subsidence of the foundations, and buildings of the 3rd stage were caused by a design error associated with the choice of an insufficient section of the columns. No deformations of the bearing walls caused by mutual influence were found. 3. Considering next factors: the service life of the attached building is 22nd years; complex engineering and geological conditions of construction; considerable age of buildings (Table 1) located in the zone of influence, in general, this project can be considered very successful, and the engineering solution for the use of bored pile foundations in attached high-rise buildings is recommended to be used in such situations.

References 1. Nasser A-BAY, Ledenyov VV, Savinov YV, Umnova OV (2020) Survey of the damaged closely located buildings in the historical part of the Sanaa city (Yemen). IOP Conf Ser Mater Sci Eng 913:022017 2. Nasser A-BAY, Keita Y, Ledenyov VV, Savinov YV, Umnova OV (2021) Research of the additional building influence on the foundation in a stress superposition existing along the radius zone. IOP Conf Ser Mater Sci Eng 1083:012014 3. Monastyrev P, Mischenko E, Kuznetsova N (032045) Problems of integration of cultural heritage objects with architectural and historical environment of the city. IOP Conf Ser Mater Sci Eng 463(3):032045 4. Anastasopoulos J (2013) Structural damage of a 5-storey building: differential settlement due to construction of an adjacent building or because of construction defects ? In: Seventh in teznetional confezence on case histozies in geotechnicae cngimeezing, Chicage, pp 1–10 5. Stuazt JG (1962) Intellizence between foundations with special defence of surface footings in sand. Geotechnique 12:15–23 6. Finno RJ, Calvello M (2005) Supported excavations: the observational method and inverse modelling. J Geotech Environ Eng ASCE 131(7) 7. Borja RI, Lee SR (1990) Cam-clay plasticity, part 1: implicit integration of elasto-plastic constitutive relations. Comput Methods Appl Mech Eng 78:48–72 8. Butterfield R (1979) A natural compression law for soils (and advance on e-log p). Géotechnique 29:469–480 9. Muir Wood D (1990) Soil behaviour and critical state soil mechanics. Cambridge University Press, Cambridge 10. Bowles JE (1997) Foundation analysis and design, 5th edn. McGraw-Hill Pub, New York City 11. Triton (2004) Geotechnical Investigation at the area of Moshato, Technical Report (confidential) 12. Ghosh P, Rajesh S, Sai Chand J (2017) Linear and nonlinear elastic analysis of closely spaced strip foundations using Pasternak model. Front Struct Civil Eng 11(2):228–243 13. Das BM, Larbi-Cher If S (1986) Ultimate bearing capacity of closely spaced strip foundations. Department of Civil-Engineering, Indian Institute of Science, Bangalore, 560012, India

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14. Singh A, Punmia BC, On ML (1973) Intellizence between adjacent gmaze footings on cohesionless soil. Indian Geotech J 13(4):275–284 15. Ledenev VV, Skrylev VI (2017) Accidents, destruction and damage. Causes, consequences and warnings. Publishing house of the Federal State Budgetary Educational Institution of Higher Education “TSTU”, Tambov, p 440 16. Ledenev VV (2018) Deformation and destruction of foundations, foundations, building materials and structures (theoretical experiment). publishing center of the Federal State Budgetary Educational Institution of Higher Education “TSTU”, Tambov, p 469 17. Savinov YaV (2003) The main causes of damage to load-bearing wall structures and recommendations for their prevention on the example of the city of Tambov . Cand those Sciences, Tambov, p 235 18. Shashkin AG, Shashkin KG (2002) Interaction of buildings and foundations: methods of calculation and their application in design, p 48

The Effect of Reinforced Concrete for Crack Resistance and Rigidity Based on Mechanics of Fracture Under Bending with Torsion Vladimir Kolchunov

Abstract The author obtained the effect of reinforced concrete for crack resistance and rigidity based on fracture mechanics in bending with torsion. Its physical essence lies in the additional deformation effect of the reaction of reinforcement and concrete in the form of an ellipsoid for an alternative kinematic crack, associated with a violation of the continuity of concrete using dual-console element. A complete picture of the different types of cracks lcr c,i has been developed from the limit strain condition εbt,u for functional or discrete level values of lcr c . The distance between cracks and the width of the opening are developed from the differential equation. Crack opening is the accumulation of relative concentrated mutual displacements of reinforcement and concrete on both sides of the crack in the areas where there is a discontinuity in the concrete from the elliptical crack instead of their kinematic form. Here the scientific hypothesis of Thomas and the author of the article was developed. The rigidity of reinforced concrete structures under bending with torsion in elastoplastic compressed concrete is obtained, and the coefficients ϕij , v(λ) for projection from the tensors of compressed concrete and reinforcement diagrams are obtained. The approximation of the rectangular cross-sections using the small-square of matrix with the elements for the rigidity characteristics D pq is performed. The rigidity of reinforced concrete structures under bending with torsion in elastoplastic compressed concrete is obtained, as well as the coefficients ϕij , v(λ) to project from the tensors of diagrams of compressed concrete and reinforcement using the functionals, hypotheses of deformation, displacement from tearing off acr c , transverse cr c (y, z) and longitudinal cr c (x, z) shear, coefficients ψs,m and ψsw,m , in the form of simple expressions (synthesis) and in full expanded form (analysis). Keywords Reinforced concrete effect · Crack width · Hypotheses · Bending · Torsion · Crack spacing · Rigidity

V. Kolchunov (B) Southwestern State University, 50 let Oktyabrya Street, 94, Kursk 305040, Russian Federation e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_9

79

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1 Introduction More and more researchers are devoting their attention to the development of models of deformation of reinforced concrete using the basic principles of fracture mechanics in bending with torsion [1–9]. The research of crack resistance and rigidity of reinforced concrete structures under bending with torsion has been conducted in many (theoretical and experimental) works [10–13], but the problem of crack opening widths has significant errors. In [2–4, 7, 8, 14–18, 20–23], the influence of the Professor Kolchunov effect has been observed for an alternative elliptical crack form. It causes movement and crack opening at a distance of two diameters from the axis of the working reinforcement. Such significant deformations of reinforced concrete have not yet actually been considered. Continuing research, the paper presents the main points of the development of a universal dual-console element (DCE) for solving the problem of complex resistance of reinforced concrete structures. This was made possible by technologies of experimental research, providing further improvement of safety of structural systems of buildings and structures under conditions of accident-free operation [19–22]. The object of this research is reinforced concrete structures of industrial and civil buildings. The purpose is the development of the effect of reinforced concrete in the form of deformation impact in the violation of the continuity of concrete and reinforcement reaction for crack resistance and rigidity based on the fracture mechanics under the action of bending with torsion. The main objectives of the research: – development of the dual-console element for a spatial crack based on fracture mechanics relations; – construction of equations for finding the length of spatial cracks and crack opening widths using the obtained effect of reinforced concrete; – determination of the physical essence of the phenomenon of crack resistance and rigidity development using approximation of rectangular cross sections by means of small squares in matrix elements.

2 Methods Opening of Spatial Cracks and the Rigidity of Reinforced Concrete Structures Under Bending and Torsion. To obtain scientific results, spatial crack modeling was used for the Professor Kolchunov effect of reinforced concrete. Its physical essence lies in the additional deformation effect [2–4, 7–8, 14–18, 20–23, etc.] of the reaction of reinforcement and concrete in the form of an ellipsoid crack, associated with a violation of the continuity of concrete for a dual-console element (DCE) at a

The Effect of Reinforced Concrete …

81

distance of two diameters oof the working reinforcement axis or from an alternative kinematic crack. The main aspects of fracture mechanics are focused on the peculiarities of the stress–strain state in areas with disrupted continuity including cracks. The mechanism of crack shear during its development is embedded in the pre-fracture zone with localized deformation w and the formation of specific crack surfaces. The determination of the energy release rate ζbu is based on the fracture mechanics functional:  ζbu = lim

δ A→0

δW − δV δA

 =

dW dV − , dA dA

(1)

where δV —the decrease in the potential energy of the body when the crack advances by a small increment δa; δW —the additional work performed on the body when the crack advances by a small increment δa. Let’s consider basic provisions and features of the dual-console element, which includes a crack for the development of the calculation apparatus of reinforced concrete. For a solid body, the stress–strain state has analyzed by methods of the theory of elasticity and plasticity. An elementary cube describing the relationship between stresses and strains at a point is distinguished. In the transition to the section, the established relation has integrated over the whole section. As a result, the problem has obtained in differential equations, the exact solution of which is usually very difficult. The hypothesis of planar deformations for the whole cross-section, which simplifies the solution of the problem, is adopted in the strength of materials. For a body with a crack, the methods developed in the theory of elasticity, plasticity and strength of materials are inapplicable in establishing the relationship between stresses and displacements. But the use of the method of sections to the material with cracks brings its positive results for the approximate determination of the stress intensity coefficient. This method can also be used to isolate a special DCE in fracture mechanics. The application of the dual-console element for rod reinforced concrete elements has its own peculiarities. First, if the long dual-console is allocated for the entire length of the crack, and not for some elementary section of it, then the crack length h cr c is determined by the following condition of fracture mechanics: dζbu = 0. dh cr c

(2)

At the same time, the difficulties arising here are the main reason (along with the need to use complex numbers) why the detailed tools of fracture mechanics, which allow us to study the features of the stress–strain state in the vicinity of the crack, have not yet found proper application in the theory of reinforced concrete. Formula (2) has conditioned by Saint–Venant’s principle as applied to near reinforcement zones of working reinforcing bars near a crack, and confirmed by a number of experimental research [13].

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The short dual-console element of known length is located at half the length of the area adjacent to the crack between the working reinforcing bars, for example, between the transverse or multilevel longitudinal reinforcing bars, Fig. 1. The condition ∂ζbu /∂h cr c = 0 (from which the crack length h cr c is found) have replaced by the condition for finding the projection of the spatial crack C using the Lagrange function for many variables   f qsw , x B , σs , x, σb , σs,I , σb,I , C2 ...λ1 , λ2 , λ3 , λ4 , λ5 , λ6 , λ7 , ... and F1,2 = Lagrange multipliers λi .

Fig. 1 Universal DCE for the dependences of fracture mechanics in a separate (average) strip of reinforced concrete of spatial cracks: a the characteristic stress diagrams in the tensile concrete and DCE in the vicinity of the spatial crack adjacent to the working axis reinforcement X s Ys Z s using the i-axis X i Yi Z i for tearing (±0, 5a∗ ), transverse (±0, 5b∗ ) and longitudinal shear (±0, 5c∗ ); b drawing node for the stress–strain state features at the crack tip

The Effect of Reinforced Concrete …

⎫ 1 2 m + λ1 ∂ϕ + λ2 ∂ϕ + ... + λm ∂ϕ =0 ⎪ ⎪ ∂ x1 ∂ x1 ∂ x1 ⎪ 1 2 m + λ1 ∂ϕ + λ2 ∂ϕ + ... + λm ∂ϕ =0 ⎬ ∂ x2 ∂ x2 ∂ x2 , .......................................⎪ ⎪ ⎪ ∂f 1 2 m + λ1 ∂ϕ + λ2 ∂ϕ + ... + λm ∂ϕ =0 ⎭ ∂ xn ∂ xn ∂ xn ∂ xn ∂f ∂ x1 ∂f ∂ x2

83

(3)

The projection of the spatial crack C has found from the extremum condition of the function of many variables and the ensuing equality to zero of the corresponding partial derivatives. Secondly, the forces in the sections at distances t and b from the crack must be connected with the required parameters of the stress–strain state of the reinforced concrete element. Thirdly, there are virtual movements of the DCE cantilevers when the neutral axis of the reinforced concrete element rotates and the working reinforcing bar rotates, caused by the dowel forces, i.e. the cantilever pinch from both sides may not be absolutely rigid. Thus, the application of the DCE, which is transformational between the dependencies of fracture mechanics and the theory of reinforced concrete, is a very important and challenging problem. It should be linked not only with the problem of determining the stress–strain state of the cross-section of a reinforced concrete element, but also with the problem of the distribution of bond between the reinforcement and the concrete. The appearance of a crack in a solid body can be considered as a certain deformation effect, which is reflected in the peculiarities of the bond between the reinforcement and the concrete in the areas adjacent to the crack. The connection between the stress–strain state and the ζbu value in the pre-fracture zone seems to be most successful with the DCE, in contrast to the use of the Gourse function with complex numbers. The crack edge compliance for the value ζbu , is determined using the fracture mechanics functional. Thus, the DCE is used as a link between the dependencies of solid mechanics and fracture mechanics. The above conclusions were used in the development of a universal short dualconsole element to solve the problem of resistance of reinforced concrete structures in torsion with bending (Fig. 1).

3 Results As a result, the effect of reinforced concrete for the opening of spatial cracks and rigidity of reinforced concrete structures in bending with torsion was developed [2– 4, 7–8, 14–18, 20–23, etc.]. In calculation models A and B for the new dual-console elements, the left and right elements are located up to half the width of the structure from the neutral axis to the lower and upper edges of length equal to lt,∗ (Fig. 2, a and b).

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Fig. 2 The dual-console element in bending with torsion for a single (middle) strip of spatial crack DCE 1, rig; DCE 1, lef—first (bottom) right and left elements; DCE 2, rig; DCE 2, lef—second (top) right and left elements: a model A; b model B

The first (bottom) right (DCE1, rig) and left (DCE1, lef) element in a separate middle strip in the shape of a propeller of width bi and length lt,∗ has the length: lt,i,∗,m,rig1 =

lt,1−3d ,∗ + lt,2−4d ,∗ , 2

(4)

lt,i,∗,m,le f 1 =

lt,1−3d ,∗ + lt,2−4d ,∗ . 2

(5)

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85

The second (top) right (DCE2, rig) and left (DCE2, lef) element in a separate middle strip of width bi and length lt,∗ has the length: lt,i,∗,m,rig2 =

lt,1−3up ,∗ + lt,2−4up ,∗ , 2

(6)

lt,i,∗,m,le f 2 =

lt,1−3up ,∗ + lt,2−4up ,∗ . 2

(7)

bt,∗,m = const1 was taken as an approximation for the right and left parameters bt,i,∗,m,rig1 , bt,i,∗,m,rig2 , bt,i,∗,m,le f 1 , bt,i,∗,m,le f 2 and tt,∗,m = const2—for tt,i,∗,m,rig1 , tt,i,∗,m,rig2 , tt,i,∗,m,le f 1 , tt,i,∗,m,le f 2 . A universal dual-console element (DCE) for implementing the dependences of fracture mechanics in reinforced concrete of spatial cracks in its surface for a single (average) strip has obtained. The characteristic stress diagrams in the tensile concrete and DCE in the vicinity of the spatial crack adjacent to the working axis reinforcement X s Ys Z s using the i-axis X i Yi Z i for tearing (±0, 5a∗ ), transverse (±0, 5b∗ ) and longitudinal shear (±0, 5c∗ ) have been developed (Figs. 1 and 2). We also have made a successive displacement of the axes on xi = xc ± 0.5a∗,i , yi = yc ± 0.5b∗,i , z i = z c ± 0.5c∗,i and rotation by angle αi (for cosine l), βi (for cosine m), θi (for cosine n). xi = xc · (±li ), yi = yc · (±m i ), z i = z c · (±n i ). The joint displacement and rotation of the axes have the form (Fig. 2): ⎧ ⎪ ⎨ xi = (xc ± 0.5a∗,i ) · (±li ); yi = (yc ± 0.5b∗,i ) · (±m i ); ⎪ ⎩ z i = (z c ± 0.5c∗,i ) · (±n i ).

(8)

t is a parameter in accordance with the Saint–Venant principle and the studies of the zone near the reinforcement using semi-analytical and numerical methods equal to half the diameter of the reinforcement in the first approximation. The tensile stresses in the selected sections are distributed according to the square parabola law from the neutral axis to the point where the stress sign changes. In this case, their maximum value is limited to Rbt , so in a significant area the actual distribution of tensile stresses is close to a rectangle, regardless of the law of their distribution in the elastic stage. Compressive stresses in the same sections in the areas adjacent to the reinforcement have a triangular diagram. b in the zone adjacent to the reinforcement is taken equal to the value of the sum of the protective layer and half of the diameter. This value is doubled as the strip is highlighted on both sides of the reinforcing bar. In bending (tension–compression), expression (9) is not used because the geometric dimensions of the crack do not change in thickness b. The spatial crack profile changes in thickness during torsion. b = 2(as − 0.5d),

(9)

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b has taken no more than 4 diameters of the working reinforcement. Here as and d are the distance from the center of the working armature to the bottom face of the cross section and the diameter of the working armature, respectively. For the isolated DCE at thickness b according to formula (9), it is logical to simplify the surface by taking its slope constant within b. Angle  is the slope angle of the spatial crack in the plane of the cross section. The angle acr c of inclination of the spatial crack in the vertical longitudinal plane perpendicular to the cross-section has also assumed constant within the distance between the transverse reinforcement. Since one half of the thickness b of a rectangular reinforced concrete structure, it has taken equal to α1,cr c , and for the other half it has taken equal to α2,cr c : α2,cr c = α1,cr c ± 90◦ .

(10)

The sign “plus” or “minus” are taken depending on the beginning of the angle readout relative to the side surface (right or left). The adopted simplifications make it possible to greatly simplify the resolving equations of the spatial crack surface (at each iteration step) using it discretely for a selected strip of thickness b. The iterative process is organized using a transitive (transformational) DCE. The dual-console element is a transformational element between the dependencies of fracture mechanics and the equations of reinforced concrete theory. To determine the unknown X 1 = T , …X n , author used the expression of the value ζbu as a function of the suppleness. The element’s compliance is determined e0 = C · P0 ; V =

2 · P 2 · C; 3 0

dV 3 δP 2 δC = ·C · P · + · P2 · . dA 4 δA 3 δA

(11) (12) (13)

Similarly, we can transform dW/d A: δe δP 2 dW δC =P· = P ·C · + · P2 · . dA δA δA 3 δA

(14)

Substituting expressions (11), (12) into Eq. (1), we have obtained: ζbu =

  δP 1 δC P2 · . −C · P · 3 δA δA

(15)

For the dual-console element under the action of a number of forces (T, P1 , P2 , q, Mcon ), expression (13) has taken the form:

The Effect of Reinforced Concrete …

87

1 = 3 i=1 n

ζbu



 Pi2 · δCi δ Pi − Ci Pi . δA δA

(16)

Displacements (1 ...i ) in any sections are determined by structural mechanics methods. The displacements associated with the rotation of the console by an angle ϕ2 are determined from the geometric relations: δ I = ϕ2 · h cr c ;   1 δ I I = ϕ2 · h cr c − t ; 3   5 δ I I I = ϕ2 · h cr c − t − m . 8

(17) (18) (19)

The element’s compliance is of the form: CI =

2 · I ; T

(20)

CI I =

2 · I I ; −PI

(21)

CI I I =

2 · I I I ; P2

(22)

2 · ϕ2 . Mcon

(23)

C0 =

In this case, the definition of the parameters included in formulas (20)–(23) does not cause difficulties, for example: 

P1 = 0.5 · σbt · b · t;

(24)

2 · Rbt · b · m. 3

(25)

P2 =

The compliance for a distributed load, can be expressed as: Cq =

2 · Aq , q

(26)

 where q = b · Rbt Aq —the area of the displacement diagram at the section of the distributed load. The other parameters in Fig. 2 are found in the same way.

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When all parameters in formula (15) are expressed as a function of the parameter hcr c , we can proceed to transformations of this formula:   1 ∂C I ∂C I I ∂C I I I 2 · ∂Cq + M 2 · ∂C 0 + b2 Rbt · T 2 · + P12 · + P22 · con 3b ∂h cr c ∂h cr c ∂h cr c ∂h cr c ∂h cr c ∂T ∂ P1 ∂ P2 ∂ Mcon −C I · T − C I I P1 · − C I I I P2 · − C0 Mcon · . ∂h cr c ∂h cr c ∂h cr c ∂h cr c ζbu =

(27)

Performing differentiation after algebraic transformations, we obtain the  dependence (function) linking the tangential force near the crack  T h cr c , ζτ , εq1 el , b, t, η1 , η2 , η5 , η7 , η8 , η14 , η15 with the length h cr c using the concrete constant ζbu . The relative mutual displacements of reinforcement and concrete are determined from the dependence (Fig. 3): εg (x) = εs (x) − εbt (x) ,

(28)

where εs (x)—the relative deformations of the reinforcement; εbt (x)—the relative deformations of the concrete in section x. The calculation of the distance between cracks lcr c is obtained from the condition according to which the elongation of the concrete on the surface of the structure in the average cross section (in the area between the cracks) is equal to εbu . Thus, the relative deformations of concrete from the dependence (28) and the equilibrium condition of the reinforcing bar are designed to determine the value of lcr c . The differentiation of the condition (28) has the form:

Fig. 3 Deformations of concrete and reinforcement: a deformation diagrams of concrete, reinforcement εs (x or z) and their relative displacements εg (x or z) in the section between inclined (for flat model) or spatial (for spatial model) cracks in reinforced concrete structures; b deplanation in the section with a crack for dependence of reinforcement diameter ds and radius of boundary layer r on coefficient kr

The Effect of Reinforced Concrete …

89

dεg (x) + Bεg (x) = 0. dx

(29)

The solution of the homogeneous first-order differential equation has the form: εg (x) = C · e−Bx .

(30)

The integration constant C can be found from the boundary condition x = 0, εbt,c (x) = −σbt,c /(vb E b ): C=

  1 σbt,c B3 . + − B B(1 − K ) vb E b

(31)

Taking into account many years of experimental and numerical studies given in [2–4, 13], based on the replacement of the reinforced concrete element with a calculation model having properties close to real, for simplification purposes, and substituting in (31) after appropriate conversions, we have obtained values 1/K = 1 + As E s : (ωbt (x)Abt (x)E b · vbt (x)) = 1 + δ · μs · n(h 0 + x · (γ − 1)) : (0.32 · h 0 · (γ − ξ )(γ + 0.03ξ )); B = (Ss · G)/(K · As · E s ); B2 = (δ · Q · t · B) : (G · vb · Ab );B3 = εs + T /(E s · As ) − σbt,c /(vb · E b ) − B2 . After substituting C and the corresponding transformations, the equation has taken the form: εbt (x) = (1 − K )B3 (1 − e−Bx ) −

σbt,c . vb E b

(32)

Taking into account (32), we have obtained: e−B(0.5lcr c −t∗ ) = 1 + εbt,u +

σbt,c vb E b B3 (K − 1)

(33)

and ln B4 = −B(0, 5lcr c − t∗ ).

(34)

From (34) the distance between cracks has equal: lcr c =

2(ln B4 − Bt∗ ) . −B

(35)

The parameters used here take into account the boundary deformations of concrete and reinforcement, deformation characteristics, the effect of the discontinuity of concrete, the geometric characteristics of the section, and the bonding characteristics of reinforcement and concrete: Abt (x)—the area of the tensile concrete in

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section x; Ss —cross-sectional perimeter of the reinforcement; G—notional deformation modulus of bonding of reinforcement and concrete, G = 0, 3E b ; δ = (1 − ξ ) : (γ − ξ )—coefficient taking into account the section height and the height of the compressed zone ξ = x B : h 0 —relative height of the concrete compression zone; γ = h : h 0 —the ratio of the section height to the working section height; Q—the greatest lateral force acting in the cross-section (usually we can take Q = Rsup ); εs = σs : (vs E s )—strains of the tensile reinforcement in the crack; T = ω · τb · Ss · t—the resultant conditional tangential stress in the local zone adjacent to the crack; σbt,c —stress in the compressed zone of concrete equal to σbt,c = 3, 05Rbt until the results of research are specified; ω—coefficient of filling the shear stress diagram equal to ω = 0, 67 until the results of research are specified; τb —tangential stresses in the concrete of the local zone adjacent to the crack equal to τb = 2, 9Rbt until the results of research are specified; t—distance from the bottom edge of the concrete to the axis of the stretched reinforcement; vb — elasticity coefficient for tensile concrete (for the second group is taken as equal to vb = 0, 45); εbt,u —ultimate tensile deformations of concrete; ωbt (x) and vbt (x), the coefficient of filling of the deformation diagram and the coefficient of elasticity of tensile concrete in the section x between cracks (ωbt (x) · vbt (x) ≈ 0.5)); the parameter B4 = 1 + σbt,c /((K − 1)B3 νb E b ) + εbt,u . Dependence (34) takes into account the influence of important factors. These are deformations of reinforcement in the section with a crack, parameters of the bond of reinforcement B with concrete, geometrical characteristics of the section and characteristics of concrete and reinforcement, deformation effect (arising in a reinforced concrete element after the breach of continuity), etc. The distance between cracks is the most important parameter needed to determine the width of crack opening in reinforced concrete structures. The crack opening width grows with increasing strain and with decreasing distance between cracks. When comparing the functional or discrete level values of lcr c for several levels, the new level of cracking corresponds to the load level at which the following inequality is observed: lcr c,i ≤ η · lcr c,i−1 ,

(36)

lcr c,i,rig + lcr c,i,le f = lcr c,i−1 .

(37)

A complete picture of the different types of cracks adjacent to the concentrated for cracking lasts until fracture occurs. Several levels of cracking were distinguished for the system of inequalities, instead of one, as it is accepted in a number of known methods:

The Effect of Reinforced Concrete …

⎫ ⎪ lcr c > lcr c,1 − no cracks; ⎪ ⎪ ⎪ ⎪ lcr c,1 ≥ lcr c ≥ lcr c,2 − f ir st level; ⎬ . lcr c,2 ≥ lcr c ≥ lcr c,3 − second level; ⎪ ⎪ ....................................⎪ ⎪ ⎪ ⎭ lcr c ≥ 6t∗

91

(38)

The minimum value of the distance between spatial cracks is 6d ≤ lcr c,min ; b ≤ lcr c,i ≤ 0, 5lcr c,i−1 for beam width; h ≤ lcr c,i ≤ 0, 5lcr c,i−1 for plate height. Experimental research of the crack opening width has values that differ by up of two to three. Crack opening is the accumulation of relative concentrated mutual displacements of reinforcement and concrete on both sides of the crack in the areas where there is a discontinuity in the concrete from the elliptical crack instead of their alternative kinematic forms—a development of the scientific hypothesis of Thomas and Vl. Kolchunov. Corollary. The deplanation of concrete in the section with a crack depending on the distance to the surface of the contact with the reinforcement has been taken into account. The coefficient kr at a distance of two diameters from the axis of the working reinforcement or the protective layer of the reinforcement was used. As a result, the crack opening width has taken the following form   2B3 2T + (1 − e−B·(0.5lcr c −t∗ ) ) + 2B2 (0.5lcr c − t∗ ) , acr c = ϕ1 · ϕ2 · ϕ3 · kr · − G·t B (39) where ϕ1 —the coefficient, taking into account the duration of the load, (taken equal to 1.0—at short-time action of load; 1.4—at continuous action of load); ϕ2 —the coefficient taking into account the profile of the longitudinal reinforcement, (taken equal to 0.5—for periodic and wire rope reinforcement; 0.8—for smooth reinforcement); ϕ3 —coefficient taking into account the type of loading (taken equal to 1.0—for bending and eccentrically compressed elements; 1.2—for tensile elements); kr —coefficient according to the research results. Rigidity and Approximation of Rectangular Cross Sections Using Small Squares in Matrix Elements. The rigidity of reinforced concrete structures D pq (p, q–1, 2, 3, 4) in bending with torsion has been obtained from the approximation of rectangular cross-sections using small squares in matrix elements ai j . n—the total number of small squares; j—cross sections along the x-axis, j = 1–6. Author has obtained the bending moment Mbend,ij , torsional moment Mt,i j , longitudinal force Nij , and lateral force Q i j for cross sections 1–6. The bending moments from the external load are located relative to the coordinate selected axes within the  =M +M /η + N · e + Q · a − c transverse (in the XOZ and YOZ planes). M x x,d t x j j  = M · η + M +N · φ+Q · χ ; N = M /e +M /φ+N + Pi · a; M t x t,d x x t d    ; Mt,i /Mx ; χ = Mt /Q + Mt / Pi ; φ = Mt /N + Mt,i /N ; η = Mt /Mx +

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Mx = Q · a = Rsup · a; Q = Mx /(a j − c j ) + Mt /χ + Q d ; lateral force for transverse ∗ ∗ · c j + Mt /χ − Q b =σsw,d · Asw · c j /sw + Mt /χ − Q b . reinforcement Q sw = qsw,d In structural mechanics for internal and external forces, for example Msup = Mbend − Rsup · am,b − N · ex − Mt /η. The rigidity of the cross-sections has the form of a matrix. The relative longitudinal deformation εb,0,x, j,i of the neutral axis bending fiber (second functional and hypothesis of linear deformations [23, etc.]), the curvature rx,1j,i of the longitudinal axis in the considered cross section and the twist angle ϕ A, j,i (first functional and hypothesis of angular deformations [23, etc.]) were found for compressed concrete, longitudinal and transverse reinforcement. The dependencies connecting the relative deformations and stresses of concrete and reinforcement have the form εb, j,i = ε0,b, j,i + rx,1j,i · Z bx, j,i ; εs, j,i = ε0,s, j,i + · Z sx, j,i , σbi = E b · vbi · εbi ; σs j = E s j · vs j · εs j ; τb, j,i = G b · vb, j,i · γb, j,i ; E b —initial modulus of elasticity of concrete; E s j —modulus of elasticity of the jth reinforcement bar; vbi —coefficient of elasticity of concrete of the i-th section; vs j —coefficient of elasticity of the j-the reinforcement bar. Then additionally have found forces and displacements (in the crack), “Nagel” forces, relative angular deformations, torsional rotation angle ϕ A,b,l2 ,sum, j,i = ϕb,l2 +   ϕb,l2 ,add = ϕ2,A, j (Mt,i ·l j ·Y3,i (z, y))/(Mt · Ab,c,i ·z b,t,i ) ± 0, 5cr c,zx ± 0, 5cr c,yx · force ofcompressed concrete and working reinforcekr , displacement of lateral      Pi · ment ( Q,b, j,i =  Q b, j,i · η Q,b / G b (λ) · Ab, j,i + add,b = Rsup− η Q,b / G b (λ) · Ab, j,i + cr c,zx,Q ;  Q,s = Q s, j,i · η Q,s / G s (λ) · As, j,i + add,s ); G(λ) = (v(λ)E b )/(2(1 + v(λ))). The transverse shear cr c (y, z) and longitudinal shear cr c (x, z) (see Figs. 1 and 2) are obtained from the realization of fracture mechanics dependences for the dual-console element in reinforced concrete. We obtained detachment (displacement ±0, 5a∗ for width of opening 0, 5acr c ), transverse shear (for isplacement ±0, 5b∗ for 0, 5cr c (y, z)); longitudinal shear (for displacement ±0, 5c∗ for 0, 5cr c (x, z)) of the spatial crack. 1 r x, j,i

cr c (x, z) = 2 · (u gz · sin α − u gx · cos α),

(40)

cr c (y, z) = 2 · (u gz · sin θ − u gy · cos θ ).

(41)

where u gx , u gz , u gy —longitudinal, vertical and transverse movements for the strip lt,i,∗,m,rig1 , lt,i,∗,m,rig2 , lt,i,∗,m,le f 1 , lt,i,∗,m,le f 2 ; ψs , ψsw coefficients for compressed concrete and working reinforcement; As /μ = A j,i for small squares of width bi and height h i ). As a result, we have and inverse transition, where we know r1x , ϕ, ε0 and  Q , but do not know Mx , Mt , N , Q. Thus, we have got the transitions from the first to the third: direct transition 1 from internal forces Mx , Mt ,N , Q, reverse transition 2 relative deformations r1x , ϕ, ε0 ,  Q , direct transition 3 internal forces Mx , Mt , N , Q and algebraic levels from the first to the fourth.

The Effect of Reinforced Concrete …

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Thus, we obtain the elements of the matrix, where the physical meaning can be determined using functionals, deformation hypotheses and coefficients ψs,m , ψsw,m without concrete tension, bending and torsional moments, as well as longitudinal and transverse forces [23].

4 Conclusions 1.

2.

3.

4. 5.

6.

7.

The author has discovered the effect of reinforced concrete. Its physical essence lies in the additional deformation effect of the reaction of reinforcement and concrete in the ellipsoid crack shape profile, associated with a violation of the continuity of concrete and reinforcement reactions for a dual-console element (DCE) from the main spatial crack at a distance of two diameters of the working reinforcement axis.Analysis of the character of the diagram using many years of experimental data shows that the deformations of concrete in the areas adjacent to the cracks change in direction. In this case, there is a need to determine the reaction and deformation effects of concrete and reinforcement in the spatial crack using a dual-column element. On the surface of the spatial crack the dependence of fracture mechanics in the form of a universal DCE for a separate strip has been implemented. The characteristic stress diagrams in the tensile concrete adjacent to the working axis reinforcement X s Ys Z s using the i-axis X i Yi Z i for tearing (±0, 5a∗ ), transverse (±0, 5b∗ ) and longitudinal shear (±0, 5c∗ ) have been developed. The dual-console element for the parameters has constructed for parameters bt,i,∗,m,rig1 , bt,i,∗,m,rig2 , bt,i,∗,m,le f 1 , bt,i,∗,m,le f 2 after the joint displacement and rotation of the axes xi = (xc ± 0.5a∗,i ) · (±li ); yi = (yc ± 0.5b∗,i ) · (±m i ); z i = (z c ± 0.5c∗,i ) · (±n i ). In helical spatial cracks for their longitudinal cr c,z and transverse cr c,y shear have determined using cosines l, m, n in its separate DCE strip. Different levels of cracking of spatial cracks have been identified for the distance between adjacent spatial cracks lcr c,i (main cracks) in determining the full pattern of cracks during loading Distances between spatial cracks have been found from the formula lcr c = 2(ln B4 − Bt∗ ) : (−B). εs = σs : (vs E s )—deformation of the tensile reinforcement in the crack; T = ω · τb · Ss · t—resultant of the conditional tangential stresses in the local zone adjacent to the crack and σbt,c —stresses in the compressed zone of concrete, the deformation effect occurring in a reinforced concrete element after the violation of continuity; parameters of coupling B of reinforcement with concrete and parameters B2 , B3 , B4 . A complete picture of the different types of cracks adjacent to the concentrated force and to the support is constructed for the levels of cracking along the longitudinal and transverse reinforcement of the reinforced concrete structure, comparing the functional or discrete level value of lcr c .

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8.

Crack opening is the accumulation of relative concentrated mutual displacements of reinforcement and concrete on both sides of the crack in the areas where there is a discontinuity in the concrete from the elliptical crack instead of their kinematic forms—a development of the scientific hypothesis of Thomas and Vl. Kolchunov. The deplanation of concrete in the section with a crack depending on the distance to the surface of the contact with the reinforcement has been taken into account. The coefficient kl at a distance of two diameters from the axis of the working reinforcement or the protective layer of the reinforcement was used. 9. Analysis of the ratios has shown that the crack opening width increases with increasing strain and with decreasing distance between the cracks. 10. The rigidity and opening of spatial cracks of reinforced concrete structures under bending with torsion in elastoplastic compressed concrete have been obtained. The approximation of the rectangular cross-sections using the small-square 4 × 4 matrix with the elements for the stiffness characteristics of D pq has been performed. The inverse transition has been obtained, where the known r1x , ϕ, ε0 and  Q , but unknown Mx , Mt , N , Q using functionals, deformation hypotheses and coefficients ψs,m , ψsw,m . In this case, the expressions have a convolute and a fully expanded form.

References 1. Karpenko NI (1996) General models of reinforced concrete mechanics. Stroyizdat, Moscow. ISBN 5-274-01682-0 2. Golyshev AB, Kolchunov VlI (2009) Reinforced concrete resistance. Osnova, Kiev 3. Bondarenko VM, Kolchunov VI (2004) Design models of the power resistance of reinforced concrete. Publishing House ABC, Moscow. ISBN 5-93093-279-4 4. Veruzhsky YuV, Kolchunov VlI (2005) Methods of reinforced concrete mechanics. NAU, Kiev 5. Veryuzhsky YuV, Golyshev AB, Kolchunov VlI, Klyueva NV, Lisitsin BM, Mashkov IL, Yakovenko IA (2014) A reference guide to structural mechanics: Volume II. Publishing House ABC, Moscow. ISBN 978-5-4323-0007-2 6. Kolchunov VlI, Fedorov VS (2020) Conceptual hierarchy of models in the theory of resistance of building structures. Promyshlennoe i grazhdanskoe Stroitelstvo [Industrial Civ Eng]. 8:16– 23. https://doi.org/10.33622/0869-7019.2020.08.16-23 7. Golyshev AB, Kolchunov VlI (2015) Resistance of reinforced concrete structures, buildings and structures erected in difficult engineering and geological conditions, Kiev 8. Fedorov VS, Kolchunov VI, Pokusaev AA, Naumov NV (2020) Calculation models of deformation of reinforced concrete constructions with spatial cracks. Russian J Build Constr Archit 6–26. https://doi.org/10.36622/VSTU.2020.47.3.001 9. Karpenko NI, Kolchunov VI, Travush VI (2021) Calculation model of a complex stress reinforced concrete element of a boxed section during torsion with bending. Russian J Build Constr Archit 7–26. https://doi.org/10.36622/VSTU.2021.51.3.001 10. Kim C, Kim S, Kim K-H, Shin D, Haroon M, Lee J-Y (2019) Torsional behavior of reinforced concrete beams with high-strength steel bars. ACI Struct J 116:251–233. https://doi.org/10. 14359/51718014 11. Bernardo L (2019) Modeling the full behavior of reinforced concrete flanged beams under torsion. Appl Sci 9:2730. https://doi.org/10.3390/app9132730

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12. Lin W (2021) Experimental investigation on composite beams under combined negative bending and torsional moments. Adv Struct Eng 24:1456–1465. https://doi.org/10.1177/136 9433220981660 13. Travush VI, Karpenko NI, Kolchunov VI, Kaprielov SS, Dem’yanov AI, Konorev AV (2018) The results of experimental studies of structures square and box sections in torsion with bending. Build Reconstr 6:32–43 14. Kolchunov V, Smirnov B, Naumov N (2020) Physical essence of the “nagel effect” for main reinforcement in an inclined crack of reinforced concrete structures. IOP Conf Ser Mater Sci Eng 896:012055. https://doi.org/10.1088/1757-899X/896/1/012055 15. Kolchunov V, Dem’yanov A, Naumov N (2020) Analysis of the “nagel effect” in reinforced concrete structures under torsion with bending. IOP Conf Ser Mater Sci Eng 953:012052. https://doi.org/10.1088/1757-899X/953/1/012052 16. Kolchunov VI, Dem’yanov AI, Naumov NV, Mikhaylov MM (2019) Calculation of the stiffness of reinforced concrete structures under the action of torsion and bending. J Phys Conf Ser 1425. https://doi.org/10.1088/1742-6596/1425/1/012077 17. Kolchunov VI, Dem’yanov AI, Naumov NV (2020) The second stage of the stress-strain state of reinforced concrete constructions under the action of torsion with bending (theory). IOP Conf Ser Mater Sci Eng 753:032056. https://doi.org/10.1088/1757-899X/753/3/032056 18. Kolchunov VlI, Dem’yanov AI (2019) The modeling method of discrete cracks and rigidity in reinforced concrete. Mag Civil Eng 4(88):60–69. https://doi.org/10.18720/MCE.88.6 19. Demyanov A, Kolchunov VI (2017) The dynamic loading in longitudinal and transverse reinforcement at instant emergence of the spatial srack in reinforced concrete element under the action of a torsion with bending. Istraz i Proj za privredu 15:377–382. https://doi.org/10.5937/ jaes15-14663 20. Kolchunov VlI, Dem’yanov AI (2018) The modeling method of discrete cracks in reinforced concrete under the torsion with bending. Mag Civil Eng 5(81):160–173. https://doi.org/10. 18720/MCE.81.16 21. Kolchunov VlI, Dem’yanov AI, Mikhaylov MM (2020) Static-dynamic deformation of compressed concrete in an indeterminate reinforced concrete frame during bending with torsion. News of higher educational institutions. Construction 4:5–21 22. Kolchunov VI, Kolchunov VlI, Fedorova NV (2018) Deformation models of reinforced concrete under special impacts. Promyshlennoe i grazhdanskoe Stroitelstvo [Industrial Civ Eng]. 8:54–60 23. Kolchunov VI, Demyanov AI, Protchenko MV (2021) Moments in reinforced concrete structures under bending with torsion. Build Reconstr 95:27–46. https://doi.org/10.33979/20737416-2021-95-3-27-46

Numerical Modeling of Steel Joints Anastasia Alekseeva , Nina Buzalo , Jens Otto , and Alexey Bulgakov

Abstract A method for modeling and determining the stress fields at the junction of a beam with a column is presented. The study was carried out on the basis of experimental studies of the unit under cyclic loads by S.V. Polyakov and co-authors. On the basis of experimental data, a numerical model was created to assess the influence of the geometric parameters of the assembly elements on its bearing capacity, and to determine the effective stress concentration factor. For the analysis, the finite element method in specialized software was used. The resulting model makes it possible to more accurately determine the bearing capacity of the joint and identify areas with an increased level of stress. Specific values of the effective concentration factor were obtained, ranging from 1.9 to 4.5. The results obtained open up prospects for further research on the optimization of joints of steel structures and their successful application in civil engineering. Keywords Numerical modeling · Steel structures · Connections · Stress concentration factors · Equivalent stresses

1 Introduction In the steel frames of multi-storey civil and industrial buildings, one of the most responsible and important places are the joints of columns with beams [1], which are performed mainly during installation. The improvement of the nodal joints of the frame in order to reduce steel consumption is achieved, as a rule, through the use of A. Alekseeva · N. Buzalo South-Russian State Polytechnic University, Prosveshcheniya Street 132, 346428 Novocherkassk, Russia J. Otto Technical University of Dresden, Mommsen St. 10, 01069 Dresden, Germany e-mail: [email protected] A. Bulgakov (B) Southwest State University, 50 let Oktyabrya Street 94, 305040 Kursk, Russia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_10

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high-strength steels, the development of new effective types of structural units, the introduction of optimal design methods [2]. When designing joints of steel structures, a large amount of information is required for an objective assessment of the effect of the connection parameters on the strength resistance of the frame elements [3]. In order to reduce the consumption of materials and the cost of construction, it is impossible to discount the requirements of increasing the reliability and durability of structures, improving the technology of their design and manufacture, which is directly related to the refinement of design schemes and the creation of adequate design models [4]. The accuracy of the computational model is based on the results of physical studies of real operational structures and numerical studies of computer models, studies of real operating loads, especially seismic ones. The research results make it possible to identify real operating conditions, study the processes of deformation and destruction of the structure and establish acceptable limits of idealization of computational models [5]. The introduction of numerical modeling of steel frame assemblies makes it possible to refine the design schemes, take into account the spatial operation of structures, the real properties of materials, including the behavior of the material beyond the elastic limit, inhomogeneities causing stress concentration (stresses increase in small areas adjacent to the places of heterogeneity) [6].

2 Method In this article, the task is to determine the stress distribution in the node of the rigid connection of an I-beam with a square column made of four corners (Fig. 1). This design is investigated and analyzed in [7]. All connection elements are made of C235 steel. The mechanical properties of steel are accepted according to GOST 2777288: σt = 235 MPa; σw = 360 MPa. The computational model of the test sample is presented in the form of a volumetric thin-walled body. Such a model is usually used for products made of sheet and rolled steel, provided that the thickness of the walls is more than 10 times smaller than the dimensions of the section. The model is made of flat linear plate elements (Fig. 1) of the appropriate thickness for beam and column parts, as well as one-dimensional rigid elements (RBE-2 in terms of the Nastran solver) for welded and bolted joints. The use of plate elements in this task is permissible, since the thicknesses of all the parts used are not variable (as, for example, in shelves of I-beams with a shelf slope), and also satisfy the condition of falling into the category of thin-walled structures [8]. It is important to note that the use of RBE2 elements for modeling welded joints introduces errors in the calculation model, since it is an absolutely rigid element that causes large stress spikes [9] in neighboring elements of finite rigidity (Fig. 2). To assess the strength of parts of welded structures modeled using rigid elements, the technique of indenting two thicknesses from the welding line is used [10, 11]. According to the stresses acting at the distance of such an indentation in the finite element model, it is possible to correctly estimate the strength of the near-shock zone.

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Fig. 1 The finite element model

Fig. 2 Surge of stresses near a rigid element

For this model, we assume that the welds are made qualitatively, and the strength of the welds is not lower than the strength of the near-seam zone. Also in the model, friction contacts are assigned between the overlay (part “1” in the Fig. 3) and the bolt shelf (part “2” in the Fig. 3) for the correct distribution of contact interaction forces among the assembly parts. The model is fixed along the upper and lower base plate from the condition of ensuring the immobility of the studied structure as a rigid body. Hinges are implemented in the upper and lower base plate, rotation along the Z axis in the coordinate system of the model is also limited.

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Fig. 3 Layout of elements

Fig. 4 Two variants of the calculation scheme in general form

Such restrictions of movements in total provide sufficient anchoring for the calculation of the model. Loads on the beam and on the columns are transmitted to a small area using an interpolating element. The model implements 2 different loading schemes (Fig. 4): 1) the forces on the beams are directed downward, the moments of forces at the point of contact with the column are balanced; 2) the forces on the beams are directed in different directions, the moments of forces at the junction with the column are not balanced. To conduct a numerical experiment, a complete factor experiment of the type was 2k chosen as the main technique, which allows, with a known number of factors, to find the number of experiments necessary to implement all possible levels of factors N = 2k , where «N» is the number of experiments, «k» is the number of factors, «2» is the number of levels. The factors determining the process are: the thickness of the lining X1, the length of the lining X2, the force on the column X3, the force on the

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101

Table 1 Results №

X1

X2

X3

X4

Var. 1 Beam σmax , MPa

Var. 1 Column σmax, MPa

Var. 2 Beam σmax , MPa

Var. 2 Column σmax, MPa

1

+

+

−

−

154.1

206.6

198.1

230.1

2

+

+

−

+

184.9

231.0

203.9

271.7

3

+

+

+

−

239.2

276.2

288.5

283.0

4

+

+

+

+

233.8

298.2

294.2

324.4

5

+

−

−

−

201.4

230.0

242.9

250.1

6

+

−

−

+

207.5

253.1

250.0

295.0

7

+

−

+

−

295.9

313.4

353.7

330.9

8

+

−

+

+

299.1

334.0

360.8

352.6

9

−

+

−

−

372.0

235.6

416.2

255.0

10

−

+

−

+

380.2

258.2

424.5

299.9

11

−

+

+

−

545.7

322.7

611.7

348.2

12

−

+

+

+

553.8

342.7

620.1

360.6

13

−

−

−

−

379.7

235.2

429.0

253.9

14

−

−

−

+

387.9

257.7

437.2

298.7

15

−

−

+

−

572.1

322.4

631.4

346.9

16

−

−

+

+

565.8

342.2

639.4

358.8

beam X4. When considering a problem in which the number of factors studied is 4, it is necessary to perform 24 = 16 various combinations of experiments. According to the previous experiment [4] natural parameter values is: X1(+) = 10 mm, X1(−) = 6 mm, X2(+) = 50 mm, X2(−) = 30 mm, X3(+) = 800 kN, X3(−) = 600 kN, X4(+) = 50 kN, X4(−) = 60 kN.

3 Results and Discussion According to the experimental plan, 16 calculations were carried out for each loading scheme. The results are shown in Table 1. Based on the data summarized in the Table 1, it becomes clear that only those samples in which the parameter X1 is equal to its upper limit correspond to the strength condition. Figure 5 shows graphs of voltage changes depending on the value of the parameter X1 and X2. As a result of the calculation, distributions of equivalent stresses over the structure were obtained. The general nature of the distributions is similar for all variants of the experiment, and varies only in the values of stresses (Fig. 6).

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A. Alekseeva et al. 400 350 Stress, MPa

300 250 200 150 100 50 0

-

+ parameter boundary

Parameter

Parameter X1(X2+)

Parameter

Parameter X2(X1+)

Fig. 5 Graph of the influence of the parameter values X1 and X2

Fig. 6 Distribution of equivalent stresses. 1 is the compression zone of the column; 2 is the effect of the bending moment of the beams on the stress state of the column at the junction

The rated voltage in the dangerous section is calculated by the formulas of the resistance of materials without taking into account the concentration. As a rule, these stresses correspond to the stresses in the design elements located at a distance from the geometric concentrators. The ratio of the magnitude of the greatest local voltage to the magnitude of the nominal voltage is called the theoretical stress concentration coefficient [12, 13] (Table 2): ασ = σmax /σn

(1)

ατ = τmax /τn

(2)

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Table 2 Concentration coefficients X1

X2

X3

X4

Var. 1 ασ

1

+

+

−

−

1.937

2

+

+

−

+

1.909

96.9

1.974

103.26

3

+

+

+

−

2.163

110.6

2.543

113.46

4

+

+

+

+

2.111

110.8

2.470

119.13

5

+

−

−

−

2.585

77.9

2.672

6

+

−

−

+

2.709

76.6

2.701

92.553

7

+

−

+

−

2.486

119.0

2.641

133.905

8

+

−

+

+

2.542

117.6

2.661

135.588

9

−

+

−

−

2.647

140.6

2.956

140.799

10

−

+

−

+

2.695

141.1

3.017

140.72

11

−

+

+

−

2.592

210.5

2.884

212.11

12

−

+

+

+

2.627

210.8

2.916

212.62

13

−

−

−

−

3.934

96.5

4.487

95.615

14

−

−

−

+

3.993

97.1

4.317

101.252

15

−

−

+

−

3.974

143.9

4.402

143.43

16

−

−

+

+

3.915

144.5

4.468

143.09

№

Var. 1 σn 79.5

Var. 2 ασ 2.305

Var. 2 σn 85.94

90.896

4 Conclusions Thus, the following conclusions were obtained: 1. Changing the parameter X1 from its lower limit to the upper one, all other things being equal, increases the coefficient by an average of 1.36 times; 2. Parameter X2 from its lower border to the upper one, all other things being equal, increases the coefficient by an average of 1.49 times; 3. Parameter X3 from its lower border to the upper one, all other things being equal, increases the coefficient by an average of 1.11 times; 4. Changing the X4 parameter from the “−” border to the “+” border reduces the concentration factor by 1.02 times. 5. The stresses obtained in 1, 2, and 5 out of 16 numerical experiments satisfy the condition of strength in the yield point of the material, the stiffness condition is fulfilled in all variants. The development of options for a constructive connection solution is the goal of further research. Acknowledgements The reported study was funded by RFBR, project number 20-38-90046\20.

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References 1. Itskov IE (2008) Calculated seismic loads on high-rise buildings erected in the Republic of Kazakhstan. Seismic construction. Safety Struc 2:32–35 2. Zlochevsky AB (1983) Experimental methods in structural mechanics. Stroyizdat, Moscow, p 192 3. Pavlov AB (2002) Taking into account the real behavior of joints in the calculation of steel frames. Ind Civil Constr 6:37–39 4. Polyakov SV (1984) Earthquake-resistant buildings and the development of the theory of seismic resistance, Moscow, p 254 5. Svyatoshenko AE (2006) Improving the reliability of frame elements of steel frames in multistorey buildings. N. Novgorod, p 25 6. Martemyanov AI (1985) Design and construction of buildings and structures in earthquakeprone areas. Stroyizdat, Moscow, p 255 7. Polyakov SV (1983) Earthquake-resistant structures of buildings. Higher School, Moscow, p 304 8. Trufyakova VYa (ed) Strength of welded joints under variable loads. Naukova dumka, Kiev, p 256 (1990) 9. Neuber G (1947) Stress concentration. I.L.: OGIZ, p 114 10. Odessa PD, Vedyakov II, Gorpinchenko VM (1998) Prevention of brittle destruction of steel building structures. IP “INTERMET ENGINEERING”, Moscow, p 220 11. Lampsi BB (1979) Thin-walled steel support structures under local loads: theory of local stresses. Stroyizdat, Moscow, p 272 12. Novozhilov VV (1969) On the foundations of a theory of equilibrium cracks in elastic solids. PMM 33(5):797–812 13. Savin GN (1968) Stress distribution around the holes. Naukova dumka, Kiev, p 887 14. Evtushenko SI, Petrov IA, Shutova MN, Chernykhovsky BA (2021) Bearing capacity of eccentrically compressed bisteel columns. Mag Civ Eng 102. https://doi.org/10.34910/MCE. 102.1 15. Buzalo N, Gontarenko I, Chernikhovski B (2020) Force resistance of steel columns of industrial buildings with corrosion damage. IOP Conf Ser Mater Sci Eng 896:012044. https://doi.org/10. 1088/1757-899X/896/1/012044 16. Evtushenko SI, Petrov IA, Alexeev SA (2019) Optimization task when calculating the bi-steel thin-walled rod. Presented at the. https://doi.org/10.1063/1.5138445 17. Buzalo N, Gontarenko I, Chernykhovsky B (2020) Reducing the force resistance of steel columns in industrial buildings with corrosion damage during operation. Constr Archit 8:9–13. https://doi.org/10.29039/2308-0191-2020-8-4-9-13 18. Ragheb WF (2015) Local buckling of welded steel I-beams considering flange–web interaction. Thin-Walled Struct 97:241–249. https://doi.org/10.1016/j.tws.2015.09.026

Component Compositions of Mixtures of Cement-Wood Heat-Insulating Material N. V. Kuznetsova

and A. D. Seleznev

Abstract The research object is a cement-based heat-insulating material with wood waste. The preparation of wood-cement mixtures was carried out using the selected technological parameters by dispersing in a vibro-rotary mill of periodic action. The aim of the study is to establish the dependence of the physical and technical properties (a thermal conductivity coefficient, compressive strength and density) of cement heat-insulating material on the ratio of the components of mixtures with sawdust. The research was carried out by the method of experiment planning, taking into account the interpolation capabilities of the models. Based on the results of the experiment, mathematical models were constructed and graphs of the dependence of the thermal conductivity coefficient and compressive strength on the sawdust/cement and water/cement ratios were presented with constant sand/cement and lime/cement ratios. It was found that with an increase in the content of sawdust in the mixture (sawdust/cement ratio is in the range from 0.25 to 0.75), the strength of the samples significantly decreases (up to 64%), and the coefficient of thermal conductivity decreases on average by 15%. Compositions of mixtures with given values of the thermal conductivity coefficient have been selected, having compressive strength indicators in the range from 0.4 to 1.1 MPa, which make it possible to obtain heatinsulating wood-cement materials. Possible areas of application of these cement heatinsulating materials with the use of wood waste have been determined: insulation of floor of the ground floor, wall and partition blocks. Keywords Cement heat-insulating materials · Wood-cement composites · Woodworking waste · Thermal conductivity coefficient

N. V. Kuznetsova (B) · A. D. Seleznev Tambov State Technical University, Sovetskaya street, 106, 392000 Tambov, Russia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_11

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1 Introduction Currently, the rational use of natural resources is a topical subject in all spheres of human manufacturing activity. This issue is especially important in the construction materials industry, since one of the most important directions of its development is to reduce the consumption of primary raw materials and increase the use of secondary raw materials. This can be achieved in the following ways: the introduction of wastefree and low-waste technologies, a decrease in the resource intensity of products, the active use of local raw materials, as well as an improvement in the quality of processing industrial waste, such as, for example, woodworking waste. The volume of timber procurement in Russia is approximately 200 million m3 per year. At the same time, waste from wood processing is about 32% of the initial material [1]. Most of it is sawdust, shavings and chipped wood. At the same time, most of it is stored at landfills or burned [2], which is economically unprofitable both for enterprises related to woodworking and for the national economy. Up to 21% of woodworking waste is used in the production of building materials [1], such as arbolite [3], cement-bonded particle boards (CBPB), wood-particle boards (WPB) [4]. At the same time, substances that are used in the production of these materials, such as phenol–formaldehyde resins, reduce environmental friendliness, and sometimes pose a danger to human health [5]. In this paper, it is proposed to use wood shavings in the manufacture of cement composite heat-insulating materials, which can be used, for example, in three-layer monolithic structures with a heat-insulating layer of wood-cement material [6]. It is assumed that there is a possibility of obtaining a relatively cheap, environmentally friendly, high-quality material. Its main advantages can be the availability of components and an uncomplicated production process in comparison with other heat-insulating materials. The proposed material is made on the basis of a mineral binder: cement, the particles of which, in the process of hydration when mixed with particles of wood waste, are exposed to the aggressive action of the components of cellulose-containing fillers, including easily soluble simplest sugars: sucrose, glucose, fructose [7], therefore, the primary task is to neutralize these substances in cement mixtures. Various methods are used to reduce the negative effect of the simplest sugars on cement hardening processes. For example, various chemical additives are introduced into a wood-cement mixture: aluminum sulfate, calcium chloride, liquid glass, and others [8]. In the paper [9], wood particles are proposed to be pretreated with a lime solution, and in the paper [10] it is recommended to remove sugars from organic filler by fermentation by using microorganisms contained in a substrate of animal origin: manure. Thus, the main problem of using wood waste as a filler in cement composite materials is the need to neutralize the simplest sugars they contain. It is proposed to solve this issue by adding slaked lime to the cement mixture. One of the most important physical and mechanical properties of a cement heatinsulating material is the coefficient of thermal conductivity. In the paper [11],

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107

detailed studies of the dependence of this property on the size of wood filler particles are presented; however, there is insufficient information on the strength of the samples under study and the component composition. The aim of the study is to select the ratio of the components of mixtures of cement heat-insulating materials using wood shavings. The thermal conductivity coefficient is taken as the objective function considered in the study.

2 Methods The process of obtaining cement-based heat-insulating materials with desired properties can be conditionally divided into two main stages: determining the regularities of the influence of various factors on the physical and mechanical properties of the material and determining the composition and production technology of the material with the required properties. Portland cement grade M400, corresponding to Russian State Standard GOST 10,178–85 “Portland cement and portland blastfurnace slag cement”, was used as a binder in the design of the compositions of mixtures of cement heat-insulating materials. The filler was fine quartz sand (Russian State Standard GOST 8736–2014 “Sand for construction works”) and woodworking waste: spruce shavings [12, 13]. Also, slaked lime (Russian State Standard GOST 9179–2018 “Lime for building purposes”) was used as an additive to neutralize the simplest sugars in wood, such as sucrose, glucose. Due to the heterogeneity of the components included in the mixture, traditional mixing methods did not give the desired result, so the components were dispersed in a vibratory-rotary mill of periodic action. The technological mixing mode was determined during preliminary studies. The process of changing the physical and mechanical properties of a composite building material proceeds under the influence of various factors, the nature of the influence of which is difficult to describe. The use of experiment planning in the study of the physical and mechanical properties of a composite building material presupposes purposeful control of the course of the experiment, which is implemented under conditions of an incomplete understanding of the mechanism of change in physical and mechanical properties depending on a number of factors. This approach makes it possible to implement the main planning principle: obtaining the required accuracy of the mathematical description with a limited number of experiments. Experiment design implies randomization and simultaneous variation of all factors, which makes it possible to more accurately assess the effects of the influence of factors and their interactions in comparison with a one-factor (when one factor changes) experiment, and an increase in the number of factors leads to an increase in the accuracy of estimates [14]. The logically thought-out design of the study includes the choice of independent variables, the area of the factor space and the mathematical model for describing the process under consideration.

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Table 1 Intervals of variation of factors Factors

Ranges of change of factors

X1

−1

X2

X3

X4

0.25

0

0.5

+1

0.75

−1

1

0

1.5

+1

2

−1

0%

0

7.5%

+1

15%

−1

2

0

2.5

+1

3

Based on the analysis of preliminary information, the factors that most significantly affect the physical and mechanical properties of the cement heat-insulating material are identified: x1 x2 x3 x4

– sawdust/cement ratio (Sawd/C); – sand/cement ratio (S/C); – proportion of lime content in cement (L/C); – water/cement ratio (W/C).

When planning the experiment, the following intervals of variation of factors were considered (Table 1). The choice of the number of levels of variation was determined by the curvilinear nature of the dependence of the physical and mechanical properties of the cement heat-insulating building material on these factors. The choice of the factor space was made taking into account the interpolation capabilities of the constructed model according to the following plan (Table 2). It was assumed that the dependence of the physical and mechanical properties of cement heat-insulating materials with the use of woodworking industry waste can be described by a reduced polynomial of incomplete third order, the coefficients of which depend on the values of the factor levels (x1 , x2 , x3 , x4 ). Samples with 25 different compositions were prepared for the experiment. The number of samples in the experiment (3 duplicate samples were prepared) when testing for central compression, density and thermal conductivity was 75 cubes with an edge of 100*100*100 mm. Based on the results of tests for compressive strength, density and thermal conductivity for each property, a mathematical model was obtained that describes its dependence on all the above factors.

Component Compositions of Mixtures …

109

Table 2 Experimental research plan Experiment number

X1

X2

X3

X4

1

−1

−1

−1

−1

2

+1

−1

−1

−1

3

−1

+1

−1

−1

4

+1

+1

−1

−1

5

−1

−1

+1

−1

6

+1

−1

+1

−1

7

−1

+1

+1

−1

8

+1

+1

+1

−1

9

−1

−1

−1

+1

10

+1

−1

−1

+1

11

−1

+1

−1

+1

12

+1

+1

−1

+1

13

−1

−1

+1

+1

14

+1

−1

+1

+1

15

−1

+1

+1

+1

16

+1

+1

+1

+1

17

−1

0

0

0

18

+1

0

0

0

19

0

−1

0

0

20

0

+1

0

0

21

0

0

−1

0

22

0

0

+1

0

23

0

0

0

−1

24

0

0

0

+1

25

0

0

0

0

For clarity of the data obtained, surfaces were constructed with two fixed values of the factors and two changing ones (Figs. 1 and 2).

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Fig. 1 Dependence of the thermal conductivity coefficient λ, W/(m · ºC), on the factors x1 and x4 with unchanged x2 = 1.5 and x3 = 0%

Fig. 2 Dependence of strength R, MPa, on factors x1 and x4 with unchanged x2 = 1.5 and x3 = 0%

3 Results and Discussion The graphs show the following regularities: the strength of the material increases from 0.4 to 2.8 MPa with a decrease in the Waste/C ratio and an increase in W/C, since the introduction of wood waste into the mixture increases its water demand and porosity [15]; the thermal conductivity coefficient decreases from 0.38 to 0.19 W/m ºC with an increase in Waste/C and a decrease in W/C. One of the significant factors affecting strength is the W/C ratio, the effect of which on the change in physical and mechanical properties with a quartz sand filler and with different Waste/C ratios is significantly different. The strength of the samples with an increase in the W/C ratio from 2 to 3 increased on average by 25%. With an increase in the Waste/C ratio from 0.25 to 0.75, the strength, on the contrary, decreases on average by 64%. With an increase in the S/C ratio, varying from 1 to 2, a decrease in strength was observed on average by 30%.

Component Compositions of Mixtures …

111

Table 3 Compositions of mixtures of cement heat-insulating materials with specified characteristics Compositions λ = 0.25 W/(mºC)

λ = 0.3 W/(mºC)

Composition number

Component ratios

Properties

Waste/C

S/C

L/C

W/C

R, MPa

ρ, kg/m3

1

0.25

1.8

1.5

2

1.1

1300

2

0.25

1

6

2

0.8

1050

3

0.5

1.6

0

2.6

0.9

1200

4

0.5

1.9

7.5

2.4

0.4

1180

5

0.25

1.6

10.5

2

1

1270

6

0.25

1.1

15

2

0.7

1120

7

0.5

1.4

0

3

1.1

1060

8

0.1

2

0

2.2

1.8

1520

The coefficient of thermal conductivity of the samples with a change in the W/C ratio from 2 to 3 increases by an average of 30%. With an increase in the Waste/C ratio from 0.25 to 0.75, on the contrary, a decrease in the thermal conductivity coefficient by an average of 15% is observed, since with the introduction of a larger amount of sawdust, lighter and more porous materials are obtained. Analyzing the resulting graphic material, it is possible to determine the compositions of cement heat-insulating materials with predetermined physical and mechanical properties. The method for determining the composition of materials with predetermined physical and mechanical properties is that a line with equal values of the response function is selected on the constructed surface. Then this line is projected onto the plane of arguments, after which it is possible to find unknown factors by dropping perpendiculars from the point of interest on the axis of arguments. When using this technique, several compositions of mixtures of cement heatinsulating materials were selected with a coefficient of thermal conductivity λ = 0.25 W/m ºC and λ = 0.3 W/m ºC (Table 3). By changing the ratio of the components in the mixture, it is possible to achieve a significant change in strength (from 0.7 to 1.8 MPa – mixtures No. 6 and No. 8), or to change the ratio of the components with practically unchanged properties of the material (mixtures No. 2 and No. 3). Using the obtained compositions, it is possible to manufacture building products with the required properties. The final composition of the mixture is selected based on the physical and technical requirements and technical and economic ones. Fields of application of the obtained products: products for filling in partitions and separation walls, small wall blocks in low-rise construction (subject to protection from external atmospheric influences), partition blocks, thermal insulation of floors of the ground floor.

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4 Conclusions On the basis of the experiments made and the study of the physical and mechanical properties of the material with the use of waste from the woodworking industry, the possibility of using sawdust as a filler was revealed. 1. On the basis of the experiments carried out and the study of the physical and mechanical properties of cement materials using wood waste, the possibility of using sawdust as a filler in an amount of 0.25 to 0.75% of the binder mass under special technological conditions for preparing a mixture (selected dispersion parameters in vibro-rotary mill of periodic action) is proven. 2. As expected, with an increase in the sawdust content in the mixture (Waste/C in the range from 0.25 to 0.75), the strength of the samples significantly decreases (up to 64%), and with an increase in the W/C ratio from 2 to 3 it increases by an average of 25%. 3. The coefficient of thermal conductivity of the samples increases to 30% with an increase in the W/C ratio from 2 to 3; with an increase in the Waste/C ratio from 0.25 to 0.75, a decrease in the thermal conductivity coefficient by an average of 15% is observed. 4. For the practical use of the research results, the compositions of mixtures of cement heat-insulating materials with predetermined values of the thermal conductivity coefficient have been determined.

References 1. Kolesnikova AV (2013) Analiz obrazovaniya i ispol’zovaniya drevesnyh othodov na predpriyatiyah lesopromyshlennogo kompleksa Rossii [Analysis of the formation and use of wood waste at the enterprises of the Russian timber industry complex]. Aktual’nye voprosy ekonomicheskih nauk [Topical issues of economic sciences], no 33, pp 116–120. (rus). https://www.eli brary.ru/download/elibrary_20722278_22216470.pdf. Accessed 18 Nov 2021 2. Borzunova AG, Zinov’eva IS (2012) Kompleksnaya pererabotka drevesnogo syr’ya. Utilizaciya drevesnyh othodov [Complex processing of wood raw materials. Utilization of wood waste]. Uspekhi sovremennogo estestvoznaniya [Advances in modern natural science], no 4, pp. 180– 181. (rus). https://natural-sciences.ru/ru/article/view?id=29983. Accessed 18 Nov 2021 3. Shevchenko VA, Lebedeva TG, Kiselev VP, Chuprova NA, Ivanova LA, Terekhova II (2018) Issledovanie svojstv vtorichnogo drevesnogo zapolnitelya dlya arbolita [Study of the properties of recycled wood filler for wood concrete]. Sovremennye naukoemkie tekhnologii [Modern high technologies], no 3, pp 112–116. (rus). https://top-technologies.ru/ru/article/view?id= 36946. Accessed 18 Nov 2021 4. Gornostaeva EYU, Lasman IA, Fedorenko EA, Kamoza EV (2015) Drevesno-cementnye kompozicii s modificirovannoj strukturoj na makro-, mikro- i nanourovnyah [Wood-cement compositions with structures modified at macro-, micro- and nano- levels]. Stroitel’nye materialy [Construction Materials], no 11, pp 13–17. (rus). https://journal-cm.ru/images/files/2015/ 2015_11_013-016.pdf. Accessed 18 Nov 2021

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5. Leonovich AA, Vojtova TN (2014) Povyshenie ekologicheskoj bezopasnosti drevesnostruzhechnyh plit [Improvement of the environmental safety of wood particle boards]. Izvestiya vysshih uchebnyh zavedenij. Lesnoj zhurnal [Russian Forestry Journal], no 6, pp 120–129. (rus). https://www.elibrary.ru/download/elibrary_22595409_22592751.pdf. Accessed 18 Nov 2021 6. Zaprudnov VI, Karpachyov SP (2017) Tekhnologiya izgotovleniya trekhslojnyh monolitnyh konstrukcij s teploizolyacionnym sloem iz drevesno-cementnogo materiala [Manufacturing technology of three-layer monolithic structures with a heat-insulating layer of wood-cement material]. Lesnoj vestnik [Forestry Bulletin], vol 21, no 5, pp 83–88. (rus). https://doi.org/10. 18698/2542-1468-2017-5-83-88 7. Polishchuk AI, Rubinskaya AV (2012) Himicheskaya agressivnost’ zapolnitelya rastitel’nogo proiskhozhdeniya po otnosheniyu k cementu [Chemical aggressiveness of the filler of plant origin in relation to cement]. Aktual’nye problemy lesnogo kompleksa, Bryansk, “Bryanskaya gosudarstvennaya inzhenerno-tekhnologicheskaya akademiya” [Actual problems of the forestry complex, Bryansk, “Bryansk State Engineering and Technological Academy”], no 34, pp 72–74. (rus). https://www.elibrary.ru/download/elibrary_21979272_46052682.pdf. Accessed 18 Nov 2021 8. Shitova IYU, Samoshina EN, Kislicyna SN, Boltyshev SA (2015) Sovremennye kompozicionnye stroitel’nye materialy, Penza, “Penzenskij gosudarstvennyj universitet arhitektury i stroitel’stva” [Modern composite building materials, Penza, “Penza State University of Architecture and Construction”], p 136. (rus) 9. Rudenko BD, Plotnikov SM (2012) Formirovanie struktury cementno-drevesnogo kompozita pri obrabotke izvest’yu drevesnogo zapolnitelya [Formation of structure of cement-wood composite the limingwoodfiller]. Aktual’nye problemy lesnogo kompleksa, Bryansk, “Bryanskaya gosudarstvennaya inzhenerno-tekhnologicheskaya akademiya” [Actual problems of the forestry complex, Bryansk, “Bryansk State Engineering and Technological Academy”], no 34, pp 82–84. (rus). https://www.elibrary.ru/download/elibrary_22573951_41321694.pdf. Accessed 18 Nov 2021 10. Mironov VA (2004) Razrabotka tekhnologicheskih variantov polucheniya stroitel’nyh materialov na osnove othodov derevoobrabotki [Development of technological options for obtaining building materials based on woodworking waste]. Zapiski Gornogo instituta, Sankt-Peterburg, “Sankt-Peterburgskij gornyj universitet” [Notes of the Mining Institute, St. Petersburg, “St. Petersburg Mining University”], vol 158, pp 245–247. (rus) 11. Titova SA, Vasil’ev SB (2016) Vliyanie razmera drevesnyh chastic zapolnitelya na teploprovodnost’ drevesno-cementnogo kompozita [The influence of aggregate wooden particles size on thermal conductivity of wood composite with cement binder]. Fundamental’nye issledovaniya [Fundamental research], no 5–1, pp 53–57. (rus). https://fundamental-research.ru/ru/article/ view?id=40249. Accessed 18 Nov 2021 12. Nanazashvili IH (1990) Stroitel’nye materialy iz drevesno-cementnoj kompozicii [Building materials made of wood-cement composition]. Strojizdat, p 415. (rus) 13. Dvorkin LI, Dvorkin OL (1999) Proektirovanie sostavov betonov s zadannymi svojstvami [Design of concrete compositions with specified properties]. Rovno: Izd-vo RGTU, p 197. (rus) 14. Krasovskij GI, Filaretov GF (1982) Planirovanie ehksperimenta [Experiment planning], Izd-vo BGU. Minsk, p 302. (rus) 15. Zaprudnov VI, Sanaev, VG (2012) Makroskopicheskie svojstva drevesno-cementnyh kompozitov [Macroscopic properties of wood-cement composites]. Vestnik Moskovskogo gosudarstvennogo universiteta lesa–Lesnoj vestnik [Moscow State Forest University Bulletin – Forestry Bulletin], no 6 (89), pp 168–171. (rus). https://www.elibrary.ru/download/elibrary_ 18485022_53707406.pdf. Accessed 18 Nov 2021

Experimental Establishment of the Required Number of Experiments Per Point in Determining the Thermal Fluctuation Constants of the Generalized Zhurkov for the Method of Direct Temperature and Control Point A. V. Erofeev

and T. I. Gorokhov

Abstract For the newly developed method of determining the thermal fluctuation constants of the generalized Zhurkov equation, the scope of possible application is established. The technique is based on finding the thermal fluctuation constants for one direct temperature, plotted in the coordinates lgτ − σ, and one control point obtained at a different temperature. The required number of experiments conducted under identical conditions to obtain adequate values of thermal fluctuation constants has also been experimentally established. The studies were carried out on polyvinyl chloride plates with transverse bending. The initial set of experimental original data consisted of 8 values. In the future, it increased in increments of one value to 16 values. For each set the thermal fluctuation constants of the generalized Zhurkov equation were determined and their comparative analysis was carried out. Keywords Direct temperature · Durability · Operability · Prediction · Reference point · Thermofluxtution constants

1 Introduction Various forecasting methods are used to determine the durability of building materials [1–5]. However, the concept of thermal vibrations of solid fracture and deformation is currently becoming widespread [6–10]. In order to carry out prediction within its framework, an experimental determination of four thermal fluctuations constants included in the generalized Zhurkov equation is required [11]. The very method of determining the thermofluxtual constants of the generalized Zhurkov equation is quite time-consuming. To obtain reliable results, it is necessary to obtain a dependence of durability on stress at least at three test temperatures of the sample. Considering that at least 5 points are also required for each temperature, for each of which at least 6 samples are tested, a hundred samples are eventually tested. Due to the fact, the A. V. Erofeev · T. I. Gorokhov (B) Tambov State Technical University, Tambov, Russia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_12

115

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A. V. Erofeev and T. I. Gorokhov

classical method of determining thermal fluctuations constants is labor-intensive a technique was proposed that allows determining constants from one direct temperature and one control point at a different temperature [12]. The technique is based on the linearity hypothesis of angular coefficients of direct temperatures, constructed in the coordinates of the logarithm of time from voltage. Due to the fact that the method is new, it is required to establish the required number of experiments conducted under identical conditions to obtain a point in the coordinates lgτ – σ. The object of this study is the thermal fluctuation constants determined by the direct and temperature method. The subject of the study is to determine the required number of experiments. The aim of the study is to reduce the complexity of conducting experiments while maintaining the necessary accuracy of determining the thermal fluctuation constants by the direct and temperature method. To achieve this goal, it is necessary to solve a number of tasks: – to determine the thermal fluctuation constants for different initial experimental data; – to analyze the results obtained; – specify the required minimum number of experiments conducted under identical conditions to obtain a single point in the coordinates lgτ − σ.

2 Methodology Thermal fluctuations constants were determined for polyvinyl chloride plates at transverse bending [13]. To establish the minimum number of experimental trials to obtain one point for constructing a straight line, as well as to select a control temperature at which only one point is determined, it is possible and sufficient to establish the relationship between the number of experiments and the obtained deviations in constant values. For this purpose, thermal fluctuations constants are determined at the given direct temperature in coordinates lgτ – σ (in this case T = 15 °C), the sample of the original data for which gradually increased by one value, and points at a different temperature (the number of experiments per point—16). The initial sample consisted of 8 values, which are given in [13]. For example, for the first set of data, a straight line is drawn from the points obtained in the tests of 9 samples, and the point value at a different temperature is taken from the data obtained in the tests of 16 samples. Further, the data obtained from the tests of 10 samples, etc., are used. Thermal fluctuations constants were determined in a program made in the form of a web application and available at http://thermofluctuation-constants.herokuapp. com/thermo. The program automatically performed statistical data processing at a confidence probability of 95% [14, 15].

Experimental Establishment of the Required Number of Experiments Per Point …

117

Table 1 Values of thermal fluctuations constants at different number of tests carried out under identical conditions for one point Number of tests

τ 0. s

T m. K

kJ U 0 . mole

kJ γ. mole·MPa

Straight T = 15 ºC; the point at σ = 5.6 MPa and T = 30 ºC 9

−5.58

439

353.779

41.777

10

−5.15

439

318.002

36.741

11

−4.66

439

306.599

36.256

12

−4.81

439

308.155

36.057

13

−5.02

439

310.537

35.822

14

−4.79

439

395.116

35.901

15

−4.22

439

288.259

34.194

16

−4.91

439

300.927

34.444

Straight T = 15 ºC; the point at σ = 5.6 MPa and T = 45 ºC 9

−2.85

439

326.075

41.777

10

−3.80

439

296.333

36.741

11

−3.44

439

281.027

36.256

12

−3.56

439

288.017

36.657

13

−3.60

439

287.780

35.822

14

−3.58

439

276.293

33.901

15

−3.04

439

269.341

34.194

16

−3.04

439

278.118

34.444

Straight T = 15 ºC; the point at σ = 5.0 MPa and T = 30 ºC 9

−4.40

439

334.956

41.777

10

−2.27

439

271.784

36.741

11

−1.39

439

254.172

36.256

12

−1.70

439

258.199

36.057

13

−1.82

439

259.319

35.822

14

−1.81

439

247.959

33.901

15

−1.11

439

238.393

34.194

16

−1.25

439

242.215

34.444

Straight T = 15 ºC; the point at σ = 5.0 MPa and T = 45 ºC 9

−3.20

439

315.711

41.777

10

−2.25

439

271.536

36.741

11

−1.96

439

264.302

36.256

12

−2.02

439

263.411

36.057

13

−2.05

439

263.005

35.822

14

−1.66

439

245.510

33.901

15

−1.73

439

248.473

34.194

16

−1.80

439

251.010

34.444

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A. V. Erofeev and T. I. Gorokhov

3 Results The set of values of thermal fluctuations constants at different number of tests carried out under identical conditions per one point is shown in Table 1. Values of deviations of thermal fluctuations constants from their average value are given in Table 2. In addition, it is necessary to find the values of deviations of the thermal fluctuation constants from the values taken as reference. The results obtained are included in Table 3.

4 Conclusion Analysis of the obtained values of τ0 (Tables 2 and 3), namely their significant spread (from 1.31 to 64.06% relative to the average value and from 3.14 to 58.03% relative to the reference value) allows us to conclude that the accuracy of determining the location of the control point significantly affects the final result of determining the thermal fluctuation constants. In addition, the analysis of the data obtained shows that with an increase in the sample, the values of γ and U0 decrease by 18% and by 15…28%, respectively. Regardless of the selected control point, with the same number of experiments conducted at one point, the values of the thermal fluctuation constant γ remain constant. At the same time, the values of U0 change [16–19]. Thus, the results obtained allow us to conclude that the considered method for determining thermal fluctuation constants can be applied in cases where it is necessary to determine their approximate values with insignificant labor costs. To increase accuracy, it is necessary to use other techniques.

Experimental Establishment of the Required Number of Experiments Per Point …

119

Table 2 Values of deviations of thermal fluctuations constants from their average value at different number of tests under identical conditions per one point Number of tests

lgτ 0

Δlgτ 0 . %

T m. K

Δ T m. %

U0

kJ mole

ΔU 0 . %

kJ γ . mole·MPa

Δ γ. %

15.31

Straight T = 15 ºC; the point at σ = 5.6 MPa and T = 30 ºC 9

−5.58

44.81

439

0.00

353.779

24.21

41.777

10

−5.15

40.25

439

0.00

318.002

11.65

36.741

1.41

11

−4.66

34.00

439

0.00

306.599

7.65

36.256

0.07

12

−4.81

36.04

439

0.00

308.155

8.19

36.057

0.48

13

−5.02

38.70

439

0.00

310.537

9.03

35.822

1.14

14

−4.79

35.78

439

0.00

395.116

38.72

35.901

0.92

15

−4.22

27.03

439

0.00

288.259

1.21

34.194

5.95

16

−4.91

37.37

439

0.00

300.927

5.65

34.444

5.19

Straight T = 15 ºC; the point at σ = 5.6 MPa and T = 45 ºC 9

−2.85

7.46

439

0.00

326.075

14.48

41.777

15.31

10

−3.80

18.99

439

0.00

296.333

4.04

36.741

1.41

11

−3.44

10.57

439

0.00

281.027

1.35

36.256

0.07

14

−3.58

14.04

439

0.00

276.293

3.09

33.901

6.87

15

−3.04

1.31

439

0.00

269.341

5.75

34.194

5.95

14

−3.58

14.04

439

0.00

276.293

3.09

33.901

6.87

15

−3.04

1.31

439

0.00

269.341

5.75

34.194

5.95

16

−3.04

1.31

439

0.00

278.118

2.41

34.444

5.19

Straight T = 15 ºC; the point at σ = 5.0 MPa and T = 30 ºC 9

−4.40

30.09

439

0.00

334.956

17.60

41.777

15.31

10

−2.27

26.34

439

0.00

271.784

4.80

36.741

1.41

11

−1.39

54.79

439

0.00

254.172

12.06

36.256

0.07

12

−1.70

44.90

439

0.00

258.199

10.31

36.057

0.48

13

−1.82

40.71

439

0.00

259.319

9.83

35.822

1.14

14

−1.81

41.12

439

0.00

247.959

14.87

33.901

6.87

15

−1.11

64.06

439

0.00

238.393

19.48

34.194

5.95

16

−1.25

59.36

439

0.00

242.215

17.59

34.444

5.19

Straight T = 15 ºC; the point at σ = 5.0 MPa and T = 45 ºC 9

−3.20

3.87

439

0.00

315.711

10.84

41.777

15.31

10

−2.25

26.84

439

0.00

271.536

4.89

36.741

1.41

11

−1.96

36.28

439

0.00

264.302

7.76

36.256

0.07

12

−2.02

34.34

439

0.00

263.411

8.13

36.057

0.48

13

−2.05

33.23

439

0.00

263.005

8.30

35.822

1.14

14

−1.66

45.96

439

0.00

245.51

16.01

33.901

6.87

15

−1.73

43.62

439

0.00

248.473

14.63

34.194

5.95

16

−1.80

41.53

439

0.00

251.01

13.47

34.444

5.19

Average value

−3.08

439.00

284.82

36.23

120

A. V. Erofeev and T. I. Gorokhov

Table 3 Values of deviations of the thermal fluctuation constants from their reference value for a different number of tests conducted under identical conditions at one point Number of tests

lgτ 0

Δlgτ 0 . %

T m. K

Δ T m. %

U0

ΔU 0 . %

kJ γ . mole·MPa

Δ γ. %

1

2

3

4

5

6

7

8

9

kJ mole

Straight T = 15 ºC; the point at σ = 5.6 MPa i T = 30 ºC 9

−5.58

58.03

439

0.24

353.779

12.72

41.777

4.96

10

−5.15

54.56

439

0.24

318.002

1.32

36.741

19.35

11

−4.66

49.81

439

0.24

306.599

2.36

36.256

20.95

12

−4.81

51.36

439

0.24

308.155

1.85

36.057

21.61

13

−5.02

53.38

439

0.24

310.537

1.07

35.822

22.41

14

−4.79

51.16

439

0.24

395.116

25.89

35.901

22.14

15

−4.22

44.51

439

0.24

288.259

8.88

34.194

28.24

16

−4.91

52.37

439

0.24

300.927

4.29

34.444

27.31

Straight T = 15 ºC; the point at σ = 5.6 MPa i T = 45 ºC 9

−2.85

17.82

439

0.24

326.075

3.90

41.777

4.96

10

−3.80

38.39

439

0.24

296.333

5.91

36.741

19.35

11

−3.44

31.99

439

0.24

281.027

11.68

36.256

20.95

12

−3.56

34.19

439

0.24

288.017

8.97

36.657

19.62

13

−3.60

35.00

439

0.24

287.78

9.06

35.822

22.41

14

−3.58

34.63

439

0.24

276.293

13.59

33.901

29.35

15

−3.04

22.94

439

0.24

269.341

16.53

34.194

28.24

16

−3.04

22.94

439

0.24

278.118

12.85

34.444

27.31

Straight T = 15 ºC; the point at σ = 5.0 MPa i T = 30 ºC 9

−4.40

46.84

439

0.24

334.956

6.72

41.777

4.96

10

−2.27

3.14

439

0.24

271.784

15.48

36.741

19.35

11

−1.39

40.55

439

0.24

254.172

23.48

36.256

20.95

12

−1.70

27.55

439

0.24

258.199

21.55

36.057

21.61

13

−1.82

22.03

439

0.24

259.319

21.03

35.822

22.41

14

−1.81

22.57

439

0.24

247.959

26.57

33.901

29.35

15

−1.11

52.74

439

0.24

238.393

31.65

34.194

28.24

16

−1.25

46.57

439

0.24

242.215

29.57

34.444

27.31

Straight T = 15 ºC; the point at σ = 5.0 MPa i T = 45 ºC 9

−3.20

26.89

439

0.24

315.711

0.59

41.777

4.96

10

−2.25

3.80

439

0.24

271.536

15.58

36.741

19.35

11

−1.96

16.21

439

0.24

264.302

18.75

36.256

20.95

12

−2.02

13.65

439

0.24

263.411

19.15

36.057

21.61

13

−2.05

12.21

439

0.24

263.005

19.33

35.822

22.41

14

−1.66

28.94

439

0.24

245.51

27.84

33.901

29.35

15

−1.73

25.87

439

0.24

248.473

26.31

34.194

28.24

16

−1.80

23.12

439

0.24

251.01

25.03

34.444

27.31

Average value

−2.34

437.95

313.85

43.85

Experimental Establishment of the Required Number of Experiments Per Point …

121

Acknowledgements The team of authors would like to give a special thanks to Nina Bunina for her help in translating the article.

References 1. Alexandrovsky SV (2004) Durability of external enclosing structures. M.: NIISF RAASN, 332 p 2. Kolupaev VA (2017) Generalized strength criteria as functions of the stress angle. J Eng Mech 143(9). ctat N0 04017095 3. Lo KH, Miyase A, Wang SS (2018) Failure strength predictions for closed-cell polyvinyl chloride foams. J Comp Mater 52(30):4185–4201 4. Kumar D, Alam M, Zou PXW, Sanjayan JG, Memon RA (2020) Comparative analysis of building insulation material properties and performance. Renew Sustain Energy Rev 131. Article N0 110038 5. Sokova S, Smirnova N (2018) Reliability assessment of waterproofing systems of buildings underground parts. IOP Conf Ser Mater Sci Eng 365:052028. https://doi.org/10.1088/1757899X/365/5/052028 6. Gusev BV, Yezersky VA, Monastyrev PV (2005) Heat-conductivity of mineral wool slabs when subjected to operation effects. Promyshlennoe i Grazhdanskoe Stroitel’stvo 1:48–49 7. Gusev BV, Ezerskij VA, Monastyrev PV (2004) Change in the linear dimensions of mineral wool slabs subjected to operation effects. Promyshlennoe i Grazhdanskoe Stroitel’stvo 8:32–34 8. Mamontov SA, Yartsev VP, Monastyrev PV (2017) An artificial and natural aging of woodfiber composite. In: Izvestiya Vysshikh Uchebnykh Zavedenii, Seriya Teknologiya Tekstil’noi Promyshlennosti, January 2017, no 1, pp 95–100 9. Erofeev AV, Yartsev VP, Monastyrev PV (2017) Decorative and protective plates for facade decoration of buildings. In: Izvestiya Vysshikh Uchebnykh Zavedenii, Seriya Teknologiya Tekstil’noi Promyshlennosti, January 2017, no 1, pp 101–104 10. Regel VR, Slutsker AI, Tomashevsky EE (1974) The kinetic nature of the strength of solids. Science, Moscow, p 560 11. Yartsev VP (1998) Physical and technical foundations of the performance of organic materials in parts and structures. Dissertation of doctor of technical sciences (Voronezh), p 350 12. Drannikov RN, Erofeev AV Certificate of state registration of a computer program. № RU 2021612651. Calculation of thermal fluctuation constants of the generalized Zhurkov equation 13. Potapova LB, Yartsev VP (2005) The mechanics of materials in a complex stress state. How is the ultimate stress predicted? Publishing House Mashinostroyenie-1, Moscow, p 244 14. Drannikov RN (2020) Determination of the initial data for calculating the thermal fluctuation constants of the generalized Zhurkov equation of polyvinyl chloride plates. In: Drannikov RN, Erofeev AV, Gorokhov TI (eds) Modern science: theory, methodology, practice - materials of the 2nd All-Russian (National) Scientific and practical conference. electronic resource, pp 116–119 15. Musatov MV, L’vov AA (2009) Analyzing the models of the least squares method and derivation of estimates estimates methods. Vestnik Saratovskogo gosudarstvennogo tekhnicheskogo universiteta. Sci J Saratov State Tech Univ 4(2):137–140 16. Golovanchikov AB, Doan MK, Petrukhin AB, Merentsov NA (2020) Comparison of the accuracy of experimental data approximation using the least relative squares method with the least squares method. Model Optim Inf Technol 8 1(28):38 17. Miyase A, Wang SS (2018) Test method development and determination of three-dimensional stiffness properties of polyvinyl chloride structural foams. J Comp Mater 52(5):679–688 18. Perelmuter MN (2020) Modeling of crack self-healing kinetics. Phys Mesomech 23(4):301–308 19. Kienzler D, Wan Y, Erickson SD, Wu JJ, Wilson AC, Wineland DJ, Leibfried D (2020) Quantum logic spectroscopy with ions in thermal motion. Phys Rev X 10(2). ctat № 021012

Effects of Basalt Fibre on the Strength of Concrete Alexey Bulgakov , Klaus Holschemacher , Iuliia Davidenko , and Vladimir Bredikhin

Abstract The effect of basalt fiber on the strength characteristics of concrete is considered and the experiments of compression tests are described. The study showed that the effect of adding basalt fiber (fiber length 6 and 12 mm) in amounts of 0.5 and 1% in three different concrete compositions can both increase the strength characteristics and decrease them, and a comparison with control specimens without fiber was carried out. Experimental results showed that the use of 6 mm basalt fiber gave the best results. The addition of 1% basalt fiber increased the compressive strength of the sample by 14% and the addition of 0.5% fiber increased the compressive strength by 4%. Keywords Fiber-reinforced concrete · Steel fiber · Polypropylene fiber · Fiberglass · Polyamide fiber · Basalt fiber

1 Introduction Nowadays, concrete is an indispensable element in construction. Most of the supporting and enclosing structures are made from concrete. But only with correctly selected proportions, concrete can serve longer and fulfill its main functions. Today there is an increasing need for high-strength concrete, it is due to the fact that the load on the supporting and long-span structures is growing. However, the use of high-strength concrete entails some difficulties associated with insufficient concrete strength in bending, significant shrinkage deformations and low crack resistance, which increases the risk of brittle fracture of structures.

A. Bulgakov (B) · I. Davidenko · V. Bredikhin Southwest State University, 50 let Oktyabrya Street 94, 305040 Kursk, Russia e-mail: [email protected] K. Holschemacher Leipzig University of Applied Sciences, Karl-Liebknecht-St. 132, 04277 Leipzig, Germany e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_13

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However, in the post-industrial society, there are many solutions to the problems of high-strength concrete. The use of various additives can solve these problems, which in turn can improve the quality of concrete at times [1]. Additives can be a wide variety of liquids, powders and fibrous materials. Previously, rebars were used to increase the strength of concrete, but a thick screed is not always necessary. For this, various fiber materials and liquid additives are added to the solutions. They, in turn, are designed to strengthen structures for bending and compression [2]. In recent years, fiber is gaining popularity as a reinforcing material in various concrete mixtures. There are different types of fibers: steel, polypropylene, fiberglass, polyamide and basalt fibers [3]. From all the variety of materials used for the production of fiber, basalt fiber stands out for its mechanical, chemical and thermal characteristics. Only carbon fiber can compete with basalt fiber, but the last is more expensive. Basalt fiber is produced from basalt rocks by melting them and converting the melt into fibers. Basalts are rocks of igneous origin, natural raw materials [4]. Basalt fiber comes in two varieties: • Staple fiber. The main parameter of this type is the diameter of the individual fibers. There are the following types of fibers: micro-thin have a diameter of 0.6 µ, ultra-thin—from 0.6 to 1 µ, super-thin—from 1 to 3 µ, thin—from 9 to 15 µ, thickened—from 15 to 25 µ, thick—from 25 to 150 µ, coarse—from 150 to 500 µ. • Continuous fiber. This variety contains fibers that can either be twisted into a thread or wound into a roving, and are sometimes sliced into chopped fiber. Nonwoven and woven textile bases can be produced from such material, it can also act as fiberglass. Basalt fiber is an effective micro-reinforcing additive in cement-based or gypsumbased mortars. First of all, it increases the resistance of concrete without destruction in the critical period of 2–6 h after laying. At a later stage, when the concrete has hardened and begins to shrink, the basalt fiber prevents cracking of the concrete, thus significantly reducing the risk of the element’s break, and therefore reducing the amount of scrap. The use of basalt fiber in concrete solutions lowers the formation of shrinkage cracks at an early stage by 90%, for comparison—the use of reinforcing mesh reduces by only 6%. But here it is permissible to use basalt plastic reinforcement as a replacement for structural steel reinforcement in monolithic housing construction. The use of basalt fiber allows to reduce the hydration of concrete, thereby reducing internal loads during temperature fluctuations [5–7]. The object of the study is fiber-reinforced concrete. The aim of the study is to study the effect of basalt fiber on the strength characteristics of the concrete, as well as to identify the length of the fiber demonstrating greater strength. To achieve this goal, the following tasks were formulated:

Effects of Basalt Fibre on the Strength of Concrete

125

1. Experimentally determine the strength of cubes of various compositions by compression 2. To conduct a comparative analysis of samples of various compositions.

2 Methods For the experiment, 4 different compositions were taken to find out which composition could withstand the greatest load. The concrete samples include the following components: • • • • •

Portland Cement PC-500; crushed stone fractions 5–10 mm; crushed stone fractions of 10–20 mm; water; AlfaBet concrete hardening accelerator.

The first sample, which was the main one, included the above written components. A 6 mm fiber was added to the second sample, a 12 mm fiber was added to the third and fourth ones. In the last two samples, it was decided to find out at what percentage of fiber the samples will show its compressive strength characteristics higher, so we added 4 kg of fiber to the third sample, and 8 kg of fiber to the fourth. The compositions of the mixtures are presented in detail in Table 1. For the experiment, a fiber with the following technical characteristics was taken (Table 2) [8]. The experiment consisted in testing different compositions, at which the compressive strength in MPa was determined [9, 10]. The tests were carried out on a testing machine that provided compression of the compositions, measuring the load with an error of no more than ±1% of the measured value. Table 1 Concrete composition Compositions

Crushed stone fractions 5–10 mm, kg

Crushed stone fractions 10–20 mm, kg

Portland Cement, kg

Water, l

AlfaBet, l

Fiber length 6 mm, kg

Fiber length12 mm, kg

C1

525

525

850

235

11

−

−

C2

525

525

850

235

11

8

−

C3

525

525

850

235

11

−

4

C4

525

525

850

235

11

−

8

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Table 2 Technical specifications of the basalt fibers Technical characteristics

Basalt fiber

Tensile strength, MPa

3000–4840

Modulus of elasticity, Gpa

79.3–93.1

Elongation at break, %

3.1–6.0

Specific gravity, N/m3

2.65–2.8

Fiber diameter, microns

6–21

Melting point, °C

1450

Density, g/m3

2.65

3 Results and Discussion The tests were carried out on samples in the form of cubes with dimensions of 10 × 10 × 10 cm. After 7, 14, 28 and 60 days, after pouring, four different compositions were placed under the press and each value was recorded. The results of the strength test of the samples are shown in Table 3. Table 3 shows that the best results were obtained by samples from high-strength concrete with the addition of basalt fiber with a 6 mm length. With the addition of 1% of the basalt fiber, the compressive strength of the sample increased by 14%, and with the addition of 0.5% fiber increased by 4%. Table 3 Test results Days

Compositions

Cubic strength, MPa

7

C1

34.356

C2

40.488

C3

34.820

14

28

60

C4

33.170

C1

52.281

C2

57.991

C3

54.194

C4

49.396

C1

74.687

C2

85.131

C3

77.413

C4

69.105

C1

78.64

C2

87.818

C3

82.092

C4

71.25

Effects of Basalt Fibre on the Strength of Concrete

127

Fig. 1 Graph of the strength gain of concrete

On the basis of the table a graph of the strength gain of concrete was made for a visual comparison of the samples (Fig. 1).

4 Conclusions As a result of the study, it was found that the samples to which the basalt fiber was added have greater strength than the samples without fiber, except for the fourth sample. It can also be added that samples with a fiber length of 6 mm (sample C2) had greater strength than samples with a fiber length of 12 mm (sample C4). On the basis of experimental data, can be formulated the following conclusions: 1. The addition of basalt fiber in the composition of the concrete, increases its strength characteristics in compression compared to conventional concrete. 2. Concrete samples with a 6 mm basalt fiber have greater strength than samples with a 12 mm fiber.

References 1. Bazhenov YM (2005) Concrete technology of the XXI century. Academic readings of RAASN. New scientific directions of building materials science, Belgorod (1):9–20 2. Bazhenov YM (1977) High-strength concrete with chemical additives. Concr Reinforced Concr 8:29–31 3. Types of fiber. https://cemmix.ru/clauses/vse-fibry-betona. Accessed 21 Oct 2021 4. Rybin VA (2016) Physicochemical study of basalt fiber with protective alkali-resistant coatings. Novosibirsk, p 143 5. Kljuev SV (2012) High-strength fiber concrete for industrial and civil construction. Mag Civil Eng 34(8):61–66

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6. Kosior-kazberuk M (2013) Variation in fracture energy of concrete subjected to cycling freezing and thawing. Arch Civil Mech Eng 13(2):254–259 7. Neocleous K, Angelakopoulos H, Pilakoutas K, Guadagnini M (2011) Fibre - reinforced rollercompacted concrete transport pavements. Proc ICE Transp 164(2):97–109 8. Okolnikova GE, Novikov NV, Starchevskaya AY, Pronin GS (2019) Strengthening concrete with basalt fiber. Building 37–40 9. Volkov IV (2005) Fiber concrete - the state and prospects of application in building structures. Build Mater Equip Technol XXI Century 4:24–25 10. Buchkin AV, Stepanov VF (2006) Cement compositions of increased corrosion resistance, reinforced with basalt fibers. Constr Mater 7:12–16 11. Okolnikova GE, Belov AP, Slinkova EV (2018) Analysis of the properties of various types of fiber-reinforced concrete. Syst Technol 26:206–210 12. Ulybin AV (2012) On the choice of concrete strength inspection methods of readybuilt structures. Mag Civil Eng 34(8):42–46 13. Sprince AA, Pakrastinsh LA, Korjakins AB (2011) Experimental study on creep of new concrete mixtures In: Civil engineering 11 - 3rd international scientific conference, proceedings, vol 3, pp 20–26 14. Nikolskiy SG (1990) Acoustic emission control of strength. Probl Strength 252(6):102–106

Experimental Studies of the Effect of Reinforcement on the Bearing Capacity of a Sandy Base Under Static and Cyclic Loading Vasiliy M. Antonov , Ibtehal Abdulmonem Al-Naqdi , Pavel V. Monastyrev , Sergey Emelianov , and Ekaterina Pakhomova Abstract This article presents the results of laboratory experiments to assess the effect of reinforcement on the bearing capacity of the base and the rate of settlement development under static and cyclic loading. The experiments were carried out in a metal tray with rigid sides walls. The soil was fine sand. Reinforcement was carried out in one and two layers. Metal grids with dimensions of 145 × 125 mm were used as reinforcing elements. It was shown that by comparison between single-layer reinforcement and two-layers, the values of the ultimate load were 1.8–2.8 times higher by static loading transfer scheme, and for a cyclic one by 1.9–3.4 times, depending on the distance to the reinforcement. The optimal location of the reinforcing element with single-layer reinforcement, both under static and cyclic application of loads was h s = 0.1 ∼ 0.2D. The total values of settlement during cyclic application of loads are greater due to the accumulation of residual deformations during repeated application of loads. Keywords Reinforced soil · Plate · Reinforcement · Cyclic loads · Static loads

1 Introduction At the construction stage, foundations and bases initially experience a gradual increasing load, and then, if equipment is used in the technological process that experiences repeated or repeatedly variable loads, then cyclic loads are applied. As experience showed, that the loss of bearing capacity and strength of the soil base under the action of cyclic loads occurs due to the accumulation of shifts of individual volumes of soil with subsequent loss of strength. It is possible to increase the rigidity of the base due to the redistribution of shear stresses and the inclusion of an additional volume of soil due to its reinforcing [1–15]. V. M. Antonov · I. A. Al-Naqdi · P. V. Monastyrev (B) Tambov State Technical University, Tambov, Russia e-mail: [email protected] S. Emelianov · E. Pakhomova Southwest State University, Kursk, Russia © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_14

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The scope of previous experimental studies of reinforced bases under cyclic loads is very limited [16]. The purpose of the previous studies was to develop empirical formulas used in design [17], while not considering the effect of reinforcement on the rate of settlement development and bearing capacity under the action of cyclic and repeatedly variable loads. Determining the optimal depth of the reinforcing elements, comparing the bearing capacity and the rate of settlement development in the base when applying static and cyclic loads, in the case of single-layer and multi-layer reinforcement in the base is the purpose of this study.

2 Materials and Methods The experiments were carried out in a metal tray with rigid sides walls measuring 70 × 55 × 55 cm. The sand was fine, homogeneous, with a natural humidity of 11%. The sand base was formed through layer-by-layer compaction using a metal tamper to a density of 1.53 g/cm3 . The thickness of each compacted layer was 5 cm, a reinforcing grid was laid to the desired depth, if necessary. The granulometric composition of sand is shown in Fig. 1 and in Table 1. During the tests, the settlement was determined over the entire load range by ICH-10 h-type indicators mounted on a reference frame. A rigid metal plate with a diameter = 120 mm was used as a foundation model. The load on the plate was transmitted using a lever system with a gear ratio of 1:5. The loading stages were assumed to be equal to 0.1 of the previously found ultimate load. Each stage was maintained until the settlement was conditionally stabilized (20 min). The loading

Fig. 1 Sand uniformity curve

Table 1 Grain composition of sand Particle sizes, mm

2

1

0.5

0.25

0.1

Less than 0.1

Percentage content, %

0

0.4

1

89.8

8.6

0.2

Experimental Studies of the Effect of Reinforcement …

131

was carried out either till failure, accompanied by the extraction of soil, or to a sharp increase in settlements, or until the conditional maximum settlement of the foundation was obtained [s]u . Static and cyclic application of loads were considered. With cyclic transmission of loads, the load was brought up to F = 0.6Fu and then transmitted for 20 cycles. After that, the application of the load continued in stages until failure. Reinforcement was carried out in one and two layers. As reinforcing elements, were used grids with dimensions of 145 × 125 mm, the diameter of the grid rods was 4 mm, the pitch of the rods was 35 mm. The grids were placed under the sole of the plate. The reinforcement scheme is shown in Fig. 2. The distance from the sole of plate to the reinforcement with single-layer reinforcement was changed in the range of 0.1–0.5 D, with an interval of 0.1 D, with double-layer reinforcement was changed in accordance with Table 2.

Fig. 2 Reinforcement schemes with: a single-layer, b double-layers

Table 2 The distance from the plate sole to the reinforcing elements

0.1

hs2 / D

0.2

hs1 / D

0.1

0.2

0.6 0.3

0.3 0.1

0.4

0.4

0.2

0.5

0.1

0.2

0.1

0.5 0.3

0.2

0.1

0.3

0.2 0.7 0.4

0.3

0.4

0.5

0.6

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Table 3 Pressure and settlement values corresponding to the ultimate static loading Single-layer reinforcement

Double-layers reinforcement

Distance to the grid, hs qu(R), MPa Su, mm Distances to the grids qu(R), MPa Su, mm hs1 /D, hs2 /D hs = 0.1D

0.144

19.2

hs1 = 0.1, hs2 = 0.6 0.265

18.12

hs = 0.2D

0.128

17.7

hs1 = 0.2, hs2 = 0.6 0.33

20.5

hs = 0.3D

0.106

17.2

hs1 = 0.3, hs2 = 0.6 0.305

21.79

hs = 0.4D

0.088

16.24

hs1 = 0.4, hs2 = 0.6 0.181

18.19

hs = 0.5D

0.088

14.8

hs1 = 0.5, hs2 = 0.6 0.145

18.08

Table 4 Limit values of pressure and settlement due to cyclic loading application Single-layer reinforcement

Double-layers reinforcement

Distance to the grid, hs qu(R), MPa Su, mm Distances to the grids qu(R), MPa Su, mm hs1 /D, hs2 /D hs = 0.1D

0.154

21.18

hs1 = 0.1, hs2 = 0.6 0.296

29.06

hs = 0.2D

0.149

19.81

hs1 = 0.2, hs2 = 0.6 0.3

30.7

hs = 0.3D

0.097

17.8

hs1 = 0.3, hs2 = 0.6 0.336

34.27

hs = 0.4D

0.106

19.11

hs1 = 0.4, hs2 = 0.6 0.203

20.35

hs = 0.5D

0.097

17.12

hs1 = 0.5, hs2 = 0.6 0.238

28.44

3 Results and Discussion Table 3 shows the values of pressure, MPa and settlement, mm, corresponding to the ultimate static loading with single-layer and double-layers reinforcement, and Table 4 shows the same values with cyclic loading. Figures 3 and 4 show the pressure-settlement dependence during static and cyclic loading application for unreinforced base and base reinforced with one layer and two layers of reinforcement, with varying distances to the upper layer.

Experimental Studies of the Effect of Reinforcement …

133

Fig. 3 Pressure-settlement dependence with static loading application and variable distances to the top layer with single-layer and double-layer reinforcement h s1 = (0.1 − 0.3)D, h s2 = 0.6D (a), h s1 = (0.4 − 0.5)D, h s2 = 0.6D (b)

Figures 5 and 6, show a comparison of the results of settlement values for a base reinforced with two layers of reinforcement (Fig. 5) and single-layer reinforcement (Fig. 6) at a fixed pressure under the sole of the plate foundation and at varying distances to the reinforcing elements.

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Fig. 4 Pressure-settlement dependence under cyclic loading application and with variable distances to the top layer with single-layer and double-layer reinforcement h s1 = (0.1 − 0.3)D, h s2 = 0.6D (a), h s1 = (0.4 − 0.5)D, h s2 = 0.6D (b)

Fig. 5 Settlement values for a base reinforced with two layers of reinforcement at a fixed pressure of 0.07 MPa

Experimental Studies of the Effect of Reinforcement …

135

Fig. 6 Settlement values for a base reinforced with a single layer of reinforcement at a fixed pressure of 0.04 MPa

4 Conclusions According to the results of the experiments, the effectiveness of two-layer reinforcement is noticeable. Compared with the non-reinforced base, the maximum load values are almost 4 times higher for both static and cyclic loads. Compared with single-layer reinforcement, the values of the ultimate load are 1.8–2.8 times higher for a static load transfer scheme, and for a cyclic one by 1.9–3.4 times, depending on the depths to the reinforcement. The optimal location of the reinforcing element with singlelayer reinforcement was h s = 0.1 ∼ 0.2D, both with static and cyclic application of loads. With two-layer reinforcement, the maximum effect was observed when the upper layer of reinforcement was located at the same distance h s1 = 0.1 ∼ 0.3D, that is, in the zone of development of maximum shear stresses. In this case, the upper grid played the role of a fake sole, while the optimal location of the second layer of reinforcement was h s2 = 0.4 ∼ 0.6D. The total values of settlement during cyclic transfer of loads are greater due to the accumulation of residual deformations during repeated applications of loads.

References 1. Antonov VM, Al-Naqdi IA (2020) Experimental study of the influence of sand base reinforcement on the development of deformations under static and cyclic loading. In: IOP conference series: materials science and engineering, vol 918, no 1. IOP Publishing, p. 012008

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2. Antonov VM, Al-Naqdi IA (2020) Use of program ANSYS in the analysis of interaction between a rigid foundation and reinforced soil. In: IOP conference series: materials science and engineering, vol 786, no 1. IOP Publishing, p 012060 3. Chen Q, Abu-Farsakh M (2015) Ultimate bearing capacity analysis of strip footings on reinforced soil foundation. Soils Found 55(1):74–85 4. Azzam WR, Nasr AM (2015) Bearing capacity of shell strip footing on reinforced sand. J Adv Res 6(5):727–737 5. Cicek E, Guler E, Yetimoglu T (2015) Effect of reinforcement length for different geosynthetic reinforcements on strip footing on sand soil. Soils Found 55(4):661–677 6. Abu-Farsakh M, Chen Q, Sharma R (2013) An experimental evaluation of the behavior of footings on geosynthetic-reinforced sand. Soils Found 53(2):335–348 7. Alawaji HA (2001) Settlement and bearing capacity of geogrid-reinforced sand over collapsible soil. Geotext Geomembr 19(2):75–88 8. Raghavendra HB (2008) Analysis of soil-reinforcement interaction in reinforced soil beds. Proc Inst Civil Eng Ground Improve 161(1):9–15 9. Sharma R, Chen Q, Abu-Farsakh M, Yoon S (2009) Analytical modeling of geogrid reinforced soil foundation. Geotext Geomembr 27(1):63–72 10. Chakraborty M, Kumar J (2014) Bearing capacity of circular foundations reinforced with geogrid sheets. Soils Found 54(4):820–832 11. Khing KH, Das BM, Puri VK, Cook EE, Yen SC (1993) The bearing-capacity of a strip foundation on geogrid-reinforced sand. Geotext Geomembr 12(4):351–361 12. Basudhar PK, Saha S, Deb K (2007) Circular footings resting on geotextile-reinforced sand bed. Geotext Geomembr 25(6):377–384 13. Latha GM, Somwanshi A (2009) Bearing capacity of square footings on geosynthetic reinforced sand. Geotext Geomembr 27(4):281–294 14. Madhav MR, Poorooshasb HB (1988) A new model for geosynthetic reinforced soil. Comput Geotech 6(4):277–290 15. Li J, Tang C, Wang D, Pei X, Shi B (2014) Effect of discrete fibre reinforcement on soil tensile strength. J Rock Mech Geotech Eng 6(2):133–137 16. Wang JQ, Zhang LL, Xue JF, Tang Y (2018) Load-settlement response of shallow square footings on geogrid-reinforced sand under cyclic loading. Geotext Geomembr 46(5):586–596 17. Ashmawy AK, Bourdeau PL (1995) Geosynthetic-reinforced soils under repeated loading: a review and comparative design study. Geosynth Int 2(4):643–678

The Effect of Long-Term Storage on the Compressive Strength Along the Grain of Pine Timber Alexander Masalov

and Viktoriia Solodilova

Abstract Long-term storage of apolymer, including natural polymer, could significantly affects all its mechanical characteristics. For the accuracy of the experiment, specimens of the same size, breed and humidity were used. The ultimate strength of pine wood was determined in laboratory conditions in 1981 and in 2019 years. The specimens in tests conducted 38 years ago had compressive strength varying from 39.32 to 53.75 MPa, the accuracy rate was 2.77%, which ensures sufficient reliability of the experiment data. In 2019, the average compressive strength of the specimens was from 47.04 MPa to 64.67, and the accuracy rate was 2.68%. The average value of compressive strength along the grain of the core part of wood according to the tests of 1981 was equal to M = 48.83 MPa. The average value of compressive strength along the grain of the heartwood after long-term storage was, according to the tests of 2019, M = 52.89 MPa. The difference between the average values of 48.83 MPa < 52.89 MPa was noted. The value of the compressive strength along the grain of sapwood after long-term storage was slightly higher: by 52.89–48.83 = 4.06 MPa or 7.9%. The reliability of the obtained data was checked by means of the Student’s criterion. Keywords Wood · Compressive strength · Long-term storage · Heartwood · Sapwood · Timber · Experiment

1 Introduction Any building structure and material alters its properties during their operation. There are various reasons that could cause degradation of mechanical properties of materials and structures. Among them are atmospheric impacts, duration of loading under the static and cyclic loading. Wood is a natural polymer and has its special properties. Long-term loading of timber structures by static and cyclic load in Southwest state university was investigated by A. Prokofiev, V. Kabanov [8–11], A. Smorchkov. S. A. Masalov · V. Solodilova (B) South West State University, 50 Years of Octoberst., 92, 305040 Kursk, Russia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_15

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Povetkin. Stability of statically indeterminate timber structures was investigated by V. Kolchunov [1–3] and K. Dubrakova [4–7]. Mechanical properties of wood have the characteristics inherent in all polymers. In this work, it was experimentally investigated the possibility of reducing the value of the ultimate strength in compression of pine wood as a result of long-term storage. Changes in the values of the mechanical characteristics of structural materials during their operation or storage should be taken into account in verification and design calculations. The obtained data reflect a significant difference in the testing of “fresh” sapwood and storage sapwood was obtained: compressive strength slightly increased with storage time. In this experiment, statistically significant values of the reduction in compressive strength of sapwood and pine heart will be determined.

2 Materials and Methods Wood as a structural material can be considered as a composite consisting of two main components—lignin and cellulose. Lignin performs functions similar to concrete, provides compressive strength. Cellulose is a natural reinforcement that allows wood to withstand the load. Due to oxidation during long-term storage or long-term operation, the development of degradation of the mechanical properties of wood components is possible. This phenomenon should be taken into account when assessing the service life of structures. To identify the regularities of the influence of long-term storage on the strength characteristics of wood, specimens of standard size 20 × 20 × 30 mm were used, were selected according to the scheme shown in Fig. 1. The specimens were dried in two stages to achieve an equilibrium moisture content of 10%. The marking of the specimen was carried out according to the following scheme: “1a2”, where 1 is the sector designation, a is the designation of the bar, 15 is the designation of the specimen along the length of the bar (Fig. 1). To determine of the regularity of long-term storage on the strength characteristics, short-term load tests were carried out on 64 specimens to determine the compressive strength. Tests of the first series of specimens in accordance with GOST 16,483.20– 7373 Wood. Methods for determination of ultimate strength in compression parallel the grain were carried out in the laboratory of the Kursk Polytechnic Institute of the Department of Structural Mechanics and Strength of Materials in 1981 under the guidance of prof. A.A. Smorchkov. The tests were carried out on a press of the UM-5 type (Fig. 2a) The data on the strength properties of wood specimens were entered into the test log. After the compression tests were performed, moisture tests were performed and the test results of the specimens were adjusted to values at 12% moisture. The untested specimens were stored for 38 years in the laboratory of the Department of Industrial and Civil Engineering at Southwest State University. In 2019, the stored specimens were prepared and tested.

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Fig. 1 Scheme of sampling from a pine block. Specimen before testing

a)

b)

Fig. 2 a Mechanical press UM-5 b Hydraulic press PGM-100MG4A

The wood moisture was measured by method of GOST 16,483.7-71 Wood. Methods for determination of moisture content using a low-temperature laboratory electric furnace SNOL 67/350 with forced air circulation. Before the tests, each specimen was weighed on the laboratory scale VLTE-1100. Compressive strength measurements along the grain of wooden specimens in 2019 were carried out in the laboratory of industrial and civil construction using a hydraulic press PGM-100MG4A (Fig. 2b).

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To study the statistical variability of compressive strength and establish the distribution law of the set of measurements, specimens of various series (1a, 3a, 5b) were taken. For (1.0 ± 0.5) minutes after the start of the test, the specimens were fractured, with the constant loading rate.

3 Results and Discussion The obtained experimental data of 2019 are comparable with the results of the experiments of 1981, which will allow us to assess the regularities of the influence of long-term storage on compressive strength characteristics. The results of the tests of 1981 are given below. The results of sapwood tests. 1981-year test results of the sapwood specimens. For statistical processing of the obtained data, we adjusted the values obtained during the experiment of 1981 to the moisture equal to 12% in accordance with the formula (1). σ12 = σW × (1 − α(W − 12),

(1)

where α—is the coefficient equal to 0.04; σW —the ultimate compressive strength of the specimen at the time of testing, MPa; W—moisture content of aspecimen at the time of testing, %. Specimen 1a10 σ12 = 46.83 × (1 − 0.04(10 − 12) = 50.58 MPa Specimen 1a20 σ12 = 44.12 × (1 − 0.04(10 − 12) = 47.65 MPa Specimen 1a40 σ12 = 36.41 × (1 − 0.04(10 − 12) = 39.32 MPa Specimen 3a10 σ12 = 47.1 × (1 − 0.04(10 − 12) = 50.88 MPa Specimen 3a20 σ12 = 45.72 × (1 − 0.04(10 − 12) = 49.38 MPa Specimen 3a40 σ12 = 48.66 × (1 − 0.04(10 − 12) = 52.55 MPa Specimen 5c2 σ12 = 49.77 × (1 − 0.04(10 − 12) = 53.75 MPa Specimen 5c10 σ12 = 46.21 × (1 − 0.04(10 − 12) = 49.91 MPa Specimen 5c20 σ12 = 44.13 × (1 − 0.04(10 − 12) = 47.66 MPa Specimen 5c30 σ12 = 46.34 × (1 − 0.04(10 − 12) = 50.08 MPa Specimen 5c40 σ12 = 52.34 × (1 − 0.04(10 − 12) = 56.52 MPa Table 1 shows some statistical parameters for the test data of specimens of sapwood in 1981.

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Table 1 Determination of statistical parameters for the test data of 1981 for the specimen of pine sapwood Specimen

V*. MPa

X**. MPa

X2 ***. (MPa)2

1a10

50.58

0.74

1a20

47.65

−2.19

0.5476 4.7961

1a40

39.32

−10.52

110.6704

3a10

50.88

1.04

1.0816

3a20

49.38

−0.46

0.2116

3a40

52.55

2.71

7.3441

5b2

53.75

3.91

15.2881

5b10

49.91

0.07

0.0049

5b20

47.66

−2.18

4.7524

5b30

50.08

0.24

0.0576

5b40

56.52

6.68

44.6224

V = 548.28

−15.35

V = 189.3768

15.39 * In

the first column, denoted as V, the obtained numbers (variants) are written; **in the second column, designated as X, the deviation of an individual variant from the arithmetic mean M is written with the sign “+” or “−”; ***in the third column, denoted as X2 —the square of deviations 

V = 548.28 = 49.84 MPa n 2 11  X Standard deviation: δ = ± n−1 = ± 189.3768 = 4.3517 MPa 10

Arithmetic mean: M =

δ √ == ± 4.3517 = 1.38 MPa. Average sampling error: m = ± √n−1 n−1

Coefficient of variation: ε = Xδ · 100% = 100·4.3517 = 8.73% 49.84 m 100·1.38 Accuracy indicator: %P% = X ∗ 100% = 49.84 = 2.77%. P% = 2.77 < 5 this of the experiment is provided.

2019-year test result of the sapwood specimens. Statistical procedure here and further is the same as for the previous test data. Specimen 1a16 σ12 Specimen 1a32 σ12 Specimen 1a36 σ12 Specimen 1a41 σ12 Specimen 3a18 σ12 Specimen 3a23 σ12 Specimen 3a27 σ12 Specimen 3a30 σ12 Specimen 5c14 σ12 Specimen 5c24 σ12 Specimen 5c27 σ12 Specimen 5c42 σ12

= 48.83 × (1 − 0.04(8 − 12) = 56.64 MPa = 45.28 × (1 − 0.04(8 − 12) = 52.52 MPa = 42.93 × (1 − 0.04(8 − 12) = 49.80 MPa = 40.55 × (1 − 0.04(8 − 12) = 47.04 MPa = 49.18 × (1 − 0.04(8 − 12) = 57.05 MPa = 49.65 × (1 − 0.04(8 − 12) = 57.59 MPa = 52.95 × (1 − 0.04(8 − 12) = 61.42 MPa = 55.75 × (1 − 0.04(8 − 12) = 64.67 MPa = 46.7 × (1 − 0.04(8 − 12) = 54.17 MPa = 46.95 × (1 − 0.04(8 − 12) = 54.46 MPa = 49.35 × (1 − 0.04(8 − 12) = 57.25 MPa = 50.90 × (1 − 0.04(8 − 12) = 59.04 MPa

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Table 2 Determination of statistical parameters for the test data of 2019 for pine sapwood Specimen

V*. MPa

X**. MPa

X2 ***. (MPa)2

1a16

56.64

0.67

0.4489

1a32

52.52

−3.45

11.9025

1a36

49.80

−6.17

38.0689

1a41

47.04

−8.93

79.7449

3a18

57.05

1.08

1.1664

3a23

57.59

1.62

2.6244

3a27

61.42

5.45

29.7025

3a30

64.67

9.2

84.64

5c14

54.17

−1.8

3.24

5c24

54.46

−1.51

2.2801

5c27

57.25

1.28

1.6384

5c42

59.04

3.07

9.4249

V = 671.65

−21.86

V = 272.0404

22.37

Table 2 shows some statistical parameters for the test data of sapwood specimens in 2019: 

V = 671.25 = 55.97 MPa n 12 272.0404 = 4.973 MPa Standard deviation: δ = ± 11 4,973 Average sampling error: m = ± √12−1 = 1, 50 MPa = 8.885% Coefficient of variation: ε = 100·4.973 55.97 Accuracy indicator. %:P% = 100·1.50 = 2.68% 55.97

Arithmetic mean: M =

P% = 2.68 < 5 means that sufficient reliability of the experiment is provided. Comparison of 1981 and 2019-year sapwood test results. The average value of the compressive strength along the grain of the sapwood specimen according to the 1981 test data was equal to M = 49.84 MPa. The same after long-term storage was, according to test data in 2019, M = 55.97 MPa. There is a difference in the average values of 49.84 MPa < 55.97 MPa. Average value of the compressive strength of pine sapwood appeared to be greater in the tests of 2019 than in the tests of 1981 year on 12,2%. Let us estimate the reliability of the difference between the results of two samples in accordance with Students criterion. The value of the Student’s criterion, t is calculated as |55, 97 − 49, 84| |x1 − x2 | = √ = 3, 01 t= 1, 9 + 2, 25 m 21 + m 22

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143

where x1 is arithmetic mean of the first group; x2 is arithmetic mean of the second group; m 1 is average sampling error of the first group; m 2 is average sampling error of the first group; The obtained value of the t-criterion is greater than the tabular value for the number of degrees of freedom 11 + 12–2 = 21. 3.01 < 2.09—therefore. the difference in the mean values of the samples is statistically significant. The results of heartwood tests. 1981-year test results of the heartwood specimens. Specimen 1b1 σ12 = 56.76[1 + 0.04(10 – 12)] = 52.22 MPa Specimen 1b10 σ12 = 56.63[1 + 0.04(10 – 12)] = 52.1 MPa Specimen 1b20 σ12 = 47.93[1 + 0.04(10 – 12)] = 44.09 MPa Specimen 1b30 σ12 = 50.26[1 + 0.04(10 – 12)] = 46.24 MPa Specimen 1b40 σ12 = 52.71[1 + 0.04(10 – 12)] = 48.49 MPa Specimen 8b1 σ12 = 53.45[1 + 0.04(10 – 12)] = 49.17 MPa Specimen 8b10 σ12 = 53.94[1 + 0.04(10 – 12)] = 49.62 MPa Specimen 8b20 σ12 = 55.53[1 + 0.04(10 – 12)] = 51.09 MPa Specimen 8b30 σ12 = 49.03[1 + 0.04(10 – 12)] = 45.11 MPa Specimen 8v40 σ12 = 54.55[1 + 0.04(10 – 12)] = 50.19 MPa Table 3 shows some statistical parameters for the test data of specimens of heartwood in 1981. 

Arithmetic mean: M = Standard deviation: δ =

V = 488.32 = 48.83 MPa n 10   2 X ± n−1 = ± 72.02 = 2.85 MPa 9

Table 3 Determination of statistical parameters for the test data of 1981 for the specimen of pine heartwood Specimen

V*. MPa

X**. MPa

X2 ***. (MPa)2

1v1

52.22

3.39

1v10

52.1

3.27

10.69

1v20

44.09

−4.74

22.47

1v30

46.24

−2.59

6.71

1v40

48.49

−0.34

0.12

8v1

49.17

0.34

0.12

8v10

49.62

0.79

0.62

8v20

51.09

2.26

5.11

8v30

45.11

−3.72

13.84

8v40

50.19

1.36

1.85

V = 488.32

11.39

V = 73.02

11.41

11.49

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δ √ = 0.317 MPa. Average sampling error: m = ± √n−1 == ± 2.85 9

Coefficient of variation: ε = Xδ · 100% = 100·2.85 = 5.84% 52.89 = 0.65%. Accuracy indicator. % P% = mX ∗ 100% = 100·0.317 48.83 P% = 0.65 < 5 this means that sufficient reliability of the experiment is provided. 2019 year test result of the sapwood specimens. Statistical procedure here and further is the same as for previous test data.

Specimen 1a16 σ12 Specimen 1a32 σ12 Specimen 1a36 σ12 Specimen 1a41 σ12 Specimen 3a18 σ12 Specimen 3a23 σ12 Specimen 3a27 σ12 Specimen 3a30 σ12 Specimen 5c14 σ12 Specimen 5c24 σ12 Specimen 5c27 σ12 Specimen 5c42 σ12

= 48.83 × (1 − 0.04(8 − 12) = 56.64 MPa = 45.28 × (1 − 0.04(8 − 12) = 52.52 MPa = 42.93 × (1 − 0.04(8 − 12) = 49.80 MPa = 40.55 × (1 − 0.04(8 − 12) = 47.04 MPa = 49.18 × (1 − 0.04(8 − 12) = 57.05 MPa = 49.65 × (1 − 0.04(8 − 12) = 57.59 MPa = 52.95 × (1 − 0.04(8 − 12) = 61.42 MPa = 55.75 × (1 − 0.04(8 − 12) = 64.67 MPa = 46.7 × (1 − 0.04(8 − 12) = 54.17 MPa = 46.95 × (1 − 0.04(8 − 12) = 54.46 MPa = 49.35 × (1 − 0.04(8 − 12) = 57.25 MPa = 50.90 × (1 − 0.04(8 − 12) = 59.04 MPa

2019-year test results of the heartwood specimens. Specimen 1v6 σ12 = 54.42[1 + 0.04(7 − 12)] = 43.54 MPa Specimen 1b8 σ12 = 55.9[1 + 0.04(7 − 12)] = 44.72 MPa Specimen 1b13 σ12 = 50.23[1 + 0.04(7 − 12)] = 40.18 MPa Specimen 1b17 σ12 = 55.8[1 + 0.04(7 − 12)] = 44.64 MPa Specimen 1b19 σ12 = 55.38[1 + 0.04(7 − 12)] = 44.3 MPa Specimen 1b24 σ12 = 60.48[1 + 0.04(7 − 12)] = 48.38 MPa Specimen 1b27 σ12 = 62.05[1 + 0.04(7 − 12)] = 49.64 MPa Specimen 1b33 σ12 = 59.7[1 + 0.04(7 − 12)] = 47.76 MPa Specimen 1b38 σ12 = 56.98[1 + 0.04(7 − 12)] = 45.58 MPa Specimen 1bv40 σ12 = 68.34[1 + 0.04(7 − 12)] = 54.67 MPa Specimen 8b4 σ12 = 79.83[1 + 0.04(7 − 12)] = 63.86 MPa Specimen 8b7 σ12 = 75.13[1 + 0.04(7 − 12)] = 60.1 MPa Specimen 8b12 σ12 = 77.03[1 + 0.04(7 − 12)] = 61.62 MPa Specimen 8b18 σ12 = 77.7[1 + 0.04(7 − 12)] = 62.16 MPa Specimen 8b22 σ12 = 75.2[1 + 0.04(7 − 12)] = 60.16 MPa Specimen 8b25 σ12 = 79.48[1 + 0.04(7 − 12)] = 63.58 MPa Specimen 8v28 σ12 = 76.6[1 + 0.04(7 − 12)] = 61.28 MPa Specimen 8v31 σ12 = 77.13[1 + 0.04(7 − 12)] = 61.7 MPa Specimen 8b35 σ12 = 64.68[1 + 0.04(7 − 12)] = 51.74 MPa Specimen 8b42 σ12 = 60.35[1 + 0.04(7 − 12)] = 48.28 MPa Table 4 shows some statistical parameters for the test data of specimens of heartwood in 2019.

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Table 4 Determination of statistical parameters for the test data of 2019 for the specimen of pine heartwood Specimen

V*, MPa

X**, MPa

X2 ***, (MPa)2

1v6

43.54

−9.35

1v8

44.72

−8.17

66.75

1v13

40.18

−12.71

161.54

1v17

44.64

−8.25

68.06

1v19

44.3

−8.59

73.79

1v24

48.38

−4.51

20.34

1v27

49.64

−3.25

10.56

1v33

47.76

−5.13

26.32

1v38

45.58

−7.31

53.44

1v40

54.67

1.78

8v4

63.86

10.97

120.34

8v7

60.1

7.21

51.98

8v12

61.62

8.73

76.21

8v18

62.16

9.27

85.93

8v22

60.16

7.27

52.85

8v25

63.58

10.69

114.28

8v28

61.28

8.39

70.39

8v31

61.7

8.81

77.61

8v35

51.74

−1.15

1.32

8v42

48.28

−4.61

21.25

V = 1057.89

−73.03

87.42

3.17

V = 1243.55

73.12 

V = 1057.89 = 52.89 MPa n 20   2 X = ± 1243,55 = 8.09 MPa Standard deviation: δ = ± n−1 19 δ 8.097 √ √ Average sampling error: m = ± n−1 == ± 19 = 1.86 MPa, Coefficient of variation: ε = Xδ · 100% = 100·8.09 = 15.3% 52.89 Accuracy indicator, % P% = mX ∗ 100% = 100·1,86 = 3.51%, 52.89

Arithmetic mean: M =

P% = 2,77 < 5 this means that sufficient reliability of the experiment is provided, 2019 year test result of the sapwood specimens. Statistical procedure here and further is the same as for previous test data. Specimen 1a16 σ12 Specimen 1a32 σ12 Specimen 1a36 σ12 Specimen 1a41 σ12 Specimen 3a18 σ12

= 48.83 × (1 − 0.04(8 − 12) = 56.64 MPa = 45.28 × (1 − 0.04(8 − 12) = 52.52 MPa = 42.93 × (1 − 0.04(8 − 12) = 49.80 MPa = 40.55 × (1 − 0.04(8 − 12) = 47.04 MPa = 49.18 × (1 − 0.04(8 − 12) = 57.05 MPa

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Specimen 3a23 σ12 Specimen 3a27 σ12 Specimen 3a30 σ12 Specimen 5c14 σ12 Specimen 5c24 σ12 Specimen 5c27 σ12 Specimen 5c42 σ12

= 49.65 × (1 − 0.04(8 − 12) = 57.59 MPa = 52.95 × (1 − 0.04(8 − 12) = 61.42 MPa = 55.75 × (1 − 0.04(8 − 12) = 64.67 MPa = 46.7 × (1 − 0.04(8 − 12) = 54.17 MPa = 46.95 × (1 − 0.04(8 − 12) = 54.46 MPa = 49.35 × (1 − 0.04(8 − 12) = 57.25 MPa = 50.90 × (1 − 0.04(8 − 12) = 59.04 MPa

Comparison of 1981 and 2019-year heartwood test results. The average value of the compressive strength along the grain of the heartwood specimens according to the 1981 test data was equal to M = 48,83 MPa. The same after long-term storage was, according to test data in 2019, M = 52.89 MPa. There is a difference in the average values of 48.83 MPa < 52.89 MPa. Average value of the compressive strength of pine sapwood appeared to be greater in the tests of 2019 than in the tests of 1981 year on 8.31%. Let us estimate the reliability of the difference between the results of two samples in accordance with Students criterion. The value of the Student’s criterion, t is calculated as |52.89 − 48.83| |x1 − x2 | = √ = 1.86 t= 1.317 + 3.46 m 21 + m 22 The obtained value of the t-criterion is greater than the tabular value for the number of degrees of freedom 20 + 10–2 = 28;1.86 < 2.05—therefore, the difference in the mean values of the samples is statistically insignificant. Here it is important to note that the obtained experimental distribution curves for the experimental data on sapwood, as well as for heartwood, did not agree satisfactorily with the theoretical distribution curves, apparently due to the small number of tests and the rather large variability of the wood strength characteristics [14–16]. Therefore, to assess the statistical significance of the difference in mean values, we will use the Student’s criterion conditionally, with the provision that the hypothesis of a normal distribution of values in statistical samples has not been confirmed.

4 Conclusion Some statistically significant difference in the tests of “fresh” and storage sapwood was obtained compressive strength slightly increased over time of storage. Statistically insignificant difference of increase of the compressive strength over time in the tests of heartwood was obtained. Nevertheless, the obtained results should be considered with the grain of salt. The reasons of it: first, it is not the increase but the decrease of strength was expected because of possibly degradation processes in wood over the time; second, the obtained experimental distribution curves for the

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experimental data on sapwood, as well as for heartwood, did not agree satisfactorily with the theoretical distribution curves, apparently due to the small number of tests and the rather large variability of the wood strength characteristics. A statistically significant value of the reduction in the compressive strength of sapwood and heartwood of pine on a time base of 38 years has not been established.

References 1. Travush VI, Kolchunov VI, Dmitrieva KO (2015) Long-term strength and stability of compressed wood rods. Stroitel’stvo I reconstruccija 5:40–46. https://www.elibrary.ru/item. asp?id=24395117 2. Travush VI, Kolchunov VI, Dmitrieva KO (2016) Stability of compressed rods made of wood at the simultaneous appearance of power and environmental exposures. Stroitel’nayamekhanikairaschetsooruzhenij 2:50–53. https://www.elibrary.ru/item.asp?id=267 00902 3. Travush VI, Kolchunov VI, Dmitrieva KO Experimental and theoretical research of durabilities and stability the squeezed cores from wood at power and environmental influence. Izvestiyavysshihuchebnyhzavedenij. tekhnologiyatekstil’nojpromyshlennosti 3:280– 285. https://www.elibrary.ru/item.asp?id=26378375 4. Dubrakova KO, Dubrakov SV, Altuhov FV, Galaeva DH (2019) The buckling of the physically nonlinear frame-rod structural system. 2019 IOP Conf Mater Sci Eng 698:022007 5. Dubrakova KO (2018) The stability of statically indeterminate systems of wood. BST Byulleten’stroitel’nojtekhniki 11:54–55. https://www.elibrary.ru/item.asp?id=36380438 6. Klyueva NV, Dmitrieva KO (2016) Issues of sustainable rod elements design systems of different wood species in force and environmental loading moisture. Stroitel’stvoireconstrukcia 5:60–68. https://www.elibrary.ru/item.asp?id=26703111 7. Kabanov V (2001) Reliability of elements made of glued beams under fatigue load. Dissertation. Svk STU, Bratislava 8. Kabanov V, Masalov A, Solianik J (1998) Normalization of exploitation loading of wood composites for building structures. In: Proceedings of the 5th world conference on timber engineering, Montreux, Switzerland, vol 2, pp 796–797 9. Kabanov V (2001) The reliability of glued laminated timber members under fatigue loading. Dissertation. SvF STU, Bratislava 10. Stupishin L, Kabanov V, Masalov A (2014) Fracture resistance of bended glued timber elements with flaws. Adv Mater Res 988:363–366 11. Kanocz J, Bajzecerova V (2013) Timber - concrete composite elements with various composite connections Part 1: screwed connection. Wood Res 58(4):555–570 12. Ali MA, Bajzecerova V, Kvocak V (2017) Design methods of timber-concrete composite ceiling structure. Mag Civil Eng 5(73):88–95. https://doi.org/10.18720/MCE.73.8 13. Yehia A, Ali Z (2018) Flexural behavior of FRP strengthened concrete-wood composite beams. Ain Shams Eng J 9(4). https://doi.org/10.1016/j.asej.2018.06.003 14. Yemelyanov SG, Pakhomova EG, Dubrakova KO, Dubrakov SV (2019) Stability of statically indefinite physically nonlinear timber structural systems. J Appl Eng Sci. https://doi.org/10. 5937/jaes17-21686

Fast-Hardening Slag-Alkaline Heat-Resistant Aerated Concrete of Increased Heat Resistance with Additives of Fly Ash of Novocherkassk SDPP Sergey Emelianov , Alexey Bulgakov , Jens Otto , Arsen Avakyan , Kirill Protsenko , Gennadiy Skibin , and Alexander Mikheev Abstract One suggests technology for the production of quick-hardening, heatresistant aerated concrete with an application temperature of up to 600 °C. To improve the strength and heat resistance of aerated concrete, liquid glass was used as a binder and—Cherepovets granulated blast-furnace slag as a filler hardener. Increasing the reactivity of liquid glass and its plasticity was carried out by reducing the silicate modulus of liquid glass and introducing sodium hydroxide. The addition of fly ash up to 50% of the mass of the slag in the composition of aerated concrete allowed to reduce the cost of concrete and reduce its density while maintaining sufficient strength. To simplify the technological process, hydrogen peroxide was used as a gasifier instead of aluminum powder. As a result of the thermal reaction of the interaction of liquid glass, granulated blast-furnace slag, and hydrogen peroxide the aerated concrete is self-heating, bulking, and hardening. Such concrete allows not only to obtain casings and monolithic areas comparable in strength to autoclaved concrete but also to carry out repair and reconstruction work with thermal insulation. Aerated concrete can be made in a low-mechanized section and retain its properties in a humid environment when the furnace is not in operation. Keywords Blast furnace granular slag · Fly ash · Technical perhydrol · Sodium hydroxide · Heat-resistant cellular concrete

S. Emelianov · A. Bulgakov (B) Southwest State University, 50 let Oktyabrya Street 94, 305040 Kursk, Russia e-mail: [email protected] J. Otto Technical University of Dresden, Mommsen St. 10, 01069 Dresden, Germany e-mail: [email protected] A. Avakyan · K. Protsenko · G. Skibin · A. Mikheev South-Russian State Polytechnic University, Prosveshcheniya Street 132, 346428 Novocherkassk, Russia © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_16

149

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1 Introduction Dehydration and recrystallization of hydrate new formations of artificial stone during high-temperature firing into anhydrous, incapable of forming a single crystalline aggregate, results in destructive stresses and loss of strength. The formation of solidification products modified by Na+ ions and alkaline and alkaline-earth hydroaluminates (analogs of natural durable minerals—nepheline, calyophyllite, leucite, albite, orthoclase) is necessary for the smooth course of dehydration processes without breaking the structure. Formation of the microstructure of cement stone of high heat resistance due to self-reinforcing crystallization of oriented new formations of one structure in another is carried out by the introduction of alkali metal compounds (5–10% by mass) into compositions with a formation by eutectic melts heating. Thus, in order to obtain heat-resistant bundles of slag-alkaline composition, it is necessary to ensure: – recrystallization of hydrate neoplasms into anhydrous compounds without destructive stresses; – formation of 5–10% melts from the mass of the mixture for the processes of mixture self-reinforcement: – the formation of crystallization intergrowths of the precipitating phases; – optimal ratio of vitreous and crystalline phases of the burnt artificial stone for the formation of fragmentary structure.

2 Materials and Methods 2.1 Materials The following alkaline components were used as starting materials for the production of aerated concrete: technical sodium hydroxide, density 1.34 g/cm3 GOST R 550642012 and sodium liquid glass silicate module Ms = 3, initial density 1.42 g/cm3 GOST 13078-81. As a gas-forming agent—technical perhydrol, with a density of 1.1 g/cm3 GOST 10929-76. The chemical composition of the fillers is shown in Table 1. Table 1 Chemical composition of fillers Components

Chemical composition, % by weight SiO2

Al2 O3

37.88

Fly ash of the Nk SDPP 44.61

Cherepovets blast furnace granulated slag

Fe2 O3

CaO

MgO

7.50

1.39

48.31

4.22

22.74

9.90

2.35

1.11

Calcination losses

Other 0.70

12.22

7.07

Fast-Hardening Slag-Alkaline Heat-Resistant Aerated Concrete …

151

2.2 Methods 2.2.1 Selection of Components of Slag-Alkaline Binders 2.2.1.1 The Ratio of the Components of the Slag-Alkaline Binder and Their Effect on the Basic Properties The properties of building materials based on aqueous solutions of sodium silicates depend on the degree of interaction of sodium silicate with mineral filler and can be regulated by technological methods in a wide range [1]. According to the theory of condensation of dispersed substances and polystructural theory [2], the structure of slag–alkaline concrete depends on the degree of filling (liquid–solid ratio (L/S)), the activity modulus of the filler and its dispersion, the silicate modulus of liquid glass. So the fillers used in this work solve various problems. Ground granulated slag has increased chemical activity in relation to liquid glass, and fly ash has a low density and is a waste product. This makes it possible to obtain aerated concrete with improved thermal characteristics and reduce its cost. Considering the importance of the ratio between the fillers used, the influence and selection of the optimal filler on the strength properties of aerated concrete at the age of 1 day and 28 days was studied. normal hardening, as well as an indicator of the average density of dry samples. The determination of the flow rate of an aqueous solution of liquid glass was determined by the mobility of the slag—alkali mixture by the spread on the Suttard device equal to 27 = 28 cm. For liquid glass with a silicate modulus (Ms ) 3 and a density equal to 1.1; 1.2; 1.25; 1.28 g/cm3 at blast furnace slag -fly ash ratios 0.66; 1.0; 1.5; 2.0, the beginning of the setting time was determined (Table 3). The research results have shown that the most optimal slag- ash ratio (S/A) is 2:1. Table 2 shows the compositions of slag-alkaline compositions. Tables 3, 4, 5, 6 and Figs. 1, 2, 3 show the test results. As follows from the data in Table 3, the increased content of fly ash (S/A = 0.66) slows down the setting time. Table 2 Variable compositions of slag-alkaline compositions Components

The content of components in mass parts at a ratio of (S/A) 0.66

1.0

1.5

2.0

Ground granulated slag

1.0

1.0

1.5

2.0

Fly ash of Novocherkassk SDPP

1.5

1.0

1.0

1.0

Aqueous solution of sodium silicate liquid glass density, g/cm3 1.1

0.86

0.78

0.75

0.65

1.2

0.82

0.73

0.64

0.59

1.25

0.85

0.79

0.66

0.49

1.28

0.90

0.84

0.75

0.62

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Table 3 Setting time of slag-alkaline compositions Liquid glass density, g/cm3

Setting time of slag-alkaline compositions at the slag-ash ratio, min. Beginning

1.10

End

0.66

1.0

1.5

2.0

0.66

1.0

1.5

2.0

80

70

65

55

140

130

115

–

1.20

65

40

35

30

90

70

60

–

1.25

140

130

115

105

–

–

–

–

1.28

95

70

60

50

–

–

–

–

Table 4 Dependence of strength on density of liquid glass at the age of 1 day of normal hardening Density of liquid glass, g/cm3

Strength, MPa at a ratio of S/A 0.66

1.0

1.5

2.0

1.10

0/0.23

0/0.57

0/0.61

0/0.71

1.20

−/0.57

−/1.61

0/2.41

0/2.82

1.25

0.41/1.06

0.63/1.31

0.74/1.63

0.87/1.83

1.28

0.17/0.73

0.21/0.85

0.34/0.97

0.44/1.21

* The

numerator contains flexural strength; the denominator contains during compression

Table 5 Dependence of strength on density of liquid glass at the age of 28 days of normal hardening Density Liquid glass,

Strength, MPa at a ratio of S/A g/cm3

0.66

1.0

1.5

2.0

1.1

0.20/0.37

0.67/0.73

0.71/0.91

0.84/1.56

1.2

1.42/3.64

1.68/9.84

3.22/9.93

3.85/10.24

1.25

1.85/8.55

2.43/10.46

3.85/11.83

4.32/12.31

1.28

1.24/3.02

1.44/3.41

2.23/7.66

3.04/8.86

* The

numerator contains flexural strength; the denominator contains during compression

Table 6 Dependence of the density of the slag-alkali composition on the density of liquid glass Liquid glass density, g/cm3

Density, kg/cm3 with a S/A ratio 0.66

1.0

1.5

2.0

1.1

680

762

840

920

1.2

1052

1170

1250

1270

1.25

1090

1190

1200

1230

1.28

900

937

980

1100

Fast-Hardening Slag-Alkaline Heat-Resistant Aerated Concrete …

153

Min. 160 140 120 1 100 2 80 3

60

4

40 20 0

0.66 0.66

1.00 1.00

1.50 1.50

S/A

2.00 2.00

Fig. 1 The dependence of the setting time on the slag-ash ratio (S/A) and the density of liquid glass. 1—1100 kg/m3 ; 2—1200 kg/m3 ; 3—1250 kg/m3 ; 4—1280 kg/m3 S, МPа 33 2.5 2.5 1

22

2 1.5 1.5

3

1 1

4

0.5 0.5 0 0

0.66 0.66

11

1.5 1.5

22

S/A

Fig. 2 Compressive strength (S) from the slag-ash ratio (S/A) at the age of 1 day of normal hardening at a density of liquid glass: 1—1100 kg/m3 ; 2—1200 kg/m3 ; 3—1250 kg/m3 ; 4—1280 kg/m3

S. Emelianov et al.

S, MPa

154

14 12 10 1 8

2

6

3 4

4 2 0

0.66 0.66

11

1.5 1.5

22

S/A

Fig. 3 Compressive strength (S) from the slag-ash ratio (S/A) at the age of 28 days of normal hardening at a density of liquid glass: 1—1100 kg/m3 ; 2—1200 kg/m3 ; 3—1250 kg/m3 ; 4—1280 kg/m3

Based on the conducted studies, it was found that a decrease in the proportion of slag and an increase in fly ash significantly reduces the strength at the age of 1 and 28 days, the density of hardened compositions decreases with an increase in the fly ash content. As noted above, this is due to the high chemical activity of blast furnace slag and the low density of fly ash [3–10]. A significant influence on the strength characteristics of the composition has a change in the density of liquid glass [11–15]. A decrease in density from 1.28 to 1.1 g/cm3 leads to a sharp decrease in strength, however, the high viscosity of liquid glass compositions will negatively affect the processes of aerated concrete swelling, therefore it is advisable to use liquid glass with a density of 1.20 g/cm3 . 2.2.1.2 Determination of the Optimal Flow Rate of Liquid Glass While using liquid-glass binders, the homologation of compositions is possible when creating a continuous film of binder on the surface of the filler grains, while the production technology on liquid-glass compositions requires the introduction of hardeners. In this case, the role of the hardener is played by finely ground granulated blast furnace slag. As follows from the fundamental theory of adhesives and surfaces, an increase in the thickness of the seam leads to a decrease in the strength of the composition. With an increased thickness of the adhesive seam, an intermediate (middle) layer is formed, the strength of which is lower than the strength of the layers bordering the hardener and entering into a chemical reaction with it. For concretes

Fast-Hardening Slag-Alkaline Heat-Resistant Aerated Concrete …

155

on liquid glass, the decrease in strength is associated with a high water content in the binder composition—50–65%. In the process of water removal, shrinkage and the formation of a porous structure occurs. Such adhesive seams are characterized by increased defectiveness, in which cracks develop, which increase brittleness and reduce heat resistance. For aerated concrete, the strength of the slag-alkaline substance (frame) is crucial. According to, the strength of the stone decreases by 25 at 10% porous structure, by 2 times at 30%, and by 4–5 times at 50–60%. According to the Suttard device, the optimal liquid–solid ratio was selected with a height of 16, 21 and 27 cm with a slag-ash-entrainment ratio (S/A) 1:1; 1:1.5; 2:1. The compositions and results of the studies are given in Table 7 and in Figs. 4, 5 and 6. Analysis of the data obtained showed that an increase in the density of liquid glass increases its consumption for mixtures. The increased content of fly ash (S/A = 1:1.5) increases the liquid–solid ratio and reduces the strength both during bending and compression. At a liquid glass density of 1.1 g/cm3 , the liquid–solid ratio increases Table 7 Dependence of the basic properties of slag-alkali compositions on the ratio of fillers and mobility of liquid glass S/A ratio

Mobility, cm

1:1

Liquid glass with a density of 1.1 g/cm3

1:1

1.0:1.5

2:1

1:1

L/S

Bending strength, MPa

Compressive strength, MPa

1 day

1 day

28 day

28 days

Average dry density, kg/m3

16

0.51

0.4

0.9

0.58

1.60

762

21

0.60

0.5

0.65

0.6

1.25

820

27

0.71

–

0.58

0.68

0.74

762

Liquid glass with a density of 1.2

g/cm3

16

0.528

1.58

1.91

4.15

10.53

1250

21

0.61

0.60

2.66

1.91

10.04

1200

27

0.73

–

1.93

1.64

9.82

1170

16

0.64

–

1.88

0.39

6.54

1090

21

0.71

–

1.75

0.82

5.07

1090

27

0.92

–

1.36

0.56

3.63

1052

1.82

10.52

1150

Liquid glass with a density of 1.25 g/cm3 16

0.45

0.75

3.9

21

0.46

1.78

4.9

3.77

15.24

1190

27

0.49

0.88

1.82

4.33

12.367

1230

Liquid glass with a density of 1.28 g/cm3 16

0.55

–

2.85

1.74

8.92

1230

21

0.69

0.18

1.59

1.33

4.68

976

27

0.84

0.2

0.84

1.46

3.44

937

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S. Emelianov et al.

L / S0.9 0.9

0.8 0.8 0.7 0.7

1

0.6 0.6 0.5 0.5

2

0.4 0.4 3

0.3 0.3 0.2 0.2 0.1 0.1 0

0

M, cm 16

21

27

S, МPa

Fig. 4 The dependence of the L/S ratio on the mobility (M) and density of liquid glass (at a slag-ash ratio (S/A) = 1:1) at a density of liquid glass: 1—1100 kg/m3 ; 2—1200 kg/m3 ; 3—1280 kg/m3

12 10 1 8 2 6

3

4 2 0

0.5 0.55 0.6 0.85 0.6 0.65 0.65 0.7 0.7 0.75 0.75 0.8 0.85

L/S

Fig. 5 The dependence of the compressive strength (S) of slag-alkali compositions on the liquid– solid ratio at the age of 28 days at a density of liquid glass: 1—1100 kg/m3 ; 2—1200 kg/m3 ; 3—1280 kg/m3 ; at a ratio of S/A = 2:1

Fig. 6 The dependence of the compressive strength (S) of slag-alkali compositions on the liquid–solid ratio at the age of 28 days at a density of liquid glass of 1250 kg/m3 ; at a ratio of S/A = 2:1

S,МPa

Fast-Hardening Slag-Alkaline Heat-Resistant Aerated Concrete …

157

20 15 10 5 0

0.45 0.45

0.46 0.46

0.47 0.47

0.48 0.48

0.49 0.49

L/S

for all the mobility of mixtures and the density and strength of the hardened binders decreases [5, 16–19]. The density of liquid glass depends on the amount of silicate formations dissolved in it, which react between the alkalis of silicates and the main oxides that make up the slags, in particular with CaO. The insufficient amount of alkaline silicates explains the reduced density on liquid glass (1.1 g/cm3 ). Compositions with liquid glass have the lowest liquid–solid ratio (L/S) at a density of 1.25 g/cm3 and S/A = 2:1. The same compositions have the highest strength (Table 7). 2.2.2 Design of Compositions of Slag-Alkaline Aerated Concrete When designing the compositions of slag-alkaline aerated concrete [20–25], binders with a ratio of solid components S/A (2–2.5): 1 were used. An aqueous solution of sodium silicate with a density of 1.25, 1.28 g/cm3 and a silicate modulus from 1.45 to 3. To obtain aerated concrete, the mixture during the gas formation period must have the necessary plastic viscosity and gas-retaining ability to prevent the tendency of the formed bubbles to break out. The release of gas in the mixture must be accompanied by its thickening, otherwise it will lead to the settling of the unshagged mass. The gas release process must be completed before the mixture begins to set. Based on the research, perhydrol was used as a gas-forming agent for the production of cellular concrete (Table 8). The use of perhydrol makes it possible to simplify the technology of preparing the technological mixture due to the fact that it is evenly distributed over the volume of the mixture and, unlike aluminum powder, does not require calcination and degreasing, and also slows down the onset of setting of the aerated concrete mixture, which allows for more thorough mixing in an energy-saturated mixer. 2.2.3. Dependence of the Strength Properties of Aerated Concrete on the Amount of the Gas-Forming Agent As a result of the reaction of the interaction of liquid glass and hydrogen peroxide, gaseous oxygen is released and vitreous SiO2 falls out, which turns into a jelly-like

158

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Table 8 Dependence of strength parameters of aerated concrete on the quantity and type of gasforming agent Type and quantity of the gas-forming Dry density, kg/m3 agent, % of the sum of dry components

Compressive strength in dry condition, MPa

Aluminum powder, % 0.04

890

5.43

0.07

1150

6.91

Perhydrol, % 1.0

1210

8.77

2.0

900

5.13

3.0

850

5.26

state within about two hours, i.e. the reaction of the interaction of hydrolytically formed caustic alkali and weak acid—hydrogen peroxide. As a result of the neutralization of the acid by the base, the coagulation of silica is formed. The more concentrated the hydrogen and the lower the modulus of the liquid glass, the more intense the reaction proceeds. To determine the optimal silicate modulus of liquid glass and the content of the alkaline component (in terms of Na2 O), the silicate modulus was changed from 1.6 to 3 by introducing an aqueous NaOH solution with a density of 1.34 g/cm3 to obtain a 27 cm spread of the raw mixture on the Suttard device. The physical and mechanical properties were determined on samples of size 7.07 × 7.07 × 7.07 cm. Previously, the samples were dried at 105 °C. Table 9 and Figs. 7, 8 and 9 show the compositions and characteristics of slagalkaline aerated concrete. As follows from the Table 9, by reducing the silicate modulus increases the strength of aerated concrete The silicate modulus of liquid glass was reduced by the introduction of NaOH. The increase in alkalinity contributes not only to a more energetic reaction of hydrogen peroxide with alkaline oxide Na2 O, but also to a greater solubility of slag oxides. The dissolved oxides of slag are hydrated to form hydroxides, which subsequently react with alkaline silicates to form oxides with lower solubility. The introduction of Na2 O in the form of a solution not only reduces the silicate modulus, but also increases the plasticity of the slag-alkali mixture. As follows from the Table 9, by reducing the silicate modulus increases the strength of aerated concrete The silicate modulus of liquid glass was reduced by the introduction of NaOH. The increase in alkalinity contributes not only to a more energetic reaction of hydrogen peroxide with alkaline oxide Na2 O, but also to a greater solubility of slag oxides. The dissolved oxides of slag are hydrated to form hydroxides, which subsequently react with alkaline silicates to form oxides with lower solubility. The introduction of Na2 O in the form of a solution not only reduces the silicate modulus, but also increases the plasticity of the slag-alkali mixture.

5.32 0.46

– in NaOH solution

Features: compressive strength, MPa: – at the age of 1 day

− 7.2 · 10–6 0.16 600

water heat exchange

Coefficient of linear thermal expansion, grad−1

Coefficient of thermal conductivity at 20 °C, W/(m·K)

Maximum application temperature, °C

600

0.16

7.2 · 10–6

0.66

0.33

2.54

7.53

0.535

−

10.31

Caustic sodium from the slag mass (in terms of Na2 O) total, in %: – including in liquid glass

25

0.528

Liquid–solid ratio

0.048

0.90

0.048

Perhydrol from the mass of dry components, mass part

2.0

0.5

42

1.45

Silicate module of liquid glass

Thermal resistance: air heat exchange

0.5

Liquid glass, from the sum of dry components, mass part

1

2

540

2

– at the age of 28 day

1

Ash-entrainment, mass part

540

1 2

kg/m3

Compositions

Slag, mass part

Density,

Name

600

0.16

7.2 · 10–6

−

32

0.75

0.36

3.36

8.36

0.535

0.048

1.8

0.5

1

2

540

3

Table 9 Properties and compositions of slag—alkaline heat—resistant aerated concrete

600

0.12

7.4 · 10–6

−

22

0.53

0.26

1.05

6.05

0.528

0.048

2.48

0.5

1

2

510

4

600

0.09

7.8 · 10–6

−

20

0.49

0.29

1.56

7.58

0.552

0.061

2.5

0.57

1

2

420

5

600

0.19

7.0 · 10–6

−

18

0.36

0.34

3.23

3.03

0.461

0.42

3.0

0.322

1

2.5

690

6

600

0.16

7.1 · 10–6

−

48

0.95

0.72

5.42

5.02

0.505

0.042

3.0

0.536

1

2.5

580

7

600

0.25

6.8 · 10–6

17

140

4.3

2.3

1.54

6.52

0.472

0.042

1.8

0.323

1

2.5

845

8

Fast-Hardening Slag-Alkaline Heat-Resistant Aerated Concrete … 159

Fig. 7 Dependence of the strength (S) of aerated concrete on the silicate module (Ms) of liquid glass: 1—at the age of 1 day; 2—at the age of 28 days for foam concrete with a density of 540 kg/m 3

S. Emelianov et al. S,МPa

160 11 0.9 0.8 0.7 0.6 0.5

1 2

0.4 0.3 0.2 0.2 0.1 0.1

Fig. 8 The dependence of the strength (S) of aerated concrete on the content of Na2 O (for the ratio S/A = 1:1): 1—at the age of 1 day; 2—at the age of 28 days

S,МPa

00

1.451.45

1.8 1.8

2 2

2.48 2.48

МS

11 0.9 0.9 0.8 0.8 0.7 0.7 0.6 0.6

1

0.5 0.5

2

0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 00

6.05 6.05

7.5

8.36

10.3

% Na2O

Fig. 9 Dependence of the strength (S) of aerated concrete on the Na2 O content (for the ratio S/A = 2.5:1) 1—at the age of 1 day; 2—at the age of 28 days

S , MPa

Fast-Hardening Slag-Alkaline Heat-Resistant Aerated Concrete …

161

55 4.5 4.5 44 3.5 3.5 33 1

2.5 2.5 22

2

1.5 1.5 11 0.5 0.5 00

33

55

6.5 6.5

%Na2О

3 Results and Discussion The conducted studies allow us to conclude that in order to obtain a fast-hardening heat-resistant self-supporting aerated concrete, characterized by increased heat resistance with an application temperature of up to 600 °C, it is advisable to introduce a NaOH solution into the composition of slag-alkaline aerated concrete based on Cherepovets blast furnace granulated slag to reduce the silicate modulus of liquid glass, and to reduce the cost and density, dry selection fly ash is used. As a poreformer, the use of hydrogen peroxide is rational, since this makes it possible to simplify the production technology of aerated concrete and slow down the beginning of setting of the raw mixture to increase the manufacturability of the process of mixing and laying the aerated concrete mixture. When comparing slag-alkaline binders with cement binders, the following features can be noted. The contraction of slag-lime binders is 4–5 times less than that of Portland cement ones, as a result, they have lower porosity. This provides high water impermeability, frost resistance, low shrinkage rates. Heat release of slag-lime binders is low, despite the intense increase of strength in the early periods of hardening. Slag-lime binders have high corrosion resistance and biostability. Alkaline components act as antifreeze additives, so the binder hardens even at subzero temperatures [26–29].

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Alkaline binders are of high economic efficiency. Specific capital investment for the production of these binders is 2–3 times less than in the production of Portland cement. Their prime cost is 1.7–2.9 times lower than that of Portland cement, specific consumption of fuel equivalent is 3–5 times lower, electric power consumption is 2 times lower than that for Portland cement production. For cellular concrete, in terms of creating a strong matrix and high physical and mechanical characteristics autoclave production is mainly used. It is widely known how difficult and costly autoclave production is, which is profitable only with large volumes of products. When several autoclaves are in operation, the waste steam is bypassed to the next autoclave, thus saving money. Slag-lime non-autoclaved aerated concrete allows to get comparable characteristics of autoclaved cement cellular concrete, if not higher, on low-mechanized sections. At the same time, the high rate of setting of slag-lime concrete requires a higher culture and improvement of production technology [30–34].

4 Conclusions 1. A reasonable ratio of 2:1 between the flow rate of slag and fly ash was established in the slag-lime binder. It determines the maximum strength characteristics at the liquid–solid ratio equal to 0.45–0.49. Under the same conditions, the maximum compressive strength of 2.3 MPa was obtained at one day of age without heat treatment. Thermal resistance is 140 air heat cycles and 17 water heat cycles. 2. The practicability of using hydrogen peroxide, namely technical hydrogen peroxide, as a gasifier was established. 3. The influence of the silicate modulus of liquid glass on the physical and mechanical properties of aerated concrete was determined. The dependence of the strength of aerated concrete on the change in the liquid glass modulus from 2.48 to 1.25 was obtained; as the silicate modulus decreases, the strength increases. 4. The effect of caustic soda content (converted to Na2 O) in the aerated concrete mixture on the properties of aerated concrete was studied. It was found that increasing Na2 O from 6 to 10% increases the strength properties by half. 5. It was established that heating the developed compositions of aerated concrete to t = 600 °C does not reduce the strength of aerated concrete, and for some compositions, there is an increase in strength by 5–7%. Burning shrinkage is not higher than 1.3%. 6. Self-hardening of aerated concrete is carried out within 10 min. 7. The main physical and mechanical properties of non-autoclaved slag-alkaline aerated concrete correspond to the properties of autoclaved cement aerated concrete.

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The Temperature Control Methods for the Heat Supply System of Buildings and Structures Dmitry Tyutyunov , Aleksey Pihtin, and Aleksey Borodin

Abstract Testing and controlling algorithms for the temperature conditions in the heat supply systems of buildings and structures provide necessary information and support the control of the flows of the working medium (liquid, gas) in the heat load. This approach allows to monitor the distribution of heat flows in real time. The purpose of controlling this process is to create a mathematical model to determine the time interval for restarting the heat flow control algorithm in the heat supply system with a dependent connection to the heat source, on the basis of which a discretization interval of the heat supply system state probing time should be obtained. This approach is accompanied by appropriate microprocessor support according to the “smart home” scheme. The task was set to use the differential heat balance equation to achieve the aforementioned goal. It is expected to use the dependencies of the functioning of the heating system in stationary and quasi-stationary modes, taking into account transient processes in the event of start, shutdown or emergency stoppage. The methods of mathematical analysis are used to obtain the desired relation. In addition, the solution to this problem is accompanied by a graphical illustration in the Mathcad software environment. An important part of this article is a relatively simple schematic and technical implementation of the obtained solution. As a part of the study of the heat supply process for buildings and structures, a study of the differential equation of the heat balance of the dependent heat supply system of buildings and structures was performed. A working formula for the discrete interval for controlling the parameters of the specified heating system was obtained. The discretization interval of the heat supply time was obtained, which is supported by the real time schematic solution. As a result of the study, the main elements of diagnostics of the heat supply system were obtained: the diagnostic interval, the discretization interval, the control scheme, which allows monitoring in real time according to the «smart building» principle. Keywords Dependent heat supply system · Heat balance equation · Heat carrier temperature · The diagnostic interval · The discretization interval · Smart home D. Tyutyunov · A. Pihtin (B) · A. Borodin Southwest State University, 94. 50 Let Oktyabrya ul., Kursk 305040, Russia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_17

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1 Introduction Improving the methods of management and control over the distribution of heat flows is the most relevant task in the plans for the implementation of the governmentsanctioned program of the Russian Federation in the field of energy preservation and energy efficiency for the period up to 2030. In works [1–4], automation record data algorithms are used, including data on physical characteristics, parameters of the state of the heat supply system and operating conditions of enclosing structures. However, the data is stored in the controller’s memory, but not analyzed automatically; instead, the assessment of the operation of the systems carried out only in case of system failures or in emergency. The site operation engineer, who uses their own experience to interpret the data obtained, carries out the analysis. The authors obtain and analyze data on the operation of adsorption coolers using the X-variable algorithm to automate the determination of the state of the system. In the study [5, 6], as the most popular, the method of integrating a building automation system is used, which includes remote control technology that allows real-time monitoring of energy consumption by end-users of energy, as well as implementation of optimization functions. The main goal of works [7–10] is to present an integrated system of energy efficient building automation. The proposed system is based on some software tools for modeling and optimizing energy consumption in the building sector, increasing the interactivity of building automation systems. The system can include energy efficient automation functions for heating, cooling and lighting. The proposed methods and algorithms are very promising, but they have a number of significant disadvantages associated with the lack of automatic scanning and operational analysis of the distribution of heat energy flows in the heat supply system according to the dependent scheme. At the same time, the above named algorithms have a high degree delay and sampling time step of monitoring the state of microclimate systems [11–14]. This study uses the method of data analysis based on the differential equation of heat balance with automated collecting and analysis of the data, with further presentation of all the necessary information to users in real time with a low sampling time of the system state monitoring of all relevant components of a heat supply system [15, 16]. One of the control options for a heat supply system with dependent connection to heat networks: Figure 1 shows a diagram of the equipment and devices required for the functioning of a “smart home”: a) HCMCT – heat consumption metering and control unit, containing a heat meter with a set of primary measuring instruments, a controller TC; b) A set of elements of the heating system: a control valve V1 with an actuation mechanism M1, a circulation pump N1 with a frequency converter M2; outdoor

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Fig. 1 Schematic diagram of the control of a dependent heat supply system

air temperature sensors t n (TE1), indoor air temperature sensor t k (TE2); temperature sensor of the supply heat carrier t 1 (TE3) and in the return pipeline t 2 (TE4); R is the building heat load. Let us consider a mathematical model of heat and mass transfer for the case shown in Fig. 1. Let us assume that in the area under consideration in a cylindrical pipe there is a continuous medium in the form of a heated liquid (water), in which the main transfer characteristics are continuous functions of time and coordinates [8]. To solve non-stationary problems of forced convective heat transfer, it is common to use the differential equation of heat transfer in a medium moving at a constant speed: λt Qv − Q ∂t ∂t ∂t ∂t + wx + wy + wz = + ∂τ ∂x ∂y ∂z cρ cρ

(1)

where t is the heat carrier (hot water) temperature, °C; τ is the time, s; x, y, z are the coordinates in a rectangular Cartesian coordinate system, m; wx , wy , wz are the heat 2 2 ∂2 carrier speed vector projections, m/s/; t = ∂∂x 2 + ∂∂y 2 + ∂z 2 is the Laplace operator in a rectangular Cartesian coordinate system; λ is the heat conduction coefficient, W/m °C; c is the heat capacity of the heat carrier (hot water), J/kg·°C; ρ is the density of the heat carrier (hot water), kg/m3 ; Qv and Q are the intensities of internal sources and heat losses of the cooled heat carrier, respectively, W/m3 .

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Relation (1) is most applicable for steel thin-wall electrically welded pipes according to GOST 10,704–91 with the ratio of the inner diameter to the outer diameter dd21 < 0, 98. In order to determine Qv and Q it should be assumed that Qv ≈ 0, and the Q value is determined by the formula: Q = k p · π · d2 · l(t−tk )

(2)

where t is the heat carrier (hot water) temperature, °C; t k is the indoor air temperature, °C; d 2 is the effective diameter of the pipeline, m; l is the heat load pipeline circuit length, m; k p is the heat transfer coefficient of the pipeline circuit to the heat load, W/m °C. The k p value is determined by the formula: kp =

1 1 α1

+

δ λp

+

(3)

1 α2

where α 1 is the coefficient of heat transfer from the heat carrier to the pipeline, W/m2 °C; α 2 is the coefficient of heat transfer from the pipeline to the heat load, W/m2 °C; δ is the pipeline wall thickness, m; λp is the heat conduction coefficient of the pipeline wall, W/m °C. The heat transfer coefficient is determined from the relation: αi =

N u l,d · λi di

(4)

where i = 1,2; λi is the heat conduction coefficient of hot water and air in a heated room, W/m °C; N u l,d is the Nusselt number for turbulently flowing hot water in a circular pipe. The N u l,d value is determined by the formula:  0,8 N u l,d = 0, 021Rel,d · Prl0,43 ·

Prl Prw

0,25 · εi

(5)

where Rel,d is the Reynolds criterion for hot water in a circular pipe (Rel,d ~ 105 ); Pr l , Pr w are the Prindtl numbers for hot water and the inner surface of the pipeline wall, respectively; εi is the coefficient that indicates the change in the average heat transfer coefficient for the pipe. If dl1 ≥ 50, then εi = 1 [15, 16].

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2 Experimental Let us consider two modes of the heat supply to the facility: stationary and nonstationary [10]. In the stationary mode, the heat supply of the circuit of the heat load of the movement of the medium occurs only along the Ox axis (Fig. 2), flow rate and temperature of the medium passing through the valve V1 are constant, the circulation pump N1 does not function. ∂t = 0, w y = wx = 0. Assuming that Qv ≈ 0, we have: In this case, in Eq. (1) ∂τ wx

λ ∂ 2t ∂t Q = · 2− ∂x c · ρ ∂x c·ρ

(6)

Taking into account (2) and (3), we get: k p · π · d2 · l · t k p · π · d2 · l · tk ∂ 2t c · ρ ∂t − wx · − =− 2 ∂x λ ∂x λ λ

(7)

The general solution to the non-homogeneous differential Eq. (4) is the expression: t O H (0) = c1 exp(a1 x) + c2 exp(a2 x) + tk

(8)

where c1 , c2 , a1 , a2 – const. Taking into account the boundary conditions, it is possible to determine the constants c1 and c2 : ton (0) = c1 + c2 + tk = t1 → ton (l) = c1 exp(a1l) + c2 exp(a2 l) + tk

Fig. 2 Heat transfer in a medium moving at a constant speed

(9)

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The stationary mode provides for the constancy of the temperature difference at point A, Fig. 1: t A − t2 = const

(10)

This is true if the temperatures tA and t2 are constant. In the non-stationary mode, the parameters of the heat load (hot water temperature, density, etc. in an arbitrary cross-section x) change over time. And in this case, the operation of the circulation pump N1 is blocked. Then in the differential Eq. (1) 2 2 ∂t ∂2t = 0, wx = w y = wz = 0, ∂∂x t2 + ∂∂yt2 + ∂z the following relations are true: ∂τ 2 = ∂t ∂t ∂t 0wx ∂ x + w y ∂ y + wz ∂z = 0, Q v ≈ 0. After eliminating partial derivatives, we have: Qv ∂t =− ∂τ c·ρ

(11)

∂t kρ · π · d2 · l · (t − tk ) =− ∂τ c·ρ

(12)

c·ρ =T kρ · π · d2 · l

(13)

∂t t − tk =− ∂τ T

(14)

Taking into account (2), we get:

After the substitution:

As a result, we have:

Expression (14) is especially relevant for transient processes caused by a sudden change in temperature t n or t 1 , t 2 in case of a possible accident or starting (shutdown) of the heating system. Let us transform (14) in a differential equation corresponding to the first order lag: t+T

∂t = k · tk ∂τ

(15)

where k ≈ 1 is the amplification coefficient, T is the time constant. The transfer function w1 (P) can be expressed as follows: w1 (P) =

k 1 ≈ 1 + PT 1 + PT

(16)

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where P is the experimentally determined parameter. The corresponding transition function h(τ ) can be expressed as follows:   τ  h(τ ) = k 1 − exp − T

(17)

The pure delay transfer function w2 (P), taking into account the pure delay element, can be expressed as follows: w2 (P) = e− pτd

(18)

where τ d is the pure delay time, s. From (15)–(18) it follows that the control of the heat supply process can be carried out taking into account the sequential connection of the pure delay elements and the first order lag element. In this case, the resulting transfer function of the heating system wco (P) can be expressed as follows: wco (P) = w1 (P) · w2 (P) = e− pτd ·

1 1 + PT

(19)

Let us solve the differential Eq. (13), taking into account that t > t k [15]: τ dt d(t − tk ) =∫ t − t t1 τd T k   τ − τd t A = tk + (t1 − tk )exp − t tA

∫

(20) (21)

where t 1 , t A are the temperatures of hot water at the inlet to the heating system and at point A, respectively, °C; τ z , T are the time of the complete delay in the transient process and the time constant, respectively, s; R is the heat load.

3 Results Taking into account (15)–(21), the characteristics of the functions w1 (P) and w2 (P) are graphically illustrated in Figs. 3 and 4, respectively. It should be noted that, according to (12), the parameter T sets the time for the medium to reach the temperature t, °C in a circular pipe in a section with an outer diameter d 2 at a distance l from the origin of coordinates, Fig. 2 [16]. It should be noted that both in stationary and non-stationary modes, the circulation pump is turned off if the temperatures t n , t 1 , t 2 , t k do not change. If there is a change, then, based on the theory of “smart home” maintenance, it is possible to regulate and balance the state of the heat supply system by using the circulation pump N1 or the control valve V1. In our case, we are solving the problem of finding the diagnostic

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Fig. 3 Temperature characteristic of the input signal t k of the iterative link, K=1

Fig. 4 Temperature characteristic of the input signal t 1 with a net delay, K =1

interval and the discretization interval, which helps to solve the previous problem in real time. If we take into account that the temperature of hot water t A at point A (Fig. 1) should always be higher than the temperature t 2 in the return pipeline by some value t, then the following inequality is true [16]: t A ≥ t2 + t

(22)

Taking into account (20), we have:   τ − τd ≥ t2 + t tk + (t1 − tk )exp − T

(23)

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From (23) it follows that: τd ≤ τ ≤ τd + T ln

t 1 − tk t2 − tk + t

(24)

Inequality (23) sets the so-called “time interval for restarting the heat flow control algorithm” with a dependent connection scheme, which allows to scan the heat supply state of a facility with a certain observation discretization period. Such a period can be called a “discretization interval” and denoted as τ g . The τ g value can be determined based on (23), according to the formula: τg = γ T ln

t1 − tk t2 − tk + t

(25)

where γ ∈ (0; 1]. Let us introduce the most common limitation for the parameters of the heat supply system (Fig. 1): t 1 = 95…150 °C, t 2 = 70 °C, t k = 20 °C, τ d = 0…600 c, T = 50…200 °C, Δt = 10 °C. Based on these data, we can graphically illustrate the function τ g = τ (t 1 , T ), γ = 1, Fig. 5, using the Mathcad software environment.

Fig. 5 Graph of the function τ g = τ (t 1 , T )

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Fig. 6 Diagram for determining the “discretization interval” τ g in the control mode of the heat supply system with dependent connection to the heat source

Below is a schematic solution for determining τg for linking to control in the “smart home” operating mode, Fig. 6.

4 Discussion It should be noted that the choice of the control parameter at γ ∈ (0; 1] depends on the range of variation of the values of T, τ d and t 1 . Taking into account this note and relation (25), it is possible to obtain a marking on the abscissa axis (time axis τ, s) with marking according to the iterative formula: τn = τd + (n − 1)τg

(26)

where n = 1, 2, etc. In this case, the n-th interval can be expressed as follows: τd + (n − 1)τg ≤ τ ≤ τd + (n − 1)τg

(27)

In the process of finding a solution, a study of the functioning of the heat supply system of a building (structure) operating according to the “smart house” scheme was performed. During the research, the desired solution was obtained using the methods of mathematical analysis and the Mathcad software environment. The task of finding a solution was completed, the results were obtained according to the purpose of the study. A working formula for real-time scanning of the heat supply process was obtained.

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5 Conclusion As a result of solving the problem in accordance with the set goal, a mathematical model was created, which made it possible to: 1. Obtain the time interval for restarting the heat flow control algorithm with a dependent connection to the heat source; 2. Obtain the discretization interval for the time of probing the state of the heat supply system; 3. Carry out probing and monitoring of the state of the heat supply system in real time according to the “smart home” principle.

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13. Tian Y, Guo S, Jin G, Pang Y, Wang X, Wu W, Zhao J (2019) A two-step approach to solve the issue of dew condensation for displacement ventilation and chilled ceiling system. Energy Procedia 158:6527–6531. https://doi.org/10.1016/J.EGYPRO.2019.01.106 14. Shi Z, Chen Q (2021) Experimental and computational investigation of wall-mounted displacement induction ventilation system. Energy Build 241. https://doi.org/10.1016/J.ENBUILD. 2021.110937 15. Ezhov V, Semicheva N, Tyutyunov D, Burtsev A, Perepelitsa N (2021) Version of a mathematical model of purge ventilation system with a complex recuperative heat exchanger. J Appl Eng Sci 19(1):246–251. https://doi.org/10.5937/JAES0-30068 16. Yezhov VS, Semicheva NE, Tyutyunov DN, Burtsev AP, Perepelitsa NS, Burtsev AP (2021) Mathematical model for automated heat flow control of an energy efficient ventilation system. Proc Southwest State Univ 25(1):38–52. https://doi.org/10.21869/2223-1560-2021-25-1-38-52

The Mathematical Model of Automated Control of Heat Flows in the Supply and Exhaust Ventilation System Dmitry Tyutyunov , Alexey Burtsev , Nikita Perepelitsa , and Alexander Burtsev

Abstract The aim is to study a mathematical model of optimal control of heat flows of a supply and exhaust ventilation system with a built-in integrated heat exchangerrecuperator. To achieve these goals, the methods of mathematical modeling and the creation of a computational model were used in the work. The automatic control of air conditioning system is based on the principle of feedback. An experimental supply and exhaust system with a plate heat exchanger-recuperator, operates in a quasistationary heat transfer mode. Exhaust air removed from the room is used as a heating medium. At the same time, the system is controlled with an independent connection scheme to the heat supply system. The air heated in the room is considered as an incompressible gas, the heat exchange between the heating and heated heat carriers is a stationary process, the turbulence of the heating and heated coolant flows is isotropic. As a result of the study, a mathematical model of heat flow control in the supply and exhaust ventilation system with a built-in integrated heat exchangerrecuperator was obtained. The optimal values of the consumed thermal energy and the parameters of the ventilation system operation are obtained. Keywords Supply and exhaust system · Utilization · Heat transfer coefficient · Electric power · Efficiency · Autonomy · Ventilation gases · Thermoelectricity

1 Introduction In ventilation and air conditioning systems, one of the main components is an automatic control system (ACS), which performs various functions, and also provides highly efficient operation in the range from shutdown functions to centralized regulation and control of climatic parameters (temperature, humidity, control of concentrations of hazards, air velocity). In studies [1–4], methods of model-predictive control (MPU) are used, which allows predicting the heat and humidity behavior of the energy management system D. Tyutyunov · A. Burtsev (B) · N. Perepelitsa · A. Burtsev Southwest State University, 94, 50 Let Oktyabrya ul., Kursk 305040, Russia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_18

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of buildings based on changes in climatic conditions. When comparing the thermal models of a passive house with concentrated parameters and an integrated photovoltaic system, the complexity and necessity of describing the main thermal characteristics of the building is assessed, as well as an extended Kalman filter (EKF) is used online to analyze the reduction of implementation costs, along with an assessment of unmeasured heat from residents. At the same time, it is worth noting that the proposed MPU algorithm requires high computing power and processing speed. In [5, 6], a numerical model of a hybrid system for converting solar energy into electricity and heat using solar cells was developed. To cool the elements, a fan air flow is used, providing hybrid ventilation. The model has automatic roller blinds that help regulate the load on heating and cooling, as well as control the level of daylight in the room. At the same time, the main disadvantage of the system is not the possibility of efficient and deep use of excess heat. Studies [7–9] have shown that the exhaust duct can be connected to the supply unit in order to increase the cooling capacity and reduce the vertical temperature gradient through the bypass line. However, when recirculating the air, along with the flow of warm air removed from the room, air pollution enters the supply duct, reducing the air quality in the serviced area. Therefore, it is important to develop a comprehensive system to ensure optimal thermal comfort and indoor air quality with associated deep utilization of excess heat in the exhaust air with associated generation of thermoelectricity, which can be used to ensure the autonomy of the supply and exhaust system [10, 11]. The developed mathematical model [12], which is based on the principle of feedback - regulation of processes by obtaining information from external sensors based on mathematical modeling of physical processes occurring in a serviced building or structure, provides prediction of thermal and ventilation parameters of the system in real time with low response time and computing power costs, creating a comfortable and healthy indoor environment.

2 Materials and Methods The experimental supply and exhaust system under study with a plate heat exchangerrecuperator, a ventilation system operating in a quasi-stationary heat transfer mode, is shown in Fig. 2. Exhaust air removed from the room is used as a heating medium. At the same time, the system is controlled with an independent connection scheme to the heat supply system. The air heated in the room is considered as an incompressible gas, the heat exchange between the heating and heated heat carriers is a stationary process, the turbulence of the heating and heated coolant flows is isotropic. The schematic diagram of the supply and exhaust mechanical ventilation system with ACS is shown in Fig. 1.

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Fig. 1 Control scheme of the supply and exhaust ventilation system with a recuperator: D1 - Supply air damper; D2 – Exhaust air damper; F1 – Supply filter; F2 –Exhaust filter; M1 – Supply fan; M2 – Exhaust fan; Q1 – water heater; FS1 – Channel humidity sensor; FS2 – room humidity sensor; SM1, SM2 – Electric drive of the regulating damper; SM3 – Electric bypass drive; SM4 – Electric drive of the 3–way valve of the water heater; TE1 - Outdoor air sensor; TE2 – Air temperature sensor after the heat exchanger; TE3 - Temperature sensor against freezing of the water heater; TE4 - Temperature sensor of the reverse coolant; TE5 - Channel temperature sensor; TE6 - Room temperature sensor; DD1 - Dry running protection relay; M3 - water heater circulation pump; 1 plate heat exchanger; 2 - room with control panel; 3 - street; 4 - controller

Fig. 2 Design scheme of the installation: RK1 - plate heat exchanger; F1 - Supply filter; F2 -exhaust filter; M1 - Supply fan; M2 - Exhaust fan; P1 - control panel; Q1 - water heater; T1 and T2 - supply and exhaust air temperatures. Ta – air temperature at point A at the bypass inlet; Tc, - respectively, the air temperature in the heated room and at the outlet from it; K1 - the proportion of full opening of the bypass valve V1 (0 ≤ K1 ≤ 1); K N - the proportion of full capacity of the supply fan M1; M1 (0 ≤ K N ≤ 1); K is the heat transfer coefficient of the heat exchanger, W/m ·°C

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Let’s present the diagram in Fig. 1 in a simplified form - Fig. 2. in order to obtain the optimal mode of heat use. In this case, the ventilation system of a room or groups of rooms will be considered a thermal load R, consuming heat Q 1 .

3 Results The transferred amount of heat is determined, W: (1) This heat can be used partially:Q 1 for outdoor air heating, Q 2 to receive thermopods: Q = Q 1 + Q 2

(2)

Terms Q 1 , Q 2 in formula (2), it can be represented as: Q 1 = a1 · Q 1 + a2 · Q 2

(3)

a1 = 0, 85 . . . 0, 88; a2 = 0, 12 . . . 0, 15 accordingly, the proportion of components Q 1 , Q 2 in the heat balance. From Eq. (3) follows: a1 + a2 = 1

(4)

In the presence of a thermal load R, the heat balance equation will have the form: Q in = Q ent

(5)

Q in , Q ent – accordingly, the total heat flows at the inlet and outlet of the ventilation system. In this case, the formula (6) follows: Q ent = Q A + Q M + Q F + Q V

(6)

Q 1 , Q 2 , Q M , Q k , Q v , Q A , Q F - heat flows in a ventilated room. In expression (6), the ratio is valid: Q F = QV ≈ 0

(7)

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Fig. 3 Thermal characteristic of valve V1

When installing the valve V1 and the supply fan M1 (Figs. 1, 2 and 3) between the supply and exhaust ducts of the ventilation system, in accordance with the requirements, the air consumption G1 , GM and the mixing coefficient at point A of hot and cold and air masses U should be taken into account: U=

T1 − T A T A − T2

(8)

It is important to note that the air flow in the quasi-stationary mode has a directly proportional dependence on the heat flows: Q 1 = G 1 · c1 · (T1 − T2 )

(9)

Q M = G M · c M · (T1 − T2 )

(10)

where the temperatures T1 and T2 are taken in the range of 15…65° C. At the same time, it can be assumed that the specific heat capacities at constant pressure c1 and cN are equal to 1,005 kJ / kg ·°C; G1 , G2 , GA – respectively, the air flow in the supply and exhaust ducts, kg/s; Gm air flow through the supply fan M1 and point A. We will consider the coordinated operation of the valve V1 and the supply fan M1, respectively, on their linear sections M N , PL in Figs. 3 and 4. The specified agreement is made taking into account the mixing coefficient U: Q M = μ · U · Q1

(11)

gde μ ≥ 1, μ = const. The heated coolant passes through the adjustable flap V1 with a fraction of the opening K1, then the flow using the supply fan M1 with a thermal load R, functioning with a fraction of the full capacity K N , then the values of the heat flows Q1A , QMA at point A can be determined by the formulas: Q 1A = k1 · Q 1

(12)

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Fig. 4 Thermal characteristics of the mixing pump M1

Q M A = μ · U · Q 1 · k1 · k M

(13)

The heat flow of a ventilated room with heat R has a temperature T int = 293 K (t int = 20 °C). In the quasi-stationary mode, the Qk flow is transmitted through the wall of the heat exchanger-recuperator, while the equation will have the form: Q K = k · (tint − text ) · F = k · (Tint − Text ) · F

(14)

Text = text + 273 - the temperature of the supply air in the room; F – the area of the inner surface of the recuperator, m2 . The ventilation process in the nominal mode is stationary – over time, the values of the main parameters do not change. Based on these features, the heat balance equation must take into account Tint − Text = tint − text : Q ent = Q k + Q 2

(15)

Q ent = k · (tint − text ) · F + Q 2

(16)

Q 2 = const As a result, we get the balance at point A: k1 · Q 1 = μ · Q 1 · U · k1 · k M = k · (tint − text ) · F + Q 2

(17)

k1 · Q 1 · (1 + μ · U · k M ) = k · (tint − text ) · F + Q 2

(18)

Let ‘s introduce the notation: 1 · (k1 · (tint − text ) · F + Q 2 ) = C = const Q1

(19)

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From (19) follows: kM =

c 1 − μ · U · K1 μ·U

(20)

c 1 ;b= μ·U μ·U

(21)

Denoting: a= a, b = const, we get: KM =

a −b k1

(22)

a > 0, b > 0 with 0 < K 1 ≤ ab ≤ 1, t.k. 0 < K N ≤ 1. Graphically, the dependence (20) is presented in Fig. 5 as a family of curves I, II, III, and text I < text I I < text I I I : The coefficients K M and K 1 from expression (22) are inversely proportional. With an increase in the temperature of the supply air text, the corresponding curve of the family approaches the abscissa axis and intersects it at a point ab . In Fig. 6, curves I, II, III correspond to temperatures text I < text I I < text I I I . Data T 1 , T 2 , T M , U, Q1 , Q2 , F in nominal mode, they are stored in a ROM (permanent storage device) built into the controller. Let’s analyze the operation of the circuit in Fig. 2, based on the heat balance Eq. (18). We will assume that violations of the temperature pressure tkext = tint −text if there are no internal sources of heat (cold) in a ventilated room with a thermal load, Fig. 5 Dependence of K M on K 1

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Fig. 6 Condition for determining the local extremum

R occurs due to a change in the temperature of the outside air Text by a certain amount ΔT ext . Such dynamics, respectively, leads to a change in the temperature of the T int . We will conduct a study of the thermal balance when the temperature regime changes in the diagram in Fig. 2. Let’s assume that the temperature of the supply air Tint has decreased by the value of ΔT ext degrees, which, with the positions K 1 and K m unchanged, will lead to a decrease in the temperature of the thermal load R by the value of ΔT int degrees. To restore the thermal balance, it is sufficient to increase the proportion of K 1 of the full opening of the valve V1 by the value of ΔK 1 , respectively, to reduce the proportion of K N of the full capacity of the mixing pump M1 by the value of ΔK m : Q 1 · (k1 − k1 ) · (1 + μ · U · (k M − k M )) = k · ((tint − text ) − (text − text )) · F + Q 2

(23)

In the extreme case when the pump is completely stopped N1 (ΔKm = 0): k1 =

k · F · (text − text ) Q 1 · (1 + μ · U · k1 )

(24)

If we consider that ΔK1 ≥ 0, then obviously the condition must be met: text ≥ tint

(25)

Let’s assume that the temperature of the supply air T ext has increased by ΔT ext degrees, which, with the positions K 1 and K M unchanged, will lead to an increase in the temperature in the room R by the value of ΔT int degrees. In this case, to restore the thermal balance, it is sufficient to increase the proportion of K M of the full capacity of the supply fan M1 by the value of ΔK m and, accordingly, reduce the proportion of K 1 of the full capacity of the valve V1 by the value of ΔK 1 : Q 1 · (k1 − k1 ) · (1 + μ · U · (k M + k M )) = k · (tint + tint ) − (text + text ) · F + Q 2

(26)

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In the extreme case when the valve is completely closed V1 (ΔK1 = 0): k M =

tint − tint Q 1 · k1 · μ · U

(27)

where from the requirement ΔKm = 0 it follows the fulfillment of the condition: tint ≥ text

(28)

Combined ratio (20–25) we obtain a combined formula for controlling heat flows:   k · F · ((tint ∓ tint ) − (text ∓ text )) + Q 2 − k1 k1 = ± Q1 · (1 + μ · U · (k N ∓ k N ))

(29)

the upper signs “ + ” or “–” correspond to the fall of the T ext by the value of ΔT ext , the lower signs “–” correspond to the growth of the T ext by the value of ΔT ext . In both cases, ΔT ext ≥ 0, ΔT int ≥ 0. The system allows you to implement the dependence (24) in real time, taking into account the moment of delay when the nominal temperature T int is reached. Consider the option of ventilation with minimal energy consumption while maintaining the nominal temperature of t int . Taking into account the expressions and the given temperature difference Δt int = t int - t ext , we investigate the function for a local extremum: F(k1 , k N ) = F(k1 ) = k1 + k N = k1 +

a − f → min k1

(30)

Differentiate expressions (31): d F(k1 ) a =1− 2 dk1 k1

(31)

We define critical points of the first kind:  √ d F(k1 ) a = 1 − 2 = 0 ⇒ k11 = − a, k12 = a dk1 k1

(32)

√ If we consider that K1 > 0, then you should√leave k12 = a. From Fig. 6 it follows that the point k12 = a is the point of the local minimum. Based on the illustration of the graph of the second derivative of the function F(K 1 ) in Fig. 7, we can conclude that there are no inflection points. √  √ 2 F(k1 ) So, Fmin = F a = 2 a − b. On the other hand: d dk = Fk1 ,k2 (k1 ) = 2 1   1 − ka2 = 2a > 0, t.e. graph of the function F(K 1 ) on the interval (0;1]. k3 1

k1

1

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Fig. 7 Definition of dependency Fk1 ,k2 (k1 ) on the half -interview (0;1]

4 Conclusion As a result of the work carried out, a mathematical model of heat flow control in the supply and exhaust ventilation system with a built-in integrated heat exchangerrecuperator is proposed and investigated. The optimal values of the consumed thermal energy and the parameters of the ventilation system operation are obtained. The developed mathematical model, which is based on the principle of feedback - process regulation by obtaining information from external sensors based on mathematical modeling of physical processes occurring in a serviced building or structure, provides real-time forecasting of thermal and ventilation parameters of the system with low response time and computing power costs, creating a comfortable and healthy indoor environment.

References 1. Sha H, Qi D (2020) Investigation of mechanical ventilation for cooling in high-rise buildings. Energy Build 228. https://doi.org/10.1016/J.ENBUILD.2020.110440 2. Pekdogan T, Tokuç A, Ezan MA, Ba¸saran T (2021) Experimental investigation of a decentralized heat recovery ventilation system. J Build Eng 35. https://doi.org/10.1016/J.JOBE.2020. 102009 3. Imal M (2016) A new system design for energy management in HVAC control systems for textile plants. Acta Phys Pol A 130(1):245–248. https://doi.org/10.12693/APHYSPOLA.130.245 4. Ioannidis Z, Buonomano A, Athienitis AK, Stathopoulos T (2017) Modeling of double skin façades integrating photovoltaic panels and automated roller shades: analysis of the thermal and electrical performance. Energy Build 154:618–632. https://doi.org/10.1016/J.ENBUILD. 2017.08.046 5. Zhou W et al (2020) Optimization of dust removal performance of ventilation system in tunnel constructed using shield tunneling machine. Build Environ 173. https://doi.org/10.1016/J.BUI LDENV.2020.106745

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6. Shi Z, Lai D, Chen Q (2020) Performance evaluation and design guide for a coupled displacement-ventilation and passive-chilled-beam system. Energy Build 208. https://doi.org/ 10.1016/J.ENBUILD.2019.109654 7. Serale G, Fiorentini M, Capozzoli A, Bernardini D, Bemporad A (2018) Model Predictive Control (MPC) for enhancing building and HVAC system energy efficiency: problem formulation, applications and opportunities. Energies 11(3). https://doi.org/10.3390/EN1103 0631 8. Ruiz GR, Segarra EL, Bandera CF (2019) Model predictive control optimization via genetic algorithm using a detailed building energy model. Energies 12(1). https://doi.org/10.3390/EN1 2010034 9. Gutiérrez González V, Ramos Ruiz G, Fernández Bandera C (2021) Impact of actual weather datasets for calibrating white-box building energy models base on monitored data. Energies 14(4). https://doi.org/10.3390/EN14041187 10. Ezhov V, Semicheva N, Tyutyunov D, Burtsev A, Perepelitsa N (2021) Version of a mathematical model of purge ventilation system with a complex recuperative heat exchanger. J Appl Eng Sci 19(1):246–251. https://doi.org/10.5937/JAES0-30068 11. Yezhov V, Semicheva N, Burtsev A, Perepelitsa N (2021) Experimental calculation of the main characteristics of thermoelectric EMF source for the cathodic protection station of heat supply system pipelines. In: Murgul V, Pukhkal V (eds) International Scientific Conference Energy Management of Municipal Facilities and Sustainable Energy Technologies EMMFT 2019. EMMFT 2019. Advances in Intelligent Systems and Computing (AISC), vol 1259, pp 225–237. Springer, Cham. https://doi.org/10.1007/978-3-030-57453-6_19 12. Yezhov VS, Semicheva NE, Tyutyunov DN, Burtsev AP, Perepelitsa NS, Burtsev AP (2021) Mathematical model for automated heat flow control of an energy efficient ventilation system. Proc Southwest State Univ 25(1):38–52. https://doi.org/10.21869/2223-1560-2021-25-1-38-52

Prognostic Approach to Sustainable Development in Urban Planning Analysis of Green Areas Yana Zolotukhina , Ekaterina Prokshits , Semyon Podvalny , and Yulia Pashchenko

Abstract With an accurate and correct statement of the tasks of the project, its development, it is necessary first of all to identify the problem, to analyze the object of design or renovation, the next stage is to solve the problem with the help of forecasting. The landscape and ecological organization of the citywide center is an important element of the natural and ecological framework of urban systems and an important aspect in achieving the goals of sustainable development of the region. The current state of the natural complex of the city of Voronezh is studied according to the ecological and planning parameters of green areas, including parks and squares. The correlation between the ecological state and the functional and planning organization of landscaping sites has been revealed. Organizational and planning measures for the preservation and development of the natural complex are proposed. Keywords Sustainable development · Ecological framework · Standard of living · Socio-economic development of regions · Landscaping · Comfortable urban environment · The quality of the urban environment · Public space

1 Introduction Improving and modernizing the infrastructure of the region for the purpose of its effective sustainable development is one of the most important tasks of the modern policy of the region, in order to achieve these goals. Forecasting in the urban planning context is based on types of planning that are not projects, programs, but fall under the definition of the word “forecast”, this is a type of foresight of the development of events based on scientific methods.

Y. Zolotukhina (B) · E. Prokshits · S. Podvalny · Y. Pashchenko Voronezh State Technical University, 20 letiya Oktyabrya street, 84, 394006 Voronezh, Russia e-mail: [email protected] S. Podvalny The Russian Presidental Academy of National Economy and Public Administration, Moscow, Russia © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_19

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Only an integrated approach to the analysis of the territory, covering the ecological, urban planning, social, landscape-recreational and cultural aspects of urban life, will be able to give an objective assessment of the quality of life of the population. In the research Klimanova O. A. and Illarionova O. I. with the help of a comprehensive assessment of 13 indicators, the quality of housing and communal services in 15 major cities of Russia was assessed. The research showed that Ufa, Nizhny Novgorod, Kazan, Yekaterinburg, Perm and Voronezh have satisfactory ratings both in terms of recreational indicators and integrity indicators. However, this method, being relatively fast and easy to use, makes it possible to assess not only the general availability of GI, but also its quality and distribution, which is important for urban spatial planning [1]. In the work “Ecological planning of urbanized areas in the south of the Far East (Birobidzhan city as an example)” the authors proposed the principles and features of the ecological organization of the urban area. It was revealed that the basis of environmental planning is the ecological and functional zoning of urban areas. The developed algorithm of ecological and functional zoning and the possibility of using the basic conditions of the ecological framework in the planning of urban areas contribute to optimizing the quality of the urban environment [2]. Many authors in their works highlight various aspects of human perception of the environment, the specific features of the subjective assessment of its condition and attitude to the quality of the environment. The authors B. I. Kochurov, Yu. A. Khaziakhmetova, I. V. Ivashkina, E. A. Sukmanova note the ever-increasing demand for landscape as a result of the significant transformation of modern cities, the change of architectural styles, the growth of urban space and communications, the desire to improve the quality of the urban environment and the comfort of living of the urban population [3]. In the work “Environment in the human perception: geographical aspects” it is noted that the population considers the further development of the landscape to improve its living conditions, which is the most important part of the concept of integrated geoecological analysis [4]. Kapustin, P. V. notes that the methods of working with the urban environment are first structured according to the types of knowledge surrounding the environment, the proximity of research and design approaches is noted when it comes to the urban environment [5]. Similarly, in the work “Urban environment design: new methodological approaches based on the biosphere compatibility paradigm”, a methodology is proposed for the development of a draft territory development plan - planning documentation of urban planning elements of the planning structure (blocks, neighborhoods, residential areas) based on the paradigm of biosphere compatibility of cities and settlements developed in RAACS, which a person develops [6]. The mutual influence of processes occurring in landscape-recreational spaces and their elements is noted, the use of a system of methods and techniques for the formation of an artificial environment of landscape recreation are prerequisites for the stability of landscape-recreational space as a demoecosystem [7, 8].

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The scheme formed by the authors for developing a comprehensive strategy for sustainable development of urban areas based on the principles of goal-setting and the proposed priority rules contribute to the objective formation of complex development goals [9–11]. There are a number of problems that directly depend on the sustainable development of the region, such as: economic, social, political, cultural, financial and the state of the natural environment. The model of sustainable development of the region is a set of interrelated components: environmental, economic, social, political, financial, ethnic, cultural [12–14].

2 Materials and Methods The initial materials for the urban planning analysis of the main park zones of the city of Voronezh were a topographic map, historical references, the general plan of the Voronezh City District for 2021–2041. The objects of the research were 7 key public spaces of the city of Voronezh: Voronezh Central Park, Victory Park, Scarlet Sails Park, Petrovsky Square, Tanais Park, Koltsovsky Square, Orlyonok Park. The research was based on the idea of the ecological framework of the city as a set of undeveloped territories with landscaping. The most important part of the ecological framework of the city are the territories occupied by woody vegetation (trees over 5 m high). The vegetation data was obtained using the Global Forest Change service, supported by the University of Maryland, which provides access to data for 2020 obtained from the analysis of satellite images taken from the Landsat satellite at different times. Statistical data on the area of districts, public areas, and population were taken from the database of the Voronezh Statistical Yearbook of the Federal State Statistics Service for the Voronezh Region. The main research methods were informational-analytical, comparativegeographical, cameral methods, as well as the method of thematic mapping. The cameral research consisted in collecting and processing stock materials on the characteristics of the sites under consideration, as well as the results of scientific research on the ecological state of natural components and the urban landscape as a whole. All the works were based on a systematic approach. The city was considered as a complex integral system. The principle of analyzing the interrelationships of natural and anthropogenic conditions, the ratio of functional zones, taking into account the disturbance of the territory under the influence of various influences, economic and household activities of the population were the main ones when choosing optimal solutions to improve the quality of the urban environment.

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3 Evaluation The ecological condition of the central part of the city is characterized by an abundance of unfavorable factors, such as chemical and mechanical pollution of the air and soil, increased background noise, high level of electromagnetic pollution, and so on. Currently, citywide centers of large and major cities are the most dynamically developing territories. The active transformation of the functional and planning structure is accompanied by both positive and negative aspects, including the consolidation of buildings, the complication of the functional organization, an increase in the intensity of traffic. In this regard, due to good transport and walking accessibility, good location and environmental component, there is a prospect of development of nearby areas to the central one [13, 14]. According to the regional standards of urban planning design of the Voronezh region, the level of provision of landscaping of public areas of the city of Voronezh at the moment is: – – – – – –

Zheleznodorozhny district: 130,79 ha; Kominternovsky district: 199,95 ha; Levoberezhny district: 129,64 ha; Leninsky district: 32,4 ha; Sovetsky district: 270,89 ha; Central district: 197,44 ha.

According to statistical data, a calculated indicator of the minimum allowable level of security was obtained and shown in Fig. 1. At the moment, 961.11 hectares of territories have been planted in Voronezh, which is 56.77% of the required level. We will analyze the significant green areas of the city [15]. 1. Voronezh Central Park The park was founded in 1844, has the status of a city park of culture and recreation. The history of the Voronezh Central Park has more than 170 years. During the battles for Voronezh in 1942–43, the front line passed on the site of the park, and there were fierce battles. In peacetime, the park was restored. In 1986, the park was heavily flooded during the spring flood. There were no funds for its restoration, and therefore the park was in an abandoned state for a long time. The major renovation of the park took place in 2014, according to the reconstruction project developed by

Fig. 1 The calculated indicator is minimal acceptable level of security

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the French landscape architect Olivier Dame and the Moscow company Megapark, which included the repair of the central alley and the Green Theater, the installation of fountains, volleyball and basketball courts, a children’s “town”, tennis courts, bike paths, etc. During the reconstruction, the historical originality of the old park was preserved. 2. Park of Victory The park was founded in 1974, according to the detailed planning project of the district, developed in 1974, this territory was defined as a public center of the district with a park area. On September 4, 2010, a monument was opened on the territory of the park, around which landscaping was carried out with the installation of pedestrian paths, lighting and landscaping. 3. Park «Alye Parusa» The park was founded on July 8, 1975, the status of the park of culture and recreation. In the 1990s, the infrastructure of the park began to collapse, the green zone was littered and gradually fell into disrepair. In 2011, a large-scale reconstruction was carried out. The work was carried out under the supervision of French architect and landscape designer Olivier Dom. The main structure of the park, developed back in the 1970s, remained unchanged, but large-scale works were carried out in accordance with modern requirements of park art. In the new design of the park, wood was mainly used as a material to emphasize its natural component. 4. Petrovsky Square The square was founded in 1860. The first monument in Voronezh was dedicated to Emperor Peter the Great, from that time the name of Petrovsky Square was fixed for the green zone. In 1901, a fountain appeared, benches were installed. During the Great Patriotic War, the monument suffered and was restored in 1956. The next reconstruction was carried out in 2007. 5. Park Tanais In the 1940s, pine trees were planted on the territory of the current park, and in 1974 the forest gradually began to turn into a park. In 2011, the covering of paths and roads was updated, lighting was installed. At the moment, a project of renovation and modernization of the territory is being developed. 6. Koltsovsky Square The opening of the monument to A.V. Koltsov took place on October 27, 1868. In 1871, the construction of a fence around the perimeter of the square was completed. In the same square, during 1876–1877, one of the two very first fountains of the city was built, there were no global reconstructions of the square. 7. Park «Orlyonok» The park was founded in 1954 and has the status of a culture and recreation park. In 1954, a park with a fountain and an architectural entrance gate was opened, which have been preserved to this day. In 1979, a large-scale reconstruction took place in the park. In the 1990s, the park was destroyed, but 40 years later in 2009, after the

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second large-scale reconstruction, the park was closed for the third. To date, the park is preparing for a new opening after a large-scale modernization and renovation, it will be a modern park of culture and recreation [16, 17]. According to field studies, the main advantages and disadvantages of these territories were identified and included in Table 1. The analysis of the functional and planning organization of the landscape complex indicates some trends in its development, both positive and negative. The 1946 master plan, developed by Academician Rudnev, laid down the principles of the center’s landscaping system, which could only partially be implemented. The system of interconnected boulevards and parks was to become the basis of landscape organization, such a structure, combined with landscaping of streets facing the Voronezh River, could provide good ventilation of the central part of the city and significantly improve the microclimatic and environmental parameters of the air environment. At the moment, the existing popular recreational places in the city do not have a logical mutual connection, there is no general concept and integrity of green areas [18–20]. Such a structure of boulevards, parks and squares could not only enrich the architectural appearance of the city, but also actively affect the ecological state of the over-compacted buildings. The irrational and ill-thought-out development of residential quarters in the last 10–15 years has affected the lack of the possibility of enriching the overall architectural, spatial and landscape planning organization and has narrowed the potential for the development of the natural complex of the urban environment [21]. As a result of the ongoing changes, the landscaping system is transformed into a network of single, small-sized, linear and point elements that are not connected by a single planning and compositional idea. The boundaries of the city are expanding every year in all directions, new public buildings appear, such as shopping and entertainment centers, supermarkets, pedestrian streets and landscaped landscaped spaces, the number of residential complexes with thoughtful courtyard spaces is increasing, public spaces have ceased to serve only the central part of the city, many residential areas are forming their own district center [22]. This specificity of the development of modern cities cannot be ignored, as it directly affects the general idea of the layout of recreational areas. Based on the schemes of development of recreational public spaces of the city, according to the forecasting methodology, it is necessary to draw up a scheme of historical changes in the main public spaces, the periods of their reconstruction and modernization, the years of creation of new places of attraction. The development of information technologies, which are rapidly growing and changing, leads to the fact that the way of life of people, their activities, needs are also changing rapidly, and architecture and urban planning does not have time to adapt to these changes. This may lead to the abolition of recreational spaces that carry only one function. Modern life requires a flexible system and the versatility of each object. Public space cannot be limited only to local squares, parks and squares, but should have the appearance of a developing network of territories throughout the city. When forming modern urban public spaces, one of the most important features can be identified-these are the functional and content characteristics of the territory,

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Table 1 Characteristics of the state of green areas Location of the object

Dignities

Disadvantages

1. Voronezh Central Park 1. Availability of functional Not revealed areas, including parking, food outlets 2. Good level of landscaping and landscaping 3. Uniform stylistics of park objects, playgrounds and small architectural forms that do not violate the architectural appearance 4. Security system (video surveillance)

2. Park of victory 1. Availability of functional areas, food outlets 2. Good level of landscaping and landscaping 3. Amusement area for children

1. Lack of a public toilet 2. Lack of public security (CCTV cameras, security points) 3. There is no uniform style of playgrounds, attractions and commercial outlets, which violates the architectural appearance

1. Availability of functional areas, food outlets 2. Availability of a public toilet 3. Separate territory for walking dogs 4. Park library with wi-fi access point and bookshelves 5. Security system (video surveillance). 6. A good level of landscaping and landscaping

Not revealed

3. Park «Alye parusa»

(continued)

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Table 1 (continued) Location of the object

Dignities

Disadvantages

1. Formed walking areas 2. Unified style of small architectural forms 3. The presence of an object of historical heritage

1. Unsatisfactory condition of covering pedestrian zones 2. Outdated small architectural forms 3. In places, not rational hiking routes with obstacles in the form of trees 4. Degradation of landscaping 5. Lack of a security system

The park is at the stage of renovation, therefore there were no decent indicators at the time of analysis

1. The park’s attractions do not allow a holistic perception of the recreational environment 2. The desolation of the park, there is no lighting, and a number of small architectural forms are dangerous for the life and health of citizens 3. There is no public toilet, rest shelters, a safe playground for children

4. Petrovsky Square

5. Park Tanais

6. Koltsovsky Square 1. Good level of landscaping and Not revealed landscaping 2. The presence of the installation 3. The presence of a public toilet

(continued)

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Table 1 (continued) Location of the object

Dignities

Disadvantages

7. Park «Orlyonok» A renovation project has been developed, work is underway on the reconstruction of the park

their complexity, which is determined by a variety of forms and components of the environment, urban planning conditionality, open fragments of the territory, the relative stability of the main types of urban interiors, which depends on the types of urban life. These characteristics of spaces form two types: – architectural and spatial characteristics and features of the territory (structure, compositional structure, geometry); – practical conditions and parameters (operation, natural and climatic conditions, landscape, subject content of the environment). To assess the importance of the needs and consumer behavior of citizens in the functioning of urban spaces, it is necessary to develop criteria for the value of the territory, which will allow us to consider the issues of urban planning programming, functional planning organization, architectural and spatial fullness of objects differently. The quality of life in a significant ratio is characterized by the quality of public spaces. The necessary conditions for the transformation of the urban environment include: – development of the composition of the urban environment on the scale of the city, not the district; – formation of a common urban network of public recreational spaces; – formation of the silhouette and iconic characteristics of all recreational areas; – introduction of a design code in landscaping; – the use of small architectural forms with a visual transition to the scale of a person. Analytical tools are rarely used when choosing scenarios for the development of the territory and forecasting their consequences when making urban planning decisions. At the same time, the achievements of the last decade in the field of information technology have contributed to the development of various methods of analyzing the urban environment (Space matrix, Space sintax, Mixed Use Index (MXI)), including integration with geoinformation systems designed to quantify the

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spatial properties of buildings, study its relationship with socio-economic processes. The analytical tool of the system is based on the new generation BI-platform Prognoz Platform (PP), which was originally designed to create high-tech turnkey business applications. Prognoz Platform allows you to conduct operational analysis, visualize data, model and predict processes, has its own data warehouse designer and builds multifunctional industrial BI systems. The tool has great capabilities from the point of view of analytics, but it does not work with spatial data, respectively, it does not allow for a comprehensive urban planning analysis [23].

4 Conclusions 1. The experience of designing and forming iconic public spaces of the city of Voronezh is analyzed and summarized. 2. The experience of studying urban public recreational spaces has shown that the social significance of any public space, whether it is an event venue or a public garden for walking, grows with its functional and cultural value, but is rather relative. The need to preserve the characteristic spaces of the city, their interconnection, the concept of unity, their outstanding historical elements-this will be a reflection of the era. Only with the creation, preservation and development of public recreational spaces in the concept of sustainable development, the city will be able to increase the artistic expressiveness not only of individual territories and districts, but also of the urban area as a whole. 3. The main task of general planning as a procedure is to ensure the elaboration of promising directions for the development of urban settlements, including in terms of a comfortable urban environment, needs significant methodological updating. The methodology implies the use of an infrastructural approach that allows using any green urban spaces based on preliminary identification for the layout of a full-fledged ecological framework. A parallel assessment of the full range of ecoservice functions would increase the “competitive” capabilities of the elements of the ecological framework in any projects and strategic development plans. 4. Trends and patterns of formation and long-term development within the framework of sustainable development of the region are revealed. 5. The necessity of developing the concept and principles of designing a network of public spaces in the city is revealed. 6. The dynamics of the development of the urban center should be accompanied by an adequate transformation of the natural landscape complex towards differentiation and integration of various functions, complication and enlargement of the structure of natural territories, enrichment of their visual appearance while preserving the historical landscape heritage as the core of the system. 7. It is recommended to create an information and analytical system (IAS) that allows, based on the analysis of statistical data on the socio-economic development of the city and spatial GIS data on the state of the urban environment,

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to understand the processes taking place in the urban planning system, make informed decisions about its development and adjust the urban situation. 8. Generalization of the design experience of recent years reveals the need to develop a flexible strategy and techniques for the formation and functioning of communication spaces as an element of the organization of lifestyle in public space. Forecasting in urban planning allows you to study the specifics, factors and patterns of the formation of public spaces of the city, performing a retrospective analysis, which will allow you to anticipate the consequences of making a decision, as a consequence, to propose a new approach to their design.

References 1. Klimanova OA (2020) Geography, Environment, Sustainability, vol 13, no 1, pp 251–259 2. Kalmanova VB (2018) IOP Conference Series: Earth and Environmental Science, vol 107, no 012130, pp 2–6 3. Kochurov BI, Haziahmetova YA, Ivashkina IV, Sukmanova EA (2018) South of Russia: ecology, development, vol 13, no 3, pp 71–82 4. Dushkova D, Lentz S, Micheel M (2011) Geography, Environment, Sustainability, vol 4.4, pp 48–56 5. Kapustin PV (2021) Russian J Build Constr Archit 3(51):114–127 6. Ilyichev VA, Kolchunov VI, Ptichnikova GA, Kormina AA (2019) Russian J Build Constr Archit 2(46):94–108 7. Grosheva TI (2019) Russian J Build Constr Archit 4(44):103–120 8. Skryabin P, Sergeeva N (2020) Archit Eng 5(4):65–73 9. Murzin AD, Anopchenko TY (2014) Archit Eng 5(4):65–73 10. Maksimova E, Abakumov E, Shamilishvili G (2019) Springer Geography, pp 279–288 11. Spiridonov V, Shabiev S (2020) IOP Conf Ser Mater Sci Eng 962, 032034. https://doi.org/10. 1088/1757-899X/962/3/032034 12. Golov AG (2011) J Sociol Soc Anthropol 5:304–312 13. Lapshina KN, Bakaeva NV, Sotnikova OA (2017) International Scientific Conference: Sustainable Growth in Small open Economies, vol 1, pp 143–146 14. Enin AE, Sheveljov VP, Stupak EV (2018) Constr Reconstr 4(78):64–75 15. Podvalny SL, Sotnikova OA, Zolotukhina IA (2020) Russian J Build Constr Archit 4(48):50–63 16. Bystrova TY, Larionova VA (2017) Akademicheskiy vestnik UralNIIproekt RAASN, pp 513– 523 17. Firsova NV, Ivashkina IV (2020) Gradostroitelstvo 5(69):26–31 18. Duani A, Talen E J Am Plan Assoc 80(4):449–450 (2015) 19. Weller R (2008) Lands J 27(2):255–278 20. Pauleit S (2003) English nature’s accessible natural greenspace standards model. Built Environ 29(2):157–170 21. Zeng C, Deng X, Xu SH, Wang Y, Cui J (2016) An integrated approach for assessing the urban ecosystem health of megacities in China, vol 53, pp 110–119 22. Ragheb A, El-Shimy H, Ragheb G (2015) Procedia Soc Behav Sci 216:778–787 23. Zavyalov AYU, Maksimova SV, Mel’cova ES, Lorens PZ (2015) Archit Mod Inf Technol 2(31):2–5

The Construction Technique Employed in the Erection of the Masonry Dome of the Mosta Rotunda, Malta Lino Bianco

Abstract Spanning large roofs had always been a challenge in the history of architecture. A leap was made by the Romans with the construction of structures such as the Pantheon in Rome. This building was the model on which the Mosta Rotunda was constructed. This rotunda, which supports the third largest circular masonry dome in Christian Europe, is erected in Lower Globigerina Limestone. Although there exists a reliable description on its construction, the erection of M˙garr dome is a good illustration. Albeit elliptical instead of circular, the parish priest of M˙garr during the construction of the church was well versed in the historical documents – including the architect’s drawings and his technical submission/s – relating to the Rotunda and both the architect-engineer and master mason of the M˙garr church hailed from Mosta. Photographic images taken during the building of M˙garr dome fit squarely with the concise descriptions of the construction technique used in the erection of Mosta dome. These photos illustrate the notching of a course to the one below; the overlap is nearly a third of the length of the voussoir, which tallies with published descriptions on the Mosta dome. Keywords Masonry dome · Building construction · Mosta rotunda · Mosta dome · M˙garr dome · Lower globigerina limestone

1 Introduction Citing George Gilbert Scott (1811–1878), who claimed that the dome is “‘the noblest of all forms’, and it appears as a powerful symbol in secular and religious architecture throughout history”, architectural historian Gavin Stamp notes that in the Maltese archipelago, “the craze for dome-building reached astonishing heights” [1: 74]. Following a brief overview of the history of domes which falls short of Cowan’s [2], he made reference to the domed Roman Catholic churches which litter the islands, L. Bianco (B) University of Malta, Msida MSD 2080, Malta e-mail: [email protected] University of Architecture, Civil Engineering and Geodesy, 1046 Sofia, Bulgaria © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_20

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Fig. 1 The Mosta Rotunda: a exterior and b interior of the dome

in particular the Mosta Rotunda and its circular dome (Fig. 1a and 1b). The design of this church was inspired by the Pantheon in Rome, albeit that it had been argued that the then contemporary domed church of San Francesco di Paola in Naples could have been a case study [1]. The Xewkija Rotunda – reminiscent of Santa Maria della Salute in Venice – on the sister island of Gozo, is the other case study which Stamp cited. Completed in 1971 in the Baroque style, its dome is a reinforced shell clad in Lower Globigerina Limestone (LGL), which acted as formwork for the concrete. Most of the domes erected in post-Second World War Malta are such constructions [3]. The paper focuses on the construction technique employed in the erection of the masonry dome of the Mosta Rotunda without centring. Such domes have been studied by Guerra [4], Davey [5] and Sanpaolesi [6]. Reference is made to primary sources, particularly documents of the architect. Notably, secondary sources include Edgar Salomone [7, 8] and Emmanuel Benjamin Vella [9]. The dome of the M˙garr Church, Malta, erected in identical limestone on a smaller scale on an elliptical plan, was used as a comparative study. Photographic images shot during the construction of the dome of this case study provide insight into the technique used in the erection of Mosta dome.

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2 The Mosta Rotunda 2.1 Background Musta, as the town was known in the earlier part of the nineteenth century, was included in a travel guide published in 1839 [10]. The main part of the description of the town was on the erection of the Rotunda. At the time, it was reported that “the whole mass of the temple [of Mosta], has arrived at several layers, beyond the spring of the cornice, and the portico, or facade, is in a very advanced state. … [The Pronaos] of the undertaking is finished, so far as stone work goes, and is terraced” [10: 125]. The significance of the Rotunda in the history of world architecture can be inferred from its inclusion in the seminal publication written by the architectural historian James Fergusson (1808–1886) [11]. The church, designed in load-bearing masonry in the Neoclassical idiom by the Maltese architect of French descent Giorgio Grongnet de Vassé (1774–1862) – hereafter referred to as Grognet as he is known in the literature – is roofed over by a 37.2 m-diameter dome (Fig. 2). The third largest in the ecclesiastical history of Europe, this dome is a feat in building engineering inspired by the concept of corbelling (Table 1; conversion factor used is 1 foot = 0.3048 m). Its construction commenced in 1833 and was completed by 1861, and it was consecrated a decade later. The lantern was constructed in 1889 to the design of George Schinas (1834–1894). The dome was erected without falsework. This implies that the builders opted for optimising efficiency in construction through minimising expenses involved in such props. The Rotunda was constructed around the original parish church in order not to interfere with divine worship and not to disturb the tombs located beneath the flooring. The building is constructed in LGL in its entirety, locally known as franka, freely translated as freestone due to the absence of a specific direction of stratification. Aquitanian in age, this limestone member – the oldest of the Globigerina Limestone Formation – consists mainly of globigerinid planktonic foraminifera [21, 22]. The built heritage of the Maltese archipelago is essentially constructed in this primary industrial mineral which outcrops across the islands [23]. The quality of the limestone varies [24, 25]. Only the highest grade type was utilised in the construction of the Rotunda. It was quarried from Ta’ Qali, a fact established through the recent application of geohistorical retrospective analysis [26]. Grognet was publicly challenged on the technical feasibility of the Rotunda by several local periti, plural of perit, the architect-engineer profession as known in Malta dating to the period when the Order of the Knights Hospitallers of St John ruled Malta (1530–1798). By 1800, the mode of collapse of arches, vaults and domes was well understood; Grognet was challenged on the structural stability of the drum. A commission of four practising periti was appointed by the British Governor General of Malta – Malta and its dependencies were established as a Crown Colony from 1813 until 1964 – to assess the design proposal. To support his design and its feasibility, Grognet used the Pantheon as a case-study. Thus, based on [26], arguing that the

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Fig. 2 Design proposal for the Mosta Rotunda: a main elevation [19] and b plan [20]

Table 1 Comparative study undertaken by Vella (Based on [9: 162]) Building

Internal diameter of dome (m)

Internal height (m)

External height (m)

Pantheon, Rome

43.3 [12: 220]

42.7 [12: 220]

44.8 [13: 311]

St Peter’s Basilica, Vatican

42.0 [14: 371]

123.4 [14: 371]

132.5 [14: 371]

S. Maria del Fiori, Florence

41.5 [15: 335]

101.2 [15: 335]

114.3 [15: 335]

Mosta Rotunda, Malta

36.0

54.9

59.7

St Paul’s Cathedral, London

33.0 [16: 90–91]

68.6 [17: 354]

111.0 [16: 90–91]

Hagia Sophia, Istanbul

33.0 [18: 38]

54.9 [18: 38]

56.1 [15: 447]

Rotunda was inspired by this Roman building is an understatement. With respect to the structural properties of LGL, Grognet made reference to Milizia [27]. At the time, knowledge and experience were available [28–30]. Yet, no formal empirical knowledge on the properties of LGL was available; with respect to the timeline of the construction of the Rotunda, petrography as a science was established a few decades post the commencement of its construction, whilst the first systematic attempt to assess the physical characteristics of the local limestone was published decades after its completion [31]. The Rotunda was used in a recent publication as an illustration of building science and professional practice in nineteenth-century ecclesiastical architecture in Malta [32].

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2.2 The Building Team The frieze on the portico reads “Vergini Syderibus Restitutæ T. H. Mustenses. FF. A.S. M. CCM. LVII”, which translates as “To the Assumption of Virgin Mary, this temple was built by the people of Mosta in 1857”. Although the building of the Rotunda was entrusted to a master mason, the building team included not only masons but also a significant number of parishioners. The people of Mosta were neither equipped nor had the capacity to build the church. The Malta Penny Magazine published in July 1841 stated [19: 118]: “the greatest expense was that of labourers and masons. To obviate this, as much as possible, the church hit upon the happy expedient of promising and bestowing indulgences to all who would work there gratuitously on Sundays. As many as two or three hundred pious volunteers, may have been seen labouring there on the same day; … and the advancement of the church to its present state may in a great measure be attributed to these labours of the Sabbath”. This fact is corroborated in a guide published a few years earlier [10: 125–126]: “Funds, we believe, are rather short, for the finishing of this sublime edifice; but it will go gradually on, to a termination, from the slender means which exist, and from the enthusiasm of the lower orders, who work gratis, on Sundays, and other church holydays”. Not only men contributed free labour; women and children likewise contributed by unloading and storing cartloads of soil, sieving soil and LGL powder locally known as xaèx, carrying water and preparing mortar [9: 151]. Although it was widely held that the population of the village numbered 6,000 in 1841 [20: 121], the year when the building was a third of the final height, the official census undertaken in 1842 stated that the population numbered 3,386 [33: 58]; it reached 3,828 by 1861 [34: 2]. This gives an insight into the significant fraction of the parishioners which was engaged in the building works. Cash came from the selling of donations ranging from livestock to poultry to crops to donations of land through wills of the deceased. Inhabitants who could not donate due to extreme poverty would contribute, alongside others, labour hours on Sundays and holidays. At the time, poverty due to lack of employment was rampant throughout the island; the inhabitants of Mosta were more impoverished: the locality listed the highest number of beggars and there were years where people died of hunger [9: 149].

2.3 Construction of the Dome In his submission to the commission set up by the British Governor General, discussed in [32], Grognet addressed the structural engineering calculations. This report included a drawing, hereby reproduced as Fig. 3a, which illustrated the following [35]: PQ: base at a scale of 20 canes of the Rotunda, that is 160 palmi. ADFEB: catenary curve or dome. MF: along its axis, its height of 26 canes or 208 palmi.

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Fig. 3 Design proposal for the Mosta Rotunda: a structural schematic drawing [35: 22] and b cross section through the main axis (after [11: 32])

VP/VY: ACB: CF:

width of the drum. hemispherical dome. height of 34 palmi of the catenary curve over the hemispherical one.

To comprehend this sketch in the context of his design, the proposed section of the church is reproduced as Fig. 3b (after [11: 32]). With respect to the thickness of the shell, this report states [35: 17]: “Il massiccio della cupola sara’ al piu’ dalla sua nascita della grossezza di una canna maltese e cominciando gradatamente ad estremarsi in su, sinchè termina al suo ombelico, nella grossezza di palmi tre, circa” (The thickness of the dome will be at the utmost from the springing of one Maltese cane in thickness and gradually decrease as it rises, until it terminates at the navel which is about three palmi in thickness). This recalls the construction of the Pantheon: the thickness of the shell decreases towards the top, although unlike Mosta, using lighter building material. Furthermore, coffering present in the interior helps in reducing the dead load of the dome. Making reference to the corbelled domes in antiquity – notably the domed interior of the Treasury of Atreus, Mycenae – Torpiano [3: 24] poses the problem of the roofing of the same accordingly: “the trick is to support parts of the ring until the whole is completed”. He paraphrased the architectural historian James Fergusson thus: “[Mosta dome was] built, without centring, in a series of rings, each notched on to the previous one” [3: 24–26]. Edgar Salomone (1882–1969), a priest brought up in Mosta and who held his first mass in the Rotunda in 1909, published two booklets on this town, one specifically focussing on the Rotunda [7, 8]. His concise description of the construction of the dome reads [7: 21–22]: “The building of the dome over this church forms by itself a marvel of architecture: for no scaffolding was used and

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neither stone nor wooden work set up to direct its curvature. It was done by simply notching each course to the one below: in other words, when the circular foundation on which the dome rests was finished, the first row of the dome was built with heavy blocks of stone, having one edge cut off, so as to give the right concavity, and so placed as to overlap their supports by one third of their length: then another layer was built on this, overlapping it in the same way. This process went on until the dome was completed”. Another description which falls squarely with that of Salomone is by Emmanuel Benjamin Vella (1899–1946). This versatile writer [36], born in Mosta, outlined concisely the construction method used [9: 139–140]: “Din il-koppla fiha bi˙cc˙ a xogèol kbira tal-in˙ginerija imma dak li jgèa˙gg˙ eb lil kullèadd huwa kif kellhom il-èila jtellgèu saqaf bèal dak mingèajr armar taètu, kif soltu jsir f’gèeluq minn dik ix-xorta! Il-bini tagèha sar billi kienu jqegèdu filata dawwara mejt, u minn flok il-mollijiet li kienu ju˙zaw bil-bi˙cc˙ a t’isfel tal-knisja, hawn kellhom iz-zintlu. Imbagèad wara li tkun lesta dik il-filata jibdew l-oèra ta’ fuqha. Il-èa˙gra z˙ z˙ omm li ma taqax gèal isfel imèabba li kella l-gargnu mill-maqgèad, mir-rjus u mill-faqqani; u gèal hekk waèda ti˙gi ngastata ma’ l-oèra, u s-soda ta’ taèt dejjem i˙zz˙ omm l-oèra ta’ fuqha” (This dome contains a great deal of engineering work but what amazes everyone is how they [the master mason and the masons] had the ability to erect a roof like that without scaffolding under it, as is usually done in an enclosure like that! Its construction was done by placing a course all around, and instead of the templates they used in the lower part of the church, here they had the centre. Then after that course is finished the other one on top will be placed. The dimension stone is prevented from falling down by means of rebates from the lower face, the head and from the upper face; and thus one is notched to the other, and the lower course always holds the one above). The critical Maltese word in Vella’s version is ‘gargnu’, which the authoritative publication by Aquilina translates as “the overlapping joint between two steps in a stone staircase” [37].

3 The M˙garr Church as a Case Study 3.1 Background Established as a parish in 1898, the Neo-Classical–inspired parish church of M˙garr was erected over the period 1912–1946 (Fig. 4). The construction of the dome was completed by 1939; the lantern was built after the Second World War [38]. A caption to an illustration contained in a booklet published in 1966 states that the ‘builders’ of the M˙garr church were the first parish priest Jerome Chetcuti (1863–1949) and Edgar Salomone [39: 21]. The initial concern of Chetcuti was to erect a larger parish church. He, the former administrator of the Mosta Rotunda [39], engaged Gio Maria Camilleri (1860–1917) as architect-engineer – a surveyor and foreman engaged in government services [38,

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Fig. 4 M˙garr Parish church as at present: a elevation and b ceiling

˙ Maria, known as Gamri, ˙ 40] – and Gio Camilleri (1895–1978) as master mason, both personalities from Mosta. The design was approved by the Superintendent of Public Works [38]. Salomone came to live in M˙garr in 1919. He was assistant to the parish priest from 1921 until 1931, when Chetcuti was appointed a member of the Cathedral Chapter, a post Salomone occupied until 1954 [36]. It was during his term in office – that is, from 1931 until the opening of the church in 1939 – when the phase of the erection of the dome gathered momentum, It is claimed that the quarry used to extract the building stone for the church was located at Ta’ Vnezja, within the limits of Ta’ Qali. Another quarry was opened at Tar-Ragèad for second grade building stone to be used as filler in the cavity of the walls. In the 1930s, another quarry was opened at Ta’ Mrejnu to extract ferrogenous stone (Maltese, g˙ ebel tal ferran˙gin) for the infilling of cavities and thus reducing the costs and accelerating the construction work [38]. Until the 1930s, when tracks were laid to transport stone to the building site, farmers made use of mule driven carts. M˙garr was, and still is, predominantly a farming community. It has long been claimed that the residents of the village contributed to the construction of the church through (i) voluntarily working on the project and (ii) funds generated by selling farm products, notably eggs [41]: “the church itself is shaped like an egg, a tribute to the devout hens that financed it” [42: 173]. A week prior to its consecration, The Catholic Times of England labelled it the ‘“Eggs and Poultry’ Church” (cited in [39: 20]). This is factually not true on two counts: 1. Chetcuti aspired for the new church to have a dome similar to the Carmelite church in the old capital, Mdina, which is elliptical; and

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2. when Chetcuti was parish priest, he collected £5,408 for the construction of the church. Whilst money collected from the selling of eggs was the highest item, amounting to £876, it was followed by legacies and donations which amounted to £692 [38]. Thus, funds generated from the selling of eggs during this period accounted for 16% of the total sum collected. Perit Annetto Mifsud Ellul (1889–1942), from Qormi but residing in Mosta, was entrusted to prepare the drawings for the erection of the dome. He engaged head˙ master Ganni Cilia (1904–1999) to study the works of Giacomo Barozzi da Vignola (1507–1573) [38].

3.2 Relevance Photographs shot during the erection of its masonry dome provide an illustrative insight into the art and science of building construction at the time and the likely technique used in the erection of the dome of the Rotunda. The initial plans for the M˙garr church were draughted less than half a century after the completion of the dome of the Rotunda. Indeed, it was only a generation or two removed from the period when the dome of the Rotunda was completed. The M˙garr church shares with the Rotunda and its parishioners the following known facts: 1. it was conceived and overseen by parish priests from Mosta; 2. both the original architect-engineer and the master mason were from Mosta; 3. the building stone for its construction – LGL – was extracted presumably from Ta’ Vnezja, within the limits of Ta’ Qali; and 4. the dome was erected without falsework. Further to these four facts, Scerri includes the use of an identical construction technique [43]. To support his claim, he reproduced labelled photos of the construction of M˙garr dome posted on Facebook by David Vella whose maternal grandfather was ˙ Gamri Camilleri, nicknamed ‘Is-Saqqafi’ which literally translates as ‘The Roofer’. Scerri also included the quote from Vella stated above, although he made use of the text printed in an edited version published some decades later [44], which quote was included in David Vella’s post on Facebook [45] as reproduced in Muscat [46]. These images, likely shot in 1937/8 – hereunder reproduced as Figs. 5 and 6, where reproduced on the same portal by Neal Camilleri, Is-Saqqafi’s great grandson [47]. The author concurs with Scerri’s opinion that the method used in the construction of M˙garr dome as illustrated by these images helps comprehend how Mosta dome was erected. They read as a free transliteration of the quote from Vella into a pictorial image. Coupled with Salomone’s, which includes the dimensions of the notches, this transliteration is more faithful to the construction technique used in the erection of the dome of the Rotunda. Each voussoirs was carried by four labourers (Fig. 5a). Once laid, each voussoir is temporarily tied to a voussoir from the lower course (ring) by means of pseudo

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Fig. 5 Construction of M˙garr dome ( © M˙garr Parish Office): a carrying of voussoirs, b placing a ˙ voussoir, c master mason Gamri Camilleri (standing on platform dressed in white [46, 47]) checking the position of the voussoir, and d master mason pointing the voussoir

sash clamps (Fig. 5b). The position of the voussoir is first checked by the master mason Camilleri (Fig. 5c) and then the joints are pointed (Fig. 5d). The placing of a voussoir next to the marker shown in Fig. 5c and 5d, is shown in Fig. 6a. Such markers were standalone voussoirs placed through the foci of the ellipse in order to be used as guides for placing the remaining voussoirs. Interesting is the notch of the course to the one below (Fig. 6b), the gargnu; the overlap is nearly a third of the length of the voussoir, which tallies with the description of the construction of Mosta dome given by Salomone [7]. The completion of a course/ring can be appreciated in Fig. 6c. Albeit of different geometry, the domes of the Mosta Rotunda and the M˙garr Parish Church were both erected without centring, the virtual centres being where the respective radii converge. The type of construction employed is what Rafael Guastavino (1842–1908) labels as mechanical in contrast with cohesive [48]. They are essentially corbelled domes – built in a series of closed, self-supporting rings, each

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Fig. 6 Construction of M˙garr dome (© M˙garr Parish Office): a placing of a voussoir next to a marker, b the notch/step/overlap is nearly a third of the length of the voussoir; the position of each voussoir is offset by circa half the width of the one below which ensures discontinuity in vertical joints, and c completion of a course/ring

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rendered stable once complete. For their structural integrity, a mechanical system relies on the “resistance of any solid to the action of gravity when opposed by another solid” [49: 125]. Thus, during construction, the lower ring supports the partially completed overlying ring and ensures that its overall geometry, and eventually that of the whole structure, is maintained. Once erected, a dome is a shell with intrinsic stiffness arising primarily from its geometry and the nature of the material in which it is constructed. Equilibrium is attained independently of the cohesive properties of the material in which the dome is erected; “the only major consideration is that of the physical quality of hardness, i.e., in essence, whether or not the material is able to support itself without crushing” [50: 20].

4 Final Comments The construction technique used in the building of the dome of M˙garr Parish Church as illustrated through photographic images taken during its erection fits accurately the description outlined by Salomone [7] and Vella [9] on Mosta dome, the local scholars most versed in the history of the building of the Rotunda. It involves the notching of a course to the one below; the overlap is nearly a third of the length of the voussoir. The result recalls a corbelling technique without falsework on a grand scale. This knowledge in the building of M˙garr dome is not coincidental. The key personalities which oversaw its design and execution were just a generation or two removed from the time when the dome of the Rotunda was completed: the parish priest at the time of its construction was the same Salomone who, prior, had been the assistant parish priest of the locality. Furthermore, both the architect-engineer and the master mason of M˙garr church were from Mosta. Acquaintance with the construction technique is of significance not only with respect to understanding the structural dynamics of the dome but also as a useful tool to undertake effective restoration of deteriorated voussoirs, interventions which must respect the integrity of the monument as built. Acknowledgements The author would like to thank Architect-Engineer Innocent, known as Vincent, Centorrino for valuable discussion on the historical material with respect to the architectural design of domes, the late Rev. Paul Caruana from Naxxar for his help in the translation of the original sources on Mosta Dome from Italian into English and Alessandra Bianco for her assistance in gathering historical photographic material. Special gratitude to Rev. George J. Schembri, the Parish Priest of M˙garr, for allowing the reproduction of images in Figs. 5 and 6. Although these photos were uploaded on Facebook by David Vella [45], Neal Cammileri [47] and Ivan Scerri [43], the copyright lies with the M˙garr Parish Office.

References 1. Stamp G (2012) Domes. Apollo 175(595):74–75

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2. Cowan HJ (1977) A history of masonry and concrete domes in building construction. Build Environ 12:1–24 3. Torpiano A (1987) On the design of masonry shell structures. Ph.D. thesis. University of Bath 4. Guerra G (1958) Statica e tecnica costruttiva delle cupole antiche e modern. Instituto de Architettura Tecnica, Napoli 5. Davey N (1961) A History of Building Materials. Phoenix House, London 6. Sanpaolesi P (1971) Strutture a cupola autoportanti. Palladio XXI:3–64 7. Salomone E (1911) Musta: Memories and Charms. The Orphans’ Press, Rochdale 8. Salomone EG (1913) La Rotonda della Musta: Relazione architettonica del Grongnet: documenti editi. Casa San Giuseppe, Malta 9. Vella EB (1930) Storja tal-Mosta bil-knisja tagèha. Empire Press, Malta 10. MacGill T (1839) A Hand Book, or Guide, for strangers visiting Malta. Luigi Tonna, Malta 11. Fergusson J (1862) History of the Modern Styles of Architecture: Being a Sequel to the Handbook of Architecture. John Murray, London 12. Anderson WJ, Spiers RP (1907) The Architecture of Greece and Rome: A Sketch of Its Historic Development. Batsford, London 13. Fergusson J (1874) A History of Architecture in All Countries, From the Earliest Times to the Present Day, vol I. John Murray, London 14. Baumgarten PM (1913) Basilica of Saint Peter. In: Catholic encyclopaedia. The Encyclopaedia Press, New York, vol. XIII, pp 369–374 15. Fergusson J (1874) A History of Architecture in All Countries, From the Earliest Times to the Present Day, vol II. John Murray, London 16. Bumpus TF (1906) The Cathedrals of England and Wales. T. W. Laurie Ltd., London 17. Rivoira GT (1921) Architettura Romana: Construzione e statica nell’ eta’ imperiale. U. Hoepli, Milan 18. Jackson TG (1925) Architecture. Macmillan, London 19. Anon 1 (1841) Colossal Church of Musta. Malta Penny Mag 98(24 July):117–119 20. Anon 2 (1841) Church at Musta. Malta Penny Mag 99(31 July):120–122 21. Oil Exploration Directorate (1993) Geological map of the Maltese Islands: Sheet 1. Office of the Prime Minister, Malta 22. Baldassini N, Mazzei R, Foresi LM, Riforgiato F, Salvatorini G (2013) Calcareous plankton bio-chronostratigraphy of the Maltese Lower Globigerina Limestone member. Acta Geol Pol 63:105–135 23. Bianco L (2017) Techniques to determine the provenance of limestone used in Neolithic architecture of Malta. Rom J Phys 62(1–2):901 24. Bianco L (1993) Some factors controlling the quality of Lower Globigerina building stone of Malta. M.Sc. dissertation. University of Leicester 25. Bianco L (2021) Geochemistry, mineralogy and textural properties of the Lower Globigerina Limestone used in the built heritage. Minerals 11(7):740 26. Bianco L (2019) A geohistorical retrospective analysis of cultural heritage buildings: the case of Mosta Dome, Malta. Geo J 84:291–302 27. Milizia F (1785) Principii d’ Architettura Civile, vol 3. Remondini, Bassano 28. Bianco L (1999) Geocultural activity in seventeenth and eighteenth century Malta. Geo J 48(4):337–340 29. Bianco L, Cardona K (2020) Seventeenth-century building engineering in the central Mediterranean: a case study from Malta. Terra Sebus. Acta Musei Sabesiensis 12:329–353 30. Hughes JQ (1967) The Building of Malta During the Period of the Knights of St John of Jerusalem, 1530–1975. Alec Tiranti, London 31. Crown Agents for the Colonies (1885) Resistance of Malta and Gozo stone to thrusting stress. David Kirkaldy and Son, London 32. Bianco L (2018) Building science and professional ethics in nineteenth-century ecclesiastical architecture in Malta. Terra Sebus. Acta Musei Sabesiensis 10:413–424 33. Godfrey C (1842) Population of the islands of Malta and Gozo: an abstract statement. Malta Gov Gazette 1551(31 December):57–59

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34. Giglio A (1863) Census of the Islands of Malta and Gozo for the Year 1861. Government Printing Office, Malta 35. : Grongnet de Vassé, G (1913) Relazione sul mio Progetto per la nuova Chiesa da Fabricarsi di pianta in Casal Musta (1833). In: Salomone EG (ed) La Rotonda della Musta: Relazione architettonica del Grongnet: documenti editi, pp 15–22. Casa San Giuseppe, Malta. Grongnet 1833 36. Schiavone MJ (2009) Dictionary of Maltese biographies. Pubblikazzjonijiet Indipendenza, Pieta’ 37. Aquilina J (1987) Maltese-English Dictionary. Midsea Books, Malta 38. Deguara A (1999) L-Im˙garr: Il-èajja u l-èidma ta’ niesu mill-qedem sa llum. Colour Image, M˙garr 39. Chronicler (1966) Mgarr-Malta: Its remote and recent history. s.n., s.l. 40. Mangion F (1972) Gio Maria Camilleri Arkitett Mosti. In: Vella EB et al (eds) Storja tal-Mosta bil-Knisja Taghha, pp 278–279. Empire Press, Malta 41. Guillaumier A (1987) Bliet u Rèula Maltin. Valletta Publishing & Promotion Co., Valletta 42. Fiott C (1997) Towns and villages in Malta and Gozo; part 3: the north. Conventual Franciscans, Rabat 43. Scerri I (2007) L-Arkitett Gio Maria Camilleri–90 sena minn mewtu. Il-Mosta 5. http://mostaa rchives.smashyouagainstthewall.com/ArkitettGioMariaCamilleri.htmllast. Accessed 16 Oct 2021 44. Vella EB et al (1972) Storja tal-Mosta bil-Knisja Taghha. Empire Press, Malta 45. Vella D (2020) Malta Vintage History. Facebook, 24 April 2020. https://www.facebook.com/ groups/768456500209072/permalink/1337125190008864/. Accessed 16 Oct 2021 46. Muscat S (2020) Mgarr Church/The construction of the dome. Facebook, 5 November 2020. https://www.facebook.com/groups/1233039633440130/search/?q=mgarr%20church%3A. Accessed 16 Oct 2021 47. Camilleri N (2021) Nostalgia Malta. Facebook, 14 March 2021. https://www.facebook.com/ groups/1233039633440130/user/100004410632901. Accessed 16 Oct 2021 48. Guastavino R (1893) Essay on the Theory and History of Cohesive Construction Applied Especially to the Timbrel Vault. Ticknor & Company, Boston 49. Guastavino R (1893) Cohesive construction: its past, its present, its future. Am Archit Build News XLI(August 26):922 50. Milkovich AK (1992) Guastavino tile construction: an analysis of a modern cohesive construction technique. Masters thesis. University of Pennsylvania

Optimization of the Routing of Heating Networks Ekaterina Kopytina , Evgeny Umerenkov , Anastasia Chuikina, Natalya Petrikeeva , and Dmitry Chudinov

Abstract For optimal routing of heating networks during reconstruction and new construction, various methods and main optimization criteria are proposed. It is possible to significantly reduce labor-intensive calculations at the design stage by using various software and computing systems. The implementation of the software part of the work was carried out in a high-level free object-oriented programming language Python. At the same time, the interface of the calculation program for the optimization of the heating network route is considered. The program is designed to select an option or options for routing a heating network by methods of expert assessments and partial optimization. The program has the following functionality: selection of a method for tracing a heating network; selection of optimization criteria; input of initial data; input of thermal resistance of heat transfer for each pipe diameter; selection of end-user temperatures; viewing the selected calculated optimization criteria for each scheme; comparison of schemes by the enlarged values of the optimization criteria for the selected partial optimization; performing a comparison of schemes for the enlarged values of the optimization criteria after the input of the criteria weights with the selected method of expert evaluations; building a radar chart. Keywords Organization of construction · Resource saving · Heating networks · Network routing · Multi-criteria optimization · Partial optimization · Optimization · Expert assessment method · Applied programs in construction

E. Kopytina (B) Voronezh State University, University Square, 1, 394018 Voronezh, Russia e-mail: [email protected] E. Umerenkov Southwest State University, 94, 50 Let Oktyabrya ul., Kursk 305040, Russia A. Chuikina · N. Petrikeeva · D. Chudinov Voronezh State Technical University, 20-Letiya Octyabrya Street, 84, 394006 Voronezh, Russia © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_21

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1 Introduction The heating networks of Russia have a considerable length due to the climatological features of our country. This, in turn, leads to an economic rise in the cost of heat supply facilities. In addition, earthworks and the further process of their operation with inspection and repair work are quite laborious and specific. Therefore, the issues of optimal routing during reconstruction and new construction are always relevant [1]. The problem of tracing and optimal tracing is considered quite often in the works of a number of authors [2–4]. At the same time, various techniques and basic criteria for optimization and analysis are proposed. Even at the stage of urban planning analysis, certain studies are carried out. As a result of a review of the available literature sources, it seems relevant to use the methods of multicriteria optimization [5–7]. Obviously, the more connected consumers, the more ramified the heating network should be, and, consequently, the more laborious are the calculations at the design stage. They can be reduced through automation using various software and computing systems. At the same time, there are not many software and computing systems for finding such solutions, which are convenient, fairly simple and intuitive, and described in special literature. Previously, the implementation of the software part of the work was carried out by us in the high-level free object-oriented programming language Python [8, 9]. In a number of works, we have also considered the issue of partial and multicriteria optimization. Thus, in [9], an original computer program was developed and presented for tracing a heating network using multicriteria optimization methods. The program is designed to select an option or several options for routing a heating network by methods of expert assessments and partial optimization. It seems to be quite convenient at this stage of calculations for routing optimization. Let’s take a closer look at the interface of this program.

2 Methods Let’s consider some dependencies that were chosen as optimization criteria and were included in this program as defining ones. Due to the limited initial data at the initial design stage, a number of values can be determined by aggregated characteristics. Heat losses in the heating network can be determined by the formula [8–10] qm.n = q · Mcon ,

(1)

where q is the specific annual heat losses attributed to 1 m2 conditional material characteristics of the heating network, Gcal/(year · m 2 ); Mcon is the conditional

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material characteristic of the heating network, calculated on the outer surface of the insulation, m2 . The dependence for determining the material characteristics of the network, taking into account the reduction, has the form M=

n 

Mi =

i=1

Abd Rl0,19

· li ,

(2)

where Abd is the correction factor; Rl is the specific pressure loss, kg /( m 2 · m); li is the length of the section under consideration, m. A generalized indicator determined by the formula can serve as a reliability criterion  Q j ωi   Q(t)  1 − e−ωi t , =1− ωi Q0 Q0 j=1 j=l

Rsys (t) =

(3)

where Q(t) is the mathematical expectation of the characteristics of the quality of the system functioning; Q 0 is the estimated heat consumption, MW; Q i is the undersupply of heat, MW; t is time, year; ωi is the failure flow parameter, 1/ year, defined as. N 

ω=

mi

i=1

N t

=

m mean (t) , t

(4)

where m i is the number of refusals, pcs.; N is the the number of identical sections of the heating network, pcs.; t is the observation time, year; m mean is the average number of refusals, pcs. Using the value of the actual heat turnover, it is possible to analyze the magnitude of the branching of the heating network [8, 9] zφ = p



z φi =



p

(Q i × li ),

(5)

where Q i is the calculated heat load, Gcal/ h. Note that it is desirable to minimize some criteria in the process of integral optimization, while the values of other criteria, on the contrary, should be increased (if possible). To simplify the discussions (while maintaining their general character), it is proposed to replacethe values of the reliability criterion, for example, with its inverse value Rsys → 1 Rsys (since only this criterion, in the considered problem, must be maximized). Then, during the optimization process, it will be desirable to reduce all criteria [8, 11]. The most common method for solving transport subproblems [8, 12] is based on solving the function

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S=

n 

x k pk ,

(6)

k=1

where xk is the optimality parameter; pk is the parameter weight. In this case, the key problem here will be the determination of the parameter weight. It is customary to determine it with the help of expert assessments. As noted in the work, the most appropriate method for determining the weight is a method based on the search for the relative frequencies of the transformed ranks [8], which can be represented as m 

ai =

Ai j

j n  m  i

,

(7)

Ai j

j

where Ai j is the criterion rank after transformation.

3 Results and Discussion On the basis of the above dependencies, the problem of optimal tracing of the heating network was solved. In the course of solving the problem [8, 9], the application “Tracing the heating network using multi-criteria optimization methods” was developed, which contains the following modules: • • • • •

Main.py; Choose_form_ui.py; Input_data_form_ui.py; Result_form_ui.py; Temperature_form_ui.py.

Choose_form_ui.py, Input_data_form_ui.py, Result_form_ui.py, Temperature_form_ui.py are converted program interfaces. The Main.py module describes the main logic of the program. Main.py contains several classes such as: – the Choose_Characteristic() class contains the load_characteristic() method, which serves to select the optimization method by the user of this software product and those characteristics that must be calculated: the material characteristics of the heating network, the moment of heat load, the reliability of the heating network, the time spent on construction or reconstruction, annual heat loss, temperature dispersion. This class interacts with the Choose_form.ui interface, which is shown in Fig. 1.

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Fig. 1 Optimization method and characteristics selection form

Fig. 2 Input form of thermal resistance of heat transfer

– the Input_data() class interacts with the Input_data_form.ui form and is responsible for drawing the data input elements necessary for making calculations according to the given formulas, handling user input errors, calculating the characteristics previously selected by the user, as well as generating a dialog box for the user to enter the thermal resistance of heat transfer for each diameter, which is shown in Fig. 2. This functionality is implemented by the load_table() and load_inp_data() methods. – The Temperature() class interacts with the Temperature_form.ui form and is responsible for user selection of consumer temperatures, as shown in Fig. 3.

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Fig. 3 Consumer temperatures selection form

– the Result() class works with the Result_form.ui form and is required to display the values of the calculated characteristics depending on the previously selected optimization method in three views, such as: • table of optimization criteria; • table of optimal options; • graphical presentation. The optimization criteria table displays the values of the calculated criteria in a table view using the give_data() method. The best-case table allows you to compare schemas when aggregating values. The interface of the table of optimal options using the expert judgment method is shown in Fig. 4. The interface of the best-case table using partial optimization is shown in Fig. 5. The graphical representation allows the user to set the diagram number and view the result in the form of a radar diagram thanks to the implemented plot_graph() method.

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Fig. 4 Applying partial optimization

Fig. 5 Application of the method of expert assessments

A petal chart is a specific image that allows you to display the data of each category along a separate axis. Each axis starts at the center of the figure and ends at the outer circle. The radar chart is shown in Fig. 6. A class diagram showing the methods of the software product developed in the course of research is shown in Fig. 7. The authors of [13–15] also considered models of optimal pipeline transport systems using the method of computer programming. In this case, linear programming and the method of purposeful enumeration of trees are used. In this case, the interface of the program in question is simpler and more intuitive.

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Fig. 6 Radar chart view

Fig. 7 Class diagram

4 Conclusions Due to the peculiarities of the method used for determining the weight values, the criterion with the minimum value of the relative frequency of the converted ranks is of greatest importance ai . As a result, it is necessary to obtain the most advantageous option for tracing the heating network, or several options, if this method is without expert judgment [8, 16].

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The main disadvantage in the above optimization method is the subjective choice of the criterion weight by experts, while the wrong choice can lead to an erroneous decision. This can be avoided by using a method that limits the obviously disadvantageous options for tracing, while choosing not one optimal option, but groups of options. Thus, those route options are removed that will be unprofitable for any values of the weights [8, 9]. The use of modern software products allows you to reduce time and labor costs during design. The implementation of the software part of the work was carried out in a high-level free object-oriented programming language Python and is intended to select the option for tracing the heating network using expert estimates and partial optimization. The paper considers the interface of the program, presents an analysis of the main modules of the working block of the program, shows an example of its work in the form of working windows and building a diagram. The program has the following functionality: selection of a method for tracing a heating network; selection of optimization criteria; input of initial data; input of thermal resistance of heat transfer for each pipe diameter; selection of end-user temperatures; viewing the selected calculated optimization criteria for each scheme; comparison of schemes by the enlarged values of the optimization criteria for the selected partial optimization; performing a comparison of schemes for the enlarged values of the optimization criteria after the input of the criteria weights with the selected method of expert evaluations; construction of a radar diagram [8, 9]. This visually facilitates and simplifies the work of both the expert and the designer when making the best decision.

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8. Chuikina AA, Sotnikova OA (2021) Razrabotka metodiki i programmy rascheta optimal’nogo marshruta truboprovodnoy trassy sistemy teplosnabzheniya. Santekhnika otoplenie konditsionirovanie 4:46–48 9. Kopytina EA, Chuikina AA, Bokhan AR (2021) Trassirovka teplovoy seti metodami mnogokriterial’noy optimizatsii, Svidetel’stvo o registratsii programmy dlya EVM 2021617373 10. Petrikeeva NA, Chudinov DM, Kopytina YA, Sotnikova OA (2018) Version of the solution of the problem of optimization of thickness of the heat-insulation layer in heat supply. Russ J Build Constr Arch 4:40–49 11. Melkumov VN, Tulskaya SG, Chuykina AA, VYu, Dubanin (2021) Solving the multi-criteria optimization problem of heat energy transport. Adv Intell Syst Comput 1258:3–10 12. Penkovskii A, Stennikov V, Postnikov I (2019) Unified heat supply organization: mathematical modeling and calculation. Energy Procedia 10:3439–3444. https://doi.org/10.1016/j.egypro. 2019.01.930 13. Abramov SV, Egorov SY, Karpov SV, Karpushkin SV, Kornilov KS, Druzhinina VN (2013) Reshenie zadachi trassirovki truboprovodov s ispol’zovaniem tekhnologii CUDA. Perspektivy nauki 8:106–109 14. Furman I, Allashev A, Piskarev A, Bovchaliuk S (2017) Evelopment and study of technological visual programming of logic control problems. East-Eur J Enterp Technol 2:23–31. https://doi. org/10.15587/1729-4061.2017.118833 15. Stennikov VA, Sokolov DV, Barakhtenko EA (2020) The development of an algorithm based on dynamic programming for optimization of tree-like energy pipeline system. In: E3S web of conferences. Mathematical models and methods of the analysis and optimal synthesis of the developing pipeline and hydraulic systems 2020, p 02005. https://doi.org/10.1051/e3sconf/202 021902005 16. Stennikov V, Postnikov I, Mednikova E (2021) Determination of an effective heating radius in district heating systems in terms of reliability. Energy Syst Res 1:54–62. https://doi.org/10. 38028/esr.2021.01.0007

Hydrodynamics of the Flow of an Ideal Liquid When It Flows Out of the Bottom Hole of a Parabolic Tank Boris Kumitskiy , Svetlana Tul’skaya , Viktor Morozov , Egor Aralov , and Victor Budnikov

Abstract In order to clarify the relationship between the geometry of the tank and the physical content of its emptying process, experimental studies were carried out to determine the expiration time through the bottom holes of vessels pre-filled with water of various geometric shapes with equal overall dimensions (cylinder, cone, paraboloid). The dependence of the time of complete emptying on the shape of the vessel was found. A feature was observed when the liquid flows out of the paraboloid: the uniformity of the level decrease and the deformation of the free surface. To explain such an anomaly of the process of outflow from a vessel of a parabolic shape, a hydrodynamic model is proposed based on the idea of the movement of particles of an ideal liquid through current tubes of various curvature that completely fill the volume of the paraboloid. Analytical expressions of the main kinematic parameters of the outflow (emptying time, acceleration of liquid particles), as well as the equation of the deformed free surface and its rate of decrease are obtained. The proposed work provides for a series of experiments on emptying vessels of various geometric shapes of the same overall dimensions, as well as a description of the results obtained using a hydrodynamic model based on the flow of liquid through curved current tubes. Keywords Current tube · Axisymmetric emptying · Paraboloid · Hydrodynamic model · Bottom hole

1 Introduction With unsteady fluid movement, an example of which is emptying the tank with decreasing pressure, most of the flow characteristics (pressure, volume flow, flow rate) change. At the same time, the process of fluid outflow from the bottom hole

B. Kumitskiy · S. Tul’skaya · E. Aralov (B) Voronezh State Technical University, 84, 20-letiya Oktyabrya ul., Voronezh 394006, Russia e-mail: [email protected] V. Morozov · V. Budnikov Southwest State University, 94, 50 Let Oktyabrya ul., Kursk 305040, Russia © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_22

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acquires the significance of an independent task of hydromechanics and is its main component [1–3]. Against the background of increasing needs for the intensification of oil production, artificial irrigation, and the safety of the use of hydraulic equipment, there is a need to change many hydromechanical parameters, the implementation of which by experimental methods causes certain difficulties. Therefore, preference is given to theoretical research and development [4]. There is a need in an integrated approach to analysis and development related to the main liquid storage tanks [5]. In order to clarify the mechanism of emptying the vessel and describe the process of unsteady fluid flow through the holes and nozzles, physical and mathematical models have been developed [5–11]. Some of them are based on the assumption of the occurrence of intense funnels, the cause of which is the rotation of the liquid around the axis, which is the center of symmetry of the bottom hole [7–9]. The spontaneous formation of funnels is indicated by experimental results [9, 12]. The idea of funnel formation is stated in the hydrodynamic model of work [13], which assumes the movement of liquid particles along a helical line on curved sections of the trajectory. The mechanism of funnel formation during the emptying of parabolic vessels is proposed in the hydromechanical model [8, 11], which is based on the occurrence of surface forces during the movement of inviscid liquid particles along curved current tubes. Unfortunately, most of the listed physico-mechanical models represent a formal, descriptive development without hidden physical content of the fluid outflow process. There is practically no information about the existing features when emptying tanks of various geometric shapes, in particular, vessels of the shape of a paraboloid of rotation. The paper considers axisymmetric emptying of a container of the shape of a paraboloid of rotation, pre-filled with an inviscid liquid. The existence of a connection between the physical content of the outflow process and the geometry of the reservoir, which includes an economic component, is proved. In addition, a feature of expiration (observed in practice and theoretically confirmed) is of research interest: when emptying parabolic vessels, the level of the free surface decreases uniformly. To explain such an anomaly and obtain analytical dependences of the main parameters of the outflow, a hydrodynamic model is proposed, which is based on the idea of the movement of liquid particles through curved current tubes. They completely fill the axisymmetric flow in the paraboloid, have a curvature increasing from the axis of symmetry to the vessel wall, and are limited by the free surface and the plane of the bottom hole.

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2 Methods As part of the experiment, a container was used, which is a cyclone nozzle for a household vacuum cleaner and meets almost all the parameters of the paraboloid of rotation according to the equation: h = Ar 4 , by A = 4 · 10−5 mm−1 and maximum height h max = Ho = 250 mm and the radius rmax = Ro = 50 mm. To clarify the dependence of the emptying time on the geometric shape of the vessel, similar studies were also carried out with conical and cylindrical tanks with the same overall dimensions and diameter of the bottom hole. The results of the experiment are shown in Fig. 1. This experiment shows that for each diameter of the bottom hole, the emptying time of the parabolic vessel is 2.5 times longer than the conical one, and the emptying of the conical one is 5 times slower than the cylindrical one, although the volume of the 2 2 cylinder (Vu = π 4D H ) only 3 times less than the volume of the cone (VK = π12D H ), 2 and the volume of the paraboloid (Vn = π 8D H ) 1.5 times the volume of the cone. This indicates the relationship between the fluid outflow process and the geometry of the vessel. It should be noted that, starting from the diameter of the bottom hole equal to 6 mm, when emptying the paraboloid, a curvature of the free surface of the liquid was observed, a deflection in the form of a vortex-free funnel can be observed. The Fig. 1 Experimental dependence of the time of complete emptying of vessels of the shape of the surface of rotation on the diameter of the bottom hole

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Fig. 2 Distribution of the axial component of acceleration az on the free surface of the liquid, the filling paraboloid of rotation: 1- undisturbed free surface; 2 - deformed surface (funnel surface)

formation of a funnel can cause the appearance of features of the outflow of liquid from the reservoir of a parabolic shape, as well as a decrease in the level at a constant rate during emptying. Indeed, the formation of a funnel during emptying occurs due to the uneven distribution of the axial component of the acceleration of liquid particles on the free surface, the plot of which is shown in Fig. 2. It can be seen that the acceleration of the particles of the free surface of the liquid az decreases from the maximum on the axis of symmetry to zero on the vessel wall. Such a distribution is satisfied, for example, by the equation:   r2 αz = q 1 − 2 , R

(1)

where q is the acceleration of gravity, r and R are the current and maximum radii of the surface of rotation with the coordinate z. Equation (1) satisfies the pattern of fluid outflow in a water clock (az = 0 by r = R).

3 Results and Discussion It is assumed that the current tubes (elementary trickles), the curvature of which decreases from the vessel wall to the axis of symmetry, completely fill the axisymmetric fluid flow when emptying the paraboloid (Fig. 3). A liquid particle, being in a rectilinear current tube, moves with acceleration directed along the axis of the tube, which balances the pressures at opposite points of the cross section of the elementary trickle. In the places of curvature of the current tube, the particle moves with centripetal acceleration, and the centripetal force acting on it, directed to the center of curvature, leads to the appearance of a pressure gradient on opposite sides of the cross section of the current tube [8]. To describe the experimental results obtained in the work, which is a continuation of the research [8, 11], and to explain the features of emptying the paraboloid,

Hydrodynamics of the Flow of an Ideal Liquid …

229

Fig. 3 Distribution of mass and surface forces acting on a particle of an ideal fluid M moving in an arbitrarily selected stream of axisymmetric flow in coordinates (r, z). Here H0 , r0 , R0 is the overall height, the radius of the paraboloid and the radius of the bottom hole, respectively

a hydrodynamic model is used, which is based on the movement of an inviscid fluid particle along curved current tubes. It is assumed that the curved current tubes (elementary trickles) completely constitute an axisymmetric fluid flow during the emptying of the paraboloid (Fig. 3). Based on the basic equation of dynamics, we obtain a differential equation for particles of an ideal fluid [5, 6]: q − az =

υz2 dr · , r dz

(2)

where dr this value shows the ratio between the level of the free surface and its dz radius. Combining expressions (1) and (2), we obtain an equation describing the cross section of the level of the curved free surface of the liquid flowing through the bottom hole of the parabolic vessel: 2(R 2 − r 2 ) dz = dr z r2

(3)

Solving differential Eq. (3) under boundary conditions r0 ≤ r ≤ R, we obtain the algebraic equation of the free surface: z=H

R2 R2 exp(1 − 2 ), 2 r r

(4)

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where H and R are the height of the liquid level, and the radius of the rotation surface corresponding to the z coordinate. It can be seen that the liquid level in the paraboloid depends on the radius of the surface z. Therefore, the height of the level acquires the meaning of the average value, which is determined by the well known formula [14]: H z = R − r0

  R  2 R R2 exp 1 − 2 dr r r

(5)

r0

Integration (5) leads to the expression for the average value of the free surface level: 

r0 z = H R

2 (6)

Taking into account the expression for the average value (6), it is possible to determine the volume flow of liquid for containers of this shape in the form: Q=

πr03  2g H R

(7)

To calculate the velocity of the liquid level during the emptying of a vessel of parabolic shape, we use the expression for the velocity υz when emptying a vessel of an arbitrary surface of rotation [1]: υz =

 r 2  0 2qz R

(8)

It is known that for vessels of the shape of a paraboloid of rotation υz = const. This means that expression (8) is valid for all z and R, including H 0 and R0 , then:  υz =

r0 R0

2



2q H0 ,

(9)

and the time of complete emptying of the parabolic shaped container is equal to H0 = T0 = υz



r0 R0

2

H0 2q

(10)

It should be noted that the obtained formula (10) is quite suitable for calculating the time of experimental outflow of water from the bottom hole of the paraboloid in accordance with Fig. 1.

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4 Conclusions The presented research materials allow us to highlight the main results: a) experimental studies conducted on emptying pre-filled vessels of various geometric shapes with the same overall dimensions and diameters of bottom holes indicate a connection between the outflow process and the geometric shape of the tank; b) in the process of emptying the paraboloid with small pressures and diameters of the bottom hole greater than 5 mm, a «deflection» of the free surface in the form of a vortex-free funnel is detected; c) the effect of a uniform decrease in the wall boundary of the free surface of the liquid during the emptying of the container was found; d) the mechanism of uniform reduction of the liquid level in the process of emptying the paraboloid is proposed; e) formulas are obtained that are suitable for determining the rate of decrease in the liquid level during the outflow process, and describing the shape of the deformed free surface. The elements of the proposed hydrodynamic model can be useful in mastering academic disciplines using an idealized continuum model.

References 1. Konstantinov AV, Limarchenko OS (2017) Effect of the viscosity and capillarity of fluid on the nonlinear dynamics of a tank partially filled with a fluid. Int Appl Mech 53(2):130–138 2. Rusanov NA, Kitaev DN (2017) Calculation of the time of gravity discharge of light oil products at gas stations, Urban planning. Infrastructure. Communications 2(7):66–72 3. Belonogov OB (2016) Discharge and non-dimensional parameters of fluid Flows in throttles of spool hydraulic valves of electrohydraulic amplifiers. Vestnik Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Mashinostr 5:4–23 4. Buzina VA (2013) Unsteady spatial outflow of gas-saturated liquid from axisymmetric vessels. Vestnik Bashkir University 3(18):636–639 5. Orlov VV, Temnov AN, Tovarnykh GN (2011) Experimental study of the outflow of a rotating fluid, Vestnik Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Mashinostr 2:23–34 6. Kumitskiy BM, Tul’skaya SG, Aparina IA, Sarychev MA (2017) Simulation of fluid flow at variable pressure from a vertical pipeline, Urban planning. Infrastructure. Communications 4(9):19–23 7. Baskakov VD, Zarubina OV, Karnaukhov KA, Tarasov VA (2016) Mathematical modeling of the collision process of plane jets of an ideal liquid, Vestnik Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Mashinostr 2:79–90 8. Kumitskiy BM, Savrasova NA, Afonichev DN (2019) The use of the principles of hydromechanics in solving the problems of water supply to agricultural consumers. Vestnik Voronezh State Agrarian Univ 2(61):84–91 9. Massoudi M (2020) Mathematical modeling of fluid flow and heat transfer in petroleum industries and geothermal applications. Energies 13:1344

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10. Gorlov AS, Gubarev AV, Gorlov KA (2016) Mathematical and simulation modeling of vortex flow in short vortex chambers, Vestnik Belgorod State Technological University named after V. G. Shukhov 9:137–142 11. Kumitskiy BM, Savrasova NA, Likhachev ER (2019) Hydrodynamic model of axisymmetric outflow of an ideal fluid from the bottom hole of a tank shaped like a paraboloid of rotation. Vestnik Dagestan State Univ 1:15–23 12. Kopysov SP, Tonkov LE, Chernova AA (2015) Application of VOF and SPH to solve problems with a developed free surface. Proc Inst Math Comput Sci Udmurt State Univ 2(46):76–84 13. Mazur SV, Strelets VN, Strilest OR, Stepaniuk AA (2017) Fluid movement along the groove in the form of an Archimedes spiral of a rotating ring of a mechanical seal of increased tightness, Vestnik Azov State Technical University. Ser Tech Sci 35:117–123 14. Konstantinov AV, Limarchenko OS, Mel’nik VN, Semenova IY (2017) Generalizing the Faraday problem of the parametric oscillations of a cylindrical tank partially filled with a fluid. Int Appl Mech 53(1):59–66 15. Belashov VY, Kharshiladze OA (2019) The modified method of contour dynamics and modeling of vortical structures, Uchenye Zapiski Kazanskogo Universiteta. Seriya FizikoMatematicheskie Nauki 161(1):5–23 16. Wang T, Faria D, Stevens LJ, Tan JSC, Davidson JF, Wilson DI (2013) Flow patterns and draining films created by horizontal and inclined coherent water jets impinging on vertical walls. Chem Eng Sci 102(1):585–601 17. Yang X (2018) Numerical analysis of water film flow characteristics on the large flat plate. Proc Nuthos 12:655–662

Experimental Study of Deformation of Flexible Timber Compressed Elements Under Environmental Loading Alexey Bulgakov , Jens Otto , Sergei Dubrakov , and Denis Shvartcer

Abstract In the laboratory of Southwest State University, experimental studies were carried out on the stability of the compressed elements of the experimental frames during the subsidence of the base of the middle rack and the influence of the negative properties of the heaving soil on the stability of the compressed elements of the experimental frames. Experimental values of stability parameters of frame-rod timber structures working in conditions of subsidence soils were determined by a specially developed technique. The scheme and general view of the pilot plant are given. The mechanical characteristics of the timber were determined in accordance with the current standards for the determination of physical and mechanical characteristics. The compressed elements of the prototype frames with a cross section of 40 × 30 mm racks and crossbars were tested according to a specially developed technique. The essence of the method under study is explained by drawings. The research program included testing of three series of frame-rod timber structures, three samples in each. Experimental studies of the stability of compressed elements of frame-rod timber structural systems with various coupling conditions were carried out at relatively low economic costs. The results of short-term tests of samples are presented. The significant influence of the negative properties of the heaving and subsidence soils on the critical stability parameters of the compressed elements of the experimental frames is shown. The following conclusion was obtained: Depending on the geometric parameters and the load application scheme, the elements of frame-rod timber structural systems may lose stability. At the same time, taking into account the level of operating stresses, as well as the influence of negative properties of heaving and subsidence soils have a significant impact on the value of critical stability parameters of the systems under consideration. Keywords Frame-rod structures · Critical strength · Stability A. Bulgakov (B) · S. Dubrakov · D. Shvartcer Southwest State University, 50 let Oktyabrya Street 94, 305040 Kursk, Russia e-mail: [email protected] J. Otto Technical University of Dresden, Mommsen Street 10, 01069 Dresden, Germany e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_23

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1 Introduction During the operation of structures, there is a change in the magnitude of the loads acting on the structural elements, as well as a change in the size of sections, a change in natural factors, etc. [1–13]. For structures with timber load-bearing constructions, the critical stability parameters in the structural system depend on many factors, including the level of operating tense [14–16]. In this regard, it is necessary to investigate the deformation of the core elements of structural systems when these factors change in conditions of constrained bifurcation and to establish their influence on the critical stability parameters. An experimental study of the stability of frame-rod timber structures was carried out in order to test the developed calculation apparatus for determining the critical force of compressed timber rods, based on the hypothesis that the relative deficit of the current value of the investigated factor of no equilibrium force resistance of wood is described by a function that is invariant with respect to physical and mechanical characteristics of this material.

2 Methods of Experimental Research. Designs of Experimental Frames The research program included testing of three series of frame-rod timber structures, three samples in each. The main parameters of the experimental frames are given in Table 1, the number of tested structures is taken into account the possibility of statistical processing of research results. The mechanical characteristics of the timber were determined in accordance with the current standards for the determination of physical and mechanical characteristics. Experimental values of stability parameters of frame-rod timber structures working in conditions of subsidence soils were determined by a specially developed technique. The scheme and general view of the pilot plant are shown in Figs. 1, 2, 3, 4 and 5. In an experimental study of the effect of the subsidence of the base on the stability of frame-rod structural systems, a test bench was made on which a structural scheme was assembled in the form of a frame-rod system, support racks with a support beam were fixed, while one of the racks was fixed on a movable part mounted on a screw jack. Crossbars and racks are connected or solidly concreted. Then strain gages are installed on the support racks. Next, the frame-rod system is loaded with a given design static load through a loading device represented by a lever system. Next, with the help of a screw jack, the movable part of the support beam is lowered, thereby creating an artificial subsidence of the base. The result of this study is the ability to accurately determine the load at which the load-bearing element of the tested structural system is switched off.

150,0 4 3,00

9 16 0,8660

1,15 173,21

Length, cm

Height, cm

Width, cm

Moment of inertia min

Moment of inertia max

Radius of inertia min

Radius of inertia max

Flexibility

Loading scheme of the experimental frame

Р-2

Series

Table 1 Main parameters of experimental samples of frames

173,21

1,15

0,8660

16

9

3,00

4

150,0

Р-1

Loading scheme of the experimental frame

Flexibility

Radius of inertia max

Radius of inertia min

Moment of inertia max

Moment of inertia min

Width, cm

Height, cm

Length, cm

Series

Experimental Study of Deformation of Flexible Timber Compressed Elements … 235

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Fig. 1 Experimental setup diagram

Fig. 2 Diagram of an experimental setup for studying the effect of base deformations on critical stability parameters

The essence of the method under study is explained by the drawings, which show the structural diagrams of the lever system and the frame-rod structure. The lever system (Fig. 1) consists of: 1-support beam, 2-lever-load system, 3-support racks, 4-cargo platform. Frame-rod construction consists of: 1-distribution beam, 2-support posts, 3-frame crossbars, 4-support beam, 5-switch-off rack, 6-movable part of the support beam, 7-screw jack.

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Fig. 3 Experimental setup diagram

Fig. 4 General view of the installation for assessing the stability of frame-rod timber structural systems

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Fig. 5 General view of the installation for assessing the stability of frame-rod timber structural systems

The experiment is carried out as follows. Support posts 2 are fixed (see Fig. 2) using a support beam 4. Crossbars 3 and posts 2 are connected or solidly concreted. One of the racks 5 is fixed to the movable part of the support beam 6 mounted on a screw jack 7. The reinforced concrete frame-rod system and, accordingly, its racks are loaded with a given design static load using a lever system through the distribution beam 1. The movable part of the support beam 6 is lowered with a screw jack 7, thereby creating an artificial subsidence of the base. With the help of strain gages mounted fixed on support posts 2, the load is measured, at which the loss of stability of one of the elements of the tested structural system occurs. During the experiment, deformations of the upper fibers are recorded using strain gauges mounted on the surface of the frame racks. The deflection and change in the length of the rod during loading was measured by an electronic deflection meter. Thus, with the help of the described installation, a compressive force N is created in the racks of the experimental frame. This makes it possible, by increasing the load, to investigate the stability of the compressed elements of the frame-rod timber structural system. The device for experimental determination of the critical strength of the core elements of timber frames allows experimental studies of the stability of compressed elements of frame-core structural timber systems with various coupling conditions at relatively low economic costs.

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2.1 Stability of the Compressed Elements of the Experimental Frames During Subsidence of the Base of the Middle Rack Experimental studies of the stability of experimental samples of frames for qualitative and quantitative assessment of analytical dependencies were carried out in the laboratory of the Department of PGS of Southwest State University. The compressed elements of the prototype frames with a cross section of 40 × 30 mm racks and crossbars were tested for central compression according to a specially developed technique [13–16]. The graph of the results is shown in Fig. 6. When compiling Tables 2, 3, 4 and 5, based on the results of experiments, the following were determined: the average value of the critical force: n Pκp =

i

Pκp,i , n

(1)

Pκp,i · pi ,

(2)

where n is the number of tests; mathematical expectation: E(x) =

n i

where p_i—probability of critical force value P_(kp,i);

Fig. 6 Results of the study of the influence of the subsidence of the base of the central rack of frames of the P-1, P-2, P-3 series on the value of the critical force

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A. Bulgakov et al.

Table 2 Test results of the R-1 series frames Length, cm

Height cm

Width cm

Mom. in. min

Mom. in. max

Radius in. min

Radius in. max

Flexibility

Euler. Power, kN

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

817,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

812,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

810,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

818,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

807,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

805,00

Average value

811,50

Mean square deviation

11,73

Coefficient of variation

1,44

The standard deviation of the mean value

4,79

Critical force with a confidence probability of 0.95

802,12

Table 3 Results of the study of the effect of the critical subsidence of the base of the central rack of the P-1 series frames Length, cm

Height cm

Width cm

Mom. in. min

Mom. in. max

Radius in. min

Radius in. max

Flexibility

Critical drawdown of Ssl, cr. at α = 1, mm

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

31,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

35,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

34,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

31,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

29,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

32,00

Average value

32,00

Mean square deviation

4,90

Coefficient of variation

15,31

The standard deviation of the mean value

2,00

Critical Ssl drawdown,kr. with a confidence probability of 0.95

28,08

Standard deviation:  σ =

2 n  i Pκp − Pκp,i . n−1

(3)

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241

Table 4 Results of the study of the effect of the critical subsidence of the base of the central rack of the P-2 series frames Length, cm

Height cm

Width, cm

Mom. in. Min

Mom. in. Max

Radius in. min

Radius in. max

Flexibility

Critical drawdown Ssl, cr. at α = 0.8, mm

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

19,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

21,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

22,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

23,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

20,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

22,00

Average value

21,17

Mean square deviation

3,29

Coefficient of variation

15,55

The standard deviation of the mean value

1,34

Critical Ssl drawdown,kr. with a confidence probability of 0.95

18,53

Table 5 Results of the study of the influence of the critical subsidence of the base of the central rack of the P-3 series frames Length, cm

Height, cm

Width, cm

Mom. in. min

Mom. in. max

Radius in. min

Radius in. max

Flexibility

Critical drawdown Ssl, cr. at α = 0,6, mm

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

72,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

70,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

69,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

74,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

73,00

150,00

4

3,00

9

16

0.8660

1,1547

173,2051

71,00

Average value

71,50

Mean square deviation

4,18

Coefficient of variation

5,85

The standard deviation of the mean value

1,71

Critical Ssl drawdown,kr. with a confidence probability of 0.95

68,15

the standard deviation of the mean value: σ σR = √ , n coefficient of variation:

(4)

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V =

σ . x

(5)

The value of the critical force with probability p = 0.99 was determined by the formula: x = x − σr · t,

(6)

where t—Student’s coefficient, determined according to Table D.1 GOST R 8.7362011.

2.2 Investigation of the Influence of the Negative Properties of the Heaving Soil on the Stability of the Compressed Elements of the Experimental Frames A qualitative assessment of the above analytical dependencies was carried out in relation to the study of the influence of the heaving properties of the foundation soil on the stability of experimental frames in the laboratory of Southwestern State University. Experimental frames with a cross section of racks and crossbars 40 × 30 mm with a span of 1.5 m were tested for central compression according to a specially developed technique [13–16]. The graph of the results is shown in Fig. 7. Fig. 7 Results of the study of the influence of the negative properties of the heaving soil of the base of the central rack of the frames of the P-1, P-2, P-3 series on the value of the critical force

Experimental Study of Deformation of Flexible Timber Compressed Elements …

243

The results obtained and presented in the Tables 6, 7 and 8 show a significant influence of the negative properties of the heaving and subsidence soils on the critical stability parameters of the compressed elements of the experimental frames. Table 6 Results of the study of the influence of the negative properties of the heaving soil of the base of the central rack of the P-1 series frames on the value of the critical force Length, cm

Height cm

Width, cm

Mom. in. min

Mom. in. max

Radius in. min

Radius in. max

Flexibility

Critical heave deformation  cr., at α = 1, mm

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

81,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

84,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

82,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

83,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

81,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

82,00

Average value

82,17

Mean square deviation

2,61

Coefficient of variation

3,18

The standard deviation of the mean value

1,07

Critical heave deformation cr. with a confidence probability of 0.95

80,07

Table 7 Results of the study of the influence of the negative properties of the heaving soil of the base of the central rack of the P-2 series frames on the value of the critical force Length, cm

Height cm

Width, cm

Mom. in. Min

Mom. in. Max

Radius in. min

Radius in. max

Flexibility

Critical heave deformation  cr., at α = 0,8, mm

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

28,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

29,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

30,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

32,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

30,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

32,00

Average value

30,17

Mean square deviation

3,58

Coefficient of variation

11,88

The standard deviation of the mean value

1,46

Critical heave deformation cr. with a confidence probability of 0.95

27,30

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Table 8 Results of the study of the influence of the negative properties of the heaving soil of the base of the central rack of the P-3 series frames on the value of the critical force Length, cm

Height cm

Width, cm

Mom. in. min

Mom. in. max

Radius in. min

Radius in. max

Flexibility

Critical heave deformation  cr., at α = 0,6, mm

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

40,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

38,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

42,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

40,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

38,00

150,00

4

3,00

9

16

0,8660

1,1547

173,2051

41,00

Average value

39,83

Mean square deviation

3,58

Coefficient of variation

8,99

The standard deviation of the mean value

1,46

Critical heave deformation cr. with a confidence probability of 0.95

36,97

3 Conclusions According to the results of experimental studies of the stability of the compressed elements of the experimental frames with the subsidence of the base of the middle rack, it was found that the critical drawdown decreases at 1 ≥ α ≥ 0.85, and at α < 0.85 the critical drawdown increases. According to the results of an experimental study of the influence of the negative properties of the heaving soil on the stability of the compressed elements of the experimental frames, it was revealed that the critical heave deformation decreases at 1 ≥ α ≥ 0.75, and at α < 0.85 the critical heave deformation increases. Based on numerical studies, the following conclusion can be drawn: Depending on the geometric parameters and the load application scheme, the elements of frame-rod timber structural systems may lose stability. At the same time, taking into account the level of operating stresses, as well as the influence of negative properties of heaving and subsidence soils have a significant impact on the value of critical stability parameters of the systems under consideration.

References 1. Alexandrov AV, Travush VI, Matveev AV (2004) Investigation of the stability of the structures of the arched covering of the hall using the criteria for identifying the most dangerous elements. Bulletin of the Department of construction Sciences RAACS, pp 14–21

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2. Alexandrov AV, Matveev AV (2003) Criteria for the identification of the most hazardous elements and their use in problems of stability of structures. In: Traffic Safety of Trains: 4th Conference 2003, FSAEIHE 3. Alexandrov AV, Travush VI, Matveev AV (2002) On the calculation of core structures for stability. Ind Civ Constr 16–20 4. Alexandrov AV (2001) The role of individual elements of the core system in the loss of stability. Bulletin FSAEIHE, vol 46 5. Dmitrieva KO, Klyueva NV (2016) Questions of stability of core elements of structural timber systems under force and environmental loading. Constr Reconstr 13–18 6. Dubrakova KO (2018) Issues of stability of statically indeterminate timber systems. Bull Constr Mach 54–55 7. Klyueva NV, Dmitrieva KO (2016) Stability analysis of core timber structures under force loading and variable humidity. Sci Bull Voronezh State Univ Archit Civ Eng Constr Archit 17–24 8. Klyueva NV, Dmitrieva KO (2016) Issues of stability of core elements of structural timber systems of various breeds under power and environmental loading in conditions of high humidity. Constr Reconstr 60–68 9. Morchkov AA, Orlov DA, Kereb SA, Baranovskaya KO (2013) Safety of glued timber structures at the manufacturing stage. Ind Civ Constr 74–75 10. Travush VI, Kolchunov VI, Dmitrieva KO (2015) Long-term strength and stability of compressed timber rods. Constr Reconstr 40–46 11. Travush VI, Kolchunov VI, Dmitrieva KO (2016) Stability of compressed timber rods with simultaneous manifestation of force and environmental effects. Constr Mech Calculation Struct 50–53 12. Travush VI, Kolchunov VI, Dmitrieva KO (2016) Experimental and theoretical study of the strength and stability of compressed timber rods under force and environmental impact. News of higher educational institutions. Technol Textile Ind 280–285 13. Matveev AV (2002) Some issues of creating a specialized software package for the analysis of bridge structures. Bull FSAEIHE 76–83 14. Pyatikrestovsky KP, Travush VI (2015) On programming a nonlinear method for calculating timber structures. Academia. Archit Constr 115–119 15. Pyatikrestovsky KP, Khuganov HS (2013) Nonlinear deformations of statically indeterminate timber structures. Izvestia of higher educational institutions. Construction 21–30 16. Pyatikrestovsky KP (2014) Nonlinear methods of mechanics in the design of modern timber structures, vol 320. MGSU

Hardening Mode and Foam Concrete Properties Mikhail Novikov , Andrey Goykalov , Elvira Semenova , and Vladislav Pakhomov

Abstract The results of experimental studies of mechanical properties of cement foam concrete with average density from 1200 to 1600 kg/m3 at different age and for different hardening conditions are presented. Concrete hardening took place in an unloaded state in laboratory conditions, under conditions of long-term load action and under conditions of natural physical-climatic actions, when the material was affected by degradation processes from humidification, drying, freezing–thawing, carbonization. The mechanical properties of foam concrete were determined according to standard test methods. It was found that during hardening in laboratory conditions in non-autoclave cement foam concrete there is a greater increase in strength and modulus of elasticity in time than during hardening in full-scale conditions, and the greater the lower the average density of concrete. The effect of strengthening foam concrete under the influence of a long-term applied load with respect to the same concrete, which was in the same temperature and humidity conditions, but without the load, was revealed. Keywords Foam concrete · Strength · Modulus of elasticity · Deformation · Mechanical properties · Central compression · Long-term tests

1 Introduction The need for inexpensive and heat-efficient construction material requires the creation of new and co-improvement of existing technologies and equipment for its production. The construction materials that most fully satisfy the requirements of modern conditions include the so-called, hardest in normal conditions porous concrete (hereinafter foamed concrete), the macroporosity of which is provided by air entrainment with stirring in the presence of modern high-efficiency surface-active M. Novikov (B) · A. Goykalov · E. Semenova Voronezh State Technical University, Moskovsky prospekt, 14, 394026 Voronezh, Russia e-mail: [email protected] V. Pakhomov Southwest State University, 94, 50 Let Oktyabrya ul., Kursk 305040, Russia © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_24

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additives [1–3]. According to the technical and economic indicators of production and use, monolithic foam concrete is one of the most competitive materials at present [4–8]. However, the widespread use of new generation non-autoclave cement foam concrete in modern construction is constrained by the unresolved problems of rationing its construction and technical properties. Foam concrete as a building material for load-bearing and enclosing structures of buildings shall have long-term operational reliability under conditions of constant impact of operating environment and mechanical loads. It is known [9–11] that the hardening of concrete is influenced by many factors: the type and grade of cement, the composition of concrete, the value of the water cement ratio, the type and type of additives, humidity and tempera-tour of the environment. Concrete hardening is subject to certain laws. The general law of concrete strength increase is gradual decrease of strength growth intensity with increase of concrete age. When subjected to freezing–thawing, saturation-drying cycles, the process of destruction of concrete is accelerated. Many works of domestic and foreign researchers were devoted to the influence of these factors on the structure of concrete and the rate of strength growth [12–18]. In this regard, of particular interest is the study of the strength and deformation properties of foam concrete over time during their hardening. The process of hardening cement in foam tones in the presence of surfactants known to be retardants of melting and hardening requires further study. Thus, in view of the variety of factors influencing the growth of the strength and modulus of foam concrete elasticity over time, accurate quantification of their increase requires special experiments. Therefore, the purpose of the present work was to study the time variation of the strength and deformation properties of foam concrete during its hardening under various conditions. The object of the study was cement fine-grained and micro-grained foam concrete of natural hardening with an average dense-style of 1200 to 1600 kg/m3 . The experimental studies have been carried out using the facilities of the Collective Research Center named after Professor Yu. M. Borisov, Voronezh State Technical University, which is partly supported by the Ministry of Science and Education of the Russian Federation, Project No 075- 15-2021-662.

2 Materials and Methods Foam concrete of two modifications in the spectrum of densities of 1200–1600 kg/m3 was subjected to research: fine-grained natural granulometry on quartz sand and micro-grained concrete on fly ash. The matrix material was dense concrete made without the use of an air-entrapping additive. As raw materials for the manufacture of concrete samples, the following were used: Portland cement of the brand PC-500DO; “Penostrom” air-entrapping surfactant; ash-fly with Sud = 300 m2 /kg was used as filler for micro-grained concrete,

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249

quartz sand with Mk = 1.4 was used for fine-grained concrete. The concrete composition according to the cement-filler ratio was considered optimal to ensure minimum shrinkage and increased crack resistance, according to the results of previous studies [19–20]. For these types of concrete, the cubic and prism strengths, the up-range modulus, the Poisson coefficient and the ultimate compressibility under short-term load were experimentally evaluated. Their values were determined according to standard methods on sample cubes with a size of 100 × 100 × 100 mm and sample prisms with a size of 100 × 100 × 400 mm at a certain age after their manufacture. Based on the results of tests of concrete samples, graphs of changes in concrete properties over time were built (Fig. 1). The change in these characteristics over time was evaluated with dimensionless coefficients representing their ratio in the 1-year to 28-day age considered (Table 1). At the same time, the average values of the characteristics of experimental data are shown in the graphs and in the table.

40 R, МPа

D 1700 30

D 1600

20

D 1400

10

D 1200

Rb, МPа

0 30 0

100

200

300

D1600

20

D 1400 10

D 1200

0 15 0 Еb·103, МPа

400 D 1700

100

200

300

400 D 1700 D 1600 D 1400 D 1200

100

200

300

400

10 5 0 0

Duration of hardening, day

Fig. 1 Kinetics of changing properties of micro-grained concrete over time

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Table 1 Results of testing of foam concrete properties in time Look structures foam concrete

Grade by average density

Cube strength R365 /R28

Prism strength Rb 365 /Rb 28

Modulus of elasticity Eb 365 /Eb 28

Poisson’s ratio m365 / m28

Ultimate compressibility εub 365 /εub 28

Rb 365 /Rb 28 after creep

Fine-grained

D1200

1.34

1.36

1.24

0.94

0.89

1.58

D1400

1.27

1.28

1.18

0.98

0.90

1.47

D1600

1.23

1.2

1.14

1.02

0.91

1.3

Plotn.

1.15

1.14

1.09

0.95

0.9

1.19

D1200

1.5

1.54

1.38

0.97

0.85

1.76

D1400

1.44

1.41

1.26

1.04

0.87

1.58

D1600

1.32

1.30

1.24

0.95

0.88

1.43

Plotn

1.20

1.21

1.15

1.01

0.88

1.36

Microgranular

Once and temporarily, with control prisms stored in laboratory conditions, prisms were tested that were observed for a long time under the influence of load, which made it possible to identify the effect of long-term loading on the short-term strength and modulus of elasticity of concrete. Deformations of prism samples were measured by tensoresistors with a base of 50 mm glued to samples in the center of each side face, as well as using hour-type indicators. The readings of the sensors were taken by a strain gauge at each loading stage, which was 0.1 of the destructive load. Studies of foam concrete with an average density of 1200 kg/m3 , hardened for 15 years under natural environmental conditions, deserve special attention. Tests were carried out on cubes and prisms of a similar size, sawn from monolithically molded masses of walls 400 mm thick.

3 Results and Discission Based on the results of the studies, it was established that foam concrete and concrete of a dense structure on different types of aggregate gain strength and increase the modulus of elasticity in time during hardening in laboratory conditions (Fig. 1, Table 1). The annual increase in strength and modulus of elasticity of foam concrete on fly ash is more than that of foam concrete on quartz sand comparable in average density by 10% on average, and the value of increase with increase in average density decreased. This phenomenon is explained by the relatively higher hydraulic activity and water release of the concrete on the fly ash, and therefore by the better humidity conditions under which the hardening concrete structure was located. For fine and micro-grained concretes of a dense structure, the strength to 365 days increased by 15–20%, and the modulus of elasticity by 10–15%. For foam concrete, depending on the type of aggregate, the strength and modulus of the up-depth increased significantly (respectively by 20–50% and 15–40%) and the more, the lower the average density of concrete. This nature of growth of strain-strength characteristics of foam concrete is explained by the fact that air-entrapping additives slow

Hardening Mode and Foam Concrete Properties

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cement hardening at an early age of concrete. Therefore, with prolonged hardening, the cement stone with additives increases its strength and modulus of elasticity to a greater extent. The results of the change in the strength of foam concrete over time were quite successfully approximated by the exponential dependence: R(t) = R0 [1 − b1 · e−a1 t − b2 · e−a2 t ],

(1)

where t - age of concrete, days; R0 - limit value of concrete strength, MPa; b and a -parameters determined from experience. To describe the change in the elasticity modulus of foam concrete E(t) over time, a similar expo-non-social relationship (1) was adopted, replacing R(t) and R0 with E(t) and E0 , respectively. Quantitatively, the functions R(t) and E(t) and the rate of their approximation to the limit values should be judged by the data of Table 2. As can be seen from the comparison of the given results, the maximum deviation of experimental data from the values determined by formula (1) does not exceed 5%, and the standard deviation for the entire observation period is 1%. Compression strength of foam concrete grades D1200 on sand of natural granulometry, ground sand and with the addition of fly ash, hardened in natural conditions, Table 2 Parameter values for expression (1) Predicted value

Cube strength

Parameters

Fine-grained

Modulus of elasticity

Microgranular

D1200

D1400

D1600

dense

D1200

D1400

D1600

dense

R0 , MPa a1 , day−1 a2 , day−1

8.0

16.3

23.3

51.2

10.6

21.2

30.1

32.3

0.0035

0.003

0.0026

0.003

0.0035

0.004

0.0035

0.0035

0.074

0.088

0.080

0.09

0.075

0.095

0.081

0.08

b1

0.19

0.21

0.15

0.10

0.28

0.33

0.21

0.10

b2

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

−2.70 0.112

+3.07 0.283

−3.41 0.560

−2.35 0.716

−2.61 0.125

−2.00 0.167

−3.54 0.420

−3.84 0.614

13.9

19.4

41.7

10.6

18.1

25.3

27.3

Deviation in % Prism strenght

Structure type and grade by average density of concrete

R0 , MPa a1 , day−1 a2 , day−1

7.3 0.003

0.003

0.002

0.003

0.004

0.004

0.0033

0.004

0.074

0.080

0.077

0.085

0.086

0.084

0.084

0.084

b1

0.21

0.19

0.12

0.07

0.37

0.28

0.20

0.12

b2

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

Deviation in %

−4.02 0.128

−4.48 0.300

+4.14 0.480

−3.63 0.794

+2.61 0.096

−2.50 0.264

−1.49 0.273

−1.68 0.227

E0 · 103 , MPa a1 , day−1 a2 , day−1

7.5

12.4

16.4

28.7

11.6

12.9

5.9

8.7

0.004

0.0045

0.0052

0.006

0.005

0.005

0.005

0.006

0.076

0.135

0.14

0.13

0.10

0.10

0.10

0.10

b1

0.19

0.19

0.18

0.07

0.36

0.26

0.22

0.10

b2

0.50

1.00

1.00

1.00

0.36

0.65

0.75

1.00

-2.76 0.082

-1.06 0.072

+3.47 0.233

+0.95 0.121

+1.52 0.049

+3.00 0.095

-2.31 0.142

-1.24 0.111

Deviation in %

M. Novikov et al.

R, МPа

252

-o-

Duration of hardening lg(t), day Fig. 2 Increase in compression strength of foam concrete over time D1200 natural hardening

increased over the year compared to the design 28-day age, respectively, by 1.2, 1.15 and 1.1 times, and over 15 years increased by 1.5, 1.4 and 1.3 times, respectively. A graphical interpretation of this change is shown in Fig. 2. A graphical interpretation of this change is shown in Fig. 2. It is noted that the strength of natural hardening concrete on ash is less than the strength of foam concrete on sand by 25% at the age of 28 days, by 30% at the age of 1 year and by 35% at the age of 15 years, and therefore less and the value of strength gain over time. Analysis of the results of the studies shows that foam concrete hardened in laboratory conditions at quasi-stationary parameters of temperature and humidity has a higher increase in compression strength than the foam concrete equal in average density, which was in natural physical and climatic conditions during periodic humidification-drying, freezing–thawing. The greater increase in strength in foam concrete hardened in laboratory conditions is explained by the better conditions for cement hydration. The effect of hardening time on the deformation of foam concrete during axial compression is represented by the characteristic diagrams in Fig. 3. In all types of foam concrete, the inclination angle of the curves of longitudinal and pop-river deformations to the horizontal axis increased, which indicates a decrease in deformability and an increase in the modulus of elasticity. Poisson coefficient during concrete hardening changed slightly, in media within 5%. Compared with the initial (28 days after manufacture) deformations, pre-single compressibility decreased by an average of 10% in fine-grained foam concrete and by 13% in micro-grained. Plastic deformations of fast-flowing creep with a load of less than 0.3–0.4 Rb have practically disappeared. Thus, these temporary resistance loads are nothing more than limits of concrete elasticity, which increase during the year by an average of 10 and 15%, respectively, for fine and micro-grained foam concrete. As for natural hardening foam concrete, its elasticity limit for 15 years has increased to a relative level of 0.7 and 0.6 of the temporary resistance, respectively, for fine and micro-grained concrete.

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253

σb, МПа 10

8

6

4

2

1

4

2 3

5 6

0 -50

0

+ l2 · 105

50

100

150

200

250

– l1 · 105

Fig. 3 Foamed concrete compression strain diagram using D1200 grade example: 1, 2, 3 - fine foam concrete, respectively, at age 28 days, 1 year and 15 years; 4, 5, 6 - micro-grained foam concrete, respectively, at the age of 28 days, 1 year and 15 years

After the prism creep test at a load of 0.3 Rb , the strength of fine-grained concrete increased by 20–60%, and micro-grained concrete by 35–75%, especially significantly in foam concrete with a lower average density. Here is given the ratio of prism strength at the end of loading to the strength at the beginning of loading. Comparative data on the strength of prisms under load and previously nena-loaded make it possible to conclude that the increase in the strength of prisms under load was on average 12% for both fine and micro-grained foam concrete. It should be noted that the effect of increasing the strength under the influence of a long-acting load for concretes of lower average density is higher than for concretes of higher density. Thus, the experiments revealed a natural strengthening of foam concrete under the influence of a long-term applied load with respect to the same concrete, which was in the same temperature and humidity conditions, but without the load.

4 Conclusions 1. When hardening in laboratory and natural physical and climatic conditions, foam concrete of all compositions shows a steady increase in strength and modulus of elasticity over time and the greater the lower the average density of concrete.

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2. A natural hardening of foam concrete was revealed under the influence of a longterm applied load on the same concrete, which was in the same temperature and humidity conditions, but without load. 3. Due to the increase in strength and modulus of elasticity in time, the initial provision of normative and design resistance of foam concrete to compression and, therefore, bearing capacity of structures from it is increased. This makes it possible to increase its characteristics when calculating structures for the first group of limit states by 5–10%. In addition, this creates a prerequisite for reducing the consumption of reinforcement or cement without reducing the bearing capacity of the structure. 4. Thus, the properties of non-autoclave cement foam concrete on various types of aggregate improve over time, which characterizes it as a reliable and promising structural and structural-thermal insulation material.

References 1. Novikov MV, Chernyshov EE, Prokshits EE (2021) Key Eng Mater 887:711–717 2. Novikov MV, Prokshits EE, Goykalov AN (2018) in Solid State Phenomena (Trans Tech Publications Ltd, 2018), pp 936–943 3. Novikov MV, Sotnikova OA, Goikalov AN (2021) Engineering and Construction Bulletin of the Caspian Region 112:05–10 4. Zuhua Z, John L, Provis B, Andrew R, Hao W (2014) Constr Build Mater 56:113 5. Colangelo F et al (2018) Mechanical and thermal properties of lightweight geopolymer composites 86:266–272 6. Remnev VV (2020) Bulletin of SRC Stroitelstvo 1(24):91–97 7. Lee SJ, Eom TS, Yu E (2021) Int J Concr Struct Mater 15 8. Piriev YS, Pirieva YL (2014) Ind Civ Eng 8:25–27 9. Pi T, Du Z, Zhang H, Wang S (2021) Int J Concr Struct Mater 15 10. Chernousov NN, Chernousov RN, Suxanov AV, Bondarev BA (2015) Russian J Build Constr Archit 1(37):41–50 11. Vesova LM (2019) Materials Science Forum 945:76–79 12. Rakhimbayev SHM, Anikanova TV, Pogromsky AS (2020) Chemistry, Physics and Mechanics of Materials 2(25):4–16 13. Rakhimbayev SHM, Tolypina NM, Khakhaleva EN, Tolypin DA (2021) Mater Sci Forum 1017:133–142 14. Rybakov V, Smirnov A, Volkova A, Seliverstov A, Petrov D in (EDP Sciences, 2018), pp 3–15 15. Berlinov M, Berlinova M (2016) MATEC Web of Conferences, p 04014 16. Sharanova AV, Lenkova DA, Panfilova AD (2018) In: IOP Conference Series: Materials Science and Engineering (Institute of Physics Publishing, 2018), p 012014 17. Rakhimbaev SHM, Polovneva AV, Rakhimbaev IS (2013) Middle East J Sci Res 11:1640–1645 18. Slavcheva GS, Chernyshov EM (2016) Stroitel’nye materialy 9:58–64 19. Slavcheva GS, Buimarova TK (2020) The Far Eastern Federal University: School of Engineering Bulletin 2(43):124–131

Two-Dimensional Temperature Fields of Variants Design of a Double-Skin Facade Structure Angelina Tkachuk , Elina Umerenkova , Andrey Goikalov , and Mikhail Novikov

Abstract The use of a double facade structure in cold climates is relevant today. The global interest in the Arctic territories requires a new approach to design, which will ensure the sustainability of these regions. The promising Double-Skin Facad design predicts a solution to a range of problems. But, it is worth noting that this design has been little studied and requires scientific substantiation. A study was made of the effect of the width of the buffer zone of the double facade on the results of thermal engineering calculations of two-dimensional temperature fields. The Arctic city of Murmansk was chosen as the base region for the study. Six variants of the construction of the “floor—outer wall” node were considered. Thermal calculations for each of the options were performed using the Elcut 6.4 software. The calculation results are summarized in a single table and confirm the hypothesis of the relevance of using a double facade structure in a cold region. The relationship between the width of the buffer zone and the thermal conductivity of the double facade structure is found. With an increase in the buffer zone, the average temperature of the two inner surfaces increases systemically, and, accordingly, the difference in their temperatures decreases. The Double-Skin Facad creates the self-illuminated effect required for the Arctic regions and demonstrates sufficient energy efficiency. Keywords Heat engineering · Double skin facade · Thermal conductivity · Energy saving · Arctic regions · Lighting · Architecture

1 Introduction Today, interest in the Arctic is on the world level. This territory is a clash of economic, geopolitical and strategic interests of the leading powers of the world, which in their zeal are ready to invest in these territories. This interest is due to the broad prospect A. Tkachuk (B) · A. Goikalov · M. Novikov Voronezh State Technical University, Moskovsky prospekt, 14, 394026 Voronezh, Russia e-mail: [email protected] E. Umerenkova Southwest State University, 94, 50 Let Oktyabrya ul., Kursk 305040, Russia © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_25

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of these regions with the richest potential, including in the transport, food and energy sectors. However, many Arctic regions do not have a stable situation of the migration issue, often tending to negative migration [1]. This problem is often associated with the low quality of the social component of such regions. The problem of social sustainability of the Arctic regions is influenced by various factors, including the natural features of the geographical location of the territories. One of which is the polar night, its duration at the North Pole is six months. In this case, in terms of architecture, we need a new look at combining the utilitarian function of a building, combining solutions for energy saving and architectural lighting. One such solution is the Double Skin Facade. It is a multi-layer construction of an outer and inner glass circuit with an air gap between them. The external circuit protects against thermal, solar, aerodynamic, acoustic and other influences, ensuring a favorable quality of the internal environment in buildings through natural ventilation, daylight, the required level of sound insulation, heat and solar energy control [2–4]. According to the method “The method for evaluation the characteristics of architectural lighting of buildings” [5] Double Skin Facade refers to the lighting of architecture on the principle of “self-illuminated” buildings. In this project, the double façade takes on this role. Scientists all over the world are interested in the design of the double façade and its energy saving effect. In work [6], the average value for saving thermal energy by double facades is given, which is 33%. Analytical studies [7] have established energy savings from 10 to 50%. The authors of the studies [8] obtained energy savings of 70.5, 27.6 and 31% for different regions, respectively. The energy efficiency of this design is mainly ensured by the formation of an air gap between the two contours of the wall. Energy saving is achieved by returning a part of the lost heat to the room from the outer fences in winter and by increasing the heat transfer resistance of the outer fencing when installing closed air layers in the summer. The Double-Skin Facad is the subject of this study based on the above. The purpose of which is to substantiate and prove the advantages of this design in relation to cold climatic regions and to identify the most optimal design, including the width of the buffer zone.

2 Methods Within the framework of this article, for the study of two-dimensional temperature fields of the variant design of the structure of a double glass facade, the base region was chosen—the Arctic city of Murmansk. Murmansk is the largest city in the world beyond the Arctic Circle, which is a major maritime transport hub and fishing center of Russia, occupying a leading position in the region’s economy, as well as its financial, business and cultural center.

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According to the schematic map of climatic zoning for construction On the territory of Russia, the city of Murmansk is confined to region II, subdistrict II A. The city of Murmansk is located in a rather severe subarctic zone in terms of climatic conditions. But due to the influence of the warm North Cape Current, which is a continuation of the Gulf Stream, its climate is characterized as temperate with relatively cool, wet summers, high air humidity, high clouds and monsoon winds. An important condition for the formation of the climate of Murmansk is the inflow of total solar radiation. The midday sun height ranges from 0 (the sun does not rise above the horizon during the polar night) to 440 (during the polar day). The length of the day ranges from 0 to 24 h. The polar night in Murmansk begins on November 29 and ends on January 13, i.e. lasts 44 days, and the polar day—from May 22 to August 22—lasts more than 2 months. The total inflow of total radiation to the horizontal surface per year is 61.4 kcal/cm2 . It changes from 0 in December up to 13.1 kcal/cm2 in June. At the same time, the percentage of the possible total radiation for the year is 56%, and in March and April, due to the decrease in cloudiness, it reaches 70–71%. The radiation balance is negative throughout the winter and in the second half of autumn (from September to March inclusive), i.e. the underlying surface loses more heat from radiation than it receives from the sun; in the rest of the year, the opposite phenomenon occurs. The radiation balance for the year is equal to 14.7 kcal/cm2 . Within the framework of this study, a thermal engineering calculation of twodimensional temperature fields was carried out according to the presented design options (Fig. 1). The following values were taken in the calculations: {{1}}—indoor air temperature 20 °C; – outdoor air temperature −27 °C (corresponds to the temperature of a cold fiveday period with a provision of 0.92 for Murmansk according to Russian Code of Rules (SP) 131.13330.2020); – αv = 8.7 W/(m * o C) (Russian Code of Rules (SP) 131.13330.2020); – αn = 23 W/(m * o C) (Russian Code of Rules (SP) 131.13330.2020); – to determine the dew point air humidity is taken equal to 55% (rel.), in accordance with the sanitary and hygienic requirement SP 50.13330.2012; – humidity regime of premises—normal (Russian Code of Rules (SP) 131.13330.2020); – area of humidity—wet (Russian Code of Rules (SP) 131.13330.2020); – operating condition—B (Russian Code of Rules (SP) 131.13330.2020); – standardized temperature difference tn = 4.5 °C (Table 5, Russian Code of Rules (SP) 131.13330.2020).

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Fig. 1 Variants of the construction of the slab assembly. Outer wall

Accepted indoor temperature and humidity its air corresponds to a dew point temperature of 10.7 °C. Coefficients of thermal conductivity taken in the calculation: – – – –

reinforced concrete monolithic floor: λ = 1.92 W/(m * o C); masonry from gas silicate blocks: λ = 0.18 W/(m * o C); Channel Glass: λ = 0.49 W/(m * o C); buffer zone (air): λ = 0.0259 W/(m * o C).

Today, the separation of the bearing and heat-insulating functions of building materials in building structures is the basis of the concept of a heat-efficient building and increasing the level of its thermal protection [9–11]. The normalized value of the reduced resistance to heat transfer of the enclosing structure, R0nor m , m2 * C/W, should be determined by the formula:

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m Rnor = Rtr0 × mr , 0

(1)

where R0tr is the base value of the required resistance to heat transfer of the enclosing structure, m2 * °C/W, should be taken depending on the degree-day of the heating period, GSOP, °C * day/year, the construction region and determined according to Table 3 Russian Code of Rules (SP) 60.13330.2020; mr —coefficient taking into account the peculiarities of the construction region. Within the framework of these studies, the main goal was to justify the use of a double facade design with the identification of the most optimal width of the buffer zone, taking into account the fulfillment of the sanitary and hygienic requirements (clause 5.7 of Russian Code of Rules (SP) 50.13330.2020), which regulates that the surface temperature should be higher than the dew point under design conditions … The studies were carried out by calculating the temperature fields of structures. All calculations to reduce the number of nodes are logically fragmented along the axis of symmetry. The Elcut 6.4 software was used for calculations [12, 13].

2.1 Heat Engineering Calculation of Option 1. Gas Silicate Masonry (400 mm) Figure 2 shows the result of heat engineering calculation of option 1. Gas silicate masonry with the image of isolines and heat flow.

Fig. 2 Heat engineering calculation of option 1. Gas silicate masonry (400 mm)

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Fig. 3 The graph of temperature change in the section of the structure along the line a-b

Table 1 Calculation results for option 1. Gas silicate masonry (400 mm) Node description

F

T

Ts

Tf

Option 1. Gas silicate masonry (400 mm)

29.118

3.5787

17.319

9.128

Figure 3 shows a graph of temperature changes in the section of the structure along the line a-b indicated in Fig. 2. These temperature fields (Fig. 2, 3) correspond to the following numerical results (Table 1). In this table and the following, the following designations are used: F—heat flux over two internal surfaces, W; T—temperature difference between two internal surfaces, o C; Ts—average temperature two internal surfaces, o C. Tf—surface temperature in the corner between the floor and the wall, o C.

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Fig. 4 Heat engineering calculation 2 options. Double facade, buffer zone width 200 mm

Fig. 5 The graph of temperature change in the section of the structure along the line a-b

2.2 Thermal Engineering Calculation 2 Options. Double Facade, Buffer Zone Width 200 mm Figure 4 shows the result of the heat engineering calculation of 2 options. A double facade, the width of the buffer zone is 200 mm.

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Table 2 Calculation results for option 2. Double facade, buffer zone width 200 mm Node description

F

T

Ts

Tf

2 option. Double facade, buffer zone width 200 mm

3.7181

0.92161

19.669

19.124

Table 3 Calculation results for option 3. Double facade, buffer zone width 400 mm Node description

F

T

Ts

Tf

3 option. Double facade, buffer zone width 400 mm

2.0441

0.44794

19.822

19.523

Figure 5 shows a graph of temperature change in the section of the structure along the line a-b indicated in Fig. 4. These temperature fields (Fig. 4, 5) correspond to the following numerical results (Table 2).

2.3 Heat Engineering Calculation 3 Options. Double Facade, Buffer Zone Width 400 mm Figure 6 shows the result of the heat engineering calculation of 3 options. Double facade, the width of the buffer zone is 400 mm. Figure 7 shows a graph of temperature changes in the section of the structure along the line a-b indicated in Fig. 6.

Fig. 6 Heat engineering calculation 3 options. Double facade, buffer zone width 400 mm

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Fig. 7 The graph of temperature change in the section of the structure along the line a-b

These temperature fields (Fig. 6, 7) correspond to the following numerical results (Table 3).

2.4 Heat Engineering Calculation 4 Options. Double Facade, Buffer Zone Width 600 mm Figure 8 shows the result of the heat engineering calculation of 4 options—a double facade, the width of the buffer zone is 600 mm. Figure 9 shows a graph of temperature changes in the section of the structure along the line a-b indicated in Fig. 8. These temperature fields (Fig. 8, 9) correspond to the following numerical results (Table 4).

2.5 Heat Engineering Calculation of the 5th Option. Double Facade, Buffer Zone Width 800 mm Figure 10 shows the result of the heat engineering calculation of the 5th option—a double facade, the width of the buffer zone is 800 mm.

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Fig. 8 Heat engineering calculation 4 options. Double facade, buffer zone width 600 mm

Fig. 9 The graph of temperature change in the section of the structure along the line a-b Table 4 Calculation results for option 4. Double facade, buffer zone width 600 mm Node description

F

T

Ts

Tf

4 option. Double facade, buffer zone width 600 mm

1.3307

0.40418

19.878

19.687

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Table 5 Calculation results for option 5. Double facade, buffer zone width 800 mm Node description

F

T

Ts

Tf

5 option. Double facade, buffer zone width 800 mm

1.0533

0.23279

19.907

19.758

Fig. 10 Heat engineering calculation of the 5th option—double facade, buffer zone width 800 mm

Figure 11 shows a graph of temperature change in the section of the structure along the line a-b indicated in Fig. 10. These temperature fields (Fig. 10, 11) correspond to the following numerical results (Table 5).

2.6 Heat Engineering Calculation of the 6th Option—Double Facade, Buffer Zone Width 1000 mm Figure 12 shows the result of the heat engineering calculation of the 6th option— double facade, the width of the buffer zone is 1000 mm. Figure 13 shows a graph of temperature changes in the section of the structure along the line a-b indicated in Fig. 12. These temperature fields (Fig. 12, 13) correspond to the following numerical results (Table 6).

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Fig. 11 The graph of temperature change in the section of the structure along the line a-b

Fig. 12 Heat engineering calculation of the 6th option. Double facade, buffer zone width 1000 mm

3 Results and Discussion The results of the study of two-dimensional temperature fields of the variant design of the structure of a double glass facade, in particular six variants, are summarized in Table 7 and Fig. 14.

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Fig. 13 The graph of temperature change in the section of the structure along the line a-b

Table 6 Calculation results for option 6. Double facade, buffer zone width 1000 mm Node description

F

T

Ts

Tf

6 option. Double facade, buffer zone width 1000 mm

0.75515

0.26211

19.925

19.812

Node description

F

T

Ts

Tf

Option 1. Gas silicate masonry (400 mm)

29.118

Table 7 Summary of the results of 6 options 3.5787

17.319

9.128

2 option. Double facade, buffer zone width 200 mm

3.7181

0.92161

19.669

19.124

3 option. Double facade, buffer zone width 400 mm

2.0441

0.44794

19.822

19.523

4 option. Double facade, buffer zone width 600 mm

1.3307

0.40418

19.878

19.687

5 option. Double facade, buffer zone width 800 mm

1.0533

0.23279

19.907

19.758

6 option. Double facade, buffer zone width 1000 mm

0.75515

0.26211

19.925

19.812

From the data obtained, it can be observed that with an increase in the buffer zone from 200 to 1000 mm, the average temperature of the two inner surfaces (Ts) increases systemically. Accordingly, with an increase in the width of the buffer zone, the temperature difference between the two inner surfaces (T) decreases. The most optimal widths for the buffer zone can be taken as 200 and 600 mm if it is necessary to provide a passage in the buffer zone. For the variant with a technical passage, a cantilever base for the passage should be provided, in addition, ventilation openings in it should be designed.

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20

оС

15

10

5

0 1 opon

2 opon

3 opon

4 opon

5 opon

6 opon

Opons Тs

Tf

Schedule Тf

Fig. 14 Graph of Ts and Tf changes, °C

4 Conclusions 1. The use of a double facade structure in a cold region is justified, the fulfillment of the sanitary and hygienic requirements (clause 5.7 of Russian Code of Rules (SP) 50.13330.2020) is taken into account, which regulates that the surface temperature must be above the dew point under design conditions. 2. With an increase in the buffer zone, the average temperature of the two inner surfaces increases systemically, and, accordingly, the difference in their temperatures decreases. 3. The most optimal widths for the Double-Skin Facad buffer zone in Murmansk can be assumed to be 200 and 600 mm if it is necessary to provide a passage in the buffer zone. For the variant with a technical passage, a cantilever base for the passage should be used, in addition, design ventilation openings in it. 4. The Glass Channel as part of the Double-Skin Facad offers a stunning alternative to traditional opaque building walls and flat architectural glass, creating virtually seamless façade surfaces. 5. The use of the Double-Skin Facad for architectural solutions in cold climatic regions is justified not only as a self-illuminated effect, but also demonstrates sufficient energy efficiency due to the selection of the optimal width of the buffer zone.

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References 1. Shelomentsev AG, Voronina LV, Smirennikova EV, Ukhanova AV (2017) Ars Administrandi (The Art of Management) 418:396–418 2. Khairdzira N, Taibb N (2020) Malaysia Archit J 2(2):65–72 3. Borodach M, Shilkin N (2015) AVOK-PRESS 33–45 4. Pomponi F, Piroozfar PAE, Southall R, Ashton P, Farr ERP (2016) Energy performance of double-skin façades in temperate climates: a systematic review and meta-analysis Renew Sust Energ Rev 1525–1536:54 5. Tkachuk AE, Sotnikova OA, Goikalov AN (2021) Astrakhan: GAOU JSC VO “AGASU” 2(36):47–53 6. Qahtan AM (2019) Case studies in thermal engineering 14(February):100419 7. Stribling D, Stigge B (2002) A critical review of the energy savings and cost payback issues of double facades 8. Vasilieva IL, Nemova DV, Vatin NI (2020) Housing and communal infrastructure 3(14):17–25 9. Novikov MV, Goikalov AV (2021) Raschet i konstruiro-vanie ehlementov zdanii iz yacheistykh betonov, Moscow, Znanie-M, vol 212 10. Goykalov AN, Novikov MV, Gulak LI (2020) IOP Conf Ser Mater Sci Eng (Inst Phys Publ) 11. Novikov MV, Sotnikova OA, Goikalov AN (2021) Engineering and construction bulletin of the Caspian region 2(36):5–10 12. Margolis BI, Mansoor GA (2019) Software and Systems 2:313–317 13. Huang Y, Niu JL (2016) Energy and Buildings 117:387–398

Using Linear Equations in Calculating the Heat Capacities of Gases Dmitry Kitaev , Svetlana Tulskaya , and Vitaly Zhmakin

Abstract The object of research is the dependence of the true molar heat capacity of ideal gases on temperature. To describe the dependence of heat capacity on temperature, equations of polynomials of various degrees are used. There is no data on the optimal degree of the polynomial that provides the highest accuracy of the approximation equations. Based on a comparison of the reference data on heat capacities and linear equations obtained by dividing the temperature interval into two, it was found that the greatest deviations are observed for carbon dioxide and averaged 3.9%. The average deviations for hydrogen sulfide are 3.34% in the temperature range 0– 1200 °C. Based on the existing experimental data on the true mass isobaric heat capacities of ideal gases using the least squares method, approximation equations are obtained that provide the highest accuracy. It was found that for most of the gases under consideration the best results are provided by polynomials of the eighth degree, and for water vapor and hydrogen of the ninth degree. With the specified degree of polynomials, the maximum values of the absolute error do not exceed 0.1%. Keywords Heat capacity · Ideal gas · Interpolation · Approximation · Linear equation · Absolute error · Polynomial

1 Introduction It is known that the temperature dependence of the heat capacity of an ideal gas is characterized by a nonlinear dependence. One of the expressions that make it possible to determine the true heat capacity of a mole of gas at constant pressure, obtained on the basis of the quantum-statistical theory of heat capacity and spectroscopic data, D. Kitaev (B) · S. Tulskaya Voronezh State Technical University, st. 20-letiya Oktyabrya, 84, 394006 Voronezh, Russia e-mail: [email protected] S. Tulskaya e-mail: [email protected] V. Zhmakin Southwest State University, 94, 50 Let Oktyabrya ul., Kursk 305040, Russia © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_26

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has the form [1, 2] ⎡  cp =

5 ⎢ R + R⎣ 2

i

 hc 2 εi kT pi e−εi



pi e

hc −εi kT

 hc kT

−

 i

hc εi kT

 

i

pi e

pi e

−εi

−εi

2 ⎤ hc kT

2 hc kT

⎥ ⎥ ⎥ ⎦

(1)

i

εi —the energy of a molecule in the quantum state i (when calculating this value, spectroscopic data are used); pi —is the number of levels with the same energy or statistical weight for the i state. An alternative approximation method based on the Karpov equation [3] as well as various interpretations of the equation [4, 5] can be used c0p (T ) = a + bt + cT −2 + dT 2 + eT −3 + f T 3 + gT −0,5 + hT −1 + i ln T. (2) Other universal equations in the form of polynomials have been proposed [6– 8]. When calculating in specific areas of technology, modified equations are used, adapted for operating temperature ranges [9, 10]. In [11], an interpolation formula in the form of a third-order polynomial with a maximum average relative approximation error of 7.7% is recommended for calculating the specific heat capacity of nitrogen and oxygen in vapor and liquid states. In [12, 13], linear and quadratic regression equations were obtained for the heat capacities of gases (CO2 , N2 ) and water vapor (H2 O) depending on temperature. On their basis, linear and more accurate quadratic dependences of the average heat capacity of the combustion products of compressed gas fuel of grades “A” and “B” are proposed, which differ by 1.4%. When compared with the heat capacities of the combustion products of gas engine fuel (pure natural gas) [13], the difference in the calculated values for fuel grade “A” at a temperature of 300 K is 1%, at a temperature of 1800 K the error is 1.5%; for fuel grade “B” at a temperature of 300 K the error is 5.2%, at a temperature of 1800 K the error is 7.8%. In [8], when determining the heat capacity of an ideal gas, a third degree polynomial is used as a component of the heat capacity of a real gas when calculating processes in a diesel engine. The work [15] indicates the need to take into account the change in the heat capacity of the mixture during a fire, since the error can be up to 75%. The author uses third degree polynomials for oxygen, carbon monoxide and carbon dioxide, and fourth degree for nitrogen. In the practice of modern heat engineering calculations and even scientific research, the method of calculating heat capacities by linear equations is widely used, when interpolation formulas are set for the ranges from 0 to 1000 (1500) °C and from 1000 (1500) to 3000 °C [16]. Linear equations are used to calculate the isobaric heat capacity in the temperature range 500–1000 K [16]. In the example considered, the deviation according to the linear formula is about 1%. The paper indicates an increase in the error in determining the temperature at the end of the adiabatic expansion in the turbine, since the heat capacity is part of the exponent. In the example considered in the work, the deviation is 5°. Linear dependences of heat

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capacity on temperature are given in textbooks, teaching aids and methodological developments [17, 18]. The question of the required accuracy of calculations and the need to use polynomial equations of various degrees is solved individually in each case. Let us consider an example of determining the value of the average mass isobaric heat capacity of carbon dioxide in the temperature range from 100 to 600 °C. We use an interpolation formula of the form [17]. c pm = 0.8725 + 0.00024053t.

(3)

Substituting the temperature range, we get c pm = 0.8725 + 0.00024053(100 + 600) = 1.040871 kJ /(kg · K) Let us use the tabular values of the heat capacities given with an interval of 100 °C [18]: c pm =

1.0396 · 600 − 0.8658 · 100 = 1.07436 kJ /(kg · K). 600 − 100

The values obtained differ by 3.2%. For other gases and temperature ranges, the difference can be much larger, especially when calculating the heat capacities of mixtures. It is also interesting that a number of old textbooks present a different equation from (3) for the gas under consideration, the type of heat capacity and the temperature range c pm = 0.8654 + 0.0002443t.

(4)

Equation (4) for the case under consideration gives the value 1.03641. Equations (3) and (4) differ insignificantly, but the deviation from the exact value will increase and amount to 3.66%. It is also interesting that in some textbooks the heat capacity equations for oxygen, nitrogen, carbon monoxide, water vapor, and air are presented for the temperature range from 0 to 1500 °C, in collections of problems in the range from 0 to 1000 °C and from 1000 to 2700 °C. Figure 1 shows the linear dependences constructed according to the equations proposed in various literature for the average mass isobaric heat capacity. Figure 1 it follows that the equations for CO and CO2 have the greatest difference, and for other gases in the range from 0 to 1000 °C they practically coincide.

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Fig. 1 Linear dependence of heat capacity on temperature

2 Materials and Methods Let us present on one graph the results of plotting the dependence of the true molar isobaric heat capacity using linear interpolation formulas and the most accurate tabular data. Figure 2 shows the plotting results for some gases. Tabular dependencies are shown in the figure by blue lines, and interpolation ones by red lines. Figure 2 shows that when using linear interpolation formulas for gases, the largest deviations will be observed for SO2 and CO2 . The closest is the linear dependence for O2 in the temperature range from 1000 to 2700 °C, for H2 O and air in the range from 0 to 1000 °C. In other cases, the deviations depend on the temperature. For CO2 at temperatures above 1500 °C, the linear equation does not intersect the tabular curve, in which case the values will be overestimated. It can be seen from the graphs in Fig. 2 that significant deviations will be observed at the boundary of the partition intervals (1000, 1500 °C). Also, in the initial temperature ranges from 0 to 100–300 °C, deviations are observed for most gases.

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Fig. 2 Dependences of the true molar isobaric heat capacity on temperature

3 Results Table 1 shows the values of the arithmetic mean absolute deviations of the results of calculating the heat capacities ,%, obtained by tabular and linear formulas. The minimum min and maximum max values are also indicated. The data in Table 1 are consistent with the conclusions drawn from Fig. 2. It follows from Table 1 that the greatest deviations are observed for CO2 in the temperature range from 0 to 1500 °C, the average value is 3.9% and the maximum is 13.3%. In

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Table 1 The values of the absolute deviations of the values of the true molar isobaric heat capacity Gas

Interval, °C

,%

min,%

O2

0–1000

0.982

0.507

max,%

Interval, °C

,%

min,%

max,%

1.742

1000–2700

0.327

0.018

0.676

N2

0–1000

0.642

0.056

2.147

1000–2500

0.684

0.056

1.076

CO

0–1000

0.503

0.053

1.334

1000–2500

0.517

0.006

1.626

Air

0–1000

0.424

0.075

1.103

1000–2500

0.386

0.056

1.215

H2O

0–1000

0.614

0.118

2.017

1000–2900

1.146

0.074

3.248

SO2

0–1200

3.340

0.080

9.383

–

–

–

–

H2

0–1500

0.868

0.031

1.634

1500–2700

0.703

0.021

1.894

CO2

0–1500

3.901

0.286

13.297

1500–2500

1.189

0.856

1.968

Fig. 3 Dependence of the true mass isobaric heat capacity of oxygen on temperature

the range from 1500 to 2500 °C for CO2 , the average deviation reaches 1.2%, and the maximum deviation is 2%. Significant deviations are observed for SO2 , on average 3.34% in the temperature range 0–1200 °C. In the temperature range from 1000 to 2900 °C for H2 O, the average error values are 1.15%, and the maximum is 3.25%. For other gases, the average error does not exceed 1%, but the maximum values can be more than 1%. The most accurate linear equations are for N2 , CO and air. Let us consider the approximation of the dependence of the heat capacity on the temperature of the tabular data using the example of oxygen. Figure 3 shows tabular data (blue) and approximating polynomials of degree k = 1,2,3. Let us find the regression equation in the form of a polynomial of degree k of the form

Using Linear Equations in Calculating the Heat Capacities …

cˆ p =

k

277

ajt j.

(5)

j=0

To find the coefficients of Eq. (5), we use the least squares method according to which ⎡ ⎤2 n n k

 2 j ⎣c i − = ci − cˆi = a j ti ⎦ ⇒ min, i=1

i=1

(6)

j=0

ci —tabular value of heat capacity; cˆi —is the value calculated according to (5); n—is the number of experimental points. A necessary condition for the minimum of functional (6) (for k = 3) is the equality to zero of the partial derivatives:   n k

∂ j l = −2 ci − al ti ti = 0, j = (0, 1, . . . k). ∂ a` j i=1 l=0 Expanding the brackets, we obtain a system of k + 1 linear normal equations for k + 1 unknowns al n

i=1

j

ci ti =

k n

l=0 l=1

l+ j

al ti

=

k

l=0

al

n

l+ j

ti

.

(7)

l=1

After substituting the values of the sums into system (7), (l, j = 0,1,2,3), it takes the form ⎫ 1.69522E21a3 + 7.19659E17a2 + 3.14206E14a1 + 1.42884E11a0 = 1.73353E11, ⎪ ⎪ ⎪ ⎬ 7.19659E17a3 + 3.14206E14a2 + 1.42884E11a1 + 693E5a0 = 83346.39844E3, ⎪ 3.14206E14a3 + 1.42884E11a2 + 693E5a1 + 37.8E3a0 = 44.72235313E3, ⎪ ⎪ ⎭ 1.42884E11a3 + 693E5a2 + 37.8E3a1 + 28a0 = 0.316331E2.

(8)

After solving the system of Eqs. (8) using the Cramer method and substituting the found coefficients, the regression Eq. (5) will take the form c p = (909.096 + t(335 − t(0.14816 + 2.636E − 4t))E − 3)E − 3.

(9)

Checking the adequacy of Eq. (9) according to Fisher’s criterion with a confidence level of p = 0.95 gives a positive result. As calculations have shown for the gas under consideration and the type of heat capacity in the temperature range from 0 to 2700 °C, with a confidence level of p = 0.95, the equation of the second degree is also adequate (c p =

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   9322 + t 2.222 − 4.14E − 4t 2 E − 4). A linear equation was also obtained that is not adequate with a given probability. Lowering the degree of the polynomial (2nd degree), determining the regression equation, checking the adequacy, we come to the conclusion about the adequacy of the second degree polynomial. A linear regression equation was also calculated, but it is not adequate. Therefore, with a confidence level of p = 0.95, the second-degree equation can be considered adequate to the tabular data. The maximum value of the relative error for the second degree polynomial k = 2 is 2.1%, for k = 3 the error is 0.8%, and for a linear dependence it is 7.2%. According to the authors, such accuracy is not sufficient in modern conditions. As is known, on the basis of the data of the true heat capacity, the average heat capacity is obtained in the temperature range of a specific process, for example, cooling the exhaust flue gases in a gas turbine plant in order to obtain hot water. The use of linear equations for a wide range of temperatures can lead to significant errors in the calculation of the amount of heat. An equation that is adequate from the point of view of mathematical statistics may have an unacceptable error when calculating the amount of heat and its cost in monetary terms. Table 2 Regression coefficients O2

N2

Air

CO2

CO

a8

12.00398E–27

−84.68933E–28

−43.44547E–28

−48.44547E–28

−59.97242E–28

a7

−14.51865E–23

83.75999E–24

38.56751E–24

54.20747E–24

53.71133E–24

a6

73.22529E–20

−32.16041E–20

−11.75786E–20

−25.61333E–20

−16.88087E–20

a5

−19.90618E–16

56.42511E–17

79.65546E–18

67.35382E–17

14.63975E–17

a4

31.27974E–13

−29.64653E–14

33.43216E–14

−11.18083E–13

35.57831E–14

a3

−27.73659E–10

−43.52230E–11

−83.58055E–11

13.23860E–10

−98.96410E–11

a2

11.42046E–7

63.99645E–8

68.90151E–8

−13.01332E–7

83.58093E–8

a1

10.26171E–5

−52.46643E–6

−27.54852E–7

11.04033E–4

−36.41346E–6

a0

91.46970E–2

103.5434E–2

100.4117E–2

81.48627E–2

104.0033E–2

H2

Water vapor (H 2 O)

H2 S

N 2O

SO2

a9

10.50463E–29

−83.34864E–31

–

–

–

a8

−14.02408E–25

11.12322E–26

−53.87152E–25

−51.61486E–27

−16.01046E–25

a7

80.17741E–22

−61.86433E–23

26.66847E–21

81.03372E–23

76.92693E–22

a6

−25.70128E–18

18.57165E–19

−54.07811E–18

−30.54343E–19

−14.59963E–18

a5

50.72448E–15

−32.76883E–16

57.37717E–15

53.04754E–16

13.53410E–15

a4

−63.27742E–12

35.58973E–13

−33.36609E–12

−51.19093E–13

−58.91546E–13

a3

48.17688E–9

−26.16702E–10

96.70310E–10

31.53129E–10

84.31632E–11

a2

−19.24455E–6

14.09027E–7

−78.74939E–8

−16.92100E–7

−29.94127E–8

a1

39.26051E–4

20.66147E–5

34.23536E–3

11.33520E–4

58.03996E–5

a0

1419.732E–2

185.8979E–2

99.23027E–2

85.0749E–2

60.64823E–2

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As the main criterion for evaluating the accuracy of the equation, a relative error of 0.1% was taken in relation to the tabular data. Were obtained regression equations for some gases used in technology, with a relative error not exceeding 0.1%. The results in the form of coefficients of the polynomial ai are presented in Table 2. It follows from Table 2 that for most of the gases under consideration, the best accuracy is ensured when using polynomials of the 8th degree. The exception is water vapor and hydrogen for which the optimal degree of the polynomial of the approximation equation is 9.

4 Conclusions 1. The values of the error are determined when using linear equations of the dependence of the true heat capacity of some ideal gases in a wide range of temperatures. It is shown that the use of linear interpolation equations obtained by dividing the entire temperature interval into two can lead to significant errors. In the temperature range from 1500 to 2500 °C for CO2 , the average deviation is 1.2%, and the maximum deviation is 2%. Significant deviations are observed for SO2 , on average 3.34% in the temperature range 0–1200 °C. In the temperature range from 1000 to 2900 °C for H2 O, the average error values are 1.15%, and the maximum is 3.25%. 2. Using the example of the dependence of the true mass isobaric heat capacity of oxygen on temperature, it is shown that the maximum error value for the approximation equations in the entire temperature range of the first degree is 7.2%, for the second degree, 2.1%, and for the third degree, 0.8%. 3. On the basis of the calculations, it was found that for most of the gases considered, to obtain the values of the true molar isobaric heat capacity with the maximum value of the absolute error not exceeding 0.1%, it is sufficient to use approximation polynomials of the eighth degree. The coefficients of the polynomials providing the required accuracy are obtained.

References 1. Kitaev DN, Chernykh EM (2008) Voronezh State Technical University Bulletin 4(12):36–40 2. Grigoriev BA, Gerasimov AA, Alexandrov IS (2019) Thermophysical properties of oil hydrocarbons, gas condensates, natural and associated gases. MPEI Publishing House, vol 1, p 735. ISBN 978-5-38-301322-9 3. Bychinskii VA, Tupitsyn AA, Mukhetdinova AV, Chudnenko KV, Fomichev SV, Krenev VA (2013) Russ J Inorganic Chem 58(12):1639–1645. https://doi.org/10.7868/S0044457X131 20064

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4. Lemire RJ, Palmer DA, Taylor P, Schlenz H (2020) Chemical thermodynamics of iron. Part 2, Nuclear Energy Agency Data Bank, Organisation for Economic Co-operation and Development, Ed., vol. 13b, Chemical Thermodynamics, OECD Publications 5. Malomuzh NP, Makhlaichuk PV, Khrapaty SV (2014) J Phys Chem 88(9):1284–1290. https:// doi.org/10.7868/S0044453714090246 6. Coufal O (2013) Computer Physics Communications 184:194–200 7. Puidomènech I, Rard JA, Plyasunov AV, Grenthe I (1999) OECD Nuclear Energy Agency, p 96 8. Kuznetsov NM, Frolov SM (2020) Combustion and explosion 13(2):113–117. https://doi.org/ 10.30826/CE20130212 9. Gnitiev PA (2017) Bulletin of the Donbass national academy of civil engineering and architecture issue engineering systems and industrial safety, vol 5, no 127. ISSN 2519-2817 online 10. Aristova NM, Belov GV, Sineva MA, Morozov IV (2016) Scientific service on the internet: proceedings of the XVIII All-Russian scientific conference, Novorossiysk, pp 46–50, 19–24 September 2016. https://doi.org/10.20948/abrau-2016 11. Khvostov AA, Zhuravlev AA, Tselyuk DI (2018) Information technology in construction, social and economic systems 3(13):21–27 12. Sobolenko AN (2019) Bulletin of the Astrakhan state technical university. Series: marine engineering and technology 2:48–55. https://doi.org/10.24143/2073-1574-2019-2-48-55 13. Sobolenko AN, Florianskaya MV (2021) Bulletin of the Astrakhan state technical university. series: marine engineering and technology 2:65–74. https://doi.org/10.24143/2073-1574-20212-65-74 14. Frolov CM, Ivanov VS, Tukhvatullina RR, Frolov FS, Kuznetsov NM, Basara B (2019) Combustion and explosion 12(1):73–83. https://doi.org/10.30826/CE19120109 15. Pylenok DA, Naumov VA (2017) Youth Sci Bull 5(12):20–25 16. Karyshev AK, Zhinov AA, Shevelev DV (2015) Electron J Sci Technol Educ 4(4):29–37 17. Bulygin YuA, Galdin DN (2015) Thermodynamics and heat transfer: textbook. Manual. Voronezh State Technical University, Voronezh, p 110 18. Ostrovskaya AV, Korolev VN (2020) Technical thermodynamics: textbook. In: Sapozhnikov BG (ed) Ural Federal University the first President of Russia B. N. Yeltsin. - Yekaterinburg: Ural University Publishing House, p 240. ISBN 978-5-79-963089-8

Method for Analysis of Hierarchies for Development of Gas Industry Enterprises Galina Martynenko , Vitaly Zhmakin , Vera Ukhlova , Vladimir Lukyanenko , and Maria Popova

Abstract The paper poses the task of developing an algorithm for conducting a scenario analysis of the options for the development of the gas economy of cities, as one of the effective tools for strategic planning. In turn, this determines one of the tasks of the work as the formation of a model for assessing gas projects for the possibility of scenario analysis. As a solution, a method for analyzing hierarchies and a model for assessing gas projects is proposed, which makes it possible to implement a scenario analysis of possible solutions within the framework of strategic planning for the development of the gas industry. The mathematical model makes it possible to take into account such factors of choice as the payback of the project, the complexity of implementation, compliance with the industry development trends and the consumer preferences of society. The resulting model is based on the concept of the hierarchy analysis method, which makes it possible to take into account both quantitative and qualitative indicators. Due to this, it maximally reflects the logic of experts in the selection of projects, but the assessment itself is based on a rigorous mathematical calculation. Application of the proposed algorithm makes it possible to obtain significance weights for each proposed project (scenario), which makes it possible to rank decisions under the conditions of the considered evaluation criteria. Keywords Scenario analysis · Multi-criteria optimization · Hierarchy analysis method · Evaluation model · Gas supply

G. Martynenko (B) · V. Lukyanenko Voronezh State Technical University, Moskovsky prospect, 14, 394026 Voronezh, Russia e-mail: [email protected] V. Zhmakin · M. Popova Southwest State University, 94, 50 Let Oktyabrya ul., Kursk 305040, Russia V. Ukhlova Voronezh State University, Universitetskaya Square, p. 1, 394045 Voronezh, Russia © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_27

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1 Introduction In order to increase the efficiency of the functioning of companies, strategic management should be based on strategic planning [1]. It is the strategic planning system that allows the management, shareholders, founders and other interested parties to determine the direction of the company’s development, in particular, to identify organizational and structural changes that need to be made in the organization, to choose effective tools to achieve goals. This is due to the fact that strategic planning is a process of modeling the future, i.e. creation of a management model that will allow maintaining a strategic balance between the company’s goals, its potential capabilities and probable development prospects. Situational and scenario analysis are effective tools of analytical strategic planning. Situational analysis is traditional for the gas industry. It allows you to determine the current situation, marketing opportunities and problems that the company may face in the future. In the process of situational analysis, they study the environment, look for opportunities, evaluate the organization’s ability to use them, identify strengths and weaknesses in comparison with competitors and evaluate the reaction of competitors to a particular company strategy. However, it does not allow predicting the dynamics of the company’s development, taking into account the assessment of internal and external factors of development, as well as the prospects for the development of the industry market. Scenario analysis is based on an assessment of the picture of the future, consisting of coordinated, logically interrelated events and a sequence of steps that with a certain probability lead to a predictable final state (the image of the company in the future, projects being implemented). In contrast to forecasts, scenarios take into account not only quantitative indicators, but also qualitative ones obtained as a result of processing expert opinions, and not by calculation.

2 Methods The process of forming a scenario with this approach includes three main stages: 1) an assessment of the current situation of the company, whose task is to understand the dynamics of the influencing factors; 2) formation of a variety of development alternatives (“future scenarios”); 3) assessment of the probability of the implementation of various scenarios in the future; 4) development of a strategy to achieve the desired scenarios. The advantage of the scenario approach is the ability, in accordance with the expected scenario of the development of the company’s situation, to timely identify the danger of unsuccessful managerial influences or predict adverse developments. This approach allows you to temporarily adjust management decisions. In the process

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of evaluating scenarios (projects), the choice of a particular variant (development scenario) is evaluated, taking into account the opinions of all interested parties. The paper proposes an approach to strategic planning of the gas industry, which is not traditional. The relevance of the work is determined by the relevance of the problems of strategic management in the industry in difficult economic conditions associated with uncertainty in decision-making.

3 Results and Discussion To carry out scenario analysis, we will use a hierarchical scenario assessment model, which most fully reflects the planning system characteristic of gas sector enterprises. Its main elements are: Hierarchy focus, actors, goals, policies, outcomes and generalized outcome [2, 3, 5–8]. The focus of the hierarchy is understood as the general purpose of the problem under study. Actors are the acting forces that influence the outcome to varying degrees. Goals are understood as the desired limits or values that are sought to be achieved. Sanctioned means of achieving goals provided through generally accepted decision-making procedures are considered as policies. Outcomes are potential options for the future state of the company, which are possible after the application of policies. The generalized outcome allows you to integrate the values of individual outcomes to assess the consequences of decisions taken during planning. The planning process begins with defining the purpose of planning and building a hierarchy (Fig. 1). At the first level, one element is indicated in the hierarchical model—focus F, which is understood as the overall goal of planning. At the second level, the actors— Ak, who can influence the development of events in the future are indicated. At the third level, there are goals C, which the actors strive to achieve. The fourth level

Fig. 1 Hierarchy for implementing the scenario analysis procedure

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provides policies P, means to achieve the desired goals. At the fifth level—outcomes J (scenarios). The application of this procedure to a gas sector enterprise makes it possible to obtain a hierarchical model for evaluating projects implemented within the framework of strategic planning (Fig. 2). The focus of scenario analysis is a project that will satisfy the wishes (requirements) of all interested parties. The goals in the model are dictated from the positions of administrative and industry customers who are actors. The Ministry of Energy, the administration of the Voronezh region (city), and other persons interested in the development of the gas industry of the region can act as an administrative contractor. The representatives of the industry customer include the management of the operating companies and the regional supplier of the resource. As goals at the third level of the model, the satisfaction of such aspects of projects as economic, technological, social and political is considered. In turn, each of them is determined by the specific characteristics of the projects. The economic aspect characterizes the project with respect to the possibility of profit (income) and expenses. In turn, the profitability (profitability) of the project depends on the tariffs that can be applied when delivering the resource, the volume of supply, which depends on the performance of the gas system and the service life. The costs of the project are determined in the future, respectively, the costs of construction and operation are taken into account. The technological aspect allows us to evaluate the project from the perspective of implementation and further operation. It takes into account the technological solution and the safety of the project. In particular, the technological solution is viewed from the perspective of specialists (availability, qualifications, cost), equipment (complexity of installation and operation, cost) and efficiency (demand

Fig. 2 Project evaluation model

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in the future). By safety we mean both the safety of construction and the safety of operation. The social aspect allows you to evaluate the project from the perspective of the consumer. Important here safety of operation (minimal risks to life and health), acceptability of consumption rates, ease of operation (simple connection and minimal control), choice and cost of user equipment. Political aspects make it possible to assess the risks of projects related to financing by the state, the supply of equipment in the case of the use of foreign solutions (sanctions, exchange rates). As scenarios (outcomes, alternatives), the model considers options for possible projects for the development of the gas sector of the region, which can be offered by customers. Projects are understood as solutions that are possible within the framework of solving the issue of gasification of an object (a block of development, a separate structure). In this regard, many projects may include such options as: Construction of a new segment using existing technology, construction of a new segment using new technology, modernization of the existing segment, abandonment of the facility in favor of the option of choosing an alternative energy source (the use of renewable energy sources instead of traditional sources). The resulting hierarchical assessment model corresponds to the concept of the hierarchy analysis method (MAI) and allows us to apply this method to determine the most “promising” development scenario [3, 4]. The choice of the method is also optimal from the position that a number of evaluation criteria presuppose not only quantitative, but also qualitative values. In addition, the model provides an assessment taking into account the opinion of both one expert and several. The project evaluation model in MAI designations is shown in Fig. 3. According to MAI, at the first step of the algorithm, expert assessments of the preference of elements of the levels of the compiled hierarchy are revealed. Expert assessments consist in comparing elements of the same level of the model and are obtained through a survey of experts. At the same time, tables of paired comparison matrices are formed and filled in. Both the row and the column contain all the elements of the assessed level (Fig. 2 and 3). Experts are asked to what extent the element in the row has a stronger (weaker) impact on the future of the company than the element in the column. The obtained qualitative assessments are translated into quantitative ones using the assessment scale proposed by T. Saati [4]. At the intersection of the row and the column, the value of the quantitative assessment (Oc) is recorded (Table 1). Based on the values of the matrix of paired comparisons, local weights of importance (preference) of the level elements are calculated. Local weights of level C: C=



cn ,

 Cn = cn C .

(1)

4

Similarly to finding the local weights of level C (1), the importance weights of the other levels of the hierarchy are found. Next are the global weights of all levels, representing generalized estimates of the importance of these elements according to the formula (2).

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Fig. 3 Project evaluation model in MAI designations

Table 1 Matrix of paired comparisons for level C Level C

C1

C2

C3

C4

Amount per line

C1 C2

1

Oc

Oc

Oc

c1

Oc

1

Oc

Oc

C3

c2

Oc

Oc

1

Oc

c3

C4

Oc

Oc

Oc

1

c4

Local weight

C1

C2

C3

C4

C

Global C-level weights: OC1 = O B2 · C1 , OC2 = O B1 · C2 + O B2 · C2 OC3 = O B1 · C3 OC4 = O B1 · C4

(2)

where OB1 , OB2 —global higher-level estimates; OB1 , OB2 —second-level estimates, are equal to local weights, respectively, B1 and B2 . The global weights of the elements of the subsequent levels are similar. The algorithm is repeated to the level of outcomes (scenarios). At the last level, the scenario most appropriate to the preferences of experts is determined. The method assumes that each alternative from the set of possible options (S) is also evaluated by the method of paired comparison. When filling in the matrices of paired comparisons, the expert is asked the question: To what extent the scenario in the row corresponds to the selected criterion to a greater extent. Next, the score is compared with the T. Saati scale and the resulting value

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Table 2 Matrix of paired comparisons for evaluating alternatives (scenarios) Criterion N

Sc1

Sc2

Sc3

….

ScS

Sc1

1

Oc

Oc

….

Oc

……

Oc

Oc

Oc

….

Oc

ScS

Oc

Oc

Oc

….

1

Local weight

I1

I2

I3

….

Is

is entered into the matrix of paired comparisons (Table 2). Matrices are formed to evaluate projects with respect to each criterion, respectively, their number is equal to the number of criteria of the model. A set of criteria is determined based on the evaluation model (E1–E8, D5–D8) (Fig. 3). The matrix of paired comparisons in all cases must be positive definite, inversely symmetric, having a rank equal to 1. A feature of the inverse symmetric matrix of paired comparisons is: 1) there should always be a score equal to 1 on the main diagonal, which means that the score of the Oc at the intersection of the row column and the column row with the same numbers should be the same, i.e. Ocij = Ocji ; 2) a ratio must always be maintained that meets the condition: If an estimate is made when comparing the i-th factor with the j-th factor Ocij , then when comparing the j-th factor with the i-th, an estimate Ocji = 1/Ocij [8]. In addition, the matrix of paired comparisons must be consistent. This means that the eigenvector of the matrix λ is greater than (or equal to) the number of its criteria, i.e. λ ≥ n. Based on the estimates entered in the table, the local weights of alternatives are calculated (Im , n = 1, S), they are also entered in the table, the calculation formulas are similar to (1). Next, the global weights of scenarios (OI) are calculated: OI1 = I1 · OE1 + I1 · OE2 + . . . + I1 · OE9 + I1 · OD5 + . . . + I1 · OD8 OIS = IS · OE1 + IS · OE2 + . . . + IS · OE9 + IS · OD5 + . . . + IS · OD8

(3)

where S—is the number of scenarios. In accordance with the resulting final weights, the expected scenarios are ranked. The scenario with a higher weight is more preferable in these evaluation conditions. The algorithm of the scenario analysis procedure is shown in Fig. 4. It is a set of steps performed sequentially, which makes it intuitive and easy to use. The input data for the algorithm are the criteria for evaluating projects and the set of projects to be evaluated. Set of evaluation criteria is formed on the basis of a set of indicators characterizing projects. At the same time, it is important that each project proposed for selection can be described with respect to the selected indicators. Many projects are recommended to choose no more than seven options. The model obtained in step 2 can be used for different expert councils and different projects. Its change is

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recommended when the organization changes the key indicators by which projects are evaluated. At the same time, it is allowed to form a model with an excessive number of criteria, which will make it universal for all gas sector organizations. The identification of the expert opinion implemented in step 3 can be carried out both with the involvement of one or several specialists. At the same time, all experts should use a single model. The expert evaluates the criteria by qualitative or quantitative values. At the same time, it is recommended to compare the elements in pairs. The expert is asked to compare which criterion from the pair is more significant. It is also allowed to arrange the criteria in order of significance or in order of non-decreasing values, if there are quantitative indicators. The use of dimensionless priorities in the approach makes it possible to compare heterogeneous factors. At step 4, the estimates are recalculated into values according to the scales used in MAI. To translate qualitative assessments, it is recommended to use the T. Saati scale. It is allowed to use their prioritization when comparing criteria. Priority is the importance of the criterion expressed by a number. The higher the number assigned to the priority, the more significant the criterion is. When recalculating to the MAI scales, it should be borne in mind that the sum of the priorities of all elements subordinate to an element of a higher level should be equal to one. At step 5, the local weights of the model criteria are calculated. For the second level, the importance of criteria for directly achieving the main goal is assessed. For the third level—the significance of the criteria relative to the criteria of the overlying level. Step 6 consists in linear convolution of weights of importance of criteria of each level and calculation of weights of evaluation indicators, i.e. calculation of global weights of elements for each level from the second to the fourth. In step 7, possible projects (scenarios) are compared with respect to each criterion of the last level. Step 8 is the step of the final calculation of the weight of the significance of the project. At step 9, the projects under consideration are ranked according to the received values of significance. The alignment of the series is performed according to the non-decreasing values of the weights. The highest value of the weight corresponds to the highest priority of the significance of the project, and the lowest—the least importance. In case of equality of the weights of two or more projects, the first in the list is the one whose weight according to the subcriteria is higher than the standing level. At the same time, the most significant criterion is selected, starting from the top level. Step 10 allows you to get the result both in the form of a list of projects in a row of significance from the position of the expert(s), and with the value of weight coefficients.

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Fig. 4 Scenario analysis algorithm

4 Conclusions 1. The global weights of scenarios can also be interpreted as the probabilities of the implementation of the scenarios under consideration under the conditions of the accepted evaluation criteria. In this case, further analysis of these probabilities is carried out. If the obtained values suit the decision-maker, then the research process is completed. If the decision-maker wishes to see a different probability distribution, then it is possible to adjust the significance of the criteria based on the changes obtained during the application of the algorithm of the reverse

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planning process. The reverse process allows you to see the criteria that affect the final result. 2. The applied method of hierarchy analysis makes it possible to evaluate the indicators dimensionlessly, which is important when using qualitative assessments in the evaluation model along with quantitative ones, when quantitative assessments do not allow judging the significance of the project only on the basis of values. 3. The software implementation of the presented algorithm will allow for an assessment with minimal time, and decisions on the selection of projects will be more objective. 4. The developed assessment model and the adapted algorithm of the hierarchy analysis method can be used as the basis for a decision support system for selecting projects (scenarios) for the development of the gas industry in the regions [9–15].

References 1. Ukhlova VV, Martynenko GN, Luk’yanenko VI (2021) Sistemy upravleniya i informatsionnyye tekhnologii 1(83):43–48 2. Volokobinskiy MYu, Pekarskaya OA, Razi DA (2016) Ekonomika i upravleniye narodnym khozyaystvom. Vestnik finansovogo universiteta 2:33–42 3. Mitsel’ AV, Telipenko YeV (2011) Ekonomicheskiy analiz: teoriya i praktika 27(234):57–64 4. Ozherel’yev DA, Shalay VV (2020) Omskiy nauchnyy vestnik. Ser. Aviatsionno-raketnoye and energeticheskoye mashinostroyeniye 4(4):75–81. https://doi.org/10.25206/2588-0373-2020-44-75-81 5. Shapkin AS, Shapkin VA (2021) Teoriya riska i modelirovaniye riskovykh situatsiy: ucheb-nik 880 6. Nekrasova VV, Sleptsova KR (2018) Aktual’nyye voprosy upravleniya i ekonomiki. Trudy mezhdunarodnoy nauchno-prakticheskoy konferentsii: pod. Red. V.V. Nekrasovoy, A.A. Gorbachevoy 170–174 7. Ukhlova VV, Lyulina YeV (2018) Rol’ i mesto informatsionnykh tekhnologiy v sovre-mennoy nauke: sbornik statey Mezhdunarodnoy nauchno – prakticheskoy konferentsii 2(2):6–8 8. Ukhlova VV, Derevyanko AV (2019) Innovatsionnyye issledovaniya kak lokomotiv razvitiya sovremennoy nauki: ot teoreticheskikh paradigm k praktike: elektronnyy sbornik nauchnykh statey po materialam XVI Mezhdunarodnoy nauchno-prakticheskoy konferentsii 192–198 9. Luk’yanenko VI, Martynenko GN, Panov MYA (2012) Fiziko-tekhnicheskiye problemy energetiki, ekologii i energoresursosberezheniya. Trudy nauchno-tekhnicheskoy konferentsii molodykh uchenykh, aspirantov i studentov 89–94 10. Isanova AV, Martynenko GN, Sedaev AA (2018) Russ J Build Constr Archit 4(40):6–14 11. Kolodyazhnyi SA, Kolosov AI, Panov MY (2014) Scientific herald of the Voronezh state university of architecture and civil engineering. Constr Archit 1(21):16–33 12. Panov MY, Semyonov VN (2009) Scientific herald of the Voronezh state university of architecture and civil engineering. Constr Archit 1(1):35–41 13. Medvedeva ON, Astashev SI, Melkumov VN (2020) Sci J Constr Archit 2(58):9–19 14. Melkumov VN, Chuikin SV, Papshitsky AM, Sklyarov KA (2015) Scientific bulletin of the Voronezh state university of architecture and civil engineering. Constr Archit 2(38):41–48 15. Mel’kumov VN, Chujkin SV, Papshickij AM, Sklyarov KA (2015) Scientific herald of the Voronezh state university of architecture and civil engineering. Constr Archit 4(28):33–40

Improving the Reliability of Gas Distribution Networks Kuznetsov Sergey , Kolosov Aleaxander , and Kuznetsova Galina

Abstract On the basis of the queuing theory, a model of the work of repair units of gas distribution organizations has been developed. To determine the optimal number of personnel for repair departments, the model uses the reliability indicators of the gas distribution system. An equation is obtained for the number of serviceable elements of the gas distribution network, depending on the number of faults and parameters of restoration work. To speed up the work, a method has been developed for choosing the optimal routes for the movement of workers using the branch and bound method. The use of the results obtained in the work of the repair departments of gas distribution organizations will improve the reliability of the gas distribution networks. Keywords Reliability of gas pipelines · Gas distribution network · Operation of gas pipelines

1 Introduction The safe operation of gas distribution networks is becoming increasingly important. There is a deterioration in the safety performance of gas equipment. The technical condition of gas distribution networks and their maintenance need to be improved. There is a tendency to reduce the number of personnel serving gas distribution networks, which also leads to a decrease in their reliability. In this situation, an important task to improve the reliability of gas distribution networks is to justify the number of maintenance personnel and improve the organization of their work. Recently, a number of works have been published on this topic. In works [1– 6], the issues of assessing the reliability of gas distribution systems are considered. Prediction of the reliability of gas distribution systems is considered in works [7– 9]. Optimal control of gas transportation taking into account the reliability factor is

K. Sergey (B) · K. Aleaxander · K. Galina Voronezh State Technical University, 20 let Oktyabrya, 84, 394006 Voronezh, Russia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_28

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considered in [10]. So far, the problems of the effective work of the repair departments of organizations distributing gas have not been considered. The paper deals with the problems of improving the organization of the work of repair departments to improve the reliability of gas distribution networks.

2 Methods The planning of the work of the repair departments of gas distribution organizations is based on the choice of the correct methods of using equipment and personnel, which allow you to control the reliability of the equipment and regulate the workload of workers. Repair departments perform the following types of work: maintenance of gas distribution networks, including: checking the tightness of gas pipelines, equipment and instruments; inspection and check of valves; checking the operation of safety and locking devices, etc. bypassing gas pipelines and checking for gas contamination of wells, basements, underground structures, etc.; maintenance of valves of overground, underground and internal gas pipelines; current repair, which consists in the elimination of minor malfunctions and damage to gas pipelines and structures; preventive maintenance of gas equipment, while work is carried out related to the current repair and adjustment of gas equipment; works on localization or elimination of accidents; repair of locking devices, etc. To construct a mathematical model of the work of repair departments of a gas distribution organization, it is proposed to use the theory of queues. The work of the repair departments must ensure the required level of reliability of the elements of gas distribution networks. The repair department is a multi-channel queue system [11–14]. The work of repair departments must ensure a certain ratio of serviceable and faulty elements of the gas distribution network [15]: K (t) =

m(t) , N

(1)

where: m(t)—mathematical expectation of the number of serviceable elements of the gas distribution network; N—total number of elements of the gas distribution network.

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Repair service load indicator: ρ=

Z , V

(2)

where: Z—number of malfunctions of elements of the gas distribution network, units ·year−1 ; V —number of repaired elements of the gas distribution network, units ·year−1 . Average workload per employee: α=

ρ . l

(3)

where: l—number of employees. The likelihood that all workers are not busy: p=

 l  lk k=0

l l αl+1 α + k! l! 1 − α

−1

k

.

(4)

Average number of faults in the queue: n q = lα +

l l αl+1 p0 . l! (1 − α)2

(5)

Average waiting time for faults in the queue: tq =

αl+1 ll p0 . n  (1 − α)2 V l!

(6)

i=1

The equation for the number of serviceable elements of the gas distribution network has the form:    d m(t) N m(t) m(t) = −λ · +μ· 1− , (7) dt N N where: λ—the flow of failures of the elements of the gas distribution network, 1·year−1 ; μ—recovery flow of elements of the gas distribution network, 1·year−1 .

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Fig. 1 An example of a worker’s movement scheme when servicing a gas distribution network

By solution (7) with the initial condition K (t0 ) = K 0 : K (t) =

 μ μ + e−(λ+μ)(t−t0 ) K 0 − . λ+μ λ+μ

(8)

The gas distribution network of large cities is a highly ramified geographically distributed system. Maintenance of such a system involves significant movement of workers. To speed up work, it is advisable to choose the optimal routes for the movement of workers, Fig. 1. We will develop a system for finding optimal routes for servicing the gas distribution network. Let there be n service points of the gas distribution network. We build a matrix C with the initial data on the distances between service points: ⎛

c11 ⎜ c21 C =⎜ ⎝ ... cn1

c12 c22 ... cn2

... ... ... ...

where: cij —distance between service points i and j.

⎞ c1n c2n ⎟ ⎟, ... ⎠ cnn

(9)

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The length of the route will be determined by the following relationship: l(z) =

n−1 

cik ik+1 ,

(10)

k=0

Set of all routes P. It is required to find z0 ∈ P: l(z 0 ) = min l(z). z∈P

(11)

The combined block diagram of the model for troubleshooting the gas distribution network and the choice of routes for the movement of workers is shown in Fig. 2 [16, 17]. To select the optimal routes for the movement of workers, the branch and bound method is used. The branch and bound method has a tree structure for finding the optimal solution [18, 19]. The branch-and-bound algorithm is as follows: the set of routes is divided into 2 categories, containing a direct transition from vertex to vertex and not containing it. For each category, a lower score is found; division of one of the already existing subsets into two subsets is performed according to the method described above. If one of them is an already constructed route, then the minimum changes; the selection of the minimum values of the constructed routes is performed. It is advisable to implement the system for choosing the optimal routes for the movement of workers together with the GPS monitoring system for the movement of workers. This allows you to monitor the movement of workers, get accurate statistics on the location of workers at the facilities. The main advantage of a GPS monitoring system is that all parameters can be tracked in real time. With the introduction of this system, the efficiency of work is increased, the management of business processes is improved and funds are significantly saved. GPS monitoring enables optimal control and helps to analyze and evaluate performance.

3 Results and Discission In Fig. 3 shows a simulation modeling module that implements the developed mathematical model of the work of repair departments of a gas distribution organization. It is developed in the MatLab-Simulink environment and consists of separate Simulink functional blocks connected by links.

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Based on the survey data, the flow of refusals is determined

Determine the minimum recovery flow

We accept the initial headcount l

Increase in the number of staff

No

K>Kmin Yes Number of staff

Organization of staff work

Building a distance matrix C

Selection of branch edges (i,j)

No

Yes Optimal headcount with optimal employee relocation

Fig. 2 Block diagram of the algorithm for determining the optimal number repair units and routes of movement of workers

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Fig. 3 A simulation module that implements a mathematical model of the work of repair departments of a gas distribution organization in the environment of the MatLab-Simulink

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To simulate the real flow of gas equipment malfunctions and the work of repair services, the following information was accumulated in the database: description of the operating mode of the repair services of gas distribution organizations; description of the flow of repair requests typical for the operation of the gas distribution organization; description of the gas equipment recovery flow typical for the operation of the gas distribution organization. Modeling the execution of requests for the repair of gas equipment consists of the following stages: control of continuous model time; the time of receipt of repair requests is set from the database of real requests; the service time for repair requests is selected from the database of real repair requests. Determine the moments of occurrence of events: receipt of a repair request from the dispatcher for service; receipt of a repair request in the queue; transfer of the repair request for service to the contractor; leaving the repair request from the queue; completion of servicing the repair request by the contractor. Simulate the execution of requests for the repair of gas equipment and accumulate statistical data on the process. Indicators of the quality of service of repair requests are determined by processing the results of modeling by methods of mathematical statistics. To build expansion blocks for the simulation modeling module for executing requests for equipment repair, a top-down construction scheme was used. Building begins with defining the goals and objectives of the blocks and moves from top to bottom. In the development process, detailing of individual blocks is carried out. This ensures the systemic integrity of the simulation model. The blocks of the model are consistent across all areas of development. Using the developed simulation model for servicing gas equipment, calculations of the work of services of a gas distribution organization were carried out on the example of the city of Voronezh. In Fig. 4 shows the results of calculations of the work of the repair services of the gas distribution organization. As a result of the simulation, all the characteristics of the work of a real repair service of a gas distribution organization were obtained when working with a real flow of faults. An assessment of the sensitivity of each indicator to a change in the value of the intensity of the flow of faults and the intensity of the flow of repairs is obtained. This made it possible to identify shortcomings in the work of repair departments and determine the main directions of its improvement.

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Fig. 4 Results of calculations of the work of the repair service of the gas distribution organization: a incoming flow of faults; b the number of faults in the queue and at the stage of repair

4 Conclusions 1. On the basis of the queuing theory, a model of the work of repair units of gas distribution organizations has been developed. To determine the optimal number of personnel for repair departments, the model uses the reliability indicators of the gas distribution system. Relationships have been obtained linking the number of malfunctions of the elements of the gas distribution system and the number of maintenance personnel. 2. Maintenance of gas distribution networks is associated with significant movements of workers. To speed up the work, a method has been developed for

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choosing the optimal routes for the movement of workers using the branch and bound method. 3. It is advisable to implement the system for choosing the optimal routes for the movement of workers together with the GPS monitoring system for the movement of workers. With the introduction of this system, the efficiency of work is increased, the management of business processes is improved and funds are significantly saved. 4. Application of the results obtained in the practical activities of the repair departments of gas distribution organizations will improve the planning of their work and increase the reliability of gas distribution networks. 5. The approach used can be used when planning the work of repair departments of any geographically distributed engineering networks.

References 1. Medvedeva ON (2018) Comparative evaluation of the energy and economic efficiency the gas supply systems of small towns. Russ J Build Constr Archit 1:29–41 2. Yu W, Wen K, Min Yu, He L, Huang W, Gong J (2018) A methodology to quantify the gas supply capacity of natural gas transmission pipeline system using reliability theory. Reliab Eng Syst Saf 175:128–141 3. Yu W, Wen K, Li Y, Huang W, Gong J (2018) A methodology to assess the gas supply capacity and gas supply reliability of a natural gas pipeline network system. In: Proceedings of the international pipeline conference, American Society of Mechanical Engineers, V002T07A006 4. Li J, Yan M, Yu J (2018) Evaluation on gas supply reliability of urban gas pipeline network. Eksploat Niezawodn 20(3):471–477 5. Yu W et al (2018) Gas supply reliability assessment of natural gas transmission pipeline systems. Energy 162:853–887 6. Zhu J, Gong Zh, Guo Yu, Wang Q (2020) The stability and robustness analysis of SNG and PNG supply. MethodsX 7:100802 7. Chen F, Wu Ch (2016) A novel methodology for forecasting gas supply reliability of natural gas pipeline systems. Front Energy 8. Li J, Qin Ch, Yan M, Ma J, Yu J (2016) Hydraulic reliability analysis of an urban loop highpressure gas network. J Nat Gas Sci Eng 28:372–378 9. Zhu J et al (2019) Dynamic analysis of SNG and PNG supply: the stability and robustness view. Energy 185:717–729 10. Grudz V et al (2020) Optimal gas transport management taking into account reliability factor. Manag Syst Prod Eng 28(3):202–208 11. Melkumov VN, Kuznetsov SN, Kuznetsova GA (2020) Use of Kohonen maps for planning the repair of heating networks. Alternativnaya i intelektualnaya energetica. Materialy II mezhdunarodnoy nauchno-practicheskoy konferencii 70–71 12. Kolosov GA, Kuznetsova OA, Gnezdilova (2018) Management of work of emergency and recovery services of a gas-distributing organization. Russ J Build Constr Archit 2(38):19–26 13. Kuznetsov SN, Kuznetsova GA (2020) Digital models of gas equipment reliability management. Nauchny Zhurnal. Inzhenernie sistemy i soruzhenia 1(38):90–94 14. Melkumov VN, Panov MY (2012) Increasing the reliability of in-house gas equipment. Nauchni vestnic Voronezhskogo gosudarstvennogo arhitecturno-stroitelnogo universiteta. Stroitelstvo I arhitectura 4(28):32–40

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15. Melkumov VN, Sklyarov KA, Gorskikh AA (2011) Reliability monitoring of heat supply networks. Scientific Herald of the Voronezh State University of Architecture and Civil Engineering. Constr Archit 1(9):42–49 16. Melkumov VN, Kobelev AN (2012) Using cluster analysis to improve the reliability of engineering networks. Vestnic VGTU 11(8):141–145 17. Melkumov VN (2013) Modeling the process of repairing indoor gas equipment. Nauchny vestnic VGASU. Stroitelstvo i arhitectura 1(29):101–108 18. Golovinsky PA, Cheremisin AV (2010) Control of gas distribution network reliability. Scientific Herald of the Voronezh State University of Architecture and Civil Engineering. Constr Archit 2(6):12–20 19. Pavlucov SP (2012) Analysis of the composition and duration of operation of gas equipment. Inzhenernie sistemy i soruzhenia 3(8):16–23

Determination of Homogeneous Foundation’s Settlement Based on the Integral Estimation Method Ksenia Dubrakova , Alexey Bulgakov , and Thomas Bock

Abstract To meet the requirements of Federal Law No. 384 “Technical regulations on the safety of buildings and facilities”, it is necessary to prevent the unacceptable strain level of the building base. Consequently, the design of foundations should be carried out taking into account the limiting base settlement. In this regard, pride of place goes to the issue of projecting the settlement of foundations on compressible bases, the determination of their unevenness and settlement progress. This article proposes the development of a new determining method for homogeneous foundation’s settlement based on the integral estimation method, that can help reduce the number of performed calculations. Assuming that the ground deformations occur mainly in a zone of some thickness directly under the foundation base, and the ground distortion decreases with depth, it may be concluded that it is possible to predict the ultimate settlement of a homogeneous foundation tell by the settlement of one layer of some finite thickness. Assume that the total foundation base settlement is proportional to the ratio of the total stress in a layer of some finite thickness tending to 0, to the total additional stress in a layer with a thickness tending to infinity. Using developed coefficient Kα makes it possible to determine foundation settlement by calculating the deformations of one ground layer located directly under the foundation base, which greatly simplifies the underground structure design. The value of the coefficients α Kα is calculated under various parameters η; with ξ integration by parts and is presented in the article as a table. The settlement values determined by the current regulatory documents and by the developed methodology coincide, which allows us to conclude that the proposed method has a sufficient degree of reliability and can significantly facilitate the process of determining base deformations of buildings and structures. Keywords Foundation · Settlement · Base · Compressed strata · Method of layer-by-layer summation · Integral estimation method K. Dubrakova · A. Bulgakov (B) Southwest State University, 50 let Oktyabrya Street 94, 305040 Kursk, Russia e-mail: [email protected] T. Bock Technical University of Munich, Arcis Street 21, 80333 Munich, Germany e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_29

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1 Introduction To meet the requirements of Federal Law No. 384 “Technical regulations on the safety of buildings and facilities”, it is necessary to prevent the unacceptable strain level of the building base. Consequently, the design of foundations should be carried out taking into account the limiting base settlement. In this regard, pride of place goes to the issue of projecting the settlement of foundations on compressible bases, the determination of their unevenness and settlement progress. Nowadays, there are many methods for determining the deformations of the “building-base” system. They differ in accuracy, the number of factors taken into account, the design schemes used, and the assumptions in describing the ground behaviour. In [16], a refined method for calculating the settlement of shallow foundations was developed based on the method of layer-by-layer summation. This method made it possible to take into account the division into components of the diagrams of additional external normal loading, leading to the occurrence of elastic and elastoplastic deformations, and a change in the total deformation modulus E of the ground base layers depending on the stress state. The [8] considers the possibility of taking into account the ground deformability in the vertical and horizontal directions under the action of vertical σzp and horizontal σxp ,α additional stresses calculated for the points of the half-plane. The points are located on the central vertical in the middle of the layers hi . The analysis results of the stress–strain state of anisotropic bases, which were loaded through a rigid stamp, uniform and nonuniform strip loads using the finiteelement method, and the experiment plan with a wide range of changes in anisotropy indices are presented in the research [9]. Also, there was proposed a practical method for predicting foundation settlement, which allows taking into account the strain anisotropy of the ground. Proposals for improving the calculation of the foundation settlement, which take into account the anisotropic ground properties, are presented in [4]. Considering the natural anisotropy of grounds will make it possible to more reasonably assign the sizes of foundation base and determine the settlement, which allows obtaining a significant economic effect. In [3, 11], a method is proposed for determining the strip foundation settlement, taking into account the horizontal displacements of the ground by changing the coefficient β in calculating the bases for deformations. Experimental studies of bearing capability and settlement of clay base of foundations under block regime cyclic loading are presented in [11]. As a result, it was concluded that under such loads, soil deformations increase within the compressed strata, and also in all load blocks, the base is deformed with different intensities. The most intensive soil deformations and foundation subsidence occurred at the initial stage of loading, and during the transition to the second stage, stabilization took place. Bearing-capacity failure occurs at the third stage of loading after reaching the limiting state of the soil body in the compressible strata of the slab foundation.

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In [10, 19] was proposed a new approach to solving an engineering problem of determining the foundation settlement of large areas using a design model of an elastic half-plane of limited distribution capacity, which takes into account the discreteness and strength characteristics of the soil ground. Methods for determining the consolidation and creep coefficients from experimental curves are described in [13]. Calculation formulas for determining foundation settlement, taking into account the creep of quasi homogeneous soils of the foundations, obtained based on the results of experimental data, are also given. The structural strength influence of soils on foundation settlement calculations and the comparison of the settlement obtained using the normative method and taking into account the structural ground strength are considered in [14]. A new method for determining an average additional vertical pressure for calculating the consolidation settlement is presented in [6, 17]. The article also presents an algorithm for obtaining a simplified influence coefficient formula for calculating the stresses that arise in the center of a uniformly loaded shallow foundation, a numerical example of the practical application of the obtained formula is given. The study issues of pore space of moraine clay soils using the analysis of SEM images of the surface of samples prepared by a special technique are given in [7, 18]. The authors’ studies of the moraine clay soil microstructure have shown that soils are characterized by the presence of large micropores with a specific anisometric crescent shape. These micropores are formed at the boundary between the surface of large sandy-silty quartz or feldspar grains and a finely dispersed unoriented clay matrix. It was concluded that such micropores can work as ways of filtering groundwater through the soil body and significantly change its properties. A brief overview of nonlinear models of soil work, which are used in popular mathematical calculating programs of soil behavior in a complex stress state, is given in [21]. The author analyzes the applicability of these models and also provides methods for checking the reliability of the calculation results that can be obtained using nonlinear models. The methodology for predicting engineering-geological processes within an urban region is given in [5, 20]. The paper shows the possibility of using cluster analysis to integrate dissimilar engineering-geological and geodynamic parameters on the example of the Khanty-Mansiysk city.

2 Methods Currently, the settlement of the foundation base using a design scheme in the form of a linearly deformable half-space is calculated by the layer-by-layer summation method. Assuming that the ground deformations occur mainly in a zone of some thickness directly under the foundation base, and the ground distortion decreases with depth, it may be concluded that it is possible to predict the ultimate settlement of a homogeneous foundation tell by the settlement of one layer of some finite thickness.

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Let us assume that the total foundation base settlement is proportional to the ratio of the total stress in a layer of some finite thickness tending to 0, to the total additional stress in a layer with a thickness tending to infinity. To significantly reduce the amount of calculations contained in the analysis of the settlement homogeneous foundation erected in pits less than 5 m deep, using the method of layer-by-layer summation, it is proposed to introduce a correction factor reflecting the settlement proportion in the considered layers: σzp,1 − σzγ ,1 σzp,lim −σzγ ,lim

Kα =

(1)

where σzp,1 − σzγ ,1 —total additional stresses in a layer of some finite thickness; σzp,lim − σzγ ,lim —total additional stresses in base. The coefficient α is determined by the formula:     ξ η 1 + η2 + 2ξ 2 2 η α= + arctg    π ξ 2 + η2 1 + ξ 2 1 + ξ 2 + η2 ξ 1 + ξ 2 + η2

(2)

. where: η = bl , ξ = 2z b Knowing the correction factor Kα and the settlement of one layer of some finite thickness, it is possible to determine the foundation base settlement by the formula: s=

S1 Kα

(3)

where S1 —settlement of one layer of some finite thickness; Kα —correction factor. The settlement of one layer of some finite thickness can be determined by the formula: S1 = β

hi (p−σzγ,0 ) E

(4)

where hi —is the layer thickness in which the settlement is determined. By reference to (2.4 *), formula (4) takes the form: s=β

hi (p−σzγ,0 ) EKα

(5)

where β—the coefficient taking into account the lateral expansion of the ground, equal to 0.8; hi —the layer thickness in which the settlement is determined; p—the average pressure under the foundation base, kPa; σzγ, σzγ,0 —vertical stress by own ground weight at the level of the foundation base, kPa (when planning by cutting σzγ, 0 = γ / d, where γ—the unit weight of soil located above the base; d—footing depth from the planning level); E—deformation modulus of the i-th soil layer along the primary loading branch; Kα —correction factor.

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To determine the total value of the coefficient in a layer of some finite thickness α1 and the total value of the coefficient in foundation base αlim it is necessary to calculate an integral (3) for different values of ξ. In this case, for αi, the integration should be extended within the thickness of the considered layer, and in case of αlim —within all foundation base. The ξ-values for the total value of the coefficient in a layer of some finite thickness vary from 0.05 to 12. As the total value of coefficient at the foundation base should be taken the values of a certain improper integral with a lower limit equal to 0 and an upper infinite limit.

3 Results The value α0,05 is calculated when η = 1; ξ = 0,05 integration by parts:   2 ξ η(1 + η2 + 2ξ 2 ) η  α0,05 + ar ctg  π ξ 1 + ξ 2 + η2 (ξ 2 + η2 )(1 + ξ 2 ) 1 + ξ 2 + η2 0    ξ(1 + 12 + 2ξ 2 ) 2 1  + = ar ctg  π ξ 1 + ξ 2 + 12 (ξ 2 + 12 )(1 + ξ 2 ) 1 + ξ 2 + 12    1 2 ξ 4  dξ = ar ctg  dξ + π π ξ ξ2 + 2 (ξ 2 + 1) ξ 2 + 2 

0,05

Further calculations for each value of ξ and η are performed similarly and are summarized in Table 1. Let us calculate the values of correction factor Kα according to formula (2) for each value of ξ and η: Kα =

α1 0,05 αlim 2,244

Further calculations are performed in the same way. The results are summarized in Table 2. Within the framework of studies, the settlement was determined by the method which takes into account the integral criteria at various values of Kα . From the comparison of the results of calculating the settlement by the aforementioned methods, it follows that the closest result is given by Kα at ξ = 0.05. The maximum difference between the results of settlement calculations obtained by using the method of integral estimates and the method of layer-by-layer summation is 9.6%. This discrepancy is justified by taking into account the deformations of the base outside the compressible strata (Fig. 1).

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Table 1. αi coefficient values. ξ = 2z/b

αi coefficient for foundations Rectangular with an aspect ratio η = l/b equal to:

Strip foundations (η ≥ 10)

1,0

1,4

1,8

2,4

3,2

5,0

0,05

0,050

0,050

0,050

0,050

0,050

0,050

0,050

0,1

0,100

0,100

0,100

0,100

0,100

0,100

0,100

0,2

0,200

0,200

0,200

0,200

0,200

0,200

0,200

0,4

0,396

0,397

0,397

0,398

0,398

0,398

0,398

0,8

0,751

0,764

0,768

0,770

0,771

0,771

0,771

1,2

1,032

1,070

1,085

1,093

1,097

1,098

1,099

1,6

1,241

1,311

1,343

1,363

1,372

1,376

1,377

2,0

1,397

1,500

1,551

1,586

1,603

1,612

1,615

2,4

1,515

1,647

1,717

1,770

1,798

1,815

1,819

2,8

1,605

1,763

1,852

1,923

1,964

1,990

1,998

3,2

1,677

1,856

1,963

2,051

2,106

2,144

2,156

3,6

1,735

1,933

2,054

2,160

2,228

2,280

2,297

4,0

1,783

1,996

2,131

2,252

2,335

2,400

2,425

∞

2,244

2,633

2,935

3,288

3,647

4,209

5,089

Table 2 Values of correction factor Kα ξ = 2z/b

Correction factor Kα for foundations Rectangular with an aspect ratio η = l/b, equal to:

Strip foundations (η ≥ 10)

1,0

1,4

1,8

2,4

3,2

5,0

0,05

0,022

0,019

0,017

0,015

0,014

0,012

0,010

0,1

0,045

0,038

0,034

0,030

0,027

0,024

0,020

0,2

0,089

0,076

0,068

0,061

0,055

0,048

0,039

0,4

0,176

0,151

0,135

0,121

0,109

0,095

0,078

0,8

0,335

0,290

0,262

0,234

0,211

0,183

0,152

1,2

0,460

0,406

0,370

0,332

0,301

0,261

0,216

1,6

0,553

0,498

0,458

0,415

0,376

0,327

0,271

2,0

0,623

0,570

0,528

0,482

0,440

0,383

0,317

2,4

0,675

0,626

0,585

0,538

0,493

0,431

0,357

2,8

0,715

0,670

0,631

0,585

0,539

0,473

0,393

3,2

0,747

0,705

0,669

0,624

0,577

0,509

0,424

3,6

0,773

0,734

0,700

0,657

0,611

0,542

0,451

4,0

0,795

0,758

0,726

0,685

0,640

0,570

0,477

11,6

0,927

0,913

0,900

0,881

0,859

0,814

0,724

12,0

0,930

0,916

0,903

0,885

0,863

0,819

0,730

Determination of Homogeneous Foundation’s Settlement … Fig. 1 Dependence graph of coefficient Kα = Kα (ξ) to various parameters η

309

Kα 1.000 0.900 0.800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 0.000

0

2

4

6

8

10

12

ξ 14

4 Conclusions 1. The proposed method for calculating the foundation settlement, based on the integral estimates method, can significantly reduce the calculations and save labour resources. 2. As calculation results, the values of the correction factor Kα were obtained, the introduction of which will reduce the amount of calculations performed in comparison with the layer-by-layer summation method. 3. Calculation results of the foundation settlement using a correction factor differ from the results of the calculation using the layer-by-layer summation method, not exceeding 10%. 4. The proposed method for calculating the foundation settlement is allowed to be used with homogeneous foundations and foundations erected in pits less than 5 m deep.

References 1. Nguyen MD, Yang KH, Lee SH, Wu CS, Tsai MH (2013) Geosynth Int 20(3):207–225 2. Phoon KK, Retief JV (2016) Reliability of Geotechnical Structures in ISO2394, 249 3. Baj VF (2009) Sbornik nauchnyh trudov po materialam mezhdunarodnoj nauchnoprakticheskoj konferencii 24(4):57–60 4. Bocharova MA (2016) Vestnik nauchnyh konferencij 9–3(13):22–25 5. Zudilin AE, Savincev IA (2011) Gornyj informacionno-analiticheskij byulleten’ (nauchnotekhnicheskij zhurnal) 12:99–103 6. Ismejk M (2012) Osnovaniya, fundamenty i mekhanika gruntov 3:10–13 7. Sokolov VN, Razgulina OV, Yurkovec DI, Cernov MS (2007) Poverhnost’. Rentgenovskie, sinhrotronnye i nejtronnye issledovaniya 7:60–65 8. Korobova OA, Maksimenko LA (2015) Interekspo Geo-Sibir’ 1

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9. 10. 11. 12.

Korobova OA (2003) Izvestiya vysshih uchebnyh zavedenij. Stroitel’stvo 1(529):26–31 Lyashenko PA, Denisenko VV (2016) Stroitel’stvo i arhitektura 1(4):14–17 Mirsayapov IT, Koroleva IV, Sabirzyanov DD (2016) Izvestiya KazGASU 1(35) Mirsayapov IT, Saraf HM (2019) Izvestiya Kazanskogo gosudarstvennogo arhitekturnostroitel’nogo universiteta 1(47):175–183 Zakulin AC, Zhakulina AA, Kropachev PA, Zhautikova SA (2021) Trudy universiteta 1(82):88– 92 Osipova ON, Dyba VP (2009) Maloetazhnoe stroitel’stvo v ramkah Nacional’nogo proekta “Dostupnoe i komfortnoe zhil’e grazhdanam Rossii: tekhnologii i materialy, problemy i perspektivy razvitiya v Volgogradskoj oblasti”: materialy Mezhdunarodnoj nauchnoprakticheskoj konferencii, Volgograd, 15–16 dekabrya 2009 goda. – Volgograd: Volgogradskij gosudarstvennyj arhitekturno-stroitel’nyj universitet, 216–219 Pilyagin AV (2006) Izvestiya Kazanskogo gosudarstvennogo arhitekturno-stroitel’nogo universiteta 1(5):76–78 Pronozin YaA, Chikishev VM, Rachkov DV (2017) Vestnik PNIPU. Stroitel’stvo i arhitektura 4 Osipova MA, Noskov IV, Tejhreb NYa, Tupyakova LV (2007) Polzunovskij vestnik 1–2:72–74 Kolchunov VI, Potapov VV, Dmitrieva KO, Il’in VA (2017) Stroitel’stvo i rekonstrukciya 4(72):27–33 Subbotin AI (2018) Vestnik Volgogradskogo gosudarstvennogo arhitekturno-stroitel’nogo universiteta. Seriya: Stroitel’stvo i arhitektura 54(73):43–51 Fedorovskij VG, Bezvolev SG (2000) Osnovaniya, fundamenty i mekhanika gruntov 4:10–18 Shashkin AG (2010) Inzhenernaya geologiya 3:29–37 Shiryaeva MP, Krivonos EA (2014) Nauchnye trudy KUBGTU: elektronnyj setevoj politematicheskij zhurnal 3:18–25

13. 14.

15. 16. 17. 18. 19. 20. 21. 22.

The Use of Ash and Slag Waste in the Production of Building Materials Olga Sotnikova , Elena Zhidko, and Sergei Tenyachkin

Abstract The most appropriate solution to the environmental and economic problems associated with the disposal of ash and slag waste is the creation of a waste-free production. The use of ash and slag waste from thermal power plants allows you to save on the cost of basic expensive materials without compromising the quality of the product. The solution of the environmental problem of ash and slag waste disposal is shown by the example of experiments conducted on the use of ash. The purpose of the development is to obtain a construction material using fuel ash that meets modern requirements in terms of strength and lightness. To find the composition, mathematical planning of a step-by-step optimum search experiment was used. The use of mathematical methods of step-by-step improvement of the plan made it possible to experimentally find the composition of ash concrete used in construction. Blocks made using ash are used for the construction of thermal chambers and laying the foundations of pumping stations on wells. And also Keywords Environmental problem · Environment · Fuel ash · Waste · Solobetone · Waste disposal

1 Introduction An increasing risk to human life and health due to a decrease in the quality of the natural environment, the constant threat of major man-made disasters and degradation of natural ecosystems, an exorbitant load of production and consumption waste is becoming an increasingly urgent problem of the world community [1–3]. Most O. Sotnikova · E. Zhidko (B) Voronezh State Technical University, 20th Anniversary of October, 84, Voronezh, Russia e-mail: [email protected] S. Tenyachkin Military Training and Research Center of the Air Force “Air Force Academy named after Professor N.E. Zhukovsky and Yu. A. Gagarin”, Voronezh, Russia O. Sotnikova · E. Zhidko · S. Tenyachkin Voronezh State Technical University, Voronezh, Russia © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_30

311

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alarming are the trends indicating that the situation is improving. Air, water and soil in areas of large industrial centers often contain substances whose concentration exceeds the maximum permissible norm. Safe and sustainable (anti-crisis) development of economic entities in modern conditions can be achieved through timely provision of decision makers with high-quality information about the state of the external and internal environment of the facility [4–6]. A serious problem is the task of recycling the ash of thermal power plants (CHP), which is stored in the ash dumps of Russia over 85 million tons as of the beginning of the XXI century.

2 Methods Consider the mathematical planning of experiment for the production of structural solobetone [26]. The purpose of the development is to obtain a building material using fuel ash, namely structural heat-insulating corrugated concrete with a bulk density of 600– 800 kg/m3 and with a compressive strength class B 2 (tensile strength not lower than 50 kg/cm2 ) [11, 12]. The composition is set by six components: Cement, water, ash, lime, aluminum powder and soda. Mass fractions of these components zi =

mi b  mi

(1)

i−1

are related by

b 

zi = 1

(2)

i=1

In formula (1), mi denotes the mass of the i-th component. The output depends on the composition: σ—ultimate strength at compression, kg/cm2 ; γ—bulk weight solobetone, kg/m3 and others. f the mass fractions zi are used as factors, then for studying the compositionproperty diagrams it will be necessary to apply Scheffe’s cumbersome plans on multidimensional simplex tetrahedra with vertices corresponding to pure substances, which is physically meaningless for a concrete mix. At the same time, it is known from literature sources and the experience of factory studies [7, 8, 13–15] that the strength and the usual mass of aerated concrete, in which sand is used instead of ash, is determined by the mass ratios of water, sand, D3-24 , etc., respectively. to the mass of cement. Therefore, we take as factors the following values:

The Use of Ash and Slag Waste in the Production …

313

(3) the ratio of the masses of water. Ash, lime, additives D3-24, soda, respectively, to the mass of the cement. To find the composition, the mathematical planning of the experiment of a stepby-step search for the optimum was used. At the first stage, five factors varied: – the ratio of the mass of water to the mass of cement in the range from 0.45 to 0.85; – the ratio of the mass of ash to the mass of cement in the range from 1.4 to 2; – the ratio of the mass of lime by weight of cement in the interval from 0.01 to 0.03; – the ratio of the mass of D3–24 by weight of cement in the interval from 0.9 to 1.1; – the ratio of the mass of soda ash by weight of cement in the range from 0.0026 to 0.006. The problem is formulated as follows: It is required to put the experiment in this way, so that at a minimum cost for its conduct, to obtain information on its results, sufficient for the construction of adequate mathematical models. 

σ = f 1 (x1 , x2 , x3 , x4 , x5 ) 

γ = f 1 (x1 , x2 , x3 , x4 , x5 )

(4) (5)

to find the values of the factors (i = 0…5) notifies the response function (4) to (5) extreme values: σ ≥ 50 κ/CM2 .

(6)

γ ≤ 700 κ/M3

(7)

To build a surface response (4), (5) use economical method of steep climbing [16–18]. In this method each of the factors (3) varies on two levels. As used factor values that are close to the same in the production of conventional concrete. Assessment for levels of ash translation run on the sand content of dioxide of aluminium in them. The lower level is coded as –1, top +1. The plan of the experiment, the results calculated by the regression equations   obtained on the basis of the experiment, responses σ and γ and the transition formula for coded variables are given in Table 1.

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Table 1 Factors and their levels in the first series of experiments № experience

Name of factors

Factor designation

Levels Lower

Basic (zero)

Upper

The formula for the transition to code variables

1

The ratio of the mass of water to the mass of cement

X1

0.45

0.65

0.85

X1 =

x1 −0,65 0,2

2

Ratio of ash mass to cement mass

X2

1.4

1.7

2

X2 =

x2 −1,7 0,3

3

The ratio of lime mass to cement mass

X3

0.01

0.02

0.03

X3 =

x3 −0,02 0,01

4

The ratio of the mass of the additive D3−24 to the mass of cement

X4

0.9

1

1.1

X4 =

x4 −1 0,1

5

The ratio of the mass of soda to the mass of cement

X5

0.0026

0.0043

0.006

X5 =

x5 −0,004 0,0017

As a first approximation we assume that model (4) and (5) linear: σˆ = a0 + a1 · X 1 + a2 · X 2 + a3 · X 3 + a4 · X 4 + a5 · X 5

(8)

γ ∧ = b0 + b1 · X 1 + b2 · X 2 + b3 · X 3 + b4 · X 4 + b5 · X 5

(9)

To estimate the six coefficients ai (i = 0…5) in the model (8) and the six coefficients bi (i = 0…5) in the model (9) the results of the experiment is enough to have eight experiments to plan TEU-25−2 (fractional factorial, which is a quarter of a replica from the plan PPE-(full factorial experiment), obtained, for example, generating ratios: X 5 = X 1 · X 2, X 4 = X 1 · X 3

(10)

This plan is given in Table 2 Experience No. 9 (zero experience) needed to assess curvature of the response surface and check of adequacy (matching the experimental data within the margin of error) of linear model (8), (9) or model, enhanced interactions (products of factors):

The Use of Ash and Slag Waste in the Production …

315

Table 2 Plan TEU-25−2 (X 5 = X 1 · X 2 , X 4 = X 1 · X 3 ) and the results of the experiment № experience

Response σ, kg/cm2

Factor levels



γ

908

23,25

906,5

801

14,5

803,5

845

5,5

845

743

−3,25

742

50

856

48,5

856,5

−1

42

755

39,75

753,5

– 1

32

794

30,75

795

1

17

692

22

692

0

25 (23; 24; 25; 28)

794,5 (781; 787; 793; 817)

22,625

799,25

X2

X3

X4

X5

1

−1

−1

−1

1

1

22

2

1

−1

−1

−1

−1

12

3

−1

1

−1

1

−1

4

4

1

1

−1

−1

1

2

5

−1

−1

1

−1

1

6

1

−1

1

1

7

−1

1

1

– 1

8

1

1

1

1

9

0

0

0

0

γˆ = a0 +

5 i=1

5 i=1

Calculated using regression equations σ

X1

σˆ = a0 +

Response γ, kg/m3



ai · X i + a23 X 2 · X 3 + a123 · X 1 X 2 X 3

(11)

bi · X i + b23 X 2 · X 3 + b123 · X 1 X 2 X 3

(12)

Experiment in conditions of zero-experience n 9 was repeated four times with the purpose of obtaining information for statistical evaluations. The results of the parallel experiments were calculated: Arithmetic mean n y=

i=1

yk

(13)

n

and the sample variance n S y2 =

− y)2 = n−1

i=1 (yk

n i=1

yk2 − n · y 2 , n−1

(14)

where n is the number of replications. The number of degrees of freedom for the variance equals f = n – 1.

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3 Results and Discussion Analyze the results of repeated experiments on the presence of coarse (rather than random) errors. Suspected gross error are popping out of the total number of values. Then carry out check according to a statistical criterion of Grubbs: popping a value Umax (or Umin ) excluded from the sample as a gross measurement, if the value calculated by the formulae: (15)

is greater than the table value of the criterion of Grubs at a given confidence level and number of degrees of freedom f = n – 2. The calculated values of dispersion is the dispersion of reproducibility. Them estimated variance for the coefficients of the regression equation by the formula: 2 = Sbj

2 SBOCP , N ·m

(16)

where N—is the number of experiments m -is the number of their repetitions. These variances are estimated, critical values of coefficients ai and according to the formula:  2 , (17) bκp = t p (t) × Sbj where t p (t)-the table value of student’s t test. If the absolute value of the coefficient of the regression equation will be smaller than the critical (17), the term with this factor as a minor is excluded from the regression equation. The first eight experiments from Table 2, it is sufficient to calculate the coefficients of the models (11) and (12) based on the method of least squares from the condition of minimum total for all the experiments, the quadratic deviation of the parameter values yˆ from experienced y (bj) =

n k=1



yˆk − y k

2

=

n k=1



bo +

m j=1

b j X jk +

 y

b ji X ik X jk − yˆk

2

→ min

(18)

Here m—is the number of factors, X jk —the value of the factor j in the k-th experience n—number of independent experiments. Equating to zero the derivatives of functions (18) at b0 b j bi j , get to determine the N unknown coefficients of a system of N linear equations with N unknowns. Plans for PPE and TEU have significant orthogonality property:

The Use of Ash and Slag Waste in the Production … N 

X ik X jk = 0 in i = j, j = 1, 2 . . .

317

(19)

k=1 N 

X ik X ik = N ; i = 1, 2 . . .

(20)

k=1

In addition n 

X ik = 0 i = 1, 2 . . .

(21)

k=1

Therefore, the calculation formulas for the coefficients of regression Eqs. (11) and (12) are simple: The coefficient of the regression equation before factor X j equal to the scalar product of the vector-column response y the column vector of this factor in the planning matrix, divided by the number of experiments (without zero) bj =

N N 1  1  X ik Y k , bi j = X ik X jk Y k N k=1 N k=1

(22)

Using these formulas, according to the Table 2 calculated values of the coefficients a0 , a1 , a2 , a3 , a4 , a5 , a23 , a123 b0 , b1 , b2 , b3 , b4 , b5 , b23 , b123 The results of the experiment the first stage of the method the steep ascent was selected and implemented a plan of the experiment of the 2nd phase. Factors and their levels for the second series of experiments are presented in Table 3. The regression equations have the following form: σ = 39 + 6, 25X1 − 7, 5X2 + 7X3

(23)

γ = 787, 875 − 42, 125X3 + 24, 125X2 X3

(24)

Calculated according to these equations, the values in all experiments are given in Table 4.

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O. Sotnikova et al.

Table 3 Factors and their levels for the second series of experiments № experience

Name of factors Factor designation

Levels Lower

Lower

Lower

The formula for the transition to code variables

1

The ratio of the mass of water to the mass of cement

X1

0.54

0.58

0.62

X1 =

x1 −0,58 0,04

2

Ratio of ash mass to cement mass

X2

1.35

1.49

1.63

X2 =

x2 −1,49 0,14

3

The ratio of lime mass to cement mass

X3

0.025

0.03

0.035

X3 =

x3 −0,03 0,005

4

The ratio of the mass of the additive D3−24 to the mass of cement

X4

1

1

1

Does not vary

5

The ratio of the mass of soda to the mass of cement

X5

0.0043

0.0043

0.0043

Does not vary

Table 4 Plan PPE-23 and the results of the experiment № experience

Factor levels

X1

X2

Response σ, kg/cm2

Response γ, kg/m3

X3

Calculated using regression equations σ



γ



10

−1 −1 −1 34

891

33.25

854.125

11

1

−1 −1 45

837

45.75

854.125

12

−1 1

−1 18

803

18.25

805.875

13

1

−1 31

789

30.75

805.875

14

−1 −1 1

47

717

47.25

721.625

15

1

−1 1

60

746

59.75

721.625

16

−1 1

1

32

764

32.25

769.875

17

1

1

1

45

756

44.75

769.875

18

0

0

0

40.25 (37; 40; 41; 43 801 (788; 789; 802; 39 825)

1

787.875

The Use of Ash and Slag Waste in the Production …

319

4 Conclusions 1. In modern conditions increases the severity of the problem of disposing of ash and slag materials from combustion of coal in thermal power plants. Their accumulation in increasing volumes leading to a rapid increase of environmental, social and economic costs because of the extremely low level of utilization. 2. The use of ash waste saves on the cost of basic expensive materials without compromising the quality of the product, simultaneously solving the disposal problem saleslady materials. 3. The use of waste increases profitability. 4. Slabosolenym waste processing allows to stabilize the environmental situation in the country. 5. Complex use of natural raw materials and waste leads to an increase in the level of national economy of materials and goods, rational distribution of productive forces, to reduce different cost items and, therefore, enhances the efficiency of capital investments in the national economy. 6. The use of mathematical methods for phased improvement plan allowed experimentally to find the composition of Solomona used in construction for strength and lightness meet the requirements [18]. 7. Blocks are used for the construction of heating chambers and laying the foundations of the pumping stations at the wells. And for low-rise buildings for production purposes (boilers, pumping and pumping stations, and water lifting stations).

References 1. Malinina LA, Volkov JuS, Rekitar JaA (2012) Jekologicheskie i tehnologicheskie aspekty razvitija stroitel’stva i proizvodstva stroitel’nyh materialov v mire, vol 5. Moscow: «BINTI» 2. Gourley JT (2013) Geopolymers, opportunities for environmentally friendly construction material. In: Gourley JT (ed) Proceedings of the international conference and exhibition on adaptive materials for a modern society (Materials ‘2003). Sydney, Australia 3. Nekrasova AS, Sinjak JuV (2017) Perspektivy razvitija toplivno-jenergeticheskogo kompleksa Rossii na period do 2030 goda. Probl Forecasting 4:21–52 4. Putilin EI, Cvetkov VS (2013) Obzornaja informacija otechestvennogo i zarubezhnogo opyta primenenija othodov ot szhiganija tverdogo topliva na TJeS .Soyuzdornii, p 60, Moscow 5. Burdonov AE, Barahtenko VV, Zelinskaja EV, Suturina EO, Burdonova AV, Golovina AV (2014) Fiziko-mehanicheskie harakteristiki kompozicionnyh materialov na osnove othodov proizvodstva s real’nymi recepturami. Mag Civ Eng 9(35):14–22 6. Barahtenko VV, Burdonov AE, Zelinskaja EV, Tolmacheva NA, Golovina AV, Samorokov VJe (2013) Issledovanie svojstv sovremennyh stroitel’nyh materialov na osnove promyshlennyh. Fundam Res 10–12:2599–2603 7. Sirotyuk VV, Lunev AA (2017) Strength and deformation characteristics of ash and slag mixture. Mag Civ Eng 6(74):3–16 8. Panibratov JuP, Staroverov VD (2015) K voprosu primenenija zol TJeS v. Technol Concr 1–2:43–47

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9. Hardjito D (2012) Development and Properties of Low-Calcium Fly Ash-based Geopolymer Concrete. Research Report GC1 / D. Hardjito, B. V. Rangan, vol 103. Curtin University of Technology, Perth 10. Lamb DW (2016) Ash disposal in dams, mounds, structural fills and retaining walls. In: Proceedings of the third international ash utilization symposium, U.S. Bureau of Mines, Information Circular, vol 86, pp 170–179 11. GOST 10180–2012 (2013) Betony. Metody opredeleniya prochnosti po kontrolnym obraztsam, p 36. Moscow 12. Asaturjan VI (1983) Teoreticheskoe planirovanie, vol 248. Radio and Communication, Moscow 13. Hardjito D (2015) Development and Properties of Low-Calcium Fly Ash-based Geopolymer Concrete. Research Report GC1 / D. Hardjito, B. V. Rangan, vol 103. Curtin University of Technology, Perth 14. Haleema A, Luthrab S, Mannana B, Khuranaa S, Kumarc S (2016) Critical factors for the successful usage of fly ash in roads and bridges and embankments: analyzing Indian perspective. Resour Policy 49:334–348 15. Hadbaatar A, Mashkin NA, Stenina NG (2016) Study of AshSlag wastes of electric power plants of Mongolia applied to their utilization in road construction. Procedia Eng 15:1558–1562 16. Bol’shev LM, Smirnov NV (1983) Tablicy matematicheskoj statistiki. Moscow: Science. The main edition of physical and mathematical literature, vol 416 17. Louson Ch, Henson R (1986) Chislennoe reshenie zadach metodom naimen’shih, vol 232. Nauka, Moscow 18. Linnik JuV (1958) Metod naimen’shih kvadratov i osnovy matematiko-statisticheskoj teorii obrabotki nabljudenij. Moscow: Fizmatliz 334

Thermofluctuation Constants of Built-Up Section Wooden Beams Without Special Ties A. V. Erofeev and P. V. Monastyrev

Abstract Predicting the performance of building materials, products and structures can be carried out from the standpoint of a thermofluctuation concept of destruction and deformation of solids. According to the concept, the decisive role in the destruction and deformation of solids belongs to the thermal movement of kinetic units. To make the forecast, it is necessary to determine the thermal fluctuation constants included in the generalized Zhurkov equation on the basis of experimentally obtained data on the dependence of durability on temperature and voltage. The given paper presents experimental data on the determination of thermal fluctuation constants for built-up section wooden beams without special ties. The height of built-up elements is different. The obtained thermofluctuation constants have been compared with the previously obtained constants for solid section and built-up section wooden elements. The height of the elements is the same. Keywords Wooden beams · Generalized Zhurkov equation · Prediction of durability · Built-up section · Thermofluctuation concept

1 Introduction The thermofluctuation concept of destruction and deformation of solids appeared in the middle of the last century and became the next step in the study of destruction and deformation mechanisms [1, 2]. In the thermofluctuation concept, the destruction of a body is considered as a thermoactivation process that develops over time when a load is applied to the body. It reduces the binding energy, which in its turn leads to a change in the distance between the atoms [3]. Consequently, with an increased mechanical field, the process of breaking interatomic or intermolecular bonds accelerates. The directivity of the applied load makes this process irreversible due to the accumulation of elementary discontinuities.

A. V. Erofeev (B) · P. V. Monastyrev Tambov State Technical University, Tambov, Russia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 N. Vatin et al. (eds.), Modern Problems in Construction, Lecture Notes in Civil Engineering 287, https://doi.org/10.1007/978-3-031-12703-8_31

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During the experimental study of temperature–time dependence of strength, S. N. Zhukov derived a formula for determining the durability of the material. The development of scientific foundation of the thermofluctuation concept allowed one to explain the mechanism of destruction and reveal the physical meaning of the constants included in the resulting formula [4]:  U0 − γ σ , τ = τ0 exp RT 

(1)

where τ —durability, s; τ 0 —period of atoms motion in a solid, s; U 0 —effective energy of destruction activation, kJ/mol; γ —structure-sensitive constant, kJ/(mol·MPa); R—universal gas constant, kJ/(mol·K); σ —stress, MPa; T —temperature, K. Later, S. B. Ratner and V. P. Yartsev modified the formula by introducing a limit on the maximum temperature at which a material can work, while the physical meaning of constants and the interpretation of heat motion of atoms as the decisive factor of destruction remained unchanged [5]. The formula came to be known as the generalized Zhurkov equation and currently has the following form:  τ = τm · exp

  U0 − γ · σ  −1 · T − Tm−1 , R

(2)

where T m —limit temperature of solid body existence. To predict the durability, it is necessary to experimentally determine the thermofluctuation constants for each material. At present, these constants are determined for a wide range of building materials, including for wooden elements [6, 7]. However, in the case of built-up sections, constants may differ from the constants of solid section. Therefore, this work concerns determining the thermofluctuation constants of built-up section wooden beams, which is the purpose of this work. The objectives of the work are to determine and compare the thermal fluctuation constants of composite wooden beams. The object of the study is wooden beams of composite cross-section. The subject of the study is their thermal fluctuation constants. The built-up section elements possess different heights (Fig. 1). Two variants of the elements’ arrangement relative to each other are considered.

2 Methodology For cross-bending tests, a hexagonal bench consisting of 6 levers with the possibility of varying the gear ratio was used. During the tests, the gear ratio of a lever was 4.125. The increased temperature was created by rod electric elements and maintained with the help of a heat shield.

Thermofluctuation Constants of Built-Up Section Wooden Beams …

323

Fig. 1 Schematic view and dimensions of samples

Tests for fracture by cross-bending were carried out in the mode of specified constant stresses and temperatures (in the range from 6 to 36 °C) according to the standard procedure [8]. In a general way, the ultimate breaking stresses of samples were determined by the formula: σp =

M , W

(3)

where σ p —ultimate strength of built-up element, MPa; M—ultimate bending moment, kN·m; W —moment resistance, cbsm. For example, for built-up section wooden samples consisting of two different elements, one should take into account that their height h is not the same. Accordingly, each element will work relative to its center of gravity, for the first element we have z 1 = h6 , and for the second element—z 2 = h3 (with the total height of these two elements h, Fig. 2). Accordingly, the values of I and W will also be different:  3 2 2 bh 3 bh 3 h 4 = cm ; W = = 6·bh = bh sm3 ; – for element 1: I1 = b(h/3) 1 12 12·27 12·27 6 12·27 54

Fig. 2 Section of a built-up wooden element consisting of two different parts

324

A. V. Erofeev and P. V. Monastyrev  b

2h/ 3

3

– for element 2: I2 = = 12 – for built-up element as a whole: I =

bh 3 12·27

3 8·bh 3 = bh 12·27 36 5·bh 2 σ p = Pl 4 54

+

8bh 3 12·27

sm4 ; W =

sm4 ;W2 =

bh 2 54

+

4bh 2 54

=

3·8·bh 2 12·27

5bh 2 54

=

4bh 2 54

sm3 ;

sm3 .

54·Pl Hence: = 20·bh 2. Based on the fact that l is a constant (l = 20 cm), formula (3) for the convenience of calculation can be converted as follows:

σp =

5400Pp . bh 2

(4)

To obtain each point, at least six samples were tested under identical conditions. In the course of the experiments aimed at determining the durability, the time from the start of load application by a non-destructive load (0,88σ p , …, 0,98σ p ) to the destruction of a sample was recorded. Under the same conditions, six samples were tested to obtain a single point. The straight line in coordinates lg τ − σ was built on 5 points (5 loading stages at a fixed temperature) [9]. The obtained results were subjected to statistical analysis. Subsequently, according to the test results, the empirical constants included in the generalized Zhurkov equation were determined by a graphic analytic method.

3 Results and Discussion The short-term strength for the first variant was determined at temperatures of 10, 20 and 33 °C, for the second variant—15, 25, 36 °C. The results are presented in Table 1. From the results obtained, it can be seen that the higher the temperature of the test, the less stress must be created in the material for its destruction. Table 1 Values of breaking stresses for three element built-up section samples, at different temperature Temperature at which the tests were carried out, for the first variant T 1 = 10 °C

T 2 = 20 °C

T 3 = 33 °C

σ p = 78.00 MPa

σ p = 69.40 MPa

Breaking stresses σ p = 91.20 MPa

Temperature at which the tests were carried out, for the second variant T 1 = 15 °C

T 2 = 25 °C

T 3 = 36 °C

σ p = 72.10 MPa

σ p = 62.50 MPa

Breaking stresses σ p = 89.60 MPa

Thermofluctuation Constants of Built-Up Section Wooden Beams …

325

During the tests, it was noticed that the samples have a different nature of destruction. Some built-up components broke down with the rupture of wood fibers at the place of load application, the others—under significant deformations. The general nature of the samples’ destruction is shown in Fig. 3. The results of determining the durability for variant 1 are summarized in Table 2. Based on the results obtained (Table 2), the thermofluctuation constants for the first variant of built-up section sample were determined by means of the graphic analytic method (Fig. 4). It should be noted that for built-up section wooden beams, as well as for solid section wooden beams, the inverse sheaf is implemented [10]. Straight lines converge to a point (pole) at a stress of σp = 53.5 MPa in this case lgτ = 12.4. Straight-line correlation lgτ = f(σ ) at a temperatue of 10 °C is described by equation: lgτ = −0.2918σ + 27.589; at T = 20 °C: lgτ = –0.4853σ + 37.8; and at T = 33 °C: lgτ = –0.7781σ + 53.42.

Fig. 3 Destruction of built-up section wood samples

Table 2 Test results of built-up section samples (variant 1) Temperature at which the tests were carried out T 1 = 10 °C

T 2 = 20 °C

T 3 = 33 °C

Breaking stresses σ p = 91.20 MPa

σ p = 78.00 MPa

σ p = 69.40 MPa

σ, MPa

lgτ

σ, MPa

lgτ

σ, MPa

lgτ

89.4

0.9

76.4

0.4

68.0

0.2

87.6

2.1

74.9

1.6

66.6

1.6

88.4

2.5

73.3

2.4

65.2

3.2

82.1

3.5

71.8

3.0

63.8

3.8

80.3

4.2

70.2

3.5

62.5

4.5

326

A. V. Erofeev and P. V. Monastyrev lgτ

16 14 12 10 8 6 4 2 0

10 градусов 20 градусов 33 градуса

σ, MPa 40

20 18 16 14 12 10 8 6 4 2 0

50

60

70

80

90

100

110

lgτ 55 МПа 60 МПа 65 МПа

3.00

3.25

3.50

3.75

4.00

σ, MPa

U, kJ / mol

600 500 400 300 200 100 0

54 55 56 57 58 59 60 61 62 63 64 65 66 σ, MPa

Fig. 4 Graphic analytic determination of thermofluctuation constants of built-up section wooden beams consisting of two elements, variant 1 (“inverse sheaf”)

Straight-line correlation lgτ = f(1000/T) for stresses 55 MPa, that is stress line 55 MPa, is described by the following equation: lgτ = 11.169(1000/T) − 27.889. Stresses line 60 MPa is described by the following equation: lgτ = 18.656(1000/T) − 54.751; and stresses line 65 MPa: lgτ = 29.596(1000/T) − 94.01. From the pole state we obtain constants: lgτm∗ = 12.4; Tm∗ = 279. Straight-line correlation U0∗ = f(σ ) is described by the following equation: U0∗ = 35.285σ – 1737.8. Hence we obtain the two remaining constants: U0∗ = −1737.8, γ * = −35.285. Thus, according to the tests’ results and processing of the data obtained, the following thermofluctuation constants of the generalized Zhurkov equation have been

Thermofluctuation Constants of Built-Up Section Wooden Beams …

327

Table 3 Test results of built-up section samples (variant 2) Temperature at which the tests were carried out T 1 = 15 °C

T 2 = 25 °C

T 3 = 36 °C

Breaking stresses σ p = 89.60 MPa

σ p = 72.10 MPa

σ p = 62.50 MPa

σ, MPa

lgτ

σ, MPa

lgτ

σ, MPa

lgτ

87.8

0.8

70.7

0.9

61.3

0.2

86.0

1.7

69.2

1.3

60.0

0.9

84.2

2.1

68,5

2.0

58.8

1.9

82.4

2.4

67.1

2.3

56.3

4.4

80.6

2.9

65.6

3.3

55.0

4.9

obtained for built-up section wooden samples consisting of two elements (variant 1): lgτ∗m = 12.4; Tm∗ = 279; U0∗ = −1737.8; γ* = −35.285. The results of durability test for variant 2 are summarized in Table 3. Based on the results obtained (Table 3), the thermofluctuation constants for the second variant of built-up section sample were determined through a graphic analytic method (Fig. 5). Straight lines converge to a point (pole) at a stress of σp = 45.5 MPa in this case lgτ = 12.5. Straight-line correlation lgτ = f(σ ) at a temperature of 15 °C is described by equation: lgτ = −0.2734σ + 25.01; at T = 25 °C: lgτ = −0.4693σ + 33.968; and at T = 36 °C: lgτ = −0.8037σ + 49.277. Straight-line correlation lgτ = f(1000/T) for stresses 50 MPa, that is stress line 50 MPa, is described by the following equation: lgτ = 9.5088(1000/T) − 21.511. Stresses line 55 MPa is described by the following equation: lgτ = 20.979(1000/T) − 62.575; and stresses line 60 MPa: lgτ = 32.494(1000/T) − 103.79. From the pole state we obtain constants: lgτm∗ = 12.5; Tm∗ = 279. Straight-line correlation U0∗ = f(σ ) is described by the following equation: U0∗ = 45.894σ − 2124.2. Hence we obtain the other two constants: U0∗ = −2124.2, γ * = −45.894. Thus, according to the tests performed and processing of the data obtained, the following thermofluctuation constants of the generalized Zhurkov equation have been obtained for built-up section wooden samples consisting of two elements (variant 2): lgτ∗m = 12.5; Tm∗ = 279; U0∗ = −2124.2; γ * = −45.894. The obtained constants are summarized in Table 4 which also shows the constants for a solid wooden section. Table 3 shows that constant lgτm∗ for all types of section has approximately the ∗ = 12.4) for a built-up section same value (lgτm∗ = 12.5). The difference by 0.1 (lgτ2m sample consisting of 2 different elements (variant 1) is caused by the occurrence of a number of errors in determining the constants by the graphic analytic method. From this we can conclude that lgτm∗ is a constant value that does not depend on the type of section (solid section or built-up one).

328

A. V. Erofeev and P. V. Monastyrev lgτ

16 14 12 10 8 6 4 2 0

15 градусов 25 градусов 36 градусов

40 20

50

60

70

80

90

100

σ, MPa

110

lgτ 50 МПа

15

55 МПа 60 МPа

10 5 0

700 600 500 400 300 200 100 0

3.00

3.25

3.50

3.75

σ, MPa

4.00

49 50 51 52 53 54 55 56 57 58 59 60 61 σ, MPa

Fig. 5 Graphic analytic determination of thermofluctuation constants of built-up section wooden beams consisting of two elements, variant 2 (“inverse sheaf”)

Table 4 Values of the constants obtained Section type

Empirical constants lgτ∗m

Tm∗

U0∗

γ*

Solid section [8]

12.5

235

−172.14

−7.363

Built-up section of two elements (variant 1

12.4

279

−1737.8

−35.285

Built-up section of two elements (variant 2)

12.5

279

−2124.2

−45.894

Comparing the obtained values of constant Tm∗ , it can be seen that for solid section wooden samples T∗m = 235 K, for built-up section samples consisting of two different elements (variant 1, variant 2) T∗m = 279 K. A slight difference in this case is not critical.

Thermofluctuation Constants of Built-Up Section Wooden Beams …

329

This difference may occur as a result of the following factors: – differences in the equipment used for testing (design, gear ratio, etc.); – differences in the grades and quality of wood from which the samples were made, hence the possible difference in their quality; – environmental factors (temperature, humidity, etc.); – man-made factor that also plays a significant role. Taking into account the errors mentioned above, we can conclude that Tm∗ is a constant value that does not depend on the type of section. According to Table 3, it can be noted that in comparison with the results of early studies for solid section samples, the values of constants U 0 and γ change sharply and by several times: – for built-up section samples consisting of two different elements (variant 1): by 10.1 and 4.8 times, respectively; – for built-up section samples consisting of two different elements (variant 2): by 12.34 and 6.2 times, respectively. This difference in results is due to the factors mentioned above (equipment, test conditions, physical and mechanical factors, etc.).

4 Conclusion Based on the above said and the results obtained, the following conclusions can be drawn: 1. it has been confirmed that, as in previous works [11], constants lgτm∗ and Tm∗ are constant values and are the same for each of the sections (solid or built-up ones); 2. constants U 0 and γ , when compared with the results obtained for solid section samples [11], do not have a common factor. At the same time, based on the results of Table 3, we can see that the modulus for U 0 is about 2 times greater than the modulus for γ. Perhaps this phenomenon is also a dependency and requires further clarification.

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3. Regel VR, Slutsker AI, Tomashevsky EE (1974) The kinetic nature of the strength of solids. Science, Moscow, p 560 4. Yartsev VP (1998) Physical and technical foundations of the performance of organic materials in parts and structures Dissertation of doctor of technical sciences (Voronezh), p 350 5. Potapova LB, Yartsev VP (2005) The mechanics of materials in a complex stress state. How is the ultimate stress predicted? Publishing House Mashinostroyenie-1, Moscow, p 244 6. Sokova S, Smirnova N (2018) Reliability assessment of waterproofing systems of buildings underground parts. IOP Conf Ser Mater Sci Eng 365:052028. https://doi.org/10.1088/1757899X/365/5/052028 7. Lo KH, Miyase A, Wang SS (2018) Failure strength predictions for closed-cell polyvinyl chloride foams. J Comp Mater 52(30): 4185–4201 8. Yartsev VP, Kiseleva OA (2019) Prediction of the building materials performance in products and structures. Adv Mater Technol 4(16):35–52 9. Golovanchikov AB, Doan MK, Petrukhin AB, Merentsov NA (2020) Comparison of the accuracy of experimental data approximation using the least relative squares method with the least squares method Modeling, optimization and information technologies, vol 8, no 1(28), p 38 10. Erofeev AV, Skvortsov P, Mukhortov PA (2017) The mechanism of destruction of solid and composite wooden beams without special connections from the thermal fluctuation position. Bull Kyrgyz-Russian Slavic Univ 17(12):80–84 11. Erofeev AV, Skvortsov, SP, Mukhortov PA (2017) Determination and analysis of thermal fluctuation constants of wooden beams of various cross-sections. Young people’s view on the problems of regional economy - 2017: materials of the All-Russian Open competition of university students and young researchers: Publishing House of the Federal State Educational Institution of Higher Education “TSTU”, pp 168–176