Burried Flexible Steel Pipe: Design and Structural Analysis 0784410585, 978-0-7844-1058-5

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ASCE Manuals and Reports on Engineering Practice No. 119

Buried Flexible Steel Pipe Design and Structural Analysis Prepared by the Task Committee on Buried Flexible (Steel) Pipe Load Stability Criteria & Design of the Pipeline Division of the American Society of Civil Engineers

Edited by William R. Whidden, P.E.

Library of Congress Cataloging-in-Publication Data Buried flexible steel pipe : design and structural analysis / prepared by the Task Committee on Buried Flexible (Steel) Pipe Load Stability Criteria & Design of the Pipeline Division of the American Society of Civil Engineers; edited by William R. Whidden. p. cm.—(ASCE manuals and reports on engineering practice; no. 119) Includes bibliographical references and index. ISBN 978-0-7844-1058-5 1. Water-pipes. 2. Underground pipelines. 3. Pipe, Steel. 4. Flexible couplings. I. Whidden, William R. II. American Society of Civil Engineers. Task Committee on Buried Flexible (Steel) Pipe Load Stability Criteria & Design. TD491.B865 2009 628.1′5—dc22 2009025043

Published by American Society of Civil Engineers 1801 Alexander Bell Drive Reston, Virginia 20191 www.pubs.asce.org Any statements expressed in these materials are those of the individual authors and do not necessarily represent the views of ASCE, which takes no responsibility for any statement made herein. No reference made in this publication to any specific method, product, process, or service constitutes or implies an endorsement, recommendation, or warranty thereof by ASCE. The materials are for general information only and do not represent a standard of ASCE, nor are they intended as a reference in purchase specifications, contracts, regulations, statutes, or any other legal document. ASCE makes no representation or warranty of any kind, whether express or implied, concerning the accuracy, completeness, suitability, or utility of any information, apparatus, product, or process discussed in this publication, and assumes no liability therefor. This information should not be used without first securing competent advice with respect to its suitability for any general or specific application. Anyone utilizing this information assumes all liability arising from such use, including but not limited to infringement of any patent or patents. ASCE and American Society of Civil Engineers—Registered in U.S. Patent and Trademark Office. Photocopies and reprints. You can obtain instant permission to photocopy ASCE publications by using ASCE’s online permission service (http://pubs.asce.org/permissions/ requests/). Requests for 100 copies or more should be submitted to the Reprints Department, Publications Division, ASCE (address above); e-mail: [email protected]. A reprint order form can be found at http://pubs.asce.org/support/reprints/. Copyright © 2009 by the American Society of Civil Engineers. All Rights Reserved. ISBN 978-0-7844-1058-5 Manufactured in the United States of America. 16 15 14 13 12 11 10 09 1 2 3 4 5

MANUALS AND REPORTS ON ENGINEERING PRACTICE (As developed by the ASCE Technical Procedures Committee, July 1930, and revised March 1935, February 1962, and April 1982) A manual or report in this series consists of an orderly presentation of facts on a particular subject, supplemented by an analysis of limitations and applications of these facts. It contains information useful to the average engineer in his or her everyday work, rather than findings that may be useful only occasionally or rarely. It is not in any sense a “standard,” however; nor is it so elementary or so conclusive as to provide a “rule of thumb” for nonengineers. Furthermore, material in this series, in distinction from a paper (which expresses only one person’s observations or opinions), is the work of a committee or group selected to assemble and express information on a specific topic. As often as practicable, the committee is under the direction of one or more of the Technical Divisions and Councils, and the product evolved has been subjected to review by the Executive Committee of the Division or Council. As a step in the process of this review, proposed manuscripts are often brought before the members of the Technical Divisions and Councils for comment, which may serve as the basis for improvement. When published, each work shows the names of the committees by which it was compiled and indicates clearly the several processes through which it has passed in review, in order that its merit may be definitely understood. In February 1962 (and revised in April 1982) the Board of Direction voted to establish a series entitled “Manuals and Reports on Engineering Practice,” to include the Manuals published and authorized to date, future Manuals of Professional Practice, and Reports on Engineering Practice. All such Manual or Report material of the Society would have been refereed in a manner approved by the Board Committee on Publications and would be bound, with applicable discussion, in books similar to past Manuals. Numbering would be consecutive and would be a continuation of present Manual numbers. In some cases of reports of joint committees, bypassing of Journal publications may be authorized.

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Title Urban Subsurface Drainage Hydraulic Modeling: Concepts and Practice Conveyance of Residuals from Water and Wastewater Treatment Groundwater Contamination by Organic Pollutants: Analysis and Remediation Underwater Investigations Guide to Hiring and Retaining Great Civil Engineers Recommended Practice for FiberReinforced Polymer Products for Overhead Utility Line Structures Animal Waste Containment in Lagoons Horizontal Auger Boring Projects Ship Channel Design and Operation Pipeline Design for Installation by Horizontal Directional Drilling Biological Nutrient Removal (BNR) Operation in Wastewater Treatment Plants Sedimentation Engineering: Processes, Measurements, Modeling, and Practice Reliability-Based Design of Utility Pole Structures Pipe Bursting Projects Substation Structure Design Guide Performance-Based Design of Structural Steel for Fire Conditions Pipe Ramming Projects Navigation Engineering Practice and Ethical Standards Inspecting Pipeline Inatallation Belowground Pipeline Networks for Utility Cables Buried Flexible Steel Pipe: Design and Structural Analysis

We dedicate this manual of practice to Dr. Reynold King Watkins, our beloved mentor. This book would not have been possible without your tireless efforts. With our warmest gratitude and appreciation, we thank you.

William R. Whidden, P.E., Chair Brent Keil, P.E., Vice Chair Robert J. Card, P.E., Secretary Spyros A. Karamanos, Ph.D. Randall C. Hill, P.E. J. Edward Barnhurst, P.E. David L. McPherson, P.E. Stephen F. Shumaker, P.E. Bruce VanderPloeg Henry H. Bardakjian, P.E. John L. Luka, P.E. George F. Ruchti

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PREFACE

Most Americans take for granted that every time they open the faucet, clean, clear water flows out. There is never any thought to the reality that the piping systems used to transport the water is vitally important. But when service is interrupted, then the importance of buried pipe systems to the community becomes a reality and a priority. Without a reliable buried pipe system, an entire community can be momentarily incapacitated. The purpose of this manual is to provide information on the structural design and analysis of buried steel water and wastewater pipe consistent with the latest pipe and soil design concepts of the industry. Structural design of welded steel pipe ensures adequate performance for the service life of the pipe. Design must be based on required lifetime performance and on limits of performance, sometimes referred to as “failure.” This manual also covers the performance limits, which are based on principles of pipe mechanics and soil mechanics, and on the analysis of pipe–soil interaction. This manual, however, does not describe manufacturing procedures, which are satisfactorily addressed by standards from the American Water Works Association and other standards-setting organizations. An understanding of the principles included in this manual is essential before applying the individual concepts to a design. Otherwise, extracting single design excerpts without that understanding may lead to an erroneous evaluation. In 1958, Spangler and Watkins published the Modified Iowa Formula for predicting the ring deflection of buried flexible pipe. Flexible pipe deflects under soil load. Ring deflection is a function of stiffness of the ring and support of the ring by soil at the sides of the pipe. The term E’ was first promulgated in the Modified Iowa Formula as a measure of that horizontal passive soil support at the sides of the flexible pipe influenced vii

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by a size factor. With adequate E’ values, predicted ring deflection is “controlled” within allowable limits. Unfortunately, E’ has been used as the basis for design of the pipe rather than the soil, from the inception of the formula up to the present day. This use of E’ is improper. E’ was never intended as a means for pipe design. It was originally intended to be a method of predicting the ring deflection that could be verified by field measurement. Furthermore, there is no procedure for testing soil to determine the value of this original E’. For the purpose of this manual, the use of the term E’ refers to the secant modulus of the soil, not to the E’ of the Modified Iowa Formula. This manual provides appropriate analytical concepts to address the external loading principles of steel pipe design. Since the 1950s, Dr. Reynold King Watkins of Utah State University—and others—developed these external loading design concepts. Also, there has long been confusion as to the definition of flexible pipe. Terms such as flexible, semiflexible, semirigid, and rigid have been used and only add to this confusion. In effect, there are just two basic philosophies of pipe design: flexible and rigid. What differentiates the two design principles is the method of analyzing resistance to internal and external forces. For rigid pipe design, these forces are additive. A combination internal and external loading analysis is required, in which the stress in the pipe wall created by both thrust and bending forces is evaluated. The structural design of the pipe wall is developed to resist these forces. In flexible steel pipe design, internal and external pressures are analyzed independently. Any combination analysis would show a reduction of the stress to be resisted. Therefore, independent analyses develop a more conservative design for flexible pipe than would a combined stress analysis. Flexible pipe deflects and conforms with soil embedment as soil is compressed. When designing steel pipe, the designer must consider issues beyond the thickness of the steel cylinder. These considerations include the type of coating and linings to be applied and the type of joint configuration consistent with the application. Certain coatings and linings are appropriate for some installation conditions and inappropriate for others. The same holds true for the various joint configurations. As with any design, the designer should always be aware of the nature of the input data and the impact the results of a calculation have on the economics of a project. Rules of thumb do not have to be considered as absolute values. The designer should use discretion when evaluating requirements for project design. Performance limits are not synonymous with failures. Both performance limits and failure mechanisms must be recognized.

PREFACE

ix

Pipes are an efficient and economical means of transporting anything that can flow—fluid, slurry, gas, wire conduits, pedestrians, traffic, and so on. Pipes even provide storage. The first step for transportation of fluids in pipe is to determine: • What is to be transported? • What is the rate (quantity) of flow? • What are the pressure and pressure variations? Basic fundamentals of design are pipe design, soil design, and pipe– soil interaction. This Manual of Practice, Buried Flexible Steel Pipe: Design and Structural Analysis, has been organized to provide a structured, chronological design or analysis process for the student or design professional. Here is an overview of each chapter and appendix. Chapter 1 provides the historical sequence of events leading to our understanding of relationships between buried steel pipe and soil. Chapter 2 lists the notations as used in the manual. Chapter 3 establishes the basis for design of the pipe, not the piping system. This is an important concept in understanding buried steel pipe design. Essentially, the steel pipe resists the internal forces, and the soil support resists the external forces. This chapter provides the design criteria and parameters to analyze pipe stresses and strains as well as explaining limitations on those strains for pipe lining or coating issues. Chapter 4 provides the geotechnical principles that relate to buried pipe design and analysis. The project’s geotechnical report should address certain data to assist the design engineer in analyzing and designing the soil embedment. Significant parameters include the soil unit weight, soil compressibility, and strength at soil slip. Chapter 5 begins the process of analyzing the relationship between pipe and soil that leads to a successful design, which is detailed in Chapter 6. Chapter 6 contains several design examples that demonstrate the design process outlined in the previous chapters. Chapter 7 addresses additional design and analysis topics. These may be uncommon to the majority of buried pipeline installations, such as seismic loading or pipe on supports, or they may be supplemental to a complete design, such as longitudinal thrust forces. There is also information on optional methods of obtaining passive side support, such as flowable fill. Appendix A is about the Iowa Formula. The Iowa Formula was originally intended to show that ring deflection is primarily a function of soil embedment and was not intended for the design of pipe. This formula has been misused for design for many years. This appendix explains the proper application of the formula.

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PREFACE

Appendix B is about soil slip analysis. “Soil slip” is the common description of a shearing failure in soil. By analyzing an infinitesimal soil cube using a Mohr stress circle, we can determine or establish soil stability. In Appendix C, an example is presented to provide the engineer with a representative finite element model. The parallel trench condition was selected to provide a guide to understanding the benefits and procedures of this powerful tool. Appendix D deals with external fluid pressure. Because external fluid pressure may be capable of collapsing a pipeline, this appendix provides information and examples to assist the engineer in recognizing and evaluating this condition and remedying any potential problem. Appendix E is called “The Story of Buried Steel Pipes and Tanks.” Students committed to an area of expertise should understand the background and history of their chosen field. Dr. Watkins, a pioneer in this field, witnessed—and made—history in the area of buried steel pipes and buried tanks, much of which he personally experienced. This appendix is his historical account and provides a fascinating snapshot of that history and why many of the established concepts evolved. Appendix F demonstrates that nonuniform ring pressure is statically indeterminate. To approximate the condition, both static equilibrium equations and deformation equations are required. Examples of this condition are presented by applying a dummy force or bending moment to the ring. Appendix G presents the rationale associated with the development of impact factors for live loads.

CONTRIBUTORS

This Manual of Practice was prepared by the Buried Flexible (Steel) Pipe Load Stability Criteria and Design task committee under the supervision of the Pipeline Division’s Technical Committee. William R. Whidden, P.E., Chair, PBS&J Brent Keil, P.E., Vice Chair, Northwest Pipe Company Robert J. Card, P.E., Secretary, Lockwood, Andrews & Newnam, Inc. Reynold K. Watkins, Ph.D., P.E., Utah State University Loren R. Anderson, Ph.D., P.E., Utah State University James A. Bay, Ph.D., Utah State University Spyros A. Karamanos, Ph.D., University of Thessaly Randall C. Hill, P.E., Camp Dresser & McKee Inc. J. Edward Barnhurst, P.E., MWH Americas, Inc. David L. McPherson, P.E., MWH Americas, Inc. Stephen F. Shumaker, P.E., Camp Dresser & McKee Inc. Bruce VanderPloeg, Northwest Pipe Company Henry H. Bardakjian, P.E. John L. Luka, P.E., American SpiralWeld Pipe Company George F. Ruchti, American SpiralWeld Pipe Company

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BLUE RIBBON REVIEW COMMITTEE

George J. Tupac, Chair, G. J. Tupac and Associates, Inc. Roger L. Brockenbrough, R. L. Brockenbrough and Associates, Inc. Sam Arnaout, Hanson Pressure Pipe

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CONTENTS

1

HISTORY OF BURIED STEEL PIPE ............................................... 1.1 1.2 1.3 1.4

2

3

1

The Ancient World......................................................................... The History of Iron and Steel Pipes............................................ The Pioneers in Pipe Design ........................................................ Contributors to Design .................................................................

1 3 7 12

NOMENCLATURE, CONSTANTS, AND TERMINOLOGY.......................................................................

15

2.1 Nomenclature ................................................................................. 2.2 Constants ......................................................................................... 2.3 Terminology ....................................................................................

15 20 21

PIPE MECHANICS .............................................................................

23

3.1 3.2 3.3 3.4 3.5 3.6

23 23 25 26 27

Introduction .................................................................................... Internal Pressure Design ............................................................... Minimum Thickness for Handling ............................................. Ring Stiffness .................................................................................. Ring Compression.......................................................................... Performance Limits of Cement Mortar Linings and Cement Mortar Coatings ...................................................... 3.7 Ring Deflection ............................................................................... 3.8 Yield Stress ......................................................................................

xv

28 31 31

xvi

4

5

6

CONTENTS

SOIL MECHANICS.............................................................................

33

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19 4.20 4.21

Introduction .................................................................................. Notation ......................................................................................... Soil Conduit .................................................................................. Flaws In Applying Elastic Theories to Soil ............................. Unit Weights of Soil..................................................................... Vertical Soil Pressures (Stresses) ................................................ Soil Strength .................................................................................. Soil Slip .......................................................................................... Soil Particle Size and Gradation ................................................ Soil Friction Angle ....................................................................... Passive Resistance ........................................................................ Cohesion in Soil ........................................................................... Soil Compression ......................................................................... Embedment ................................................................................... Select Fill ....................................................................................... Liquefaction .................................................................................. Quick Condition ........................................................................... Soil Movement.............................................................................. Earthquakes .................................................................................. Soil Specifications ........................................................................ Finite Element Analysis ..............................................................

33 33 34 34 35 36 38 39 39 42 42 43 45 46 46 47 47 48 48 49 50

PIPE–SOIL INTERACTION ..............................................................

55

5.1 5.2 5.3 5.4 5.5 5.6

Introduction .................................................................................... Ring Deflection ............................................................................... Relative Effect of Pipe and Soil on Ring Deflection ................. Hydrostatic Collapse in a Fluid Environment .......................... Ring Deformation Failure of Buried Flexible Pipe ................... Minimum Cover.............................................................................

55 56 58 60 61 65

DESIGN ANALYSIS ...........................................................................

73

6.1 6.2 6.3 6.4

74 75 77

Case 1—Internal Pressure and Handling................................... Case 1A—Ring Stability................................................................ Case 1B—Ring Stability With Vacuum....................................... Case 1C—Ring Stability With Vacuum and Water Table Above Pipe ........................................................ 6.5 Case 2A—Ring Stability at a Given Depth with Partial Vacuum ...................................................................... 6.6 Case 2B—Pipe Stiffness to Prevent Collapse ............................

80 82 85

CONTENTS

7

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SPECIAL CONSIDERATIONS .........................................................

87

7.1 Introduction .................................................................................... 7.2 Parallel Pipes in a Common Trench............................................ 7.3 Parallel Trenches ............................................................................ 7.4 Trenches in Poor Soil ..................................................................... 7.5 Flowable Fill ................................................................................... 7.6 Longitudinal Forces ....................................................................... 7.7 Buried Pipe on Bents ..................................................................... 7.8 Seismic Considerations ................................................................. 7.9 Encased Pipe ................................................................................... References...............................................................................................

87 87 94 96 98 99 110 118 123 124

APPENDIX A

THE IOWA FORMULA—WHAT IT IS AND IS NOT ........................................................................... 127

APPENDIX B

SOIL SLIP ANALYSIS ................................................ 131

APPENDIX C

FINITE ELEMENT DESIGN EXAMPLE TRENCH PARALLEL TO A BURIED PIPE ........... 141

APPENDIX D

EXTERNAL FLUID PRESSURE................................ 149

APPENDIX E

THE STORY OF BURIED STEEL PIPES AND TANKS ................................................................ 161

APPENDIX F

RING ANALYSIS......................................................... 177

APPENDIX G

IMPACT FACTORS IN SOIL .................................... 185

GLOSSARY ................................................................................................. 189 BIBLIOGRAPHY........................................................................................ 191 INDEX .......................................................................................................... 195 SI CONVERSION TABLE........................................................................ 201

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CHAPTER 1 HISTORY OF BURIED STEEL PIPE

Long before buried pipelines evolved as a means of improving people’s standards of living, the concept of buried pipes existed in nature. Such “structural engineering” was evident in life forms, from the one-gut worm to the complexity of the human body. In the insect world, communities of insects bored intricate underground tunnels and systems. Rodents burrowed underground in buried pipes that served as their habitats. The history of buried pipes starts with pipes that serve communities.1 About 2500 bc, the Chinese delivered water through bamboo pipes. In some Mediterranean countries, clay pipes supplied water to villagers at a central well. Ancient buried pipes in Persia, called ghanats, were rocklined tunnels, dug by hand under the mountains, to collect clean water and pipe it as much as 30 miles to parched cities on the plains. The mountain streams flowed into wetland swamps—all contaminated by sewage, livestock, garbage, snakes, and mosquitoes.

1.1 THE ANCIENT WORLD In ancient Greece, pipelines and tunnels were constructed to transport and distribute water in urban areas (Fig. 1-1). The most renowned public work of water transportation of the era was the Eupalinos aqueduct in the city of Samos, the capital of an island east of the Aegean Sea. Its construction started in 550 bc (during the ruling of Polycrates), by the 1

For more on the history of buried pipes, refer to Appendix E.

1

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BURIED FLEXIBLE STEEL PIPE

Figure 1-1. Exhibits in an Athens Metro Station (Evangelismos) of Clay Pipes from Peisistratos’s Aqueduct (from Athens, Greece, Circa 540-530 BC).

engineer Eupalinos, and lasted 10 years. Some years later, some time between 540 bc and 530 bc, the ruler of Athens, Peisistratos, constructed a 2,800-m-long aqueduct, which transported water to the city of Athens from the nearby mountain of Hymettos. The water was distributed in the city through a buried pipeline system. During 100 to 300 ad, in Rome, with plenty of low-cost slave labor, pipes became an important part of the infrastructure for the emperor and the elite. Water was delivered to Rome via aqueducts and then distributed via lead pipes to the mansions of the elite and to their luxurious Roman baths. The fall of Rome may have been brought about, in part, by those lead pipes. Over time, the acidic water dissolved lead from the pipes, which resulted in lead poisoning. But the problem of lead poisoning did not end there. Lead was also found in cooking kettles that were used to boil acidic grape juice down into a sweet syrup. Pompeian red lead paint that flaked off the floor where babies crawled also contributed to the Romans’ health issues. Lead poisoning caused impotence, and the few successful pregnancies that did occur produced offspring with brain defects. During the Renaissance, buried sewer pipes channeled the foul smell of raw sewage in the streets of cities such as Paris and London. These underground sewers were brick-lined tunnels that formed arches. The arch had already been used in the remarkable Roman arches for buildings and aqueducts. In fact, mortar was not needed because the blocks (brick

HISTORY OF BURIED STEEL PIPE

3

Figure 1-2. A Wood-Stave Pipe from the Early 1900s That Is Still in Service.

or stone) were held in place by compression. Later in the 1900s, the concept of arching was rediscovered as it applied to soil arching action over buried pipes. In North America, the first European settlers fashioned pipes by boring out logs. Later, they made wooden pipes from carefully sawed staves held together by steel hoops. The concept was adapted from coopers, who made wooden barrels and tubs. Some old wood-stave pipes are still serviceable, such as the one pictured in Fig. 1-2.

1.2 THE HISTORY OF IRON AND STEEL PIPES Since 1000 bc, iron had been around; but before the Renaissance, iron was used mostly to make spears, swords, and shields. By 1346 ad, iron was used to make guns. These guns became the incentive for making iron pipe—the dream of “ingeniators” (ingenious ones, or engineers)— because of the demand for water in burgeoning cities and because iron is stronger than bamboo or clay. In 1824, iron pipes were developed in England when James Russell invented a device for welding iron tubes (gun barrels) together into pipes. Costly, handmade iron pipes supplied gas for the gas lamps in the streets and the dwellings of the elite. In 1825, Cornelius Whitehouse made long iron pipes by drawing flat strips of hot iron through a bell-shaped die. Next came the Bessemer process for making steel, and the open-hearth furnace for production of large quantities of steel. Steel pipes became reality. The urban way of life had changed. Communities had expanded into metropolises. Steel pipes for water and clay pipes for sewage became the “guts of the city.” The development of the steel pipe is summarized in the following

4

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four major stages as abstracted from History of Steel Water Pipe (Cates 1971). 1. In 1830, the first furnace was built in the United States for making wrought iron pipe. More furnaces were soon built. The demand for pipes was enormous because of the need for water distribution in fast-growing cities. Those wrought iron pipes were made in small diameters. Production was limited because iron was not available in large quantities. 2. The age of steel was born in 1855 in England, where Bessemer developed a process for production of steel. Development of the open-hearth furnace in 1861 made steel available in large quantities—thousands of tons. Before then, steel had been produced by the pound. Steel made it possible to cold-form sheets into pipes of any diameter. Soon after the 1849 gold rush in California, sheet steel was formed into tubes with longitudinal, riveted seams. One end of each pipe “stick” was crimped so that it could be stabbed into the next stick like stovepipes. Sections were joined by simply hammering them together. From 1860 to 1900, virtually all water pipe was cold-formed from steel sheets and riveted. More than 2 million ft of steel pipe were installed during that period in the United States (Fig. 1-3). 3. The third major development was lock-bar pipe in 30-ft lengths (Fig. 1-4). It was first fabricated in 1905 in New York. Two semicircular pipe halves were joined by inserting the edges of each into two longitudinal lock-bars with an H-shaped cross section. The edges of

Figure 1-3. Riveted Steel Pipe.

HISTORY OF BURIED STEEL PIPE

5

Figure 1-4. Lock-Bar Steel Pipe. the pipe halves were designed to a slightly greater thickness to form a shoulder for engaging the lock-bar. The two halves were then press-fit together. The pipe edges were clamped in the lock-bars. The longitudinal seam was 100% efficient. Riveted seams were only 45% to 70% efficient. The interior of this pipe was smoother than that of

6

BURIED FLEXIBLE STEEL PIPE

riveted pipe. Carrying capacity was increased from 15% to 20%. From 1915 to 1930, 3.3 million ft of lock-bar was installed and 1.5 million ft of riveted pipe. 4. The fourth major development was automatic electric welding. Electric welding started as a novelty in 1920 but made progress during the 1930s, when welding machines and fluxes were developed. From 1920 to 1940, approximately 7 million ft of welded steel pipe was installed. During World War II, virtually all steel production was diverted into the war effort. Welding was essential to the construction of warships. Welding techniques used on U.S. Navy ships helped to shorten construction time, and welding techniques improved. In the late 1940s, pipe manufacturers began fabricating welded steel pipe by straight-seam electrical resistance and fusion welding. Helical (spiral) seam welding was just coming on line. During the 1950s, the maximum size of pipes increased. Joints in the larger diameter steel pipes were welded. Initially, design of the welding followed procedures already established in other practices, such as pressure vessels. After World War I, welded steam boilers replaced riveted boilers because riveted joints leaked at high pressures. The need for safety requirements after boiler explosions compelled the American Society of Mechanical Engineers (ASME) to write an ASME Boiler and Pressure Vessel Code, based on good safe practice. The welding of joints was mostly butt welds, or the equivalent, “joggle joints.” Safety factors were high. The American Petroleum Institute proposed a code based on less restrictive safety factors, resulting in the formation of a joint API– ASME committee in 1934 to standardize welded joints. It wasn’t until 1968 that agreement was finally achieved in a standard, ASME Section VIII, Division I, Rules for Construction of Pressure Vessels. The boiler code for high-pressure, high-temperature welded joints was not applicable to welded steel water pipes at lower temperatures and pressures. Lap welds, especially during installation of buried pipes, were found to be more dependable than butt welds. The joint could be more easily stabbed, and field welding could be more easily controlled. A single lap weld could be either on the inside or outside of the joint, while a double lap weld was on the inside and the outside. However, the double weld provided an opportunity to check for a leak in the joint. A valve (like a tire valve stem) could be tapped into the bell between welds. Air pressure could be applied, and any leak in the joint could be discerned by loss of pressure. From pipe tests cited (Brockenbrough 1990), single-welded lap joint efficiencies vary from 75% to 100%. Double-welded lap joint efficiencies vary from roughly 85% to 100%. The increase in efficiency of the doublewelded lap joint is small because the two welds tend to fail in sequence.

HISTORY OF BURIED STEEL PIPE

7

1.3 THE PIONEERS IN PIPE DESIGN The development of pipes was by trial and error. How many Persian lives were lost in cave-ins while excavating tunnels before rock lining? How could Romans predict that lead pipes would cause lead poisoning? Who could predict that welding would make obsolete rivets, lock-bars, and stovepipes? Evolution of pipes proceeded empirically—not by design. The design of buried pipes is fairly recent. It started in 1913 when Anson Marston became the first dean of engineering at Iowa State College. He noted, with concern, how transportation became bogged down during every rainstorm and that with every spring thaw dirt roads became quagmires of mud. So he sought a remedy and called for action with a publicized resolve: “Let’s get Iowa out of the mud.” Marston recognized that to get roads out of the mud, they had to get the water out of the roads. The remedy: bury drainpipes along the roads. The nation took note, and a federal highway research board was formed, with Anson Marston as its first director. Marston led the first engineered design of buried drainpipe. He derived an equation for soil load on pipe. In those days, drainpipes were clay or concrete—both rigid materials. He left details of the design of pipe up to the manufacturers to make pipe that could withstand his “Marston load” in a three-edge-bearing test (Fig. 1-5). It was a radical design concept based on a performance specification—not on the typical volumes of details in procedure specifications. The Marston load was for rigid pipe—clay or concrete. The Armco Company had developed flexible pipe of corrugated steel. Steel was available in coils from which corrugated pipe could be fabricated. But the flexible pipe could not support the Marston load in a three-edge-bearing

Figure 1-5. The Marston Load on Rigid Pipe (Left) Is the Weight of the Backfill (Cross-Hatched), Reduced by the Friction of the Trench Walls. The Three-EdgeBearing Test (Right) Is for D-Load Strength at the Failure of a Pipe.

8

BURIED FLEXIBLE STEEL PIPE

test. From exploratory installations in the yard, an Armco engineer named Kelly was convinced that corrugated steel pipes would work as culverts. He sponsored a test program at Iowa State College. The project was assigned to a young faculty member named M. G. Spangler. Using a “soil box,” Spangler showed that flexible pipe deflects under soil load and develops horizontal soil support on the sides of the pipe. With soil support, flexible pipes could be used as culverts. Spangler (1941) introduced the concept of pipe–soil interaction. He derived the Iowa Formula for predicting the horizontal expansion of buried, flexible pipe based on a horizontal soil modulus, E′. Kelly was pleased. He plotted graphs of the formula to expedite the design and sale of corrugated steel culverts, but the graphs were unreasonable. Kelly was disappointed, and Spangler was devastated. In 1956, Spangler asked his student, Watkins, to rederive the formula. Spangler’s math was elegant and correct, but his horizontal soil modulus, E′, was flawed dimensionally. E′ was corrected; the plots were reasonable. The Modified Iowa Formula was published by Watkins and Spangler (1958). The Iowa Formula had predicted ring deflection in elastic soil—not inelastic soil. The E′ concept was simplistic. The formula did show that ring deflection is controlled primarily by the soil, not the pipe. The formula is not the basis for design of pipe, but rather, is a prediction of long-term deflection of the circular pipe into an oval during the time of soil placement and subsequent settlement. M. G. Spangler, known as the father of buried, flexible pipe analysis, developed his Iowa Formula, which is shown in Fig. 1-6. Spangler recognized that flexible pipe deflects under soil load and develops horizontal

Figure 1-6. Spangler’s Assumptions for Derivation of the Iowa Formula.

HISTORY OF BURIED STEEL PIPE

9

soil support. Using the method of virtual work, Spangler solved for horizontal pipe expansion: ∆x =

D f KWc r 3 EI + 0.061E′ r 3

where ∆x = increase in horizontal diameter, Df = deflection lag factor (about 1.0), K = bedding factor (about 0.1), Wc = PD = Marston load on the pipe, P = soil pressure on top of the pipe, D = pipe diameter, r = pipe radius = D/2, E = modulus of elasticity of pipe I = t3/12 for plain pipe wall, t = wall thickness, and E′ = modulus of elasticity of soil. The assumptions in Fig. 1-6 include an elastic soil modulus and parabolic soil support on the sides of the pipe over 100° of arc. In fact, the horizontal soil support, σx, is more nearly rectangular, not parabolic, over the full diameter. The bedding factor is based on the assumption that support on the bottom of the pipe is effective only over an angle, α. In theory, the coefficient, K, varies from 0.110 to 0.083 as α increases from zero to 180°. In fact, angle α increases as the ring deflects under soil pressure. Therefore, K is not constant. Moreover, the imprecision of soil placement and compaction, especially under pipe haunches, can only justify an approximate value of K = 0.1. The deflection lag factor, Df, allowed for settlement of soil after installation. Spangler opined that in a year, the deflection lag factor might be as much as 1.5. This notion was speculation that could apply only to poorly compacted soil embedment. If embedment is well compacted, deflection does not lag, and the lag factor is unity. Moreover, internal pressure in a pressurized pipe tends to reround the oval pipe and nullify any deflection lag. The horizontal soil modulus, E′, is not constant but varies with depth of burial, soil density, and soil compression caused by both soil cover and ring deflection. Constant values were published by the U.S. Bureau of Reclamation (USBR), which were backcalculated from existing installations without regard for depth. To understand pipe–soil interaction, the Iowa Formula can be rewritten for vertical ring deflection, δ = ∆y/D, in the form

10

BURIED FLEXIBLE STEEL PIPE

δ (%) =

10 P Σ ( EI r 3 ) + 0.06E′

(Pipe) (Soil ) The summation ∑ may include lining and coating. From this form of the Iowa Formula, the relative effects on ring deflection of ring stiffness (EI/r3) and soil stiffness (0.06E′) can be evaluated. It is easily shown that ring stiffness for steel pipe is usually insignificant compared to soil stiffness, especially if soil embedment is select and compact. The history of allowable ring deflection starts with Spangler’s colleague, William Schlick, who as a graduate student, was assigned by Dean Marston to inspect the deflection of culverts in the county. The culverts were all concrete. Schlick decided that ring deflection was best observed by cracks inside the pipe at crown and invert. For preliminary investigation, he picked up a scrap of steel shim stock that happened to be onehalf-inch wide and 0.01-in. thick, and he rounded one end. Then he went into the field and recorded the percent of culverts with cracks wider than 0.01 in. Marston published the results, which became the standard. Crack widths must not exceed 0.01 in. History has shown that the “hundredthinch crack” is overly conservative—especially for mortar lining and coating in steel pipe. And ring deflection is not a realistic function of crack width. Spangler’s soil box tests on flexible steel pipes showed that at a ring deflection of 20%, the pipe appeared almost flat on top on the verge of inversion. With a safety factor of 4, Spangler recommended an upper limit of 5% for steel pipe. This limit is commonly accepted as the maximum allowable ring deflection. Development of steel pipe was redirected during World War II to special-use pipes, such as thick-wall, high-pressure torpedo tubing. During the 1950s, the United States was still recovering from World War II. The nation’s infrastructure had been neglected. Buried pipes were urgently needed—for culverts and drainage, water supply, sewage disposal, gas and petroleum, and power lines and telephone lines. Innovations were introduced. In the early 1960s, steel pipes with cement mortar lining and coating were tested in a parallel plate device at Utah State University for the Smith-Scott Company of California (Watkins 1965). The first mortarlined-and-coated steel pipes were crude but showed potential, not only for protection against corrosion, but also for increased ring stiffness. Because steel was the strongest and stiffest material used in pipes, wall thickness could be less than with other pipes. However, because ring stiffness is a function of wall thickness to the third power, thin-walled

HISTORY OF BURIED STEEL PIPE

11

steel pipes were so flexible that holding them in shape during installation was a problem. Mortar lining and coating increased ring stiffness and, consequently, facilitated handling and installing. In the parallel plate tests, the mortar cracked longitudinally, but the ring could be deflected more than 6% before mortar broke loose. So how wide could the cracks be and still protect the pipe against corrosion? And how important was loss of bond? And was radius of curvature of a deformed ring at a flat spot more important than ring deflection? And how could the radius of curvature of a flat spot be measured? These concerns were resolved by tests and by field experience. Design became based on realistic performance limits. Performance limits include stresses that exceed yield strength, excessive deformations, and leaks. Leaks are caused by excessive deformation but also by abrasion (wear) and by corrosion. Corrosion of pipes (rust), in the early days of steel pipes, was mitigated by increasing the steel thickness by one or more sixteenths of an inch to allow for corrosion of the surface. A coating of rust became a protection against further corrosion. But in some cases, electrolysis or aggressive environment caused corrosion clear through the wall. Corrosion experts developed cathodic protection. And coatings were developed, such as polyethylene tape coating, that would not crack or disbond. Mortar coatings and linings showed promise. Linings were spun into place centrifugally so that mortar thickness could be reduced. The spun-in-place lining surface was smooth, with less frictional resistance to fluid flow, than earlier surfaces. Reduced mortar thickness allowed greater ring deflection based on allowable crack width. Small cracks in mortar lining close by autogenous healing because calcium carbonate forms in the moist environment. Under the patronage of the American Iron and Steel Institute (AISI), the persistent attention of the American Water Works Association (AWWA) and the Steel Plate Fabricators Association (SPFA) helped advance the design of buried steel pipe during the last half of the 20th century. Committees were formed from representatives of steel pipe manufacturers and users. Tests were sponsored. Field installations were monitored. Manuals were written. Seminars were presented. The Steel Water Pipe Manufacturers Technical Advisory Committee (SWPMTAC) and the American Society for Testing and Materials (ASTM) contributed. As a result of their contributions, the twenty-first century began with a surge of effort to update standards for steel pipe. With research and performance records available, the American Society of Civil Engineers (ASCE) formed a task group to write an ASCE steel pipe manual of practice. The effort was strengthened by creation of a joint committee of both the Steel Tank Institute (STI) and the SPFA. The buried steel pipe effort became a worldwide engineering response to a dire, worldwide need for water

12

BURIED FLEXIBLE STEEL PIPE

during the next century of increasing demand and decreasing availability of clean water. By the end of the twentieth century, design of buried steel pipe followed a sequence. Design starts with internal pressure. Thickness of the steel must keep hoop stress below allowable tensile strength. Under external pressure, pipe wall thickness must be great enough that ring compression stress does not exceed allowable compression strength of steel. Ring stiffness must be sufficient to hold the pipe in shape. While transporting and installing pipe, ring deflection is often controlled by stulls, or props, in the pipe. Ring stiffness prevents local deformations. Ring stiffness includes stiffness of mortar lining and coating. However, cracks in the mortar may reduce the contribution of mortar to pipe ring stiffness. Ring stiffness is of greatest importance during handling and installation. After installation, the soil holds the pipe in shape. However, soil support can be lost if the embedment liquefies or moves. Ring stiffness must be sufficient to prevent buckling under wheel loads with minimum soil cover. Under external hydrostatic pressure, ring stiffness must prevent collapse of the pipe. After installation, ring deflection is nearly equal to (no greater than) vertical strain of the side-fill soil. Ring deflection is controlled primarily by soil specifications: soil type and density, and placement and compaction of soil. When the pipe is pressurized, it rerounds. Ring deflection is no longer an issue except at flat spots, i.e., impressions created by hard, high points in the bedding or by point loadings (e.g., boulders or alignment sills) against the pipe. The need for care in placement of the pipe and for placement and compaction of the bedding and embedment is obvious. The future for buried, welded steel pipe is well established. From available records, a few steel pipelines installed more than 100 years ago are still in service. A significant percentage of steel pipes installed more than 75 years ago are still in service. Buried pipes have become the arteries of communal life—the guts of civilization’s infrastructure.

1.4 CONTRIBUTORS TO DESIGN Contributors to the design of buried flexible steel pipe include the following: American Iron and Steel Institute (AISI) sponsored research, including full-scale tests, at universities and state departments of transportation and published papers and manuals on buried steel pipe. American Water Works Association (AWWA) contributed standards for good practice.

HISTORY OF BURIED STEEL PIPE

13

Cates, Walter H., a civil engineer, was a major influence on cooperative efforts to improve the design of buried pipe. Katona, Michael, Ph.D., was one of the first to develop a program for finite element analysis. His CANDE program is still in use with modifications. Other finite element analysis programs are now available. Numerous researchers from the University of California, New York (Albany), Northwestern University, the University of Ohio, Sacramento State University, Utah State University, and others, recognized the need for design of buried flexible pipe. With computers, finite element analysis has become a contribution to design and analysis. Steel Plate Fabricators Association (SPFA), with funding from AISI and pipe manufacturers, presented seminars throughout the United States and Canada on the design of buried steel pipe. Transportation Research Board (TRB) sponsored conferences and published papers on pipes required for highway and airfield construction. Tupac, George, retired from U.S. Steel, was chairman of committees to write and upgrade manuals for steel pipe. Such manuals include AWWA Manual M11, and AISI manuals on welded steel water pipe and buried steel penstocks. U.S. Bureau of Reclamation (USBR) developed testing facilities in Colorado and monitored installation and performance of numerous USBR pipelines. Results were published. White, Howard, an engineer with Armco Company, noted the findings of full-scale tests and proposed the ring compression procedure for analysis of external soil pressure on steel pipe.

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CHAPTER 2 NOMENCLATURE, CONSTANTS, AND TERMINOLOGY

2.1 NOMENCLATURE α αs β δ ∆ ∆T ∆x ∆y ε εs φ γ γ′ γb γc γd γdmax γdmin γe γs γsat γt γw υc υs

= Coefficient of thermal expansion and contraction of steel (°F) = Circumferential angle of contact of saddle support (deg) = One half the bedding angle of flowable fill (deg) = Percent ring deflection of pipe = Pipe deflection under an applied load, general (in.) = Change in temperature (°F) = Horizontal pipe deflection (in.) = Vertical pipe deflection (in.) = Strain, general = Percent vertical compression of side-fill embedment = Soil friction angle (deg) = Unit weight of soil, general (pcf) = Effective soil unit weight (pcf) = Buoyant unit weight of backfill (pcf) = Unit weight of cement mortar (pcf) = Unit weight of dry backfill (pcf) = Maximum unit weight of dry backfill (pcf) = Minimum unit weight of dry backfill (pcf) = Unit weight of embedment slurry (pcf) = Unit weight of steel (pcf) = Unit weight of saturated backfill (pcf) = Total unit weight of backfill (pcf) = Unit weight of water (pcf) = Poisson’s ratio for cement mortar = Poisson’s ratio for steel 15

16

BURIED FLEXIBLE STEEL PIPE

ϕ tanϕ′ θ θf θx σ σf σ1 σ2 σ3 σH σmax σmin σP σrc σs σT σY σx σy σU σz σ σx σy τ Ψ A A1 A2 As Ax B Bd Bs c c1 d D DI Dm

= Angle of soil slip (deg) = Coefficient of friction between pipe and soil = Angle variable for mortar crack analyses (deg) = Angle of plane of soil slip (deg) = Angle variable for mortar crack analyses (deg) = Stress, general (psi) = Stress at wall crushing (psi) = Maximum principal stress for soil analyses (Appendix B) (psi) = Intermediate principal stress for soil analyses (Appendix B) (psi) = Minimum principal stress for soil analyses (Appendix B) (psi) = Hoop stress from internal pressure (psi) = Maximum principal soil stress (psi) = Minimum principal soil stress (psi) = Stress from internal pressure (psi) = Ring compression stress (psi) = Stress at saddle support (psi) = Longitudinal stress from temperature change (psi) = Yield strength (psi) = Horizontal soil stress (psi) = Vertical soil stress (psi) = Ultimate tensile strength (psi) = Longitudinal stress (psi) = Effective intergranular soil stress, submerged (psi) = Horizontal effective intergranular soil stress, submerged (psi) = Vertical effective intergranular soil stress, submerged (psi) = Shear stress in soil, general (psi) = Frictional resistance term for saddle support design = Cross-sectional area of pipe wall (ft2 or in.2) = Cross-sectional area of large end of reducer (in.2) = Cross-sectional area of small end of reducer (in.2) = Modified area of pipe wall for saddle support analysis (in.2) = Area of pipe wall per unit length for saddle support analysis (in.) = Breadth of applied surface live load (in.) = Trench width at top of pipe (in.) = Breadth of saddle support (longitudinal length) (in.) = Cohesion of soil (psi) = Distance from neutral axis to outermost fiber in beam bending analyses (in.) = Percent ring deflection in decimal form = Nominal diameter of pipe (in.) = Inside diameter of steel cylinder (in.) = Mean diameter of pipe (in.)

NOMENCLATURE, CONSTANTS, AND TERMINOLOGY

DO DP Dr D/t Dx Dy e

= = = = = = =

17

Outside diameter of steel cylinder (in.) Outside diameter of pipe coating (in.) Relative density Ring flexibility Horizontal diameter of pipe (in.) Vertical diameter of pipe (in.) Middle ordinate measurement when determining radii of noncircular pipe (in.) e = Soil void ratio e′ = End ordinate measurement when determining radii of noncircular pipe (in.) e″ = End ordinate measurement when determining radii of noncircular pipe (in.) emax = Maximum soil void ratio emin = Minimum soil void ratio E = ASME weld efficiency (Appendix E) E = Modulus of elasticity, general (psi) E′ = “Elastic” soil modulus (psi) Ec = Modulus of elasticity of cement mortar (psi) EI/D3 = Ring stiffness, general (psi) EI/r3 = Ring stiffness, general—alternate version (psi) Es = Modulus of elasticity of steel (psi) f = Friction factor for saddle stress analysis F = Applied load to cylinder when determining pipe stiffness (lb) FB = Buoyant force (lb) Ff = Frictional resistance (lb) Fy = Minimum specified yield strength (psi) G = Specific gravity of soil particles h = Height of water surface above ground (ft) hw = Height of water surface above pipe (in.) H = Height of dry backfill over saturated backfill (in.) H′ = Height of saturated backfill over embedment (in.) H″ = Height of saturated embedment over top of pipe (in.) Hc = Height of soil cover over top of pipe (in.) I = Moment of inertia of pipe cylinder (in.4) Ic = Moment of inertia of coating cross section per unit length (in.3) Il = Moment of inertia of lining cross section per unit length (in.3) Is = Moment of inertia of pipe wall cross section per unit length (in.3) k = Ratio of principal stresses at soil slip ka = Active soil pressure (psi) kp = Passive soil pressure (psi) Ks = Bedding factor (Appendix A) l = Unit arc length for mortar crack analyses (in.)

18

BURIED FLEXIBLE STEEL PIPE

L L′ L2 L3 m M N N.S. ps P P PA PB Pd Pext Pf Pl Po Ps Pt Pv Pvac Pw Px Py Q Q Q Q Q′ Qf Qx r r′ ra rb rmax rmin rp rr

= Length of applied surface live load (in.) = Length of measuring device used to determine radii of noncircular pipe (in.) = Overall length of pipe for beam analysis (ft) = Longitudinal length of pipe for frictional analysis (ft) = Ring flexibility = Circumferential bending moment in pipe (lb-in.) = Normal soil pressure (lb/ft) = Neutral surface for bending analyses = Saddle pressure on pipe (psi) = External fluid pressure (Appendix D) (psi) = Pressure, general (psi) = Total vertical soil pressure at top of pipe (psi) = Total horizontal soil pressure at springline of pipe (psi) = Vertical soil pressure due to dead load (psi) = External pressure (psi) = Internal field test pressure (psi) = Vertical soil pressure due to surface live load (psi) = Portion of vertical soil pressure, Pv, supported by ring stiffness (psi) = Internal hydraulic transient pressure, surge (psi) = Test pressure (psi) = Vertical soil pressure (psi or psf) = Vacuum pressure (psi) = Internal working pressure, or sustained operating pressure (psi) = External horizontal soil pressure (psi) = External vertical soil pressure (psi) = Angle variable for mortar crack analyses (deg) = Buoyancy of an empty pipe (lb) = First moment of cross-sectional area above or below the neutral survace (in.3) = Vertical load on parallel pipes (lb) = Load supported by soil between parallel pipes (lb) = Angle of plane of soil slip (deg) = Angle variable for mortar crack analyses (deg) = Radius of curvature of ring, general (in.) = Radius of curvature at a “flat spot” (in.) = Radius at top of pipe (in.) = Radius at bottom of pipe (in.) = Maximum radius of curvature for mortar crack analyses (in.) = Minimum radius of curvature for mortar crack analyses (in.) = Outside radius of pipe (in.) = Ratio of vertical to horizontal radii of an ellipse

NOMENCLATURE, CONSTANTS, AND TERMINOLOGY

rs rx ry R R Rs R′s sf S S′ t tc tl ts T TA u uB UA V VA w w w1 w2 w3 wd wl W Wc Wp X X1 y y1 Y Z Z1

19

= Outside radius of steel cylinder (in.) = Radius of curvature of ring at springline (in.) = Radius of curvature of ring at crown (in.) = Distance from pipe centerline to applied live load (ft) = Radius of longitudinal bending (in.) = Stiffness ratio (determined by calculation) = Stiffness ratio (determined by testing) = Safety factor = Degree of saturation of the soil = Vertical soil compression strength (psi or psf) = Thickness, general (in.) = Coating thickness (in.) = Lining thickness (in.) = Steel cylinder thickness (in.) = Thrust, general (force) = Radial compressive force per foot in pipe cylinder (lb/ft) = Pore water pressure (psi) = Hydrostatic pressure at soil cube B (psi) = Additional hydrostatic pressure at A due to flood level above ground surface (psi) = Vertical shear load at saddle support (lb) = Vertical shear force per foot in pipe cylinder (lb/ft) = Weight of soil lifted when soil environment settles relative to the pipe (lb) = Width of crack for mortar crack analyses (in.) = Unit weight of pipe (lb/ft) = Unit weight of pipe + contents + fill over pipe (lb/ft) = Unit weight of pipe (lb/in.) = Dead load per unit length of pipe (lb/ft) = Live load per unit length of pipe (lb/ft) = Surface wheel load (lb) = Load on pipe per unit length of pipe (Appendix A) (lb/ft) = Weight per foot of pipe and contents (lb/ft) = Distance at springline between parallel pipes (ft) = Distance at springline from a buried pipe to an adjacent cut trench wall (in.) = Deflection (sag) of a fixed end beam under uniform load (in.) = Deflection (sag) of a continuous pipe on bents under uniform load (in.) = Frictional resistance term for saddle support design = Maximum depth of vertical trench wall (in.) = Dimensional constant

Note: Nomenclature in appendices may differ from that in the chapters.

20

BURIED FLEXIBLE STEEL PIPE

Figure 2-1. Nomenclature for Cross Section of the Trench and the Pipe.

2.2 CONSTANTS α = Coefficient of thermal expansion and contraction of steel = 6.5 × 10−6/°F γc = Unit weight of cement mortar = 144 pcf γs = Unit weight of steel = 490 pcf γw = Unit weight of water = 62.4 pcf for freshwater, or 64 pcf for seawater υc = Poisson’s ratio for cement mortar = 0.25 υs = Poisson’s ratio for steel = 0.30 π = 3.14 Ec = Modulus of elasticity of cement mortar = 4 × 106 psi Es = Modulus of elasticity of steel = 30 × 106 psi g = 32.2 ft/sec2

NOMENCLATURE, CONSTANTS, AND TERMINOLOGY

21

2.3 TERMINOLOGY Figure 2-1 identifies common terminology for various locations of the trench and pipe.

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CHAPTER 3 PIPE MECHANICS

3.1 INTRODUCTION Structural design of welded steel pipe is based on the principles of pipe performance and the conditions for performance limit. A performance limit may be a leak or excessive deformation—either ring deformation or longitudinal deformation. Deformation is based on pipe mechanics, soil mechanics, and pipe–soil interaction. Soil is part of the conduit structural system—not simply a load on the pipe. Typically, design of pipe proceeds as follows: 1. 2. 3. 4. 5. 6. 7.

internal pressure—steel cylinder (wall) thickness; handling and installation—ring stiffness; external pressure—ring compression; ring deflection (deformation); longitudinal stress analysis; joints, linings, and coatings; miscellaneous, special design cases.

3.2 INTERNAL PRESSURE DESIGN The thickness of the steel cylinder (wall) is computed on the basis of limiting the hoop tensile stress in the steel to a defined maximum value for the internal pressure that is being analyzed. To determine the hoop stress, σH, we make a cut and construct a small slice as in Fig. 3-1. 23

24

BURIED FLEXIBLE STEEL PIPE

Figure 3-1. Free-Body Diagram of a Pressurized Shell. The free body is in static equilibrium. Equating horizontal forces, 2σHt = P2r, from which σ H = Prt Rewriting the hoop stress formula to a more common form to solve for the steel cylinder thickness, ts =

PDO 2 σp

(3-1)

where σp = stress from internal pressure (psi), P = pressure, general (psi), DO = outside diameter of steel cylinder (in.)*, ts = mainline steel cylinder thickness (in.). The most common internal pressure analyzed for design considerations is the operating pressure, which is often referred to as the working or design pressure (Pw). When designing the steel cylinder for this internal pressure, it is common to limit the allowable hoop tensile stress to a value equal to 50% of the specified minimum yield strength of the material. Another design condition for internal pressure is the transient pressure. This pressure is typically an infrequent, momentary pressure spike; hence, a greater hoop tensile stress is permitted. For this internal pressure * To be exact, the steel cylinder I.D., DI, should be used, but for conservative practical reasons, DO is commonly used.

PIPE MECHANICS

25

condition, a limiting hoop tensile stress equal to 75% of the specified minimum yield strength of the material is used. It is typical in the field to hydrostatically test the completed pipeline. For this internal pressure design case, the analysis of the field hydrotest pressure condition could be similar to the transient pressure, i.e., an allowable hoop tensile stress up to 75% of the specified minimum yield strength of the material should be used.

3.3 MINIMUM THICKNESS FOR HANDLING The minimum thickness for the steel cylinder of the pipe is often governed by what can be safely handled and installed in the field. Designers commonly use D/ts ratios up to 240. With special design, manufacturing, shipping, and installation considerations, increased D/ts ratios of 288 and higher have been successfully installed. Irrigation and hydroelectric systems are two examples that use these higher D/ts values.

Example 3-1: Minimum Wall Thickness, ts What is the minimum wall thickness, ts, to satisfy internal pressure requirements and handling? Pipe size, D = 48 in.; Cylinder O.D., DO = 49.875 in.; Working pressure, Pw = 150 psi; Transient pressure, Ps = 220 psi; Field test pressure, Pf = 200 psi; Steel minimum yield, σY = 36,000 psi. a. Working pressure design: ts =

150 ( 49.875) = 0.208 in. 2 ( 0.5) 36 , 000

b. Transient pressure condition: ts =

( 220 )( 49.875) = 0.203 in. 2 ( 0.75) 36 , 000

c. Field test pressure condition:

26

BURIED FLEXIBLE STEEL PIPE

ts =

200 ( 49.875) = 0.185 in. 2 ( 0.75) 36 , 000

d. Minimum thickness for handling: ts =

48 = 0.200 in. 240

Therefore, select steel cylinder thickness equal to 0.208 in. nominal to satisfy internal pressure and handling requirements.

3.4 RING STIFFNESS Stiffness is resistance to deflection (Fig. 3-2). Pipe stiffness is defined as the ratio of the concentrated load F applied to a cylinder over the resulting deflection D, or F/D. Ring stiffness is defined as EI/r3 per unit length of pipe; the dimensions of ring stiffness are force per unit area, commonly psi. Because I = t3/12 per inch length of pipe, EI/r3 = 2E/3(D/t)3. For steel, Es = 30 × 106 psi and t = ts; therefore, ring stiffness is

Figure 3-2. Deflection and Stiffness.

PIPE MECHANICS

EI ( 20 × 106 ) = r3 ( D t s )3

27

(3-2)

Clearly, ring flexibility (D/t) is an inverse measure of ring stiffness. Pipe stiffness is related to ring stiffness and ring flexibility: From elastic analysis, F/D = 6.72(EI/r3) and therefore, F/D = 4.48E/(D/t)3.

3.5 RING COMPRESSION If the pipe ring is held in circular shape when external pressure is applied, stress in the pipe wall is ring compression stress, s = P(DO)/2ts (Fig. 3-3). Performance limit for common pipe diameters and thicknesses is wall crushing or wall buckling at yield stress, σY. External pressure is caused by the soil embedment and the pipe does not fail at yield stress, but any additional pressure must be supported by the embedment. Nevertheless, for design, yield stress is set as the performance limit. With the safety factor, sf, the ring compression design equation is σ Y P ( DO ) σ Pr = or approximately Y = 2ts sf sf ts

(3-3)

Ring deflection is usually limited by specification such that it is small enough to be neglected. If ring deflection, d, were not negligible, ring compression stress at springline, B, would be increased by the increase in span from DO to DO(1 + d), where d is the horizontal ring deflection. The ring compression design equation would then become

( PDO ) (1 + d ) ( 2ts ) = σ Y sf

Figure 3-3. Ring Compression Stress, σ, Due to External Pressure, P. Ring Compression Stress Is σ = Pr/ts.

28

BURIED FLEXIBLE STEEL PIPE

Example 3-2: Factor of Safety Using a steel pipe of 48-in. I.D. and ts of 5/16 in., ring deflection is limited by specification to a small (negligible) value. Use DO = 49.875 in., σY = 36 kip/in.2, and assume a load of 25 psi. What is the factor of safety? Substituting into the ring compression stress equation for circular pipe, σY = P(DO)/2ts, we get σY = 25(49.875)/(2 × 0.3125) = 1,995 psi. Solving for the sf against yield of the material, we find sf = 36,000/1,995 = 18. Analysis is based on the assumption that side fill holds the ring in its circular shape. The assumption is valid except for instability discussed in Chapter 6.

3.6 PERFORMANCE LIMITS OF CEMENT MORTAR LININGS AND CEMENT MORTAR COATINGS Small cracks in mortar linings and coatings are inevitable but not critical. In fact, small cracks in a moist environment close by autogenous healing, the formation of calcium carbonate in the cement. From experience, cracks no greater than the thickness of a dime are considered small cracks. Pressure in the pipe tends to reround the pipe and close cracks due to deflection. If the pipe ring is permanently deformed (by lowpressure or gravity flow) and cracks are so wide that water could circulate to the steel, the exposed steel may corrode. The widest cracks occur in the tensile zones of the pipe. For coatings, this situation usually occurs at springline (Fig. 3-4). If multiple cracks open, the widths are less than a single crack. The widest cracks in a lining usually occur at the crown and invert. For analysis, the widest possible single crack width, w, is predicted from the following equations: w 2tc = 1 rmin − 1 r coating w 2tl = 1 r − 1 rmax lining where w tc rmin tl r rmax unit arc length

= width of crack, = thickness of mortar coating, = minimum radius, = thickness of mortar lining, = circular radius of pipe, = maximum radius, = 1.

PIPE MECHANICS

29

Figure 3-4. Cross Section of Pipe at Springline Showing Crack Width, w, as a Function of Mortar Coating Thickness, t, and Change in Radius from Circular, r, to Minimum, rmin. N.S. = Neutral Surface. (The Neutral Surface Is Close to the Steel. For Analysis, Assume That a Crack Penetrates to the Steel Surface.)

If ring deflection is less than 5%, cracks are generally narrower than the thickness of a dime (1/16 in.). Pressure in a pipe tends to reround the pipe, which leaves only hairline cracks that are uniformly distributed and that heal in a moist environment. Ring deflection is not the best basis for predicting crack width. Permanent deviations in radii of curvature are more reliable.

Example 3-3: Maximum Calculated Crack Width A flat spot in a 48-in.-diameter pipe with 1/2-in. cement mortar lining thickness has a radius of 120 in. What is the maximum calculated crack width? Use the equation, w/2tl = 1/r − 1/rmax, to find the crack width in the cement mortar lining. Rewrite to solve for the crack width, therefore, w = 2tl(1/r − 1/rmax). Solving for w, crack width is then 0.03 in. In practice, it is often necessary to measure the radius of curvature of a deformed pipe. This measurement can be done from either inside or outside the pipe, as shown in Fig. 3-5. From the outside, e can be found by laying a tangent of known length L and by measuring the offsets to the pipe wall at each end of the tangent. The average of the two (e′ and e″) is the value of e.

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BURIED FLEXIBLE STEEL PIPE

Figure 3-5. Procedure for Calculating the Radius of Curvature of a Ring from Measurements of a Chord Length, L, and the Middle Coordinate, e. The radius of curvature of the pipe wall can be calculated from the following equation: r=

( 4e 2 + L2 ) 8e

(3-4)

However, the measurement of e is not exact, and an approximation can be made by simplifying Eq. 3-4 to r=

L2 8e

(3-5)

To further simplify the calculation, a measuring device (stick), cut to 12⅝ in. long yields the following: r=

20 e

Example 3-4: Radius of a Pipe Find the radius of a pipe with a measured offset of ¾ in. when using a measuring stick cut to 12⅝ in. Answer: r = 20/0.75 = 26.7 in.

PIPE MECHANICS

31

Figure 3-6. Relationship of Ratio of Radii to Elliptical Ring Deflection.

3.7 RING DEFLECTION The assumption of elliptical ring deflection, as shown in Fig. 3-6, is based on theoretical analysis of a pipe buried in a homogeneous, isotropic, elastic medium. From field experience, if pipe is in soil embedment, it is prudent to consider nonelliptical ring deflection. A more accurate analysis of a nonelliptical ring is based on maximum and minimum radii of curvature. Some pipe installers attempt to locate where ring deflection is nonelliptical by measuring ring deflection, d, by an equivalent procedure, d = (Dx − Dy)/(Dx + Dy). If the numerator is zero, or if (Dx − D) differs significantly from (D − Dy), the ring deflection is nonelliptical and analysis should be based on maximum and minimum radii of curvature rather than elliptical ring deflection.

3.8 YIELD STRESS Yielding in steel is not necessarily a failure condition. Steel is ductile and can perform in the ductile range. However, designers consider yield stress, σY, to be a conservative performance limit for design. Yield stress is evaluated by standard uniaxial tension tests. For steel pipe, worst-case yield stress is biaxial. As an example, in steel pipe with

32

BURIED FLEXIBLE STEEL PIPE

Figure 3-7. Von Mises Compound Yield.

internal pressure, hoop tension stress is σx. Longitudinal stress, σz, causes biaxial stress. Among conditions for longitudinal stress is a longitudinal bend in a pipeline. The bend causes longitudinal stresses, i.e., tension on the outside of the bend and compression on the inside of the bend. Stresses, σx and σz, are compound stresses that alter yield stress. From beam mechanics, longitudinal strain is σz/E = r/R, where r is radius of the pipe and R is radius of the longitudinal bend in pipe. E is modulus of elasticity, 30,000,000 psi. Compound yield is shown in Fig. 3-7. If longitudinal stress and ring stress are of the same sign (either tension or compression), yield is slightly greater than the tensile test, σY. But if longitudinal and ring stress are of opposite sign, yield stress is less than tensile test, σY.

CHAPTER 4 SOIL MECHANICS

4.1 INTRODUCTION Structural behavior of buried pipe is not elastic, especially at performance limits. Design and analysis is based on pipe–soil interaction using correct properties of both pipe and soil. At performance limit (beyond elastic limit), steel pipes are ductile. Soil varies from particulate (granular) to viscous (mud). Basic principles of soil mechanics are required for rational design and analysis of buried pipe.

4.2 NOTATION γ γd γsat γt γb γw φ φ e c Z

= unit weight of soil; = dry unit weight; = saturated unit weight; = total unit weight; = buoyant unit weight; = unit weight of water = 62.4 pcf for freshwater, and 64 pcf for seawater; = soil friction angle (approximately the maximum angle of repose of a soil slope); = 30° = the lower limit for most embedment soils (35–45° for compacted embedment); = void ratio = ratio of volume of voids to volume of soil grains; = cohesion of soil (essential for vertical wall in an open trench); = maximum depth of an open trench with vertical walls;

33

34

BURIED FLEXIBLE STEEL PIPE

Zγ/c = 2/tan(45° − φ/2), in dimensionless terms for evaluating maximum depth of trench, Z; σ = normal (principal) stress in the soil (the subscript indicates the direction of the stress); τ = shear stress in soil (the subscript indicates the direction of the plane on which shear stress acts); k = soil strength = ratio of maximum to minimum principal stresses on an infinitesimal cube of soil at soil slip; k = (1 + sinφ)/(1 − sinφ) = 3 at φ = 30°, 3.7 at φ = 35°, 4.6 at φ = 40°, and 5.8 at φ = 45°; s = degree of saturation of soil = ratio of volume of water to volume of voids; ε = normal strain (notably, vertical compression of the side-fill embedment); d = ring deflection ratio (∆/D) of flexible pipe = e, vertical compression strain of the side-fill embedment; θf = angle of the plane of soil slip = (45° + φ/2); G = specific gravity of soil grains (typically about 2.7); H = height of soil cover or height of each soil stratum; h = height of the water table; P = vertical pressure = Pd + Pl; Pd = dead load pressure = 3γH; Pl = live load pressure = W/2H2; W = surface wheel load; u = hydrostatic pore water pressure = hγw. 4.3 SOIL CONDUIT Flexible pipe is a liner and form for a soil conduit. Soil embedment is the major structural component of the conduit. The soil embedment holds the pipe in shape, strengthens the pipe, protects the pipe, and supports much of the load. Analysis must include the structural performance of both pipe and soil and the pipe–soil interaction based on the properties of each. Performance limit is usually the simultaneous failure of both pipe and soil. 4.4 FLAWS IN APPLYING ELASTIC THEORIES TO SOIL For pipe–soil interaction, especially at performance limit, elastic theories neglect • soil arching action (as in a masonry arch), • soil slip (shear planes in the soil), and

SOIL MECHANICS

• nonlinear soil relationships.

compression

and

35

nonlinear

stress–strain

Failure is excessive deformation—the nonelastic deformation of pipe and nonelastic soil slip and soil compression. Excessive deformation may result in leaks, damage to lining and coating, and collapse of pipe.

4.5 UNIT WEIGHTS OF SOIL Pressure in the soil depends on weight per unit volume, g.

)

G + Se γt =  γ w = total unit weight  1+ e

)

G+e γ sat =  γ = saturated unit weight  1+ e w

) )γ

G γd = γ = dry unit weight 1 + e w G−1 γb =  1+ e

w

= buoyant unit weight ( weight of soil reduced by weight of water displaced )

Figure 4-1 shows a three-phase diagram.

Figure 4-1. Three-Phase Diagram for Soil.

36

BURIED FLEXIBLE STEEL PIPE

Example 4-1: Dry, Saturated, and Buoyant Unit Weights What are typical values of dry unit weight, saturated unit weight, and buoyant (effective) unit weight? From the soils laboratory, specific gravity, G, of the soil is about 2.7. Void ratio, e, depends on the gradation of particle size and density (compaction). Typical values range from 0.4 to 0.7. If e = 0.5, unit weights are γd = 112 pcf dry, γsat = 133 pcf saturated, and γb = 71 pcf buoyant. In examples to follow, assume unit weights of 110 pcf dry, 130 pcf saturated, and 70 pcf buoyant. Imprecision of soil properties seldom justifies more than two significant figures.

4.6 VERTICAL SOIL PRESSURES (STRESSES) P = Pl + Pd = vertical pressure, Pd = dead load pressure = γH, Pl = live load pressure = W/2H2 (Boussinesq, Pl = 0.477 W/H2). Figure 4-2 demonstrates vertical live load stress.

Example 4-2: Vertical Live Load Stress What is the stress, Pl? H = 2.5 ft of soil cover and W = 16-kip dual wheel load. Pl = W/2H2 = 1,280 psf.

Figure 4-2. Vertical Live Load Stress, Pl, at Depth H, Under Wheel Load W = 16 Kip.

SOIL MECHANICS

37

What is Pl if H = 10 ft? Substituting, Pl = 80 psf.

Example 4-3: Vertical Dead Load Stress What is the dead load stress? Pd = γH = dead load stress. H = 2.5 ft of soil depth and g = 110 pcf = dry unit weight. Solving, Pd = 275 psf.

4.6.1 Below a Water Table Below a water table, intergranular (effective) stress is total stress, σ, reduced by the weight of water displaced by soil (Fig. 4-3).

Figure 4-3. Total, Vertical, Dead-Load Stress (Pressure Pd) at the Level of the Top of Pipe.

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BURIED FLEXIBLE STEEL PIPE

–=σ−u σ where σ = total vertical stress = Pd, – = intergranular stress, σ u = pore water pressure = hγw. Both total and intergranular stresses are required for pipe–soil analyses. 4.6.2 Under Multiple Strata σ = ΣγH.

Example 4-4: Total and Intergranular Stresses What are the total and intergranular stresses at the level of the top of pipe in Fig. 4-3? γd γsat H1 H3 σ

= = = = =

110 pcf = dry unit weight of both sand and clay, 130 pcf = saturated unit weight, 9 ft, H2 = 6 ft, 11 ft, ΣγH = 990 + 780 + 1,430 = 3,200 psf.

Total vertical stress at the top-of-pipe level is σ = 3,200 psf = 22.2 psi = Pd. Pore water pressure is u = γwh = (11 ft)(62.4 pcf) = 686 psf. Intergranular stress is 3,200 − 686 = 2,514 psf. Intergranular stress at top-of-pipe level is s = 2,514 psf = 17.5 psi. Total vertical stress is used to calculate ring compression stress in an empty pipe. Intergranular stress is used to calculate vertical compression (strain) of the side-fill embedment soil. Flexible ring deflection is approximately equal to the vertical compression of the side-fill soil.

4.7 SOIL STRENGTH Performance limit (failure) of granular embedment is either excessive soil compression or soil slip. Soil slip is shearing of soil on a slip plane

SOIL MECHANICS

39

Figure 4-4. Mohr Stress Circle, Showing Strength k = σmax/σmin = (1 + sinφ)/(1 − sinφ), the Strength Envelopes, Stresses at Soil Slip (at φ = 30°, k = 3, at φ = 40°, k = 4.6), and Soil Slip Planes Correctly Oriented at θf at φ = 30°, and Slip Plane θf = 45° + φ/2 = 60°. (Fig. 4-4). Soil stresses around buried pipes are two-dimensional and can be analyzed by the Mohr stress circle (see Appendix B). 4.8 SOIL SLIP Soil slips if the Mohr stress circle is tangent to the strength envelopes at soil friction angle φ. Angle φ is roughly the angle of repose (maximum slope) of a windrow of cohesionless soil. Strength at soil slip is the ratio of maximum to minimum principal stresses; σmax/σmin = k where k = (1 + sinφ)/(1 − sinφ) = strength at soil slip = ratio of maximum to minimum principal stresses. Increase in φ by compaction increases strength, k. See Section 4.12 for increased soil strength via cohesion. Example: What is soil strength, k, at a conservatively low soil friction angle, φ = 30°? Solving, k = 3 (Fig. 4-4). 4.9 SOIL PARTICLE SIZE AND GRADATION Based on the Unified Soil Classification (Table 4-1), particle sizes fall into categories from boulders down to cobbles and smaller as follows:

40

Table 4-1. Unified Soil Classification Important Properties

Typical Names of Soil Groups

Clayey gravels, poorly graded gravel–sand–clay mixtures Well-graded sands, gravelly sands, little or no fines Poorly graded sands, gravelly sands, little or no fines Silty sands, poorly graded sand– silt mixtures

Permeability When Compacted

Shearing Strength When Compacted and Saturated

Compressibility When Compacted and Saturated

Workability as a Construction Material

GW

Pervious

Excellent

Negligible

Excellent

GP

Very pervious

Good

Negligible

Good

GM

Good

Negligible

Good

GC

Semipervious to impervious Impervious

Good to fair

Very low

Good

SW

Pervious

Excellent

Negligible

Excellent

SP

Pervious

Good

Very low

Fair

SM

Semipervious to impervious

Good

Low

Fair

BURIED FLEXIBLE STEEL PIPE

Well-graded gravels, gravel–sand mixtures, little or no fines Poorly graded gravels, gravel– sand mixtures, little or no fines Silty gravels, poorly graded gravel–sand–silt mixtures

Group Symbols

Inorganic silts, micaceous or diatomaceous fine sandy or silty soils, elastic silts Inorganic clays of high plasticity, fat clays Organic clays of medium to high plasticity

SC

Impervious

Good to fair

Low

Good

ML

Semipervious to impervious

Fair

Medium

Fair

CL

Impervious

Fair

Medium

Good to fair

OL

Poor

Medium

Fair

Fair to good

High

Poor

CH

Semipervious to impervious Semipervious to impervious Impervious

Poor

High

Poor

OH

Impervious

Poor

High

Poor

MH

SOIL MECHANICS

Clayey sands, poorly graded sand–clay mixtures Inorganic silts and very fine sands, rock flour, silty or clayey fine sands with slight plasticity Inorganic clays of low to medium plasticity, gravelly clays, sandy clays, silty clays, lean clays Organic silts and organic silt– clays of low plasticity

Source: USBR 1963.

41

42

BURIED FLEXIBLE STEEL PIPE

Gravel

Sand

Fines (Silt and Clay)

75 3 —

4.75 0.2 No. 4

0.075 0.03 No. 200

Particle size (mm) Particle size (in.) Sieve (mesh per inch)

Well-graded soil has uniform distribution of particle sizes. Poorly graded soils contain same-size particles throughout.

4.10 SOIL FRICTION ANGLE Soil friction angle Φ, unit weight γ, cohesion c, and vertical soil compression ε are the major soil properties for buried pipe analysis. Other soil properties may have significant effect under special circumstances, e.g., permeability, minimum density at liquefaction, and Atterberg limits. Soil friction angle Φ is important because it affects soil strength. Friction angle is roughly the steepest angle of repose (slope) of a windrow of cohesionless soil. Precise values of soil friction angle Φ can be found from direct shear and triaxial tests in the soils laboratory. Figure 4-5 is a typical graph of values for friction angle Φ for granular, cohesionless soil as a function of density and soil type. It is intended for preliminary analysis.

γ d max  emax − e  × 100% = Relative density is Dr =   emax − emin  γd

 γ d − γ d min  × 100%  γ d max − γ d min 

4.11 PASSIVE RESISTANCE Passive resistance is maximum horizontal resistance to pressure, sx, (as of pipe) at soil slip (Fig. 4-6a.)

Example 4-5: Passive Soil Resistance Given: Granular embedment soil, Φ = 30°, H = 2.5 ft, D = 36 in., and γ = 110 pcf. What is passive soil resistance, σx, at springline? Vertical principal stress is σy = γ(H + D/2) = 3 psi. At soil slip, k = σmax/σmin = (1 + sinφ)/(1 − sinφ) = 3. Solving, soil slips at passive resistance, σx = 9 psi. Horizontal pipe pressure, σx, could be caused by a heavy wheel load crossing the pipe.

SOIL MECHANICS

43

Figure 4-5. Approximate, Conservatively Low Values of Soil Friction Angle φ for Average Native Granular Embedment. Values Are Higher for Crushed Rock and Select Embedment. Relative Density Is Not Relative Compaction, Which Is Understood (by Rule-of-Thumb) to Be RC = 80% + 0.2Dr.

4.12 COHESION IN SOIL Cohesion in the soil increases strength. This concept is used in flowable fill. Portland cement is added to poor soil (with excessive fines) with enough water to flow the mixture under the pipe. Flowability is the objective. Cohesion, like glue, is shearing strength, which spreads the strength envelopes vertically (c on the shear stress axis, τ) (Fig. 4-6b.)

Example 4-6: Maximum Principal Stress By adding half a sack of Portland cement per cubic yard, unconfined compression strength is 70 psi. From Fig. 4-6b, cohesion is c = 20 psi. If φ = 30° and minimum σy = 10 psi at springline (Fig. 4-6a), what is the maximum principal stress, σx (passive resistance)? From Fig. 4-7, σx = 100 psi.

44

BURIED FLEXIBLE STEEL PIPE

Figure 4-6. Typical Principal Soil Stresses. (a) Maximum Horizontal Resistance to Pressure, σx, at Soil Slip, and (b) Shearing Strength.

Figure 4-7. Comparison of Maximum Principal Stresses in Granular Embedment and the Same Embedment with Half a Sack of Portland Cement per Cubic Yard. σx Increases from 30 to 100 psi.

SOIL MECHANICS

45

4.13 SOIL COMPRESSION In the design of buried flexible steel pipe, soil compression is soil strain, e. Excessive soil compression causes the pipe to shift and deflect. The embedment, in particular, must not exceed allowable limits of compression. Nonuniform bedding allows deflection of adjoining pipes at a joint, which causes a lever action and the risk of a leak. Excessive compression of soil under the haunches causes the bottom of the pipe to flatten. Ring deflection ratio (∆/D) of the flexible pipe is roughly equal to the vertical strain of the side-fill embedment. Strain is a function of stress. The stress– strain relationship is not elastic. Figure 4-8 shows typical stress–strain curves for granular soil at various densities from confined compression tests. Clearly, at any given stress level, the greater the compaction, the smaller the vertical strain (compression). The laboratory confined compression test is used typically to predict the vertical compression of side fill, which is useful for predicting ring deflection. Confined compression is conservative because it overpredicts side-fill compression. The confined compression test is uniaxial. At the springline of a flexible pipe, side-fill compression is biaxial (vertical and radial). Consequently, vertical strain of side fill is less than is predicted by the laboratory confined compression test. For finite element analyses, sections of the stress–strain curves are assumed to be linear. This linearity provides stiffness, E′ (secant modulus), for analysis. Figure 4-8 shows one

Figure 4-8. Stress–Strain Diagram for a Silty Sand from Confined Compression Tests at Varying Density (ASTM D698) Showing a Soil Stiffness, E′, from σ = 0 to 3.6 ksf.

46

BURIED FLEXIBLE STEEL PIPE

such stiffness, E′ = 800 psi, at 80% density for a stress increase from zero to 3.6 ksf. If density is 90%, stiffness is E′ = 1,500 psi from zero to 3.6 ksf.

4.14 EMBEDMENT Embedment is the soil placed around a pipe after the pipe is positioned and aligned on bedding (Fig. 4-9). Embedment is an essential component of the conduit. Some specifications call for select fill that is screened with a specified distribution of grain sizes. Some specifications call for flowable fill, which includes Portland cement (or fly ash) and enough water to form a slurry that flows under the pipe to ensure uniform bedding and embedment. Some specifications allow “backpacking” adjacent to the pipe with a soil arch over the backpacking to support load. Embedment must hold the pipe in alignment and protect the pipe from heavy wheel loads. Embedment must prevent soil liquefaction that could collapse the pipe or cause flotation of an empty pipe under a high water table. Embedment and bedding must prevent piping (washout of soil from under the pipe) caused by groundwater flow channels under the pipe.

4.15 SELECT FILL Select fill is well-graded granular material with specified gradation of particle sizes and usually less than 12% fines. It is compacted at specified moisture content and in lifts of limited height.

Figure 4-9. Typical Embedment.

SOIL MECHANICS

47

Well-graded soil provides a soil filter that prevents fines in the embedment from migrating out into the trench wall and prevents fines from the trench wall from migrating into the embedment. If adequately compacted, the gradation prevents piping. If vertical compression of the embedment is controlled (in terms of soil type and density), the embedment forms a soil arch over the pipe that protects the pipe and supports the load of backfill and live loads above the pipe. Arching action of embedment is highly desirable (it will work without it; we design for full overburden) if an embankment is to be built up over the pipe. A cover of embedment over the pipe is essential. The arching action also allows for backpacking—a less dense zone of embedment at the pipe–soil interface where there is potential for impact damage to the pipe during compaction.

4.16 LIQUEFACTION The conditions for liquefaction of soil are loose soil, saturation (below a water table), and shock waves (seismic action). The shock wave could be caused by earthquake or vibration from traffic, pile driving, blasting, or heavy equipment. Unit weight of liquefied soil is roughly twice the unit weight of water. Liquefied soil can collapse a pipe or cause it to float out of alignment. The critical soil density for liquefaction of granular soil is approximately 85% standard Proctor density. However, under high-amplitude shock waves, liquefaction could occur at higher densities.

4.17 QUICK CONDITION “Quicksand” is soil liquefied by seepage of water in the soil. An obvious quick condition is the result of artesian flow of water up through soil. Figure 4-10 is a schematic sketch of a laboratory procedure for determining the head of water, h, above the soil surface at which an aquifer below the soil stratum of height H causes soil to liquefy. Buoyant unit weight of soil is roughly equal to the unit weight of water; and so, as a rule of thumb, at h ≈ H, soil is liquid. This quick condition could cause a pipe to float and is of concern for buried pipe on hillsides where seepage from above could liquefy the soil embedment of a pipe. Flow nets become useful. Hillsides pose additional problems for pipes. In regions of freeze–thaw, surface layers of soil creep downhill with each cycle of freeze–thaw. Creep is also caused by cycles of change in temperature and in water content. Landslides are an obvious problem.

48

BURIED FLEXIBLE STEEL PIPE

Figure 4-10. Equating Buoyant Weight to Uplift Force at Which the Soil Is Liquefied (Quick Condition).

4.18 SOIL MOVEMENT In tidal basins, soil rises and falls. Deep pumping of groundwater, as well as crumbling tunnels and mines below the surface, can cause soil settlement. Flexible couplings or gasketed bell-and-spigot joints may be required for longitudinal flexibility. Pipes crossing earthquake faults require pairs (or double pairs) of flexible couplings.

4.19 EARTHQUAKES Earthquakes in general require seismic analyses that include types of waves and the amplitude and direction of the waves. A seismologist or geotechnical engineer should be consulted. If seismic waves move parallel to a buried pipe, shear waves (S waves) cause longitudinal bending (undulations) that can cause leaks at bell-andspigot joints by lever action. Pressure waves (P waves) can cause leaks at joints by jamming and withdrawing adjoining pipes. If seismic waves cross a buried pipe, the soil could be displaced or liquefied, depending on the soil conditions. The result could be displacement, flotation, or collapse of buried pipe.

SOIL MECHANICS

49

4.20 SOIL SPECIFICATIONS The critical soil specifications are maximum allowable compression (based on allowable ring deflection) and minimum allowable strength at soil slip. Additional specifications may be required for special conditions. Soil specifications are based on the mechanical properties and on the performance limits of soil (conditions for failure). The most basic performance limits for the soil in pipe–soil interaction are excessive compression and soil slip. Performance limits could also include • soil liquefaction; • migration of fines through coarser particles, especially where groundwater seepage occurs; • soil permeability that may affect seepage on slopes. A soil filter (for gradation of particle size) could be specified to control seepage and soil particle migration. Soil slip can be measured by penetrometers. Penetrometers are easy to use and can be used without slowing down the project. They predict resistance to soil slip directly. Conventional control of soil slip (strength) and soil compression is achieved by specifying minimum soil density. Density is controlled by compaction and water content. Density is measured by sand cones or by nuclear gauges. Soil compression is measured by laboratory stress–strain tests. Confined compression tests (Fig. 4-11) are approximate because they are uniaxial. They are conservative for predicting strain of soil embedment for buried structures because stress in soil embedment is biaxial. Confined compression tests predict compression of a soil stratum under vertical pressure. The compression (vertical strain) is a function of vertical stress,

Figure 4-11. Typical Confined Compression Test.

50

BURIED FLEXIBLE STEEL PIPE

soil type, and degree of compaction. Soil compression is related inversely to soil stiffness. If soil were elastic, the stiffness would be E′ = σ ε where E′ is soil stiffness, σ is soil stress, ε is strain. If vertical pressure on an uncompacted soil stratum is increased from σ1 to σ2, the vertical soil strain (compression) is ε2 − ε1. This increase would cause ring deflection of a flexible pipe in the stratum. Because soil is not elastic, stress–strain curves are not linear. A specific soil stiffness, E′, is the slope of a secant between initial stress (ε1, σ1) and the stress after pressure is applied (ε2, σ2). Specific values of E′ are used in finite element analyses but are only approximate in predicting vertical compression of embedment. Horizontal compression of embedment complicates elastic soil stiffness. Horizontal values of E′ are not accurate in predicting ring deflection of flexible pipes. Buried pipe design is better served by stress– strain data than by published values of E′. E′ is not constant; it varies with soil type, soil compaction, and depth of soil cover. Minimum soil density is often specified for embedment soil. Soil density is of less value than stress–strain data for predicting compression. Soil particle size (gradation) is often specified for select embedment, but it does not determine accurately the basic soil properties of soil compression and soil strength.

4.21 FINITE ELEMENT ANALYSIS Katona et al. (1976) pioneered the application of the finite element method for the solution of buried pipe problems. Their project, sponsored by the Federal Highway Administration (FHWA), produced the wellknown public domain computer program CANDE (Culvert ANalysis and DEsign). CANDE has been upgraded several times and is now available for use on a personal computer. Others also made early contributions in the use of the finite element method for buried structures problems (Katona 1982; Leonards et al. 1982; Sharp et al. 1984; Sharp et al. 1985; and Spitzley 1987). The basic idea behind the finite element method for stress analysis is that a continuum is represented by a number of elements connected only at the element nodal points (joints), as shown by the two-dimensional representation of a buried pipe in Fig. 4-12. A structural analysis of the

SOIL MECHANICS

51

Figure 4-12. Typical Finite Element Mesh for a Buried Pipe Installation. finite element assemblage can be made in a manner similar to the structural analysis of a building. The process involves solving for the nodal displacements and then, based on the nodal displacements, the stresses and strains within each element of the assemblage can be determined. The elements shown in Fig. 4-12 are the basic structural units of the soil–pipe continuum, just as beams and columns are the basic structural units of building frames. Each element is continuous, and stresses and strains can be evaluated at any point within the element. The major difference between the analysis of a continuum and a framed structure is that even though a continuum is only connected to adjacent elements at its nodal points, it is necessary to maintain displacement compatibility between adjacent elements. Special shape functions are used to relate displacements along the element boundaries to the nodal displacements and to specify the displacement compatibility between adjacent elements. Once the continuum has been idealized, as shown in Fig. 4-12, an exact structural analysis of the system is performed using the stiffness method of analysis (Zienkiewicz 1977; Dunn, Anderson, and Kiefer 1980; and Gere and Weaver 1980). The output of a finite element analysis includes the stresses and strains at any point in the system and, more importantly, the displacement, moment, shear, and thrust at any point in the buried pipe. An example of a finite element analysis is presented in Appendix C. The power of using the finite element method is that once the model is set up, many cases can be analyzed and the sensitivity of assumptions can be tested. Furthermore, a finite element analysis can be performed for many buried pipe applications that are difficult to analyze using conventional analysis procedures. Multiple pipes in a trench, the effect of excavating a trench adjacent to an existing pipe, and other applications can conveniently be accommodated by a finite element analysis.

52

BURIED FLEXIBLE STEEL PIPE

There are limitations in using a finite element analysis. The problem is usually analyzed as a two-dimensional problem, even though the system is clearly three-dimensional. For long culverts, treating the problem as a plane-strain two-dimensional problem is generally not a serious limitation, but in some cases the three-dimensional effects cannot be neglected. There are three-dimensional finite element analysis programs available, but generally they do not have the proper constitutive relationship for modeling soil and do not provide interface elements that allow slip between the soil and the pipe. In these cases, it may be necessary to compare two- and three-dimensional solutions for conditions that can be modeled and then to extrapolate to the real case. Evans (2004) used this technique to study the effects of modeling a point load on a long pipe. Abdel-Motaleb (1995) used a three-dimensional analysis to investigate the behavior of steel storage tanks where the behavior at the ends of the tanks was important. A finite element analysis of a soil–structure interaction system, such as a buried pipe, is different from a finite element analysis of a simple linearly elastic continuum in several ways, according to Watkins and Anderson (2000): • The soil properties, such as the elastic modulus, are stress- and strain-dependent (nonlinear). • A different element type must be used to represent the pipe than that used for the soil. • It may be necessary to allow movement between the soil and the walls of the pipe, requiring the use of an interface element. • It may be necessary to use a geometric nonlinear solution for flexible pipes that involve large displacements. Many commercial finite element analysis software packages are available for the solution of various stress analyses. In selecting a finite element program for use in solving soil–structure interaction problems such as buried pipe, it is important to make sure that the program has the attributes listed above. 4.21.1 Stress- and Strain-Dependent Soil Properties In many buried pipe applications, the stress–strain properties of the soil are nonlinear over most of the operational stress and strain range. In general, the soil modulus increases with increasing effective normal stresses and exhibits strain-softening behavior with increasing shear strain. The nonlinear stress–strain properties of soils can be modeled by simulating the construction process. In the finite element model, soil is placed in layers similar to the construction sequence. As each new layer

SOIL MECHANICS

53

is added, the stresses in the layers below are increased; the increased stresses increase the strain in the soil as well as contributing to the deformation of the pipe, and in turn the strain-dependent soil parameters change. The finite element program that is used must allow the adjustment of soil parameters as the construction progresses. 4.21.2 Pipe Elements In a two-dimensional finite element analysis, the pipe is generally modeled as a series of beam elements that model the shear, moment, and thrust in the pipe as well as the deflection of the pipe. In a three-dimensional analysis, the pipe would likely be modeled with a series of shell elements. 4.21.3 Interface Elements In the analysis of buried pipes, it is frequently important to allow for movement (slip) between the soil and the pipe. Slip can be accommodated by using interface elements. The interface element compares the shear stress induced along the pipe with the frictional strength at the soil–pipe interface and then allows movement if the frictional strength is exceeded. Because it is difficult to determine when the use of interface elements is important, it is probably best to always include the interface element in the analysis. 4.21.4 Geometric Nonlinearity In many conventional finite element analysis applications, the displacements are small. In such cases, the geometry of the system changes little, and it is common practice to define the global stiffness matrix based on the original geometry of the system. This practice may limit the use of the finite element analysis for buried pipe applications, where the deflections of the system may be substantial. For example, in analyzing the rerounding of a buried pipe due to internal pressures, it is essential to follow and adjust the geometry of the pipe to simulate the rerounding of the pipe. If the initial shape of a pipe is circular before adding external loads and elliptical after loading, then pressurizing the loaded pipe should cause it to seek a circular shape as the internal pressure is increased. A finite element analysis of this problem does not work if the global stiffness matrix of the soil–pipe system is based on the original circular shape of the pipe because the analysis would be that of a circular pipe rather than an elliptical pipe. Therefore, as the pipe deflects under the external or internal loads, the global stiffness matrix must also be adjusted for the changed geometry.

54

BURIED FLEXIBLE STEEL PIPE

Finite element analysis can be an efficient and valuable tool for understanding the behavior of buried pipes under a variety of geometric and loading conditions. Commercial user-friendly computer programs are available that make it possible to model the soil–pipe system and to obtain reliable results.

CHAPTER 5 PIPE–SOIL INTERACTION

5.1 INTRODUCTION Soil, or pipe ring, stiffness, which is a material property, is defined as resistance to deflection. Soil stiffness usually provides most of the resistance to buried flexible steel pipe deflection. Ring stiffness is important during installation because it helps to keep the pipe in shape while embedment is placed and compacted. The performance limit of ring stability is instability. Ring instability is a spontaneous deformation that progresses toward inversion (reversal of curvature). Pipes can invert only if the ring deflects and the soil slips at the same time. Instability is analyzed as a soil–structure interaction. Structural performance of buried flexible steel pipe is dependent on the pipe to soil (embedment around the pipe) and native soil interaction. Pipe–soil interaction is critical to maintain the ring stability of the pipe under external earth, construction and surface loads, and also to prevent collapse, or buckling, under external hydrostatic or soil pressure. A finite element analysis of pipe to soil interaction system may become a useful tool to predict the performance of pipe installed under different loading conditions in soils with nonlinear properties (see Chapter 4 and Appendix C). The representation of pipe to soil interaction requires capabilities generally not included in most finite element analysis applications. For buried flexible steel pipe applications, it is critical to determine the minimum soil cover required to avoid pipe damage from wheel traffic or construction loads, to prevent pipe flotation, and to prevent the effects of weather conditions, such as freezing and thawing, on the pipe embedment. 55

56

BURIED FLEXIBLE STEEL PIPE

5.2 RING DEFLECTION As soil and surface loads are placed over a buried flexible steel pipe, the ring tends to deflect primarily into an ellipse with a decrease in vertical diameter, ∆y, and approximately equal increase in horizontal diameter, ∆x. Any deviation from elliptical cross section is a secondary deformation that may be due to nonuniform soil pressure. The increase in horizontal diameter develops lateral soil pressure and support that increase the load-carrying capacity of the ring. The decrease in the vertical diameter partially relieves the load on the ring. The soil above the pipe takes more of the load in arching action over the pipe. Although some pipe deflection is beneficial in supporting the load on the pipe, it should not exceed a practical performance limit so as not to impair the structural properties of the pipe and the protective properties of the linings and coatings. Therefore, the prediction of ring deflection is important. The ring deflection is elastic up to the formation of permanent ring deformations. In tests conducted at Utah State University, it was observed that the ring deflection ratio of a buried flexible pipe did not exceed the vertical compression strain of the side-fill soil (Fig. 4-8). Ring deflection ratio, d, (d = ∆/D) is d≤ε

(5-1)

From Fig. 4-8, ε is the average side-fill unit settlement or soil strain = ∆D/D. Vertical soil strain ε is predicted from laboratory compression tests data, such as the stress–strain graphs of Fig. 4-8 for cohesionless silty sand. Soil stiffness E′ is the slope of a secant to the anticipated soil pressure P on the stress–strain diagram for a specific soil density, as shown in Fig. 4-8. Figure 5-1 is a graph of the ring deflection term as a function of stiffness ratio Rs or R′s where Rs = E′D3/EI and R′ = 0.0186 Rs. Therefore, ring deflection can be predicted by the use of Figs. 4-8 and 5-1.

Example 5-1: Predicted Deflection If a 48-in. diameter by 1/4-in. wall bare steel pipe is to be placed in embedment compacted to 80% dry density (AASHTO T 180) below 15 ft of cohesionless silty sand weighing 120 pcf, then what is the predicted deflection?

PIPE–SOIL INTERACTION

57

Vertical soil pressure = 15 × 120 = 1,800 psf = 1.8 ksf. At 80% density, from Fig. 4-8, the soil strain at 1.8 ksf is ε = 1.7%. The soil secant, E′, from 0 to 1.8 ksf on the 80% graph is E′ = 12.5/0.017 = 735 psi. Rs = stiffness ratio = E′D3/EI ≈ 2,800. At Rs = 2,800, from Fig. 5-1, d/ε = 1. Therefore d = ε = 1.7%. Because soil strain is 1.7%, the predicted ring deflection is d = 1.7% (1) = 1.7%. The proper procedure for design of flexible pipes is to specify the allowable ring deflection and to make sure that the vertical compression of the side-fill soil does not exceed this value. Predicted ring deflection is a basic performance limit. Therefore, it is controlled by a performance specification. One performance specification can replace many procedural specifications. An example is a specification for ring deflection in the following form: “The backfill soil quality, placement, density, etc., shall be such that maximum ring deflection does not exceed (some percent to be specified).” This format is responsive to a basic performance limit, allowable ring deflection. One caveat is for nonelliptical deformations with flat spots. For this case, the radius of curvature should be determined by the procedure in Chapter 3 and should be used to determine ring deflection.

Figure 5-1. Ring Deflection Term as a Function of Stiffness Ratio.

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BURIED FLEXIBLE STEEL PIPE

5.3 RELATIVE EFFECT OF PIPE AND SOIL ON RING DEFLECTION Because the soil provides most of the resistance to ring deflection, the soil controls ring deflection. The ring stiffness is usually insignificant compared to soil stiffness. For any pipe stiffness, the ring is able to support part of the vertical load as it deflects. This part of the vertical pressure supported by ring stiffness is Po, as shown in the right side of Fig. 5-2. Po can be calculated by the Castigliano theorem: Po = Ed m3 = 96 ( ΣEI D3 ) d

(5-2)

where ∑EI/D3 = the sum of ring stiffnesses of cylinder, mortar lining, and mortar coating and m = r/t. The contribution of mortar lining or coating to ring stiffness is based on the assumption that the mortar acts as a laminar ring and is not bonded to the steel cylinder.

Figure 5-2. Unsaturated Soil. Left, Free-Body Diagram of an Infinitesimal Cube at Springline, B, Showing Stresses at Incipient Soil Slip. Right, Vertical Soil Pressure, Po, Supported by the Pipe due to Ring Stiffness.

PIPE–SOIL INTERACTION

59

The following examples show the portion of the soil overburden supported by the pipe, based on the hypothetical assumption that the soil offers no side resistance to pipe deflection.

Example 5-2: Vertical Load What part of the vertical load in Example 5-1 is supported by the bare pipe? Modulus of elasticity for steel is 30 × 106 psi. The predicted deflection in the example was 1.7%. Therefore, d = 0.017. Ei = ( 30 × 106 ) × ( 0.253 12) = 39, 063 lb-in.2 in. Substituting values into Eq. 5-2: Po = 96 ( ΣEI D3 ) d = 0.58 psi = 83.5 psf Based on the 120 pcf soil weight, the equivalent earth cover that the pipe can support is 83.5/120 = 0.7 ft. Therefore, the bare pipe supports about 5% of the total earth cover.

Example 5-3: Another Vertical Load Problem What part of the vertical load in the above example can be supported by the pipe if the 48-in. bare steel pipe in the previous example was lined with 0.50-in. mortar and coated with 0.75-in. mortar? Modulus of elasticity for mortar is 4 × 106 psi. ∑EI for the three (lining, cylinder, and coating) laminar rings = (4 × 106) × (0.503/12) + (30 × 106) × (0.253/12) + (4 × 106) × (0.753/12) = 41,667 + 39,063 + 140,625 = 221,355 psi/in. Substituting values into Eq. 5-2, PO = 3.27 psi = 470 psf. Therefore, the pipe with the cement mortar lining and coating can support 470/120 = 3.9 ft of earth cover or 26% of the total earth cover. The soil has to support 74% of the earth cover.

Because ring deflection is a common performance limit, it is noteworthy that the ring deflection can be controlled more effectively by quality and compaction of soil embedment than by increased ring thickness. Ring deflection is controlled by placement and compaction of the embedment and by control of heavy construction loads that might pass over the pipe before height of soil cover is adequate.

60

BURIED FLEXIBLE STEEL PIPE

The ring stiffness of steel cylinder plus mortar lining (and possible coating) is of greatest importance during installation when ring stiffness helps to hold the pipe in shape while embedment is placed and compacted. The installer must control ring deflection. Longitudinal hairline cracks that appear in the mortar due to ring deflection are not detrimental to the pipe performance after installation. These cracks close partially when the pipe is pressurized and rerounded. In moist environments, cracks close by autogenous healing (i.e., a buildup of calcium carbonate in the cracks). 5.4 HYDROSTATIC COLLAPSE IN A FLUID ENVIRONMENT The formula for the collapse of pipe under external hydrostatic pressure (including internal vacuum) by the classical theory (Fairbairne, Presse, Brian, and Timoshenko) is Pr3/EI = 3, which, for mortar-lined (and coated) steel pipe, becomes P = 3 ΣEI r 3

(5-3)

Example 5-4: External Hydrostatic Pressure at Collapse What is external hydrostatic pressure at collapse of a 37.5-in. I.D. steel pipe with 0.1875-in. wall? Modulus of elasticity for steel is 30 × 106 psi. Therefore, EI/r3 = E/12(D/t)3 = 2.46 psi, and substituting values, P = 7.4 psi. What is external pressure at collapse of the same pipe with mortar lining 0.375-in. thick? Modulus of elasticity for mortar is 4 × 106 psi. Therefore, for the steel cylinder and mortar lining, ∑EI/r3 = 2.46 + 2.75, making P = 15.6 psi. Collapse is a function of modulus of elasticity and pipe ring stiffness. By way of comparison, if the pipe is held in shape by good embedment, performance limit is wall crushing, which is a function of yield strength.

Example 5-5: Wall-Crushing Pressure Limit For the pipe in the above example, find the wall-crushing pressure limit for the pipe that has steel with yield strength equal to 42,000 psi. Ignore the strength of the cement mortar lining. σf = 42,000 psi, and P = σr(t/r), therefore, P = 420 psi. Wall crushing is a function of yield strength of the material. The value of embedment is obvious. The soil embedment is an integral component of the conduit.

PIPE–SOIL INTERACTION

61

5.5 RING DEFORMATION FAILURE OF BURIED FLEXIBLE PIPE Performance limit of buried flexible steel pipe is either by wall crushing (ring compression) or excessive wall buckling (inversion). If the ring could be held circular, analysis would be simple ring compression. But flexible ring analysis anticipates ring deflection before vacuum is applied. Ring deflection depends on ring stiffness and stiffness of embedment soil. Performance limit is failure that occurs if the ring either crushes due to ring compression or buckles due to side-fill slip at B, as shown in Fig. 5-2. 5.5.1 Wall Crushing Failure by wall crushing: σ f = ( Pext + Pvac ) DO 2T + 3Ed (T DO )

(5-4)

where σf = ring compression stress at yield stress in the pipe wall at B T = wall thickness DO = outside diameter Pext = external pressure at top of pipe Pvac = internal vacuum d = ∆/D = ring deflection, E = modulus of elasticity It is recommended that a factor of safety of 2 be applied to the ring compression stress at yield. The first term on the righthand side of Eq. 5-4 represents the uniform axial stress due to external hydrostatic or soil pressure depicted in Fig. 5-3a, and the second term represents bending stress due to ring bending, as depicted in Fig. 5-3b.

Example 5-6: Maximum Negative Pressure Consider a 48-in. steel pipe with 0.25-in. wall with yield strength of 42,000 psi and E = 30 × 106 psi. The earth cover load is 15 ft with a unit soil weight of 120 pcf. The measured deflection of the pipe after installation is 3%. What is the maximum negative pressure, Pvac, the pipe can withstand at ring compression? Compare this pressure to a full vacuum (14.7 psi) to demonstrate the factor of safety. External pressure due to a 15-ft earth load with a 120-pcf soil weight is Pext = 12.5 psi. Axial compressive stress at external pressure of 12.5 psi is 1,200 psi. Ring compression stress due to 3% ring deflection is

62

BURIED FLEXIBLE STEEL PIPE

Figure 5-3. Depiction of Axial and Bending Stresses for Eq. 5-4. 14,062.5 psi. Based on yield strength of 42,000 psi, the calculated vacuum pressure using Eq. 5-3 is 279 psi. This result assumes that stability is maintained until wall crushing occurs. Therefore, the factor of safety at full vacuum is 279/14.7 = 18.9. If we apply the recommended factor of safety of 2 against the yield strength, then the calculated vacuum pressure will be 60 psi.

5.5.2 Ring Buckling (Inversion) Over time, shearing stresses between pipe and soil become negligible due to such things as water seepage, temperature change, and vibration. Vertical and horizontal soil pressures are related as follows: PA rA = PB rB = Pr For an ellipse, rr = rA rB = (1 + d )3 (1 − d )3

(5-5)

PB = PA (1 + d )3 (1 − d )3 = PA rr

(5-6)

Therefore,

Pressure Against Soil at Springlines The horizontal pressure of the pipe against the soil at B is reduced by PO, the vertical soil pressure supported by the pipe due to ring stiffness.

PIPE–SOIL INTERACTION

63

PB = ( PA + Pvac − PO ) rr − Pvac (See Fig. 5-2 for a free-body diagram and assumptions.) Substituting PO, PB = ( PA + U A + Pvac − Ed m3 ) rr − Pvac

(5-7)

Where UA = additional hydrostatic pressure at A due to the flood level above ground surface (flood level h is shown in Fig. 5-4). If soil at B does not have adequate strength, the soil slips and the ring inverts. Strength of Soil at Springlines The following is analysis of strength for granular side fill (Fig. 5-4.) σ x = k σy where – = horizontal effective soil stress at B, σ x – = vertical effective soil stress at B, σ y k = ratio of horizontal to vertical effective stress at soil slip = (1 + sinΦ)/(1 − sinΦ), Φ = friction angle of embedment, – can be evaluated by methods in Chapter 4. σ y

Figure 5-4. Saturated Soil. Free-Body Diagram of an Infinitesimal Soil Cube at B, Showing the Stresses Acting on It at Incipient Soil Slip and Showing the Shear Planes at Soil Slip.

64

BURIED FLEXIBLE STEEL PIPE

Vacuum at Collapse of Buried Pipes The total horizontal soil pressure at springline B at soil slip is PB = k σ y + uB

(5-8)

where PB = total horizontal pressure on soil at B – = horizontal effective soil slip stress at B, kσ y uB = hydrostatic pressure in soil at B. When the horizontal pressure PB from Eq. 5-6 is equal to PB from Eq. 5-7, the soil is on the verge of slipping, which is defined as instability. The equation of equilibrium of side fill at soil slip for collapse by ring inversion is Pvac ( rr − 1) = k p V y + uB − ( PA + πrγ w 2 − dE m3 ) rr

(5-9)

where Pvac = vacuum collapse, rr = (1 + d)3/(1 − d)3 = ratio of vertical to horizontal radii of elliptical pipe, m = r/t, r = mean radius of circular pipe, t = wall thickness, d = ∆/D = initial ring deflection, which usually occurs because of backfilling, kp = (1 + sinφ)/(1 − sinφ) at passive resistance, φ = friction angle of embedment, γw = unit weight of water, – σ = vertical effective soil stress at B, y uB = hydrostatic pressure at B if a water table is above the pipe, PA = soil and water pressure at A, E = modulus of elasticity of pipe material, E/m3 = 96 EI/D3 where EI/D3 = ring stiffness, I = moment of inertia of the wall cross section per unit length of pipe, and F/∆ = pipe stiffness = 53.77 EI/D3. Note: πrγw/2 is uplift buoyancy pressure of empty pipe. If the embedment is not cohesionless as assumed in the above analysis, the same procedure may be used, except that the relationship between the horizontal and vertical stresses at soil slip must be evaluated for each particular embedment. Below a groundwater table, the hydrostatic pressure on the bottom of the pipe is greater than on the top. Collapse may occur from the bottom.

PIPE–SOIL INTERACTION

65

Example 5-7: Internal Vacuum A 48-in.-diameter welded steel pipe with 0.25-in. wall is buried in embedment of dry uncompacted sand to 6 ft above the top of the pipe. Unit weight of sand is 110 pcf. The soil friction angle is 25°. Ring deflection was not controlled during backfilling, so the average ring deflection was 8%. What is the internal vacuum at collapse? D = 48 in., t = 0.25 in., E = 30,000,000 psi, I = t3/12 = 0.0013, 3 EI/D = 30,000,000 × 0.0013/483 = 0.353 psi, d = 0.08, H = 6 ft, γ = 110 pcf, uB = 0, Φ = 25°, kp = (1 + sin 25°)/ (1 − sin 25°) = 2.464, rr = (1 + 0.08)3/(1 − 0.08)3 = 1.618, PA = 6(110)/144 = 4.58 psi, σy = 8(110)/144 = 6.11 psi. Substituting into Eq. 5-9, Pvac = 19.4 psi. Therefore, the internal vacuum pressure at soil slip is 19.4 psi.

5.6 MINIMUM COVER In pipeline design, analyses of minimum soil covers required are essential to protect the integrity of the buried pipe under different loading and environmental conditions. Soil is the major component of a flexible buried pipe system. Soil protects the pipe by holding the pipe in shape and in alignment. The following are analyses of minimum soil covers required for protection against wheel loads, flotation, uplift, and frost. 5.6.1 Wheel Loads Two conditions for minimum cover, H, should be considered for a wheel load, W, crossing over the pipe. The first condition is when W is directly over the pipe. The second condition occurs when W approaches the pipe. Figure 5-5 shows the wheel load, W, directly over the pipe. The scenario for failure is soil slip at springlines. For empty, flexible pipe, Pxrx = Pyry.

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BURIED FLEXIBLE STEEL PIPE

Figure 5-5. Wheel Load, W, Directly over the Pipe. The horizontal pressure of pipe on soil at springline is Px = Pyrr, where Py = γH + W/2H2, which is dead load plus live load; and rr = ry/rx, the ratio of radii. For elliptical ring deflection, rr = [(1 + d)/(1 − d)]3, where d is ring deflection. d = 2% rr = 1.13

5% 1.35

10% 1.83

The activating horizontal stress of pipe on soil at springline is Px = rr ( γH + W 2 H 2 )

(5-10)

The resisting (passive) soil strength at springline is σ x = k p γ ( H + D 2)

(5-11)

where γ = unit weight of the soil and kp = (1 + sinΦ)/(1 − sinΦ) = passive strength coefficient. Equating Px = σx, and solving, W = 2 γH 3 [( k p rr ) (1 + D 2 H ) − 1] Φ = 15° kp = 1.7

30° 3.0

45° 5.8

(5-12)

PIPE–SOIL INTERACTION

67

Figure 5-6. Example of Maximum Wheel Load as a Function of Soil Cover over a Flexible 48-in. Pipe Buried in Granular Embedment.

Example 5-8: H with Respect to W How does H vary with respect to W if γ = 120 pcf, D = 48 in., and Φ = 30°? The results are given in Fig. 5-6. But this analysis assumes that the pipe does not fail on approach of wheel load. Figure 5-7 shows the critical location of wheel load W on approaching the pipe from the left side that “punches through” a truncated pyramid and deforms the pipe ring. Location of the load is critical on the left side of centerline, as shown. Maximum moment M is critical on the right side of the centerline. This critical location has been determined by tests. Pressure on the pipe is not uniform. Consequently, ring stiffness is needed to resist ring deformation. Deformation is caused by punch-through of a truncated pyramid of soil under the wheel. If ring stiffness is not adequate, top of the pipe inverts as the wheel rolls across the pipe. Inversion is triggered by the maximum moment, M = 0.022Pr2, about 10° to the right of centerline. The moment, M, causes bending stress σ = Mc/I. The ring compression stress is σ = (P/2)(D/t) for flexible pipe, where P = γH = negligible. Equating, pressure, P, can be found from the equations: P = ( 30 σ Y ) ( D t )

2

P = ( 30 σ Y ) ( D t )

2

elastic yield stress

(5-13)

ductile hingee

where P = vertical pressure on buried pipe due to the surface wheel load, = yield stress in steel (usually 42,000 psi for steel pipe), and σY (D/t) = ring flexibility = diameter/wall thickness for plain pipe.

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Figure 5-7. Exaggerated Sketch of the Inversion Mechanics of Flexible Pipe Under a Surface Load.

Figure 5-8 shows vertical soil pressure, P, under a dual wheel. For an HS-20 truck, the tire print is B = 7 in. and L = 22 in. (tire pressure at 105 psi). Wheel load, W, on compacted granular soil punches out a pyramid with slopes of about 1h:2v (slope angle = 37°). From Fig. 5-8, pressure on the pipe is P = W (B + H ) ( L + H )

(5-14)

Minimum cover, H, can be evaluated from simultaneous Eqs. 5-13 and 5-14.

Example 5-9: Minimum Height of Soil Cover What is the minimum height of soil cover over a plain steel pipe at the initiation of yielding if an AASHTO HS-20 truck crosses over? The cover is granular soil compacted such that ruts are insignificant. Reaching the yield stress is not inversion; the formation of a ductile hinge is incipient inversion. But limiting the stress to the yield point provides an additional safety factor:

(D t ) = 240 AASHTO HS-20 dual wheel load with

PIPE–SOIL INTERACTION

69

Figure 5-8. Pressure, P, on the Top of a Flexible Pipe at Minimum Cover When a Truncated Pyramid Is “Punched Through” by Surface Live Load. W = 16-kip wheel load, B = 7 in., L = 22 in., σY = 42,000 psi yield strength. From Eq. 5-13, P = 21.88 psi (3 kip/ft2). Substituting into Eq. 5-14 and solving, H = 13.6 in. Considering dynamics, an engineer would probably call for H = 1.5 ft. Tests show that this analysis is conservative. Analysis ignores soil support, longitudinal strength of the pipe, and ductile hinge at inversion. From tests with a smooth approach, H = 1 ft. Mortar linings and coatings increase the stiffness of the pipe and increase the safety factor. In the example above, the stiffness of lining and coating were neglected because tensile strength is low and hairline cracks further decrease effectiveness of the mortar. 5.6.2 Flotation The obvious case of flotation is empty pipe under water. If the pipe is below the water surface, a minimum soil cover, H, is needed to prevent flotation. Many pipes are below water surface, e.g., near a high groundwater table or a river crossing, under a lake or bay, or below flood level. A full pipe does not float.

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Figure 5-9. Minimum Cover of Buoyant Soil Under Water to Prevent Flotation of Empty Pipe (Crosshatched Area Based on Tests Conducted at Utah State University).

Figure 5-9 shows a cross section of minimum cover for granular soil. Buoyancy, Q, of the empty pipe is the weight of water displaced: Q = γ w ( πD2 4 ) ↑ where γw = 62.4 pcf = weight of water and D = pipe diameter. Weight of soil is the weight of soil wedges bounded by the soil slip planes at an angle equal to the soil friction angle. For cohesionless soil, a reasonable soil friction angle is 37°, for which soil slips at roughly 1h : 2v, shown in outer bounds in Fig. 5-9. Based on tests conducted at Utah State University, granular soil slips on parabolic surfaces rather than 1 : 2 planes. The resisting force, W, is the buoyant weight of soil cover, shown cross-hatched: W = γbA↓ where γb = 62.4 pcf = γw (approximate buoyant, i.e., effective, unit weight) and A = area shown cross-hatched = (DZ + Z2/3 − πD2/8). A safety factor is recommended. For design purposes, increase the calculated H by a factor of 2.0.

PIPE–SOIL INTERACTION

71

Example 5-10: Minimum Cover of Granular Soil Under Water What is minimum cover, H, of granular soil under water to prevent flotation when a pipe is empty? The empty pipe floats if Q exceeds W. Equating Q = W, Q = γ w πD2 4 5, Q = 20 γD2.

Example 5-11: Uplift Load What is the uplift load, Q, on a 48-in.-diameter pipe with 8 ft of cohesionless soil cover at γ = 110 pcf? From the pipe uplift equation, Q/γD2 = 4.2. Solving, Q = 7,392 lb/ft.

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BURIED FLEXIBLE STEEL PIPE

Figure 5-10. Inverted Terzaghi Model for Uplift Force on a Pipe Buried Under High Soil Cover.

Example 5-12: Another Uplift Load Problem What is the uplift load, Q, in the above example if the cover was 4 ft, which is the minimum recommended cover for flotation of empty pipe? From pipe uplift equation, Q/γD2 = 1.9 Solving, Q = 3,344 lb/ft.

5.6.4 Frost For pipes in which the contents could freeze or pipes that could be deformed by cycles of freezing and thawing of the embedment, the minimum soil cover is usually the deepest penetration of frost. Frost depths are available from U.S. government agencies. In the northern contiguous states, frost depth is less than 2.5 ft. At a depth greater than approximately 5 ft, temperature is constant year round—about 55 °F. In extremely cold climates, permafrost exists, wherein frost is much deeper and never melts except for a few inches on the surface during midsummer. Special design is required for permafrost.

CHAPTER 6 DESIGN ANALYSIS

In this chapter, case scenarios will illustrate analysis of buried pipe, and examples will show design for internal pressure and handling. Various conditions of external loading will be analyzed to show that flexible pipe ring stability depends on soil properties. Buried pipe design analysis, which was introduced in the previous three chapters, follows three basic procedures. The first step in buried pipe design, as shown in Chapter 3, is to determine the wall thickness required because of internal pressure. This step assumes that pipe diameter, flow, pressure, and routing have been determined. The second step is to check for minimum steel wall thickness for handling, which is also shown in Chapter 3. And finally, the pipe–soil embedment system is analyzed for external loading during construction, which involves earth loads, live loads, and water table conditions and can also include negative pressure in the pipeline (Chapters 4 and 5). After a pipeline is installed and pressurized, the internal pressure tends to decrease any ring deformation. Basically, pipe does not deflect more than the vertical compression of the surrounding soil. Critical deflection of soil, or the performance limit, is the vertical deflection at which soil slip occurs. When soil slip occurs, a flexible pipe will collapse. By specification, pipe deflection may be much more limited than that for critical soil compression or soil slip, due to such things as coating and lining constraints. These deflection limits can be controlled by selection and control of embedment material and installation techniques, rather than by pipe stiffness. The following examples illustrate pipe wall thickness design and analysis of ring stability under various conditions. 73

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BURIED FLEXIBLE STEEL PIPE

• Case 1—Determine Wall Thickness for Internal Pressure and Handling. • Case 1A—Ring Stability—External Pressure and No Water Table or Vacuum Pressure. Analyzing amount of deflection to cause soil slip. • Case 1B—Ring Stability—External Pressure and Vacuum Pressure. Analyzing amount of vacuum pressure to cause soil slip. • Case 1C—Ring Stability—External Pressure with Water Table and Vacuum Pressure. Analyzing amount of deflection to cause soil slip with added vacuum pressure and water table. • Case 2A—Ring Stability at a Given Depth and Ring Deflection. Determine amount of deflection that allows ring collapse. • Case 2B—Ring Stability at a Given Depth and Ring Deflection. Determine pipe stiffness required for given conditions. Note: The outside diameter of the steel cylinder is used for many of the calculations in the problems rather that the inside diameter or neutral axis diameter. This usage has been common practice in the industry and is generally more conservative. Additionally, soil properties do not lend themselves to a high level of precision.

6.1 CASE 1—INTERNAL PRESSURE AND HANDLING Determine steel wall thickness (ts) required to withstand internal pressure requirements for working, surge, and test pressures. Also, check steel thickness for handling. Given: Nominal pipe size, D = 48 in. Cylinder O.D., DO = 49.75 in. Internal working pressure, Pw = 150 psi Surge pressure, Ps = 220 psi

Specified Manufacturer’s standard Specified Specified surge allowance of 70 psi Specified

Internal field test pressure, Pf = 188 psi Cement mortar lining (CML), tl = 0.5 in. (flexible coated) Cement mortar coating (CMC), tc = 0 in. Cylinder minimum yield strength, σY = 42 ksi

DESIGN ANALYSIS

Internal Pressure Calculations ts =

75

Using the hoop stress formula, PDO 2σ

(3-1)

Working pressure design, Pw, where σ = 0.5 σY, therefore, ts =

( Pw DO ) (150 × 49.75) = = 0.178 in. ( 2σ ) ( 2 × 21, 000 )

Surge pressure design, Ps, where σ = 0.75 σY, therefore, ts =

( Ps DO ) ( 220 × 49.75) = = 0.174 in. ( 2σ ) ( 2 × 31, 500 )

Field test pressure design, Pf, where σ = 0.75 σY, therefore, ts =

( Pf DO ) ( 2σ )

=

(188 × 49.75) = 0.148 in. ( 2 × 31, 500 )

Minimum Thickness for Handling Per Chapter 3, ts = D/288 for flexible lined and coated pipe, or D/240 for cement mortar lined and flexible coated pipe. This pipe is cement mortar lined and flexible coated. Therefore, ts = D/240 = 48/240 = 0.200 in. Summary Use a wall thickness of 0.200 in. to satisfy all of the above pressure and handling conditions for the cement mortar lined and flexible coated pipe.

6.2 CASE 1A—RING STABILITY Analyze with • external pressure analysis with soil support, • water table below pipe, • no internal or vacuum pressures. The performance limit is soil slip at springline. Find the vertical deflection at which soil slip occurs. Consider the infinitesimal cube shown in the Fig. 6-1. At soil slip, the pressure of the pipe against the soil is equal to the passive soil resistance,

76

BURIED FLEXIBLE STEEL PIPE

Figure 6-1. Cross Section of Buried Pipe Considered in Case 1A.

Prr = kσ y

(6-1)

P is the soil pressure at the top of the pipe and  (1 + d )  rr =   (1 − d ) 

3

(6-2)

where d = ring deflection in decimal form. At soil slip, k=

(1 + sinΦ ) (1 − sinΦ )

(from Chapter 4)

where Φ is the soil friction angle. σy is the vertical soil stress at B. Problem Statement Determine vertical deflection at which soil slip occurs. Looking at the 48-in.-diameter pipe from case 1 where diameter, DO = 49.75 in., wall thickness, ts = 0.200 in., CML thickness, tl = 0.5 in., allowable deflection, d = 0.03 = 3%. Conditions Fill height above top of pipe, Hc = 10 ft with dry, cohesionless soil (sand),

DESIGN ANALYSIS

77

soil weight, γd = 120 pcf, water surface above the top of pipe, hw = 0 ft, water weight, γw = 62.4 pcf with freshwater, vacuum = 0 psi, soil friction angle, Φ = 30 deg from Fig. 4-5 (conservative for dry sand), soil compaction = 85% (ASTM D698), live load, Pl = 0 psf. Ring Stability (at Hc Depth) Check for deflection at which soil slip occurs. The performance limit is soil slip at springline. With soil support and no external radial pressure, the deflection at which soil slip occurs is calculated as follows: At top—of pipe, P = γdHc/144 = (120 × 10)/144 = 8.33 lb/in.2; At springline, σy = γd(Hc + DO/2)/144 = 120 × (10 + 2.07)/144 = 10.06 psi; k = (1 + sinΦ)/(1 − sinΦ) 1.5/0.5 = 3. At soil slip, Prr = kσy, therefore rr = kσy/P = 3 × 10.06/8.33 = 3.62 and rr0.33 = 1.54. To determine the critical ring deflection, substitute rr into the following equation and solve for d:

( rr0.33 − 1)  (1 + d )  rr =  or d = 0.33   (1 − d )  ( rr + 1) 3

d=

(1.54 − 1) 0.54 = = 0.213 = 21.3% (1.54 + 1) 2.54

Summary This answer is seven times the specified allowable deflection of 3% to which the pipe is being maintained due to the cement mortar lining limit. Therefore, soil slip cannot occur at the specified deflection limit.

6.3 CASE 1B—RING STABILITY WITH VACUUM Analyze with • external pressure analysis with soil support, • water table below the pipe, • internal vacuum pressure. Determine the vacuum pressure at which soil slip occurs with soil support in unsaturated soil. Consider the infinitesimal cube shown in the Fig. 6-2.

78

BURIED FLEXIBLE STEEL PIPE

Figure 6-2. Cross Section of Buried Pipe Considered in Case 1B.

The performance limit for internal vacuum and/or external soil pressure is inversion. To solve for critical vacuum or external radial pressure, a ring stiffness component is added to the previous formula because critical vacuum, Pvac, is sensitive to the radius of curvature. Pvac ( rr − 1) = kσ y − ( PA − dE m3 ) rr

(5-9)

(this is Eq. 5-9 with uB and πrγw/2 equal to 0) where E = modulus of elasticity of pipe and m = r/t = ring flexibility, and the buoyancy term is dropped for this case. For design of pipe to withstand internal vacuum pressure, a safety factor of 2 is recommended. Determine the allowable vacuum or external radial pressure while maintaining this recommended safety factor. Problem Statement Look at the 48-in.-diameter pipe from Case 1A with reduced earth cover of lower density soil, where diameter, DO = 49.75 in., wall thickness, ts = 0.200 in., CML thickness, tl = 0.5 in., allowable deflection, d = 0.03 = 3% (specified). Conditions Fill height above the top of pipe, Hc = 2 ft of dry sand; soil weight, γd = 100 pcf; water surface above the top of pipe, hw = 0 ft (water table);

DESIGN ANALYSIS

79

water weight, γw = 62.4 pcf of freshwater; vacuum = 14.7 psi; soil friction angle, Φ = 30 deg (conservative for dry sand); soil compaction = 85% (ASTM D698); live load, Pl = 0 psf; ratio of radii (at allowable d), rr = 1.20. rr = [(1 + d ) (1 − d )] = (1.03 0.97 ) 3

3

What vacuum pressure can this buried pipe withstand?

Calculations At top-of-pipe pressure, PA = γdHc/144 = 100 × 2/144 = 1.39 psi and Z = H c + DO 2 = 2 + ( 49.75 12) 2 = 2 + 2.08 = 4.08 ft. At springline, σy = γdZ/144 = 100 × 4.08/144 = 2.83 psi. At soil slip, k = (1 + sinΦ)/(1 − sinΦ) = 1.5/0.5 = 3. Ring stiffness, E/m3, is the sum, S, of ring stiffnesses of steel pipe, lining, and coating. For steel, Es = 30 × 106 psi, and m = rs/ts, where rs ≈ Do/2 = 48.75/2 = 24.875 in., and ts = steel pipe wall thickness. For mortar, Ec = 4 × 106 psi, r ≈ rs, and t = mortar wall thickness. Therefore, E/m3 = 30 × 106/(r/t)stl3 + 4 × 106/(r/t)cml3 + 4 × 6 10 /(r/t)cmc3, where stl is steel cylinder. Ring stiffness = 30 × 106/(24.875/0.2)stl3 + 4 × 106/(24.875/0.5)cml3 + 0cmc = 48.1 psi; d = 0.030 (3% specified); rr = 1.2. Rewriting this equation: Pvac(rr − 1) = kσy − (PA − dE/m3)rr to solve for Pvac: Pvac = (kσy − (PA − dE/m3)rr)/(rr − 1) = (3 × 2.83 − (1.39 − 0.03 × 48.1) × 1.2)/(1.2 − 1) = 42.8 psi. Summary This is a safety factor of 2.9 against a 14.7 psi full vacuum pressure. Critical vacuum pressure increases significantly by limiting ring deflection and by compacting the embedment (increase soil friction angle). The most significant variables here are the ring deflection and the soil density.

80

BURIED FLEXIBLE STEEL PIPE

6.4 CASE 1C—RING STABILITY WITH VACUUM AND WATER TABLE ABOVE PIPE Analyze with • external pressure analysis with soil support, • water table above pipe, • internal vacuum pressure. The soil does not liquefy if the density of the embedment is 90% standard Proctor. The height of the water table, h, above ground surface is an external pressure that must be added to the internal vacuum pressure. Determine the internal vacuum pressure or flood pressure, or both, at h at which soil slip occurs. Consider the infinitesimal cube shown in Fig. 6-3. The worst case is an empty pipe with the water table at flood level. The equation of stability is Pvac ( rr − 1) = kV y + uB − ( PA − πrγ w 2 − dE m3 ) rr

(5-9)

where uB is water pressure at B and πrγw/2 is the uplift buoyancy pressure of the empty pipe. Problem Statement Look at the 48-in.-diameter pipe from Case 1B with increased earth cover of higher density saturated soil, where

Figure 6-3. Cross Section of Buried Pipe Considered in Case 1C.

DESIGN ANALYSIS

81

diameter, DO = 49.75 in.; wall thickness, ts = 0.200 in.; CML thickness, tl = 0.5 in.; allowable deflection, d = 0.03 = 3% (specified). Conditions Fill height above the top of pipe, Hc = 4 ft, soil weight, γsat = 130 pcf of saturated sand, water surface above ground surface, h = 10 ft (water table), water weight, γw = 62.4 pcf for freshwater, vacuum = 0 psi; soil friction angle, φ = 30 deg, soil compaction = 90% (ASTM D698), live load, Pl = 0 psf, ratio of radii (at allowable d), rr = 1.20 = [(1 + d)/(1 − d)]3 = (1.03/0.97)3. What vacuum or flood level can the buried pipe withstand? Calculations At top-of-pipe pressure, PA = (γsat × Hc + γw × h)/144 = 7.94 psi; r = (DO/12)/2 = (49.75/12)/2 = 2.07 ft; uB = water pressure at springline = (h + Hc + r)γw/144 = 6.1 psi. At springline, σy = PA + γsat × r/144 − uB = 3.71 psi. At soil slip, k = (1 + sinΦ)/(1 − sinΦ) = 1.5/0.5 = 3. Ring stiffness, E/m3, where m = (rs/t), with rs = DO/2 = 49.75/2 = 24.875 in. E = ∑ steel + CML + CMC moduli. Therefore, E/m3 = 30 × 106/(r/t)stl3 + 4 × 106/(r/t)cml3 + 4 × 106/(r/t)cmc3. Ring stiffness = 30 × 106/(24.875/0.2)stl3 + 4 × 106/(24.875/0.5)cml3 + 0cmc3 = 48.1 psi. d = 0.03; rr = 1.2. Use the equation Pvac(rr − 1) = kσy + uB − (PA + πrγw/2 − dE/m3)rr to rewrite and solve for external pressure, Pvac: Pvac = (kσy + uB − (PA + πrγw/2 − dE/m3)rr)/(rr − 1) = [3 × 3.71 + 6.1 − (7.94 + π × 2.07 × 62.4/2/144 − 0.03 × 48.1) × 1.2]/ (1.2 − 1) = 38.6 psi Converting Pvac to an additional flood level, 38.6 × 2.31 + 10 = 99 ft.

82

BURIED FLEXIBLE STEEL PIPE

Summary At 3% deflection, the safety factor with respect to vacuum pressure would be 38.6/14.7 = 2.6. Again, the most significant variables above are the ring deflection and the soil density. An increase in the water table above the pipe reduces the allowable vacuum pressure, thus reducing the factor of safety against a full vacuum pressure. In general, the height of ground surface should be greater than DO/2 to resist flotation, with the soil denser than critical density. The minimum specified density is generally 90% (ASTM D698). If the soil is looser than critical density, it has the potential to liquefy.

6.5 CASE 2A—RING STABILITY AT A GIVEN DEPTH WITH PARTIAL VACUUM Analyze with • partial vacuum pressure and • water table above the pipe. Figure 6-4 shows a 96-in.-outside diameter × 3/8-in.-wall pipe, full of water, buried in an embedment of silt and fine sand. The cover is 16 ft. At certain times during the year, the water table rises to within 2 ft below the ground surface. Soil friction angle is 15 deg. Maximum vacuum pressure is 11.4 psi. What is the elliptical ring deflection at which collapse occurs? – + u − (P + dE/m3)r The equation of stability is Pvac(rr − 1) = kσ y B A r

(5-9)

Note: The uplift buoyancy pressure term from Eq. 5-9 was omitted because it is not a factor in this sample calculation, and the general case k is used. Problem Statement Look at a bare steel cylinder 96-in.-diameter pipe, where diameter, DO = 96 in., wall thickness, ts = 0.375 in., CML and CMC thickness = 0 in. Conditions Fill height above the top of pipe, Hc = 16 ft of silt and fine sand; soil weight, γd = 100 pcf of dry silt; soil weight, γsat = 125 pcf of saturated silt; water surface above the top of pipe, hw = 14 ft (water table);

DESIGN ANALYSIS

83

Figure 6-4. Cross Section of Buried Pipe Considered in Cases 2A and 2B. water weight, γw = 62.4 pcf of freshwater; vacuum, Pvac = 11.4 psi; soil friction angle, Φ = 15 deg; soil compaction = unknown; live load, Pl = 0 psf. What is the critical ring deflection with the high water table and the partial vacuum pressure? Calculations At top-of-pipe pressure, PA = γd(Hc − hw)/144 + γsat × hw/144; = 100(16 − 14)/144 + 125 × 14/144 = 13.54 psi. At springline, σy = PA + γsat × rs/144 − uB = 13.54 + 125 × 4/144 − 7.80 = 9.21 psi,

84

BURIED FLEXIBLE STEEL PIPE

where rs = (DO/12)/2 = (96/12)/2 = 4 ft and uB = water pressure at springline = (hw + rs)γw/144 = 7.80 psi. At soil slip, k = (1 + sinΦ)/(1 − sinΦ) = 1.259/0.741 = 1.7. Ring stiffness, E/m3, where m = (r/t) , with rs = DO/2 = 96/2 = 48 in. and E = ∑ steel + CML + CMC moduli. Therefore, E/m3 = 30 × 106/(r/t)stl3 + 4 × 106/(r/t)cml3+ 4 × 106/(r/t)cmc3. Ring stiffness = 30 × 106/(48/0.375)stl3 + 0cml+ 0cmc. = 14.3 psi. Solve by iteration using the following equations: Equation 5-5 is the first equation: rr = [(1 + d)/(1 − d)]3 = ry/rx for ellipses and rr = [(1 + 0.03)/(1 − 0.03)]3 = 1.20. Equation 5-9 (without the uplift component) is the second equation: – + u − (P + dE/m3)r or rewriting to solve for r : Pvac(rr − 1) = kσ y B A r r rr = ( kσ y + uB + Pvac ) ( Pvac + PA − dE m3 ) = (1.7 ( 9.21) + 7.8 + 11.4 ) (11.4 + 13.54 − 0.03(14.3 ) = 1.42 Then, solve for various deflections until solution is determined:

Deflection (%)

3 4 5 6 6.2

rr from First Equation

rr from Second Equation

1.20 1.27 1.35 1.43 1.45

1.42 1.43 1.44 1.45 1.45

Therefore, the critical elliptical ring deflection at soil slip is 6.2%. For a variation of the above example, if the deflection is limited to 3%, what is the maximum vacuum or radial external pressure? Again, at 3% using the first equation, rr = [(1 + d)/(1 − d)]3 = [(1 + 0.03)/(1 − 0.03)]3 = 1.20. Then, using the second equation, – + u − (P + dE/m3)r )/(r − 1) Pvac = (kσ y B A r r = [1.70 × 9.21 + 7.80 − (13.54 − 0.03 × 14.30) 1.20]/(1.20 − 1) = 39.4 psi. Summary At the 3% deflection limit, the safety factor against a full vacuum pressure is 2.7. Or the allowable water level over the top of pipe in an emergency flood situation, with an 11.4-psi vacuum pressure, is as follows: (39.4 psi − 11.4 psi) 2.31 ft/psi = 64.4 ft.

DESIGN ANALYSIS

85

6.6 CASE 2B—PIPE STIFFNESS TO PREVENT COLLAPSE Analyze with • water table above the top of pipe, • partial vacuum pressure, • limit on ring deflection. Figure 6-4 shows a 96-in.-outside diameter pipe, full of water, buried in an embedment of silt and fine sand, as in the previous example. The cover is 16 ft. At certain times during the year, the water table rises to within 2 ft below the ground surface. Soil friction angle is 15 deg. If ring deflection is limited to a maximum of 5%, what pipe stiffness is required, F/∆, to prevent collapse? Use a safety factor of 2 against the vacuum pressure for design. Problem Statement pipe from Case 2A:

Look at the bare steel cylinder 96-in.-diameter

diameter, DO = 96 in. and CML and CMC thickness = 0 in. Conditions Fill height above the top of pipe, Hc = 16 ft of silt and fine sand; soil weight, γd = 100 pcf of dry silt; soil weight, γsat = 125 pcf of saturated silt; water surface above the top of pipe, hw = 14 ft (water table); water weight, γw = 62.4 pcf of freshwater; vacuum, Pvac = 11.4 psi; soil friction angle, Φ = 15 deg; soil compaction = unknown; live load, Pl = 0 psf; allowable deflection, d = 5% (specified); ratio of radii, rr = 1.35. rr = [(1 + d)/(1 − d)]3 = (1.05/0.95)3 – + u − (P + dE/m3)r The equation of stability is Pvac(rr − 1) = kσ y B A r

(5-9)

Note: The uplift buoyancy pressure term from Eq. 5-9 was omitted because it is not a factor in this sample calculation and the general case k is used. Pipe stiffness, from Chapter 3, for plain pipe is F/∆ = (53.77 EI)/D3 = (4.48 E)/(D/ts)3 = E/1.786 m3.

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BURIED FLEXIBLE STEEL PIPE

Calculations

First, solve the above stability equation for m3: m3 = ( dErr ) ( Pvac ( rr − 1) − kσ y − uB + PA rr ) .

At top-of-pipe pressure, PA = γd(Hc − hw)/144 + γsat × hw/144 = 100(16 − 14)/144 +125 × 14/144 = 13.54 psi. – = P + γ × r /144 − u = 13.54 + 125 × 4/144 − 7.80 = At springline, σ y A sat s B 2 9.21 lb/in. , where rs = (DO/12)/2 = (96/12)/2 = 4 ft and uB = water pressure at springline = (hw + rs)γw = 7.80 psi. At soil slip, k = (1 + sinΦ)/(1 − sinΦ) = 1.259/0.741 = 1.7. Ring stiffness, E/m3, where m = (r/t), with r = DO/2 = 96/2 = 48 in. Use a safety factor of 2 applied to Pvac = 2 × 11.4 = 22.8 psi. m3 = ( dErr ) ( Pvac ( rr − 1) − kσ y − uB + PA rr ) = ( 0.05 × 30 , 000 , 000 × 1.35) [ 22.8 (1.35 − 1) − 1.7 × 9.21 − 7.8 + 13.54 × 1.35] = 722, 698 And m = 89.7 = r/ts, resulting in ts = r/89.7 = 48/89.7 = 0.535 in. For mortar-lined and -coated pipes, pipe stiffness, F/∆, can be used for determination of ring stiffness, E/m3. Pipe stiffness is measured by a three-edge bearing test, which is essentially a parallel plate test. Measured values are more accurate than theoretical values for which neutral surface is assumed and bond of mortar to steel is neglected. The relationship of pipe stiffness to ring stiffness is F/∆ = (E/m3)/1.786. For calculations involving mortar-lined and mortar-lined-and-coated pipes, ring stiffness can also be found from measured pipe stiffness. For this example, based on ring stiffness, the equivalent pipe stiffness is F ∆ = E 1.786 m3 = 30 , 000 , 000 1.786 (722, 698 )3 = 23.3 psi , which is conservatively low. Measured values of pipe stiffness would be greater. Summary Pipe stiffness can be increased with cement mortar lining or cement mortar coating. However, it might be more effective to use a pipe zone material with a higher friction angle than 15 deg to reduce the resulting wall thickness.

CHAPTER 7 SPECIAL CONSIDERATIONS

7.1 INTRODUCTION Designers are at times confronted with situations that are outside the confines of what is generally considered standard buried pipe design and analysis. In these situations, standard design and analysis may apply but in conjunction with special considerations. This chapter presents several such situations, and the associated designs and analyses.

7.2 PARALLEL PIPES IN A COMMON TRENCH The situation where two pipes are installed in a common trench can cause a designer to question the applicability of basic design principles for buried flexible pipe. Although the basic principles are still valid, this section offers additional analysis for the region of soil between the pipes with respect to heavy surface loads. Surface loads at three critical locations need to be reviewed: • On approaches where, under minimum soil cover, the pipe deforms. Resistance of the pipe ring to deformation is a function of ring stiffness (see Chapter 5). • Directly above a pipe where the pipe fails in ring compression or where the soil slips at the springline (see Chapter 5). • Directly above the soil column between the parallel pipes. Once the pipe strength is found to be adequate for the surface load on approach and directly over the pipe, the final step is determination of the minimum pipe separation. 87

88

BURIED FLEXIBLE STEEL PIPE

Figure 7-1. Pipe–Soil Column Between Parallel Pipes. Section AA Must Support Part of the Surface Live Load, W, Plus the Dead Load, Shown Crosshatched. When buried pipes are installed in parallel, principles of analysis for single pipes still apply, including the requirement for minimum soil cover. However, the design of parallel, buried pipes requires an additional analysis for heavy surface loads. Consider a free-body diagram of the pipe– soil column between two parallel pipes (Fig. 7-1). Section AA is the minimum cross section. This column must support the full weight of the soil mass, shown crosshatched, plus part of the surface load, W, shown as a live load pressure diagram. The soil column is critical at its minimum section AA at the springlines, where the adjacent pipe walls confine it. For design, the strength of the column at section AA must be greater than the vertical load. 7.2.1 Strengths The performance limit of the column is either the ring compression strength of the pipe wall or the vertical compressive strength of the soil column at section AA. The lesser of these two values governs the design. Ring compression strength of the pipe wall is yield strength σY of the steel. Strength of the soil is the ratio of vertical stress, σy, to horizontal stress, σx, at soil slip. For cohesionless embedment, soil slips when the ratio of

SPECIAL CONSIDERATIONS

89

vertical to horizontal soil stresses equals σy/σx = (1 + sinΦ)/(1 − sinΦ). The vertical stress on the soil column at section AA is σy = [dead weight of soil (crosshatched)]/X + live load effect, 0.477 W/(Hc + rp)2 (Fig. 7-1). The horizontal soil stress, σx, is the pressure of pipe walls acting against the soil column. For flexible pipes, the horizontal pressure at section AA is equal to vertical soil pressure, Pd, on top of the pipes. Therefore, σx = Pd. In general, live load pressure has little or no effect because the live load is not directly above the pipe. For cohesive soil, approximate soil strength, σy/σx, at soil slip, may be found through triaxial shear tests in which interchamber pressure is equal to the horizontal pressure of the pipe wall against the soil. If the water table is above section AA, the compressive soil strength would be the effective vertical stress, σy, confined by horizontal stress, σx, where, at soil slip, the ratio σy/σx = (1 + sinΦ)/(1 − sinΦ). Water pressures outside and inside of the pipe may enter into the stress calculations. 7.2.2 Stresses If the bond between the soil and the pipe wall could be ensured, the column would be analyzed as a reinforced concrete column based on an equivalent, or transformed, section. But the bond between soil and pipe cannot be ensured because of fluctuations in temperature, moisture, and loads, all of which tend to break down the bond. To be conservative, the bond is assumed to be zero. Therefore, stresses in the pipe and soil are each calculated independently. 7.2.3 Design of Pipe Before the soil column is analyzed, the pipe must be reviewed for adequacy. From Chapter 3, design starts with Eq. 3-3 for ring compression, PDO/2ts = σY/sf, which can also be written as PVDO/2ts = σY/sf where DO = outside diameter of the steel cylinder (in.); ts = pipe wall area per unit length of pipe (in.); σY = ring compression strength of the wall = minimum specified yield strength of steel (in psi); sf = safety factor; Pv = maximum vertical soil pressure on top of the pipe (psi). For worst-case ring compression, live load W is directly above the pipe where Pv = Pl + Pd. The live load effect, Pl, can be found by either the

90

BURIED FLEXIBLE STEEL PIPE

Boussinesq or Newmark (Dunn et al. 1980) method. If W is assumed to be a line load, Chapter 4 showed that according to Boussinesq, Pl = 0.477 W/Hc2. Alternatively, if live load W is assumed to be a distributed surface pressure, the Newmark integration can be used. Below a depth equal to the greatest width of tire print, the Newmark integration gives essentially the same results as the Boussinesq method. For simplicity, use the simpler Boussinesq method. In either case, soil cover must be greater than the required minimum by the pyramid–cone analysis method discussed in Chapter 5.

Example 7-1: Pipe with Live Load The proposed pipe is steel, with DO = 73.750 in., ts = 0.313 in., σY = 36,000 psi, and Hc = 1.5 ft, with a soil of unit weight γt = 120 pcf. A surface wheel load of W = 20 kip is anticipated. Is the proposed pipe adequate for the given loading? Two conditions must be evaluated. The first condition is that where the live load is directly above the pipe. The second condition is that where the live load is approaching the pipe. a. Live Load Directly Above the Pipe. pressure at the top of the pipe, Pv.

First, find the vertical soil

Pv = Pl + Pd = 0.477 ( 20,000 ) (1.5 )2 144 + ( 73.75 12 ) (1.5 )(1) 120 144 = 29.4 + 7.7 = 37.1 psi.

(7-1)

Second, verify stress in steel cylinder because of Pv. PvDO/2ts must be less than or equal to σY/sf. Pv DO 2ts = σ Y sf 37.1 ( 73.75 ) [ 2 ( 0.313 )] = 36 ,000 sf 4 ,371 = 36 ,000 sf sf = 36 ,000 4 ,371 = 8.2 b. Live Load on Approach to the Pipe. Refer to Chapter 5 for the basis of analysis. Assume a standard AASHTO HS-20 dual wheel tire print of 8 in. × 24 in. at 104 psi tire pressure. Neglect impact, such as sudden braking or wheel drop. What is the minimum required soil cover, Hc?

SPECIAL CONSIDERATIONS

91

From Chapter 5, with minimum cover, the maximum bending moment M = 0.022 Pvrs2. Therefore, M = 0.022Pv(73.75 2 ) = 29.91Pv 2

Also, σ = Mc1/Is = 36,000 psi at yield; Is = ts3/12 = 0.31253/12 = 0.00254 in.3; c1 = ts/2 = 0.3125/2 = 0.1563 in. Therefore, M = σIs/c1 = 36,000 (0.00254)/(0.1563) = 585 lb-in. at yield. Equating Ms and solving for Pv, 29.91Pv = 585 Pv = 19.6 psi. Also from Chapter 5, Pv = W/(Hc + 8 in.)(Hc + 24 in.), where W = 20 kip. Therefore, 19.6 = 20,000 ( H c + 8 ) ( H c + 24 ) H c 2 + 32 H c + 192 = 20,000 19.6 Solve for Hc by completing the square,

( Hc + 16 )2 = 20,000

19.6 − 192 + 256 = 1,084.4

H c + 16 = 32.9 H c = 16.9 in. Minimum cover is conservative because the longitudinal strength of pipe is neglected and a line load is assumed. Nevertheless, if Hc = 17 in., or about 1.5 ft, the approach of a 20-kip wheel load must be made with caution. With a safety factor, a reasonable minimum depth of cover would be 3 ft.

7.2.4 Design of Soil Column The following is an analysis for flexible pipes only, and it assumes that the pipe has been found adequate for resistance to the ring compression loads. Referencing Fig. 7-1, the vertical load on the two flexible pipe walls at section AA is no less than 2PvDP/2 = PvDP. In the design of the soil column, it is assumed, conservatively, that the pipe wall takes a vertical load of PvDP, which is only part of the total load. The remainder of the

92

BURIED FLEXIBLE STEEL PIPE

load must be supported by the soil. The greatest load occurs when the heavy live load W is centered above section AA—not over the top of the pipe. At this location, the live load pressure at AA is the maximum. Pipe walls carry γtHcDP due to the dead load. Live load pressure Pl on the pipes is small enough to be neglected. Moreover, it is already supported by the ring stiffness required for minimum cover. What cannot be neglected is the live load on section AA. Vertical soil stress, σy, on section AA must be less than vertical soil compression strength, S′. Vertical stress is soil load divided by the cross-sectional area.

σ y = Q ′ X ≤ S′ sf

(7-2)

where σy = vertical soil stress on section AA (psf), Q′ = Q − γtHcDP = load supported by the soil at section AA = total load less load supported by the pipe walls (lb/ft), Q = vertical load on section AA = wd + wl (lb/ft), γt = unit weight of soil (pcf), Hc = height of soil cover (ft), DP = outside diameter of pipe (ft), X = width of section AA between pipes (ft), S′ = vertical soil compression strength (psf), sf = safety factor. Per unit length, Q is the sum of the dead weight of the crosshatched soil mass wd and that portion of wl of the surface live load W that reaches section AA. The dead load wd per unit length (l) of pipe is soil unit weight times the crosshatched area: wd = ( l ) ( X + DP ) ( H c + DP 2 ) − π ( DP 2 ) 2  γ t 2

(7-3)

The live load wl is the volume under the live load pressure diagram of Fig. 7-1 at section AA. It is calculated by means of Boussinesq or Newmark, as described in Chapter 4. The pyramid–cone punch-through stress analysis does not apply because the height of cover is greater than the required minimum. From the Boussinesq method, the live load wl per unit length is wl = 0.477WX ( H c + DP 2 )

2

(7-4)

Example 7-2: Vertical Soil Stress and Safety Factor The pipe from Example 7-1 is installed in parallel, with a separation between pipes, X = 1 ft, and with the same trench conditions. Again, a

SPECIAL CONSIDERATIONS

93

surface wheel load of W of 20 kip is anticipated. The pipe is tape coated, resulting in DP ≈ DO = 73.750 in. a. What is the vertical soil stress at section AA of Fig. 7-1? b. What is the safety factor against soil slip? a. Vertical Load on Section AA. First, the vertical load on section AA, Q, must be found. Q = wd + wl. The dead load, wd, is found by Eq. 7-3, with l = 1. 2 wd = ( l ) ( X + DP ) ( H c + DP 2 ) − π ( DP 2 ) 2  γ t 2 = ( l ) ( 1 + 73.75 12 ) ( 1.5 + 73.75 12 2 ) − π ( 73.75 12 2 ) 2  120 = 2,148 lb

The live load, wl, is found by Eq. 7-4. wl = 0.477WX ( H c + DP 2 ) 2 = 0.477 ( 20,000 )(1) [1.5 + ( 73.75 12 ) 2 ] b = 456 lb 2

Therefore, Q = 2,148 + 456 = 2,604 lb Q′ = Q − γ t H c DP = 2,604 − 120 ( 1.5 ) ( 73.75 12 ) ( 1) = 2,604 − 1,106 = 1, 498 lb From Eq. 7-2, the vertical soil stress, σy = Q′/X. Therefore, for a unit length of 1 ft,

σ y = 1, 498 [(1)(1)] = 1, 498 psf. b. Safety Factor. The safety factor is sf = Px/σx (resisting stress/active stress) (Fig. 7-2). At section AA in the soil column, the granular soil slips if

V x V y = ( 1 − sin Φ ) ( 1 + sin Φ ) For a flexible ring, Px = Pd = γcHc. Therefore, Px = 120(1.5) = 180 psf. At soil slip, the soil column widens horizontally and the pipes narrow. If the soil is lightly compacted, such that the soil friction angle is Φ = 30°,

σ x = σ y (1 − sin Φ ) (1 + sin Φ ) = σ y 3 = 1, 498 3 = 499 psf

94

BURIED FLEXIBLE STEEL PIPE

Figure 7-2. Detailed Pipe–Soil Column Between Parallel Pipes.

Therefore, the safety factor is sf = 180/499 = 0.36, which is less than 1.0, so the soil will slip. Increasing the soil friction angle to 45° only increases the safety factor to 0.7, which still results in soil slip. Other options to eliminate the potential for soil slip include increasing either X or H, placing soil cement between the pipes, or a combination of the three. Analyses of a soil column bound between two pipes are conservative. Longitudinal resistance of the pipes and soil cover is neglected. Additionally, the arching action of the soil cover is neglected. Based on this inherent conservatism, safety factors can be small, such as less than sf = 1.5.

7.3 PARALLEL TRENCHES Buried flexible pipes depend on embedment for stability. Compacted soil at the sides supports and stiffens the top arch. So what happens when a trench is excavated parallel to a buried flexible pipe? The fundamental questions relate to minimum separation between the newly excavated trench and pipe and the variables that relate to collapse of the trench. These issues were the objectives of research at Utah State University in 1968. To reduce the number of variables, ring stiffness was assumed to be zero. The results of the test are conservative because no pipe has zero stiffness. Most flexible steel pipes have D/t ratios of less than 300. The D/t ratio was 600 in an attempt to approach zero stiffness. The pipe shape was maintained by mandrels during placement of the backfill. In general, if the native soil is cohesionless, the trench wall is at an angle of repose no greater than the soil friction angle, Φ. The trench slope at this angle of repose should not cut into the embedment of the buried pipe. If the native soil is cohesive, the trench wall can stand in a vertical cut, as shown in Fig. 7-3.

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Figure 7-3. Maximum Depth of a Vertical Cut.

The primary concern when using separate parallel trenches is having sufficient separation to maintain the stability of the trench wall adjacent to the existing buried pipe. Vertical soil pressure on the buried pipe creates a horizontal pressure, which if large enough can result in punchout of the adjacent trench wall (Fig. 7-3). The ability of the adjacent trench wall to sustain the imposed load is a function of the soil properties and the height of cover and diameter of the buried pipe. From this information, the minimum distance, X1, of undisturbed soil from the adjacent trench wall to the buried pipe can be calculated. Tests performed on moist, granular soil have shown that X1 = 1.4 HcDP/Z at complete collapse of a flexible pipe under a vertical prism of soil. Applying a safety factor of approximately 2 results in X1 = 3HcDP/Z. Z is the maximum depth of self-sustaining vertical cut, a measure of the “soil strength,” the value of which is determined by excavation of a test pit, or by the equation Z = 2c/[γttan(45° − Φ/2)]. This analysis is conservative, though, because it does not account for any support due to the ring stiffness of the pipe. Inclusion of the ring stiffness could allow for a reduction in the value X1, but this change would need to be verified based on tests of the proposed pipe–soil system.

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Z = maximum depth of trench with vertical walls, at cave-in. (ft), X1 = minimum separation (ft), Hc = depth of cover (ft), DP = diameter of pipe (ft), γt = unit weight of soil (pcf), c = soil cohesion (lb/in.2), Φ = soil friction angle (deg).

Example 7-3: Minimum Trench Separation Assume that a 48-in. flexible pipe is buried to a depth of cover of 5 ft in soil with cohesion c = 4 psi, a soil friction angle of Φ = 30°, and γt = 125 pcf. What is the minimum separation between an adjacent trench of maximum depth and the buried pipe? First, the maximum depth of the adjacent trench must be determined. From the above, Z = 2c [ γ t tan ( 45° − Φ 2 )] = 2 ( 4 )( 144 ) [125 tan ( 45° − 30° 2 )] = 15.96 ft = 16 ft The minimum separation is then calculated as X1 = 3 H c DP Z = 3 ( 5 ) ( 48 12 ) 16 = 3.75 ft = 3.75 ft

7.4 TRENCHES IN POOR SOIL Poor soil can pose a concern for the buried flexible pipe designer. Soil strength (soil bearing capacity) can be measured by driving a 2-in.diameter split-barrel sampling tube into the soil using a 140-lb hammer falling 30 in. The blow count is the number of blows per foot of penetration. The tube can be driven to depths below the surface. Generally, soils achieving 4 blows per foot or less are considered poor. In such conditions, the trench width may need to be increased to achieve the necessary support for the embedment material. Additionally, soil particle migration may need to be addressed as well to maintain long-term support for the pipe–embedment system.

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7.4.1 Minimum Trench Width If the trench walls are of poor quality soil, the trench width may need to be up to twice the diameter of the pipe, and a trench box should be used for excavation. Figure 7-4 shows how vertical pressure, P, on a flexible pipe is transferred horizontally to the trench wall, where it can be supported by roughly half of the pressure on the pipe. This trench width analysis is conservative. In fact, theoretically, the trench wall could be mud, but in this unlikely case, the pipe would need to be designed for external fluid pressure. Generally, if the trench wall can stand in vertical cut, it has sufficient strength to provide horizontal support for the pipe in a trench of width equal to 2DP. 7.4.2 Soil Particle Migration Soil particle migration is generally a function of either groundwater flow that washes trench wall fines into the voids in a coarser embedment or wheel loads and earth tremors that shove or shake coarser particles from the embedment into the finer soil of the trench wall. If fines migrate from the trench wall into the embedment, the trench wall may settle, but the pipe is unaffected. If the embedment particles migrate into the trench

Figure 7-4. Soil Wedge at Incipient Slip of Sidefill in the Trench Width Bd = 2DP.

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wall, the shift in sidefill support may allow a slight ring deflection. This migration could occur only if the trench wall soil is loose enough or plastic enough that the embedment particles can be shoved into it. The conditions for soil particle migration are unusual. Nevertheless, they must be considered. Remedies for soil particle migration include embedment with enough fines in it to filter out migrating particles in groundwater flow and trench liners. Geotextile trench liners may be specified in severe cases.

7.5 FLOWABLE FILL Some installations are subject to extremely narrow trenches where placement and compaction of embedment is impractical. In other situations, the process for compacting the embedment to its desired density may be impractical. For these and other select instances, the use of a freeflowing material, called flowable fill, for bedding and embedment is beneficial. Pipe is typically placed on small soil berms or sand bags for support and vertical alignment in the trench, which also allows the material to flow under and around the pipe. The supports should be of a material that is less rigid than the proposed fill to avoid the possibility of introducing localized stress risers in the pipe. The benefits and desired characteristics of flowable fill are discussed in the next sections. 7.5.1 What Is Flowable Fill and What Are Its Benefits? Common practice is to specify select, imported soil for bedding and embedment. An alternative to imported materials is recycling the native soil as flowable fill, also referred to as controlled low-strength material. Flowable fill is granular soil, usually composed of native materials with enough fines and cementitious material to result in a slurry. It is a fullcontact bedding and can also be used as a sidefill, or even as embedment over the top of the pipe. Flowable fill reduces or eliminates problems such as uneven bedding, voids under the haunches, and excessive ring deflection. The objectives of flowable fill are to recycle native soil and to place bedding and embedment in fewer steps, in a narrower trench, and with improved quality assurance. If flowable fill is used properly, the trench width may be reduced. Care should be exercised to prevent flotation of the pipe. 7.5.2 Desired Characteristics The slurry must be fluid enough to flow under and maintain full contact with the pipe but be structurally sound after curing. The slurry

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must include cementitious material but may also include silt and some clay. Many native soils containing fines can be used for flowable fill, provided the clay content is not over two-thirds of the fines. Large rocks must be screened out of flowable fill. As shown earlier, the ring deflection of a buried pipe is approximately equal to the vertical compression of the sidefill soil. Therefore, if the flowable fill is placed as a sidefill, its vertical compression and shrinkage must be within the defined limits for the deflection of the pipe. Flowable fill must also have enough bearing capacity to support the backfill and hold the pipe in shape without excessive deflection. High strength is not a primary requirement, but some cement is recommended so the material flows properly. Compressive strength should be kept low—a minimum of 40 psi—but no greater than the pipe’s internal pressure. Tests show that flowable fill embedment can be of good quality with as little as one sack of cement per cubic yard of native soil. Flowable fill with excessive strength creates two problems: • Embedment cannot be easily excavated in case the pipe must be uncovered at some future time. • If high-strength embedment cracks due to soil movement, high stresses can be concentrated on the pipe.

7.6 LONGITUDINAL FORCES Stresses develop in buried pipe as a result of longitudinal forces at special sections (e.g, valves, tees, elbows, wyes) caused by pressure, temperature change, beam action, and relative longitudinal pipe–soil movement. A general understanding must be reached regarding the applicable stresses involved: the interaction of thrust force stresses, the longitudinal stresses resulting from internal pressure (Poisson’s effect stress), and stresses resulting from a thermal gradient. Longitudinal performance and performance limits can be analyzed by fundamentals of engineering mechanics and mechanics of materials. Typically, a pipeline is welded to a special section to restrain that section from longitudinal movement due to thrust forces. The thrust could be due to the effect of internal pressure on an appurtenance, such as an elbow, reducer, bulkhead or valve, or it could result from thermal stresses, all of which result in a longitudinal force of some magnitude being imparted to the pipe. The frictional resistance between the pipe and the surrounding backfill material achieves restraint of that force. General analysis assumes that maximum thrust is present at the appurtenance, and, with uniform soil cover, a linear reduction of the thrust force from the appurtenance to the free end of the pipe by resistance of the soil

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Figure 7-5. Linear Decrease of Thrust Force in Restraint Length.

embedment as the pipe shortens or lengthens. A more detailed analysis is offered in Section 7.6.3. Figure 7-5 is an example of longitudinal force, F. A section of buried pipe is attached to an appurtenance at the fixed end but is free to shorten or expand from the free end (at a coupling or gasketed joint). The pipe shortens when the temperature drops or when the pipe is pressurized. The shortening generates frictional resistance of the soil embedment, which accumulates from the free end to maximum thrust T at the appurtenance. Thrust T must not cause the stress in the pipe wall to exceed yield. If both ends of the pipe are restrained, soil friction is eliminated, but the pipe feels the thrust caused by temperature decrease and internal pressure. If the pipe is bent, longitudinal stresses can be analyzed by bending moment analysis. The pipe connected to the appurtenance is subject to the total applied thrust at the appurtenance, which is equal to the frictional resistance of the soil for some distance, as the pipe shortens. With this shortening comes a longitudinal strain, and in turn a longitudinal stress. If the pipe could not shorten, then the thrust force would be resisted by a bearing force of the embedment material and not translated as longitudinal stress in the pipe. The total applied thrust as referenced here does not necessarily depict a maximum thrust value of PA acting on a pipe of diameter D, where P is pressure in the pipe and A is the pipe cross-sectional area = πD2/4, but rather the full value of the thrust generated by the special section in question. For instance, pipe adjacent to a closed valve or bulkhead would be subject to a full thrust force equal to PA, whereas pipe adjacent to a reducer would be subject to a full thrust force equal to P(A1 − A2), where A1 and A2 are the cross-sectional areas of the adjoining pipes. As will be shown below, stress due to thrust is the primary influence in the analysis of longitudinal forces. However, fundamentally the longitudinal stress created by a thrust force can never be greater than 50% of the

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stress in the hoop direction resulting from internal pressure, as is easily shown by the following. For hoop stress, the formula is σ = PDP/2ts. For longitudinal stress due to a maximum, dead-end thrust force the formula is σz = [Pπ(DP)2/4]/[π(DP)ts] = PDP/4ts, or 50% of the hoop stress. For a section of pipe that is fully restrained longitudinally, the result of internal pressure is the generation of a longitudinal Poisson’s effect stress. Because Poisson’s ratio is 0.3 for steel, the resulting Poisson’s effect stress is 0.3 times the hoop stress due to internal pressure. As noted above, though, pipe immediately adjacent to an appurtenance generating a thrust has to have some degree of movement, or no stress due to thrust could exist. Therefore, the pipe is not fully restrained and has the ability to contract and to relieve the Poisson’s stress. Because Poisson’s stress is directly proportional to hoop stress, which is a primary stress, it too would be considered a primary stress. (Primary stresses are discussed in more detail in a later section.) As such, stress due to the Poisson’s effect should be subject to the same limits as hoop stress. However, Poisson’s effect by itself is never a concern in a design relating to longitudinal forces because it cannot impart a stress greater than 30% of the hoop stress. The pipe is inherently capable of accepting the same stress level in the longitudinal direction as in the hoop direction, or 100% of the hoop stress. The final stress comes from temperature variations that create thermal stresses in the steel cylinder. As discussed above, pipe must shorten for tension stresses to be created in a pipe. If the pipe is free to shorten (or lengthen) incrementally until equilibrium is reached between the tension force and the resistive frictional force of the embedment, then it is free to move in response to thermal cycling. If the pipe is restrained (fixed) longitudinally so that it cannot move at all, then the pipe is subject to stresses due to thermal cycling. With the pipe in this condition, Poisson’s stress would be additive to the thermal stress if the thermal condition is one of cooling because the pipe cannot shorten to relieve either stress. When the thermal condition is one of heating, the pipe is in compression due to the thermal condition and in tension due to Poisson’s effect, thereby counteracting one another. Thermal stress is considered a secondary stress, for which allowable stress can be significantly increased over primary stresses, both of which are discussed next. Both ASME (2006) and ASCE (1993) define two basic types of stress: primary and secondary. ASME (2006) defines primary stress as that required to satisfy the laws of equilibrium. Primary stress is not selflimiting, and once it exceeds the yield strength of the material through the entire thickness of a component, the prevention of failure depends on the strain hardening properties of the material. Hoop stress in a cylinder due to internal pressure is primary stress. ASME (2006) defines secondary stress as self-limiting, where local yielding can redistribute stress to a tolerable level without causing failure. Bending stress that develops at the

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attachment of a body flange to a shell and thermal stress are examples of secondary stress. Because secondary stress is self-limiting, ASME (2006) and ASCE (1993) both dictate that the allowable stress can be increased beyond primary stress. ASCE places no limit on secondary stress that is acting alone. For secondary stress acting in combination with primary stress, ASME and ASCE both dictate a stress limit equal to three times that used for analysis of the primary stress alone. ASME further limits this value to twice the yield strength of the material at temperature. Depending on the material, the tensile strength could be a design stress limit before either of the values stated above. Based on the above analyses and barring extraordinarily unique conditions, welded joint buried pipes can be expected to perform satisfactorily throughout their expected design lives by use of a single fillet weld. As shown in the following analyses, the stress on the weld for the various conditions falls well within cited standard engineering guidelines, which are very conservative. Ingenuity in installation can eliminate much of the longitudinal stress problem. For example, AWWA Standard C206-03 recommends various methods to reduce thermal stresses, such as shading the pipe in the trench, using backfill as insulation, making certain joint welds (particularly closure joints) at a time of day when temperature is the lowest, or a combination of these methods. In fact, the temperature of the pipe can be adjusted to compensate for anticipated internal pressure as well as temperature. Temperature variations can also be reduced by use of the weld after backfill installation method, where embedment and backfill material are placed up to at least 1 ft over the top of the pipe before welding the joint. By using this installation method, the steel cylinder has the opportunity to achieve thermal equilibrium with the surrounding soil before welding. Based on this prewelded equilibrium, the potential for substantial thermal stress due to installation has been removed. With an equilibrium temperature of 60 °F, which is reasonable for depths of cover below the frost line, a thermal gradient of ± 30 °F is generally accepted in the industry as adequate for design. Steel is adaptable to longitudinal stresses because of its low coefficient of thermal expansion, high strength, and ductile yield capability. So what if longitudinal stress reaches the yield point? The steel stretches, but fracture is not inevitable. 7.6.1 Temperature and Pressure Change For changes in temperature and pressure, longitudinal stress can be reduced by inserting into the pipeline such things as slip couplings, bellows, and pipe elbows. Regardless of installation method, when a straight section of welded pipe has fixed ends or is restrained over a

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Figure 7-6. Longitudinal Stress in Restrained Pipes Due to Decrease in Temperature and Internal Pressure.

considerable length by friction between the pipe and the embedment, longitudinal stresses due to decrease in temperature and increase in internal pressure (Poisson’s effect) are as shown in Fig. 7-6. When both effects are combined, the resultant stress is

σ z = α Es ∆T + ν P ( D ) 2ts

(7-5)

where σz = longitudinal stress (psi); α = coefficient of thermal expansion = 6.5 × 10−6 (°F); Es = modulus of elasticity of steel = 30 × 106 (psi); ∆T = change in temperature (°F); P = internal pressure in the pipe (psi); D = nominal inside diameter of the pipe (in.); ts = steel cylinder thickness (in.); ν = Poisson ratio = 0.30.

Example 7-4: Longitudinal Stress A straight steel pipeline of 51-in. inside diameter with 0.187-in. steel cylinder thickness is fixed at both ends. The temperature drops 30 °F when

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internal cold water is introduced: ∆T = 30 °F. An internal water pressure, P = 120 psi, is then applied to the pipe. Assume that no relative movement occurs between the pipe and embedment. What is the longitudinal stress, σz, in the pipe? Substituting into Eq. 7-5,

σ z = 6.5 × 10 −6( 30 × 106 ) ( 30 ) + 0.30 (120 )( 51) [ 2 ( 0.187 )] = 5,850 + 4 ,910 = 10,760. 7.6.2 Beam Action Longitudinal stresses due to beam action are analyzed by classical methods. High spots can occur in the bedding, as shown in Fig. 7-7, for a variety of reasons, such as improper installation techniques or bedding evacuation due to adjacent, postinstallation excavations. Even with soil compacted under the haunches, there is still a possibility that soil mounds or timbers placed somewhere near the ends of the pipe sections for vertical alignment may become hard spots (reactions) supporting the pipe sections. Because soil support is not concentrated, bedding reactions may be distributed somewhat like the sine curve shown in Fig. 7-8. The worst condition results when the reactions are spaced at half of the pipe length. It turns out that the maximum moment in the beam for the sine curve distribution of reactions is 0.4 times the maximum moment on concentrated reactions. A word of caution is appropriate for any buried pipes on piles or bents. When the sidefill settles with respect to the pipe, moments can be extreme due to the weight of the pipe, its contents, and the soil wedge above it. Longitudinal beam stresses in buried pipe should be limited to 50% of the specified minimum yield strength of the steel cylinder.

Figure 7-7. Section of Pipe Acting as a Beam Simply Supported on the Ends.

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Figure 7-8. Pipe as a Simply Supported Beam with Reactions at Quarter Points and Distributed as Sine Curves.

Example 7-5: Longitudinal Stress in a Simply Supported, Empty Pipe Suppose the 51-in.-inside diameter pipe in Example 7-4 has a specified minimum yield strength of 42,000 psi and is welded into 60-ft sections before aligning it in the trench. After it is aligned on concentrated reactions at each end, but before the 60-ft sections are welded together, what is the maximum longitudinal stress in this simply supported beam due to only the weight of the pipe? From basic mechanics of solids, σz = Mc1/I, with the balance of the data as follows: DI = 51.000 (in.); ts = 0.187 (in.); σz = longitudinal stress in the beam due to bending (psi); M = maximum longitudinal bending moment in the beam (lb-in.); = w1L22/8 for a simply supported beam (lb-in.); w1 = the weight of the pipe per unit length (lb/ft); I = moment of inertia of the cross section of the steel cylinder (in.4); ≈ π(Dm3)ts/8 c1 = DI/2 + ts (in.); L2 = length of the pipe section acting as a beam = 60 (ft); γs = density of steel (pcf); w1 = π(DO2 − DI2)/4γs = 3.14(51.3742 − 512)/4(490/1,728)12 = 102.3 (lb/ ft); M = w1L22/8 = 102.3(60)2/8 = 46,035 (lb-ft) = 552.42 (kip-in.); c1 = DI/2 + ts = 51/2 + 0.187 = 25.687 (in.); I ≈ π(Dm)3ts/8 = 3.14(51.187)3(0.187)/8 = 9,844 (in.4).

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Therefore, σz = Mc1/I = 552.42(25.687)/9,844 = 1.44 ksi. This level of stress is minor and insignificant compared to the allowable stress of 50% of the specified minimum yield strength. Although, as can be seen in the following example, once the pipe is buried and filled with water, the stresses need to be addressed.

Example 7-6: Maximum Longitudinal Stress The pipe in Example 7-5 is welded, covered with 4 ft of soil (γt = 120 pcf) and filled with water. What is the maximum longitudinal stress? In this condition, each 60-ft beam has fixed ends. Again, σz = Mc/I, with the balance of the data as follows: σz = longitudinal stress in the beam due to bending (psi); M = maximum bending moment in the beam (lb-in.); = w2L22/12 (lb-in.) for a beam fixed at each end (Fig. 7-9); w2 = the weight of the pipe + contents + backfill per unit length (lb/ft); I = moment of inertia of the cross section of the steel cylinder (in.4); c1 = DI/2 + ts (in.); L2 = length of the pipe section acting as a beam (ft); Hc = height of cover (ft); γs = density of steel (pcf); γw = density of water (pcf); w2 = 102.3 + πγwD2/4 + H(Dp)γt; = 102.3 + 3.14(62.4)(51/12)2/4 + 4(51.374/12)(120); = 102.3 + 885.2 + 2,055.0; = 3,043 (lb/ft);

Figure 7-9. Longitudinal Sag of a Fixed-End Pipe.

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M = w2L22/12 = 3,043(60)2/12 = 912,900 (lb-ft) = 10,954,800 (lb-in.); c1 = 25.687 (in.); I ≈ 9,844 (in.4). Therefore, σz = Mc1/I = 10,954,800(25.687)/9,844 = 28,586 psi. This stress exceeds the 21,000 psi allowable design stress, and it must be addressed. Prevention of this beam action through the use of uniform bedding is the best solution. The bedding should be adequately designed and properly placed to support the pipe throughout the entire length. A general question posed regarding beam action is, “What effect does a longitudinal bend in the pipe have on ring deflection?” Ring deflection due to longitudinal bend or sag in a pipe results in a flattening of the pipe’s cross section into an ellipse. The percent decrease in diameter due to flattening is a function of the radius of curvature of the bend, R, and is found from Brazier’s equation, d = 2Z1/3, with the balance of the data as follows: d = ring deflection; Z1 = dimensional constant = 1.5(1 − ν2)Dm4/16ts2R2; ν = Poisson ratio = 0.30; Dm = mean diameter of steel cylinder (in.); ts = wall thickness of steel cylinder (in.); R = radius of longitudinal bend (in.); Es = modulus of elasticity = 30 × 106 (psi); L2 = length of span (see Fig. 7-9); y = deflection at mid-length (in.). As shown in Chapter 3, longitudinal stress due to bending is σz = Esr/R. Bending stress is also Mr/I. Standard beam analysis for a fixed-end pipe defines the maximum moment at the fixed end as M = w1L22/12. Therefore,

σ z = Es rp R = Mrp I ⇒ Es rp R = ( w1L2 2 12 ) rp I ⇒ Es I = w1L2 2 R 12 Additionally, from standard beam analysis, the longitudinal sag at the center of the pipe is y = w1L24/(384EsI). Rearranging the standard longitudinal sag equation yields EsI = w1L24/(384y). Therefore, Es I = w1L2 2 R 12 = w1L2 4 ( 384 y ) ⇒ R = L2 2 ( 32 y )

(7-6)

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Example 7-7: Ring Deflection and Bending Stress Given a 60-in.-diameter steel pipe with a wall thickness of 0.25 in., what is the ring deflection at the center of a fixed-end pipe if L2 = 100 ft and y = 2 in.? What is the bending stress associated with this deflection? Z1 = 1.5 ( 1 −Q 2 ) D 4 16ts 2 R2 = 1.5 1 − ( 0.3 )2  D 4 = 0.0853 ( D ts ) ( R D ) 2

(16t 2 R2 )

2

For the pipe in question, Z1 = 0.0853(60/0.3)2/(R/D)2 = 3,412.5/(R/D)2. From Eq. 7-6, R = L22/32y = 1002/[32(2/12)] = 1,875 ft and % ring deflection, d = 2Z1/3 = 2[3,412.5/(R/D)2]/3, which is due to ovality resulting from longitudinal bending with radius R. d = 2,275 ( R D )

2

R D = 1,875 ( 60 12 ) = 375 Therefore, d = 2,275/3752 = 0.0162 = 1.6%. Longitudinal stress caused by bending to a radius, R, is σ = Mc1/I, where c1 is the length from the horizontal neutral surface (N.S.) to the outside surface of the pipe. If ring deflection is d = 1.6%, c1 is reduced to 98.4% of circular radius, rp. The moment of inertia of the cross section, I, is also reduced. Analysis is complicated. For only 1.6% reduction in c1, the theoretical change in stress does not justify the complicated analysis. For design, assume a circular pipe, where I/c1 ≈ πrp2ts. Maximum longitudinal stress is σz = Esrp/R = 30 × 106 (60/2)/[(1,875) (12)] = 40,000 psi. A basic assumption here is that the ovality that occurs in the pipe crosssection (Brazier’s effect) is not included in the computation of maximum stress or strain. This effect can be included, but the complexity of the equations and the little extra accuracy suggests that the above formulae stay as they are and that this effect is not included. From Chapter 3, maximum circumferential bending stress due to ring deflection is σ = 3Esd/(D/ts) = (3) 30 × 106 (0.016)/(60/0.25) = 6,000 psi. If the stress calculated by this elastic theory is greater than the yield stress, steel enters the ductile range, where elastic theory is conservative and where a permanent set occurs, but not failure of the pipe if failure is defined as yield stress. The longitudinal stress of 40,000 psi in the above example is conservative because it is based on analysis of a round cylinder.

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The above analysis is for an empty pipe. On pressurization, the pipe tends to reround. If the fixed end is on a sill or block for the purposes of vertical alignment, when pressurized the pipe will lift a soil weight greater than the prismatic load assumed in the example. Consequently, at the sill, the pipe will not reround but may, in fact, increase flattening on the bottom. The tangential stress could increase above 10 ksi. Concentrated shearing stresses due to bearing on the sill could become critical. To avoid such situations, uniform bedding should be ensured throughout the length of the pipe. 7.6.3 Relative Longitudinal Pipe–Soil Movement Longitudinal stresses due to relative longitudinal pipe–soil movement can be calculated approximately from the free-body diagram of Fig. 7-10.

Figure 7-10. Longitudinal Friction Due to Contraction of the Pipe. Friction is analyzed throughout a distance L3/2 from a slip coupling to the effective restraint where maximum allowable stress is reached.

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If the pipe changes length with respect to the soil, frictional resistance of Ff = N(tanφ′) is developed per unit length of the pipe. N is the normal soil pressure against the pipe. For a flexible ring, N includes the weight of the pipe and its contents, plus the soil pressure, Pv, on top times the circumference, π(Dp).

Example 7-8: Length of Pipe Between Slip Joints What is the maximum length of the pipe of Example 7-6 between slip joints if temperature and pressure cause the pipe to slip and if allowable longitudinal stress at midlength is not to exceed σz = 18 ksi; Ff = frictional resistance (lb/ft); N = normal soil pressure against pipe (lb/ft); Pv = soil pressure at the top of the pipe = γtHc (psf); Wp = weight of pipe and contents (lb/ft); A = cross-sectional area of the pipe cylinder (ft2); tanφ′ = coefficient of friction of the pipe–soil interface = 0.3 (assumption based on experience); Hc = soil cover (ft); γt = density of backfill = 120 (pcf); σz = longitudinal stress (psi); N = πDpPv + Wp = 3.14 (51.374/12) (120) (4) + (102.3 + 885.2) = 6,455.8 + 102.3 + 885.2 = 7,443 (lb/ft); Ff = Ntanφ′ = 7,443(0.3) = 2,233 (lb/ft). For longitudinal equilibrium, Ff(length)/2 = σzA. A = π(DO2 − DI2)/4 = 3.14[(51.374/12)2 − (51/12)2]/4 = 0.2088 ft2; length = 2σzA/Ff = 2(18,000)(0.2088)(144)/2,233 = 484.7 ft.

7.7 BURIED PIPE ON BENTS In certain soil conditions, such as marsh areas, standard direct bury installation methods are not possible. The soil in these areas is such that stability of the embedment around the pipe cannot be achieved for the long term, or possibly not at all, without excessively deep installation, which is generally cost prohibitive. The pipe must be supported to avoid the possibility of both sinking and floating. One solution for installation in these conditions is to support the pipe below the surface on bents (Fig. 7-11). The bents are anchored in stable material below the poor soil, and they provide 100% of the vertical support of the pipe. Lateral support

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111

Figure 7-11. Buried Pipe on Bents.

from the surrounding soil is assumed to be zero, but to be conservative the weight of the soil above the pipe is accounted for in the design. 7.7.1 Fundamental Assumptions The fundamentals of analysis begin with four assumptions for the installation conditions. These assumptions are valid for poor soil conditions, where no vertical or lateral support for the pipe is possible. In such soils, the worst assumed conditions would be as follows: • The vertical soil pressure, Pv, on the entire pipeline is equal to the vertical soil pressure at the level of the top of the pipe. It might be argued that vertical soil pressure on the pipe would be greater than Pv because the bents resist settlement of the pipeline, whereas the compressible soil would tend to settle and so drag the pipe down with it. Such drag-down occurs in tidal basins, marshes, and landfills that settle over time. See Chapter 5 for soil drag-down weight analysis. • Lateral soil pressure is Pv/3. As noted in Taylor (1948), if the soil at the side of the pipe is highly compressible but nonviscous, the least ratio of horizontal to vertical soil pressure at failure is one-third. An example of this type of soil is loose, fine sand, which is often encountered. • Support of the pipe occurs only at bents. Soil bedding under the pipe between the bents is neglected. It is assumed that the soil bedding settles away from the pipe. This is the worst case. • It is also assumed that the pipe is filled with liquid. 7.7.2 Analyses Based on the assumptions, the following analyses are possible. 1. For a continuous beam supported by equidistant spans, standard analysis identifies the longitudinal bending moment as maximum at the supports. This analysis can be used to calculate the flexural

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BURIED FLEXIBLE STEEL PIPE

stress in the wall of the pipe using the classical Eq. 7-7, as for any beam in bending:

σ z = Mc1 I

(7-7)

where σz = stress in the pipe wall (psi); M = longitudinal bending moment at the saddle = 0.11w3L22 (lb-in.); w3 = PvDO + Wp/12 + πDO2/4(γw/1,728) (lb/in.); Pv = vertical soil pressure on the pipe (psi); DO = outside diameter of pipe (in.); Wp = weight of pipe per unit length (lb/ft); γw = unit weight of liquid in pipe, which is assumed to be flowing full (pcf); L2 = spacing of bents (in.); c1 = DO/2 (in.); I = moment of inertia of steel cylinder ≈ πDm3ts/8 (in.4); ts = steel cylinder thickness (in.). 2. The shearing stress at the bents can also be calculated as for any beam (Fig. 7-12):

τ = VQ ( 2 Its )

(7-8)

where τ = longitudinal shearing stress at the neutral surface (psi); V = shearing load = w3L2/2 (lb); Q = first moment of cross-sectional area above (or below) the neutral surface = DO2ts/2 (in.3).

Figure 7-12. Bent Saddle Configuration and Loading.

SPECIAL CONSIDERATIONS

113

3. Ring compression stress, (circumferential direct stress) in the wall of the ring due to vertical bearing pressure on the saddle is calculated as follows:

σ rc = Pv DO ( 2 Ax )

(7-9)

where σrc = ring compression stress (tangential direct stress) (psi); Pv = vertical soil pressure on the ring (psi) (Fig. 7-1); Ax = wall cross-sectional area per unit length of pipe = ts(1 in.)/(1 in.) (in.). Equation 7-9 must be modified from its classical form at the saddles if the pipe is on bents. Modification includes revising the definition of both Pv and Ax. The maximum vertical pressure of pipe on the saddle is not Pv, but ps, which is defined as follows: ps = 2V [ Bs DO sin ( α s 2 )] where ps = maximum pressure of pipe on saddle (psi); Bs = breadth of the saddle minus the longitudinal length along the pipe centerline (in.); αs = circumferential angle of contact of saddle (deg). This definition is based on the assumption that there is no frictional resistance between the pipe and the saddle. Consequently, ps is too high, but a good first approximation. ps is simply the total vertical load on a bent divided by the horizontal projection of the pipe–saddle contact area. A more exact value of ps results by modifying the previous equations to account for the inevitable friction between the pipe and the saddle as follows: ps = 2V (1 − Ψ ) [ Bs DO sin (α s 2 )]

(7-10)

where Ψ = frictional resistance term = f[(1 − cos(αs/2))/sin(αs/2)] and f = coefficient of friction between the pipe and the saddle. This is the sum of the vertical components of frictional resistance due to the radial pressure ps. Of course, being a first approximation it is slightly high because the radial pressure is reduced slightly by the friction. However, the reduction is small. Friction, f, breaks down and approaches zero in time.

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BURIED FLEXIBLE STEEL PIPE

The cross-sectional area of the pipe wall also requires revision at a bent. The effective wall area becomes As = ts( Bs + 20ts )

(7-11)

The effective length of cylinder wall becomes the breadth of the saddle support, Bs, plus 10 times the wall thickness on either side of the support. The stress in the cylinder pipe wall diminishes linearly from maximum at the saddle to zero at 10 thicknesses away. Taking ps from Eq. 7-10 and As from Eq. 7-11 and substituting them in Eq. 7-9 for Pv and Ax, respectively, yields

σ s = V (1 − Ψ ) [ts( Bs + 20ts ) sin (α s 2 )]

(7-12)

The stress defined in Eq. 7-12 is the maximum ring compression stress at the saddle, also referred to as circumferential direct stress. 4. Punching stress, also referred to as shearing stress, around the saddles of the bents can be calculated by the following:

τ = πα sV ( 1 − Ψ ) [ts ( πDOα s + 360°Bs ) sin (α s 2 )]

(7-13)

This stress is the average shearing stress throughout the wall thickness around the perimeter of contact between the pipe and the saddle. Equation 7-13 is simply total radial load of the saddle against the pipe wall divided by the steel area in shearing stress. It is assumed that the radial pressure is constant with the vertical component of the radial load equal to the total vertical load, 2V. 5. Ring deflection or flattening down of the ring due to pipe weight and soil pressure can be predicted as well. The effect of liquid in a pipe is negligible if the pipe is buried without being placed on saddles. For pipe on saddles, the ring deflection at the bent can be found from a Castigliano analysis. The result of such analysis is as follows for each saddle contact angle noted: d = 0.015 ps rs 3 Es I s for α s = 120°

(7-14a)

d = 0.0034 ps rs 3 Es I s for α s = 180°

(7-14b)

where d = % ring deflection in decimal form; ps = saddle pressure on pipe (psi); rs = outside radius of steel cylinder (in.);

SPECIAL CONSIDERATIONS

115

Es = modulus of elasticity of steel (psi); Is = moment of inertia of pipe wall cross section per unit length = ts3/12 (in.3). At the bent, it is assumed that the vertical pressure of the pipe on the saddle, ps = w3L2/(DOBs). Substituting ps, Is, and rs into Eqs.7-14a and 7-14b yields ring deflection, d, as follows: d = 0.023 [ w3 L2 DO 2 ( EBsts 3 )] for α s = 120°

(7-14c)

d = 0.005 [ w3 L2 DO 2 ( EBsts 3 )] for α s = 180°

(7-14d)

These equations for ring deflection are conservative. They are based on soil loading on top of the pipe without regard to side soil support or soil support on the bottom of the pipe between the bents. Soil on the sides would help to restrain the ring deflection, and soil between the supports would support the pipe some and reduce the loads at the bents. Additionally, the third-dimensional effect is ignored, so longitudinal stiffness of the pipe over the bent is neglected. Conservatism is prudent, however, because the saddle may not fit the pipe to hold it fixed within the saddle angle, αs. Also, the saddle may not be perfectly rigid at the edges. Clearly, the saddle must be structurally adequate to hold the pipe fixed within the saddle angle, αs. 6. The maximum longitudinal deflection of the pipe as a beam between the bents can be calculated based on standard beam deflection theory as follows: y1 = w3 L2 4 ( 384Es I )

(7-15)

where y1 = deflection of pipe at center span between bents (in.).

Example 7-9: Buried Pipe on Bents A 54-in. nominal diameter pipe is installed on bents with saddles in a buried condition where the unit weight of the soil, γt, is 125 pcf. The height of soil cover over the pipe, Hc, is 5 ft. The pipe has a steel cylinder outside diameter of 56.000 in., a steel cylinder thickness of 0.500 in. with material yield strength of 42 ksi, thin-film, spray-applied lining, and tape coating. Each saddle encompasses 120° of the pipe and measures 12 in. longitudinally along the pipe. The bents are spaced at a distance of 20 ft.

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BURIED FLEXIBLE STEEL PIPE

The saddles are coated, resulting in a coefficient of friction of 0.15 at the saddle–pipe interface. Find the following for the pipe: 1. 2. 3. 4. 5. 6.

bending stress at a bent, shearing stress at a bent, ring compression stress at a saddle, shearing stress at a saddle, ring deflection at a saddle, and deflection of the pipe at center span.

1. Calculate bending stress at a bent. From Eq. 7-7, σz = Mc1/= 2.256 × 106(28.000)/33,550 = 1,883 psi, where M = 0.11w3L22 (in.-lb) = 0.11(356)(240)2 = 2.256 × 106 in.-lb; w3 = PvDO + Wp + (πDO2/4)(γw/1,728) (lb/in.) = 4.34(56.000) + 24.49 + [3.14(56.000)2/4](62.4/1728) = 356 lb/in.; γw = 62.4 pcf; Pv = Hcγt/144 = 5(125)/144 = 4.34 psi; DO = 56.000 in.; Wp = (DOts − ts)π(0.2836) = [56.000(0.500) − 0.500](3.14)(0.2836) = 24.49 lb/in.; L2 = 20(12) = 240 in.; c1 = 56.000/2 = 28.000 in.; I ≈ πDm3ts/8 (in.4) = 3.14 (55.500)3 (0.500)/8 = 33,550 in.4; ts = 0.500 in. 2. Calculate shearing stress at a bent. From Eq. 7-8, τ = VQ/(2Its) and τ = 42,720(784)/[2(33,550)(0.500)] = 998 psi, where V = shearing load = w3L2/2 = 356(240)/2 = 42,720 lb and Q = DO2ts/2 = (56.000)2(0.500)/2 = 784.0 in.3 3. Calculate ring compression stress at a saddle. From Eq. 7-12, σrc = V(1 − Ψ)/[ts(Bs + 20ts)sin(αs/2)] = 42,720(1 − 0.0866)/{0.500[12 + 20(0.500)]sin(120/2)} = 4,096 psi, where Ψ = f[(1 − cos(αs/2))/sin(αs/2)] = 0.15[(1 − cos(120/2))/sin(120/2)] = 0.0866; f = 0.15; Bs = 12 in.; αs = 120°.

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117

4. Calculate shearing stress at a saddle. From Eq. 7-13, τ = παsV(1 − Ψ)/[ts(πDOαs + 360°Bs)sin(αs/2)] = 3.14(120)(42,720)(1 − 0.0866)/[0.500(3.14(56.000(120)+360(12)) sin(120/2)] = 14,702,905/11,008 = 1,336 psi 5. Calculate ring deflection at a saddle. From Eq. 7-14c, for a 120° saddle, d = 0.023(w3L2DO2/EBsts3) = 0.023(356)(240)(56.000)2/[30 × 106(12)(0.500)3] = 0.137 = 13.7% A deflection of 13.7% is excessive but not totally unexpected, given the design conditions. An increased breadth of saddle, saddle angle, or wall thickness should be investigated to reduce the calculated deflection. Based on the size of the previously calculated deflection, the saddle breadth, Bs, can be increased to 18 in., and the wall thickness can be increased to 0.75 in. From Eq. 7-14c, for a 120° saddle, d = 0.023(w3L2DO2/EBsts3) = 0.023(373)(240)(56.500)2/[30 × 106(18)(0.75)3] = 0.029 = 2.9% where DO = 56.500 in.; ts = 0.750 in.; w3 = PvDO + Wp + [πDO2/4](γw/1,728) (lb/in.) = 4.34 (56.500) + 37.07 + [3.14 (56.500)2/4] (62.4/1728) = 373 lb/in.; Wp = (DOts − ts) π(0.2836) = [56.500 (0.750) − 0.750] (3.14) (0.2836) = 37.07 lb/in.; Bs = 18 in.; I ≈ πDm3ts/8 (in.4) = 3.14 (55.750)3 (0.750)/8 = 51,008 in.4 This deflection is reasonable. Therefore, the increased saddle angle and wall thickness is recommended. 6. Calculate pipe cylinder vertical deflection at center span. From Eq. 7-15, y1 = w3L24/(384EsI) = 373 (240)4/[384 (30 × 106) (51,008)] = 0.0021 in.

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BURIED FLEXIBLE STEEL PIPE

7.7.3 Conclusion Combination of the stresses by Mohr’s circle is usually unnecessary because no combination of stresses is critical and because a stress value equivalent to yield point at an isolated location is not failure in most pipes. Nevertheless, Mohr’s circle can be used and should be available for analysis if needed. Differential settlement of a bent between two bents that do not settle would increase the stress in general. Assuming that the middle bent settled completely away from the pipe, the flexural stress would increase to something less than four times the stress calculated by Eq. 7-7. The shearing stress would increase to about twice the stress calculated by Eq. 7-8. The ring compression stress would increase to about twice that calculated by Eq. 7-9, or less if some soil support is developed between the bents that do not settle. The saddle punching stress would increase to approximately twice the stress calculated by Eq. 7-12. The ring deflection would approximately double, and the sag between the bents would increase almost four times.

7.8 SEISMIC CONSIDERATIONS Buried pipelines in seismic regions should be designed to resist earthquake-induced stresses and deformations. The main purpose of pipeline seismic design is to ensure a minimum required operational (functional) level after a strong seismic event. 7.8.1 Seismic Hazards The seismic hazards to be taken into consideration in pipeline design can be summarized as follows: • permanent ground deformations due to seismic fault displacement (surface faulting), • earthquake-induced soil failures due to liquefaction and lateral spreading, • earthquake-induced soil landslides, • ground shaking caused by seismic wave propagation. A description of each of the above seismic hazards is given below: 1. Surface faulting. When a surface fault ruptures, permanent ground displacement occurs along the rupture in the form of a single trace or many parallel traces in a fault zone. Most of the movement occurs

SPECIAL CONSIDERATIONS

119

in the major fault zone, but nearby faults may also have displacements. In case of a significant fault displacement, pipelines that cross the fault may not survive this type of offset unless special provisions were made in their design and construction. 2. Liquefaction and lateral spreading. Liquefaction is the state where water-saturated cohesionless soils lose shear strength and temporarily turn from solid to liquid. Cohesionless soils are typically sands but can also be silts or wind-blown deposits, such as loess. This type of soil resists shear stresses due to friction between the grains. When earthquake waves shake the sand, the grains move slightly relative to each other. The shearing motion is accompanied by a reduction in volume, but if the sand is saturated, the water resists the decrease in volume and the load is transferred from the grains to the water. If there is insufficient compressive stress between grains, friction no longer holds the solid together, and it can become a liquid. Usually, several strong loading cycles are required for the liquefaction state to occur. Liquefaction causes lateral spreading, flow failure, or loss of bearing capacity. Because saturation and cohesionless soil are required for liquefaction, there are often a few to tens of feet of competent soil above the liquefied layer. Lateral spreading occurs when large blocks of competent soil move horizontally on top of the liquefied layer. Areas prone to lateral spreading include mild slopes near riverbanks and other waterfront, the toes of alluvial fans, and flood plains. In contrast to lateral spreading, flow failures involve the movement of the liquefied soil. Blocks of competent soil may also be carried within the flow. In general, pipelines buried in soils that liquefy and move can be subjected to large movements and may experience large strains. In lateral spreading, there can be large local strains in pipe at the block boundaries. 3. Soil landslides. In the course of a seismic event, soil on slopes loses shear strength and rocks become dislodged, so that landslides may occur. Landslides may be caused by liquefaction (as described above), or they may occur in unsaturated soil (e.g., rock slides, slumps and shallow landslides, and deep translational and rotational landslides). Small rock slides are commonly triggered by earthquakes in mountainous areas, whereas slumps and shallow slides typically occur in cut-and-fill slopes, embankments, and in shallow soil overlaying steep rock slopes. The performance of fill is highly dependent on the density and material of the fill (compaction). Well-compacted fills perform better than loose fills. Deep translational and rotational slides typically involve large volumes of soil and rock. Liquefaction of a sand lens or underlying sand deposits often contribute in triggering a large landslide, but they may not be the only causes. The large motions often associated with

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BURIED FLEXIBLE STEEL PIPE

landslides can severely affect pipe contained in the moving material. Landslides and rockfalls can also sweep away or crush the pipeline in their paths. 4. Ground shaking. Seismic events are associated with waves traveling in the rock and soil at speeds that depend on both the type of wave (e.g., dilatational, shear, or surface) and the properties of the rock or soil medium (the stiffer the material, the faster the wave travels and the higher its frequency). Waves cause ground shaking and, consequently, strains in the ground. Ground-shaking intensity is usually quantified by the peak acceleration of the ground surface and is most commonly expressed as a percentage or fraction of the acceleration of gravity. Ground strains due to shaking are transferred to the buried pipeline and may cause overstress, leading to failure. General Note on Seismic Hazards Hazards 1, 2, and 3 are associated with permanent deformations of the soil and the pipeline; they constitute the primary causes of pipeline failure in a seismic event. On the other hand, hazard 4 (ground shaking), in general, is not the predominant hazard to welded-joint steel buried pipelines. Nevertheless, seismic wave effects can be important in special cases, where a strong earthquake hits a thin-walled pipeline, a pipeline with relatively weak joints (e.g., belland-spigot joints), or a pipeline locally weakened by the presence of significant corrosion pits. 7.8.2 Seismic Hazard Assessment The selection of an appropriate quantitative definition of seismic hazard constitutes an important issue toward seismic hazard pipeline assessment. The definition may be made deterministically or in a probabilistic manner. In a deterministic evaluation of seismic hazard, the earthquake is typically defined by one to several earthquake scenarios felt to be credible for the local region. An earthquake scenario is defined by an earthquake of a specified magnitude occurring at a particular epicenter location or along a specified fault. This event is normally the one that produces the maximum ground motion at the site. The earthquakes chosen for the scenarios are often based on a large historical event or a best estimate of an event on a hypothetical or well-established fault system. Although questions regarding the actual numbers associated with the magnitude and location of the design earthquake are sometimes difficult to resolve, this approach eliminates one variable, the earthquake recurrence, which must be incorporated in the probabilistic approach. Defining the earthquake in a probabilistic fashion requires consideration of the potential variation in earthquake magnitude, location, and

SPECIAL CONSIDERATIONS

121

frequency of occurrence. In a highly seismic region, a probabilistic definition of hazard for a particular location includes the effects of multiple earthquake sources. One consequence of this method is that the predominant earthquake hazard may not be the same for different portions of a long pipeline. Information on the geology, seismicity, and the groundmotion attenuation of a region are typically integrated into a probabilistic model to compute the probabilities of exceeding various levels of ground motion in some time period. This probability is sometimes translated into an average return period for each ground motion level. Selection of a probabilistic or deterministic approach depends on the goals of the seismic evaluation. Deterministic approaches are preferred when the goals of the evaluation are related to emergency planning and emergency response. Probabilistic approaches are most appropriate for evaluating potential financial loss, prioritization of capital for seismic upgrade, and determining strategic location of company resources, such as parts, new pipeline, and headquarters facilities. 7.8.3 Design Recommendations General Recommendations for Fault Crossing When a pipeline crosses a fault, • It is suggested that the pipeline alignment is such that tensile rather than compressive stresses are introduced in the pipeline wall. • Within the anticipated fault rupture zone, the number of pipe bends, tees, valves, and other appurtenances, which confine pipe movement, should be avoided or, at least, minimized. • The design may consider an increase of wall thickness within an adequate length on each side of the fault (e.g., 150 ft on each side of the fault). • To accommodate severe permanent deformations, the use of flexible pipe joints or couplings may be also considered. The number of joints and their spacing should be determined with respect to the estimated magnitude of fault movement, as well as the deformation capacity of the joint. • The minimum ground cover should be used, so that the pipeline is flexible to deform and follow the imposed deformation of the surrounding soil. • Furthermore, it is possible to use loose backfill, such as pea gravel, allowing movement of the pipe in the trench. However, in such a case, special care should be paid to avoid overall (beam-type) compression buckling of the loosely confined pipeline.

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BURIED FLEXIBLE STEEL PIPE

Besides the above general design requirements, the use of isolation valves is an important issue of pipeline design to isolate segments of the distribution system, especially in areas where strong seismic action is anticipated. On the other hand, shut-off values activated on strong seismic action should be used only when their triggering level is justified experimentally, so that their proper activation is ensured. Structural Analysis and Design In the course of a seismic pipeline design, due to the relatively large deformations associated with earthquake actions, which may go beyond yielding, strains rather than stresses should be controlled. In particular, one has to account for both tensile and compressive strains not to exceed certain prescribed limits: • The steel material must be ductile enough to deform in the inelastic range without rupture. The maximum tensile strain in the pipeline wall should remain less than 5%. • Compressive strain shall not exceed the critical strain that causes wrinkling of the pipe wall. This critical strain can be considered equal to 0.4ts/DO. To estimate the strains at the pipeline wall due to a specific permanent ground deformation, a three-dimensional structural analysis model should be used. The model should consist of structural beam elements (or special-purpose structural pipe elements) for the simulation of the pipe and spring elements to model the surrounding soil. The structural elements should consider the inelastic behavior of the steel material, and the springs should be nonlinear to take into account the nonlinear behavior of the soil. Friction elements to account for the interaction between the soil and the pipe may also be used for a more efficient analysis. The properties of all elements used in such a model should be based on reliable and safe estimates of the real properties of steel pipe material and soil material. 7.8.4 Relevant Standards and Guidelines The following three documents provide information regarding seismic design concerns. American Lifelines Alliance. (2005). Seismic guidelines for water pipelines, Prepared by G&E Engineering Systems, Oakland, Calif. ASCE. (1984). Guidelines for the seismic design of oil and gas pipeline systems, ASCE Technical Council on Lifeline Engineering, New York.

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Comité Européen de Normalization. (1998). “Silos, tanks and pipelines,” Eurocode 8, Part 4, Annex A, Comité Européen de Normalization, Brussels, CEN ENV-1998-4.

7.9 ENCASED PIPE If pipe is encased in concrete, the shape is fixed. The pipe becomes a liner. The encasement supports soil and live loads. Because concrete is permeable, if the pipe is below the water table, over time, external water pressure can build up on the pipe liner. Pressure is distributed uniformly around the pipe. Therefore, ring compression stress in the pipe wall is σ = PextDO/2ts, or PextDO/2A, where A is the pipe wall cross-sectional area per unit length. The liner buckles when the ring compression stress reaches yield strength. The liner is “blown to one side” and inverts (Fig. 7-13a). Seepage through concrete is so slow that it may take years to build up to critical pressure. The encasement could be concrete, soil cement, or grout when the liner is placed in a leaky host pipe for rehabilitation or when a liner is installed in a tunnel and then encased in grout. The major problem with encasement is the “flat spot” (Fig. 7-13b). If a liner is held in vertical alignment on sills or if it floats up against crossbars when the fluid concrete is placed, flat spots can occur. For plain steel pipe, the flat spot must be more than a dent in the pipe. From field experience, to be of concern the flat spot must be longer, along the pipe, than one pipe diameter.

a

b

Figure 7-13. a, Encased Pipe That Has Buckled, and b, Encased Pipe with a Flat Spot.

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REFERENCES ASME. (2006). Companion guide to the ASME boiler and pressure vessel code, 2nd ed., American Society of Mechanical Engineers, New York, NY. ASME. (2006). Guidebook for the design of ASME Section VIII pressure vessels, 3rd ed., American Society of Mechanical Engineers, New York, NY. ASCE. (1993). Manuals and reports on engineering practice No. 79, Steel Penstocks, Chapter 3, ASCE, New York, NY. AWWA. (2003) AWWA Standard C206, Field Welding of Steel Water Pipe, American Water Works Association, Denver, CO. Taylor, D. W. (1955). Fundamentals of soil mechanics, John Wiley and Sons, New York.

PREAMBLE TO THE APPENDICES

The materials found in these appendices were written by Dr. Reynold K. Watkins. Most of the material discussed in this manual was derived from the teachings and achievements that Dr. Watkins has contributed over his lifetime. Whether it was a white paper, lesson plans, or material quickly jotted on pieces of paper, as a committee, we found his writings and research in the area of buried pipe design and analysis to be profoundly influential on the subject matter. While some material may appear redundant to the reader, we believe the knowledge imparted by Dr. Watkins found within the context of these appendices is an invaluable part of the learning process and, therefore, worth reiterating. —Task Committee on Buried Flexible Steel Pipe Load and Stability Criteria and Design

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APPENDIX A THE IOWA FORMULA—WHAT IT IS AND IS NOT

M. G. Spangler (1941) is known as “the father of buried flexible pipe analysis.” He recognized that flexible pipe deflects under soil load and develops horizontal soil support. Pipe–soil interaction is the basis for the structural behavior of buried flexible pipes. Spangler first published his Iowa Formula for predicting the ring deflection in 1941. Initially flawed, the Iowa Formula was modified by Watkins and Spangler (1958) and published in the form ∆x =

Dl K sWc r 3 ( EI + 0.061E′r 3 )

(A-1)

where d = ring deflection ratio = ∆y/D based on vertical decrease in diameter, ∆y; ∆x = horizontal increase in diameter due to vertical soil pressure, P; Dl = deflection lag factor (= 1 if embedment is compacted or pipe is pressurized); Ks = bedding factor = 0.1 (0.083 to 0.110, depending on the bedding angle); Wc = PD = load on pipe per unit length of pipe (prismatic load); P = vertical soil pressure on top of the pipe; D = diameter of the pipe (for flexible pipe, (I.D.) ≈ (O.D.) ≈ D within justifiable precision); r = radius (assumed equal to D/2 in the derivation of the Iowa Formula); I = moment of inertia of the pipe wall per unit length = t3/12; 127

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Figure A-1. Notation for Ring Deflection, d = ∆y/D (left) and an adjusted form of the Iowa Formula (right) for analyzing vertical ring deflection, d.

t = wall thickness for plain (bare) pipe; E = modulus of elasticity of the pipe material = 30,000,000 psi for steel; E′ = horizontal modulus of soil reaction (a modulus of elasticity—a constant). The Iowa Formula was derived to predict horizontal ring deflection. It demonstrates the importance of the horizontal soil support on ring deflection. It overpredicts ring deflection because horizontal compression of side-fill soil is not uniaxial and elastic but, rather, is biaxial compression of particulate soil. For pipe design, the vertical ring deflection ratio, d, is of greater value than horizontal ring deflection. Vertical ring deflection ratio is approximately (and conservatively) d = e = vertical compression of side-fill soil where e = vertical strain (compression) of side-fill soil due to pressure, P (see Fig. A-1 for notation). The Iowa Formula for predicting ring deflection was not intended for design of pipe. On the contrary, it shows that ring deflection is primarily a function of the soil embedment. Ring deflection caused by soil does not determine ring stiffness of the pipe. Moreover, the properties of soil are nonlinear and imprecise. E′ is a function of height of soil cover and, therefore, is not a constant for a given soil type and density. A good form for discussion of the Iowa Formula is the following: d=

∑ (EI

10P r 3 ) + 0.06E ′

ring deflection

(A-2)

The effects of soil and pipe are in the denominator. The following example compares the effects on ring deflection, d, of ring stiffness, EI/r3, and soil stiffness, E′. Soil stiffness is predominant.

APPENDIX A

129

Figure A-2. Section of Mortar-Lined Steel Pipe, 48-in. I.D. D/t = 240.

EXAMPLE A 48-in. mortar-lined, tape-coated steel pipe is buried in granular embedment. In this case, ring stiffness is, conservatively, the sum of ring stiffnesses, ∑EI/r3, of the lining and the steel pipe. The tape coating has negligible effect on the ring stiffness. Bond between mortar and steel is conservatively neglected. A typical value of soil stiffness is E′ = 2,000 psi with height of soil cover ignored. In the denominator of Eq. A-2, what are the relative contributions of soil stiffness and pipe stiffness? Pipe (∑EI/r3) Steel r = 24 in., ts = 0.2 in., I = t3/12 E = 30,000,000 psi EI/r3 = 1.447 psi Mortar tm = 0.5 in., I.D. = 48 in. E = 4,000,000 psi EI/r3 = 2.833 psi ∑EI/r3 = 4.3 psi (3% of the denominator) Soil (0.06E′) E′ = 2,000 psi 0.06 E′ = 120 psi (97% of the denominator) The pipe ring stiffness is negligible compared to the soil stiffness. In fact, the ring stiffness is only a third of the typical standard deviation of 10% for soil stiffness (Fig. A-2).

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Two conclusions are salient. 1. What is the Iowa Formula? It is an elastic model for predicting horizontal deflection of a buried flexible pipe. It is based on pipe–soil interaction. It emphasizes the importance of soil. 2. What the Iowa Formula is not? It is not a model for design of buried steel pipes. It is not a basis for specifying minimum ring stiffness. Ring deflection is limited by other conditions than ring stiffness. Spangler’s recommended allowable ring deflection of 5% usually covers the “other conditions,” such as cleaning equipment, attachments to special sections, flow capacity, and leaks at joints.

APPENDIX B SOIL SLIP ANALYSIS

Soil slip is the common description of a shearing failure in soil. Examples of soil slip are landslides and cave-ins. The soil slips when the ratio of maximum principal stress to minimum principal stress exceeds its limit. This limit is the soil strength. Following is an analysis of soil slip. Figure B-1 is an infinitesimal soil cube on which the principal stresses are σ1 = maximum principal stress, σ2 = intermediate principal stress, σ3 = minimum principal stress. Soil embedment about a buried pipe is usually two-dimensional. Worst-case analysis is the ratio of maximum to minimum principal stresses, σ1/σ3, at which the soil slips. Soil strength is k = σ1 σ 3 Otto Mohr derived an equation for stresses: normal stress, σ, (perpendicular to) and shearing stress, τ, (parallel to) a plane at angle, θ, through the infinitesimal cube (Fig. B-2). He recognized that the equation plots as a circle on the τ–σ axes shown on Fig. B-3. This is known as the Mohr stress circle. The center of the circle always falls on the σ-axis. It is noteworthy that cube, O, can be superimposed on the Mohr circle at the correct values for σ1 and σ3. This O becomes the origin of axes. It always falls on the Mohr circle. σ1 acts on an x-plane. σ3 acts on a y-plane. The x and y axes are oriented the same as the axes of the cube. Any plane 131

132

BURIED FLEXIBLE STEEL PIPE

Figure B-1. Principal Stresses on a Soil Cube.

Figure B-2. Plane on Which Normal Stress, σ, and Shearing Stress, τ, Can Be Calculated and Plotted on the Mohr Stress Circle.

Figure B-3. Mohr Stress Circle on σ–τ Axes. Center of the Circle Is on the σ-Axis. Angle of the Plane Plots as 2θ.

APPENDIX B

a

133

b

Figure B-4. Strength Envelope for Soil Slip in Granular Soil. Any Combination of σ and τ That Falls Outside of the Strength Envelope Is Failure (Soil Slip). (a) Reaction, R, at Soil Slip Is at Angle φ, Which Is the Soil Friction Angle. (b) Soil Slip Rotated 90° and Superimposed on the Mohr Stress Axes. φ Is Angle of Repose.

through the origin of axes, O, intersects the circle at the shearing stress and normal stress acting on that plane. Compression is positive, and counterclockwise shearing couple is positive. Figure B-4 is the strength envelope for granular, noncohesive soil shown plotted on σ–τ axes. The concept is based on the frictional resistance on a soil cube that slips past the bedding. The resultant force (reaction R) is at angle φ, called the soil friction angle. Conceptually, the strength envelope is the angle of repose of granular soil when dumped into a pile or windrow. If the Mohr circle becomes tangent to the strength envelope, the soil slips. The ratio of principal stresses, σmax/σmin, at soil slip and the plane θf, on which soil slips are solved by trigonometry. The procedure involves the construction of three diagrams: Mohr stress circle, orientation diagram, and strength envelope. The diagrams are superimposed as shown. From the superimposed diagram, soil strength, k (at soil slip), is the ratio of maximum to minimum principal soil stresses, i.e., k = σ max σ min where k = (1 + sin φ ) (1 − sin φ ) θf = 45° + F/2 where θf is the plane of failure (soil slip plane) The infinitesimal soil cube can also include shearing stresses, such as cohesion (glue) in the soil. For typical buried pipe analysis, the variables are maximum principal stress, minimum principal stress, and soil friction angle. If two of the three are known, the other variable can be found.

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BURIED FLEXIBLE STEEL PIPE

SOIL STRESS MODEL Free-Body Diagram Infinitesimal unit cube of soil principal stresses (basic case): a. σ1 = maximum principal stress and b. σ3 = minimum principal stress.

I. Mohr Stress Circle. σ = normal stress – horizontal axis. Compression is positive. τ = shearing stress – vertical axis. Counterclockwise shearing couple is positive. Center is on the σ-axis. Principal stresses are on the σ-axis where shearing stresses are zero.

II. Orientation Diagram. x = horizontal plane and y = vertical plane.

Orientation of planes on which stresses act:

III. Strength Envelope. The soil slips (failure) if the Mohr circle touches the strength envelope. Soils labs provide strength envelopes.

APPENDIX B

135

Superimposed Diagrams • Superimpose orientation diagram on the Mohr stress diagram. • The origin of axes, O, always falls on the Mohr circle. • Any plane through O intersects the Mohr circle at the stresses acting on that plane. • Orientation is correct for all planes through soil cube O on which stresses σ and τ act. • Superimpose strength envelopes. k = (1 + sin φ ) / (1 − sin φ ) = σ 1 σ 3 θ f = 45° + φ 2 = failure plane.

Example 1. Find surface load W at soil slip (active soil pressure at springline) as the surface load approaches a buried flexible pipe (Fig. B-5). The soil is granular and uncompacted; unit weight is γ = 110 pcf; and soil friction angle is φ = 30°. Soil slips at springline if σ y σ x = k for active soil pressure, σ x

(B-1)

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BURIED FLEXIBLE STEEL PIPE

Figure B-5. Conditions for Soil Slip on Approach of a Surface Load, W.

Figure B-6. Conditions for Soil Slip with Surface Load Directly Above Pipe.

From the Mohr circle, k = (1 + sinφ)/1 − sinφ) = 3. Because the pressure on a flexible ring is constant, σx = Pd = 220 psf (active soil pressure), where Pd = γH. Live load pressure is Pl = W/(H + D/2). σ y = 550 psf + W 50 ft 2

(B-2)

Substituting Eq. B-2 into B-1 and solving, W = 5,500 lb = 5.5 kip. Example 2. Find the surface load, W, at soil slip when W is directly above the pipe (Fig. B-6). σ x σ y = k = 3 for passive soil resistance , σ x , at the springline σ x = 220 pcf + W 8 ft 2 ( passive soil resistance ) σ y = 550 pcf = γ ( H + D 2 )

(B-3) (B-4)

APPENDIX B

137

Substituting Eq. B-4 into B-3 and solving, W = 11,400 lb = 11.4 kip. If uncompacted, the soil slips on approach of surface load, W = 5.5 kip from Example 1. Example 3. Find W on approach (Fig. B-5) if the soil is compacted such that γ = 120 pcf and F = 40°. k = (1 + sinφ)/(1 − sinφ) = 4.6 σx = γH = 240 psf active soil pressure σy = 600 psf + W/50 ft2 Substituting into Eq. B-1 and solving, W = 25,190 lb = 25.2 kip. Example 4. Find W directly above the pipe (Fig. B-6) for compacted soil. From the procedure of Example 2 but with γ = 120 pcf and φ = 40°, W = 20,160 lb = 20.2 kip. If compacted, the soil slips when surface load is W = 20 kip directly above the pipe from Example 4. Example 5. What is the maximum diameter of a tunnel before soil slip (collapse) if soil cohesion is c = 7 psi (1 ksf); soil unit weight is γ = 120 pcf; height of cover is H = 6 ft; and friction angle is φ = 30°?

Figure B-7. Tunnel Analysis.

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BURIED FLEXIBLE STEEL PIPE

Based on elastic theory of stresses around a hole in an infinite matrix, the stress at the side of the hole is increased threefold. An approximate radius is found by equating stress = strength at the springline, O: 3γ(H + R) = 2c/tanα (Fig. B-7) where

Figure B-8. Infinitesimal Cube of Soil at Soil Slip. σy = Maximum Principal Stress and σx = Minimum Principal Stress.

Figure B-9. Mohr Circle Analysis for Soil Slip on Top of a Flexible Pipe.

APPENDIX B

139

α = (90° − φ)/2 = 30°. Solving, R = 3.7 ft D = 7.4 ft (approximate). Example 6. Derive equations for soil strength, k, and soil slip plane, θf, in cohesionless soil with friction angle, φ = 30°. Figure B-9 is the Mohr stress circle for analysis of soil slip of an infinitesimal soil cube (as on top of a pipe, see Fig. B-8), showing correctly oriented stresses, strength envelope, and soil slip planes. k = σ y σ x = (1 + sin φ ) (1 − sin φ ) = 3 and θ f = 45° + φ 2 = 60°

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APPENDIX C FINITE ELEMENT DESIGN EXAMPLE TRENCH PARALLEL TO A BURIED PIPE

BACKGROUND The example in this appendix illustrates the use of a two-dimensional plane strain finite element analysis to model the behavior of a buried pipe using the software PLAXIS 7.2. A hardening soil model is used in this example. The hardening soil model is a nonlinear soil model that uses a Mohr–Coulomb failure envelope to model the shear strength of the soil, a hyperbolic model to describe the stress–strain behavior of soil, a hardening model to account for the effect of confinement on the soil stiffness, and a cap model to account for differences in loading and unloading behavior in soil. The pipe is modeled using elastic–plastic beam elements. Interface elements are used around the pipe to allow for slippage between the soil and the pipe element. The pipe modeled is a 48-in.-diameter steel pipe with a wall thickness of 0.2 in. The pipe has 2 ft of cover and a load approximating the wheel load from a 16-kip dual-truck tire was positioned above the crown of the pipe. Exact modeling of a wheel load requires a three-dimensional analysis. To approximate this loading using a two-dimensional plane strain analysis, an elastic analysis was performed to determine a distributed strip load that applies the same maximum normal stress at the depth of the pipe crown as a rectangular wheel load. This example evaluates the effects of excavating a trench parallel to a buried pipe. The excavation is modeled by removing soil from the model in 2-ft-thick layers. Four layers are removed, resulting in an 8-ft-deep trench. Details from the analysis of a trench 2 ft from the pipe are presented below. Additional analyses were performed for a trench 4 ft from the pipe. The results of this analysis are summarized. 141

142

BURIED FLEXIBLE STEEL PIPE

MODEL GEOMETRY Figure C-1 shows the model with a trench 2 ft from the pipe. The trench is the rectangular region in the left part of the model. Geometry lines in the trench delimit the 2-ft-thick layers to be removed in subsequent analyses. The distributed strip load can be seen above the pipe crown. The dashed line around the pipe indicates the limits of the boundary elements used between the soil and pipe. The finite element mesh used in these analyses is shown in Fig. C-2. It should be noted that the program generates elements inside the pipe. These elements were deactivated to model an empty pipe. PLAXIS uses random distribution of nodal points to avoid effects from evenly spaced nodal points.

Figure C-1. Model of 48-in.-Diameter Steel Pipe with Parallel Trench 2 ft. from the Pipe.

Figure C-2. Finite Element Mesh Used to Model 48-in.-Diameter Steel Pipe with Parallel Trench.

APPENDIX C

143

ANALYSIS SEQUENCE The sequence in which loads are applied and removed has a significant effect in all soil–structure interaction problems. The loading–unloading sequence used in this analysis is as follows: 1. 2. 3. 4. 5.

Weight of the soil was applied. The wheel load was applied. The first 2 ft of the trench was excavated. The second 2 ft of the trench was excavated. The third 2 ft of the trench was excavated.

RESULTS FOR A TRENCH 2 Ft FROM THE PIPE The first phase of modeling involved applying the weight of the soil. Pipe deflections and bending moments were very small at this stage and therefore of little interest. The next phase of loading was to apply the distributed load simulating a truck wheel load. The ring deflection of pipe due to this loading was 0.17 in. The deformed finite element mesh is shown in Fig. C-3. The mesh deformations are exaggerated 10 times. Figure C-4 is the bending moment diagram for the pipe and shows a maximum bending moment of 52.9 ft-lb/ft. The trench was excavated by removing soil in 2-ft thick layers, as shown in Figs. C-5 through C-8. These figures show deformed meshes after removal of each layer. Again, deformations are exaggerated 10 times. Figure C-9 shows the deformed mesh at the completion of excavation at true scale. Figure C-10 shows the pipe bending moment diagram at the end of excavation; the dashed lines in the diagram indicate the plastic

Figure C-3. Deformed Finite Element Mesh After Applying Distributed Load. Deformations Are Exaggerated 10 Times.

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BURIED FLEXIBLE STEEL PIPE

Figure C-4. Pipe Bending Moment Diagram After Applying Distributed Load. Maximum Bending Moment Is 52.9 ft-lb/ft.

Figure C-5. Deformed Finite Element Mesh After Excavating First Layer of Trench. Deformations Are Exaggerated 10 Times.

Figure C-6. Deformed Finite Element Mesh After Excavating Second Layer of Trench. Deformations Are Exaggerated 10 Times.

APPENDIX C

145

Figure C-7. Deformed Finite Element Mesh After Excavating Third Layer of Trench. Deformations Are Exaggerated 10 Times.

Figure C-8. Deformed Finite Element Mesh After Excavating Fourth Layer of Trench. Deformations Are Exaggerated 10 Times.

Figure C-9. Deformed Finite Element Mesh After Excavating Fourth Layer of Trench. Deformations Are at True Scale.

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BURIED FLEXIBLE STEEL PIPE

Figure C-10. Pipe Bending Moment Diagram After Completing Excavation. Maximum Bending Moment Is 252 ft-lb/ft.

Table C-1. Details from Each Stage of Excavation Excavation Stage

1 2 3 4

Crown to Invert Deflection (in.)

Springline to Springline Deflection (in.)

Maximum Pipe Bending Moment (ft-lb/ft)

0.21 0.64 0.67 2.19

0.09 0.36 0.39 1.89

64.6 144 149 251

moment. The maximum bending moment is 252 ft-lb/ft at the crown of the pipe, where a single plastic hinge has formed. Maximum bending moment is 252 ft-lb/ft. Table C-1 provides additional details of pipe deflections and bending moments during each stage of excavation.

SUMMARY OF RESULTS FOR TRENCH 4 Ft FROM PIPE An additional analysis was performed for a trench 4 ft from the pipe. As expected, this condition results in much lower pipe deflections and bending moments. The deformed mesh with the trench excavated to full depth is shown in Fig. C-11. Again, deformations are exaggerated 10 times. The maximum bending moment is 170 ft-lb/ft, as shown in Fig. C-12.

APPENDIX C

147

Figure C-11. Deformed Mesh for Trench 4 ft from Pipe. Deformations Are Exaggerated 10 Times.

Figure C-12. Pipe Bending Moment Diagram for Trench 4 ft from the Pipe. Maximum Bending Moment Is 170 ft-lb/ft.

CONCLUSION These sample analyses illustrate the power of the finite element method for evaluating complicated buried steel pipe problems. High-quality analyses require sophisticated soil and pipe models, and PLAXIS 7.2 is one example of a software package that has implemented such models. Great care is required in using the finite element method to model the behavior of buried structures. The results can be sensitive to the parameters used and the limitations of the model. Those performing such analyses should have an understanding of soil behavior, the soil and pipe models used in the analyses, and the limitation of the model and analyses.

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BURIED FLEXIBLE STEEL PIPE

The primary strength of using the finite element method is the ability to evaluate the behavior of buried pipe performance under unusual conditions. Evaluating the effect of making an excavation adjacent to a pipe has been illustrated in this example, but the method can be used to understand many other conditions. Multiple pipes in a trench, including pipes of different sizes, poor compaction, and unsymmetrical and extreme loading conditions are examples of unusual conditions that can be understood better through the use of the finite element method. Sensitivity studies can be easily carried out to better understand the influence of different design conditions. However, whenever possible, finite element models should be calibrated and verified with careful field measurements and full-scale model studies.

APPENDIX D EXTERNAL FLUID PRESSURE

External fluid pressure on flexible steel or plastic pipes can cause pipe collapse. External fluid pressure can occur if the pipe is immersed in water, liquefied soil, grout, flowable fill, or atmospheric pressure. The atmospheric pressure is commonly referred to as internal vacuum. External fluid pressure may also be applied around a pipe that is buried in soil or even encased in concrete. Under those confined conditions, the pipe may buckle and collapse. This constitutes a challenging analysis and design problem. The analyses in this appendix are of collapse for steel pipes.

D.1 FLUID EMBEDMENT If the pipe is circular and is immersed in fluid, collapse can occur due to buckling when the external pressure p becomes equal to a critical value given by the following expression: pcr =

( )

2E t 1 − ν2 D

3

(D-1)

where p = applied external fluid pressure (plus internal vacuum); pcr = critical external fluid pressure (plus internal vacuum) of a circular pipe at collapse; E = modulus of elasticity = 30,000,000 psi (210,000 MPa) for steel; ν = Poisson’s ratio = 0.3 for metals (including steel);

149

150

σy D t D/t

BURIED FLEXIBLE STEEL PIPE

= = = =

yield stress of steel; pipe diameter; pipe wall thickness of plain pipe; ring flexibility (diameter-to-thickness ratio).

Sometimes, Poisson’s ratio effects are neglected. Therefore, Eq. D-1 is written as follows: pcr = 2E

( ) t D

3

(D-2)

Buckling shape is an oval, shown in Fig. D-1a. Equations D-1 and D-2 come from the classical analysis of elastic ring collapse (Timoshenko and Gere 1961; Brush and Almroth 1975). Equation D-2 can be written in the following form:

( pcr E )( D t )3 = 2 Collapse in the case of a circular pipe under fluid embedment is a sequence of the following: 1. For applied external pressure levels p less than the critical pressure pcr, the pipe slightly shrinks uniformly but remains circular. 2. Buckling occurs when p = pcr. 3. At buckling, the pipe cross section changes shape from a circle to an oval (Fig. D-1a).

Figure D-1. (a) Buckling of a Circular Pipe from Circular to Oval Shape and (b) Development of Four Plastic Hinges at θ = 0, π/2, π, and 3π/2.

APPENDIX D

151

4. In this configuration, the four points of the pipe, depicted in Fig. D-1b, are locations of maximum stress and deformation. Beyond the elastic regime, plastic hinges form. 5. A four-hinge mechanism is developed, which leads to collapse (i.e., cross-sectional flattening). Example D.1 The ring diameter to thickness ratio of a steel pipe is D/t = 240. If the pipe is assumed initially to be circular, what is the external fluid pressure that causes buckling? Answer. From Eq. D-2, substitute 240t for D and solve for the buckling (critical) pressure, por = 4.3 psi. Equations D-1 and D-2 are approximate because of simplifying assumptions in the analyses and most importantly out-of-roundness. They are based on elastic buckling theory of rings, as stated in classical textbooks. In practice, the pipe will always be imperfect, in the sense that its cross section will not be circular. Therefore, instead of a “perfect” pipe, an “imperfect” pipe should be considered for realistic analysis. The “imperfect” pipe cross section is not circular, and the maximum pressure, pmax, is less than pcr calculated from Eq. D-1, should be reduced, i.e., pmax < pcr. For the sake of simplicity in the analysis, initial imperfection in shape (out-of-roundness) is assumed to be in the form of an oval (Fig. D-1). It can be shown mathematically that this is a conservative assumption, leading to useful results. The ultimate (maximum) pressure, pmax, is a function of the initial imperfection (ovality). Timoshenko’s quadratic formula (Timoshenko and Gere 1961) is often used to predict the maximum pressure, pmax, in terms of the initial imperfection, δ0; pipe flexibility, D/t; and yield stress of the steel, σY. The initial imperfection, δ0, is the radial distance from the out-of-round oval to the circle of radius, R. The term, δ0/R, is a form of ring deflection which reduces maximum pressure to pmax in the equation: 3D  δ 0    2 pmax −  pY +  1 + pcr pmax + pcr pY = 0   t  R   

(D-3)

where pY = 2σ Y

( ) t D

(D-4)

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BURIED FLEXIBLE STEEL PIPE

Figure D-2. Reduction of Maximum Pressure Sustained by an Imperfect Pipe in Terms of Imperfection Amplitude, According to Eq. D-5. Results Are Shown for a Yield Stress Equal to 40 ksi (275 MPa). is the pressure that causes the entire pipe cross section to reach the yield stress and pcr is given by Eq. D-1 or D-2. Note that, for thin-walled pipes (e.g., pipes with D/t > 50), pY is much higher than both pcr and pmax. Assuming a value of maximum acceptable imperfection amplitude δ0 equal to 0.01 of the pipe radius (δ0/R = 0.01), then the above formula becomes

(

)

D 2 pmax −  pY + 1 + 0.03 pcr  pmax + pcr pY = 0   t

(D-5)

The predictions of Eq. D-3 for the maximum pressure pmax (normalized by pY) are depicted in Fig. D-2 for various values of D/t and δ0/R for a steel material with yield stress equal to 40 ksi. It can be readily verified that very similar curves apply for yield stress ranging between 36 ksi and 45 ksi. Equation D-3 does not apply directly to local pipe initial deformations, such as a localized dent or a kink. A different analysis is required for local dents, but this is outside of the present discussion. Example D.2 The ring flexibility parameter and the yield stress of a steel pipe are D/t = 240 and σY = 45 ksi, but the ring is not circular. The amplitude of out-of-roundness is 2% of the pipe radius. What is the maximum external fluid pressure that could be sustained by the pipe?

APPENDIX D

153

Answer. pY = 375 psi, por = 4.34 psi. Applying Eq. D-3, one has to solve the following quadratic equation: 2 pmax − 441.8 pmax + 1627.5 = 0

which gives (the smallest root) pmax = 3.72 psi The maximum pressure is less than pcr = 4.34 psi.

D.2 PIPE ENCASED IN CONCRETE A pipe encased in concrete is confined. Concrete is undeformed, so that the pipe is restrained in the sense that outward displacements of the pipe are prevented by the concrete. The pipe becomes a liner. The concrete encasement supports the soil loads. Under those confinement conditions, the pipe may buckle due to external pressure. This may happen because concrete is permeable, and if the pipe is below the water table, over time, external pressure builds up on the pipe liner. Initially, under low external pressure, the circumference decreases slightly, bond breaks down, pressure is distributed uniformly around the pipe, and ring compression stresses develop in the pipe wall. Those stresses may cause buckling in the form of a single-lobe shape (Fig. D-3). This phenomenon is accentuated in the presence of small initial imperfections (deformations) around the pipe, as well as the presence of a small gap between the pipe and the concrete. Seepage through concrete is sometimes so slow that it may take years for the pressure to reach a critical level and buckling to occur. Pipe deformation can be described in detail by the following steps: • At low levels of pressure p less than the critical pressure pcr of Eq. D-1 or D-2, the pipe shrinks uniformly by a small amount; this creates a gap between the pipe and the concrete. This gap is added to any gap from the initial imperfections and construction. Usually this gap is located in the bottom of the liner, where pressure p is maximum. • At critical pressure level pcr, the cylinder buckles. However, the oval shape cannot be obtained due to confinement. • Thus, upon buckling, the cylinder accommodates itself within the confinement boundary and is able to sustain further increase of external pressure.

154

BURIED FLEXIBLE STEEL PIPE a

b

Figure D-3. (a) Buckling of Pipe Encased in Concrete; (b) Buckled Portion of the Pipe.

• Under those conditions, the part of the cylinder with the gap (usually at the bottom) behaves similar to an arch subjected to uniform external pressure, supported at the two “touchdown” points B and B’ (Fig. D-3b). This leads to the so-called “inversion buckling,” followed by pipe collapse. The maximum pressure pM sustained by the pipe can be computed within good accuracy by the following semi-empirical equation proposed by Montel (1960), in terms of the material yield stress σy, the cylinder flexibility R/t, the initial imperfection δ0 and the initial gap g between the cylinder and the stiff boundary: pM =

5σ y

(R t)

[1 + 1.2 (δ 0 + 2 g ) t ]

1.5

(D-6)

Montel (1960) proposed Eq. D-6 for 30 ≤ R/t ≤ 170, 250 MPa ≤ σy ≤ 500 MPa [36 to 72 ksi], 0.1 ≤ δ0/t ≤ 0.5, g/t ≤ 0.25, and g/R ≤ 0.025, but recent finite element results (Vasilikis and Karamanos 2008) demonstrated

APPENDIX D

155

Figure D-4. Comparison of Montel’s Equation with Finite Element Results.

its very good accuracy for values of δ0 and g outside the above range, as shown in Fig. D-4, for a pipe with flexibility D/t = 200 [R/t = 100] and yield stress σY = 45.3 psi (313 MPa). Example D.5 A steel pipe with ring flexibility D/t = 240, diameter D = 60 in. (1,524 mm) and yield strength σY = 42 ksi (290 MPa) is encased in concrete. Assuming initial out-of-roundness amplitude δ0 equal to 1% of the radius and a gap g equal to 1% of the pipe radius, what is the maximum external water pressure, pM, that can be sustained by the pipe? Answer. Thickness is t = 60/240 = 0.25 in. Initial imperfection and gap are δ0 = 0.3 × (60/2) = 0.3 in., and g = 0.3 × (60/2) = 0.3 in. Therefore, pM =

5 × 42,000 = 30 psi (120 )1.5[1 + 1.2 ( 0.3 + 2 × 0.3 ) 0.25 ]

Example D.6 A steel pipe under a dam (Fig. D-5) with ring flexibility parameter D/t = 180, diameter D = 60 in. (1,524 mm), and yield strength σY = 42 ksi (290 MPa), is encased in concrete. Over time, pressure builds up on the

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BURIED FLEXIBLE STEEL PIPE

Figure D-5. Encased Pipe in Dam.

pipe to p = 142 psi. Flat spots have been detected in the pipe with maximum radius of ry = 3R. Assuming a gap equal to 0.1% of the pipe radius, is the pipe safe against wall buckling? Answer. Thickness is t = 0.25 in., and gap is g = 0.03 in. What is the initial imperfection to be used? This should be calculated from the flatspot geometry. Recall from analytical geometry that the curvature of an arch is related to the chord length L and the mid-ordinate distance Δ as follows (Fig. D-6): ∆=

L2 8r

For the “perfect” circular pipe, ∆ (1) =

L2 8R

∆ ( 2) =

L2 8ry

For the “flat-spot” pipe,

Thus, the initial displacement δ0 to be used as an initial imperfection is

δ 0 = ∆ (1) − ∆ ( 2) =

L2  1 1  − 8  R ry 

APPENDIX D

157

Figure D-6. Geometric Analysis of a Flat Spot; Bottom Part of the Pipe at Flat Spot.

Pipe radius is R = 60/2 = 30 in., and the thickness is t = 60/180 = 0.33 in. Considering (empirically) L = 0.25R and taking into account that ry = 3R, one obtains δ0 = 0.02R, so that δ0 = 0.6 in. Therefore, from Eq. D-6, pM =

5 × 42, 000 = 245 lb in.2 ( 90 )1.5[1 + 1.2 ( 0.6 + 2 × 0.03 ) 0.33 ]

This pressure is greater than 142 psi. Therefore, the pipe is safe against buckling. Remedies Against External Fluid Pressure Collapse in Concrete Embedment Conditions. Two possible remedies to prevent buckling in concrete encased pipes are • Reduce hydrostatic pressure on the concrete encasement by installing a horizontal drain pipe along the encasement. This can be accomplished by directional drilling. • Bore small holes (weep holes) in the pipe wall to relieve external pressure on the pipe.

D.3 PIPE UNDER SOIL EMBEDMENT If a pipe is embedded in soil, external fluid pressure can be applied around the pipe due to soil permeability. In this case, the pipe is partially

158

BURIED FLEXIBLE STEEL PIPE

restrained for outward displacements, in the sense that outward displacements are resisted by the deformable soil. For very stiff soils, pipe behavior is similar to the case of concrete confinement, whereas for very soft soils, the embedded pipe behaves similar to the case of fluid confinement. In other words, for typical soil conditions, the maximum pressure sustained by the pipe is between the maximum pressure of Eq. D-3 and Montel’s collapse pressure of Eq. D-6. pcr < pmax < pM

(D-7)

An exact analytical solution of the problem is not possible, due to its complexity; the soil interacts with the deforming pipe, and this interaction is crucial to determine the external pressure capacity. Therefore, the use of numerical solution methodologies, such as finite element analysis, is necessary. The reduction of ultimate pressure of pipes depends on the soil conditions. The main parameter that expresses the rigidity of the confinement medium is the Spangler horizontal soil modulus E′. Finite element analysis (Vasilikis and Karamanos 2008) has shown that the soil modulus E′ has a significant effect on the ultimate pressure capacity. For design purposes, a reduction factor of the pressure for concrete pM developed by Montel (Eq. D-6) is suggested. This reduction factor, denoted as f, is shown graphically in Fig. D-7 in terms of the soil modulus E′ expressed in psi. The validity of this formula has been verified using finite elements for 1,000 lb/in.2 ≤ E′ ≤ 3,000,000 lb/in.2, where the upper limit corresponds to 10% of the steel modulus (similar to concrete confinement), and the lower limit of 1,000 psi corresponds to a soft soil.

Figure D-7. Reduction Factor for Calculating External Pressure Capacity of a Pipe Buried in Soil.

APPENDIX D

159

Example D.7 A steel pipe with ring flexibility parameter D/t = 240, diameter D = 60 in. (1,524 mm), and yield strength σY = 42 ksi (290 MPa) is encased in a soft soil with E′ = 10,000 lb/in.2 = 10 kip/in.2 Assuming initial out-ofroundness amplitude δ0 equal to 1.5% of the radius and a gap g equal to 0.5% of the pipe radius, what is the maximum external water pressure that can be sustained by the pipe? Answer. Thickness is t = 0.25 in. Initial imperfection and gap are δ0 = 0.45 in., and g = 0.15 in. Therefore, pM =

5 × 42,000 = 34.7 lb in.2 (120 )1.5[1 + 1.2 ( 0.45 + 2 × 0.15 ) 0.25 ]

From Fig. D-7, the reduction factor for E′ = 10 ksi is about 0.4. Thus, the maximum pressure is pmax = f ⋅ pM = 0.4 × 34.7 = 13.9 psi

D.4 ADDITIONAL NOTES AND RECOMMENDATIONS • The fluid pressure to be resisted is the internal “vacuum” plus external fluid pressure, such as a water table above an empty pipe. • Soil conditions are very important for the external pressure resistance of the confined pipe. Therefore, specify good soil with enough soil cover to ensure adequate passive soil resistance. Furthermore, specify compaction (i.e., soil density) of the embedment in order to ensure the soil friction angle required to prevent soil slip. • Check on the allowable ring deflection. If the deflection is too large, it may affect critical fluid pressure. Ring deflection occurs during installation. Internal pressure usually rerounds the deflected ring. Deformation must be controlled in order to prevent “flat spots” and excessive ring deflection. • Initial imperfections (i.e., deviation from roundness) play a key role in maximum pressure, and this is expressed explicitly in Montel’s equation (Eq. D-6) through term δ0 in the denominator. The validity of this formula has been verified using finite element results, where initial imperfections were assumed in the form of a localized deformation pattern, rather than a flat spot, which is a smoother type of initial out-of-roundness. In any case, the value of δ0 should be the maximum deviation of the real (imperfect) pipe cross section from the “perfect” circular geometry.

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APPENDIX E THE STORY OF BURIED STEEL PIPES AND TANKS* Reynold K. Watkins

We can write rational recommendations for the future about as far ahead as our knowledge of the past.

Water is the lifeblood of the arid Great Basin. The Great Basin is a large, dry lake bed between the Rockies and the Sierras. When I joined the faculty at Utah State, all of the water for irrigation was delivered in ditches. Loss of water was serious. Too much water was sucked up by grass and willows along ditch banks. Too much water seeped into the sandy soil. Too much water evaporated from the warm, wet ditch banks. A ditch, one mile long, could deliver maybe a third of the inflow.

* The material in this appendix was written by Reynold K. Watkins, Professor Emeritus, Department of Civil and Environmental Engineering, Utah State University, Logan, UT 84322-4110 on March 1, 2006.

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And there was always erosion of the banks, and silting up of the ditch, and rodent holes, and ice damage to gates. But the worst problem was loss of children. When my neighbor family found the body of their twoyear-old in the ditch, they were inconsolable, and so was I. I resolved to learn about buried pipes as alternatives to open ditches. On sabbatical leave, I studied pipes under Spangler at Iowa State College. The nation had not yet recovered from World War II. So office space for graduate students was limited. But Professor Spangler graciously invited me to share his office with him. “The office is never locked,” he said, “And the outside door to the building has no lock.” How times have changed. Professor Spangler was more than a teacher. He was my mentor and my colleague. He would take time to relate his buried pipe experiences and research. On one occasion in his office, Professor Spangler turned to me and said, “I derived a formula for predicting ring deflection of buried flexible pipe, specifically for culverts under roads. I call it the Iowa Formula. But it doesn’t work. Would you care to find what is wrong with the formula?” I would, and I did. His mathematics were complex and elegant—and correct—except for the dimensions of a modulus of elasticity of the soil. We corrected the dimensions and published the Modified Iowa Formula in 1958. I was caught up in pipes. The legacy of Marston and Spangler is the design of culverts, an essential component of the interstate highway system. In fact, the development of buried pipeline systems is connected inextricably to the development of highway systems. It’s all about earth-moving. After World War II, roads were a maze of disconnected local roads (state, county, and town) at a time of desperate need for interstate transportation. Roads had been neglected during the war. On June 29, 1956, President Eisenhower signed the Federal Aid Highway Act. The interstate highway system was about to be born. But its conception occurred much earlier—after World War I. In July 1919, an army company departed from Washington, D.C., in a crosscountry automobile caravan. The objective was to evaluate transportation by automobile as the inevitable replacement of horse-and-wagon transportation before World War I. A young officer in the company was Captain Dwight Eisenhower. It took 62 days to reach San Francisco. Captain Eisenhower noted that the wagon roads were a more serious detriment to transportation than were the automobiles, despite tire blowouts, overheated engines, and broken axles. After World War II, General Eisenhower surveyed the effect of Allied bombing. He noted that a German railway could be knocked out by a single bomb. But the German Autobahn was indestructible. A bomb could

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Figure E-1. President Dwight Eisenhower, Key Contributor to Transportation in the United States, Signed the Federal Aid Highway Act in 1953. not knock out two parallel multilane highways. Moreover, Germany could be crossed in two days. In 1953, President Eisenhower (Fig. E-1) remembered the 62 days on rough wagon roads across America and only two days on a speedway across Germany. He got onto the case for an American interstate highway system—for rapid deployment of troops and equipment and for emergency evacuation routes, but also for urgent civilian needs, which were transportation and commerce. The timing was right; the need was obvious. The president prioritized the needs of the U.S. troops above pork-barrel politics, and the knowhow was available. Highway technology had been progressing, albeit unnoticed.

AS FOR THE KNOW-HOW? Before World War I, Anson Marston (Fig. E-2) was coerced, as his professional responsibility, to become the first dean of engineering at Iowa State College. He accepted reluctantly, “But only for two years, mind you.” Anyway, why was engineering needed at an agricultural college in corn-and-hog country? Dean Marston found out why. Each spring, Iowa farmers were bogged down in roads that were quagmires of mud

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Figure E-2. Anson Marston, First Chairman of the Highway Research Board (Circa 1920).

(Fig. E-3). Marston responded with a call for action. “Let’s get Iowa out of the mud.” He had support from farmers who put pressure on the state government. The Iowa road project was launched. Marston realized that to get Iowa out of the mud, they had to get the water out of the roads. And that, he declared, could be accomplished by drain pipes and culverts. Marston himself led out by deriving a formula for the earth load on a buried pipe. It is simply the weight of backfill soil reduced by friction of the trench walls (Fig. E-4). Then it became the responsibility of pipe manufacturers to make pipe that could support the Marston load. The D-load test for pipes became a performance specification. Performance specification was a new concept for pipe design. The Iowa road drainage project was a success. Pipe manufacturers were pleased with the performance specification. They could utilize their own expertise in making pipe that could support the D-load and not be encumbered by volumes of procedural specs. State highway departments took notice. Iowa was not the only state bogged down in muddy roads. So the federal government established the Highway Research Board. Anson Marston was its first director. Highway drain pipes were part of a remark-

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Figure E-3. A Reason for Dean Anson Marston’s Call for Action, “Let’s Get Iowa Out of the Mud.”

Figure E-4. A Marston Load on Buried Concrete Culverts Was the Weight of the Backfill Reduced by the Friction of the Trench Walls and the D-Load Test for Manufacturers to Meet the Marston Load Requirement. The D-Load Is Load at Pipe Failure in the Three-Edge-Bearing Test.

able development of buried pipes—for culverts and drains—but also for transmission of water, gas, power, and oil; and for disposal of sewage and stormwater; and for subways and shopping malls. Buried pipes were becoming the arteries of communal life—the guts of civilization’s infrastructure. Evolution of pipes that serve communities originated in antiquity. About 2500 bc, the Chinese delivered water through bamboo pipes. In Greece, terra cotta pipes supplied water to villagers at a central well. In Persia, rock-lined tunnels called ghanats were dug by hand to deliver freshwater from the mountains to the parched cities on the plains.

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During 100 to 300 ad in Rome, with plenty of low-cost slave labor, pipes became an important part of the infrastructure for the emperor and the elite. Water was delivered to Rome in aqueducts. Then the water was distributed in lead pipes to the mansions of the elite and their luxurious Roman baths. The fall of Rome may have been brought about, in part, by those lead pipes. The acidic water dissolved lead from the pipes. The elite were lead-poisoned. Lead caused impotence, and the few successful births produced heirs who were mentally retarded. Caligula? Nero? During the Renaissance, the foul smell of raw sewage in the streets of cities like Paris and London led to buried sewer pipes. Underground sewers were brick-lined tunnels. The bricks formed arches like the remarkable Roman arches in buildings and aqueducts. Mortar was not needed because the blocks (brick or stone) were held in place by compression. The concept of arching action was “rediscovered” in the 1900s as it applied to soil arching action over buried pipes. Development of pipes was empirical, labor intensive, and fraught with failures. Who knows how many Persian lives were lost in underground cave-ins while excavating tunnels ahead of rock lining? How could the Romans know that acid water in lead pipes would cause lead poisoning, infertility, and mental retardation of their children?

IRON Iron had been known since 1000 bc, but before the Renaissance, iron was used mostly to make spears, swords, and shields. By 1346 ad, iron was used to make guns. These guns became the incentive for iron pipe— the dream of “ingeniators” (engineers) because of the demand for water in burgeoning cities and because iron is stronger than bamboo or clay. Iron pipes became reality in England in 1824 when James Russell invented a device for welding iron tubes (gun barrels) together into pipes. Costly, hand-made iron pipes supplied gas for the gas lamps in the streets and dwellings of the elite. In 1825 Cornelius Whitehouse made long iron pipes by drawing flat strips of hot iron through a bell-shaped die. Then came the Bessemer process for making steel, and the openhearth furnace for production of large quantities of steel. Steel pipes became reality. The urban way of life was changed. The community expanded into a metropolis. The “guts of the city” became steel pipes for water and for sewage, clay pipes and brick-lined tunnels. Walter Cates identified four stages in the development of steel pipe in History of Steel Water Pipe (1971). 1. In 1831 the first furnace was built in the United States for making wrought iron pipe. More furnaces were built. The demand for pipes

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was enormous because of the need for water distribution in fastgrowing cities. Pipe production was limited, however, because iron was not available in large quantities. 2. The second stage was the age of steel. Steel was born in England in 1855 with the Bessemer process for making iron into steel. Then the open-hearth furnace (1861) made steel available in thousands of tons—not just pounds. After the gold rush, in California sheet steel was formed into tubes with longitudinal, riveted seams. One end of each pipe “stick” was crimped so it could be stabbed into the next stick like stove pipes. Sections were joined by simply forcing them together. From 1860 to 1900, virtually all water pipe was cold-formed from steel sheets and riveted. Two million feet were installed. 3. The third major development was Lock-bar pipe in 30-ft lengths (Fig. E-5). It was first fabricated in New York. Two semicircular pipe halves were joined by inserting the edges of each into two longitudinal Lock-bars with an H-shaped cross section. The edges of the pipe halves were “up-set” to form shoulders for engaging the lockbar. The seam was 100% efficient. Three million feet of Lock-bar was installed—and only half as much riveted pipe. 4. The fourth major development was automatic electric welding. Welding started as a novelty in 1920, but in only 20 years, welding took over steel pipe production. Seven million feet of welded pipe was installed. But back to the story. The Marston load applied only to rigid pipes—concrete and clay. The

Figure E-5. Sketch of Lock-Bar Pipe.

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“failure” (or performance limit) was cracks in the pipe. Crack width was limited to 0.01 in. I was studying rigid pipe design and came upon the unreasonable hundredth inch crack standard. Crack width depends upon wall thickness, pipe diameter, and multiplicity of cracks. I asked Professor Spangler, “Why the 0.01-in. crack for concrete and clay pipe?” Professor Spangler laughed, sneezed, put down his cigar, and said, “Come with me.” We walked down the hall to an office with nameplate, William Schlick. “Bill, this student wants to know why the hundredth inch crack.” Bill Schlick related this story: Dean Marston called two students into his office: M. G. Spangler and Bill Schlick. Marston said to M. G., “Spangler, I want you to construct a soil box in which you are to prove the Marston load theory.” And to Bill, Marston said, “Schlick, you are to inspect every culvert in Story County and report back to me.” The next morning, Bill went into the field and crawled through concrete culverts all day. Late that evening he returned to the laboratory, tired and covered with mud. Then it occurred to him that he was supposed to report back to the dean. But he had nothing to report except that he had crawled through a hundred muddy culverts. Despondent, he happened to notice a scrap of steel shim stock on the floor. It was a half in. wide, 0.01 in. thick. He cut off a few inches, rounded one end, and stuck it in his pocket. The next morning, he returned to the field and found how many of the culverts had a crack inside that was wide enough for him to stick in the gauge. That evening he reported to the dean the percent of culverts with cracks wider than one-hundredth of an inch. “That’s good; we’ll publish!” the dean exclaimed. And suddenly, the hundredth-inch crack became the standard.

After the Marston load specifications for rigid pipes comes Armco Company, with flexible corrugated steel pipe. From tests in their yard in Ohio, corrugated steel pipes performed well as buried culverts, but they collapsed under the “standard” D-load. So why did flexible pipes perform as culverts? In the late 1930s Dean Marston assigned the flexible pipe question to a young instructor, M. G. Spangler (Fig. E-6). From soil box tests, Spangler discovered the effectiveness of soil support at the sides of flexible pipe. It became clear that buried pipe performance is pipe–soil interaction. And soil is a major component of the conduit. Spangler derived his Iowa Formula for predicting flexible ring deflection as a function of pipe ring stiffness, and horizontal soil support. Spangler demonstrated that good embedment is the basic structure. Production costs of corrugated steel pipes were reduced by forming pipes from coils of steel helically wound, like toilet paper spools, with welded seams. Coatings evolved from asphalt to zinc (galvanized) to aluminum and to polymer coatings.

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Figure E-6. Merlin Grant Spangler, Professor, Iowa State University; Father of Buried Flexible Pipe Design; Chairman of the Culvert Committee of the Transportation Research Board.

PLASTIC PIPES APPEARED ON THE SCENE During World War II, German water distribution was damaged by Allied bombs. Steel plants had been destroyed. So without steel pipes, how could damaged water pipes be replaced? A “quick fix” was temporary replacement using plastic PVC pipe. After the war, “temporary” became permanent. In good soil embedment, plastic pipes survive for long life. Now, plastic pipes abound in gas distribution, in electrical conduits, in indoor plumbing, etc. Plastic tubes are ubiquitous.

SOIL HANDLING AND EXCAVATING At the same time as the evolution of pipes, there was an evolution of soil handling and excavating equipment. World War II advanced mechanized equipment phenomenally. The Nazis invaded neighboring nations with “blitzkrieg” (lightning strike) mechanized artillery. Horse-drawn artillery was suddenly obsolete. Steam engines were replaced by diesels. Steam shovels were replaced by backhoes. Mule-drawn scrapers and fresnos were replaced by graders, bulldozers, carry-all loaders, and gigantic dump trucks. The grade-all was developed for shaping cuts and fills. Major contributions were the remarkable inventions of R. G. LeTourneau (Fig. E-7). Legend has it that LeTourneau sought inspiration from on high in his conference room, where a conference table was surrounded by 12 empty chairs with a pad of paper and pencil at each place. In this

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Figure E-7. R. G. LeTourneau, Author of Mover of Men and Mountains. Courtesy of LeTourneau University, used with permission.

sanctuary, Bob paced around the table. When a revelation descended, he would drop onto the nearest chair and make notes. From his autobiography, Mover of Men and Mountains, we discover his story of road construction equipment. The beginning of men moving mountains was in 1885 in California, where the first “tractor” was built. It was a steam engine that had largedrive wheels with cleats on them. Diesel power soon replaced the boilerfired steam engine. One of these monsters could do the work of 100 mules. But in poor soil, the cleated wheels would spin and dig down under the weight of the tractor. In a rain-soaked field, Benjamin Holt was watching one of his tractors, when the wheels started to spin and quickly dug down to the axles. In a flash of inspiration, he remembered treadmills—treadmills?—on which a horse would plod to turn the gears that ground the corn. Why couldn’t a tractor, riding on a treadmill, spread the weight of the tractor on the soggy ground? It was a winner. The result was the new 1905 model “tractor-on-a track” that crawled along over mud like a “caterpillar.” “Caterpillars” suddenly appeared everywhere. Mules became dog food. Then Europe became embroiled in World War I. The British Ministry, knowing about the “caterpillar,” proceeded to armor-plate tractors and

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mount cannons on them. They called the monster a “tank.” Quoting LeTourneau: It wallowed through water-filled shell holes and crashed over sand bags to straddle German trenches. It knocked down stone walls and trees, crushed machine gun nests, and blew up ammunition dumps.

LeTourneau’s story is wild, but there was little doubt as to the earthmoving possibilities for tracked “tractors.” The fresno was invented in Fresno. It was simply a big scoop shovel pulled by mules. The scoop shovel was 3 ft wide for a two-mule team and 5 ft wide for a four-mule team. The operator, walking behind, manipulated the handle of the scoop shovel by raising it to load and then by lowering it to drag the load. It was risky. Mule skinners reported gory accidents when the fresno hit a rock and flipped the operator up over the load. The fearsome handle was eliminated in 1915 by a scraper with a blade that could be raised and lowered by electric motors. The operator rode on the scraper. The scraper was pulled by a “caterpillar.” Coordination of the operators was troublesome—all of that hollering back and forth. So, LeTourneau came up with the idea of a fully mechanized scraper mounted on a tractor and controlled by a single operator who could control the scraper by pushing buttons and levers. And LeTourneau expanded the scoop shovel into a box-shaped bucket with high sides that could handle larger quantities of soil. And he powered the tractor wheels with electric motors that smoothed out the pulling force. The demand for moving large quantities of earth resulted in scrapers that were bigger and faster and with a front panel on the bucket that could be dropped into place to prevent soil from spilling out during hauling. Speed was increased by lifting the bucket after it was loaded so it was not dragging and by replacing tracks with high-speed rubber tires. This became the Tournapull in 1937 (Fig. E-8). It was the carry-all “mover of mountains.” In his autobiography, LeTourneau describes the bombing of Hickam Field during the attack on Pearl Harbor. The objective of the bombing was to destroy U.S. air power in the Pacific. Quoting the ever-exuberant LeTourneau: Yet minutes after the attack, out lumbered a weird assortment of earthmoving machines, neglected by the enemy as a worthless target. Scrapers powered by Tournapulls filled in the bomb craters on the runways and aprons, packing and spreading the dirt so swiftly that the planes that had gone into the air to challenge the attackers were able to return to their own base.

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Figure E-8. The Tournapull—One of LeTourneau’s Inventions—Became the Carry-All Loader.

Figure E-9. Carry-All Loaders during World-War II—on the Burma Road and the Alcan Highway. During World War II, earth-moving equipment was essential in construction of the Burma Road and the Alcan Highway in 1942 (Fig. E-9.) And since then, earth-moving equipment has revolutionized construction of highways and airfields, and mines, and dams, and railways. Excavation equipment has made practical the installation of buried pipes, culverts and tanks, and underground subways and traffic tunnels. Excavation can-do makes possible underground homes, office complexes, and shopping malls. President Eisenhower’s highway project of 1956 was conceived on the basis of culvert and drainage know-how and earth-handling know-how. The can-do was returning servicemen and American citizens of the “Greatest Generation,” who provided a disciplined, well-trained, and determined can-do work force. The interstate highway system was born. The miracle of birth of the interstate highway system occurred in 1956. Could our nation now give birth to such a miracle? The future may, or may not, need another interstate highway system, but how about alternatives such as railways, subways, and buried pipes? The cost of transportation decreases from airways, to highways, to railways, to ships, and into

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pipes. The opportunities for innovation are unlimited if the know-how is not expropriated and if the can-do is not squandered. American know-how and can-do can lead out toward a better world. But we can grasp the future about as far ahead as our memory of the past. Before the memory fades, let us remember the interstate highway project of 1956 and the power of know-how and can-do.

PIPE WELDING The equipment for forming pipes from coils of sheet steel could not have happened except for advances in welding of seams and joints. So, to the story of welding. Welding started in pressure vessels designed for steam engines. The first steam engine boilers were riveted. But rivets leaked at high pressures. Welding promised a leak-proof remedy. Temperatures were hot, pressures were enormous, and failures were catastrophic. Pressure vessel codes were conservative. Welding in pipes and tanks was more recent. So, it was inevitable that welding standards for buried tanks and pipes would have been influenced by the older pressure vessel codes. But there are significant differences between high-pressure vessels and pipes for successful transmission and distribution of water to 280 million people and buried tanks, like a million tanks buried under service stations in the United States. Successful lap-welded tanks and pipes provide a large pool of information on the performance and performance limits of lap welds (Fig. E-10).

Figure E-10. Single-Welded Lap Joint (Fillet Weld): Outside Weld (Top) and Inside Weld (Bottom). Double-Welded Lap Joint Is Both Combined.

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Single-welded lap welds are adequate in general. Double-lap welds are roughly 10 percent stronger. Before World War I, pressure vessels were riveted and leaked at high pressures. Welding was a novelty that showed promise for sealing leaks, but only if the strength of the weld was adequate. The authors of the ASME pressure vessel code reluctantly allowed welding, but only with large safety factors. From successful field experience, the American Petroleum Institute prepared a code with less restrictive safety factors. In 1934 a joint API–ASME committee adopted a modified code, but controversy continued until 1951 when pressure codes merged into a single code, which by 1968 became ASME Rules for Construction of Pressure Vessels. Example For Fig. E-11, what is the minimum wall thickness of a pressure vessel with a welded joggle joint? From the pressure vessel code, an example of the ASME formula for wall thickness is t = PD/(2SE + 1.8P) where t = wall thickness; P = pressure = 100 psi; D = diameter = 48 in.; S = allowable stress = 21 ksi; E = weld efficiency = 55%. Substituting values, wall thickness is t = 0.208 in. Longitudinal stress is PD/4t = 5.82 ksi. But yield strength is 42 ksi. The safety factor is strength/stress = 7.2. Writers of the pressure vessel code were cautious because of many infamous boiler explosions at high pressures. But for buried tanks and pipes containing liquids (not steam) and with low pressure (like 100 psi), the pressure vessel formula is overly conservative. And hoop stress is more critical than longitudinal stress on welded joints. Moreover, the pressure vessel code is based on forces parallel to the weld. In lap-welded joints, the force is perpendicular to the weld. From tests and from analytical theories, the perpendicular weld is 1.5 times as strong as the parallel weld (Fig. E-12).

Figure E-11. Joggle Joint for Pressure Vessels.

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Figure E-12. Relationship of Direction of Forces to the Direction of Fillet Welds on Lap-Welded Joints. From tests of full pipe sections, longitudinal strength of the singlewelded lap joint is 75% as strong as the cylinder wall. Longitudinal stress is usually no greater than half of the hoop stress.

FIELD EXPERIENCES THAT MADE HISTORY Experiences from the field have made history. A typical example is leaks in welds in buried gasoline storage tanks owned by the Church Universal and Triumphant located in Montana. Elizabeth Clare Prophet was the charismatic leader of the church. Wealthy widows had been converted under the assurance of resurrection in the lap of the Lord if they would consecrate all of their worldly wealth to the church. Then came the prediction from on high that the “great and dreadful day of the Lord” was coming soon. The elect would be saved, and the earth would be cleansed by fire. It was essential that the “elect” protect themselves against the onslaught of frenzied infidels who would attempt to invade the enclave of the elect on that terrible day. The remedy for the elect was to arm themselves and to go underground. They purchased a beautiful canyon, Mol Heron Creek, from Randolph Hearst on the boundary of Yellowstone Park. There they buried steel pipes, 14 ft in diameter which, like submarines, were fitted to sustain the lives of 1,200 of the most elect. But they needed fuel. They purchased 35 steel tanks, 9 ft in diameter and 42 ft long, for storage of fuel—oil for heat and gasoline for power. The tanks were to be buried uphill from the living units. That was late in the fall of 1990. Excavation for the tanks was proceeding in partially frozen soil. Then came the Word of the Lord. His coming was to be in April of the following spring (1991). Burial and filling of tanks suddenly became urgent. Backfill soil was bulldozed over the tanks with no attempt to compact the soil. Early in the spring, a fisherman on the Yellowstone River, near the confluence of Mol Heron Creek, smelled gasoline. He reported to the Montana state officials. The church was ordered to remove the tanks.

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The Prophet was instructed by the Lord to seek compensation for replacement by suing the tank manufacturer. This required a determination of the cause of the leaks. As the loose soil (much of it frozen) began to thaw in the spring, the backfill soil settled and dragged down the tanks. The tanks squatted. Flat spots developed on the bottoms. The flattened welds opened and leaked. Some of what has been learned from the history of tank and pipe leaks is the need for care in backfilling. The pipe or tank must be held in shape. During installation, “It’s the soil, stupid.” In St. Louis, circa 1970, a 6-ft-diameter buried steel water pipe burst. The result was a geyser that blew open a 100-ft-diameter crater. Water supply was out of service for much of the city. The pipe was designed for test pressures of 150 psi. The design was precise and correct. Explanations were in demand. The failure occurred on Christmas Eve during a television commercial when everybody ran to the bathroom, flushed the toilet, and took a drink of water. Suddenly water flow was enormous. Then everybody shut off the water. The result was a water hammer in the pipeline that developed a pressure many times greater than the 150-psi design pressure. And so, from history, the precision of structural analysis is questioned. Design for strength of materials may be precise to three significant figures, but assumed pressure may not be as precise; neither is the soil pressure, the deformations of the pipe, or the dynamics, but we are learning. We are still making history, all of which portends an expanding future for buried steel pipes and tanks. Let us pay attention to the history in order to plan well for the future.

APPENDIX F RING ANALYSIS

Pipe ring stresses and deformations are functions of pressure patterns. The ring under nonuniform pressure is statically indeterminate. Therefore, both equations of static equilibrium and equations of deformations are required for analysis. Deformations are analyzed by applying a “dummy” force (or dummy bending moment). This dummy does virtual work as it moves during deformation of the ring. For ring analysis, the most useful equation was derived by Castigliano. To find relative rotation of point A on the ring with respect to point B, Castigliano’s equation is ψ A B = I ( M EI )(∂ M ∂ m) rdθ where ψA/B = relative rotation of A with respect to B; M = bending moment at a point, C, on the ring; E = modulus of elasticity of the pipe material; I = moment of inertia of pipe wall cross section per unit length of pipe = t3/12 for plain pipe; r = radius of the circular pipe to neutral surface of the wall; dθ = infinitesimal angle of the pipe; m = “dummy” moment at point A, in direction of relative rotation, ψA/B, of A with respect to B. B is assumed to be fixed. Example 1 What is the rotation of A with respect to B for the quadrant of a pipe in Fig. F-1? EI is constant. F is force per unit length of the pipe.

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Figure F-1. Quadrant of Circle Loaded by Force, F, from Which Relative Rotation of A with Respect to B Is to Be Found.

At point C, M = Frcosθ + m, where m approaches zero. ∂M/∂m = 1. Substituting, ΨA/B = (Fr2/EI)∫cosθdθ = (Fr2/EI)sinθ from θ = 0 to θ = 90° ΨA/B = Fr2/ EI. The dimensionless rotation is in radians. Example 1 demonstrates application of the Castigliano equation. More appropriate for pipe analysis is the use of the equation when relative rotation of A with respect to B is zero. Also more useful is the linear deflection of A with respect to B, either horizontal or vertical. Instead of a dummy bending moment, m, a dummy, p, in the direction of deflection is applied. This is demonstrated in the following example. Example 2 What is the vertical deflection of point A under the force, F? (See Fig. F-2.) y A B = ∫ ( M EI )(∂ M ∂ p ) rdθ where p = “dummy” force at point A in direction of the relative displacement, yA/B, of A with respect to B. At point C, M = (F + p)rcosθ, where p approaches zero. ∂M/∂p = rcosθ. Substituting, yA/B = (Fr3/EI) ∫cos2θ dθ = (Fr3/EI)[θ/2 + (sin2θ)/4] from θ = 0 to θ = 90°.

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Figure F-2. Quadrant of Circle with a Force, F, from Which the Vertical Deflection of A with Respect to B Is to Be Found. y A B = πFr 3 4EI It is noteworthy that the quadrant of a circle analyzed above is statically determinate. Bending moment at B is MB = Fr. From static equilibrium at B, thrust T = F, and shearing force V = 0. Example 3 A pipe is subjected to parallel plate load, F (Fig. F-3). It is statically indeterminate. The pipe ring is symmetrical about both the vertical and horizontal axes. One quadrant is the smallest repeating section. There are six forces, three at A and three at B. Known (by symmetry of adjacent quadrants): VA = 0 and VB = 0. F is given. Unknowns (four): MA, TA, MB, and TB. Equations of equilibrium (three):

[SFx = 0]

TA = 0 TB = F 2 [SM = 0 ] MB = M A − Fr 2

[SFy = 0]

Equation of deformation (fourth): ΨA/B = 0, rotation of A with respect to B. Four equations are needed to solve. From Castigliano, add dummy, m, in the direction of rotation.

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Figure F-3. Stress Analysis of Pipe Ring Subjected to a Parallel Plate Load, F.

ψ A B = ∫ ( M EI )(∂ M ∂ m ) rdθ = 0 At C, M = MA + m − (F/2)r(sinθ). ∂M/∂m = 1 when m → 0. Substituting and integrating from limits of θ = 0 to θ = π/2, MA = Fr/π. With MA, VA, and TA known, stresses anywhere in the ring can be found. Once MA is known, the Castigliano equation for vertical deflection can be used for finding the ring deflection δ = δ/D. The procedure is the same as presented above for the circular quadrant. Some of the more common analyses of stresses and deflections are listed in tables and texts on ring analysis. See, for example, Roark’s Formulas for Stress and Strain. It is noteworthy that Castigliano analyses above are based on bending moment in the pipe ring. The effects of shear and thrust in the pipe wall are neglected. In fact, the Castigliano equation is based on the method of

APPENDIX F

181

Figure F-4. Flowable Fill Bedding under Flexible Pipe with Soil Pressure (on Top). Side Support of the Pipe by Embedment Is Neglected for Worst-Case Assumptions. virtual work for which the variables are scalar. Therefore, if shear and thrust are significant, they can be included in the Castigliano equations just by adding them in. The effects of shear and thrust on the deflection of pipes are negligible in virtually all steel pipe analyses. Example 4 Flowable fill: What are the ring analyses for pipe subjected to vertical pressure, P, but supported by flowable fill? (See Fig. F-4.) Flowable fill is soil–cement grout that flows under the pipe and becomes a uniform bedding. Uniform bedding prevents differential settlement of adjoining pipes and fracture of welded joints and pipe bells. Portland cement (or fly ash) is added to improve flowability and to add strength. Advantages of flowable fill include the following: 1. 2. 3. 4.

The need to level and compact bedding is avoided or ameliorated. Native soil can be used rather than imported select soil. Multifunctional trenching and installing techniques are facilitated. Trenches can be narrow. Tunnels need to be only slightly larger in diameter than the pipe. 5. Flowable fill helps to protect the pipe in the event of future excavations. Flowable fill must be fluid enough to flow under the pipe, strong enough to hold the pipe in shape, and noncompressible enough to prevent

182

BURIED FLEXIBLE STEEL PIPE

ring deformation. A slump of 10 in. on a flow table of 12-in. diameter is recommended by some users. If flowable fill is used as side-fill embedment, it must not compress or shrink vertically more than the allowable ring deflection of the pipe. Ring deflection is roughly equal to vertical compression of side fill. Flowable fill must set up in a short period of time so that pipe installation is not hampered by delay of backfilling. Strength should be low. Only a small amount of Portland cement is needed if the native soil has enough fines to make the slurry flowable. Low strength facilitates future excavation. If the pipe deflects longitudinally, lowstrength flowable fill fractures in multiple cracks. When high-strength encasement fractures, cracks are few, but stresses are concentrated at potential fracture points on the pipe. Suggested strengths of flowable fill are within a range of 40 to 100 psi in unconfined compression tests. Installers must prevent the pipe from floating when flowable fill flows under it. Much of the native soil in the world has fines in it. Fines are silt and clay. Flowable fill does not require select, concrete-quality aggregate. As much as 60% silt in sandy native soil with one sack of Portland cement per cubic yard of soil cement has been used successfully. Trenches can be narrow. Tunnels can be just slightly larger in diameter than the pipe. Notation. α = angle of flowable fill; r = radius of the ring; P = vertical pressure; E = modulus of elasticity of pipe; I = moment of inertia of wall; MA = moment in wall at A (comparable outside surface); d = ring deflection = yA/D. For pipe designers of flexible pipe with flowable fill bedding, from Castigliano analyses, the following table shows approximately the effect of the angle, α, of flowable fill on the ring. The ratios show decreases due to increasing angle, α, on moment, MA, and deflection, d, when compared to moment and deflection, α = 0. The values of increasing α are significant. Ratios α (°)

MA/Pr

d(EI/Pr3)

0 30 60 90

0.299 0.195 0.112 0.047

0.116 0.040 0.015 0.0034

σ

d

1.0 0.7 0.4 0.2

1.00 0.34 0.13 0.03

APPENDIX F

183

Figure F-5. Bending Moment at A as a Function of α.

Figure F-6. Ring Deflection as a Function of Angle α.

From symmetry of ring quadrants, shearing force at A is VA = 0. Stress at A is σ = MA/(I/c), where I/c = t2/6 for plain pipe. Ring deflection is d = yA/D. Figure F-5 is a plot of bending moment, MA, in the ring as a function of angle, α. Noteworthy is the reduction in bending moment, MA, as the angle of flowable fill, α, increases. Figure F-6 is a plot showing the decrease in ring deflection, d (shown as δ), as the angle of flowable fill, α, increases.

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APPENDIX G IMPACT FACTORS IN SOIL

Impact factor is the ratio of a dynamic impact force to its static weight. The static weight is usually a surface wheel load. The dynamic impact force is the maximum vertical force felt by the soil when the wheel is dropped from a given height. Some departments of transportation design roads and bridges with a very conservative impact factor of 2.0. Others make rational designs using published tables and design specifications. The following example shows the rationale for using a factor of 2.0 (Fig. G-1.)

EXAMPLE What is the impact factor for a tire wheel dropped from a height of first contact of tire to surface? F = impact force, W = wheel weight, y = height of drop, impact factor = F/W. According to the principle of conservation of energy, the work of the dropped weight equals the energy transferred to the tire. From Fig. G-1, Wy = Fy 2 where F W = impact factor = 2 If the drop is from some height, z, greater than drop y from first contact with the ground surface, the work of the dropped weight must include Wz. Work = W(y + z), and F = 2W(y + z)/y. 185

186

BURIED FLEXIBLE STEEL PIPE

Figure G-1. Sketch of Impact Force of a Surface Wheel Load.

Figure G-2. Distribution of Vertical Stresses, σ, (After Boussinesq) under a 16 kip/ft Line Load at Depth of H = 1 ft and H = 2 ft. The Line Load Is Reasonable Because of Wheels on Axles and Vehicles Crossing in Parallel. At a Depth of 4 ft Directly Below the Wheel Load, W, σ = 0.477 ksf.

For buried steel pipe, the impact factor is the ratio of dynamic force, F, to static surface load, W. The vertical pressure on a buried pipe may be obtained from Boussinesq analysis (Fig. G-2) of vertical stress at pipe depth, H, using the surface line load, F = W times the impact factor. Accordingly, at depth, H, vertical soil stress is σ = F/2H2 where F = W times the impact factor. The value of the impact factor is based on field experience. Impact factors are published by the American Association of State Highway Transportation Officials (AASHTO), the American Railway

APPENDIX G

187

Engineering Association (AREA), the American Society for Testing and Materials (ASTM), and the Federal Aviation Administration (FAA). Height of Cover (ft)

0 to 1 1 to 2 2 to 3 Over 3′ a b

Highways

Railways

Runways

1.50 1.35 1.15 1.00

1.75

1.00 1.00 1.00 1.00

a a a

Taxiways, Aprons, Hardstands, Run-Up Pads

1.50 b b b

Refer to data available from American Railway Engineering Association (AREA). Refer to data available from Federal Aviation Administration (FAA).

R/H N

0.0 0.477

0.1 0.465

0.3 0.385

0.6 0.221

1.0 0.084

1.5 0.025

2.0 0.008

2.5 0.003

3.0 0.0015

For impact analysis, the worst case occurs when load, W, crosses the pipe (R = 0 in Fig. G-2). Accordingly, N = 0.477 or, conservatively, N = 1/2, and σ = F/2H2, where F = W times the impact factor. σ is the vertical stress on top of the pipe. An impact factor of 2 is conservative. Impact is mitigated by paving on the surface, by low vehicle speeds, and by a smooth, level surface. Installers can mitigate the concern for impact by requiring any minimum cover crossing to have a sign that reads, “Cross slowly and carefully.”

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GLOSSARY

Active soil pressure: ka = σx. Autogenous healing: The formation of calcium carbonate in cracks in cement mortar lining, resulting in sound, continuous material. Backfill: Compacted material placed from the top of the embedment to the soil grade. Bedding: A layer of uncompacted material placed in the bottom of the trench, on which the pipe is laid. CMC: Cement mortar coating. CML: Cement mortar lining. Cohesive soil: A sticky soil, such as clay or silt; its shear strength equals about half its unconfined compressive strength. Cohesionless soil: A soil that when unconfined has no significant cohesion when submerged and no significant strength when air-dried, such as sand. Controlled low-strength material (CLSM): See flowable fill. Crown: The point of highest flow line in a given pipe cross section. D-load: The three-edge bearing load at failure for reinforced concrete pipe. Depth of cover: The distance from soil grade to the top of the pipe. Depth of pipe trench: The distance from soil grade to unexcavated, bottom-of-trench material. Embedment: Compacted material extending vertically from the bottom of the pipe for some predetermined distance—typically to 1 ft over the top of the pipe. Equilibrium: Pr is constant around the circumference of a pipe (Pxrx = Pyry).

189

190

BURIED FLEXIBLE STEEL PIPE

Flowable fill: A mixture of soil, water, and cementitious material used to fill the pipe zone as an alternate to bedding and compacted embedment. It is also called soil–cement slurry or controlled low-strength material (CLSM). Haunch: The region under a pipe extending from the bedding to the springline of the pipe. Hoop stress: σP = PDO/(2ts), circumferential stress in a material of cylindrical form subjected to internal pressure. – = σ − u, total vertical stress minus pore water Intergranular soil stress: σ pressure. Invert: The point of lowest flow line in a given pipe cross section. Liquefaction: The transformation of a soil from a stable state to a flowable state. Marston load: Theory of earth loads on rigid pipe, developed by Anston Marston in the early 1900s. Performance limit: Set criteria to which a design value must conform. Pipe zone: The region of the trench that encompasses both the bedding and embedment. Pore water pressure: u = hγw. Radius of curvature: r = DO/2 for a circular cylinder. Radius of curvature: r = L2/8e for an out-of-round cylinder (see Fig. 3-5). Ring compression stress: σ = P(DO)/2ts, wall stress in a perfectly circular pipe. Ring deflection (percent): d = ∆/D = (Dx − Dy)/(Dx + Dy) (see Fig. 3-6). Side fill: The region of embedment located between the pipe and the trench wall. Soil arching: The ability for soil to be self supporting, it reduces the effective load on pipe. Soil compression: εs, soil strain due to an applied stress (see Fig. 4-8). Soil friction angle: φ, roughly the steepest angle of repose (slope) of a windrow of cohesionless soil. Soil stiffness: E′, secant modulus, slope of soil stress–strain diagram (see Fig. 4-8). Soil void ratio: e, ratio of volume of voids to volume of soil grains (see Fig. 4-1). Springline: The point on the physical pipe cylinder, inside or outside, that is level with the centerline of a given pipe cross section. Unit weight—buoyant: Weight of material reduced by weight of water displaced by soil. Unit weight—dry: Weight of dry soil per unit of total volume. Unit weight—saturated: Weight of saturated soil per unit of total volume. Unit weight—total: Weight of soil and water per unit of total volume.

BIBLIOGRAPHY

Contributors. Contributors to the design of buried flexible steel pipe include the following: American Iron and Steel Institute (AISI) sponsored research, including full-scale tests, at universities and state departments of transportation and published papers and manuals on buried steel pipe. American Water Works Association (AWWA) contributed standards for good practice. Cates, Walter H., a civil engineer, was a major influence on cooperative efforts to improve the design of buried pipe. Katona, Michael, Ph.D., was one of the first to develop a program for finite element analysis. His CANDE program is still in use with modifications. Other finite element analysis programs are now available. Numerous researchers from the University of California, New York (Albany), Northwestern University, the University of Ohio, Sacramento State University, Utah State University, and others, recognized the need for design of buried flexible pipe. With computers, finite element analysis has become a contribution to design and analysis. Steel Plate Fabricators Association (SPFA), with funding from AISI and pipe manufacturers, presented seminars throughout USA the United States and Canada on the design of buried steel pipe. Transportation Research Board (TRB) sponsored conferences and published papers on pipes required for highway and airfield construction. Tupac, George, retired from U.S. Steel, was chairman of committees to write and upgrade manuals for steel pipe. Such manuals include AWWA Manual M11, and AISI manuals on welded steel water pipe and buried steel penstocks. 191

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U.S. Bureau of Reclamation (USBR) developed testing facilities in Colorado and monitored installation and performance of numerous USBR pipelines. Results were published. White, Howard, an engineer with Armco Company, noted the findings of full-scale tests and proposed the ring compression procedure for analysis of external soil pressure on steel pipe.

REFERENCES American Association of State Highway and Transportation Officials (AASHTO). (2004). “Standard method of test for moisture–density relations of soils using a 4.54-kg (10-lb) rammer and a 457-mm (18-in.) drop,” American Association of State Highway and Transportation Officials, Washington, D.C., T180. American Iron and Steel Institute (AISI). (1992). Buried steel penstocks, American Iron and Steel Institute, Pittsburgh, Pa. American Iron and Steel Institute (AISI). (2007). Welded steel water pipe, American Iron and Steel Institute, Pittsburgh, Pa. American Lifelines Alliance. (2005). Seismic guidelines for water pipelines, (June 17, 2009). API–ASME. (1968). ASME Section VIII, Division I, Rules for construction of pressure vessels, American Petroleum Institute and American Society of Mechanical Engineers, New York. American Society of Civil Engineers (ASCE). (1993). Steel penstocks, ASCE Manuals and Reports on Engineering Practice No. 79, ASCE, New York. ASCE. (1984). Guidelines for the seismic design of oil and gas pipeline systems, ASCE, New York. American Society of Mechanical Engineers (ASME). (2007) ASME boiler and pressure vessel code, ASME, New York. ASME. (1968). Rules for construction of pressure vessels, ASME, New York. ASME. (2006). Companion guide to the ASME boiler and pressure vessel code, 2nd ed., K. R. Rao, ed., ASME, New York. ASME. (2006). Guidebook for the design of ASME Section VIII pressure vessels, 3rd ed., ASME, New York. American Water Works Association (AWWA). (2005) Field welding of steel water pipe, Standard C206. AWWA, Denver, Colo. AWWA. (2004). Steel water pipe: A guide for design and intallation, 4th ed., Manual M11, AWWA, Denver, Colo. Brockenbrough, Roger L. (1990). “Strength of bell-and-spigot joints,” J. Struct. Engrg., 116(7), 1983–1991. Brush, D. O., and Almroth, B. O. (1975). Buckling of bars, plates, and shells, McGraw-Hill, New York.

REFERENCES

193

Cates, Walter H. (1971). History of steel water pipe: Its fabrication and design development. Available at (June 17, 2009). Comité Européen de Normalization. (1998). “Silos, tanks and pipelines,” Eurocode 8, Part 4, Annex A, Comité Européen de Normalization, Brussels, CEN ENV–1998–4. Dunlop, C. A. (1939). “Trends and developments in API Pipe Standard.” American Petroleum Institute. Dunn, I. S., Anderson, L. R., and Kiefer, F. W. (1980). Fundamentals of geotechnical analysis, Wiley and Sons, New York. LeTourneau, R. G. (1967). Mover of Men and Mountains, Moody Publishers, Chicago. Montel, R. (1960). “Formule semi-empirique pour la détermination de la pression extérieure limite d’instabilité des conduits métalliques lisses noyées dans du béton.” La Houille Blanche 5, 560–568. Spangler, M. G. (1941). “The structural design of flexible pipe culverts,” Bulletin 153, Iowa State College, Ames. Taylor, D. W. (1948). Fundamentals of soil mechanics, Wiley, New York. Vasilikis, D., and Karamanos, S. A. (2008). “Buckling of unconfined and confined thin-walled steel cylinders under external pressure,” Pipelines 2008: Maximizing performance of our pipeline infrastructure, S. Gokhale and S. Rahman, eds., ASCE, Reston, Va., 1–10. Watkins, R. K. (1965). Report on parallel plate tests on mortar lined and coated steel pipe, for Smith-Scott Company of California. Watkins, R. K., and Spangler, M. G. (1958). “Some characteristics of the modulus of passive resistance of soil—A study in similitude,” Proc. of the Highway Research Board, Highway Research Board, Washington, D.C. Young, W. C. (1989). Roark’s formulas for stress and strain, 6th ed., McGrawHill, Dallas, Texas.

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INDEX

Abdel-Motaleb, I. M., 52 American Petroleum Institute, 6, 174 American Society of Civil Engineers (ASCE), 101, 102 American Society of Mechanical Engineers (ASME), 6, 101, 102 ancient China, 165 ancient Greece, 1–2, 165 ancient Rome, 2, 166 aqueducts, 1–2 Armco Company, 7, 168 ASME Boiler and Pressure Vessel Code, 6 automatic electric welding, 6 AWWA Standard C206–03, 102 backpacking, 46, 47 beam action, longitudinal stresses due to, 104–109 bending moment, 143, 144, 146, 147 bending stress, 101–102, 107, 108 bents: analyses for, 111–115, 118; assumptions for installation conditions, 111; example of, 115– 117; explanation of, 110–111 Bessemer process, 3, 4, 166, 167 boiler code, for high-pressure, hightemperature welded joints, 6 Boussinesq method, 90, 92 Brazier’s equation, 107, 108 buoyant unit weight of soil, 35, 36, 47, 48 buried flexible pipe: on bents, 110–118; in common trenches, 87–94; design

of, 7–12; finite element analysis method and, 50–54; historical background of, 1–3; longitudinal forces affecting, 99–110; ring deflection of, vii–viii, 56–60; ring deformation failure of, 61–65; soil compression and, 45; structural performance of, 55. See also design analysis scenarios butt welds, 6 CANDE (Cuvert ANalysis and DEsign) program, 50 Castigliano’s equation, 58, 114, 177, 178, 180–181 Castigliano’s theorem, 58, 114 caterpillar, 170–1711 Cates, Walter, 166 cave-ins, 131. See also soil slip cement mortar coatings, 28–30 cement mortar linings, 28–30 Church Universal and Triumphant (Montana), 175–176 clay pipe, 3 constants, 20 corrosion, 11 crack width, 28–30, 168 dead load stress, vertical, 37 deformation: analysis of, 177; in encased pipe, 153; pipe mechanics and, 23; results of excessive, 35; ring stiffness and, 67

195

196

INDEX

design analysis scenarios: internal pressure and handling, 74–75; overview of, 73–74; pipe stiffness to prevent collapse, 85–86; ring stability, 5–77; ring stability at given depth with partial vacuum, 82–84; ring stability with vacuum, 77–79; ring stability with vacuum and water table above pipe, 80–82 D-load test, 164 dry unit weight of soil, 35, 36 ductile hinge, 67 dummy bending moment, 177 E’: correction of, 8; explanation of, 8; in Modified Iowa Formula, vii–viii; use of, viii earth-moving equipment, 169–173 earthquakes, 48, 118, 120–122. See also seismic hazards Eisenhower, Dwight, 162–164, 172 elastic yield stress, 67 electric welding, 6 embedment: explanation of, 46, 94; fluid, 149–153; pipe under soil, 157– 159; select fill and, 47 encased pipe, 123, 153–157 Eupalinos, 2 Eupalinos aqueduct (Samos), 1–2 external fluid pressure: effects of, 149; fluid embedment and, 149–153; issues related to, 159; pipe encased in concrete and, 153–157; pipe under soil embedment and, 157–159 fault crossing, 121122 Federal Aid Highway Act (1956), 162, 164, 172 Federal Highway Administration (FHWA), 50 field test pressure design, 75 fines, 182 finite element analysis: explanation of, 50–51; geometric nonlinearity and, 53; interface elements and, 53; limitations in use of, 52; pipe elements and, 53; software for, 52, 141, 142, 147; stress- and strain-

dependent soil properties and, 52–53; two-dimensional plane strain, 141–148; value of, 54, 55 flexible pipe: deflection of, 8–9; development of, 7–8, 168; explanation of, viii; external fluid pressure on, 149–159; steel, viii flotation, minimum cover and, 69–71 flowable fill, 98–99, 181–182 fluid embedment, 149–153 fluid pressure. See external fluid pressure Formulas for Stress and Stain (Roark), 180 fresno, 171 frost, minimum cover and, 72 geotextile trench liners, 98 ghanats, 1, 165 ground shaking, 120 helical seam welding, 6 Highway Research Board, 164 highway technology, 163–164 History of Steel Water Pipe (Cates), 4, 166–167 hoop stress: explanation of, 23–25, 101; formula for, 24, 74–75 horizontal pipe expansion, 9 hydrostatic pressure, pipe collapse under, 60 impact factors: explanation of, 185– 186; publication of, 186–187 intergranular stress, 37–38 internal pressure, 23–25, 74–75 Inverted Terzaghi Model for uplift force, 72 Iowa Formula: application of, ix, 129– 130; development of, 8, 127; explanation of, 127–129; modified, vii–viii, 162; rewritten for vertical ring deflection, 9–10 Iowa State College, 8 iron pipe: historical background of, 3, 166–168; manufacture of wrought, 4 joints, welded, 6

INDEX landslides, 119–120, 131. See also soil slip lap joints, 6 lap welds, 6 lateral spreading, 119 LeTourneau, R. G., 169–171 liquefaction: conditions for, 47, 48; explanation of, 119 live load: on approach to pipe, 90–91; directly above pipe, 90, 92; vertical, 36–37 Lock-bar pipe, 167 lock-bar pipe, 4–6 longitudinal forces: beam action and, 104–109; explanation of, 99–101; longitudinal pipe-soil movement and, 109–110; temperature and pressure change and, 102–104 longitudinal sag equation, 107 Marston, Anson, 7, 10, 162–165, 168 Marston load, 78, 167 maximum allowable ring deflection, 10 maximum negative pressure, 61–62 minimum cover: analysis of, 65; flotation and, 69–71; frost and, 72; uplift and, 71–72; wheel loads and, 65–69 minimum thickness for handling, 25–26, 75 minimum trench separation, 96. See also trenches Modified Iowa Formula, vii–viii, 162 modulus of elasticity, 59, 60 Mohr, Otto, 131 Mohr-Coulomb failure envelope, 141 Mohr stress circle, 39, 118, 131–136, 138 Montel, R., 154 Montel’s collapse pressure, 158 Montel’s equation, 157, 159 Mover of Men and Mountains (LeTourneau), 170 Newmark integration, 90, 92 nomenclature, 15–20

197

partial vacuum pressure, 82–84 passive resistance, 42 Peisistratos, 2 penetrometers, 49 permafrost, 72 Persia, 165, 166 pipe: clay, 3; cracks in, 28–30; encased, 123, 153–157; function of, ix; historical background of, 1–3, 165– 168; internal pressure design and, 23–25; iron, 3; minimum thickness for cylinder of, 25–26; parallel, in common trench, 87–94; pioneers in development of, 7–12; plastic, 169; pressure at collapse of, 60; radius of, 29, 30; rigid, viii, 7, 168; ring stability with water table above, 80–82; yield stress of, 31–32. See also buried flexible pipe; specific types of pipe pipe bending moment, 143, 144, 146, 147 pipe design: contributors to, 12–13; pioneers in, 7–12 pipe mechanics: deformation and, 23; elements of, 23; internal pressure design and, 23–25; minimum thickness for handling and, 25–26; performance limits of cement mortar linings and cement mortar coatings and, 28–30; ring compression and, 27, 28; ring deflection and, 31; ring stiffness and, 26–27; yield stress and, 31–32 pipe-soil interaction: deformation and, 23; elastic theories and, 34–35; hydrostatic collapse in fluid environment and, 60; longitudinal stress and, 109–110; minimum cover and, 65–72; overview of, 55; performance limits for, 49; ring deflection and, 56–60; ring deformation failure of buried flexible pipe and, 61–65 pipe stiffness: explanation of, 26–27; to prevent collapse, 85–86; ring deflection and, 58 pipe uplift, 71–72

198

INDEX

plastic pipe, 169 PLAXIS 7.2, 141, 142, 147 Poisson’s effect stress, 101, 103 Poisson’s ratio, 150 pressure vessel code, 174 pressure waves, 48 primary stress, 101 Prophet, Elizabeth Clare, 175 quicksand, 47 Renaissance, 2–3, 166 rigid pipe, viii, 7, 168 ring analysis, 177–183 ring buckling, 62–64 ring compression: explanation of, 27; factor of safety and, 28; parallel installations and, 88, 89, 91, 92; at saddle, 113, 114 ring compression design equation, 27 ring deflection: bending stress and, 108; compression and, 27; cracks and, 28, 29; equation to determine critical, 77; explanation of, 31, 38, 159; history of allowable, 10; Iowa Formula and, 9–10, 127–130; longitudinal bend or sag in pipe and, 107; maximum allowable, 10; pipe-soil interaction and, 56–57; prediction of, vii, 8, 56–57, 59; relative effect of pipe and soil on, 58–60; soil slip and, 77; stiffness and, 26; vertical, 9–10, 128 ring deflection ratio, 56 ring flexibility, 27 ring stability: analysis of, 75–77; explanation of, 55; at given depth with partial vacuum, 82–84; with vacuum, 77–79; with vacuum and water table above pipe, 80–82 ring stiffness: explanation of, 26–27; function of, 12; installation and, 55, 60 Rules for Construction of Pressure Vessels (American Society of Mechanical Engineers), 6, 174 Russell, James, 3

saturated unit weight of soil, 35, 36 Schlick, William, 10, 168 secondary stress, 101–102 seismic hazards: assessment of, 120– 121; design recommendations for, 121–122; explanation of, 118–120; standards and guidelines related to, 122–123 seismic waves, 48, 120 select fill, 46–47 shock waves, 47 slurry, 98–99 Smith-Scott Company, 10 soil: cohesion of, 43, 44; developments in handling and excavating, 169– 173; flowable fill, 98–99; impact factors in, 185–187; specifications for, 49–50; stiffness of, 55; strength of, 38–39 soil compression: explanation of, 38, 45–46; measurement of, 49–50 soil conduit, 34 soil filters, 49 soil friction angle, 42, 43 soil landslides, 119–120 soil mechanics: critical soil specifications and, 49–50; deformation and, 23; elastic theories and, 34–35; embedment and, 46; finite element analysis and, 50–54; liquefaction and, 47; notation for, 33–34; passive resistance and, 42–43; quick condition and, 47, 48; select fill and, 46–47; soil cohesion and, 43, 44; soil compression and, 38, 45–46; soil conduit and, 34; soil friction angle and, 42, 43; soil movement and, 48; soil particle size and gradation and, 39–42; soil slip and, 39; soil strength and, 38–39; unit weights of soil and, 35–36; vertical soil pressures and, 36–38, 111 soil particles: migration of, 97–98; size of, 39–42 soil pressure: lateral, 111; vertical, 36–38, 111 soil slip: equation of equilibrium of side fill at, 64; explanation of, x,

INDEX 38–39, 131–133; internal vacuum pressure at, 65; measurement of, 49; at passive resistance, 42; ring stability and, 75–77; safety factor against, 93–94; soil stress model and, 134–139; vacuum pressure and, 77 Spangler, Merlin Grant, vii, 8, 127, 162, 168, 169 springlines: pressure against soil at, 62, 64; strength of soil at, 63 steel pipe: corrosion of, 11; developments in, 10–12, 167, 168; historical background of, 3–4; lockbar, 4–6 steel production, in United States, 6 stiffness, ring, 26–27. See also pipe stiffness stress: bending, 101–102, 107, 108; longitudinal, 99–109; primary, 101; secondary, 101–102 stress analysis. See finite element analysis stress-strain properties, 52–53 stress-strain tests, 49, 50 surface faulting, 118–119 surge pressure design, 75 Taylor, D. W., 111 temperature, longitudinal stress and, 102–104 tidal basins, 48 transient pressure, 24–25 trenches: flowable fill and, 98–99; parallel, 94–96; parallel pipes in

199 common, 87–94; parallel to buried pipe, 141–148; in poor soil, 96–98

Unified Soil Classification, 39–41 uplift load, 71–72 Utah State University, 10, 56, 70, 161 vacuum pressure: partial, 82–84; ring stability and, 77–79; water table above pipe and ring stability with, 80–82 vertical dead load stress, 37 vertical live load stress, 36–37 vertical load, 58, 59 vertical ring deflection, 9–10, 128 vertical ring deflection ratio, 128 vertical soil stress, 92–93 Von Mises compound yield, 32 wall crushing, 60, 61 wall thickness, 74, 75 Watkins, Reynold King, vii, x, 8, 52, 125, 127, 161n welded joints, 6 welded steel pipe: manufacture of, 6, 167, 173–175; structural design of, vii, 23 wheel loads, 65–69 Whitehouse, Cornelius, 3, 166 wood-stave pipe, 3 working pressure design, 75 wrought iron pipe, 4 yield stress evaluation, 31–32

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SI Conversion Table Unit

SI Unit

= 25.4 millimeters (mm) = 4.448 Newtons (N) = 0.454 kilograms (kg) = 47.9 Pascals (Pa) = 6.9 kilopascals (kPa) = 1 meter (m)

1 inch (in.) 1 pound (lb) 1 pound (lb) 1 pound/foot2 (psf) 1 pound/square inch (psi) 3.28 feet (ft)

201