Hydraulics of Stepped Spillways: Proceedings of the International Workshop on Hydraulics of Stepped Spillways, Zurich, Switzerland, 22-24 March 2000 905809135X, 8022763837, 9789058091352

Table of contents :
Cover......Page 1
Half Title......Page 2
Title Page......Page 4
Copyright Page......Page 5
Table of Contents......Page 6
Preface......Page 10
Organization......Page 12
Sponsors......Page 14
Introductory lecture......Page 16
Spillways for high velocities......Page 18
Case studies......Page 26
Field testing of Brushes Clough stepped block spillway......Page 28
The stepped spillway for the Mhlathuzane dam, Swaziland......Page 36
Hydraulic design of Nakasujigawa dam stepped spillway......Page 42
Ashton stepped spillway - Design and construction......Page 50
Aeration characteristics and cavitation risk......Page 58
Stepped spillways, a dissolved gas abatement alternative......Page 60
Scale effects in modelling two-phase stepped spillway flow......Page 68
Air inception in skimming flow regime over stepped spillways......Page 76
Air entrainment and safety against cavitation damage in stepped spillways over RCC dams......Page 84
Air-water flow and gas transfer at aeration cascades: A comparative study of smooth and stepped chutes......Page 92
Energy dissipation......Page 100
Stepped spillway studies at CEDEX......Page 102
Flow resistance in skimming flow: A critical review......Page 110
Dissipation efficiency of stepped spillways......Page 118
Energy dissipation comparison among stepped channel, drop and ramp structures......Page 126
Nappe flow in stepped channels - Occurrence and energy dissipation......Page 134
Internal flow features......Page 142
Backwater and drawdown curves in stepped spillway flow......Page 144
Pressure field in skimming flow over a stepped spillway......Page 152
Characteristics of plunging flows in stepped channel chutes......Page 162
Design......Page 168
The CIRIA guide for the design of stepped-block spillways......Page 170
Guidelines for the hydraulic design of stepped spillways......Page 178
Roller compacted concrete and stepped spillways......Page 186
Design of concrete stepped overlay protection for embankment dams......Page 194
Hydraulic design of stepped spillways over RCC dams......Page 202
Design of stepped spillway for skimming flow regime......Page 210
Author index......Page 216

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HYDRAULICS OF STEPPED SPILLWAYS

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PROCEEDINGS OF THE INTERNATIONAL WORKSHOP ON HYDRAULICS OF STEPPED SPILLWAYS/ZURICH/SWITZERLAND/MARCH 22-24,2000

Hydraulics of Stepped Spillways Edited by

H.-E. Minor & W H. Hager Versuchsanstaltfiir Wasserbau, Hydrologie und Glaziologie, VAW, ETH- Zentrum, Zurich, Switzerland

A.A.BALKEMA/ROTTERDAM/BROOKFIELD/2000

The texts of the various papers in this volume were set individually by typists under the supervision of each of the authors concerned.

Authorization to photocopy items for internal or personal use, or the internal or personal use of specific clients, is granted by A.A. Balkema, Rotterdam, provided that the base fee of US$ 1.50 per copy, plus US$ 0.10 per page is paid directly to Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, USA. For those organizations that have been granted a photocopy license by CCC, a separate system of payment has been arranged. The fee code for users of the Transactional Reporting Service is: 90 5809 135 X/00 US$ 1.50 +US$ 0.1 0.

Published by A.A. Balkema, P.O. Box 1675, 3000 BR Rotterdam, Netherlands Fax: +31.1 0.413.5947; E-mail: [email protected]; Internet site: www.balkema.nl A.A. Balkema Publishers, Old Post Road, Brookfield, VT 05036-9704, USA Fax: 802.276.3837; E-mail: [email protected] ISBN 90 5809 135 X © 2000 A.A. Balke rna, Rotterdam Printed in the Netherlands

Hydraulics of Stepped Spillways, Minor & Hager (eds) © 2000 Balkema, Rotterdam, ISBN 90 5809 135 X

Table of contents

Preface

IX

Organization

XI

Sponsors

XIII

Introductory lecture Spillwfiys for high velocities

3

H-E.Minor

Case studies Field testing of Brushes Clough stepped block spillway

13

R.Baker

The stepped spillway for the Mhlathuzane dam, Swaziland

21

UDrewes & T.Gehrke

Hydraulic design of Nakasujigawa dam stepped spillway

27

N.Hakoishi & T.Sumi

Ashton stepped spillway- Design and construction

35

L.ANigus, K.MSteiger & CMarti

Aeration characteristics and cavitation risk Stepped spillways, a dissolved gas abatement alternative

45

ML.Ahmann & E.T.Zapel

Scale effects in modelling two-phase stepped spillway flow

53

R.MBoes

Air inception in skimming flow regime over stepped spillways MR.Chamani

v

61

Air entrainment and safety against cavitation damage in stepped spillways over RCC dams J.Matos, MSdnchez, A Quintela & 1Dolz

69

Air-water flow and gas transfer at aeration cascades: A comparative study of smooth and stepped chutes L. Toombes & H Chanson

77

Energy dissipation Stepped spillway studies at CEDEX C Mateos Igudcel & V. Elviro Garcia

87

Flow resistance in skimming flow: A critical review HChanson, Y.Yasuda & I.Ohtsu

95

Dissipation efficiency of stepped spillways U Fratino, A F Piccinni & G. de Marinis

103

Energy dissipation comparison among stepped channel, drop and ramp structures A Peruginelli & S. Pagliara

111

Nappe flow in stepped channels- Occurrence and energy dissipation AN. Pinheiro & CS.Fael

119

Internal flow features Backwater and drawdown curves in stepped spillway flow WHHager & R.MBoes

129

Pressure field in skimming flow over a stepped spillway M Sanchez J uny, 1 Pomares & 1 Dolz

137

Characteristics of plunging flows in stepped channel chutes Y.Yasuda & I.Ohtsu

147

Design The CIRIA guide for the design of stepped-block spillways R.Baker

155

Guidelines for the hydraulic design of stepped spillways R.MBoes & H.-E. Minor

163

Roller compacted concrete and stepped spillways E.1Ditchey & D.B.Campbell

171

Design of concrete stepped overlay protection for embankment dams K.H.Frizell, 1Matos & AN. Pinheiro

179

VI

Hydraulic design of stepped spillways over RCC dams J.Matos

187

Design of stepped spillway for skimming flow regime S.P.Tatewar & R.N. Ingle

195

Author index

201

VII

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Hydraulics of Stepped Spillways, Minor & Hager (eds) © 2000 Balkema, Rotterdam, ISBN 90 5809 135 X

Preface

Stepped spillways have been successfully applied for roller compacted concrete dams (RCC-dams ), but they have also been constructed on existing fill dams to increase the discharge capacity and to improve environmental concerns. It is worthwhile to study the possibilities to increase the range of application to dams with higher heads and larger floods, since this type of spillway is a highly economic solution. Therefore, a workshop was organized bringing together scientists and engineers to discuss the major aspects of the hydraulics of stepped spillways such as: Air entrainment characteristics, Free surface profile development, Turbulence effects of step flow, Cavitation characteristics, Energy dissipation in air-water flow, and Discharge capacity of stepped spillways. In addition, successful design cases are presented and experience with spillway refurbishing is described. This book contains the papers presented at the International Workshop 'Hydraulics of stepped spillways' held in March 2000 at ETH Zurich, Switzerland. It gives an overview of the state-of-the-art in the field of stepped spillways and addresses in particular currently still open questions. The editors gratefully acknowledge the sponsorship of the International Association ofH ydraulic Engineering and Research (IAHR), the American Society of Civil Engineers (ASCE), the Schweizerische Wasserwirtschaftsverband (SWV) and the Swiss National Committee on Large Dams (SNGT), as well as the support of the scientific committee. We appreciate the financial support of Electro watt Engineering Limited, Zurich; Colenco Power Engineering Limited, Baden, and Lombardi Engineering, Minusio, which helped to produce this book. The organization of the symposium and the preparation of the book at hand was carried out by the Laboratory of Hydraulics, Hydrology and Glaciology (VAW) of ETH Zurich. The main work was carried out by R.M.Boes, secretary of the workshop, who deserves our sincere thanks. H.-E. Minor & W. H. Hager Zurich, March 2000 IX

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Hydraulics of Stepped Spillways, Minor &Hager (eds) © 2000 Balkema, Rotterdam, ISBN 90 5809 135 X

Organization

SCIENTIFIC COMMITTEE Dr A.Goubet Prof. Dr W. Kinzel bach Prof. Dr J. Knauss Prof. Dr H. Kobus C. Mateos Igm'icel

Dr P. Rutschmann Prof. Dr A. Schleiss

Dr P.Volkart

Ministere de l'Industrie et du Commerce Exterieur, Paris, France Institute of Hydromechanics and Water Resources Management (IHW), ETH Zurich, Switzerland Oskar-von-Miller Institute, Technical University of Munich, Germany Institute of Hydraulic Engineering, University of Stuttgart, Germany Hydraulics Laboratory ofCEDEX, Madrid, Spain VAW, ETH Zurich, Switzerland, Laboratory of Hydraulic Structures (LCH), Federal Institute of Technology (EPF), Lausanne, Switzerland VAW, ETH Zurich, Switzerland

XI

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Hydraulics of Stepped Spillways, Minor & Hager (eds) © 2000 Balkema, Rotterdam, ISBN 90 5809 135 X

Sponsors

ASCE, Water Resources Engineering Division, USA Colenco Power Engineering Ltd., Baden, Switzerland Electrowatt Engineering Ltd., ZUrich, Switzerland IAHR, Hydraulic Structures Section, Netherlands Lombardi Engineering Ltd., Minusio, Switzerland Swiss Association of Water Resources (SWV), Baden, Switzerland Swiss National Committee on Large Dams (SNGT), Switzerland

AmeriAn Society of Civil EnginHrs Eidgenossische Technische Hochschule Zurich

II

SNGT-CNSGB

SCHWEIZERISCHER WASSERWIRTSCHAFTSVERBAND

•

IAHR ""-'

""-' AIRH XIII

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Introductory lecture

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Hydraulics of Stepped Spillways, Minor & Hager (eds) © 2000 Balkema, Rotterdam, ISBN 90 5809 135 X

Spillways for high velocities Hans-Erwin Minor Laboratory of Hydraulics, Hydrology and Glaciology (VAW), ETH Zentrum, Zurich, Switzerland

ABSTRACT: The high velocities in high head spillways have in the past caused considerable damage to spillway structures. The example of Shahid Abbaspour is used to demonstrate the causes in detail. The remedial measures are discussed. Further the consequences for the design of spillways with high velocities are outlined. The questions resulting from these consequences concerning stepped spillways are formulated. 1 LESSONS LEARNT FROM SHAHID ABBASPOUR (KARUN I) SPILLWAY FAlLURE 1.1 History

Spillways for high heads and consequently for high velocities have suffered from severe cavitation damage. One example is the spillway of Shahid Abbaspour Hydroelectric Plant in Khuzestan, Iran. The first dam on the Karun River which was finished in 1977, is a double curvature arch structure of 200 m height. The initial powerhouse at the toe of the dam was equipped with four turbines with a total capacity of 1000 MW. To meet the demand of peak capacity in the future, an additional underground powerplant downstream of the left abutment was foreseen already in the feasibility studies. The spillway has three bays, each of 18.5 m width, and is equipped with three tainter gates, each 15 m wide and 21.26 m high; it is designed for a maximum discharge of 16,200 m 3/s. The specific discharge amounts to 290 m 3/s·m. At the foot of the straight spillway chute, a flip-bucket which is curved also in the horizontal plane, throws the water into the river bed. The energy dissipation takes place in a plunge pool. The first test operations of the spillway and the gates were performed in April 1977, apparently without any problems. The discharge, however, did not exceed 250 m 3/s through any one bay until June (in bay 2), and July (in bay 3). For a very short period of less than one day, the maximum discharge through any one bay at this time was approximately 600 m 3/s. No reports exist of any damage resulting from this operation. In December 1977, a flood with a return period of approximately 2.5 years made necessary the opening of the gates for spilling of around 1200 m 3/s. Bays 1 and 2 were used, and each bay thus discharged up to 600 m 3/s. After nine days of operation, severe damage to the lower sections of the spillway chutes was recognised. The gates of bays 2 and 3 were closed and bay 1 was used to spill the remaining 1100 m 3/s, but after a short time damage of the lower part of the spillway in this bay was also noted. 1.2 Observations The damage occurred at a specific discharge between 32 m 3/s·m and 60 m 3/s·m. The spillway invert damage is shown in Figs 1 and 2. In each bay a considerable area of the concrete had

3

Figures 1 and 2 Shahid Abbaspour spillway after cavitation damage in March 1978

been eroded to a maximum depth of 2.80 m, which means that not only the concrete (slab thickness is 1.50 m) but also part of the rock had been tom out. When the author visited the dam site in March 1978 (Minor 1978), the spillway was operating with all three bays and a discharge of some 600 m3Is, i.e. about 200 m 3Is through each bay. After closing the gates, all bays could be inspected. Approximately 25 m (measured vertically) above the flip-bucket, at which point the flow velocity was around 37 m/s with 600 m31s discharging through one bay, the cavitation damage started at construction joints or bolt holes and increased rapidly in a downstream direction. The deepest holes had already been filled with rich concrete in order to protect the rock, but in some places the rock, the drainage system and rock anchors were still visible. In the undamaged part of the spillway a waviness of the concrete surface (corrugated surface) was observed. These waves were of up to several centimeters height in the chute and up to about 10 em in the flip-bucket (Fig 3). Especially in bay 3, but also in the other two bays, dozens of holes for the bolts which had been used as fixation points during construction could be seen. Most of them had been filled with special mortar or dry pack but the water flowing across these repaired areas at high velocity had removed many of the fillings (Fig 4). The construction joints had also been repaired from the start as shown in Fig 5. 1.3 Reasons for erosion damage

The observations made clear that the main reason for the erosion damage was cavitation. Once damage had developed normal erosion due to the impact of the water on the damaged area and "sawing" by the vibrating reinforcement steel rods caused worsening of the damage. Several types of cavitation damage could be observed. The wavy surface of the concrete (Fig 3) led to the build up of sub-atmospheric pressures just downstream of the peaks (Fig 6a) of such waves. The velocities are so high that the pressure drops below the vapour pressure of the water and vapour cavities or zones with vapour bubbles 4

Uneven surface in flip bucket with starting cavitation damage

Figure 3

Figure 4 Bolthole with tom out filling and starting cavitation damage

Figure 5 Repaired construction joint with starting cavitation damage

A- A

;;;~

vapor cavities ~damage

~~ffi:W

c) offset into the flow

Plan view

. A

Hole~ damage

-

vapor cavities

A

-

~on~~w-e~ --- - --

'x

damage

~

a) hole in the surface

d) offset away from the flow

~

~

b) wavy surface

Figure 6

e) groove in bottom slab

Flow action and cavitation damage for various surface irregularities

5

developed downstream of the wave peak. These cavities or bubbles travel further downstream into zones of higher pressure where they collapsed, thus creating very high pressure peaks which are the actual cause of the damage to the concrete surface. Fig 3 shows the onset of such damage. Another -type of cavitation damage occurred when, as a result of pressure changes, the epoxy mortar or dry pack plugs of the bolt holes were tom out (Fig 4). The flow entered the hole and was forced to a sharp curvature at the lower edge, thus again creating vapour cavities (Fig 6b). At construction joints where the discharge flows against or over small irregularities (offsets) (Figs 6c, d), or over small transverse grooves (Fig 5), the same cavitation phenomena as already described led to damage downstream. The grooves at the construction joints resulted from the concreting procedure which started at the top of the chute and advanced down the slope with the concreting of the individual slabs of course being done from bottom to top. The construction joints therefore opened up when the concrete settled slightly before getting hard. Concreting the double curvature surface of the flip-bucket was very difficult, with the result that the waviness and surface irregularities in that part of the spillway were more pronounced (Fig 3). These large irregularities are such that even high pressures in the flip-buckets, due to the vertical curvature of the flow, are insufficient to prevent cavitation damage. At the side walls no cavitation damage was noted, and this fact can be explained by the low water depths which had occurred there. It thus seems likely that at the irregularities which existed along the side walls, air had been able to enter the space separating the flow from the side wall, and consequently prevent cavitation. The low pressures causing cavitation damage depend, of course, on the flow velocities. In Fig 7, the flow velocities along the spillway are plotted against the discharge through one bay for several positions on the spillway chute. The calculations of the velocities were done assuming Strickler's friction factor, (kst), equal to 80 m 113 s· 1• The heavy cavitation started at an elevation that corresponds to point No. l 0 in the longitudinal section (Fig 7), where the velocity was around 37 m/s for a discharge of600 m3/s at which the damage had occurred. 50

v m Is

14 10 9

40 7

30

.

I

20

Discharge I bay 10~---;----~--~-----r--~----· 1000 3000 5000

Figure 7 Flow velocities in spillway against discharge in one bay Insert: Longitudinal section through spillway

6

Figure 8

Damage due to cavitation erosion at Shahid Abbaspour spillway in September 1993

1.4 Countermeasures taken and further damage

The spillway was repaired i.e. the surface of the chute was re-established and the quality of the surface was improved using epoxy-resin for better durability. But already in 1979 serious cavitation damage occurred (Krumdieck et al. 1993). The chute was repaired again without design changes. The situation at Shahid Abbaspour is such that the spillway has to operate every year. The flood volumes routed through between 1974 and 1992 were small but the chute showed signs of cavitation damage after each flood season and had "continuously" to be repaired (lndermaur 1993, Fouladi 1994). A large flood occurred a the beginning of 1993. The discharge through the spillway was reported to have peaked at about 4000 m 3/s. Cavitation started to cut through the bottom slab of the chute until eventually the training wall between bays 2 and 3 and the outer, right hand side training wall were undermined and collapsed. This occurred in April. Because of sustained high inflow to the reservoir, the spillway gates had to be kept open and the damages propagated. The large volume of concrete which constitutes the flip buckets together with the left bay chute were lifted and rotated. The upstream part of the flip buckets of bays 2 and 3 and the bottom slab of the same chute bays were completely destroyed (Fig 8). The water also dug into the foundation rock and undercut the bedding planes. This caused sliding of the rock. A large scour developed in the river bed where the jet impinged, aggravating the mass movement of the left abutment of the dam (Krumdieck et al., 1993). 1.5 Rehabilitation ofspillway chute The spillway chute was completely reconstructed after extensive rock protection measures had been carried out. Aeration grooves were introduced and the flip bucket was moved upstream, (Fouladi, 1997), measures that were already proposed after the first damage (Minor, 1978).

7

2. CONSEQUENCES FOR THE DESIGN OF SPILLWAYS WITH HIGH VELOCITIES The conclusion from the initial failure of Karun I spillway and reports on other damages of spillways and bottom outlets (Colgate, 1959; Wagner and Jabara, 1971; Douma, 1972; Ball, 1976) together with the basic work of Peterka (1953) led to a new design philosophl,. Specific discharge was limited to 100 to 150 m3/s·m and 150m3/ s·m to 200 m"/ s·m for the design flood and the safety check flood, respectively. Aeration of the bottom slab of the spillway chutes and tailrace channels of the bottom outlets (total wetted perimeter) were introduced in cases where the design velocities exceeded 30 rn/s. The aeration slots were designed and spaced so that for maximum discharge the air content at the bottom was always above 5 % (Volkart and Rutschmann, 1991). The results were excellent concerning cavitation damage (Galperin et al., 1977; Quintela 1980; Pinto et al., 1982; Minor 1987a; Minor 1987b; Minor 1988a). However, the hydraulic models used to optimise the aeration slots and the uncertainty concerning the rate of air detrainment led to a design which provoked an air concentration in the flow that was too high as e.g. test operation at the Alicura spillway revealed. The rate of detrainment that is still very often used today in design is 0,4 to 0,5 % per meter flow length comes from Russian measurements (Galperin et al., 1977). Experience with prototypes having aeration slots, suggests that a value of 0, 15 - 0,2 % per meter would be more appropriate. However, more detailed studies are necessary. Another point is that the aeration system should not be designed optimally for the design flood (if we talk about spillways) which normally has a return period of 1000 years (Minor, 1998; ICOLD Bulletin 82). It seems much more appropriate to design the aeration system for a flood that occurs once in a lifetime, i.e. once in 100 years and accept small damages to the spillway for large floods, if they occur at all. Additionally the surface irregularities must be minimised. The commonly applied specifications for deviation from the theoretical line as well as offsets must be strictly applied which is not easy on a spillway chute with large inclination. Construction procedure must be adjusted so that longitudinal joints are in positions where they can be treated. Bolt holes, as well as horizontal joints should be avoided completely (Minor 1988b). As could be shown for Alicura spillway (Minor 1987a) bottom slabs can be concreted without horizontal joints between aeration slots thus avoiding one major inception point of cavitation. 3. STEPPED SPILLWAYS

3.1 Spillways at RCC "-Dams Roller compacted concrete is a relatively young technique of constructing dams. It is very economic, mainly because of its rapid construction procedure (Schrader 1995). The dis face of RCC dams which are normally of the gravity or arch gravity type has a stepped surface which results from the construction procedure. The height of the steps is very often 120 em and since the dis slope for gravity sections is close to 3/4 the horizontal portion of the steps normally measures 90 em. For arch gravity sections the slope is steeper. For smaller dams the ungated spillways are designed so that the water runs down the steps into a stilling basin. Only at the crest a smooth ogee like shape is constructed, followed by some smaller steps before the spillway changes into a stepped chute that is in fact the dis face of the RCC-dam (Fig 9) (Boes 1999). Sometimes the steps in the spillway are made smaller, i.e. half the height of the steps of the dam body. Today, RCC dams are planned with a hight far above 100 m and in areas with extreme floods. In these projects, it is economically and often technically not possible to rely on ungated spillways. Or, in other words, the specific discharge has to be in the order of 100-200 m 3/s·m. In these cases, today a conventional spillway structure is put on top of an RCC structure (Fig 10), thus eliminating part of the advantages ofRCC method.

8

F.S.L. 900.00

~

903.00

y

885.50

y

\ Figure 9 Stepped spillway of Peterson Dam, Colorado (from Boes, 1999)

Figure 10 Egiin Dam, Mongolia, study of conventional gated spillway on RCC dam with ski jwnp

3.2 Other applications ofstepped spillways Recently, existing dams with too small spillway capacities have been rehabilitated by applying RCC as an overtopping protection to a portion of the dis slope of the dam, thus increasing the discharge capacity during extreme floods (McLean and Hauser, 1993). Even new dams have been designed with spillways that are an integrated part of the dam. The spillway is founded on the fill (Strobl and Schmid, 1997). Here also RCC could be an interesting alternative. Then the spillway would not be smooth but stepped. Very often spillways for high dams are excavated into the abutments and the chute is concreted at high cost. Using RCC could here also help to reduce cost; especially if a stilling basin would be needed that could be kept smaller.

3.3 Open questions concerning high velocity flow and energy dissipation at stepped spillways Several points still require further clarification. The energy dissipation along stepped spillways sometimes seems to be overestimated. Two question may be asked in this respect: 1. How can a practising engineer estimate the energy losses along a stepped spillway in order to be able to design the spillway and the stilling basin correctly? 2. How and with which restrictions can results from model tests be scaled up to the prototype? The other main topic is the erosion of the steps over which the water is flowing. We should be able to give answers to the following questions: 3. Are the edges of the steps eroded - by attack ofthe water - or by cavitation damage as discussed in paragraph I? 4. Is the natural aeration process sufficient to suppress the cavitation risk completely? 5. Which additional measures have to be taken to make sure that no cavitation damage occurs? 6. What is the limit for the specific discharge at stepped spillways? Can the value of 2530 m3/s·m be increased considerably? Only if the specific discharge could be raised by a factor of 3 to 4 would it be possible to design gated spillways with stepped chutes and thus apply stepped spillways for projects with high discharges.

9

4. CONCLUSIONS Spillways of conventional type can be designed so that even for high velocity flow the risk of cavitation damage is very limited. For velocities above 30 mls, aerators are today state of engineering practice. Special design rules and construction procedures have been developped that ensure cavitation free structures up to specific discharges of 150m3/sand more. For stepped spillways, the situation is different. The accepted load is considerably lower and a number of questions is still to be answered.

REFERENCES Ball, J.W. (1976). Cavitation from surface irregularities in high velocity flow. ASCE Journal of Hydraulics Division, September 1976. Boes, R. (1999). Gewichtsstaumauem aus Walzbeton. Wasser, Energie, Luft 91 (112) 11-15. Colgate, D. (1959). Cavitation damage of roughend concrete surfaces. ASCE Journal of Hydraulics Division., October 1959. Douma, J.H. (1972). Field experience with hydraulic structures. 1UTAM I IAHR Symposium on flow induced vibrations, Karlsruhe 1972. Fou1adi, C. (1994). Karun I spillway damage and construction of a new flip-bucket. 18'h Congress on Large Dams, Durban 1994, Vol. 5, 632-640. Galperin, R.S. et al. (1977). Protection against cavitation by boundary flow aeration. Cavitation in Hydraulic Structures, Moscow, 1977. /COLD Bulletin 82. Selection of Design Flood. Indermauer, W. (1993). Personal communication. Krumdieck, A., Riemer, W. Brenner, P. (1993). Shahid Abbaspour hydraulic plant- Report on spillway rehabilitation assessment. Project /RA/189/025 Dam Construction Programme, United Nations Development Programme, Zurich/Teheran, September 1993, unpublished. McLean, F.U. and Hansen, K.D. (1993). Roller compacted concrete for embankment overtopping protection. Proc. Specialty Conf. on Geotechnical Practice in Dam Rehabilitation, ASCE, Raleigh, USA 188-206. Minor, H.-E. (1978). Report on the spillway erosion at Reza Shah Kabir dam for Khuzestan Water and Power Authority. Elektrowatt Engineering Services Ltd., Zurich, April 1978, unpublished. Minor, H.-E. (1987a). Experience with chute aeration. Wasserwirtschaft 77, 6, 292-295. Minor, H.-E. (1987b). The bottom outlet of the hydroelectric project Alicura in Argentina. Wasserwirtschaft 77, 6, 309-312. Minor, H.-E. (1988a). Design of spillways for large dams. Indian Journal of Power & River Valley Development, Special Issue, March, 89-93. Minor, H.-E. (1988b). Konstruktive Details zur Vermeidung von Kavitationsschiiden. Int. Symposium Erosion, Abrasive und Kavitation im Wasserbau, ETH Zurich 1988. Mitteilung der Versuchsanstaltfiir Wasserbau, Hydrologie und Glaziologie der ETH-Ziirich, 307-378 Minor, H.-E. (1998). Report of the European R&D Working Group "Floods" Proceedings. Int. Symposium in New Trends and Guidelines on Dam Safety, Barcelona. Dam Safety, A.A. Balkema 1541-1550. Peterka, A.J. (1953). The effect of entrained air on cavitation pitting. IAHRIASCE Proceedings, Minnesota International Hydraulics Convention, Minneapolis, Minnesota, September 1953. Pinto, N.L., Neidert, S.H. and Ota, J.J. (1982). Aeration at high velocity flows. Water Power and Dam Construction, Feb. 1982 Quintela, A. C. ( 1980). Flow aeration to prevent cavitation erosion water power and dam construction, January 1980. Schrader, E. (1995). RCC: Current practices, controversies and options. Hydropower and Dams, September 1995. Strobl, Th. and Schmid, R. (1997). Muscat Dam, Oman- Flood alleviation for the Sultanate's capital. Dam Engineering in Kenya, Nigeria, Oman and Turkey, Technical Reports Strabag Brochure No. 52, 1997 43-53. Volkart, P. and Rutschmann, P. (1991). Aerators on Spillways. Air entrainment in free-surface flows, IAHR Hydraulic Structures Design Manual No. 4, 84-113. Wagner, W. and Jabara, M. (1971). Cavitation damage downstream from outlet works. 14'h IAHR­ Congress, Paris, 1971.

10

Case studies

Stagecoach dam, Colorado, USA (Courtesy of R.M.Boes, VAW)

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Hydraulics of Stepped Spillways, Minor &Hager (eds) © 2000 Balkema, Rotterdam, ISBN 90 5809 135 X

Field testing of Brushes Clough stepped block spillway Ray Baker Environmental Systems Research Institute, University of Salford, Manchester, UK

ABSTRACT: Brushes Clough was the first stepped block spillway constructed outside of Russia and in order to find out more about prototype operation the spillway was regularly monitored for the first two years of its life. There were no significant rainfall events in this time and so to obtain hydraulic data the spillway was subjected to two sets of artificially created high flow tests. The paper gives a brief outline of the Brushes Clough spillway design along with the detailed findings of the routine monitoring and high flow test programme. I INTRODUCTION Brushes Clough is a disused reservoir in the Pennine hills above the town of Shaw in Greater Manchester, UK. As part of decommissioning of the reservoir in 1992 the darn was breached and a new spillway constructed down the remnant of the embankment. The invert of the new spillway was lined with stepped blocks using methodology outlined in a draft version of the Design Guide for Stepped Block Spillways (Hewlett et a!, 1997) and was the first use of stepped block technology in the United Kingdom. Due to the uniqueness of the site the UK Construction Industry Research and Information Association (CIRIA) sponsored a project to monitor the site for the first two years of operation and to carry out simulated flood testing, Baker ( 1997). 2 STEPPED BLOCK PRINCIPLE The stepped block principle was first recognised in Russia and used on a number of State Farm dams the oldest of which has been in service since 1976. As flow passes over the edge of a step it separates from the surface, re-attaching part way along the tread of the downstream step. When flow develops to the skimming regime the lee of the step fills with water and a turbulent eddy forms. Pressure in the eddy is sub-atmospheric, reducing with increasing flow rate. The stepped block concept connects this low pressure zone to the underside of the block by holes or slots which allow sub-block seepage flows to be drawn back into the main flow and effectively sucks the block onto the underlying embankment. Stepped blocks also have three other hydraulic benefits. Firstly, the upstream edge of the blocks are shielded from the flow preventing the creation of stagnation pressure against an upstand which has been shown to be the key factor affecting the stability of flat block systems, Baker (1992). Secondly, the system is inherently stable, if a block lifts off the surface the curving streamlines generate a force to push it back into position. Thirdly, the high surface roughness of the steps reduces the flow velocity and hence the size of any necessary stilling arrangement at the toe.

13

3 BRUSHES CLOUGH DESIGN At Brushes Clough the designers, North West Water Engineering, used larger blocks than the minimum allowed in the Design Guide (Hewlett et a!, 1997) because of a fear that smaller blocks might be removed by vandals. Drainage provision was by slots, partly cast into the underside of the overlap and part in the tail of the downstream block, Figure I. 400

•

\F

SECTION F-F

ELEVATION

VIEW ON E

Figure 1

Block detail

wedge shaped blocks to base stone pitching to sides

1:1 trapezoidal channel with pitched base and sides 1.6

I OOmm dia perforated pipe

PLAN

60.88

LONG-SECTION

Figure 2 Brushes Clough spillway arrangement

14

The main spiiJway channel was of trapezoidal cross-section, designed for the 1:50 year flow rate of 3.66 m3/s. The spillway arrangement is shown on Figures 2 and 3. Stone pitching was used for the side slopes with five wedge blocks across the invert. Two half blocks were used in alternate rows to allow the blocks to be laid in stretcher bond. The blocks were pre- - -

(2)

v'> v8 cos¢

(3)

PwdB

where d8 and v8 are the bubble diameter and bubble rise velocity, respectively. With decreasing model size the bubbles become relatively larger, leading to an increased de­ trainment rate and a decreased transport rate of the air phase. The near-bottom air concentration is therefore larger for prototypes, which reduces the risk of cavitation on spillways as compared to model prediction. In the upper flow region, marked (2), the ( 1-C) values, i.e. the water phase, increase with in­ creasing model size and turbulence intensity, because water droplets are ejected further and in larger quantities from the underlying air-water mixture. For the same reason the characteristic mixture flow depth h90 , which is important for the design of chute training walls, also increases with model scale. The water is displaced by the air phase from the near-bottom region (I) to higher flow depths for a given prototype discharge qw. In general, three distinct flow regions can be distinguished from the concentration profiles: (I) a region with mainly pure water flow comprising small air bubbles for C(z) < 0.3 to 0.4, (2) a region with mainly air flow comprising water droplets for approximately C(z) > 0.6 to 0.7, and (3) an intermediate region with true two-phase flow of about equal water and air contents in terms of discharge for about 0.3 to 0.4 :S C(z)::; 0.6 to 0.7. 6 VELOCITY PROFILES By analogy to the air concentration profiles, Figure 6 shows results in prototype dimensions for different approach Froude numbers and ¢ = 30° at about 18 and 30 steps downstream from the inception point, whereas Figure 7 refers to Fr 0 = 3.5, r/J = 50° at a downstream distance of 4 and approximately 33 steps. Figure 6 and corresponding figures given by Boes (2000) suggest that the velocity decreases with increasing model size or scale for a chute inclination angle of 30°. For all experimental results considered, the difference between the largest and the medium­ sized model with AL = 6.6 and 13 .2, respectively, is significantly smaller than between AL = 13.2 and 26.4. When the smallest model size is compared to the medium-sized one, the mean depth­ averaged velocity increases by 3.6%. Regarding the steep inclination angle of 50°, there is also a slight velocity decrease with in­ creasing model scale, but the average difference becomes small for all experimental data given by Boes (2000). Because for both inclination angles the experimental runs over the small models with AL = 26.4 and 19.6 had maximum Reynolds and Weber numbers of Re = 6.93·104 and We= 86, respectively, compared toRe?_ I0 5 and We?_ I 00 for }oL :S 13.2, it is concluded from the velocity profiles that Re"' 10 5 and We"' I 00 are limiting values for modelling two-phase cascade flow without significant scale effects. A minimum scale of about I: I 0 to I: 15 is thus recommended for typical flow rates and standard step height of stepped spillways.

58

1000

1200~-------------------,

z[mm]

z[mm]

800 600 400

•

200 0 0

10

5

5

~

•

15

20

25

~

Figure 6. Velocity distribution um (z) for¢= 30° and a) Fr, = 4.0, hjs = 1.04 and AL = ( +) 6.6 with Re = 4 3.70·105, We= 247, A1. = (o) 13.2 with Re = 1.28·10 5, We= 134, and AL = (T) 26.4 with Re = 4.53·10 , We= 69 at ( +) 18, (o) 19 and (T) 15 steps from inception point, b) Fro= 6.0, h0 1s = 1.04 and AL = ( +) 4 13.2 with Re = 1.92·10 5, We= 164, and AL = ( ) 26.4 with Re = 6.93·10 , We= 86 at ( +) 30 and ( ) 29 steps downstream from inception point.

1200,------------------,

1200,-----------------~

z[mm]

z[mm]

I

1000

600:-

•

400 200

OL_____ 0 ~

L_~~L---~----~

5

10

15

OL_--~L_~~~--~----~

20

0

5

10

15

20

~

Figure 7. Velocity distribution um(z) for¢= 50°, Fro= 3.5, hjs= 1.06 and Af.= (+) 6.5 with Re= 3.53·105 , We mean"' 219, and AL = ( ) 19.6 with Re = 6.67·10 4 , We mean"' 74 at a) 4 steps, b) ( +) 34 and ( ) 33 steps downstream from inception point.

Although there is still a noticeable difference in air concentration when the Reynolds and Weber numbers increase above the critical values mentioned, the error with respect to prototype conditions is rather small. This is suggested for example by comparing the C results of liL = 6.6 and 13.2 with Re = 3. 70·1 05 and 1.28·10 5, Wemean"' 24 7 and 134, respectively, for almost uni­ form flow in Figure 4b. The difference inC is smaller than that between li1. = 13.2 and 26.4, which indicates that the effects of scale become almost negligible for an increase of model size beyond li1. = 13.2. Even the results from smaller models using Froude scaling are on the safe side for desii,'Tl purposes with respect to air concentration, flow velocity and energy loss, be­ cause aeration tends to be underestimated and velocity overestimated. Both tendencies imply 59

more favourable conditions for cavitation to occur than are expected in the prototype. The con­ trary holds for the required training wall height, however, as the two phase flow depths increase with increasing model size and turbulence intensity and are therefore underestimated in model studies. 7 CONCLUSIONS The use of model families revealed that the results from small-scale models can be scaled to prototype dimensions by the Froude similarity law with negligible scale effects, provided the Reynolds and Weber numbers are at least Re"" 1·10 5 and We"" 100, respectively. For typical unit discharges over stepped spillways up to about q = 20 m2/s and step heights s"" 0.6 m this implies a minimum scale of I: 10 to I: 15. For smaller models scale effects will increase due to viscosity and surface tension effects, but the results obtained are on the safe side for design purposes except for the required training wall height. 8 REFERENCES Bayat, H.O. ( 1991 ). Stepped spillway feasability investigation. Proc. 171h I COLD Congress, Vienna, Austria, Q.66(R.98): 1803-1817. Boes, R. (1998). Fiberoptische Messung von lokalen Luftkonzentrationen und FlieBgeschwindigkeiten in Zweiphasenstromungen. Wasserbauliche Mitteilungen 13: 205-214, Institut ftir Wasserbau und Tech­ nische Hydromechanik, TU Dresden (in German). Boes, R.M. (2000). Zweiphasenstromung und Energieumsetzung aufGrosskaskaden (Two-phase flow and energy dissipation on cascades). Doctoral Dissertation. ETH Zurich, Switzerland (in German): in re­ View.

Boes, R.M. & Hager, W.H. (1998). Fiber-optical experimentation in two-phase cascade flow. Proc. inti. RCC Dams Seminar, Denver, USA (K. Hansen, ed.). Chamani, M.R. & Rajaratnam, N. (1999). Characteristics of skimming flow over stepped spillways. Jl. of Hydr. Eng. 125(4): 361-368. Eccher, L. & Siegenthaler, A. ( 1982). Spillway aeration of the San Roque project. Inti. Water Power & Dam Constr. 34(9): 37-41. Ervine, D.A. & Falvey, H.T. (1987). Behaviour of turbulent water jets in the atmosphere and in plunge pools. Proc. Instn. Civ. Engrs., Part 2, 83(3): 295-314. Hager, W.H. (1992). Spillways. Shockwaves and air entrainment. I COLD Bulletin 81, Paris, France. Kobus. H. (1984). Local air entrainment and detrainment. Proc. IAHR Symp. on Scale Effects in Model­ ling Hvdraulic Structures (H. Kobus, ed.), Esslingen, Germany, 4.10: 1-10. Matos~ J. & Frizell, K.H. ( 1997). Air concentration measurements in highly turbulent aerated flow. Proc. 2i IAHR Congress, San Francisco, USA (S.S.Y. Wang & T. Carstens, eds.) A: 149-154. Pegram, G.G.S., Officer, A.K. & Mottram, S.R. (1999). Hydraulics of skimming flow on modeled stepped spillways. Jl. of Hvdr. Eng. 125(5): 500-510. Pinto, N.L. deS. (1984). Model evaluation of aerators in shooting flow. Proc. IAHR Symp. on Scale Ef­ fects in Modelling Hydraulic Structures (H. Kobus, ed.), Esslingen, Germany, 4.2: 1-6. Rajaratnam, N. (1990). Skimming flow in stepped spillways. Jl. ofHvdr. Eng. 116(4): 587-591. Rutschmann, P. (1988). Beliiftungseinbauten in Schussrinnen (Aerator devices in spillways). Doctoral Dissertation. Mitteilung Nr. 97, Versuchsanstalt fiir Wasserbau, Hydrologic und Glaziologie, ETH Zurich (in German). Schwall, M. & Hager, W.H. (1992). Die Strahlbox (The jetbox). Schweizer Ingenieur und Architekt 110(27-28): 547-549 (in German). Speerli, J. (1999). Stromungsprozesse in Grundablassstollen (Flow phenomena in bottom outlets). Doc­ toral Dissertation. Mitteilung Nr. 163, Versuchsanstalt fur Wasserbau, Hydrologic und Glaziologie, ETH Ziirich (in German). Tozzi, M.J. ( 1994 ). Residual energy in stepped spillways. Inti. Water Power & Dam Constr. 46(5): 32-34. Vischer, D., Volkart, P. & Sigenthaler, A. (1982). Hydraulic modelling of air slots in open chute spill­ ways. Proc. Hydraulic modelling of civil engineering structures, Coventry, UK: 239-252. Wahrheit-Lensing, A. ( 1996 ). Selbstbeliiftung und Energieumwandlung beim Abfluss iiber treppenfO."'"oOOoo::iQOoOoo 20"), data from CHAMANI and RAJARATNAM (1999) and the present study suggest higher friction factors for low aspect ratios (i.e. Wlh::; 10) with identical flow conditions and geometry. Note that both studies used a constant channel breadth, 0.3-m and 0.4-m respectively, and the effect of the channel width was not specifically investigated.

5.

CONCLUSION

In skimming flows down stepped chutes, the external edges of the steps form a pseudo-bottom over which the flow passes. Beneath this, recirculating vortices develop and are maintained through the transmission of shear stress from the waters flowing past the step edges. Skimming flows are characterised by a large !low resistance which is caused by FORM LOSSES. The flow resistance is consistently larger than on smooth-invert channels. Unsteady interactions between the recirculating cavities and the main stream are important. Flow visualisations suggest irregular fluid ejections from the cavity into the main stream, the process being sequential from upstream to downstream. On flat chutes, the flow resistance is a combination of skin friction on the horizontal faces of the steps and form drag associated with the recirculating cavity. The flow resistance data differ from steep chute data and they may be correlated with the relative step roughness (Eq. (10)). On steep chutes, the flow resistance must be analysed as a form drag. It may be estimated from the maximum shear stress in the shear layers: Equation (12) presents a simple model of form loss that agrees well with steep chute data. Although they exhibit some scatter, the data are distributed around two dominant values (f- 0.17 and 0.30). The study emphasises the complexity of skimming !low on stepped chutes. The flow resistance and energy dissipation processes arc dominated by the form losses and cavity recirculation. Acknowledgments : The authors thank a large number of people for providing their experimental data including Dr BAKER, Univ. of Salford, Prof. KNAUSS, MUnich Univ. of Tech., Mr ROYET, CEMAGREF. Source of data: BaCaRa (1991,1997), BAKER (1994), BAY AT (1991), BINDO eta!. (1993), CHAMANI and RAJARATNAM (1999), CHRISTODOULOU (1993), DIEZ-CASCON eta!. (1991). FRIZELL (1992), GORDIENKO (1967), GRINCHUK et a!. (1994), NOORI (1984), PEYRAS et a!. (1991,1992). SORENSEN (1985). TOZZI ( 1992), TOZZI eta!. ( 1998). and Present Study. (Full bihliographic details in CHANSON 1995a, pp. 210-229)

APPENDIX I- ESTIMATING BOUNDARY SHEAR STRESS ALONG A RECIRCULATING CAVITY At each step, the cavity flow is driven hy the developing shear layer and the associated transfer of momentum (Fig. I). The mixing layer is hasically a free shear layer. The equivalent houndary shear stress of the cavity flow equals the maximum shear stress in the shear layer that may he modelled hy a mixing length model: To = Tmax = P * vT

*

(aa:)

(I-ll

Y=Y5o

where VT is the momentum exchange coefficient, Y50 is the location of the streamline V = V j2, and V 0 is the free-stream velocity (e.g. Goertler model). The equivalent friction factor equals : f

=

8 * 1 max p*Vo2

2

(I-2)

= ~*K

where IlK is the dimensionless rate of expansion of the shear layer. In air-water mixing layers of plane plunging jets, BRATTBERG and CHANSON ( 1998) observed K - 6 for velocities ranging from 2 to 8 m/s. For monophase flows, K- 12. Equation (1-2) predicts a form drag: f = 0.2 for skimming !low, a result close to friction factor data in steep stepped !lows. BRATTBERG and CHANSON (1998) showed further that Y5ofd 0 = -0.094*(x/d 0 +5.3), implying the presence of a stagnation point associated with maximum pressures on the horizontal face of the step. This is consistent with the pressure measurements of FRIZELL ( 1992) and LEJEUNE and LEJEUNE ( 1994 ).

101

REFERENCES BaCaRa (1997). "Roller Compacted Concrete. RCC for Dams." Presses de /'Ecole Nationale des Pants et Chaussies, Paris, France, 181 pages. BAKER, R. (1994). "Brushes Clough Wedge Block Spillway - Progress Report No. 3." SCEL Project Report No. SJ542-4, University of Salford, UK, Nov., 47 pages. BRATfBERG, T., and CHANSON, H. (1998). "Air Entrapment and Air Bubble Dispersion at Two-Dimensional Plunging Water Jets." Chemical Engineering Science, Vol. 53, No. 24, Dec., pp. 4113-4127. CHAMANI, M.R., and RAJARATNAM, N. (1999). "Characteristics of Skimming Flow over Stepped Spillways." Jl of Hyd. Engrg., ASCE, Vol. 125, No.4, pp. 361-368. CHANSON, H. (1995a). Hydraulic Design of Stepped Cascades, Channels, Weirs and Spillways. Pergamon, Oxford, UK. CHANSON, H. (1995b). "Air Bubble Diffusion in Supercritical Open Channel Flow." Proc. 12th Australasian Fluid Mechanics Conference AFMC, Sydney, Australia, Vol. 2, pp. 707-710. CHANSON, H. ( 1997). Air Bubble Entrainment in Free-Surface Turbulent Shear Flows. Academic Press, London, UK. CHANSON, H. (1999). The Hydraulics of Open Channel Flows: An Introduction. Edward Arnold, London, UK. DJENEDI, L, ANSELMET, F., and ANTONIA. R.A. (1994). "LOA Measurements in a Turbulent Boundary Layer over aD-Type Rough Wall." Experiments in Fluids, Vol. 16, pp. 323-329. ELAVARASAN, R., PEARSON. B.R., and ANTONIA, R.E. (1995). "VIsualization of Near Wall Region in a Turbulent Boundary Layer over Transverse Square Cavities with Different Spacing." Proc. 12th Australasian Fluid Mech. Conf AFMC, Sydney, Australia, Vol. I, pp. 485-488. FRIZELL. K.H. (1992). "Hydraulics of Stepped Spillways for RCC Dams and Dam Rehabilitations. " Proc. Jrd Specialty Cunf on Roller Compacted Concrete, ASCE, San Diego CA, USA, pp. 423-439. HENDERSON, F.M. (1966). Open Channel Flow. MacMillan Company, New York. USA. KAZEMIPOUR. A.K., and APELT. C.J. ( 1983 ). "Effects of Irregularity of Form on Energy Losses in Open Channel Flow." Aust. Civil Engrg Trans .. I.E.Aust., Vol. CE25, pp. 294-299. LEJEUNE, A., and LEJEUNE. M. (1994). "Some Considerations on the Hydraulic Behaviour of Stepped Spillways." Proc. Inti Conf Modelling, Testing and Monitoring for Hydo Powerplallls, UNESCO-IAIIR, Budape,t, Hungary, July. MATOS, J., SANCHEZ, M .. QUINTELA. A., and DOLZ. J. (1999). "Characteristic Depth and Pressure Protllcs in Skimming Flow over Stepped Spillways." Proc. 28th IAHR Congress, Graz, Austria, Session B 14 (CD-ROM). OHTSU. 1.0., and YASUDA, Y. (1997). "Characteristics of Flow Condrtions on Stepped Channels." Proc. 27th IAHR Biennal Congress, San Francisco, USA, Theme D, pp. 5S3-588. RUFF, J.F., and FRIZELL, K.H. (1994). Proc. Hvd. En~;. Con}:, ASCE, Buffalo USA, Vol. 2. pp. 999-lOOJ. TOZZI, M., TANIGUCHI. E .. and OTA, J. (1998). ''Air Concentration in Flows over Stepped Spillways." Proc. 1998 ASME Fluids Eng. Con(, FEDSM'98, Washington DC. USA, Paper FEDS'vl98-5053, 7 pages (CD-ROM) YASUDA, Y., ami OHTSU, 1.0. (1999). "Flow Re,istance of Skimming Flow in Stepped Channels." Proc. 2Rth IAHR Congress. Gra7, Austria, Session B 14, 6 pages (CD-ROM).

102

Hydraulics of Stepped Spillways, Minor &Hager (eds) © 2000 Balkema, Rotterdam, ISBN 90 5809 135 X

Dissipation efficiency of stepped spillways U. Fratino & A. F. Piccinni Dipartimento di Ingegneria delle Acque, Politecnico di Bari, Italy

G.de Marinis Dipartimento di Meccanica, Strutture, Ambiente e Territorio, Universita di Cassino, (FR), Italy

ABSTRACT: This study on hydraulic structures used for dissipating energy downstream from dams offers interesting suggestions for applied research aiming to improve hydraulic effi­ ciency and constrain construction costs without neglecting environmental aspects. Extensive experimental tests have been carried out in the laboratory of Dipartimento di Ingegneria delle Acque at Bari Polytechnic. Three different geometric configurations were ana­ lysed, each characterised by a constant step number and step height, but with different chute slopes. The experimental study focused on two aspects of physical interpretation of the phe­ nomenon: the first concerned with the definition of the flow conditions, as defined by the device geometry and the flow dynamics, and the second with the evaluation of the rate of energy dissi­ pation. The results seem to confirm the notorious difficulties in understanding the problem, even if the experimental data show the same trend as those obtained by other researchers. I INTRODUCTION Stepped spillways are assuming a new role following developments in the field of construction technology and in view of the need to improve the visual impact of the hydraulic structures used for dissipating energy downstream from dams. The renewed interest in this type of spillway stems from the awareness that the steps increase energy dissipation and thus effectively reduce the size of the energy dissipation basin required downstream and, hence, cut costs. The use of such structures as flood release facilities for large dams has ancient origins, the first examples being found on the Khosr River dam in Iraq as far back as 700 B.C. However, these structures always played a purely structural role, and it was not until the early 201h century (New Croton dam, 1906) that their shape was used to increase the energy dissipation rate. Used essentially for recreational purposes for a large part of the century, thanks partly to an increased knowledge of the behaviour of the hydraulic jump stilling basins and the reliability of their design procedures, the study of such structures made limited progress until about twenty years ago when research began to tackle the issue systematically, even if many aspects, such as the relationship between the flow regime, the hydrodynamic variables and the flow characteris­ tics are still far from a universally approved definition. The renewed interest in these structures stems from the new awareness that not only the steps significantly increase the dissipation energy rate and help contain the size of the structure, but they also cut the construction costs of the downstream stilling basin and reduce effects such as cavitation and the lifting of lining slabs due to bottom pressure fluctuations. Therefore, the goal of this study is to conduct new experimental tests on structures having particular geometric characteristics in order to confirm advanced hypotheses concerning the pa­ rameters and the limits of validity of different flow typologies and the dissipation characteristics of the structure.

103

Figure I. Nappe flow (h/1 =0.24- Q=I0.21/s)

Figure 2. Skimming flow (h/1 =0.48 - Q=29.2 1/s)

2 STATEMENT OF PROBLEM Stepped spillways were exhaustively developed by Essery & Homer (1978), Sorensen (1985) and Rajaratnam (1990), in addition to the book published by Chanson (1994). The above studies identified two principal regimes of flow, defined by geometric and hydraulic conditions, called "nappe flow" and "skimming flow" respectively, and characterised by very different kinematic conditions (Figs. 1-2). The first regime determines a succession of free-falling nappes and the flow bounces from one step to the next forming a complete or partially developed hydraulic jump, while the second occurs for larger discharges for the same geometric characteristics, the water flows down in a coherent stream where external edges determine a pseudo-bottom defined by the straight line that connects the edges of each step (Fig. 2( However this distinction does not seem to create well defined limits as for each geometric configuration, there may be an 'or' of the other typology, according to the hydraulic characteris­ tics of the approaching flow. Indeed, the passage from one regime to the other seems to follow a transition phase that is hard to define and inside which the flow regime assumes intermediary characteristics typical of the above flow types. The inherent difficulty in defining the variables that determine the existence of one or the other regime means that we are still unable to provide a universally accepted criterion for the definition of the flow regime that a combination of geometric and hydraulic parameters induces. Only nappe flow with a fully developed hydraulic jump has a reliable criterion, as a simpli­ fied kinematic hypothesis may allow the analytical determination of the longitudinal distance needed to contain the falling jet and the length of a fully developed hydraulic jump. This is be­ cause the sum of these quantities must necessarily be lower than the step length/, assuming that the motion is purely gravitational, an acceptable hypothesis for the nappe flow regime. Under the hypothesis of gravitational flow, the distance Ld, at which the impact of the jet with the following step takes place, is for a uniformly accelerated flow: (1)

where h is the step height, k is the critical flow depth and d6 is the brink water depth of the step, to be evaluated using the expression by Rouse ( 1936). The length Lr. needed for the complete development of the hydraulic jump, is defined by Hager ( 1992) as: 1 According to Chanson's criteria each flow regime could be divided into three sub-regimes. For the nappe flow re­ gime three types can be distinguished: nappe flow with a fully developed hydraulic jump, nappe flow with a partially developed hydraulic jump and nappe flow with no hydraulic jump. At the same time, for the skimming flow regime. it is possible to identity the wake-step interference sub-regime, the wake-wake interference sub-regime and the recir­ culating cavity flow sub-regime.

104

(2)

where dd is the water depth immediately upstream of the hydraulic jump. In this context, the simplified approaches proposed by Rajaratnam ( 1990) and Chanson (1994) play a fundamental role. The former empirically identified the value k/h = 0.80 as the limit for which it is possible to observe the nappe flow regime, while the latter analysed experi­ mental data and defined a functional relationship between k/h and h/1 to identify the onset of the skimming flow regime. Chanson obtained, in a range of± 20%, the following expression:

konset =1.06 -0.465!!._, h I

(3)

where konset is the critical flow depth corresponding to the discharge for which the passage be­ tween the two regimes takes place. Ohtsu & Yasuda ( 1997) interpreted the experimental data while operating in perfect analogy with other hydraulic phenomena and introduced a third "transition regime". This approach ap­ pears to fit the experimental data better, even if some uncertainties remain. In a recent paper (Yasuda & Ohtsu, 1999), their analysis resulted in two equations that can be used to define the upper limit for the nappe flow regime and the lower for the skimming flow regime as: k

h)0.26 (1.4--1

h

1.4

(4)

(h)-0/65

k -=0.862h l

(5)

The dissipation efficiency and the mechanisms that determine and improve its effectiveness are defined using different evaluation processes for nappe and skimming flow regimes. In the first case, energy dissipation is due to jet impact on the underlying water cushion and hydraulic jump. In contrast, most of the energy is dissipated in maintaining the recirculation vortices be­ neath the pseudo bottom formed by the edges of the steps in the skimming flow regime (Fig. 3). The definition of dissipation plays fundamental role because it is the most important design factor. Although the nappe flow regime could, under ideal conditions, achieve the total dissipa­ tion of the head between the spillway crest and the downstream river bed, the limitations im­ posed by environmental constraints and the approaching flow characteristics render such a structure technically infeasible. The flow regime efficiency must therefore be evaluated in rela­ tion to the external conditions imposed on the spillway, with a design choice that is determined

a

Figure 3. Vorticity structures in skimming flow regime

105

Figure 4. Experimental set-up

by technical and economic considerations. The dissipated energy is evaluated by means of the following expression: &f H --=1-____!E_=JHmax

Hmax

d

k3

I

+1_-

2

d2 I

Hdam

+1k

=1-

A+ L A-2 2

Hdam

k

+.l

(6)

2

in which Hmax is the maximum head available, Hres is the downstream residual energy, d1 is the water depth under the hypothesis of uniform flow on the spillway and A is a dimensionless pa­ rameter expressing the relationship between the water depth d 1 and the critical depth k. For nappe flow regime, this parameter can be defined using theoretical considerations by White (1943)as: (7)

The definition of d1 for skimming flow regime is much more complex because of the differ­ ent way in which the dissipation phenomena occur. The different nature of the dissipation phe­ nomenon leads to the A parameter being defined according to the friction characteristics result­ ing from the steps that determine the pseudo-bottom on which the water flows. Under the hypothesis that the water reaches uniform flow condition, the friction factor according to Darcy­ Weisbach is: 2

f

=8gsinad R q2 4'

(8)

where q [m 2/s) is the discharge per unit width, a the channel bottom angle, R [m] the hydraulic radius and d [m] the uniform flow depth. From the previous equation we immediately obtain the amount of dissipated energy in the skimming flow regime as:

&! = H max

1

-

_f ( 8sina

)i cos a+ L(_f)-: 2

Hdam -··--·

k

8sina

+-3

(9)

2

in which the friction factor f is strongly subjected by the flow conditions, i.e. whether or not the flow is aerated. 3 EXPERIMENTAL SET-UP The experimental tests were performed in the laboratory of Dipartimento di Ingegneria delle Acque at Bari Polytechnic using a varying slope channel, 40 m long and 0.75 m wide. The stepped spillway model contained 24 mm thick PVC plates, arranged in such a way as to achieve different geometric configurations (Fig. 4). With the channel set in a horizontal posi­ tion, three different geometrical models were defined: the number of steps ( 14) and the step height (24 mm) were constant but different slopes were selected (0.48, 0.24 and 0.12). The discharge was varied by means of a pump up to a maximum 0.20 m 2/s although, in actual fact, the tests were performed with a maximum discharge of only 0.05 m 2/s in order to assure stability of the experimental structure. The discharge measurement involved an orifice plate and a water differential manometer. Two metallic tanks controlled by a sluice gate were located at the ends of the channel. At the upstream section there was a damper to assure the hydraulic feed having negligible kinetic com­ ponents. The discharge was checked by the broad-crested weir equation and this verification

106

furnished an absolute relative error always smaller than 7%. The water depths were measured at several points upstream, downstream and along the stepped channel and, for this purpose, a hydrometer connected to an electronic integrator capa­ ble of measuring the mean value in a predefined temporal interval was used. These values were, subsequently, employed in order to minimise accidental errors and to guarantee the correctness of the subsequent numerical elaborations. A digital camera was also used to validate the qualita­ tive analyses with recorded images. 4 ANALYSIS OF RESULTS

In the first phase of analysis the flow regimes were checked and compared with Rajaratnam (1990), Chanson (1996) and Yasuda and Othsu's criteria (1999) (Tab. 1), and a certain correspondence was found, even if they did not match completely. Table I. Experimental tests compared with several analytical definitions of flow regimes. Configuration I h/1 q [m 2/s]

RC

0.0053 N 0.0082 N 0.0096 s 0.0143 s 0.0187 s 0.0191 s 0.0213 s 0.0262 s 0.0305 s 0.0359 s 0.0408 s 0.0471 s

cc

=

0.12

OYC

Configuration 2 h/1 q

RC

=

s s s s s s s s s

N

T T T

s s s s s s s s

0.0029 N 0.0052 N 0.0096 s 0.0124 s 0.0136 s 0.0153 s 0.0158 s 0.0186 s 0.0205 s 0.0232 s 0.0287 s 0.0343 s 0.0380 s 0.0384 s 0.0429 s

Configuration 3 h/1 = 0.48

OYC

q [m2/s]

N N

N N

0.0015 N 0.0045 N 0.0071 N 0.0113 s 0.0160 s 0.0211 s 0.0232 s 0.0319 s 0.0389 s 0.5130 s

[m 2/s] N N N

0.24

cc

s s s s s s s s s s s s s

T T

s s s s s s s s s s s

RC

cc

OYC

N N N

N N

s s s s s s s

T T

s s s s s s

The notations RC, CC and OYC refer to methodological criteria defined by Rajaratnam (RC), Chanson (CC) and Ohtsu and Yasuda (OYC) respectively, while the letters N, T and S indicate the flow regimes (Nappe, Transition or Skimming) obtained by their application. The visual interpretation made it possible to attribute a specific character to each flow regime, leaving a large subjectivity to the intermediate conditions in which the observed flows were characterised by gravitational behaviour with a partial hydraulic jump in the initial steps and the formation of whirling zones along the last steps. Figure 5 shows the experimental observations in addition to the curves that define the analytical criteria. The figure points at the variety of the approaches and the different ways in which the researchers interpreted the limited amount of available data for an identification criterion. It should be stressed, however, that there is an ap­ preciable coincidence between our experimental data and the analytical data derived by Yasuda and Ohtsu's criterion. This last approach seems to interpret the evolutionary process of the flow, although its defini­ tion requires a finer detail that must be achieved by means of a large scale and extensive labora­ tory and field study. In this context, it must be underlined that our data was insufficient to give a better definition of the results already available. The experimental analysis of the dissipation processes made reference to the different natures of the phenomenon, using different approaches according to the investigated flow regime. For nappe flow configurations, the experimental data confirmed the theoretical considerations with an almost total correspondence between the analytical and experimental values (Fig. 6), with differences of less than 5%.

107

k/h 2,8

•s 2,6 2.4 2.2

1.6 1,4

1.2

0

• s • s • s • s

1,8

~--

'

• s

---------

Essery & Horner(l978) Bettz & Lawless (1992)

•s

0

• s

•s •s

Montes (1994) Upper hm1t for nappe flow Ohtsu & Yasuda (1999)

---6··· Lowerhmit forsktmmmg

• s

•s

flow Ohtsu & Yasuda (1999 ~--Chanson's cntena

I

.-

• s • s • s •s •s

•s •s

"'• ·r~..• rs

•s

··----.

-

•

RaJaratnam's critena Expenmental data

Skimming flow

0.8

X

•N

0,4

Nappe flow

o·x

•N

0.2

06

O,J

0,0

1,2

h/1

1,5

Figure 5. Classification of flow conditions

!

100%

1\.H/Hmax

~·

---~=--='-~•--.!o?.fl~~1•!.._--.l!o~~.:___.:_jt

I

A

.:

-- T

80%

-·

~

I

-.-~--~

t _ - !

60%

- I--

I

-,-

40%

o i

I

h/L=0.12

20% 0,2

0,4

0,6

0,8

klh

1,2

Figure 6. Dissipation energy rate in nappe flow regime

The analysis of the dissipation efficiency in the transition and skimming flow regimes was more complex. In general terms, for all the examined configurations, a reduction in the dissipa­ tion efficiency was observed when the discharge increased or when the channel slope increased for a fixed discharge. A possible interpretation of this behaviour should be sought in the hydrau­ lic characteristics of the skimming flow regime, in which the influence of the pseudo-bottom should be evaluated as macro-equivalent roughness through the definition of the friction factor f An analytical verification of the dissipation efficiency in the above interpretation shows how, for the analysed configurations, Chanson's assumption to consider a constant friction factor, equal to one, is not correct Besides, this assumption gives rise to some perplexities as the physical nature of the examined variable has a close analogy with the friction factors character­ ising steeper rivers and for which an estimate, independent of discharge and mean slope, ap­ pears rather forced. 108

ozs 02

j :

-.c.

0,1S

I.

·:~- :~ -7-

·; i

0.1

o... 10

20

30

Qi>'tl

Figure 7. Friction factor vs. discharge

40

"'"

0.5

_____ 1_5_ _ _

-~- ~~h 3,51

i]T_ _- ~-----I

90%

0.6

70%

'"" 40%

T

L

I

-r

o

so~

1

I 30% 0

10

___::_ -_ ,... I 1 ----;___ ___:__

20

30

I

t ..

.o.s1.r

I

1

j

:'J 1J ! ~-

'""

.

I

Figure 8. Energy dissipation vs. discharge

100"k

50%

II[

10

40

Figure 9. Dissipation efficiency in skimming flow regime

~

~

I

i

I

~

~

oo

ro

ro

u [']

Figure 10. Friction factor vs. channel slope

To this end, an indirect evaluation of the friction factor was performed. This was achieved by measuring the water depths at several points along the structure, starting from the point where uniform flow was reached (Fig. 7). The figure shows an increase in the f parameter when the discharge increases or when channel slope increases for fixed discharge, confirming, as fully predictable, the dependence of the friction factor on these factors. In order to simplifY the analysis, a similar approach to that one proposed by Chanson was used to calculate the mean value of the friction factor. These results, expressed in terms of dissi­ pation efficiency, are reported in Figure 8 for each geometric configuration. The good agree­ ment between the experimental and analytical data shows how, along with the other experimen­ tal data. lower slope spillways have a better dissipation behaviour for the same discharge. The conclusions of this study find further confirmation in the experimental data of Yildiz & Kas ( 1998). who worked with larger channel slopes and determined dissipation efficiencies lower than those derived analytically assuming f equal to one, while, recently, Yasuda & Ohtsu ( 1999), using a similar approach, found experimentalfvalues in close agreement to our data. The dissipation rate in our and Yildiz and Kas's laboratory experiments 2 are reported in Fig­ ure 9. The figure confirms best dissipation efficiencies when the stepped spillways slope de­ creases, even if it shows decreasing performance levels when the discharge increases. The con­ tinuous curves obtained from the application of equation (9), withf equal to one and a equal to 6° and to 60° respectively, largely overestimate the experimental data, once again underlining the limited reliability of this kind of analytical procedure. The availability of further experimental data with different channel slopes, number of steps and discharges was a stimulus for a new preliminary verification of the calculatedfvalues. This verification used a minimisation process of the mean square error to estimate a mean value of 2

The e~pcrimcntal data by Yildiz and Kas. represented in Figure 9. are related to stepped spillway models ha1·ing a step height equal to 2.5 em.

109

the friction factor able to justify the experimental results. The results of this analysis are re­ ported in Figure 10, where the calculated friction factors are represented versus the channel slope. The trend confirms the previous conclusions, showing larger friction factors for increas­ ing channel slope.

5 CONCLUSIONS This study focused its attention on two important aspects concerning the physical interpretation of stepped spillways: the determination of the flow condition and the evaluation of dissipation efficiency. Despite the considerable interest of the scientific community, some uncertainties and a certain approximation in the methodological approach still exist. In particular, the difficulties regarding the definition of the criteria for determining and classifying the flow regimes and all the inherent uncertainties in the definition of a structure's hydraulic behaviour. As with other hydraulic phenomena characterised by the transition between two very differ­ ent flow typologies, there clearly exists a transition zone in which the nature of the two regimes overlaps. This eventuality, which can be observed in our experimental data, shows how a differ­ ent approach could fit the experimental data fairly well, even with some uncertainties. This ex­ perimental deduction, therefore, provides a valid input to future studies on this subject, furnishes further stimula and confirms the need for a general re-examination ofthe methodical approaches utilised for the solution of this problem. As far as the determination of the dissipation efficiency is concerned, the definition of a unique evaluation procedure still seems to be lacking. While for the nappe flow regime, the theoretical hypotheses are confirmed by the experimental data, the estimate of the fricticn factor f represents the true issue of the problem for the skimming regime, as it cannot be attributed with a constant value independent of discharge and channel slope, as demonstrated by the new experimental data.

REFERENCES Chanson, H. 1994. Hydraulic design of stepped cascades, channels, weirs and spillways. Oxford: Perga­ mon. Chanson, H. 1996. Prediction of the transition nappe/skimming flow on a stepped spillway. Journal of Hydraulic Research, 34 (3): 421-429.

Esse;.(, I.T.S., Homer, M.W. 1978. The hydraulic design of stepped spillways. London: ClRIA Report 33, 2" edition. Hager, W.H. 1983. Hydraulics of plane free overfaiL Journal of Hydraulic Engineering ASCE, I 09 (12): 1683-1697.

Hager, W.H. 1992. Energy dissipators and hydraulic jump. Water Science and Technology Library 8, Dordrecht: Kluwer Academic Pub!. Ohtsu, 1., Yasuda, Y. 1997. Characteristics of flow conditions on stepped spillways. Proc. 27'h IAHR Congress, San Francisco, Theme D, 583-588. Peyras, L., Royet, P., Degoutte, G. 1992. Flow and energy dissipation over stepped gabion weirs. Journal of Hydraulic Engineering ASCE, 118 (5): 707-717.

Rajaratnam, N. 1990. Skimming flow in stepped spillways. Journal of Hydraulic Engineering, ASCE, 116 (4): 587-591. Discussion: 118 (!): 111-114. Rouse, H. 1936. Discharge characteristics ofthe free overfaiL Civil Engineering, 6: 257. Sorensen, R.M. 1985. Stepped spillway hydraulic model investigation. Journal of Hydraulic Engineering, ASCE, Ill (12): 1461-1472. Discussion: ll3 (8): 1095-1097. White, M.P. 1943. Energy loss at the base of a free overfall- Discussion. Transaction, ASCE, I 08: 13611364.

Yasuda, Y., Ohtsu, I. 1999. Flow resistance of skimming flow in stepped channels. Proc. 28'h IAHR Con­ gress, Graz, 814.

Yildiz, D. & Kas, I. 1998. Hydraulic performance of stepped chute spillway. Journal of Hydropower & Dams, 5 (4): 64-70.

110

Hydraulics of Stepped Spillways, Minor & Hager (eds) © 2000 Balkema, Rotterdam, ISBN 90 5809 135 X

Energy dissipation comparison among stepped channel, drop and ramp structures Alessandro Peruginelli & Stefano Pagliara Dipartimento di lngegneria Civile, University of Pisa, Italy

ABSTRACT: The work describes the results of experiments conducted at the Hydraulic Laboratory ofthe University ofPisa. Tests were conducted for stepped channels, drops, smooth and block ramps by equipping two models. For the case of stepped channels different step types were used: smooth steel steps, artificial rough steps and smooth steps with the presence of end sills; different runs, with respectively 20, 14 and 9 steps, have been considered. Experiments refer to "nappe flow" and "skimming flow" configurations. The main purpose of the work is the comparison of the energy dissipation among the different hydraulic structures. I INTRODUCTION Energy dissipation is one of the most important feature in the design of many hydraulic structures. Actually, cascades are of great interest for the engineering community. Poggi (I 949, 1956) conducted the earlier experimental studies on stepped channels for the case of nappe flow regime. Essery and Homer (I 978) made the first comprehensive work on this kind of hydraulic structure, giving numerous graphs useful for design. Stephenson (1991) presented graphs relative to energy dissipation. Recently, Rajaratnam (1990), Diez-Cascon et al. (1991), Peyras et. al. (1991) and Christodoulou (1993) made consideration and experiments on energy dissipation in case of stepped channels. Chamani et al. (1994) introduced a method for estimating the energy loss of nappe flow. Chanson (1994) gave the equations for energy dissipation for both nappe and skimming flow for both un-gated and gated spillways. The discussion of the paper of Chanson produced new experimental data (Ohtsu and Yasuda 1995, Kells 1995, Matos and Quintela 1995). Chanson (1995) gave a general overview of stepped channels and other types of hydraulic structures together with their historical evolution. Chanson (1997) also extended the consideration on energy dissipation for low slopes cascades. In the present work the energy dissipation relative to stepped channels is compared with the drop, the smooth and block ramp structures. Drop structures have been investigated by Moore (1943) and Rand ( 1955). Hager and Bretz ( 1986) studied the case of submerged drop structures.

Figurel. Different hydraulic structures compared in this work 111

L

1

·~""~ ~ h~o.on7 m -·-y I

·'-.___/

---~gate

-

p1ezometers

0

end sill

_.L...lo

.__I

Figure 2.Sketch of the stepped channel model

+-----

080m

Figure 3. Sketch of the experimental setup for drop, smooth and block ramp

r--·- - -L-

0.8

~

c

1.19474-0.59501 X - , h l

___.£.

d

___.£.

h

> 0.78145-0.17725

h

X-,

I

for concrete or rock steps;

(3)

for gabions steps.

(4)

Chanson (1996) presented the following formula to determine the onset of skimming flow, together with the comparison of experimental data collected by several authors

120

(5)

h

a

where is the initial angle of the streamlines with the horizontal, Frb is the Froude number at the step edge. Eq. (1), (2) and (3) are represented in Fig. 2, along with Eq. (5) for Frb=l.65 and 2.70. The discussion of Fig. 2 is presented in section 4.2, together with the results obtained in the present study. As far as known, there are currently no criteria to determine the occurrence of the different types of nappe flow. However, there is more information about the onset of skimming flow then on the occurrence of isolated nappe flow with fully developed hydraulic jumps. There are also no criteria to determine the occurrence of nappe flow. or the onset of the skimming flow for raising steps or for steps with end sills.

2.2 Energy dissipation and residual head For a stepped channel with nappe flow having enough steps so that uniform flow can be reached at least in the last step, the residual head, H,, immediately downstream of the channel can be expressed as 2

H r =d+-q~

(6)

2gd-

where d is the flow depth, q the discharge per unit spillway width and g the acceleration due to gravity. The energy dissipation, &!, is expressed as (7)

M-f=Hmax-Hr,

where Hmax is the maximum head (Hmax= Hd + 1.5 de, with Hd being the dam height from the toe up to the spillway crest) and H, is the residual head at the toe of the stepped channel. It must be emphasised that. the residual head is a more direct information for the designer, because it will be used to evaluate the necessity and possibly to design an energy dissipation structure. Following this idea, Chanson (1994b) presented the following expression valid for free flow spillways and nappe flow with a fully developed hydraulic jump

H,

de 0.54( h

)0.275 +].4](dc_· )-0.55 - .. 2

h

(8)

Chamani and Rajaratnam (1994) by introducing the concept of average energy loss per step presented the following equation, based on the data published by Essery and Horner ( 1978) (8:o; N :o;30; 0.03:o; h(m) :o;0.45 ; 0.421:o; hll :o;0.842)

121

Hr

(9)

Ho

(10)

where N is the number of steps. Eq. (9) is represented in Figs. 3 and 4 for different values of hi/ and N. The discussion of these figures is presented in section 4.3, together with the results obtained in the present study. 3 EXPERIMENTAL FACILITY The study described in the present paper was developed in an experimental facility built at the Laboratory of Hydraulics and Water Resources of the Instituto Superior Tecnico, Technical University of Lisbon. The facility, shown in Fig. I, comprises a 0.70 m wide and 8.00 m long flume, with glass walls. Upstream of the flume there is a flap gate, which controls the discharge flowing out of the upstream reservoir. At the downstream boundary there is a flap gate to control the water level downstream of the stepped channel. The ten steps, built with PVC, are 0.05 m high and have variable length comprised within 0.10 and 0.25 m. The water supply to the facility used a centrifugal pump with a maximum discharge of 40 1/s. An electromagnetic flowmeter was installed in the supply pipe. The accuracy of the flowmeter was checked with a Bazin weir temporarily installed at the downstream end of the. flume. The water levels upstream and downstream of the steps were measured either by a hydrometer installed over the flume walls, or in external lateral hydrometers installed on the right wall of the flume. The simultaneous use of both measuring systems reassured the accuracy of the water level measurements. The residual head was obtained by the indirect or non-intrusive method, measuring the downstream sequent depth, d2, of the hydraulic jump imposed at the toe of the last step. The momentum equation was applied to compute the upstream sequent depth, d1 . The hydraulic jump position was controlled with the flap gate installed at the downstream extremity of the flume.

Fig. I- Nappe Oow facility ot lhe Lab. of Hydraulics a.nd Water Resources, 1ST, Lisbon.

122

ck/h 16 / [q

(5)

Frbo=o2 70

------ - . Essery and Horner (1978)

--~----

----~

?eyros e\ ol (I 991) Stephenson ( 1 99 1) Be.tz urHJ Luwless ( 1992) Kells (I 'j'J'') Shu-- Xun et ol ~lalos

( 1'YJL)

(1997):Fr=2 70

•

Present study

-"

Present study 1;m;t of ;soloted nappe flow

lwnit of isolated nappe flow

with partially developed hydraulic jump

0

---~----

0

0 2

0.4

h/1

-------~- ---~--

0.6

0.8

1.0

. 2

1.4

Fig. 2. Nappe and skimming !low occurrence.

4 RESULTS AND DISCUSSION 4.1

Scope of the experimental research

The experimental research was conducted with two main purposes: establish nappe flow occurrence criteria and determine the residual energy at the toe of the stepped spillway. Until today, the tests were carried out for 1:3 and l :4 slopes. It is intended to perform identical tests for l :2 and l :5 slopes, in order to obtain a more complete set of data, which will allow more general conclusions. The results already obtained for the slopes referred to are presented and compared with other authors' data and criteria. 4.2 Nappe flow occurrence

The nappe flow occurs from q=O up to the onset of skimming flow. This last aspect was previously reviewed in this paper. In the present study, the onset of skimming flow was considered to occur when the cavities beneath the free falling nappes disappeared in all steps of the spillway, since it was verified that some cavities showed a tendency to exist up to slightly higher discharges than others. In Fig. 2, data and criteria from other authors are presented together with the two data points corresponding to slopes h/l = l :3 and I :4. Two other points corresponding to the limit of the isolated nappe flow (impact of the whole nappe in the step) are also presented. The analysis of Fig. 2 shows that: There are no data for the slopes considered in the present study_ Most of the data was obtained for larger slopes, corresponding to situations of stepped spillway over concrete gravity dams, where skimming flow occurs for lower specific discharges. The onset of the skimming flow occurs for higher values of d/h, when the spillway slope decreases, as would be expected. In the proximity of the axis d/h, the shape of the curves derived from Eq. (5) does not seem adequate, once an asymptotic tendency should occur. This tendency is underlined by the two data points obtained in the present study. The two data points corresponding to the occurrence of isolated nappe flow arc close to the curve proposed by Chanson (1994•), which refers to the occurrence of nappe flow with a fully developed hydraulic jump.

123

4.3 Energy dissipation and res1dual energy

As previously mentioned, the non-intrusive method was used to determine the residual head a t the toe of the stepped spillway. For each slope (I :3 and I :4), several experiments were carried out, varying the discharge from a minimum value of 2.5 Vs, which was considered as minimum value compatible with accuracy of discharge and water level measurements, up to a maximum value corresponding to the onset of the skimming flow. The data are represented in two different ways, together with other authors' data: the dimensionless total head loss (Fig. 3) and the dimensionless residual head (Fig. 4). Although the present authors prefer the second plot, because it gives a more clear indication to the user, it was considered that the first plot should also be included because several other authors have presented it. The analysis of Fig. 3 raises the following comments: The tendency of &-l!Hmax increasing with Hide, already observed by other authors, 1s verified with the data collected in the present study. The data of the present study fill the gap for low values of Hide. According to the present study, the measured dissipation agrees relatively well with curves corresponding to Eq. (9) for N= 10 and h!/=0.333 and 0.25, although these apply for 0.42]: 10, and the hydrostatic term cos¢ may be neglected compared to the hydrodynamic term F 2 • Accordingly (2) may be simplified and expressed simply as (Hager and Blaser 1998)

dY --=-a(Y -l)Y

(3)

dx

with Y=hlh 11 , x=xlxs where x,=h ~ !(h ~sin¢) is a scaling length, and o=l 0/3 for turbulent rough flow, based on the Gauckler-Manning-Strickler (GMS)-formula. The general solution of (3) subject to the boundary (subscript a) condition Y(x=O)=Yo where Yo=h/h, is

[ Y-1 YJ=-a-x

In yo _ · ; 1

(4)

.

Solving for Y(X) results explicitly in

Y(x)=[t-(1- yo- 1 ) exp(- a-x

W

(5)

This formulation is advantageous in terms of generalized presentation of results. Note, however, that both Y and X involve h,, i.e. either the uniform flow depth hw11 for blackwater, or the uniform mixture flow depth h111 , for white water. The results are presented subsequently.

131

4 DRAWDOWN CURVES Figure 3 relates to two typical experiments with rjF=30° and 50°. At the upstream channel end (subscript o) with a flow depth hwo, i.e. Ya=h~.jhwr, the corresponding abscissa Xo is introduced such that the boundary value satisftes (5). The solid data points then follow the prediction. At the inception point, there is no change of normalization because the equivalent blackwater drawdown curve Yw(x+Xo) is plotted. For both cases, agreement between observation and prediction is noted. For all drawdown curves collected, these profiles were checked with Eq.(5) and Figure 4 shows principal agreement. For ¢F30° the standard deviation of data is less than ±5%, whereas it is almost ±I 0% for ¢ =50°.

2

21

Yw

\

: Yw 1.5 ~

1.5

'

••

I

0.5 -

0.5

L __

0 0

_ _ j_ __ j __ __ L _ _

0.5

1.5

OL_____

~+Xo 2

~

_ L_ _ _ _ _ _~----~

1.5

0.5

0

2.5 ~

Figure 3. Drawdown curve Y"(x+Xol relating to blackwater condition with ( t) x$x, and (0) x>x1, for (a) t/F30°, (b) t/F50°.

(-)

Eq.(5)

2n----------------------,

2.8 1.6

2.4

0

0 ~

Yw

2

0

0

3

4

0

5 ~

2

3

Figure 4. Plot of all drawdown curves Y"(x+Xo) for (a) ¢F30°, (b) ¢F50°; Notation Figure 3.

132

4

5 BACKWATERCURVES Speerli and Hager (2000) investigated backwater curves in bottom outlets for a relatively small bottom slope. Their approach may be directly applied for stepped spillway flow. Boes (2000) demonstrated the applicability for blackwater conditions, which occurs under selected configurations, yet not being very typical in applications. The following thus refers exclusively to whitewater conditions, starting from the point of inception. The basic differential equation for hypercritical air-water mixture flow can be demonstrated to be again df/dx=l~Y 3 • Its solution is available but complicated by transcendental functions (Chow 1959). An approximation within ±5% reads (Speerli and Hager 2000) Y9o(xJ=tanh(1.1xJ,

(6)

where tanh is the tangent hyperbolic function. Further Yq 0 =h 9r/hqo, with h90 =hm(C=0.9) as mixture flow depth with a surface air concentration of 90%, and xm=xlxm, where

xm=h ~ l(h ~" sin¢) is the mixture normalizing length. In order to plot all data on one curve, one will again select an abscissa %( f 90 = Y90 ,.)= Xo at the inception point and then move in the downstream direction. Figure 5 compares the data with Eq.(6) and agreement is again noted. A typical standard deviation is ±5% for ¢=30° and ±2% for ¢=50°. These deviations are so small for air-water flows that one can talk of almost perfect agreement.

6 UNIFORM FLOW Skimming flow eventually develops into a uniform aerated flow of depth h90,. Boes (2000) established a uniform flow equation for 0.55,h 90,,/s0.50 approximately

Xn

l

(17)

= U(0.95-Y;),

or (18)

This has the same form as Eq.(l3) for the drawdown length. Again, the effect of h!h 90 , is significant. Eq.(l8) can be developed by accounting for the inception flow depth (Boes 2000)

he_ - -l - (. sm'f'A.Fs )1/9 • hi 0.316

(19)

Inserting Eqs.(8) and (19) in Eq.(18) gives (20) For typical spillway angles rjF-30° and rjF-50°, the term (sin I/Jr 119 is 1.08 and 1.03, respectively. For an average of 1.05 one has 0.575(sini/Jr 119=0.60 and, therefore, X8 exclusively in terms ofFs 135

(21) Given that Fs= F. sin2 ¢by definition, the step Froude number is typically smaller than 30. For l9.0 2.5:i!hjdc:i!9.0

o• < 8 ~ 14"

- 19•

a)

b)

=-----~­ ~»7 »nnQ....--::. ?'7"777>7>>

::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Figure 4. Defillilion sketcb in plunging flow.

Figure 5. Flow patterns due to a change of downstream depth in stepped channels.

148

tions (Table I). In order to examine the velocity decay in plunging flows, an electromagnetic velocity meter was used [sampling time= 120 s, sampling frequency= 40 ms]. Also, the flow condition was recorded by using a video camera. 3 FLOW CONDITIONS OF PLUNGING FLOWS The flow condition of plunging flows in stepped channels changes with the discharge Q (or dis­ charge per unit width q), channel slope tan B , and downstream depth hd under a given dam height (total height of stepped channel) H 0 and step heightS (Fig. 4). Flow patterns with a change of downstream depth can be classified into two types. 3.1 FlowConditionsfor0° ::

0.3

.~

.c -'

.z;0

0.2

1---------,L--i-------:;?'""'=------;---------+---=~-'--l

::0 c a:l

~

f-+

0.1

--

/ / ~ / _:;;.. ..-+- - - . : m momm•od•d c,= 0 lm 1

/~--:::::...

.__..-

S ~sin slope

!

0 L-------~------~-------------------------" 40 30 20 10 0

Unit discharge q (ml's)

Figure 4

Design Chart for blocks in skimming flow

4. 2 Geotechnical considerations The problem of embankment stability is of course site specific and it is stressed in the Design Guide that a proper ground investigation must be carried out prior to the start of design work, with the determination of undrained and/or drained shear strength parameters. These need to be used to assess the spillway stability; during construction; under dry conditions; during operation when the embankment may become partially or fully saturated and immediately following operation as the embankment drains. 4. 3 Stilling arrangements Failure of loose blocks has been witnessed in the laboratory under a hydraulic jump. There are two modes of failure: individual blocks lifting about their upstream edge and rotating backwards and group of blocks lifting together in a wave. Three design methodology to avoid failure are proposed in the Guide: the use of large blocks in the stilling area, Fig. 2; the construction of a mass concrete toe anchor block, Fig. 3; or termination of the pre-cast blocks upstream of the expected hydraulic jump zone the and construction a conventional reinforced concrete stilling basin. On all spillways built outside of Russia to date, the latter option has been selected. 4. 4 Underdrain An important feature of the system design is a free-draining layer between the blocks and the protected embankment. This serves as an underdrain to collect seepage flow and facilitate its evacuation via the drainage holes to the low pressure zone. It also acts as a filter to prevent the embankment material from being eroded and sucked through the holes, and as a regulating iayer to assist construction. In the Russian prototype installation the drainage layer has been constructed from layers of graded stone whilst in the West combinations of stone and geotextilc have normally been adopted. With all designs it is important that the smallest size of stone in the underdrain can not be carried through the holes or slots in the block. The only kno"n prototype failure, at Jelyvski in the Ukraine , Pravdivets (1982) was caused by loss of the underdrain and embankment material through the holes in the blocks during first operation.

158

Drainage vents 8==350mm

\~~-'1 _____00::_

[:Z25rr.J22.5rr.J

Vent deton

----~------------~--

Figure 5

Minimum block dimensions recommended in the Design Guide

4.5 Minimum block size

For block sizing away from the toe regime design charts are provided, Fig. 4, but the Design Guide recognises that for many sites the block geometry will be fixed by concrete casting and handling considerations. A minimum average block thickness of I OOmm is recommended with a step height of 60mm and seven I 0 x I Omm drainage slots cast into the underside of the overlap, Fig 5. Whilst this would be adequate for hydraulic considerations at most sites it is recognised that the designer may wish to make the blocks larger to make them less vulnerable to vandalism and to reduce the number of blocks and hence the laying effort. When considering block shape and size it is important that the designer sticks to the geometric provisions of the Design Guide. In laboratory tests the blocks have been shown to work best with a step height to length ratio of 1:5 and with between 2.5 and 5% of the exposed block area being provided as drainage holes or slots in the Icc of the step. Smaller step height to length ratios or less open area for drainage will lead to instability. Larger step-height to length ratios make the system ineffective and large hole areas allow significant quantities of water to enter the underdrain during low flow when the spillway is operating in nappe flow regime 4. 6 Spillway construction

Throughout the design process the designer should give consideration to the construction methodology and the safety of those involved in the construction operation. Points to consider include the method of block production, which could include dry or wet casting in a factory with transport to site, or wet casting in a pre-cast yard on site. Block handling is also an important criteria, large blocks may need lifting eyes for cranage. The access, reach and safe operation of suitable equipment on the embankment slope must be considered. With overlapping block shapes as recommended in the Design Guide, laying must commence at the toe and work up hill.

159

(j)

0

'KEY:

wo

WO

BRUSHES CLOUGH (UK)

BW

WADI SAHALNAWT (OMAN)

WO

BW

JIANG SHE WANAN (CHINA)

OTHER

JELYEVSKI

TRANSBAIKAL

KOLYMA

ONEISTER COFFERDAM

0.125

0.2

0.52,-

OS - Overlapping slabs

0.59,0.725

1.0,1.2

2.12

3

2

1

0.4

1.0

2.12

2

2

1

0 333

0.285

0.2

0.125

0.4

0.5

0.222

0.154

2

980

12

115

6

20

14.2

12

7.5

15

12

CHANNEL WIDTH (m)

BW - Butl-jointed and wedge shaped

0 212

0.2

0.74

0.35

0.25

0.25

0.8

wo

DNEIPER POWER STATION

3.0

0.167

0.16

3.0

1.3, 1.5

OS

SOSNOVSKI

0.5,-

0.154

0.16

3.0

1.3,1.5

OS

MASLOVO

2.6,3.0

0.159

0.16

3.0

1.3,1.5

0.12-0.2

CHANNEL SLOPE J

OS

(J,)

THICKNESS

KLINBELDIN

(m)

WIDTH B

0.16

0.2,-

lmf" 3.0

6

STEP HEIGHT

1.3,1.5

LENGTH L, L, (m)

OS

BLOCK TYPE

BOLSHEVIK

RUSSIA

LOCATION

Table I Known prototype installations

-,8

2.2

5.1

36.5

18

5

13

63

8

23

7.5

v

(m/s)

1993

1991

1978

1981

1976

1980

DATE BUILT

FULL SCALE TRAPEZOIDAL TEST CHANNEL

AQUIFER RECHARGE DAM

FAILED

SMALL EMBANKMENT DAM

FULL-SCALE TEST CHANNEL

FARM DAM

FARM DAM

FARM DAM

FARM DAM

COMMENTS

WO - Wedge-shaped and overlapping

13,8.5

20,-

7

37,-

3.3

3.0

-,7.5 13,11

3.0

3.3

(my/s)

FLOW

7.5,5.5

-,11.5

z\'mT"

HEAD

I

4. 7 Post construction

The Design Guide also covers the post-construction inspection and maintenance of the spillway giving a list of possible problems, such as settlement, cracking of the concrete or blockage of the drainage holes, which could result in incorrect operation. It is suggested that because of the interlocking nature of the construction faulty or damaged blocks may have to be repaired by insitu-concretc. 5 APPENDICIES The Design Guide contains four very useful appendices. Appendix I lists all of the known prototype sites, Table 1, with photographs and more detailed description of many of the sites. Appendix 2 gives details of the laboratory work conducted in Russia, U.K., U.S.A. and elsewhere which have led to the detailed design criteria for minimum block thickness, best step height to length ratio, minimum area of holes and other criteria necessary for the safe usc of the technology. Samples of some of the data arc provided. Appendix 3 gives additional information on the detail design of the undcrdrain when gcotcxtiles are to be used. Appendix 4 is a worked example based upon a 12.5m v.1dc spillway passing a flow of 60 m3/s down a I in 2.5 slope. This utilizes a 150mm average thickness block on the main spillway increasing to 550mm average thickness at the toe. An alternative toe design using the mass concrete anchor block is also provided. 6 CONCLUSIONS The CIRIA Design Guide for Stepped Block Spillways gives a comprehensive coverage of the methodology for the planning, detail design and post construction maintenance of such spillways, mth examples of laboratory and prototype work, to give designers the confidence to usc the technology. REFERENCES Baker, R. (1992). Concrete blocks for dam spillways. Thesis for the degree of PhD, University ofSalford, U.K. Hewlett, H.W.M., Baker, R., May, R.W.P. & Pravdivets, Y.P. (1997). Design ofstepped-block spillways. Special Publication 142, C.I.R.I.A., London. Pravdivets, Y.P. (1982). Peculiarities of work on spillways ofpre-cast concrete blocks. Gidrotckniehe e Melioratsiya No. 1. January, pp23-25 (In Russian, translation DoE, U.K.).

161

Taylor & Francis

Taylor & Francis Group http://taylorandfrancis.com

Hydraulics of Stepped Spillways, Minor &Hager (eds) © 2000 Balkema, Rotterdam, ISBN 90 5809 135 X

Guidelines for the hydraulic design of stepped spillways Robert M. Boes & Hans-Erwin Minor Laboratory ofHydraulics, Hydrology and Glaciology (VAW), ETH-Zentrum, Zurich, Switzerland

ABSTRACT: Based on model experiments design guidelines for stepped spillways are devel­ oped for two different chute slopes. Particular emphasis is placed on the onset of skimming flow, the location of the inception point of air entrainment, the maximum unit discharge possi­ ble without cavitation risk, the energy dissipation characteristics, the length to attain uniform flow and the required training wall height. I INTRODUCTION Stepped spillways have regained popularity over the last one and a half decades with the evolu­ tion of the RCC dam construction technique. A stepped chute can be economically integrated on the downstream face of an RCC gravity dam. Another common application is the use of stepped overlays on the downstream face of embankment dams as emergency spillways to safely pass the PMF over the crest of the dam. Advantages of stepped spillways include ease of construction, reduction of cavitation risk potential, and reduction of the stilling basin dimen­ sions at the downstream toe of the dam due to continuous energy dissipation along the chute. Overviews of spillways with particular focus on stepped chutes are given by Chanson (1994a), Vischer & Hager (1998) and Minor (2000). Because general design guidelines for stepped spillways are still not available despite in­ creased research activities around the world, hydraulic model investigations on skimming flow were conducted at VAW of ETH Zurich, Switzerland. Details on the experimental set-up and the novel fiber-optical instrumentation used are given by Boes & Hager ( 1998) and Boes ( 1998, 2000). 2 TRANSITION FROM NAPPE FLOW TO SKIMMING FLOW Two distinct flow regimes are found on stepped spillways, so-called nappe flow and skimming flow. Whereas in nappe flow the steps act as a series of overfalls with the water plunging from one step to another (Figure Ia), the water flows as a coherent stream over the pseudo-bottom formed by the step comers in skimming flow. Generally speaking, nappe flow is found for low discharges and large steps. For small steps or larger discharges such as the design discharge the water skims over the step comers, and recirculating zones develop in the triangular niches formed by the step faces and the pseudo-bottom (Figure I b). The transition from nappe to skimming flow can be expressed by the ratio of critical flow depth he and step height s. Ac­ cording to Boes (2000), skimming flow sets in for ratios larger than he = 0.91-0.14tan'l'. A. s

(1)

-

163

~

~

Figure I. a) Nappe flow with h!s"' 0.2 on Urft Dam stepped spillway, Germany, with ¢"' 34 o (courtesy of Dr. V. Spork, RWTH Aachen, Germany), b) Skimming flow over model steps with h!s"' 1.73, ¢= 30°. Eq.(l) is in approximate agreement with the transition functions given by Rajaratnam (1990), Stephenson ( 1991) or Yasuda & Ohtsu ( 1999) and is applicable for chute inclination angles of approximately 25° < ¢< 55°. A certain risk of acoustic noise due to vibrations of the falling jets exists in the nappe flow regime, especially for wide spillways where the cavity below the nappe is not aerated over the entire width. However, as is illustrated by a typical prototype example in Figure I a, the nappe aeration at the free surface is rather large due to the high degree of turbu­ lence caused by the macro-roughness of the steps, so that excessive sub-pressures beneath the falling nappe are unlikely to occur. Further studies on the pressure distribution for the transition between nappe and skimming flow are recommended. 3 AIR ENTRAINMENT Where the turbulent boundary layer reaches the free surface, the degree of tubulence is large enough to entrain air into the water flow at the so-called inception point of air entrainment. For the designer of a stepped chute, knowing the location of the inception point is important to have an idea of the unaerated spillway zone which is potentially prone to cavitation damage due to large sub-pressures. According to Boes (2000), the unaerated or black water length L; (Figure 2a) from the spillway crest to the inception point can be described by (Figure 2b)

L; = 9. 72 Fr. 0.86, K

(2)

where K = s cos¢ denotes the roughness height perpendicular to the pseudo-bottom, Fr.= q/(gsin,Ps 3) 112 is a roughness Froude number containing the relevant parameters of stepped spillway flow such as unit discharge q, step heights and chute inclination angle ¢, and g is the acceleration of gravity (Figure 2a). If Eq.(2) is written in dimensional form

L; = 9. 72

q

0.86

A. COSY'

g0.43 (sin¢)0.43 so.29

(3)

'

the small influence of the step height becomes obvious, whereas it can be seen that the unit dis­ charge predominantly determines the location of the inception point. If in case of high velocities the hydrodynamic pressures on the step surfaces or at the step corners fall below the vapour pressure, cavitation might cause severe damage to the spillway concrete. The placement of an aerator to artificially entrain air is therefore of interest in the black water region of a stepped spillway. This can also be achieved by bridge-supporting piles downstream of the spillway crest as for the Puebla de Cazalla Dam in Spain (Mateos Iguacel & Elviro Garcia 1992). Further research on the hydrodynamic pressure fluctuations should shed more light on the cavitation risk potential of stepped spillways, particularly of the unaerated spillway zone. 164

300 250

L/K

200 150 100 50

~

.;v

~ 10

~

h

/

,/

,/.

Fr. 20

30

40

50

~

Figure 2. a) Side view of a stepped spillway: (---)pseudo-bottom, flow region with (I) equivalent clear water of depth hw and CD mixture of depth h90 , (·-·-·)energy head, and (o) inception point, b) Non-di­ mensional length L/K(Fr. )for ¢ = 30° and K = (•) 20, (•) 40 and ( +) 80 mm, tjJ = 50° and K = (.6.) 20 and (V) 60 mm, ( - ) Eq.(2). 4 SELECTION OF STEP HEIGHT When designing a stepped spillway, the height and downstream slope of the dam as well as the design discharge are normally given. The maximum unit discharge is either determined by the spillway width due to limited site conditions, or by hydraulic constraints as discussed below. In selecting the step height of a cascade spillway, the designer usually chooses from a certain range of values determined by the dam construction procedure. For RCC dams, for example, the step height is usually one to four times the thickness of a compacted lift of typically 0.3 m, i.e. between 0.3 and 1.2 m. Two main aspects have to be considered when selecting the step height and are discussed in the following, (I) cavitation risk potential, and (2) energy dissipation rate of a cascade. 4.1 Cavitation risk

Based on the fundamental work of Peterka (1953) and experience with aerated high velocity flow (e.g. Minor 1987), a local air concentration of about 5 to 8% is a minimum value widely accepted today by design engineers to avoid cavitation damage to concrete faces. Boes (2000) examined the air concentration Cb at the step comers (index b) for two different inclination an­ gles and found the following values for fully aerated uniform flow (Index u, Figure 3a), with Fr. as defined above Cb.u =0.068-6.21·10-4 Fr.

(4a)

Cbu =0.268-5.69·10- 3 Fr.

(4b)

The concentration distribution along a stepped chute is given by (Figure 3b) Cb (X)= (1-exp( -0.035(X + lO))Cb.J Cb (X)= (1-exp( -0.025(X + 2))Cb.u)

for~= 30°,

(Sa) (Sb)

The non-dimensional streamwise coordinate X= (x- L;)lh90,,, with x starting at the spillway crest, denotes the distance x- L; from the inception point (index i) normalized with the charac­ teristic mixture flow depth for uniform flow h90 ,,.

165

If Cb = 0.05 is considered a minimum value to avoid cavitation damage, the maximum rough­ 112 ness Froude number must not exceed Fr•max= qmaAs 3 sin¢) = 29.0 and 38.3 for¢= 30° and ¢= 50° according to Eq.(4a) and (4b), respectively. The maximum unit discharge qmax to pro­ vide a bottom air concentration in uniform flow large enough to avoid cavitation damage even 2 for very high flow velocities thus amounts to values between qmax = 10.5 and 84.4 m /s for step heights between s = 0.3 and 1.2 mat an angle of¢= 30°. For a gravity dam with a typical¢"" 2 50°, qmax increases from 17.3 m2/s for s = 0.3 m to 138.0 m /s for s = 1.2 m. The latter value is far beyond the maximum unit discharge of about 25 to 30 m2/s (Minor 2000) commonly ac­ cepted a limiting value so far. Mateos Iguacel & Elvira Garcia ( 1992) were even more careful 2 and recommended a critical unit discharge of only q..a,= 10 m /s. It should be noted however, that all C-results presented are on the safe side for design purposes because due to a higher de­ gree of turbulence in the prototype, the aeration tends to be more pronounced than suggested by model results (Boes 2000). It can be concluded from the definition of the roughness Froude number that qnuu increases with 312 s , i.e. increasing the step height by a factor of 4 increases qmax by 8. Regarding cavitation risk, higher steps allow a considerably larger maximum water discharge to be released over a stepped spillway than small steps. In other words, higher steps have a smaller cavitation poten­ tial than small steps for a given discharge. Furthermore, the spillway length needed to attain uniform aerated flow decreases with increasing step height (see Eq.(6), Christodoulou 1999, Hager & Boes 2000). It should be borne in mind, however, that the range of discharges in the nappe flow regime increases with increasing step height according to Eq.(l). Like the black water region upstream of the inception point, the downstream developing region up to X( Cb = 0.05) might also be prone to cavitation damage in case of high velocities greater than approximately 13 m/s (Mateos Iguacel & Elvira Garcia 1992). An aerator placed in the unaer­ ated spillway region downstream from the crest as previously proposed is again required to attain a sufficient air content at the step comers along a stepped chute. Regarding the horizontal and vertical step faces in the step niches, the experimental results of Boes (2000) show that a minimum air concentration of between 5 and 25% can be found in the near-uniform region of a stepped spillway with a bottom inclination angle of 50°. The higher air concentrations are found in the upper half of the vertical face, where the negative pressure minima occur according to the experimental results of Sanchez Juny et a!. (2000). For all dis­ charges tested, the minimum pressures were well above the critical cavitation values, however.

0.3

f 0

1.4

Cb(X)/Cb.u A

P~'·.

0.2r

A

0

0

A

A AA

0

·o

0.6

w

'V

'V

'V 'V

'V

A

A

0

0.1

• 10

~

• 20

0.4

•

0.2

•

Fr.

30

40

X

00

50 ~

50

100

150

200

Figure 3. Bottom air concentration: a) in uniform flow Cb.u(Fr.) for¢= (•) 30° and (o) 50°, (--) Eq.(4a) and(---) Eq.(4b); b) along the chute Cb(X)!Cbu for¢= 50° with model steps ofs =(A) 31.1 and (v) 93.3 mm, ( - ) Eq.(5b).

166

Therefore, no risk of cavitation damage is expected in the step niches of stepped spillways for fully aerated flow. 4.2 Energy dissipation For the designer of a stepped spillway, knowledge of the energy dissipation along the chute is essential for an adequate design of the downstream stilling basin or any other energy dissipator. Two methods to compute the residual energy head Hres at the spillway toe should be distin­ guished, whether uniform aerated flow (index u) is attained or not. According to Yildiz & Kas (1998) and Matos & Quintela ( 1995a) this is the case for approximate relative dam heights Hdan.lhc~ 20 and Hdan.lhc?. 25 to 30, respectively, whereas Christodoulou (1999) gives a distance L, parallel to the pseudo-bottom of L

86

=

.

5 001

u

q

0.71

(6)

(cost/J)0.07(sint/J)028'

where Lu is measured from the spillway crest. The data of Boes (2000) on relative residual en­ ergy as function of the relative dam height are plotted in Figure 4 for chute inclination angles of 30° and 50° together with the analytical curve proposed by Chanson ( 1994b) for uniform flow

Hres

(7)

Hmax

where Hmax denotes the reservoir head, fw.u is the friction factor for uniform equivalent clear water flow and a is the kinetic energy correction coefficient. According to the experimental re­ sults of Boes (2000), the kinetic energy coefficient a= 1.21 on the average, which approxi­ mately agrees with the value of 1.16 proposed by Matos (1999) for stepped spillways and with 1.20 scd condtul air ilow (T I 00), where a quasi-uniform fully aerated flow might be attained at the spillway toe. the mean air concentration can be assumed equal to that obtained in a smooth chute of identical slope (sec e.g .. Hager 1991 ). 4.3

Trwning Hoff he;ght

The design of the training walls should take into account free-surface aeration. The estimation of the characteristic depth Y9o requires the knowledge of the mean air concentration Cnean (Eq. 4) and also of the equivalent clear water depth. d (Eq. I) The above parameters can be estimated from Eq. 4 and 6. for!= 0.08. 4.4

Residual energ_v

The specific energy at the spillway toe (residual energy) can be estimated by Chanson ( 1994. p. I 03). wherc(can be assumed equal to 0.08. It 1s important to note that the above formula is only precise if quasi-uniform flow conditions arc reached at the toe of the spillwav. 4.5

l'otential{i1r cavitation damage

To the authors· knowledge, cavitation damage has not occurred during operation of stepped spillways. Stepped block protection systems have been successfully used on t1at slopes on sev­ eral Russian dams \\ ith design discharges up to 20 m 2/s (Pravdivcts 1987). Prototype tests have also been conducted for unit discharges up to 60 m 2/s on a special test chutc at the Dnciper hy­ droplant (Pravdivcts and Bramley 1989). Ho\\ever, if the stepped chute is designed for signifi­ canth higher unit discharges, the likelihood of cavitation should be investigated.

:'i NON-CONVENTIONAL SPILLWAYS CHARACTERISTICS Three types of non-conventional spillways founded on the downstream slope of earth dams \\ere considered: TYpe I - Reinforced concrete channel. Type II - Gabions stepped channel. and Type Ill - Pre-cast concrete blocks stepped channel. From a hydraulic point of view. the type I spillway is similar to chute spillways founded in one of the dam abutments. However. if found..:d on the embankment. some special precautions must be taken in the design of the slab joints and in the drainage layer (Albert et al .. 1992). Gabions forming stepped channel spillways (type II) increase the energy d1ssipation relative to an impcrv1ous stepped channel. Flow through the gabions increases the energy dissipation. Peyras eta/. ( Jl)l) I) showed that using of gabions in stepped channels with nappe t1ow allows a reduction in the energy dissipation basm length up to 30 percent compared to conventional smooth chute spill\,ay basins. Pcyras eta/. presented design criteria for gabion overflow struc­ tures. The type Ill spillway was developed in the former USSR (Pravdivcts and Slisskv. 1981) Its fundamental characteristic is the usc of wedge-shaped pre-cast concrete blocks. Th~ blocks are used with a drainage layer. which ftltcrs the seepage flow and protects the subsoil from tlow erosion. The blocks are inherentlY stable due to the hydrodynamic forces generated by the sktmming tlow (Baker et ol.. 1994: FrizelL 1997) To improve the block stability and the per-

184

formanct.: of th..: drainag..: lay..:r. dramag..: hoks arc made in the blocks, assurnu~, together with the drainage: lavc:r. that uplift forces arc negligible. The channel is lined with rows of blocks, placed t1ghtly. in shingle-fashion from the downstream toe with no longitudinal joints aligned. 5 I Design criteria and cost estimate

To rapidly evaluate the economic advantages of the construction of non-conventional spillways just described, Rclvas (I 997) developed a computer program for conducting preliminary designs of non-conventional spillways. The program computes the main characteristics of several solu­ tions, with d1ftcn.:nt channel widths for each spillway type. With input of a set of unit costs for the main types of works included in the spillway·s construction, the program also computes the respective cost cstimat~:s. following an iterative cycle converging to minimum cost. 5. 2 Case studies

The costs of non-conventional spillways founded on the downstream slope of embankment dams were compared with the costs of conventional spillway solutions. Following arc brief de­ scriptions of three Portuguese dams that were selected for comparison (Table I): - Foz do Guadiana dam is 22 m high with an ogcc crest and chute spillway dt.:signcd for . 24 m3/s - Enxoc dam 1s 21 m high with a non-conventional stepped chute spillwav designed for 42 111 'Is It mcludes an X-m-wide horizontal free flo\\· control structure follo~\'cd by a 6X.5m-long stt.:ppcd concrete rectangular channel of the same width. adJacent to downstream slope of the dam. Tht: steps arc 1.50 m high. The first spillway reach is followed by a 50-m-long stt.:pped trapezoidal channel lined with Reno mattresses forming I m h1gh steps. The adoption of a steppc:d spill\\ay \\as intended to eliminate a downstream energy dissipation structure (LNEC. 1996) - Ribeira de Ociras dam is 27m high with a chute spillway \~ith an agee crest designed for 291 m3/s. Table I. -Minimum cost estimates of non-conventional

SJ!illwa~s

for the three case studies.

Spillway costs (I 000 E1 JR) and percentage di!Terences to conventional solution

Dam Conventional

T\'pe I

T\'pe II

------

~~"-~~--

Tvpe Ill

Foz do ( iuach