diseñoescalones

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COMMISSION INTERNATIONALEDES GRANDS BARRAGES

-------VINGT QUATRIME CONGRS

DES GRANDS BARRAGESKyoto, Juin 2012

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GUIDELINES ON THE DESIGN AND HYDRAULIC CHARACTERISTICS

OF STEPPED SPILLWAYS 1

Robert Michael BOESProf., Director of Laboratory of Hydraulics, Hydrology and Glaciology (VAW),

ETH Zurich

SWITZERLAND

1. INTRODUCTION

Spilling floods safely from a reservoir to the tailwater of a dam is a key issueregarding dam safety. Stepped cascades are both spillways and energy dissipatorscombining a number of advantages. On the one hand, the free-surface flow onsurface spillway chutes allows for a safe passage of water even under flood events

larger than the design flood, i.e. for an overload scenario such as the safety checkflood. On the other hand, a stepped chute can easily be incorporated into the dambody of concrete structures such as RCC dams, leading to economic savings due torelatively simple and fast construction both of new dams and for armouring ofexisting embankment dams. Moreover, the high amount of energy dissipationachieved along stepped spillways enables savings on the stilling basin, the length ofwhich can be considerably reduced compared to those downstream fromconventional smooth chutes. The energy dissipation is due to the step macro-roughness, leading to air entrainment and greatly reduced flow velocities andconsequently limiting the cavitation risk. The aeration produces flow bulking,however, and therefore requires higher sidewalls.

1Guide pour le dimensionnement et les caractristiques hydrauliques des vacuateurs decrue en marches descalier.

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2. GENERAL DESIGN ASPECTS

A standard stepped spillway typically consists of a control section at its upperportion, e.g. a standard ogee-crested weir, the spillway chute with uniformly sizedsteps (Fig. 1) and a terminal dissipator structure at the chute toe, mostly a stillingbasin. Two different stepped spillway types should be distinguished:

(1) Large-width stepped spillways with small maximum unit discharges up to about30 m2/s, featuring no bottom aerator and only a small terminal energy dissipater.

(2) Narrow stepped spillways with peak unit discharges above 30 m2/s or so,including bottom aerator and terminal energy dissipator.

Fig. 1Definition sketch of stepped spillway with standard ogee-crested weir as control

structure and step-aerator on first step (adapted from [1])Schma dun vacuateur de crue en marches descalier avec dversoir standard

comme ouvrage de contrle et arateur de marche (adapt de [1])

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Type (1) is the favorite spillway if the hydrologic and topographic boundaryconditions are favorable, i.e. if the peak flood discharge Qmax is either relatively smallor the spillway width B large, resulting in maximum unit discharges qmax=Qmax/B < 30 m

2/s. However, these conditions are often not met, resulting in qmaxconsiderably above the mentioned threshold. Then, type (2) should be selected toavoid cavitation damage to the structure. In the following, the need for a bottomaerator will be discussed and criteria for its application are given. Furthermore, thehydraulic design procedure will be explained.

2.1. CAVITATION RISK AND COUNTERMEASURES

It is well known (e.g. [2]) that cavitation on chutes is initiated for high velocityflows and local pressures below the vapour pressure, resulting in the local cavitationindex

= (hp + ha hv)/[v2/2g] [1]

below a threshold value c, where hp = bottom pressure head, ha= atmosphericpressure head, hv= vapour pressure head, v= local flow velocity and g=acceleration of gravity. The higher the flow velocity and the smaller the pressuredifference between the actual and the vapour pressure, the smaller the cavitationindex. Whereas the critical (subscript c) lower threshold is commonly taken asc= 0.2 for smooth chute inverts, that for a singular step is of the order ofc= 1.00.1 according to [2] and [3], see [4]. For stepped spillways as a series ofisolated steps the critical cavitation index is higher than on smooth chutes butsmaller than for a singular step due to the following reasons: (i) steps form largeoffsets away from the flow direction, preventing cavitation from residing on the

boundary ([5]) and (ii) a uniformly rough surface has a lower cavitation potential thanan isolated roughness of the same geometry due to reduced velocities and wakeeffects ([5]) and [6]). In a recent laboratory study, [7] report of incipientcavitation at= 0.6 to 0.7 and 1.3 for steps inclined by an angle to the horizontal of= 21.9and 68.1 (slopes of 1V:2.48H and 1V:0.4025H), respectively, and of critical c-values of roughly 0.4 and 0.6 to 0.7, respectively. According to [6][6], the criticalcavitation index is roughly four times the friction factor fb both for smooth and roughsurfaces, i.e. c= 4fb. For the typical slope range of stepped spillways of 1:2.9(= 19) to 1:0.7 (= 55) this would amount to values between c= 0.27 (= 45)and c= 0.8 (= 19). Taking into account that no evidence exists so far that astepped spillways has ever experienced cavitation damage ([1], [7]), even those

submitted to unit discharges largely superior to 30 m

2

/s, the limit cavitation index isassumed to be around 0.5 for stepped spillways in the common slope range of 1:2.9(= 19) to 1:0.7 (= 55).

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2.2. REQUIREMENTFOR BOTTOM AERATOR

As shown above, for a given velocity and pressure head, a stepped invertwould be more prone to cavitation than a smooth chute along the un-aerated chute

portion, i.e. upstream from the inception point of self-entrainment, because of ahigher critical inception number. Once air is entrained at the free surface, it is quicklytransported by turbulent mixing to the step surfaces, where the compressible air-water mixture may counteract the strain on the concrete surface resulting fromcollapsing vaporized bubbles caused by cavitation pitting. According to a commondefinition formulated by [8], the inception point bottom (subscript b) air concentrationat the step edge is Cb = 0.01. It has been demonstrated by [9], among others, that asmall local air concentration of 1% may be sufficient to prevent or at leastconsiderably reduce cavitation damage.

Fig. 2 shows the inception number as a function of unit discharge for steppedspillways of various step heights and pseudo-bottom (PB) slopes. Also given is thecritical index of 0.5, as discussed above. The -values have been computedaccording to [10] for water temperatures of 14C. The larger the step height, thelarger the cavitation index for a given unit discharge. For a given step height, the unitdischarge at critical cavitation index c= 0.5 decreases with increasing inclinationangle. Depending on step height and slope, -values fall below the critical thresholdfor unit discharges of between roughly q = 20 and 40 m2/s. This corroborates thehesitation to design classical stepped spillways without aerators for greater unitdischarges. An aerator to artificially entrain air is therefore required upstream fromthe inception point for unit discharges larger than the limit values given in Table 1.

2.3. SELECTIONOF CONTROL STRUCTURE

The following control structures may be combined with stepped chutes:

(i) Ogee-crested weir with or without steps(ii) Broad-crested weir with or without gates(iii) Piano key weir

Most spillway crests are designed as an uncontrolled smooth ogee weiraccording to the US Army Corps of Engineers Hydraulic Design Criteria ([11]). Forstepped chutes, transitional steps of increasing height along the standard ogee-

crested profile down to the point of tangency (e.g. [12]) may be used to reducenappe deflection along the first steps (see also 0). However, if a bottom aeratorbecomes necessary (see 2.2. and 3.1), the standard crest should have no steps so

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that the nappe velocity at the aerator is sufficiently large to ensure its properperformance.

Stepped spillways may have an unregulated broad-crested weir as describedby [13]. If a broad-crested weir is to be regulated by tainter or flap gates, it should befollowed by a sufficiently long and rather mildly sloped smooth chute connected to aconstantly-sloped stepped chute by a parabolic transition, see e.g. [7] for FolsomDam in California, USA. Otherwise, there is a risk of jet deflection, resulting in aconsiderably spray and weak energy dissipation ([13]).

Stepped spillways may even feature a piano key weir as upstream controlstructure as for the case of the Gloriettes Dam in France ([14]).

Fig. 2Cavitation indices as function of unit discharge q for various

chute inclination angles and step heights s

Indices de cavitation en fonction du dbit spcifique q pour de nombreuxangles dinclinaison et hauteurs de marche

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2.4. SELECTION OF STEP HEIGHT

The determination of the step height should primarily be based upon theconstruction procedure. RCC dams are often constructed in layers of 0.3 m andformwork heights of 0.6 to 1.2 m, so that step heights between 0.3 and 1.2 m areconvenient. Larger steps of 2 to 3 m or so may be favourable for stepped spillwayscut into rock such as in the valley flanks at embankment dams to facilitate theconstruction by drilling and blasting.

Results of model tests indicate that large step heights are preferable in termsof hydraulic behaviour. Firstly, the location of the inception point of air entrainmentmoves slightly towards the spillway crest with increasing step height, so that the un-aerated spillway portion prone to cavitation damage is shorter, see equation [6].Secondly, energy dissipation slightly increases with increasing step height ([15],[16]), see also equation [14].

The step height should be selected in such a way that for both the design andthe safety check floods the flow regime on the chute is either distinctively in theskimming flow or nappe flow regimes (see 3.3), i.e. at least about 20% larger orsmaller than hc/s given by equation [5] ([16]). Otherwise the maximum hydraulic loadoccurs in the transition regime with potential hydrodynamic instabilities resulting froma change from aerated to un-aerated nappe flows, or vice versa ([17]). Obviously, forun-gated spillways, the transition regime cannot be avoided if the chute is designedfor skimming flow.

Table 1Unit discharge q [m2/s] at critical inception index c= 0.5 for various chute

inclination angles and PB slopes, respectively, and step heights sDbit spcifique q [m2/s] pour lindex critique de cavitation c= 0.5, denombreux angles dinclinaison et hauteurs de marche

slope (V:H) 1:2.5 1:2 1:1.5 1:1 1:0.8 1:0.7

q

[m2/s] [] 21.8 26.6 33.7 45.0 51.3 55

s[

m]

0.3 27 24 20 17 16 16

0.6 33 29 25 21 19 19

1.2 41 35 30 25 23 23

2.4 51 43 36 30 28 27

3.0 54 46 39 32 30 29

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3. HYDRAULIC DESIGN

3.1. AERATOR DESIGN (IF APPLICABLE)

Different types of bottom aerators on stepped spillways have been thoroughlymodel-tested at VAW over several years, among which deflector- and step-aerators([4], [10], [18]). A step-aerator as shown in Fig. 3 Fig. 3has proved to be the bestoption to entrain a small but sufficient quantity of air remaining close to the chutebottom, thereby hardly affecting the depth-averaged air concentration Ca, the mixtureflow depths h90 or the energy dissipation along the chute while still preventingcavitation damage. Although no aerator blockage was observed by [18] even forlarge unit discharges of up to q = 113 m2/s (based on a prototype step height of2.4 m) and q = 40 m2/s (based on a prototype step height of 1.2 m), respectively,step-aerators may not be apt to sufficiently entrain air for so high unit discharges(see [19]). For these, a deflector-type aerator (see [4]) may be the best option, asthese generally cause higher bottom aeration than step-aerators. Deflector-aeratorsmay be placed in an existing stepped chute at any step, if required. However, adrawback of deflector-aerators is the higher spray production for small unitdischarges, see 3.2.

Fig. 3Definition sketch of step-aerator on stepped spillways, with PB = pseudo-bottom

Schma dun arateur de marche avec PB =pseudo-fond

A step-aerator should be placed at the first step of constant step height(Fig. 3). The optimum dimensions are c/cd= 0.90 to 0.95, where c= horizontal base

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length of the step-aerator and cd= base length from the vertical step face to the PB.The tip angle should be identical to the chute angle of the PB ([18]).

Depending on the unit discharge and the step height, a second step-aeratormay become necessary if the bottom air concentration falls below Cb= 0.01, see 2.2.Manipulating the equations given by [10] and [18], the latter can be determined asfunction of the streamwise coordinatexoriginating at the first step (Fig. 1) as

c

cc

c

b

h

x

h

s

h

x

h

xxC

3

083015

21

21

tanh

.)(

/

/

[2]

Equation [2] is limited to 0


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3.2. SPRAY REDUCTION

Spray results from the impact of a relatively thin jet flow onto the first horizontalstep face ([10], [18]). For small discharges, the jet impinging onto the horizontal stepface is deflected at about the same angle to the atmosphere (Fig. 4a). Accordingly,the spray height may become much larger than the flow depth under designdischarge. There are generally two options to reduce the spray height along the firststeps of the constantly-sloping stepped chute at small discharges. It is suggested by[12] to insert transitional steps of increasing height along the standard crest profiledown to the point of tangency as shown in Fig. 5. It was further found by [10] and[18] that steps with broken edges along the constantly-sloped stepped chute reducethe spray height significantly, as schematically shown in Fig. 4b. The broken stepedges are finished with a formwork containing the negative of the inset shape. Theheight of the sloping portion should be around 0.20s.

A step-aerator placed on the first step partially lifts the flow over the first twosteps and therefore reduces their effect. Broken edges downstream of this reach(n 3) reduce the spray height effectively. The tests performed at VAW indicatedthat a step aerator combined with 5 treated step edges provides optimum chuteperformance under minimum unit discharges.

3.3. FLOW REGIME

Two distinct flow regimes occur on stepped spillways, namely the so-callednappe flow and skimming flow ([17]). Nappe flow occurs for low discharges and largestep heights with the water plunging from one step to another. For small steps and

large discharges the water usually skims over the step edges, and recirculatingzones develop in the triangular niches formed by the step faces and the pseudo-bottom. Strictly speaking, a distinction between an upper limit for nappe flow and alower limit for skimming flow may be considered, with a transition regime separatingthese characteristic limits ([21]). The transition from nappe to skimming flow can beexpressed by the ratio of critical depth and the step height hc/s. The VAWexperimental results indicate the onset of skimming flow for approximately26


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a) b)

Fig. 4Definition sketch comparing (a) standard step with (b) improved step (with

inset in light grey; step-aerator in dark grey) (after [1])Schma comparant (a) marche standard avec (b) marche amliore (avec

insertion en gris clair; arateur de marche en gris fonc) (selon [1])

3.4. AIR ENTRAINMENT

A main advantage of the significant aeration along stepped spillways is thereduction of the cavitation risk potential, see 2.2. Knowing the inception pointlocation is thus important to determine the un-aerated spillway zone potentially proneto cavitation damage ([15]) and to decide whether an aerator is required, or not.

3.4.1. Location of inception point

The inception (subscript i) point location is usually expressed either in terms oflength Li of the black-water reach, or by the vertical distance wiLisin from thespillway crest (Fig. 1). According to [15] Li is defined as

2041

21905

..

.

)(sin

.

s

hL

c

i

[6]

Equation [6] indicates that the critical depth hc or the unit discharge q predominantlygovern the value ofLi, whereas the effect ofs is small. By doubling s, Li is reducedby only 13%, whereas doubling q leads to an increase of 74%. The steeper the

spillway slope, the more upstream the water becomes aerated. An increase of slopefrom 1:2 to 1:0.8 (= 26.6 to 51.3) reduces Li and wi by about 54% and 20%,respectively.

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Fig. 5Crest profile of stepped spillway with steps of increasing step height fitted to

standard ogee-crested weir profile down to point of tangency (adapted from [12]12]Crte dun dversoir marches descalier avec hauteurs de marche

croissantes insres dans le profildun dversoir standard (adapt de [12]12]

3.4.2. Inception flow depth

For 26< < 55 the flow depth at the inception point hm,i is ([15])

30

1090400.

..

)(sin

.

shh cm,i [7]

Here again, hc has a greater effect on hm,i than s. Because the flow is alreadyaffected by aeration at the inception point ([12]) the depth-averaged inception airconcentration Ca,i is useful for the computation of the so-called equivalent clear-waterinception depth hw,i. According to [8], it is given by

)(., 24010213

iaC [8]

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3.5. UNIFORM FLOW CHARACTERISTICS

Once the flow on stepped spillways becomes aerated, a distinction should bemade between the equivalent clear-water depth hw and the mixture flow depth h90,the later being defined as the flow depth with an air concentration of 90% at thesurface. The term equivalent implies that hw= h90 (1Ca) is a computed value intwo-phase flow determined analytically with the characteristic mixture flow depth h90and the depth-averaged air concentration Ca.

3.5.1. Attainment of uniform flow

The normalized vertical distance from the spillway crest needed for uniformflow (subscript u) to be attained increases almost linearly with and follows thepower formula ([15], {16])

3224 /sinc

u

hw

[9]

3.5.2. Flow depths

The uniform equivalent clear-water depth hw,u is given by ([15], [16])

312150 /)(sin. c

w,u

h

h. [10]

The ratio hw,u/hc thus varies exclusively with the chute angle , independent from sand q.

The uniform mixture flow depth h90,u partly determining the sidewall height(see 3.8.20) is described by ([15], {16]).

50.1tan090,0.50F

.

*

s

hu

, [11]

where F* = q/(gsins3)1/2 is the characteristic roughness Froude number. For agiven relative discharge hc/s, both hw,u and h90,u decrease with increasing chuteslope.

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3.6. FRICTION FACTOR

The friction factor of uniform two-phase flow may be used to calculate the flowvelocities and energy heads on relatively long spillways on which uniform flow isattained, equation [9]. Based on the findings of [16] the bottom roughness frictionfactor fbon stepped chutes with 1955 and 0.1 < K/Dh,w,u < 1.0 is approximatedby

h,w,ubD

K

flog25001

)2sin(42050

11..

.. , [12]

where Dh,w,u 4hw,u is the hydraulic diameter of uniform flow in wide rectangularchannels and K= scos the step roughness perpendicular to the PB. Equation [12]indicates that the effect of chute angle is much larger than that of the relative

roughness K/Dh,w,u. Flow aeration is taken into account using the uniform equivalentclear-water depth hw,u. Also, equation [12] accounts for both a shape correction factorand a sidewall correction method ([16)].

Interestingly, no difference in friction factors results for stepped chutes withequal roughness spacing K/Ls where Ls =s/sin= K/(sincos) = 2K/sin(2) is thedistance between step edges along the pseudo-bottom. For instance, for given s andq, the friction factor is equal for chutes with = 40 and = 50, because sin(240) =sin(250).

3.7. ENERGY DISSIPATION

Knowledge of the residual kinetic flow energy at the toe of a stepped spillwayis important to design the downstream energy dissipator. The residual head abovethe pseudo-bottom at any section along a stepped spillway (Fig. 1), regardless ofuniform or non-uniform flow conditions, is expressed by

2

2

2g wwres

h

qhH cos

, [13]

where 1.1 is the energy correction coefficient. To determine the residual energyheads on stepped chutes, a distinction is made between conditions where uniform

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flow is attained, or not. For uniform flow, i.e. forw/hc 15 to 20 according to equation[9], the normalized residual head is expressed by [16]

3231

sin82

cossin8

with,

bb

c

res ffF

Fh

w

F

H

H

max

forw/hc 15 to 20[141a]

with the friction factor fb computed from equation [12]. If the spillway chute is tooshort for uniform flow to be attained, the following approximation of [16] [16] basedupon an approach of [17] may be used

ch,w

res

h

w

D

K

H

H 8010

)(sin0450exp ..

max

.

forw/hc< 15 to 20 [14b]

3.8. TRAINING WALL DESIGN

While the local flow depths in the upper portion of a stepped spillway aremainly governed by a considerable spray formation for small discharges, the uniformmixture flow depth h90,u at design discharge may serve as a guide for the design ofspillway training walls in the aerated or white-water region further downstream,where considerable aeration leads to flow bulking.

3.8.1. Upper spillway portion

The required training wall (subscript t) heights along the upper chute portion(subscript 1) ht,1 where jet deflection causes spray (subscript s) is designedaccording to the envelope of spray profiles given by [1] and [18][18]. With thedimensionless coordinates Xs=(xxo)/(sFo) and Zs=(hs,1ho)/(hs,maxho), where

xo = (3s)/sin is the origin of the spray flow and hs,1 = spray height due to jetdeflection, the spray profiles follow

Zs = [0.65MXsexp(10.65MXs)]1/2 for 0


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The exponent =(1+n)-1/3 accounts for the number n of treated step edges,see 3.2. Equation [15] indicates that for chutes below a step-aerator, the jetreattaches further downstream than on standard-stepped chutes without aerator dueto the slightly lifted lower jet trajectory beyond its contact with the step-aerator ([18]).Note that equations [15] and [16] are applicable for gravity dam chutes with 50.

A safety factorshould be employed when computing the design training wall heightht,1, such that

ht,1= hs,1. [17]

Depending on the erosion potential along the chute sidewalls, = 1.2 forconcrete dams with no concern of erosion of the downstream face and = 1.5 foremergency spillways on embankment dams or on valley flanks prone to erosion.

3.8.2. Lower spillway portion

The proposed design height ht,2 for the training walls along the aerated lowerspillway portion (subscript 2) reads

ht,2= h90,u, [18]

again with a safety factor taking into account the erosion potential of the spillwaychute sides as given in 3.8.1 above. Note that equation [18] is valid for the wholerange of spillway angles 1955 and is based upon the skimming flow regime.For nappe flow, the nappe impact onto the steps may cause a considerable sprayovertopping the training walls designed after [Erreur ! Source du renvoiintrouvable.], so that the sidewalls should be designed according to equations [15]

and [17], see 3.8.1.

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REFERENCES

[1] PFISTER M., HAGER W.H. & MINOR H.-E. Step aerator and sprayreduction for stepped chutes. Proc. 32 IAHR Congress, Venice, 282, pp. 1-10, 2007.

[2] FALVEY H.T. Cavitation in chutes and spillways. Engineering Monograph42, Bureau of Reclamation, Denver, 1990.

[3] DREWES U. Oberflchentoleranzen bei Betonschussrinnen im Hinblick aufKavitation (Tolerances of concrete surfaces in spillway chutes with regard

to cavitation). VAW-Mitteilung 99 (D. Vischer, ed.), ETH Zurich, pp. 11-33,1988 (in German).

[4] Pfister M., HAGER W.H. & MINOR H.-E. Bottom aeration of steppedspillways. Journal of Hydraulic Engineering132(8), pp. 850-853, 2006.

[5] FRIZELL K.H., MEFFORD, B.W. Designing spillways to prevent cavitationdamage. Concrete International13(5), pp. 58-64, 1991.

[6] ARNDT R.E.A., IPPEN A.T. Rough surface effects on cavitation inception.ASMEJournal of Basic Engineering9(3), pp. 249261, 1968.

[7] FRIZELL K.H., RENNA F.M. Laboratory studies on the cavitation potentialof stepped spillways. Proc. 34 IAHR Congress, Brisbane, pp. 2420-2427,2011.

[8] BOES R.M., HAGER W.H. Two-phase flow characteristics of steppedspillways. Journal of Hydraulic Engineering129(9), pp. 661-670, 2003.

[9] RASMUSSEN R.E.H. Some experiments on cavitation erosion in watermixed with air. Intl. Symposium Cavitation in Hydrodynamics 20, pp. 1-25,National Physical Laboratory, London, 1956.

[10] PFISTER M., HAGER W.H. & MINOR H.-E. Stepped chutes: Pre-aerationand spray reduction. Intl. Journal of Multiphase Flow 32(2), pp. 269-284,2006.

[11] Hydraulic Design of Spillways, Technical Engineering and Design Guides,as adapted from the U.S. Army Corps of Engineers, No. 12, ASCE, 1995.[12] MATEOS IGUCEL C., ELVIRO GARCIA V. Stepped spillways. Design for

the transition between the spillway crest and the steps. Proc. HYDRA 2000London UK (D.A. Ervine, ed.): 1(1B11), pp. 260-265. Thomas Telford,London UK, 1995.

[13] PFISTER M. Effect of control section on stepped spillway flow. Proc. 33IAHR Congress Vancouver10229, pp. 1964-1971, 2009.

[14] BIERI M., LEITE RIBEIRO M., BOILLAT J.-L., SCHLEISS A., LAUGIER F.,LOCHU A., DELORME F., VILLARD J.-F. Rhabilitation de la capacitdvacuation des crues intgration de PK-Weir sur des barrages existants

(Rehabilitation of the spillway capacity integration of PK weir on existingdams). Proc. Colloque CFBR-SHF Dimensionnement et fonctionnementdes vacuateurs de crues (CD-ROM), Paris, 2009 (in French).

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[15] BOES R.M., MINOR H.-E. Hydraulic design of stepped spillways for RCCDams. Hydropower & Dams 9(3), pp. 87-91, 2002.

[16] BOES R.M., HAGER W.H. Hydraulic design of stepped spillways. Journal ofHydraulic Engineering129(9), pp. 671-679, 2003.

[17] CHANSON H. Hydraulic design of stepped cascades, channels, weirs andspillways. Pergamon, Oxford UK, 1994.

[18] SCHIESS ZAMORA A., PFISTER M., HAGER W.H., Minor H.-E. Hydraulicperformance of step aerator. Journal of Hydraulic Engineering 134(2), pp.127-134, 2008.

[19] SCHIESS ZAMORA A., PFISTER M., HAGER W.H., MINOR H.-E. Closureto Hydraulic performance of step aerator. Journal of Hydraulic Engineering135(7), pp. 621-622, 2009.

[20] PFISTER M., HAGER W.H., MINOR H.-E. Closure to Bottom aeration ofstepped spillways. Journal of Hydraulic Engineering134(8), pp. 1183-1185,2008.

[21] YASUDA Y., OHTSU I. Flow resistance of skimming flows in steppedchannels. Proc. 28 IAHR Congress Graz (H. Bergmann, R. Krainer, H.Breinhlter, eds.), CD-ROM, Theme B14, 1999.

[22] MATOS J., SNCHEZ M., QUINTELA A., Dolz J. Air entrainment and safetyagainst cavitation damage in stepped spillways over RCC dams. Proc. Intl.Workshop on Hydraulics of Stepped Spillways VAW, ETH Zurich (H.-E.Minor, W.H. Hager, eds.), Balkema, Rotterdam, pp. 69-76, 2000.

SUMMARY

Stepped spillways are commonly used as a flood evacuating structure at dams

combining spillway chute and energy dissipator. Most stepped chutes have beenlimited to design unit discharges of some 30 m2/s due to risk of cavitation damage.For high design floods this requires wide spillway structures. Therefore, as a ratherrecent measure to increase the applicability of stepped chutes to higher unitdischarge, aerators have been developed to artificially entrain air into the flowupstream of the inception point of free surface air entrainment. This paper discussesthe need to apply these aerators and presents general design recommendations.Furthermore, a comprehensive analysis of the flow features of stepped chutes ispresented together with design guidelines for the hydraulic and structural layout of astepped spillway, including the aspects of: control structure and measures to limitspray height along the chute, flow regimes and air inception characteristics, uniform

flow features, friction factor and energy dissipation as well as design of training walls.

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RSUM

Les vacuateurs de crue en marches descalier sont actuellement souventutiliss comme ouvrages dvacuation de crues combinant le coursier et ledissipateur dnergie. La plupart de ces vacuateurs de surface ont t limits desdbits spcifiques denviron 30 m2/s en raison des risques de dgts dus lacavitation. Ceci ncessite des coursiers larges pour des dbits de crue importants.Des arateurs de marche ont donc t rcemment dvelopps pour entraner de lair

dans lcoulement en amont du point dentranement dair de la surface deau, afin

damliorer lapplicabilit des vacuateurs de crue en marches descalier desdbits spcifiques plus levs. Dans cet article, lopportunit dappliquer de tels

arateurs est discute et des recommandations de dimensionnement sont donnes.De plus, une analyse dtaille des phnomnes dcoulement sur des vacuateursen marches, ainsi quun guide de dimensionnement la fois hydraulique et

structurel, sont prsents. Les aspects suivants sont abords: ouvrage de contrleet mesures pour limiter la hauteur de spray le long du coursier, rgimesdcoulement et caractristiques de lentranement dair ainsi que de lcoulement

uniforme du mlange eau-air, coefficient de frottement et dissipation dnergie,dimensionnement des parois latrales.

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