Stepped Spillway as an Energy Dissipater

Canadian Water Resources Journal / Revue canadienne des ressources hydriques ISSN: 0701-1784 (Print) 1918-1817 (Online) Journal homepage: http://www.tandfonline.com/loi/tcwr20 Stepped Spillway as an Energy Dissipater Jean G Chatila & Bassam R Jurdi To cite this article: Jean G Chatila & Bassam R Jurdi (2004) Stepped Spillway as an Energy Dissipater, Canadian Water Resources Journal / Revue canadienne des ressources hydriques, 29:3, 147-158, DOI: 10.4296/cwrj147 To link to this article: https://doi.org/10.4296/cwrj147 Published online: 23 Jan 2013. Submit your article to this journal Article views: 2362 View related articles Citing articles: 3 View citing articles Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalinformation?journalcode=tcwr20 Download by: [37.44.196.55] Date: 10 December 2017, At: 09:05

Stepped Spillway as an Energy Dissipater Jean G. Chatila and Bassam R. Jurdi Abstract: This paper describes an experimental investigation into the hydraulics of ogee-profile stepped spillways, examines their viability as an alternative to smooth-back spillways and investigates their efficiency in reducing the downstream energy and length of the hydraulic jump. Tests were performed in a long rectangular flume with glass walls on both sides. One smooth model was used as a benchmark for comparison with stepped models made out of a combination of crests and bottoms of different step heights. Significant reductions in terminal velocities and total energies were observed, where the stepped spillway profiles tested proved to be very effective in terms of energy dissipation for flows of the order of the design head or lower. For flows beyond the design head, the effectiveness of the stepped spillway configuration was reduced and became negligible for heads greater than one and a half times the design head. It was concluded that the number of steps is the overbearing factor in expending flow kinetic energy and, therefore, reducing the length of the downstream forming hydraulic jump. Résume : Le présent article décrit une étude expérimentale sur l hydraulique des déversoirs en marches d escalier en doucine et examine leur viabilité en tant que solution de rechange aux déversoirs à dos lisse. Il est également question de leur efficacité pour ce qui est de réduire l énergie en aval et la longueur du ressaut. Des essais ont été menés dans un long chenal rectangulaire flanquée de parois de verre de chaque côté. Un modèle lisse a été utilisé comme point de repère à des fins de comparaison avec des modèles en marches d escalier fabriqués à partir d une combinaison de crêtes et de fonds de différentes hauteurs de marche. Des réductions considérables des vitesses limites et des énergies totales ont été observées, les profils des déversoirs en marches d escalier testés s étant avérés très efficaces en fait de dissipation d énergie pour les débits de l ordre de la chute brute ou d un degré moindre. Pour les débits dépassant la chute brute, l efficacité de la configuration du déversoir en marches d escalier a été réduite et est devenue négligeable pour les hauteurs de chute supérieures à une fois et demie la chute brute. Il en a été conclu que le nombre de marches constitue un facteur décisif pour ce qui est de l expansion de l énergie cinétique du débit et, par conséquent, de la réduction de la longueur du ressaut se formant en aval. Jean G. Chatila 1 and Bassam R. Jurdi 1 1 Department of Civil Engineering, Lebanese American University, P.O. Box 36 Byblos, Byblos, Lebanon. Submitted February 2003; accepted February 2004. Written comments on this paper will be accepted until March 2005. Canadian Water Resources Journal Vol. 29(3): 147 158 (2004) Revue canadienne des ressources hydriques

148 Canadian Water Resources Journal/Revue canadienne des ressources hydriques Introduction A spillway is a hydraulic structure that is usually provided at storage and detention dams to release surplus or flood water that cannot be safely stored in the reservoir. Since the failure of dams and their related appurtenances may cause serious loss of life and property, their design and maintenance are commonly controlled by government regulation. Historically, spillways of improper design or insufficient capacities have caused failures of dams. Also, many embankment dams were identified as being unable to pass their design flows without failure due to overtopping (Frizell, 1991). Thus, the spillway must be hydraulically and structurally adequate. When the reservoir s storage capacity is exceeded, water flows over the spillway crest and accelerates down the spillway face to produce high velocities at the spillway toe, which may cause dangerous scour in the natural channel below the structure. Some form of stilling basin structure located at the foot of the spillway has been used for energy dissipation. Depending on the expected Froude Number (Fr) of the incoming flow, the form of the stilling basin can range from a simple concrete apron to a complex structure that may include rows of chute blocks, baffle piers and a plain or dentated end-sill. If the basin requires all three features, this can add substantially to the overall costs. Consequently, alternative solutions to the problem are worth investigating. One possible solution is to consider a stepped spillway instead of the traditional smooth ogee-profile spillway, where a series of drops in the invert are provided from near the crest to the toe. Over a wide range of operating conditions, the stepped spillway is expected to generate substantial energy losses on the spillway structure itself, thereby reducing the need for a more costly form of stilling basin. The steps act as roughness elements to reduce flow acceleration and hence terminal velocity. Moreover, excessive turbulence induced by the steps helps speed the development of a boundary layer and the entrainment of air to bulk the flow. Both the reduced velocity and the cushioning effect of the entrained air thus reduce the cavitation potential. Stepped Spillways Considerable interest in stepped spillways is shown mainly because of the technical advances in the Roller- Compacted Concrete (RCC) construction method for building gravity dams, where including stepped spillway construction concurrent with horizontal RCC placement can be easily accomplished, which reduces the cost and time of construction. In addition, stepped spillways contribute to the stability of the dam. Several researchers have performed studies on stepped spillway physical models. However, the results obtained for each case were valid only for that case and could only be used as a guide for other similar cases. Young (1982) studied the feasibility of a stepped spillway for the Upper Stillwater Dam and managed a 75% energy reduction. Sorensen (1985) performed a physical model investigation for stepped spillways, where he found that adding a few steps to the face of the spillway eliminated the deflecting water jet. Christodoulou (1993) found that energy loss due to the steps depends primarily on the ratio of the critical depth to the height of the step, as well as on the number of steps. Sorensen (1985) studied the design of steps and their spacing on the spillway face in order to optimize the energy dissipation. Degoutte et al. (1992) stated: The size requirements for stilling basin downstream of stepped spillway were not well known. A practical guideline for the design of stepped spillways has been published (CIRIA, 1978). However, this document provices no indication as to what degree the spillway step configuration may impact the energy dissipation. Chamani and Rajaratnam (1999a, b) developed an equation to predict the incipient value of the ratio of the critical depth to step height, which agreed well with most of their experimental observations. Chanson (1999) proposed a pre-design calculation method that provides a general trend for preliminary designs. Experimental Study The literature indicates that there are considerable gaps in knowledge in the design of stepped spillways. The choice of an experimental model, computational model, or interpolating/extrapolating the necessary information from the U.S. Army Corps of Engineers (USACE) or the U.S. Bureau of Reclamation (USBR) design/performance curves can be a difficult and dangerous task (USACE, 1990; USBR, 1977). This is especially true if scaling effects in experimental modelling are ignored, basic assumptions and capabilities in computational modelling are not taken

Chatila and Jurdi 149 into consideration and interpolation/extrapolation of design curves leads to physically incorrect situations. From a computational standpoint, simulating the flow is difficult due to non-linearity and other factors. The flow changes from subcritical upstream of the crest to supercritical along the spillway and then it must pass through a hydraulic jump to reach the subcritical tailrace channel. Furthermore, the curvature of the spillway profile may be significant, thus causing pressure variations due to centripetal fluid acceleration, which rival the hydrostatic pressure component. Many researchers have discussed the topic of stepped spillways and tried to implement some numerical finite element techniques for solving the flow field (Chamani and Rajarantnam, 1999b; Pegram et al., 1999; Sanchez et al., 2000; Yildiz and Kas, 1998). However, it is crucial to have reliable data against which mathematical models can be calibrated and validated. Chen et al. (2002) report that stepped spillways have increasingly become effective energy dissipaters. When the hydraulic performance of the overflow is clearly known, the energy dissipation could be increased. Thus, it is of great importance to thoroughly examine the hydraulics of stepped spillways through experimentation in order to optimize the energy dissipation, where different step heights have to be tested. If both gravitational and viscous forces are important, then dynamic similitude requires both Froude and Reynolds numbers be held constant. Thus, one degree of freedom in the modelling exercise is lost and the length ratio is no longer arbitrary but depends on the choice of the fluid viscosity. To overcome this obstacle, the Froude number is held constant since gravitational forces are predominant, and the Reynolds number is maintained in the same flow regime as the prototype. The general modelling laws can be developed and the specific equation involving the additional constraint of the Froude number modelling introduced. Geometric, kinematic, and dynamic laws of similitude apply in this instance (Prasuhn, 1992). Rice and Kadavy (1996) report that, according to the U.S. Bureau of Reclamation, it is recommended that models of large dams and spillways be constructed to scale ratios of 1:30 to 1:100, and for medium size structures the Bureau recommends that models should not be smaller than 1:60 scale. In 1953, the USBR recommended that flow heads larger than 3 cm should be used in order to avoid surface tension problems. However, Rice and Kadavy (1996) reported that if the water depth exceeds a few centimetres, the effects of the surface tension, and thus the Weber number, could be disregarded as well. This complies with the conditions of the experiments performed in this study. Flow Regimes Flow regime over a stepped spillway can either be nappe or skimming flow. In nappe flows, water from each step hits the step below as a falling jet, with the energy dissipation occurring by jet breakup in the air and mixing on the step, with or without the formation of a partial hydraulic jump. When the upstream-directed flow meets the vertical step wall, it is forced to reverse direction and a pool is formed. This flow is recirculated in the pool and joins the downstream-directed flow with a lesser velocity. Rajaratnam (1990) suggested that nappe flow occurs when y c /h < 0.8. A nappe flow regime is possible for higher discharges, but this needs a very flat slope. In the skimming flow regime, water flows down the stepped face as a coherent stream, skimming over the steps and is cushioned by the recirculating fluid trapped between them. Skimming flow occurs at moderate to high discharges. No nappe is visible and the external edges of the steps form a pseudo-bottom over which the flows pass. Vortices, which transmit shear stresses, develop and large friction losses characterize skimming flows. Downstream of the point of inception, a layer containing a mixture of air and water extends through the fluid and the flow becomes uniform far downstream, where measurements may not vary for a given discharge. Chanson (1994) reported that as the skimming flow becomes fully developed the stepped spillway behaves similar to a smooth one with high roughness. Rajaratnam (1990) defined the onset of skimming flow for values of the ratio y c /h > 0.80, which is the case throughout the current experimental program. Although the mechanisms of energy loss are quite different between the nappe flow and skimming flow regimes, both flows can dissipate a major proportion of the flow energy. Experimental Setup The tests were performed in the Hydraulics Laboratory at the Lebanese American University, Byblos Campus, Lebanon. Experiments were conducted in a 6.0 m long

150 Canadian Water Resources Journal/Revue canadienne des ressources hydriques flume, 30.4 cm wide and 40.0 cm deep. The walls of the flume are glass on both sides (Figure 1). An end weir controlled the position of the downstream forming hydraulic jump. Two pumps supplied the flow into the channel through calibrated orifice meters located in the feed pipes into the channel, with two independent valves to control the flow. Discharge was measured using these meters. The channel was kept at zero slope throughout the experiments. Depth of water at any point was measured using a point gauge with accuracy to the nearest millimetre, or division thereafter. In the case of a fluctuating water surface profile, average values of depths were taken based on several measurements. The models had a height of 25.7 cm, a base length of 29.7 cm, and a width equal to that of the channel. The hydraulic design charts 111-2-/1 of USACE-WES were used for the design of the spillway model profiles (USACE-WES, 1952). A vertical upstream face and a curved surface defined by the radii 0.2H d and 0.5H d in front of the crest centreline were selected. The profile downstream of the crest centreline is defined by x n = KH 1-n y (1) d Using K = 2, n = 1.85, H d = 5.08 cm, yields the following equation for the spillway profile at the crest y = 0.12559x 1.85 (cm) (2) A face slope = 60 (or slope 1.73:1) was used after the point of tangency with the crest curve. A smooth transition, at the toe of the spillway, is needed to avoid excessive vibration and structural damage. Thus, a circular curve, or bucket, tangent to the foundation and the spillway s terminal downstream slope, is used. Steps in the stepped spillway models were introduced at a point just downstream of the spillway crest so that the envelope of their tips follows the standard smooth profile down to the toe (Figure 2). Two stepped spillway models, built of plexi-glass, were used in the study. In general, step geometries may be horizontal, inclined or pooled. Horizontal steps were selected in this instance for more effectiveness and ease of manufacturing. The models, which had the same overall height and general crest shape, had different step heights. Since the crest sections of the two models were removable and interchangeable, this permitted a wider combination of step heights to be tested. A smooth ogee-profile spillway was manufactured and used as a benchmark for comparison purposes. The literature indicates that step sizes are classified in either one of two categories: (i) large-step sizes of height = 1/20 H dam, and (ii) small-step sizes of height = 1/40 H dam (Sorensen, 1985; Christodoulou, 1993; Bindo et al., 1993; and Rice and Kadavy, 1996). When applied to the experimental spillway models, steps of 0.6 to 1.3 cm are used. However, these are only general guidelines for step sizes and in the current study steps of 0.5 to 1.5 cm were utilized. As for the stepped model geometries, bottom 1 (B1) had a total of 14 steps, each with a 1.0 cm drop. Bottom 2 (B2) had a total of nine steps, with a 1.5 cm drop. Crest 1 (Cl) had a total of 19 steps, each with a 0.5 cm drop. Crest 2 (C2) had a total of 12 steps, with a 0.75 cm drop (Figure 2). Smaller step sizes were implemented for the crests as compared to the bottoms in order to have a smooth flow transition. In general, one has to be careful about the significance of scale effects on the experiments and the consequent interpretation of results. Primary concerns included the amount of energy dissipated by the steps, the optimum size of the steps for maximum energy dissipation and the effect of steps on the downstream-forming hydraulic jump, which affects the length of stilling basin required. While conducting the experiments, measurements were repeated to ensure that the results are reproducible with minimal measurement errors. In some instances, average values were considered. The following measurements were recorded for a wide range of flows over the smooth and stepped spillway models (Figure 1): (i) water head at the upstream of the spillway, H (m), defined as the upstream vertical difference between crest level and water level; (ii) water head at the crest of the model spillway, (m); (iii) profile of free surface for different discharges; (iv) depth of flow at the bottom or the toe of the model, Y1 (m), which is the upstream depth of the hydraulic jump; (v) depth of flow at the downstream end of the hydraulic jump, Y2 (m); (vi) differential head across the orifice metres, (m), and (vii) length of the hydraulic jump, L j (m). The longitudinal element of the jump is, without doubt, the most difficult to measure. This is partially due to the differences in opinion as to exactly where the terminus of the jump lies (Elevatorski, 1959). It was easier to determine the section at which the hydraulic jump has started than where it ended. In this instance, a dye-tracer, Rhodamine WT, was dropped at different locations in

Chatila and Jurdi 151 Figure 1. Experimental Facility with Flow over a Stepped Spillway Model. Figure 2. Typical Crest and Bottom Configurations of a Stepped Spillway Model.

152 Canadian Water Resources Journal/Revue canadienne des ressources hydriques the vicinity of the hydraulic jump. The termination of the hydraulic jump was determined visually through the circulation of the dye. Results and Discussion A major concern for stepped spillways is providing smooth transition flow from the spillway crest to the first few steps. Based on experimental observations, the flow at the transition is very good with no undesirable disturbance of flow, no tumbling action, and no separation of the flow at the break in slope. This was the case for all discharges and models tested. It was seen that there may be some air entrained at low discharges but this disappeared at high discharges. Average flow velocities were calculated from the measured flow rates and depths using the continuity equation. The discharge over an uncontrolled crest structure can be defined as Q = CLH 3/2 (3) where C = discharge coefficient (in m 0.5 /s), L = the crest length (in m), and H is as previously defined. Figure 3 shows the variation of the flow rate with the flow head over different spillway models. Theoretically, such a plot, on a log-log scale, should yield a straight line with a slope of 1.5 and an intercept of log(c L). Based on a regression analysis of the 0.020 measured data with r² = 0.88, the computed value of the slope was 1.54, which is close to the expected theoretical value for a spillway. Based on the intercept, a value of C = 2.35 m 0.5 /s is obtained. This value is close to that computed by Sorenson (1985) and also falls within the range recommended by King and Brater (1963). Baban (1995) reported a C value of 2.225 when H/H d > 1.33. The available energy in the different models was computed for each flow condition at the toe of the spillway close to the upstream end of the hydraulic jump. The aim was to determine the efficiency of step configuration in releasing energy. The percentage energy dissipated in each stepped model was calculated in reference to the available energy for the smooth model. Figure 4 shows the variation of the percentage energy dissipated at the toe of the spillway with H/ H d, the ratio of the flow head (H) to the design head (H d ) of the spillway. Figure 4 shows that model C1B1 produced the highest value of energy dissipation for the models under consideration. For flow heads less than 60% of the design head (H/H d = 0.6), most of the models produced more than 60% energy dissipation with model C1B1 reaching up to 80%. All models had relatively low energy dissipation at H/H d = 1.40. In addition, energy dissipation was in the range of 20 to 30% for flows around the design head and increased to 30 to 40% for H/H d in the vicinity of 1.25. The energy dissipation rate will then decrease with increasing discharge as it reaches a stage where the effect of the C1B1 C2B2 C2B1 C1B2 Smooth Flow Rate, Q (m 3 /s) 0.015 0.010 0.005 0.000 0 3 6 9 Flow Head, H (cm) Figure 3. Variation of Flow Rate with Flow Head over Different Spillway Models.

Chatila and Jurdi 153 % Energy Dissipated 100 80 60 40 20 C1B1 C2B2 C2B1 C1B2 0 0.0 0.5 1.0 1.5 2.0 H/H d Figure 4. Variation of Percent Energy Dissipated at the Spillway Toe with (H/H d ). steps is very small and a stepped spillway acts similar to a smooth one. The amount of energy dissipated for various discharges is determined and for all discharges the flow was found to be a skimming flow. Figure 5 shows the variation of the Fr1 at the upstream side of the hydraulic jump with H/H d. This figure shows that for model C1B1 with H/H d = 0.45, Fr1 was reduced by about 82% as compared to the smooth model. In general, for all models and with H/ H d < 1.0, Fr1 was considerably reduced. The reduction in Fr was not significant for H/H d > 1.20 and became negligible for H/H d > 1.40. Froude Number, Fr1 14 12 10 8 6 4 2 Figure 6 shows the variation of the dimensionless quantity L j /H d with H/H d. It clearly indicates that L j is reduced approximately by 64% or more for model C1B1 as compared to the smooth model. Considerable reduction in L j is also noticed for all other models. As a result, the length of the stilling basin is also reduced. Figure 7 shows the variation of L j with the difference between downstream and upstream depths (Y2 Y1) or conjugate depths. In general, L j is about five to seven times the difference in conjugate depths. Performing a regression analysis on the data plotted in Figure 7 produces a ratio of L j /(Y2 - Y1) = 5.16 with r 2 = 0.84. This is well within the normally accepted values. C1B1 C2B2 C2B1 C1B2 Smooth 0 0.0 0.5 1.0 1.5 2.0 H/H d Figure 5. Variation of Froude Number (Fr1) at the Upstream Side of the Hydraulic Jump with H/H d.

154 Canadian Water Resources Journal/Revue canadienne des ressources hydriques 14 12 C1B1 C2B2 C2B1 C1B2 Smooth 10 L j /H d 8 6 4 2 0 0.00 0.50 1.00 1.50 2.00 H/H d Figure 6. Variation of L j /H d with H/H d. L j, (cm) 70 C1B1 60 C2B2 C2B1 C1B2 Smooth 50 40 30 20 10 0 0 3 6 9 12 (Y2-Y1), (cm) Figure 7. Variation of L j with the Difference in Downstream and Upstream Depths.

Chatila and Jurdi 155 Figure 8 shows that the percentage energy dissipated due to the steps depends primarily on the Y c /h ratio, where Y c = critical depth of flow passing over the spillway and h = step height, as well as on N, the number of steps. For Y c /h = 2.5, the stepped surface was very effective in dissipating energy. For values of 2.5 < Y c /h < 6, the effect is still appreciable. However, for values of Y c /h > 6, the effect starts to reduce. Using model results, a relation between the ratio L j /H d and the parameter Y c /Nh is presented in Figure 9. This figure shows that L j is reduced with Y c /Nh. As the number of steps increases, the energy dissipated is increased, and L j is reduced. A similar conclusion was reached by Chamani and Rajaratnam (1994), where they reported that the number of steps is more important than the size of the steps. The results of the study indicated that the model consisting of bottom B1 and crest C1 (C1B1) produced higher energy dissipation as compared to combinations of models with other crests and bottoms. In this instance, for flows lower than the design discharge, the energy dissipated amounted to approximately 80% as compared to the equivalent smooth spillway model. At the design discharge, approximately 25% of the energy was dissipated. Consequently, using such a stepped spillway design reduced the required length of the stilling basin. Although the use of a stepped spillway was recommended for 1.2H d, our results showed that about 15 to 20% % Energy Dissipated 100 of the energy, as compared to a smooth spillway flow, was dissipated even at 1.4H d. Finally, Fr1 at the toe of the spillway was significantly reduced for the optimal stepped spillway geometry. More steps on the spillway face mean a better expenditure of energy and a shorter hydraulic jump. This is evidenced by the fact that, under similar 80 60 40 20 0 C1B1 C2B2 C2B1 C1B2 2 4 6 8 Y c /h Figure 8. Variation of Percentage Energy Dissipated with Y c /h. L j/hd 12 10 8 6 4 2 0 C1B1 C2B2 C2B1 C1B2 0.05 0.10 0.15 0.20 0.25 Figure 9. Variation of L j /H d with Y c /Nh. Y c /Nh conditions, model C1B1 (33 steps) displayed the most efficient energy dissipation ratio and shortest L j /H d, as compared to models C2B2 (19 steps), C1B2 (28 steps), or C2B1 (26 steps). This is mainly due to the fact that steps act as macro-roughness elements that increase friction in a sustainable way thus changing the flow s kinetic energy into heat or thermal energy. Therefore,

156 Canadian Water Resources Journal/Revue canadienne des ressources hydriques having more steps means more energy drops to slow down the flow. Summary and Conclusions Based on the analysis of the experimental results of this study, the following can be summarized. The water flow over a spillway presents a difficult mathematical problem. In this instance, physical models are built to examine the amount of energy dissipated by a particular stepped spillway design. In this study, physical models, with different step sizes, were tested to determine the optimum amount of dissipated energy. In general, compared to the equivalent smooth spillway flows, significant reductions were observed in the terminal velocities and total energies of the stepped spillway flows. The stepped spillway profiles tested proved to be very effective in terms of energy dissipation for flows in the order of H d or lower. For flows beyond H d, the effectiveness of the stepped spillway configuration was reduced and diminished for heads greater than 1.4H d. Also, more steps on the spillway face mean a better expenditure of energy and a shorter hydraulic jump. Finally, it can be concluded that stepped spillways, with the maximum possible number of steps, are an efficient and desirable alternative to traditional smooth-back spillways. They are a viable option when considering the design of a dam, provided that a well-studied model is experimented upon for the spillway prototype. In addition, one should not forget the drawbacks of stepped spillways such as noise and erosion of the steps. Experience shows that flow conditions at the transition between the nappe and skimming flow must be avoided. Further, the design of stepped chutes requires a higher quality of construction and more maintenance work than conventional smooth spillways. Acknowledgements This work was supported in part by the Lebanese American University Research Council through a grant. References Baban, R. 1995. Design of Diversion Weirs. John Wiley & Sons Ltd., UK. Bindo, M., J. Gautier and F. Lacroix. 1993. The Stepped Spillway of M Bali Dam. Journal of Water Power and Dam Construction, 14(1): 35-36. Chamani, M.R. and N. Rajaratnam. 1994. Jet Flow on Stepped Spillways. Journal of Hydraulic Engineering, ASCE, 120(2): 254 259. Chamani, M.R. and N. Rajaratnam. 1999a. Onset of Skimming Flow on Stepped Spillways. Journal of Hydraulic Engineering, ASCE, 125(9): 969-971. Chamani, M.R. and N. Rajaratnam. 1999b. Characteristics of Skimming Flow over Stepped Spillways. Journal of Hydraulic Engineering, ASCE, 125(4): 361 368. Chanson, H. 1994. Comparison of Energy Dissipation in Nappe and Skimming Regimes on Stepped Chutes. Journal of Hydraulic Research, IAHR, 32(2): 213 218. Chanson, H. 1999. Current Expertise and Experience on Stepped Chute Flows: Hydraulics of Stepped Spillways. April 27, Lecture presented as an invited speaker at Kyoto University, Disaster Prevention Research Institute. Chen, Q., G. Dai and H. Liu. 2002. Volume of Fluid Model for Turbulence Numerical Simulation of Stepped Spillway Overflow. Journal of Hydraulic Engineering, ASCE, 128(7): 683-688. Christodoulou, G.C. 1993. Energy Dissipation on Stepped Spillway. Journal of Hydraulic Engineering, ASCE, 119(5): 473-482. CIRIA. 1978. The Hydraulic Design of Stepped Spillways, Second Edition, R033M, CIRIA, currently available on microfiche. Degoutte, G., L. Peyras and P. Royet. 1992. Skimming Flow in Stepped Spillway. Discussion, Journal Hydraulic Engineering, ASCE, 118(1): 111-114.

Chatila and Jurdi 157 Elevatorski, E. 1959. Hydraulic Energy Dissipaters, McGraw-Hill Inc., New York. Frizell, K.H. 1991. Stepped Spillway Design for Flow over Embankment. Proceedings, The 1991 National Conference Hydraulic Engineering, ASCE, Nashville, Tennessee, July 29 to August 2, 118-123. Yildiz, D. and I. Kas. 1998. Hydraulic Performance of Stepped Chute Spillway. Hydropower and Dams, (4): 64 70. Young, M.F. 1982. Feasibility Study of a Stepped Spillway. Proceedings, Hydraulics Division Speciality Conference, ASCE, New York, 96-106. King, H.W. and E.F. Brater. 1963. Handbook of Hydraulics, fifth edition, McGraw-Hill Book Company, Inc., New York. Pegram, G.G.S., A.K. Officer and S.R. Mottram. 1999. Hydraulics of Skimming Flow on Modeled Stepped Spillways. Journal of Hydraulic Engineering, ASCE, 125(5): 500 510. Prasuhn, A.L. 1992. Fundamentals of Hydraulic Engineering, Oxford University Press. Rajaratnam, N. 1990. Skimming Flow in Stepped Spillways. Journal of Hydraulic Engineering, ASCE, 116(4): 587 591. Rice, C.E. and K.D. Kadavy. 1996. Model Study of a Roller Compacted Concrete Stepped Spillway. Journal of Hydraulic Engineering, ASCE, 122(6): 292 297. Sanchez, J.M., J. Pomares and J. Dolz. 2000. Pressure Field in Skimming Flow over a Stepped Spillway. Proceedings, International Workshop on Hydraulics of Stepped Spillways, Zurich, Switzerland. Sorensen, R.M. 1985. Stepped Spillway Hydraulic Model Investigation. Journal of Hydraulic Engineering, ASCE, 111(12): 1461-1472. USACE. 1990. Hydraulic Design of Spillways. United States Army Corps of Engineers, EM 1110-2-1603, Department of the Army, Washington D.C. USACE-WES. 1952. United States Army Corps of Engineers Waterways Experiment Station, Corps of Engineers Hydraulic Design Criteria. USBR. 1977. Design of Small Dams. United States Bureau of Reclamation, U.S. Government Printing Office, Washington D.C.