Abstract
In this study, the hydraulics of cascade spillways were investigated by conducting a series of laboratory experiments; twenty different cascade spillways tested in a horizontal laboratory flume. A wide range of discharge values, three weir slope angles (15, 25 and 45 degrees), and different step numbers ranged from 3 to 50 on ogee surface were considered. Some data-based models were developed to explain the relationships between hydraulic parameters. Multiple regression equations were developed based on dimensional analysis theory to compute energy dissipation over cascade spillways. For testing the robustness of developed data-based models, genetic programming (GP) was used as a new computing technique. A GP approach was developed to relate the input and output (energy dissipation) variables. It was found that formulation based on the GP approach in solving energy dissipation problems over cascade spillways is more successful than the method based on the regression equation.
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Abbreviations
- B :
-
Spillway width
- E 1 :
-
Energy at the downstream of spillway before hydraulic jump
- E 0 :
-
Total energy at the upstream of spillway
- ΔE :
-
Difference between energy at the upstream and at downstream of the spillway (ΔE = E0 − E1)
- F r :
-
Supercritical Froude number = \(V_{1} /\sqrt {gy_{1} }\)
- g :
-
Acceleration due to gravity
- h:
-
Each step height
- H w :
-
Total spillway height from flume bed
- l:
-
Each step length
- q :
-
Discharge per unit width
- Q :
-
Discharge
- S :
-
Spillway slope (V: H)
- V a :
-
Approach velocity = q/y
- V 1 :
-
Velocity at the toe of the spillway
- y 0 :
-
Depth of flow about 0.60 m distance from upstream in spillway above the spillway crest
- y 1 :
-
Depth before hydraulic jump at the spillway toe
- y2 :
-
Depth after hydraulic jump
References
Aytek A, Kişi Ö (2008) A genetic programming approach to suspended sediment modeling. J Hydrol 351(3–4):288–298. https://doi.org/10.1016/j.jhydrol.2007.12.005
Azamathulla HMd (2012) Gene expression programming for prediction of scour depth downstream of sills. J Hydrol 460–461C:169–172. https://doi.org/10.1016/j.jhydrol.2012.06.034
Azamathulla HMd, Jarrett RD (2013) Use of gene-expression programming to estimate manning’s roughness coefficient for high gradient streams. Water Resour Manage 27(3):715–729. https://doi.org/10.1007/s11269-012-0211-1
Azamathulla HMd, Ghani AA, Leow CS, Chang CK (2011) Gene-expression programming for the development of a stage-discharge curve of the Pahang River. Water Resour Manage 25(11):2901–2916. https://doi.org/10.1007/s11269-011-9845-7
Chamani MR, Rajaratnam N (1999) Characteristics of skimming flow over stepped spillways. J Hydra Eng 125(4):361–368. https://doi.org/10.1061/(ASCE)0733-9429(1999)125:4(361)
Chanson H (2001) The hydraulics of stepped chutes and spillways. Balkema, Lisse, p 418p
Chanson H, Toombes L (2004) Hydraulics of stepped chutes: the transition flow. J Hydra Res 42(1):43–54. https://doi.org/10.1080/00221686.2004.9641182
Dorado J, Rabuñal JR, Pazos A, Rivero D (2003) Prediction and modeling of the rainfall-runoff transformation of a typical urban basin using ANN and GP. Appl Artif Intell 17:329–343. https://doi.org/10.1080/713827142
Felder S, Chanson H (2009) Energy dissipation down a stepped spillway with non-uniform step heights. J Hydra Eng ASCE 137(11):1543–1548. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000455
Felder S, Chanson H (2011) Energy dissipation, flow resistance and gas-liquid interfacial area in skimming flows on moderate-slope stepped spillways. Environ Fluid Mech 9(4):427–441. https://doi.org/10.1007/s10652-009-9130-y
Ghorbani MA, Khatibi R, Aytek A, Makarynskyy O, Shiri J (2010) Sea water level forecasting using genetic programming and comparing the performance with Artificial Neural Networks. Comput Geosci 36:620–627. https://doi.org/10.1016/j.cageo.2009.09.014
Guven A, Aytek A, Md Azamathulla H (2013) A practical approach to formulate stage-discharge relationship in natural rivers. Neural Comput Appl 23(3–4):873–880. https://doi.org/10.1007/s00521-012-1011-5
Jarrett RD (1984) Hydraulics of high gradient streams. J Hydra Eng ASCE 110(1):1519–1539. https://doi.org/10.1061/(ASCE)0733-9429(1984)110:11(1519)
Kisi O, Guven A (2010) Evapotranspiration modeling using linear genetic programming technique. J Irrigat Drain Eng 136(10):715–723. https://doi.org/10.1061/(ASCE)IR.1943-4774.0000244
Koza JR (1992) Genetic programming: on the programming of computers by means of natural selection. The MIT Press, Cambridge
Osman-Tugrul B, Egemen A (2018) Estimation of BOD in wastewater treatment plant by using different ANN algorithms. Membrane Water Treatment 9(6):455–462. https://doi.org/10.12989/mwt.2018.9.6.455
Pegram GGS, Officer AK, Mottram SR (1999) Hydraulic of skimming flow on modeled stepped spillways. J Hydra Eng 125(5):500–509. https://doi.org/10.1061/(ASCE)0733-9429(1999)125:5(500)
Rajaratnam N (1990) Skimming flow in stepped spillway. J Hydra Eng 116(5):587–591
Rand W (1955) Flow geometry at straight drop spillway. Proc Am Soc Civ Eng 81 Paper 791:1–13
Roushangar K, Akhgar S, Salmasi F, Shiri J (2014) Modeling energy dissipation over stepped spillways using machine learning approaches. J Hydrol 508(16):254–265. https://doi.org/10.1016/j.jhydrol.2013.10.053
Salmasi F (2004) Hydraulic investigation of stepped spillways by physical modeling, Ph.D thesis, Shahid Chamran University. Ahvaz-Iran
Salmasi F, Samadi A (2018) Experimental and numerical simulation of flow over stepped spillways. Appl Water Sci 8(229):1–11. https://doi.org/10.1007/s13201-018-0877-5
Salmasi F, Sattari MT (2017) Predicting discharge coefficient of rectangular broad-crested gabion weir using M5 tree model. Iran J Sci Technol Trans Civ Eng 41(2):205–212. https://doi.org/10.1007/s40996-017-0052-5
Salmasi F, Cahamani MR, Farsadi-Zadeh D (2012) Experimental study of energy dissipation over stepped gabion spillways with low heights. Iran J Sci Technol Trans B Eng Civ Eng 36(C2):253–264. https://doi.org/10.22099/IJSTC.2012.640
Toombes L, Chanson H (2008) Flow patterns in nappe flow regime down low gradient stepped chutes. J Hydra Res 46(1):4–14. https://doi.org/10.1080/00221686.2008.9521838
Whigham PA, Crapper PF (2001) Modelling rainfall-runoff using genetic programming. Math Comput Model 33:707–721. https://doi.org/10.1016/S0895-7177(00)00274-0
Yilmaz B, Aras E, Nacar S, Kankal M (2018) Estimating suspended sediment load with multivariate adaptive regression spline, teaching-learning based optimization, and artificial bee colony models. Sci Total Environ 15(639):826–840. https://doi.org/10.1016/j.scitotenv.2018.05.153(Epub 2018 May 26)
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Appendix: Experimental Results
Appendix: Experimental Results
The number of data points are totally 154. A decision was made to use 110 data points for training and 44 data points for testing the model in its prediction model.
See Table 7.
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Salmasi, F., Sattari, M.T. & Nurcheshmeh, M. Genetic Programming Approach for Estimating Energy Dissipation of Flow over Cascade Spillways. Iran J Sci Technol Trans Civ Eng 45, 443–455 (2021). https://doi.org/10.1007/s40996-020-00541-3
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DOI: https://doi.org/10.1007/s40996-020-00541-3