Flooding Probability Constrained Optimal Design of Trapezoidal Channels
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VIEW THE REPLYPublication: Journal of Irrigation and Drainage Engineering
Volume 133, Issue 1
Abstract
Trapezoidal open channels are designed for specified slope, specific lining materials, and for a specified design flow. These input design parameters are prone to uncertainties. The freeboard is used to confine the flow within the limits of the channel cross section and to accommodate the uncertainty effects. Because of the size of uncertainty, the flow can overtop the freeboard with a “flooding probability.” To design an optimum channel cross section for safety against overtopping, the flooding probability constrained optimum channel design concept is introduced. An optimization model was developed which has two objective functions of minimizing the total cost of the channel and minimizing the flooding probabilities subject to uniform flow equation as constraint. The constraint method of multiobjective optimization is used in which the objective of minimizing the flooding probability is converted to a constraint, and the resulting single objective optimization problem is solved. The flooding probability constraint is developed by using the first order analysis. The final single objective optimization model is highly nonlinear and requires the use of the projected augmented Lagrangian technique. The optimization model is applied for two cases, namely, channels having composite roughness and channels having uniform roughness. The solution results of the analysis established the potential of the model.
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References
ASCE. (1993). “Design and construction of urban stormwater management systems.” ASCE Manuals and Reports on Engineering Practice No. 77, ASCE, ISBN 0872628558.
Chow, V. T. (1959). Open channel hydraulics, McGraw-Hill, Singapore.
Chow, V. T., Maidment, D. R., and Mays, L. W. (1988). Applied hydrology, McGraw-Hill, Singapore.
Cohon, J. L., and Marks, D. H. (1975). “A review and evaluation of multiobjective programming techniques.” Water Resour. Res., 11(2), 208–220.
Das, A. (2000a). “Optimal channel cross section with composite roughness.” J. Irrig. Drain. Eng., 126(1), 68–72.
Das, A. (2000b). “Optimization based simulation and design of tile drainage systems.” J. Irrig. Drain. Eng., 126(6), 381–388.
Easa, S. M. (1992). “Probabilistic design of open drainage channels.” J. Irrig. Drain. Eng., 118(6), 868–881.
Einstein, H. A. (1934). “Der hydraulische oder profile-radius [The hydraulic or cross-section radius].” Schweizerische Bauzeitung, Zurich, 103(8), 89–91 (in German).
Froehlich, D. C. (1994). “Width and depth-constrained best trapezoidal section.” J. Irrig. Drain. Eng., 120(4), 828–835.
Guo, C. Y., and Hughes, W. C. (1984). “Optimal channel cross section with freeboard.” J. Irrig. Drain. Eng., 110(3), 304–314.
Horton, R. E. (1933). “Separate roughness coefficients for channel bottom and sides.” Eng. News-Rec., 111(22), 652–653.
Jain, A., Bhattacharjya, R. K., and Sanaga, S. (2004). “Optimal design of composite channels using genetic algorithm.” J. Irrig. Drain. Eng., 130(4), 286–295.
Lee, H. L., and Mays, L. W. (1986), “Hydraulic uncertainties in flood levee capacity.” J. Hydraul. Eng., 112(10), 928–934.
Lotter, G. K. (1933). “Soobrazheniia k Gidravlicheskomu Raschetu Rusel s Razlichnoi Sherokho-vatostiiu Stenok (Considerations on hydraulic design of channels with different roughness of walls).” Izvestiia Vsesoiuznogo Nauchno-Issledovatel’skogo Instituta Gidrotekhniki (Trans. All-Union Sci. Res. Inst. Hydraulic Eng.), Leningrad, Vol. 9, pp. 238–241.
Monadjemi, P. (1994). “General formulation of best hydraulic channel section.” J. Irrig. Drain. Eng., 120(1), 27–35.
Murtagh, B. A., and Saunders, M. A. (1993). “MINOS 5.4 user’s guide.” Tech. Rep. SOL 83-20R, System Optimization Laboratory, Dept. of Operations Res., Stanford Univ., Stanford, Calif.
Tung, Y. K., and Mays, L. W. (1980). “Risk analysis for hydraulic design.” J. Hydr. Div., 106(5), 893–913.
Yen, B. C. (2002). “Open channel flow resistance.” J. Hydraul. Eng., 128(1), 20–39.
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© 2007 ASCE.
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Received: Aug 2, 2005
Accepted: May 17, 2006
Published online: Feb 1, 2007
Published in print: Feb 2007
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