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Information Journal Paper

Title

Optimal design of trapezoidal open channel section considering the lined free board as a design variable

Pages

  61-69

Abstract

 Introduction In this study, two optimization models for trapezoidal open channel cross-sectional design have been investigated. In one optimization model the lined free board is not considered and in the other the lined free board is considered. In fact, in this study, for the first time in the field of the optimization of open channels, in addition to the total free board, the lined free board is also considered as a design variable. In the two optimization models mentioned above, the first objective function is considered as a cost function. The discharge, manning's roughness coefficient and the longitudinal bed slope of the channel were random variables, because in real life situation, the actual flow may exceed the design flow because of probable fault in the control of flow at the off take point, and the uncertain lateral inflow. The actual manning roughness values may exceed the assumed design values because of imperfections in fabrication. The physical bed slope achieved may differ from the design values because of fabrication faults. These variations can cause the occasional flooding of man-made open channels. To maintain provisions for these possible variations within the designed cross-sectional dimensions, a flooding probability constraint must be incorporated in the optimal design model. The manning flow equation is also considered as a constraint. Overall in the two models of optimization, the first objective is to minimize the cost of excavation and the lining channel cost and the second objective is to minimize the probability of overflow from its cross section. The manning flow equation is also considered as a constraint. These models have solved with Wolfram Mathematica software. Methods Due to the probability of the second objective function, the model is classified into random optimization models and this is a two-objective optimization problem. To obtain the answers to the two-objective optimization problem, the multi-objective constrained programming method is used, which converts the vector optimization into a numerical one. This conversion from vector to numerical formulas with regard to the first objective is to minimize the total cost of the channel as the single objective in this problem and the second objective which seeks to minimize the overflow, as an additional constraint. In this study, the flooding probability constraint is developed by using the first order analysis that essentially uses the calculus based differentiation of the manning uniform flow. The numerical and deterministic form of the previous modeling are solved with Wolfram Mathematica software for a numerical example. Results The results of solving models with the Wolfram Mathematica software for a numerical example showed that in both optimization models (with lined free board and no lined free board), for the probability of overflow, the total cost was greater and with increasing probability of overflow from 0. 225 to 0. 3, the total cost, the bottom width of the channel, the total free board and the lined free board have decreased. On the other hand, the depth of flow in the channel and side slopes have increased. But in general, the total cost for the construction of a channel in a model with a lined free board is lowered compared to that in which the lined free board is not considered. In other words, considering the lined free board in the open channel, the optimal section has been created at a lower total cost. These results are presented in the form of tables and probability overflow – cost diagrams. According to the results of this study, the cost of channel construction has increased for both models with decreasing the possibility of overflow. Also for low values of overflow, it is necessary to increase the total free board (and lined) and make the channel wider. Comparison of the free board model with a model that did not include the free board showed that considering the lined free board or somehow the unlined part, reduced the total cost. On the other hand, in general, the best choice among all the optimized responses obtained with different overflow probabilities in each model is up to the design engineer, who can determine the budget, importance, and usability of the channel and many other factors. It should be noted that it is suggested that land acquisition and water loss costs (evaporation, transpiration) be included in the objective function to develop the current design in future research and it is also possible to compare the results with current design standards.

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    APA: Copy

    AHMADI, ANIS, Khoshfetrat, Ali, & MALEKI, MOHAMMAD. (2020). Optimal design of trapezoidal open channel section considering the lined free board as a design variable. IRANIAN WATER RESEARCH JOURNAL, 14(2 (37) ), 61-69. SID. https://sid.ir/paper/964967/en

    Vancouver: Copy

    AHMADI ANIS, Khoshfetrat Ali, MALEKI MOHAMMAD. Optimal design of trapezoidal open channel section considering the lined free board as a design variable. IRANIAN WATER RESEARCH JOURNAL[Internet]. 2020;14(2 (37) ):61-69. Available from: https://sid.ir/paper/964967/en

    IEEE: Copy

    ANIS AHMADI, Ali Khoshfetrat, and MOHAMMAD MALEKI, “Optimal design of trapezoidal open channel section considering the lined free board as a design variable,” IRANIAN WATER RESEARCH JOURNAL, vol. 14, no. 2 (37) , pp. 61–69, 2020, [Online]. Available: https://sid.ir/paper/964967/en

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