Abstract
Abstract In this paper, several analytical models are presented for the optimal design of a trapezoidal composite channel cross-section. The objective function is the cost function per unit length of the channel, which includes the excavation and lining costs. To define the system, design variables including channel depth, channel width, side slopes, freeboard, and roughness coefficients were used. The constraints include Manning’s equation, flow velocity, Froude number, and water surface width. The Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm was used to solve the optimization problem. The results are presented in three parts; in the first part, the optimal values of the design variables and the objective function are presented in different discharges. In the second part, the relationship between cost and design variables in different discharges is presented in the form of conceptual and analytical models and mathematical functions. Finally, in the third part, the changes in the design variables and cost function are presented as a graph based on the discharge variations. Results indicate that the cost increases with increasing water depth, left side slope, equivalent roughness coefficient, and freeboard.
Highlights
The optimal design of a channel cross-section reduces the cost along the channel
The results indicated that using HBP, compared to bat algorithm (BA), particle swarm optimization (PSO), LINGO, the Lagrange multiplier method, and the shuffled frog-leaping algorithm, led to a 32% saving in construction cost
The optimal design for trapezoidal composite channel cross-sections was prepared with different discharge values by presenting both conceptual and analytical models
Summary
The optimal design of a channel cross-section reduces the cost along the channel. The optimal geometric dimensions of a channel’s cross-section are determined such that the cost of channel construction is minimized and the flow passing through it is maximized [1]. In all the above studies, the uniform roughness coefficient was considered along the bed and sides of the channel cross-section. Swamee et al [6] designed the optimal shape of the open channel cross-section with the objective function of the channel construction cost including excavation and lining costs and water loss. The advantage of Lotter’s equation compared to Horton’s is that the velocity varies in channel bed and sides that have different roughness coefficients. Chahar [9] presented the optimal parabolic cross-section design equations without considering the freeboard. These equations were used to minimize the excavation and lining costs and were obtained in an explicit shape using the Fibonacci search method. Bhattacharjya [10] presented the optimal design of a trapezoidal composite
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