Optimization of the cross-section and free board of trapezoidal channels based on the minimum probability of overflow and excavation and covering costs

Subject Areas : Analysis, design and construction of water structures

Maryam Ghasemi Khiadani ¹ , Ali Khoshfetrat ^{2 *} , Mohammad Maleki ³

1 - Graduated from Civil Engineering Department, Isf.C., Islamic Azad University, Isfahan, Iran
2 - Department of Civil Engineering, Isf.C., Islamic Azad University, Isfahan, Iran
3 - Department of Mathematics, Isf.C., Islamic Azad University, Isfahan, Iran

Received: 2024-10-20 Accepted : 2025-04-22 Published : 2025-04-27

Keywords: Channel section design, Nonlinear optimization, Free board, Minimum overflow probability, Excavation and cover costs,

Abstract :

In general, the efficiency of water conveyance channels is often below the acceptable level, one of the reasons being the lack of appropriate optimization methods in channel design. The objective of channel cross-section optimization is to design a channel in the most hydraulically favorable condition while ensuring economic feasibility. Additionally, minimizing the risk of overflow is essential in channel design.

In the present study, the goal is to minimize the total costs of excavation and lining, along with minimizing the probability of flow overflow in a trapezoidal channel under varying discharge rates. Furthermore, the effect of discharge variation on channel dimension optimization is investigated. The freeboard and flow discharge are considered as design variables. Due to the constraint of satisfying Manning’s equation, the problem formulation leads to a nonlinear optimization, which is solved using Wolfram Mathematica software.

The results indicate that as the discharge increases, the optimal depth and bottom width also increase, leading to higher construction costs. However, with increasing discharge, the channel’s freeboard decreases.

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