Abstract
This study proposes a methodology for the design of trapezoidal cross-sections of open channels with minimum construction cost subject to uniform flow and stability constraints. The proposed methodology integrates the application of the Weighted Superposition Attraction–Repulsion (WSAR) method for finding economically optimized geometric parameters with iterative search methods that calculate the seismic stability factor of the slope. Compared to existing research, which mainly used the Fellenius method and did not consider seismic loading adequately, seismic loading is used explicitly in this research through consideration of the Fellenius, Bishop, and Janbu methods simultaneously. The WSAR algorithm is applied for the optimum design of open channel sections for the first time in literature. The results prove that most economical channel designs are obtained from the Janbu method in all cases. In non-seismic conditions, cost savings varied from 2.78% to 3.29% for varied discharge values. Under seismic conditions, this advantage is more significant. In the case of seismic conditions, K h = 0.01, the Janbu approach accounted for cost savings of up to 12.13% for Q = 100 m³/s and up to 9.16% for Q = 500 m³/s. In the case of seismic conditions, K h = 0.02, these savings amounted to 50.91% and 25.82% for Q = 100 m³/s and Q = 500 m³/s, respectively.