A simplified direct method for finding optimal stable trapezoidal channels

An economical channel with trapezoidal cross-section is determined in this paper by considering the criterion for the side slope stability (soil conditions). This cross-section prevents the slope failure after construction. To implement this slope stability criterion, Taylor's stability chart is converted to a polynomial surface equation (using multiple regression analysis) that was found to be very accurate. This equation facilitates the modelling of the optimal channel cross-section and was integrated with the flow and geometric constraints to determine the optimal channel cross-section that minimizes the total construction cost. The proposed optimization model is direct and determines the safety factor without iterations. The computer running time of the proposed model is only about 1% of the running time of the existing hybrid model. The efficiency of the proposed model, which substantially aids the conduct of sensitivity analysis, should be of interest to irrigation and drainage professionals.