Genetic algorithms for optimizing stepped spillways to maximize energy dissipation

Stepped spillways are important water-management structures that are used for energy dissipation. Use of these spillways has increased in recent decades, they can reduce construction time and they are effective for reducing the flow's downstream kinetic energy. In this study, the width and height of the steps as well as the slope and height of the overflow spillway were considered as variables. Due to the large number of variables, non-linearity of the objective function and constraints, and the lack of an explicit relationship between decision variables, a genetic algorithm (GA) was used. A stepped spillway with optimal dimensions was proposed as a replacement of the smooth spillway of Sarogh Dam located in West Azerbaijan province, Iran. The proposed steps increase energy dissipation; for constant discharge and varying slopes, the changes in the optimal height of the steps were insignificant. Sensitivity analysis using the objective function showed that the relative energy dissipation for a constant discharge is independent of the optimal height of the steps and decreases with increasing spillway slope. In addition, for fixed slopes, increasing the flow rate leads to a decrease in relative energy dissipation and an increase in the optimal height of the steps.