Numerical Analysis of Slope Stability under Surcharge Effects Using Convex Crossover Optimization

An important problem in geotechnical engineering is slope stability analysis, yet it remains highly complex due to the nonlinear nature of failure mechanisms. The evaluation requires determining the critical failure surface (CFS) and the minimum factor of safety (FOS), which poses a challenging optimization problem. In this study, the limit equilibrium method (LEM), based on the Fellenius approach, is applied to assess slope stability under varying surcharge conditions, including surcharge intensity, position, and width. Results show that higher surcharge intensity combined with reduced position distance and width significantly undermines slope stability. Traditional optimization algorithms are often inadequate for such problems, as they rely on initial guesses and may converge only to local optima. To address this, a Multi-Parametric Genetic Algorithm (MPGA) with a Convex Crossover (CC) operator is developed. The CC operator parameters are calibrated using benchmark test functions, while a time-dependent decay factor is incorporated to improve variable interaction and prevent premature convergence. The proposed MPGA consistently identifies more accurate critical failure surfaces and provides lower safety factors compared to conventional approaches. Overall, the method demonstrates superior efficiency and robustness, offering a reliable tool for slope stability optimization under surcharge conditions.