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One of the most crucial problems in geo-engineering is the instability of unsaturated slopes, causing severe loss of life and property worldwide. In this study, five novel meta-heuristic methods are employed to optimize locating the Critical Failure Surface (CFS) and corresponding Factor of Safety (FOS). A Finite Element Method (FEM) code is incorporated to convert the strong form of the Richard’s differential equation to the weak form. More importantly, the derived code can consider both the seismic and seepage conditions additional to the static loading. Eventually, the proposed optimization procedure is validated against benchmark examples and some insights are provided.

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This study presents a novel approach for optimizing critical failure surfaces (CFS) in homogeneous soil slopes by incorporating seepage and seismic effects through the Self-Adaptive Enhanced Vibrating Particle System (SA_EVPS) algorithm. The Finite Element Method (FEM) is employed to model fluid flow through porous media, while Bishop's simplified method calculates the Factor of Safety (FOS). Two benchmark problems validate the proposed approach, with results compared against traditional and meta-heuristic methods. The SA_EVPS algorithm demonstrates superior convergence and accuracy due to its self-adaptive parameter optimization mechanism. Visualizations from Abaqus simulations and comprehensive statistical analyses highlight the algorithm's effectiveness in geotechnical engineering applications. The results show that SA_EVPS consistently achieves lower FOS values with smaller standard deviations compared to existing methods, indicating more accurate identification of critical failure surfaces.