An improved finite element limit equilibrium method for three-dimensional slope stability analysis under seismic condition

The finite element limit equilibrium method (FELEM) is increasingly applied in slope stability analysis due to its time efficiency and use of realistic stress fields. However, traditional limit equilibrium methods (LEM) are limited by simplified inter-slice stress assumptions, hindering accurate representation of earthquake-induced complex failures. This study introduces FELEM combined with an improved particle swarm optimization (PSO) algorithm (FELEM-PSO) for pseudo-static and nonlinear seismic time-history analyses. A “rough-to-precise” two-stage search strategy achieves dynamic slip surface optimization in a time-varying stress field, and its effectiveness is evaluated using a slope containing a weak interlayer. Numerical examples under strong seismic conditions revealed a failure mechanism involving the elevation amplification effect. The computed safety factor showed a relative difference of 0.39%∼0.78% compared to the strength reduction finite element method (SRFEM). This demonstrates the method’s potential to capture complex failure mechanisms. The presented method also improved computational efficiency, with reductions of 85.3%∼91.4% versus SRFEM, primarily by avoiding the elasto-plastic strength-reduction iteration loop. FELEM-PSO thus offers a promising balance of numerical precision and efficiency for preliminary seismic slope stability evaluation. It should be noted that these metrics derive from a limited set of deterministic examples and should not be viewed as statistical bounds for arbitrary slopes or ground motions.