A 3D finite element limit equilibrium framework for reliability analysis of complex slopes: Demonstrating the superiority of horn-shaped failure mechanisms

Existing applications of the finite element limit equilibrium method (FELEM) have primarily focused on deterministic analyses of simple slopes, with limited attention given to reliability assessments of complex three-dimensional slopes that account for spatial variability and intricate failure mechanisms. To address this gap, a novel 3D FELEM framework based on a rigid finite element formulation is proposed. Three rotational failure mechanisms—spherical, ellipsoidal, and horn-shaped—are incorporated to identify the most critical slip surface in complex terrains. Spatial variability of soil properties is further considered through the Modified Linear Estimation (MLE) method for reliability analysis. Results indicate that the slope length-to-height ratio (L/H) significantly influences stability: for narrow slopes (L/H < 6), 3D safety factors are markedly higher than their 2D counterparts, whereas for long slopes (L/H > 6), the two approaches yield comparable results due to an increased likelihood of localized failure. Among the three failure mechanisms, the horn-shaped mechanism consistently identifies the most critical slip surface and provides the most accurate stability assessments for regular, convex, and multilayer slopes. Reliability analysis further reveals that while both the coefficients of variation of cohesion and friction angle reduce the reliability index, their correlation coefficient exerts an even more pronounced effect. The proposed framework offers a robust and versatile approach for 3D slope stability and reliability evaluation under spatially variable soil conditions.