Probabilistic Evaluation of Three-Dimensional Slope Stability under Steady Unsaturated Seepage Conditions Using Sparse Polynomial Chaos Expansions

This study proposes an efficient probabilistic framework for the stability analysis of three-dimensional (3D) unsaturated soil slopes by integrating the sparse polynomial chaos expansion (SPCE) with Monte Carlo simulation. The deterministic stability of the slope is first evaluated using the kinematic approach of limit analysis, in which the suction stress-based Mohr–Coulomb criterion is incorporated to account for steady-state unsaturated seepage conditions. To address the computational intensity of 3D analytical models, a surrogate model based on SPCE is constructed using a limited number of training samples, enabling rapid and accurate reliability evaluations. The accuracy of the proposed approach is rigorously validated through comparative studies against established semianalytical solutions and FLAC3D (version 7.0) numerical simulations. Subsequently, a comprehensive parametric study is conducted to investigate the effects of parameter uncertainty, correlations, and distribution types, as well as the impact of water table variations. The results demonstrate that parameter uncertainties and hydrological conditions have pronounced influences on the stability of unsaturated 3D slopes. Specifically, the rising water table is found to cause a nonlinear increase in the failure probability due to the dissipation of matric suction. Among the parameters considered, the effective internal friction angle and the effective cohesion are identified as the most influential factors. This framework provides a robust and conservative tool for the reliability assessment of 3D slopes in complex hydromechanical environments.