Assessing the average maximum failure probability of unsaturated slopes over a given exposure period under stochastic rainfall

Rainfall-induced landslides pose a significant threat to infrastructure and safety. Traditional deterministic approaches and many probabilistic methods are limited in their ability to evaluate the cumulative risk induced by multiple rainfall events over a specified time horizon. This study proposes a novel probabilistic framework to assess the average maximum failure probability (AMFP) of unsaturated soil slopes over a given exposure period ( T ) under multiple stochastic rainfall. The framework integrates rainfall randomness, geotechnical uncertainty, and unsaturated hydro–mechanical coupling, while addressing key challenges related to exposure-period aggregation and computational efficiency. The dependence structure between rainfall duration and intensity, including long-tail characteristics of extremes, is modeled using a Frank Copula based on historical rainfall data. Coupled seepage–stability simulations are implemented in FLAC3D through customized FISH scripting. To enable large-scale Monte Carlo analysis, a high-accuracy Support Vector Regression (SVR) surrogate model is constructed to replace computationally expensive numerical simulations. Application to a homogeneous slope in Baotou, China, indicates that the AMFP increases monotonically with exposure duration, rising from 2.52% ( T  = 0.5 year) to 3.08% ( T  = 5 years), demonstrating cumulative amplification of failure risk under stochastic rainfall. For T  = 1 year (34 rainfall events), the AMFP is 2.69%, corresponding to a reliability index of 1.927. Sensitivity analysis shows that rainfall duration and intensity exert comparable influences on failure probability, while soil strength parameters remain the dominant controlling factors. By linking stochastic rainfall occurrence with exposure-period-based extreme response, the proposed framework provides a rigorous and computationally efficient tool for time-dependent slope reliability assessment and risk-informed engineering decision-making.