Fully analytical method for probabilistic stability analysis of the rainfall-induced landslide considering variability of saturated hydraulic conductivity and rainfall uncertainty

Characteristics of a rainfall event (e.g., rainfall duration D and intensity I) have a significant influence on the probabilistic stability analysis of the rainfall-induced landslides. However, most previous probabilistic stability analyses of rainfall-induced landslides have been performed under a given rainfall pattern without considering the uncertainty of the rainfall characteristics. The Monte Carlo simulation method, which takes a lot of computing resources and time, has been widely used in previous studies. In this paper, a fully analytical method is proposed to estimate the slope failure probability induced by a random rainfall event (P_F1) and the annual slope failure probability (P_FA), which considers both rainfall uncertainty and the variability of saturated hydraulic conductivity K_s. Triple integration is used by the analytical method to avoid repeated sampling and calculation. Compared with the Monte Carlo simulation method, the analytical method greatly improves the calculating efficiency. The outcomes based on the analytical method are consistent with those obtained by the Monte Carlo simulation method, which verifies the accuracy of the analytical method. When the mean of the saturated hydraulic conductivity (μ_Ks) is large, P_F1 decreases with the increase in the coefficient of variation (COV) of K_s. When μ_Ks is small, P_F1 and P_FA increase with the increase in COV of K_s (COV_Ks).