Analytical solutions for annual probability of slope failure induced by rainfall at a specific slope using bivariate distribution of rainfall intensity and duration

In risk assessment and management of rainfall-induced landslides, annual frequency or probability of slope failure has often been used as a straightforward index for quantitatively measuring landslide risk. It is therefore of great interest to predict the annual failure probability of a specific slope when subjected to rainfall infiltration. This study derives analytical solutions, respectively, for assessing the probability of slope failure caused by a single rainfall event, the annual probability of slope failure induced by rainfall, and slope failure probability over some years. The analytical solutions rely on two key elements: (1) a bivariate distribution of rainfall intensity and duration which reflects local rainfall characteristics for a given slope, and (2) a critical rainfall pattern curve (CRPC) that comprehensively represents a slope's rainfall-induced performance under a wide spectrum of rainfall patterns. The proposed method is illustrated and verified by an engineered cut slope in South Korea. The estimated high annual failure probability is consistent with the observed slope failure in the field. The proposed method can be implemented easily and efficiently. The proposed method can also be used to quantitatively evaluate the landslide risk (e.g., annual failure probability) with or without stabilization, leading to risk-informed slope designs.