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 esti-mated 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.

Automated summary

In the assessment and management of rainfall-induced landslides, the probability of slope failure is often used as an index to measure landslide risk. This study provides analytical solutions to assess the probability of slope failure caused by rainfall events, annual probability of slope failure induced by rainfall, and slope failure probability over multiple years. The proposed method utilizes a bivariate distribution of rainfall intensity and duration and a critical rainfall pattern curve to represent a slope's performance under different rainfall patterns. The method is validated using a cut slope in South Korea, showing consistent results with observed slope failures.