A probabilistic framework for rainfall-induced instability in unsaturated slopes using bivariate rainfall and multivariate soil random fields

Rainfall is a critical factor in triggering landslides globally, with slope failure probability serving as a key metric for assessing landslide risks. While the spatial variability of soil properties and rainfall uncertainty significantly influence slope failure probability, limited studies have addressed these factors concurrently. Most existing research either emphasizes the spatial variability of soil properties or rainfall uncertainty, often neglecting their combined effects. To address this gap, this study introduces an integrated probabilistic framework that incorporates soil spatial variability and rainfall uncertainty into a slope model for the probabilistic slope seepage analysis based on Monte Carlo simulations. Multivariate soil random fields are employed to represent spatial variability, while rainfall uncertainty is modeled using a bivariate distribution of intensity and duration. This approach allows for the derivation of critical metrics, including the probability of slope failure under single rainfall events, annual failure probabilities, and failure probabilities over multiple years. The proposed framework was applied to a soil slope from the Sawala Laska road project in Ethiopia to demonstrate its effectiveness. Compared to traditional methods that consider only rainfall uncertainty or treat soil properties as deterministic, the framework provides a broader range of safety factor values and more precise estimates of critical rainfall durations. It also reveals that the probability of failure during a single rainfall event decreases, while annual failure probability increases gradually with more frequent rainfall events. By integrating spatial soil variability and rainfall uncertainty within a unified framework, this study advances landslide risk assessments and provides practical tools for slope stability analysis under real-world conditions.