Efficient System Reliability Analysis of Slope Stability in Spatially Variable Soils Using Monte Carlo Simulation

Monte Carlo simulation (MCS) provides a conceptually simple and robust method to evaluate the system reliability of slope stability, particularly in spatially variable soils. However, it suffers from a lack of efficiency at small probability levels, which are of great interest in geotechnical design practice. To address this problem, this paper develops a MCS-based approach for efficient evaluation of the system failure probability $P_{f\text{,}s}$ of slope stability in spatially variable soils. The proposed approach allows explicit modeling of the inherent spatial variability of soil properties in a system reliability analysis of slope stability. It facilitates the slope system reliability analysis using representative slip surfaces (i.e., dominating slope failure modes) and multiple stochastic response surfaces. Based on the stochastic response surfaces, the values of $P_{f\text{,}s}$ are efficiently calculated using MCS with negligible computational effort. For illustration, the proposed MCS-based system reliability analysis is applied to two slope examples. Results show that the proposed approach estimates $P_{f\text{,}s}$ properly considering the spatial variability of soils and improves the computational efficiency significantly at small probability levels. With the aid of the improved computational efficiency offered by the approach, a series of sensitivity studies are carried out to explore the effects of spatial variability in both the horizontal and vertical directions and the cross-correlation between uncertain soil parameters. It is found that both the spatial variability and cross-correlation affect $P_{f\text{,}s}$ significantly. The proposed approach allows more insights into such effects from a system analysis point of view.