Locating the Multiple Failure Surfaces for Slope Stability Using Monte Carlo Technique

Owing to the complicated slope stratigraphy (e.g., multiple soil layers and multiple benches or gradients in side slopes), multiple failure surfaces for slope stability have been recognized in geotechnical discipline. This paper aims to develop a systematic and probabilistic approach to locate the multiple failure surfaces combining the traditional limit equilibrium method with Monte Carlo Simulation. Each of the multiple failure surfaces is selected from a large pool of failure surfaces and the correlation coefficient between two failure surfaces in factor of safety (FS) is adopted to characterize the extent to which two failure surfaces are correlated. After eliminating those highly correlated failure surfaces, the multiple failure surfaces can be gradually identified. The number of failure samples and the number of exclusive failure samples corresponding to each of multiple failure surfaces are determined within the proposed methodology. These data are reanalyzed to find the critical failure surface with the maximum failure probability, the critical failure surface with maximum simplified risk, and those failure surfaces dominating the risk of slope failure. The proposed approach is illustrated through two examples excerpted from the literature and validated against the results from the commercial software package and literature. The comparative study manifests that the critical failure surface with the minimum FS does not always coincide with that with the maximum failure probability and with the maximum simplified risk. In addition to FS, the failure surfaces should be received much attention. The proposed methodology provides an effective tool in decision making for slope stabilization and rehabilitation process.