Adaptive Monte Carlo simulation method for system reliability analysis of slope stability based on limit equilibrium methods

A slope fails if it slides along any slip surface. Proper assessment of slope failure risk in geological and geotechnical engineering needs to account, rationally, for a large, or even unlimited, number of circular and/or non-circular potential slip surfaces, which can be modeled as components of a series system. Nevertheless, the computational efforts for incorporating a large number of potential slip surfaces into slope system reliability analysis might be prohibitively expensive, particularly if non-circular slip surfaces are considered. This paper develops an efficient direct Monte Carlo simulation (MCS) method, called adaptive MCS, for slope system reliability analysis based on limit equilibrium methods (LEM), in which a novel sample manipulation strategy is proposed in lieu of brute-force exploration of failure samples amongst direct MCS samples. Equations are derived for the proposed approach and are illustrated using two slope examples considering circular and non-circular potential slip surfaces, respectively. Results show that the proposed approach provides proper estimates of slope system failure probability considering a large number of circular and/or non-circular potential slip surfaces. It significantly improves the computational efficiency of LEM-based slope system reliability analysis compared with brute-force exploration of failure samples.