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Uncertainty is an inevitable factor that influences the function analysis, design, and safe operation in engineering systems. Due to the complexity property and unclear failure mechanism, uncertainty is an intrinsic property of slope engineering. Hence, stability analysis and design cannot meet the demands of slope engineering based on the traditional deterministic method, which cannot deal with uncertainty. In this study, a practical reliability approach was developed to consider the uncertainty factor in slope stability analysis by combining the multiplicative dimensional reduction method (MDRM) and first-order second moment (FOSM). MDRM was used to approximate the complex, nonlinear, high-dimensional, and implicit limit state function. The statistical moment of safety factor was estimated based on the moment method using MDRM. FOSM is adopted to compute the reliability index based on the statistical moment of the safety factor. The proposed method was illustrated and verified by an infinite slope with an analytical solution. The reliability index and failure probability were compared with Monte Carlo simulations (MCS) in various cases. Then, it was applied to a slope based on numerical solutions. The results show that the proposed method is feasible and effective for probabilistic slope stability analysis. The reliability index obtained from the proposed method shows high consensus with the traditional response surface method (RSM). It shows that the proposed method is effective, efficient, and accurate. MDRM provides a practical, simple, and efficient probabilistic slope stability analysis approach.

Dimensional Reduction-Based Moment Model for Probabilistic Slope Stability Analysis