Probabilistic Analysis of a Three-Dimensional Slope Based on Limit Analysis

In traditional stability analyses of three-dimensional slopes, soil has often been treated as a homogeneous material with single-parameter properties, overlooking the variability inherent in the strength parameters and unit weight of natural soil. This oversight can lead to an overestimation of slope stability and reliability. To address this issue, this manuscript introduces a novel approach. Initially, a horn-shaped double logarithmic spiral failure mechanism for three-dimensional slopes is constructed based on the kinematic approach within the framework of limit analysis theory. The critical height of the three-dimensional slope is calculated using the mean values of soil properties. Subsequently, the stochastic response surface method is employed to formulate a limit state equation for three-dimensional slopes, with three different algorithms utilized to analyze failure probability. Two cases are employed to validate the proposed method and to assess the efficiency and accuracy of the algorithms. Further, a back analysis of the probabilistic distribution of strength parameters for three-dimensional slopes is performed using the stochastic response surface limit state equation. The findings reveal that the relative width of the three-dimensional slope, the coefficient of variation (COV) of strength parameters, and unit weight significantly affect slope reliability. An increase in relative width leads to higher failure probability, while larger COV values for strength parameters and unit weight correspond to higher failure probability. Through back analysis, the results considering parameter variability align more closely with strength parameters obtained from in situ experiments.