Local failure probability of the anti-dip slope susceptible to flexural toppling

Abstract

Anti-dip slope that fails in the form of flexural toppling is commonly encountered in rock engineering. This paper presents an approach to calculate the local failure probability of the anti-dip slope susceptible to flexural toppling. The realization of this approach consists of four major steps: (1) establishing geo-mechanical model of the slope and generating physical parameters randomly using Monte Carlo simulation, (2) determining the demarcation of the toppling and sliding failure zones, (3) evaluating the stability state of each single column, and (4) deriving the local failure probability by an iterative calculation. A case study of the Mari landslide is analyzed by employing the proposed approach, and the Maxwell model is applied to reduce physical parameters with time. The results show that the instability grade increases gradually throughout the whole evolution process of the slope. In the incipient stage, particular attention should be paid to the middle–upper columns, which have the highest failure probabilities. However, as the slope deformation increases, all the columns should be taken into account since they have approximately the equal possibility of failure. A simplified slope model is employed to perform a parametric analysis. The results show that (1) the local failure probability of the slope tends to decrease with increases in the rock friction angle, rock tensile strength or interface friction angle, while increasing the rock unit weight leads to a higher probability of local failure; (2) the computation results are more sensitive to the uncertainty in the interface friction angle than that in the other three above-mentioned parameters; and (3) the maximum failure probability depends on the geometric parameters, including the column interface angle, slope angle, crest angle, slope height and column thickness.