Probabilistic slope stability analysis by risk aggregation

Abstract This paper develops a probabilistic slope stability analysis approach that formulates the slope failure event as a series of mutually exclusive and collectively exhaustive events using conditional probability and utilizes Monte Carlo Simulation (MCS) to determine the occurrence probability for each of the mutually exclusive and collectively exhaustive events in a progressive manner. Then, these probabilities are aggregated to represent the overall slope failure probability p f . Equations are derived for the proposed approach, and the implementation procedures are illustrated using a cohesive slope example. The p f values obtained from the proposed approach are shown to agree well with those p f values that have been obtained by searching a large number of potential slip surfaces for the minimum factor of safety (FS) in each MCS sample. The computational time, however, is shown to reduce by, at least, an order of magnitude. In addition, a sensitivity study is performed to explore the effect of a key parameter in the proposed approach, i.e., the correlation coefficient threshold ρ 0 , on both the accuracy of p f and computational cost. When the spatial variability is significant, the effect of ρ 0 on the accuracy of p f is significant, and a relatively large ρ 0 value is needed to ensure the accuracy of p f . On the other hand, the computational time reduces substantially as the ρ 0 value decreases. At an extreme case of ρ 0  = 1.0, the risk aggregation approach becomes equivalent to an approach where a large number of potential slip surfaces are searched for the minimum FS in each MCS sample. In contrast, at the other extreme case of ρ 0  = 0, the risk aggregation approach is the same as an approach that has been used in many previous studies and relies on only one slip surface. The risk aggregation approach deals rationally with the possibility of slope failure along more than one distinct slip surface (i.e., multiple failure modes) with significantly reduced computational efforts.