Probabilistic analysis of rock slope stability with first-order approximation

Abstract

Based on the theory of probability, the probabilistic analysis of slope stability is conducted. Equations for the estimation of slope failure probability are first derived using direct integrations. However, the complexity of the integrations is formidable. In order to overcome the limitation of the direct integration, the first-order second-moment approximation of the slope failure probability is employed for more complex slope stability problems. The study indicates that the distributions of parameter values play a significant role in slope stability, which can not be disclosed by the conventional methods of stability analysis. Greater dispersiveness of the parameter values will lead to a different probability of failure, although the factor of safety estimated by conventional methods remains the same if the mean values of the parameters are unchanged. By taking consideration of the distributions of the parameters, the probability model can provide more reliable designs of rock slopes.