Probabilistic Model of Progressive Failure of Slopes

A probabilistic model for the progression of failure in a soil slope is presented. Failure progression is defined as a spatial and continuous extension of the failure zone along a potential slip surface in a statistically homogeneous medium. The local safety margin of any segment of the slip surface is assumed to follow a normal distribution; cohesive and frictional parameters of shear strength being considered as independent random variables. The joint distribution of the safety margin of any two adjacent segments of the slip surface is assumed to be bivariate normal. After defining the model and outlining the rules of transition, expressions for the probability of failure progression are derived. The model and its formulation are illustrated by a worked example and the significance of the proposed model is discussed. The suggested approach to the study of progressive failure gives insight into the interdependence of the stability of adjacent elements or sections of a soil mass. Consequently, it is potentially valuable in clarifying the real behavior of soil masses and expecially slopes.