Probabilistic Critical Slip Surface for Earth Slopes Based on the First Order Reliability Method

Abstract

The paper presents a computational procedure for reliability analysis of earth slopes in which the probabilistic critical slip surface is located using a mathematical programming formulation similar to that used to search for the deterministic critical slip surface in a conventional slope stability analysis. The procedure is based on the First Order Reliability Method (FORM) in conjunction with the Spencer method for evaluation of factor of safety of general slip surfaces and the Sequential Quadratic Programming (SQP) technique of optimization. When applied to two benchmark illustrative examples, the procedure yields the probabilistic critical slip surfaces which are reasonable and the values of the associated minimum reliability indices are close to or lower than those reported by different investigators using different methodologies, and compare well with those from the direct Monte-Carlo simulation method (MCS). Further, the developed procedure has been made use of to investigate another important aspect of reliability analysis, namely, how the results of reliability analyses vary with the probability distributions assumed for the basic random variables. Three most commonly assumed distributions, namely, normal, lognormal and truncated normal distributions have been considered. The results indicate that the lognormal assumption used solely to ensure non-negativity of the basic variables might lead to non-conservative prediction of probability of failure. Whether the effect of such distributional assumption is consistent when the coefficients of variation (COVs) of the basic random variables vary within their respective ranges has also been investigated.