A probabilistic slope stability analysis using deterministic computer software

Abstract

A designation of the probability of failure of a slope can add further understanding to its behaviour, over and above a conventional factor of safety. The purpose of this paper is to illustrate how a deterministic slope stability package can be made into a probabilistic software package or used in a probabilistic manner. The same general procedure could be applied to any deterministic computer program. A slope stability example was set up to be solved in the conventional manner using a deterministic software package (i.e., PC-SLOPE). Additional, independent code was developed to generate statistical data in order that the deterministic solution could be repeatedly executed to give a probabilistic evaluation of the same example. Normal frequency distributions relative to variations in cohesion, angle of internal friction and pore-water pressure were studied. From the mean values and the standard deviations of the cohesion, angle of internal friction and pore-water pressure, along with the correlation relationship between cohesion and angle of internal friction, sets of random values of the cohesion, angle of internal friction and pore-water pressure were generated using the Monte Carlo method and the Point Estimate method. Each set of these values of cohesion, angle of internal friction and pore-water pressure generated were then used in the deterministic software package to compute a factor of safety. Further code was written to read the output factors of safety files and to analyze the results. In this way, the probability distribution of the factor of safety was obtained for a specific slip surface. The reliability in terms of the probability of factor of safety being greater than or equal to 1.0 was also computed.