Monte Carlo simulation method for reliability analysis of slope stability

Abstract

In Hong Kong, slope design has to comply with the requirement of the “Geotechnical manual for Slopes” published by the Geotechnical Engineering Office (GEO) which stipulates the minimum factor of safety (FOS) to be attained. There is no requirement and information on the probability of failure of the slope. Generally, a lager factor of safety may associate with a smaller probability of failure, but it depends inter alia on the probability density function (pdf) of input parameters, notably, the shear strength parameters. This project aims to evaluate the probability of failure of selected man-made soil slopes under the HK Government’s Landslip Prevention and Mitigation Programme (LPMitP) by constructing reliable pdf of shear strength parameters from triaxial tests. This project will focus on (a) whether FOS can give meaningful information on the probability of failure of a slope; (b) methods to calculate the probability of failure in a reliable and economical way and (c) apply the Monte-Carlo method to slopes under LPMitP before and after upgrading works. Slopes were selected from GEO Stage three study reports which included the before upgrade sections (without soil nails) and upgraded sections (with soil nails). A method was devised to generate the pdf of effective shear strength parameters from the consolidated undrained and drained triaxial tests. Statistical information such as mean, standard deviation and Coefficient of Variance (COV) of the pdfs are obtained. With the help of a well known commercial software SLOPE/W, Monte-Carlo simulations were performed to obtain the probability of failure of each slope. In order to obtain reliable and economical results, the optimal number of Monte Carlo simulations was also evaluated. The project provides insights and understanding on the relationship between factor of safety and probability of failure of slopes before and after upgrading. Moreover, the effect of pdf of input parameters cannot be over-emphasized.