Implementing Reliability Analysis of a Soil Slope using First-Order Second Moment Method, Monte-Carlo Simulation Method and Subset Simulation Method in a MS-Excel Spreadsheet

Abstract

The spatial variation in the soil properties affects the analysis and design of geotechnical structures such as slope stability analysis. This paper presents the reliability analysis of a soil slope using three different methods namely, first-order second moment (FOSM) method, Monte-Carlo simulation (MCS) method and Subset simulation (SS) method. The analysis has been carried out by considering the spatial variation of the soil properties of the slope. The correlation function and the correlation distance (λ) for the uncertain parameters are modelled using random field theory developed by Vanmarcke. The factor of safety (FOS) of the slope is determined using Ordinary method of slices. The reliability based probabilistic slope stability analysis has been carried out in a MS-Excel spreadsheet to determine the probability of failure (P_f ) and reliability index (β) of the slope. The spreadsheet mainly consists of three parts i.e., deterministic analysis, uncertainty analysis and uncertainty propagation. The study shows that the SS method has shown better performance as compared to FOSM method and MCS method especially at low failure probability levels. Also, SS method ensures the generation of samples in the failure region which is not always possible in MCS method.