Probabilistic Based Reliability Slope Stability Analysis Using FOSM, FORM, and MCS

Abstract

Soil uncertainties play an important part in the analysis and design of geotechnical structures. The effect of uncertainties on the geotechnical structures and their influence on the probability of failure or reliability of the structure is of great interest for geotechnical researchers. Probabilistic-based slope stability analysis incorporates the uncertainties present in the soil, as expressed in terms of mean, variance, and autocorrelation. In this paper, reliability analysis of a finite cohesive soil slope based on the probabilistic approach is presented using the First Order Second Moment (FOSM) method, First Order Reliability Method (FORM), and Monte Carlo Simulation (MCS) method. Stability analysis has been performed using the ordinary method of slices to calculate the Factor Of Safety (FOS) of the slope under undrained conditions. The reliability analysis has been implemented in the MS-excel spreadsheet environment and was mainly focused on the two models, namely the deterministic model for calculating the FOS of the slope and the uncertainty model for generating the random variables of uncertain soil parameters. The reliability index (β) of the soil slope and its corresponding probability of failure (Pf) was calculated using the above methods. The obtained result shows that the MCS method has significantly shown better performance than FOSM and FORM because of its robustness and simple approach to calculate Pf and β of the slope.