Comparative study of deterministic and probabilistic critical slip surfaces applied to slope stability using limit equilibrium methods and the First-Order Reliability Method

Abstract

This work presents the validation of the Morgenstern-Price method implemented in the Risk Assessment applied to Slope Stability (RASS) computational program to carry out deterministic and probabilistic analyses of slope stability. Deterministic analyses, based on the factor of safety approach, are performed using limit equilibrium methods. The probabilistic ones, on the other hand, are carried out through the direct coupling of these methods to the First Order Reliability Method (FORM). Initially, two benchmark cases are presented for validation of the computational routine related to the Morgenstern-Price method. Next, two illustrative examples are presented, with the investigation of the critical surfaces defined by deterministic and probabilistic criteria, which correspond to the minimum factor of safety, the maximum probability of failure, and the maximum quantitative risk. In the set of stability analyses, it was verified that both the numerical responses and the geometry of the critical surfaces can vary depending on the choice of the limit equilibrium method and the criterion for identifying the critical surface. The different possibilities presented by the methodology used in this study define not only a critical surface, but a set of critical surfaces that can help in the engineering decision-making process and slope risk management, complementing the widely used purely deterministic analyses in geotechnics.

Keywords
Slope stability; Limit equilibrium methods; Factor of safety; Direct coupling; Reliability; Quantitative risk assessment