Stratified Response Surfaces for System Probabilistic Evaluation of Slopes

TLDR

Probabilistic slope analysis must account for soil property uncertainty, yet traditional single‑mode failure approaches often underestimate failure probability, making system reliability analysis a more rational alternative. This study seeks to enhance slope reliability analysis by incorporating system reliability concepts. The authors propose a stratified response‑surface method that constructs multiple response surfaces for each failure mode, enabling efficient system reliability evaluation via a dispersion‑ellipsoid FORM or Monte Carlo simulation. When applied to case studies, the stratified RSM produced results that closely matched those from Monte Carlo simulations.

Abstract

The need for probabilistic slope analysis that takes into account the uncertainty of soil properties has been acknowledged by the geotechnical profession. Traditionally, probabilistic slope analysis involves only single-mode failure that is considered based on the critical slip surface. This may result in underestimating the failure probability. In contrast, system reliability analysis for slopes is deemed more rational. This study aims at improving the existing methods of slope reliability analysis by considering system reliability. A stratified response surface method (stratified RSM) is proposed to describe the performance functions of possible failure modes. The proposed method differs from conventional response-surface–based slope reliability analysis (which constructs a single approximate performance function) by generating a group of (stratified) response surfaces. Based on these stratified response surfaces, system reliability analysis can be efficiently carried out by means of either a first-order reliability method (FORM) or Monte Carlo simulations. The efficient FORM based on the concept of a dispersion ellipsoid in the space of the original variables is used. Application of the proposed approach to probabilistic assessment of slopes is illustrated by case studies, and the results obtained are compared with Monte Carlo simulations.