A Study of Probabilistic FEMs for a Slope Reliability Analysis Using the Stress Fields

Abstract

In this paper, the applicability and the effectiveness of the probabilistic finite element methods (FEMs) such as the perturbation method, and the Spectral Stochastic Finite Element Method (SSFEM) applied to the reliability analysis of the slope stability have been studied. The results were checked by the Monte Carlo simulation and a direct coupling ap-proach combining the deterministic finite elements code and First Order Reliability Method (FORM) algorithm. These methods are presented considering the spatial variation of soil strength parameters and Young modulus. The random field is used to describe the spatial variation. Also, the reliability analysis is conducted using a performance function formulat-ed in terms of the stochastic stress mobilized along the sliding surface. The present study shows that the perturbation method and SSFEM can be considered as practical methods to conduct a second moment analysis of the slope stability taking into account the spatial variability of soil properties since good results are obtained with acceptable estimated rela-tive errors. Finally, the perturbation method is performed to delimit the location of the critical probabilistic sliding surfac-es and to evaluate the effect of the correlation length of soil strength parameters on the safety factor. In addition, the two methods are used to estimate the probability density and the cumulative distribution function of the factor of safety.

Stress-weighted spatial averaging of random fields in geotechnical risk assessment

“…where r(x;y) = r(xy) because of the assumed homogeneity; the expression (10) has only loose ties with the approximate variance reduction factor proposed for practical applications by Vanmarcke (2010):…”

“…The integral equations ( 7)- (10) apply not only to shearing resistance, but also to settlement analysis and to any linear operator, in fact. In a simplified linear form suggested by the Eurocode 7 (EN 1997-1), the foundation settlement w (m) can be estimated as follows:…”

An Overview on Methods for Slope Stability Analysis

“…Thus, the probability of failure can be estimated. In this study, the values evaluated by the Monte Carlo simulation and direct coupling approach are considered as reference values [9].…”