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

Khaled Farah*, 1, 2, Mounir Ltifi1, 2, Hedi Hassis1
1 University of Tunis El Manar, National Engineering School of Tunis, Civil Engineering Laboratory, 1002, Tunis, Tunisia
2 National Engineering School of Gabés, Tunisia

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© 2015 Farah et al;

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the National Engineering school of Tunis, Tunisia BP 37, Le Belvédère 1002 Tunis; Tel: +21671875726; Fax: +21671875726; E-mail:


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.

Keywords: FORM algorithm, monte carlo simulation, perturbation method, random field, slope stability, spatial variability.