264 Kh. Farah, M. Ltifi, T. Abichou, H. Hassis Technical Note Comparison of some probabilistic methods for analyzing slope stability problem Kh. Farah 1 , M. Ltifi 1 , T. Abichou 2, *, H. Hassis 1 Received: March 2013, Revised: May 2013, Accepted: July 2013 Abstract The study aims at comparing the results of different probabilistic methods such as the perturbation method, Spectral Stochastic Finite Element Method (SSFEM) and Monte Carlo Method. These methods are developed for a linear soil behavior. In this study, by assuming soil strength properties and Young modulus are random variables, a preliminary search of critical slip surface is established. One-dimensional random field is used to conduct a parametric study. The proposed probabilistic slope stability analysis is performed using a performance function formulated by the stochastic stress field mobilized along the slip surface. The results have shown that the Young modulus has no significant effect on the factor of safety. In addition, the studies have found that the perturbation method is valid than SSFEM to conduct the slope stability analysis. Moreover, SSFEM performed with high orders of expansion to reach the convergence of solution can lead to intractable calculations, while Monte Carlo method is too time consuming for a slope stability reliability analysis using modeling the spatial variability of soil properties by the random field’s theory. Finally, the numerical results have shown that the correlation lengths of the soil strength properties have effect on the position of the critical sliding surface. Keywords: Slope stability, Stochastic finite element method, Random field, Probabilistic methods, Monte Carlo. 1. Introduction Uncertainty and hazard are unavoidable in the geotechnical engineering domain. The adopted analytical models are mathematical simplifications of more complex physical phenomena, and soil parameters introduced in some equations present a spatial variability. For many years, the analysis of slope stability has been studied by deterministic approaches that have considered these uncertainties by determining a safety factor. One such example is the finite element method. Since risks have begun to be quantified and discussed, probabilistic methods are now required to overcome this deficiency. Researchers quantify the uncertainty in the soil properties, either by random variable or by the random field’s theory. In recent years, several probabilistic approaches have been developed for the analysis of slope stability [1, 2,3,4]. In considering, the spatial variability of soil properties, the random fields can be considered as an appropriate tool for reliability analysis in the geotechnical engineering. * Corresponding author: abichou@eng.fsu.edu 1 Civil Engineering Laboratory, National Engineering school of Tunis, Tunisia BP 37 Le Belvédère 1002 Tunis Tunisia 2 Department of Civil and Environmental Engineering, Florida State University, 2525 Pottsdamer Street, Tallahassee, FL, 32310 USA Most methods can take into account the spatial variability of soil properties that are modeled by the random field’s theory. The random field is completely defined by a mean, standard deviation and autocorrelation function. The work presented here aims to compare the perturbation method, spectral stochastic finite element method SSFEM and Monte Carlo simulation to calculate the statistical parameters of safety factors for a probabilistic slope stability analysis of homogeneous soil within the linear behavior law. A discussion of the applicability and effectiveness of these methods is presented for evaluation of probability density safety factor as well as its mean and standard deviation. The discretization procedure is necessary to approximate with an estimation error and is divided into three major types: point discritization, average discritization and series expansion methods [5, 6, 7]. The probabilistic methods proposed in this article, which belong to the stochastic finite element method, are applied to various domains by different formulations. Among them are the perturbation method and the spectral method [7, 8, 9, 10, 11]. However, most of these formulations are used for linear constitutive law. There are only a few documents that study the reliability problem with elastoplastic material behavior [9, 10, 11,12, 13]. Similar works with convergence study and the evaluation Geotechnique