A Comparison of 1D and 2D Spatial Variability in Probabilistic Slope Stability Analysis

Abstract

Slope stability analysis is a highly challenging task in geotechnical engineering as the influence of uncertainty involved in geotechnical properties on failure behavior of slopes is inevitable. Traditional deterministic slope stability approach, based on a single factor of safety (FoS) parameter, cannot explicitly encounter the uncertainties involved in geotechnical properties and failure mechanism, leading to erroneous results of slope stability. Hence, slope stability practice is highly persuadable to probabilistic treatment, which allows quantification of the uncertainty and rationally integrating the same into the analysis. The present study investigates the influence of inherent spatial variation of soil domain in probabilistic slope stability analysis. To accomplish this, a hypothetical slope is analyzed, considering 1D spatial variation, with the aid of GeoStudio 2007, using Morgenstern-Price limit equilibrium method (LEM) coupled with Monte Carlo simulation (MCS). The results are compared with those of Griffiths et al. (2007), wherein 2D random field for soil shear strength was considered and the analysis was carried out with the help of random finite element method (RFEM). The influence of correlation lengths on the probabilities of failure is compared. The results reveal that the probability of failure highly depends on spatial variation of soil property in both the methods. When correlation length is small, the failure probability is essentially zero; failure probability increases rapidly for intermediate correlation lengths, and for large correlation lengths, the failure probability becomes constant. It is also found that combining LEM with one-dimensional random field gives lower probabilities of failure than RFEM, as RFEM is more efficient in simulating the field uncertainty. Moreover, RFEM can search and identify the weakest path through the soil domain for the failure to occur, whereas LEM presumes a predefined failure plane.