Sensitivity Study of Local Average Size on the Failure Probability of Spatially Variable Slope Stability

Abstract

This paper explores the influence of local average size, Δz, on the failure probability, pf, of spatially variable slope failure along a given slip surface and along a combination of two slip surfaces. The spatial variability of statistical geotechnical property with depth is modeled by a lognormal random field with an exponentially decaying correlation structure. The probabilistic slope stability analysis incorporating random field theory with Monte Carlo simulation is adopted to conduct the sensitivity study. The variance reduction due to local averaging and the correlations between local averages are considered (denoted M1), and a simplified approach (denoted M2) neglecting the variance reduction and simulating correlations between local averages at the mid-points of local averages is compared with M1. The results of sensitivity study on an undrained slope have shown that the influence of Δz on pf of slope failure along a given slip surface hinges on the given slip surface. As the ratio of Δz to the scale of fluctuation, λ, varies in the range of 0.0 to 0.4, M1 and M2 can predict the results within 10% normalized discrepancy for the pf of slope failure along a given slip surface. As Δz/λ is greater than 0.4, the performance of M1 is superior to that of M2. As Δz increases, a larger value of Δz cannot identify the additional contribution to pf if slope failure along more than one slip surface is taken into account.