In fluence of a firm stratum on probabilistic slope stability analyses with spatially variable undrained soil strength

The influence of a firm stratum on the stability of a slope under undrained conditions has long been of interest to geotechnical investigators, which has been studied in a number of previously important works in relation to slope stability analyses without considering soil spatial variability. This paper proposes another look at such a problem in the context of probabilistic slope stability analyses considering soil spatial variability. Here, the random field (RF) is used to simulate the spatially variable undrained soil strength. It is found that under stationary RF and non-stationary RF with the soil strength at the top ground surface (s_u0) larger than 0, the depth of the firm stratum (H_f) has a significant influence on the mean and standard deviation of factor of safety (i.e., μ[FS] and σ[FS], respectively). By contrast, under non-stationary RF with s_u0 = 0, H_f has a slight influence on μ[FS], but its influence on σ[FS] is non-negligible. In addition, the autocorrelation distance is found to have an insignificant impact on the influential effect of H_f on μ[FS]. However, for σ[FS], this impact is not negligible. When the autocorrelation distance is smaller, the influence of H_f on σ[FS] would be more significant. Under non-stationary RF, the influence of H_f on σ[FS] would be slight if the autocorrelation distance is large enough. Furthermore, the impacts of slope ratio, s_u0, isotropic and anisotropic features on the influential effects of H_f are also investigated and discussed.