Probabilistic Slope Stability Analysis with Stochastic Soil Hydraulic Conductivity

The effects of stochastic hydraulic conductivity on the slope stability of an embankment dam are investigated using a combination of random field simulation, seepage analysis, and slope stability analysis. The hydraulic conductivity distribution is treated as a spatially stationary random field following a lognormal distribution. The turning band method is used to generate the spatial variability of the saturated hydraulic conductivity K_s in the domain. Different standard deviations of log hydraulic conductivity ${\sigma }_{\mathit{lnKs}}$ are investigated. For each value of ${\sigma }_{\mathit{lnKs}}$, various realizations of hydraulic conductivity were generated and combined with a numerical model to simulate water flow in an earth dam with variable K_s. The first-order second-moment reliability index β was employed to characterize the influence of the variability of K_s, and hence, pore-water pressures, on the stability of the downstream slope. A linear relationship between ${\sigma }_{\mathit{lnKs}}$ and the standard deviation of the factor of safety σ_F was obtained from the simulation results. A relationship between β and ${\sigma }_{\mathit{lnKs}}$, in which every 0.1 increment of ${\sigma }_{\mathit{lnKs}}$ results in a decrease of 1.0 in β, is deduced based on the simulation results. Results of a Shapiro-Wilk test for goodness of fit indicate that the factor of safety can be assumed to be normally or lognormally distributed when the saturated hydraulic conductivity follows a lognormal distribution and ${\sigma }_{\mathit{lnKs}}$ is small (≤0.5). When ${\sigma }_{\mathit{lnKs}}$ is large (>0.5), neither normal nor lognormal distributions provide a reasonable approximation of the factor of safety. Simulation results show that neither standard deviation nor coefficient of variation of the factor of safety is constant when only the variability of hydraulic conductivity is considered. While the results presented are directly applicable only to the particular earth dam geometry and boundary conditions studied, the methodology is general and may be extended to embankments with different boundary conditions.