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 simu lation, seepage analysis, and slope stability analysis. The hydraulic condu ctivity distribution is treated as a spatially stationary random field foll owing 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( ln Ks) are investigated. For each value of sigma(ln Ks) various realization s of hydraulic conductivity were generated and combined with a numerical mo del to simulate water flow in an earth dam with variable K-s. The first-ord er second-moment reliability index beta was employed to characterize the in fluence of the variability of K-s, and hence, pore-water pressures, on the stability of the downstream slope. A linear relationship between sigma(ln K s) and the standard deviation of the factor of safety sigma(F) was obtained from the simulation results. A relationship between beta and beta(ln Ks), in which every 0.1 increment of sigma(ln Ks) results in a decrease of 1.0 i n beta, is deduced based on the simulation results. Results of a Shapiro-Wi lle test for goodness of fit indicate that the factor of safety can be assu med to be normally or lognormally distributed when the saturated hydraulic conductivity follows a lognormal distribution and sigma(ln Ks) is small (le ss than or equal to 0.5). When sigma(ln Ks) is large (>0.5), neither normal nor lognormal distributions provide a reasonable approximation of the fact or of safety. Simulation results show that neither standard deviation nor c oefficient of variation of the factor of safety is constant when only the v ariability of hydraulic conductivity is considered. While the results prese nted 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.