Probabilistic Slope Stability Analysis with Stochastic Soil Hydraulic Conductivity

Abstract

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 distri- bution. The turning band method is used to generate the spatial variability of the saturated hydraulic conductivity Ks in the domain. Different standard deviations of log hydraulic conductivity are investigated. For each sln Ks value of various realizations of hydraulic conductivity were generated and combined with a numerical s , ln Ks model to simulate water flow in an earth dam with variable Ks. The first-order second-moment reliability index b was employed to characterize the influence of the variability of Ks, and hence, pore-water pressures, on the stability of the downstream slope. A linear relationship between and the standard deviation of the factor sln Ks of safety sF was obtained from the simulation results. A relationship between b and , in which every 0.1 sln Ks increment of results in a decrease of 1.0 in b, is deduced based on the simulation results. Results of a sln Ks 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 is sln Ks small (#0.5). When is large (>0.5), neither normal nor lognormal distributions provide a reasonable s ln Ks 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. INTRODUCTION AND BACKGROUND Natural soils are highly variable and heterogeneous (Lamb 1966; Peck 1967; Vanmarcke 1977a; DeGroot and Baecher 1993). In practice, methods used for the analysis of slope sta- bility typically are deterministic, with soil properties charac- terized as constants for a given soil layer and each specified layer assumed to be homogeneous. The variability of soil properties presumably is taken into account indirectly for de- sign purposes by selecting a factor of safety, which is chosen based on experience and/or some design criteria (Griffiths and Fenton 1993; Duncan 1996). Many authors have pointed out the limitations of deterministic methods because they do not account explicitly for variability and uncertainty related to soil parameters (Vanmarcke 1977b; Oka and Wu 1990; Soulie et al. 1990; Kulhawy et al. 1991). Methods are needed to quan- tify uncertainties associated with soil properties and to include them in slope stability analysis (Anderson et al. 1982; Whit- tlestone et al. 1995). By incorporating uncertainties quantita- tively, reliability analysis can enhance engineering judgment and facilitate improved decision making (Li and Lumb 1987). Many water-retaining structures in North America are em- bankment dams (Fenton and Griffiths 1996) and the prediction of dam slope stability is of great importance. Hydraulic con- ductivity of the embankment soils is used to calculate all of the hydraulic parameters associated with dam performance, in- cluding seepage rates and amounts, pore-water pressures, and therefore, the state of effective stress. It follows that uncer- tainty associated with the spatial variability of hydraulic con- ductivity leads to uncertainty in estimating pore-water pres-