Stochastic Evaluation of Hydraulic Hysteresis in Unsaturated Soils

The effect of hydraulic hysteresis on the analysis of seepage in unsaturated soils is evaluated stochastically. A hysteretic seepage model is introduced by coupling the governing Richards equation with a hysteretic soil-water retention curve. The first-order second-moment (FOSM) method is used to study the effect of uncertainty in the input parameters on the one-dimensional seepage behavior of a soil column. A performance function is established in terms of the capillary-barrier effect in a multilayered capillary soil cover system. The contribution of variations in the flux at the top boundary on the performance of the soil cover is first investigated with both the traditional nonhysteretic model (NHM) and the hysteretic model (HM). Comparisons show that the HM model is comparatively conservative in the seepage analysis of unsaturated soils and that stochastic seepage behavior is closely associated with the hydraulic history of the soil. In addition, the effects of key input parameters in the HM model on the output statistics are studied in detail, including the saturated hydraulic conductivity $k_s$, the exponential index in the unsaturated hydraulic conductivity function ${\lambda }_k$, the fitting parameters in the van Genuchten soil water characteristic curve (SWCC) equation $\alpha$ and $n$, the residual volumetric water content ${\theta }_r$, the slope of the scanning SWCC curve ${\kappa }_0$, and the top-boundary flux condition $Q$. The SD of hydraulic head is sensitive to the uncertainty inherent in these random input parameters, and for the specific case studied here, the significance of those parameters is found to decrease in the following order: $n$, $Q$, $\alpha$, ${\kappa }_0$, $k_s$, ${\lambda }_k$, ${\theta }_r$. Hydraulic hysteresis is suggested to be considered in the seepage analysis of unsaturated soils.