First-order Probabilistic Analysis of the Effects of Heterogeneity on Pore-water Pressure in a Hillslope

Abstract:

Pore-water pressure in a hillslope is a critical control of its stability. The main objective of this paper is to introduce a first-order moment analysis to investigate the pressure head variability within a hypothetical hillslope, induced by steady rainfall infiltration. This approach accounts for the uncertainties and spatial variation of the hydraulic conductivity, and is based on a first-order Taylor approximation of pressure perturbations calculated by a variably saturated, finite element flow model. Using this approach, the effects of variance (σ²_lnKs) and spatial structure anisotropy (λ_h/λ_v) of natural logarithm of saturated hydraulic conductivity, and normalized vertical infiltration flux (q/k_s) on the hillslope pore-water pressure are evaluated. We found that the responses of pressure head variability (σ²_p) are quite different between unsaturated region and saturated region divided by the phreatic surface. Above the phreatic surface, a higher variability in pressure head is obtained from a higher σ²_lnKs, a higher λ_h/λ_v and a smaller q/k_s; while below the phreatic surface, a higher σ²_lnKs, a lower λ_h/λ_v or a larger q/k_s would lead to a higher variability in pressure head, and greater range of fluctuation of the phreatic surface within the hillslope. σ²_lnKs has greatest impact on σ²_p within the slope and λ_h/λ_v has smallest impact. All three variables have greater influence on maximum σ²_p within the saturated region below the phreatic surface than that within the unsaturated region above the phreatic surface. The results obtained from this study are useful to understand the influence of hydraulic conductivity variations on slope seepage and stability under different slope conditions and material spatial distributions.