Stochastic Analysis of Unsaturated Flow in Heterogeneous Soils: 2. Statistically Anisotropic Media With Variable α

Steady unsaturated flow in heterogeneous soil with an arbitrarily oriented mean hydraulic gradient is analyzed using spectral solutions of the stochastic perturbation equation which describes the capillary pressure head ψ. The unsaturated hydraulic conductivity is related to ψ by K = K_s exp (−αψ), where K_s is the saturated hydraulic conductivity and α is a soil parameter, and both K_s and α are treated as three‐dimensional statistically homogeneous, anisotropic random fields. Analytical results are obtained for the capillary pressure head variance and the effective (mean) unsaturated hydraulic conductivity. The head variance depends upon the degree of anisotropy of the ln K_s covariance; when α is random, the head variance increases with mean capillary pressure head. The effective hydraulic conductivity for arbitrary orientation of the mean hydraulic gradient J is shown to have tensorial properties, but its components depend on the magnitude and direction of J and the orientation of the stratification in the soil. When α is random, the degree of anisotropy of the effective conductivity depends strongly on mean capillary pressure.