Stochastic Analysis of Unsaturated Flow in Heterogeneous Soils: 1. Statistically Isotropic Media

Steady unsaturated flow with vertical mean infiltration through unbounded heterogeneous porous media is analyzed using a perturbation approximation of the stochastic flow equation which is solved by spectral representation techniques. The hydraulic conductivity K is related to the capillary pressure head ψ by K = K_s exp (−αψ), where K_s is the saturated conductivity, and α is a soil parameter. A general formulation is presented for the case with K_s and α represented as statistically homogeneous spatial random fields. In part 1, solutions are developed assuming α is constant and representing K_s variability by one‐dimensional and three‐dimensional isotropic random fields. Results are obtained for head variances and covariance functions, effective hydraulic conductivities, variances of the unsaturated hydraulic conductivity, flux variances, and variance of pressure gradient. When the parameter α is relatively large, corresponding to coarse textured soils, the head variance decreases and all of the results demonstrate a trend toward gravitationally dominated one‐dimensional vertical flow. The effective conductivity is dependent on the correlation scale of ln K_s and the mean hydraulic gradient.