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

T. ‐C Jim Yeh, Lynn W. Gelhar, Allan L. Gutjahr

Research output: Contribution to journalArticlepeer-review

335 Scopus citations


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 = Ks exp (−αψ), where Ks is the saturated conductivity, and α is a soil parameter. A general formulation is presented for the case with Ks and α represented as statistically homogeneous spatial random fields. In part 1, solutions are developed assuming α is constant and representing Ks 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 Ks and the mean hydraulic gradient.

Original languageEnglish (US)
Pages (from-to)447-456
Number of pages10
JournalWater Resources Research
Issue number4
StatePublished - Apr 1985

ASJC Scopus subject areas

  • Water Science and Technology


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