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Stochastic Analysis of Unsaturated Flow in Heterogeneous Soils: 1. Statistically Isotropic Media
Author(s) -
Yeh T.C. Jim,
Gelhar Lynn W.,
Gutjahr Allan L.
Publication year - 1985
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr021i004p00447
Subject(s) - hydraulic conductivity , isotropy , covariance , pressure head , hydraulic head , permeameter , infiltration (hvac) , mathematics , soil water , richards equation , covariance function , porous medium , vadose zone , soil science , geotechnical engineering , statistics , physics , geology , porosity , thermodynamics , quantum mechanics
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.