Effective hydraulic conductivities of transient unsaturated flow in stratified soils

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Abstract
The effective hydraulic conductivities of transient unsaturated flow in stratified soils are evaluated using a three‐dimensional stochastic approach. Because of the disparity of the correlation scales in a stratified soil, the general stochastic equations are simplified, and this allows analytical evaluation and derivation of generic expressions for the effective hydraulic conductivities. Simple asymptotic expressions, valid at particular ranges of the soil property and the mean flow characteristics, are also derived. Several examples illustrating the results using data from two real soils are also presented. It was found that the effective hydraulic conductivities show significant hysteresis and are anisotropic with a degree of anisotropy depending on the mean flow conditions (wetting or drying). Such hysteresis and anisotropy are produced by the spatial variability of the hydraulic soil properties rather than hysteresis or anisotropy of the local parameters. A physical interpretation of the results is given along with a qualitative comparison with field observations. The ramifications of this study need to be further investigated and be considered in field applications such as waste disposal control.