Effective unsaturated hydraulic conductivity for one‐dimensional structured heterogeneity

Abstract

Effective hydraulic conductivities of unsaturated soils are defined for one‐dimensional structured heterogeneity. The heterogeneity is defined using homogeneous sublayers forming repeated unit cells of length L. The effective conductivity is defined as the steady downward Darcian velocity in an infinitely deep profile. The dependence of the hydraulic conductivity upon the pressure head is found by computing the average value of pressure head within the repeating unit cells for each effective conductivity. For a cell of length L approaching zero, the effective conductivity becomes the harmonic average of the individual sublayer hydraulic conductivities weighted according to the cell fraction each occupies. In that case, as the profile approaches saturation, the effective conductivity is the same as the well‐known result for flow through an “array” of saturated layers. For a large cell length L, the effective hydraulic conductivity approaches an arithmetic average of the pressure heads which develop in each sublayer. Examples are computed for finite cell lengths L for both binary and tertiary systems. The effective hydraulic conductivity functions for the finite cell lengths fall within the envelope formed by the two limiting cases for small and large cell lengths. For the binary system, all of the hydraulic conductivity functions fall between the envelopes formed by the two hydraulic conductivity functions for the individual sublayer materials.