On the tensor concept of unsaturated anisotropic hydraulic conductivity

Abstract

Unsaturated hydraulic conductivity can be regarded as a second order tensor, the coefficients of which depend on soil moisture suction or soil moisture content. General equations for the three‐dimensional anisotropic unsaturated flow of water in porous media must involve nine coefficients of the hydraulic conductivity tensor, all of which are, in general, nonzero. Equations for horizontal anisotropic unsaturated flow can be reduced to an orthotropic form with principal hydraulic conductivities Kx′,Ky′, and Kz′ provided the principal axes of the conductivity tensor do not rotate when the moisture content or the soil moisture suction changes. This condition is fulfilled only for a certain constant ratio of hydraulic conductivities in different directions that is independent of the soil moisture suction or soil moisture content. In this case the flow velocity is given by the simple Darcy type equation without the cross coefficients of hydraulic conductivity. A simple experimental method is proposed to determine the diagonal and cross coefficients of the hydraulic conductivity as functions of the soil moisture suction for horizontal unsaturated steady flow in anisotropic porous media.