On the hydraulic conductivity of unsaturated soils

Abstract

Unsaturated steady flow of mixtures of a liquid and a gas through sands and similar porous media at low Reynolds numbers obeys Darcy's law. The relative liquid permeability K is not constant, but a universal function of the degree of liquid saturation. An approximate theory gives its form, which is a cubic parabola. A similar expression is found for the gas permeability. Numerous experiments by Wyckoff ami Botset confirm the theory. This is in agreement with Gardner's hypothesis that K is a function of the concentration in water, and indirectly with Richards' hypothesis that it is a function of the capillary potential. The degree of liquid saturation seems to be a more useful unit of liquid percentage than any other.