Anisotropy factor of saturated and unsaturated soils

Abstract

Variations in the degree of anisotropy in soil hydraulic conductivity with changes in water saturation (Se) may adversely impact predictability of flow and transport processes. The conceptual “layered cake” model was extended to consider effects of bulk density variations within a particular soil type. The anisotropy factor as function of matric potential A(ψ) exhibits different behavior for different soil textures. For example, A(ψ) for sand shows complex behavior with a local maximum just before A(ψ) drops to a minimum where sand becomes isotropic (A(ψ) = 1) near ψ = −1.0 bar. Experimentally determined relationships between soil bulk density and hydraulic properties show existence of strong correlation between A(Se) and the ratio of extreme hydraulic conductivity values K(Se)max/K(Se)min for each soil for the entire saturation range and across several soil types. The strong dependency of anisotropy factor on extreme values Kmax and Kmin was investigated for four simple and continuous probability density functions of bulk density. Additionally, simple analytical expressions for a binary system of alternating layers with Kmax and Kmin only were derived. An upper bound for A(Se) is obtained with equal weight for Kmax and Kmin (w = 0.5). The experimental data and model predictions agreed for certain values of weight assigned to either Kmax or Kmin (∼w = 0.02). Other approximations based on Kmax and Kmin provide simple estimates for anisotropy factor that could be related to shape of statistical distribution of hydraulic conductivity.