Anisotropy factor of saturated and unsaturated soils

Variations in the degree of anisotropy in soil hydraulic conductivity with changes in water saturation (S-e) 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(psi) exhibits different behavior for different soil textures. For example, A(psi) for sand shows complex behavior with a local maximum just before A( y) drops to a minimum where sand becomes isotropic (A(psi) = 1) near psi = - 1.0 bar. Experimentally determined relationships between soil bulk density and hydraulic properties show existence of strong correlation between A(S-e) and the ratio of extreme hydraulic conductivity values K(S-e)(max)/K(S-e)(min) for each soil for the entire saturation range and across several soil types. The strong dependency of anisotropy factor on extreme values K-max and K-min 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 K-max and K-min only were derived. An upper bound for A(S-e) is obtained with equal weight for K-max and K-min ( w = 0.5). The experimental data and model predictions agreed for certain values of weight assigned to either K-max or K-min (similar to w = 0.02). Other approximations based on Kmax and K-min provide simple estimates for anisotropy factor that could be related to shape of statistical distribution of hydraulic conductivity.