Steady infiltration from spheroidal cavities in isotropic and anisotropic soils

Abstract

Solutions are given for quasilinear steady infiltration from spheroidal cavities (with axis of rotational symmetry vertical) of arbitrary aspect ratio v into isotropic and anisotropic homogeneous soils. The conductivity tensor is assumed to have principal components K(Ψ), K(Ψ), and μ2K(Ψ), the third of these in the vertical direction. Here μ2 is the anisotropy, and Ψ is the moisture potential. Scattering analog techniques are used to secure the required solutions. The exact solutions involve spheroidal wave functions; but, more usefully, we express the far field wetting function and the discharge function as expansions appropriate for small and large values of s, the dimensionless transformed equatorial radius of the cavity. A joining technique is used to establish estimates of the discharge function throughout the ranges 0 ≤ s ≤ ∞, 0 ≤ ω ≤ 20, with transformed aspect ratio ω = μ−1 v. The effect of anisotropy on cavity discharge increases systematically both as v decreases from ∞ to 0, and as σ( = μ−1 s) increases from 0 to ∞. This behavior is explained physically in terms of interaction between, on the one hand, cavity configuration and orientation, and, on the other, the relative importance of capillarity and gravity. The analysis provides means of improving the approximate analysis of the borehole permeameter in isotropic soils, and of investigating the properties of borehole and disc permeameters in unsaturated anisotropic soils.