Steady Three-dimensional Absorption in Anisotropic Soils1
- J. R. Philip2
Exact solutions are given for steady absorption from spheroidal cavities into soils with axisymmetric anisotropy independent of moisture potential. The needle, sphere, and disc are special cases. Apart from their direct relevance to systems with gravity negligible, our results yield the leading terms of expansions describing steady infiltration into such soils for small and moderate values of the dimensionless cavity length. The effectively wetted region is a spheroid with aspect ratio µ, where µ2 is the anisotropy. The analysis suggests that, in anisotropic soils, vertical conductivity influences the capillary component of flow much more strongly for disc permeameters than for borehole permeameters. Generalizations of the problem solved in detail involve (i) inequality of the three conductivity principal components, (ii) cavity axes skew to conductivity axes, (iii) ellipsoidal cavities. Any one, combination of two, or all three, of these generalizations leads to essentially the same mathematical problem with the solution expressible in terms of the incomplete elliptic integral of the first kind.Please view the pdf by using the Full Text (PDF) link under 'View' to the left.
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