Steady Infiltration From Buried Discs and Other Sources

Abstract

Scattering analog techniques are used to analyze steady quasilinear infiltration from buried discs and to develop related results. The exact solution involves 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 disc radius. Other simple techniques for estimating the moisture field include boundary layer and Green's function methods. Further aspects of the study include: useful comparisons with Wooding's classical results for the surface disc; and small s expansions, not hitherto available, for steady infiltration from cylindrical and spherical cavities. Buried discs (with aspect ratio h = 0), oblate spheroids (0 < h < 1), spheres (h = 1), and prolate spheroids (h > 1) form an ordered sequence. Both capillary effects and the difficulty of matching small and large s expansions increase markedly with h. The surface disc is an exceptional “least capillarity” case. The foregoing considerations lead to design principles for permeameters to measure the saturated hydraulic conductivity of unsaturated field soils. The customary borehole permeameter has h large and consequently strong capillary effects; but saturated conductivity has greatest influence on permeameter discharge when capillary effects are least. Accordingly, the optimal design is the surface disc permeameter, with h = 0 and minimal capillary effects.