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Steady Infiltration from Buried, Surface, and Perched Point and Line Sources in Heterogeneous Soils: I. Analysis¹

ABSTRACT

The quasilinearized steady infiltration equation is generalized to apply to heterogeneous soils with conductivity depending exponentially on both moisture potential and depth. Mathematical developments, including a theorem connecting surface and buried source solutions, follow closely those established previously for homogeneous soils. Solutions are found for buried, surface, and perched point and line sources. Physically relevant solutions are limited to the following ranges of β, the dimensionless coefficient of dependence of conductivity on depth: for buried and surface sources, β 0; for perched point sources, β –1; for perched line sources, β < –1. It is of interest that the homogeneous medium (β = 0) is an extreme case for existence of buried and surface source solutions; and that perched source solutions (relevant to subirrigation) exist only for soils with conductivity increasing rapidly enough with height above the impermeable base. Detailed mapping of flows and general discussion is left to Part 2.

¹ Contribution from CSIRO, Australia.

² Chief, CSIRO Division of Environmental Mechanics, P.O. Box 821, Canberra City, A.C.T., Australia 2601.

Received for publication July 28, 1971. Accepted for publication November 29, 1971.