The steady distribution of moisture beneath a two‐dimensional surface source

Abstract

The steady distribution of moisture beneath a two‐dimensional strip source is analyzed by applying the quasi‐linear approximation. The source is described by specifying either the moisture content or the infiltration rate. A water table is specified at some depth D below the surface, the depth varying from shallow to semi‐infinite. Numerical solutions are determined, via the boundary integral equation method, as a function of the material inverse sorptive length α, the width of the strip source 2 L , and the depth to the water table. The moisture introduced at the source is broadly spread below the surface when α L ≪ 1, for which absorption by capillary forces is dominant over gravity‐induced flow. Conversely, the distribution becomes fingerlike along the vertical when α L ≫ 1, where gravity is dominant over absorption. For a source described by specifying the moisture content, the presence of a water table at finite depth influences the infiltration through the source when α D is less than about 4; infiltration rates obtained assuming the water table depth is semi‐infinite are of sufficient accuracy for greater values of α D . When the source is described by a specified infiltration flux, the maximum allowable value of this flux for which the material beneath the source remains unsaturated is determined as a function of nondimensional sorptive number and depth to the water table.