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Unsteady Two-Dimensional Flow of Water in Unsaturated Soils Above An Impervious Barrier¹

ABSTRACT

The unsteady two-dimensional, water flow equation for unsaturated soils is solved by use of a finite difference approximation and an alternating-direction implicit (ADI) method. The two-dimensional flow medium is a homogeneous soil with an impervious barrier at some depth from the soil surface and having equally spaced trenches. The bottom of the trenches are wetted at time zero and are kept at a constant 0.50 cm³/cm³ water content, the initial soil water content of the flow medium is 0.20 cm³/cm³. Water movement from the walls of the trenches and the soil surface is neglected. Computer results of the water content with time at all locations in the flow medium are obtained for physical data from an Ida silt loam soil for two geometries. For trenches at 120 cm spacing, 30 cm deep, and 30 cm wide, the wetting front reaches a depth of 30 cm in 35 min, and reaches the soil surface in 140 min. For trenches at 60 cm spacing, 15 cm deep, and 15 cm wide, the wetting front reaches a depth of 30 cm in 45 min, and reaches the soil surface in 30 min. The ADI method proves valuable for use with a modern computer to solve unsteady two-dimensional flow problems.

¹ Journal Paper no. J-6963 of the Iowa Agr. & Home Econ. Exp. Sta., Ames. Projects no. 1819 and 1888. Supported by the Office of Water Resources Research, U.S. Dep. of the Interior, as authorized under the Water Resources Research Act of 1964, Public Law 88-379, through Project A-026-IA of the Iowa State Water Resources Research Institute, and by National Science Foundation Grant No. GK-31137.

² Research Assistant and Professor of Soils and Physics, respectively, Department of Agronomy, Iowa State Univ., Ames. Iowa, 50010.

Received for publication December 19, 1972. Accepted for publication March 22, 1973.