Analytical solutions for unsteady multidimensional infiltration in heterogeneous soils

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Abstract
Appendix is available with entire article on microfiche. Order from American Geophysical Union, 2000 Florida Avenue, N.W., Washington, DC 20009. Document W91‐003; $2.50. Payment must accompany order.The problem of unsteady multidimensional infiltration in heterogeneous soils is approached analytically. By assuming that the hydraulic conductivity is an exponential function of the soil matric potential and a linear function of the soil moisture, the governing flow equation is linearized for a special variation of the saturated hydraulic conductivity in space. By using integral transform methods, analytical solutions to the one‐ and two‐dimensional flow problem are derived and shown to be generalized versions of known results for homogeneous soils. The development aims at obtaining quantitative criteria for the validity of the one‐dimensional approximation, which is commonly used in hydrologic applications.