Numerical Solution of the Moisture Flow Equation for Infiltration into Layered Soils 1

A numerical solution of the moisture flow equation was devised and programmed for an IBM 650 computer. Solutions obtained for infiltration into a loam over a silt loam and vice versa showed that infiltration was governed by flow through the less permeable soil, provided the wetting front had extended well into the second layer. Solutions were also obtained for vertical upward and vertical downward infiltrations and for horizontal infiltration into two soils. The numerical solution was found to give excellent results when compared with the methods of E. J. Scott et al. and J. R. Philip for horizontal infiltration into homogeneous soils at a uniform initial water content. T MOISTURE FLOW EQUATION has been used by many workers to describe the isothermal flow of water into soil (4, 5, 6, 7). All of these methods require that the soil be homogeneous throughout. The method of Scott et al. (9) requires, in addition, that moisture diffusivity be exponentially or linearly related to moisture content. The method of Philip (7) is the only one treating vertical infiltration. This paper describes a method to estimate the solution of the moisture flow equation for vertical infiltration into layered soils without a specific mathematical relation between moisture diffusivity and water content. THEORY OF THE METHOD To meet the objective outlined above, it was necessary to devise a numerical solution of the flow equation. The numerical solution proved too tedious and time consuming for hand calculation. Consequently, the method was programmed on an IBM 650 computer. The general form of the flow equation in one dimension can be written as follows: [1] JL? = JL (K 55) at ax ax Here, 6 is water content, H is hydraulic head, x is distance, t is time, and K is conductivity. The numerical form of this equation for the vertical infiltration case discussed here is: 'H^Hii^i^-iir-«:;;>