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This article in SSSAJ

  1. Vol. 52 No. 6, p. 1526-1533
    Received: Dec 7, 1987

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Constant Rate Rainfall Infiltration in a Bounded Profile: Solutions of a Nonlinear Model

  1. P. Broadbridge *,
  2. J. H. Knight and
  3. C. Rogers
  1. CSIRO Division of Environmental Mechanics, GPO Box 821, Canberra, ACT 2601, Australia
    Dep. of Applied Mathematics, Univ. of Waterloo, Waterloo, Ontario, Canada N2L 3G1



We present new exact solutions to a versatile analytic nonlinear model of single phase vertical unsaturated flow during constant rate rainfall infiltration in a bounded soil profile with an impermeable base. The nonlinear flow equation in a fixed finite region is transformed to a linear diffusion problem with boundary conditions on a shrinking domain. The linear problem is treated by King's method of Laplace-transform boosts. The analytic solutions illustrate the theoretical differences in the basement moisture build-up when the water content dependence of the soil hydraulic properties varies from strong to weak. When the rainfall rate exceeds a critical value which is estimated here, surface ponding precedes basement saturation. In this case, time to ponding is approximated well by the expression for the infinite column. When the rainfall rate is less than the critical value (which is greater than the conductivity at saturation), basement saturation precedes surface ponding. In this case, the time to basement saturation is close to the time taken for the rainfall to fill the available pore space.

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