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Constant Rate Rainfall Infiltration in a Bounded Profile: Solutions of a Nonlinear Model
Author(s) -
Broadbridge P.,
Knight J. H.,
Rogers C.
Publication year - 1988
Publication title -
soil science society of america journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.836
H-Index - 168
eISSN - 1435-0661
pISSN - 0361-5995
DOI - 10.2136/sssaj1988.03615995005200060002x
Subject(s) - ponding , laplace transform , saturation (graph theory) , infiltration (hvac) , nonlinear system , bounded function , mathematics , hydraulic conductivity , soil science , richards equation , mathematical analysis , geology , water content , geotechnical engineering , thermodynamics , soil water , physics , ecology , combinatorics , quantum mechanics , drainage , biology
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.