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New Analytic Solution Related to the Richards, Philip, and Green–Ampt Equations for Infiltration

^a Soils and Agricultural Engineering Dep., Paraná State Univ., Rua dos Funcionários 1540, CEP 80030-035, Curitiba, PR, Brazil
^b Civil Construction Dep., Paraná State Univ., CEP 81531-990, Curitiba, PR, Brazil
^c Soil Physics Lab., CENA/Univ. of São Paulo, Av. Centenário 303, CEP 13418-900, Piracicaba, SP, Brazil
^d Dep. of Land, Air and Water Resources, Univ. of California, Davis, CA

Correspondence: ^* Corresponding author (Klaus{at}cena.usp.br).

Received for publication 9 May 2008. Based on physical laws of similarity, an analytic solution of the soil water potential form of the Richards equation was derived for water infiltration into a homogeneous sand. The derivation assumes a similarity between the soil water retention function and that of the soil water content profiles taken at fixed times. The new solution successfully described soil water content profiles experimentally measured for water infiltrating downward, upward, and horizontally into a homogeneous sand and agrees with that presented by Philip in 1957. The utility of this analysis is still to be verified, but it is expected to hold for soils that have a narrow pore-size distribution before wetting and that manifest a sharp increase of water content at the wetting front during infiltration. The effect of van Genuchten's parameters and n on the application of the solution to other porous media was investigated. The solution also improves and provides a more realistic description of the infiltration process than that pioneered by Green and Ampt in 1911.

Abbreviations: TZ, transmission zone • WF, wetting front • WZ, wetting zone