Infiltration of Constant-Flux Rainfall Into Soil as Analyzed by the Approach of Green and Ampt

Infiltration of water into soil from an application of constant water flux r is analyzed theoretically by treating the resulting soil-water profiles as step functions, as assumed in the approach of Green and Ampt (1911). Important features of the infiltration process then follow in fairly straightforward mathematical form. As r decreases toward the near-saturated soil hydraulic conductivity Kb, the time to of onset of surface-water excess is sufficiently increased so that the curves of infiltration flux i versus cumulative time t are shifted toward larger times, progressively away from the curve of i versus t for continuous ponding. But i is not a simple function of t, primarily because the cumulative water infiltration I is an implicit function of t. Two explicit-form equations are then proposed for i versus t, both equations being integrable into explicit forms of I versus t. The one explicit equation is matched with the implicit function within ±11 percent, over the whole range from r = Kb to r → ∞ at continuous ponding. The other explicit equation is more suitable for r nearer to Kb, the error of matching to the implicit function being within ±5 percent for 1 < r/Kb < 10. Thus, both explicit equations appear to have promise for expressing infiltration phenomena (flux and cumulative) as a function of time.