Derivation of the Relationships between Green-Ampt Model Parameters and Soil Hydraulic Properties

Abstract

The Green–Ampt model (GAM) is a widely used water infiltration model. However, it lacks a reliable theoretical basis to independently and simultaneously determine the GAM parameters of effective hydraulic conductivity (Kₑ) and the average matric pressure head at the wetting front (Hf) from those commonly measured soil hydraulic properties. In this paper, we derived an approximate analytical solution similar to GAM for one-dimensional vertical infiltration into soils with initially uniform soil moisture distribution, with Kₑ and Hf being simultaneously related to the Brooks–Corey (BC) model parameters. The new relationships are not restricted to the piston-type moisture profile or delta-type water diffusivity like in the traditional GAM (TGAM). Infiltration experiments on three soils of various textures were conducted to validate the new approximate analytical solution and the corresponding GAM parameters. It was demonstrated that the predicted cumulative infiltrations and soil moisture profiles by the GAM with Kₑ and Hf calculated by the new expressions (new GAM, NGAM) generally agreed well with the numerical solutions, especially for initially dry soils. In contrast, cumulative infiltrations were considerably over-predicted by the TGAM using Kₑ = Kₛ and Hf calculated by Neuman’s equation. Our theoretical analysis further indicated that even without air entrapped during infiltration, the effective hydraulic conductivity can still be less than the saturated hydraulic conductivity Kₛ. The relative effective hydraulic conductivity ζ (Kₑ/Kₛ) and the relative average matric pressure head at the wetting front η (-Hf/hd where hd is absolute value of the air-entry suction) show a dependency only on soil pore structure index (n) and effective initial soil-water saturation (Sᵢ). The values of ζ increased but η decreased with Sᵢ and n. The theoretical ranges of ζ and η were from 0.5 and 2 for dry heavy-texture soils to 1 and 0 for saturated soils, respectively, which are consistent with the experimental values reported in literatures.