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Derivation of the Relationships between Green–Ampt Model Parameters and Soil Hydraulic Properties
Author(s) -
Ma DongHao,
Zhang JiaBao,
Lu YunXuan,
Wu Laosheng,
Wang QuanJiu
Publication year - 2015
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/sssaj2014.12.0501
Subject(s) - hydraulic conductivity , infiltration (hvac) , soil water , water content , pressure head , soil science , water potential , geotechnical engineering , environmental science , geology , thermodynamics , physics
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 ( K e ) and the average matric pressure head at the wetting front ( H f ) 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 K e and H f 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 K e and H f 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 K e = K s and H f 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 K s . The relative effective hydraulic conductivity ζ ( K e / K s ) and the relative average matric pressure head at the wetting front η (‐ H f / h d where h d is absolute value of the air‐entry suction) show a dependency only on soil pore structure index ( n ) and effective initial soil‐water saturation ( S i ). The values of ζ increased but η decreased with S i 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.