Generalization of the Green–Ampt Theory for Horizontal Infiltration into Homogeneous Soils

Abstract

Core Ideas The Green–Ampt theory may be now generalized for the unsaturated zone. This theory is applicable in any homogeneous soil for θi ≠ 0. The centenary limitation of the Green–Ampt theory for horizontal infiltration has been solved. In past work, an analytic solution of the Boltzmann transform as a function of matric potential was proposed to estimate the soil water content profile for horizontal water infiltration into porous media. However, it could only be successfully described for sands, but with singularity at position x = 0. Later, others introduced the concept of air‐entry pressure to divide the soil water retention curve into saturated and unsaturated domains to provide an exact solution of the Bruce and Klute equation, with no restrictions, while assuming the initial soil water content to be zero before the infiltration process. The problem remained that the above‐mentioned analytical solution was limited to sands, while the Bruce‐ and Klute‐based approach was limited to zero water content at the beginning. This study was based on both previous studies, and the objective was to develop a solution that works for all soil types and does not depend on zero initial soil moisture content. As a result, an alternative solution is presented that generalizes the centenary theory of Green and Ampt for any homogeneous soil.

Feasibility Investigation of Improving the Modified Green–Ampt Model for Treatment of Horizontal Infiltration in Soil

“…However, Prevedello et al [11] also emphasized that this analytical solution was restricted to sands with very abrupt soil water retention curves, which exist in coarse sand but rarely found in fine sand, silt, or clay. Barry [33] suggested a power law relationship between the hydraulic head and Boltzmann variable, and extended the theories of Prevedello et al [11,29,30]. However, neither Prevedello nor Barry considered the effect of gravity on horizontal infiltration.…”

“…Prevedello et al [11,29,30] proposed an analytical solution of the GA model for horizontal infiltration, which has a wider range of applications than the traditional Philip's solution [31]. This analytical solution was derived from the relationship between the Boltzmann transform and the matric potential.…”

“…In their studies, the only force that drives water infiltration is matric suction. They characterized the moisture profile as being composed of three regions: (i) the back transmission zone (TZ), (ii) the middle wetting zone (WZ), and (iii) the wetting front (WF) [11,29,30]. It was assumed that the TZ is fully saturated throughout the infiltration process, which is very similar to the "piston" hypothesis adopted by Green and Ampt [34].…”

“…As a trend descriptor of the primary moisture profile, the MGA model has two limitations: (i) the MGA model does not account for the influence of adsorbed water on soil water suction; and (ii) it can be clearly seen that the moisture profiles measured by Prevedello et al [29,30] cannot be described by the straight lines of the MGA model. Hence, some improvements are needed to fill these gaps and make more accurate estimates of soil moisture changes in soil.…”

“…As shown in Figure 1, the soil moisture profile function in the TZ, θ 1 (x), is used to estimate the soil moisture profile shape of this zone which was defined by Prevedello et al [29,30]. Soil moisture profile function, θ 2 (x), is used to reflect the shape of the WZ.…”