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

Abstract

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 α 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.

Column-scale unsaturated hydraulic conductivity estimates in coarse-textured homogeneous and layered soils derived under steady-state evaporation from a water table

“…In order to validate the applicability of Eq. (10), we employed data and hydraulic parameters from the Loveland sand in Anat (1965), the sand studied by Smits et al (2012) (Sand 1), the sand studied by Prevedello et al (2009) (Sand 2), and three coarsetextured soils from van Genuchten (1980) including Hygiene sandstone, Touchet silt loam, and Silt loam G.E.3 with VG parameters listed in Table 1.…”

The recent similarity hypotheses to describe water infiltration into homogeneous soils

“…The similarity solutions of Prevedello et al (2008 and2009) are here tested with measurements of water infiltrating into laboratory columns of Columbia silt loam and Hesperia sandy loam (Davidson et al, 1963). Their measured soil water properties and wetting parameters are given in Table 1.…”

“…Recognizing that these similarity solutions are approximations of classical solutions of Richard's equation, Prevedello et al (2008Prevedello et al ( , 2009) specifically stated that the use and acceptance of the hypotheses remained open for future research. Here, without deriving additional mirror image hypotheses, we merely explore the potential use and associated restrictions of the two recent similarity hypotheses illustrated in Figure 1.…”

Modelling of acid mine drainage (AMD) in columns

“…The existence of a similarity relationship between the water retention function (h) θ and the water content profiles (z) θ , taken at fixed times as proposed by Prevedello et al (2009), was assumed in this study. Due to this assumption, the hydraulic model is valid only for porous media with narrow size distribution (such soils show an abrupt humidity increase during water percolation).…”

“…(6), proposed by Prevedello et al (2009), was used to describe the transient downward water infiltration inside the column. It must be highlighted that Eq.…”