The Similarity Hypothesis and New Analytical Support on the Estimation of Horizontal Infiltration into Sand

A method based on a specific power-law relationship between the hydraulic head and the Boltzmann variable, presented using a similarity hypothesis, was recently generalized to a range of powers to satisfy the Bruce and Klute equation exactly. Here, considerations are presented on the proposed similarity assumption, and new analytical support is given to estimate the water density flux into and inside the soil, based on the concept of sorptivity and on Buckingham-Darcy's law. Results show that the new analytical solution satisfies both theories in the calculation of water density fluxes and is in agreement with experimental results of water infiltrating horizontally into sand. However, the utility of this analysis still needs to be verified for a variety of different textured soils having a diverse range of initial soil water contents. 1. Introduction Based on physical laws of similarity applied to the rate of work required for water to wet and move through a soil, Prevedello et al. [1] presented an analytic solution of a Boltzmann transformed equation of continuity for horizontal infiltration which is derived without invoking the concept or use of the soil water diffusivity function. The derivation assumes that a similarity exists between the shapes of the soil water retention function and the Boltzmann transformation , and the solution successfully described soil water content profiles experimentally measured for different infiltration times into a homogeneous sand. More recently, an extension of this theory generalized the solution to a range of powers to include the saturated zone [2], to satisfy the Bruce and Klute equation exactly. With a similar assumption, but not exactly as expressed by Prevedello et al. [1], Prevedello et al. [3] obtained a new analytic solution of the Richards equation for the infiltration into the same sand that holds for all infiltration times from zero to infinity, including vertical directions without making use of empirical constants. In this case, the derivation assumed that a similarity exists between the soil water retention function and the soil water content distribution within the soil profile during infiltration. Although the similarity assumptions used by [1, 3] seem different, we now show that the mathematical development of both leads to the same equation for the description of the soil water content profiles for horizontal infiltration. We also present an analysis to obtain analytical equations to estimate the water density flow into and inside the soil, according to the sorptivity concept and the