Scaling analysis of water retention curves for unsaturated sandy loam soils by using fractal geometry

Fractal geometry was deployed to analyse water retention curves (WRC). The three models used to estimate the curves were the general pore-solid fractal (PSF) model and two specific cases of the PSF model: the Tyler & Wheatcraft (TW) and the Rieu & Sposito (RS) models. The study was conducted on 30 undisturbed, sandy loam soil samples taken from a field and subjected to laboratory analysis. The fractal dimension, a non-variable scale factor characterizing each water retention model proposed, was estimated by direct scaling. The method for determining the fractal dimension proposed here entails limiting the analysis to the interval between an upper and lower pressure head cut-off on a log-log plot, and defining the dimension itself as the straight regression line that interpolates the points in the interval with the largest coefficient of determination, R-2. The scale relative to the cut-off interval used to determine the fractal behaviour in each model used is presented. Furthermore, a second range of pressure head values was analysed to approximate the fractal dimension of the pore surface. The PSF model exhibited greater spatial variation than the TW or RS models for the parameter values typical of a sandy loam soil. An indication of the variability of the fractal dimension across the entire area studied is also provided.