The water retention function for a model of soil structure with pore and solid fractal distributions

We present a development of the fractal approach to modelling the soil water retention characteristic based on a recent model of soil structure called the Pore-Solid Fractal. This model, in its most general form, exhibits symmetry between the solid phase and pore phase, in marked contrast to the asymmetry between phases present in a mass fractal model. As a consequence, the general expression of the water retention characteristic associated with this model exhibits a structural parameter, appearing as a power-law exponent, related to the scaling of not only the pore-size distribution but also the solid-size distribution of the model. The model thus provides a theoretical framework for the prediction of the water retention characteristic from measurement of the solid-size distribution. Three special cases of the model are considered. Two correspond to those arising from mass fractal models, and the third is shown to be consistent with established empirical power-law models of the water retention function. Two examples of application allow us to examine the suitability of the new approach to predict the water retention function of a soil from measurement of its particle-size distribution. A power-law model is fitted to the particle-size distribution data. Despite questionable fits on the two available data sets, a fractal dimension is inferred and used to predict the water retention characteristic. The results are encouraging and show the need for further theoretical and practical investigations using the new theory.