A New Fractal Approach to Account for Capillary and Adsorption Phenomena in the Water Retention and Transfer Properties of Unsaturated Soils

To describe the water retention and transfer properties of an unsaturated soil over the whole range of matric suction, it is necessary to account for both capillary and adsorption phenomena. Existing models combine well-known empirical functions for capillary water at lower suctions and more physically based ones for adsorptive water at higher suctions. To determine their full set of parameters, they however require different optimization procedures, among which those coming from capillary models are empirical. In this context, the main objective of this work is to develop a simple and robust physically based model of the water retention and transfer properties of unsaturated soils valid from saturation to oven dryness. To do so, new capillary-based water retention and hydraulic conductivity functions founded on the fractal approach have been derived from the pore size distribution, by means of the Young-Laplace law and Mualem's model. To describe adsorption phenomena, these functions are combined with those used in the Peters-Iden-Durner (PID) model, providing a model along the full range of suctions, with less parameters than the existing models. Our work also shows that some parameters are directly determined from the experimental grain size distribution data (the fractal dimension), or from the water retention data (air entry suction and residual water content), leaving only two parameters to be optimized. The model was successfully validated with respect to published experimental data from 10 different coarse, sandy, and clayey soils.