Calculation of unsaturated hydraulic conductivity using a fractal model for the pore-size distribution

Abstract

The hydraulic conductivity of unsaturated soils with constant volume is a function of the saturation degree or matric suction, and can be obtained based on currently available procedures. However, each procedure has its limitations and consequently cares should be taken in the selection of a proper procedure. Fractal approach seems to be a potentially useful tool to describe hierarchical systems and is suitable to model the structure and hydraulic properties of porous media. In this paper, the soil–water characteristic curve and hydraulic conductivity function of unsaturated soils were derived from the fractal model for the pore-size distribution, and were expressed by only two independently physical parameters, the fractal dimension and the air-entry value. The predictions of the proposed soil–water characteristic curve and unsaturated hydraulic conductivity were in good accord with the published experimental data. Comparisons between the experimental results and the predictions of both the fractal model and the van Genuchten–Mualem model were performed, and it was found that the predictions of the fractal model were better than that of the van G–M model.