Fractal approach to hydraulic properties in unsaturated porous media

Modelling flow and Solute transport in unsaturated porous media on the basis of the Richards equation requires specifying values for unsaturated hydraulic conductivity and water potential as a function of saturation. The high cost and large spatial variability of measurements makes the prediction of these properties a viable alternative. 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 fractal model for the pore-size distribution of unsaturated soils is constructed. The soil-water characteristics, hydraulic conductivity and soil-water diffusivity of unsaturated soils are derived and expressed by only two parameters, the fractal dimension and the air-entry value, which can be evaluated from the fractal model for the pore-size distribution. The predictions of the soil-water characteristics, hydraulic conductivity and soil-water diffusivity of unsaturated soils are in good accord with the published experimental data. Correlation between the pore-size distribution and the grain-size distribution is also studied, and it is found that both the pore-size distribution and the grain-size distribution satisfy the fractal model and they have the same fractal dimension. The fractal dimension of the grain-size distribution can be used to determine the unsaturated hydraulic conductivity, instead of the fractal dimension of the pore-size distribution. (C) 2003 Elsevier Ltd. All rights reserved.