Fractal-based models for the unsaturated soil hydraulic functions

- New semi empirical models based on fractal geometry designed to predict the relative permeabilities
- The proposed models reflect the interaction between water and soil.
- The models is their applicability over the full range of pore sizes in a soil.

Reliable estimates of the unsaturated soil hydraulic properties are needed in many research and engineering projects. Fractal based approaches have become popular for describing the hydraulic functions. New models based on fractal geometry are presented to describe the wetting phase relative permeability (unsaturated hydraulic conductivity) of porous media. Analytical expressions were derived using the fractal capillary pressure (water retention) model proposed by Alfaro Soto and Vilar (2006) and the statistical pore size distribution models of Mualem (1976a) and Burdine (1953) for the unsaturated hydraulic conductivity. The newly derived models provide predictions of the relative permeability to water, as well as of the fractal dimension for modeling the pore structure of a soil. Results are compared with previous formulations by Brooks and Corey (1964), van Genuchten (1980) and Kosugi (1996), as well as with experimental water retention and hydraulic conductivity data of four soils having widely different soil textures. The proposed models agreed closely with observed data. The analytical models may be attractive alternative for estimating the unsaturated hydraulic conductivity when no laboratory or field measurements are available.