A review of fractal, prefractal and pore-solid-fractal models for parameterizing the soil water retention curve

Ghanbarian-Alavijeh, B., Millán, H. and Huang, G. 2011. A review of fractal, prefractal and pore-solid-fractal models for parameterizing the soil water retention curve. Can. J. Soil Sci. 91: 1–14. The soil water retention curve is an important hydraulic parameter for characterizing water flow and contaminant transport in porous media. Therefore, many empirical, semi physical, and physical models of the soil water retention curve have been proposed. Among them, fractal models appear to be a useful approach for modeling soil as a heterogeneous porous medium and its hydraulic characteristics. Fractal models are mathematically based, and their parameters have physical meanings. In this study, we review published fractal, prefractal and pore-solid-fractal models for soil water retention curves including Tyler and Wheatcraft, Rieu and Sposito, Perrier et al., Perfect, Bird et al., Millán and González-Posada, and Cihan et al. models. In the pore-solid fractal (PSF) approach the pore phase and matrix phase have a finite volume even for an infinite number of iterations. The results of fitting the PSF model to measured soil water retention data indicate that this model works well, particularly at lower water contents.