A Fractal Model to Interpret Porosity-Dependent Hydraulic Properties for Unsaturated Soils

Abstract

This paper presents a simple fractal model to quantify the effects of initial porosity on the soil-water retention curve and hydraulic conductivity of unsaturated soils. In the proposed conceptual model, the change of maximum pore radius, which largely determines the change of the air-entry value, is directly related to the fractal dimension of pore volume (D) and porosity change. The hydraulic properties of unsaturated soils are then governed by the maximum pore radius, the fractal dimension of pore volume (D), and the fractal dimension of drainable pore volume (Dd ≤ D). The new fractal model removes the empirical fitting parameters that have no physical meaning from existing models for porosity-dependent water retention and hydraulic behaviour and employs parameters of fractal dimensions that are intrinsic to the nature of the fractal porous materials. The proposed model is then validated against experimental data from the literature on soil-water retention behaviour and unsaturated conductivity.