Statistical Mixing Model for the Apparent Dielectric Constant of Unsaturated Porous Media

A statistical model is proposed that relates the apparent dielectric constant of an unsaturated porous medium to its porosity and volumetric water content. It is assumed that the solid, water, and air components are randomly distributed in space. The unsaturated soil, or other porous media, are considered as a three-dimensional network of capacitors, with a distribution of capacitance values according to the volume fractions of the three components. Taking into consideration the simplifying assumptions embedded in the model and the fact that no calibration is required, a fair agreement was demonstrated between its prediction and the widely used empirical function ofTopp. The basic model presented can be further developed to account for other soil properties by lifting some of the simplifying assumptions. The objectives of this study were to provide some additional insight into the way the volume fractions of the three soil phases determine its apparent dielectric constant, and to introduce a new approach for further investigation of this phenomenon. It is not intended to propose a new universal model relating the volumetric water content to its measured apparent dielectric constant.