A Theory of the Complex Dielectric Permittivity of Soil Containing Water: The Semidisperse Model

A model of soil composed of a multiphase mixture of solid particles, water, and air voids is proposed from which the complex permittivity, or dielectric constant and conductivity, is calculated. It is based on the Hanai/Bruggelman/Wagner theory of mixtures and considers the ionic conducting water as partly dispersed and partly the dispersing medium, an important distinction with this theory. The permittivity as a function of frequency and water content is predicted. The increase in dielectric constant with water volume fraction does not differ greatly with soil type in the high-frequency limit and is approximated by a normal curve specified by the theory. A normal curve and the marked increase in dielectric constant at lower frequencies has been observed experimentally. It is concluded that this semidisperse theory of the dielectric permittivity is successful in describing the behavior of soils containing moisture in the high-frequency range (1 MHz-1 GHz). Approximations to the more detailed theory and a series-parallel RC equivalent circuit are given.