Assessing the permittivity of an unsaturated sand by combining a Lattice Boltzmann Method simulation, electromagnetic homogenization models and measurements

Abstract

Dielectric permittivity is a prevailing property used for the estimation of water content in heterogeneous materials like soils and concrete. Troubles are frequently encountered when searching for the relationship between a material's permittivity and its degree of saturation. Building an electromagnetic model of the material is thus of critical importance. This paper focuses on the study of an unsaturated sand. Analytical and numerical electromagnetic homogenization procedures are confronted. Dielectric permittivity of the sand is measured at different saturation degrees within the frequency range [200 MHz; 1 GHz] thanks to a large open-ended coaxial probe. A numerical procedure is then built to calculate the effective permittivity of the medium. First, a representative elementary volume of the dry sand is created. Pore domain is then separated into water and gas phases through the use of a Lattice Boltzmann Method algorithm. The effective permittivity is then estimated using numerical homogenization. Results obtained at different water contents were eventually compared with analytical homogenization models like the Bruggeman and Maxwell-Garnett equations. A close match is obtained between measurements, numerically derived results and a Bruggeman model based on a spheroidal description of the air and water phases.