Geometrical Factors Affecting the Bulk Electrical Properties of Soils and Rocks: Measurements and Continuum Mean Field Computations

Abstract

Understanding the relationship between the effective electrical conductivity and dielectric permittivity of soils and rocks and their porosity and volumetric water content is important because measurements of electrical properties are used to determine porosity and water content. In this lecture we are going to report experimental and theoretical studies aimed at improving our understanding of the way the geometrical attributes of granular materials determine their effective conductivity and permittivity [2-5]. In order to avoid interfacial surface conductivity and bound water effects we have used coarse granular materials of low surface area such as glass beads, quartz sand grains, tuff and mica particles. Accurate measurements of the effective electrical conductivity [4,5] and permittivity [2-5] of anisotropic packings of mica particles [2] and isotropic packings of glass beads, sand grains and tuff particles [3-5] have demonstrated: 1, an alteration of the directional effective conductivities and permittivities of anisotropic packings attributed to particle shape and orientation; 2, a reduction in the permittivity of isotropic packings due to deviation from a spherical particle shape and an increased broadness of particle size distribution. The measured effective conductivities and permittivities are predicted reasonably well by modified classical mixing formulas [2-4], reviewed in e.g. [1]. ] . Particle shape effects were modeled using the depolarization factors of equivalent oblate particles [2-4] and those of particle size distribution using a finite number of inclusion-intermediate background mixing [3]. For dense granular packings of various particle shapes and size fractions, of a background/inclusion conductivity ratio of 1/8 to 80 the effects of the neighboring particles can be accounted for with a single value, a = 0.2, of a heuristic pa rameter a defined in the range of 0 (Maxwell/Clausius-Mossotti mixing law) to 1 (coherent potential approximation).