Particle shape characterization using angle of repose measurements for predicting the effective permittivity and electrical conductivity of saturated granular media

Abstract

The particle shape of sediments, soils, and rocks affects the packing of the material and the subsequent pore geometry; it therefore influences important transport properties, such as electrical conductivity, dielectric permittivity, diffusion coefficient, thermal conductivity, and hydraulic conductivity. It is difficult to quantify the “average” shape characteristics of a granular material so a method, which would capture the three‐dimensional shape characteristics of a granular material in regards to its packing geometry, would be of great benefit. In this article we examine the use of the angle of repose and the maximum angle of stability of a slope of granular material poured into water, as a simple and rapid method of quantifying its “effective” particle shape. A two‐stage concept is discussed relating the measured slope angles to the aspect ratio of an equivalent oblate ellipsoidal particle and using this aspect ratio for predicting the effective permittivity and bulk electrical conductivity of isotropic packings of granular materials. The slope angle‐aspect ratio relationships were established using measurements of bulk electrical conductivity of monosized spherical glass beads and nonspherical sand and tuff grains packed in water to different porosities. This empirical relationship, the choice of an oblate geometry to represent particle shape, and a heuristic mixing model accounting for the effect of neighboring particles on the internal electrical field were tested using measurements of the effective permittivity for those granular media. Good agreement was found between the model predictions and measurements, indicating the physical significance of the above relationships and quantifiers. We have also tested and found high correlations between slope angles and a shape factor determined by image analysis of two‐dimensional particle micrographs. We do not, however, propose to use it for routine particle shape characterization because of the insufficiently informative viewing of oblates from above and because of the expensive equipment and extensive work involve with it. Instead, we propose to use the easily measurable slope angles for routine particle shape characterization because of its simplicity and also because of its beneficial sensitivity to surface roughness and particle angularity effects beyond the aspect ratio of a smooth equivalent ellipsoid.