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

Abstract

[1] 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 threedimensional 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 angleaspect 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 twodimensional 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.INDEX TERMS: 1866 Hydrology: Soil moisture; 5109 Physical Properties of Rocks: Magnetic and electrical properties; 5139 Physical Properties of Rocks: Transport properties; KEYWORDS: particle shape, geometry, angle of repose, granular media, dielectric permittivity, electrical conductivity Citation: Friedman, S. P., and D. A. Robinson, Particle shape characterization using angle of repose measurements for predicting the effective permittivity and electrical conductivity of saturated granular media, Water Resour.

Granular materials composed of shape-anisotropic grains

“…The grain shapes of sediments, soils, and rocks affect the packing of the material and the resulting pore geometries. They influence important transport properties, such as electrical conductivity, dielectric permittivity, diffusion, thermal conductivity, and hydraulic conductivity [22]. The stress distribution in a sandpile of shape-anisotropic ('anisometric') particles is very different from that in a pile of spherical grains, owing particularly to orientation effects [23].…”

Measurement and Modeling of the Influence of Grain Size and Pressure Gradients on Swash Zone Sediment Transport

“…Although should physically vary with sediment properties (size, shapes, angularity, packing density) and condition (degree of saturation, immersed or dry) (Friedman andRobinson, 2002, Carrigy, 1970), no analytical formulation exists that links all these properties and conditions to . For example, experimental studies of Miller and Byrne (1966, Table I, pg 307) and Carrigy (1970, Table V, pg157) show that average for quartz sand is around and increases by an order of 1% for sand submerged in water.…”

A 2D numerical study of the effect of particle shape and orientation on resistivity in shallow formations

“…The use of these m values is supported by experimental data on sphere-like and cylindrical inclusions. Several authors (among others, Atkins and Smith, 1961, Jackson et al, 1978, Friedman and Robinson, 2002 made experiments on natural sands and found m values close to 1.5 for reported sphericity values ranging from 0.73 to 0.83. Their results compare well with the Bussian's predictions for non-conducting particles and m values of 1.5 (Figure 2).…”

“…If non-spherical (oblate or prolate) particles have some preferential alignment, the soil becomes anisotropic and its resistivity depends on the direction in which it is measured. Several authors examined the effect of particle shape and/or orientation on the electrical properties of the material, through laboratory investigation (Willye, 1953;Atkins and Smith, 1961;Jackson et al, 1978;Kujiper et al, 1996;Friedman and Robinson, 2002) or theoretical models (Sen et al, 1981;Mendelson and Cohen, 1982;Bussian, 1983;Kuijper et al, 1996;Zimmerman, 1996). About the influence of the particle shape, the main conclusion is that the mixture resistivity generally increases when particles are elongated, for both 2D or 3D, leading to higher values of the cementation exponent m. As mentioned before, theoretical works highlighted that m is higher in 2D than in 3D, showing the higher sensitivity of resistivity to porosity (or particle concentration) in 2D.…”