NUMEV Seminar: What grain size distribution produces the densest arrangement in a pile of frictional spheres?

Revisiting and rediscovering Fuller and Thompson's century-old distribution.

By Nicolas Estrada.

Using a discrete element method, we study the effects of grain size distribution (GSD) on the structure of three-dimensional samples composed of spherical grains. More specifically, we compress these systems isotropically and then analyze their density, connectivity, and uniformity and curvature coefficients. Our study focuses on GSDs described by a power-law distribution, and in particular on the Fuller–Thompson distribution, proposed over a century ago. We show that, among all the DTGs studied, this particular distribution produces the densest and most highly connected systems. Next, we compare the Fuller–Thompson distribution with two well-known DTGs: that of a stack of Apollonian spheres and that toward which granular systems evolve after intensive grain fracturing. Surprisingly, we find that these three DTGs are virtually indistinguishable in the limit of large size ranges, despite having been introduced or discovered in different scientific contexts (namely, engineering, mathematics, and earth sciences, respectively).