NUMEV seminar: Which grain size distribution produces the densest arrangement in a frictional sphere stack?

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

By Nicolas Estrada.

Using a discrete element method, we investigate the effects of grain size distribution (GSD) on the structure of three-dimensional samples composed of spherical grains. Specifically, we compress these systems isotropically, and then analyze their density, connectivity, uniformity and curvature coefficients. Our study focuses on DTGs described by a power law, and in particular on the Fuller and Thompson distribution, proposed more than a century ago. We show that, among all the DTGs studied, this particular distribution produces the densest and best-connected systems. Next, we compare Fuller and Thompson's distribution with two well-known DTGs: that of the Apollonian sphere stack and that towards which granular systems evolve after intensive grain fracture. Surprisingly, we find that these three DTGs are virtually coincident in the limit of large size ranges, despite their introduction or discovery in different scientific contexts (i.e., engineering, mathematics and earth sciences, respectively).