NUMEV Seminar: What grain size distribution produces the densest arrangement in a stack of friction 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, and in particular on the Fuller and Thompson distribution, proposed over a century ago. We show that, among all the GPDs studied, this particular distribution produces the densest and best-connected systems. We then compare the Fuller and Thompson distribution with two well-known GPDs: that of the stacking of Apollonian spheres and that towards which granular systems evolve after intensive grain fracturing. Surprisingly, we find that these three DTGs are practically coincident in the large size range, despite their introduction or discovery in different scientific contexts (i.e., engineering, mathematics, and earth sciences, respectively).