A random method for simulating loose packs of angular particles using tetrahedra

Abstract

The problems posed by the need to consider angular shapes in order to achieve more realistic micro-mechanical models of rock particulates are introduced. A relatively simple and fast particle deposition algorithm for packing simulations is developed. The details of the algorithmic procedures for deposition of tetrahedron-shaped particles of different size and aspect ratio are outlined. Numerical results including predictions of porosity for spheres, tetrahedra, different particle size distributions, binary mixtures and tetrahedron shapes are presented. For the loose packing of spheres extrapolated to zero wall effect, the porosity obtained was 0·414. Mono-sized tetrahedron packs with wall effects for a 3·288 cm edged equilateral tetrahedron packing in a 30 × 30 × 30 cm box produced an average porosity of 0·627 with a value of 0·584 when extrapolated to zero wall effect. Binary mixtures of tetrahedra show the characteristic minimum in porosity for a size mixture. The minimum is less well defined than for spheres. Continuous size distributions of tetrahedra based on a truncated Schuhmann distribution from 0·28 to 2·8 cm edge length in a 10 × 10 × 10 cm box do not indicate that distributions with a lower uniformity will necessarily produce a minimum in porosity. For tetrahedra of constant volume the porosity increases with decreasing sphericity in tetrahedra with different aspect ratios.