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.

Maximum packing densities of basic 3D objects

“…For random packing, Chaikin et al [20] declared that the optimal packing density of tetrahedron which they measured in experiments was above 0.75, while the packing densities in experiments of Dong and Ye [9] were all less than 0.5. Latham et al [21] found from numerical simulation that the random loose packing density of tetrahedra was 0.416. Random close packings of tetrahedra were simulated with sphere assembly model and relaxation algorithm [22], and the results are shown in Figure 3.…”

Validation of a stochastic digital packing algorithm for porosity prediction in fluvial gravel deposits

“…Traditional ways to construct an irregular particle require the user to place spherical elements within a meshed polyhedral body (e.g., Wang et al, 2007;Matsushima et al, 2009;Ferellec and McDowell, 2010;Fukuoka et al, 2013), which consumes high computational costs with large numbers of components (spheres) involved (Hubbard, 1996;Song et al, 2006). Although techniques using 3D polyhedral (Latham et al, 2001) or continuous superquadric functions (Williams and Pentland, 1992;Lu et al, 2012) provide a straightforward way to generate irregular particle shapes, complex contact-detection algorithms are needed, leading to deterioration in simulation speed as particle complexity increases (Johnson et al, 2004). In order to overcome these difficulties, a stochastic digital packing algorithm was developed (Jia and Williams, 2001).…”

Continuum and discrete element coupling approach to analyzing seismic responses of a slope covered by deposits

“…But for an earthquake-induced slide of a slope covered by deposits, some important information (e.g., processes of collapse and disintegration of the deposits) could be lost during the numerical simulation using traditional method based on continuum assumption. On the contrary, discrete element method (DEM) (Cundall and Strack 1979) is now developed and accepted to be an effective tool for studying problems of large displacements and rotations of the non-continuum under static and dynamic loads (Latham et al 2001;Potyondy and Cundall 2004;Itasca Consulting 2004;HUANG and LU 2006;Munjiza 2004;Onate and Rojek 2004;Nakashima and Odia 2004). However, due to the difficulty of eliminating the radiation damping, and considering the boundary effects, DEM is still not widely used to study seismic responses of a slope covered by deposits.…”