Abstract
This paper is a study of the dependence of the volume of voids in a granular material on the particle size distribution. It has previously been proposed that the volume of voids is proportional to the volume of the smallest particles. In a particle size distribution which is progressively becoming wider (e.g. as occurs due to crushing during the compression of sand), the smallest size of particle decreases, yet there are only ever a few of these particles out of many thousands or millions. This paper attempts to identify which particles govern the overall density of a granular material, and a new definition of the ‘smallest particles’ is proposed. These particles are shown to govern the void space in a range of simulations of spherical and non-spherical crushable particles. The theory also applies to idealised Apollonian sphere packings.
Highlights
The packing characteristics of granular materials have been studied for over a century
All simulations demonstrate tend towards the same slope, which is to be expected as all materials have the same size-effect on average particle strengths
The initial motivation for trying to relate the particle size distribution (PSD) to the current voids ratio was in the derivation of a compression law, able to predict the compressibility of crushable soil
Summary
The packing characteristics of granular materials have been studied for over a century. The density determines the dilatancy and peak strength when sheared (Bolton, 1986); the size and interconnectivity of the voids govern the permeability (Hazen, 1892); whilst the distribution of interparticle contacts affects the induced particle stresses which govern particle breakage (McDowell and Bolton, 1998). The above theory was based on the assumption of a fractal particle size distribution and the kinematics of particle fracture This was subsequently investigated using DEM (McDowell and de Bono, 2013) by performing simulations of crushable sands, and led to a new compression law in which the normal compression line can be expressed as: e ∝ σ −1/2b (1). The parameter b describes the rate at which the average strength increases with decreasing particle size (a common observation for most brittle materials), and is related to the distribution of imperfections/flaws in the material
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