ised in terms of porosity, coordination number and radial distribution function, and the particle–particle or pore–pore connectivity is analysed with the Voronoi or Delaunay tessellation. The force structures and their link with jamming states are also discussed. Structural properties are shown to be correlated with porosity which links directly to the cohesive force acting on a particle.

We present a numerical study of the packing of uniform spheres under three-dimensional vibration using the discrete element method (DEM), focusing on the effects of vibration condition (amplitude and frequency) and inter-particle frictions (sliding and rolling frictions). The results are analysed in terms of packing density, coordination number (CN), radial distribution function (RDF) and pore structure. It is shown that increasing either the vibration amplitude or frequency causes packing density to increase initially to a maximum and then decrease. Both vibration frequency and amplitude should be considered to characterize the effect of vibration process on packing structure. The sliding and rolling frictions between particles can decrease packing density since they dissipate energy, although the effect of rolling friction is less significant. In line with the change of packing density, microstructural properties such as CN, RDF and pore distribution also change: a looser packing often corresponds to smaller CN, less peaked RDF and larger but more widely distributed pores.

We present a numerical method capable of reproducing the densification process from the so-called random loose to dense packing of uniform spheres under vertical vibration. The effects of vibration amplitude and frequency are quantified, and the random close packing is shown to be achieved only if both parameters are properly controlled. Two densification mechanisms are identified: pushing filling by which the contact between spheres is maintained and jumping filling by which the contact between particles is periodically broken. In general, pushing filling occurs when the vibration intensity is low and jumping filling becomes dominant when the vibration intensity is high.