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.

This paper presents a study of the structural transition of the packing of uniform spheres with a wide range of packing fractions. Several critical states are identified including the onset of local jamming, onset of global jamming and maximally random jammed (MRJ) states. With the increase of packing fraction , the packing structure transforms from one-dimensional chains to two-dimensional triangles and finally three-dimensional tetrahedra, correspondingly undergoing phase changes from non-jamming to local jamming, global jamming, MRJ and finally crystal structure. There is a competition between FCC (face-centred cubic) and HCP (hexagonal closed packed) in the transition from disordered to ordered structure with the increase of . HCP can transform to FCC after reaching its maximum at =0.7