Internal states of model isotropic granular packings. I. Assembling process, geometry, and contact networks

This is the first paper of a series of three, in which we report on numerical simulation studies of geometric and mechanical properties of static assemblies of spherical beads under an isotropic pressure. The influence of various assembling processes on packing microstructures is investigated. It is accurately checked that frictionless systems assemble in the unique random close packing (RCP) state in the low pressure limit if the compression process is fast enough, higher solid fractions corresponding to more ordered configurations with traces of crystallization. Specific properties directly related to isostaticity of the force-carrying structure in the rigid limit are discussed. With frictional grains, different preparation procedures result in quite different inner structures that cannot be classified by the sole density. If partly or completely lubricated they will assemble like frictionless ones, approaching the RCP solid fraction ${\ensuremath{\Phi}}_{\mathrm{RCP}}\ensuremath{\simeq}0.639$ with a high coordination number: ${z}^{*}\ensuremath{\simeq}6$ on the force-carrying backbone. If compressed with a realistic coefficient of friction $\ensuremath{\mu}=0.3$ packings stabilize in a loose state with $\ensuremath{\Phi}\ensuremath{\simeq}0.593$ and ${z}^{*}\ensuremath{\simeq}4.5$. And, more surprisingly, an idealized ``vibration'' procedure, which maintains an agitated, collisional regime up to high densities results in equally small values of ${z}^{*}$ while $\ensuremath{\Phi}$ is close to the maximum value ${\ensuremath{\Phi}}_{\mathrm{RCP}}$. Low coordination packings have a large proportion $(>10%)$ of rattlers---grains carrying no force---the effect of which should be accounted for on studying position correlations, and also contain a small proportion of localized ``floppy modes'' associated with divalent grains. Low-pressure states of frictional packings retain a finite level of force indeterminacy even when assembled with the slowest compression rates simulated, except in the case when the friction coefficient tends to infinity. Different microstructures are characterized in terms of near neighbor correlations on various scales, and some comparisons with available laboratory data are reported, although values of contact coordination numbers apparently remain experimentally inaccessible.