The three-dimensional structure of large packings of monosized spheres with volume fractions ranging between 0.58 and 0.64 has been studied with x-ray computed tomography. We search for signatures of organization, classifying local arrangements and exploring the effects of local geometrical constrains on the global packing. This study is the largest and the most accurate empirical analysis of disordered packings at the grain-scale to date, mapping over 380,000 sphere coordinates with precision within 0.1% of the sphere diameters. We discuss topological and geometrical methods to characterize and classify these systems emphasizing the implications that local geometry can have on the mechanisms of formation of these amorphous structures. Some of the main results are (1) the observation that the average number of contacts increases with the volume fraction; (2) the discovery that these systems have a very compact contact network; (3) the finding that disordered packing can be locally more efficient than crystalline packings; (4) the observation that the peaks of the radial distribution function follow power law divergences; (5) the discovery that geometrical frustration plays no role in the formation of such amorphous packings.

Using sedimentation to obtain precisely controlled packings of noncohesive spheres, we find that the volume fraction RLP of the loosest mechanically stable packing is in an operational sense well defined by a limit process. This random loose packing volume fraction decreases with decreasing pressure p and increasing interparticle friction coefficient . Using x-ray tomography to correct for a container boundary effect that depends on particle size, we find for rough particles in the limit p ! 0 a new lower bound, RLP 0:550 0:001.

We have discovered an invariant distribution for local packing configurations in static granular media. This distribution holds in experiments for packing fractions covering most of the range from random loose packed to random close packed, for beads packed both in air and in water. Assuming only that there exist elementary cells in which the system volume is subdivided, we derive from statistical mechanics a distribution that is in accord with the observations. This universal distribution function for granular media is analogous to the Maxwell-Boltzmann distribution for molecular gasses. Granular materials are complex systems characterized by unusual static and dynamic properties. These systems are comprised of large numbers of dissipative macroscopic particles assembled into disordered structures. The microscopic description of the system-state requires a very large number of variables. However, there is a very large number of microscopic configurations corresponding to the same macroscopic properties. Edwards and coauthors [1,2] have proposed that the complexity of static granular systems could be disentangled by means of a statistical mechanics approach reducing the description of the system state to a few parameters only [3,4,5,6,7,8,9,10,11,12]. An essential part of Edwards' idea is that in static granular media volume plays the role held by energy in usual thermodynamics. Therefore, an understanding of the volume distribution function is the key to connect microscopic details of the system with macroscopic state variables.Since granular materials are dissipative, they can change their static configurations only when energy is injected into the system. The general idea underlying a statistical mechanics description is that the properties of the system do not depend on the kind of energy injections, but only on the portion of the configurational space that the system explores under such action. For instance, some classical experiments [13,14,15] obtained different average packing fractions by tapping the container with different intensities and different numbers of times. Similarly, in an experiment by Schröter et al. [16], reproducible average packing fractions were obtained by driving the system with periodic trains of flow pulses in a fluidized bed. More generally, various controlled perturbations (tapping, rotating, pouring, etc.) can produce packings with characteristic average packing fractions. Within a statistical mechanics framework, if the system volume (V T ) is the relevant state variable, the system properties should depend only on the achieved packing fraction and not on the preparation history. This hypothesis is examined in this paper using the largest sets of experimental data on particle positions presently available.Experiments.-We analyze the structural properties of static granular packings produced in 18 different experiments, 6 with acrylic spheres in air and 12 with glass beads in water. The packing fractions ρ range from 0.56 to 0.64. Three-dimensional density maps have been obtaine...

Bead packs of up to 150,000 mono-sized spheres with packing densities ranging from 0.58 to 0.64 have been studied by means of X-ray Computed Tomography. These studies represent the largest and the most accurate description of the structure of disordered packings at the grain-scale ever attempted. We investigate the geometrical structure of such packings looking for signatures of disorder. We discuss ways to characterize and classify these systems and the implications that local geometry can have on densification dynamics.