Influence of a reduced gravity on the volume fraction of a monolayer of spherical grains

Stability of a tilted granular monolayer: How many spheres can we pick before the collapse?

The triggering of avalanches is investigated using discrete element simulations for a process of random extraction of spheres. A monolayer, formed by identical spheres in a hexagonal configuration, is placed on a tilted plane surrounded by a small fence that sustains the spheres, mimicking the disposal of fruits in the market. Then, a random continuous extraction process of spheres is imposed until the collapse. For this simple numerical experiment, a phase diagram was obtained to visualize the occurrence of avalanches triggered by vacancies as a function of the tilting angle, system size, and friction coefficient. More importantly, a subzone was found where we can predict the critical number of extractions until the avalanche takes place. The prediction is made from an evolution model of the average coordination number based on statistical considerations. The theoretical prediction also gives a constant critical void fraction of spheres, which implies the system collapses at a critical packing fraction.

Arches and contact forces in a granular pile

Assemblies of granular particles mechanically stable under their own weight contain arches. These are structural units identified as sets of mutually stable grains. It is generally assumed that these arches shield the weight above them and should bear most of the stress in the system. We test such hypothesis by studying the stress born by in-arch and out-of-arch grains. We show that, indeed, particles in arches withstand larger stresses. In particular, the isotropic stress tends to be larger for in-arch grains whereas the anisotropic component is marginally distinguishable between the two types of particles. The contact force distributions demonstrate that an exponential tail (compatible with the maximization of entropy under no extra constraints) is followed only by the out-of-arch contacts. In-arch contacts seem to be compatible with a Gaussian distribution consistent with a recently introduced approach that takes into account constraints imposed by the local force balance on grains.