Effect of friction in a toy model of granular compaction

A toy model of granular compaction which includes some resistance due to granular arches is proposed. In this model, the solid/solid friction of contacting grains is a key parameter and a slipping threshold omega(c) is defined. Realistic compaction behaviors have been obtained. Two regimes separated by a critical point omega(c)* of the slipping threshold have been emphasized: (i) a slow compaction with lots of paralyzed regions and (ii) an inverse logarithmic dynamics with a power-law scaling of grain mobility. Below the critical point omega(c)*, the physical properties of this frozen system become independent of omega(c). Above the critical point omega(c)*-i.e., for low friction values-the packing properties behave as described by the classical Janssen theory for silos.