  We proposed a toy model of granular compaction which includes some resistance
due to granular arches. In this model, the solid/solid friction of contacting
grains is a key parameter and a slipping threshold Wc is defined. Realistic
compaction behaviors have been obtained. Two regimes separated by a critical
point Wc* 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
Wc*, the physical properties of this frozen system become independent of Wc.
Above the critical point Wc*, i.e. for low friction values, the packing
properties behave as described by the classical Janssen theory for silos.
