[en] We report numerical investigations for the compaction dynamics of dense granular assemblies. The studies are based on the non-smooth contact dynamics model. Our work suggests that the dimensionless acceleration parameter Gamma, used by a large majortiy of authors, is not appropriate for rescaling the data. We prove that the dimensionless energy Xi, injected in the granular system at lift-off, is more appropriate and leads to robust interpretations of the compaction dynamics. Indeed, the injected energy allows to pass energy barriers that separate local equilibrium states. Using the Eyring picture of relaxation dynamic, we show that the consideration of Xi leads to a new law for compaction.