The compaction behavior of deformable grain packings beyond jamming is a process widely investigated because of its great industrial and engineering significance, yet it remains misunderstood. Many numerical and experimental approaches have enabled the exploration of the physics of deformable granular media and the definition of some theoretical models with reliable predictions for the relations between pressure and density. However, these models have some limitations such as the use of nonphysical parameters, the lack of accuracy at extreme pressures, and the missing physical derivation of the compaction equations. We study the compaction behavior of soft sphere packings beyond the jammed state by numerical simulations (see Fig. 1) using the non-smooth contact dynamic method. The results show that the evolution of packing fraction - as a function of the applied pressure - is well described using only micromechanical parameters. This is obtained based on the stress tensor, together with the limit too small deformation of the particles' strain. Our work also suggests that it is possible to extrapolate the compaction behavior of an elementary Voronoi cell that contains a single particle to the packing scale.