  We study the history dependence of the mechanical properties of granular
media by numerical simulations. We perform a compaction of frictional disk
packings in a two-dimensional system by controlling the area of the domain with
various strain rates. We then find the strain rate dependence of the critical
packing fraction above which the pressure becomes finite. The observed behavior
makes a contrast with the well-studied jamming transitions for frictionless
disk packings. We also observe that the elastic constants of the disk packings
depend on the strain rate logarithmically. This result provides a experimental
test for the history dependence of granular systems.
