  We report the simultaneous softening and compaction of a confined dense
granular pack in acoustic resonance experiments. Elastic softening is
manifested by a reduction of the shear-wave speed, as the wave amplitude
increases beyond some threshold. No macroscopic rearrangement of grains or
dilatancy is observed; instead, elastic softening is accompanied by a tiny
amount of compaction on the scale of grain asperities. We explain these
apparent contradictory observations using a theoretical model, based on shear
transformation zones (STZs), of soft spots and slipping contacts. It predicts a
linear shear stress-strain response with negligible macro-plastic deformation
due to the small-amplitude acoustic oscillation. However, these waves reduce
the interparticle friction and contact stiffness through the acoustic
lubrication of grain contacts, resulting in an increase in the structural
disorder or compactivity and softening of dynamic modulus. The compaction
associated with this microscopic friction decrease is consistent with the
prediction by an Ising-like correlation between STZs in the subyield regime.
