  The behavior of granular media under quasi-static loading has recently been
shown to attain a stable evolution state corresponding to a manifold in the
space of micromechanical variables. This state is characterized by sudden
transitions between metastable jammed states, involving the partial
micromechanical rearrangement of the granular medium. Using numerical
simulations of two-dimensional granular media under quasistatic biaxial
compression, we show that the dynamics in the stable evolution state is
characterized by scale-free avalanches well before the macromechanical
stationary flow regime traditionally linked to a self-organized critical state.
This, together with the non-uniqueness and the non-monotony of macroscopic
deformation curves, suggests that the statistical avalanche properties and the
susceptibilities of the system cannot be reduced to a function of the
macromechanical state. The associated scaling exponents are non-universal and
depend on the interactions between particles. For stiffer particles (or samples
at low confining pressure) we find distributions of avalanche properties
compatible with the predictions of mean-field theory. The scaling exponents
decrease below the mean-field values for softer interactions between particles.
These lower exponents are consistent with observations for amorphous solids at
their critical point. We specifically discuss the relationship between
microscopic and macroscopic variables, including the relation between the
external stress drop and the internal potential energy released during kinetic
avalanches.
