  We investigate statistics and scaling laws of avalanches in two-dimensional
frictional particles by numerical simulations. We find that the critical
exponent for avalanche size distributions is governed by microscopic friction
between the particles in contact, where the exponent is larger and closer to
mean-field predictions if the friction coefficient is finite. We reveal that
microscopic ``slips" between frictional particles induce numerous small
avalanches which increase the slope, as well as the power-law exponent, of
avalanche size distributions. We also analyze statistics and scaling laws of
the avalanche duration and maximum stress drop rates, and examine power spectra
of stress drop rates. Our numerical results suggest that the microscopic
friction is a key ingredient of mean-field descriptions and plays a crucial
role in avalanches observed in real materials.
