  We introduce a stochastic microscopic model to investigate the jamming and
reorganization of grains induced by an object moving through a granular medium.
The model reproduces the experimentally observed periodic sawtooth fluctuations
in the jamming force and predicts the period and the power spectrum in terms of
the controllable physical parameters. It also predicts that the avalanche
sizes, defined as the number of displaced grains during a single advance of the
object, follow a power-law, $P(s)\sim s^{-\tau}$, where the exponent is
independent of the physical parameters.
