  A variety of studies have modeled the physics of material deformation and
damage as examples of generalized phase transitions, involving either critical
phenomena or spinodal nucleation. Here we study a model for frictional sliding
with long range interactions and recurrent damage that is parameterized by a
process of damage and partial healing during sliding. We introduce a failure
threshold weakening parameter into the cellular-automaton slider-block model
which allows blocks to fail at a reduced failure threshold for all subsequent
failures during an event. We show that a critical point is reached beyond which
the probability of a system-wide event scales with this weakening parameter. We
provide a mapping to the percolation transition, and show that the values of
the scaling exponents approach the values for mean-field percolation (spinodal
nucleation) as lattice size $L$ is increased for fixed $R$. We also examine the
effect of the weakening parameter on the frequency-magnitude scaling
relationship and the ergodic behavior of the model.
