A damage model based on failure threshold weakening

Abstract

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

A possible mechanism for aftershocks: time-dependent stress relaxation in a slider-block model

“…However, the RJB model is advantageous to research the basic physical principles contributing to earthquake scaling laws due to its simple rules, ease of programming and speed of simulations. For these reasons it has often been used to test additional physical principles, such as damage and threshold weakening (Serino et al 2010; Gran et al 2011).…”