title: Probabilistic model of waiting times between large failures in sheared media.
abstract: Using a probabilistic approximation of a mean-field mechanistic model of sheared systems, we analytically calculate the statistical properties of large failures under slow shear loading. For general shear F(t), the distribution of waiting times between large system-spanning failures is a generalized exponential distribution, ρ_{T}(t)=λ(F(t))P(F(t))exp[-∫_{0}^{t}dτλ(F(τ))P(F(τ))], where λ(F(t)) is the rate of small event occurrences at stress F(t) and P(F(t)) is the probability that a small event triggers a large failure. We study the behavior of this distribution as a function of fault properties, such as heterogeneity or shear rate. Because the probabilistic model accommodates any stress loading F(t), it is particularly useful for modeling experiments designed to understand how different forms of shear loading or stress perturbations impact the waiting-time statistics of large failures. As examples, we study how periodic perturbations or fluctuations on top of a linear shear stress increase impact the waiting-time distribution.
authors: Department of Physics, University of Illinois at Urbana-Champaign, Illinois 61801, USA.
authors: Braden A W
authors: BA
authors: Brinkman
authors: Department of Physics, University of Illinois at Urbana-Champaign, Illinois 61801, USA.
authors: Michael P
authors: MP
authors: LeBlanc
authors: Department of Physics, University of Illinois at Urbana-Champaign, Illinois 61801, USA.|Department of Earth Sciences, University of Southern California, Los Angeles, California 90089-0740, USA.
authors: Jonathan T
authors: JT
authors: Uhl
authors: Department of Earth Sciences, University of Southern California, Los Angeles, California 90089-0740, USA.
authors: Yehuda
authors: Y
authors: Ben-Zion
authors: Department of Physics, University of Illinois at Urbana-Champaign, Illinois 61801, USA.
authors: Karin A
authors: KA
authors: Dahmen