Review of the Physical Basis of Laboratory-derived Relations for Brittle Failure and their Implications for Earthquake Occurrence and Earthquake Nucleation

A laboratory-derived crack growth-based constitutive relation for brittle faulting is developed. The relation consists of two rheologic components, a nonlinear Arrhenius dependence of strain rate on temperature and stress, corresponding to subcritical crack growth, and a linear slip-weakening behavior associated with dilatancy, crack coalescence and supercritical crack growth. The implications of this general behavior for the onset of rapid slip- (earthquake nucleation) are considered. Laboratory observations of static fatigue and time- dependent failure from rock fracture and rock friction experiments are consistent with this simple constitutive description, as are the predictions of rate- and state- dependent equations for the onset of rapid frictional slip between bare rock surfaces. I argue that crack growth is the physical process that controls time-dependent rock fracture and the time-dependent onset of unstable frictional sliding. Some similar and related arguments made in the past 1/2 century in the fields of rock mechanics and earthquake seismology are reviewed. For stressing rates appropriate for the San Andreas fault system, the simple constitutive relation with lab-derived constants predicts a minimum time for nucleation of ~ 1 yr. General predictions are a minimum nucleation patch radius of 0.06 to 0.2 m, and a minimum earthquake moment of 8.5 · 107 Nm.