TEMPORAL VARIATIONS IN SEISMIC EVENT RATE AND B-VALUES FROM STRESS-CORROSION CONSTITUTIVE LAWS

A model is developed to characterise the state of damage for a fractal population of cracks in terms of a mean energy release rate [G]which depends on the stress sigma, the event rate N and the seismic b-value. N is assumed to be proportional to the total number of potentially active cracks, and b to be proportional to the exponent D of the crack length distribution. [G]is then positively correlated with N and negatively correlated with b, consistent with experimental observation based on stress intensity as a constitutive variable. The model predicts that higher b-values are associated either with lower stress intensity or greater material heterogeneity. Both experiment and theory predict intermediate-term seismic quiescence of similar magnitude to that observed in the field (45-90%), for only a small simultaneous reduction in stress and stress intensity (2-7%) or the equivalent mean energy release rate. The theoretical model predicts three different types of quiescence associated with increasing, constant or decreasing b-value. The first two are associated with stable intermediate-term quiescence due to a reduction in [G], and the third is associated with unstable short-term quiescence associated with constant or increasing [G]. The theory can be used to infer relative changes in [G] from acoustic emissions in the laboratory. Experiments to date show that quiescence of the order 10% can be seen in the laboratory at strain rates of 10(-5) s-1, but that this has the characteristics of short-term rather than intermediate-term quiescence.