Stress corrosion constitutive laws as a possible mechanism of intermediate-term and short-term seismic quiescence

Abstract

SUMMARY Three types of seismic quiescence are recognized in the earthquake cycle. Post-seismic quiescence occurs due to the stress drop caused by a previous major earthquake, and results in long-term seismic gaps; infermediate-term quiescence occurs due to a small stress relaxation in the volume around the next mainshock area; and short-term quiescence during foreshock sequences occurs due to slipweakening or dilatancy hardening concentrated on the nucleation point. In this paper a single quantitative model for intermediate-term and short-term quiescence is developed from (a) observation of subcritical crack growth due to stress corrosion, and (b) a general model-for subcritical damage development where a fractal population of fractures results, irrespective of the underlying mechanism. In the former the stress intensity K of a single dominant macrocrack is the appropriate constitutive variable, while the latter more general formulation relies on a mean potential strain energy release rate (G) proportional to (a) the square of the applied effective stress and (b) the mean fracture length. Stress corrosion provides an important concrete example as well as a useful analogy for interpreting the general theory. We then consider the effect of a stress decrease in the intermediate-term on seismic event rates using the approporiate constitutive laws for both variables. Simple calculations for a material of stress corrosion index n = 30 show that a 45 per cent reduction in event rates is consistent with only a 2 per cent reduction in K, and a 90 per cent reduction results from only a 7 per cent decrease in K. A similar order of magnitude of quiescence can be predicted theoretically by considering the effect of similar small changes in (G) for a fractal pupulation of faults or cracks averaged over a range of length scales. Such intermediate-term quiescence occurs in the model when K or (C) decreases because of the reduction in applied stress, during a phase of strain softening late in the earthquake cycle. Such a decrease in K or (G) moves the system temporarily further from the failure condition K = K, (or (G) = (G),) and is therefore stable. This temporary stability is consistent with the relatively long duration of intermediate-term quiescence (months or years). Observed intermediate-term seismic quiescences are relatively easily explained in the model by stable, regional decreases in stress in a volume much larger than the mainshock area, but prior to the period when concentrated accelerating crack growth in the nucleation zone dominates the strain softening. The general mechanism is compared to the Kaiser effect as a possible alternative explanation for intermediate-term seismic quiescence. The two models are not necessarily mutually exclusive, though the Kaiser effect involves local stress and strain relaxation, and predicts more abrupt changes in event rate when the stress decreases. Short-term quiescence is also a feature of the general model, and is predicted when a concomitant decrease in seismic b-value occurs, as the larger events near the nucleation zone begin to dominate the stress relaxation, thereby inhibiting fracture