Power Laws, Precursors and Predictability during Failure

– We investigate the dynamics of a modified Burridge-Knopoff model by introducing a dissipative term to mimic the bursts of acoustic emission (AE) from rock samples. The model explains many features of the statistics of AE signals observed in experiments such as the crossover in the exponent value from relatively small amplitude AE signals to larger regime, and their dependence on the pulling speed. Significantly, we find that the cumulative energy dissipated identified with acoustic emission can be used to predict a major slip event. We also find a data collapse of the acoustic activity for several major slip events describable by a universal stretched exponential with corrections in terms of time-to-failure. Predicting failure of materials is of interest in science and engineering (electrical breakdown , fracture of laboratory samples to engineering structures) particularly so in seismology due to the enormous damage earthquakes can cause. Whether it is at a laboratory or geological scale, this amounts to identifying useful precursors at a statistically significant level. One important non-destructive tool in fracture studies is the acoustic emission (AE) technique as it is sensitive to the microstructural changes occurring in the sample. Insight into earthquake dynamics has been obtained through fracture studies of (usually precut samples to mimic slip on preexisting tectonic faults) rock samples [1]. Such studies have established that there is a considerable overlap between AE and seismology as both are concerned about the generation and propagation of elastic waves. Quite early, the statistics of the AE signals was shown to exhibit a power law [2, 1, 3] similar to the Gutenberg-Richters law for the magnitudes of earthquakes [4] and Omori's law for aftershocks [2, 5]. These prompted further investigations to look for precursor effects that can be used for earthquake predictability [5, 6, 7, 8]. Apart from the power laws observed in the AE signals during fracture, acoustic activity of unusually large number of situations as varied as volcanic activity [9], micro-fracturing process [10, 11, 12], and collective dislocation motion [13], exhibits power laws. Though the general mechanism attributed to AE is the release of stored strain energy, the details are system specific. Thus, the ubiquity of the power law statistics of AE signals suggests that the