PERFORMANCE OF THE GUTENBERG-RICHTER LAW IN NUMERICAL AND LABORATORY EXPERIMENTS

摘要

The activity of fault sources is typically estimated from paleo-seismological and geomorphological investigations, whereas for area sources the activity is determined by statistical analysis of earthquakes catalogues in the region. The probability distribution of magnitude is then assumed to follow a doubly-bounded exponential distribution for area sources, which is a modified form of the famous Gutenberg-Richter equation. For fault sources, a characteristic distribution is often used, a special case of which is the maximum magnitude model. A justification of the ubiquitous GR law on physical grounds has been sought with limited success. On the other hand, during compression tests on concrete or rock specimens, the statistical analysis of acoustic emission (AE) signals emerging from the growing microcraks constitutes an effective damage assessment criterion. It has been observed that the signals amplitudes are distributed according to the GR law, and characterized through the Zvvalue, which decreases systematically with damage growth. In experimental studies, AE signals are captured by sensors on the external surfaces of specimens subjected to compression. Test specimens were also analyzed using a 3D Discrete Element Method (DEM) lattice model by numerical simulation. The simulation closely reproduced the experimental results, not only in terms of stress-time global response, but also in terms of typical AE parameters, such as AE count rate, cumulative counts, and b-value variations. Using the DEM model, the relation between AE signals magnitude and the energy released in each localized rupture were also analyzed. The results are compatible with the GR energy-magnitude relation. Finally the numerical simulations present the same tendency observed in laboratory tests, which show a perceptible shift to lower AE frequencies during the evolution of the damage process. These promising results suggest that some features of the probability distribution of earthquake magnitudes may be correlated to the evolution of the damage process for the source under consideration and that these features may be assessed using numerical models.