13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- 4. Comparison between numerical and experimental AE statistics Since the studies of Mogi and Scholz [19,20] on AE, we know that the Gutenberg-Richter empirical law can be observed at the laboratory sample scale. They showed that a significant overlap exists between the definition of AE and earthquake. This is further reinforced by the evidence that brittle fracture obeys similar statistics from tectonic earthquakes to the dislocation movements smaller than micron size. Moreover, in recent years, experiments employing acoustic emission have established remarkable results concerning the model of process zone and the quasistatic fault growth. Such experiment-based knowledge is expected to be useful for studying the fundamental behavior of natural earthquakes, because it is widely accepted that fault systems are scale-invariant [21, 22] and there exist universal similarities between faulting behaviors, from small-scale microcracking to large-scale seismic events. For example, AE events caused by microcracking activity [19–23] and stick-slip along a crack plane [24, 25] are similar to those generated by natural earthquakes. By analogy with seismic phenomena, in the AE technique the magnitude may be defined as follows [26, 27]: m=LogAmax + f r( ), (4) where Amax is the amplitude of the signal expressed in μV and f r( ) is a correction coefficient whereby the signal amplitude is taken to be a decreasing function of the distance r between the source and the AE sensor. In seismology, the Gutenberg-Richter empirical law [28]: LogN ≥m ( ) =a−bm, (5) expresses the relationship between magnitude and total number of earthquakes in any given region and time period, and is the most widely used statistical relation to describe the scaling properties of seismicity. In Eq. (5), N is the cumulative number of earthquakes with magnitude ≥m in a given area and within a specific time range, while a and b are positive constants varying from a region to another and from a time interval to another. Eq. (5) has been used successfully in the AE field to study the scaling laws of AE wave amplitude distribution. This approach evidences the similarity between structural damage phenomena and seismic activities in a given region of the Earth, extending the applicability of the Gutenberg-Richter law to structural engineering [29]. Figure 10: Frequency magnitude bilinear diagram: a=40.4, b=1.97.
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