The acoustic emission b value is an important and widely used parameter for the early prediction of rock fractures. In this study, five groups of true triaxial compression tests were conducted on granite specimens to analyze changes in b value during the process of rock failure, and to investigate the b value characteristics of acoustic emission events. First, the acoustic emission events that simultaneously triggered at least four sensors were located using P-wave arrivals and sensor coordinates. Then, considering various intervals of acoustic emission event counts, stress magnitude, and stress proportion, b values were calculated using the values of the maximum amplitude, average amplitude, maximum absolute energy, and average absolute energy of the acoustic emission events. In addition, the goodness of the fitting curves was used to evaluate the fitting reliability of the b values. The results indicated higher accuracy of b value when calculated using the average amplitude setting for intervals of acoustic emission event counts of 200 or greater, stress magnitude of 20 MPa or greater, and stress proportion of 10% or greater. Moreover, the interval of event counts of 200 is suggested as a window parameter for b value calculations, and the b values are observed to exhibit a decreasing trend before fracture for more than 80% of the specimens. Furthermore, the b value tends to decrease with an increase in confining pressure. Thus, the b value can be used as an indicator for validating the stress concentration area, including magnitudes and accumulative probability density distribution of events, which is a beneficial complement to clarifying precursor information of rock mass instability.

The Gutenberg‐Richter (G‐R) relationship has been regarded as the fundamental description of the size distribution from large‐scale‐earthquake to small‐scale‐laboratory rock ruptures. However, because deviation from the G‐R relationship has often been reported, especially when the amplitude distribution is used for b value estimation in rock acoustic emission testing, the effect of attenuation should be considered. Here, we perform a detailed analysis on the deviation of the size distribution from a G‐R law and discuss modification of the attenuation on the doubly truncated size distribution from a more general perspective. We find that the attenuation will not modify the size distribution, and the b value is theoretically verified to be unchanged within an interval specified by the minimum and maximum amount of attenuation. Based on these discussions, we propose a new b value estimation procedure for rock acoustic emission testing and apply it to a dilation rupturing test; the results confirm that b value depends on material heterogeneity and stress.

The b value is a critical parameter that has been used to describe spatial and temporal size distribution characteristics in data from both natural seismicity and laboratory rock acoustic emission (AE) tests. However, unlike the magnitude used for b value estimation in earthquakes which corrects for hypocentral distance, the apparent amplitude of the AE, is most commonly used for b value estimation in the rock AE test. This ignores the effect of attenuation, which may modify the frequency–amplitude distribution and affect the b value results. Here, we investigate the attenuation effect on the estimate of b value from synthetic data generated by random sampling of a doubly truncated frequency–amplitude distribution and a known underlying b value from a statistical perspective. We generated AE source amplitudes that obey an exponential distribution with different theoretical b values and applied an attenuation operator to obtain apparent frequency–amplitude data for comparison with the true underlying distribution. The results show that the b value is unchanged within a specific interval of amplitude distribution after accounting for attenuation under the conditions examined here, and that data truncation is the primary cause of modification of the frequency–amplitude distribution in the presence of attenuation, rather than attenuation alone. In addition, we employed the same synthetic data simulation scheme to estimate the minimum data volume for accurate estimation of the underlying b value from the apparent amplitude distribution. We found that the determination of the minimum data volume is influenced by the theoretical b value of the underlying distribution: the higher the theoretical b value, the larger the minimum data volume required, varying from 200 events from b < 1.5 to 300 for b > 1.5.

In this study, mode I fracture tests on cracked straight-through Brazilian disc (CSTBD) and notched semi-circular bend (NSCB) shale specimens with different sizes were conducted to investigate the difference between maximum tangential stress fracture criterion and the size effect law (SEL) model in predicting apparent fracture toughness (K_a) of shale. In addition, the effects of specimen size and geometry on the K_a and the selection of fracture criterion on the prediction of the inherent fracture toughness (K_Ic) were also studied. The results show that the K_a increases with the increase of specimen size, and the difference between K_Ic of shale specimens with different sizes predicted by the fracture process zone length determined by the further improved maximum tangential stress (FIMTS) criterion is the smallest. For the prediction of K_a of NSCB specimen, the results predicted by the FIMTS criterion are the closest to the tested fracture toughness. However, the effect of SEL model applied to the prediction of K_a of NSCB specimens is poor. The effective establishment of SEL model requires high accuracy for test data, especially for the configuration with large variation of the dimensionless stress intensity factor (Y*) with normalized crack length (α).