## 6 Conclusions  
In conclusion, the authors investigated the seismic \(b\)-value for AE events during repeated stick-slip cycles of pre-cut faults in granite under triaxial compression conditions (confining pressure: 40 MPa). The pre-cut fault had an angle of 45\({}^{\circ}\) with the axial stress and thus is unfavorably oriented. Using a multi-channel AE waveform recording system, AE waveforms were recorded at 16 bits and at a sampling rate of 25 MHz. At the same time, two peak detectors were used to record the maximum amplitude of AE events. Acoustic emission amplitude data, ranging over three orders of magnitude, show the frequency-magnitude relation of [PERSON] and Richter.  
At first, the \(b\)-value, event rate, and surface strain for the intact specimen demonstrate three distinct phases: the primary, secondary, and nucleation phases. This pattern is similar to that observed for other fine-grained granites, such as Westerly granite and Oshima granite [7].  
The results of the present study indicate that the static frictional coefficient decreased from the maximum value prior to the first stick-slip event to a stable mean value of approximately 0.6 after several stick-slip events, while the dynamic frictional coefficient fluctuated between 0.45 and 0.52. The pre-failure static slip accounts for approximately 30% of the dynamic slip. AEs during the pre-failure static slip stage were concentrated on the fault surface.  
Prior to the first stick-slip event, the seismic \(b\)-value decreased gradually from approximately 1.8 to 1.0 with a fault slip of approximately 0.6 mm. For later stick-slip events, the seismic \(b\)-value decreased from 1.2 to 1.5 to approximately 0.6 as the shear stress increased, and then quickly jumped back up to 1.0 to 1.3 before the stress decreased. The time of the minimum \(b\)-value, which coincided with the maximum event rate, corresponded to a stress level of 70-95% of the shear strength.  
Our results on \(b\)-value evaluation preceding repeated stick-slips demonstrate that the seismic \(b\)-value can be used as an indicator of fault slip history or the degree of fault maturity and shear stress acting on the fault, which is important in seismic hazard assessment and earthquake prediction, especially for injection-induced seismicity in fields in which reactivated shear rupture of unfavorable and immature faults or tensile fractures is important. For individual earthquakes, there are no significant differences, in a wide aspect of earthquake seismology, between induced-earthquakes by fluid injection and earthquakes related to tectonic activity [2]. A combination of multi pieces of statistical behaviors is required making reliable discrimination. This study indicates \(b\)-value evaluation is an important parameter.  
All authors designed the project and participated in the experiments and the interpretation of the results. [PERSON] processed and analyzed the data and wrote the manuscript.  
Figure 7: Magnitude-frequency distributions and seismic \(b\)-values for induced earthquakes at two shale gas sites, Weiyuan and Shangluo, in Sichuan China. (The plot for Shangluo was modified from [PERSON] et al. 2017 [2].) In the figure, \(Mc\) indicates the lower cut magnitude for completeness, and SE indicates the standard error of the \(b\)-value.  
**Acknowledgments:** The present study was partly supported by the National Science Foundation of China (NSFC 41174046).  
**Conflicts of Interest:** The authors wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.