## 5 Research on the Frequency-Domain Characteristics of AE Signals
### Discussion on AE Signal Distribution and Peak Stress Precursor
#### 5.1.1 Frequency-Domain Distribution of AE Signals and the Definition of Prediction Signals  
To study the variation of crack degree and peak AE signal frequency by the triaxial compression test under different confining pressures of the deep granite samples A1, B1, and C1, the relation scatter plots of amplitude, peak frequency, and frequency centroid with respect to normalized axial stress (\(\sigma_{1}/\sigma_{\text{max}}\)) were drawn, as shown in Figures 6-8, respectively, to acquire the frequency domain distribution law of deep granite AE signals and the precursory characteristics before reaching peak stress. Figure 5: Configuration of peak frequency and frequency centroid. The figures indicate that during the test, the AE signals with an amplitude of 35-80 dB account for the majority. The peak frequency presents an obvious stratification phenomenon, while the distribution of frequency centroid band shows the law from thin to wide. In general, the distribution characteristics of the three AE parameters show some similar regularity during the test. Therefore, the study of the frequency-domain characteristics of AE signals before loading to the peak stress in the triaxial test can more comprehensively grasp the change patterns of fracture corresponding to various AE signals. It can better define the AE signals of rock failure prediction before loading to the peak stress from the perspective of the frequency domain. The amplitude distribution of AE signals clearly shows that the number of AE signals is less in the crack closure stage and the early stage of linear elastic deformation. The corresponding results can also be obtained in the distribution of the other two signals. The maximum amplitude in each stage shows a similar trend with stress; it increases with increasing stress, before reaching the peak stress. Beyond this, the amplitude distribution breaks in the range of 35-80 dB and some signals larger than 80 dB begin to appear. Figure 8: Relationship between frequency centroid distribution and normalized axial stress. (**a**) A1, (**b**) B1, (**c**) C1. Figure 6: Relationship between amplitude distribution and normalized axial stress. (**a**) A1, (**b**) B1, (**c**) C1. Figure 7: Relationship between peak frequency distribution and normalized axial stress. (**a**) A1, (**b**) B1, (**c**) C1. The peak frequency spectrum can be divided into three parts: low-frequency band (0-200 kHz), medium-frequency band (200-350 kHz), and high-frequency band (350-500 kHz). The low-frequency signals exist in the entire testing process. The frequency band around 75 and 160 kHz begins to widen with stress. When the normalized axial stress value reaches 50-60%, a large number of medium-frequency signals begin to appear and are concentrated around 225 and 300 kHz. Compared with the low- and medium-frequency signals, the practical significance of high-frequency band signals is more obvious. These signals appear almost at the same time when the amplitude crosses 80 dB, and only a little earlier than the time the stress peak is reached. Therefore, the appearance of signals with a peak frequency greater than 350 kHz has a strong correlation with rock failure. As shown in Figure 5 and the concept of frequency centroid mentioned above, the higher the energy of AE signals in a certain frequency band, the closer the frequency centroid value will be to that frequency band. The frequency centroid distribution diagram shows that the AE energy is mainly concentrated in the frequency band of 150-175 kHz at the beginning of crack closure. With increasing stress, the AE energy is concentrated at approximately 225 kHz until the peak stress is reached. The frequency centroid shows the same characteristics as the values of amplitude and peak frequency. That is, its bandwidth widens, and most importantly, more signals larger than 275 kHz appear.