## 3 Results and Analysis
### \(b\)-Value and \(\gamma\)-Value Analysis  
Based on the calculation methods outlined in Section 3.2, the evolution curves of the \(b\)-value and \(\gamma\)-value during the entire loading process are depicted in Figure 7. Since both basalt and granite rocks exhibited similar results, this paper only displays the results for basalt rock Samples 0-1 and 0-2. Combining the analysis of stress and AE curves (as shown in Figure 3), we can observe that for Specimen 0-1, stress drops occurred at 996 s and 1172 s. At these moments, high-amplitude AE signals were generated, resulting in a sudden decrease in the \(b\)-value (0.3), while the \(\gamma\)-value concurrently increased rapidly. At 1399 s, Specimen 0-1 collapsed, leading to a decrease in the \(b\)-value and a sharp increase in the \(\gamma\)-value. Notably, whenever stress drops and sudden collapses occurred in the specimens, the \(b\)-value and \(\gamma\)-value consistently exhibited opposing trends. Similar patterns were observed in Specimen 0-2. This indicates that both the \(b\)-value and \(\gamma\)-value can effectively reflect the rock damage process, especially showing sensitivity to stress drops. When specimens undergo catastrophic collapse, both parameters undergo significant changes, thus serving as valuable precursor indicators of rock catastrophic instability.  
Figure 6: Calculation Process of \(\gamma\)-value: AE waveform (**a**); Power spectrum of the signal, a negative slope in the fitted curve represents the \(\gamma\)-value (**b**).  
Figure 7: The time evolution curve of \(b\)-value and \(\gamma\)-Value: Specimen 0–1 **(a**); Specimen 0–2 (**b**).  
Compared to Specimen 0-1, the \(b\)-value of Specimen 0-2 exhibits an overall trend of fluctuating decline, whereas the \(b\)-value of Specimen 0-1 experiences multiple sudden drops. Simultaneously, the \(\gamma\)-value of Specimen 0-2 shows a continuous overall increase, while Specimen 0-1 only undergoes sudden increases at certain moments. This discrepancy arises from the differences between the two samples. The scale of crack propagation during the rock failure process is significantly related to the AE signals. The generation of microcracks corresponds to signals with low amplitude and high frequency, while the occurrence of penetrating cracks, macroracks, and collapse-induced unstable cracks corresponds to signals with high amplitude and low frequency in AE.  
According to Equation (2), the \(b\)-value of AE is entirely dependent on the relationship between AE magnitude and frequency. Signals with high amplitude and low frequency correspond to lower \(b\)-value, whereas signals with low amplitude and high frequency correspond to higher \(b\)-value. Therefore, the \(b\)-value can reflect the scale of rock crack propagation from a time-domain perspective. Similarly, according to Equation (3), the magnitude of the \(\gamma\)-value in AE is related to frequency and power spectral density. Signals with low amplitude and high frequency correspond to high power spectral density and high amplitude. Thus, the \(\gamma\)-value can reflect the scale of rock crack propagation from a frequency-domain perspective.  
After the initial stress drop, internal cracks develop in Specimen 0-1, continuously generating signals with high amplitude as stress increases. In contrast, Specimen 0-2 does not further expand cracks after the initial stress drop, producing signals with high amplitude only when complete failure occurs. This discrepancy contributes to the differences between the parameters of the two specimens.