## 3 Experimental Results and Analysis
### Analysis of the Acoustic Emission Parameters  
The phenomenon of elastic waves generated in all directions by material damage is called material acoustic emission [14]. Its trend corresponds to the change in stress and strain in the damage process of rock under loading. Therefore, acoustic emission signals can be monitored to reflect the accumulation of damage, crack initiation, and crack penetration in the rock. Further, acoustic emission ringing can describe the number of cracks inside the rock according to the number of signals generated by rock damage, while the acoustic emission b-value can reflect the intensity of rock damage development through fluctuations [23,24]. It can be used as a characteristic parameter of the rock damage signs, thus introducing the acoustic emission b-value and acoustic emission ringing to analyze the development of the internal damage rule of change in the rock, as follows:  
\[\mathrm{lg}N=\mathrm{a}-\mathrm{b}M \tag{1}\]  
where \(M\) is the magnitude, the value of which can be obtained by dividing the acoustic emission amplitude by 20; \(N\) is the number of shocks within the range of values of \(M\), which is usually taken to be the number of impacts exceeding the acoustic emission amplitude; a is a constant, usually depending on the type of rock; and b is the proportion of small-value events relative to large-value events.  
To calculate the b value accurately, the minimum number of window samples should be greater than 2000 when using the least squares method [25], and the amplitude should be calculated as 20 dB. The b value derived from Equation (1) is depicted alongside the acoustic emission ringing, acoustic emission energy, and stress and strain curves in Figure 3. Additionally, curves illustrating the changes in the acoustic emission parameters at various temperatures under different loading rates are presented, with the peak value corresponding to the \(\sigma_{\mathrm{m}}\)-stress.  
Figure 3 shows that the acoustic emission characteristic parameters of each granite specimen under different loading rates and temperatures closely align with the stress-strain curves. The b-value of granite under each condition exhibits an overall fluctuating and decreasing trend. During the elastic deformation and crack development stages, a higher loading rate correlates with greater volatility in the b-value. At each temperature, an increase in the loading rate leads to a sudden decrease in the b-value from 90% to 80% of the peak stress, indicating accelerated internal damage of the specimen. This decrease in the b-value occurs earlier with larger loading rates, highlighting its potential as a characteristic parameter for detecting rock damage signs. Furthermore, the b-value serves as a key indicator of rock damage. Under the same loading rate, the magnitude of the b-value change is approximately 0.3 at 30 \({}^{\circ}\)C, 0.5 at 40 \({}^{\circ}\)C, 0.6 at 60 \({}^{\circ}\)C and 80 \({}^{\circ}\)C, suggesting that the magnitude of the b-value change increases with temperature, exacerbating internal rock damage.  
Figure 3 clearly shows that under the same loading rate, higher temperatures result in greater acoustic emission ringing counts during the unstable crack development and damage stages. Granite specimens at 60 \({}^{\circ}\)C and 80 \({}^{\circ}\)C exhibit a certain degree of centralized and delayed internal damage. Additionally, at the same temperature, the total number of ringing events at a loading rate of 0.005 mm/s is 1.7 times greater than that at 0.01 mm/s and 0.02 mm/s, indicating more complex internal crack development in the granite specimens at the 0.005 mm/s loading rate.