## 3 Experimental Results and Analysis
### Granite Damage Development and Three-Dimensional Evolution of Cracks  
To some degree, acoustic emission ringing and energy provide insights into the extent of crack development in rock at specific stages, while the b-value predicts rock damage. However, these metrics do not comprehensively represent the crack development trends, energy magnitudes, and resultant damage across different locations. To delve deeper into the crack development and evolution patterns of granite under varying temperatures and loading rates, we further analyzed the crack development process. This analysis combines the ratio of acoustic emission damage and energy with the distribution of acoustic emission signal points at each stage of the granite loading process. Figure 3: Variations in the acoustic emission characteristic parameters at different loading rates and temperatures. The real-time signal point size represents the acoustic emission energy, with various colors indicating the acoustic emission ringing counts. Equations (2) and (3) were utilized to calculate the damage and energy shares at each stage of rock fracture development [26], as follows:  
\[D = \frac{N_{\mathrm{d}}}{N_{\mathrm{m}}} \tag{2}\] \[R = \frac{E_{\mathrm{d}}}{E_{\mathrm{m}}} \tag{3}\]  
where \(N_{\mathrm{d}}\) represents the number of acoustic emission ringing events at a specific moment in \(\mathrm{pcs};N_{\mathrm{m}}\) represents the total number of acoustic emission ringing events after the conclusion of rock compression; \(E_{\mathrm{d}}\) represents the total energy at a specific stage; \(E_{\mathrm{m}}\) represents the total energy generated after the conclusion of rock compression; \(D\) signifies the rock damage variable; and \(R\) represents the energy share. By applying the aforementioned analytical methods to scrutinize the acoustic emission spatial signal point variation pattern of granite at each stress stage, we obtained the acoustic emission spatial signal point evolution process of granite specimens at each stress stage under various temperatures and loading rates. These findings are illustrated in Figures 4-7. Figure 4 shows that when the temperature is 30 \({}^{\circ}\)C, the acoustic emission signals are first distributed discretely in the lower left corner of the specimen at 0.2 under a loading rate of 0.005 mm/s. With increasing axial loads, the number of acoustic emission signals increases and increases to the upper right corner of the specimen, while the acoustic emission signals become increasingly intense at the lower left corner of the specimen. The acoustic emission signals become increasingly powerful, which means that the cumulative damage of the rock specimen is accompanied by cumulative damage. With increasing specimen strength, the penetrating main crack inside the specimen gradually forms. Meanwhile, when the specimen is pressurized, the main crack in the specimen forms, and the bearing capacity begins to decrease. At a stress value of 0.9, the number of acoustic emission signals continues to increase, albeit with low energy, suggesting that the specimen retains its load-bearing capacity. Microcracks persist within the specimen until eventual failure, with analytical findings aligning closely with the final test results (Figure 4). At loading rates of 0.005 mm/s and 0.01 mm/s, the damage-to-energy ratio primarily emphasized the early and middle stages of fracturing, indicating greater damage during these phases than during the later stages. This trend is consistent with the distribution of the acoustic emission signals, which are particularly evident during the middle and early stages of uniaxial compression under both loading rates. These observations suggest that higher loading rates are more detrimental to the rock specimen during the early and late stages of the compression process. Figure 5 reveals that at 40 \({}^{\circ}\)C, the acoustic emission signals under loading rates of 0.005 mm/s and 0.01 mm/s initially concentrate centrally in the lower right corner of the specimen.