## 3 Experimental Results and Analysis
### Fractal Features of the AE Signal Points
This suggests that during the process of damage destruction, the distance from the acoustic emission signal points to the origin of the granite, which exhibits fractal characteristics. These computations yield the fractal dimension of the acoustic emission signal under various temperatures and loading rates, as depicted in Figure 9.  
Figure 9 shows that the fractal dimension fluctuates under different loading rates and temperatures, and the fractal dimension generally decreases, then fluctuates, and then decreases. The stages of decreasing fractal dimension in the granite specimens are the compaction stage and the destruction stage. This is attributed to the closure of internal pores during the rock compaction stage, leading to a reduction in fractal dimension. Subsequently, in the rock damage stage, as the main cracks penetrate through, the fractal dimension further decreases. Moreover, with increasing temperature, the magnitude of change in the fractal dimension during the destruction stage increases. The fractal dimension fluctuation stage includes the elastic deformation stage, stable crack development stage, and unstable crack development stage. During this stage, the crack initiation, expansion, or closure of the rock specimen, and orderly, disorderly changes of the cracks occur. This is an overall change in the direction of increasing order; thus, the fractal dimension fluctuation changes, and the amplitude of the overall crack development increases. Under identical temperature conditions, an increase in the loading rate results in a decrease in the magnitude of the fractal dimension within the range of 0.1-0.7. Specifically, a higher loading rate correlates with a lower degree of compactness in the granite specimens. The fluctuations in fractal dimension occur within the range of 0.02-0.52, transitioning between 0.15-0.52 with increasing loading rates, then to 0.1-0.3, further transforming to 0.002--0.320, and subsequently to 0.002-0.520. Notably, the fractal fluctuation between 0.002-0.212 significantly diminishes, indicating a reduction in cracks within the specimen during compression. At constant loading rates, as the temperature increases, the fractal dimension decreases within the range of 0.1  
0.4, signifying stages of specimen compression density and crack distribution during the damage stage. Additionally, the amplitude of fractal dimension fluctuations increases from 0.05-0.52 at temperatures of 30 \({}^{\circ}\)C and 40 \({}^{\circ}\)C to 0.1-0.3 at temperatures of 60 \({}^{\circ}\)C and 80 \({}^{\circ}\)C. The amplitude of the change in amplitude decreases, indicating that the greater the temperature of the crack development process is, the greater the crack distribution, and the greater the temperature is, the greater the crack distribution. In the development process, with a more decentralized crack distribution, cracks cannot form in an obvious direction, and the cracks clearly form a network. The analysis indicates that the fractal dimension of R and L can somewhat portray the rock's traits across stages, such as compression density, stable crack development, unstable crack development, and rock damage. Furthermore, the crack evolution within the rock follows a pattern of initial enhancement, subsequent reduction, and then another enhancement. Thus, the fractal dimension provides a numerical depiction of crack evolution and destruction intensity in granite. Such an understanding can assist in predicting rock destruction and evolution processes in practical engineering scenarios. Figure 9: The fractal dimension of the R and L values of the specimen.