## 4 Results
### Acoustic Emission and Energy  
In PFC, particles are used to construct a computational model, and when the stress exceeds the bond strength between particles, the bond breaks and releases energy, corresponding to an acoustic emission event [48]. In addition, from the energy point of view, assuming that the heat exchange from the sample to the outside world is not taken into account, the total input energy is all converted into the strain energy and dissipation energy of the rock:  
\[U=U^{e}+U^{d} \tag{3}\]  
where \(U\) denotes the boundary energy, which is the work performed by the upper and lower walls on the sample; \(U^{e}\) is the strain energy, including the strain energy of the particles themselves and the model strain energy; \(U^{d}\) is the frictional energy, including the frictional energy, damping energy, kinetic energy, etc., between particles. Through the built-in Fish language in PFC, real-time monitoring and recording of acoustic emission events and energy evolution during the loading process are conducted. Eventually, different temperature-dependent full-process acoustic emission and energy development curves of granite under uniaxial compression are obtained, as shown in Figure 13.  
For the room temperature samples, as shown in Figure 13a, the results correspond to the four stages of stress-strain curve and crack development of the granite mentioned above, with different characteristics in acoustic emission activity and energy evolution. In the initial densification stage, there are very few acoustic emission signals. The bonds between particles are not yet broken, and the energy is still in an accumulation state. The boundary energy is entirely converted into strain energy stored between the bonds. The strain energy curve coincides with the boundary energy curve, exhibiting a nonlinear parabolic growth, with a very small growth rate. In the elastic stage, acoustic emission events gradually appear, but the amplitude and frequency are still small. With the increase in stress, the frictional energy slightly increases, and the boundary energy begins to separate from the strain energy curve. In the plastic strengthening stage, acoustic emission activity gradually becomes frequent, with an increase in amplitude and frequency. Although the strain energy still shows an increasing trend, the growth rate gradually decreases and drops to zero at the peak point. The strain energy stored between particles is released. Upon entering the post-peak failure stage, the number of acoustic emission events sharply increases, and the amplitude intensifies. When reaching the peak stress, the number of acoustic emission events does not reach its peak but lags behind the peak stress point. At this point, the strain energy is at a critical value, and the work performed by external forces mainly converts into frictional energy. Figure 12: Cracking hotspot map of granite at different temperatures. As shown in Figure 13b-f, for the granite subjected to high-temperature effects, its acoustic emission activity differs significantly from that at the room temperature state. In the initial densification stage, there are minor acoustic emission events starting at 200 \({}^{\circ}\)C. When the temperature reaches 400 \({}^{\circ}\)C, acoustic emissions become active in the early stages of loading. This indicates that with the increase in temperature, the thermal damage caused to the sample gradually increases, and internal cracks develop and begin to release energy earlier than at room temperature. Upon entering the elastic stage, the level of acoustic emission activity shows a slight increase due to the higher temperature. In the post-peak stage, the higher the temperature, the more pronounced the multi-peak phenomenon of acoustic emissions becomes. However, the amplitude intensity is less intense than that at room temperature. This is because the higher temperature enhances the ductility of the granite, resulting in more energy being released near the peak stress, while the energy released at the peak stress decreases [49].