# Study on Damage Behavior and Its Energy Distribution of Deep Granite at High-Temperature Conditions
## 3 Acoustic Emission Test Results and Analysis of Fractured Rock under Triaxial Loading
### Effect Analysis of Equivalent Damage Factors on Rock Energy Evolution  
According to the law of conservation of energy  
\[W=U^{d}+U^{e} \tag{3}\]  
where \(W\) is the energy input to rock sample by press; \(U^{e}\) is the elastic energy; and \(U^{d}\) is mainly damage energy during rock deformation and plastic energy used for rock particles to produce plastic deformation. Taking the loading curve of rock as an example, assume that OA is the loading curve and AB is the unloading curve. Then, the area enclosed with the strain below AB is \(u_{i}^{e}\), and the area enclosed below OA and above AB is the \(u_{i}^{d}\). \[u_{i}^{e}=\int_{\varepsilon_{b}}^{\varepsilon_{c}}\sigma_{i}d\varepsilon_{i} \tag{4}\]  
\[u_{i}^{d}=\int_{0}^{\varepsilon_{c}}\sigma_{i}d\varepsilon_{i}-\int_{ \varepsilon_{b}}^{\varepsilon_{c}}\sigma_{i}d\varepsilon_{i} \tag{5}\]  
where \(\varepsilon_{b}\) and \(\varepsilon_{c}\) are the strain values at the point where the stress is 0 after unloading and at the beginning of unloading, respectively. In this paper, the elastic modulus \(E_{0}\) of the elastic segment before the peak is taken as the unloading elastic modulus \(E_{i}\) in the calculation of energy. For uniaxial compression test, the elastic energy \(U_{i}^{e}\) can be released at stress \(\sigma_{i}\). \[U_{i}^{e}=\sigma_{i}^{2}/2E_{0} \tag{6}\]  
For triaxial test, the stored elastic energy mainly consists of axial and circumferential parts. However, the circumferential stored elastic energy is far less than the axial elastic energy, so Equation (6) is still used to calculate the elastic energy. According to the stress-strain curve obtained from the conventional triaxial compression test, the evolution of total input strain energy density, elastic energy density, and dissipated energy density with \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Confining** & \multicolumn{3}{c}{**Equivalent Damage Factor (D)**} \\ \cline{2-4}
**Pressure/MPa** & \(D\) = 0.16 & \(D\) = 0.36 & \(D\) = 0.51 & \(D\) = 0.89 \\ \hline
0 MPa & & & & \\
10 MPa & & & & \\
20 MPa & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Failure modes of fractured rock under different confining pressures. strain under different confining pressures was obtained by combining energy calculation Equations (3)-(6), as shown in Figures 5 and 6. It can be seen from Figures 5 and 6 that energy characteristic curves evolve similarly under different confining pressures. At the stage of fracture compaction and stable development, the mechanical energy input from the outside is mainly transformed into elastic energy and stored in the rock interior. This part of energy accounts for about 90\(\sim\)96% of the total energy, and only about 5% is used for fracture closure and the generation and expansion of new fractures. In the unstable development stage of fracture, both elastic energy and dissipative energy continue to increase, but the proportion of dissipative energy in total energy begins to increase gradually due to the plastic deformation of rock samples and the further initiation and expansion of microcracks. In the post-peak stage, macroscopic main cracks appear. The elastic energy is released quickly, and most of the energy is converted into dissipated energy, which is used for macroscopic crack sliding and friction heat energy. At the same time, a certain amount of elastic energy is stored in the post-peak residual stage under confining pressure. The maximum dissipated energy of samples with different initial thermal damage under confining pressures of 10 MPa and 20 MPa is shown in Figure 7. The result shows that, under the same fracture degree, with the confining pressure increases, the maximum dissipative energy becomes larger. Under the same confining pressure, with the increase in rupture degree, the maximum dissipated energy increases first and then decreases, and the change rate is first slow and then fast.