## 3 Results
### Laws of Energy Evolution During Uniaxial Compression of Basalt After Microwave Irradiation  
Microwave radiation modifies the structural properties of rocks, particularly in terms of porosity and crack formation, which subsequently influences their mechanical behavior. In this study, the damage inflicted on basalt specimens by microwaves is quantitatively assessed by analyzing the strain energy prior to the peak of the specimens' stress-strain curves. The methodology follows the principles of uniaxial loading and unloading experiments, as depicted in Figure 8.  
The stress-strain curve generated from the uniaxial loading and unloading test mirrors that of the uniaxial compression test up to the unloading point. To quantify the extent of damage, this study measures the elastic strain energy (\(u_{c}\)), dissipation energy (\(u_{d}\)), and total input energy (\(u_{t}\)) of the rock specimens by performing three cycles of loading and unloading on each group of specimens, as illustrated in Figure 9. The calculations for these energy components are based on the following formulas:  
\[u_{t}=\int_{0}^{\epsilon_{1}}f_{1}(\epsilon)d\epsilon \tag{2}\]  
\[u_{\epsilon}=\int_{\epsilon_{2}}^{\epsilon_{1}}f_{2}(\epsilon)d\epsilon \tag{3}\]  
\[u_{d}=u_{t}-u_{\epsilon}=\int_{0}^{\epsilon_{1}}f_{1}(\epsilon)d\epsilon-\int _{\epsilon_{2}}^{\epsilon_{1}}f_{2}(\epsilon)d\epsilon \tag{4}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Microwave Power** & **Radiation** & **Peak Axial Stress, \(\sigma_{c}\)(MPa)** & **Modulus of Elasticity, \(\mathcal{E}\)(GPa)** \\ \hline
0 kW & 0 s & 102.25 & 30.31 \\ \hline \multirow{4}{*}{3 kW} & 30 s & 100.78 & 28.22 \\  & 60 s & 95.43 & 26.88 \\  & 90 s & 94.10 & 26.78 \\  & 120 s & 93.72 & 26.49 \\ \hline \multirow{4}{*}{6 kW} & 30 s & 97.20 & 26.15 \\  & 60 s & 89.07 & 21.86 \\ \cline{1-1}  & 90 s & 85.55 & 20.60 \\ \cline{1-1}  & 120 s & 83.49 & 19.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The main mechanical parameters of basalt specimens under different microwave radiation power and time. Figure 8: Uniaxial loading and unloading experiment original diagram. (**a**) Stress–time diagram. (**b**) Stress–strain diagram. where \(f_{1}\) represents the stress-strain curve of the rock during the initial loading, and \(f_{2}\) represents the curve obtained by unloading the rock specimen at the unloading point. \(\varepsilon_{1}\) is the strain of the basalt specimen at the unloading point, and \(\varepsilon_{2}\) is the strain of the specimen when the unloading stress reaches zero. The total input energy (\(u_{t}\)), dissipation energy (\(u_{d}\)), and elastic strain energy (\(u_{e}\)) for each uniaxial loading and unloading experiment can be calculated according to the formulas, as shown in Figure 10. [PERSON] et al. [38] posit that an external load is a prerequisite for the accumulation of energy in the rock, and there is a linear relationship between energy storage and external load at different temperatures, which aligns with the law of energy storage:  
\[u_{e}=Au_{t}+B \tag{5}\]  
Assuming the same linear relationship between \(u_{e}\) and \(u_{t}\) for basalt under microwave radiation:  
\[u_{d}=Ku_{t}+M \tag{6}\]  
where \(K\) is the compression energy dissipation factor, and \(M\) is the fitting constant. When the external input energy (\(u_{t}\)) is 0, meaning there is no input energy, \(u_{d}\) (the dissipation energy) must also be 0, which leads to \(M=0\). In this formula, the magnitude of \(K\) reflects the energy storage capacity of the specimen. A larger \(K\) value indicates that more of the external input energy is converted into dissipative energy, signifying that the specimen's energy storage capacity is weaker, and consequently, the greater the damage the specimen has sustained. The investigation revealed that the energy storage capacity of rock specimens showed minimal changes after just 30 s of microwave irradiation. As a result, the specimens were divided into seven groups for further analysis of the effects of prolonged exposure times.