## 3 Analysis of Dynamic Performance and Energy Consumption
### Analysis of Cyclic Impact Energy  
After the sandstone specimen is subjected to cyclic dynamic impact, its internal damage gradually increases. The initiation, development, propagation, and penetration of cracks all need to absorb energy from the outside. The laws of thermodynamics show that energy transformation is the intrinsic nature of a change in physical characteristics and that the internal damage of rock is closely related to energy dissipation. Based on the energy conservation law and one-dimensional stress wave theory, the incident energy, reflected energy, and transmitted energy can be obtained by Equation (1) to Equation (3). \[W_{I} =\frac{\text{AC}}{\text{E}}\int_{0}^{t}\sigma_{I}^{2}(t)\text{dt} \tag{1}\] \[W_{R} =\frac{\text{AC}}{\text{E}}\int_{0}^{t}\sigma_{R}^{2}(t)\text{dt}\] (2) \[W_{T} =\frac{\text{AC}}{\text{E}}\int_{0}^{t}\sigma_{T}^{2}(t)\text{dt} \tag{3}\]  
where \(W_{I}\), \(W_{R}\), and \(W_{T}\) represent the incident energy, reflected energy, and transmitted energy, respectively; A, C, and E are the cross-sectional area, longitudinal wave velocity, and elastic modulus of the pressure bar, respectively; \(\sigma_{I}^{2}(t),\ \sigma_{R}{}^{2}(t),\ \text{and}\ \sigma_{T}{}^{2}(t)\) are incident stress, reflected stress, and transmitted stress at time \(t\), respectively. \[W_{L} =W_{I}-W_{R}-W_{T} \tag{4}\] \[\zeta =W_{L}/W_{I} \tag{5}\]  
The dissipated energy and dissipated energy ratio of sandstone specimens can be obtained according to Equation (4) and Equation (5). The calculations of the cyclic impact energy of sandstone after different high-temperature treatments are presented in Table 3 and Figure 12. Four conclusions can be achieved. (1) When the impact velocity increases, the incident energy increases gradually and is approximately linearly distributed. The peak stress increases with the transmitted energy. (2) When T \(\leq\) 600 \({}^{\circ}\)C, the energy dissipated ratio of the first impact is greater than that of the second impact. According to the energy conservation law, the kinetic energy of sandstone specimen is converted into the energy consumption and other loss energy absorbed by sandstone fracture during impact. For the dissipated energy, due to a deformation of pore body, micro-plastic deformation of the solid medium occurs around the pore and there is a rupture of the solid medium. When the stress wave around the pore passes through the pore body, part of the energy is consumed. This indirectly reflects the damage failure mechanism inside the solid and further indicates that the rock deformation failure is a comprehensive result of energy release and energy dissipation. (3) When the temperature is 25 \({}^{\circ}\)C, 200 \({}^{\circ}\)C, and 800 \({}^{\circ}\)C, the dissipated energy of the sandstone under the last impact is far greater than that under the previous impact. The reason may be that there are many cracks in the sandstone in the previous impact, but they are not completely destroyed. At the last impact, a large amount of energy is lost from cracks, and the reflected energy and transmitted energy actually acting on the sandstone are small, resulting in an increase in dissipated energy. (4) At the first impact, the dissipation energy of sandstone decreases sharply at treatment temperatures of 800 \({}^{\circ}\)C and 1000 \({}^{\circ}\)C, indicating that high-temperature thermal damage had  
Figure 12: Analysis of cyclic impact energy of sandstone. (**a**) Relationship between impact velocity and incident energy. (**b**) Relationship between peak stress and transmitted energy.