# Experimental Study on Dynamic Mechanical Properties of Sandstone Under Different Damage Degrees
## 3 Uniaxial and Triaxial Dynamic Loading Apparatus Based on SHPB  
The dynamic impact experiment on rock specimens utilizes the split Hopkinson pressure bar (SHPB) apparatus, as illustrated in Figure 3. During the dynamic uniaxial compression experiment, there is no need to apply axial or confining pressure to the rock specimen; dynamic loading is achieved solely through the impact stress wave generated by the spindle-shaped striker. In contrast, the triaxial dynamic compression experiment requires both an axial pressure apparatus and a confining pressure apparatus to apply axial and confining pressures to the rock specimen, while the spindle-shaped striker generates the impact stress wave for dynamic loading. Figure 3: Split Hopkinson pressure bar (SHPB) apparatus [31]. (**a**) Conventional uniaxial SHPB experimental system. (**b**) Triaxial SHPB experimental system. Figure 2: Schematic diagram of sandstone sample combination loading model. (**a**) Specim loading mechanical model. (**b**) Load-time curve. After the spindle-shaped striker completes the impact, the stress wave will undergo multiple reflections within the striker and rod system, eventually reaching equilibrium. The compressive stress wave starts propagating to the right from the impact surface, due to the difference in wave impedance between the rock and the incident bar, the compressive stress wave will undergo transmission and reflection at the contact surface between the incident bar and the rock. The transmitted stress wave will advance in the direction of the transmission bar, while the reflected stress wave will travel back to the incident bar and propagate to the left, but with an intensity much lower than the incident wave. This phenomenon can be observed in Figure 4. When the stress wave transmitted through the rock propagates within the rock, it will be affected by the internal microcracks and other defects, causing a decrease in its intensity and propagation speed. When the weakened stress wave reaches the contact surface between the rock specimen and the transmission bar, due to the difference in wave impedance between the two, transmission and reflection phenomena will occur. As shown in Figure 4, the amplitude of the green transmitted wave is lower than that of the incident wave on its left. This is because the propagation of stress waves inside rocks promotes the expansion of internal microcracks, thereby consuming part of the energy brought by stress waves. As shown in Figure 5, according to one-dimensional wave theory, the relationship between stress, strain, and strain rate of rock specimens over time can be obtained. \[\sigma(t)=[\sigma_{I}(t)-\sigma_{R}(t)+\sigma_{T}(t)]\cdot A_{e}/(2A_{s}) \tag{1}\]  
\[\epsilon(t)=\frac{1}{\rho_{e}C_{e}L_{s}}\int_{0}^{t}{[\sigma_{I}(t)+\sigma_{R }(t)-\sigma_{T}(t)]dt} \tag{2}\]  
\[\dot{\epsilon}(t)=\frac{1}{\rho_{e}C_{e}L_{s}}[\sigma_{I}(t)+\sigma_{R}(t)- \sigma_{T}(t)] \tag{3}\]  
The incident stress wave propagates to the right towards the rock specimen, and after reflection and transmission occur on the left and right sides of the rock specimen, the incident energy and reflection energy on the incident bar, as well as the transmission energy on the transmission bar, are expressed as follows:  
Figure 4: Impact experiment waveform. Figure 5: Schematic diagram of stress wave transmission and reflection on both sides of the rock specimen. \[ \begin{split} E_{I}&=\frac{A_{e}}{\rho_{e}C_{e}}\int_{0}^{t} \sigma_{I}^{2}(t)dt\\ E_{R}&=\frac{A_{e}}{\rho_{e}C_{e}}\int_{0}^{t} \sigma_{R}^{2}(t)dt\\ E_{T}&=\frac{A_{e}}{\rho_{e}C_{e}}\int_{0}^{t} \sigma_{T}^{2}(t)dt\\ \end{split}  \tag{4}\]  
As shown in Figure 5, after the spindle-shaped striker hits the incident bar, it propagates its kinetic energy to the rock specimen in the form of a stress wave. A portion of the energy is reflected back from the left side of the rock specimen, and another portion is transmitted out from the right side.