## 2 Material and Methods
### Experimental System
#### 2.2.2 LT-SHPB System  
As shown in Figure 4, a LT-SHPB system developed by China University of Mining and Technology was adopted to conduct the impact tests. The system consists of five main components: an impact loading system, a compression bar system, a data acquisition system, a damping system, and a low-temperature freezing system. In the experimental system, the bars and the striker are made of high-strength Cr40 alloy steel with diameters, P-wave velocities, yield strengths, and elastic modulus of 50 mm, 5400 m/s, 800 MPa, and 208 GPa, respectively. The low-temperature freezing system consists of a temperature controller, a liquid nitrogen tank, an electric heating wire sensor, and a cold chamber. The cold chamber, as the key structure of the system, has a good insulating effect. Its inner insulation layer is mainly composed of aluminum silicate acupuncture blanket and insulating brick.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(V_{\text{p}}\)**(m/s)** & \(\rho_{d}\)**/(g\(\cdot\)cm\({}^{-3}\))** & \(\rho_{sat}\)**/(g\(\cdot\)cm\({}^{-3}\))** & \(n\)**/(\%)** & \(\sigma_{p}\)**/(MPa)** & \(\eta\)**/(\%)** \\ \hline
2459 & 2.14 & 2.31 & 16.57 & 13.84 & 7.94 \\ \hline \hline \end{tabular} Notes: \(V_{\text{p}}\), P-wave velocity; \(\rho_{d}\), dry density; \(\rho_{sat}\), saturation density; \(n\), porosity; \(\sigma_{p}\), uniaxial compressive strength; \(\eta\), water content.  
\end{table}
Table 1: The physical and mechanical parameters of selected samples.  
Figure 3: Experimental procedure and equipment.  
Before the test, the chamber temperature was set to \(-25\)\({}^{\circ}\)C. The frozen sandstone sample was then quickly placed in the cold chamber. Molybdenum disulfide was applied at the ends as a lubricant to reduce the friction effect between the bars and the sample. It is worth mentioning that the sample should remain in the chamber for at least 0.5 h [5]. To obtain the desired waveform, a circular rubber pad with a diameter of 15 mm and a thickness of 2 mm was used as a pulse shaper. A compressive wave was generated when the high-pressure gas propelled the striker against the incident bar. Part of the compressive wave propagated through the sample to the transmission bar. As a result, the strain signal generated on the bar was measured by the strain gauges, as shown in Figure 5. Based on the one-dimensional stress wave propagation theory, the three-wave analysis method was used to calculate the strain and stress [26], as shown in Equation (1).  
\[\left\{\begin{array}{l}\sigma=\frac{A_{\mathrm{r}}E_{\mathrm{0}}}{2}[\varepsilon _{\mathrm{i}}(t)+\varepsilon_{\mathrm{r}}(t)+\varepsilon_{\mathrm{r}}(t)]\\ \varepsilon=\frac{C}{\mathrm{s}}\int\limits_{0}^{t}{[\varepsilon_{\mathrm{i}}( t)-\varepsilon_{\mathrm{r}}(t)-\varepsilon_{\mathrm{t}}(t)]dt}\\ \dot{\varepsilon}=\frac{C}{\mathrm{s}}[\varepsilon_{\mathrm{i}}(t)- \varepsilon_{\mathrm{r}}(t)-\varepsilon_{\mathrm{t}}(t)]\end{array}\right. \tag{1}\]  
where \(\sigma\), \(\varepsilon\), and \(\dot{\varepsilon}\) refer to dynamic stress, dynamic stress, and strain rate, respectively; \(A_{\mathrm{r}}\) is the ratio of the cross-sectional area of the bar to the sample; \(E_{\mathrm{0}}\), \(C_{\mathrm{s}}\), and \(L_{\mathrm{s}}\) are the elastic modulus, the wave velocity of the bar, and the length of the sample, respectively; \(\varepsilon_{\mathrm{i}}(t)\), \(\varepsilon_{\mathrm{r}}(t)\), and \(\varepsilon_{\mathrm{t}}(t)\) refer to the incident, reflected, and transmitted strain, respectively. In addition, the striker impact velocity is measured by a laser beam measurement system.