## 2 Materials and Methods
### Dynamic Test Introduction  
For the dynamic test, we used the Split Hopkinson Pressure Bar, which consists of a striker, an incident bar, a transmitted bar, an absorbed bar, a confining pressure device, and a data acquisition system. The total length of the incident bar is 2400 mm, the end in contact with the striker is a variable cross-section, the length of the variable cross-section is 170 mm, and the diameters of the two ends are 37 mm and 50 mm, respectively. The diameter of the striker is 37 mm, and the length is 400 mm. The length of the transmitted  
Figure 1: Some granite samples. bar is 1200 mm, and the diameter is 50 mm. The wave speed of the bars is 5190 m/s, the density is 7800 kg/m\({}^{3}\), and Young's modulus is 210 GPa. The confining pressure device consists of an oil pumping device, a pressure chamber, and a pressure control system. When using the device, we first use the hot melt pipe to fix the rock samples in the pressure chamber and then fill the oil into the pressure chamber through the oil pumping device; when the pressure chamber is full of oil, we turn off the oil pumping device and then set the predetermined value of the pressure chamber on the pressure control system and click the button of pressurization, where the system will then be like a syringe squeezing the oil into the chamber to increase the pressure to the preset value. The Split Hopkinson Pressure Bar is shown in Figure 2.  
When using the Split Hopkinson Pressure Bar, the size of the impact air pressure is set on the gas pressure control device first and nitrogen gas is released when the value of the air pressure in the gas gun is added to the set value. The rapidly released gas produces a larger pressure to drive the bullet to hit the incident bar to produce a shock wave to be transmitted to the rock samples, which are deformed at high speed under the impact loading. The whole process is recorded as a pulse signal by strain gauges and collected by the DH8302 dynamic signal test system designed by Donghua Company. The dynamic stress and strain parameters of the rock samples are analyzed by the supporting computer software. The Hopkinson test satisfies two basic assumptions:  
One-dimensional elastic stress wave assumption: the propagation path of the stress wave in the Hopkinson bar is one-dimensional, and the stress wave in any cross-section in the bar is in the same horizontal plane. That is, the axial strain measured at the surface of the compression bar can represent the axial strain of the entire cross-section. Stress-strain uniformity assumption: that is, the stress and strain of the rock sample in the length direction are uniform. Based on the above two assumptions, the equation for the average stress \(\sigma(t)\), average strain \(\varepsilon(t)\), and average strain rate \(\varepsilon(t)\) of the specimen can be obtained [27, 28]:  
\[\sigma(t) =\frac{A_{e}}{2A_{s}}\;E_{s}\;[\varepsilon_{I}\left(t\right)- \varepsilon_{R}\left(t\right)-\varepsilon_{T}\left(t\right)], \tag{2}\] \[\varepsilon(t) =\frac{C_{s}}{L}\int_{0}^{t}\;[\varepsilon_{I}(t)-\varepsilon_{R} (t)-\varepsilon_{T}(t)]\;dt,\] (3) \[\varepsilon(t) =\frac{C_{s}}{L}\;[\varepsilon_{I}(t)-\varepsilon_{R}(t)- \varepsilon_{T}\left(t\right)], \tag{4}\]  
where \(A_{e}\) and \(A_{s}\) are the cross-sectional area of the incident bar and sample, mm\({}^{2}\). \(E_{s}\) is the modulus of elasticity of the incident bar, GPa. \(\varepsilon_{I}\left(t\right)\), \(\varepsilon_{R}\left(t\right)\), and \(\varepsilon_{T}\left(t\right)\) are the strain signals  
Figure 2: Schematic diagram of the Split Hopkinson Pressure Bar. of incident wave, reflected wave, and transmitted wave at the moment of \(t\), respectively. \(C_{s}\) is the longitudinal wave speed of the incident bar, m/s. \(L\) is the length of the sample. Based on the above rationale, a pre-experiment was carried out. The strain signals obtained after impact were analyzed, as shown in Figure 3. The waveform is generally smooth, and no dispersion effects are observed during the propagation of the stress waves.