## 2 Experiments
### Experimental Apparatus  
Figure 2a shows the setup of the SHPB that is used in this study. In a rock dynamic test using a SHPB, the pressure of the gas chamber when the striker bar is released is typically regulated to generate various strain rates [21; 22]. This method is utilized herein to provide strain rates of the incident bar within the range 83.1-259.0 s\({}^{-1}\). Figure 3 plots the strain rates that are used in this study: these are generated in the SHPB by regulating the pressure of the gas chamber in the range 0.4-1.3 kg/cm\({}^{2}\) while the striker bar is released. The stress can be determined from the Young's modulus of the incident bar. Figure 3 plots both the stress increment per unit time and the strain rate. The loading rates that are generated in this study are in the range 3403-8467 GPa/s when no specimen is embedded between the incident bar and transmitted bar. The applicability of the SHPB technique needs to be examined carefully before reliable dynamic experimental data can be obtained. The appearance of a discontinuity, for instance, the vacant one in-between the incident and transmitted bars, can interfere with the stress equilibrium during the application of dynamic impact since the mechanical impedance of the discontinuity is extremely small compared to that of solid bars and thus affects the dynamic stress propagation. Dynamic equilibrium is conventionally checked by comparing the transmitted signal and the difference between the incident and reflected signals [37]. The error, \(e_{\varepsilon}\), can be evaluated by subtracting the measured strain that is generated by the transmitted wave from the sum of the strains that are generated by the incident wave and the back (reflected) wave at incidence: \(e_{\varepsilon}=e_{i}-e_{r}-e_{t}\). Only the dynamic equilibrium in early process during a SHPB test is concerned in this study since the failure of the embedded rock specimen  
Figure 3: Relationship between pressure of gas chamber when striker bar is released and loading rate. Figure 2: Setup of experiment with the Split Hopkinson Pressure Bar (SHPB) test (**a**) and interpretation on measured waveforms of strain histories (**b**). leads to a non-equilibrium state. Therefore, the first waveforms of the recorded \(\varepsilon_{i}(t)\), \(\varepsilon_{r}(t)\), and \(\varepsilon_{t}(t)\) are evaluated. The linearly increasing portion of recorded strain histories are extended to intercept the time axis to determine their corresponding arrival times, i.e., \(t_{0}^{i}\), \(t_{0}^{r}\), and \(t_{0}^{t}\)(Figure 2b). The time for incident pulse to reach its peak (\(t_{p}^{i}\)) is selected as half of the integration period, \(\Delta t=(t_{p}^{i}-t_{0}^{i})\), and the average error in the early dynamic equilibrium state is then determined as:  
\[e_{\varepsilon}=\frac{1}{2\Delta t}\int_{t_{0}^{i}}^{t_{0}^{i}+2\Delta t}( \varepsilon_{i}-\varepsilon_{r}-\varepsilon_{r})dt \tag{1}\]  
where \(t_{0}^{i}\) are \(t_{0}^{i}\), \(t_{0}^{r}\) and \(t_{0}^{t}\) for the integration of \(\varepsilon_{i}(t)\), \(\varepsilon_{r}(t)\), and \(\varepsilon_{t}(t)\), respectively. The value of \(e_{\varepsilon}\) is in the range 0.5-51.9% (Figure 4). The pressure measurement film (referred to as PMF herein) of the Fujifilm product is also adopted to examine the force equilibrium between the two ends of the specimen during a SHPB test (Figure 2a). Both low- and medium-pressure types of measurement film are used. Two PMFs of appropriate pressure scale are embedded between the two ends of specimen and the incident bar (the front PMF) and the transmitted bar (the rear PMF), respectively. Notably, only two PMFs are used in case no specimen is embedded. Table 1 illustrates typical results of some SHPB tests for various specimens under various pressures of the gas chamber while the strike bar is released. The area of PMF is decomposed into 64 parts to interpret corresponding densities of red patches and the average of these parts is used to represent the peak stress during the SHPB test.