## 2 Materials and Methods
### Quasi-Static Uniaxial Compression and SHPB Impact Test  
The standard cylindrical specimens with a diameter of 50 mm and height of 100 mm were tested by the TAW-2000 rock mechanics test system to perform conventional uniaxial compression tests, using displacement control for loading with a loading rate of 0.01 mm/s.  
The SHPB impact test was performed using the SHPB system (Figure 2) at the mechanics laboratory of Wuhan University. The striker, incident, and transmitted bars were manufactured from high-strength 40 Cr alloy steel with a material density of 7800 kg/m\({}^{3}\)  
Figure 1: Layered sandstone core specimen and optical microscopy images of the specimen core. (**a**) Image of the layered sandstone core; (**b**) relationship between the bedding plane and loading directions; (**c**) reflected light image of layered sandstone under the microscope; and (**d**) transmitted light image of layered sandstone under the orthogonal polarization system.  
The pressure bar had a diameter of 50 mm, an elastic modulus of 210 GPa, a Poisson's ratio of 0.3, and a longitudinal wave velocity of 5670 m/s. Both the incident and transmitted bars had a diameter of 50 mm and a length of 2500 mm. The striker bars had a diameter of 37 mm and a length of 400 mm. To ensure that the test specimen can be fractured but not crushed under impact loading, a trial impact was conducted on the test specimen before the experiment. Finally, an impact pressure of 0.1 MPa was selected for the experiment. The average strain rate ranged from 15.7 s\({}^{-1}\) to 29.1 s\({}^{-1}\). Before impact loading, Vaseline petroleum jelly was evenly applied to both ends of the specimen to reduce the friction between the specimen and pressure bar. Figure 3 shows the stress waveforms of the elastic pressure bars at both ends of the specimen under impact compression. The curve of the transmitted wave aligns closely with the curves of the incident wave + reflected wave, indicating that before the peak stress was reached and the specimen failed, the stresses at both ends were generally in equilibrium, and therefore, satisfied the stress equilibrium conditions defined in the one-dimensional stress wave theory. According to this theory, the mean axial stress \(\sigma(t)\), mean strain \(\varepsilon(t)\), and mean strain rate \(\varepsilon(t)\) of the specimen can be calculated using the strain pulse data and the following equations:  
\[\sigma(t)=\frac{A_{\mathrm{e}}E_{\mathrm{e}}}{2A_{\mathrm{s}}}[\varepsilon_{i }(t)+\varepsilon_{r}(t)+\varepsilon_{t}(t)] \tag{1}\]  
\[\varepsilon(t)=\frac{\varepsilon_{e}}{L_{\mathrm{s}}}\int_{0}^{t}[\varepsilon _{i}(t)-\varepsilon_{r}(t)-\varepsilon_{t}(t)] \tag{2}\]  
\[\dot{\varepsilon}(t)=\frac{\varepsilon_{e}}{L_{\mathrm{s}}}[\varepsilon_{i}( t)-\varepsilon_{r}(t)-\varepsilon_{t}(t)] \tag{3}\]  
where \(A_{\mathrm{e}}\) and \(A_{\mathrm{s}}\) are the cross-sectional areas of the bar and granite specimen, respectively; \(E_{\mathrm{e}}\), \(\varepsilon_{\mathrm{e}}\), and \(L_{\mathrm{s}}\) are the Young's modulus of the elastic bar, velocity of the 1D elastic longitudinal wave, and length of the granite specimen, respectively; and subscripts \(i\), \(r\), and \(t\) correspond to the incident, transmitted, and reflected wave signals recorded by the strain acquisition system, respectively.