## 3 SHPB Test Results of the Prefabricated Fractured Sandstone Specimens
### Dynamic Mechanical Parameters of the Prefabricated Fractured sandstone Specimens  
The variation in dynamic mechanical parameters of the prefabricated fractured sandstone specimens with different fracture thicknesses is shown in Figure 6.  
From Figure 6a, the results indicate that the dynamic compressive strength of the sandstone specimens decreased as the prefabricated crack thickness increased. The dynamic compressive strength of intact sandstone specimens was 99.17 MPa, which was higher than that of the prefabricated crack specimens. Compared with the intact specimens, the dynamic compressive strength of the sandstone specimens with a prefabricated crack thickness of 1.5-3.5 mm decreased by 11.43%, 22.97%, 24.82%, 35.18%, and 42.64%, respectively. The dynamic compressive strength and thickness of the prefabricated crack showed a linear negative correlation, and the fitting function is shown in Equation (2).  
\[\sigma_{d}=-14.804a+108.998\left(\mathrm{R}^{2}=0.970\right) \tag{2}\]  
Compared to the specimens with larger prefabricated crack openings, cracks with smaller openings were almost closed. At this time, the normal stress acting on the surface of prefabricated cracks was greater, and the frictional resistance generated on the crack  
Figure 5: Dynamic stress–strain curve of the prefabricated fractured sandstone specimens.  
Figure 6: Dynamic mechanical parameters of the prefabricated fractured sandstone specimens varied with crack thickness. (**a**) Dynamic compressive strength. (**b**) Dynamic strain. (**c**) Dynamic modulus of elasticity.  
surface also increased, thereby weakening the stress concentration at the crack tip. As the crack opening increased, the frictional resistance generated by the crack surface gradually decreased until it reached 0. The normal stress acting on the crack surface gradually transformed from frictional resistance to the driving force promoting crack propagation, resulting in a gradual decrease in the dynamic compressive strength of the specimen.  
Figure 6b shows that the dynamic strain of the pre-cracked sandstone specimens decreased gradually as the pre-crack thickness increased, and this became smaller. The dynamic strain of intact sandstone specimens was 5.51 \(\times\) 10\({}^{-3}\), and the dynamic strain of sandstone specimens with the prefabricated crack thickness of 1.5-3.5 mm was 4.19 \(\times\) 10\({}^{-3}\), 3.50 \(\times\) 10\({}^{-3}\), 3.45 \(\times\) 10\({}^{-3}\), 3.24 \(\times\) 10\({}^{-3}\), and 2.65 \(\times\) 10\({}^{-3}\), respectively. The dynamic strain of sandstone specimens was negatively correlated with the thickness of prefabricated cracks, and the fitting relationship is shown in Equation (3).  
\[\epsilon_{d}=-6.80a^{3}+5.115a^{2}-12.916a+14.346\ \ (\mathrm{R}^{2}=0.997) \tag{3}\]  
From Figure 6c, the results show that the dynamic elastic modulus of the sandstone specimens decreased as the crack thickness increased. The dynamic elastic modulus of the intact sandstone specimen was 47.94 GPa, and the dynamic elastic moduli of the sandstone specimen were 35.01, 31.93, 23.04, 18.21, and 12.61 GPa, respectively, when the prefabricated crack thickness was 1.5-3.5 mm. There was a linear negative correlation between the dynamic elastic modulus and the thickness of the prefabricated crack. The fitting function is shown in Equation (4).  
\[E_{d}=-11.703a+53.419\ \ (\mathrm{R}^{2}=0.984) \tag{4}\]  
When the fractured specimen is subjected to impact compression, the upper and lower surfaces of the crack first close. As the crack opens, the compressible space on the crack surface decreases. Therefore, the dynamic elastic modulus of the fractured sandstone specimen increases as the crack opens.