## 3 Numerical Simulation Analysis
### Parameter Analysis  
#### 3.3.1 Effect of Impact Velocity on Penetration Performance  
The impact velocity range of the projectile was 600 m/s-1200 m/s and the interval between two adjacent impact velocities was 100 m/s. The damage to the target after penetration is shown in Figure 10. The depth versus time curves, penetration speed versus time curves and acceleration versus time curves of the projectile penetrating red sandstone and limestone are shown in Figures 11 and 12, respectively. Figure 10 shows that after the projectile penetrated the rock target, there were obvious crater regions, tunnel areas, compaction areas, plug blocks and cracks on the target. When the projectile hits the target, it produced a strong impact force. The projectile was squeezed into the target, resulting in the fragmentation of nearby rocks into fine particles. Then, it was squeezed between the projectile and the undamaged target and compacted to form a compaction area (red area in the figure). As the impact force of the projectile decreased with increasing penetration depth, the farther away it was from the projectile surface, the smaller the diameter of the compaction area. With increasing projectile impact velocity, the diameter of the compaction area of the red sandstone target increased slightly, and the diameter of the compaction area of the limestone target obviously increased. The diameter of the compaction area of red sandstone was generally larger than that of limestone. This was because the strength of red sandstone was less than that of limestone, and the material had a granular clastic structure, which was easier to crush. With increasing projectile impact velocity, the penetration depth of the projectile increased gradually. When the projectile impact velocity was greater than 1000 m/s, the projectile penetrated the red sandstone target. There were large cracks across the entire target around the tunnel area, and the number of cracks gradually increased with increasing projectile impact speed. There were fewer large cracks in the red sandstone target than in the limestone target because the red sandstone material had a better energy absorption effect and did not easily form large cracks. Figure 10 shows that when the impact speed of the projectile was 1141 m/s, the projectile penetrated the 1 m thick limestone target, an obvious blanking block was formed behind the target, and the crack extended behind the target. Figures 11a and 12a show that the limit velocity of the projectile penetrating the 1 m thick red sandstone target was 900-1000 m/s, whereas the limit velocity of the projectile penetrating the 1 m thick limestone target was 1100-1200 m/s. Taking the intermediate values for their limit speed, the anti-aggressive ability of limestone compared with that of red sandstone increased by 23.8%. Figures 11b and 12b show the curves of the velocity of the projectile penetrating the red sandstone and limestone targets with time. The curves of the projectile penetrating velocity with time were basically similar. When the impact velocity was 1000 m/s, the residual velocity after the projectile penetrated the target was 146 m/s; when the impact velocity was 1107 m/s, the residual velocity after the projectile penetrated the target was 220 m/s. Figures 11c and 12c show the time-varying curves of the acceleration of the projectile penetrating the red sandstone and limestone targets with time. The time-varying curve of the acceleration of the projectile penetrating the red sandstone target was similar to that of the limestone target. In the process of penetration, the acceleration of the projectile first increased sharply, then decreased at a faster speed, and then decreased slowly to 0. Regardless of the impact velocity of the projectile, the maximum acceleration of the  
Figure 12: Data of projectile penetration into limestone target: (**a**) penetration depth versus time curve; (**b**) penetration velocity versus time curve; (**c**) penetration acceleration versus time curve.