## 3 Numerical Simulation Analysis
### Model Verification
Area 1 is the crater region; zone 2 is the radial crack zone; zone 3 is an oblique crack zone extending along the penetration direction; zone 4 is the compaction zone and tunnel zone; and zone 5 is the back crater area caused by scouring. Figure 9a,b are divided into four areas, which are the same as the first four areas in Figure 8.  
Figure 8a shows the red sandstone target. When the projectile entered the target at certain angles, the penetration trajectory was tilted. Figure 8a depicts a large red sandstone particle falling off the blue frame, which was due to the large crack indicated by the black arrow at the tail of the target that resulted in the fragmentation of some red sandstone particles during target cutting. In the process of target cutting, due to the cracks under the target surface and the soft material of red sandstone, the hole diameter and depth of the target were increased. Figures 8 and 9 show that in zone 1 of the target, after the projectile penetrated the red sandstone and limestone targets, a more standard conical crater was formed. However, the opening diameter in the simulation model was slightly smaller than that of the test results because the test target fell off and was damaged during the target cutting process. Figures 8 and 9 show that in zone 2 of the target there were many cracks in the red sandstone target, but most of the cracks were narrow, whereas there were few cracks in the limestone target, but these cracks were wide. Compacted cracks were found in zone 2 of the red sandstone target, as shown by the red arrow in Figure 8a. The numerical simulation was in good agreement with the number, trend and position of cracks in the test results. Figures 8 and 9 show that in zone 3 of the target, the number of cracks along the penetration direction in the limestone target was increasingly obvious. The numerical simulation agreed well with the trend and position of cracks in the test results, but the number of cracks was slightly different. Zone 4 in Figures 8b and 9b shows that the diameter of the compacted zone of red sandstone was significantly larger than that of limestone because the red sandstone material was easier to crush and damage at the same speed. The diameter of the compacted zone was similar to that of the test results. In Figure 8a, the upper part of zone 5 became detached during target cutting and the lower part had two oblique cracks along the penetration direction, which caused the red sandstone near the penetration hole to fall off and form a back crater area in the red sandstone. There were two short cracks along the penetration direction in the upper/lower part of zone 5 in Figure 8b, which is very similar to Figure 8a. Since the limestone target was not penetrated, there was no back crater area. In summary, after the projectile penetrated the rock, the cracks formed on the limestone target were few and wide, whereas the cracks formed on the red sandstone target were dense and fine. The diameter of the compaction zone of red sandstone was larger than that of limestone, and the damage to the penetration path was more serious. The penetration resistance of red sandstone was obviously weaker than that of limestone, but the surface collapse area of the red sandstone target was smaller. In the process of penetration, red sandstone was more sensitive to the attitude of the projectile. The numerical simulation results were very similar to the experimental results, which shows the reliability of the material parameters and constitutive equation. The Forrestal penetration formula was also applicable to the penetration calculation of red sandstone and limestone. When the projectile penetrated red sandstone at low speed and limestone at medium speed, the three results demonstrated the best agreement, and the error was no more than 5%.