## 4 Numerical Simulation
### Comparative Analysis of Numerical Simulation and Impact Test Results  
Figure 12a-c, respectively, expressed the axial force curve of rockbolt and the shear stress curve of I and II interface in PFC2D. As can be seen from the figure, the axial force of rockbolt gradually decreases from the load end to the other end, which is similar to the result in the laboratory test. Peak values appear at the shear stress curves of I and II interface in the latter half of the anchoring structure, and the shear stress is slightly larger than the laboratory data. Because strain gauge pasted numbers are few in the lab test, the measurement positions are adjacent to the interface, making it impossible to accurately measure the shear stress of interfaces. However, numerical simulations can obtain the axial force and shear stress of measured circles. The particles of the adjacent measured circle may exist at different bonding states, rotation capacity, contact force and so on, which affects shear stress. Shear stress fluctuation in PFC simulation is slightly large, and there is some error with laboratory test, but the curve obtained by PFC is more comprehensive, and variation tendency is similar to the result of the laboratory test. Figure 13 shows the relationship between the loading step and the total number of cracks. With loading, the total number of cracks in the anchorage structure increase gradually. The total number of cracks includes old cracks and new cracks, and it is a cumulative number. Figure 14 shows the debonding evolution process of the simulation test. In order to highlight the cracks, cracks are presented as red. Figure 14b-e corresponds to Figure 10 of the laboratory test. The whole impact process can be divided into three stages:  
Figure 11: Dynamic impact test model and measuring circle location figure of PFC2D. (**a**) Dynamic impact test model of PFC2D (**b**) Measuring circle plan. Figure 12: Axial force and interfacial shear stress distribution curve. (**a**) Distribution curve of bolt axial force (**b**) Shear stress curve of I interface (**c**) shear stress curve of II interface. Figure 13: Cracks number curve. Figure 14: Evolution process of anchorage debonding. Crack initiation stage (O-B), which is when the particles' stress is greater than the particles' bonding force, about 3000 steps, and the bonding force chain shows breakage. At this stage, the cracks generated are only 5% of the total number of cracks, and the growth rate of the crack is small and slow; II interface cracks are more than I interface, as shown in Figure 14b. In the crack coalescence stage (B-C), the number of cracks accounts for about 75% of the total number of cracks, about 5000 steps, and the crack accumulation curve is nearly vertical in a short time. When the crack tip produces concentrated stress, some force chains are broken and new cracks appear. The number of cracks generated in the latter half is more than the former half, and the number of cracks generated in the II interface is more than I interface, as shown in Figure 14c. In the debonding slip stage (C-E), the crack accumulation curve gradually depresses and the crack development rate slows down. When the loading step reaches 7500 steps, the crack accumulation curve is almost horizontal. This indicated that II interface generates many cracks, and the friction force cannot resist the impact load. The rockbolt-anchor agent moves along the impact load direction and fewer new cracks generate, as shown in Figure 14d. After loading 12,500 steps, a large displacement occurs in the rockbolt-anchoring agent, resulting in debonding failure; total cracks number is 793, as shown in Figure 14e. The results of the rockbolt debonding simulation test are similar to those of the laboratory impact test, but the displacement of the rockbolt and anchorage agent is small. The reasons are as follows: the bullet accelerates through electromagnetic force, and the bullet experiences the process of acceleration, uniform speed and deceleration in the laboratory test.