# Analysis and Design of Protection Device for Anchor Cable Pull-Out in High-Stress Roadways
## 4 Numerical Simulation of Impact Protective Devices for Anchor Wire Breaking
As shown in Figure 17, the maximum elastic strain of the spring was 6.1% and maximum deformation was 0.087 m. The lower part of the spring of the protective device was deformed considerably, whereas the upper part was hardly deformed. The limit impact load of the protective device with Specification I was only 70 m/s. The lower part of the spring was rapidly stretched and deformed after being hit, and the diameter was reduced, due to the thin wire diameter of the spring. The inner wall of the spring was locked up upon contact with the outer wall of the anchor end, leading to the tensile failure of the lower part of the spring. The upper part was hardly stretched, significantly weakening the energy absorption performance of the spring, which was considerably less than the energy absorption data measured via the spring tensile test. Increasing the wire diameter of the spring can slow down the stretching speed of the spring and enhance its energy absorption performance during stretching. Anchor protective device with Specification II: At an anchor wire breaking and ejection speed of 160 m/s, the maximum principal stress of the protective devices is shown in  
Figure 16: Diagram of the maximum shear force distribution of the protective device. Figure 17: Distribution diagram of total deformation and equivalent elastic deformation. Figure 18, the maximum shear stress is displayed in Figure 19, and total deformation and equivalent elastic deformation are exhibited in Figure 20.  
Figure 19: Diagram of the maximum shear force distribution of the protective device. Figure 20: Distribution diagram of total deformation and equivalent elastic deformation. of the peak shear stress was about 4330 MPa, resulting in shear failure. The middle and lower sections of the spring experienced local shear failure, while the upper and middle sections displayed complete shear failure. At complete shear failure, the cross-section stress of the spring presented an asymmetric annular distribution. The maximum shear stress at the center of the cross section was about 891 MPa, and the maximum shear stress at the outer ring was around 8190 MPa. As shown in Figure 20, the maximum elastic strain of the spring was approximately 11.4%, and maximum deformation was 0.27 m. The middle and lower parts of the spring of the protective device were deformed considerably, while the upper part was not. The ultimate impact load of the anchor protective device with Specification II was 160 m/s, which was considerably higher than the anchor protective device with a wire breaking and ejection speed of 48 m/s. As the spring wire diameter of the protective device increased from 4 mm to 5 mm, the elastic coefficient of the spring was improved. After the protective device was hit, the large deformation of the lower part of the spring was improved, and the middle part of the spring was not locked up with the anchor end, avoiding stress concentration in the lower part of the spring that will result in failure. The tensile deformation of the middle section of the spring absorbed a large amount of impact kinetic energy, which increased the ultimate impact load of the protection device from 70 m/s to 160 m/s, meeting the protection requirements for anchor wire breaking and ejection. However, the upper section of the spring was still locked up upon contact with the anchor end, limiting the energy absorption effect of the spring. In summary, spring texture  
Figure 12:0 Distribution diagram of total deformation and equivalent elastic deformation. Figure 12:1 Diagram of the maximum shear force distribution of the protective device. can be improved or spring wire diameter can be increased to improve its elastic coefficient further. In addition, spring diameter and spacing between the spring and the anchor can be increased to prevent the upper spring section from being locked up upon contact with the anchor, further improving the energy absorption effect of protective devices.