# 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  
Due to the limitations of tensile tests on protection devices and the absence of dynamic impact verification, dynamic simulations of the anchor cable protection device were executed using ANSYS Workbench software. Initially, the model was constructed utilizing Rhino software and subsequently imported into ANSYS Workbench software. The model comprised a total of 50,772 units and 25,396 nodes. The explicit dynamics module was employed to solve the model. Contrasting with the tensile test in Section 3, which involves static load tension, ANSYS Workbench software simulates the impact of dynamic loading. Given that dynamic loading impacts  
Figure 8: Force–displacement curves of the protective devices with a wire diameter of 4 mm. Figure 9: Force–displacement curves of the protective devices with a wire diameter of 5 mm. necessitate superior material strength properties, it is anticipated that the energy absorbed by the spring in the numerical simulation will be less than that in the test. The protective device of Specification I had a 65 Mn spring with a wire diameter of 4 mm and 16 turns. The protective device of Specification II had a 65 Mn spring with a wire diameter of 5 mm and 13 turns. The other structural materials of the model were structural steel. Considering that 65 Mn conformed to the GB/T61 standard, structural steel was the default material of ANSYS, and the permissible shear stress coefficient of the materials was 0.7 [31]. The boundary conditions were the roof and the fixed supporting points on the roof. Different initial velocities were applied to the cross section of the broken anchor wire above the roof as the load was applied. The length and diameter of anchor wire breaking and ejection were 0.3 m and 6 mm, respectively. The numerical simulation results are analyzed in accordance with first strength theory and third strength theory to determine whether the anchor cable protection device is damaged. The geometric structure and the load and constraint positions of the anchor cable protection device are shown in Figure 10. The flowchart of the ANSYS Workbench simulation is shown in Figure 11. The material parameters of the anchor cable protection device are provided in Table 1. The technical parameters of the anchor cable protection device are listed in Table 2.  
The ejection energy was 163 J at an anchor wire breaking and ejection speed of 70 m/s. In accordance with first strength theory and combined with Figure 12, stress concentration was determined to occur on the surface of the middle spring section. The peak principal stress was about 2253 MPa, indicating tensile failure, while the local principal stress was 884 MPa, reflecting no failure. The cross section of the spring demonstrated local tensile failure, and stress in the middle section of the spring was distributed in a ring shape, which was small inside and large outside. The principal stress in the center of the cross section was about 728 MPa, and the principal stress in the outer ring was about 4565 MPa. That is, the spring was intact inside, and tensile failure occurred outside. In accordance with third