## 3 Three-Dimensional Numerical Model
### Existing Tunnel Operation  
The overall displacement cloud, overall vibration velocity cloud, and Von Mises stress cloud of the rock layer under train dynamic loading were extracted and analyzed for the purpose of determining the area affected by the dynamic loading of train operation in existing tunnels. Figure 16 shows a cloud diagram of the overall displacement of the rock formation under the dynamic load of the train. The overall displacement of the rock layer under the dynamic train load is along the axis of the existing tunnel. The influence range is largest in the center of the dynamic train load application area, the symmetry decreases to both sides, and the overall course is ellipsoidal. Taking the section at the center of the dynamic load application area of the existing tunnel as the benchmark, three impact zones are quantitatively described: the first zone is distributed within 5 m below the track surface, with an irregular semicircular shape and an overall displacement of 0.10-0.14 mm; the second zone is distributed within 40-50 m around the tunnel section, with an irregular ellipsoidal shape and an overall displacement of 0.07-0.10 mm; the third zone is distributed within 40-50 m around the tunnel section, with an irregular ellipsoidal shape and an overall displacement of 0.10 mm; and the third zone is distributed in the tunnel section, with an overall displacement of 0.10 mm. The third zone is distributed in the range of 70-100 m around the tunnel section, with an irregular oval shape and an overall displacement of 0.69-0.07 mm. As shown in Figure 17, the overall vibration velocity of the rock layer under the dynamic load of the train is shown in the cloud diagram. In Figure 17, it can be seen that the overall vibration velocity of the rock layer under dynamic train loads varies irregularly along the axis of the existing tunnel, but the overall influence area does not change much. Taking the cross-section at the center of the dynamic load application area of the existing tunnel as the reference, three impact zones are quantitatively described: the first zone is distributed in the track surface area, and the overall vibration velocity is in the range of 1.29-1.94 m/s; the second zone is in the range of 6 m below the track surface, with the shape of an irregular semicircle, and the overall vibration velocity is in the range of 0.34-1.29 m/s; and the third zone is in the range of 10 m below the track surface, with an  
Figure 16: Clouds of the overall displacement of the rock layer under the dynamic load of the train. irregular semicircle, and the left side wall is in the range of 3 m. The third zone is in the area of an irregular semicircle in the range of 10 m below the track surface, the area is in the range of 3 m on the left side wall, and the overall vibration speed is 0.18-0.34 m/s. The Von Mises stress cloud of the rock formation under the dynamic train load is shown in Figure 18. In Figure 18, it can be seen that the Von Mises stresses under dynamic train loads change irregularly along the axis of the existing tunnel, but the overall influence area does not change much. Taking the section at the center of the dynamic load application area of the existing tunnel as the reference, three impact zones are quantitatively described: the first zone is distributed in the track area, and the Von Mises stresses are in the range of 0.18-0.30 MPa; the second zone is in the irregular semicircular area within 3 m below the track surface and in the area within 2 m of the left side wall, and the Von Mises stresses are in the range of 0.05-0.18 MPa; and the second section is in the irregular semicircular area within 5 m below the track surface and the area within 3 m on the left side wall, and the Von Mises stress is 0.03-0.05 MPa.