## 3 Three-Dimensional Numerical Model
### New Tunnel Blasting  
The overall displacement cloud, overall vibration velocity cloud, and Von Mises stress cloud of the rock layer under blasting action were extracted and analyzed in order to determine the area affected by blasting dynamic loads in the new tunnel excavation. The Von Mises stress cloud can accurately represent the stress distribution in the formation when only tensile stresses are considered [32].  
Figure 13 shows the overall displacement of the rock layer under blasting load. As can be seen from Figure 13, with the centerline of the tunnel section as the reference point, the overall displacement of the rock layer under the dynamic blasting load is divided into three zones: the first zone is a circle with a diameter of 19.72 m centered on the reference point, and the overall displacement is 0.88\(\sim\)2.11 mm; the second zone is a circle with a diameter of 27.09 m, and the overall displacement is 0.35\(\sim\)0.88 mm; the third zone is a circle with a diameter of 35.24 m, and the overall displacement is 0.35\(\sim\)0.18 mm.  
As shown in Figure 14, the overall vibration velocity of the rock layer under blasting load is shown in the cloud diagram. As can be seen in Figure 14, with the centerline of  
Figure 12: Combination of track surface settlement curves of the existing tunnels with different timing steps.  
Figure 13: Clouds of the overall displacement of the rock layer under blasting loads.  
the tunnel section as the reference point, the overall vibration velocity of the rock layer under the dynamic blasting load is divided into three zones: the first zone is a circle with a diameter of 19.72 m centered on the reference point, and the overall vibration velocity is in the range of 2.53-6.07 cm/s; the second zone is a circular domain extending outward from the circular domain of the first zone to a circular domain with a diameter of 25.63 m, and the overall displacement is in the range of 1.01-2.53 cm/s; the third zone is a circular domain extending outward from the circular domain of the second zone to a circular domain with a diameter of 35.24 m; and the third section is the circular domain of the second section extended outward to the circular domain with a diameter of 35.24 m, and the overall displacement is in the range of 0.51-1.01 cm/s.  
The Von Mises stress cloud of the rock formation under blasting load is shown in Figure 15. As can be seen in Figure 15, with the centerline of the tunnel section as the reference point, the Von Mises stress in the rock layer under dynamic blasting load is divided into three zones: the first zone is a circle with a diameter of 19.72 m centered on the reference point, and the Von Mises stress is in the range of 1.25-3.01 MPa; the second zone is a circle extending outward from the circle in the first zone to a circle with a diameter of 25.63 m, and the Von Mises stress is in the range of 0.50-1.25 MPa; and the third zone is a circle in the second zone, and the Von Mises stress is in the range of 0.50-1.25 MPa. The second section is the circular domain of the first section extending outward to 25.63 m in diameter, and the Von Mises stress is in the range of 0.50-1.25 MPa; the third section is the circular domain of the second section extending outward to 30.03 m in diameter, and the Von Mises stress is in the range of 0.25-0.50 MPa.  
Figure 14: Clouds of the overall vibration velocity of the rock formation under blasting loads.  
Figure 15: Von Mises stress cloud of the rock formation under blasting loads.  
Considering the overall displacement map, overall vibration velocity map, and Von Mises stress impact area of the rock layer under the action of blasting dynamic load, combined with the impact characteristics of blasting load in tunnel excavation, it is determined that is it best to take the center of the datum point in the tunnel section and the circular domain with a diameter of 25.63 m as the impact area of blasting dynamic load in the excavation of the new tunnel.