## 2 Engineering Background
### Analysis of Numerical Simulation Results
#### 3.3.2 Displacement of Bridge Piles  
Pile #2 and pile #3 nearest the shield tunnel (see Figure 7) were selected for analysis. Figure 9 shows the horizontal and vertical displacement and deformation of pile #2. It can be seen from the figure that the vertical displacement of pile #2 decreases with the deepening of the pile body, and the maximum vertical displacement is 2.1 mm at the pile top. This may lead to additional compressive stress in the vertical direction of the piles and reduce the bearing capacity of the piles. The horizontal deformation of the pile body is related to the relative position of the tunnel. The upper half of the pile body is deformed towards the tunnel side due to the volume loss during shield tunnelling, while the lower half of the pile body is deformed away from the tunnel side. The maximum horizontal displacement occurs at 5 m of the pile body, which is 0.5 mm. Similar to the deformation of pile #2, the vertical displacement of pile #3 decreases with the deepening of the pile body, and the maximum vertical displacement is 3.0 mm at the pile top. Within 18 m of the upper half of the pile, affected by the volume loss during shield tunnelling, it deforms towards the tunnel side, while the rest of the pile deforms away from the tunnel side. The maximum horizontal displacement occurs at 6 m of the pile body, which is 0.7 mm.  
Figure 10 shows the internal force of pile #2 after excavation. It can be seen from the figure that the axial force of the pile is \(-500\)--\(-4681\) kN, and the whole is in a compression state. Under the influence of negative friction within 7.5 m below the pile top, the pile body of the axial force tunnel increases with the deepening of the pile body, while within 7.5-23 m below the pile top, the pile body of the axial force tunnel decreases with the deepening of the pile body. Affected by the horizontal displacement of the pile body, the bending moment of the pile body in the direction perpendicular to the tunnel is more significant than that in the direction parallel to the tunnel. The maximum bending moment occurs at the 4 m position of the pile body, which is 83 kN\(\cdot\)m. Figure 10 also shows the internal force of pile #3 after excavation. It can be seen from the figure that the axial force of the pile is \(-500\)--\(-4577\) kN, and the whole pile is under compression. Under the influence of negative friction within 5m below the pile top, the pile body of the axial force tunnel increases with the deepening of the pile body, while within 5-23 m below the pile top, the pile body of the axial force tunnel decreases with the deepening of the pile body. The maximum bending moment of the pile body is 138 kN\(\cdot\)m, which occurs at the position of  
Figure 8: Map of the entire model settlement.  
16m of the pile body. Generally speaking, the stress and displacement of pile #3 are similar to that of pile #2, but the stress and displacement are more significant than that of pile #2.  
Due to the grouting reinforcement treatment of the soil around the pile body, the stiffness of the surrounding soil layer is improved so that the surface settlement and the horizontal and vertical displacement of the pile can meet the deformation control standard. In the process of side crossing bridge pile excavation of the shield tunnel, the shield tunnelling attitude is controlled, and the tunnel face pressure is controlled to achieve continuous, balanced and stable construction. At the same time, synchronous grouting and grouting behind the wall is strengthened to avoid significant disturbance to the stratum, and the assembly quality of segments is strictly guaranteed.  
Figure 9: Deformation of piles #2 and #3. (**a**) Horizontal displacement. (**b**) Vertical displacement.  
Figure 10: Internal forces in piles #2 and #3. (**a**) Axial force. (**b**) Bending moment parallel to tunnel direction. (**c**) Bending moment in vertical tunnel direction.