## 5 Results and Analysis
### The Results of the Impact on Vertical Displacement  
The vertical displacement variations of four points, namely, the horizontal direction nodes N61174 (near end) and N59140 (far end) and the vertical direction nodes N5792 (upper end) and N7569 (lower end), in the circumferential cross-section under the three different excavation sequence plans are plotted in Figure 11. Since the existing railway tunnel has been completed during the actual excavation (Plan 1), and the soil removal process (Plan 2) has been finished, these two conditions are set to have zero displacement in the numerical software. The numerical analysis only considers the phase starting from diaphragm wall construction (Plan 3), corresponding to the actual construction conditions. Figure 11: Comparison chart of vertical displacement variation at various nodes for different excavation sequence scenarios. **(a)** Node: 61174, **(b)** Node: 5792, **(c)** Node: 59140, **(d)** Node: 7569. Figure 10: Radial analysis section selection diagram. Although the different steps of each construction phase represent different meanings in the graph, the results show a consistent trend in the upward vertical displacement of tunnel nodes and their relative magnitudes throughout the entire construction period across different excavation plans. Sequential excavation (Plan 1) exhibits lower vertical displacement in the first half of the construction period. This is because the plan primarily focuses on excavating the circular junction well at the initial stage, resulting in a relatively small amount of soil removal and, consequently, a smaller degree of uplift in the nearby tunnel. However, in the second half of the construction period, as the volume of soil removal increases, the vertical displacement also increases. Simultaneous excavation (Plan 2) maintains relatively high vertical displacement throughout the entire excavation period. This may be attributed to the simultaneous excavation on both sides, leading to a relatively large volume of soil removal. Comprehensive excavation (Plan 3) combines the characteristics of the first two plans. In the early stages, it is similar to simultaneous excavation, and then it switches to sequential excavation. This results in a vertical displacement curve showing a trend similar to but not entirely consistent with the first two plans at different stages. The variation in vertical displacement is related to the method and volume of soil excavation. In a given construction phase, a smaller volume of soil excavation may lead to lower vertical displacement, while a larger volume may result in increased vertical displacement. The comprehensive excavation plan (Plan 3), combining the characteristics of the first two plans, may have advantages in certain situations. It adopts simultaneous excavation in the early stages, allowing for the earlier completion of a portion of the project. It then switches to sequential excavation to reduce later-stage vertical displacement. This integrated approach may offer more flexibility in balancing project progress and vertical displacement. The observations in Figure 12 provide important spatial insights for evaluating the impact of soil excavation on nearby tunnels. In terms of overall vertical displacement, the deformation trends of circumferential cross-section points under the same plan are generally consistent, showing an overall uplift trend. However, it is important to note that soil excavation on one side of the foundation pit may have different effects on stress distribution and displacement. Therefore, in specific spatial locations, there may be variations in the uplift values of each node. In the horizontal direction, the vertical uplift value of node N59140 on the side closer to the foundation pit is relatively smaller compared to node N61174 on the far side, with a difference of 13.02% in uplift values.