## 3 Analysis of Influencing Factors
### Influences of Basement Plan Dimensions  
In this section, the vertical deformation of the tunnel for six different cases (basement length \(L\) = 36 m, 63 m, 90 m and basement width \(B\) = 36 m, 63 m, 90 m) is analyzed. Figure 8 shows the vertical deformation of the tunnel for different basement plan dimensions. It can be seen that tunnel vertical deformations increase significantly with the increase in \(L\) or \(B\). However, for the same increment, the vertical tunnel deformation induced by increasing \(L\) is significantly larger than that induced by increasing \(B\). The scope of vertical tunnel deformation due to basement excavation is expanded significantly by an increase in \(L\), but remains almost constant with the increase in \(B\). Although the scope of vertical deformation is expanded, the ratio \(X/(L/2)\) gradually decreases and tends to 0.5 \(L\). The  
Figure 7: Schematic diagram of the basement–tunnel interaction problem: (**a**) cross section 1; (**b**) cross section 2.  
results indicate that the diaphragm wall is a constraint on tunnel deformations, but this constraint gradually weakens with the increase in \(L\). Figure 9 shows the relationship between the maximum vertical deformation of the tunnel, \(\mu_{\text{max}}/H_{\text{c}}\), and basement dimensions. The maximum vertical deformation of the tunnel increases with the increase in \(L\) or \(B\). But the increase in the maximum deformation due to \(L\) is larger than that due to \(B\). When the ratio of \(L/H_{\text{c}}\) or \(B/H_{\text{c}}\) is less than 3, the maximum vertical deformation increases rapidly, while the change is relatively small for ratios larger than 3, and it keeps constant for ratios larger than 7. Therefore, when the ratio of \(L/H_{\text{c}}\) is larger than 7, the problem of the maximum vertical tunnel deformation below the center of the basement can be considered a planar problem. Figure 8: Vertical deformation of the tunnel for different basement plan dimensions: (**a**) vertical deformations along the tunnel; (**b**) normalized vertical deformations along the tunnel. Figure 9: Relationship between maximum vertical tunnel deformation and basement plan dimensions. Influence of the Tunnel Cover Depth, \(H_{\rm c}\), and the Basement Excavation Depth, \(H_{\rm e}\)  
The maximum vertical deformation of the tunnel \(\mu_{\rm max}\) affected by the basement depth, \(H_{\rm e}\), for the five different tunnel cover depths (\(H_{\rm c}\) = 12 m, 24 m, 36 m, 48 m, 60 m) is analyzed. Figure 10 shows the maximum vertical deformation of the tunnel, \(\mu_{\rm max}\), with different \(H_{\rm c}\) and \(H_{\rm e}\). It can be seen that the maximum vertical deformation of the tunnel increases with increasing \(H_{\rm e}\) and decreases with increasing \(H_{\rm c}\). The non-linear relationship between maximum vertical deformation and \(H_{\rm e}\) becomes more significant with increasing \(H_{\rm c}\). At the same \(H_{\rm e}\), the tunnel with larger \(H_{\rm c}\) produces smaller maximum vertical deformation. This is due to a larger \(H_{\rm c}\) corresponds to a smaller relative excavation depth. The ratio of basement depth, \(H_{\rm e}\), to tunnel cover depth, \(H_{\rm c}\), is defined as the unloading ratio, \(\alpha\), which describes the degree of excavation depth above the tunnel. The value of \(\alpha\) ranges from 0 and 1, with a higher \(\alpha\) indicating a greater excavation depth above the tunnel. Figure 11 shows the relationship between the maximum vertical deformation of tunnel, \(\mu_{\rm max}\), and the unloading ratio, \(\alpha\). It can be seen that the vertical deformation increases with increasing \(\alpha\). There exists a critical unloading ratio \(\alpha\) of 0.6. The vertical deformation of the tunnel shows a linear increase with increasing \(\alpha\) for a value of \(\alpha\) less than 0.6, while it increases rapidly for an \(\alpha\) larger than 0.6.