## 2 Numerical Model of Centrifuge Test
### Numerical Results  
The ground and tunnel deformations as measured from the centrifuge tests were compared and discussed with the numerical simulation results in terms of prototype units. The tunnel cover depth, \(H_{c}\), was used as a normalized parameter to normalize the calculation results.  
\begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Value** \\ \hline \(\gamma/\mathrm{kN}\cdot\mathrm{m}^{-3}\) & 15.5 \\ \(E_{50}^{ref}/\mathrm{MPa}\) & 20.0 \\ \(E_{oct}^{ref}/\mathrm{MPa}\) & 20.0 \\ \(E_{ut}^{ref}/\mathrm{MPa}\) & 60.0 \\ \(m\) & 0.5 \\ \(v\) & 0.2 \\ \(c^{\prime}/\mathrm{kPa}\) & 2 \\ \(\varphi^{\prime}/^{\circ}\) & 35 \\ \(\psi/^{\circ}\) & 6 \\ \hline \end{tabular}
\end{table}
Table 1: Foundation soil material parameters.  
Figure 2: Schematic diagram of the numerical model.  
Figure 4 shows the measured and computed ground settlement of sections A-A and B-B (shown in Figure 2). It can be seen that the computed profiles of ground surface settlement agree reasonably well with the measurements. The maximum settlement occurs near the edge of the basement, with a settlement of 0.06% \(H_{\rm c}\). The settlement decreases gradually with increasing distance, with a settlement of 0.02% \(H_{\rm c}\) at a distance of 2.0 \(H_{\rm c}\) from the wall edge.  
Figure 5 shows the measured and computed soil heave at the formation level of the basement. It can be seen that the computed profiles of soil heave agree reasonably well with the measurements when the basement depth is shallow (\(H_{\rm e}\) = 3.1 m, 6.2 m). However, when the basement depth, \(H_{\rm e}\), is 9 m, there are some differences between the measured and computed soil heave. The soil heave at the basement center is 0.099% \(H_{\rm c}\) (the measured heave is 0.08% \(H_{\rm c}\)) and decreases to 0.096% \(H_{\rm c}\) (measured heave is 0.07% \(H_{\rm c}\)) at 0.4 \(L\) away from the basement center. According to the computed results, the variation in the soil heave is relatively small within 0.4 \(L\) from the basement center but decreases rapidly beyond this distance. The heavy fluid (ZnCl\({}_{2}\)) in the centrifuge model test is isotropic, and the stresses in the ZnCl\({}_{2}\) solution are isobaric. However, the ratio of horizontal to vertical stresses  
Figure 4: Ground surface settlement behind the diaphragm wall.  
Figure 3: Schematic diagram of the calculated working conditions.  
in the sand is less than \(1\) in the numerical simulation. So, there are some relatively large differences between the measured and computed results.  
Figure 6 shows the measured and computed vertical deformation of the tunnel with excavation depth. It can be seen that the computed profiles of vertical deformation agree reasonably well with the measurements. The vertical deformation of the tunnel increases with increasing excavation depth. The non-linear relationship of the computed vertical deformations is more obvious than the measurements. Within the scope of the basement, the closer the measurement point is to the diaphragm wall, the greater the reduction in vertical deformation of the tunnel, while outside the scope of the basement, the vertical deformation of the tunnel is relatively small. Finally, the vertical deformation of the tunnel decreases to zero at a distance of 1.5 \(L\) away from the basement center, which indicates that the main influence area of basement excavation on the lower tunnel is 1.5 times the length of the basement.  
Figure 5: Soil heave at the formation level of the basement.  
Figure 6: Vertical displacement along the tunnel.  
Comparisons of the measured and computed results of the ground surface settlements, soil heave at the formation level of the basement, and vertical displacement along the tunnel indicate that the numerical model is reasonably accurate in its analysis of the influence of basement excavation on the existing tunnel.