## 4 Ground Surface Settlement Law over the Shield Tunnel
### Shape of the Ground Surface Settlement Curve
#### 4.3.3 The Influence of burial Depth and Spacing on the Surface Settlement  
To study the influence of burial depth and spacing on the surface settlement curve, the cut-off standard of the single and double peaks are obtained for the surface settlement curve. A total of 16 different conditions are designed, as shown in Table 6. The cross section of the double-O-tube tunnel is shown in Figure 18. The left line tunnel is first to be excavated, followed by the right line tunnel.  
When the burial depth is relatively shallow, the tunnel spacing has a great impact on the ground settlement. When the tunnel spacing increases by 0.1 \(D\), the ground surface settlement subsequently decreases by approximately 23%, as shown in Figure 19a. As the burial depth increases, the ground settlement gradually increases, but the effect of tunnel spacing on the sensitivity of ground surface settlement decreases. When the tunnel spacing increases by 0.1 \(D\), the decrease in the ground surface settlement is within 7%. The range of the decrease for the maximum settlement clearly decreases during tunnel construction, but the influence range of the settlement increases, as shown in Figure 19b-d. This is due to the burial depth reaching a certain degree where the soil forms a soil arch effect, which slows down ground settlement [(39; 40)].  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Tunnel location** & & & \(\boldsymbol{L/D}\) & \\ \hline \(Z/D\) & (1.0, 0.5) & (2.0, 1.1) & (2.5, 1.5) & (3.0, 2.0) \\  & (1.0, 0.6) & (2.0, 1.2) & (2.5, 1.6) & (3.0, 2.1) \\  & (1.0, 0.7) & (2.0, 1.3) & (2.5, 1.7) & (3.0, 2.2) \\  & & (2.0, 1.4) & (2.5, 1.8) & (3.0, 2.3) \\  & & & (2.5, 1.9) & \\ \hline \hline \end{tabular}
\end{table}
Table 6: Parameters of the tunnel location.  
Figure 17: Ground surface settlement curves.  
For double-O-tube tunnels, the ground settlement curve is superimposed by the settlement caused by the two single tunnels. When the buried depth remains unchanged, the shape of the settlement curve will change as the tunnel spacing changes. Based on the above 16 conditions, single and double peak boundary points for the ground surface settlement curves caused by the construction of a double-O-tube tunnel are summarized. The cut-off function, shown in Equation (25), is obtained by fitting as follows:  
\[y=0.81x-0.24. \tag{25}\]  
Figure 19: Ground surface settlement under different buried depth and spacing: (**a**) 1.0 \(D\); (**b**) 2.0 \(D\); (**c**) 2.5 \(D\); (**d**) 3.0 \(D\).  
Figure 18: Layout of the double-O-tube tunnel.  
When the coordinate point is located at the lower side of the fitting curve, the ground surface settlement curve takes on a single peak state. Otherwise, the ground surface settlement curve takes on a two-peak form, as shown in Figure 20. According to the engineering case described here, \(Z/D=2.71\) and \(L/D=1.03\) are obtained, and the coordinate point is located at the lower side of the fitting curve. According to Equation (25), it can be predict that the ground surface settlement curve is a single-peak, which is consistent with the surface settlement curve determined from field measurements. This proves the correctness and rationality of the cut-off function proposed here.