## 4 Parametric Analyses
### Influence of the Tunnel Geometric Parameters  
The impact of the tunnel radius, ring width, and lining thickness on the LEBS of the shield tunnel are investigated under the combined action of bending moment \(M\) = 40 MN\(\cdot\)m and residual jacking force. The value ranges of the tunnel geometry parameters are based on the conventional tunnel, and the remaining parameters are shown in Table 1.  
As shown in Figure 4(a), when the residual jacking force is 0 MN, the LEBS of the shield tunnel increases with increasing tunnel radius, whereas the effective ratio of LEBS decreases almost linearly from 0.0724 to 0.0506. When the residual jacking force is small (i.e., N less than 6 MN), the effective ratio of LEBS decreases with increasing radius, while it increases with increasing radius as the N is more than 6 MN. As shown in Figure 4(b), when the tunnel radius increases from 3 m to 4.4 m, the maximum increase in the LEBS of the shield tunnel reaches 387.4%.  
The study shows that the LEBS and the effective ratio of LEBS increase nonlinearly with increasing residual jacking force and eventually tend to a stable value. Under the same residual jacking force (i.e., axial pressure), the larger the tunnel radius, the greater the LEBS and the effective ratio of LEBS.  
Figure 4: Effects of bending moment on the LEBS.  
Figure 6 shows that the LEBS and the effective ratio of LEBS for the shield tunnel increase linearly with the ring width, nonlinearly with increasing residual jacking force, and eventually tend to stabilize.  
As shown in Figure 7, when the residual jacking force is 0 MN, the effective ratio of LEBS decreases with increasing lining thickness, the \(\eta\) decreases from 0.1143 to 0.0335, while the LEBS of the shield tunnel increases with increasing lining thickness from 6.2 \(\times\) 10\({}^{7}\) kN\(\cdot\)m\({}^{2}\) to 7.26 \(\times\) 10\({}^{7}\) kN\(\cdot\)m\({}^{2}\). Figure 7b shows that the LEBS increases from 17.1% to 300% with increasing residual jacking force as the lining thickness increases from 0.2 m to 0.8 m. There is a nonlinear proportional relationship between the LEBS, the effective ratio of LEBS, and the residual jacking force. When the N is greater than 12 MN, the LEBS increases nonlinearly with the residual jacking force.  
Figure 7c clearly shows the change rule of the LEBS with lining thickness. The LEBS of the shield tunnel increase from 6.2 \(\times\) 10\({}^{7}\) kN\(\cdot\)m\({}^{2}\) to 7.26 \(\times\) 10\({}^{7}\) kN\(\cdot\)m\({}^{2}\) as lining thickness increases, but the increment of LEBS gradually decreases. According to the slope change point of the LEBS and the effective ratio of LEBS for the shield tunnel, it is suggested that  
Figure 5: Effects of tunnel radius on the LEBS.  
Figure 6: Effects of ring width on the LEBS.  
the lining thickness should be approximately 0.35 m when the tunnel is subjecting a small bending moment. Compared with similar projects at home and abroad, the tunnel segment lining thickness in China is greater than that in European countries but less than that in Southeast Asian ones [26].  
The results show that the LEBS of shield tunnels is variable stiffness, and the influential order on the LEBS of shield tunnels is the tunnel diameter > lining thickness > ring width. When the effective ratio of the LEBS is greater than or equal to 0.85, it is not related to the ring width and lining thickness.