# A New Design Method of Shield Tunnel Based on the Concept of Minimum Bending Moment
## 4 Cross-Section Design and Case Analysis for Minimum Bending Moment Shield Tunnel in Soft Soil Area
### Case Analysis for Minimum Bending Moment Shield Tunnel  
The shield tunnel of one metro line in Shanghai passes through soft soil 3, 4, 5, and 6, as shown in Table 1, all of which feature a small soil-resistance coefficient, so it is important to consider reducing the bending moment as much as possible. According to the line design, the thickness of the overlying soil ranged between 6.5 and 28.8 m, combined with the geological investigation data of the tunnel, several designs have been made based  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Engineering Condition** & \(\mathbf{P_{1}}\) & \(\mathbf{P_{2  
on the different working conditions for the shield tunnel of this metro line. The cross-section parameters of the zero bending moment shield tunnel under different working conditions were obtained as presented in Table 5. Finally, the cross-section of the shield tunnel conditional on the minimum bending moment is shown in Figure 15. The shape of the cross-section of the shield tunnel conditional on the minimum bending moment was similar to a vertical ellipse. The finite element software Midas GTS NX was adopted for the numerical simulation analysis in order to compare the bending moments of two differently shaped shield tunnel cross-sections due to the surrounding earth pressure shown in Figure 15 (take the bending moment for the tension on the inner side of the tunnel as positive). With reference to one metro line in Shanghai that travels through soft soil areas, simulation analysis was conducted for four working conditions, where the thickness of the overlying soil of the shield tunnel was 7 m, 13 m, 19 m, and 25 m. Due to the constant cross-section shape of the shield tunnel, the 2D model was utilized to simulate the cross-section bending moment [29; 30]. The 2D plane strain model was utilized to simulate the different soils, and the soil constitutive model was a modified Mohr-Coulomb model. The soil parameters and material properties were the same as those of the soft area of the above-mentioned metro line in Shanghai, as shown in Table 6. The beam element model was utilized to simulate the tunnel lining with reference to the Shanghai metro shield tunnel in light of the  
Figure 15: Comparison between minimum bending moment shield tunnel cross-section and circular shield tunnel cross-section in Shanghai. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Engineering** & & & & & &  
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**Condition** & & & & & & & & & & & & & \\  
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dimension and mechanical parameters, as shown in Figure 11. The interaction between the tunnel and the soil was simulated using a compressed elastic spring, as shown in Figure 16, the vertical elliptical cross-section can be taken as an example. The soil model of this article was designed to be 80 m wide and 40 m tall, constituted by three types of soil. From the top to the bottom, the soils were clay, mucky silty clay, and mucky clay and the thickness of the soils were 4.5 m, 11.5 m, and 29 m, respectively. The soil model was divided into 17,055 mixed grids. The radius of the circular cross-section tunnel model was 3 m and was divided into 38 grids through size control. The long-axis of the vertical elliptical cross-section tunnel model was 6 m long and the short-axis was 4.4 m long. It was divided into 62 grids through size control. The grid division of the numerical simulation model is shown in Figure 17.  
The maximum bending moment and the minimum bending moment of the two differently shaped cross-sections of the tunnel under the different working condition were obtained using the simulation analysis, as shown in Table 7. It can be learnt through Table 7 that the bending moments of the two differently shaped cross-sections increased