## 4 Structural Design
### Sensitivity Analysis of Key Load Parameters  
In the shield tunnel design, the deformation and internal forces of the structure stand as crucial design indicators. Moreover, the influence of surrounding environmental disturbances on structures is becoming increasingly important [47; 48]. In this Section, the influence of different load parameters on structural response is investigated using the ESHR model and the direct calculation method. The investigated load parameters include the lateral pressure coefficient \(\eta\), offset load, and buried depth, with their respective values summarized in Table 7. These three load parameters are visually depicted in Figure 16. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Position**} & \multicolumn{2}{c}{**Direct Calculation Method**} & \multicolumn{2}{c}{**Three-Stage Calculation Method**} \\  & **Bending Moment** & **Axial Force** & **Bending** & **Axial Force** \\  & **(kN\(\cdot\)m)** & **(kN)** & **Moment (Kn\(\cdot\)M)** & **(kN)** \\ \hline Top & \(1764\) & \(-982\) & \(1772\) (+0.5\%) & \(-992\) \\ Right waist & \(-1861\) & \(-2066\) & \(-1890\) (+1.6\%) & \(-2089\) \\ Bottom & \(1629\) & \(-1480\) & \(1759\) (+8.0\%) & \(-1492\) \\ Left waist & \(-1660\) & \(-1950\) & \(-1688\) (+1.7\%) & \(-1972\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of internal forces between the three-stage calculation method and the direct calculation method. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Load Parameter** & **Unit** & **Design Value** & **Values for Sensitivity Analysis** \\ \hline Lateral pressure coefficient \(\eta\) & / & 0.54 & 0.4, 0.5, 0.54, 0.6, 0.7 \\ Offset load & kPa & 30 & 0, 15, 30, 45, 60 \\ Buried depth & m & 13 & 5, 10, 13, 15, 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Values of different load parameters for sensitivity analysis. For ease of understanding, the influence of evolving load parameters on the bending moment (absolute value) at critical positions on the structure is presented in Figure 17. According to the calculation results, when the lateral pressure coefficient \(\eta\) decreases from 0.7 to 0.4, the positive bending moments at the top and bottom of the structure increase by 6.8-11.7%, while the negative bending moment at the waist increases by 21.8%. The results show that with the gradual decrease in the lateral pressure coefficient \(\eta\), i.e., lateral unloading condition, the overall structural response shows an unfavorable trend and the most sensitive part is the negative moment regions at the waist of the structure. When the offset load increases from 0 to 60 kPa (right side), the positive bending moments at the top and bottom of the structure increase by 12.2-12.4%, while the negative bending moment at the right waist of the structure increases by 27.8%. However, the negative bending moment on the left waist of the structure decreases by 1.8%. The results show that the offset load primarily affects the internal force of the structure on its offset side, especially for the negative moment region at the offset side waist of the structure. When the buried depth of the structure increases from 13 m to 20 m, the bending moments generally exhibit a 47.1% to 48.5% increase. When the buried depth of the structure decreases from 13 m to 5 m, the bending moments generally exhibit a 53.8-55.4% decrease. As the buried depth changes, the changes in the overall response of the structure maintain a similar changing ratio, with similar sensitivity. In summary, adverse alterations in the lateral pressure coefficient \(\eta\) and offset load particularly impact the negative bending moment regions at the waists of the structure. Figure 16: Illustration of three load parameters for sensitivity analysis. Figure 17: Influence of different load parameters on bending moments at critical positions on the structure: (**a**) Lateral pressure coefficient \(\eta\); (**b**) Offset load; (**c**) Buried depth. Conversely, changes in the buried depth correlate proportionally with structural responses.