## 4 Structural Design  
### Structural Design during the Construction Process  
In addition to considering the structural bearing state during the service stage, as highlighted in Sections 2 and 3, special attention must be paid to ensuring the structural safety of column-free QRST structures during the construction stage [43; 44], including the assembly condition and simultaneous grouting condition. Among these conditions, the simultaneous grouting condition is one of the governing conditions during the tunnel design, potentially inducing substantial structural responses [20]. To ensure structural safety, as shown in Figure 15, a temporary column is utilized to regulate the structural response starting from the assembly condition; this will then be removed when the structure enters the service stage. Similar construction solutions are often applied. During the construction of large-section tunnels, non-circular tunnels, or tunnels with considerable openings, the structure is often subjected to high external temporary loads or the structural system itself has not yet been fully completed. Therefore, necessary temporary supports are needed [45]. For example, during the construction of connecting aisles using the mechanized drilling method, auxiliary facilities such as internal supports are needed to control the structural response during the cutting process, thereby ensuring the stability of the structure [46]. Given the applicability of the ESHR model for tunnel design, it serves as a tool for comprehensively assessing the structural behavior throughout the construction process, facilitating both understanding and engineering applications. The simulation of structural behavior during the entire construction process is divided into the following three stages:  
* Synchronous grouting condition. After the tunnel structure comes out from the shield tail, the external soil-water pressure and grouting pressure are resisted by the column-free QRST structure and the temporary support, the load-bearing state of which is similar to that of the typical QRST structure, as shown in Figure 15. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Condition**} & \multicolumn{2}{c}{**Deformation of Short Axis (mm)**} \\  & **Analysis** & \\  & **Total (Joint Contribution)** & **Test** \\ \hline
9 m service stage & 79.73 (52.74) & 72.00 \\
10 m service stage & 95.59 (66.35) & 94.88 \\
13 m service stage & 111.31 (74.49) & 108.64 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Analysis of the deformation mechanism on the short axis of the structure (mm). Figure 15: Bearing state of the column-free QRST structure with the temporary column subjected to simultaneous grouting condition: (**a**) Loading state; (**b**) 3D illustration. * Stable load condition. As the grouting pressure gradually dissipates and the external load stabilizes, the structure undergoes an unloading process while the structural form remains unchanged. * Column removal condition. Subsequently, the temporary column is removed slowly to ignore the dynamic structural response. During this process, soil-structure interaction is simulated by a set of foundation springs surrounding the tunnel structure. The final state of the structure is the same as that depicted in Figure 6b. Based on the above-mentioned three-stage calculation method, total results of structural responses are obtained. The method outlined in Section 3, which involves directly applying the external load during the service stage, is called the direct calculation method. Subsequently, a comparative analysis of internal forces at critical positions is conducted between the direct calculation method and the three-stage calculation method, as outlined in Table 6. Compared with the results calculated by the direct calculation method, those calculated by the three-stage calculation method exhibit a slight elevation of up to 8%.