## 4 Discussion of the Results
### Parametric Study  
The choice for the exact configuration of the longitudinal joints is a critical point in shield tunnel projects [52; 53]. It influences the lining's mechanical response, including structural deformations and bending moment distribution, and additionally may affect the safety and applicability of tunnel linings [54; 55; 56]. The stiffness of the joint is one of the most important factors for the decision for the joint type [57]. As a new shield tunnel lining structure, the effect of stiffness of the longitudinal joints in quasi-rectangular tunnels is unknown. The effects of some parameters in the full-ring model, including the rotational and shear stiffnesses of longitudinal joints, and the size of the rigid zone, are discussed here, as well as of the width of the internal column, whose size is also a point of attention in practical applications. In the parametric study, the values of the parameters are changed to detect the variation tendencies of the structural response. Considering the practical ranges of the parameters, the ranges of the magnification factors for the parametric values are listed in Table 7. When one variable is changed, the other parameters remain constant. Figure 16: Layout of joints in middle and neighboring rings. Calculation Case 2 (in Section 4.2), with an overburden of 17 m and a coefficient of lateral pressure of 0.6, is taken as the basis for the parametric study. The calculation results of the deformation at D3 and the bending moments at JM2, JM8 and JM10 (shown in Figure 17) are selected as the target objects to detect the effect of the aforementioned parameter variations. The choice is determined by the observation that in Calculation Case 2, the largest deformations take place at D3 while JM2 and JM10 are the sections with the largest positive and negative bending moment respectively. Additionally, relatively large negative moments also occur at the ends of the long axis at JM3 and JM8 (Figure 6). The deformations and internal forces at these sections act as the main controlling factors for the structural design. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{2}{c}{**Range of the**} & \multirow{2}{*}{**Value of x**} \\  & **Magnification Factors** & & \\ \hline Rotational stiffness & 2x & \(\pm\)4, \(\pm\)3, \(\pm\)2, \(\pm\)1, 0 \\ Shear stiffness & 2x & \(\pm\)4, \(\pm\)3, \(\pm\)2, \(\pm\)1, 0 \\ Size of rigid zone & 0 and 2x & \(\pm\)2, \(\pm\)1, 0 \\ Width of interior column & 2x & \(-\)2, \(-\)1, 0, 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Ranges of parameters. Figure 17: Results of parameter analysis: (**a**) deformation of D3; (**b**) bending moment at JM2; (**c**) bending moment at JM8; (**d**) bending moment at JM10. In the graphs presented in Figure 17, the exponent \"x\" is the variable on the abscissa axis. The value of the corresponding input parameter is multiplied by \(2^{\text{x}}\). The contrasts of the results with the magnified or reduced parameters to the results with the original parameters are shown in full lines with the left ordinate axes. In Figure 17a, the convergence deformation is calculated by dividing the deformation of D3 by the original length of D3, while the difference ratios of the bending moments at JM2, JM8 and JM10 to those with the original parameter settings are summarized in Figure 17b-d. Moreover, the slopes of these curves are calculated, equivalent to the change rate of the selected target objects, and are shown in dashed lines with reference to the right axes. The reader should pay attention to the magnification factor of 0 in the row of \"size of rigid zone\" in Table 7. The \"0\" indicates that there is no rigid zone in the model, and the related \"x\" is taken as \(-3\) in Figure 17, in order to compare with the actual range of \"x\" from \(-2\) to \(2\).