## 4 Discussion of the Results
### Comparison between Variable and Constant Rotational Stiffness  
In the presented model, the rotational stiffness changes are taken into account through an incremental method, based on experimental and 3D numerical results. In this section, however, constant rotational stiffness values for all segmental joints are used to replace the variable stiffness defined by the incremental method. This allows us to investigate the effect of the incremental method on the bending moments at key sections JM1 to JM10 and the convergence deformations at key deformation points D1 to D3. In the following, a range of constant stiffness values in increments of 25,000 kNm/rad is considered, and the differences between the predicted and experimental values from the indoor full ring experiment are recorded. The evaluations show that only values between 50,000 kNm/rad and 125,000 kNm/rad render reasonably good numerical results, as shown in Figure 12. Results for axial forces in the linings are not presented in this paper, as no significant differences were found between the iterative nonlinear and constant value predictions.  
Firstly, considering the bending moments, Figure 12 reveals for a joint stiffness of 125,000 kNm/rad, differences up to 13% in Case 1, up to 15% in Case 2, up to and 36% in Case 3. For the other joint stiffnesses, the maximum differences are 28% (100,000 kNm/rad in Case 3), 19% (75,000 kNm/rad in Case 3), and 21% (50,000 kNm/rad in Case 1). This means that if a reasonable constant stiffness value is used, the bending moment differences can be kept within reasonable limits. However, the differences rise with the increase in pressure level around the tunnel linings, and the constant stiffness fitting the experimental results in the best way, also changes for the different load cases.  
Secondly, considering the key deformations, Figure 12 reveals for a joint stiffness of 125,000 kNm/rad differences up to 11% in Case 1, up to 16% in case 2, and up to 75% in Case 3. For other joint stiffnesses, the maximum differences are 54% (100,000 kNm/rad Case 3), 21% (75,000 kNm/rad Case 1), and 51% (50,000 kNm/rad Case 3).  
Figure 11: Measured deformations from experiment and numerical model in Experimental Case 1.  
Figure 12: Difference comparison between predictions and experiments: (**a**) Experimental Case 1; (**b**) Experimental Case 2; (**c**) Experimental Case 3 (rotational stiffness in \(10^{3}\) kNm/rad).  
In contrast to the previous conclusion for the bending moments, it is obvious that the convergence deformations of key deformation points vary significantly with different stiffnesses. This means that the structural deformation is very sensitive to the rotational stiffness input. If the adaption of a constant stiffness value is not supported by full ring tests, the method of constant rotational stiffness in segmental joints may lead to non-negligible deformation prediction errors. On the other hand, the method presented in this paper can consider the joint's nonlinear behavior, and the results obtained by this method can match the experimental results of both deformations and bending moments for all load cases well within the range of about 10% in all but a few measurement points. When the bending moments around the joint's vicinity are large, which may exist in large-diameter and special-section shield tunnels, the joint nonlinear behavior needs to be considered in the calculation model. In general, it can be concluded that a proper constant joint rotational stiffness is difficult to determine, and its deduced deviations may influence the structural design and safety evaluation. The presented incremental method in this paper is able to solve this problem.