# Study on the Seismic Response of Shield Tunnel Structures with the Preload Loss of Bolts
## 3 Validation of Joints Model  
To validate the modelling process and the accuracy of data extraction, modelling verification tests for relevant joints were conducted following the modelling approach of this study. Material parameters for all components were derived from reference literature for control experiments. A solid model of the segment joint was established and subjected to model loading verification. With regard to the placement and loading conditions of the joint test blocks during the experimental process, the constraints and loading application in the finite element simulation are depicted in Figure 5. At the two end sections, only the vertical displacement at the bottom and the vertical rotation along the symmetrical axis of the segment were constrained. The loading used local pressure loading with a limited area, neglecting the influence of the segment's curved surface on the vertical forces [37; 38].  
Figure 4: The acceleration time–history and Fourier spectrum of Kobe earthquake motion. (**a**) Acceleration time course curve (0.1 g Kobe). (**b**) The seismic wave Fourier spectrum.  
Figure 5: Pipe segment joint test. (**a**) Test loading machine. (**b**) Test loading model.  
During the loading process, the bolt moment is calculated based on an eccentricity (M/N) of 0.3 m, with horizontal force N incrementally loaded by 50 kN at each stage. Consequently, the vertical load can be obtained from Equations (3) and (4). The loading continues until the horizontal force reaches 600 kN, after which the horizontal force is increased by 25 kN at each stage [12].  
\[P=\frac{N(e+H_{1})}{L-L_{1}} \tag{3}\]  
\[e=\frac{M}{N} \tag{4}\]  
The numerical simulation results and experimental data are shown in Figure 6, where component deflection, concrete cross-section strain, bolt cross-section strain, and joint opening value are compared. It can be observed that the variation patterns of the numerical simulation results closely match the experimental results. Although there are errors in vertical deformation and joint opening, this is mainly due to the boundary conditions not being able to fully replicate real-world conditions and the influence of gravity. In summary, it can be concluded that the numerical simulation has correct material parameters.  
To further investigate the impact of preload on the segment joint, the cooling method was used to apply varying levels of preload to the connecting bending bolts. It has been observed that under the influence of static overload, the impact of different preload levels on the structural performance of segment joints is quite significant. Preload can effectively reduce the deformation of the segments in the initial stages. Additionally, the simulated ultimate bearing moment of the joint without preload is 246.42 kN\(\cdot\)m. However, with a preload force of 160 kN, it increases to 270.84 kN\(\cdot\)m, which represents a 9.02% improvement. Similarly, based on the comprehensive comparison of joint simulations at various preload levels, it has been found that the application of a preload of 160 kN has a more pronounced  
Figure 6: Results of positive joint. (**a**) Component deflection. (**b**) Concrete cross-section strain. (**c**) Bolt cross-section strain. (**d**) Joint opening value.  
constraining effect on joint deformation compared to no preload and 120 kN preload. Furthermore, in comparison to the condition with preload of 280 kN, the ultimate bearing capacity of the structure is greater. Therefore, it can be concluded that the optimal preload for bolts in this study is 160 kN. Additionally, based on Figure 6c, it has been observed that preload can tighten the adjacent segments, preventing the joint opening under relatively small loads.