# Study on the Seismic Response of Shield Tunnel Structures with the Preload Loss of Bolts
## 4 Result Analysis
### Radial Deformation Analysis  
Radial deformation was taken at various points along the circumferential centre line of the middle ring at the end of the first stage, the end of the second stage, and the end of the fourth stage. The differences were calculated to obtain the following parameters: radial displacement deformation caused by preload loss during the static stage (end of the second stage-end of the first stage); radial displacement deformation caused by different preload loss rates under dynamic loading (end of the fourth stage-end of the second stage); non-recoverable deformation caused by preload loss during the entire stage (end of the fourth stage-end of the first stage). To facilitate the observation of the impact of preload loss, all data are compared by taking the normal condition (with a preload of 280 kN) as the reference, and the tunnel structure deformation is compared by calculating the differences. Figure 11: Arias intensity at the monitoring points. (**a**) Arias intensity of arch spandrel with 0.1 g. (**b**) Arias intensity of arch spandrel with 0.3 g. (**c**) Arias intensity of arch spandrel with 0.5 g. (**d**) Average Arias intensity with 0.1 g. (**e**) Average Arias intensity with 0.3 g. (**f**) Average Arias intensity with 0.5 g. (**g**) Proportion of loss at each stage. Figure 12 illustrates the influence of preload loss in the static phase on the structural radial displacement deformation. It can be observed that the radial deformation exhibits a distribution pattern symmetric about the 90-270\({}^{\circ}\) axis. As the level of preload loss increases, the radial deformation of the segment gradually increases, and the radial deformation is mostly positive. This indicates an outward expansion of the segment ring. The maximum relative deformation is 0.035 mm and occurs when the preload is completely lost. In terms of overall structural deformation, compared to the situation with no preload loss, there is a tendency for inward contraction only at the crown and some joint locations. In this case, the relative deformation between the inner and outer segments (offset) is 0.038 mm when no preload is lost. However, when preload is completely lost, it is 0.094 mm, an increase of 147.37%. This indicates that as the degree of preload loss increases, the overall stiffness of the segment ring decreases. Figure 13a-c is the radial deformation of the segments under seismic loading. It can be observed that the radial deformation of the segments is positively correlated with the degree of preload loss. As the intensity of seismic loads increases, the difference in radial deformation between the cases with no preload and with preload gradually increases. This indicates that the effect of bolt preload increases with the strengthening of seismic load intensity. When the PGA is 0.1 g, the segments in the range of 180\({}^{\circ}\)-285\({}^{\circ}\) exhibit an inward contraction tendency under various conditions. The deformation is positively correlated with the degree of preload loss, and the overall pattern presents a central symmetrical shape about the 135-315\({}^{\circ}\) axis. The overall unrecoverable deformation is shown in Figure 14a-c. It can be observed that during the dynamic phase with PGA = 0.1 g and 0.3 g, the influence on the radial deformation of the structure remains relatively consistent. However, when the PGA is 0.5 g, it is evident that as the degree of preload loss increases, the unrecoverable radial deformation gradually increases. Furthermore, compared to the static phase, the impact of dynamic loads on unrecoverable deformation is more pronounced during this phase. Figure 12: Radial deformation amount in the static phase. Figure 14: The radial deformation amount cannot be recovered. (**a**) The overall unrecoverable radial deformation, PGA = 0.1 g. (**b**) The overall unrecoverable radial deformation, PGA = 0.3 g. (**c**) The overall unrecoverable radial deformation, PGA = 0.5 g.  
Figure 13: Radial deformation amount in the dynamic phase.