# Seismic Resilience Evolution of Shield Tunnel with Structure Degradation
## 5 Evolution of Tunnel Seismic Resilience  
### Performance of Tunnel Lining  
(A) Ellipticity  
The overall deformation of the structure adopts ellipticity as the primary measure during the seismic loading. Due to the variability of the radial deformation axes during dynamic loading, it has been observed that the compression deformation of the shield tunnel structure is more significant in the 45\({}^{\circ}\) or 135\({}^{\circ}\) directions under seismic loading. Therefore, it is assumed that the axes along the diameters in the counterclockwise 45\({}^{\circ}\) and 135\({}^{\circ}\) directions from the center of the shield tunnel are designated as Axis I and Axis II, respectively. As shown in Figure 10a, the radial displacement time-history relationships of four reference points are extracted, namely, the left and right shoulders and the springing points of the middle ring. The variation of ellipticity during the seismic loading is obtained based on the following formula:  
\[T(t)=\frac{D_{I}(t)-D_{II}(t)}{D_{0}}\times 1000\% \tag{9}\]  
Figure 9: Radial deformation of the lining structure. **(a)** Static phase; **(b–d)** Dynamic phase with PGA = 0.1 g/0.3 g/0.5 g; **(e–g)** Unrecoverable radial deformation with PGA = 0.1 g/0.3 g/0.5 g.  
where \(D_{I}(t)\) represents the radial deformation variation with time along Axis I; \(D_{II}(t)\) represents the radial deformation variation with time along Axis II; \(D_{0}\) represents the outer diameter of tunnel structures before deformation. Axis I is the major axis when the ellipticity is a positive value, which is shown in Figure 10b. Axis II is the major axis when the ellipticity is a negative value, which is shown in Figure 10c. Figure 11 depicts the time-history curves of structural ellipticity under the seismic waves with peak accelerations for various loading conditions. As the seismic load is applied, the ellipticity shows an overall fluctuation. The results under 0.5 g acceleration are taken as an example. Under a seismic wave peak acceleration of 0.5 g, when the preload is 280 kN, the ellipticity reaches a maximum of 4.325%., a minimum of \(-\)4.367%, with an amplitude of 8.692%. When the preload is 240 kN, the ellipticity reaches a maximum of 4.332%, and a minimum of \(-\)4.371%, with an amplitude of 8.703%. It is shown that the deformation amplitude increases by 0.127% when the preload loss is 40 kN. And when the preload is 0 kN, the ellipticity reaches a maximum of 4.372%, and a minimum of \(-\)4.401%, with an amplitude of 8.773%. It is shown that the deformation amplitude increases by 0.932% when the preload loss is 280 kN. The elliptical deformation of the tunnel structure keeps increasing as the preload continues to increase. At the same time, when the preload is 280 kN, the irreversible ellipticity is \(-\)0.095%, while for a preload of 0 kN, this value is \(-\)0.105%. This indicates the constraining effect of preload on the overall deformation of the tunnel structure. Figure 10: Ellipticity detection point and the deformation type. (**a**) Layout of the axis for ellipticity detection; (**b**) Axis I is the major axis; (**c**) Axis II is the major axis. Additionally, under seismic waves peak accelerations of 0.3 g and 0.1 g, the deformations of the tunnel structure with complete preload are 4.994% and 1.610%, respectively. The greater the peak value of the earthquake, the more pronounced the impact of seismic loading on the overall deformation of the tunnel structure. At the same time, it can be observed from the figure that there is a certain degree of recovery in the tunnel structure after the seismic wave ends. But, the complete recovery of the tunnel structure is not achieved. There is some residual deformation on the tunnel structure. When the peak acceleration is 0.1 g, 0.3 g, and 0.5 g, the residual deformations of the tunnel structure are \(-0.018\%\), \(-0.0363\%\), and \(-0.096\%\), respectively. It can be observed that the residual deformation of the tunnel structure increases with the increase in peak acceleration of the seismic wave.