## 3 Results and Discussion
### Damage Assessment of the Tunnel Lining  
The tunnel lining experiences intricate mechanical impacts due to the combined effects of fault dislocation and earthquakes, resulting in significant damage to the lining structure. To assess the overall tunnel damage more comprehensively, this study utilizes the overall structural damage index, which is commonly employed in above-ground structures, to evaluate the tunnel lining damage. In the Concrete Damaged Plasticity (CDP) model, the extent of concrete damage is represented by the compression damage factor C and the tensile damage factor T. These damage factors range from zero to one, where a value of zero signifies no damage to the concrete, and a value of one indicates complete destruction of the concrete. The overall  
Figure 10: Energy dissipation time history. lining damage index can be divided into two parts: the overall lining damage index in compression (OLDC) and the overall lining damage index in tension (OLDT) [33]. OLDC and OLDT are calculated based on the weighted average of the damage values of each cross-sectional element of the tunnel lining in the model, where the dissipated energy of the element serves as a weighting factor. This approach reflects the overall damage condition of each cross-section of the lining. The equations for calculating OLDC and OLDT are as follows:  
\[\text{OLDT} =\sum_{i=1}^{n}\left[d_{i}^{\epsilon}\left(E_{i}^{\epsilon}/\sum_{i=1 }^{n}E_{i}^{\epsilon}\right)\right] \tag{8}\] \[\text{OLDC} =\sum_{i=1}^{n}\left[d_{ci}^{\epsilon}\left(E_{i}^{\epsilon}/\sum_ {i=1}^{n}E_{i}^{\epsilon}\right)\right] \tag{9}\]  
According to several studies and in conjunction with the definition of damage states of lifeline projects in earthquake damage statistics [34; 35], the damage states can be categorized into four classes based on the overall lining damage index (OLDT and OLDC), including DS1 (slight), DS2 (moderate), DS3 (severe), and DS4 (complete). Table 4 shows the damage characteristics of the tunnel at different damage levels. Figure 11a displays the distribution curves of OLDC along the axial direction of the tunnel within a 100 m range on both sides of the fault dislocation plane under the three cases. The horizontal coordinate at point zero in the figure corresponds to the location of the fault dislocation plane in the numerical model, and the yellow background area indicates the extent of the fault fracture zone. The figure illustrates that, under the sole influence of fault dislocation, the tunnel lining sustains significant damage (DS3) at the fault plane, with OLDC peaking at 0.54. Adding seismic action, the damage pattern of the tunnel lining remains largely unchanged, albeit with a marginal increase in damage values at each monitoring point. Notably, the fault plane still exhibits the highest OLDC value, now at 0.71. When subjected solely to an earthquake, the tunnel's OLDC values remain below 0.1, indicating minimal compressive damage. Figure 11b presents the OLDT distribution curve along the tunnel's axial direction under different cases. The results indicate that under fault dislocation, severe tensile damage affects the tunnel lining from \(-\)10 m to 17 m near the fault plane, with OLDT values peaking above 0.8 at \(-\)7 m and 20 m, reaching complete damage (DS4). This shows a marked increase in tensile damage over compressive damage from fault dislocation alone. Additionally, when combined with seismic forces, the damage significantly escalates at each monitoring point, with OLDT values reaching a maximum of 0.97 at 20 m, suggesting a high likelihood of complete shearing at this location. Solely under seismic influence, the tunnel lining shows severe tensile damage, with OLDT peaking at 0.76 at 5 m. Furthermore, OLDT values exceed 0.70 at all monitoring points within the fault fracture zone, highlighting more severe damage there compared to areas in the intact rock mass.