## 4 Numerical Simulation
### Parametric Study of Controls
#### 4.4.2 Shock Absorbing Layer Thickness  
In this section, the shock-absorbing layer was positioned using the \"surrounding rock-initial support-shock absorbing layer-secondary lining\" method. Four thicknesses were considered: 10 cm, 15 cm, 20 cm, and 30 cm, and compared with the condition without a shock absorbing layer. The peak horizontal accelerations (positive and negative) and peak principal stresses at critical locations in the tunnel for different shock absorbing layer thickness conditions are depicted in Figures 18 and 19.  
The findings from Figure 18 indicated that the amplification factor of the horizontal acceleration at various points of the lining at the fault zone of the extra-large section tunnel aligned with the trend of the change in the thickness of the seismic isolation layer relative to the original seismic wave acceleration. It increased with the thickness of the  
Figure 19: Effect of shock absorbing layer thickness on the first principal stress.  
Figure 18: Effect of shock absorbing layer thickness on horizontal acceleration in (**a**) positive and (**b**) negative directions.  
seismic isolation layer, and the horizontal acceleration at the crown position was slightly larger than that at the springing and the crown. In the absence of a seismic isolation layer, the maximum acceleration response peak value along the full length of the lining at the fault zone was 6.56 m/s\({}^{2}\), approximately 1.89 times larger than the original seismic wave acceleration. With a 10 cm thickness of the seismic isolation layer, the acceleration at the crown increased by 1.97 times, and with a 15 cm thickness, the acceleration at the crown was amplified by 2.09 times. At 20 cm thickness, the amplification factor of the crown acceleration was 2.11 times. The amplification factor of the acceleration exhibited a slowing trend as the thickness of the seismic isolation layer changed from 15 cm to 20 cm. When the thickness of the seismic isolation layer was 30 cm, the amplification factor of the acceleration was 2.52 times, showing an increasing trend again. Upon comparing the acceleration distribution patterns of the fault section and the intact surrounding rock section, it was found that at this point, the difference in horizontal acceleration between the two was the largest.  
Combined with related research findings, the initial analysis suggests that the trend of increasing acceleration response with the thickness of the shock absorbing layer can be attributed to the lower and softer elastic modulus of the shock absorbing layer. This leads to reduced restraint on the lining structure, resulting in an amplified acceleration response of the tunnel under seismic action. This observation underscores the need for particular attention in practical engineering anti-seismic efforts.  
Figure 19 illustrated that the inclusion of a shock absorbing layer led to a significant reduction in the first principal stress value of the lining structure at the location of the fault fractured zone in the tunnel. Compared to the absence of a shock absorbing layer, the maximum reduction in the first principal stress was nearly 62% after the installation of the shock absorbing layer, with the most pronounced effect observed at the crown and invert positions. The reduction rate slightly increased with the thickness of the shock absorbing layer absorbing layer and gradually stabilized. When the thickness of the shock absorbing layer was below 20 cm, for every 5 cm increase in thickness, the reduction rate consistently remained around 5%. However, once the thickness of the shock absorbing layer exceeded 20 cm, the additional shock absorbing effect became limited. It was recommended that the thickness of the shock absorbing layer should be 20 cm, and potentially increased conservatively if necessary.