## 4 Influence of Lining Thinning on Rock Pressure in Four-Track HSR Tunnels
### Genuine Pressure Analysis  
The stress distribution in the tunnel lining under the influence of thinning defects is illustrated in Figure 18, based on engineering conditions with a burial depth of 34 m and Grade IV rock. The defect parameters are identical to those presented in Figure 14. On the outer side of the lining, the contact pressure between the lining and rock within the active thinning zone is significantly reduced, with localized contact failure observed in some areas. This indicates that the thinning defect weakens the interaction between the lining structure and the rock. Additionally, increased contact pressure is observed at the edges of the thinning zone, suggesting a stress redistribution wherein the edge regions bear a larger portion of the load. On the inner side, the primary lining completely loses contact with the secondary lining within the active thinning zone. In the thinning-affected zone, contact is maintained but becomes markedly non-uniform. The peak contact pressure is observed at the edge of the thinning zone on the inner lining surface, reaching 1.517 MPa, 1.452 MPa, 1.911 MPa, and 1.713 MPa under the defect scenarios shown in Figure 18a-d, respectively. Areas of poor contact may become potential sites for lining cracking or water ingress. The thinning defect significantly reduces the contact stiffness and force-transfer efficiency between the lining and the rock or secondary lining. This weakens the rock's supporting function and exacerbates stress and deformation concentration in the lining, posing substantial risks to the long-term structural integrity and operational safety of the tunnel. The contact pressure contour maps were used to extract the contact pressure curves along the axial direction of the thinning defect, which represent the genuine pressure profiles. The influence of different thinning parameters (\(P_{\rm j}\), \(L_{\rm j}\), \(L^{\rm arc}\), and \(R_{\rm j}\)) on the genuine pressure curves is shown in Figure 19. To quantify the variation in genuine pressure caused by thinning, a dimensionless parameter--thinning-induced genuine pressure variation ratio (\(k_{q}\))--is defined as the ratio of the difference between the genuine pressure in the thinning-affected zone \(q_{\text{thinning}}\) and that in the thinning-free region \(q_{\text{normal}}\) to the genuine pressure in the thinning-free region \(q_{\text{normal}}\), which is expressed as follows:  
\[k_{q}=\frac{q_{\text{thinning}}-q_{\text{normal}}}{q_{\text{normal}}}\times 1 00\% \tag{1}\]  
As shown in Figure 19a, the genuine pressure distribution induced by thinning exhibits a trough-like pattern, with the minimum pressure located at the center of the active thinning zone. Interestingly, the maximum genuine pressure does not occur at the edge of the thinning zone but rather within the thinning-affected zone. When \(P_{\text{j}}\) = 1, 3, 6, 8, or 9, the thinning-induced genuine pressure variation ratio (\(k_{q}\)) ranges from 2.43% to 7.72%. When \(P_{\text{j}}\) = 2, 4, 5, or 7, the \(k_{q}\) values are 10.23%, 17.01%, 14.96%, and 16.48%, respectively. Figure 19b shows that the thinning defect causes a reduction in genuine pressure within the active thinning zone and an increase within the thinning-affected zone. The maximum genuine pressure is consistently located in the thinning-affected zone. When \(L_{\text{j}}\) = 4 m, the maximum genuine pressure is 457.04 kPa. As \(L_{\text{j}}\) increases to 16 m, the maximum pressure increases to 525.83 kPa. For \(L_{\text{j}}\) = 20 m and 24 m, the maximum genuine pressures are 489.04 kPa and 562.19 kPa, respectively. According to Figure 19c, variation in the arc length \(L^{\text{arc}}\) significantly affects both the minimum and maximum genuine pressures. When  
Figure 19: Genuine pressure distribution curves: (**a**) effect of \(P_{\text{j}}\); (**b**) effect of \(L_{\text{j}}\); (**c**) effect of \(L^{\text{arc}}_{\text{j}}\); (**d**) effect of \(R_{\text{j}}\).