## 4 Influence of Lining Thinning on Rock Pressure in Four-Track HSR Tunnels
### Deformation Analysis Results  
The stress distribution in the tunnel lining under the influence of thinning defects is shown in Figure 16, with the defect parameters identical to those in Figure 14. Thinning defects lead to significant settlement within the active thinning zone of the tunnel lining. The deformation contour plots reveal distinct elliptical or rounded-rectangle-shaped subsidence zones in the vicinity of the thinning region. Thinning defects cause pronounced vertical settlement within the active thinning zone of the tunnel lining. The deformation contour maps exhibit distinct elliptical or rounded-rectangular subsidence zones surrounding the thinning region. Under the thinning condition shown in Figure 16a, the maximum vertical settlement within the active thinning zone reaches 18.83 mm. For the case in Figure 16b, the peak settlement is also located within the active thinning zone, reaching 31.27 mm. In Figure 16c, the maximum settlement of 20.54 mm appears at the center of the thinning defect located at the vault. Similarly, in Figure 16d, the settlement peaks at the center of the active thinning zone, reaching 20.68 mm. The reduction in lining thickness results in a localized decrease in structural stiffness, weakening the lining's resistance to deformation under external loads. This leads to concentrated settlement and the formation of a \"deformation basin\", which may become a potential risk zone for crack initiation or lining failure. Such localized deformation may further induce cracking, spalling, or structural instability. These risks are especially critical under repeated operational loads, where cumulative effects can accelerate damage progression. Based on the deformation contour maps, the vertical settlement distribution curves of the lining along the axial direction of the thinning defect were extracted. The influence of different thinning defect parameters--namely, \(P_{\mathrm{j}}\), \(L_{\mathrm{j}}\), \(L^{\mathrm{arc}}\); and \(R_{\mathrm{j}}\)--on the vertical settlement of the lining is illustrated in Figure 17. The analysis is based on engineering conditions with a burial depth of 34 m and Grade IV rock. As shown in Figure 17a, when the thinning defect is located at \(P_{\mathrm{j}}=1\) to 6, the tunnel lining exhibits a settlement trough. In contrast, when \(P_{\mathrm{j}}=7\), 8, or 9, the lining shows a heating deformation pattern. Figure 17b reveals that when the thinning length \(L_{\mathrm{j}}\) is 4, 8, or 12 m, the settlement within the active thinning zone exhibits a W-shaped distribution. When \(L_{\mathrm{j}}\) increases to 16, 20, or 24 m, the settlement profile evolves into a \"W nested in M\" shape. The maximum settlements for \(L_{\mathrm{j}}=4\), 8, and 12 m are 21.03 mm, 20.37 mm, and 20.86 mm, respectively. For \(L_{\mathrm{j}}=16\), 20, and 24 m, the corresponding maximum settlements are 21.26 mm, 20.65 mm, and 20.77 mm. With the exception of \(L_{\mathrm{j}}=20\) m, the peak settlements consistently occur at the edges of the thinning zone, within the thinning-affected zone. When \(L_{\mathrm{j}}=20\) m, the maximum settlement appears at the center of the active thinning zone. As shown in Figure 17c, when the thinning arc length \(L^{\mathrm{arc}}\) is 4 m, the settlement distribution takes the form of a simple trough. For \(L^{\mathrm{arc}}\); = 8, 16, 32, and 40 m, the settlement exhibits a W-shaped pattern, with the peak settlement occurring at the base of the trough or W shape. The maximum settlement for \(L^{\mathrm{arc}}\); = 4 m is 19.93 mm. As \(L^{\mathrm{arc}}\) increases, the peak settlement also increases, reaching 20.82 mm when \(L^{\mathrm{arc}}\); = 40 m. Figure 17d shows  
Figure 17: Settlement curves: (**a**) effect of \(P_{\mathrm{j}}\); (**b**) effect of \(L_{\mathrm{j}}\); (**c**) effect of \(L^{\mathrm{arc}}\); (**d**) effect of \(R_{\mathrm{j}}\). that when the thinning-thickness ratio \(R_{\rm j}\) is 0.75, the settlement profile is trough-shaped with a peak value of 23.70 mm.