## 5 Secondary lining Support Characteristic Curve
### Calculation Results and Analysis of SCCs  
#### 5.2.1 SCCs of Secondary Lining for Different Grades of Surrounding Rock  
Taking Tunnel 3 with a tunnel spacing of 65 m as an example, the SCC of the secondary lining for different grades of surrounding rock (Grade III, IV, and V) are shown in Figure 10. \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Elastic modulus (GPa) & 30 \\ Poisson’s ratio & 0.2 \\ Compressive strength\(f_{c}\) (MPa) & 35.7 \\ Tensile strength\(f_{t}\) (MPa) & 3.20 \\ Compressive yield strength\(f_{c0}\) (MPa) & 23.8 \\ Tensile yield strength\(f_{t0}\) (MPa) & 3.20 \\ Ratio of biaxial compressive strength to uniaxial compressive strength \(f_{\text{bo}}/f_{\text{co}}\) & 1.16 \\ Characteristic length under uniaxial compression \(L_{\text{c}}\) (m) & 0.0826 \\ Characteristic length under uniaxial tension \(L_{\text{t}}\) (m) & 0.0826 \\ Fracture energy under uniaxial compression \(G_{\text{c}}\) (N/m) & 4190 \\ Fracture energy under uniaxial tension \(G_{\text{t}}\) (N/m) & 38 \\ Compressive damage parameter \(D_{\text{c}}\) & 800 \\ Tensile damage parameter \(D_{\text{t}}\) & 3000 \\ Material expansion coefficient \(a_{\text{p}}\) & 0.2 \\ Stiffness recovery coefficient \(s_{0}\) & 0.2 \\ \hline \end{tabular}
\end{table} 
Table 4: Parameter values of the CDP model. \begin{table}
\begin{tabular}{c c c c c} \hline
**Parameter** & **Density (kN/m3)** & **Elastic Modulus (GPa)** & **Poisson’s Ratio** & **Compressive Strength (MPa)** & **Tensile Strength (MPa)** \\ \hline HRB400 & 78 & 200 & 0.25 & 400 & 400 \\ \hline \end{tabular}
\end{table} 
Table 5: Material parameters of rebar. For the Grade III surrounding rock with a 0.8 m thickness lining, the SCC initially (about 0-3 cm) shows a nearly linear rapid increase in stress, which then slows down in the range of about 3 cm to 25 cm and remains almost level afterwards. The stress at a displacement of 50 cm is chosen as the peak stress, and it increases from 4.08 MPa to 4.54 MPa, with a 10.01% increase as the reinforcement ratio increases from 0.2% to 1.0%. The reinforcement enhances the lining's load-bearing capacity, mainly evident in the nonlinear growth phase, where concrete cracking allows the reinforcement to participate in the load-bearing process. The SCC for the Grade IV surrounding rock with a 1.2 m thick lining is essentially the same as that for the Grade III surrounding rock with a 0.8 m thick lining, both showing a trend of initial linear rapid growth, followed by a phase of slow growth, and finally levelling off. At a displacement of 50 cm, the peak stress increases from 5.64 MPa to 5.94 MPa with a mere 5.02% increase as the reinforcement ratio increases from 0.2% to 1.0%. Similarly, the SCC for the Grade V surrounding rock with a 1.35 m thick lining shows the same initial linear rapid growth, followed by slow growth and levelling off. At a displacement of 50 cm, the peak stress increases from 5.68 MPa to 6.34 MPa with a 10.60% increase as the reinforcement ratio increases from 0.2% to 1.0%. Figure 10: SCCs of supporting characteristics with different reinforcement ratios under different design thicknesses of surrounding rock. (**a**) Grade III surrounding rock, 0.8 m thick; (**b**) Grade IV surrounding rock, 1.2 m thick; and (**c**) Grade V surrounding rock, 1.35 m thick. In summary, the SCC of the secondary lining shows an initial linear rapid growth, followed by a slow growth phase, and finally levelling off as the displacement increases. Initially, the load is primarily borne by the concrete material, so the reinforcement ratio has almost no effect on the support stress of the lining. As the secondary lining structure cracks in the middle phase, the reinforcement gradually participates in the load-bearing process. At the same displacement, the higher the reinforcement ratio, the faster the stress growth rate.