# A Finite Element Analysis of Tunnel Lining Demolition by Blasting for Subway Tunnel Expansion
## 4 Blasting Mechanical Characteristics
### Results Analysis  
#### 4.2.1 Blasting Quality Analysis  
The numerical calculation adopts the element failure method; the element automatically exits the calculation when its stress reaches the material limit stress. That is, tunnel lining failure occurs when the compressive strength is more than 20.1 MPa or when the tensile strength is more than 2.01 MPa. According to the construction steps of the subway station newly built following the method of in situ expansion excavation of the subway tunnel, the demolition effect of the existing tunnel lining for the left drift heading at different times during the blasting process is shown in Figure 5.  
The calculation results show that damage began to occur to the pre-cut tunnel lining structure at 0.4 \(\times\) 10\({}^{-4}\) s after the dynamite blast, and it was completely crushed at 0.8 \(\times\) 10\({}^{-4}\) s after the dynamite blast. The existing tunnel lining was demolished by a blasting load within a short time. A comparison of the actual excavation outline with the design excavation contour line after the tunnel blasting using the CD excavation method, which can determine the amount of tunnel overbreak and underbreak of the excavation and evaluate the blasting effect, is shown in Figure 6.  
Using the blasting parameters in Table 2 and the CD excavation method, the subway tunnel is expanded into a subway station by blasting. It can be determined from Figure 6 that the maximum tunnel overbreak in the vault area, side wall, and inverted arch area are 15 cm, 7 cm, and 5 cm, respectively. The numerical simulation results show that the maximum tunnel overbreak value in the vault area is 15 cm, which is lower than the requirements for the excavation quality of subway tunnel cross-sections defined in the Quality Acceptance Standard for Subway Construction (GB/T 50299-2018) [25]. Therefore, the subway tunnel lining will collapse under the action of blasting impact stress and the gravity of the surrounding rock, which makes it possible to be removed quickly.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \(\rho\)/(g:cm\({}^{-3}\)) & \(A\) (GPa) & \(B\) (GPa) & \(R_{1}\) & \(R_{2}\) & \(\omega\) & \(E\) (G):m\({}^{-3}\)) \\ \hline
1.05 & 210 & 0.2 & 4.2 & 0.95 & 0.15 & 4.13 \\ \hline \end{tabular}
\end{table}
Table 4: Parameters of high-energy explosive materials.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \begin{tabular}{c} **Material** \\ **Number** \\ \end{tabular} & **Material Name** & \begin{tabular}{c} **Elastic Modulus** \\ **E (MPa)** \\ \end{tabular} & \begin{tabular}{c} **Poisson’s** \\ **Ratio \(\mu\)** \\ \end{tabular} & \begin{tabular}{c} **Bulk Density \(\gamma\)** \\ **(kN-m\({}^{-3}\))** \\ \end{tabular} & \
\begin{tabular}{c} **Cohesion \(c\)** \\ **(MPa)** \\ \end{tabular} &
\begin{tabular}{c} **Internal Friction** \\ **Angle \(\varphi\)(\({}^{c}\))** \\ \end{tabular} \\ \hline
1 & Mudstone & \(1.2\times 10^{3}\) & 0.27 & 22 & 0.6 & 22 \\ \hline
2 & Tamping plug & \(0.5\times 10^{3}\) & 0.3 & 20 & 0.25 & — \\ \hline
3 & Preliminary lining concrete & \(2.1\times 10^{4}\) & 0.18 & 24 & — & — \\ \hline
4 & Inverted arch concrete & \(2.1\times 10^{4}\) & 0.18 & 24 & — & — \\ \hline
5 & Tunnel lining concrete & \(3.15\times 10^{4}\) & 0.18 & 24 & — & — \\ \hline \end{tabular}
\end{table}
Table 3: Numerical parameters of surrounding rock and tunnel support structure.