# A Finite Element Analysis of Tunnel Lining Demolition by Blasting for Subway Tunnel Expansion
## 4 Blasting Mechanical Characteristics
### Results Analysis
#### 4.2.2 Failure Mechanism of the Vault of Tunnel Lining  
Demolishing the vault of the existing tunnel lining is the most critical step in the whole subway station construction process; subsequent construction is more convenient after the demolition of the tunnel lining structure. The stress of the vault of the tunnel lining at different times during the blasting process is shown in Figure 7.  
It can be seen in Figure 5a that the vault area of the tunnel lining is damaged at the time of 0.4 \(\times\) 10\({}^{-4}\) s. It can be seen in Figure 7a that the maximum principal stress S\({}_{1}\) (tensile stress) and S\({}_{3}\) (compression stress) of the damaged area are 10.6 MPa and 15.0 MPa, respectively. According to the principal stress nephogram analysis, the maximum principal stress S\({}_{1}\) and S\({}_{3}\) of the tunnel lining structure first increase and then decrease with the blasting time. During the blasting process, the maximum principal stress S\({}_{1}\) is 35.6 MPa at the time of 0.16 \(\times\) 10\({}^{-3}\) s, and the maximum principal stress S\({}_{3}\) is 45.3 MPa at the time of 0.4 \(\times\) 10\({}^{-3}\) s. Combined with the damaging effect of the tunnel lining in the vault area shown in Figure 5, it is convincing that tensile stress plays a leading role in damaging the existing subway tunnel lining structure. Figure 6: Expanded tunnel blasting effect caused by the CD excavation method. (1) Stress analysis of neutral axis of tunnel lining  
Through the numerical simulation results, a stress evaluation of the outer side, neutral axis, and inner side along the thickness of the lining can be carried out, as shown in Figure 8. The maximum stress of the aforementioned three measuring points on three sections (i.e., the left and right arch footing sections and the vault sections) are listed in Table 5.  
Figure 8: The measuring points of tunnel lining. Figure 7: Principal stress nephogram at different times after blasting (unit:\(10^{11}\) Pa): **(a)** principal stress nephogram at time of 0.4 \(\times\)\(10^{-4}\) s; **(b)** principal stress nephogram at time of 0.16 \(\times\)\(10^{-3}\) s; **(c)** principal stress nephogram at time of 0.4 \(\times\)\(10^{-3}\) s; **(d)** principal stress nephogram at time of 0.8 \(\times\)\(10^{-3}\) s.  
It can be seen in Table 5 that the maximum tensile stresses of all the nine points are greater than the tensile strength \(\sigma_{t}\) (2.01 MPa), and the maximum compassion stresses of three points are greater than the compressive strength \(\sigma_{f}\) (20.1 MPa). Thus, this indicates that the tunnel lining is damaged because of the combined action of the tensile stress and compressive stress based on the maximum tension theory and the maximum strain energy density theory, but tensile failure is the essential factor. The circumferential tensile stress, tangential tensile stress, and gas quasi-static pressure produced by the blasting stress wave work together to create a fracture zone. The calculation equation of the radius of the blasting fracture zone is as follows:  
\[R_{p} =r_{b}(\psi p/\sigma_{t})^{1/\alpha} \tag{3}\]  
where \(R_{p}\) is the radius of the blasting fracture zone (unit: m); \(r_{b}\) is the radius of the blast hole (unit: mm); \(\sigma_{t}\) is the tensile strength of the rock (unit: Pa); and \(\psi\) is the lateral stress ratio, it can be obtained by Equation (4):  
\[\psi=\mu/(1-\mu) \tag{4}\]  
In Equation (3), \(p\) is the peak value of the initial pressure on the wall of the blast hole (unit: Pa), and it can be obtained using Equation (5):  
\[p=\rho_{s}D^{2}(r_{c}/r_{b})\,^{6}/8 \tag{5}\]  
where \(\rho_{s}\) is the rock density (unit: kg/m\({}^{3}\)), \(D\) is the detonation velocity (unit: m/s), and \(r_{c}\) is the explosive roll radius (unit: m). In Equation (3), \(\alpha\) is the stress wave attenuation index. \[\alpha=2-\mu/(1-\mu) \tag{6}\]  
where \(\mu\) is the Poisson's ratio of the rock. The blast hole is close to the existing tunnel lining in this project.