# A Finite Element Analysis of Tunnel Lining Demolition by Blasting for Subway Tunnel Expansion
## 4 Blasting Mechanical Characteristics
### Results Analysis
#### 4.2.4 Vibration Velocity Analysis  
According to the propagation law of blasting waves [26; 27; 28], set up five vertical monitoring points that were taken every 10 m downward from the ground surface on the tunnel vault (the center of the tunnel cross-section); five horizontal monitoring points are taken every 10 m on the ground surface from the right side of the tunnel axis, as shown in Figure 4. The peak particle velocity of the measuring points caused by the blasting load at different vertical depths and horizontal distances are listed in Table 7.  
It can be seen in Table 6 that the point with the maximum PPV is closest to the explosion center in the vertical direction, and the PPVs in the directions of X, Y, and Z are 7.83 cm/s, 7.36 cm/s, and 4.82 cm/s, respectively, with a vector combined vibration velocity of 11.77 cm/s. The PPVs gradually decrease as the distance from the explosion center is in the vertical direction. However, the PPV of the vertical point V\({}_{1}\) (on the ground surface) increases again because of the influence of the freedom degrees of the ground surface, which are one more than that of the surrounding rock. For the horizontal measuring point, the PPVs in the directions of X, Y, and Z are 3.0 cm/s, 4.15 cm/s, and 4.17 cm/s, respectively, with a vector combined vibration velocity of 5.33 cm/s. The PPVs of the horizontal measuring points on the surface decrease with the increase in the distance between the tunnel vaults. The measuring point H\({}_{5}\) is 40m away from the explosion central axis, the PPVs  
Figure 9: The absolute value of principal stress evolution law after blasting.  
decrease to 2.4 cm/s. Therefore, the PPVs of the adjacent non-expanded tunnel structure within 80 m of the explosion center do not exceed the control value of 5.0 cm/s.  
The relationship between the PPVs and the distance from the blasting center is obtained by the fitting of the calculation data (the PPVs of the surface measuring point are not used considering the effect caused by the boundary freedom degrees) is shown in Figure 10.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{1}{c}{**Measuring Points**} & \multicolumn{2}{c}{
\begin{tabular}{c} **Explosion Center** \\ **Distance (m)** \\ \end{tabular} } & \(V_{x}\) **(cm/s)** & \(V_{y}\) **(cm/s)** & \(V_{z}\) **(cm/s)** & \(V_{r}\) **(cm/s)** \\ \hline \multirow{4}{*}{Vertical measuring points} & V\({}_{1}\) & 47.2 & 3.00 & 4.15 & 4.17 & 5.33 \\ \cline{2-7}  & V\({}_{2}\) & 37.2 & 2.24 & 2.12 & 3.02 & 3.45 \\ \cline{2-7}  & V\({}_{3}\) & 27.2 & 2.45 & 3.04 & 3.6 & 4.36 \\ \cline{2-7}  & V\({}_{4}\) & 17.2 & 5.44 & 4.06 & 3.08 & 6.71 \\ \cline{2-7}  & V\({}_{5}\) & 7.2 & 4.82 & 7.83 & 7.36 & 11.77 \\ \hline \multirow{4}{*}{Horizontal measuring points} & H\({}_{1}\) & 0 & 3.00 & 4.15 & 4.17 & 5.33 \\ \cline{2-7}  & H\({}_{2}\) & 10 & 2.24 & 1.05 & 2.70 & 3.53 \\ \cline{2-7}  & H\({}_{3}\) & 20 & 1.97 & 2.12 & 2.02 & 2.92 \\ \cline{2-7}  & H\({}_{4}\) & 30 & 1.46 & 1.97 & 2.47 & 2.83 \\ \cline{2-7}  & H\({}_{5}\) & 40 & 0.72 & 1.03 & 2.13 & 2.40 \\ \hline \hline \end{tabular}
\end{table}
Table 7: The PPVs of measuring points.  
Figure 10: The relationship between PPVs and distance from blasting center: (**a**) the PPV evolution law at different vertical depths; (**b**) the PPV evolution law at different horizontal distances on the surface.  
The relationships between the PPVs and the vertical distance H and the horizontal distance L from the explosion center are as follows:  
\[V_{H} =0.01H^{2}-0.734H+16.45 \tag{7}\] \[V_{L} =0.0024L^{2}-0.165L+5.20 \tag{8}\]  
Under the condition of the same stratum and charge quantity, the PPVs at different positions from the blasting center can be predicted using Equations (7) and (8) so as to provide a theoretical and design basis for the in situ expansion of subway tunnels by blasting.