## 3 Numerical Simulation of Underground Tunnel Vibration Waves
### Blasting Vibration Analysis  
#### 3.3.1 On-Site Blasting Vibration Monitoring  
In an underground blasting project, the vibration wave generated by blasting will affect the stability and safety of the adjacent roadway. The mine carries out underground blasting mining works when the ground stress is 1 Mpa, and the vibration monitoring points of the blasting site are respectively set in the interior of the adjacent roadway, at a distance of about 15m from the blasting point. Blasting site vibration monitoring points were set up in the adjacent roadway interior, about 15 m from the blast point. The orientations of the triaxial vibration sensors were as follows: X direction perpendicular to the tunnel sidewall, Y direction perpendicular to the tunnel floor, and Z direction parallel to the tunnel. The recording rate of the vibration sensors was 6000 sps, with a recording time of 4 s. In the collected vibration wave data, the maximum vibration velocity in the X direction (V\({}_{\text{X-max}}\)) was 10.454 cm/s, while in the Y direction (V\({}_{\text{Y-max}}\)), it was 6.004 cm/s, and in the Z direction (V\({}_{\text{Z-max}}\)), it was 9.126 cm/s. The triaxial vibration velocity profile measured on-site is detailed in Figure 7.  
Figure 6: Vibration velocity history curves of various measurement points under in situ stress of 1 MPa and 5 MPa.  
The location of measuring point 1 in the blasting field data collection is similar to the location of measuring point B in the simulation, and measuring point B in the simulation is 13.34 m away from the blasting point. Based on the vibration velocities shown in Figure 8, the maximum values of the three-axis vibration velocities can be determined. The comparison between the simulated blasting vibration values and the measured three-axis vibration velocities is presented in Table 6.  
According to the data in Table 6, there is a certain error between the triaxial vibration velocities in the blasting simulation and the measured data. The error range of the vibration velocity is between 0.31 and 0.50 cm/s, with relative error values ranging from 3.87% to 8.49%. These error values are within a reasonable and acceptable range given the allowable error. This indicates a certain degree of consistency between the numerical simulation of blasting vibration models and the measured values. The simulation adopted a method of initiating a single hole in every five rows, while the on-site blasting scheme used eight to nine holes in each row. Therefore, it is normal for the simulated values to be slightly smaller than the measured values. Considering factors such as the on-site detection accuracy and differences in acquisition points, the error in the blasting vibration simulation is within  
\begin{table}
\begin{tabular}{c c c c} \hline  & \(\mathbf{V_{X\_max}}\) & \(\mathbf{V_{Y\_max}}\) & \(\mathbf{V_{Z\_max}}\) \\  & **(cm/s)** & **(cm/s)** & **(cm/s)** \\ \hline Field-Measured & 7.90 & 6.37 & 5.44 \\ Simulated Measurement Point 2 & 8.21 & 5.87 & 4.98 \\ Error & \(-\)0.31 & 0.50 & 0.46 \\ Relative Error & \(-\)3.87\% & 7.81\% & 8.49\% \\ \hline \end{tabular}
\end{table}
Table 6: Comparison of simulated and field-measured vibration velocity values at measurement point 2.  
Figure 8: Graph of field-measured three-axis vibration velocity history.  
Figure 7: Layout of vibration wave monitoring points in the tunnel at the blasting site.  
a reasonable range. This validates the feasibility and accuracy of using the FEM-SPH algorithm to simulate blasting engineering vibration velocities.