# Study on Vibration Effects and Optimal Delay Time for Tunnel Cut-Blasting Beneath Existing Railways
## 3 The Mechanism and Effect of Vibration Reduction Through Waveform Interference  
### Blast Vibration Propagation Laws and Nodal Response Characteristics  
In millisecond blasting operations, the new damage in the initial detonation hole may alter the detonation dynamics of subsequent holes. To quantify this influence on vibration waveform parameters, this study conducts a comparative analysis of waveform characteristics with large delay intervals. A numerical simulation of cut-blasting scenario with 25 ms interval was conducted, wherein six cutting holes were detonated sequentially. Ground vibration data were acquired from three strategically positioned monitoring points, with time-history analyses performed on velocity components along the X, Y, and Z axes.  
As shown in Figure 4, there are six independent waveforms. Therefore, the superimposed effect of seismic waves generated by the six cut-blasting holes is weak. Then, when the charge weight in each hole is equal, the waveform and duration of single-hole blasting of one monitoring node do not change with increased blasts. The damage of previous  
\begin{table}
\begin{tabular}{c c c c c} \hline
**R (m)** & **Q (kg)** & **V (cm/s)** & **Y (lgv)** & **X (lg\(\rho\))** \\ \hline
230.9 & 107 & 0.43 & \(-\)0.36051 & \(-\)1.68708 \\ \hline
233.2 & 107 & 0.44 & \(-\)0.36957 & \(-\)1.69137 \\ \hline
222.1 & 107 & 0.47 & \(-\)0.3279 & \(-\)1.67023 \\ \hline
203.5 & 70.8 & 0.43 & \(-\)0.36351 & \(-\)1.69207 \\ \hline
205.3 & 70.8 & 0.42 & \(-\)0.37366 & \(-\)1.69575 \\ \hline
213.5 & 94.6 & 0.48 & \(-\)0.31695 & \(-\)1.67087 \\ \hline
198.1 & 73.5 & 0.46 & \(-\)0.33724 & \(-\)1.67479 \\ \hline \end{tabular}
\end{table}
Table 4: Monitoring information of measuring points.  
Figure 3: Validation of numerical simulation model (**a**) Regression equation (**b**) Data comparison.  
detonation holes does not affect the surface waveform characteristics by subsequent detonation. Therefore, the superposition effect of multi-hole blasting blasts can be analyzed by single-hole blast seismic waves. The PPVs at each point are shown in Table 5.  
The vibration velocities of the blasting seismic waves in the three directions of X, Y, and \(Z\) at the monitoring point are quite different. The vibration velocity in the Y direction is obviously larger than in the other two directions. Therefore, the Y direction is selected as the main research direction, which can better analyze the vibration effect of blasting seismic waves. Comparing Figure 4b and Figure 4c, the distances from nodes B\({}_{1}\) and B\({}_{2}\) to the tunnel face are the same, but there are differences in the waveforms and durations of the blasting seismic waves at the two nodes. This is because node B\({}_{1}\) is located on the excavated side of the tunnel. The excavated side of the tunnel forms a new free surface, which affects the propagation of the blasting seismic waves. This leads to the waveform difference between the excavated and unexcavated sides for the same distance.  
When comparing the waveform characteristics at monitoring points A (directly above the tunnel face), B\({}_{1}\), and B\({}_{2}\), the waveform at point A exhibits higher amplitudes and a more compact shape. With increasing distance from the tunnel face, the waveforms at points B\({}_{1}\) and B\({}_{2}\) become more elongated, and their duration increases. This attenuation is primarily attributed to the energy dissipation within the rock mass during propagation. Specifically, the rock medium damps the seismic waves and absorbs their energy, while seismic scattering occurs in heterogeneous rock. Consequently, the dominant frequency of the seismic wave decreases, which is the fundamental reason for the observed waveform elongation and the increase in duration. Thus, the vibration intensity significantly decreases with distance. Therefore, distance is one of the key factors in reducing the vibration effect of tunnel blasting.