# 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
### Optimal Delay Time Determination for Various Classes of Surrounding Rock  
To investigate wave superposition in distinct rock classes under varying millisecond delay conditions, single-hole blasting simulation were conducted on Class III, IV, and V surrounding rock. The results obtained the main vibration phase duration and main period at different monitoring points. The obtained parameters are summarized in Figure 12.  
As shown in the figure, both the main vibration phase duration and the main period increase with declining rock quality. When the rock quality decreases from Class III to IV, variations in the main period across monitoring nodes remain comparatively minor, whereas variations in the main vibration phase duration approximately double. Compared with Class III and IV, significant changes occur in blasting seismic wave parameters for Class V surrounding rock. When determining the optimal delay time, the fundamental principle is to reduce the vibration effect of tunnel blasting. The vibration reduction rate can directly reflect the vibration reduction effect of the different delay times. Let us select the point at the surface directly above the tunnel surface as the coordinate origin O point. Take the excavated direction in front of the tunnel as the positive direction of the coordinate axis. Select a node at the surface every 2.5 m along the axis of the excavated tunnel. Select the millisecond delay time with the largest vibration reduction rate of each point as the optimal delay time. To meet the needs of engineering practice, the rock broking effect of the tunnel face should be optimized and the construction efficiency improved. If the vibration reduction rate values of multiple millisecond times are similar, let us further screen the smallest delay time. To determine the optimal delay time for different locations, this study carries out numerical simulations of different classes of surrounding rock with different delay blasting. Figure 13 shows the optimal delay time for different classes of surrounding rock. For Class III conditions, optimal vibration reduction is achieved with 3 ms delay blasting within the ranges \(-40\) m to \(0\) m and \(10\) m to \(40\) m. Delay blasting of \(1\) ms yields a vibration reduction within the ranges \(-50\) m to \(-47.5\) m, \(0\) m to \(10\) m, and \(45\) m to \(50\) m. In the range of \(-40\) m\(-40\) m, when \(1.5\) ms \(<\Delta t_{\text{m}}<3.1\) ms, the vibration reduction through waveform separation can be achieved by using 3 ms millisecond delay time blasting. In the range of \(10\) m in front of the tunnel face, the optimal delay time is \(1\) ms. In this case, the vibration reduction through main-period superposition is better than waveform separation. At \(40\)-\(50\) m ahead/behind the tunnel face, the main period of blasting seismic waves increases with distance. Within this range, \(1\) ms millisecond delay time blasting can achieve vibration reduction through main-period superposition with better efficacy than other delay times. Figure 12: Parameters of seismic waves of different classes of surrounding rock: (**a**) \(\Delta t_{\text{m}}\); (**b**) T.  
For Class IV conditions, optimal vibration reduction is achieved with 1 ms delay blasting within the ranges \(-\)50 m\(\sim\)\(-\)35 m. A 3 ms millisecond blasting vibration reduction effect is most effective in the range of \(-\)35 m\(\sim\)\(-\)7.5 m. The 2 ms delay provides optimal vibration reduction in \(-\)7.5 m to 17.5 m. The 7 ms millisecond blasting vibration reduction effect is most effective in the range of 17.5 m\(\sim\)30 m, and the 5 ms vibration reduction effect is most effective in the range of 30 m\(\sim\)50 m. Compared to Class III, the main period T changes minimally for Class IV, but the main vibration phase duration \(\Delta\)t\({}_{\rm m}\) increases. This makes Class IV more conducive to vibration reduction through main vibration phase superimposition.