# 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
### Rock Mass Classification Effects on Blasting Wave Superposition  
To investigate blasting seismic wave effects in various rock masses, this study simulates single-hole initiation and progressive hole-by-hole initiation (2 ms delay) of cutting holes in Class III, IV, and V surrounding rock. Rock parameters for each class are listed in Table 8. Figures 9-11 present the temporal evolution of stress distributions under distinct cases. To analyze the evolution law of seismic waves generated on the surface after single-hole detonation, the surface stress evolution during this process is illustrated in Figure 9a. As shown, at t = 1.9 ms, changes appear in the stress contour map, indicating the seismic wave reaches the surface. Peak stress occurs at t = 5.4 ms. Subsequently, the seismic wave enters the attenuation phase, and due to the absence of further detonation, the stress ultimately attenuates, dissipating essentially by t = 7.4 ms. Figure 9b presents the surface stress evolution under a 2 ms delay time, where the detonation time of the second wave differs from the first by 2 ms. The second wave arrives at the surface at 3.9 ms, peaking at 7.4 ms, while the third wave arrives at 5.9 ms and peaks at 9.4 ms. Crucially, at t = 7.4 ms (when the second wave peaks), the stress from the first wave at the surface  
Figure 11: Stress contour in Class V surrounding rock under blasting. Figure 10: Stress contour in Class IV surrounding rock under blasting. has essentially dissipated, as evidenced in Figure 9a. Consequently, the second wave experiences minimal impact from the first wave. In summary, when applying millisecond delay blasting (MS Delay Blasting) with a 2 ms interval in Class III surrounding rock, the stress waves generated by sequential blasts do not produce significant superposition effects on the surface. Similarly, Figure 10 presents the stress evolution during single-hole and millisecond delay blasting in Class IV surrounding rock. Figure 10a illustrates the single-hole blasting stress contour, revealing seismic wave arrival at the surface at t = 3.0 ms, peak stress occurrence at t = 7.1 ms, and subsequent stress decay with near-complete dissipation (central zone) at t = 9.1 ms, culminating in full dissipation by t = 12.1 ms. Figure 10b depicts stress contours under 2 ms millisecond delay blasting, with the second wave arriving at 5.0 ms (peaking at 9.1 ms) and the third wave at 7.0 ms (peaking at 12.1 ms). Comparative analysis with Figure 9 demonstrates that the superposition effect between the first and second waves in Class IV is more significant. Similarly, the third and second waves also superimpose. This results in a significant stress enhancement zone above the tunnel face at 7.1 ms, 9.1 ms, and 12.1 ms. Consequently, stress wave superposition intensifies markedly in Class IV compared to Class III. Figure 11 examines the stress evolution in Class V surrounding rock under single-hole and 2 ms millisecond delay blasting. An analysis of Figure 11a,b indicates that: the first wave arrives at 4.0 ms (peaking at 10.2 ms), followed by the second wave at 6.0 ms (peaking at 12.2 ms) and the third wave at 8.0 ms. Crucially, when the second wave peaks at t = 12.2 ms, substantial residual stress from the first wave persists on the surface, resulting in significant superposition between the first and second waves. The preceding analysis indicates surface stress wave evolution across different surrounding rock classes. For Classes III and IV, superposition occurs between initial and subsequent waves but with negligible effects. In Class V surrounding rock, due to the slowed attenuation of blast-induced seismic waves, preceding and subsequent waves overlap. When the stress of the seismic wave generated by the first detonation reaches its maximum value, the seismic wave from the third detonation has already arrived at the ground surface. Moreover, when the stress of the second wave sequence peaks, the energy of the first wave sequence has not yet dissipated.