# Study on Vibration Effects and Optimal Delay Time for Tunnel Cut-Blasting Beneath Existing Railways
## 1 Introduction
[16] used a combination of theoretical analysis and case study to investigate the vibration frequency characteristics of blasting excavation in highly stressed rock masses, and discussed the vibration frequency characteristics and their influencing factors under the action of blast load and dynamic unloading. [PERSON] et al. [17] established an attenuation equation for the peak particle vibration velocity by taking into account the attenuation characteristics of P-waves, S-waves, and R-waves in the blasting vibration wave. [PERSON] et al. [18] turned to signal processing through MATLAB, explored the propagation law of blasting vibration in the stratum, and proposed a vibration reduction program to reduce the peak vibration velocity. In summary, peak vibration velocity is an important index to evaluate the hazard of blasting vibration, which is the key to ensuring construction safety. Based on the understanding of stress wave propagation and attenuation, vibration control can be realized by controlled blasting. [PERSON] et al. [19] analyzed the propagation and attenuation characteristics of blasting vibration in rock tunnels, and proposed a formula for predicting the peak particle velocity of adjacent tunnel sections, considering the amplification effect of the blasting vibration of adjacent tunnels by diffraction and reflection. [PERSON] et al. [20] analyzed the vibration response of the blasting construction sequence on the peak particle velocity (PPV) of the neighboring villages. The adjustment of the blasting sequence plays a positive role in controlling and reducing the blasting stress wave, and effectively reduces the stress propagated to the neighboring structures. [PERSON] et al. [21] used theoretical analysis and field test methods to study the safe control of the vibration reduction effect of high-frequency blasting vibration in existing tunnels and different blasting vibration reduction control techniques, which ensures the safe operation of the existing tunnels. In summary, limiting the peak vibration velocity of the mass at the surface can effectively reduce the vibration effect generated by the blasting construction of the tunnel crossing under the existing railway, thus guaranteeing the safety of the structure. Millisecond blasting is one of the most effective methods to reduce the vibration effect of blasting. It mainly serves to disperse blasting energy by detonating explosives within milliseconds. [PERSON] et al. [22] proposed a method for predicting and controlling the blasting vibration spectrum of high slopes, based on a technique for predicting the time history of blast vibrations, and determined the optimal delay time. [PERSON] et al. [23] discussed the effects of millisecond blasting time, charge length, and explosion speed on blasting vibration. Selecting the differential delay time reasonably is an effective way to control the peak vibration velocity. However, the optimal differential time interval depends on multiple factors. [PERSON] et al. [24] considered the superposition of the wave offset effect and rock fragmentation effect, theoretically analyzing the optimal delay time selection of a reasonable range. [PERSON] et al. [25] analyzed the influence of delay time on the vector peak particle velocity of superimposed vibration waveforms and established a calculation formula for the minimum delay time between adjacent boreholes based on vibration reduction. This support is crucial for optimizing millisecond blasting parameters, ultimately enabling effective control of blasting vibration hazards. The superposition of blasting seismic waves is affected by many factors. [PERSON] et al. [26; 27] explored the superposition of blasting waves in the case of confined geometries and variable cross-sectional charges, and divided different superposition regions according to different energies. [PERSON] et al. [28] analyzed the blasting vibration spectra with different delay times and core distances and studied the frequency distribution and energy characteristics of each frequency band.