# Prediction of Tunnel Blasting Vibration Velocity Considering the Influence of Free Surface
## 1 Introduction  
Tunnel blasting vibration has a negative impact on the surrounding buildings [1; 2; 3; 4], and the reasonable prediction of vibration velocity can provide a theoretical basis for field charge design. Currently, the charge in the cut hole is the primary calculation parameter in blast vibration calculations [5; 6]. When a tunnel-cutting hole blast creates a new free surface, the free surface of the non-cutting hole blasting increases, and the conversion of explosive energy into vibration energy decreases accordingly [7; 8]. The blasting-free surface and burden affect the propagation of vibration waves [9; 10]. Many scholars have conducted a lot of research on the vibration velocity of different free surfaces. [PERSON] [11] has confirmed through field tests that the cutting blashhole causes a vibration that is 1.5-2 times greater than that caused by the breaking blashhole and contour blasthole. According to [PERSON] [12], the cutting blashhole has a substantially higher blasting vibration velocity per unit charge than the non-cutting blashhole. [PERSON] [13] studied the vibration of multi-row blasthole blasting using field measurements and numerical simulations and came to the conclusion that the vibration generated by the following row was 14-22% less than that of the first row with the same charge. The blast vibration is also impacted by the burden at the same time. [PERSON] [14] believed that the blast vibration decreases as the burden reduces. Unfortunately, the above literature does not quantify the effect of the number of free faces on the peakvelocity. In China, the Sadovsky formula suggested by Chinese regulations (GB 6722-2014) is frequently used to determine the peak blast vibration prediction:  
\[v=k\bigg{(}\frac{\sqrt[3]{Q}}{R}\bigg{)}^{\alpha} \tag{1}\]  
where \(v\) is the peak vibration velocity of the particle, cm/s, and \(Q\) is the explosive amount per delay (kg). \(R\) is the distance between the blasting source and the measurement point (m), \(k\) is the blasting design and field geology coefficient, and \(\alpha\) is the attenuation coefficient.  
[PERSON] [15] and [PERSON] [16] studied the effect of free surface on blast vibration and also revised the site coefficients \(K\) and \(\alpha\). [PERSON] [17] and [PERSON] [18] modified and validated the Sadovsky formula by taking into account the number and area of free surfaces. Existing research has taken into account how the number of free surfaces affects the calculation of blast velocity, but few studies have taken into account another crucial factor--the burden. Therefore, an in-depth understanding of the influence of free surface and burdens on blast vibration is important for optimizing blast design.  
In order to develop a prediction formula for peak vibration velocity that can effectively predict the influence of blasting-free surfaces, this paper aims to investigate the effects of the number of blasting-free surfaces and burden distance on the blasting vibration velocity through single-hole tests and field engineering applications. The study's findings can quantify the effect of the free surface factor on the attenuation of blasting vibrations and offer a more precise method for predicting blasting vibrations, which can offer a theoretical basis for ensuring the security of tunnel construction and guiding the design of blasting parameters.