# Prediction of Tunnel Blasting Vibration Velocity Considering the Influence of Free Surface
## 6 Conclusions  
Through the analysis of the tunnel single-hole blasting test and field blasting prediction, the blasting vibration velocity under different free surfaces and burdens were compared and analyzed, and the following conclusions were drawn.  
1. There is a strong relationship between the number of free faces and the minimum burden, with more free faces resulting in a lower vibration velocity and a smaller minimum burden resulting in a lower vibration velocity.
2. By introducing the number of free surfaces and burden distance to the Sadovsky formula for correction, the correction formula regression coefficient is \(R^{2}=0.83\) and \(R^{2}=0.74\) for the Sadovsky formula. The correction formula significantly enhances the ability to predict blast vibration, allowing for a greater application while more correctly reflecting the decay pattern of the blast vibration brought on by the free surface.
3. Through the analysis and fitting of the measured peak value of vibration velocity, the ratio of the parameter \(\alpha\) of the proportional distance factor to the parameter \(\eta\) reflecting the free surface factor is 0.73/0.21. The contribution of the free surface factor to the attenuation of vibration velocity accounts for 21% of the total factors, which cannot be ignored.
4. The correction formula considering the number of free surfaces and burden distance can improve the accuracy of vibration velocity prediction. The prediction accuracy of the cutting blashhole is improved from 56.48% to 18.15% of the relative tolerance of the Sadovsky formula, and the average tolerance is improved from 24.79% to 13.32%. The correction formula can better predict the variation in vibration velocity at the site and provide a reliable basis for the design parameters of blasting at the site.
5. When the safe vibration velocity is known, the correction formula can be used to back-calculate the maximum charge for each series. This can be used to optimize the blasting design parameters for each series in the field.  
In this paper, the effect of free surface factors on the blast vibration was investigated through single-hole tests and field applications, and a free surface correction was made to the traditional Sadovsky formula. However, the essence of the effect of the free face on blast vibration lies in altering the confining action of the surrounding rock, and this paper fails to study the effect of the free face from the theory. Therefore, in future research, theoretical studies are needed to further reveal the mechanism of the free surface effect.  
Writing--original draft preparation, X.Z. ([PERSON]); Conceptualization, X.Z. ([PERSON]); Investigation, J.C.; writing--review and editing, X.Z. ([PERSON]); data curation, Y.D. All authors have read and agreed to the published version of the manuscript.  
Supported by the National Natural Science Foundation of China (51978671) and the Graduate Innovation Project of Central South University (1053320213139).  
Not applicable.  
The authors would like to thank [PERSON] of the Railway Development Investment Group Co., Ltd. for his support of this work.  
The authors declare no conflict of interest.