# Study on Dominant Frequency Attenuation of Blasting Vibration for Ultra-Small-Spacing Tunnel
## 7 Conclusions  
Based on the framework of this research, the following conclusions can be drawn. The dominant frequencies of blast vibration have a wide range of distribution in areas relatively close to the blast, which are mainly distributed within 200 Hz. There is a clear difference in the distribution of the dominant frequency on the primary support and the lining: (1) The distribution of the dominant frequencies on the primary support is broader than that on the lining, and (2) the dominant frequencies on the lining are concentrated in the range when the lining is far from the blast face beside a specific value. The main reasons are the cavities and gaps between the primary support and the lining have the characteristics of vibration damping and filtering, hindering the propagation of the blasting vibration waves with some frequencies. Additionally, the vibration waves are more affected by characteristics of blast design in areas relatively close to the blast, while at larger distances the propagating medium dominates the vibration response. The high-frequency part of the vibration waves attenuates rapidly on the primary support under the damping effect of the rock, whereas the Z-direction (transverse) dominant frequency decays gradually. The power function of the upper and lower bounds of the dominant frequency on the primary support with the SD was proposed. Multiple delay sequences blast contributes to a multi-structured amplitude spectrum of blast vibration waves. There are distinct differences between the global frequency of the entire vibration time series and the dominant frequencies at different delay sequences. The global frequency determined in all delays of the vibrations is close to the dominant frequency detonated in the cutting blastholes. The dominant frequencies in different sequences correspond to two parameters of the different delay sequences. Multiple free surfaces cause the overall trend of dominant frequency increase, and a large EBVS implies a low vibration frequency. The ZCFs and DFs exhibit a nonlinear relationship. This is because the DF describes the entire waveform, while the ZCF only describes the frequency of the cycle with the maximum \begin{table}
\begin{tabular}{c c c c} \hline
**Structure Type** & \(f\leq 10\) **Hz** & **10–50 Hz** & \(f>50\) **Hz** \\ \hline General civil buildings & 1.5–2.0 & 2.0–2.5 & 2.5–3.0 \\ Hydraulic tunnel & 7–8 & 8–10 & 10–15 \\ Traffic tunnel & 10–12 & 12–15 & 15–20 \\ Mine roadway & 15–18 & 18–25 & 20–30 \\ \hline \end{tabular}
\end{table} 
Table 6: Safety PPV for blasting vibration (GB6722-2014, China). amplitude. Nevertheless, the distribution of dominant frequencies in the different scaling distances obtained in this paper can be used to guide the selection of a suitable safe PPV. Because of the fluctuating drop of the vibration dominant frequency with the distance, further discussion is needed on how the different frequency components are decayed. Since the selection of safe PPV depends on the dominant frequency of blast vibration, finding a frequency that is more appropriate than the above for engineering is still worthy of further research. Conceptualization, [PERSON] ([PERSON]) and [PERSON] ([PERSON]); methodology, [PERSON] ([PERSON]) and [PERSON]; validation, [PERSON] ([PERSON]) and [PERSON]; data curation, [PERSON] ([PERSON]), [PERSON], J.M. and T.H. ; writing-original draft preparation, [PERSON] ([PERSON]); writing--review and editing, [PERSON] ([PERSON]) and [PERSON]; project administration, [PERSON], [PERSON] and T.H. ; funding acquisition, [PERSON] ([PERSON]) and [PERSON] ([PERSON]). All authors have read and agreed to the published version of the manuscript. This study was supported by the National Natural Science Foundation of China [grant number 51978671] and the Fundamental Research Funds for the Central Universities of Central South University [grant number 1053320192626]. Not applicable. Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.