## 6 Conclusions  
This study investigated the arch vibration attenuation law, structural energy response, and safety criterion using blasting vibration monitoring in the Jiaohuayu Tunnel. The primary conclusions of this study are as follows:  
1. The PPV at the vault was always larger than at the arch waist and was greater than at the sidewall regardless of direction (i.e., horizontal tangential, horizontal radial, and vertical). The vertical vibration velocity was the largest; the PPV at the vault decayed faster than the other two; the attenuation of the three-direction PPV at the same measuring point tends to be stable with increasing propagation distance. 2. The arch waist was where the greatest risk of structural damage occurred at each position of the tunnel based on the dominant frequency. The millisecond delay detonator blasting vibration signal was widely distributed in the frequency domain, but the energy was primarily concentrated at 200 Hz. 3. When the engineering structure entered the elastic-plastic stage under the action of blasting vibration, the energy dissipation mode began to change, primarily based on damping energy dissipation and hysteretic energy dissipation. This mode is of practical importance to evaluate the safety of cumulative damage of engineering structures and measure the cumulative damage of structures by hysteretic energy. 4. Existing safety criteria can be supplemented and improved using the maximum instantaneous input energy to measure the first passage damage, the hysteretic energy consumption to measure the cumulative damage, and the input-hysteretic energy criterion to judge the structural failure. The energy threshold of the first passage failure of the test section was 200 J, and the plastic cumulative damage was 3000 J. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **Natural Period (s)** & **Maximum Instantaneous Input** & **Hysteretic Energy** & **Initial Lining State** \\  & & **Energy (J)** & **Consumption (J)** & **Initial Lining State** \\ \hline
1 & 0.1428 & 213.49 & 2800.35 & cracked \\
**2** & **0.1462** & **179.73** & **1891.44** & **intact** \\
3 & 0.1394 & 130.06 & 1382.43 & intact \\
4 & 0.1428 & 227.92 & 2731.77 & cracked \\
5 & 0.1378 & 158.34 & 1711.49 & intact \\
6 & 0.1394 & 159.18 & 1804.24 & intact \\
7 & 0.1445 & 135.82 & 1488.37 & intact \\
8 & 0.1512 & 154.25 & 1712.96 & intact \\
9 & 0.1478 & 162.02 & 2746.45 & intact \\
10 & 0.1378 & 148.35 & 3032.58 & damaged \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Energy response at the sidewall. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No.** & **Natural Period (s)** & **Maximum Instantaneous Input** & **Hysteretic Energy** & **Initial Lining State** \\  & & **Energy (J)** & **Consumption (J)** & **Initial Lining State** \\ \hline
1 & 0.1428 & _230.23_ & 2319.98 & cracked \\
2 & 0.1462 & 185.99 & 2039.79 & intact \\
3 & 0.1394 & 132.4 & 1490.85 & intact \\
4 & 0.1428 & 145.79 & _3046.03_ & damaged \\
**5** & **0.1378** & **192.93** & **1845.72** & **intact** \\
6 & 0.1394 & 163.82 & 1945.75 & intact \\
7 & 0.1445 & 138.64 & 1605.11 & intact \\
8 & 0.1512 & _228.5_ & 1847.30 & cracked \\
9 & 0.1478 & 166.88 & 1883.43 & intact \\
10 & 0.1378 & 147.84 & 3270.43 & damaged \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Energy response at the arch waist. The results of this study are important when evaluating the safety of a tunnel's initial lining structure. However, the threshold of maximum instantaneous energy or hysteretic energy consumption will be different for different structures. A lot of experimental data and more engineering practice are required to improve and apply the input-hysteretic energy criterion. S.H. : writing--original draft, validation, formal analysis; F.X. : conceptualization, methodology, data curation, formal analysis, writing--review and editing; S.T. : formal analysis, writing--review and editing; S.L. : conceptualization, writing--review and editing, funding acquisition. All authors have read and agreed to the published version of the manuscript.