## 3 Dynamic Response Analysis of Ground Buildings Under Blasting  
### The Analysis of Field Monitoring of Blast Weakening Vibrations  
The vibrations near ground buildings is monitored during the blast weakening of top coal according to the above monitoring scheme. The results of vibration monitoring are shown in Table 3. (The automatic trigger of monitoring point 2-3 does not reach 0.051 cm/s, which does not monitor the data. Therefore, it is not displayed). The analysis shows that the main frequency of blasting vibrations is between 8.5 and 20 Hz, and results below 10 Hz account for a large proportion. According to 'Blasting Safety Regulations' [40], when the main frequency is within 10 Hz, the allowable value of vibration velocity is 1.5 cm/s. The blasting site is far away from the monitoring points. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Explosion Velocity** & **A** & **B** & **R11** & **R21** & **\(\mathbf{\omega}\)** & **E0** \\
**Velocity m\(\cdot\)s\({}^{-1}\)** & **GPa** & **GPa** & **R11** & **R21** & **\(\mathbf{\omega}\)** & **GPa** \\ \hline
3600 & 214.4 & 0.182 & 4.2 & 0.9 & 0.15 & 4.192 \\ \hline \end{tabular}
\end{table} 
Table 2: Explosive materials and JWL equation of state parameters. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Monitoring Point** & **Channel** & **Vibration Velocity Peak (cm/s)** & **Frequency Velocity (Hz)** & **Combined Velocity (cm/s)** & **Explosive Capacity Charge (kg)** & **Z- Directiondistance (m)** & **X- Directiondistance (m)** & **Y- Directiondistance (m)** \\ \hline \multirow{4}{*}{Point 1-1} & X & 0.151 & 12.81 & & & & & \\  & Y & 0.154 & 10.36 & 0.281 & & 166.5 & 196.3 & 497 & 326 \\  & Z & 0.181 & 9.77 & & & & & & \\  & X & 0.156 & 8.55 & & & & & & \\ Point 1-2 & Y & 0.151 & 8.84 & 0.285 & 166.5 & 196.3 & 445 & 496 \\  & Z & 0.185 & 10.74 & & & & & & \\  & X & 0.152 & 12.82 & & & & & & \\ Point 1-3 & Y & 0.165 & 10.38 & 0.286 & 166.5 & 196.3 & 426 & 492 \\  & Z & 0.176 & 14.65 & & & & & & \\  & X & 0.156 & 9.16 & & & & & \\ Point 2-1 & Y & 0.172 & 18.31 & 0.284 & 171 & 203.5 & 529 & 441 \\  & Z & 0.164 & 10.98 & & & & & & \\  & X & 0.166 & 10.26 & & & & & \\ Point 2-2 & Y & 0.162 & 16.54 & 0.282 & 171 & 203.5 & 526 & 443 \\  & Z & 0.161 & 11.25 & & & & & \\  & X & 0.168 & 9.16 & & & & & \\ Point 3-1 & Y & 0.175 & 7.94 & 0.298 & 166.5 & 208.5 & 566 & 398 \\  & Z & 0.174 & 9.22 & & & & & \\  & X & 0.154 & 5.493 & & & & & \\ Point 3-2 & Y & 0.168 & 20.14 & 0.282 & 166.5 & 208.5 & 473 & 369 \\  & Z & 0.166 & 9.77 & & & & & \\  & X & 0.153 & 9.12 & & & & & \\ Point 3-3 & Y & 0.164 & 18.31 & 0.283 & 171 & 208.5 & 437 & 378 \\  & Z & 0.172 & 7.94 & & & & & \\ \hline \end{tabular}
\end{table} 
Table 3: Monitoring results of blasting vibrations. Therefore, the peak value of the vibration velocity at each point is small. The maximum value does not exceed 0.2 cm/s, which is less than the allowable value 1.5 cm/s of blasting vibrations. When the 2303 working face advances to the remaining 400 m, the underground blast weakening uses about 170 kg of the emulsion explosive for a three-level coal mine. The ground buildings are not affected and remain in a safe state. The prediction of blasting vibration velocity is carried out using the Sadovsky formula [41; 42; 43; 44; 45]. The ORIGIN is used for fitting according to the peak velocity of the Z-direction in Table 2. The attenuation coefficient \(\alpha\) is 1.4, and the empirical coefficient K is 164.34. Equation (2) can be obtained by substituting \(\alpha\) and K into the Sadovsky formula:  
\[V=164.34(\frac{Q^{\frac{1}{3}}}{R})^{1.4}, \tag{2}\]  
where \(V\) is the allowable safe velocity of blasting vibrations, cm/s, and \(Q\) is the explosive charge. The total charge is taken during one blast, and the maximum charge is taken during segmented delayed blasting, kg.