## 3 Rock Breaking Design Program
### Dynamic Blasting
#### 3.1.2 Monitoring and Fitting  
An attempt is first made to obtain the blasting vibration fitting equations for the study area. The TC-4850 blast vibrometer (Zhongke Electric, Yueyang, China), TC-3850 blast vibrometer (Zhongke Electric, Yueyang, China), CDJ-1 type velocity sensor (China Sichuan Chengdu Zhongke measurement and Control Co., LTD, Chengdu, China), and three-direction velocity sensor (China Sichuan Chengdu Zhongke measurement and Control Co., LTD, Chengdu, China) were utilized to perform on-site PPV monitoring. The obtained PPV monitoring results were divided into three velocity directions: vertical, radial, and tangential. Since the PPV mainly occurs in the vertical direction [26; 27], only the vibration velocity in the vertical direction is regressed and analyzed in this study. The vibration test results and vertical vibration velocity are shown in Table 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Monitoring Point No.** & **R (m)** & **Q (kg)** & **PPV (cm/s)** & **Main Vibration Frequency (Hz)** \\ \hline
1 & 26 & 20 & 4.52 & 108.108 \\
2 & 28 & 22 & 4.25 & 98.199 \\
3 & 35 & 18 & 2.93 & 116.280 \\
4 & 42 & 24 & 2.64 & 166.166 \\
5 & 31 & 15 & 2.98 & 85.107 \\
6 & 39 & 18 & 2.69 & 109.863 \\
7 & 28 & 17 & 3.67 & 94.933 \\
8 & 13 & 17 & 11.78 & 88.889 \\
9 & 53 & 14 & 1.56 & 200.911 \\
10 & 50 & 12 & 1.39 & 192.667 \\
11 & 40 & 11 & 1.96 & 145.752 \\
12 & 24 & 12 & 3.79 & 90.909 \\
13 & 35 & 12 & 2.47 & 100.122 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Vibration test results. Figure 5: Schematic diagram of tunnel excavation section, borehole distribution and detonator segmentation of drilling and blasting method. (**a**) Tunnel excavation sections; (**b**) drilling and blasting hole distribution and detonator segmentation. Based on Table 2 and Equations (1)-(6), the relevant parameters can be determined as: \(K=103.02\), \(\alpha=1.377\). It can be found from Table 1 that the \(K\) is in the range of 50-150 and the \(\alpha\) is in the range of 1.3-1.5 for hard rock, which is in line with the actual rock mass conditions. The fitting equation for the vibration velocity of the explosive blasting currently is as follows:  
\[PPV=103.02\times\left(\frac{\sqrt[3]{Q}}{R}\right)^{1.377} \tag{7}\]  
Then based on Equation (7), for the inverse highway roadbed (HR), underground pipeline (UP), and high-speed rail line (HSRT) to reach the PPV control value at the nearest distance to the maximum section of the explosive charge, that is, the limit cases of the maximum section of the explosive charge without considering the possibility of practical operation, the values are, specifically, as shown in Table 3.  
(1) Drilling and blasting  
Based on the tunnel segmentation schematic, the PPV in the upper bench blasting will occur in the 13 th segment at the tunnel face of section YK9+082. The Q of the 13 th section, the explosive charge per hole, and the charge of other segments is calculated according to Table 3 and Equation (7). Finally, the vibration velocity of the highway roadbed, underground pipelines and high-speed rail line caused by blasting with explosives in each section is back-calculated to verify whether the PPV control value is exceeded, and the calculated seismic wave propagation distance is taken as the average value of the distances of each section of the gun holes. The results show that, for the upper bench blasting at the tunnel face at section YK9+082 in the 13 th section (Q is 6.8 kg), the PPV for the highway roadbed, underground pipelines and high-speed rail line are calculated to be 6.95 cm/s, 6.36 cm/s and 0.97 cm/s, respectively, which are close to but less than the limit of the specified PPV. Similarly, the PPV of each section at the lower bench of the tunnel face at section YK9+082 during blasting are calculated. Since the underground pipeline is closer to the tunnel lower bench, it is not necessary to calculate the PPV of each section of Q for the highway roadbed during blasting of the lower bench.