# Prediction of Tunnel Blasting Vibration Velocity Considering the Influence of Free Surface
## 5 Engineering Applications
### Control of Blasting Parameters  
With the large excavation section of the new tunnel and a large number of boreholes, the superimposed blasting vibration effect could lead to peak vibration velocity. Meanwhile, when the new tunnel is closest to the existing tunnel, the minimum clear distance is smaller than the excavation span and also aggravates the construction risk. Therefore, it is essential to dynamically modify the burden distance and amount per delayed charge in addition to controlling the blasting charge in the cutting blasthole. To obtain the relationship between  
Figure 10: Time history curve of the measuring point.  
Figure 9: Schematic diagram of measuring point layout.  
the proximity tunnel vibration effect and blasting parameters, the peak blast velocity of each delayed charge can be accurately predicted according to Equation (8). Once the set safe vibration velocity is selected, the optimal blasting parameters can be selected by the relationship between the amount of charge per charge \(Q\), the number of free surfaces \(m\), and the burden distance \(W_{\text{min}}\), as reflected in Equation (9).  
\[Q=R^{3}\times\exp(0.92\ln v-8.54-0.40\ln\left(\frac{W_{\text{min}}}{mR}\right)) \tag{9}\]  
When the safe vibration velocity of 5 cm/s is determined, the blasting parameters can be selected according to Figure 11. For example, when the near tunnel distance \(R=15\) m, \(W_{\text{min}}=2.0\) m for the cutting blasthole, and the maximum delayed charge is controlled within 6.5 kg, the number of blastholes in the contour blasthole is large, \(m=2\), \(W_{\text{min}}=0.5\) m, and the maximum delayed charge is controlled within 14.9 kg.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Points Number**} & **Detonator** & \multirow{2}{*}{**Q**} & \multirow{2}{*}{**\(m\)**} & \multirow{2}{*}{**\(R\)**} & \multirow{2}{*}{**\(PPV\)**} & **Sadovsky** & & **Correction** & \\  & & & & & /cm & /m & /(cm/s) & & **Formula** & **Formula** & **Tolerance** \\  & & & & & & /(cm/s) & & & /(cm/s) & & **/(cm/s)** & \\ \hline \multirow{8}{*}{\(1\)} & MS1 & 33.6 & 1 & 2.0 & 26.7 & 3.90 & 1.44 & 44.89\% & 3.08 & 18.15\% \\  & MS3 & 42.6 & 2 & 0.5 & 26.7 & 2.09 & 1.94 & 53.78\% & 1.63 & 29.43\% \\  & MS5 & 34.2 & 2 & 0.5 & 26.7 & 1.96 & 1.47 & 37.46\% & 1.29 & 20.14\% \\  & MS7 & 25.8 & 2 & 0.5 & 26.7 & 2.23 & 1.62 & 25.85\% & 1.40 & 8.52\% \\  & MS9 & 28.5 & 2 & 0.5 & 26.7 & 1.50 & 1.17 & 1.69\% & 1.06 & 11.34\% \\  & MS11 & 26.7 & 2 & 0.5 & 26.7 & 0.73 & 0.55 & 0.16\% & 0.55 & 0.14\% \\  & MS13 & 24.6 & 2 & 0.5 & 26.7 & 0.90 & 0.97 & 17.18\% & 0.90 & 8.38\% \\ \hline \multirow{8}{*}{\(2\)} & MS1 & 33.6 & 1 & 2.0 & 26.9 & 3.72 & 1.65 & 55.63\% & 3.53 & 5.19\% \\  & MS3 & 42.6 & 2 & 0.5 & 26.9 & 1.63 & 2.22 & 36.39\% & 1.87 & 14.43\% \\  & MS5 & 34.2 & 2 & 0.5 & 26.9 & 1.26 & 1.69 & 33.93\% & 1.47 & 16.69\% \\  & MS7 & 25.8 & 2 & 0.5 & 26.9 & 1.53 & 1.86 & 21.74\% & 1.60 & 4.65\% \\  & MS9 & 28.5 & 2 & 0.5 & 26.9 & 1.21 & 1.34 & 10.93\% & 1.21 & 0.27\% \\  & MS11 & 26.7 & 2 & 0.5 & 26.9 & 0.62 & 0.63 & 1.61\% & 0.63 & 1.32\% \\  & MS13 & 24.6 & 2 & 0.5 & 26.9 & 0.79 & 1.12 & 41.26\% & 1.03 & 30.24\% \\ \hline \multirow{8}{*}{\(3\)} & MS1 & 33.6 & 1 & 2.0 & 27.9 & 2.61 & 1.70 & 56.48\% & 3.63 & 7.05\% \\  & MS3 & 42.6 & 2 & 0.5 & 27.9 & 1.26 & 2.29 & 9.40\% & 1.92 & 8.27\% \\  & MS5 & 34.2 & 2 & 0.5 & 27.9 & 1.07 & 1.74 & 11.45\% & 1.51 & 22.90\% \\  & MS7 & 25.8 & 2 & 0.5 & 27.9 & 1.29 & 1.92 & 14.09\% & 1.65 & 26.20\% \\  & MS9 & 28.5 & 2 & 0.5 & 27.9 & 1.19 & 1.38 & 7.96\% & 1.24 & 17.31\% \\  & MS11 & 26.7 & 2 & 0.5 & 27.9 & 0.55 & 0.65 & 11.24\% & 0.65 & 11.55\% \\  & MS13 & 24.6 & 2 & 0.5 & 27.9 & 0.83 & 1.15 & 27.52\% & 1.06 & 17.51\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Test result statistics.  
Figure 11: Control of safe charge.