# Experimental and Numerical Studies on Ground Shock Generated by Large Equivalent Surface Explosions
## 5 Discussion  
By combining the experimental, theoretical, and numerical findings of the propagation behaviors of ground shocks, a relationship between the maximum particle vibration velocity and the propagation distance was derived for the 1 t TNT explosion, as shown in Figure 12a. Here, it is shown that the numerically simulated and theoretically derived maximum  
Figure 11: The effects of grid size on the computed velocity–time curve.  
particle vibration velocities were in good agreement (the differences were generally within 10%), and that they both decreased exponentially with increasing propagation distance.  
The first blast-resistant design standards for hazardous chemical storage facilities were based on a charge weight equivalent to 10 t TNT. Because we were unable to measure valid data from the 10 t TNT explosion experiment, the propagation behavior of the ground shock generated by the 10 t TNT charge was studied based on numerical simulation and theoretical analysis. The scaling factor for scaling a 10 t TNT explosion to a 1 t TNT explosion is \(C_{L-10\text{c:It}}=\frac{\sqrt{10,000}}{\sqrt{1000}}=2.154\). Therefore, to compute the decay in the maximum particle vibration velocity in the area near the epicenter of the 10 t TNT explosion, one simply has to multiply the temporal and spatial scales of the curve in Figure 12a by a factor of 2.154, as shown in Figure 12b.  
The _Blasting Safety Regulations_ (GB6722-2014) has defined a safety criterion for blast-induced vibrations in structures such as freshly poured large-volume concrete structures, tunnels/roadways, and high rock slopes, as shown in Table 6[29].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{4}{c}{**Safe and Permissible Particle**} \\ \cline{2-4}
**Type of To-Be-Protected Structure** & \multicolumn{3}{c}{**Vibration Velocities, \(v\) (cm/s)**} \\ \cline{2-4}  & \(f\leq\) 10 Hz & 10 Hz \(<\)\(f\leq\) 50 Hz & \(f>\) 50 Hz \\ \hline Cave dwellings, adobe houses, and & & & \\ rubble houses & 0.15–0.45 & 0.45–0.9 & 0.9–1.5 \\ Ordinary civilian buildings & 1.5–2 & 2–2.5 & 2.5–3 \\ Industrial and commercial buildings & 2.5–3.5 & 3.5–4.5 & 4.2–5 \\ Ordinary historical buildings and sites & 0.1–0.2 & 0.2–0.3 & 0.3–0.5 \\ Central control room equipment in & & & \\ operational hydropower stations and & 0.5–0.6 & 0.6–0.7 & 0.7–0.9 \\ power stations & & & \\ Hydraulic tunnels & 7–8 & 8–10 & 10–15 \\ Traffic tunnels & 10–12 & 12–15 & 15–20 \\ Mine roadways & 15–18 & 18–25 & 25–30 \\ Permanent rocky high slopes & 5–9 & 8–12 & 10–15 \\ Age: Initial setting–3 days & 1.5–2 & 2–2.5 & 2.5–3 \\ Age: 3–7 days & 3–4 & 4–5 & 5–7 \\ Age: 7–28 days & 7–8 & 8–10 & 10–12 \\ \hline \hline \end{tabular} Note: 1. The vibrational frequency refers to the dominant frequency of vibration. 2. The frequency range was determined from field measurements of the ground shock waveform or data selected based on the following criteria: cavern blasting/ \(f<\) 20 Hz; open-air deep-hole blasting: 10 Hz \(<\)\(f<\) 60 Hz; open-air shallow-hole blasting: 40 Hz \(<\)\(f<\) 100 Hz; underground shallow-hole blasting: 60 Hz \(<\)\(f<\) 300 Hz.  
\end{table}
Table 6: Safety criterion for blast-induced vibrations [29].  
Figure 12: The relationship between the maximum particle vibration velocity and the propagation distance, (**a**) 1t TNT and (**b**) 10t TNT.  
Because surface explosions are similar to open-air shallow-hole blasts, which have an \(f\) between 40 and 100 Hz, it may be assumed that the \(f\) was greater than 50 Hz during the 1 t and 10 t TNT test. Based on Figure 12b and Table 6, the minimum safe distances for a variety of to-be-protected structures (in terms of vibration safety) were derived for a 1 t and 10 t TNT blast, as shown in Tables 7 and 8.