## 4 Results  
### Blast inside the Ammunition Storage Magazine  
(1) Experimental results  
A C4 explosive was used to implement an explosion inside the ammunition storage magazine. The explosive was detonated at the portal and at 1\(\times\) the portal diameter inside the ammunition storage magazine. The experimentally measured overpressure was used for the regression analysis to obtain the empirical equations of the internal blast, as shown in Equations (7) and (8):  
\[y_{1}=1472\cdot x^{-0.6}, \tag{7}\]  
where  
\(y_{1}:\) internal blast value of the ammunition storage magazine (kPa)  
\(x:\) ratio of the distance from the measuring point to the portal inside the ammunition storage magazine (\(l\)) to the portal diameter (\(d\)). \[y_{2}=9003\cdot x^{-2.12}, \tag{8}\]  
where \(y_{2}:\) internal blast value of the ammunition storage magazine (kPa). (2) Comparison of the empirical equations  
1. Explosion at the portal  
The empirical equation of [PERSON] et al. [9] was compared with the experimental results, as shown in Figure 7. It was observed that the measured value was smaller than the Welch empirical equation when the ratio of the distance from the measuring point to the portal inside the ammunition storage magazine (\(l\)) to the portal diameter (\(d\)) ranged from 0.067 to 1, and that the relative errors were 184.67% and 115.86%. However, the Welch empirical equation was close to the experimental value when \(l/d=2\)-3, where the relative errors were 17.23% and \(-\)16.79%. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{4}{c}{**MAT\_NULL, EOS\_LINEAR\_POLYNOMINAL**} \\ \hline Air & \(\rho\) (g/cm\({}^{3}\)) & \(C_{0}\) & \(C_{1}\) & \(C_{2}\) & \(C_{3}\) \\ \cline{2-6}  & \(1.29\times 10^{-3}\) & 0 & 0 & 0 & 0 \\ \cline{2-6}  & \(C_{4}\) & \(C_{5}\) & \(C_{6}\) & \(E_{0}\) (Mbar) & \\ \cline{2-6}  & 0.4 & 0.4 & 0 & \(2.5\times 10^{-6}\) & \\ \hline  & \multicolumn{4}{c}{MAT\_HIGH\_EXPLOSIVE, EOS\_JWL} \\ \hline Explosive & \(\rho\) (g/cm\({}^{3}\)) & \(D\) (cm/\(\mu\)s) & PCJ (Mbar) & \(A\) (Mbar) & \(B\) (Mbar) \\ \cline{2-6}  & 1.601 & 0.819 & 0.28 & 6.097 & 0.1295 \\ \cline{2-6}  & \(R_{1}\) & \(R_{2}\) & OMEG & \(E_{0}\) (Mbar) & \(V_{0}\) \\ \cline{2-6}  & 4.5 & 1.4 & 0.25 & 0.09 & 1.0 \\ \hline  & \multicolumn{4}{c}{MAT\_PLAISTIC\_KINEMATIC} \\ \hline Tunnel & \(\rho\) (g/cm\({}^{3}\)) & \(E\) (Mbar) & PR & SIGY (Mbar) & \\ \cline{2-6}  & 8.0 & 2.03 & 0.3 & \(2.2\times 10^{-3}\) & \\ \hline  & \multicolumn{4}{c}{MAT\_RIGID} \\ \hline Soil Ground & \(\rho\) (g/cm\({}^{3}\)) & \(E\) (Mbar) & PR & \\ \cline{2-6}  & 1.8 & \(2.0\times 10^{-3}\) & 0.498 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material parameters of the external tunnel explosion analysis (data from [21]). Explosion at 1\(\times\) the portal diameter inside the ammunition storage magazine  
The empirical equation of [PERSON] et al. [9] and the experimental results of this study are shown in Figure 8. When the ratio of the distance from the measuring point to the portal inside the ammunition storage magazine (\(l\)) to the portal diameter (\(d\)) was 1.0, the empirical equation was smaller than the experimental value, where the relative error was \(-70.42\%\). However, the empirical equation was close to the experimental value when \(l/d=2\)\(\sim\)3, where the relative errors were 1.74\(\%\) and 10.3\(\%\). Figure 8: Comparison between the empirical equation of the internal blast extreme values and the experimental values (explosion at 1\(\times\) the portal diameter). Figure 7: Comparison of the empirical equations of the internal blast extreme values (explosion at portal). According to the empirical equation of [PERSON] et al. [9] and the experimental results of this study, the Welch empirical equation was more applicable to the explosive source in the explosion range inside the ammunition storage magazine.