## 4 Propagation Law of Near-Ground Explosion Shock Wave  
### Verification of Blast Model  
Figure 4 shows the empirical data and numerical data about the peak overpressure along \(x\) at the height of 2 m. As can be seen, the prediction values of each empirical formula in the near-field of the explosion are quite different, which is mainly because the detonation products in the near-field are quite different from the test values. In the far-field of the explosion, the influence of detonation products decreases and the predicted values of each empirical formula tend to be consistent. When scaled distance is small, different empirical formulas have a large deviation because of the test error. While when the scaled distance is big, different empirical formulas have a large consistency [44; 45; 46].  
Figure 4: Comparison of theoretical and numerical data in air explosion at the height of 2 m.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(\rho\)(g/cm\({}^{3}\)) & \(\boldsymbol{G}\)/\(\boldsymbol{\mathrm{GPa}}\) & \(\boldsymbol{B}\) & \(\boldsymbol{a_{0}}\)/\(\boldsymbol{\mathrm{GPa}}\) & \(\boldsymbol{a_{1}}\)/\(\boldsymbol{\mathrm{GPa}}\) & \(\boldsymbol{a_{2}}\)/\(\boldsymbol{\mathrm{GPa}}\) & \(\boldsymbol{\varepsilon_{\mathrm{2}}^{P}}\) & \(\boldsymbol{\varepsilon_{\mathrm{3}}^{P}}\) \\ \hline \(1.8\) & \(1.60\times 10^{-6}\) & \(1.382\) & \(3.3\times 10^{-5}\) & \(1.31\times 10^{-9}\) & \(1.23\times 10^{-3}\) & \(0.05\times 10^{-2}\) & \(9\times 10^{-4}\) \\ \hline \(\varepsilon_{\mathrm{e}t}^{p}\) & \(\varepsilon_{\mathrm{e}5}^{p}\) & \(\varepsilon_{\mathrm{e}6}^{p}\) & \(\varepsilon_{\mathrm{e}7}^{p}\) & \(\varepsilon_{\mathrm{e}6}^{p}\) & \(\varepsilon_{\mathrm{e}9}^{p}\) & \(\varepsilon_{\mathrm{e}10}^{p}\) & \(P_{2}\)/\(\mathrm{GPa}\) \\ \hline \(1.1\times 10^{-3}\) & \(1.5\times 10^{-3}\) & \(1.9\times 10^{-3}\) & \(2.1\times 10^{-3}\) & \(2.2\times 10^{-3}\) & \(2.5\times 10^{-3}\) & \(3.0\times 10^{-3}\) & \(3.42\times 10^{-4}\) \\ \hline \(P_{3}\)/\(\mathrm{GPa}\) & \(P_{4}\)/\(\mathrm{GPa}\) & \(P_{5}\)/\(\mathrm{GPa}\) & \(P_{6}\)/\(\mathrm{GPa}\) & \(P_{7}\)/\(\mathrm{GPa}\) & \(P_{8}\)/\(\mathrm{GPa}\) & \(P_{9}\)/\(\mathrm{GPa}\) & \(P_{10}\)/\(\mathrm{GPa}\) \\ \hline \(4.53\times 10^{-4}\) & \(6.76\times 10^{-4}\) & \(1.27\times 10^{-4}\) & \(2.08\times 10^{-4}\) & \(2.71\times 10^{-4}\) & \(3.92\times 10^{-4}\) & \(5.66\times 10^{-4}\) & \(1.23\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Parameters of the soil [43].  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \(\rho\)(/g/cm\({}^{3}\)) & \(\boldsymbol{E}\)/\(\boldsymbol{\mathrm{GPa}}\) & \(\boldsymbol{\mu}\) & \(\sigma_{0}\)/\(\boldsymbol{\mathrm{GPa}}\) & \(\boldsymbol{E_{p}}\)/\(\boldsymbol{\mathrm{GPa}}\) & \(\boldsymbol{\beta}\) & \(\boldsymbol{C}\) & \(\boldsymbol{P}\) & \(\boldsymbol{\mathrm{FS}}\) & \(\boldsymbol{\mathrm{VP}}\) \\ \hline \(2.65\) & \(4.0\mathrm{e}\times\) & \multirow{2}{*}{\(0.3\)} & \(1.0\mathrm{e}\times\) & \(4.0\mathrm{e}\times\) & \multirow{2}{*}{\(0.50\)} & \multirow{2}{*}{\(0\)} & \multirow{2}{*}{\(0\)} & \multirow{2}{*}{\(0\)} & \multirow{2}{*}{\(0.8\)} & \multirow{2}{*}{\(0.8\)} \\ \(10^{-1}\) & & & \(10^{-3}\) & & \(10^{0}\) & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 5: Parameters of the concrete [41].  
By comparison, simulation data is almost the same as the empirical data, and the deviation is within the permissible scope of the project. Certain deviation between the simulation result and the empirical formula is mainly because that the empirical formula is obtained by fitting according to the test results, while the simulation model is a relatively ideal result obtained by the calculation of the aerodynamic equation, and there are certain differences between the test conditions and the simulation models.