# Numerical Simulation Study of Cavity Formation in Soil under Blast Load
## 3 Numerical Simulation Results and Discussion
### Results of Numerical Simulation
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type of Explosive** & **Pressure** & **Volume of Gas Products** & **Volume of Cavity** \\  & **[GPa]** & **[dm\({}^{3}\)/kg]** & **Formation [dm\({}^{3}\)]** \\ \hline ANFO & 0.86 & 698 & 863 \\ Ammonium nitrate powder & 3.24 & 628 & 787 \\ Water gel & 5.83 & 593 & 862 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of parameters for studied explosive and cavity formation results. The simulations performed for the situations covered by the experiment showed similar dependencies, that is, the type of explosive slightly influences observable changes in the cavity volume. By introducing water gel into the simulation along with the aforementioned ANFO and AN powder explosive, cavity sizes within 10% were confirmed for all of the observed explosives. By analyzing the size of the parameter \"Power of explosives\", i.e., the product of the theoretical heat of detonation and the volume of released gasses that are the carriers  
Figure 6: The volume of cavity produced by different type of explosives (**a**) ANFO explosive, (**b**) ammonium nitrate powder, and (**c**) water gel explosive. (**d**) Comparison of the volume of cavity for different types of explosives. of the performed work, it can be confirmed that the results of the simulations and the experimental values coincide with the increase in the product QV for individual explosives. The major dissipation is with the ANFO. The properties of ANFO explosives are highly non-ideal and depend on the environmental conditions, the confinement, the shape of the charge and the type and method of initiation. The use of models describing non-ideal explosives with ideal properties is possible but is subject to corrections based on experimentally determined values of individual properties, especially detonation velocity. The detonation velocity used in the calculations was reduced to 2000 m/s, which corresponds to the measured value of a charge of 100 mm height and 131 mm diameter initiated in a borehole under experimentally simulated conditions. In contrast, the theoretical, calculated detonation velocities for ANFO explosives are given in the literature, with values for the maximum theoretical detonation velocity up to 5000 m/s and up to 3500 m/s for charges with a diameter of 60 to 80, for example. Similarly, the detonation velocity of the AN powder explosive was adjusted from 5500 m/s to 4000 m/s based on the measurement results, corresponding to the measured values in the actual charge. The correlations that are shown in Figure 7 confirm that for cavity formation, the Ansys 2020 R1 Autodyn 2D hydro code with the Compaction EOS Linear model can predict the volume of a cavity within an error limit of 12%. Also, reliable experimental data of moisture content and plasticity index can predict the volume of a cavity when using the following equations:  
\[V=10.19{w_{0}}^{2}-711.13w_{0}+12,819 \tag{4}\]  
\[V=9.6391{I_{P}^{2}}-445.81{I_{P}}+5578.3 \tag{5}\]  
Finally, it is important to mention that when explosives act in the soil, because of the process' attributes, densification in the surrounding soil and penetration of gasses in soil pores [19; 20; 21] are always present. However, this research was only focused on the prediction of cavity volume formation.