# Numerical Simulation Study of Cavity Formation in Soil under Blast Load
## 3 Numerical Simulation Results and Discussion
### Validation of Numerical Model  
The validation of a numerical model plays an important role in a numerical simulation study. In this research, the validation was performed using experimental values of cavity volumes. The used experimental results are derived from recent research in order to determine the interaction between explosives and soil properties. Those research were performed in situ in natural soil. The cavity formation in soil were produced by blasting on a test field, and ANFO and powdered AN explosives were used. Figure 2 shows the test field.  
The results of cavity volume obtained from field experiments are compared with the cavity volume calculated by a numerical model. That procedure was carried out prior to the modeling aimed at model-validation. The measurements of the cavity volume were carried out using a system with a camera and laser. The results were processed using AutoCad Civil 3D software [15; 16]. An example of the processed, measured cavity in graphical form is shown in Figure 3.  
As mentioned in Section 2, the properties of the blasted soil were determined and entered in a numerical model.  
In a borehole of 131 mm diameter and 2440 mm depth, 1 kg of a Pakaex (ANFO) explosive was placed and initiated with a plain detonator, and in a second borehole, the same procedure was repeated with a different explosive, Permonex (powdered ammonium nitrate explosive). The stem was made of sand material with a length of 0.5 m. The main  
Figure 3: Example of measured cavity shape processed using AutoCad Civil 3D software [16].  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Type of Explosive** & \begin{tabular}{c} **\(A\)** \\ **(Mbar)** \\ \end{tabular} & \begin{tabular}{c} **B** \\ **(Mbar)** \\ \end{tabular} & \begin{tabular}{c} **\(R_{1}\)** \\ **(\(\star\))** \\ \end{tabular} & \begin{tabular}{c} **\(R_{2}\)** \\ **(\(\star\))** \\ \end{tabular} & \begin{tabular}{c} **\(\omega\)** \\ **(\(\star\))** \\ \end{tabular} & \begin{tabular}{c} **\(D\)** \\ **(cm/us)** \\ \end{tabular} & \
\begin{tabular}{c} **\(P\)** \\ **(Mbar)** \\ \end{tabular} &
\begin{tabular}{c} **\(E\)** \\ **(Gerg/mm3)** \\ \end{tabular} \\ \hline ANFO (Pakaex) & 0.062805 [15] & 0.001513 & 2.193732 [15] & 0.464714 [15] & 0.177879 [15] & 0.304939 [15] & 0.01933323 [15] & 0.029706 [15] \\ Ammonium nitrate Powder (Pennoras) & 0.79023 & 0.01257 & 4.6797 & 0.9529 & 0.1903 & 0.4022 & 0.0379 & 0.0318 \\ Gel (Riopsis) & 2.38931 & 0.022655 & 5.203369 & 1.054384 & 0.158459 & 0.4587 & 0.05828 & 0.0412 \\ \hline \hline \end{tabular}
\end{table}
Table 3: JWL constants calculated by EXPLOS 07.01.01.  
Figure 2: The test field [16].  
results of the explosions were cavities with a volume of 752 dm\({}^{3}\) for ANFO [15; 16] and 835 dm\({}^{3}\) for the powdered explosive.  
The validation results of the numerical model (measured and calculated by Ansys 2020 R1 Autodyn 2D) are presented in Table 4.  
The results of the validation allow for the conclusion that the numerical model describes the soil response under the load caused by blasting within an acceptable range. The deviation between the measured and modeled values is between 6 and 12% and is acceptable, as the model is strongly dependent on the input data. Input experimental data are subjected to errors connected with the imperfection of the cavity volume measurement method and the real values of explosive parameters.