# Dynamic Response and Rock Damage of Different Shapes of Cavities under Blasting Loads
## 4 Numerical Simulation Study on the Response and Fracture Characteristics of Cavity Blasting
### Parameter Calibration and Cavity Stress Response  
In order to obtain the material parameters, samples were taken on-site in the model test to make standard tests for mechanical property tests, and atriaxial testing machine was used to carry out uniaxial compression, Brazilian splitting and straight shear tests, and the mechanical property test data are shown in Table 1. In order to study the mechanical response characteristics of the cavity, the rock material is set as an elastic material, the keyword \"MAT_ELASTIC is used, and the parameter settings are consistent with the mean values in Table 1. The foam material is used to simulate the cavity--ANSYS/LS-DYNA software simulation foam has a variety of materials available. In this paper, the MAT_SOIL_AND_FOAM material is used and the specific parameters determined by reference [26] are shown in Table 2.  
The two-dimensional elastic numerical modeling is shown in Figure 7, which is consistent with the top-view cross-section size of the similar model test, and the model is a rectangular structure with the size of 60 cm \(\times\) 30 cm, and the total number of model units is about 130,000 units. The explosive size is 2 cm \(\times\) 2 cm, and the equivalent blasting curve is used to apply the load and generate the blasting stress wave propagating to the cavity. The shapes of the cavities are circular, parallelepiped, and conical, and the diameters and side lengths are 4 cm and 12 cm, respectively, so as to realize the numerical simulation of the process of blasting stress wave incident on cavities with different cross-sectional shapes. The needle-shaped wave is used to represent the blast stress wave, in which the waveform rises rapidly and falls slowly, with the energy concentrated primarily at the front, effectively approximating the stress wave generated by blasting. Additionally, the pressure is applied along the contour of the blasthole. The stress variation and effective strain cloud diagrams of different cross-sectional shapes of the cavities under blasting loads are shown in Figures 8-10. From Figure 9a, it can be seen that the blasting load produces a significant stress concentration at the bottom of the top of the cavity when it propagates to the circular cavity. As the stress wave propagates to the right free surface, a conical region of small effective stresses appears around the cavity due to the presence of the upper and lower free surfaces. This means that the circular cavity absorbed a large amount of energy during the incidence of the blast stress wave and played \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multirow{2}{*}{\begin{tabular}{c} **Density** \\ \(\rho\)/(kg\(\cdot\)m\({}^{-3}\)) \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Static** \\ **Compressive** \\ **Strength** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Dynamic** \\ **Compressive** \\ **Strength** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Tensile** \\ **Strength** \\ **\end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Modulus of** \\ **Elasticity/GPa** \\ **Elasticity/GPa** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Poisson’s** \\ **Ratio** \\ **\(\mu\)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Cohesion** \\ **C/MPa** \\ **\end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Angle of** \\ **Hertinal** \\ **Friction** \\ **\(\varphi\)/\({}^{C}\)** \\ \end{tabular} } \\ \hline
1 & 2069.76 & 4.83 & 8.13 & 0.47 & 2.68 & 0.23 & 0.53 & 20.43 \\
2 & 2103.71 & 4.66 & 8.48 & 0.45 & 2.59 & 0.24 & 0.51 & 20.29 \\
3 & 1882.84 & 4.46 & 8.58 & 0.49 & 2.53 & 0.22 & 0.55 & 21.95 \\ Average value & 2018.77 & 4.65 & 8.4 & 0.47 & 2.60 & 0.23 & 0.53 & 20.89 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental test data for similar materials. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{ \begin{tabular}{c} **Density** \\ \(\rho\)/(kg\(\cdot\)m\({}^{-3}\)) \\ \end{tabular}  } & \multirow{2}{*}{