# 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
\begin{tabular}{c} **Tensile Strength** \\ **\(\sigma\)/MPa** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Volume** \\ **Modulus/MPa** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **a\({}_{0}\)** \\ **\end{tabular}  } & \multirow{2}{*}{\ \begin{tabular}{c} **a\({}_{1}\)** \\ **\end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **a\({}_{2}\)** \\ **\end{tabular}  } \\ \hline
400 & 0.64 & 3 & 0.0034 & 703.3 & \(0.3\times 10^{9}\) \\ vcr & ref & lcid & eps1 & eps2 & eps3 \\
0 & 0 & 0 & 0 & \(-0.104\) & \(-0.161\) \\ eps4 & eps5 & eps6 & eps7 & eps8 & eps9 \\ \(-0.192\) & \(-0.224\) & \(-0.246\) & \(-0.271\) & \(-0.283\) & \(-0.290\) \\ eps10 & p1 & p2 & p3 & p4 & p5 \\ \(-0.4\) & \(2\times 10^{5}\) & \(2\times 10^{5}\) & \(4\times 10^{5}\) & \(6\times 10^{5}\) & \(1.2\times 10^{6}\) \\ p6 & p7a good anti-detonation role. Subsequently, due to the free boundaries on the left and right sides, the reflected wave and the incident wave acted together on the cavity, resulting in the cavity being subjected to the stresses on both sides and an X-shaped high-stress distribution appeared around the circular cavity, which means that the cavity is prone to butterfly damage in the second half of the propagation of the blast stress wave, which is in line with the conclusions of the existing studies [28]. The effective strain cloud in Figure 9b is also consistent with the above analysis. The circular cavity first shows significant compressive strains on the wave-facing side, and with the propagation of the stress wave, compressive strains also appear on the back-blast side of the circular cavity. Finally, under the combined effect of the incident wave and the reflected wave, significant compressive strains appear in the whole cavity interior, but the strains on the periphery of the cavity are larger, which is due to the X-shape of the high-stress distribution. Figure 8: Effective stress and strain in a circular cavity under blasting load: (**a**) effective stress, nephogram of circular cavities; (**b**) effective strain nephogram of circular cavities. Figure 10: Effective stress and strain in a conical cavity under blasting load: (**a**) effective stress nephogram of the conical cavity; (**b**) effective strain nephogram of the conical cavity. Figure 9: Effective stress and strain in a parallelepiped-shaped cavity under blasting load: (**a**) effective stress nephogram of the parallelepiped-shaped cavity; (**b**) effective strain nephogram of the parallelepiped-shaped cavity. Figure 10 shows the process of changes in effective stress and strain within a parallelepiped cavity subjected to blast impact. Due to the large effective impact area of the parallelepiped cavity, significant stress concentration first appeared at the two corners on the left. Subsequently, the stress wave produced significant reflection and scattering between the blasthole and the cavity, resulting in a conical region of high effective stress between the blasthole and the cavity. As the stress wave propagated to the free surfaces on both sides, the incident wave and the reflected wave simultaneously acted on the parallelepiped cavity, causing sustained dynamic stress concentration on the side facing the blast, while stress concentration also appeared at the two corners on the right side of the parallelepiped cavity. From Figure 10b, it can be observed that when the blast stress wave reached the parallelepiped cavity, a significant compression strain rapidly appeared on the side facing the blast, and as the stress wave propagated, the entire cavity exhibited compression strain, although the strain on the side facing the blast was much greater than that on the upper and lower sides and the side opposite the blast, with the strain on the opposite side being the smallest. This is because the incident wave, reflected wave, and scattered waves directly acted on the side facing the blast, where the majority of the stress wave energy was consumed, while the side opposite the blast was affected the least.