# Calculation of Blasting Damage Zone Radius of Different Charge Structures in Burnt Rock
## 6 Application Example  
The special properties of burnt rock determine the 'excellent and poor' blasting effects. Due to the existence of a large number of discontinuities, such as cracks and joints, with different scales and directions in the burnt rock, the rock mass in the fire area has typical discontinuities and anisotropy. The explosion stress wave and the energy released by the explosive are affected by the cracks and cannot be fully utilized, resulting in an unsatisfactory blasting effect or even failure to complete the blasting operation. In this study, the bench blasting of burnt rock in an open-pit mine in Xinjiang was used as an example to verify the research results. The physical and mechanical indexes of burnt rock are shown in Table 1 below. The mine used a #2 emulsion explosive, and the specific explosive parameters are shown in Table 2 below. According to the derived formulas for calculating the blasting failure area of burnt rock with different charge structures (Formulas (29), (30), (33) and (36)), under the condition that the blashole (150 mm), explosive and rock parameters are known, and assuming that the initial damage of the rock was \(D=0.2\) and the damage of the blasting stress wave to rock was \(D_{0}=0.5\), the blasting failure radius of the burnt rock could be obtained. The calculation formula of the radius of the failure zone under the condition of the coupling charge structure was not affected by the variable factors. The calculated radius was 2.736 m, which was less than the failure radius of the homogeneous rock and was in line with the actual blasting situation. Under the condition of an uncoupled charge structure, the formula for the radius of the failure area is affected by the charge diameter and charge interval. Assuming that the radial uncoupling coefficient was 1.5, the calculated radius was 2.472 m. For the burnt rock step with a large number of random joint fissures, the radial uncoupled charge structure is more suitable. However, at present, most open-pit mines use mixed-emulsion explosives, which cannot be made into cartridges in advance, and the radial uncoupled charging process is complex and takes a long time. Therefore, considering the problems of charging efficiency and application, the coupling interval charging structure was selected. Since the damage radius was known, its diameter could be regarded as the row spacing in the blasting hole network parameters. Then, triangular holes were usually used in the blasting design of the open-pit mines. The relationship between the hole spacing and the row spacing was  
\[b=a\sin 60^{\circ}=0.866a \tag{49}\]  
Therefore, the hole spacing of the burnt rock step with the coupled charge structure was 6.4 m. It can be seen that after determining the damage caused by the advanced propagation of the shock wave to the rock mass, the appropriate coupling/uncoupling coefficient value could be determined according to the actual situation of the mine, and then the corresponding blasting hole spacing/row spacing parameter setting could be obtained. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Rocks** & \begin{tabular}{c} **Compressive** \\ **Strength** \\ **/MPa** \\ \end{tabular} & \begin{tabular}{c} **Tensile** \\ **Strength** \\ **/MPa** \\ \end{tabular} & \begin{tabular}{c} **Cohesion** \\ **/MPa** \\ \end{tabular} & \begin{tabular}{c} **Angle of** \\ **Internal** \\ **Friction/\({}^{c}\)** \\ \end{tabular} & \begin{tabular}{c} **Elastic** \\ **Modulus** \\ **/GPa** \\ \end{tabular} & \begin{tabular}{c} **Poisson** \\ **Ratio** \\ \end{tabular} & \
\begin{tabular}{c} **Density** \\ **/kg\(\cdot\)m\({}^{-3}\)** \\ \end{tabular} &
\begin{tabular}{c} **Porosity** \\ **/\%** \\ \end{tabular} \\ \hline Burnt rocks & 58.69 & 5.69 & 57.48 & 18.26 & 5.10 & 0.30 & 2030 & 6.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of rock property tests in burning area.