# Dynamic Response and Rock Damage of Different Shapes of Cavities under Blasting Loads
## 3 Experimental Results
### Blasting Block Size and Effectiveness  
The presence of cavities within concrete structures affects the propagation of stress waves, and the impact of these cavities varies depending on their location. For blasting experiments conducted on structures with cavities of different shapes, a corresponding size analysis is carried out. The analysis focuses on the blasting block sizes \(\mathrm{X_{50}}\) and \(\mathrm{X_{100}}\) at distances varying from the upper free surface. \(\mathrm{X_{50}}\) reflects the average size of the fragments, while \(\mathrm{X_{100}}\) represents the maximum size of the fragments, which effectively describes the proportion of large pieces generated by the explosion. Additionally, due to limitations in the experimental conditions, the spherical cavity model only yielded block size data at distances of 8 cm and 12 cm from the upper free surface. The block size distribution is shown in Figure 5.  
A large amount of measured data and literature indicate that the five-parameter Swebrec modified distribution function can well describe the distribution law of rock blasting fragments [25]. Therefore, this article, after obtaining the sizes of each rock block through ImageJ ([[https://imagej.net/ij/](https://imagej.net/ij/)]([https://imagej.net/ij/](https://imagej.net/ij/))) image processing, uses the Swebrec modified  
Figure 5: Fragments images for different distances and shapes of the rock mass: **(a,b)** the shape of the cavity is spherical, and the distances from the upper surface are 8 and 12 cm, respectively; **(c-e)** the shape of the cavity is parallelepiped, and the distances from the upper surface are 4, 8, and 12 cm, respectively; **(f-h)** the shape of the cavity is conical, and the distances from the upper surface are 4, 8, and 12 cm. distribution function to obtain the size distribution curves for each group of rock blasting tests. The basic expression of this function is as follows:  
\[P(x)=1/\left\{1+A[\ln(x_{\max}/x)/\ln(x_{\max}/x_{50})]B+(1-a)\left[\left(\frac{x _{\max}}{x}-1\right)/\left(\frac{x_{\max}}{x_{50}}-1\right)\right]^{C}\right\} \tag{1}\]  
where \(x_{\max}\) is the maximum size at \(P(x_{\max})=100\%\), which can be obtained by directly measuring the size of the largest fragment; \(x_{50}\) is the median size at \(P(x_{50})=50\%\); \(A\) is the grading coefficient, with a range of values from 0 to 1; and \(B\), \(C\) are the fitting parameters, with a range of values around 2. The distribution patterns of blasting fragment sizes under different shapes and distances from the upper free surface are illustrated in Figure 6a-c showing good fitting effects with R\({}^{2}\) values greater than 0.99. Figure 6a reveals that when the spherical cavity is 8 cm away from the upper free surface, the \(X_{50}\) value (average fragment size) is 10.64 cm, and the \(X_{100}\) value (maximum fragment size) is 35.97 cm. When the cavity is 12 cm away from the upper free surface, the \(X_{50}\) value is 6.84 cm, and the \(X_{100}\) value is 19.25 cm. The fragment size analysis indicates that a spherical cavity closer to the free surface yields a better blasting effect, resulting in smaller overall fragment sizes and a reduced proportion of large pieces. Figure 6: Fitted curves of the distribution pattern of the blasting block size for each group of specimens: (**a**) spherical cavities; (**b**) parallelepiped cavities; (**c**) conical cavities. Similarly, for concrete structures with parallelepiped cavities at different positions, different blasting effects were observed. Figure 6b shows the blast fragments from different positions of a cube. In this case, the cavity is located in three different positions. The best blasting effect was achieved when the cavity was 12 cm away from the upper free surface, with \(X_{50}=5.98\) cm and \(X_{100}=12.73\) cm, resulting in no obvious large pieces, as shown in Figure 6b. When the cavity was 4 cm or 8 cm away from the upper free surface, the blasting effect was poorer, with values of \(X_{50}\) and \(X_{100}\) being relatively close to each other.