# 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
### Three-Dimensional Numerical Modeling and Damage Characteristics of Cavities
The blue part in the figure represents the explosive elements, with a size of 4 cm \(\times\) 2 cm \(\times\) 2 cm, which is close to the 20 g charge mass in the similar model test. The red part represents the void material elements, which are shaped as cubes with an edge length of 20 cm. The yellow part represents the filled area; in this figure, an individual fracture model is used as an example, with a size consistent with the corresponding similar model test. The green part represents the rock elements, with a size of 60 cm \(\times\) 40 cm \(\times\) 30 cm, and the void material elements partially overlap with the rock elements in the modeling. Generally, when simulating the blasting of rock mass, a non-reflecting boundary is applied at the model's boundary using the keyword BOUNDARY_NON_REFLECTING to simulate different numbers of free surfaces. The 3D model is not set with a reflection-free boundary to consistency with the experimental specimen. Due to the presence of free surfaces, there is a limiting and nature-altering effect on the energy of the blast stress waves. This causes the stress wave energy to be confined within the expected range of blasting action through reflection, and it can alter the nature of the stress wave energy, converting the original compressive wave energy into tensile and shear wave energy. As a result, compared to the case without free surfaces, the rock mass is subjected to a longer duration of stress wave destructive action, leading to tensile and shear damage to the rock mass. The damage development of the rock mass during a simulated typical rock blasting process is shown in Figure 12 and is specifically manifested as follows:  
Figure 11: Three-dimensional numerical model. (1) At 0.1 ms, under the impact load of the explosive, the rock mass elements surrounding the explosive reach their failure strength and undergo massive destruction, forming a blast cavity. At 0.3 ms, the blast cavity has basically expanded to its limit, indicating that the action of the explosive impact load has essentially ended. The rock mass outside the cavity is subjected to hoop stress from the direct blast stress waves, forming radial cracks that radiate outward. At 0.7 ms, the radially spreading cracks have further developed. As the blast stress wave reaches the edge of the rock mass, due to the reflection of the stress wave at the free surface, the rock mass undergoes multi-layer fracturing under the action of the reflected wave, forming multiple cracks parallel to the free surface. (2) At 0.9 ms, the radiating radial cracks and the parallel free surface layer cracks further expand. The reflected waves from adjacent free surfaces begin to converge, and under the superimposed stress field, the rock mass exhibits angular cracks, with the angular crack cracks beginning to develop. At 4.5 ms, in addition to the already fully developed radiating radial cracks, parallel free surface layer cracks, and angular cracks, the rock mass shows a wider variety of cracks under the action of stress waves, including edge cracks at 45\({}^{\circ}\) to the free surface. These various cracks are mostly interconnected, and the rock mass is overall in a state of destruction. (3) Compared to the 4.5 ms moment, at 10 ms, the cracks have only slightly developed, and their expansion has essentially halted, indicating that the destructive effect of the rock mass blast stress waves has ceased. At this point, the cracks are primarily expanding under the quasi-static pressure of the explosive gases, and at the same time, the broken rock mass is being propelled outward by the action of the explosive gases, with the rock mass edges showing noticeable bulging. When comparing the 20 ms with the 10 ms moment, there is almost no further development of rock mass cracks, and in some cases, the edges of certain cracks have even exhibited a closure phenomenon. The main cracks have further extended, and the bulging of the rock mass at the free surface is more pronounced.