*5.2. Establishment of Finite Element Model*

The finite element model in this work was built according to actual sizes and the components were all three-dimensional solid elements (Solid164). The finite element model was meshed, and the bullet, incident and transmission rods were divided into 15 parts along the radial direction. The bullet was divided into 40 parts along the axial direction, and incident and transmission rods were divided into 200 parts along the axial direction. To more intuitively reflect the impact damage of the test piece, it was finely meshed and was divided into 30 and 20 parts along radial and axial directions, respectively (Figure 13).

**Figure 13.** Establishment of the finite element model.

The material models of the bullet and compression bars were selected from linear elastic material models. The main parameters and their values were as follows: density 7800 kg/m3, elastic modulus 2.06 GPa, and Poisson's ratio 0.36. The coal sample was input into the HJC constitutive model and its parameter values were determined according to specific values listed in Table 8. The bullet was attached to the incident rod through an automatic contact between the two faces and the pressure bar was attached through an erosive contact with the test piece. During numerical simulation, the friction between contact surfaces was ignored. The value of 2 was taken as the contact stiffness penalty function factor *f*.

#### *5.3. Waveform of the Stress Wave*

In order to allow comparison with the experimental results, impact velocities in the numerical simulation were set at 4.732 and 7.267 m/s. Here, taking the stress waveform diagram of the incident rod and the middle of the projection rod at the impact velocity of 7.267 m/s as examples, experimental data and numerical simulation results were compared. The obtained results are shown in Figures 14 and 15.

**Figure 14.** Experimental results (*v* = 7.267 m/s).

**Figure 15.** Simulation results (*v* = 7.267 m/s).

It can be seen from Figures 14 and 15 that the experimentally measured stress wave curve complied well with that drawn using simulation results, but there was a slight difference in curve volatilities. This was because the stress wave decayed with time during the propagation of the rod, and the components used in the experiment had inevitable little defects, which caused the stress wave to be weakened during propagation. Numerical simulation was carried out under ideal conditions. The end face of the rod was flat, and frictional force was neglected. Therefore, the stress wave obtained by numerical simulation was not attenuated, and the obtained stress wave curve was smoother; however, the peak value of the stress wave obtained by numerical simulation was slightly greater than that measured in real time. Although there were some differences between the simulation and experimental results obtained for the stress wave, they were generally consistent. Therefore, simulation results were considered to be accurate and reasonable.

#### *5.4. Analysis of Coal Rock Damage*

The damage process of the coal-rock SHPB experiment was captured with high-speed photography and compared to the simulated damage process, as shown in Figure 16.

Figure 16 shows that at the impact velocity of 4.732 m/s, the stress wave started to contact the coal sample at t = 578.93 μs. When t = 596.97 μs, a part of the coal body failed and obvious axial cracks appeared in the middle of the sample. When t = 623.97 μs, the number of surface cracks in the coal sample, and therefore the damage intensity, increased. When t = 725.93 μs, the coal sample broke into small pieces. When the impact velocity was 7.267 m/s, the stress wave started to contact the coal sample at t = 572.99 μs, and the coal body partially failed due to the propagation of the compressive stress wave. Radial cracks occurred at t = 584.96 μs, and when t = 583.96 μs, the internal stress of the sample gradually changed from compressive to tensile stress. At t = 617.98 μs, the coal sample was severely damaged and fell into pieces. At different impact velocities, axial cracks began to appear in the coal samples, which ultimately resulted in the failure of samples.

It can be seen from the high-speed images that when the impact velocity was 4.732 m/s, the sample was compressed by pressure, the coal was laterally deformed, and many transverse cracks were created parallel to the direction of stress wave propagation (indicated with a red circle in the Figure 16). With the development of cracks, the whole sample appeared to expand, and eventually, damage occurred under the joint action of upper crack expansion and the lower slip shear of the coal body. When the impact velocity was 7.267 m/s, first a through crack was created in the sample (shown by a red circle in Figure 16). Secondly, due to the large incident energy and high velocity of the bullet, the deformation of the coal continued to increase, and the crack expanded rapidly. Finally, the sample underwent compression expansion under impact loading, which caused tensile damage. As the speed continued to increase, the coal sample underwent a "comminuted" rupture, producing a large amount of fine granular coal dust. The severity of coal body damage positively correlated with the impact velocity, while the size of the coal block was decreased.

Comparing the experimental and simulated failure processes at impact velocities of 4.732 and 7.267 m/s revealed their high consistency. In general, numerical simulation using measured briquette HJC constitutive model parameters had a strong similarity to experimental findings, which verified the applicability of the HJC constitutive model parameters of briquette samples to simulate the failure process of coal samples under the impact of a dynamic load.

**Figure 16.** *Cont.*

Failure Process of Coal Body with Bullet Impact Velocity of 7.267 m/s.

**Figure 16.** Dynamic change process of the impact failure of a coal body.
