## 3 Analysis of Test Results
### Dynamic Mechanical Characteristics  
#### 3.2.1 Time History Curve of Stress Wave  
At the beginning of the experiment, to ensure the accuracy of the SHPB experimental results, stress balance verification was performed before processing the data [32]. Specifically, the two end faces of the specimen needed to reach stress equilibrium under the impact load, and the stress equilibrium curve of the specimens are shown in Figure 8. As shown in the figure, the superposition of the incident wave, reflected wave, and transmitted wave basically coincided with each other, indicating that the coal and rock basically reached the stress equilibrium state.  
Due to the large noise in the original signal, the data in this study were denoised and analysed using the Hilbert-Huang transformation (HHT) method [39]. Due to space limitations, only some data with different variables were analysed as an example.  
Figure 9a,b show the stress time course curves of raw coal at the same freezing temperature of \(-10\)\({}^{\circ}\)C with different saturations and speeds. As shown in the figure, (1) all curves of the incident waves have sinusoidal or half-sinusoidal curves. With the increase in the impact velocity, the peak points of the incident, reflection, and transmission curves gradually increase, the peak arrival time is advanced, and the overall duration of the impact is also shortened. At lower velocities, the reflected stress tail reaches a negative value. The reason for this phenomenon is that the specimen is not destroyed completely under incident wave loading conditions, and a large amount of strain energy is stored in the medium instead. These strain energies are released in the unloading phase of the incident wave and rebound to the bar as compression waves. (2) In the dry state and natural water-saturated state, the peak value of the transmission wave of the raw coal in the water-saturated state is higher than that in the dry state. Compared with Table 1, a denser sample in the water-saturated state occurs because a large amount of liquid water or solid water fills the internal cracks. The large amount of liquid or solid water in the internal clefts leads to a reduction in energy dissipation within the sample due to the presence of the Stefan effect.  
Figure 8: Typical dynamic stress equilibrium checks in dynamic compression tests. (Int: incident wave, Re: reflected wave, and Tra: transmitted wave).  
Figure 9: _Cont_.  
Using the same means, the same noise reduction was applied to the experimental data of the raw rock. As shown in Figure 9c,d, the graphs show the stress time-course curves of the raw rock at the same freezing temperature of \(-10\)\({}^{\circ}\)C for different saturations and velocities. The overall regularity of the coal and rock bodies has a high degree of overlap. The trend shows that with increasing speed, the peak value of the curve increases; the sample reaches the peak time earlier. Raw rock in the dry and saturated contrasting cases also had a similar pattern to raw coal, both of which had higher curves in the dry case than in the saturated state.  
Notably, the peak of the transmittance wave of the coal samples was significantly lower than that of the rock samples. Similarly, the process of reaching the peak of the stress wave in coal samples tended to be relatively slow. This was caused by the different densities of the coal and rock samples, which were determined through the wave speeds in Tables 1 and 2. A denser sample causes a faster propagation of the ultrasonic wave. This curve and wave speed could be used to validate each other.