## 3 Results and Discussion
### Analysis of Disaster Effects Caused by Different Types of Dynamic Loads  
#### 3.4.1 Velocity Field Evolution Law  
When dynamic load waves propagate in layered media, they are influenced by factors such as interlayer interfaces and the frequency of the wave itself. Their propagation attenuation mainly stems from interface scattering and medium absorption. This section investigates the attenuation process of three different dynamic load waves in coal-bearing strata, as well as their velocity response characteristics. After loading the three types of dynamic load waves, the velocity information in the \(Z\)-direction from the seismic source to the monitoring points in the roadway is obtained, as shown in Figure 12. The waveform data obtained from monitoring are subjected to spectral analysis to obtain the corresponding frequency-domain information, as illustrated in Figure 13.  
From Figure 12, it can be observed that as the three types of dynamic load waves propagate through the layers, the particle vibration velocity significantly attenuates with increasing propagation distance. When propagating to a distance of 2 m from the seismic source, the peak vibration velocity decreases to one-third of its value at the source. Subsequently, as the propagation distance increases, the attenuation trend gradually diminishes. After propagating 6 m, the attenuation trend of the signal becomes relatively stable, and the particle vibration velocity is minimally affected.  
Figure 13 reveals that as the propagation distance increases, the velocity amplitudes of the three types of dynamic load waves show a decreasing trend. Significant attenuation occurs within 0-2 m, but the frequency attenuation regions differ. The roof-type dynamic load wave exhibits significant attenuation in the low-frequency range (from 0 Hz to 35 Hz), while the fault-type dynamic load wave experiences broader significant attenuation (from  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Event** & \(\mathbf{\Delta\alpha}\) & \(\mathbf{\Delta f(\alpha)}\) & **Event** & \(\mathbf{\Delta\alpha}\) & \(\mathbf{\Delta f(\alpha)}\) & **Event** & \(\mathbf{\Delta\alpha}\) & \(\mathbf{\Delta f(\alpha)}\) \\ \hline M1 & \(1.172\) & \(-0.697\) & D1 & \(1.650\) & \(-0.570\) & B1  
0 Hz to 80 Hz). The coal pillar-type dynamic load wave shows similar attenuation regions to the fault-type, but it attenuates most rapidly in the 0-10 Hz range, with low-frequency components rapidly attenuating during propagation.  
As shown in Figure 12, after the dynamic carrier wave propagates for 6 m, the attenuation amplitude is less than 0.01%, and it has basically stopped attenuating. The peak velocity of the dynamic carrier wave at each measuring point from 0 to 6 m was selected, and the attenuation coefficient of the peak vibration velocity of the three types of dynamic carrier particles was calculated according to the formula in Section 2.4. The regression curve of the peak vibration velocity of the particle point obtained by fitting is shown in Figure 14. The peak vibration velocity of the three dynamic carrier waves decays exponentially with the increase in the propagation distance. The attenuation coefficients of the dynamic carrier waves of the roof, fault, and coal pillar are 0.0034, 0.0027, and 0.0018, respectively.  
Figure 14: Regression curves of particle peak vibration velocity.  
Figure 13: FFT spectrum of dynamic load waves in vertical direction. (**a**) Roof-type, (**b**) fault-type, (**c**) coal pillar-type.