# Evolution of Permeability and Sensitivity Analysis of Gas-Bearing Coal under Cyclic Dynamic Loading
## 4 Results and Discussion  
### The Influence of the Cyclic Loading Frequency on the Permeability  
The variation in coal permeability with the frequency of cyclic dynamic loading is illustrated in Figure 3. It is evident that there is a positive correlation between the permeability of the coal body and the frequency of cyclic dynamic loading. To better visualize the variation in permeability with the dynamic loading frequency, we defined the ratio of permeability at a given dynamic load frequency to the permeability without dynamic loading conditions as the ratio of values. When the coal body was undisturbed by dynamic loading, its permeability was approximately 0.0135 m\(\upmu\)m. However, after being subjected to cyclic dynamic loading with an amplitude of 2.5 MPa and a frequency of 6 Hz, the permeability increased to 0.0176 \(\upmu\)m\({}^{2}\), reflecting an increase of approximately 30.1%. The increases in permeability at the other three dynamic loading frequencies were 7.2% (3 Hz), 16.3% (4 Hz), and 23.8% (5 Hz), respectively. It is, therefore, evident that cyclic dynamic loading has a significantly pronounced effect on increasing the permeability of coal bodies. The pores and fractures within the coal mass serve as the primary conduits for gas seepage. Under the continuous influence of cyclic loading, the primary pores and fractures further develop, resulting in an increased permeability. As the frequency of dynamic loading increases, a certain number of secondary fractures will develop, leading to a phenomenon where permeability continues to rise with the ongoing increase in dynamic loading frequency. Moreover, under the influence of cyclic dynamic loading, the gas adsorption equilibrium within the coal matrix is disrupted, further enhancing the gas adsorption and expansion effects. Thus, it is evident that the greater the external disturbance to the coal seam, the faster the gas migration within the seam, making it more prone to abnormal gas outbursts. Simultaneously, for coal seams from which gas can be extracted,  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Number** & **Frequency and Magnitude of Dynamic Load** & **Static Load Stress Phase** & **Gas** \\ \hline
1 & 2.50 MPa, 3 Hz & 0.45 \(\sigma_{c}\) & CH4 \\
2 & 2.50 MPa, 4 Hz & 0.45 \(\sigma_{c}\) & CH4 \\
3 & 2.50 MPa, 5 Hz & 0.45 \(\sigma_{c}\) & CH4 \\
4 & 2.50 MPa, 6 Hz & 0.45 \(\sigma_{c}\) & CH4 \\
5 & 3.75 MPa, 3 Hz & 0.45 \(\sigma_{c}\) & CH4 \\
6 & 5.00 MPa, 3 Hz & 0.45 \(\sigma_{c}\) & CH4 \\
7 & 6.25 MPa, 3 Hz & 0.45 \(\sigma_{c}\) & CH4 \\
8 & 2.50 MPa, 3 Hz & 0.3 \(\sigma_{c}\) & CH4 \\
9 & 2.50 MPa, 3 Hz & 0.6 \(\sigma_{c}\) & CH4 \\
10 & 2.50 MPa, 3 Hz & 0.75 \(\sigma_{c}\) & CH4 \\
11 & 2.50 MPa, 3 Hz & 0.45 \(\sigma_{c}\) & CO2 \\
12 & 2.50 MPa, 3 Hz & 0.45 \(\sigma_{c}\) & N2 \\
13 & 2.50 MPa, 3 Hz & 0.45 \(\sigma_{c}\) & He \\ \hline \hline \end{tabular}
\end{table}
Table 1: Experimental plan.  
Figure 2: Experimental load path.  
external disturbances can enhance their permeability, thereby improving the efficiency of gas extraction. Furthermore, as the load frequency increases, the enhancement of transmittance becomes more pronounced.