## 4 Results Analysis and Discussions
### Reasons for the Changes in Permeability under Cyclic Loading and Unloading Conditions
The particle structures were rearranged resulting in the significant reduction in porosity, which was the primary reason why broken coal masses were compacted and deformed. (2) Broken coal samples were crushed further and then the broken fine particles filled the void space, resulting in the further reduction of the porosity of the coal samples. (3) The compressive deformation between particles reduced the porosity: the compressive deformation was actually elastic deformation, which can be recovered in the unloading process. Figure 13 shows the porosity change of the broken coal sample during the loading stage. The first two factors caused a significant reduction in the porosity of coal samples, so they were the main reasons causing the reduction of porosity, and this portion of porosity of coal samples cannot be recovered during stress unloading. The reduction of porosity induced by the third factor can be recovered in the unloading process, which was the reason why the porosity of coal samples increased in the unloading stage, however, the influence of the third factor on the porosity was much less significant than those of the first two factors. Therefore, the main reason for the gradually reducing loss of permeability of coal samples in the loading stage with the increase of cyclic loading and unloading times is illustrated as follows: with the increase of cyclic loading and unloading events, the particles of broken coal samples were further crushed and their corresponding structural re-arrangement capability gradually weakened, resulting in the gradual reduction of the porosity (albeit by smaller amounts each time). The main reason why the recovery amount of permeability of coal samples in the unloading stage gradually decreased with the increase of cyclic loading and unloading cycles was that, with an increased number of loading and unloading cycles, some particles being subjected to compressive deformation were constantly crushed. As a result, the recovery after compressive deformation gradually decreased, consequently leading to a gradual reduction in the increment in the porosity. During each loading and unloading cycle, the loss of permeability in the loading stage was much greater than the recovery of permeability in the unloading stage. This was mainly because the influence of structural rearrangement and breakage of particles in the loading stage on the porosity of coal samples was much greater than that of the recovery of particles after compressive deformation in the unloading stage on the porosity. Figure 13: Schematic diagram of porosity change of broken coal samples during the loading stage. The Relationship between Permeability and Strain, Porosity under Cyclic Loading and Unloading Conditions  
Based on permeability, strain and porosity data, the scatter diagrams between permeability and strain of broken coal samples were drawn and fitted to thus obtain the fitting curves between permeability and strain under cyclic loading and unloading conditions of broken coal samples, as shown in Figure 14. Besides, the scatter diagrams between permeability and porosity of broken coal samples were also drawn and fitted to thus obtain the fitting curves between permeability and porosity under cyclic loading and unloading conditions of broken coal samples, as shown in \[d_{1}=d_{0}(1-\varepsilon). \tag{7}\]0  
It can be speculated from Figures 14 and 15 that the permeability of broken coal samples decreased with increasing strain and increased with the increasing of porosity of the broken coal samples. The fitting curves between permeability and strain, and porosity are a cubic function and power function, respectively, and the fitting correlation coefficient of two functions was 0.99. In addition, under the same strain or porosity, the permeability of the broken coal sample at the loading stage in each loading and unloading stage was the same as that at the unloading stage.