## 4 Results Analysis and Discussions
### Reasons for the Changes in Permeability under Cyclic Loading and Unloading Conditions  
As shown in Figure 10, the initial height of broken coal samples was recorded as \(h_{0}\) and the compression-induced displacement recorded using the displacement transducer at the vertical direction during the triaxial seepage test was \(\Delta h\). Therefore, the axial strain (\(\varepsilon\)) on broken coal samples during the whole test can be calculated as follows:  
\[\varepsilon=\Delta h/h_{0}. \tag{6}\]  
It was assumed that the true density of coal samples, the mass of broken coal samples during each test and the initial diameter of the colloid sleeve were \(\rho\), \(m\) and \(d_{0}\), respectively. Owing to axial stress being equal to the confining stress throughout the test, that is, the sample was always in a hydrostatic-pressure state, it can be supposed that the radial strain on broken coal samples was equal to the axial strain. Therefore, the diameter (\(d_{1}\)) of coal samples during triaxial loading can be expressed as follows:  
\[d_{1}=d_{0}(1-\varepsilon). \tag{7}\]  
In accordance with Equations (6) and (7), and Figure 10b, it can be seen that the porosity (\(\phi\)) of broken coal samples during the test can be calculated as follows:  
\[\phi=\frac{\frac{\pi}{4}{d_{1}}^{2}(h_{0}-\Delta h)-\frac{m}{\rho}}{\frac{\pi }{4}{d_{1}}^{2}(h_{0}-\Delta h)}=\frac{\pi{\rho}{d_{0}}^{2}{h_{0}}(1- \varepsilon)^{3}-4m{h_{0}^{2}}}{\pi{\rho}{d_{0}}^{2}{h_{0}}(1-\varepsilon)^{3 }}. \tag{8}\]  
By substituting the data during the test monitored by using the displacement transducer into Equation (6), the stress-strain curves of coal samples under cyclic loading and unloading were calculated and drawn, as shown in Figure 11. By substituting the calculated strain into Equation (8),  
Figure 10: Calculation of strain and porosity: (**a**) before the seepage test (**b**) after the seepage test. the relationship curves between the porosity of coal samples and effective stress during cyclic loading and unloading are shown in Figure 12.  
It can be seen from Figures 11 and 12 that the increments of strains on coal samples over three cycles were 0.199, 0.079 and 0.041, respectively. Consequently, the corresponding reductions in the porosity were 0.198, 0.078 and 0.04, respectively. It indicated that with the increased cyclic loading and unloading events, the reductions in the porosity of coal samples in the loading stage gradually decreased, thus leading to the gradual reduction in the loss of permeability of coal samples. The reduction amounts of strain on coal samples during three unloading events were 0.077, 0.047 and 0.019, respectively, corresponding to increments of 0.076, 0.046 and 0.018 in porosity. This implied that with increasing loading and unloading cycles, the increment in the porosity of coal samples in the unloading stage gradually decreased, thus causing the recovery of permeability to decrease. During the three loading and unloading cycles, the reductions (0.198, 0.078 and 0.04) in the porosity of coal samples in the loading stage were much greater than the increments (0.076, 0.046 and 0.018) in the  
Figure 11: Stress-strain curves of coal samples under cyclic loading and unloading conditions. Figure 12: Changes of porosity of coal samples under cyclic loading and unloading conditions. porosity of coal samples in the unloading stage within the same cycle. Therefore, during each loading and unloading cycle, the loss of permeability of coal samples in the loading stage was much greater than the recovery thereof in the unloading stage. The reasons why the porosity of broken coal samples reduced in the loading stage involves three things [34]: (1) the structural re-arrangement of broken coal particles caused a significant reduction in porosity: in the early stage of loading of broken coal masses, there was no cohesion between particles to therefore cause slippage and rotation of particles.