## 2 Experimental Study
### Experimental Results
#### 2.2.2 Permeability Characteristics  
The stress-strain and permeability-strain curves of the two sets of comparative paths are shown in Figures 9 and 10, respectively. With an increase in the axial strain, the change in permeability mainly underwent four stages: a slow decrease, slow increase, rapid increase, and gradual stabilization.  
The change in permeability was mainly due to the change in the pores and cracks of the sample during the loading and unloading processes. As can be seen from the two figures, when the axial  
Figure 9: Stress–strain curves and permeability–strain curves under different loading paths: (**a**) \(\sigma_{3}=4\) MPa, P = 1 MPa; (**b**) \(\sigma_{3}=4\) MPa, P = 1.5 MPa; (**c**) \(\sigma_{3}=4\) MPa, P = 2 MPa; (**d**) \(\sigma_{3}=7\) MPa, P = 2 MPa; (**e**) \(\sigma_{3}=10\) MPa, P = 2 MPa.  
strain increases, the rapid increase in permeability lags behind the peak of the deviatoric stress as a whole. This showed that the rapid increase in permeability was induced by the failure of the sample and the formation of the through crack. After the failure of the sample, the gas flow increased, but it took time for the control acquisition system to register the increase in the gas flow. Therefore, a lagging phenomenon existed. Under the CTC path, when the initial radial stress and gas pressure were 10 MPa and 2 MPa respectively, the rapid increase in permeability was not obvious. This may be because no penetrating crack formed when the sample failed.  
Under the two loading paths, the original pores and cracks of the sample were first compacted, and the permeability decreased to the minimum. Then, damage occurred in the sample, and the permeability slowly increased. After the sample failed, the permeability rapidly increased and eventually almost stabilized. Figure 9 shows that under the ATC path, the corresponding axial strain was generally larger when the permeability of the sample started to rise rapidly. This showed that the axial deformation of the sample was larger, and more energy had accumulated in the sample when the sample was close to failure. Therefore, when the sample failed, the energy release was more intense and impactful.  
Under the two unloading paths, because of the loading of the axial stress, the volume of the original pores and cracks decreased, and the gas flow passage became smaller, leading to a decrease in the permeability. Then, the radial stress began to be unloaded. As a result, the deviatoric stress increased, and the average stress decreased, leading to a slow increase in the permeability. Damage occurred in the sample with the increase in the deviatoric stress, and the permeability continued to increase slowly. When the sample was destroyed, the formation of a penetrating crack caused the permeability to increase sharply and then eventually stabilize. It can be concluded from Figure 10 that, under the same conditions, the corresponding axial strain is generally smaller when the permeability begins to increase rapidly under the AUCP path. Before the unloading rate was changed, the axial deformations of the samples under the two unloading paths were the same. Then, the radial stress was continuously unloaded, and the axial strain continued to increase. However, the unloaded radial stress was smaller under the AUCP path. Therefore, the axial deformation was smaller when the sample failed. This also showed that the crack development under the AUCP path was insufficient, and the energy release was more violent and impactful.  
It could also be found that the increase in the magnitude of the permeability under the accelerated loading and unloading path was larger than that under the conventional loading and unloading path. This indicated that under the accelerated loading and unloading path, the sample was more broken after failure, which confirmed the more impactful action found in the previous analysis.