# Evolution of Permeability and Sensitivity Analysis of Gas-Bearing Coal under Cyclic Dynamic Loading
## 4 Results and Discussion
### The Permeability Behavior of Coal in the Full Stress-Strain Process  
To more intuitively illustrate the overall evolution of coal permeability under cyclic dynamic loading, we also obtained the stress-strain versus permeability relationship curves of the coal body under such loading, as depicted in Figure 7. There exists a notable coupling relationship between the stress of the coal samples, the axial strain, and the permeability. The stress-strain curve of coal can be classified into four distinct phases: the compaction stage, the elastic oscillation stage, the plastic deformation stage, and the failure stage. Correspondingly, the permeability curve is divided into four regions: the compaction reduction zone (I), the oscillation zone (II), the gradual recovery zone (III), and the abrupt increase zone of failure (IV). The compaction reduction zone (I): From the initial compression point to the lowest permeability point before the application of cyclic loading, this phase corresponds to the consolidation stage and the elastic deformation stage of the stress-strain curve. During this period, the permeability of the coal samples exhibited a non-linear decreasing trend, with the rate of decrease gradually decelerating, ultimately reducing by approximately  
Figure 6: Variation in permeability with gas adsorption. Figure 7: Stress–permeability–strain curves of coal under cyclic dynamic load. 50% of the initial permeability. The reason is that, under the gradual application of an axial load, the inherent fissures within the coal body are progressively compacted. This leads to a reduction in the connectivity of the fissures, consequently decreasing the porosity. The channels through which gas molecules flow become narrower and fewer, resulting in a noticeable decline in permeability. The oscillation zone (II): This zone exhibits a propensity towards coupled resonance in permeability during the application phase of cyclic dynamic loading, which evolves in tandem with the imposition of cyclic dynamic loads. The permeability after the application of a dynamic load should exceed that before the application, as cyclic dynamic loading induces irreversible plastic deformation in the coal matrix, leading to a gradual accumulation of damage and an increase in the pathways available for gas flow. The gradual recovery zone (III): From the end of the oscillatory zone in the permeability curve to the point of sudden slope increase, this stage corresponds to the plastic deformation phase of the stress-strain curve. During this period, with the increase in axial stress, permeability also exhibits growth. Due to the external load, the coal body framework undergoes irrecoverable plastic deformation, leading to a gradual accumulation of damage and destruction. Numerous new fissures emerge, develop, and stabilize, thereby causing the permeability to progressively recover. The abrupt increase zone of failure (IV): From the point of the sharp increase in the slope of the permeability curve until the conclusion of the test, this phase corresponds to the peak strength and post-peak phase of the stress-strain curve. During this period, the permeability curve of the coal samples exhibits an almost vertical ascent. Compared to the initial permeability, the permeability at the end of this stage has increased by approximately a factor of two. The stress-permeability temporal curve of coal under cyclic loading is illustrated in Figure 8. It is evident that the stress loading curve of the coal body and the variation in permeability exhibit a synchronous resonance pattern. When the cyclic load is applied and the stress returns to its pre-load level, the permeability fails to revert to its original state and actually increases to a certain extent. The reason for this lies in the fact that, during the application of dynamic loading, the internal fissures within the coal body further develop, leading to the widening and proliferation of seepage pathways, which, to a certain extent, increases the permeability of the coal body.