## 3 Analysis of Test Results  
Figure 3 illustrates the stress-strain curves for various cyclic periods. It is evident that the stress-strain curves create a hysteresis loop in each cycle. This hysteresis loop accurately delineates the plastic deformation caused by the opening and closing of rock fissures. The stress-strain response of the specimens remains rather uniform throughout each cyclic phase. The hysteresis loop area diminishes at all stress levels as it spirals towards the direction of escalating strain with each successive cycle. The irreversible deformations induced by these cycles exhibit less variability, with the exception of the initial cycle, which produces a markedly greater irreversible deformation. This phenomenon largely arises because the escalation of bias stress induces the initiation and propagation of cracks inside the coal samples, leading to considerable plastic deformation. Subsequently, due to the compaction effect, the extent of damage incurred during each cycle is diminished. These data indicate that the rock damage caused by elevated bias stress is far more than the fatigue damage from cyclic loading. Figure 2: Stress path program. As the stress level increases, the strain span of axial and radial strains increases, and the loading and unloading curves of the hysteresis loop to converge gradually. The configuration of the axial hysteresis loop at stress level 1 is characterized as \"shuttle\" type (in Figure 3). This phenomenon occurs because when the bias stress level in the loading section is low (about \((\sigma_{1}-\sigma_{3})<5\) MPa), the axial stress does not effectively promote the development of internal fissures and the confining stress predominantly restricts the coal samples, leading to a gradual response of axial strain as the bias stress increases. As stress levels increase, the axial hysteresis loop transforms into an extended \"streamline\" configuration. The configuration of the radial hysteresis loop resembles a \"streamline\" form, demonstrating a more distinct linearity, which indicates that the radial deformation predominantly occurs as elastic deformation. Further observations revealed that as the cyclic period increases, the angle of the stress-strain curve at the beginning of the unloading of the bias stress at the same level decreases, gradually changing from an obtuse angle to an acute angle, combined with the hysteresis effect, the \"obtuse angle\" reflects the sluggish strain feedback and rapid plastic deformation response of the coal sample when the bias stress unloading, \"acute angle\" reflects that the coal sample is sensitive at the bias stress unloading point, with a rapid response to elastic deformation. It indicates that a shorter cyclic period leads to a reduced elastic response and an increased sensitivity to plastic deformation in the coal samples at the peak of the cycle. Figure 4 shows the bias stress-volume-strain curves of the third cycle in the extraction of each stress level. Volume strain is the combined response of axial and radial strains, which characterizes the overall deformation of the coal sample, \(\varepsilon_{v}=\varepsilon_{1}+2\varepsilon_{3}\). The coal  
Figure 3: Stress–strain curves at different cyclic periods. sample undergoes shear inflation followed by shear compression during each cycle. The bias stress-volume-strain curves are roughly centrosymmetric along the axis of the line connecting the cyclic onset and peak points, and the overall phenomenon demonstrates a clear expansion and dilation. As stress levels escalate, the spectrum of volume strain values diminishes and moves towards deformation expansion, mostly due to the rise in shear stress. The key point of bias stress at the initiation of specimen shear compression was noted to be progressively nearing the peak stress point of the cycle. Comparing different cyclic periods at the same stress level, as the cyclic period decreases, the volume strain of the specimen gradually shifts to the right, indicating deformed compression.