## 3 Results
### Relationship between Disturbance Control Variables and Peak Strain  
Figures 9-11 show the relationship between different mining-induced disturbance stress and peak strain. The correlation between the mining static load disturbance rate and the peak strain is not apparent, and with the increase in the disturbance rate, the peak stress shows a changing trend of \"first lowering--then rising--then decreasing\". However, the disturbance stress level correlates well with the peak strain. As the disturbance stress level increases, the peak strain increases monotonously. It shows that the peak strain of the coal sample under static load disturbance is closely related to the stress level before the disturbance. The higher the stress level, the higher the damage after the impact and the higher the corresponding coal explosion hazard (See Figure 9).  
Figure 8: Relationship of control variables and transient stress parameters: (**a**) transient increment; (**b**) stress level.  
Figure 7: Relationship of control variables and cyclic stress parameters: (**a**) cyclic amplitude; (**b**) cyclic frequency.  
Figure 10 shows that the coal sample's peak strain gradually increases with the cyclic amplitude. With the increase of cyclic frequency, the peak strain of coal samples shows a trend of \" first increase-then decrease\". It shows that cyclic amplitude plays a vital role in the crack propagation of coal samples. High cyclic amplitude leads to the generation and development of more internal cracks, increasing peak strain at failure. Under the action of low cycle frequency, it is beneficial to crack propagation inside the sample. When the cyclic frequency is 0.6 Hz, the peak strain is 2.66. When the cycle frequency reaches 1.0 Hz, the peak strain is only 1.84. It is shown that the higher cyclic frequency limits the degree of fracture development in the sample, which causes the micro-fractures to open, close, and expand in the micro-scale. The stress-strain relationship gradually reaches the stable limit state in the macro-scale and is dynamically adjusted to the secondary stability through local instability.  
Figure 11: Relationship of transient stress control variables and peak strain: (**a**) transient increment; (**b**) stress level.  
Figure 9: Relationship of static stress control variables and peak strain: (**a**) disturbance rate; (**b**) stress level.  
As shown in Figure 11, under the action of transient disturbance, the peak strain decreases linearly with the increase of transient increment. When the transient increment is 1 MPa, the peak strain is about 2.46. When the transient increment is 5 MPa, the peak strain is only 1.14. It indicates that the specimen can withstand more times lower transient incremental perturbations, resulting in more axial strains. The higher transient disturbance increment causes more significant instantaneous damage to the sample. Therefore, when the thick and hard roof is broken, due to the more incredible kinetic energy released instantaneously, the precursory characteristics of roadway deformation before the accident may not be apparent, so it is more difficult to carry out accurate advance predictions.  
Contrary to the transient increment, the stress level under the action of mining transient load disturbance is positively correlated with the peak strain at impact failure. When the transient level is 10 MPa, the peak strain is 1.94. when the transient level is 18 MPa, the peak strain is 2.82. This law is consistent with the peak strain law under different qusci-static load levels.