## 3 Results  
### Relationship between Disturbance Control Variables and Stress Parameters  
Figure (a)a shows the relationship between different quasi-static stress rates and control variables. When the quasi-static disturbance rate is 0.01 MPa/s, the duration in the disturbance stage is about 142 s, and the peak stress at the final failure is about 26 MPa. As the quasi-static disturbance rate gradually increases, the disturbance duration decreases, and the peak stress increases in the early period and fluctuates later. When the quasi-static disturbance rate is 0.05 MPa/s, the disturbance duration is about 44 s, and the peak stress is about 34 MPa. Figure 5: Stress path of different disturbance stress: (**a**) static load; (**b**) cyclic load; (**c**) transient load. It shows that at a lower disturbance rate, the development of micro-cracks inside the sample is slower and has enough time to compact, so the sample can last longer disturbance time and finally show more substantial bearing capacity. With the increased disturbance rate, the specimen has been further damaged before the compaction closure, so the duration of the disturbance is gradually reduced. In addition, the correlation between peak stress and perturbation rate is unclear. The reason may be that the number of primary defects in different heterogeneous specimens varies greatly, resulting in peak stress not changing monotonically with changes in perturbation rate. Figure 6b shows the relationship between different quasi-static stress levels and control variables. When the sample experiences the working face mining period of \(\sigma_{1}=10\) MPa, the corresponding stress concentration factor \(K_{r}\) is 1.25, the disturbance duration is 76 s, and the stress peak when the specimen is unstable is 32.6 MPa. With the gradual mining of the working face, the disturbance duration and stress peak generally increase first and then decrease. When the stress in the \(\sigma_{1}\) direction caused by the mining is 14 MPa, the corresponding disturbance duration is 86 s, and the stress peak is 39.5 MPa. As the corresponding stress level before the disturbance gradually increases, the more internal cracks in the specimen and the bearing strength continue to decline. It shows that when the coal-rock mass is high stress, it is straightforward to cause impact damage. Figure 7a shows the relationship between different cyclic disturbance amplitudes and control variables. When the cyclic amplitude is 2 MPa, the disturbance duration is 3388 s, and the peak stress is 45.66 MPa. When the cyclic amplitude increases to 4 MPa, the disturbance duration decreases to 562 s, and the peak stress decreases sharply to 19.69 MPa. Subsequently, with the increase in cyclic amplitude, the disturbance duration and stress peak did not change significantly. It shows that the lower cyclic disturbance amplitude has less effect on the bearing capacity of the specimen. The stress amplitude of 4 MP a seems to be the critical point of a coal sample subjected to cyclic disturbance loads. Once this value is reached or exceeded, the number of internal cracks in the coal sample will increase by an order of magnitude, and the stress peak and damage of the corresponding sample will reach a relatively stable level, which is no longer affected by the cyclic amplitude. Figure 7b shows the relationship between different cyclic disturbance frequencies and control variables. When the cycle frequency is 0.2 Hz, the disturbance duration is 1526 s, and the peak stress is 39.74 MPa; when the cyclic frequency increases to 0.4 Hz, the disturbance duration decreases to 692 s, and the peak stress is 33.47 MPa. Subsequently, the disturbance duration and stress peak did not change significantly with the increase in cyclic frequency. It is shown that the lower cycle frequency has a certain effect on the bearing capacity of the sample. With the increase of the cyclic frequency, the damage to the specimen formation increases sharply, and the peak stress and ability to withstand disturbances decrease rapidly.