## 3 Experimental Results Analysis
### Effect of Loading Rate and Inclination Angle on Macroscopic Failure Characteristics of Coal Samples  
The instability failure of coal samples is the final result of crack propagation and penetration in the loading process. Its failure characteristics are not only related to its material properties, but also closely related to its loading mode [51]. Therefore, the macroscopic failure characteristics of coal samples can effectively reflect the influence of external load on its failure behavior to a certain extent. Figure 11 shows the typical macroscopic failure characteristics of coal samples under different loading rates and inclination angles. From Figure 11, firstly, at any loading rate, the change rule of macro failure mode with inclination angle is consistent, that is, with the increase of inclination angle, the failure mode of coal samples is gradually transformed from tensile splitting failure to shear failure. In general, within the inclination angle of 0\({}^{\circ}\)-5\({}^{\circ}\), a large number of tensile splitting cracks parallel to the axial direction of the sample are developed on the surface of each sample and a small number of shear cracks are locally generated. It shows that the tensile splitting failure is the main failure mode of the samples under the low inclination angle of 0\({}^{\circ}\)-5\({}^{\circ}\) and the failure mode is independent of the loading rate of the sample. Within the inclination angle of 5\({}^{\circ}\)-10\({}^{\circ}\), splitting cracks parallel to the axial direction of the samples are developed on surfaces of the most coal sample, accompanied by a large number of shear cracks. Thus, coal samples in this state present the composite failure mode of tension and shear. Within the high inclination angle of 15\({}^{\circ}\) to 25\({}^{\circ}\), macro failure surfaces with a certain angle with the axial direction of the samples are generated for most of coal samples, indicating the shear failure of the samples. The above analysis shows that the inclination angle has a significant effect on the failure mode of coal samples [49]. With the increase of the inclination angle of the sample, the failure mode is transformed from tension splitting failure (0\({}^{\circ}\)-5\({}^{\circ}\)), tension-shear composite failure (10\({}^{\circ}\)) to single shear failure (15\({}^{\circ}\)-25\({}^{\circ}\)). This is mainly because the larger shear stress component accelerates the shear crack under the high inclination angle, contributing to the shear failure [40]. Secondly, with the increase of loading rate, the fragmentation degree of coal samples increases gradually, but the macro failure law of samples is slightly different under different inclination angles. When the inclination angle of the sample is small (0\({}^{\circ}\)-5\({}^{\circ}\)) and the loading rate is low (0.05-0.50 mm/min), the failure mode of coal sample is axial splitting, and the sample is intact without debris after failure. At the medium loading rate (1.00-5.00 mm/min), the failure mode of coal samples is unchanged, which is still manifested as an axial splitting failure. However, the integrity of the sample is damaged, and fragments and debris peeled from the sample. At the high loading rate (7.50-10.00 mm/min), the failure mode is mainly the conical failure. The sample has poor integrity and more fragments, showing bursting characteristics. When the inclination angle is 10\({}^{\circ}\), axial splitting is the main failure mode at the low loading rate. At medium and high loading rate levels, the failure mode of coal samples is transformed from axial splitting to shear-slip failure, which has a high tendency of shear instability. When the inclination angle is in the range of 15\({}^{\circ}\)-25\({}^{\circ}\), the main failure mode of coal samples is shear failure at any loading rate. With the increase of loading rate, the number of debris further increases after failure of the sample, and the failure degree of the sample increases gradually.