## 3 Experimental Results Analysis
### Effect of Loading Rate and Inclination Angle on Macroscopic Failure Characteristics of Coal Samples
The above analysis shows that the loading rate and inclination angle have an important impact on the failure mode and failure degree of coal samples. As shown in Table 4, axial splitting is the main failure mode of coal samples under low inclination angle and low loading rate. After failure, the sample has high integrity. Shear failure is the main failure mode of samples under high inclination angle and high loading rate, and the sample is seriously fractured after failure. This finding is consistent with the law that inclined pillar is more prone to shear instability failure under high-strength mining. Figure 11: _Cont._  
Figure 11: Typical failure coal samples: (**a**) \(\upsilon\) = 0.05 mm/min; (**b**) \(\upsilon\) = 0.5 mm/min; (**c**) \(\upsilon\) = 1.0 mm/min; (**d**) \(\upsilon\) = 2.0 mm/min; (**e**) \(\upsilon\) = 3.5 mm/min; (**f**) \(\upsilon\) = 5.0 mm/min; (**g**) \(\upsilon\) = 7.5 mm/min; (**h**) \(\upsilon\) = 10.0 mm/min. angle. For example, when the inclination angle changes from 10\({}^{\circ}\)-25\({}^{\circ}\), the ratio of tensile cracks is less than 50%, which decreases from 42.48% to 22.65%, and decreases by 46.68%. However, the proportion of shear cracks is greater than 50%, which increases from 57.52% to 77.35% and increases by 19.83%. It shows that coal samples are mainly shear failure under this inclination angle. This law is consistent with the macroscopic failure mode of coal samples. Figure 12: The average frequency (\(AF\)) and rising angle (\(RA\)) curves under different inclination angles at a loading rate of 1 mm/min: (**a**) 0\({}^{\circ}\); (**b**) 5\({}^{\circ}\); (**c**) 10\({}^{\circ}\); (**d**) 15\({}^{\circ}\); (**e**) 20\({}^{\circ}\); (**f**) 25\({}^{\circ}\). Figure 14 shows the variation of \(AF\)-\(RA\) curve with the inclination angle at 10 mm/min. The total number of cracks at the loading rate of 10 mm/min is significantly reduced compared with that at the 1 mm/min. At the angle of 0\({}^{\circ}\)-10\({}^{\circ}\), the cracks are concentrated near the \(AF\) axis, and the number of cracks near the \(AF\) axis is significantly greater than that near the \(RA\) axis. Table 6 shows the ratio of the number of tensile and shear cracks to the total number of cracks under different inclination angles. Figure 15 shows the change curve of the ratio of tensile and shear cracks with the inclination angle. When the inclination angle is 0\({}^{\circ}\), 5\({}^{\circ}\) and 10\({}^{\circ}\), the proportion of tensile cracks is 69.56%, 67.46% and 62.75%, respectively. It indicates that the sample failure is mainly caused by tensile failure within this inclination angle range. Within the inclination angle of 15\({}^{\circ}\)-25\({}^{\circ}\), with the increase of the inclination angle, the crack distribution gradually shifts from the \(AF\) axis to the \(RA\) axis. It indicates that the shear failure of coal samples is strengthened. For example, when the inclination angle increases from 15\({}^{\circ}\) to 25\({}^{\circ}\), the proportion of tensile cracks is less than 50%, decreasing from 48.35% to 39.81%; while the proportion of shear cracks is greater than 50%, increasing from 51.65% to 60.19%. It indicates that coal samples failure is mainly caused by shear failure within this range. This law is consistent with the macroscopic failure mode of coal samples. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Inclination Angle (\({}^{\circ}\))** & **Tensile Crack/Total Crack (\%)** & **Shear Crack/Total Crack (\%)** \\ \hline
0 & 57.96 & 42.04 \\
5 & 55.78 & 44.22 \\
10 & 42.48 & 57.52 \\
15 & 36.87 & 63.13 \\
20 & 26.03 & 73.97 \\
25 & 22.65 & 77.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Proportion of tensile and shear cracks under different inclination angles at a loading rate of 1 mm/min. Figure 13: The proportion of tensile and shear cracks under different inclination angles at a loading rate of 1 mm/min.