## 3 Experimental Results Analysis
### Effect of Loading Rate and Inclination Angle on the Elastic Modulus  
Elastic modulus is an important index to characterize the deformation resistance of coal samples. In this paper, 40-60% of the peak stress in the axial stress-strain curve is selected as its experimental value. Table 3 presents the experimental values of elastic modulus of coal samples under different loading rates and inclination angles. Due to the space limitation, only the data corresponding to the maximum value of variation coefficient under each inclination angle are given. As shown in Table 3, the standard deviation and variation coefficient of the elastic modulus experimental data obtained in this experiment are, respectively, within the range of 13.81-46.91 MPa and 4.37-6.42%, indicating the reliability of the experimental data. According to Table 3, the change curve of elastic modulus with loading rate and inclination angle is drawn, as shown in Figure 10. In Figure 10a, when the loading rate is constant, with the increase of the inclination angle, the elastic modulus of the sample increases slowly and then decreases gradually, and reaches the maximum value at the inclination angle of 5\({}^{\circ}\). This finding is consistent with that described in Section 3.4. For example, at the loading rate of 5 mm/min, when the inclination angle increases from 0\({}^{\circ}\) to 5\({}^{\circ}\), the elastic modulus increases by 0.128 GPa or 16.48%; when the inclination angle increases from 5\({}^{\circ}\) to 10\({}^{\circ}\), the elastic modulus decreases by 0.352 GPa or 38.76%. Therefore, the deformation resistance of the sample at the inclination angle of 5\({}^{\circ}\) is slightly higher than that at the vertical compression, which is also related to the bonding and friction effects between particles within the material [50]. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{ \begin{tabular}{c} **Inclination** \\ **Angle (\({}^{\circ}\))** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Loading** \\ **Rate** \\ **(mm/min)** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Peak Axial** \\ **Stress (MPa)** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Absolute** \\ **Error (\%)** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Relative** \\ **Error (\%)** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Average Peak** \\ **Axial Stress** \\ **(MPa)** \\ \end{tabular}  } & \multirow{2}{*}{\ \begin{tabular}{c} **Standard** \\ **Deviation** \\ **(MPa)** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Relative** \\ **Standard** \\ **Deviation (\%)** \\ \end{tabular}  } \\ \hline
0 & 0.05 & 8.19 & 0.86 & 0.24 & 0.24 & 0.24 & 0.24 & 0.24 \\ \hline
5 & 0.05 & 10.60 & 1.11 & 11.67 & 0.49 & 0.99 & 0.24 \\
10 & 0.05 & 8.71 & 0.78 & 0.89 & 0.49 & 0.24 \\
10 & 0.00 & 6.26 & 0.0  
In Figure 10b, when the inclination angle is in the range of 0\({}^{\circ}\) to 15\({}^{\circ}\), with the increase of the loading rate, the elastic modulus of coal samples increases first and then decreases, and the larger the inclination angle, the lower the loading rate required for the sample to reach the maximum value. For example, when inclination angles are 0\({}^{\circ}\), 5\({}^{\circ}\), 10\({}^{\circ}\) and 15\({}^{\circ}\), the loading rates corresponding to the maximum elastic modulus are 3.5, 3.5, 2.0 and 0.5 mm/min, respectively. When the inclination angle is in the range of 20\({}^{\circ}\) to 25\({}^{\circ}\), the elastic modulus decreases nonlinearly with the increase of loading rate. Based on the above analysis, the variation of elastic modulus with loading rate and inclination angle is consistent with the peak axial stress. Due to the heterogeneity of coal samples, a certain deviation is generated in a small number of experimental results. However, it does not affect the conclusion.