# Energy Evolution Analysis of Coal Fracture Damage Process Based on Digital Image Processing
## 3 Analysis of Results  
### Mechanical Property Anisotropy Analysis  
The test results are summarized in Table 2, where the compressive strength and elastic modulus of the coal rocks vary evidently with the disparate dip angles of the calcite veins. In order to be able to more visually reflect the effect of calcite veins on the overall mechanical properties producing anisotropy, the data in Table 2 are plotted in Figure 4.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Material**} & \multirow{2}{*}{**Elastic Modulus**} & \multirow{2}{*}{**Homogeneity**} & \multirow{2}{*}{**Compressive Strength**} & \multirow{2}{*}{**Poisson Ratio**} & \multirow{2}{*}{**Internal Friction Angle (\(\lx@math@degree\))**} & \multirow{2}{*}{**Compression tension**} \\  & & & & & \\ \hline Coal & 7000 & 5 & 60 & 0.40 & 35 & 10 \\ Calcite & 80,500 & 3 & 101 & 0.30 & 30 & 11 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of coal numerical model [41; 42].  
Figure 3: Digital images of coal and rock at different azimuth angles.  
Figure 2: Loading diagram of coal and rock.  
From Figure 4, it could be seen that both the compressive strength and elastic modulus of the coal show apparent anisotropy with the change of calcite vein dip angle \(\alpha\). When the calcite vein has low dip angle (0\({}^{\circ}\), 15\({}^{\circ}\) and 30\({}^{\circ}\)), the compressive strength of coal is high, about 40 MPa. When calcite veins have high dip angles (45\({}^{\circ}\), 60\({}^{\circ}\), 75\({}^{\circ}\) and 90\({}^{\circ}\)), the compressive strength of coal is relatively low. When \(\alpha=0^{\circ}\), the maximum compressive strength of coal is 40.39 MPa; when \(\alpha=60^{\circ}\), it reaches the lowest value of 23.45 MPa, which is 41.94% lower than that of the 0\({}^{\circ}\) sample. This result is consistent with the strength effect of a single structural plane [43]. The trend of modulus of elasticity is opposite to the trend of compressive strength. When the calcite veins are of low dip angle, the modulus of elasticity of coal rocks is small. The modulus of elasticity is minimum at \(\alpha=0^{\circ}\) with a value of 5.4 GPa. The modulus of elasticity of the kerogen is larger when the calcite veins are of high dip angle. When \(\alpha=45^{\circ}\), the modulus of elasticity is the highest, which is 6.19 GPa, which is 14.63% higher than that of the 0\({}^{\circ}\) sample. The reason for this phenomenon is that the presence of calcite veins affects the stress distribution in the coal rock. At low dip angle, the weak cementation between coal matrix and calcite vein is not easy to be damaged, resulting in high compressive strength. At high dip angle, the weak cementation between coal matrix and calcite vein is easy to be damaged, resulting in low compressive strength. Therefore, calcite vein has apparent results on the mechanical properties of coal.  
Figure 5 shows the stress-strain curves of coal rocks containing calcite veins with diverse azimuth angles. From Figure 5, it can be seen that the deformation and damage process of coal rock has gone through three stages: linear elasticity, plasticity and failure. When calcite veins have a low dip angle, the strain from coal seam damage is large, while the strain from a high dip angle is small.