# Energy Evolution Analysis of Coal Fracture Damage Process Based on Digital Image Processing
## 3 Analysis of Results
### Failure and Deformation Characteristics of Coal Rocks  
Figure 6 shows the stress distribution in the coal rock at a stress level of about 10%. The color brightness in the graph is positively correlated with the stress. From Figure 6, it can be seen that calcite veins with different dip angles reconfigure the internal stresses in the coal rock, which is also responsible for the change of mechanical properties in Section 3.1 of the coal rock.  
Figure 4: Compressive strength and elastic modulus of coal and rock at different azimuth angles.  
Figure 7 shows the fracture process and acoustic emission diagram of coal in different directions. From Figure 7, we can find that calcite veins have a major effect on the destruction process of coal rocks, and tensile and shear damage mainly occur in the destruction process of coal rocks containing calcite veins. The crack distribution and final damage pattern of the kerogen are strongly influenced by the dip angle \(\alpha\) of calcite veins and show strong variability.  
1. When \(\alpha\) = 0\({}^{\circ}\) and 15\({}^{\circ}\), the cracks appeared first in the calcite veins, and the samples at 0\({}^{\circ}\) were uniformly distributed, and the results of the study were consistent with those of [PERSON] and [PERSON] [44,45]. When \(\alpha\) > 15\({}^{\circ}\), the initial crack initiated only locally in the calcite vein. When the azimuth angle is high (75\({}^{\circ}\) and 90\({}^{\circ}\)), the initial crack does not initiate vertically, but forms a certain included angle with the loading direction. It is worth noting that the equal-spacing cracks only appear when the inclination angle is low, but there are no equal-spacing cracks at the higher inclination angle. This may be due to the change in the inclination of the calcite veins and the change in the internal stress distribution of the coal, which in turn led to the above phenomenon.  
Figure 5: Stress\(-\)strain relation curves of coal and rock under diverse azimuth angles.  
Figure 6: Stress distribution of coal with stress level of 10%.  
2. When the calcite veins are at low inclination angles (0\({}^{\circ}\), 15\({}^{\circ}\) and 30\({}^{\circ}\)), crack extensions appear in the calcite veins, forming a larger angle with the calcite veins, and finally forming complex fracture modes, which are respectively oblique Z-shaped (0\({}^{\circ}\)), V-shaped (15\({}^{\circ}\)) and inverted V-shaped (30\({}^{\circ}\)) failure modes, and mainly shear failure. When the calcite veins have high dip angles (45\({}^{\circ}\), 60\({}^{\circ}\), 75\({}^{\circ}\) and 90\({}^{\circ}\)), the fracture mode of the coal is single, which is a type I failure mode, and the angle with the calcite veins is small, mainly tensile failure. When \(\alpha\) = 75\({}^{\circ}\) and 90\({}^{\circ}\), the coal is almost completely destroyed along the calcite vein.  
In the acoustic emission distribution in Figure 7, red indicates tensile failure, yellow indicates shear failure and black indicates failure. Generally speaking, the coal fracture process involves shear failure and tensile failure. When the dip angle of calcite veins is low (0\({}^{\circ}\), 15\({}^{\circ}\) and 30\({}^{\circ}\)), there is more shear damage inside the specimen and some amount of tensile damage. When calcite veins have high dip angles (45\({}^{\circ}\), 60\({}^{\circ}\), 75\({}^{\circ}\) and 90\({}^{\circ}\)), the form of kerogen damage changes to tensile damage and shear damage occurs in small amounts, which is consistent with the results of the above analysis.