# Energy Evolution Analysis of Coal Fracture Damage Process Based on Digital Image Processing
## 3 Analysis of Results
### Analysis of Energy Evolution during Coal Fracture Damage  
#### 3.3.1 Coal Energy Evolution Characteristic Index  
The energy value before and after rock fracture is closely related to its fracture mode. In fact, a series of energy indices (impact propensity indices) have been proposed and widely used in rock impact ground pressure and rock-burst studies to characterize the energy evolution of loaded rocks and to explain the magnitude and severity of rock fractures. The more elastic energy the rock accumulates, the stronger its propensity to impact, the less energy it dissipates, and the more energy it releases when it breaks. The less elastic energy a rock accumulates, the less it exhibits a tendency to impact, the more energy it dissipates, and the less energy it releases when it breaks [46]. These characteristic indexes mainly include elastic energy index and impact energy index. In recent years, some scholars have proposed new indicators to correct the shortcomings of the above indicators, mainly including effective impact energy index, residual energy index, etc. these indicators are important manifestations of rock energy evolution characteristics. Elastic energy index \(W_{\text{ET}}\) is defined as the ratio of elastic performance to energy consumption at 80-90% strength before the peak, as shown in Figure 8, \(W_{\text{ET}}\) = \(S_{\text{EAC}}\)/\(S_{\text{EOA}}\). Its value shows a positive correlation with the impact propensity of the rock. The criteria determined by the Polish General Institute of mining research are: \(W_{\text{ET}}\)\(\geq\) 5.0 is strong impact tendency, 2.0 \(\leq W_{\text{ET}}\) < 5.0 is medium impact tendency, and \(W_{\text{ET}}\) < 2.0 has no impact tendency. Figure 7: Fracture process and acoustic emission diagram of coal at different azimuth angles. The impact energy index \(K_{\rm E}\) is defined as the ratio of the area under the stress-strain curve before and after the peak, as shown in Figure 8, \(K_{\rm E}=S_{\rm OEEP}/S_{\rm FDHG}\). The larger the value, the stronger the impact tendency. It is generally considered that \(K_{\rm E}>2.0\) is a strong impact tendency, \(1.0\leq K_{\rm E}<\)2.0 is a medium impact tendency and \(K_{\rm E}<1.0\) has no impact tendency. The effective impact energy index \(K_{\rm eff}\) is the ratio of the elastic energy stored before the peak strength of the rock to the energy required for post-peak damage, with the expression \(K_{\rm eff}=S_{\rm FED}/S_{\rm FDHG}\). \(S_{\rm FBD}\) is the area under the peak unloading line FB in Figure 8, and \(S_{\rm FDHG}\) is the area under the post-peak curve. The expression for calculating the residual energy index \(W_{\rm R}\) is \(W_{\rm R}=(S_{\rm FBD}-S_{\rm FDHG})/S_{\rm FDHG}\). The characteristic energy parameters of each sample are calculated through the stress-strain curves of coal with 7 different calcite vein dip angles (see Figure 5), as shown in Table 3, and drawn into Figure 9. It was analyzed that:  
1. With the rise of calcite vein dip angle, the input energy density before the peak value \(E1\), the input energy density at 80% strength \(E3\) and the accumulated elastic property density at 80% strength \(E4\) show a change trend of first declining and then rising. In contrast, the pre-peak cumulative elastic energy density E2 exhibits a repeatedly increasing and then decreasing trend. 2. On the whole, when the angle of calcite vein is low, that is, the samples with low dip angle (\(0^{\circ}\), \(15^{\circ}\) and \(30^{\circ}\)), the input energy and accumulated elastic energy are large. The input energy and accumulated elastic energy of samples with high inclination angles (\(45^{\circ}\), \(60^{\circ}\), \(75^{\circ}\) and \(90^{\circ}\)) are lower. The reason for the above situation is that the coal is not easy to be damaged at low inclination angle, the number of loading steps is more, and more energy is required for damage.