# Mechanical Properties and Energy Evolution Law of Fractured Coal under Low Confining Pressure
## 5 Evolution Characteristics of Triaxial Strain Energy
### Effect of the Fracture Number Based on Energy Analysis  
Figures 13 and 14 show the energy evolution law inside the fractured coal body when the confining pressure is 0.3 MPa and 3 MPa, respectively. Similar trends can be observed from the energy evolution curves of specimens with different numbers of prefabricated cracks. The total energy of the prefabricated specimens increases with the increase of axial strain, with a low increasing rate in the early stage and a high rate in the later. In the compaction stage and elastic stage, the growth process of the elastic strain energy is consistent with the growth of the total energy, and there is little numerical difference. After reaching the peak stress point, the energy release is gradually reduced. This is because there is no obvious crack in the specimen before and during the elastic stage, the input energy is thereby almost completely transformed into elastic strain energy. With the gradual compaction of the internal openings in the specimen, the growth rate of elastic strain energy increases gradually. Then with the continuous loading of axial pressure, the internal cracks begin to sprout and expand, and the dissipation energy begins to increase rapidly. In the post-peak stage, the elastic strain energy stored in the specimen is released rapidly, and the crack propagation is accelerated. With the sharp decrease of the elastic strain energy, the dissipation energy increases significantly. Moreover, with the increase of the number of prefabricated cracks, the more obvious the'step' drop state of elastic strain energy appears after the peak, the larger the corresponding strain range of'step' is. Table 2 shows the total energy, elastic energy, dissipation energy and dissipation energy ratio of the fractured coal specimens under peak stress. As shown in Table 2, when the confining pressure is fixed, with the increase of the number of prefabricated cracks, the peak total energy and elastic energy show a trend of gradual decreasing. For example, with a confining pressure of 0.3 MPa, when the number of prefabricated cracks increases from 1 to 4, the total energy decreases by 9.59%, and the elastic energy decreases by 17.51%. With a confining pressure of 3 MPa, when the number of prefabricated cracks increases from 1 to 4, the dissipation energy increases by 6.43%, and the dissipation energy ratio  
increases from 13.53% to 21.10%. With the increase in the number of fractures, the elastic energy stored in the coal specimen decreases gradually, and the proportion of dissipated energy and dissipated energy increases gradually. This indicates an increase of energy that is consumed for developing internal cracks, and a gradual decrease of the energy to be released when the specimen fails. As a result, the failure of the coal body tends to be smoother, which corresponds to the weakening of the brittle characteristics of the fractured coal body. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Confining** & **Crack** & **Total** & **Elastic Strain** & **Dissipated** & **The Proportion of** \\
**Pressure/MPa** & **Number/Strip** & **Energy/kj** \(\cdot\)**m\({}^{-3}\)** & **Energy/kj** \(\cdot\)**m\({}^{-3}\)** & **Energy/kj** \(\cdot\)**m\({}^{-3}\)** & **Dissipation Energy/\%** \\ \hline \multirow{4}{*}{0.3} & 1 & 151.765 & 131.237 & 20.528 & 13.53 \\  & 2 & 150.147 & 127.449 & 22.698 & 15.12 \\  & 3 & 149.422 & 122.616 & 26.806 & 17.94 \\  & 4 & 137.214 & 108.257 & 28.957 & 21.10 \\ \hline \multirow{4}{*}{3} & 1 & 347.797 & 280.125 & 67.672 & 19.46 \\  & 2 & 285.442 & 215.826 & 69.616 & 24.39 \\ \cline{1-1}  & 3 & 247.890 & 177.231 & 70.659 & 28.50 \\ \cline{1-1}  & 4 & 212.963 & 140.938 & 72.025 & 33.82 \\ \hline \end{tabular}
\end{table} 
Table 2: Energy statistics at peak point of prefabricated cracked coal specimen. Figure 13: Energy evolution of coal specimens with different numbers of prefabricated cracks under confining pressure 0.3 MPa with axial strain.