## 3 Results
### The Evolution Law of Energy Absorption
Thus, when combined with the analysis of the failure morphology and mode of the specimens, it can be concluded that the severity of tensile sliding failure in sandstone decreases first and then increases with the increase in crack dip angle. Figure 14: The relationship between absorbed energy and vertical displacement ratio. Table 3 presents the maximum absorbed energy and the maximum absorbed energy ratio of specimens with different crack angles, as well as intact specimens. The data in the table reveal several key findings: the maximum absorbed energy of specimens with cracks is significantly lower than that of intact specimens, with the maximum absorbed energy of specimens with pre-existing cracks being about 40-75% of that of intact specimens. This indicates that pre-existing cracks induce substantial energy damage to the specimens. The range of maximum absorbed energy of specimens with cracks varies greatly, with a variation amplitude of about 34%, indicating that the crack angle has a significant effect on the energy required for rock failure. The specimen with the smallest maximum absorbed energy is the one with a crack angle of \(\alpha=45^{\circ}\), with a value of 6.45 J, which is only 40.56% of that of the intact specimen. The maximum value is obtained when the crack angle is \(\alpha=90^{\circ}\), with a value of 11.84 J, which is 74.4% of that of the intact specimen. The difference in maximum absorbed energy of rock specimens with crack angles of \(0^{\circ}\), \(45^{\circ}\), and \(60^{\circ}\) is relatively small, with an amplitude of variation of merely 9%. Studying the relationship between the maximum absorbed energy (i.e., the total energy required for specimen failure) and other parameters of the rock can provide an important reference for certain rock engineering. Figures 15-17 show the relationships between the maximum absorbed energy and the dip angle of pre-existing cracks, tensile strength of the rock, and acoustic emission energy, respectively. From Figure 15, it can be seen that the dip angle of pre-existing cracks has a significant effect on the maximum absorbed energy of sandstone, with a large difference in absorbed energy among specimens with different crack angles. The maximum absorbed energy of the specimen decreases first and then increases with the increase in crack dip angle, and the variation law is consistent with the relationship between tensile strength and crack angle. Figure 15: Relationship between maximum absorbed energy and pre-existing crack dip angle. \begin{table}
\begin{tabular}{c c c} \hline
**Specimen** & **Maximum Absorbed Energy/J** & **Maximum Absorbed Energy Ratio/\%** \\ \hline intact specimen & 15.91 & 100 \\ S-0 & 10.45 & 65.68 \\ S-30 & 7.78 & 48.90 \\ S-45 & 6.45 & 40.56 \\ S-60 & 7.64 & 48.01 \\ S-90 & 11.84 & 74.40 \\ \hline \end{tabular}
\end{table} 
Table 3: Maximum absorbed energy and maximum absorbed energy ratio of the rock specimen. The occurrence of tunnel collapses and other instability phenomena in rock engineering can often be attributed to the initiation, propagation, and penetration of primary defects such as cracks and joints under the influence of loads, ultimately resulting in rock instability and failure. The entire failure process is closely related to the tensile strength and energy required for the failure of the rock. Figure 16 displays a scatter plot and fitted curve between the two, indicating that there is a nonlinear relationship between the tensile strength of the rock and the maximum absorbed energy. The plot demonstrates that as the maximum absorbed energy increases, the tensile strength of the rock also tends to rise. In the field of rock engineering construction, microseismic monitoring is commonly employed to track the progression of rock mass cracks and assess the stability of rock formations in real time. In this study, indoor acoustic emission simulation tests were also conducted.