## 3 Energy Characteristics of SHIR Specimens with Different \(\alpha\)
### Evolution Process of Energy  
According to the calculation method of energy, variation of \(U\), \(U^{e}\), and \(U^{d}\) of SHIR specimens with varying \(\alpha\) under uniaxial compression conditions can be obtained. Energy evolution curves are shown in Figure 4. Based on the variation characteristics of curves, three characteristic points (compaction stress \(\sigma_{pd}\), yield stress \(\sigma_{pi}\), and peak stress \(\sigma_{p}\)) are determined. Point \(A\) corresponding to \(\sigma_{pd}\) not only represents the inflection point of the stress-strain curve from concave to straight line, but also denotes the first intersection point of the \(U^{e}\) curve and the \(U^{d}\) curve. Point \(B\) at \(\sigma_{pi}\) indicates the point where stress and \(U^{e}\) begin to transition from linear to nonlinear increments. Point \(C\), corresponding to \(\sigma_{p}\), represents the point where stress reaches its maximum value. Therefore, based on  
Figure 3: The evolution of energy during rock loading. these characteristic points, energy evolution curves of specimens with varying \(\alpha\) can be categorized into four stages: initial energy dissipation stage (\(O\)-\(A\)), stable energy storage stage (\(A\)-\(B\)), accelerating energy dissipation stage (\(B\)-\(C\)), and full energy release stage (\(C\)-\(D\)). Figure 4: The energy evolution of SHIR specimens with different \(\alpha\) during loading process: (**a**) S-0; (**b**) S-30; (**c**) S-45; (**d**) S-60; (**e**) S-90. At the initial energy dissipation stage, the \(U\) curve and the \(U^{e}\) curve exhibit a concave upward distribution, with \(U^{d}\) slightly greater than \(U^{e}\). This is because of the closure and friction of pre-existing microcracks and micropores within the SHIR specimens, resulting in minor internal damage to the rock. At this stage, the energy conversion efficiency of the rock is relatively low, mainly dominated by energy dissipation. As strain continues to increase, the slope of the \(U^{e}\) curve gradually increases while the slope of the \(U^{d}\) curve approaches 0. After the stress reaches \(\sigma_{pd}\) (point \(A\)), the \(U^{e}\) curve begins to exceed the \(U^{d}\), and the specimen enters the stable energy storage stage. The \(U^{e}\) curve at this stage shows a linear growth trend similar to the \(U\) curve. The rock exhibits strong energy storage capacity, where most of the external input energy is converted into elastic energy for storage, while dissipation energy remains relatively constant. As strain continues to increase, \(U^{e}\) far exceeds \(U^{d}\). However, when stress reaches \(\sigma_{pi}\) (point \(B\)), the rock enters the accelerating energy dissipation stage. The \(U^{e}\) curve begins to deviate from the \(U\) curve, and its slope gradually decreases. The \(U^{d}\) curve starts to increase significantly, promoting the generation and propagation of cracks. When stress reaches \(\sigma_{p}\) (point \(C\)), the rock enters the full energy release stage. The \(U\) continues to increase, and a large amount of elastic energy is released rapidly, while \(U^{d}\) increases sharply. This indicates that the stored elastic energy is converted into dissipation energy, and the cracks inside the rock continue to propagate and connect, causing the rock to lose its load-bearing capacity. From Figure 4, it can also be concluded that changes of \(\alpha\) have little impact on the initial energy dissipation stage and the stable energy storage stage. During the early loading stage, the rock generates a small amount of \(U^{d}\) due to pre-existing defects and primarily stores elastic energy once it reaches the linear elastic stage of the stress-strain curve. The variation of \(\alpha\) mainly affects the accelerating energy dissipation stage and the full energy release stage. At the accelerating energy dissipation stage, a significant amount of \(U\) is converted into \(U^{d}\) with increasing displacement, and this trend is more pronounced at lower \(\alpha\).