## 3 Energy Characteristics of SHIR Specimens with Different \(\alpha\)
### The Evolution Characteristics of Energy Ratios
Figure 7b depicts the EDR and energy ratio (\(R_{\rm DT}\) and \(R_{\rm ED}\)) curves for specimen S-45, illustrating the process of surface crack propagation. At Stages I and II, EDR amplitude is nearly zero, indicating minimal crack initiation in the rock. When the stress reaches \(\sigma_{pi}\) (6.8 MPa), shear cracks appear at the edges of the bedding planes. As the stress reaches \(\sigma_{p}\) (7.6 MPa), EDR amplitude sharply increases, with shear cracks penetrating the specimen, leading to unstable failure of the rock. This is because the shear strength of the bedding planes is much lower than that of the rock matrix; the failure of rock under loading depends solely on the bedding planes, independent of the rock matrix [32]. Figure 7c illustrates the EDR and energy ratio (\(R_{\rm DT}\) and \(R_{\rm ED}\)) curves for specimen S-90, showing the process of surface crack propagation. At Stages I and II, EDR mainly ranges between \(-0.001\) and \(0.001\) MJ/m\({}^{-3}\), indicating minimal crack formation on the rock surface. When the stress reaches \(\sigma_{pi}\) (31.6 MPa), tensile cracks appear at the bedding planes, while no cracks form on the surface of the rock matrix. At this stage, as stress continues to increase, under uniaxial compression conditions, the rock undergoes lateral strain and outward expansion. The tensile strength at the interface between soft and hard rock layers is much lower than that of the two material matrices, leading to preferential splitting failure, and the rock matrix still retains its load-bearing capacity [34]. With continuous loading, EDR amplitude expands to between \(-0.001\) to \(0.005\) MJ/m\({}^{-3}\) at 126.1 s, indicating continuous displacement and slip of internal defect surfaces within the rock. When the stress reaches \(\sigma_{p}\) (59.9 MPa), it sharply drops to 0, indicating complete crack penetration and sudden instability of the rock. This releases a significant amount of energy, causing severe structural damage to the rock. New tensile cracks propagate along bedding planes, causing extensive spalling of the rock matrix, ultimately resulting in complete failure of the rock. The above analysis indicates that the changes of \(\alpha\) significantly influence the rock fracture and damage processes. Sudden rises or drops in \(R_{\rm DT}\) and \(R_{\rm ED}\) curves can serve as precursors to rock failure, while the increased amplitude of EDR fluctuations can indicate the accelerated propagation of cracks; previous scholars have studied these characteristics [31; 35; 36]. In this study, Table 2 provides detailed stress and time data for precursor and peak points of different specimens. It is evident that \(R_{\rm DT}\) and \(R_{\rm ED}\) curves effectively predict rock failure; where the stress of the precursor point is equal to \(\sigma_{pi}\), combined with experimental images, the location of the first damage and the type of cracks produced by different rocks can be determined. It can be observed that rocks with different \(\alpha\) all experience initial failure near the bedding plane, but the types of cracks that appear first vary: specimens S-0 and S-30 first exhibit surface spalling cracks, specimens S-45 and S-60 exhibit shear cracks, and specimen S-90 exhibits tensile cracks. Additionally, due to differ ences in the fracture processes of specimens, EDR shows distinct trends. For specimens S-0 and S-30, high-amplitude EDR fluctuations mainly occur at Stage IV, with EDR before the peak much lower than after the peak, indicating more cracks forming after the peak. For specimens S-45 and S-60, EDR peaks when stress reaches \(\sigma_{p}\) and then gradually decreases, suggesting that most cracks concentrate during the instantaneous failure of rock. In the case of the specimen S-90, EDR begins fluctuating as early as Stage II, with the amplitude increasing further in Stage III, indicating that numerous cracks have already formed within the rock by this stage.