## 3 Energy Characteristics of SHIR Specimens with Different \(\alpha\)
### Macroscopic Failure Characteristics of SHIR Specimens Based on Energy  
Figure 8 illustrates the energy storage limitation (\(U_{p}^{c}\)), elastic energy release rate after the peak (\(\dot{U}^{c}\)), and failure characteristics of SHIR specimens with different \(\alpha\) under uniaxial compression. With increasing \(\alpha\), the energy storage limitation initially decreases and then increases, while the rate of elastic energy release gradually rises. Moreover, specimens with different \(\alpha\) exhibit distinct macroscopic failure characteristics under uniaxial compression. Combining the geometric shapes and propagation mechanisms of cracks, crack propagation modes can be categorized into tension cracks (T), shear cracks (S), and surface spalling cracks (S\({}_{\text{S}}\)) [37]. In Figure 8, main cracks and secondary cracks are depicted in thick red and yellow lines, respectively, with white indicating hard rock and gray indicating soft rock, while shaded areas denote regions of surface spalling. The \(\alpha\) significantly influences the growth of cracks in rocks, allowing for the classification of macroscopic failure modes into tensile failure of the rock matrix, shear slipping failure along bedding planes, and tensile splitting failure along bedding planes. At lower \(\alpha\) (\(\alpha\) = 0\({}^{\circ}\)-30\({}^{\circ}\)), main cracks primarily propagate along the loading direction, with secondary cracks and surface spalling predominantly occurring near the rock matrix adjacent to bedding planes. As \(\alpha\) increase gradually (\(\alpha\) = 45\({}^{\circ}\)-60\({}^{\circ}\)), main cracks primarily propagate and expand through shear sliding along bedding planes, with few secondary cracks observed. At the maximum \(\alpha\) (\(\alpha\) = 90\({}^{\circ}\)), main cracks similarly propagate along bedding planes. The bedding planes are parallel to the loading direction, resulting in tensile splitting failure along bedding planes, alongside internal generation of secondary cracks leading to detachment of rock surface blocks. From the above observations, it is evident that different \(\alpha\) have a significant impact on the macroscopic failure of rocks. When \(\alpha\) = 0\({}^{\circ}\)-30\({}^{\circ}\), the bedding planes are nearly horizontal. The soft and hard rocks on either side of the bedding planes experience uneven deformation due to vertical loads, leading to extensive tensile failure primarily controlled by the hard rock. When \(\alpha\) = 45\({}^{\circ}\)-60\({}^{\circ}\), due to the relatively low shear strength of the bedding planes, the rock matrix has not yet developed significant cracks, and the specimen loses its load-bearing capacity due to sliding along the bedding planes. When \(\alpha\) = 90\({}^{\circ}\), the bedding planes are parallel to the loading direction, and both the bedding planes and the rock matrix share the vertical load. However, due to the lower tensile strength of the bedding planes, the specimen experiences large-scale splitting failure along the bedding planes. The \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Specimens**} & \multirow{2}{*}{
\begin{tabular}{c} **Precursory** \\ **Point (Time, s)** \\ \end{tabular} } & \multicolumn{2}{c}{**Stress at**} & \multicolumn{2}{c}{**Time at Peak**} & \multirow{2}{*}{**Stress at Peak**} \\  & & **Precursory Point** & & **Stress Point** & & **Stress Point** \\  & & **(\(\sigma_{r}\), MPa)** & & **(s)** & **(\(\sigma_{p}\), MPa)** & \\ \hline S-0 & 51.35 & 11.27 & 139.77 & 20.85 & 0.54 \\ S-30 & 36.02 & 10.30 & 159.82 & 19.16 & 0.54 \\ S-45 & 35.87 & 6.82 & 40.64 & 7.60 & 0.90 \\ S-60 & 22.46 & 5.52 & 22.86 & 5.67 & 0.97 \\ S-90 & 57.47 & 30.61 & 141.68 & 59.88 & 0.51 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Values of stress and time at precursor points and peak stress points of SHIR specimens with different \(\alpha\). macroscopic failure of rocks is controlled by the bedding planes, with different \(\alpha\) leading to distinct types of failure.