## 3 Experimental Results and Theoretical Analysis
### Energy Dissipation Characteristics  
Experimental studies on energy dissipation characteristics have shown that the instability of rock materials is essentially the result of the internal energy stored in the rock materials being suddenly released [20; 21; 22]. Therefore, the laws of thermodynamics are often used to describe the deformation and failure of rock material. It is assumed that there is no heat exchange between the experimental system and the outside world, and the kinetic energy loss generated during the process of rock instability is also ignored. Then, the total work, elastic energy and dissipated energy for selected samples under uniaxial compression conditions are shown by Equations (1)-(4) and Figure 6[23],  
\[W=W_{e}+W_{d}, \tag{1}\]  
\[W=Al\!\int\sigma_{1}d\varepsilon_{1}=Al\!\sum_{k=1}^{n}\frac{1}{2}(\sigma_{1k }+\sigma_{1k-1})(\varepsilon_{1k}-\varepsilon_{1k-1}), \tag{2}\]  
\[W_{e}=\iiint_{V}v_{e}dV=Al\frac{\sigma_{1}^{2}}{2E}, \tag{3}\]  
\[\eta_{d}=\frac{W_{d}}{W}\times 100\%, \tag{4}\]  
where \(W\) is the total work; \(W_{e}\) and \(W_{d}\) are the elastic energy and dissipated energy for selected samples, respectively; \(\sigma_{1k}\) and \(\varepsilon_{1k}\) are the stress and strain values at each point of the axial stress-strain curve, respectively; \(v_{e}\) and \(V\) are the strain energy density and volume of selected samples, respectively; \(E\), \(A\) and \(l\) are the elastic modulus, loading area and height of selected samples, respectively; and \(\eta_{d}\) is the energy dissipation rate. From Figure 6, the energy conversions of selected samples with different flaw inclination angles present obvious step-like characteristics. Before the ends of en echelon flaws began to generate new cracks, the total work and elastic energy increased in a parabolic form, and the dissipated energy gradually increased to a stable value, which indicated that the selected samples were generally in the phase of energy storage. As the axial stress increased to the stress of point 1, crack initiation occurred at the tips of the en echelon flaws, and the dissipated energy curves exhibited a significant upward step for the first time, which could be used as an early warning signal before the final collapse happened. The selected samples failed suddenly at the peak strength, and the dissipated energy curves exhibited a significant upward step again. After the peak strength, the releasable elastic energy stored in the selected sample was suddenly released by means of kinetic energy, acoustic emission energy and so on, which resulted in a rapid increase in the dissipated energy curve and a linear decrease in the elastic energy curve. The crack further expanded to form the main fracture surface, and the selected samples eventually became unstable. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multicolumn{2}{c}{**Point 1**} & \multicolumn{2}{c}{**Point 2**} & \multirow{2}{*}{**E (GPa)**} \\ \cline{2-2} \cline{4-5}  & \(\sigma_{1}\) **(MPa)** & \(\varepsilon_{1}\) **(\%)** & \(\sigma_{1}\) **(MPa)** & \(\varepsilon_{1}\) **(\%)** & \\ \hline
**B-30** & 54.47 & 0.96 & 55.68 & 1.03 & 7.78 \\
**B-45** & 51.70 & 0.85 & 53.58 & 0.91 & 7.55 \\
**B-60** & 39.76 & 0.94 & 43.96 & 1.01 & 6.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The corresponding stress and strain values of the stress drop points (units: MPa; %; GPa). The corresponding total work and dissipated energy of stress drop points 1 and 2 are calculated, as shown in Table 2. According to Table 2, the corresponding total work of stress drop point 1 gradually decreases with increasing flaw inclination angle, which indicates that the total work required for crack initiation is affected by the flaw inclination angle.