## 3 Testing Results
### Modelling of Damage Evolution  
In the flawed rock samples depicted in Figure 5a-d, the axial strain occasionally exhibits a decreasing trend, indicating sporadic deformation, as recorded by two optical gratings. Conversely, the LVDT system, positioned at the rock bridge segment, effectively measures the deformation of the rock bridge, particularly the radial strain. Furthermore, the shape of the hysteresis loop on the radial stress-strain curve is more distinct compared to that on the axial stress curve. As seen in Figure 5e-h, the development of radial strain at each cyclic loading stage is more pronounced than that of axial strain. The rapid increase in radial deformation results from crack coalescence, leading to significant damage. Therefore, in this study, radial strain is deemed more suitable for describing the propagation of rock damage. Radial deformation is utilized to model the evolution of rock damage and establish \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**CLS**} & \multirow{2}{*}{
\begin{tabular}{c} **Maximum** \\ **Stress (MPa)** \\ \end{tabular} } & \multicolumn{4}{c}{**Axial Strain Rate [\%/N \(-\) 1]**} \\ \cline{3-6}  & & & & & \\ \hline
1 & 15 & \(6.666\times 10^{5}\) & \(1.333\times 10^{-5}\) & \(3\times 10^{-5}\) & \(1\times 10^{-5}\) \\
2 & 20 & \(1.533\times 10^{-4}\) & \(3.033\times 10^{-4}\) & \(3.866\times 10^{-4}\) & \(3.146\times 10^{-4}\) \\
3 & 35 & \(2.1\times 10^{-4}\) & \(4.666\times 10^{-4}\) & \(3.5\times 10^{-4}\) & \(3.146\times 10^{-4}\) \\
4 & 40 & \(3.933\times 10^{-4}\) & \(5.4\times 10^{-4}\) & \(3.133\times 10^{-4}\) & \(3.04\times 10^{-4}\) \\
5 & 45 & \(4.8\times 10^{-4}\) & \(6.466\times 10^{-4}\) & \(2.466\times 10^{-4}\) & \(1.6\times 10^{-4}\) \\
6 & 50 & \(6.266\times 10^{-4}\) & \(3.233\times 10^{-4}\) & \(2.266\times 10^{-4}\) & \(1.466\times 10^{-4}\) \\
7 & 55 & \(1.0011.4\) & \(5.4\times 10^{-4}\) & \(2.3\times 10^{-4}\) & \(2.346\times 10^{-4}\) \\
8 & 60 & \(0.0011.3\) & \(3.633\times 10^{-4}\) & \(3.2\times 10^{-4}\) & \(2.533\times 10^{-4}\) \\
9 & 65 & \(0.0011.63\) & \(5.033\times 10^{-4}\) & \(3.233\times 10^{-4}\) & \(3.093\times 10^{-4}\) \\
10 & 70 & & \(5.733\times 10^{-4}\) & \(3.533\times 10^{-4}\) & \(2.56\times 10^{-4}\) \\
11 & 75 & & \(5.711\pm 0.14\) & \(5.0011.5\) & \(2.746\times 10^{-4}\) \\
12 & 80 & & & \(4.0011.5\) & \(2.96\times 10^{-4}\) \\
13 & 85 & & & & \(1.0010.6\) \\
14 & & & & & \\ \hline \hline \end{tabular} Note: The green region denotes safety, the yellow region signifies uncertainty, and the red region indicates danger. The * underscores the notable volume dilatancy observed in the rock sample, marking a shift from compression dominance to expansion dominance.  
\end{table} 
Table 2: Axial strain rates for the tested rock samples at different CLSs. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**CLS**} & \multirow{2}{*}{ \begin{tabular}{c} **Maximum** \\ **Stress (MPa)** \\ \end{tabular}  } & \multicolumn{4}{c}{**Volumetric Strain Rate [\%/N \(-\) 1]**} \\ \cline{2-6}  & & & & & \\ \hline
1 & 15 & \(1\times 10^{-6}\) & \(1\times 10^{-6}\) & \(6.667\times 10^{-6}\) & \(1.666\times 10^{-6}\) \\
2 & 20 & \(4.6\times 10^{-5}\) & \(3.333\times 10^{-6}\) & \(1.04\times 10^{-4}\) & \(1.213\times 10^{-4}\) \\
3 & 35 & \(2.5\timesthe relationship between damage factors and cycles. A damage variable defined using the maximum radial strain, \(D_{\text{rs}}\), is expressed as follows:  
\[D_{\text{rs}}=\frac{\varepsilon_{\text{max}}^{n}-\varepsilon_{\text{max}}^{0}}{ \varepsilon_{\text{max}}^{f}-\varepsilon_{\text{max}}^{0}} \tag{1}\]  
where \(\varepsilon_{\text{max}}^{0}\), \(\varepsilon_{\text{max}}^{n}\), and \(\varepsilon_{\text{max}}^{f}\) are the initial maximum strain, instantaneous maximum strain after n cycles, and ultimate maximum strain, respectively. Using Equation (1), we depict the evolution of this damage variable against cycle number in Figure 9. The characteristics of damage propagation are consistent with the analysis of radial deformation.