## 3 Creep Experimental Results  
### Analysis of Strain-Time Curves  
Figure 4 presents the detailed creep characteristics of the carbonaceous slate at different loading stages. All samples evidently exhibited three distinct phases, as shown in Figure 5.  
Primary (decelerating) creep stage: In this stage, the strain rate (measured by the slope of the tangent to the creep curve) decreased with time. The strain produced in this stage can be defined as the decelerating creep strain, \(\varepsilon_{d}\).  
Secondary (steady-state) creep stage: During this stage, the creep deformation increased at a constant rate. The strain produced in this stage can be characterized as the steady creep strain, \(\varepsilon_{s}\), while the time duration can be taken as \(t_{s}\). Thus, the steady creep rate can be expressed as follows: \(\dot{\varepsilon}_{s}=\varepsilon_{s}/t_{s}\).  
Tertiary (accelerating) creep stage: This stage consisted of a rapid increase in the strain rate (measured as the slope of the tangent to the creep curve) over time.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\beta^{\prime\circ}\) & \(\sigma_{UCS}\)/MPa & \(\overset{-}{\sigma}_{UCS}\)/MPa & \(\sigma_{L}\)/MPa & \(\overset{-}{\sigma}_{UCS}\)/\(\sigma_{L}\) (\%) \\ \hline \multirow{3}{*}{0} & 75.89 & & & \\  & 78.95 & & & \\  & 73.28 & & & \\ \hline \multirow{3}{*}{15} & 47.76 & & & \\  & 47.28 & 46.61 & 33.31 & 71.47 \\  & 44.79 & & & \\ \hline \multirow{3}{*}{45} & 37.90 & & & \\  & 40.75 & 40.76 & 37.27 & 91.68 \\  & 43.63 & & & \\ \hline \multirow{3}{*}{75} & 59.46 & & & \\  & 60.92 & 62.71 & 55.41 & 88.36 \\  & 67.75 & & & \\ \hline \multirow{3}{*}{90} & 78.43 & & & \\  & 81.66 & 80.91 & 75.79 & 93.67 \\ \cline{1-1}  & 82.64 & & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: The experimental data of characteristic strength.  
The results indicate that at a relatively low loading ratio, the creep curve exhibited a primary creep stage followed by a steady-state creep stage. The curve displayed distinct primary, steady-state, and accelerated creep characteristics with high loading ratios. Carbonaceous slate exhibited unstable failure after a period of creep when \(\beta\) was set at 15\({}^{\circ}\) and 45\({}^{\circ}\). In contrast, the remaining samples rapidly reached the accelerated creep stage and experienced unstable failure after reaching the final loading level. Carbonaceous slate experienced failure after the fourth loading ratio when \(\beta<\) 45\({}^{\circ}\). This phenomenon was also observed in the creep test results of phyllite [28]. When \(\beta\geq\) 45\({}^{\circ}\), carbonaceous slate underwent creep failure after enduring at least five levels of creep loading. In comparison  
Figure 4: The strain–time curve under multi-level stress for carbonaceous slate with different foliation angles.  
to the case of \(\beta<45^{\circ}\), the slate demonstrated a significantly improved resistance against creep failure.  
Figure 6 illustrates the relationship between volumetric strain(\(\epsilon_{\beta}\)) and time. When \(\beta\leq 45^{\circ}\), the rock experienced a decrease in volumetric strain during the loading stage, which is indicative of creep failure. At \(\beta=0^{\circ}\), during the first two grades of loading, the carbonaceous slate experienced a continuous increase in strain and a simultaneous compression in volume. At the third level, the slate underwent an increase in lateral deformation and a conversion of volumetric strain to be negative. When \(\beta=45^{\circ}\), the volume strain increased and gradually decreased to be negative. The volume strain continued to increase as the loading ratio was increased for \(\beta>45^{\circ}\). The longitudinal deformation after compression was more pronounced at \(\beta=75^{\circ}\) and \(90^{\circ}\) compared with transverse deformation.