## 3 Results and Discussion  
### Mechanical Properties  
#### 3.1.1 Peak Strength  
Figure 5 demonstrates the stress-strain curves and the peak strengths of specimens at different loading-foliation angles under monotonic loading. The specimens, in a decreasing order of strength, correspond to those at loading-foliation angles of \(0^{\circ}\), \(90^{\circ}\), \(30^{\circ}\), and \(45^{\circ}\). The empirical equation first proposed by [PERSON] (1986) and then improved by [PERSON] (1987) can capture the strength variation in specimens with the loading-foliation angle Donath (1988), as expressed by  
\[\sigma_{\beta}=A-D\cos 2(\beta-\beta_{\text{min}}) \tag{1}\]  
where \(\sigma_{\beta}\) denotes the uniaxial compressive strength of the specimen at the loading-foliation angle of \(\beta\); \(\beta_{\text{min}}\) denotes the angle \(\beta\) corresponding to the minimum strength, and \(A\) and \(D\) are two constants.  
The curve fitted according to Equation (1) and the expression of the fitted equation are shown in Figure 5b. From the fitting results, it can be deduced that the strength of the specimen reaches the minimum when the loading-foliation angle is about \(53^{\circ}\).  
Figure 6 illustrates the stress-strain curves of specimens at different loading-foliation angles under cyclic loading, and the peak strengths of all specimens, including those under the monotonic loading, as a function of the loading-foliation angle. The results show that the variation trend in peak strength of specimens with the loading-foliation angle under cyclic loading is very similar to that under monotonic loading, presenting a U-type, which is consistent with the results obtained by [PERSON] et al. [PERSON] et al. (2018).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Loading Path** & **Specimen Name** & \(\beta\) (\({}^{\circ}\)) & **Cyclic Stress Step** & **Number of Cycles (Force Control +** \\  & & & **(MPa)** & **Displacement Control)** \\ \hline \multirow{4}{*}{Monotonic loading} & U-0 & 0 & \(\backslash\) & \(\backslash\) \\  & U-30 & 30 & \(\backslash\) & \(\backslash\) \\  & U-45 & 45 & \(\backslash\) & \(\backslash\) \\  & U-90 & 90 & \(\backslash\) & \(\backslash\) \\  & C-0-20 & 0 & 20 & \(6+2\) \\  & C-0-40 & 0 & 40 & \(3+1\) \\ \multirow{2}{*}{Cyclic loading and unloading} & C-30-20 & 30 & 20 & \(3+3\) \\  & C-30-40 & 30 & 40 & \(2+2\) \\ \multirow{2}{*}{3. Results and Discussion} & \multirow{2}{*}{\(3.1.1.\) Mechanical Properties} & \multirow{2}{*}{\(3.1.1.\) Peak Strength} & \multirow{2}{*}{\(3.1.\) Peak Strength} & \multirow{2}{*}{\(3.1.\) Peak Strength} \\  & C-45-20 & 45 & 20 & \(3+1\) \\ \multirow{2}{*}{3. Results and Discussion} & \multirow{2}{*}{\(3.1.\) Mechanical Properties} & \multirow{2}{*}{\(3.1.\) Peak Strength} & \multirow{2}{*}{\(3.1.\) Peak Strength} \\  & C-90-20 & 90 & 20 & \(4+4\) \\ \multirow{2}{*}{3. Results and Discussion} & \multirow{2}{*}{\(3.1.\) Mechanical Properties} & \multirow{2}{*}{\(3.1.\) Peak Strength} & \multirow{2}{*}{\(3.1.\) Peak Strength} \\  & C-90-40 & 90 & 40 & \(3+4\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Test scheme for slate specimens considering the loading path and the loading angle.  
Figure 5: Stress–strain curve and peak strengths of specimens at different loading\(-\)foliation angles under monotonic loading: (**a**) stress\(-\)strain curves and (**b**) peak strength and fitted curve.