## 3 Test Results
### Load-Displacements and Mode I Fracture Toughnesses of the SCB Tests  
The load-displacement curves of SCB tests reflect constitutive characteristics, which were useful to further study the fracture toughness of the slate. In Figure 7, the load-displacements with respect to the specimens of MA-3 (0\({}^{\circ}\)), MB-2 (30\({}^{\circ}\)), MC-1 (45\({}^{\circ}\)), MD-1 (60\({}^{\circ}\)), ME-2 (90\({}^{\circ}\)), and MF-3 (divider) are given, which exhibit a slowly increasing section until the peak load that is followed by a dramatically falling post-failure portion. From this figure, it is readily seen that as the oriented angle to the bedding increases, the corresponding peak load progressively decreases (227.5, 192.8, 166.7, 144.3, and 136.1 N), while the peak load for the case of MF-3 (divider) is 267.9 N. Before the peak loads, almost all the load-displacement curves can be described by the linear constitutive models, excluding  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{ \begin{tabular}{c} **Bedding** \\ **Angle** \\ \end{tabular}  }} & \multicolumn{2}{c}{**Tensile Strength (MPa)**} & \multicolumn{2}{c}{**Mean**} \\  & & & & **Tensile** \\  & & & & **(MPa)** \\ \hline
0\({}^{\circ}\) & 1.41 & 1.32 & 1.48 & 1.59 & 1.45 \(\pm\) 0.114 \\
30\({}^{\circ}\) & 1.12 & 0.92 & 1.10 & 1.22 &  
the result for the divider case. During the post-failure section, the typical curves under all the bedding angles and the divider type show a rather abrupt load drop, which exhibits the characteristics of brittle failure for the slate in this work. According to the recommendation by ISRM [21], the mode I fracture toughness \(K_{IC}\) of the slate can be evaluated by the following formulation,  
\[K_{IC}=\frac{P_{max}\sqrt{\pi b}}{2 RB}Y^{\prime} \tag{2}\]  
where \(P_{max}\) is the peak load; \(b\) represents the notch length; \(R\) and \(B\) denote the radius and thickness, respectively. \(Y^{\prime}\) is the dimensionless stress intensity factor under plane stress state and can be written as follows [22];  
\[Y^{\prime}=-1.297+9.516\,\left(\frac{S}{2R}\right)-\left(0.47+16.457\,\left( \frac{S}{2R}\right)\right)\beta+(1.071+34.401\,\left(S/2R\right))\beta^{2} \tag{3}\]  
where \(\beta\) = \(b/R\), \(S\) represents the span between the two bottom support rollers loaded on the SCB specimen; and \(S/2R\) is the dimensionless support distance (\(S/2R\) = 0.8 is selected in this work). The number of successful tests for the MA (0\({}^{\circ}\)), MB (30\({}^{\circ}\)), MC (45\({}^{\circ}\)), MD (60\({}^{\circ}\)), ME (90\({}^{\circ}\)), and MF (divider) is 8, 7, 7, 7, 8, and 8, respectively. By statistical analysis of the test results, \(Y^{\prime}\) and \(K_{IC}\) can be calculated from Equations (2) and (3), and are given in Table 2.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Bedding** & & & & & & & & & **Mean \(K_{IC}\)** \\
**Angle** & & & & & & & & **(MPa\(\sur\)m)** \\ \hline
0\({}^{\circ}\) & 0.173 & 0.146 & 0.176 & 0.163 & 0.17 & 0.178 & 0.186 & 0.152 & 0.168 \(\pm\) 0.0135 \\
30\({}^{\circ}\) & 0.145  
It is found in Figure 8 that the \(K_{IC}\) of the divider specimens is about 0.195 MPa\(\surd\)m, which is the maximum among the six groups, which means that in this situation the slate specimen can have the highest fracture resistance. The slate specimens in the situation of ME (90\({}^{\circ}\), i.e., short transverse direction) have the lowest fracture toughness, 0.097 MPa\(\surd\)m, which are with both the weakest fracture resistance and the worst tensile properties. The slate specimens in the situation of MA (0\({}^{\circ}\), i.e., arrester direction), are with the toughness \(K_{IC}\) of 0.168 MPa\(\surd\)m, which is close to that in the divider direction.