## 4 Numerical Modeling with Anisotropic Slate
### Results and Discussion of the SCB Tests
#### 4.3.2 SCB Results and Discussion  
This section presents the typical experimental and numerical results of anisotropic slates with different bedding angles, which cover both numerical and experimental load-displacement and typical failure patterns of the slate SCB specimens at bedding angles of 0\({}^{\circ}\) and 60\({}^{\circ}\) as detailed in Figures 14 and 15. The cases of bedding angles of 30\({}^{\circ}\), 45\({}^{\circ}\), 90\({}^{\circ}\), and divider are concisely presented in Figure 16. It is of note that the zone of interest (ZOI) is set up to present in part the detailed fracture cracks. Figure 14: _Cont._  
Figure 13: SCB computational SCB model of the carbonaceous slate under bedding angle of 0\({}^{\circ}\), (**a**) model setup, (**b**) embedded cohesive elements for the matrix, and (**c**) embedded cohesive elements for the bedding planes. Figure 14: Comparison of the tensile fracture propagation and load–displacement measured from numerically and experimentally with an inclined angle of \(0^{\circ}\), (**a–f**) corresponding to the points marked in the load–displacement curve, and (**g**) fracture failure of the representative testing specimen. Figure 15: _Cont._  
Figure 16: _Cont._  
Figure 15: Comparison of tensile fracture propagation and load–displacement measured numerically and experimentally with an inclined angle of 60\({}^{\circ}\), (**a–f**) corresponding to the marked points (**a–f**) of load–displacement curve, and (**g**) the fracture pattern of the representative slate specimen. Figure 16: _Cont._  
For the case of the inclined angle of 0\({}^{\circ}\), the tensile crack first initiates from the notch tip at the small oscillation at the peak load (Figure 14a), then the tensile crack extends rapidly as the load-displacement curve shows a rather abrupt load drop (Figure 14b) and the fracture propagation is unstable. A few cracks are generated inside the middle bedding plane as the principal opening fracture approaches the upper bedding plane and then it propagates in a zigzag manner towards the upper loading point (Figure 14c,d). Furthermore, due to the concentration of compressive stress induced by the three-point bending load on the SCB specimen, the principal fracture develops further towards the loading end (Figure 14e,f). It can be seen that the fracture evolution is almost dominated by tensile fracture, and the mechanical response and failure patterns exhibit some differences between the numerical simulations and the experimental tests. The reason is that the numerical model cannot completely take into account all of the heterogeneity of the real specimen with the micro-structure because the latter is a natural material whose micro-defects, micro weak interfaces, and micro-damage cannot be perfectly known in advance. In general, the specimens are with characteristics of significant brittle fracture that exhibit a sharp drop in loading, and evolution of interlayer cracks after the crack initiation finishes abruptly. This also matches the instantaneous 'bang' fracture during the laboratory tests. For the case of the inclined angle of 60\({}^{\circ}\), there also exists a tensile crack that initiates from the notch tip at the peak load (Figure 15a), but the fracture propagates towards the middle bedding and then rapidly travels along the bedding direction for a small distance before a snake-like macro fracture travels up to the top (see Figure 15b-f). Overall, the mechanical response and failure patterns of the numerical results agree fairly well with the typical experimental results, the fracture behavior of the numerical and typical experimental specimens were all very brittle as the load dropped sharply, while the interaction of the opening tensile fracture between the bedding and matrix occurred instantaneously after the peak load.