# Experimental and Numerical Investigations on the Slate Shearing Mechanical Behavior
## 5 Discussion
From a microscopic mechanism perspective, samples at \(45^{\circ}\) and \(60^{\circ}\) exhibit \(\tau_{\rm p}=45^{\circ}>\tau_{\rm p}=60^{\circ}\) due to the distribution characteristics of tensile force. The crack evolution reveals that, for the \(90^{\circ}\) sample, cracks mostly appear along the loading and the non-layered planes, with almost no cracks along the bedding direction, resulting in higher strength. The number of cracks for the \(30^{\circ}\) bedding angle is comparable to that at \(90^{\circ}\), though cracks at \(30^{\circ}\) are more likely to appear along the bedding plane, making the model more prone to failure. At \(\beta=60^{\circ}\), the specimen develops cracks on both the bedding plane and the matrix, which are more divergent, can expand faster, and result in lower strength. In the case of the \(0^{\circ}\) specimen, only a small number of cracks are generated on the loading surface, leading to the lowest strength; thus, \(\tau_{\rm p}=90^{\circ}>\tau_{\rm p}=30^{\circ}>\tau_{\rm p}=60^{\circ}>\tau_{ \rm p}=0^{\circ}\). Different values of \(\beta\) significantly influence the mechanical properties and failure modes of rocks, which can be explained from the stress state perspective. In a direct shear test, the \(\beta\) of the rock sample affects the transmission mode of the shear force, the shear fracture, and the failure mode. Rock shear failure is controlled by \(\tau\) and \(\sigma_{\text{n}}\). An even distribution of shear and normal stresses along the shear fracture is assumed in this study. For an element at any point on the fracture, as shown in Figure 18, and ignoring the normal stress on the left and right sides, the in-plane stress state during shear loading is represented by a combination of \(\sigma_{\text{n}}\) and \(\tau\). When the bedding planes of the slate are parallel to the loading direction, shear load transfer is relatively simple because the bedding plane facilitates shear crack formation, resulting in weak shear strength. However, for inclined \(\beta\), shear load transfer becomes more complicated. Whether from numerical simulations or experimental results, the strength of the slate is consistently lowest when the bedding angle is \(0^{\circ}\). At a \(0^{\circ}\) bedding angle, the bedding plane is parallel to the shear direction, allowing shear loads to be transmitted more easily along the bedding plane and making it easier for cracks to form, resulting in lower shear strength. This conclusion aligns with the findings in the literature [43], which conducted direct shear tests on slates in the northwest of the Iberian Peninsula (Spain). This study found that rock failure was mainly due to sliding along weak planes. When the shear direction is parallel to the bedding plane, the sample is more likely to experience shear failure along the bedding plane, demonstrating lower shear strength. The experiments in the literature further validate the impact of bedding plane orientation on rock shear behavior, highlighting the weakness when the bedding plane is parallel to the shear direction. Figure 17: The comparison of shear strength between theoretical calculation [32] and (**a**) simulation and (**b**) experimental results. Figure 18: Stress state of the slate element from the shear fracture [32]. [PERSON] et al. [22] conducted direct shear tests on Kangding slate with bedding angles of 0\({}^{\circ}\), 30\({}^{\circ}\), 45\({}^{\circ}\), 60\({}^{\circ}\), and 90\({}^{\circ}\), analyzing the effects of bedding angle on failure modes, AE characteristics, and shear strength parameters. They found that the shear strength of the samples was positively correlated with normal stress under different conditions, but the rate of increase in shear strength was negatively correlated with bedding angle. Cohesion was positively correlated with bedding angle, meaning that higher bedding angles corresponded to greater cohesion. However, at a bedding angle of 90\({}^{\circ}\), the acoustic emission count rate and energy release rate were lower.