## 3 Simulation Results and Analysis
### Mechanical Analysis Under Compression Conditions
For horizontally bedded shale, frictional constraint stress alters the stress distribution at the contact surface between the bedding and the matrix while the confining pressure further complicates the stress state. The confining pressure enhances the shale's strength and inhibits crack propagation, thereby limiting the formation of shear cracks and altering the macroscopic crack morphology (Figure 13). The inclined layered structure extracted from the shale consists of three parts: A (matrix), B (bedding plane), and C (matrix). As shown in Figure 16, under the action of stress components \(\sigma_{x^{\prime}}\), \(\sigma_{y^{\prime}}\), \(\sigma_{z^{\prime}}\), \(\tau_{xy^{\prime}}\), \(\tau_{yz^{\prime}}\), and \(\tau_{z^{\prime}x^{\prime}}\), the stress state on each part of the contact surface differs significantly from the stress state outside the contact surface. The stress state analysis of inclined bedding is more complex. To simplify the analysis, the inclined layered structure can be rotated to convert it into a horizontally layered structure. The rotated structure is then subjected to compressive stresses \(\sigma_{x^{\prime}}\), \(\sigma_{y^{\prime}}\) and \(\sigma_{z^{\prime}}\), and shear stresses \(\tau_{xy^{\prime}}\), \(\tau_{yz^{\prime}}\) and \(\tau_{z^{\prime}y}\), where the compressive stresses generate frictional constraint stresses at the contact surfaces, and the shear stresses induce shear strain. Figure 15: Horizontal bedding plane shale specimens under triaxial loading conditions. The analysis process for inclined bedding is analogous to that for horizontal bedding. Due to the differing mechanical properties of the bedding and the matrix, strain differences are induced, resulting in frictional constraint stresses. For parts A and C, the area outside the contact surface is influenced by \(\sigma_{x}\), \(\sigma_{y}\), \(\sigma_{z}\), \(\tau_{xy}\), \(\tau_{yz}\), and \(\tau_{zx}\). In contrast, at the contact surface, the matrix experiences compressive stress states (\(\sigma^{\prime}_{xA}\) and \(\sigma^{\prime}_{yA}\)) due to frictional constraints, and the bedding plane experiences tensile stress states (\(\sigma^{\prime}_{xc}\) and \(\sigma^{\prime}_{yc}\)) due to the same effect. Consequently, in the case of inclined bedding, the stress state at the contact surface between the rocks exhibits significant three-dimensional stress characteristics. The actual normal stresses \(\sigma^{*}_{xA}\) and \(\sigma^{*}_{yA}\) in the matrix are more significant than the normal stresses \(\sigma_{xA}\) and \(\sigma_{yA}\) outside the contact surface, while the actual normal stresses \(\sigma^{*}_{xC}\) and \(\sigma^{*}_{yc}\) in the bedding plane are lower than the normal stresses \(\sigma_{xC}\) and \(\sigma_{yc}\) outside the contact surface. Similarly, the actual stress combines normal, shear, and frictional constraint stress at the contact surface between parts B and C. The normal stress in matrix B is reduced by \(\sigma^{\prime}_{xB}\) and \(\sigma^{\prime}_{yB}\), while the normal stress in bedding plane increases by \(\sigma^{\prime\prime}_{xC}\) and \(\sigma^{\prime\prime}_{yc}\). Outside the contact surfaces of parts B and C, the stress conditions remain as they are outside the contact surfaces of parts A and C.  
In summary, frictional constraint stress significantly alters the stress distribution at the contact surface between the bedding and matrix for inclined bedding shale, complicating the overall stress state. Moreover, the failure behavior of inclined bedding shale is not only dependent on the strength of the bedding and matrix themselves. Still, it is  
Figure 16: Inclined bedding shale specimens. also closely related to the effects of shear stress. The presence of shear stress leads to a failure mechanism distinct from that of horizontally bedded rock masses. Compared to horizontally bedded shale, inclined bedding shale is more prone to shear slip along the bedding planes during failure, macroscopically manifested as slip failure along the bedding planes (Figures 9 and 13).