## 3 Simulation Results and Analysis
### Mechanical Analysis Under Compression Conditions  
The anisotropic behavior of shale under different loading conditions fundamentally originates from the mechanical property differences between bedding planes and the matrix in layered rock. As inherent weak structural surfaces within shale, bedding planes exhibit significant differences in stiffness, strength, and deformation characteristics compared to the matrix. These disparities directly influence stress transmission and distribution, ultimately governing the overall mechanical response of the rock. Due to this heterogeneity in mechanical properties, the failure modes of shale under varying stress states become more complex, exhibiting multiple mechanisms such as shear failure, tensile failure, or composite failure, as previously discussed. Therefore, a systematic analysis of the internal stress state of layered rocks under different loading conditions is essential for a comprehensive understanding of their failure mechanisms. Figure 14 illustrates the schematic representation of shale under uniaxial stress, with a matrix-bedding-matrix cross-layered structure extracted within the shale. When subjected to axial force, strain differences in the horizontal direction induce frictional constraint stresses of equal magnitude but opposite directions at the contact surface. If assuming the following relationships for the elastic modulus and Poisson's ratio, A (matric) = C (bedding plane) > B (matric) for the elastic modulus and A = C < B for the Poisson's ratio, the horizontal strain relationship becomes C = A < B. As a result, for parts A and B, under the action of axial compressive stress \(\sigma_{z}\), the frictional constraints on the matrix induce tensile stress states (\(\sigma^{\prime}_{xA}\) and \(\sigma^{\prime}_{yA}\)), while frictional constraints on the bedding plane induce compressive stress states (\(\sigma^{\prime}_{xB}\) and \(\sigma^{\prime}_{yB}\)). Figure 13: Triaxial failure modes and AE distribution under different bedding angles, with colors indicating varying stress levels. Due to the strain differences, parts A and B transition from a unidirectional compressive stress state to a three-dimensional stress state: matrix A experiences a combined compressive-tensile state, while the bedding plane is purely compressive. For regions outside the contact surface, the unidirectional compressive stress caused by \(\sigma_{z}\) is maintained, unaffected by frictional constraints. Similarly, frictional constraints arise for parts B and C due to strain differences between the two regions. The frictional constraints on bedding B result in tensile stress states (\(\sigma_{xB}^{\prime\prime}\) and \(\sigma_{yB}^{\prime\prime}\)), while those on the matrix induce compressive stress (\(\sigma_{xC}^{\prime\prime}\) and \(\sigma_{yC}^{\prime\prime}\)). Consequently, the bedding plane changes from a unidirectional compressive state to a three-dimensional compressive-tensile stress state, and the matrix transitions from a unidirectional compressive state to a three-dimensional compressive stress state. Parts B and C remain in the unidirectional compressive stress outside the contact surface. If the friction coefficients on the upper and lower sides of bedding B are the same, then the stress states at the contact surfaces between parts A and B and between parts B and C will be identical--both exhibit three-dimensional stress states. These states significantly differ from the unidirectional compressive stress state outside the contact surfaces. The stress state at the contact surfaces between the bedding and the matrix undergoes significant changes: a complex compressive-tensile stress state forms at the contact surface, influenced by frictional constraints. In regions outside the contact surface, the rock maintains a uniaxial compressive stress state unaffected by frictional constraints.