## 5 Conclusions  
This study investigates shale's mechanical properties and failure modes under different stress conditions by generating random bedding structures and employing numerical modeling techniques. It provides a deeper understanding of the shale fracturing mechanism, offering guidance for optimizing fracturing techniques. The key conclusions are as follows:  
(1) The compression, tension and shear properties of shale show obvious anisotropy. The properties of the bedding plane have a significant influence on mechanical properties such as the compressive strength, elastic modulus, peak strain, and tensile strength. With the increase in the bedding angle, the uniaxial compressive strength of shale shows a U-shaped change trend, while the tensile strength gradually decreases. Both failure analysis and the spatial distribution of acoustic emission signals show that under the two loading conditions, the failure mechanism of the samples is significantly different, and the influence of the bedding distribution position on the direct tensile failure mode is more significant. (2) Confining pressure enhances the compressive strength of shale by modifying the internal stress distribution and reducing both brittleness and anisotropy. By suppressing the initiation and propagation of microcracks, the strength of shale is effectively improved. When the confining pressure increases from 0 MPa to 22.5 MPa at a bedding angle of 30\({}^{\circ}\), the strength increases by about 41%, while at 0\({}^{\circ}\) bedding, it increases by only 29%. With an increasing confining pressure, the failure mode gradually shifts to shear failure across different bedding angles. The variation in the shear strength parameters obtained through principal stress fitting further explains the universality of shear slip failure in inclined bedding. (3) Frictional constraints between bedding planes and the matrix significantly influence the rock mass strength. Under uniaxial and triaxial compression, strength near the contact surface is affected by frictional stress, while the stress state outside the contact surface remains unchanged. In inclined bedding shale, shear stress promotes bedding plane slip, often leading to shear failure along the bedding planes and reducing the overall strength. Despite the valuable insights from this study, several limitations should be acknowledged. First, the numerical modeling approach relies on the assumption of idealized random bedding structures, which may not fully capture the complex heterogeneity of natural shale. Second, the study primarily focuses on the mechanical response under mono  
Figure 19: Effect of bedding plane on hoop stress. (**a**) Rectangular cross-section; **(b**) Elliptical cross-section. tonic loading conditions, while the cyclic or dynamic loading behavior remains unexplored. Future research should address these limitations by incorporating more realistic bedding structures and conducting experimental validation to further enhance the accuracy and applicability of the findings. We are particularly interested in the effect of the specimen shape and plan to conduct further experimental and numerical studies, focusing on the mechanical behavior and failure mechanisms under inclined bedding conditions. As demonstrated in this study, specimen shape has minimal influence on the failure mode when the bedding is horizontal or vertical, which aligns with existing findings in the literature on other rock types. Therefore, we aim to further investigate how sliding surface failure governs and influences layered rock masses' strength and failure characteristics under inclined bedding conditions. T.L. : Investigation, Validation, Visualization, Data curation, Writing--original draft; Z.D. : Investigation, Methodology, Funding acquisition, Writing--review and editing; B.G. : Methodology, Conceptualization, Supervision, Software, Writing--review and editing. All authors have read and agreed to the published version of the manuscript.