## 1 Introduction
[35] revealed moisture-dependent mechanical responses, with transverse laminations exhibiting superior strength and Young's modulus compared to longitudinal orientations, while water saturation paradoxically increased cohesion but reduced friction angles in Mohr-Coulomb formulations. Shale, with its finely laminated structure, natural fractures, and low permeability, is a common sedimentary rock widely distributed throughout the Earth's crust [24; 36; 37; 38; 39]. Due to its layered structure and mineral composition, shale exhibits significant mechanical properties with pronounced anisotropy [40; 41]. Recent advances in shale anisotropy research have revealed critical insights through multidisciplinary experimental approaches. [PERSON] et al. [42] employed in situ micro-CT imaging to characterize shale's internal microstructure, demonstrating how fine mineral band distributions govern fracture propagation dynamics and failure mode formation under uniaxial compression and identifying two distinct failure patterns: vertical fractures in bedding-parallel orientations and inclined fractures under transverse loading. Complementing these structural analyses, [PERSON] et al. [43] quantified microstructural evolution during in situ steam pyrolysis of oil shale, documenting a 12.2-fold porosity increase with bedding-aligned microfractures and thermal propagation extending 22.4 times beyond conductive heating zones, while subsequent experiments on rapid steam injection elucidated percolation pathway controls on thermal cracking efficiency. [PERSON] et al. [41] investigated bedding angle effects, revealing dry shale's characteristic U-shaped peak strength profile (maximum at 0\({}^{\circ}\) and 90\({}^{\circ}\) orientations) contrasted with saturated specimens' enhanced anisotropy, while high-concentration NaCl solutions demonstrated mineral-stabilizing restorative effects. [PERSON] et al. [41] mechanistically linked saline-induced mechanical degradation to fluid infiltration along bedding planes causing selective mineral dissolution, establishing quantitative correlations between solution chemistry and strength deterioration rates. [PERSON] et al. [42] delineated confinement-dependent failure regimes, observing U-shaped compressive strength variations with bedding angle alongside three distinct fracture modes: transverse shear failure under parallel loading, 45\({}^{\circ}\) shear slip at intermediate angles, and macroscopic bedding-transverse fractures under high confinement. Field studies by [PERSON] et al. [43] in the Jiyang Depression identified intersecting high-angle fracture networks and low matrix strength as primary drivers of wellbore instability, while [PERSON] et al. [44] quantified confinement effects on failure mode transitions, demonstrating progressive intensification of U-shaped strength-bedding angle relationships under elevated pressures. [PERSON] et al. [45] further differentiated mechanical responses through elastic modulus V-shaped versus strength U-shaped bedding angle dependencies, with confinement-induced anisotropy attenuation and failure mode transitions from tensile (uniaxial) to shear dominance (triaxial). Petrophysical analyses by [PERSON] et al. [46] on Sichuan Basin shales established strong anisotropy-clay content correlations (R\({}^{2}\) = 0.82), modulated by oriented clay particle arrangements and quartz-TOC associations that partially decoupled organic content from anisotropic strength relationships. Collectively, these studies provide a comprehensive framework for understanding shale's anisotropic behavior across scales, from microstructural mechanisms to macroscopic failure patterns, with critical implications for reservoir geomechanics and hydrocarbon extraction optimization. Current anisotropic strength models are broadly classified into three categories based on bedding angle-dependent strength curves: shoulder-type, U-type, and undulatory-type configurations [47; 48; 49; 50; 51; 52].