Influence of anisotropic fracture energy on the mechanical strength and fracturing behaviour of shale based on 3D finite-discrete element method

Abstract

The finite-discrete element method (FDEM) has become an increasingly valuable tool in modelling rock mechanics and microscopic fracturing behaviours in recent years. However, a reliable calibration process for 3D FDEM models, particularly for anisotropic shale, remains lacking, hindering the efficient and accurate determination of microscopic input parameters. To overcome these challenges, this study introduces a novel calibration framework for 3D FDEM anisotropic shale models by systematically investigating the sensitivity of four key fracture energy parameters: fracture energy along bedding in Mode I (GIf$${G}{I}^{f}$$), fracture energy normal to bedding in Mode I (GIf′$${G}{I}^{f{\prime}}$$), fracture energy along bedding in Mode II (GIIf$${G}{II}^{f}$$), and fracture energy normal to the bedding in Mode II (GIIf′$${G}{II}^{f{\prime}}$$). The sensitivity analysis reveals that tensile strength in shale specimens inclined at 45° and 90° is primarily governed by GIf$${G}{I}^{f}$$, while for specimens inclined at 0°, GIf′$${G}{I}^{f{\prime}}$$ plays a dominant role. In uniaxial compression, GIIf$${G}{II}^{f}$$ significantly influences the compressive strength of shale at 0° and 45° inclinations, whereas GIIf′$${G}{II}^{f{\prime}}$$ is more influential at 90°. The study also shows that Young’s modulus is independent from fracture energy. The novel 3D FDEM anisotropic shale model demonstrates strong agreement with experimental results, outperforming 2D simulations in replicating the nonlinear deformation and plastic behaviour of shale under uniaxial compression. Moreover, 3D fracture volume analysis reveals bedding-dependent secondary fracture patterns: shear-induced tensile fractures develop orthogonal to bedding-parallel shear planes at 45°, while combined principal stress and shear-induced tensile stresses generate oblique secondary fractures at 0°.