Development of the Nonlocal Deformation Constitutive Model and Its Application in Exploring the Inclination Effect on Localized Shear Deformation of Rock in FLAC3D

ABSTRACT Mastering rock local deformation and failure characteristics under different inclined loading angles is crucial for rock mass engineering stability, like that of inclined pillars. To address the inability of traditional local models to accurately describe rock's nonlocal deformation and strain localization under compression‐shear loads, this study conducts systematic innovative research. First, after briefly reviewing the core of nonlocal theory, the Mohr‐Coulomb criterion is modified by innovatively introducing a softening modulus and nonlocal internal variables, yielding an improved nonlocal constitutive model for rock deformation. Leveraging FLAC3D's large‐deformation analysis capability and open secondary development interface, an innovative and practical “double‐cycle” computational framework is proposed: the outer cycle processes nonlocal zone information and updates nonlocal internal variables in real time, while the inner cycle performs stress iterations via constitutive equations. This overcomes bottlenecks like inefficient variable updates and insufficient coupling in traditional nonlocal numerical implementations, enabling efficient and stable computation. Through combined experimentation and numerical simulation, the influence of loading inclination on rock's local deformation is explored, revealing compression‐shear deformation characteristics and proposing a rock instability prediction method. Results show the “double‐cycle” model effectively handles nonlocal variable assignment and update. The nonlocal constitutive model captures rock nonlocal deformation well, and the second‐order difference in plastic deformation element number can predict rock peak stress. At a certain dip angle, local deformation zone formation lags peak stress; as the dip angle rises, rock peak strength drops and fracture angle increases. These findings offer a theoretical basis for inclined rock strata stability analysis in engineering.