Multiscale friction-damage mechanics of layered rocks: Theoretical formulation and numerical simulation - Ren, Lu; Zhao, Lunyang; Niu, Fujun; Lai, Yuanming; Song, Danqing; Zhu, Qizhi; Shao, Jianfu (Journal of Rock Mechanics and Geotechnical Engineering, 2025)
Layered rocks (LR) exhibit inherent anisotropic stiffness and strength induced by oriented rough weakness planes, along with stress induced anisotropy and friction related plastic deformation occurs during loading. Furthermore, microcracks located in intact rock matrix (IRM) of LR are also critically important for friction and damage dissipation processes. In this paper, we first present a novel multiscale friction-damage (MFD) model using a two-step Mori-Tanaka homogenization scheme, with the aim of describing the multiscale friction-damage mechanics in LR. Physically, the initiation and propagation of flaws at different scales (i.e. microcracks and weakness planes) induced damage, and the plastic deformation is closely associated with frictional sliding along these flaws. In the thermodynamics framework, the macroscopic stress-strain relations, the local driving forces respectively conjuncted with flaws propagation and plastic deformation are derived. An analytical macroscopic strength criterion is subsequently deduced, which takes into account the variation of inclination angle and confining pressure. Notably, the failure mechanisms of IRM shearing and weakness planes sliding are inherent included in the criterion. As an original contribution, a new multisurface semi-implicit return mapping algorithm (MSRM) is developed to integrate the proposed MFD model. The robustness of MSRM algorithm is assessed by numerical tests with different loading steps sizes and convergence conditions. Finally, the effectiveness of the MFD model is confirmed using data from experiments under conventional triaxial compression, all main features of mechanical behaviors of LR are well captured by the proposed model, including initial anisotropy, stress-induced anisotropy and strain hardening/softening.