A gradient enhanced transversely isotropic damage plasticity model for rock - formulation and comparison of different approaches

The nonlinear mechanical behavior of intact rock and rock mass is characterized by irreversible deformation, associated with strain hardening, strain softening and degradation of stiffness. In the case of stratified rock types like shales or phyllites, the mechanical behavior additionally depends on the loading direction with respect to the orientation of the principal material directions, resulting in inherent anisotropic material behavior, or in many cases more specifically in transversely isotropic material behavior. On the basis of a critical review of several approaches for modeling nonlinear anisotropic material behavior, proposed in the literature, the linear mapping of the Cauchy stress tensor into a fictitious isotropic configuration, originally proposed by Boehler [1], was identified as the best choice for the application in 3D finite element simulations. Within this framework, an isotropic damage plasticity model for rock, proposed by Unteregger et al. [2], extended to inherent transversely isotropic behavior is presented. It is implemented into a FE-program by means of the return mapping algorithm and it is regularized by an over-nonlocal implicit gradient enhancement for ensuring mesh-insensitive results. For validation, numerical simulations of triaxial compression tests on Tournemire shale, documented in Niandou et al. [3], are performed at both the integration point level and the structural level. The performance of the constitutive model is assessed by its ability to predict the complex direction-dependent mechanical behavior of transversely isotropic rock and the failure modes observed in triaxial compression tests with different confining pressures and different inclination angles of the stratification planes with respect to the direction of axial loading.