A three-dimensional constitutive model for anisotropic rockmass and its numerical implementation within the framework of the FEM
This work deals with the presentation of a constitutive model for isotropic rock and its extension to anisotropic material behaviour. Beside the model definition, the focus is put on the stress update procedures, the identification strategies for the model parameters and the validation of the model by laboratory results.
In the first part a constitutive model for isotropic rock is presented. It is based on the works of Grassl and Jirasek (2006), Valentini (2011) and Unteregger (2015). In this model strain hardening is formulated within the framework of plasticity theory whereas strain softening is formulated within the framework of damage theory. A new, more flexible formulation of the damage evolution law is proposed, leading to a redefinition of the regularization scheme to assure mesh independent results in finite element analyses. Subsequently, an implicit update scheme for the elasto-plastic evolution equations is presented. Based on the results from triaxial tests on Innsbruck quartz phyllite an identification strategy for the model parameters is proposed and the model is validated.
The second part deals with approaches for considering plastic anisotropic material behaviour by means of so-called anisotropic variables. Those scalar variables render the e˙ect of the loading direction with respect to the material orientation and are based on the formulation of fabric tensors. Two approaches, one proposed by Pietruszczak and Mroz (2000, 2001) and the other one proposed by Gao et al. (2010) and Gao and Zhao (2012), are presented, critically evaluated and compared with each other. An identification strategy for the parameters of the anisotropic variables is proposed and parameters are identified for different rock types.
Finally both formulations of the anisotropic variable are used to extend an isotropic Drucker-Prager yield function and the aforementioned constitutive model for isotropic rock to anisotropic material behaviour. For each model formulation a parameter identi-fication strategy is devised and the models are calibrated for Innsbruck quartz phyllite. For both calibrated models meridional and deviatoric sections of the yield function are presented. It is shown that the anisotropic variable according to Pietruszczak and Mroz (2000, 2001) leads to loss of convexity of the yield surface, whereas the anisotropic variable according to Gao et al. (2010) and Gao and Zhao (2012) results in a discontinuous yield surface. This, in turn, leads to loss of convergence of the implicit stress update algorithm and the violation of Drucker’s stability postulate as well as the postulate of maximum plastic dissipation.