Constitutive and numerical modeling of anisotropic quasi-brittle shales

Abstract

Understanding the hydro-mechanical behavior of shale is fundamental to assess the safety of deep geological nuclear repository sites. Several countries have adopted argillaceous formations as host geological media for the repository. In Switzerland, the candidate for hosting the deep geological repository site is Opalinus Clay. This thesis aims at improving the current predicting and modeling capabilities of the hydro-mechanical behavior of shale by: (1) developing proper constitutive models; (2) validating the developed models against experimental findings. First, thermo-hydro-mechanical (THM) couplings at the constitutive level are addressed. A constitutive model that accounts for suction and temperature dependent failure is presented. Additionally, the model accounts for the true triaxial nature of strength. Numerical results showed that not accounting for true triaxial strength of geomaterials in unsaturated and non-isothermal conditions can lead to an overestimation of its strength. Then, a new constitutive model combining damage and plasticity theory for quasi-brittle geomaterials is developed. Comparison between numerical results at material point level and experimental results in triaxial compression tests show good agreement. The constitutive model is furtherly developed and modified to improve the calibration scheme and to represent a wider range of confinements. The new constitutive model is implemented with an implicit scheme in the Finite Element solver Code_Aster. Validation examples give good results and the model proves to be a powerful tool to describe the hydro-mechanical behavior of shale. The developed constitutive model is furtherly extended to account for anisotropy and true triaxial strength, both typical features of shale. Both extensions are compared separately against experimental data on several materials. The performance of the constitutive model in terms of failure stress predictions is compared to other failure criteria common in geomechanics. Results demonstrate how the proposed model gives a global smaller error between predictions and data compared to the other criteria. To avoid pathological mesh dependency, the Finite Element analyses must be carried out with a proper regularization technique. The one employed in this study is the second gradient of dilatancy formulation, which was available in Code_Aster. A series of numerical examples are presented to highlight the main characteristics of the structural response of the proposed constitutive model in combination with a second gradient of dilatancy formulation. Results demonstrate how the parameter controlling the non-associated plastic potential, the softening response, the anisotropic failure surface and the size of the problem play a major role in the final solution in presence of localized inelastic strains. Results show as well that the pathological mesh dependency is removed. A Finite Element analysis of tunnel excavation in coupled hydro-mechanical conditions is presented. The developed anisotropic plastic-damage model is employed along with the second gradient of dilatancy. Pore water pressure, tunnel walls displacement and damage around the tunnel are compared with in-situ recorded data during the excavation of the FE-tunnel at the Mont Terri site, Switzerland. The comparison between numerical predictions and recorded data is consistent and validates the concepts developed in the thesis.