Multi-scale modelling of the hydro-mechanical behaviour of argillaceous rocks

Feasibility studies for deep geological radioactive waste disposal facilities have led to an increased interest in the geomechanical modelling of its host rock. In France, a potential host rock is the Callovo-Oxfordian clay-stone. The low permeability of this material is of key importance, as the principle of deep geological disposal strongly relies on the sealing capacity of the host formation. The permeability being coupled to the mechanical material state, hydro-mechanical coupled behaviour of the clay-stone becomes important when mechanical alterations are induced by gallery excavation in the so-called excavation damaged zone (EDZ). In materials with microstructure such as the Callovo-Oxfordian clay-stone, the macroscopic behaviour has its origin in the interaction of its micromechanical constituents. In addition to the coupling between hydraulic and mechanical behaviour, a coupling between the micro (material microstructure) and macro scale will be made. By means of the development of a framework of computational homogenization for hydro-mechanical coupling, a double-scale modelling approach is formulated, for which the macro-scale constitutive relations are derived from the microscale by homogenization. An existing model for the modelling of hydro-mechanical coupling based on the distinct definition of grains and intergranular pore space is adopted and modified to enable the application of first order computational homogenization for obtaining macro-scale stress and fluid transport responses. This model is used to constitute a periodic representative elementary volume (REV) that allows the representation of the local macroscopic behaviour of the clay-stone. As a response to deformation loading, the behaviour of the REV represents the numerical equivalent of a constitutive relation at the macro-scale. For the required consistent tangent operators, the framework of computational homogenization by static condensation is extended to hydro-mechanical coupling. The theoretical developments of this extension are implemented in the finite element code Lagamine (Liege) as an independent constitutive relation. For the modelling of localization of deformation, which in classical FE methods suffers from the well-known mesh dependency, the double-scale approach of hydro-mechanical coupling is combined with a local second gradient model to control the internal length scale of localized deformation. By accepting the periodic boundary conditions as a regularization of the microscale deformation, the use of the multi-scale model in combination with the local second gradient model can be used for modelling localization phenomena in HM-coupled settings with material softening. The modelling capacities of the approach are demonstrated by means of simulations of odometer tests and biaxial compression tests. The approach is demonstrated to be a powerful way to model anisotropy in the mechanical as well as the hydraulic behaviour of the material both in the initial material state and as an effect of hydro-mechanical alterations. For the application to the modelling of Callovo-Oxfordian clay-stone, microstructural REVs are calibrated to geometrical characteristics of the inclusion that form the microstructure under consideration and to macro-scale experimental results of the mechanical behaviour. The calibrated constitutive relation is used in the simulation of gallery excavation processes. These computations give a proof of concept of the double-scale assessment of the hydro-mechanical behaviour of the excavation damaged zones around galleries in the context of nuclear waste disposal. (author)