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Coupled multi-scale modelling of mechanical degradation and transport phenomena in damaging multi-phase geomaterials for environmental applications

Final Report Summary - MULTIROCK (Coupled multi-scale modelling of mechanical degradation and transport phenomena in damaging multi-phase geomaterials for environmental applications)

MULTIROCK PROJECT - SUMMARY OF ACTIVITIES
Thierry J. Massart (International outgoing fellowship)

Objectives of the project
The main research goal of the project was to develop and apply multi-scale modelling techniques for multi-physical processes in multi-phase geomaterials such as rocks, to identify evolving macroscopic properties due to their mechanical degradation. The work focused particularly on fluid transport through porous materials with evolving damage. The outgoing phase was organised under the supervision of Prof. A.P.S. Selvadurai (Department of Civil Engineering and Applied Mechanics, McGill University, Montreal, Canada), taking benefit from the leading edge constitutive modelling research conducted in his Environmental Geomechanics group. The return phase was organised at ULB in the department of Prof. P. Bouillard.
Current day geomechanics problems require the use of modern computational tools to guide engineers in developing feasible solutions. Computational models have enhanced the development of more realistic solutions to these problems, but various issues still hinder their use. A key issue relates to the experimental identification of complex material parameters needed to utilize such tools. By combining different physical phenomena using tools capable of modelling complex geomechanical problems with environmental impacts, the developments performed were focused on multi-scale approaches, whereby several scales of representation coexist. The long-term developments targeted by the project results are firmly founded on advances in computational modelling, with long-term applications to environmental geosciences issues, for instance deep geological storage of nuclear waste, CO2 sequestration, or groundwater-borne reactive pollutant dispersion in the geosphere.

Main results
The main results are consistent with the announced work program and are related to the different scales of representation of geomaterials.
At the fine scale, tools have been developed to generate representative volume elements (RVEs) computationally for geomaterials. The first generation feature uses a 3D Voronoï tessellation algorithm for grain-based cohesive materials (granite). A new concept was developed based on the combination of level set functions and sequential addition. This RVE generator allows creating various types of complex geomaterials microstructure such as rock or soils with an arbitrary number of phases and with a porous network as illustrated below. A strong control of size distributions of components can be used, and its versatility allows envisioning its extension to many complex microstructures (composites, foams, ...). Models for the behavior of geomaterials at the fine scale were subsequently developed, and applied to simulate the cracking-induced permeability evolution. Cracking models were developed with a coupling to the fluid transport properties, as well as a poroelastic implementation. In addition, these models have been implemented within an advanced level set-based extended finite element discretisation technique, thereby allowing an integrated framework with the generation procedure.
Scale transitions have been developed and implemented in order to homogenize computationally the fine scale coupled phenomena towards the macroscopic scale. The combination of this homogenization procedure with the fine scale models can be used in order to reproduce computationally experimental measurements related to the stress-induced permeability evolution as illustrated in the following figures.


These scale transitions have subsequently been used in multi-scale computations involving two scales of representation (FE² simulations), thereby enabling the incorporation of fine scale features in larger scale computations. This implementation has been made possible by the use of a parallel computing architecture. Comparisons between full fine scale modelling and multi-scale results have shown the accuracy of the methodology.

Selected publications
Over the full period of the fellowship, the developments lead to a total of 13 submitted or published papers in impacted journals with 5 additional journal papers in preparation.
B. Sonon, S. Amalou, B.C.N. Mercatoris, B. François, T.J. Massart, XFEM-based modelling of the poromechanical behaviour of heterogeneous geomaterials, In Preparation for CMES-Computer modelling in Engineering & Sciences.
T.J. Massart, A.P.S. Selvadurai, Computational modelling of crack-induced permeability evolution in granite with dilatant cracks, Revised version submitted to International Journal for Rock Mechanics and Mining Sciences.
M.A. Hashemi, G. Khaddour, B. François, T.J. Massart, S. Salager, A tomographic imagery segmentation methodology for multiphase granular materials based on simultaneous region growing, In Press, Acta Geotechnica.
T.J. Massart, A.P.S. Selvadurai, Stress-induced permeability evolution in quasi-brittle geomaterials, Journal of Geophysical Research - Solid Earth, 117, B07207.
B. Sonon, B. François, T.J. Massart, A unified level set based methodology for fast generation of complex microstructural multi-phased RVEs, Computer Methods in Applied Mechanics and Engineering, 223-224, 2012, pp 103-122.

Training and development
In addition to the training provided by the research activities, new research lines were defined based on the interactions with the outgoing phase host. Level set based computational methodologies are central to future modelling tools for heterogeneous geomaterials. Funding sources are a crucial aspect of the implementation of such research lines. The return phase was exploited in order to obtain funding for two projects that will pave the way for the considered implementation, and show the success of the re-integration phase:
• the fellow is now partner of the Erasmus Mundus Joint Doctorate programme SEED in computational mechanics that will provide funding for 10 PhD students at ULB over the next 5 years,
• a belgian national scientific foundation project was obtained jointly with geomechanics colleagues at ULB for investigation of capillary effects in granular materials

A total of 8 PhD students are now supervised or co-supervised at ULB by the fellow in the computational mechanics group, with application fields related to geomechanics, materials science and composites, for which continued interaction with Prof. A.P.S. Selvadurai and with the scientific network built during the fellowship will be a key asset.