Un modèle lattice pour simuler la propagation de fissures sous l’effet d’une injection de fluide dans un milieu hétérogène quasi-fragile

This research study aims at developing a lattice-type numerical model allowing the simulation of crack propagation under fluid injection in a quasi-brittle heterogeneous medium. This numerical tool will be used to get a better understanding of initiation and propagation conditions of cracks in rock materials presenting natural joints where the coupling between mechanical damage and fluid transfer properties are at stake. If the final goal of the study does concern natural rocks, the model has been validated by different comparisons with experimental results obtained on cementitious materials mimicking natural rocks in term of mechanical and transport behaviours but presenting heterogeneities which are better controlled. The first part of the manuscript presents a general state of the art. The second part of the manuscript is dedicated to the study of crack propagation in quasi-brittle materials where a significant fracture process zone is evolving upon failure. Only the solid phase is studied here and a statistical tool based on Ripley’s functions is adapted in order to extract a characteristic length representative of the correlations appearing between a set of point undergoing mechanical damage. This tool is then used in the context of numerical and experimental fracture tests on 3 point bending concrete beams. The results show that the lattice-type numerical model is able to capture the global fracture process – in term of force vs. crack opening mouth displacement – but also the local fracture process – in term of dissipated energy and correlation length evolution between damage points. Moreover, this statistical tool shows how the solicitation mode may influence the development of damage within a structure. The third part presents a new elasto-plastic damage constitutive law for joint modelling. The originality of the model lies in the coupling between mechanical damage under normal strain and plasticity under tangential strain. This new constitutive law is able to reproduce indirect shear experimental tests performed on mortar specimens presenting a plaster joint where a classical Mohr-Coulomb criterion fails. The fourth part is dedicated to the representation of the full hydro-mechanical coupling within the lattice-type numerical model. The hydro-mechanical coupling is introduced through a poromechanical framework based on the intrinsic and dual hydro-mechanical description of the lattice model, which is based on a "hydraulic" Voronoi tessellation and a "mechanical" Delaunay triangulation. The total stress links the mechanical stress and the pore pressure through the Biot coefficient of the medium whereas the local permeability, which drives the hydraulic pressure gradient, depends on the local crack openings. The numerical results are compared with analytical solutions from the literature for "bi-wings" shape cracks and it is shown that both approaches present similar results for a perfect straight crack. Once the lattice-model has been successfully validated within the former parts of the manuscript, its fifth and last part is dedicated to the numerical simulation of the fully hydro-mechanical coupling problem of a free crack propagation due to fluid injection and its interaction with a natural joint in an heterogeneous rock medium. Different crack paths, which are not pre-meshed a priori, and different pressure profiles are obtained and compared for different joint inclinations. Finally, our statistical tool, which has been primarily developed for the analysis of the failure behaviour of the solid phase, is used to characterise the evolution of correlation lengths between points undergoing damage upon the crack propagation and its interaction with a natural joint. It is shown that the hydro-mechanical lattice model is able to represent different mechanism of crack stop and restart from a joint depending on its inclination.