Modélisation tridimensionnelle fortement couplée par la méthode des éléments finis étendus (XFEM) de la fracturation hydraulique avec un accent sur les barrages en béton

Abstract

In this thesis, we are interested in the modeling of cracks in large three-dimensional hydraulic structures. In this context, the development of a new numerical method to represent cracking by integrating the nonlinear fracture mechanics approach coupling a diffuse crack model in the fracture process zone with the extended finite element method (XFEM) in the area where there is coalescence of microcracks was achieved. This new model couples the benefits of the continuous damage approach with that of the extended finite elements method. Before the transition between the two models occurs, the continuous damage approach is used as predictor to determine the crack path. During the transition, energy conservation is applied while ensuring that the mode I energy dissipation is preserved. The model demonstrated a great capacity to reproduce the crack paths as well as the experimental results for many test cases. In addition, it has been shown that these results are independent of the mesh, confirming the objectivity of the model. The model initially developed in two dimensions has been extended for a three-dimensional context. A key ingredient for the method to work in 3D is the crack tracking algorithm. The so-called global method is used to follow discontinuities. This method has been applied by other authors, but in this thesis it has been extended to large problems with complex crack geometries. An important contribution was achieved to compute the crack opening in the context of the continuous damage mechanics approach. It is common to define a kind of characteristic length to link the strain in the principal direction with the crack opening. However, it was shown that in the case where an irregular mesh is used, the crack opening presents unrealistic oscillations along the crack and gives very approximate results. The proposed method, based on a local XFEM formulation and on the balance of loads, solves this problem. This algorithm was notably used in a hydrofracturation case where the permeability, linked to the crack opening, is increased during the progression of damage. Finally, a contribution was made by using the XFEM with success for the first time in an industrial-scale problem in the civil engineering sector, despite the fact that the method was published about twenty years ago. Another contribution was the proposal of a strongly coupled 3D hydromechanical method for the computation of complex and non-planar hydraulic fracturing problems. A key ingredient is the use of a sub-problem in which a hydraulic mesh is used to compute the flow in the discontinuities. The complexity of the flow, linked to the non-linearities caused by the different flow regimes and the presence of drainage, can be computed by the proposed method. The pressure computed using this sub problem can be transferred to the strongly coupled hydromechanical problem. An important aspect to consider concerns the transfer of crack openings from the structure to the hydraulic mesh and, conversely, the transfer of hydraulic pressures to the structural problem while respecting the balance of loads. The use of XFEM allows the computation of crack openings as well as the application of pressure on the crack surfaces for the simulation of the initiation and the propagation of hydraulic fracturing. The partial saturation conditions are added by coupling a non-linear diffusion model taking into account the effect of saturation by a non-linear equation varying in time and space.

Date	10 Jul 2020
Original language	French
Awarding Institution	École de technologie supérieure
Supervisor	Azzeddine Soulaïmani (Supervisor) & Pierre Léger (Co-supervisor)