Coupled fluid flow and deformation modelling of saturated fractured porous media with non-matching meshes

The consolidation of a porous medium in the presence of strong discontinuities (cracks) can prove highly challenging for computational modelling because it requires the simultaneous handling of: i) the fluid flow within discontinuities and the surrounding porous bulk, and the transition between those; ii) the mechanical deformation of discontinuities and the solid skeleton; and iii) the connection between the two, i.e. solid-fluid interaction. In the literature, significant contributions have been made to investigate those mechanisms and better understand how discontinuities can impact the fluid pressure distribution in deformable fractured porous media. For this purpose, a wide range of numerical models generally based on the finite element method have been proposed. Current approaches, however, come with a number of drawbacks, such as the large number of additional degrees of freedom required to capture the discontinuities, complicated integration procedures, and problems associated with mesh matching across discontinuities. This thesis proposes a novel multi-layered approach to deal with fluid flow in saturated fracture porous media. The new strategy is based on coupling elements that can connect the layers used to describe the fluid flow in the bulk with the flow within the fractures. Both can be modelled independently. In the first part of this thesis, the formulation is developed to account for transverse and longitudinal fluid flow in fractured porous media. The formulation allows the independent discretisation of mesh and discontinuities, which do not need to conform. Given that the formulation is developed at the element level, no additional degrees of freedom or special integration procedures are required for coupling non-conforming meshes. The proposed model is shown to be reliable regardless of the permeability of the discontinuity being higher or lower than the surrounding domain. Four verification examples are solved to demonstrate the efficiency and accuracy of the new technique when compared with results available in the literature. The results show a good agreement with other techniques available in the literature. Next, in the second part, the formulation is extended to time-dependent fluid flow modelling, which also shows reliable results in comparison with existing benchmarks. Finally, in the third part of the thesis, the model is developed to simulate coupled fluid flow and deformation – hydro-mechanical (HM) – problems in fractured porous media. The formulation includes the longitudinal fluid flow formulation developed in the first part with the discrete strong discontinuity approach (DSDA) to capture the fractured behaviour of the media. Compared to the majority of existing FEM models, this novel approach enjoys several essential advantages from a computational costs point of view such as it needs less degrees of freedom, and relies on standard integration procedures. In addition, the degrees of freedom related to the discontinuity are global and located at the crack tips, which leads to a more accurate and straightforward way of measuring the fluid pressure inside the discontinuity and corresponding mechanical deformation. To fully assess the new technique, several benchmarks and case studies have been worked out. Results show that the proposed method can effectively simulate the coupled fluid and deformation analysis in fractured porous media. In summary, a computationally robust numerical formulation based on finite element method has been developed and validated for the analysis of fluid flow whether separately, or coupled with the mechanical deformation in fractured porous media. It is worth noting that all the simulations conducted within this thesis have been implemented in Matlab