ORALS

This paper is focused on numerical analysis of the coupled hydro-mechanical response of geomaterials that contain pre-existing or newly developing zones of localized deformation, such as faults, macrocracks, shear bands, etc. In terms of mechanical response, the existence of discontinuities results in the reduction of material strength that is triggered by sliding/separation along the defects. In addition, the pre-existing cracks act as stress concentrators prompting the formation of new macrocracks that may propagate through the domain. In terms of flow properties, the hydraulic conductivity is also strongly affected by the fracture pattern and displays anisotropy at the macroscale. The numerical analysis of flow through fractured porous media is usually conducted by employing the Extended Finite Element Method (XFEM). The approach typically involves the assumption that the fluid pressure is continuous across the discontinuity, while the pressure gradient is discontinuous. Such formulation allows for the transport and storage of fluid inside the crack. The jump in the pressure gradient is achieved by partitioning the pressures at both sides of the discontinuity by a signed distance function. Although the approach is accurate, it is computationally very inefficient. The latter stems from incorporation of enriched DOSs, i.e. additional degrees of freedom that account for the presence of discontinuities, as well the need for partitioning of the domain with triangular sub-elements for the Gaussian integration scheme. Given the problems inherent to XFEM approach, a new formulation is developed here that employs the averaging of the field operators within the referential volume adjacent to macrocrack. This leads to an enriched form of Darcy’s law, which incorporates the notion of equivalent conductivity. The latter is defined as a symmetric second-order tensor whose components are function of hydraulic properties of constituents (viz. intact material and fractured region) as well as the internal length parameter. Such an approach does not require any additional degrees of freedom to account for the presence of discontinuities, which significantly improves the computational efficiency as compared to XFEM. The mechanical analysis incorporates an enhanced embedded discontinuity approach, which is conceptually similar to that employed for specification of equivalent hydraulic conductivity. It employs the same ‘characteristic dimension’ related to geometry of fractures and enables a discrete tracing of the propagation of new cracks. The formulation is illustrated by a number of examples. In particular, a series of compression tests on pre-fractured rock-like samples is simulated. Various geometric configurations of pre-existing as well as new propagating cracks are considered and the results are compared with the experimental data. In addition, a steady-state flow through the fractured domain under a prescribed hydraulic gradient is examined for different geometries of fractures. Finally, a coupled problem is considered involving a transient flow under constant traction boundary conditions.