Numerical investigation of hydro-mechanical responses of a single fracture embedded in a porous matrix

We have conducted a flow-through experiment using a Flechtingen sandstone sample containing a single macroscopic fracture. Based on this experiment, we obtained range of various intrinsic rock parameters, such as permeability and specific stiffness of the combined matrix-fracture system under hydrostatic loading. In order to quantify the processes behind the laboratory observations, we carried out coupled hydro-mechanical simulations of the matrix-fracture system. Navier-Stokes flow was solved in the 3-dimensional open rough fracture domain, and back-coupled to Darcy flow and mechanical deformation of the rock matrix.

To capture the volumetric shape of the fracture, the two fracture surfaces were scanned using a 3D-profilometer (Keyence VR-3200) before and after the experiment. The resulting fracture surfaces were aligned using a grid-search algorithm and subsequently offset to mimic the shear displacement as applied during the laboratory experiment. Based on the obtained 3D representation of the fracture volume embedded in a porous media, the stress path of the laboratory experiment was simulated numerically. By means of the simulation results, values of fracture closure, increase of contact area, fracture permeability and fracture stiffness due to normal load on the fracture surface were obtained.

The results demonstrate that the numerical simulation could capture the elastic and inelastic behaviour as well as the related permeability alteration of the fracture domain. Both, the laboratory experiments as well as the numerical simulation indicate an inelastic deformation of the single fracture even at low normal stress. The inelastic deformation is expressed by an increase of the fracture contact area and therefore fracture stiffness with increasing stress. The increase in the contact area is due to a reduction in mean aperture and is therefore accompanied by a reduction in the fracture permeability. The development of the contact area is irreversible and thus indicates the maximum stress that the sample previously experienced. We call this behaviour "stress-memory effect".

We present the workflow to obtain the numerical results and a comparison with the laboratory experiment to show that the dominant processes were captured by the simulation.