: In this work, we report on a successful benchmark program motivated by the development of robust hydro-mechanical coupled models capable of providing accurate equivalent properties, such as permeability and porosity, in larger computational cells, typical of an outcrop scale. The cells are occupied by a poroelastic fractured carbonate rock. Different research groups were invited to propose models and discretizations for the benchmark problem considering some basic premises. The construction of fine-scale models revolves around the non-linear elastic constitutive law postulated by Barton and Bandis between normal stress and normal displacement behavior. The local non-linear coupled poroelastic (matrix) - nonlinear elastic (joints) - flow (single phase) problem is solved under oedometric conditions considering a single realization of fractures locations generated through geostatistical analysis. The different research groups used a variety of techniques to solve the complex fine-scale problem. Among these techniques we may highlight embedded fracture elements [1], solid finite elements with high aspect ratio [2], augmented Lagrangian formulation [3, 4], local refinement with jump components [5] and zero thickness interface elements [6]. Numerical simulations show the magnitude of the equivalent permeabilities and local profiles, such as displacement jumps, as a function of the stress state, characterized by the pore pressure and overburden stresss. Finally, we present comparisons between the outcomes of each technique.

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