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<p>The simulation of poromechanical models in fractured (or faulted) porous rocks plays an important role in many subsurface applications such as fault reactivation by fluid injection in geological storages or the hydraulic fracture stimulation in deep geothermal systems. One of the key difficulties in simulating such models is the discretization of the contact-mechanical model which must be adapted to geological polytopal meshes and to the complex geometry of fracture/fault networks including tips, corners and intersections. In this work, we extend the first-order Virtual Element Method (VEM) combined with Nitsche s formulation, originally introduced in [<CitationRef CitationID="CR24">24</CitationRef>] for the frictionless case, to address Coulomb frictional contact. The proposed Nitsche’s formulation accounts for normal compliance and its no-penetration limit in a unified way. We first investigate the well-posedness and convergence of this VEM-Nitsche discretization and discuss its robustness with respect to the normal stiffness parameter. Then, the VEM-Nitsche scheme is compared to the VEM mixed formulation with face bubble stabilization introduced in [<CitationRef CitationID="CR17">17</CitationRef>, <CitationRef CitationID="CR18">18</CitationRef>] on several mixed-dimensional poromechanical test cases with 2D and 3D fracture networks, including a fluid-induced fault reactivation test case.</p>

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VEM fully discrete Nitsche’s discretization of Coulomb frictional contact-mechanics for mixed-dimensional poromechanical models

  • 期刊论文

  • 发表日期：

    2025年11月27日

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  • Mohamed Laaziri,
  • Roland Masson

摘要

The simulation of poromechanical models in fractured (or faulted) porous rocks plays an important role in many subsurface applications such as fault reactivation by fluid injection in geological storages or the hydraulic fracture stimulation in deep geothermal systems. One of the key difficulties in simulating such models is the discretization of the contact-mechanical model which must be adapted to geological polytopal meshes and to the complex geometry of fracture/fault networks including tips, corners and intersections. In this work, we extend the first-order Virtual Element Method (VEM) combined with Nitsche s formulation, originally introduced in [24] for the frictionless case, to address Coulomb frictional contact. The proposed Nitsche’s formulation accounts for normal compliance and its no-penetration limit in a unified way. We first investigate the well-posedness and convergence of this VEM-Nitsche discretization and discuss its robustness with respect to the normal stiffness parameter. Then, the VEM-Nitsche scheme is compared to the VEM mixed formulation with face bubble stabilization introduced in [17, 18] on several mixed-dimensional poromechanical test cases with 2D and 3D fracture networks, including a fluid-induced fault reactivation test case.