Contact between rough rock surfaces using a dual mortar method

The mechanical behavior of fractures in rocks has strong implications for reservoir engineering applications. Deformations, and the corresponding change in contact area and aperture field, impact rock fracture stiffness and permeability, thus altering the reservoir properties significantly. Simulating contact between fractures is numerically difficult as the non-penetration constraints lead to a nonlinear problem and the surface meshes of the solid bodies on the opposing fracture sides may be non-matching. Furthermore, due to the complex geometry, the non-penetration constraints must be updated throughout the solution procedure. Here we present a novel implementation of a dual mortar method for contact. It uses a non-smooth sequential quadratic programming method as solver, and is suitable for parallel computing. We apply it to a two body contact problem consisting of realistic rock fracture geometries from the Grimsel underground laboratory in Switzerland. The contributions of this article are: (1) a novel, parallel implementation of a dual mortar method with a non-smooth sequential quadratic programming method, (2) realistic rock geometries with rough surfaces, and (3) numerical examples, which prove that the dual mortar method is capable of replicating the nonlinear closure behavior of fractures observed in laboratory experiments.