A Stabilized Mortar Method for Discontinuities in Geological Media with Non-Conforming Grids
This work addresses a critical problem for subsurface engineering applications, such as performance and safety assessment, by providing a robust method for simulating discontinuities in geological media, though it appears incremental in advancing existing mortar methods.
The paper tackles the challenge of simulating fault and fracture mechanics in geological media with non-conforming grids by developing a stabilized mortar method that enforces contact constraints using Lagrange multipliers. The result is a formulation that restores inf-sup stability and recovers stable traction profiles, even in cases where other methods fail, as demonstrated through numerical experiments.
Accurate numerical simulation of fault and fracture mechanics is critical for the performance and safety assessment of many subsurface systems. The discretized representation of discontinuity surfaces and the robust simulation of their frictional contact behavior still represent major challenges. In this work, we use the mortar method to enforce the contact constraints and allow for non-conformity around the discontinuity surface, with a set of Lagrange multipliers playing the role of interface tractions. The formulation combines piecewise linear displacements with piecewise constant multipliers defined on one side of the fault interface (the non-mortar side). This choice for the Lagrange multipliers has a number of advantages from practical and computational viewpoints, but violates the inf-sup stability constraint. In order to stabilize the proposed formulation, we develop a traction-jump stabilization term to be added to the constraint equations. We use a macro-element analysis to derive an algorithmic strategy that automatically evaluates the proper scaling of the stabilization, without requiring any additional user-selected parameter. Numerical experiments demonstrate that the proposed formulation not only restores the inf-sup stability condition, but also recovers stable traction profiles in the presence of finer non-mortar sides, where other inf-sup-stable formulations fail. The proposed method is finally used to simulate non-linear contact conditions in non-conforming corner-point grids typically used in industrial geological applications.