A Stabilized Mortar Method for Discontinuities in Geological Media with Non-Conforming Grids

TL;DR

This paper introduces a stabilized mortar method for simulating discontinuities in geological media with non-conforming grids, ensuring stability and accurate traction profiles in complex fault models.

Contribution

It develops a traction-jump stabilization technique for mortar methods that automatically scales without user input, improving stability in geological fault simulations.

Findings

Restores inf-sup stability in non-conforming grid simulations

Accurately recovers stable traction profiles

Effective in complex geological fault modeling

Abstract

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.