Integrating complementarity into the 2D displacement discontinuity boundary element method to model faults and fractures with frictional contact properties

We present a two-dimensional displacement discontinuity method (DDM) in combination with a complementarity solver to simulate quasi-static slip on cracks as models for faults and fractures in an otherwise homogeneous, isotropic, linear elastic material. A complementarity algorithm enforces appropriate contact boundary conditions along the cracks so that variable friction and frictional strength can be included. This method accurately computes slip and opening distributions along the cracks, displacement and stress fields within the surrounding material, and stress intensity factors at the crack tips. The DDM with complementarity is a simple yet powerful tool to investigate many aspects of the mechanical behavior of faults and fractures in Earth's brittle crust. Implementation in Excel and Matlab enables easy saving, organization, and sharing.

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