Ovunc Mutlu

On the patterns of wing cracks along an outcrop scale flaw: A numerical modeling approach using complementarity

[1] The 2D Displacement Discontinuity Method (DDM) is combined with a complementarity algorithm to model the quasi-static formation and patterns of wing cracks that emanate from regions of stress concentration along a sliding frictional flaw in an otherwise homogeneous and isotropic elastic material. Because stress states and geometry change with sliding on the flaw and wing crack propagation, one cannot specify the boundary conditions a priori. Under these circumstances complementarity is superior to other well-known contact algorithms. We focus on meter scale phenomena where mineralogical heterogeneity (common to centimeter-scale laboratory samples) and 3D geometry (common to kilometer-scale crustal structures) reasonably can be ignored. Analytical solutions to the elastic boundary value problem of the closed sliding flaw include those that assume no friction, uniform friction, and a cohesive end zone (CEZ), and those that assume infinitesimal or straight wing cracks. Here we generalize the problem to consider linearly varying friction in the CEZ and curved wing cracks, and we allow the sliding flaw to open when mechanical interaction with the wing crack dictates that it should. Trace lengths of 135 strike-slip faults in sandstone are linearly related to wing crack lengths ranging from 0.16 to 72 m and correspond to a range of remote principal stress ratios: 0.06 < σ 2 /σ 1 ≤ 0.2. Opening displacement profiles of wing cracks from the numerical model can be significantly different from analytical solutions. These solutions may produce significant errors in stable crack length for curved propagation paths. The smeared out stress concentration in the CEZ and the heterogeneity in strength of rock suggest that multiple wing cracks may form in one slip event. The mechanical interactions of these cracks leads to kink angles that increase with distance from the flaw tip, a relationship commonly observed in nature.

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 Earths brittle crust. Implementation in Excel and Matlab enables easy saving, organization, and sharing.

Linear complementarity formulation for 3D frictional sliding problems

Frictional sliding on quasi-statically deforming faults and fractures can be modeled efficiently using a linear complementarity formulation. We review the formulation in two dimensions and expand the formulation to three-dimensional problems including problems of orthotropic friction. This formulation accurately reproduces analytical solutions to static Coulomb friction sliding problems. The formulation accounts for opening displacements that can occur near regions of non-planarity even under large confining pressures. Such problems are difficult to solve owing to the coupling of relative displacements and tractions; thus, many geomechanical problems tend to neglect these effects. Simple test cases highlight the importance of including friction and allowing for opening when solving quasi-static fault mechanics models. These results also underscore the importance of considering the effects of non-planarity in modeling processes associated with crustal faulting.