Computational Geosciences

, Volume 16, Issue 3, pp 613–624 | Cite as

Linear complementarity formulation for 3D frictional sliding problems

  • J. Ole Kaven
  • Stephen H. Hickman
  • Nicholas C. Davatzes
  • Ovunc Mutlu
Original Paper


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.


Boundary element method Friction solver Linear complementarity Fault mechanics 

Mathematics Subject Classifications (2010)

74R99 86-08 74G15 


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Copyright information

© Springer Science+Business Media B.V. (outside the USA) 2012

Authors and Affiliations

  • J. Ole Kaven
    • 1
  • Stephen H. Hickman
    • 1
  • Nicholas C. Davatzes
    • 2
  • Ovunc Mutlu
    • 3
  1. 1.U.S.G.S Earthquake Science CenterMenlo ParkUSA
  2. 2.Earth and Environmental ScienceTemple UniversityPhiladelphiaUSA
  3. 3.Weatherford InternationalHoustonUSA

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