Finite element modelling of frictional instability between deformable rocks

Earthquakes are recognized as resulting from a stick-slip frictional instability along faults. Based on the node-to-point contact element strategy (an arbitrarily shaped contact element strategy applied with the static-explicit algorithm for modelling non-linear frictional contact problems proposed by authors), a finite element code for modelling the 3-D non-linear friction contact between deformable bodies has been developed and extended here to analyse the non-linear stick-slip frictional instability between deformable rocks with a rate- and state-dependent friction law. A typical fault bend model is taken as an application example to be analysed here. The variations of the normal contact force, the frictional force, the transition of stick-slip instable state and the related relative slip velocity along the fault between the deformable rocks and the stress evolution in the total bodies during the different stages are investigated, respectively. The calculated results demonstrate the usefulness of this code for simulating the non-linear frictional instability between deformable rocks. Copyright (C) 2003 John Wiley Sons, Ltd.

[1]  B. Shibazaki,et al.  Slip-dependent friction law and nucleation processes in earthquake rupture , 1992 .

[2]  W. Brace,et al.  Stick-Slip as a Mechanism for Earthquakes , 1966, Science.

[3]  P. Bird,et al.  Thin‐shell modeling of neotectonics in the Azores‐Gibraltar Region , 2001 .

[4]  Huilin Xing,et al.  FE modeling of thermo‐elasto‐plastic finite deformation and its application in sheet warm forming , 2002 .

[5]  Tao He,et al.  Numerical Simulation of Dynamic Process of the Tangshan Earthquake by a New Method—LDDA , 2000 .

[6]  J. A. Snoke,et al.  Topographic and seismic effects of long-term coupling between the subducting and overriding plates beneath Northeast Japan , 1997 .

[7]  G. P. Nikishkov,et al.  Static-explicit FE modeling of 3-d large deformation multibody contact problems on parallel computer , 1998 .

[8]  Huilin Xing,et al.  Numerical analysis and design for tubular hydroforming , 2001 .

[9]  Tomowo Hirasawa,et al.  A numerical study on seismic coupling along subduction zones using a laboratory-derived friction law , 1997 .

[10]  C. Scholz.  Earthquakes and friction laws , 1998, Nature.

[11]  J. Dieterich.  Modeling of rock friction: 1. Experimental results and constitutive equations , 1979 .

[12]  A. Curnier,et al.  A finite element method for a class of contact-impact problems , 1976 .

[13]  Effect of fault bend on the rupture propagation process of stick-slip , 1999 .

[14]  David R. O'Hallaron,et al.  Large-scale simulation of elastic wave propagation in heterogeneous media on parallel computers , 1998 .

[15]  Richard E. Goodman,et al.  Two dimensional discontinuous deformation analysis , 1985 .

[16]  C. Marone.  LABORATORY-DERIVED FRICTION LAWS AND THEIR APPLICATION TO SEISMIC FAULTING , 1998 .

[17]  GEOFFREY KING,et al.  Role of Fault Bends in the Initiation and Termination of Earthquake Rupture , 1985, Science.

[18]  S. Cloetingh,et al.  Finite-element modelling of stress patterns along the Mid-Norwegian continental margin, 62° to 68°N , 1996 .

[19]  D. J. Andrews,et al.  Rupture propagation with finite stress in antiplane strain , 1976 .

[20]  M. Ohnaka,et al.  Scaling of the shear rupture process from nucleation to dynamic propagation: Implications of geometric irregularity of the rupturing surfaces , 1999 .

[21]  William D. Stuart,et al.  Forecast model for great earthquakes at the Nankai Trough subduction zone , 1988 .

[22]  J. C. Simo,et al.  An augmented lagrangian treatment of contact problems involving friction , 1992 .

[23]  P. Bird.  Finite element modeling of lithosphere deformation: The Zagros collision orogeny , 1978 .

[24]  A. Ruina.  Slip instability and state variable friction laws , 1983 .

[25]  John R. Rice,et al.  Dynamic motion of a single degree of freedom system following a rate and state dependent friction law , 1986 .

[26]  R. Koeller,et al.  A non-equilibrium thermodynamic theory of flow through deformable porous media , 1978 .

[27]  C. Scholz.  The Mechanics of Earthquakes and Faulting , 1990 .

[28]  J. Dieterich.  Time-dependent friction and the mechanics of stick-slip , 1978 .

[29]  Mitiyasu Ohnaka,et al.  Constitutive relations between dynamic physical parameters near a tip of the propagating slip zone during stick-slip shear failure , 1987 .

[30]  H. Xing,et al.  Three dimensional finite element modeling of thermomechanical frictional contact between finite deformation bodies using R-minimum strategy , 2002 .

[31]  H. Melosh,et al.  Mechanics of graben formation in crustal rocks - A finite element analysis , 1989 .

[32]  Genki Yagawa,et al.  Nonlinear Structural Subsystem of GeoFEM for Fault Zone Analysis , 2000 .