Modelling contact problems with friction in fault mechanics

The aim of this contribution is two-fold. First, we review the friction models applied in geophysics. These models cover: state- and rate-dependent friction, rate-dependent friction and slip-dependent friction. Second, we propose a new description of friction in the spirit of modern contact mechanics, introducing sliding rules which interrelate the contact stresses with the slip velocity. Sliding rules are formulated in a subdifferential form. Initial-boundary value problems are formulated in the strong and variational forms. By applying Green's function, the variational formulation for finding normal and tangential contact stresses is proposed.

[1]  D. Lockner.  A generalized law for brittle deformation of Westerly granite , 1998 .

[2]  Donald L. Turcotte,et al.  Geodynamics : applications of continuum physics to geological problems , 1982 .

[3]  J. Weeks,et al.  Frictional sliding of dolomite: A variation in constitutive behavior , 1985 .

[4]  Yehuda Ben-Zion,et al.  Dynamic simulations of slip on a smooth fault in an elastic solid , 1997 .

[5]  Terry E. Tullis,et al.  Frictional Behavior of Large Displacement Experimental Faults , 1996 .

[6]  C. Marone,et al.  Effects of normal stress vibrations on frictional healing , 1999 .

[7]  K. Mair,et al.  Friction of simulated fault gouge for a wide range of velocities and normal stresses , 1999 .

[8]  E. Rabinowicz,et al.  Friction and Wear of Materials , 1966 .

[9]  Stephen R. Brown.  Frictional heating on faults: Stable sliding versus stick slip , 1998 .

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

[11]  Frictional heating and the stability of rate and state dependent frictional sliding , 1995 .

[12]  John R. Rice,et al.  Slip dynamics at an interface between dissimilar materials , 2001 .

[13]  J. Dieterich.  Earthquake nucleation on faults with rate-and state-dependent strength , 1992 .

[14]  James H. Dieterich,et al.  Time‐dependent friction in rocks , 1972 .

[15]  Kim B. Olsen,et al.  Influence of friction and fault geometry on earthquake rupture , 2000 .

[16]  Friction of rocks , 1978 .

[17]  R. Madariaga,et al.  Rupture dynamics of a planar fault in a 3D elastic medium: Rate- and slip-weakening friction , 1998, Bulletin of the Seismological Society of America.

[18]  John R. Rice,et al.  Fault rupture between dissimilar materials: Ill-posedness, regularization, and slip-pulse response , 2000 .

[19]  J. Rice.  Spatio‐temporal complexity of slip on a fault , 1993 .

[20]  Peter Mora,et al.  The Lattice Solid Model to Simulate the Physics of Rocks and Earthquakes: Incorporation of Granular Friction , 1999 .

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

[22]  Vasilii S Vladimirov.  Equations of mathematical physics , 1971 .

[23]  J. Weeks,et al.  Effects of slip, slip rate, and shear heating on the friction of granite , 1998 .

[24]  M. Campillo,et al.  Influence of the shape of the friction law and fault finiteness on the duration of initiation , 1999 .

[25]  J. Rice,et al.  Elastodynamic analysis for slow tectonic loading with spontaneous rupture episodes on faults with rate‐ and state‐dependent friction , 2000 .

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

[27]  Y. Iio.  Frictional coefficient on faults in a seismogenic region inferred from earthquake mechanism solutions , 1997 .

[28]  C. Scholz.  Faults without friction? , 1996, Nature.

[29]  J. C. Jaeger,et al.  Fundamentals of rock mechanics , 1969 .

[30]  Roman Teisseyre,et al.  Earthquake thermodynamics and phase transformations in the Earth's interior , 2001 .

[31]  R. Madariaga,et al.  Modeling dynamic rupture in a 3D earthquake fault model , 1998, Bulletin of the Seismological Society of America.

[32]  K. Rybicki.  Strike-slip faulting in the presence of low-rigidity inhomogeneities , 1992 .

[33]  J. Rice,et al.  Conditions under which velocity-weakening friction allows a self-healing versus a cracklike mode of rupture , 1998, Bulletin of the Seismological Society of America.

[34]  P. Okubo.  Dynamic rupture modeling with laboratory‐derived constitutive relations , 1989 .

[35]  Raul Madariaga,et al.  Dynamic faulting under rate-dependent friction , 1994 .

[36]  Gutuan Zheng,et al.  Self-healing slip pulse on a frictional surface , 1995 .

[37]  J. J. Telega.  Topics on Unilateral Contact Problems of Elasticity and Inelasticity , 1988 .

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

[39]  Michel Campillo,et al.  Fault finiteness and initiation of dynamic shear instability , 2000 .

[40]  C. Scholz,et al.  Healing and sealing of a simulated fault gouge under hydrothermal conditions: Implications for fault healing , 1998 .

[41]  Ioan R. Ionescu,et al.  On the contact problem with slip displacement dependent friction in elastostatics , 1996 .

[42]  M. Takeo,et al.  Determination of constitutive relations of fault slip based on seismic wave analysis , 1997 .

[43]  Michel Campillo,et al.  Frequency domain inversion of strong motions: Application to the 1992 Landers earthquake , 1995 .

[44]  D. Lockner,et al.  The effect of mineral bond strength and adsorbed water on fault gouge frictional strength , 2000 .

[45]  Gregory C. Beroza,et al.  Short slip duration in dynamic rupture in the presence of heterogeneous fault properties , 1996 .

[46]  J. Rice,et al.  Slip patterns and earthquake populations along different classes of faults in elastic solids , 1995 .

[47]  J. Boatwright,et al.  Frictional constraints on crustal faulting , 1996 .

[48]  C. Marone,et al.  Earthquake nucleation on model faults with rate‐ and state‐dependent friction: Effects of inertia , 1996 .

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

[50]  James D. Byerlee,et al.  The mechanics of stick-slip☆ , 1970 .

[51]  F. Chester.  Effects of temperature on friction: Constitutive equations and experiments with quartz gouge , 1994 .

[52]  J. C. Savage,et al.  Failure in laboratory fault models in triaxial tests , 1996 .

[53]  J. Dieterich,et al.  Effect of humidity on time‐ and velocity‐dependent friction in rocks , 1984 .

[54]  M. Campillo,et al.  On the dynamic sliding with friction of a rigid block and of an infinite elastic slab , 1996 .

[55]  Michel Campillo,et al.  Initiation of in-plane shear instability under slip-dependent friction , 1997, Bulletin of the Seismological Society of America.

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