Advertisement

pure and applied geophysics

, Volume 143, Issue 1–3, pp 61–87 | Cite as

Simulation of the frictional stick-slip instability

  • Peter Mora
  • David Place
Fault Mechanics, Rupture Processes, and Fracture: Theory and Observation

Abstract

A lattice solid model capable of simulating rock friction, fracture and the associated seismic wave radiation is developed in order to study the origin of the stick-slip instability that is responsible for earthquakes. The model consists of a lattice of interacting particles. In order to study the effect of surface roughness on the frictional behavior of elastic blocks being rubbed past one another, the simplest possible particle interactions were specified corresponding to radially dependent elastic-brittle bonds. The model material can therefore be considered as round elastic grains with negligible friction between their surfaces. Although breaking of the bonds can occur, fracturing energy is not considered. Stick-slip behavior is observed in a numerical experiment involving 2D blocks with rough surfaces being rubbed past one another at a constant rate. Slip is initiated when two interlocking asperities push past one another exciting a slip pulse. The pulse fronts propagate with speeds ranging from the Rayleigh wave speed up to a value between the shear and compressional wave speeds in agreement with field observations and theoretical analyses of mode-II rupture. Slip rates are comparable to seismic rates in the initial part of one slip pulse whose front propagates at the Rayleigh wave speed. However, the slip rate is an order of magnitude higher in the main part of pulses, possibly because of the simplified model description that neglected intrinsic friction and the high rates at which the blocks were driven, or alternatively, uncertainty in slip rates obtained through the inversion of seismograms. Particle trajectories during slip have motions normal to the fault, indicating that the fault surfaces jump apart during the passage of the slip pulse. Normal motion is expected as the asperities on the two surfaces ride over one another. The form of the particle trajectories is similar to those observed in stick-slip experiments involving foam rubber blocks (Bruneet al., 1993). Additional work is required to determine whether the slip pulses relate to the interface waves proposed by Brune and co-workers to explain the heat-flow paradox and whether they are capable of inducing a significant local reduction in the normal stress. It is hoped that the progressive development of the lattice solid model will lead to realistic simulations of earthquake dynamics and ultimately, provide clues as to whether or not earthquakes are predictable.

Key words

Friction earthquakes nonlinear dynamics lattice solid numerical simulation numerical modeling 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aki, K., andRichards, P. G.,Quantitative Seismology: Theory and Methods (Freeman and Co., San Francisco 1980).Google Scholar
  2. Allen, M. P., andTildesley, D. J.,Computer Simulations of Liquids (Oxford Univ. Press, New York 1987).Google Scholar
  3. Andrews, D. J. (1976),Dynamic Plain Strain Shear Rupture with a Slip Weakening Friction Law Calculated by the Boundary Integral Method, Bull. Seismol. Soc. Am.75, 1–21.Google Scholar
  4. Archuleta, R. J. (1982),Analysis of Near Source Static and Dynamic Measurements from the 1979 Imperial Valley Earthquake, Bull. Seismol. Soc. Am.72, 1927–1956.Google Scholar
  5. Ashurst, W. T., andHoover, W. G. (1976),Microscopic Fracture Studies in the Two-dimensional Triangular Lattice, Phys. Rev. B14, 1465–1473.Google Scholar
  6. Bakun, W. H., andMcEvilly, T. V. (1984),Recurrence Models and Parkfield, California, Earthquakes, J. Geophys. Res.89, 3051–3058.Google Scholar
  7. Bowden, F. P., andTabor, D. (1950),The Friction and Lubrication of Solids (Clarendon Press, Oxford 1950).Google Scholar
  8. Brown, S. R., andScholz, C. H. (1985),Broad Bandwidth Study of the Topography of Natural Rock Surfaces, J. Geophys. Res.90, 12,575–12,582.Google Scholar
  9. Brune, J. N., Johnson, P. A., andSlater, C. (1990),Nucleation, Predictability, and Rupture Mechanism in Foam Rubber Models of Earthquakes, J. Himalayan Geol.1, 155–166.Google Scholar
  10. Brune, J. N., Brown, S., andJohnson, P. A. (1993),Rupture Mechanism and Interface Separation in Foam Rubber Models of Earthquakes: A Possible Solution to the Heat Flow Paradox and the Paradox of Large Ovethrusts, Tectonophys.218, 59–67.Google Scholar
  11. Burridge, R., Conn, G., andFreund, L. B., (1979),The Stability of a Plain Strain Shear Crack with Finite Cohesive Force Running at Intersonic Speeds, J. Geophys. Res.84, 2210–2222.Google Scholar
  12. Burridge, R., andKnopoff, L. (1967),Model and Theoretical Seismicity, Bull. Seismol. Soc. Am.57, 341–371.Google Scholar
  13. Byerlee, J. D., andBrace, W. F. (1968),Stick Slip, Stable Sliding, and Earthquakes—Effect of Rock Type, Pressure, Strain Rate, and Stiffness, J. Geophys. Res.73, 6031–6037.Google Scholar
  14. Carlson, J. M., andLanger, J. S. (1989),Mechanical Model of an Earthquake Fault, Phys. Rev. A40, 6470–6484.Google Scholar
  15. Christ, N. H., Friedberg, R., andLee, T. D. (1982),Random Lattice Field Theory, Nucl. Phys. B202, 89–125.Google Scholar
  16. Cochard, A., andMaradiaga, R. (1993),Dynamic Faulting under Rate-dependent Friction, Pure and Appl. Geophys.142, 419–445.Google Scholar
  17. Comninou, M., andDundurs, J. (1977),Elastic Interface Waves Involving Separation, J. Appl Mech.44, 222–226.Google Scholar
  18. Comninou, M., andDundurs, J. (1978),Elastic Interface Waves and Sliding between Two Solids, J. Appl. Mech.45, 325–330.Google Scholar
  19. Day, S. M. (1991),Numerical Simulation of Fault Propagation with Interface Separation, AGU 1991 fall mtg. Prog. and abstracts, published as supp. to EOS, Oct. 29, 1991.Google Scholar
  20. Dieterich, J. H. (1978),Preseismic Fault Slip and Earthquake Prediction, J. Geophys. Res.83, 3940–3948.Google Scholar
  21. Donzé, F., Mora, P., andMagnier, S. A. (1993),Numerical Simulation of Faults and Shear Zones, Geophys. J. Int.116, 46–52.Google Scholar
  22. Freund, L. B. (1978),Discussion, J. Appl. Mech.45, 226–228.Google Scholar
  23. Freund, L. B.,Dynamic Fracture Mechanics (Cambridge Univ. Press, Cambridge 1990).Google Scholar
  24. Heaton, T. H. (1990),Evidence for and Implications of Self-healing Pulses of Slip in Earthquake Rupture, Phys. Earth. Planetary Interiors.64, 1–20.Google Scholar
  25. Heaton, T. H. (1994),pers. comm. Google Scholar
  26. Heslot, F., Baumberger, T., Perrin, B., caroli, B., andCaroli, C. (1994),Creep, Stick-slip and Dry Friction Dynamics: Experiments and Heuristic Model, Phys. Rev.submitted.Google Scholar
  27. Herrmann, H. J. (1993),pers. comm. Google Scholar
  28. Hoover, W. G., Ashurst, W. T., andOlness, R. J. (1974),Two-dimensional Computer Studies of Crystal Stability and Fluid Viscosity, J. Chem. Phys.60, 4,043–4,047.Google Scholar
  29. Lomdahl, P. S., Tomayo, P., Grønbech-Jensen, N., andBeazley, D. M.,50 Gflops molecular dynamics on the Connection Machine 5. InProc. SuperComputing 93, Portland Oregon, Nov. 15–19 (IEEE Computer Soc. Press 1993a).Google Scholar
  30. Lomdahl, P. S., Beazley, D. M., Tomayo, P., andGrønbech-Jensen, N. (1993b),Multi-million Particle Molecular Dynamics on the CM-5, Int. J. Mod. Phys. C4, 1075–1084.Google Scholar
  31. Lomnitz-Adler, J. (1991),Model for Steady State Friction, J. Geophys. Res.96, 6121–6131.Google Scholar
  32. Mora, P., andPlace, D. (1993),A Lattice Solid Model for the Nonlinear Dynamics of Earthquakes, Int. J. Mod. Phys. C4, 1059–1074.Google Scholar
  33. Nielsen, S. B., andTarantola, A. (1992),Numerical Model of Seismic Rupture, J. Geophys. Res.97, 15,291–15,295.Google Scholar
  34. Pisarenko, D., andMora, P. (1994),Velocity Weakening in a Dynamical Model of Friction, Pure and Appl. Geophys.142, 447–466.Google Scholar
  35. Rice, J. R. (1993),Spatio-temporal Complexity of Slip on a Fault, J. Geophys. Res.98, 9885–9907.Google Scholar
  36. Schallamach, A. (1971),How Does Rubber Slide?, Wear17, 301–312.Google Scholar
  37. Scholz, C. H.,The Mechanics of Earthquakes and Faulting (Cambridge Univ. Press., Cambridge 1990).Google Scholar
  38. Scholz, C., Molnar, P., andJohnson, T. (1972),Detailed Studies of Frictional Sliding of Granite and Implications for Earthquake Mechanism, J. Geophys. Res.77, 6392–6406.Google Scholar
  39. Schroeder, M.,Fractals, Chaos, Power Laws (Freeman, New York 1991), p. 122.Google Scholar

Copyright information

© Birkhäuser Verlag 1994

Authors and Affiliations

  • Peter Mora
    • 1
  • David Place
    • 1
  1. 1.Institut de Physique du GlobeParis, Cedex 05France

Personalised recommendations