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 (Brune et 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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Aki, K., andRichards, P. G.,Quantitative Seismology: Theory and Methods (Freeman and Co., San Francisco 1980).
Allen, M. P., andTildesley, D. J.,Computer Simulations of Liquids (Oxford Univ. Press, New York 1987).
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.
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.
Ashurst, W. T., andHoover, W. G. (1976),Microscopic Fracture Studies in the Two-dimensional Triangular Lattice, Phys. Rev. B14, 1465–1473.
Bakun, W. H., andMcEvilly, T. V. (1984),Recurrence Models and Parkfield, California, Earthquakes, J. Geophys. Res.89, 3051–3058.
Bowden, F. P., andTabor, D. (1950),The Friction and Lubrication of Solids (Clarendon Press, Oxford 1950).
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.
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.
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.
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.
Burridge, R., andKnopoff, L. (1967),Model and Theoretical Seismicity, Bull. Seismol. Soc. Am.57, 341–371.
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.
Carlson, J. M., andLanger, J. S. (1989),Mechanical Model of an Earthquake Fault, Phys. Rev. A40, 6470–6484.
Christ, N. H., Friedberg, R., andLee, T. D. (1982),Random Lattice Field Theory, Nucl. Phys. B202, 89–125.
Cochard, A., andMaradiaga, R. (1993),Dynamic Faulting under Rate-dependent Friction, Pure and Appl. Geophys.142, 419–445.
Comninou, M., andDundurs, J. (1977),Elastic Interface Waves Involving Separation, J. Appl Mech.44, 222–226.
Comninou, M., andDundurs, J. (1978),Elastic Interface Waves and Sliding between Two Solids, J. Appl. Mech.45, 325–330.
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.
Dieterich, J. H. (1978),Preseismic Fault Slip and Earthquake Prediction, J. Geophys. Res.83, 3940–3948.
Donzé, F., Mora, P., andMagnier, S. A. (1993),Numerical Simulation of Faults and Shear Zones, Geophys. J. Int.116, 46–52.
Freund, L. B. (1978),Discussion, J. Appl. Mech.45, 226–228.
Freund, L. B.,Dynamic Fracture Mechanics (Cambridge Univ. Press, Cambridge 1990).
Heaton, T. H. (1990),Evidence for and Implications of Self-healing Pulses of Slip in Earthquake Rupture, Phys. Earth. Planetary Interiors.64, 1–20.
Heaton, T. H. (1994),pers. comm.
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.
Herrmann, H. J. (1993),pers. comm.
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.
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).
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.
Lomnitz-Adler, J. (1991),Model for Steady State Friction, J. Geophys. Res.96, 6121–6131.
Mora, P., andPlace, D. (1993),A Lattice Solid Model for the Nonlinear Dynamics of Earthquakes, Int. J. Mod. Phys. C4, 1059–1074.
Nielsen, S. B., andTarantola, A. (1992),Numerical Model of Seismic Rupture, J. Geophys. Res.97, 15,291–15,295.
Pisarenko, D., andMora, P. (1994),Velocity Weakening in a Dynamical Model of Friction, Pure and Appl. Geophys.142, 447–466.
Rice, J. R. (1993),Spatio-temporal Complexity of Slip on a Fault, J. Geophys. Res.98, 9885–9907.
Schallamach, A. (1971),How Does Rubber Slide?, Wear17, 301–312.
Scholz, C. H.,The Mechanics of Earthquakes and Faulting (Cambridge Univ. Press., Cambridge 1990).
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.
Schroeder, M.,Fractals, Chaos, Power Laws (Freeman, New York 1991), p. 122.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mora, P., Place, D. Simulation of the frictional stick-slip instability. PAGEOPH 143, 61–87 (1994). https://doi.org/10.1007/BF00874324
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00874324