Solid friction at high sliding velocities: An explicit three-dimensional dynamical smoothed particle hydrodynamics approach

Journal of Geophysical Research: Solid Earth

Volumn 104, Issue B12, 1999, Pages 28769-28788

  Maveyraud, Claude ^a,b   Benz, Willy ^b,c   Sornette, Anne ^d,e   Sornette, Didier ^b  

^a CNRS   (France)

^b UNIVERSITY OF BERN   (Switzerland)

^c INSTITUT NON LINÉAIRE DE NICE   (France)

^d UNIVERSITY OF CALIFORNIA   (United States)

^e UNIVERSITÉ CÔTE D'AZUR   (France)

Author keywords

[No Author keywords available]

Indexed keywords

FRICTION; HYDRODYNAMICS; ROCK MECHANICS;

EID: 0033545021     PISSN: 21699313     EISSN: 21699356     Source Type: Journal    
DOI: 10.1029/1999jb900217     Document Type: Article

References (87)

1. Andrews, D. J., and Y. Ben-Zion, Wrinkle-like slip pulse on a fault between different materials, J. Geophys. Res., 102, 553-571, 1997.
2. Asphaug, E., and H.J. Melosh, The stickney impact of phobos: A dynamical model, Icarus, 101, 144-164, 1993.
3. Asphaug, E., S.J. Ostro, R.S. Hudson, D.J. Scheeres, and W. Benz, Disruption of kilometre-sized asteroids by energetic collisions, Nature, 393, 437-440, 1998.
4. Batimberger, T., and L. Gauthier, Creeplike relaxation at the interface between rough solids under shear, J. Phys. I, 6, 1021-1030, 1996.
5. Beeler, N.M., T.E. Tullis, and J.D. Weeks, The roles of time and displacement in the evolution effect in rock friction, Geophys. Res. Lett., 21, 1987-1990, 1994.
6. Beeler, N.M., T.E. Tullis, M.L. Blanpied, and J.D. Weeks, Fractional behavior of large displacement experimental faults, J. Geophys. Res., 101, 8697-8715, 1996.
7. Beeman, M., W.B. Durham, and S.H. Kirby, Friction of ice, J. Geophys. Res., 93, 7625-7633, 1988.
8. Benz, W., Smooth particle hydrodynamics: A review, in The Numerical Modeling of Nonlinear Stellar Pulsations, edited by J. Buchler, pp. 269-288, Kluwer Acad., San Diego, Calif., 1990.
9. Benz, W., and E. Asphaug, Impact simulations with fracture, I, Method and tests, Icarus, 107, 98-116, 1994.
10. Benz, W., and E. Asphaug, Simulations of brittle solids using smooth particle hydrodynamics, Comput. Phys. Commun., 87, 253-265, 1995.
11. Benz, W., W.L. Slattery, and A.G.W. Cameron, The origin of the Moon and the single-impact hypothesis, Icarus, 66, 515-535, 1986.
12. Benz, W., E. Ryan, and E. Asphaug, Numerical simulations of catastrophic disruption: Recent results, Planet. Space Sci., 42, 1053-1066, 1994.
13. Ben-Zion, Y., and J.R. Rice, Earthquake failure sequences along a cellular fault zone in a three-dimensional elastic solid containing asperity and nonasperity regions, J. Geophys. Res., 98, 14,109-14,131, 1993.
14. Ben-Zion, Y., and J.R. Rice, Slip patterns and earthquake populations along different classés of faults in elastic solids, J. Geophys. Res., 100, 12,959-12,983, 1995.
15. Ben-Zion, Y., and J. R. Rice, Dynamic simulations of slip on a smooth fault in an elastic solid, J. Geophys. Res., 102, 17,771-17,784, 1997.
16. Bocquet, L., and H.J. Jensen, Phenomenological study of hysteresis in quasistatic friction, J. Phys. I, 7, 1603-1625, 1997.
17. Bowden, F.P., and D. Tabor, The Friction and Lubrication of Solids, Oxford Univ. Press, New York, 1954.
18. Brace, W.F., Laboratory studies of stick-slip and their application to earthquakes, Tectonophysics, 14, 189-200, 1972.
19. Brace, W. R., and J.D. Byerlee, Stick-slip as a mechanism for earthquakes, Science, 153, 990-992, 1966.
20. Brune, J.N., S. Brown, and P.A. Johnson, Rupture mechanism and interface separation in foam rubber models of earthquakes: A possible solution to the heat flow paradox and the paradox of large overthrusts, Tectonophysics, 218, 59-67, 1993.
21. Bullard, E.G., The interior of the Earth, in The Earth as a Planet, edited by G.P. Kuiper, pp. 57-137, Univ. of Chicago Press, Chicago, 111., 1954.
22. Byerlee, J. D., et al., Stick slip, stable sliding, and earthquakes: Effect of rock type, pressure, strain rate, and stiffness, J. Geophys. Res., 73, 6031-6037, 1968.
23. Caroli, C., and P. Nozières, Dry friction as a hysteretic elastic response, in Physics of Sliding Friction, edited by B.J.N. Persson and E. Tosatti, Kluwer Acad., Norwell, Mass., 1996.
24. Caroli, C., and B. Velicky, Dry friction as an elasto-plastic response: Effect of compressive plasticity, J. Phys. I, 7, 1391-1416, 1997.
25. Cochard, A., and R. Madariaga, Dynamic faulting under rate-dependent friction, Pure Appl. Geophys., 142, 419-445, 1994.
26. Cochard, A., and R. Madariaga, Complexity of seismicity due to highly rate-dependent friction, J. Geophys. Res., 101, 25,321-25,336, 1996.
27. Coleman, O.S., and G.V. Bicknell, Jets with entrained cloudsHydrodynamics simulations and magnetic field structure, Mon. Not. R. Astron. Soc., 214, 337-355, 1985.
28. Cox, S.J.D., Velocity-dependent friction in a large direct shear experiment on gabbro, in Deformation Mechanisms, Rheology and Tectonics, edited by R.J. Knipe and E.H. Rutter, Geol. Soc., Spec. Publ., 54, 63-70, 1990.
29. de Oliveira, C.R., and P.S. Goncalves, Bifurcations and chaos for the quasiperiodic bouncing ball, Phys. Rev. E, 56, 4868-4871, 1997.
30. Dieterich, J.H., Time-dependent friction in rocks, J. Geophys. Res., 77, 3690-3697, 1972.
31. Dieterich, J.H., Time-dependent friction and the mechanics of stick-slip, Pure Appl. Geophys., 116,790-806, 1978.
32. Dieterich, J.H., Modeling of rock friction, 1, Experimental results and constitutive equations, J. Geophys. Res., 84, 2161-2168, 1979.
33. Dieterich, J., arid B.D. Kilgore, Direct observation of frictional contacts-New insight for state-dependent properties, Pure Appl. Geophys., 143, 283-302, 1994.
34. Franaszek, M., and H.M. Isomaki, Anomalous chaotic transients and repellers of the bouncing-ball dynamics, Phys. Rev. E, 43, 4231-4236, 1991.
35. Gu, Y., and T.-F. Wong, Effects of loading velocity, stiffness, and inertia on the dynamics of a single degree of freedom spring-slider system, J. Geophys. Res., 96, 21,677-21,691, 1991.
36. Henyey, T.L., and G.J. Wasserburg, Heat flow near major strike-slip faults in California, J. Geophys. Res., 76, 79247946, 1971.
37. Herrmann, H.J., G. Mantica, and D. Bessis, Space-filling bearings, Phys. Rev. Lett., 65, 3223-3226, 1990.
38. Hirano, M., K. Shinjo, R. Kaneko, and Y. Murata, Observation of superlubricity by scanning tunneling microscopy, Phys. Rev. Lett., 78, 1448-1451, 1997.
39. Jackson, J.D., Classical Electrodynamics, 2d ed., John Wiley, New York, 1975.
40. Jensen, H.J., Y. Brechet, and B. Doucot, Instabilities of an elastic chain in a random potential, J. Phys. I, 3, 611-623, 1993.
41. Johansen, A., P. Dinon, C. Ellegaard, J.S. Larsen, and H.H. Riigh, Dynamic phases in a spring-block system, Phys. Rev. E, 48, 4779-4790, 1993.
42. Knopoff, L., The organization of seismicity on fault networks, Proc. Natl. Acad. Sci. U.S.A., 93, 3830-3837, 1996.
43. Lachenbruch, A.H., and J.H. Sass, Heat flow and energetics of the San Andreas fault zone, J. Geophys. Res., 85, 61856222, 1980.
44. Lattanzio, J.C., J.J. Monaghan, H. Pongracic, and M.P. Schwarz, Interstellar cloud collisions, Mon. Not. R. Astron. Soc., 215, 125-147, 1985.
45. Lomnitz-Adler, J., Model for steady state friction, J. Geo-phtjs. Res., 96, 6121-6131, 1991.
46. Luck, J.-M., and A. Mehta, Bouncing ball with a finite restitution-Chattering, locking and chaos, Phys. Rev. E, 48, 3988-3997, 1993.
47. Lucy, L.B., A numerical approach to the testing of the fission hypothesis, Astron. J., 82, 1013-1024, 1977.
48. Luo, A.C.J., and R.P.S. Han, The dynamics of a bouncing ball with a sinusoidally vibrating table, Nonlinear Dyn., 10, 1-18, 1996.
49. Martin, J.M., C. Donnet, T. Le Mogne, and T. Epicier, Superlubricity of molybdenum disulphide, Phys. Rev. B, 48, 10,583-10,586, 1993.
50. Mehta, A., and J.-M. Luck, Novel temporal behavior of a nonlinear dynamical model system-The completely inelastic bouncing ball, Phys. Rev. Lett., 65, 393-396, 1990.
51. Melosh, H.J., Dynamical weakening of faults by acoustic fluidization, Nature, 379, 601-606, 1996.
52. Monaghan, J.J., An introduction to SPH, Comput. Phys. Commun., 48, 89-96, 1988.
53. Monaghan, J.J., Smooth particle hydrodynamics, Annu. Rev. Astron. Astrophys., 30, 543-574, 1992.
54. Monaghan, J.J., Simulating free surface flows with SPH, J. Comput. Phys., 110, 399-406, 1994.
55. Monaghan, J.J., Gravity currents and solitary waves, Physica D, 98, 523-533, 1996.
56. Monaghan, J.J., and R.A. Gingold, Shock simulation by the particle method, J. Comput. Phys., 52, 374-389, 1983.
57. Monaghan, J.J., and R.J. Humble, Vortex particle methods for periodic channel flow, J. Comput. Phys., 107, 152-159, 1993.
58. Monaghan, J.J., and J.C. Lattanzio, A refined particle method for astrophysical problems, Astron. Astrophys., 149, 135-143, 1985.
59. National Research Council, The role of fluids in crustal processes, in Studies in Geophysics, Comm. on Gèosci., Environ, and Ressour., Nat. Acad. Press, Washington, D.C., 1990.
60. Ouillon, G., C. Castaing and D. Sornette, Hierarchical scaling of faulting, J. Geophys. Res., 101, 5477-5487, 1996.
61. Peitgen, H.-O., and D. Saupe (Eds.), The Science of Fractal Images, Springer-Verlag, New York, 1988.
62. Persson, B.N.J., and E. Tosatti (Eds.), Physics of Sliding Friction, NATO ASI Ser., 1996.
63. Pisarenko, D., and P. Mora, Velocity weakening in a dynamical model of friction, Pure Appl. Geophys., 142, 447-466, 1994.
64. Press, W.H., et al., FORTRAN Numerical Recipes, 2nd ed., Cambridge Univ. Press, New York, 1996.
65. Rice, J.R., Spatio-temporal complexity of slip on a fault, J. Geophys. Res., 98, 9885-9907, 1993.
66. Rice, J.R., and Y. Ben-Zion, Slip complexity in earthquake fault models, Proc. Natl. Acad. Sci. U.S.A., 93, 3811-3818, 1996.
67. Ruina, A., Slip instability and state variable friction laws, J. Geophys. Res., 88, 10,359-10,370, 1983.
68. Schmittbuhl, J., J.-P. Vilotte, and S. Roux, Velocity weakening friction: A renormalization approach, J. Geophys. Res., 101, 13,911-13,917, 1996.
69. Scholz, C.H., Earthquakes and friction laws, Nature, 391, 37-42, 1998.
70. Scott, D., Seismicity and stress rotation in a granular model of the brittle crust, Nature, 381, 592-595, 1996.
71. Shaw, B.E., Complexity in a spatially uniform continuum fault model, Geophys. Res. Lett., 21, 1983-1986, 1994.
72. Shaw, B.E., Fractional weakening and slip complexity in earthquake faults, J. Geophys. Res., 100, 18,239-18,251, 1995.
73. Shaw, B.E., Model quakes in the two-dimensional wave equation, J. Geophys. Res., 102, 27,367-27,377, 1997.
74. Sokoloff, J.B., Theory of dynamical friction between idealized sliding surfaces, Surf. Sci., 144, 267-272, 1984.
75. Sornette, D., Acoustic waves in random media, III, Experimental situations, Acoustica, 67, 15-25, 1989.
76. Sornette, D., P. Miltenberger, and C. Vanneste, Statistical physics of fault patterns self-organized by repeated earthquakes: Synchronization versus self-organized criticality, in Recent Progresses in Statistical Mechanics and Quantum Field Theory, Proceedings of the Conference Statistical Mechanics and Quantum Field Theory, edited by P. Bouwknegt et al., pp. 313-332, World Sci., Singapore, 1995.
77. Stauffer, D., and A. Aharony, Introduction to Percolation Theory, 2nd ed., Taylor and Francis, Bristol, Pa., 1994.
78. Stellingwerf, R.F., and C.A. Wingate, Impact modeling with smooth particle hydrodynamics, paper presented at Hypervelocity Impact Symposium, 1992.
79. Stoneham, A.M., and A.H. Harker, Purely elastic contributions to friction, Wear 80, 377-380, 1982.
80. Stoneham, A.M., M.M.D. Ramos, and A.P. Sutton, How do they stick together? The statics and dynamics of interfaces, Philos. Mag. A, 67, 797-811, 1993.
81. Streit, J.E., Low factional strength of upper crustal faults: A model, J. Geophys. Res., 102, 24,619-24,626, 1997.
82. Tanguy, A., and P. Nozières, First-order bifurcation landscape in a 2D geometry-The example of solid friction, J. Phys. I, 6, 1251-1270, 1996.
83. Tanguy, A., and S. Roux, Memory effects in friction over correlated surfaces, Phys. Rev. E, 55, 2166-2173, 1997.
84. Tillotson, J.H., Metallic equations of state for hypervelocity impact, Gen. At. Rep. GA-3216, Gen. Dyn., San Diego, Calif., 1962.
85. Tsutsumi, A., and T. Shimamoto, Frictional properties of monzodiorite and gabbro during seismogenic fault motion, J. Geol. Soc. Jpn., 102, 240-248, 1996.
86. Tsutsumi, A., and T. Shimamoto, High-velocity frictional properties of gabbro, Geophys. Res. Lett., 24, 699-702, 1997.
87. Weertman, J., Unstable slippage across a fault that separates elastic media of different elastic constants, J. Geophys. Res., 85, 1455-1461, 1980.