Modelling contact problems with friction in fault mechanics

Bielski, W. R.; Telega, J. J.

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Modelling contact problems with friction in fault mechanics

Autorzy

Bielski W. R. , Telega J. J.

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httpwww_ptmts_org_pl2001-3-bielski-t.pdf

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Abstrakty

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 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-boudary 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.

Modelowanie zagadnień kontaktowych z tarciem w mechanice uskoków geologicznych. Cel pracy jest dwojaki. Po pierwsze, omówiono modeletarcia stosowane w geofizyce. Modele te obejmują tarcie zależne od strun, prędkości i poślizgu. Po drugie, zaproponowano nowy opis tarcia w języku nowoczesnej mechaniki kontaktu, wprowadzając prawa poślizgu wiążące naprężenie poślizgu z prędkością poślizgu. Prawa poślizgu sformułowano w postaci subróżniczkowej. Zagadnienia początkowo-brzegowe sformułowano w postaci silnej i wariacyjnej. Stosując funkcję Greena zaproponowano sformułowanie wariacyjne pozwalające wyznaczyć normalne i styczne naprężenia kontaktowe.

Słowa kluczowe

fault mechanics friction contact laws state variables

Wydawca

Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej

Czasopismo

Journal of Theoretical and Applied Mechanics

Rocznik

2001

Tom

Vol. 39 nr 3

Strony

475--505

Opis fizyczny

Bibliogr. 85 poz., rys.

Twórcy

autor

Bielski W. R.

wbielski@igf.edu.pl

Institute of Geophysics, Polish Academy of Sciences

autor

Telega J. J.

jtelega@ippt.gov.pl

Institute of Fundamental Technological Research, Polish Academy of Sciences

Bibliografia

1. BEELER N.M., TULLIS T.E., BLANPIED M.L., WEEKS J.D., 1996, Frictional Behavior of Large Displacement Experimantal Faults, J. Geophys. Res., 101, 8697-8715.
2. BEN-ZION Y., RICE J.R., 1995, Slip Patterns and Earthquake Populations Along Different Classes of Faults in Elastic Solids, J. Geophys. Res., 100, 12959-12983.
3. BEN-ZION Y., RICE J.R., 1997, Dynamic Simulations of Slip on a Smooth Fault in an Elastic Solid, J. Geophys. Res., 102, 17771-17784.
4. BEROZA G., MIKUMO T., 1996, Short Slip Duration in Dynamic Rupture in the Presence of Heterogeneous Fault Properties, J. Geophys. Res., 101, 22449-22460.
5.BIELSKI W.R., TELEGA J.J., 1985, A Contribution to Contact Problem for a Class of Solids and Structures, Arch. Mech., 37, 303-320.
6. BIELSKI W.R., TELEGA J.J., 1994, Friction on Geological Faults: Modelling and Variational Formulation of Initial-Boundary Value Problems, IFTR Reports, 31, in Polish.
7. BIELSKI W.R., TELEGA J.J., 2000, A Contribution to Modelling of Friction on Tectonic Faults, Bull Pol. Acad, Sci, Ser. Earth Sci., 48, 33-43.
8. BLANPIED M.L., TULLIS T.E., WEEKS J.D., 1998, Effects of Slip, Slip Rate, and Shear Heating on the Friction of Granite, J. Geophys. Res., 103, 489-511.
9. BOATWRIGHT J., COCCO J., 1996, Frictional Constraints on Crustal Faulting, J. Geophys. Res., 101, 13895-13909.
10. BRACE W.F., BYERLEE J.D., 1966, Stick Slip as a Mechanism for Earthquakes, Science, 153, 990-992.
11. BROWN S.R., 1998, Frictional Healing on Faults: Stable Sliding Versus Stick Slip, J. Geophys. Res., 103, 7413-7420.
12. BROGLIATO B., 1999, Nonsmooth Mechanics, Springer, London.
13. BYERLEE J.D., 1970, The Mechanics of Stick-Slip, Tectonophysics, 9, 475-486.
14. BYERLEE J.D., 1978, Friction of Rocks, Pageoph., 116, 615-626.
15. CAMPILLO M., IONESCU I.R., 1997, Initiation of Antiplane Shear Instability Under Slip Dependent Friction, J. Geophys. Res., 102, 20363-20371.
16. CAMPILLO M., IONESCU I.R., PAUMIER J.C., RENARD Y., 1996, On the Dynamic Sliding with Friction of a Rigid Block and of an Infinite Elastic Slab, Phys. Earth and Planetary Interiors, 96, 15-23.
17. CAO T., AKI K., 1986, Seismicity Simulation with a Rate- and State-Dependent Friction Law, Pageoph, 124, 487-513.
18. CHESTER F.M., 1994, Effects of Temperature on Friction: Constitutive Equations and Experiments with Quartz Gouge, J. Geophys. Res., 99, 7247-7261.
19. COCHARD A., MADARIAGA R., 1994, Dynamic Faulting Under Rate-Dependent Friction, Pageoph, 142, 419-445.
20. COCHARD A., RICE J.R., 2000, Fault Rupture Between Dissimilar Materials: Ill-posedness, Regularization, and Slip-Pulsed Response, J. Geophysical Res., preprint.
21. COTTON F., CAMPILLO M., 1995, Frequency Domain Inversion of Strong Motions: Application to the 1992 Landers Earthquake, J. Geophys. Res., 100,3961-3975.
22. DASCALU C., IONESCU I.R., CAMPILLO M., 2000, Fault Finiteness and Initiation of Dynamic Shear Instability, Earth and Planetary Science Letters, 177,163-176.
23. DIETERICH J.H., 1972, Time Dependent Friction in Rocks, J. Geophys. Res.,77, 3690-3797.
24. DIETERICH J.H., 1978, Time-Dependent Friction and the Mechanics of Stickslip, Pure. Appl. Geophys., 116, 790-806.
25. DIETERICH J.H., 1979, Modeling of Rock Friction 1. Experimental Results and Constitutive Equations, J. Geophys. Res., 84, 2161-2168.
26. DIETERICH J.H., 1992, Earthquake Nucleation on Faults with Rate- and State-Dependent Strength, Tectonophysics, 211, 115-134.
27. DIETERICH J.H., CONRAD G. , 1984, Effect of Humidity on Time- and Velocity-Dependent Frictions in Rocks, J. Geophys. Res., 89, 4196-4202.
28. DIETERICH J.H., KILGORE B.D., 1994, Direct Observations of Frictional Contact: New Insights for State-Dependent Properties, Pageoph, 143, 283-302.
29. FAVREAU P., CAMPILLO M., IONESCU I.R., 1999, Initiation of In-Plane Shear Instability under Slipp-Dependent Friction, Bull., Seism. Soc. Amer., 89, 1280-1295.
30. FUKUYAMA E., MADARIAGA R., 1998, Rupture Dynamics of a Planar Fault in a 3D Elastic Medium: Rate- and Slip-Weakening Friction, Bull. Seism. Soc. Amer. , 88, 1-17.
31. IDE S., TAKEO M., 1997, Determination of Constitutive Relations of Fault Slip Based on Seismic Wave Analysis, J.Geophys. Res., 102, 27379-27391.
32. IIO Y., 1997, Frictional Coefficient on Faults in a Seismogenic Region Inferred from Earthquake Mechanism Solutions, J. Geophys. Res. , 102, 5403-5412.
33. IONESCU I.R., CAMPILLO M., 1996, On the Contact Problem with Slip Displacement Dependent Friction in Elastostatics, Int. J. Engng. Sci. , 34, 471-491.
34. IONESCU I.R., CAMPILLO M., 1999, Influence of the Shape of the Friction Law and Fault Finitness on the Duration if Initiation, J. Geophys. Res., 104, 3013-3024.
35. IONESCU I.R., PAUMIER J.-C., 1997, Instabilities in Slip Dependent Friction, ESAIM: Proc., 2, 99-111, URL: http://www.emath.fr/proc/Vol2/.
36. JAEGER J.C., COOK N.G.W., 1976, Fundamentals of Rock Mechanics, 2nd ed., London, Chapman and Hall.
37. JOHANSSON L., 1992, Elastic and Thermoelastic Contact Problems with Friction and Wear, Linkoping Studies in Science and Technology, Dissertation No. 266, Linkoping.
38. KILGORE B.D., BLANPIED M.L., DIETERICH J.H., 1993, Velocity and Normall Stress Depend Friction of Granite, Geophys. Res. Lett., 20, 903-906.
39. KING G.C.P., COCCO M., 2001, Fault Interaction by Elastic Stress Changes: New Clues from Earthquake Sequences, in: Advances in Geophysics, edit. by Dmowska R., and Saltzman B., 44, 1-38, Acadamic Press, San Diego.
40. LAPUSTA N., RICE J.R., BEN-ZION Y., ZHENG G., 2000, Elastodynamic Analysis for Slow Tectonic Loading with Spontaneous Rupture Episodes on Faults with Rate- and State-Dependent Friction, J. Geophys. Res., 105, 23765-23789.
41. LOCKNER D. A., 1998, A Generalized Law for Brittle Deformation of Westerly Granite, J. Geophys. Res. , 103, 5107-5123.
42. MADARIAGA R., OLSEN K., ARCHULETA R., 1998, Modeling Dynamic Rupture in a 3D Earthquake Fault Model, Bull. Seism. Soc. Am. , 88, 1182-1197.
43. MAIR K., MARONE C., 1999, Friction of Simulated Fault Gouge for a Wide Range of Velocities and Normal Stresses, J. Geophys. Res. , 104, 28899-28898.
44.MORROW C.A., MOORE D.E., LOCKNER D.A., 2000, The Effect of Mineral Bond Strength and Absorbed Water on Fault Gouge Frictional Strength, Geophys. Res. Lett., 27, 815-818.
45. NIELSEN S.B., CARLSON J.M., OLSEN K.B., 2000, Influence of Friction and Fault Geometry on Earthquake Rupture, J. Geophys. Res., 105, 6069-6088.
46. OKUBO P.G., 1989, Dynamic Rupture Modeling with Laboratory-Derived Constitutive Relations, J. Geophys. Res., 94, 12321-12335.
47. OGLESBYD.D., ARCHULETA R.J., NIELSEN S.B., 2000, The Dynamics of Dip-Slip Faulting: Exploration in Two Dimensions, J. Geophys. Res., 105, 13643-13653.
48. OLSEN M.P., SCHOLZ C.H., LEGER A., 1998, Healing and Scaling of a Simulated Fault Gouge Under Hydrothermal Conditions: Implications for Fault Healing, J. Geophys. Res., 103, 7421-7430.
49. PLACE D., MORA P., 1999 The Lattice Solid Model to Simulate the Physics of Rocks and Earthquakes: Incorporation of Friction, J. Comput. Phys., 150, 332-372.
50. PANAGIOTOPOULOS P.D., 1993, Hemivariational Inequalities: Applications to Mechanics and Engineering, Springer-Verlag, Berlin.
51. PERRIN G.J., RICE J.R., ZHENG G., 1995, Self-Healing Slip Pulse on a Frictional Surface, J. Mech. Phys. Solids, 43, 1461-1495.
52. PRESS F, SIEVER R., 1986, Earth, Freeman and Company, New York.
53. RABINOWICZ E., 1965, Friction and Wear of Materials, John Wiley, New York.
54. RANJITH K., RICE J.R., 2001, Slip Dynamics at an Interface Between Dissimilar Materials, J. Mech. Phys. Solids, 49, 2, 341-361.
55. RICE J.R., 1983, Constitutive Relations for Fault Slip and Earthquake Instabilities, Pageoph, 121, 443-475.
56. RICE J.R., 1993, Spatio-Temporal Complexity of Slip on a Fault, J. Geophys. Res., 98, 9885-9907.
57. RICHARDSON E., MARONE C., 1999, Effects of Normal Stress Vibration on Frictional Healing, J. Geophys. Res., 104, 28859-28878.
58. ROCKAFELLAR R.T., 1970, Convex Analysis, Princeton, New Jersey, Princeton University Press.
59. ROWSHANDEL B., NEMAT-NASSER S., 1986, A Mechanical Model for Deformation and Earthquakes on Stroke-slip Faults, Pageoph, 124, 531-566.
60. ROY M., MARONE C., 1996, Earthquake Nucleation on Model Faults with Rate- and State-Dependent Friction: Effects of Inertia, J. Geophys. Res., 101, 13919-13932.
61. RUDNICKI J., Wu M., 1995, Mechanics of Dip-Slip Faulting in an Elastic Half-Space, J. Geophys. Res., 100, 22173-22186.
62. RUINA A.L., 1980, Friction Laws and Instabilities: A Quasistatic Analysis of Some Dry Frictional Behaviour, Ph.D. Division of Engineering, Brown University.
63. RUINA A.L., 1983, Slip Instability and State Variable Friction Laws, J. Geophys. Res., 88, 10359-10370.
64. RYBICKI K.R., 1992, Strike-Slip Faulting in the Presence of Low-Rigidity In-homogeneities, Bull. Seism. Soc. Am., 82, 2170-2190.
65. SAVAGE J.C., LOCKNER D.A., BYERLEE J.D., 1996, Failure in Laboratory Fault Models in Triaxial Tests, J. Geophys. Res., 101, 22215-22224.
66. SCHOLZ C.H., 1994, The Mechanics of Earthquakes and Faulting, Cambridge University Press.
67. SCHOLZ C.H., 1998, Earthquakes and Friction Laws, Nature, 391, 37-42.
68. SCHOLZ C.H., 1996, Faults without Friction?, Nature, 381, 556-557.
69. SEGALL P., RICE J.R., 1995, Dilatency, Compaction, and Slip Instability of a Fluid-Infiltrated Fault, J. Geophys. Res., 100, 22155-22171.
70. SENATORSKI P., 2000a, Model of Earthquake Cycles with Slip-Dependent Constitutive Law. Part I-Theory, Acta Geophys. Pol., 48, 299-316.
71. SENATORSKI P., 2000b, Model of Earthquake Cycles with Slip-Dependent Constitutive Law. Part II-Simulation, Acta Geophys. Pol., 48, in press Acta Geophys. Pol.
72. SHILLOR M., SOFONEA M., TELEGA J.J., 2002, Advances in Variational Solution of Quasistatic Contact Problems, Appl. Mech. Rev., in preparation.
73. SLEEP N.H., 1995, Frictional Heating and the Stability of Rate and State Dependent Frictional Sliding, Geophys. Res. Letters, 22, 2785-2788.
74. SLEEP N.H., 1997, Application of a Unified Rate and State Dependent Friction Theory to the Mechanism of Fault Zones with Strain Localization, J. Geophys. Res., 102, 2875-2895.
75. SLEEP N.H., 1998, Rate Dependent Rate and State Friction, J. Geophys. Res., 103, 7111-7119.
76. SLEEP N.H., 1999, Effects of the Extrusion of Fault Gouge on Frictional Sliding, J. Geophys. Res., 104, 23023-23032.
77. TEISSEYRE R., 1985, Continuum Theories in Solid Earth Physics, PWN and Elsevier, Warszawa-Amsterdam.
78. TEISSEYRE R., (edit.), 1995, Theory of Earthquake Premonitory and Fracture Processes, Polish Scientific Publishers PWN, Warszawa.
79. TEISSEYRE R., MAJEWSKI E., (edit.), 2001, Earthquake Thermodynamics and Phase Transitions in the Earth's Interior, Academic Press, San Diego.
80. TELEGA J.J., 1988, Topics on Unilateral Contact Problems of Elasticity and Inelasticity, in: Nonsmooth Mechanics and Applications, J.J. Moreau, P. D. Panagiotopoulos (edit.), Springer-Verlag Wien-New York, 341-462.
81. TELEGA J.J., 1991, Quasi-Static Signorini's Contact Problems with Friction and Duality, in: International Series of Numerical Mathematics, 101, Birkhauser, 199-214.
82. TURCOTTE D.L., SCHUBERT G., 1982, Geodynamics: Applications of Continuum Physics to Geological Problems, John Wiley, New York.
83. VLADIMIROV V.S., 1984, Equations of Mathematical Physics, Mir Publishers Moscow.
84. WEEKS J., TULLIS T., 1985, Frictional Sliding of Dolomite: A Variation in Constitutive Behavior, J. Geophys. Res., 90, 7821-7826.
85. ZHENG G., RICE J.R., 1998, Conditions Under which Velocity-Weakening Friction Allows a Self-Healing Versus a Cracklike Mode of Rupture, Bull. Seism. Soc. Am., 88, 1466-1483.

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