Abstract
Constitutive relations for fault slip are described and adopted as a basis for analyzing slip motion and its instability in the form of earthquakes on crustal faults. The constitutive relations discussed include simple rate-independent slip-weakening models, in which shear strength degrades with ongoing slip to a residual frictional strength, and also more realistic but as yet less extensively applied slip-rate and surface-state-dependent relations. For the latter the state of the surface is characterized by one or more variables that evolve with ongoing slip, seeking values consistent with the current slip rate. Models of crustal faults range from simple, single-degree-of-freedom spring-slider systems to more complex continuous systems that incorporate nonuniform slip and locked patches on faults of depth-dependent constitutive properties within elastic lithospheric plates that may be coupled to a viscoelastic asthenosphere.
Most progress for the rate and state-dependent constitutive relations is at present limited to single-degree-of-freedom systems. Results for stable and unstable slip with the various constitutive models are summarized. Instability conditions are compared for spatially uniform versus nonuniform slip, including the elastic—brittle crack limit of the nonuniform mode. Inferences of constitutive and fracture parameters are discussed, based on earthquake data for large ruptures that begin with slip at depth, concentrating stress on locked regions within a brittle upper crust. Results of nonlinear stability theory, including regimes of complex sustained stress and slip rate oscillations, are outlined for rate and state-dependent constitutive relations, and the manner in which these allow phenomena like time-dependent failure, restrengthening in nearly stationary contact, and weakening in rapidly accelerated slip, is discussed.
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References
Andrews, D. J. (1976), Rupture velocity of plane-strain shear cracks, J. Geophys. Res. 81, 5679–5687.
Boatwright, J. (1980), A spectral theory for circular seismic sources: Simple estimates of source dimensions, dynamic stress drop and radiated seismic energy, Bull. Seismol. Soc. Am. 70, 1–27.
Boatwright, J. (1984a), The effect of rupture complexity on estimates of source size, J. Geophys. Res. 89, 1132–1146.
Boatwright, J. (1984b), Seismic estimates of stress release, J. Geophys. Res. (in press).
Brace, W. F. (1972), Laboratory studies of stick-slip and their application to earthquakes, Tectonophysics 14, 189–200.
Brace, W. F., and Byerlee, J. D. (1970), California earthquakes: Why only shallow focus? Science, 168, 1573–1575.
Burridge, R., Conn, G., and Freund, L. B. (1979), The stability of rapid mode II shear crack with finite cohesive traction, J. Geophys, Res. 84, 2210–2222.
Byerlee, J. (1968), Brittle—ductile transition in rocks, J. Geophys. Res. 73, 4741–4750.
Day, S. M. (1982), Three-dimensional simulation of spontaneous rupture: The effect of nonuniform prestress, Bull. Seismol. Soc. Am. 72, 1881–1902.
Dieterich, J. H. (1972), Time-dependent friction in rocks, J. Geophys. Res. 77, 3690–3697.
Dieterich, J. H. (1978), Time dependent friction and the mechanics of stick slip, Pageoph 116, 790–806.
Dieterich, J. H. (1979a), Modeling of rock friction 1: Experimental results and constitutive equations, J. Geophys. Res. 84, 2161–2168.
Dieterich, J. H. (1979b), Modeling of rock friction 2: Simulation of preseismic slip, J. Geophys, Res. 84, 2169–2175.
Dieterich, J. H., Experimental and model study offault constitutive properties, in Solid Earth Geophysics and Geotechnology (ed. S. Nemat–Nasser) (Appl. Mech. Div., vol. 42, Am. Soc. Mech. Eng., NY 1980 ), pp. 21–30.
Dieterich, J. H., Constitutive properties offaults with simulated gouge, In Mechanical Behavior of Crustal Rocks (eds. Carter, N. L., Friedman., M., Logan, J. M., and Stearns, D. W.) (Geophys. Monogr. Ser. No. 24, Am. Geophys. Union, Washington, D.C. 1981 ) pp. 103–120.
Dmowska, R., and Li, V. C. (1982), A mechanical model of precursory source processes for some large earthquakes, Geophys. Res. Lett. 9, 393–396.
Dmowska, R., and Rice, J. R., Fracture theory and its seismological applications, in Continuum Theories in Solid Earth Physics (ed. Teisseyre, R.) (Elsevier, Amsterdam, in press, 1984).
Gu, J.-C., Rice, J. R., Ruina, A. L., and Tse, S. T. (1984), Slip motion and stability ofa single degree offreedom elastic system with rate and state dependent friction, J. Mech. Phys. Solids 32 (3).
Higgs, N. G., Mechanical properties of Ultrafine Quartz, Chlorite and Bentonite in environments appropriate to upper-crustal earthquakes (Ph. D. Thesis, Texas A and M University, August 1981 ).
Ida, Y. (1972), Cohesive force across the tip of a longitudinal shear crack and Griffith’s specific surface energy, J. Geophys. Res. 77, 3796–3805.
Ida, Y. (1973), The maximum acceleration of seismic ground motion, Bull. Seismol. Soc. Am. 63, 959–968.
Li, V. C., and Rice, J. R. (1983a), Preseismic rupture progression and great earthquke instabilities at place boundaries, J. Geophys. Res. 88, 4231–4246.
LI, V. C., andRlcE, J. R. (1983b), Precursory surface deformation in great plate boundary earthquake sequences, Bull. Seismol. Soc. Am. 73, 1415 –1434.
Lockner, D. A., Okubo, P. G., and Dieterich, J. H. (1982), Containment ofstick-slip failures on a simulated fault by pore fluid injection, Geophys. Res. Lett. 9, 801–804.
Mavxo, G. M. (1980), Simulation of creep events and earthquakes on a spatially variable model (abstr), Eos, Trans. Am. Geophys. Union 61, 1120.
Mavxo, G. M. (1984), Large-scale earthquakes from a laboratory friction law, J. Geophys. Res. (in press).
Mcgarr, A. (1984), Scaling of ground motion parameters, state of stress and focal depth, J. Geophys. Res. (in press).
Okubo, P. G., and Dieterich, J. H. (1981), Fracture energy of stick-slip events in a large scale biaxal experiment, Geophys, Res. Lett. 8, 887–890.
Palmer, A. C., and Rice, J. R. (1973), The growth of slip surfaces in the progressive failure of overconsolidated day slopes, Proc. R. Soc. Lond., A332, 527.
Rabinowicz, E. (1958), The intrinsic variables affecting the stick slip process, Proc. Phys. Soc. 71, 665–675.
Rice, J. R., The mechanics ofearthquake rupture, In Physics of the Earth’s Interior (Proceedings of the International School of Physics `Enrico Fermi’, Course 78, 1979 ) (ed. Dziewonski, A. M., and Boschi, E.) (Italian Physical Society, printed by North Holland, Amsterdam 1980 ) pp. 555–649.
Rice, J. R., Shear instability in relation to the constitutive description offault slip, in Rockbursts and Seismicity in Mines (eds. Gay, N. C. and E. H. Wainwright) (Symp. Ser. No. 6, South African Institute of Mining and Metallurgy, Johannesburg, 1984 ), pp. 57–62.
Rice, J. R., and Gu, J.-C. (1983), Earthquake aftereffects and triggered seismic phenomena, Pure Appl. Geophys. 121 (2).
Rice, J. R., and Ruina, A. L. (1983), Stability of steady frictional slipping, Trans. Asme, J. Appl. Mech. 50, 343–349.
Rudnicki, J. W. (1980), Fracture mechanics applied to the earth’s crust, Annu. Rev. Earth Planet. Sci. 8, 489–525.
Ruina, A. L., Friction Laws and Instabilities: A Quasistatic Analysis of Some Dry Frictional Behavior (Brown University, Ph. D. Thesis, 1980 ).
Ruina, A. L. (1983), Slip instability and state variable friction laws, J. Geophys. Res. (in press).
Stesky, R. M. (1978), Mechanisms of high temperature frictional sliding in Westerly granite. Can. J. Earth Sci. 15, 361–375.
Stuart, W. D. (1979a), Strain softening prior to two-dimensional strike slip earthquakes, J. Geophys. Res. 84, 1063–1070.
Stuart, W. D. (1979b), Strain-softening instability model for the San Fernando earthquake, Science 203, 907–910.
Stuart, W. D., and Mavko, G. M. (1979), Earthquake instability on a strike-slip fault, J. Geophys, Res. 84, 2153–2160.
Tullis, T. E., and J. D. Weeks, (1983), Increase in frictional strength of granite during static contact (abstr), Eos, Trans. Am. Geophys. Union 64, 317.
Wong, T. -F. (1982), Shear fracture energy of Westerly granite from post failure behavior, J. Geophys. Res. 87, 990–1000.
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Rice, J.R. (1983). Constitutive Relations for Fault Slip and Earthquake Instabilities. In: Knopoff, L., Keilis-Borok, V.I., Puppi, G. (eds) Instabilities in Continuous Media. Contributions to Current Research in Geophysics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6608-8_7
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DOI: https://doi.org/10.1007/978-3-0348-6608-8_7
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