Abstract
A mathematical model is presented for the unstable deformation of rock along an existing fracture in it. It is shown that this process is essentially nonlinear and can be described by the Gordon equation. An analysis is made for the influence of geometric irregularities and friction of the contact surfaces on the evolution of the velocity of solitary slip waves which are caused by local deformation effects and propagate along the fracture.
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References
M. V. Kurlenya, V. N. Oparin, and V. I. Vostrikov, “Effect of anomalously low friction in block media,”Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 1 (1997).
R. Burridge and L. Knopoff, “Model and theoretical seismicity,” Bull. Seismol. Soc. Am.,57 (1967).
J. S. Langer and C. Tang, “Rupture propagation in a model of an earthquake fault,”Phys. Rev. Lett.,67, No. 8 (1991).
J. M. Carlson and J. S. Langer, “Mechanical model of an earthquake fault,”Phys. Rev. A 40, No. 11 (1989).
H. Nakanishi, “Earthquake dynamics driven by a viscous fluid,”ibid. Phys. Rev. A,46, No. 8 (1992).
J. M. Carlson, “Time intervals between characteristic earthquakes and correlations with smaller events: An analysis based on a mechanical model of a fault,”J. Geophys. Res.,96, No. B3 (1991).
F. M. Chester, “Effects of temperature on friction: constitutive equations and experiments with quartz gouge,”J. Geophys. Res.,99, No. B4 (1994).
J. H. Dieterich, “Earthquake nucleation on faults with rate-and state-dependent strength,”Tectonophysics,211, No. 1-4 (1992).
G. A. Sobolev, Kh. Shpettsler, and A. V. Koltsov, “Certain properties of unstable slip along an uneven fracture,” in:Physics of Rocks at High Pressures [in Russian], Nauka, Moscow (1991).
M. Solerno, M. P. Soerensen, O. Skovgaard, and P. L. Christiansen, “Perturbation theories for sine-Gordon soliton dynamics,”Wave Motion,5, No. 1 (1983).
D. McLaughlin and E. Scott, “Multi-soliton perturbation theory,” in:Solitons in Action [Russian translation], K. Longren and E. Scott (eds.), Mir, Moscow (1981).
V. G. Bykov, “Aspects of the formation of solitary seismic waves in grainy geomaterials,”Fiz.-Tekh. Probl. Razrab. Polezn. Iskop. No. 2 (1996).
J. Forsyth, M. Malcolm, and K. Mowler,Machine Methods of Mathematical Calculation [Russian translation], Mir, Moscow (1980).
B. Shibazaki and M. Matsu'ura, “Transition process nucleation to high-speed rupture propagation: scaling from stick-slip experiments to natural earthquakes,”.Geophys. J. Int.,132, No. 1 (1998).
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Institute of Tectonics and Geophysics, Far East Branch, Russian Academy of Sciences, Khabarovsk, Russia. Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 3, pp. 64–70, May–June, 2000
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Bykov, V.G. Mathematical modeling of slip in a rock along the uneven fracture. J Min Sci 36, 253–258 (2000). https://doi.org/10.1007/BF02562527
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DOI: https://doi.org/10.1007/BF02562527