Abstract
A two-dimensional planar crack which propagates along its self-plane is taken as the fault model. The static solution of the classic (linear elastic fracture mechanics) model for this study for three types of two-dimensional cracks are obtained by means of degeneration method based on the dynamic solution obtained by Kostrov (1975). The degeneration method used in this study has two points of convenience: 1 One can obtain the solutions of different types of cracks by using the unified method; 2 It is avoided to use displacement potential and stress function which physical meaning is not straight. The results obtained in this paper are just the same as that obtained by previous authors who solved the equilibrium equations by means of integral transform method. It is showed that: 1 The static solution cannot be separated from the dynamic one, because the static solution also has the meaning of duration time. 2 Both the static and the dynamic solutions of a critical crack must satisfy the same criteria, and the evolution from static to dynamic solution must be associated with some additional disturbance. Particularly, the quantity of disturbance in some form has to be imposed when a critical crack is ready to initiate.
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References
Aki, K. and Richards, P. G., 1980.Quantitative Seismology, Theory and Methods, 884–894. Freeman, W. H., San Francisco.
Andrews, D. J., 1976. Rupture velocity of plane-strain shear cracks.J. Geophys. Res.,81, 5679–5687.
Chen, X. X. and Chen, Y. T., 1985. The earthquake fault in inhomogenious stress field (abstract).Seismological Research in Fujian,6, 1/2, 25.
Chen, Y. T. and Knopoff, L., 1986. Static shear crack with a zone of slip weakening.Geophys. J. R., astr. Soc.,87, 1005–1024.
Chen, Y. T., Chen X. F. and Knopoff, L., 1987. Spontaneous growth and autonomous contraction of a two-dimensional earthquake fault. In: Wesson, R. (ed.) Mechanics of Earthquake Faulting.Techtonophysics,144, 5–17.
Chen, Y. Z., 1989. Crack problems in plate elasticity under antisymmetric loading.Int. J. Frac.,41, 2, R29-R34.
Chen, Y. T. and Wang, Z., 1989. Dynamic propagation of a two-dimensional earthquake fault with a slip weakening zone. Editorial Committee of Chinese Journal of Geophysics (Ed).Geophysics in China in the Eighties—In Commemoration of the 80th Birthday of Professor Fu Cheng-Yi. Academic Books and Periodicals Press (in Chinese).
Knopoff, L., 1958. Energy release in earthquake.Geophys. J. R. aster. Soc.,1, 44–52.
Kostrov, B. V., 1966. Unsteady propagation of longitudinal shear cracks.Journal of Applied Mathematics and Mechamics,30: 1241–1248.
Kostrov, B. V., 1975. On the crack propagation with variable velocity.Int. J. Frac.,11, 47–56.
Li, S. Y., 1991.Spontaneous Propagation of An In-Plane Shear Fault, 138–141. Ph.D. thesis, Institute of Geophysics, SSB.
Sneddon, I. N. and Lowengrub, M., 1969.Crack Problems in the Classical Theory of Elasticity, 16–39. John Wiley & Sons, Inc. New York.
Starr, A. T., 1928. Slip on a crystal and rupture in a solid due to shear.Proc. Camb. Phil. Soc.,24, 489–500.
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Contribution No. 94A0007, Institute of Geophysics, SSB, China.
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Li, SY., Chen, YT. Static solution of a crack degenerated from dynamic solution of a propagating crack. Acta Seismologica Sinica 7, 389–395 (1994). https://doi.org/10.1007/BF02650676
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DOI: https://doi.org/10.1007/BF02650676