Dynamics and scaling characteristics of shear crack propagation

Pure and Applied Geophysics

Volumn 157, Issue 4, 2000, Pages 523-538

  Silberschmidt, Vadim V ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Crack propagation; Crack damage interaction; Earthquakes; Scaling; Shear crack; Shear damage

Indexed keywords

CONTINUUM MECHANICS; CRACK PROPAGATION; EARTHQUAKE RUPTURE; FAULTING; FRACTURE MECHANICS; SCALE EFFECT; SHEAR;

EID: 0034077835     PISSN: 00334553     EISSN: None     Source Type: Journal    
DOI: 10.1007/978-3-0348-8430-3_3     Document Type: Conference Paper

References (36)

1. ALLÈGRE, C. J., LE MOUËL, J. L., CHAU, H. D., and NARTEAU, H. (1995), Scaling Organization of Fracture Tectonics (SOFT) and Earthquake Mechanism, Phys. Earth Planet. Inter. 92, 215-233.
2. BURRIDGE, R., and KNOPOFF, L. (1967), Model and Theoretical Seismicity, Bull. Seismol. Soc. Am. 57, 341-371.
3. CHEN, K., BHAGAVATULA, R., and JAYAPRAKASH, C. (1997), Earthquakes in Quasistatic Models of Fracture in Elastic Media: Formalism and Numerical Techniques, J. Phys. A: Math. Gen. 30, 2297-2315.
4. CHHABRA, A. B., MANEVEAU, C., JENSEN, R. V., and SREENIVASAN, K. R. (1989), Direct Determination of f(α) Singularity Spectrum and its Application to Fully Developed Turbulence, Phys. Rev. A 40, 5284-5293.
5. COWIE, P. A., and SCHOLZ, C. H. (1992), Growth of Faults by Accumulation of Seismic Slip, J. Geophys. Res. 97, 11,085-11,095.
6. CURTIN, W. A., and SCHER, H. (1997), Time-dependent Damage Evolution and Damage in Materials. I. Theory, Phys. Rev. B 55, 12,038-12,050.
7. CURTIN, W. A. (1998), Size Scaling of Strength in Heterogeneous Materials, Phys. Rev. Lett. 80, 1445-1448.
8. EVERTSZ, C. J. G., and MANDELBROT, B. B., Multifractal measures. In Chaos and Fractals. New Frontiers of Science (eds. Peitigen, H. O., Jürgens, H., and Saupe, D.) (Springer, Berlin 1992) pp. 921-953.
9. FRÖHLICH, C., and DAVIS, S. D. (1993), Teleseismic b Values; or, Much Ado about 1.0, J. Geophys. Res. 98, 631-644.
10. GROLEAU, D., BERGERSEN, B., and XU, H.-J. (1997), Scaling Properties of a Model for Ruptures in an Elastic Medium, J. Phys. A: Math. Gen. 30, 3407-3419.
11. GUTENBERG, B., and RICHTER, F., Seismicity of the Earth and Associated Phenomena (Princeton University 1954).
12. HALSEY, T. C., JENSEN, M. H., KADANOFF, L. P., PROCACCIA, I., and SHRAIMAN, B. I. (1986), Fractal Measures and Their Singularities: The Characterisation of Strange Sets, Phys. Rev. A 33, 1141-1151.
13. HERRMANN, H. J., and ROUX, S., Statistical Models for the Fracture of Disordered Media (North Holland, Amsterdam 1990).
14. KACHANOV, L. M., Introduction to Continuum Damage Mechanics (Nijhoff, Dordrecht, The Netherlands 1986).
15. KAGAN, Y. Y. (1991), Seismic Moment Distribution, Geophys. J. Int. 106, 123-134.
16. KAGAN, Y. Y. (1994), Observational Evidence for Earthquakes as a Nonlinear Dynamic Process, Physica D 77, 160-192.
17. KAGAN, Y. Y. (1997), Seismic-moment - Frequency Relation for Shallow Earthquakes: Regional Comparison, J. Geophys. Res. 102, 2835-2852.
18. KRAJCINOVIC, D., Damage Mechanics (Elsevier, Amsterdam 1996).
19. LEMAITRE, J., and CHABOCHE, J.-L., Mechanics of Solid Materials (Cambridge University Press, Cambridge 1990).
20. LYAKHOVSKY, V., BEN-ZION, Y., and AGNON, A. (1997), Distributed Damage, Faulting, and Friction, J. Geophys. Res. 102, 27,635-27,649.
21. LIEBOWITZ, H. (ed.), Fracture, Vol. I-VII (Academic Press, New York 1968-1972).
22. MURAKAMI, Y., Stress Intensity Factors Handbook (Pergamon Press, Oxford 1987).
23. SAHIMI, M., and ARBABI, S. (1996), Scaling Laws for Fracture of Heterogeneous Materials and Rock, Phys. Rev. Lett. 77, 3689-3692.
24. SCHOLZ, C. H., Earthquakes and faulting: self-organized critical phenomena with a characteristic dimension. In Spontaneous Formation of Space-time Structures and Criticality (eds. Riste, T., and Sherrington, D.) (Kluwer Academic Press, Amsterdam 1991) pp. 41-56.
25. SCHOLZ, C. H., Fractal transitions on geological surfaces. In Fractals in the Earth Sciences (eds. Barton, C. C., and La Pointe, P. R.) (Plenum Press, New York 1995) pp. 131-140.
26. SCHOLZ, C. H. (1997), Scaling Properties of Faults and Their Populations, Int. J. Rock, Mech. and Min. Sci. 34, paper No. 273.
27. SCHOLZ, C. H., DAWERS, N. H., YU, J.-Z., ANDERS, M. H., and COWIE, P. A. (1993), Fault Growth and Fault Scaling Laws: Preliminary Results, J. Geophys. Res. 98, 21,951-21,961.
28. SILBERSCHMIDT, V. V. (1992). The Fractal Characterization of Propagating Cracks, Int. J. Fracture 56, R33-R38.
29. SILBERSCHMIDT, V. V. (1993). Analysis of rock fracture under the localization of shear deformations. In Assessment and Prevention of Failure Phenomena in Rock Engineering (eds. Pasamehmetoglu, A. G., Kawamoto, T., Whittaker, B. N., and Aydan. Ö.) (A.A. Balkema, Rotterdam/Brookfield 1993) pp. 143-148.
30. SILBERSCHMIDT, V. V., Fractal characteristics of joint development in stochastic rocks. In Fractals and Dynamic Systems in Geoscience (ed. Kruhl, J. H.) (Springer-Verlag, Berlin 1994) pp. 65-76.
31. SILBERSCHMIDT, V. V. (1996), Fractal Approach in Modelling of Earthquakes, Geol. Rundsch. 85, 116-123.
32. SILBERSCHMIDT, V. V. (1998), Analysis of Shear Damage Accumulation, Int. J. Damage, Mech. 7, in press.
33. SILBERSCHMIDT, V. V., and CHABOCHE, J.-L. (1994a), Effect of Stochasticity on the Damage Accumulation in Solids, Int. J. Damage Mech. 3, 57-70.
34. SILBERSCHMIDT, V. V., and CHABOCHE, J.-L. (1994b), The Effect of Material Stochasticity on Crack-damage Interaction and Crack Propagation, Eng. Fract. Mech. 48, 379-387.
35. SILBERSCHMIDT, V. V., and SILBERSCHMIDT, V. G. (1990). Fractal Models in Rock Fracture Analysis, Terra Nova 2, 483-487.
36. XU, H.-J., BERGERSEN, B., and CHEN, K. (1992), Sell-organized Ruptures in an Elastic Medium: A Possible Model for Earthquakes, J. Phys. A: Math. Gen. 25. L1251-1258.