Continuum mathematical modeling of slip weakening in geological systems

Journal of Geophysical Research: Solid Earth

Volumn 112, Issue 4, 2007, Pages

  Borja, Ronaldo I ^a   Foster, Craig D ^a  

^a Stanford University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; CONTINUUM MECHANICS; FINITE ELEMENT METHOD; FRICTION; NUMERICAL MODEL; SHEAR STRAIN; SLIP;

EID: 34250652372     PISSN: 21699313     EISSN: 21699356     Source Type: Journal    
DOI: 10.1029/2005JB004056     Document Type: Article

References (54)

1. Anderson, E. M. (1951), The Dynamics of Faulting and Dyke Formation with Application to Britain, Oliver and Boyd, White Plains, N. Y.
2. Aydin, A., R. I. Borja, and P. Eichnubl (2006), Geological and mathematical framework for failure modes in granular rock, J. Struct. Geol., 28, 83-98.
3. Barenblatt, G. I. (1962), The mathematical theory of equilibrium cracks in brittle fracture, Adv. Appl. Mech., 7, 55-129.
4. Ben-Zion, Y., and J. R. Rice (1997), Dynamic simulation of slip on a smooth fault in an elastic solid, J. Geophys. Res., 102, 17,771-17,784.
5. Bilby, B. A., A. H. Cottrell, and K. H. Swindon (1963), The spread of plastic yield from a notch, Proc. R. Soc. London, Ser. A, 272, 304-314.
6. Bolt, B. A. (1970), Causes of earthquakes, in Earthquake Engineering, edited by R. L. Wiegel, pp. 21-45, Prentice-Hall, Upper Saddle River, N. J.
7. Borja, R. I. (2000), A finite element model for strain localization analysis of strongly discontinuous fields based on standard Galerkin approximations, Comput. Methods Appl. Mech. Eng., 190(11-12), 1529-1549.
8. Borja, R. I. (2002), Finite element simulation of strain localization with large deformation: Capturing strong discontinuity using a Petrov-Galerkin multiscale formulation, Comput. Methods Appl. Mech. Eng., 191(27-28), 2949-2978.
9. Borja, R. I. (2004), Computational modeling of deformation bands in granular media, II: Numerical simulations, Comput. Methods Appl. Mech. Eng., 193(27-29), 2699-2718.
10. Borja, R. I., and A. Aydin (2004), Computational modeling of deformation bands in granular media, I: Geological and mathematical framework, Comput. Methods Appl. Mech. Eng., 193(27-29), 2667-2698.
11. Borja, R. I., and R. A. Regueiro (2001), Strain localization of frictional materials exhibiting displacement jumps, Comput. Methods Appl. Mech. Eng., 190(20-21), 2555-2580.
12. Campillo, M., and I. R. Ionescu (1997), Initiation of antiplane shear instability under slip dependent friction, J. Geophys. Res., 102, 20,363-20,371.
13. Chester, F. M., and N. G. Higgs (1992), Multi-mechanism friction constitutive model for ultra-fine quartz gouge at hypocentral conditions, J. Geophys. Res., 97, 1859-1870.
14. Dieterich, J. H. (1979), Modeling of rock friction: 1. Experimental results and constitutive equations, J. Geophys. Res., 84, 2161-2168.
15. Dieterich, J. H., and B. D. Kilgore (1996), Imaging surface contacts: power law contact distributions and contact stresses in quartz, calcite, glass and acrylic plastic, Tectonophysics, 256, 219-239.
16. Dieterich, J. H., and M. F. Linker (1992), Fault stability under conditions of variable normal stress, Geophys. Res. Lett., 19(16), 1691-1694.
17. Dugdale, D. S. (1960), Yielding of steel sheets containing slits, J. Mech. Phys. Solids, 8, 100-104.
18. Evans, B., J. T. Fredrich, and T.-F. Wong (1990), The brittle-ductile transition in rocks: Recent experimental and theoretical progress, in The Brittle-Ductile Transition in Rocks, Geophys. Monogr. Ser., vol. 56, edited by A. G. Duba et al., pp. 1-20, AGU, Washington, D. C.
19. Guiton, M. L. E., W. Sassi, Y. M. Leroy, and B. D. M. Gauthier (2003), Mechanical constraints on the chronology of fracture activation in folded Devonian sandstone of the western Moroccan Anti-Atlas, J. Struct. Geol., 25, 1317-1330.
20. Hadamard, J. (1903), Lecons sur la Propagation des Ondes, Herman, Paris.
21. Hill, R. (1958), A general theory of uniqueness and stability in elastic-plastic solids, J. Mech. Phys. Solids, 6, 236-249.
22. 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.
23. Jaeger, J. C., and N. G. W. Cook (1969), Fundamentals of Rock Mechanics, CRC Press, Boca Raton, Fla.
24. Lapusta, N. (2005), Modes of dynamic rupture propagation and rupture front speeds in earthquake models that account for dynamic weakening mechanisms, Eos Trans. AGU, 86(52), Fall Meet. Suppl., Abstract S34A-07.
25. Lapusta, N., J. R. Rice, Y. Ben-Zion, and G. Zheng (2000), Elastodynamic analysis for slow tectonic loading with spontaneous rupture episodes on faults with rate- and state-dependent friction, J. Geophys. Res., 105, 23,765-23,789.
26. Leroy, Y. M., and W. Sassi (2000), A plasticity model for discontinua, in Aspect of Tectonic Faulting, edited by F. K. Lehner and J. L. Urai, pp. 77-108, Springer, New York.
27. Linker, M. F., and J. H. Dieterich (1992), Effects of variable normal stress on rock friction: Observations and constitutive equations, J. Geophys. Res., 97, 4923-4940.
28. Mandel, J. (1966), Conditions de stabilité et postulat de Drucker, in Proceedings IUTAM Symposium on Rheology and Soil Mechanics, pp. 58-68, Springer, New York.
29. Matsuoka, H., and T. Nakai (1974), Stress-deformation and strength characteristics of soil under three different principal stresses, Proc. Jpn. Soc. Civ. Eng., 232, 59-70.
30. Mitchell, J. K. (1993), Fundamentals of Soil Behavior, 2nd ed., John Wiley, Hoboken, N. J.
31. Ohnaka, M., M. Akatsu, H. Mochizuki, A. Odedra, F. Tagashira, and Y. Yamamoto (1997), A constitutive law for the shear failure of rock under lithospheric conditions, Tectonophysics, 277, 1-27.
32. Okubo, P. G., and J. H. Dieterich (1984), Effects of physical fault properties on frictional instabilities produced on simulated faults, J. Geophys. Res., 89, 5817-5827.
33. Palmer, A. C., and J. R. Rice (1973), The growth of slip surfaces in the progressive failure of overconsolidated clay, Proc. R. Soc. London, Ser. A, 332, 527-548.
34. Paterson, M. S. (1990), Rock deformation experimentation, in The Brittle-Ductile Transition in Rocks, Geophys. Monogr. Ser., vol. 56, edited by A. G. Duba et al., pp. 187-194, AGU, Washington, D. C.
35. Regueiro, R. A., and R. I. Borja (2001), Plane strain finite element analysis of pressure-sensitive plasticity with strong discontinuity, Int. J. Solids Struct., 38(21), 3647-3672.
36. Rice, J. R. (1980), The mechanics of earthquake rupture, in Physics of the Earth's Interior, edited by A. M. Dziewonski and E. Boschi, pp. 555-649, Elsevier, New York.
37. Rice, J. R. (2006), Heating and weakening of faults during earthquake slip, J. Geophys. Res., 111, B05311, doi:10.1029/2005JB004006.
38. Rice, J. R., and Y. Ben-Zion (1996), Slip complexity in earthquake fault models, Proc. Natl. Acad. Sci. U.S.A., 93, 3811-3818.
39. Rice, J. R., and M. Cocco (2007), Seismic fault rheology and earthquake dynamics, in The Dynamics of Fault Zones, Dahlem Workshop Rep. 95, edited by M. R. Handy, MIT Press, Cambridge, Mass., in press.
40. Rice, J. R., and A. L. Ruina (1983), Stability of steady frictional slipping, J. Appl. Mech., 50, 343-349.
41. Rudnicki, J. W. (1980), Fracture mechanics applied to the Earth's crust, Annu. Rev. Earth Planet. Sci., 8, 489-525.
42. Rudnicki, J. W., and J. R. Rice (1975), Conditions for the localization of deformation in pressure-sensitive dilatant materials, J. Mech. Phys. Solids, 23, 371-394.
43. Ruina, A. L. (1983), Slip instability and state variable friction laws, J. Geophys. Res., 88, 10,359-10,370.
44. Rummel, F., H. J. Alheid, and C. Frohn (1978), Dilatancy and fracture-induced velocity changes in rock and their relation to frictional sliding, Pure Appl. Geophys., 116, 743-764.
45. Scholz, C. H. (1990), The Mechanics of Earthquakes and Faulting, Cambridge Univ. Press, New York.
46. Sibson, R. H. (1986), Earthquakes and rock deformation in crustal fault zones, Annu. Rev. Earth Planet. Sci., 14, 149-175.
47. Sibson, R. H. (1989), Earthquake faulting as a structural process, J. Struct. Geol., 11(1/2), 1-14.
48. Stakgold, I. (1998), Green's Functions and Boundary Value Problems, 2nd ed., John Wiley, Hoboken, N. J.
49. Thomas, T. Y. (1961), Plastic Flow and Fracture of Solids, Elsevier, New York.
50. Uenishi, K., and J. R. Rice (2003), Universal nucleation length for slip-weakening rupture instability under nonuniform fault loading, J. Geophys. Res., 108(B1), 2042, doi:10.1029/2001JB001681.
51. Wawersik, W. R., and W. F. Brace (1971), Post-failure behavior of a granite and a diabase, Rock Mech., 3, 61-85.
52. Wawersik, W. R., and C. Fairhurst (1970), A study of brittle rock fracture in laboratory compression experiments, Int, J. Rock Mech. Min. Sci., 7, 561-575.
53. Wong, T.-F. (1982), Shear fracture energy of westerly granite from post-failure behavior, J. Geophys. Res., 87, 990-1000.
54. Wong, T.-F. (1986), On the normal stress dependence of the shear fracture energy, in Earthquake Source Mechanics, Geophys. Manogr. Ser., vol. 37, edited by S. Das, J. Boatwright, and C. H. Scholz, pp. 1-11, AGU, Washington D. C.