Modelling the time-dependent rheological behaviour of heterogeneous brittle rocks

Geophysical Journal International

Volumn 189, Issue 3, 2012, Pages 1781-1796

  Xu, Tao ^a,b   Tang, Chun An ^c   Zhao, Jian ^d   Li, Lianchong ^c   Heap, M J ^e  

^a NORTHEASTERN UNIVERSITY   (China)

^b CHENGDU UNIVERSITY OF TECHNOLOGY   (China)

^c DALIAN UNIVERSITY OF TECHNOLOGY   (China)

^d EPFL   (Switzerland)

^e UNIVERSITÉ DE STRASBOURG EOST   (France)

Author keywords

Acoustic properties; Creep and deformation; Mechanics, theory, and modelling; Microstructures; Probability distributions

Indexed keywords

AXIAL STRAIN; BRITTLE DEFORMATION; BRITTLE ROCKS; CONSTANT STRESS; CONSTITUTIVE LAW; CREEP SIMULATION; CRITICAL LEVEL; EXPERIMENTAL DATA; FRACTURE PROPAGATION; INITIAL STAGES; LOCAL FAILURE; LOCALIZED DAMAGE; MACROSCOPIC APPROACH; MATERIAL DEGRADATION; MATERIAL HETEROGENEITY; MATERIAL SOFTENING; MESOSCOPICS; PROGRESSIVE DAMAGE; RENORMALIZATION; RHEOLOGICAL BEHAVIOUR; SECONDARY CREEP; SPATIAL EVOLUTION; TERTIARY CREEP; TIME-DEPENDENT; TIME-DEPENDENT BEHAVIOUR; TIME-DEPENDENT RESPONSE; UNI-AXIAL LOADING;

ACOUSTIC PROPERTIES; CRACK PROPAGATION; CREEP; DEGRADATION; EXPERIMENTS; LOADING; MICROSTRUCTURE; PROBABILITY DISTRIBUTIONS; ROCKS; STRESS RELAXATION;

COMPUTER SIMULATION;

ACOUSTIC PROPERTY; CREEP; DEFORMATION; HETEROGENEITY; MICROCRACK; NUMERICAL MODEL; RHEOLOGY; SPATIAL ANALYSIS; STOCHASTICITY; STRESS; TEMPORAL EVOLUTION; UNIAXIAL STRENGTH;

EID: 84860839186     PISSN: 0956540X     EISSN: 1365246X     Source Type: Journal    
DOI: 10.1111/j.1365-246X.2012.05460.x     Document Type: Article

References (103)

1. Amitrano, D. & Helmstetter, A., 2006. Brittle creep, damage, and time to failure in rocks, J. geophys. Res., 111, 1-17.
2. Andrade, E.N., 1910. On the viscous flow in metals, and allied phenomena, Proc. R. Soc. London A, 84, 1-12.
3. Atkinson, B.K., 1982. Subcritical crack propagation in rock: theory, experimental results and applications, J. Struct. Geol., 4, 41-56.
4. Atkinson, B.K., 1984. Subcritical crack growth in geological materials, J. geophys. Res., 89, 4077-4114.
5. Baud, P. & Meredith, P.G., 1997. Damage accumulation during triaxial creep of darley dale sandstone from pore volumometry and acoustic emission, Int. J. Rock Mech. Min. Sci., 34, e1-e10.
6. Bell, A.F., Greenough, J., Heap, M.J. & Main, I.G., 2011a. Challenges for forecasting based on accelerating rates of earthquakes at volcanoes and laboratory analogues, Geophys. J. Int., 185, 718-723.
7. Bell, A.F., Naylor, M., Heap, M.J. & Main, I.G., 2011b. Forecasting volcanic eruptions and other material failure phenomena: an evaluation of the failure forecast method, Geophys. Res. Lett., doi:.
8. Benson, P.M., Thompson, A.B., Meredith, P.G., Vinciguerra, S. & Young, R.P., 2007. Imaging slow failure in triaxially deformed Etna basalt using 3D acoustic-emission location and X-ray computed tomography, Geophys. Res. Lett., doi:.
9. Bianco, F., Scarfi, L., Del Pezzo, E. & Patané, D., 2006. Shear wave splitting time variation by stress-induced magma uprising at Mt. Etna volcano, Earthprints,
10. Brady, B.H.G. & Brown, E.T., 2004. Rock Mechanics for Underground Mining, Kluwer Academic Publishers, London
11. Brantut, N., Schubnel, A. & Guéguen, Y., 2011. Damage and rupture dynamics at the brittle-ductile transition: the case of gypsum, J. geophys. Res., 116, B01404, doi:.
12. Challamel, N., Lanos, C. & Casandjian, C., 2005. Creep damage modelling for quasi-brittle materials, Eur. J. Mech., 24, 593-613.
13. Charles, R.J., 1958. Static fatigue of glass, J. appl. Phys., 29, 1549-1560.
14. Costin, L.S., 1985. Damage mechanics in the post-failure regime, Mech. Mater., 4, 149-160.
15. Crampin, S., Gao, Y. & Peacock, S., 2008. Stress-forecasting (not predicting) earthquakes: a paradigm shift? Geology, 36(5), 427-430.
16. Diederichs, M.S. & Kaiser, P.K., 1999. Tensile strength and abutment relaxation as failure control mechanisms in underground excavations, Int. J. Rock Mech. Min. Sci., 36, 69-96.
17. Esposito, L. & Bonora, N., 2009. Time-independent formulation for creep damage modeling in metals based on void and crack evolution, Mater. Sci. Eng., A, 510-511, 207-213.
18. Fang, Z. & Harrison, J.P., 2002. Development of a local degradation approach to the modelling of the brittle fracture in heterogeneous rocks, Int. J. Rock Mech. Min. Sci., 39, 443-457.
19. Freiman, S.W., 1984. Effects of the chemical environment on slow crack growth in glasses and ceramics, J. geophys. Res., 89, 4072-4077.
20. Grgic, D. & Amitrano, D., 2009. Creep of a porous rock and associated acoustic emission under different hydrous conditions, J. geophys. Res., 114, 1-19.
21. Gulino, R. & Phoenix, S. 1991. Weibull strength statistics for graphite fibres measured from the break progression in a model graphite/glass/epoxy microcomposite, J. Mater. Sci., 26(11), 3107-3118.
22. Gupta, V. & Bergstrom, J., 1998. Compressive failure of rocks by shear faulting, J. geophys. Res., 103(B10), 23875-23895.
23. Hadizadeh, J. & Law, R.D., 1991. Water-weakening of sandstone and quartzite deformed at various stress and strain rates, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 28, 431-439.
24. Haupt, M., 1991. A constitutive law for rock salt based on creep and relaxation tests, Rock Mech. Rock Eng., 24, 179-206.
25. Heap, M.J., Baud, P., Meredith, P.G., Bell, A.F. & Main, I.G., 2009a. Time-dependent brittle creep in Darley Dale sandstone, J. geophys. Res., 114, 1-22.
26. Heap, M.J., Baud, P. & Meredith, P.G., 2009b. The influence of temperature on brittle creep in sandstones, Geophys. Res. Lett., doi:.
27. Heap, M.J., Baud, P., Meredith, P.G., Vinciguerra, S., Bell, A.F. & Main, I.G., 2011. Brittle creep in basalt and its application to time-dependent volcano deformation, Earth planet. Sci. Lett., 307, 71-82.
28. Heap, M.J., Faulkner, D.R., Meredith, P.G. & Vinciguerra, S., 2010. Elastic moduli evolution and accompanying stress changes with increasing crack damage: implications for stress changes around fault zones and volcanoes during deformation, Geophys. J. Int., 183, 225-236.
29. Hillig, W. & Charles, R., 1965. Surfaces, stress-dependent surface reactions, and strength, in High Strength Materials, pp. 682-705, ed. Zackay, V.F., Wiley, New York, NY
30. Hirata, T., Satoh, T. & Ito, K., 1987. Fractal structure of spatial distribution of microfracturing in rock, Geophys. J. Int., 90, 369-374.
31. Horii, H. & Nemat-Nasser, S., 1985. Compression-induced microcrack growth in brittle solids: axial splitting and shear failure, J. geophys. Res., 90, 3105-3125.
32. Jeager, J.C., Cook, N.G.W. & Zimmerman, R., 2007. Fundamentals of Rock Mechanics, pp. 90-94, Blackwell Publishing, Singapore
33. Kaiser, P.K. & Morgenstern, N.R., 1981. Time-dependent deformation of small tunnels-II. Typical test data, Int. J. Rock Mech. Min. Sci., 18, 141-152.
34. Karato, S.-I. & Li, P., 1992. Diffusion creep in Perovskite: implications for the rheology of the lower mantle, Science, 255, 1238-1240.
35. Kemeny, J.M., 1991. A model for non-linear rock deformation under compression due to sub-critical crack growth, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 28, 459-467.
36. Kilburn, C.R.J., 2003. Multiscale fracturing as a key to forecasting volcanic eruptions, J. Volc. Geotherm. Res., 125, 271-289.
37. Knill, J.L., Franklin, J.A. & Malone, A.W., 1968. A study of acoustic emission from stressed rock, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 5, 87-88.
38. Kranz, R.L., 1979. Crack growth and development during creep of Barre granite, Int. J. Rock Mech. Min. Sci., 16, 23-35.
39. Kranz, R., 1980. The effect of confining pressure and stress difference on static fatigue of granite, J. geophys. Res., 85, 1854-1866.
40. Kranz, R., Harris, W.J. & Carter, N.L., 1982. Static fatigue of granite at 200°C, Geophys. Res. Lett., 9, 1-4.
41. Kranz, R. & Scholz, C.H., 1977. Critical dilatant volume of rocks at the onset of tertiary creep, J. geophys. Res., 82, 4893-4898.
42. Lemaitre, J. & Chaboche, J.L., 2001. Mécanique des Matériaux Solides, 2nd edn, Dunod, Paris
43. Lemaitre, J. & Desmorat, R., 2005. Engineering Damage Mechanics, Springer-Verlag, Berlin
44. Li, Y.S. & Xia, C.C., 2000. Time-dependent tests on intact rocks in uniaxial compression, Int. J. Rock Mech. Min. Sci, 37, 467-475.
45. Liang, Z.Z., 2005. Three-dimensional failure process analysis of rock and associated numerical test, PhD thesis, Northeastern University of China, Shenyang
46. Lin, Q.X., Liu, Y.M., Tham, L.G., Tang, C.A., Lee, P.K.K. & Wang, J., 2009. Time-dependent strength degradation of granite, Int. J. Rock Mech. Min. Sci., 46, 1103-1114.
47. Lockner, D., 1993a. The role of acoustic-emission in the study of rock fracture, Int. J. Rock Mech. Min. Sci, 30, 883-899.
48. Lockner, D., 1993b. Room temperature creep in saturated granite, J. geophys. Res., 98, 475-487.
49. Lockner, D.A., 1998. A generalized law for brittle deformation of Westerly granite, J. geophys. Res., 103, 5107-5123.
50. Lockner, D. & Madden, T.R., 1991. A multiple-crack model of brittle fracture. 2. Time-dependent simulations, J. geophys. Res., 96, 19643-19654.
51. Lockner, D.A., Byerlee, J.D., Kuksenko, V., Ponomarev, A. & Sidorin, A., 1991. Quasi-static fault growth and shear fracture energy in granite, Nature, 350, 39-42.
52. Madgwick, A., Mori, T., Withers, P.J. & Wakashima, K., 2001. Steady-state creep of a composite, Mech. Mater., 33, 493-498.
53. Maes, C., Van Moffaert, A., Frederix, H. & Strauven, H., 1998. Criticality in creep experiments on cellular glass, Phys. Rev. B, 57, 4987-4990.
54. Main, I.G., 1999. Applicability of time-to-failure analysis to accelerated strain before earthquakes and volcanic eruptions, Geophys. J. Int., 139, F1-F6.
55. Main, I.G., 2000. A damage mechanics model for power-law creep and earthquake aftershock and foreshock sequences, Geophys. J. Int., 142, 151-161.
56. Main, I.G. & Meredith, P.G., 1991. Stress corrosion constitutive laws as a possible mechanism of intermediate-term and short-term seismic quiescence, Geophys. J. Int., 107, 363-372.
57. McMeeking, R.M., 1993. Power law creep of a composite material containing discontinuous rigid aligned fibers, Int. J. Solids Struct., 30, 1807-1823.
58. Michalske, T.A. & Freiman, S.W., 1982. A molecular interpretation of stress corrosion in silica, Nature, 295, 511-512.
59. Michalske, T.A. & Freiman, S.W., 1983. A molecular mechanism for stress corrosion in vitreous silica, J. Am. Ceram. Soc., 66, 284-288.
60. Miura, K., Okui, Y. & Horii, H., 2003. Micromechanics-based prediction of creep failure of hard rock for long-term safety of high-level radioactive waste disposal system, Mech. Mater., 35, 587-601.
61. Nara, Y., Takada, M., Mori, D., Owada, H., Yoneda, T. & Kaneko, K., 2010. Subcritical crack growth and long-term strength in rock and cementitious material, Int. J. Fract., doi:.
62. Nechad, H., Helmstetter, A., El Guerjouma, R. & Sornette, D., 2005a. Andrade and critical time-to-failure laws in fiber-matrix composites: experiments and model, J. Mech. Phys. Solids, 53, 1099-1127.
63. Nechad, H., Helmstetter, A., Guerjouma, R.E. & Sornette, D., 2005b. Creep ruptures in heterogeneous materials, Phys. Rev. Lett., 94, 045501-045504.
64. Newman, W.I. & Phoenix, S.L., 2001. Time-dependent fiber bundles with local load sharing, Phys. Rev. E, 63, 021507.
65. Ngwenya, B., Main, I., Elphick, S., Crawford, B. & Smart, B., 2001. A constitutive law for low-temperature creep of water-saturated sandstones, J. geophys. Res., 106, 21811-21826.
66. Nieh, T., 1984. Creep rupture of a silicon carbide reinforced aluminum composite, Metall. Mater. Trans. A, 15, 139-146.
67. Ohnaka, M., 1983. Acoustic emission during creep of brittle rock, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 20, 121-134.
68. Palano, M., Gresta, S. & Puglisi, G., 2009. Time-dependent deformation of the eastern flank of Mt. Etna: after-slip or viscoelastic relaxation? Tectonophysics, 473, 300-311.
69. Paraschiv-Munteanu, I. & Cristescu, N.D., 2001. Stress relaxation during creep of rocks around deep boreholes, Int. J. Eng. Sci., 39, 737-754.
70. Paterson, M.S. & Wong, T.-F., 2005. Experimental Rock Deformation-The Brittle Field, Springer, New York, NYs.
71. Peng, S. & Podnieks, E.R., 1972. Relaxation and the behavior of failed rock, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 9, 699-700.
72. Pietruszczak, S., Lydzba, D. & Shao, J.F., 2004. Description of creep in inherently anisotropic frictional materials, J. Eng. Mech. ASCE, 130, 681-690.
73. Rutter, E.H., 1972. On the creep testing of rocks at constant stress and constant force, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 9, 191-195.
74. Rutter, E.H. & Mainprice, D.H., 1978. The effect of water on stress relaxation of faulted and unfaulted sandstone, Pageoph, 116, 634-654.
75. Scholz, C.H., 1968. Mechanism of creep in brittle rock, J. geophys. Res, 73, 3295-3302.
76. Scholz, C.H., 1972. Static fatigue of quartz, J. geophys. Res, 77, 2104-2114.
77. Schubnel, A., Walker, E., Thompson, B.D., Fortin, J., Guéguen, Y. & Young, R.P., 2006. Transient creep, aseismic damage and slow failure in Carrara marble deformed across the brittle-ductile transition, Geophys. Res. Lett., 33, L17301, doi:.
78. Shao, J.F., Chau, K.T. & Feng, X.T., 2006. Modeling of anisotropic damage and creep deformation in brittle rocks, Int. J. Rock Mech. Min. Sci., 43, 582-592.
79. Shao, J.F., Zhu, Q.Z. & Su, K., 2003. Modeling of creep in rock materials in terms of material degradation, Comput. Geotech., 30, 549-555.
80. Singh, D.P., 1975. A study of creep of rocks, Int. J. Rock Mech. Min. Sci., 12, 271-276.
81. Singh, M. & Behrendt, D., 1994. Microstructure and mechanical properties of reaction-formed silicon carbide (RFSC) ceramics, Mater. Sci. Eng., A, 187(2), 183-187.
82. Tang, C.A., 1997. Numerical simulation of progressive rock failure and associated seismicity, Int. J. Rock Mech. Min. Sci., 34, 249-261.
83. Tang, C.A., Chen, Z.H., Xu, X.H. & Li, C., 1997. A theoretical model for Kaiser effect in rock, Pure appl. Geophys., 150, 203-215.
84. Tang, C.A., Huang, M.L. & Zhao, X.D., 2003. Weak zone related seismic cycles in progressive failure leading to collapse in brittle crust, Pure appl. Geophys., 160, 2319-2328.
85. Tang, C.A., Tham, L.G., Lee, P.K.K., Tsui, Y. & Liu, H., 2000. Numerical studies of the influence of microstructure on rock failure in uniaxial compression-part II: constraint, slenderness and size effect, Int. J. Rock Mech. Min. Sci., 37, 571-583.
86. Tang, C.A. et al ., 2008. Fracture spacing in layered materials: a new explanation based on two-dimensional failure process modeling, Am. J. Sci., 308, 49-72.
87. Turcotte, D.L., Newman, W.I. & Shcherbakov, R., 2003. Micro and macroscopic models of rock fracture, Geophys. J. Int., 152, 718-728.
88. Tuttle, M.E. & Brinson, H.F., 1986. Prediction of the long-term creep compliance of general composite laminates, Exp. Mech., 26, 89-102.
89. Van Mier, J.G.M., Van Vliet, M.R.A. & Wang, T.K., 2002. Fracture mechanisms in particle composites, statistical aspects in lattice type analysis, Mech. Mater., 34, 705-724.
90. Voight, B., 1988. A method for prediction of volcanic eruption, Nature, 332, 125-130.
91. Voight, B., 1989. A relation to describe rate-dependent material failure, Science, 243, 200-203.
92. Wang, J.N., Hobbs, B.E., Ord, A., Shimamoto, T. & Toriumi, M., 1994. Newtonian dislocation creep in quartzites: implications for the rheology of the lower crust, Science, 265, 1204-1206.
93. Weibull, W., 1951. A statistical distribution function of wide applicability, J. appl. Mech., 18, 293-297.
94. Weiss, J. & Marsan, D., 2003. Three-dimensional mapping of dislocation avalanches: clustering and space/time coupling, Science, 299, 89-92.
95. Wiederhorn, S. & Bolz, L., 1970. Stress corrosion and static fatigue of glass, J. Am. Ceram. Soc., 53, 543-548.
96. Wong, T.-F., David, C. & Zhu, W., 1997. The transition from brittle faulting to cataclastic flow in porous sandstones: mechanical deformation, J. geophys. Res., 102, 3009-3025.
97. Wu, G. & Zhang, L., 2003. A damage mechanical constitutive model of unloading failure for brittle-elastic rock mass, in Environmental Rock Engineering, pp. 279-283, eds. Saito, T. & Murata, S., Swets & Zeitlinger B.V., Lisse
98. Xu, H., 1997. Time-dependent behaviours of strength and elasticity modulus of weak rock, Chin. J. Rock Mech. Eng., 16, 246-251.
99. Xu, X.H., Ma, S.P., Xia, M.F., Ke, F.J. & Bai, Y.L., 2004. Damage evaluation and damage localization of rock, Theor. Appl. Fract. Mech., 42, 131-138.
100. Xu, T., Tang, C.A., Yang, T.H., Zhu, W.C. & Liu, J., 2006. Numerical investigation of coal and gas outbursts in underground collieries, Int. J. Rock Mech. Min. Sci., 43, 905-919.
101. Yanagidani, T., Ehara, S., Nishizawa, O., Kusunose, K. & Terada, M., 1985. Localization of dilatancy in Ohshima granite under constant uniaxial stress, J. geophys. Res., 94, 6840-6858.
102. Yang, S. & Jiang, Y., 2010. Triaxial mechanical creep behavior of sandstone, Min. Sci. Technol., 20, 339-349.
103. Yang, M. & Toksöz, M.N., 1981. Time-dependent deformation and stress relaxation after strike slip earthquakes, J. geophys. Res., 86(B4), 2889-2901.