Visco-poroelastic damage model for brittle-ductile failure of porous rocks

Journal of Geophysical Research: Solid Earth

Volumn 120, Issue 4, 2015, Pages 2179-2199

  Lyakhovsky, Vladimir ^a   Zhu, Wenlu ^b   Shalev, Eyal ^a  

^a GEOLOGICAL SURVEY OF ISRAEL   (Israel)

^b University of Maryland   (United States)

Author keywords

brittle ductile failure; damage rheology; deformation band

Indexed keywords

BEREA SANDSTONE; BRITTLE DEFORMATION; CONFINING PRESSURE; DAMAGE MECHANICS; DEFORMATION MECHANISM; DUCTILE DEFORMATION; FAILURE ANALYSIS; NUMERICAL MODEL; POROELASTICITY; POROUS MEDIUM; RHEOLOGY; VISCOELASTICITY;

EID: 85027924503     PISSN: 21699313     EISSN: 21699356     Source Type: Journal    
DOI: 10.1002/2014JB011805     Document Type: Article

References (90)

1. Agnon, A., and, V. Lyakhovsky, (1995), Damage distribution and localization during dyke intrusion, in Physics and Chemistry of Dykes, edited by, G. Baer, and, A. Heimann, pp. 65-78, Balkema, Rotterdam, Netherlands.
2. Antonellini, M., and, A. Aydin, (1994), Effect of faulting on fluid flow in porous sandstones: Petrophysical properties, Am. Assoc. Petrol. Geol. Bull., 78, 355-377.
3. Antonellini, M. A., A. Aydin, and, D. D. Pollard, (1994), Microstructure of deformation bands in porous sandstones at Arches National Park, Utah, J. Struct. Geol., 16, 941-959.
4. Athy, L. F., (1930), Density, porosity, and compaction of sedimentary rocks, Am. Assoc. Pet. Geol. Bull., 14, 1-24.
5. Aydin, A., and, R. Ahmadov, (2009), Bed-parallel compaction bands in aeolian sandstone: Their identification, characterization and implications, Tectonophysics, 479, 277-284.
6. Aydin, A., and, A. M. Johnson, (1983), Analysis of faulting of porous sandstone, J. Struct. Geol., 5, 19-31.
7. Baud, P., E. Klein, and, T.-F. Wong, (2004), Compaction localization in porous sandstones: Spatial evolution of damage and acoustic emission activity, J. Struct. Geol., 26, 603-624.
8. Baud, P., V. Vajdova, and, T.-F. Wong, (2006), Shear-enhanced compaction and strain localization: Inelastic deformation and constitutive modeling of four porous sandstones, J. Geophys. Res., 111, B12401, doi: 10.1029/2005JB004101.
9. Baud, P., P. Meredith, and, E. Townend, (2012), Permeability evolution during triaxial compaction of an anisotropic porous sandstone, J. Geophys. Res., 117, B05203, doi: 10.1029/2012JB009176.
10. Bernabe, Y., and, W. F. Brace, (1990), Deformation and fracture of Berea sandstone, in The Brittle-Ductile Transition in Rocks, Geophys. Monograph., vol. 56, pp. 91-101, AGU, Washington, D. C.
11. Besuelle, P., (2001), Compacting and dilating shear bands in porous rock: Theoretical and experimental conditions, J. Geophys. Res., 106, 13,435-13,442, doi: 10.1029/2001JB900011.
12. Biot, M. A., (1941), General theory of three-dimensional consolidation, J. Appl. Phys., 12, 155-164.
13. Biot, M. A., (1956), General solutions of the equations of elasticity and consolidation for a porous material, J. Appl. Mech., 78, 91-96.
14. Biot, M. A., (1973), Nonlinear and semilinear rheology of porous solids, J. Geophys. Res., 78, 4924-4937, doi: 10.1029/JB078i023p04924.
15. Byerlee, J. D., (1978), Friction of rocks, Pure Appl. Geophys., 116, 615-626.
16. Cai, Z., and, D. Bercovici, (2014), Two-phase visco-elastic damage theory, with applications to subsurface fluid injection, Geophys. J. Int., 199 (3), 1481-1496.
17. Carroll, M. M., (1991), A critical state plasticity theory for porous reservoir rock, Am. Soc. Mech. Eng., 117, Book G00617-1991.
18. Casey, J., and, P. M. Naghdi, (1983), On the nonequivalence of the stress space and strain space formulations of plasticity theory, J. Appl. Mech., 50, 350-354.
19. Charalampidou, E. M., S. A. Hall, S. Stanchits, G. Viggiani, and, H. Lewis, (2014), Shear-enhanced compaction band identification at the laboratory scale using acoustic and full-field methods, Int. J. Rock Mech. Min. Sci., 67, 240-252.
20. Chemenda, A. I., (2011), Origin of compaction bands: Anti-cracking or constitutive instability?, Tectonophysics, 499, 156-164.
21. Chemenda, A. I., C. Wibberley, and, E. Saillet, (2012), Evolution of compactive shear deformation bands: Numerical models and geological data, Tectonophysics, 526-529, 56-66.
22. Collins, I. F., (2005), The concept of stored plastic work or frozen elastic energy in soil mechanics, Geotechnique, 55, 373-382.
23. Collins, I. F., and, G. T. Houlsby, (1997), Application of thermo-mechanical principles to the modelling of geotechnical materials, Proc. R. Soc. London, Ser. A, 453 (1964), 1975-2001.
24. Coussy, O., (1995), Mechanics of Porous Continua, Wiley, Chichester, U. K.
25. Das, A., G. D. Nguyen, and, I. Einav, (2013), The propagation of compaction bands in porous rocks based on breakage mechanics, J. Geophys. Res. Solid Earth, 118, 2049-2066, doi: 10.1002/jgrb.50193.
26. deGroot, S. R., and, P. Mazur, (1962), Non-Equilibrium Thermodynamics, North-Holland Co., Amsterdam.
27. DiMaggio, F. L., and, I. S. Sandler, (1971), Material model for granular soils, J. Eng. Mech. Div. ASCE, 97, 935-950.
28. Drucker, D. C., (1949), Some implications of work-hardening and ideal plasticity, Quart. Appl. Math., 7, 411-418.
29. Du Bernard, X., P. Eichhubl, and, A. Aydin, (2002), Dilation bands: A new form of localized failure in granular media, Geophys. Res. Lett., 29 (24), 2176, doi: 10.1029/2002GL015966.
30. Dunn, J. E., and, J. Serrin, (1985), On the thermodynamics on interstitial working, Arch. Ration. Mech. Anal., 88, 95-133.
31. Eichhubl, P., J. N. Hooker, and, S. E. Laubach, (2010), Pure and shear-enhanced compaction bands in Aztec Sandstone, J. Struct. Geol., 32, 1873-1886.
32. Einav, I., (2004), Thermo-mechanical relations between stress-space and strain-space models, Geotechnique, 54 (5), 315-318.
33. Einav, I., (2005a), Energy and variational principles for piles in dissipative soil, Geotechnique, 55, 515-525.
34. Einav, I., (2005b), A second look at strain space plasticity and latest applications, 18th Australasian Conference on the Mechanics of Structures and Materials, Perth, (1), 225-231.
35. Einav, I., (2007a), Breakage mechanics-Part I: Theory, J. Mech. Phys. Solid., 55, 1274-1297.
36. Einav, I., (2007b), Breakage mechanics-Part II: Modeling granular materials, J. Mech. Phys. Solid., 55, 1298-1320.
37. Fortin, J., S. Stanchits, G. Dresen, and, Y. Guéguen, (2006), Acoustic emission and velocities associated with the formation of compaction bands in sandstone, J. Geophys. Res., 111, B10203, doi: 10.1029/2005JB003854.
38. Fossen, H., R. A. Schultz, Z. K. Zhipton, and, K. Mair, (2007), Deformation bands in sandstone: A review, J. Geol. Soc. London, 164, 755-769.
39. Fossen, H., R. A. Schultz, and, A. Torabi, (2011), Conditions and implications for compaction band formation in the Navajo Sandstone, Utah, J. Struct. Geol., 33, 1477-1490.
40. Foster, C. D., R. A. Regueiro, A. F. Fossum, and, R. I. Borja, (2005), Implicit numerical integration of a three-invariant, isotropic/kinematic hardening cap plasticity model for geomaterials, Comput. Meth. Appl. Mech. Eng., 194 (50), 5109-5138.
41. Fredrich, J. T., B. Evans, and, T.-f. Wong, (1989), Micromechanics of the brittle to plastic transition in Carrara Marble, J. Geophys. Res., 94, 4129-4145, doi: 10.1029/JB094iB04p04129.
42. Grueschow, E., and, J. W. Rudnicki, (2005), Elliptic yield cap constitutive modeling for high porosity sandstone, Int. J. Solids Struct., 42 (16), 4574-4587.
43. Hamiel, Y., V. Lyakhovsky, and, A. Agnon, (2004a), Coupled evolution of damage and porosity in poroelastic media: Theory and applications to deformation of porous rocks, Geophys. J. Int., 156, 701-713.
44. Hamiel, Y., Y. Liu, V. Lyakhovsky, Y. Ben-Zion, and, D. Lockner, (2004b), A viscoelastic damage model with applications to stable and unstable fracturing, Geophys. J. Int., 159, 1155-1165.
45. Hamiel, Y., V. Lyakhovsky, and, A. Agnon, (2005), Poroelastic damage rheology: Dilation, compaction, and failure of rocks. Geochem. Geophys. Geosyst., 6, Q01008, doi: 10.1029/2004GC000813.
46. Han, D. J., and, W. F. Chen, (1986), Strain-space plasticity formulation for hardening-softening materials with elastoplastic coupling, Int. J. Solids Struct., 22, 935-950.
47. Holcomb, D., J. W. Rudnicki, K. A. Issen, and, K. Sternlof, (2007), Compaction localization in the Earth and the laboratory: State of the research and research directions, Acta Geotech., 2 (1), 1-15.
48. Issen, K. A., and, J. W. Rudnicki, (2000), Conditions for compaction bands in porous rock, J. Geophys. Res., 105, 21,529-21,536, doi: 10.1029/2000JB900185.
49. Kachanov, L. M., (1958), On the time to rupture under creep conditions [in Russian], Izv. Acad. Nauk SSSR OTN 8, 26-31.
50. Karrech, A., C. E. Schrank, R. Freij-Ayoub, and, K. Regenauer-Lieb, (2014), A multi-scaling approach to predict hydraulic damage of poromaterials, Int. J. Mech. Sci., 78, 1-7.
51. Lehane, B. M., and, B. Simpson, (2000), Modelling glacial till under triaxial conditions using a BRICK soil model, Can. Geotech. J., 37, 1078-1088.
52. Lockner, D. A., J. D. Byerlee, V. Kuksenko, A. Ponomarev, and, A. Sidorin, (1992), Observations of quasi-static fault growth from acoustic emissions, in Fault Mechanics and Transport Properties of Rocks, edited by, B. Evans, and, T.-F. Wong, pp. 3-32, Academic Press, San Diego, Calif.
53. Lyakhovsky, V., and, Y. Ben-Zion, (2008), Scaling relations of earthquakes and aseismic deformation in a damage rheology model, Geophys. J. Int., 172, 651-662.
54. Lyakhovsky, V., and, Y. Hamiel, (2007), Damage evolution and fluid flow in poroelastic rock, Izv. Phys. Solid Earth, 43, 13-23.
55. Lyakhovsky, V., Y. Ben-Zion, and, A. Agnon, (1997), Distributed damage, faulting, and friction, J. Geophys. Res., 102, 27,635-27,649, doi: 10.1029/97JB01896.
56. Lyakhovsky, V., Y. Ben-Zion, and, A. Agnon, (2005), A viscoelastic damage rheology and rate- and state-dependent friction, Geophys. J. Int., 161, 179-190.
57. Malvern, L. E., (1969), Introduction to the Mechanics of a Continuum Medium, Prentice-Hall, Inc., Englewood Cliffs, N. J.
58. Mosolov, P. P., and, V. P. Myasnikov, (1965), Variational methods in flow theory of visco-plastic media [in Russian], Appl. Math. Mech., 29, 468-492.
59. Mosolov, P. P., and, V. P. Myasnikov, (1981), Mechanics of Rigid Plastic Media [in Russian], Nauka, Moscow.
60. Naghdi, P. M., and, J. A. Trapp, (1975), The significance of formulating plasticity theory with reference to loading surfaces in strain space, Int. J. Eng. Sci., 13, 785-797.
61. Olsen, M. P., C. H. Scholz, and, A. Leger, (1998), Healing and sealing of a simulated fault gouge under hydrothermal conditions: Implications for fault healing, J. Geophys. Res., 103, 7421-7430, doi: 10.1029/97JB03402.
62. Olsson, W. A., (1999), Theoretical and experimental investigation of compaction bands in porous rock, J. Geophys. Res., 104, 7219-7228, doi: 10.1029/1998JB900120.
63. Onsager, L., (1931), Reciprocal relations in irreversible processes, Phys. Rev., 37, 405-416.
64. Paterson, M. S., and, T.-F. Wong, (2005), Experimental Rock Deformation-The Brittle Field, 2nd ed., 347 pp., Springer, Berlin.
65. Prager, W., (1959), An Introduction to Plasticity, Addison-Wesley, Amsterdam.
66. Puzrin, A. M., and, G. T. Houlsby, (2001), Fundamentals of kinematic hardening hyperplasticity, Int. J. Solids Struct., 38, 3771-3794.
67. Ricard, Y., and, D. Bercovici, (2009), A continuum theory of grain size evolution and damage, J. Geophys. Res., 114, B01204, doi: 10.1029/2007JB005491.
68. Rudnicki, J. W., (2007), Models for compaction band propagation, in Rock Physics and Geomechanics in the Study of Reservoirs and Repositories, edited by, C. David, and, M. LeRavalec, Geol. Soc. London Spec. Publ., 284, 107-126.
69. Rudnicki, J. W., and, J. R. Rice, (1975), Conditions for the localization of deformation in pressure-sensitive dilatant materials, J. Mech. Phys. Solid., 23, 371-394.
70. Shalev, E., and, V. Lyakhovsky, (2013), The processes controlling damage zone propagation induced by wellbore fluid injection, Geophys. J. Int., 193, 209-219.
71. Shalev, E., M. Calò, and, V. Lyakhovsky, (2013), Formation of damage zone and seismic velocity variations during hydraulic stimulation: Numerical modeling and field observations, Geophys. J. Int., 195, 1023-1033.
72. Shalev, E., V. Lyakhovsky, A. Ougier-Simonin, Y. Hamiel, and, W. Zhu, (2014), Inelastic compaction, dilation and hysteresis of sandstones under hydrostatic conditions, Geophys. J. Int., 197, 920-925, doi: 10.1093/gji/ggu052.
73. Stanchits, S., and, G. Dresen, (2003), Separation of tensile and shear cracks based on acoustic emission analysis of rock fracture, paper presented at the symposium Non-Destructive Testing in Civil Engineering 2003 (NDT-CE), Deutche Gesellschaft fur Zerstorungsfreie Prufugn e.V. (DGZfP), Berlin.
74. Sternlof, K. R., J. W. Rudnicki, and, D. D. Pollard, (2005), Anticrack-inclusion model for compaction bands in sandstone, J. Geophys. Res. 110, B11403, doi: 10.1029/2005JB003764.
75. Sternlof, K. R., M. Karimi-Fard, D. D. Pollard, and, L. J. Durlofsky, (2006), Flow and transport effects of compaction bands in sandstone at scales relevant to aquifer and reservoir management, Water Resour. Res., 42, W07425, doi: 10.1029/2005WR004664.
76. Sun, W., J. E. Andrade, J. W. Rudnicki, and, P. Eichhubl, (2011), Connecting microstructural attributes and permeability from 3D tomographic images of in situ shear-enhanced compaction bands using multiscale computations, Geophys. Res. Lett., 38, L10302, doi: 10.1029/2011GL047683.
77. Sun, W., Q. Chen, and, J. T. Ostien, (2014), Modeling the hydro-mechanical responses of strip and circular punch loadings on water-saturated collapsible geomaterials, Acta Geotech., 9 (5), 903-934.
78. Taylor, G. I., and, H. Quinney, (1934), The latent energy remaining in a metal after cold working, Proc. R. Soc. London, Ser. A, 143, 307-326.
79. Tembe, S., V. Vajdova, P. Baud, W. Zhu, and, T.-f. Wong, (2007), A new methodology to delineate the compactive yield cap of two porous sandstones under undrained condition, Mech. Mater., 39, 513-523.
80. Tenthorey, E., S. F. Cox, and, H. F. Todd, (2003), Evolution of strength recovery and permeability during fluid-rock reaction in experimental fault zones, Earth Planet. Sci. Lett., 206, 161-172.
81. Terzaghi, K., (1941), Theoretical Soil Mechanics, Wiley, New York.
82. Wang, H. F., (2000), Theory of Linear Poroelasticity With Applications to Geomechanics and Hydrogeology, Princeton Univ. Press, Princeton, N. J.
83. Washizu, K., (1982), Variational Methods in Elasticity and Plasticity, 3rd ed., 630 pp., Pergamon Press Ltd, Oxford.
84. Wong, T.-F., and, P. Baud, (2012), The brittle transition in rocks: A review, J. Struct. Geol., 44, 25-53.
85. Wong, T.-F., C. David, and, W. Zhu, (1997), The transition from brittle faulting to cataclastic flow in porous sandstones: Mechanical deformation, J. Geophys. Res., 102, 3009-3025, doi: 10.1029/96JB03281.
86. Yoder, P. J., and, W. D. Iwan, (1981), On the formulation of strain space plasticity with multiple loading surfaces, J. Appl. Mech., 48, 773-778.
87. Zhu, W., and, J. Walsh, (2006), A new model for analyzing the effect of fractures on triaxial deformation, Int. J. Rock Mech. Min. Sci., 43, 1241-1255.
88. Zhu, W., and, T.-F. Wong, (1997), The transition from brittle faulting to cataclastic flow: Permeability evolution, J. Geophys. Res., 102 (B2), 3027-3041, doi: 10.1029/96JB03282.
89. Zhu, W., and, T.-F. Wong, (1999), Network modeling of the evolution of permeability and dilatancy in compact rock, J. Geophys. Res., 104 (2), 2963-2971, doi: 10.1029/1998JB900062.
90. Ziegler, H., (1983), An Introduction to Thermomechanics, 2nd ed., 358 pp., North-Holland Co., Amsterdam.