Skip to main content
SpringerLink
Log in

Damage evolution and fluid flow in poroelastic rock

  • Published:
Izvestiya, Physics of the Solid Earth Aims and scope Submit manuscript

Abstract

We present a formulation for mechanical modeling of the interaction between fracture and fluid flow. Our model combines the classic Biot poroelastic theory and a damage rheology model. The model provides an internally consistent framework for simulating coupled evolution of fractures and fluid flow together with gradual transition from brittle fracture to cataclastic flow in high-porosity rocks. The theoretical analysis, based on thermodynamic principles, leads to a system of coupled kinetic equations for the evolution of damage and porosity. A significant advantage of the model is the ability to reproduce the entire yield curve, including positive and negative slopes, in high-porosity rocks by a unified formulation. A transition from positive to negative values in the yield curve, referred to as a yield cap, is determined by the competition between the two thermodynamic forces associated with damage and porosity evolution. Numerical simulations of triaxial compression tests reproduce the gradual transition from localized brittle failure to distributed cataclastic flow with increasing pressure in high-porosity rocks and fit well experimentally measured yield stress for Berea sandstone samples. We modified a widely used permeability porosity relation by accounting for the effect of damage intensity on the connectivity. The new damage-permeability relation, together with the coupled kinetics of damage and porosity evolution, reproduces a wide range of realistic features of rock behavior. We constrain the model variables by comparisons of the theoretical predictions with laboratory results reporting porosity and permeability variation in rock samples during isotropic and anisotropic loading. The new damage-porosity-permeability relation enables simulation of coupled evolution of fractures and fluid flow and provides a possible explanation for permeability measurements in high-porosity rocks, referred to as the “apparent permeability paradox.”

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Agnon and V. Lyakhovsky, “Damage Distribution and Localization during Dyke Intrusion,” in The Physics and Chemistry of Dykes, Ed. by G. Baer and A. Heimann (Balkema, Rotterdam, 1995), pp. 65–78.

    Google Scholar 

  2. O. Allix and F. Hild, Continuum Damage Mechanics of Materials and Structures (Elsevier, Amsterdam, 2002).

    Google Scholar 

  3. A. Aydin and A. M. Johnson, “Development of Faults as Zones of Deformation Bands and as Slip Surfaces in Sandstone,” Pure Appl. Geophys. 116, 931–942 (1978).

    Article  Google Scholar 

  4. A. Aydin and A. M. Johnson, “Analysis of Faulting in Porous Sandstones,” J. Struct. Geol. 5, 19–31 (1983).

    Article  Google Scholar 

  5. P. Baud, W. Zhu, and T.-F. Wong, “Failure Mode and Weakening Effect of Water on Sandstone,” J. Geophys. Res. 105, 16371–16389 (2000).

    Article  Google Scholar 

  6. Y. Bernabe and W. F. Brace, “Deformation and Fracture of Berea Sandstone,” in The Brittle-Ductile Transition in Rocks (Geophys. Monogr., 56), Ed. by A. G. Duba, W. B. Durham, J. W. Handin, and H. F. Wang (AGU, Washington, 1990), pp. 91–101.

    Google Scholar 

  7. P. Besuelle, “Compacting and Dilating Shear Bands in Porous Rock: Theoretical and Experimental Conditions,” J. Geophys. Res. 106, 13 435–13 442 (2001).

    Article  Google Scholar 

  8. M. A. Biot, “General Theory of Three-Dimensional Consolidation,” J. Appl. Phys. 12, 155–164 (1941).

    Article  Google Scholar 

  9. M. A. Biot, “Theory of Elasticity and Consolidation for a Porous Anisotropic Solid,” J. Appl. Phys. 26, 182–185 (1955).

    Article  Google Scholar 

  10. M. A. Biot, “General Solutions of the Equations of Elasticity and Consolidation for a Porous Material,” J. Appl. Mech. 78, 91–96 (1956).

    Google Scholar 

  11. M. A. Biot, “Nonlinear and Semilinear Rheology of Porous Solids,” J. Geophys. Res. 78, 4924–4937 (1973).

    Google Scholar 

  12. O. Bour and P. Davy, “Connectivity of Random Fault Network Following a Power Law Fault Length Distribution,” Water Res. Res. 33, 1567–1583 (1997).

    Article  Google Scholar 

  13. W. F. Brace, J. B. Walsh, and W. T. Frangos, “Permeability of Granite under High Pressure,” J. Geophys. Res. 73, 2225–2236 (1968).

    Google Scholar 

  14. R. M. Christensen, Mechanics of Composite Materials (Wiley-Intersci., New York, 1979).

    Google Scholar 

  15. O. Coussy, Mechanics of Porous Continua (Wiley, Chichester, 1995).

    Google Scholar 

  16. P. A. Cundall, “Numerical Experiments on Localization in Frictional Materials,” Ign. Arch. 59, 148–159 (1989).

    Article  Google Scholar 

  17. P. A. Cundall and M. Board, “A Microcomputer Program for Modeling Large-Strain Plasticity Problems,” in Proc. 6th Int. Conf. Numerical Methods in Geomechanics, Innsbruck, Ed. by C. Swoboda (Balkema, Rotterdam, 1988), pp. 2101–2108.

    Google Scholar 

  18. C. David, T.-F. Wong, W. Zhu, and J. Zang, “Laboratory Measurements of Compaction-Induced Permeability Change in Porous Rocks: Implications for the Generation and Maintenance of Pore Pressure Excess in the Crust,” Pure Appl. Geophys. 143, 425–456 (1994).

    Article  Google Scholar 

  19. S. R. deGroot and P. Mazur, Nonequilibrium Thermodynamics (North-Holland, Amsterdam, 1962).

    Google Scholar 

  20. E. Detournay and A. H.-D. Cheng, “Fundamentals of Poroelasticity,” in Comprehensive Rock Engineering: Principles, Practice and Projects, Vol. II: Analysis and Design Methods, Ed. by C. Fairhurst (Pergamon, 1993), pp. 113–171.

  21. P. Dijk and B. Berkowitz, “Precipitation and Dissolution of Reactive Solutes in Fractures,” Water Res. Res. 34, 457–470 (1998).

    Article  Google Scholar 

  22. J. Dvorkin, A. Nur, and H. Yin, “Effective Properties of Cemented Granular Materials,” Mech. Mater. 18, 351–366 (1994).

    Article  Google Scholar 

  23. J. Dvorkin and A. Nur, “Elasticity of High-Porosity Sandstones: Theory for Two North Sea Data Sets,” Geophysics 61, 1363–1370 (1996).

    Article  Google Scholar 

  24. I. Ekland and R. Temam, Convex Analysis and Variational Problems (Elsevier, Amsterdam, 1976).

    Google Scholar 

  25. A. C. Fowler and X. Yang, “Pressure Solution and Viscous Compaction in Sedimentary Basins,” J. Geophys. Res. 104, 12 989–12 997 (1999).

    Google Scholar 

  26. J. W. Gibbs, The Scientific Papers, Vol. 1: Thermodynamics (New York, 1961).

  27. Y. Hamiel, V. Lyakhovsky, and A. Agnon, “Coupled Evolution of Damage and Porosity in Poroelastic Media: Theory and Applications to Deformation of Porous Rocks,” Geophys. J. Int. 156, 701–713 (2004a).

    Article  Google Scholar 

  28. Y. Hamiel, Y. Liu, V. Lyakhovsky, et al., “A Visco-Elastic Damage Model with Applications to Stable and Unstable Fracturing,” Geophys. J. Int. 159, 1155–1165 (2004b).

    Article  Google Scholar 

  29. Y. Hamiel, V. Lyakhovsky, and A. Agnon, “Poroelastic Damage Rheology: Dilation, Compaction, and Failure of Rocks,” Geochem. Geophys. Geosyst., No. 6, Q01008 (2005a).

  30. Y. Hamiel, V. Lyakhovsky, and A. Agnon, “Rock Dilation, Nonlinear Deformation, and Pore Pressure Change under Shear,” Earth Planet. Sci. Lett. 237, 577–589 (2005b).

    Article  Google Scholar 

  31. Y. Hamiel, O. Katz, V. Lyakhovsky, et al., “Stable and Unstable Damage Evolution in Rocks with Implications to Fracturing of Granite,” Geophys. J. Int. (2006) (in press).

  32. N. R. Hansen and H. L. Schreyer, “A Thermodynamically Consistent Framework for Theories of Elastoplasticity Coupled with Damage,” Int. J. Solids Structures 31, 359–389 (1994).

    Article  Google Scholar 

  33. N. J. Hoff, “The Necking and Rupture of Rods Subjected to Constant Tensile Loads,” J. Apl. Mech 20, 105–108 (1953).

    Google Scholar 

  34. J. A. Hudson, “The Effect of Fluid Pressure on Wave Speeds in a Cracked Solid,” Geophys. J. Int. 143, 302–310 (2000).

    Article  Google Scholar 

  35. L. M. Kachanov, “On the Time to Rupture under Creep Conditions,” Izv. Acad. Nauk SSSR, Otdel. Tekhn. Nauk, No. 8, 26–31 (1958).

  36. L. M. Kachanov, Introduction to Continuum Damage Mechanics (Martinus Nijhoff, 1986).

  37. M. Kachanov, “On the Concept of Damage in Creep and in the Brittle-Elastic Range,” Int. J. Damage Mech. 3, 329–337 (1994).

    Google Scholar 

  38. D. Krajcinovic, Damage Mechanics (Elsevier, Amsterdam, 1996).

    Google Scholar 

  39. D. A. Lockner, J. D. Byerlee, V. Kuksenko, et al., “Observations of Quasi-Static Fault Growth from Acoustic Emissions,” Fault Mechanics and Transport Properties of Rocks (Int. Geophys. Series, Vol. 51), Ed. by B. Evans and T.-F. Wong (Academic, San Diego, CA, 1992), pp. 3–31.

    Google Scholar 

  40. V. A. Lyakhovsky and V. P. Myasnikov, “On the Behavior of an Elastic Cracked Solid,” Izv. Akad. Nauk SSSR, Fiz. Zemli 10, 71–75 (1984).

    Google Scholar 

  41. V. A. Lyakhovsky and V. P. Myasnikov, “On the Behavior of a Visco-Elastic Cracked Solid,” Izv. Akad. Nauk SSSR, Fiz. Zemli, No. 4, 28–35 (1985).

  42. V. Lyakhovsky, Y. Podladchikov, and A. Poliakov, “Rheological Model of a Fractured Solid,” Tectonophysics 226, 187–198 (1993).

    Article  Google Scholar 

  43. V. Lyakhovsky, Y. Ben-Zion, and A. Agnon, “Distributed Damage, Faulting, and Friction,” J. Geophys. Res. 102, 27 635–27 649 (1997a).

    Article  Google Scholar 

  44. V. Lyakhovsky, Z. Reches, R. Weinberger, and T. E. Scott, “Non-Linear Elastic Behavior of Damaged Rocks,” Geophys. J. Int. 130, 157–166 (1997b).

    Google Scholar 

  45. V. Lyakhovsky, A. Ilchev, and A. Agnon, “Modeling of Damage and Instabilities of Rock Mass by Means of a Non-Linear Rheological Model,” in Dynamic Rock Mass Response to Mining (Rock Bursts and Seismicity in Mines—RaSiM5), Ed. by G. Van Aswegen, R. J. Durrheim, and W. D. Ortlepp (South African Institute of Mining and Metallurgy, Johannesburg, 2001), pp. 413–420.

    Google Scholar 

  46. V. Lyakhovsky, Y. Ben-Zion, and A. Agnon, “A Visco-Elastic Damage Rheology and Rate-and State-Dependent Friction,” Geophys. J. Int. 161, 179–190 (2005).

    Article  Google Scholar 

  47. I. G. Main, O. Kwon, B. T. Ngwenya, and S. C. Elphick, “Fault Sealing during Deformation-Band Growth in Porous Sandstone,” Geology 28, 1131–1134 (2000).

    Article  Google Scholar 

  48. K. Mair, I. Main, and S. Elphick, “Sequential Growth of Deformation Bands in the Laboratory,” J. Struct. Geol 22, 25–42 (2000).

    Article  Google Scholar 

  49. L. E. Malvern, Introduction to the Mechanics of a Continuum Medium (Prentice-Hall, Englewood Cliffs, 1969).

    Google Scholar 

  50. G. Mavko and T. Mukerji, “Seismic Pore Space Compressibility and Gassmann’ls Relation,” Geophysics 60, 1743–1749 (1995).

    Article  Google Scholar 

  51. P. Mazur, Nonequilibrium Thermodynamics (North-Holland, Amsterdam, 1962).

    Google Scholar 

  52. D. P. McKenzie, “The Generation and Compaction of Partially Molten Rock,” J. Petrol. 25, 713–765 (1984).

    Google Scholar 

  53. B. Menendez, W. Zhu, and T.-F. Wong, “Micromechanics of Brittle Faulting and Cataclastic Flow in Berea Sandstone,” J. Struct. Geol. 18, 1–16 (1996).

    Article  Google Scholar 

  54. P. P. Mosolov and V. P. Myasnikov, “Variational Methods in Flow Theory of Visco-Plastic Media,” Appl. Math. Mech. 29, 468–492 (1965).

    Google Scholar 

  55. V. P. Myasnikov, V. A. Lyakhovsky, and Yu. Yu. Podladchikov, “Non-Local Model of Strain-Dependent Visco-Elastic Media,” Dokl. Akad. Nauk SSSR 312, 302–305 (1990).

    Google Scholar 

  56. W. I. Newman and S. L. Phoenix, “Time-Dependent Fiber Bundles with Local Load Sharing,” Phys. Rev. E 63(2) (2001).

  57. B. T. Ngwenya, O. Kwon, S. C. Elphick, and I. G. Main, “Permeability Evolution during Progressive Development of Deformation Bands in Porous Sandstones,” J. Geophys. Res. 108(B7), 2343 (2003).

    Article  Google Scholar 

  58. V. N. Nikolaevskii, K. S. Vasniev, A. T. Gorbunov, and G. A. Zotov, Mechanics of Saturated Porus Media (Nedra, Moscow, 1970) [in Russian].

    Google Scholar 

  59. A. Nur and J. D. Byerlee, “An Exact Effective Stress Law for Elastic Deformation of Rock with Fluids,” J. Geophy. Res. 76, 6414–6419 (1971).

    Google Scholar 

  60. M. P. Olsen, C. H. Scholz, and A. Leger, “Healing and Sealing of a Simulated Fault Gouge under Hydrothermal Conditions: Implications for Fault Healing,” J. Geophys. Res. 103, 7421–7430 (1998).

    Article  Google Scholar 

  61. L. Onsager, “Reciprocal Relations in Irreversible Processes,” Phys. Rev. 37, 405–416 (1931).

    Article  Google Scholar 

  62. E. Papa, “A Damage Model for Concrete Subjected to Fatigue Loading,” Eur. J. Mech., A/Solids 12, 429–440 (1993).

    Google Scholar 

  63. A. Poliakov, P. Cundall, Y. Podladchikov, and V. Lyakhovsky, “An Explicit Intertial Method for the Simulation of Viscoelastic Flow: An Evaluation of Elastic Effects on Diapiric Flow in Two-and Three-Layer Model,” in Proc. NATO Advanced Study Institute on Dynamic Modeling and Flow in the Earth and Planets, Ed. by K. E. Runcorn and D. Stone (Kluwer, Dordrecht, 1993).

    Google Scholar 

  64. I. Prigogine, Introduction to Thermodynamics of Irreversible Processes (Springfield, Ill., 1955).

  65. Y. N. Rabotnov, A Mechanism of a Long Time Failure, in: Creep Problems in Structural Members (AN SSSR. 1959) [in Russian].

  66. Y. N. Rabotnov, Mechanics of Deformable Solids (Nauka, Moscow, 1988) [in Russian].

    Google Scholar 

  67. C. I. Renshaw, “On the Relationship between Mechanical and Hydraulic Apertures in Rough-Walled Fractures,” J. Geophys. Res. 100, 24 629–24 636 (1995).

    Article  Google Scholar 

  68. C. I. Renshaw, “Influence of Subcritical Fracture Growth on the Connectivity of Fracture Networks,” Water Res. Res. 32, 1519–1530 (1996).

    Article  Google Scholar 

  69. J. R. Rice and M. P. Cleary, “Some Basic Stress Diffusion Solutions for Fluid-Saturated Elastic Porous Media with Compressible Constituents,” Rev. Geophys. Space Phys. 14, 227–241 (1976).

    Google Scholar 

  70. J. R. Rice, “Fault Stress States, Pore Pressure Distribution, and the Weakness of the San Andreas Fault,” in Fault Mechanics and Transport Properties of Rocks, Ed. by B. Evans and T. F. Wong (1992), pp. 476–503 (1992).

  71. E. L. Robinson, “Effect of Temperature Variation on the Long-Term Rupture Strength of Steels,” Trans. Am. Soc. Mech. Eng. 174, 777–781 (1952).

    Google Scholar 

  72. A. M. Rubin, “Tensile Fracture of Rock at High Confining Pressure: Implications for Dike Propagation,” J. Geophys. Res. 98, 15 919–15 935 (1993).

    Google Scholar 

  73. L. I. Sedov, “Variational Methods of Constructing Models of Continuous Media,” in Irreversible Aspects of Continuum Mechanics (Springer, 1968), pp. 17–40.

  74. B. Seront, T.-F. Wong, J. S. Caine, et al., “Laboratory Characterization of a Seismogenic Normal Fault System,” J. Struct. Geol. 20, 865–881 (1998).

    Article  Google Scholar 

  75. E. Tenthorey, C. H. Scholz, E. Aharonov, and A. Leger, “Precipitation Sealing and Diagenesis 1. Experimental Results,” J. Geophys. Res. 103, 23 951–23 967 (1998).

    Article  Google Scholar 

  76. E. Tenthorey, S. F. Cox, and H. F. Todd, “Evolution of Strength Recovery and Permeability during Fluid-Rock Reaction in Experimental Fault Zones,” Earth Planet. Sci. Lett. 206, 161–172 (2003).

    Article  Google Scholar 

  77. D. L. Turcotte, W. I. Newman, and R. Shcherbakov, “Micro and Macroscopic Models of Rock Fracture,” Geophys. J. Int. 152, 718–728 (2003).

    Article  Google Scholar 

  78. K. C. Valanis, “A Theory of Damage in Brittle Materials,” Eng. Fract. Mech. 36, 403–416 (1990).

    Article  Google Scholar 

  79. T.-F. Wong and W. Zhu, “Brittle Faulting and Permeability Evolution: Hydromechanical Measurement, Microstructural Observation, and Network Modeling,” in Faults and Subsurface Fluid Flow in the Shallow Crust (Geophys. Monogr., Vol. 113), Ed. by W. C. Haneberg, P. S. Mozley, J. C. Moore, and L. B. Goodwin (AGU, Washington DC, 1999), pp. 83–99.

    Google Scholar 

  80. T.-F. Wong, C. David, and W. Zhu, “The Transition from Brittle Faulting to Cataclastic Flow in Porous Sandstones: Mechanical Deformation,” J. Geophys. Res. 102, 3009–3025 (1997).

    Article  Google Scholar 

  81. S. Zhang, M. S. Paterson, and S. F. Cox, “Porosity and Permeability Evolution during Hot Isostatic Pressing of Calcite Aggregates,” J. Geophys. Res. 99, 15 741–15 760 (1994).

    Google Scholar 

  82. J. Zhang, T.-F. Wong, and D. M. Davies, “Micromechanics of Pressure-Induced Grain Crushing in Porous Rocks,” J. Geophys. Res. 95, 341–352 (1990).

    Article  Google Scholar 

  83. W. Zhu, C. David, and T.-F. Wong, “Network Modeling of Permeability Evolution during Cementation and Hot Isostatic Pressing,” J. Geophys. Res. 100, 15 451–15 464 (1995).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Geological Survey of Israel, 30 Malkhei Israel St., Jerusalem, 95501, Israel

    V. Lyakhovsky & Ya. Hamiel

  2. IGPP, Scripps Institution of Oceanography, University of California, San Diego, 9500 Gilman Dr., La Jolla, CA, 92093, USA

    Ya. Hamiel

Authors
  1. V. Lyakhovsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ya. Hamiel
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The text was submitted by the authors in English.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lyakhovsky, V., Hamiel, Y. Damage evolution and fluid flow in poroelastic rock. Izv., Phys. Solid Earth 43, 13–23 (2007). https://doi.org/10.1134/S106935130701003X

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S106935130701003X

PACS numbers

Search

Navigation