Skip to main content
SpringerLink
Log in

Multiscale model for predicting shear zone structure and permeability in deforming rock

  • Published:
Computational Particle Mechanics Aims and scope Submit manuscript

Abstract

A novel multiscale model is proposed for the evolution of faults in rocks, which predicts their internal properties and permeability as strain increases. The macroscale model, based on smoothed particle hydrodynamics (SPH), predicts system scale deformation by a pressure-dependent elastoplastic representation of the rock and shear zone. Being a continuum method, SPH contains no intrinsic information on the grain scale structure or behaviour of the shear zone, so a series of discrete element method microscale shear cell models are embedded into the macroscale model at specific locations. In the example used here, the overall geometry and kinematics of a direct shear test on a block of intact rock is simulated. Deformation is imposed by a macroscale model where stresses and displacement rates are applied at the shear cell walls in contact with the rock. Since the microscale models within the macroscale block of deforming rock now include representations of the grains, the structure of the shear zone, the evolution of the size and shape distribution of these grains, and the dilatancy of the shear zone can all be predicted. The microscale dilatancy can be used to vary the macroscale model dilatancy both spatially and temporally to give a full two-way coupling between the spatial scales. The ability of this model to predict shear zone structure then allows the prediction of the shear zone permeability using the Lattice–Boltzmann method.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Abe S, Mair K (2005) Grain fracture in 3D numerical simulations of granular shear. Geophys Res Lett 32:L05303

    Article  Google Scholar 

  2. Ahrenholz B, Tolke J, Lehmann P, Peters A, Kaestner A, Krafczyk M, Durner W (2008) Prediction of capillary hysteresis in a porous material using lattice-Boltzmann methods and comparison to experimental data and a morphological pore network model’. Adv Water Resour 31:1151–1173

    Article  Google Scholar 

  3. Alevizos S, Poulet T, Veveakis E (2014) Thermo-poro-mechanics of chemically active creeping faults. 1: Theory and steady state considerations. J Geophys Res Solid Earth 119:4558–4582

    Article  Google Scholar 

  4. Arns CH, Pinczewski WV, Knackstedt MA, Garboczi EJ (2002) Computation of linear elastic properties from micro-tomographic images: methodology and agreement between theory and experiment. Geophysics 67:1396–1405

    Article  Google Scholar 

  5. Babic M, Shen HH, Shen HT (1990) The stress tensor in granular shear flows of uniform, deformable disks at high solids concentrations. J Fluid Mech 219:81–118

    Article  Google Scholar 

  6. Bense VF, Gleeson T, Loveless SE, Bour O, Scibek J (2013) Fault zone hydrogeology. Earth-Sci Rev 127:171–192

    Article  Google Scholar 

  7. Bhatnagar PL, Gross EP, Krook M (1954) A model for collision processes in gases. 1.Small amplitude processes in charges and neutral one component systems. Phys Rev 94:511–525

  8. Bird RB, Stewart WE, Lightfoot EN (1960) Transport phenomena. Wiley, New York

    Google Scholar 

  9. Blunt MJ, Jackson MD, Piri M, Valvatane PH (2002) Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multiphase flow. Adv Water Resour 25:1069–1089

    Article  Google Scholar 

  10. Bui HH, Fukagawa R, Sako K, Ohno S (2008) Lagrangian meshfree particles method (SPH) for large deformation and failure flows of geomaterial using elastic-plastic soil constitutive model. Int J Numer Anal Met 32:1537–1570

    Article  MATH  Google Scholar 

  11. Campbell CS, Brennen CE (1985) Computer simulation of granular shear flows. J Fluid Mech 151:167–188

    Article  Google Scholar 

  12. Campbell CS (1993) Boundary interactions for two-dimensional granular flows. Part 2. Roughened boundaries. J Fluid Mech 247:137–156

    Article  Google Scholar 

  13. Cancelliere A, Chang C, Foti E, Rothman DH, Succi S (1990) The permeability of a random medium: comparison of simulation with theory. Phys Fluids A 2:2085–2088

    Article  Google Scholar 

  14. Cantor D, Estrada N, Azéma E (2015) Split-cell method for grain fragmentation. Comput Geotech 67:150–156

    Article  Google Scholar 

  15. Chen FF, Yang YS (2012) Microstructure-based characterisation of permeability using a random walk model. Model Simul Mater Sci Eng 20:045005

    Article  Google Scholar 

  16. Chen JK, Beraun JE, Jih CJ (2001) A corrective smoothed particle method for transient elastoplastic dynamics. Comput Mech 27:177–187

    Article  MATH  Google Scholar 

  17. Chen S, Diemer K, Doolen GD, Eggert K, Fu C, Gutman S, Travis BJ (1991) Lattice gas automata for flow through porous media. Physica D 47:72–84

    Article  Google Scholar 

  18. Cleary PW (2004) Large scale industrial DEM modelling. Eng Comput 21:169–204

    Article  MATH  Google Scholar 

  19. Cleary PW, Prakash M, Ha J (2006) Novel applications of smoothed particle hydrodynamics (SPH) in metal forming. J Mater Process Technol 177:41–48

    Article  Google Scholar 

  20. Cleary PW (2008) The effect of particle shape on simple shear flows. Powder Technol 179:144–163

    Article  Google Scholar 

  21. Cleary PW (2009) Industrial particle flow modelling using DEM. Eng Comput 26:698–743

    Article  Google Scholar 

  22. Cleary PW (2010) Elastoplastic deformation during projectile-wall collision. Appl Math Model 34:266–283

    Article  MathSciNet  MATH  Google Scholar 

  23. Cleary PW, Prakash M, Das R, Ha J (2012) Modelling of metal forging using SPH. Appl Math Model 36:3836–3855

    Article  MathSciNet  MATH  Google Scholar 

  24. Cleary PW, Morrison RD (2015) Comminution mechanisms, particle shape evolution and collision energy partitioning in tumbling mills, submitted to: Minerals Engineering

  25. Coulaud O, Morel P, Caltagirone JP (1988) Numerical modeling of nonlinear effects in laminar flow through a porous medium. J Fluid Mech 190:393–407

    Article  MATH  Google Scholar 

  26. Cundall PA, Board M (1988) A microcomputer program for modelling large-strain plasticity problems. In: Swoboda G (ed), Proceedings of the sixth international conference on numerical methods in geomechanics: numerical methods in geomechanics, vol 6, pp 2101–2108

  27. Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Geotechnique 29:47–65

    Article  Google Scholar 

  28. Chai ZH, Shi BC, Lu JH, Guo ZL (2010) Non-Darcy flow in disordered porous media: a lattice Boltzmann study. Comput Fluids 39:2069–2077

    Article  MathSciNet  MATH  Google Scholar 

  29. Combescure A, Maurel B, Potapov S (2008) Modelling dynamic fracture of thin shells filled with fluid: a fully SPH model. Mec Ind 9:167–174

    Google Scholar 

  30. Das R, Cleary PW (2008) The potential for SPH modelling of solid deformation and fracture. In: Reddy D (ed) IUTAM Proceedings book series volume on: “Theoretical, computational and modelling aspects of inelastic media”. Springer, Capetown, pp 287–296

  31. Das R, Cleary PW (2010) Application of SPH for modelling heat transfer and residual stress generation in arc welding. Mater Sci Forum 654–656:2751–2754

    Article  Google Scholar 

  32. Das R, Cleary PW (2013) A mesh-free approach for fracture modelling of gravity dams under earthquake. Int J Fract 179:9–33

    Article  Google Scholar 

  33. Das R, Cleary PW (2015) Evaluation of the accuracy and stability of the classical SPH method under uniaxial compression. J Sci Comput 64:858–897

    Article  MathSciNet  MATH  Google Scholar 

  34. Delaney GW, Cleary PW, Morrison RD, Cummins S, Loveday B (2013) Predicting breakage and the evolution of rock size and shape distributions in AG and SAG mills using DEM. Miner Eng 50–51:132–139

    Article  Google Scholar 

  35. Desrues J, Viggiani G (2004) Strain localization in sand: an overview of the experimental results obtained in Grenoble using stereophotogrammetry. Int J Numer Anal Methods Geomech 28:279–321

    Article  Google Scholar 

  36. d’Humieres D, Bouzidi M, Lallemand P (2001) Thirteen-velocity three-dimensional lattice Boltzmann model. Phys Rev 63, 066702(1-10)

  37. Elbanna AE, Carlson JM (2014) A two-scale model for sheared fault gouge: competition between macroscopic disorder and local viscoplasticity. J Geophys Res Solid Earth 119:4841–4859

    Article  Google Scholar 

  38. Ergun S (1952) Fluid flow through packed columns. Chem Eng Prog 48:89–94

    Google Scholar 

  39. Fand RM, Kim BYK, Lam ACC, Phan RT (1987) Resistance to the flow of fluids through simple and complex porous media whose matrices are composed of randomly packed spheres. J Fluids Eng 109:268–274

    Article  Google Scholar 

  40. Flodin EA, Aydin A, Durlofsky LJ, Yeten B (2001) Representation of fault zone permeability in reservoir flow models. SPE annual technical conference and exhibition, paper number 71617

  41. Giger S, Clennell B, Ciftci B, Clark P, Harbers C, Ricchetti M, Delle Piane C, Freij-Ayoub R, Middleton B, Ter Heege J, Wassing B, Orlic B (2011) Dynamic Fault Seals CSIRO Report No. EP111873, p 219

  42. Ginzburg I, D’Humières D (2003) Multireflection boundary conditions for Lattice Boltzmann models, Phys Rev E, 68:066614(1-30)

  43. Gray JP, Monaghan JJ, Swift RP (2001) SPH elastic dynamics. Comput Methods Appl Mech Eng 190:6641–6662

    Article  MATH  Google Scholar 

  44. Gray GG, Morgan JK, Sanz PF (2014) Overview of continuum and particle dynamics methods for mechanical modeling of contractional geologic structures. J Struct Geol 59:19–36

    Article  Google Scholar 

  45. Govendar I, Cleary PW, Mainza A (2013) Comparisons of PEPT derived charge features in wet milling environments with a friction-adjusted DEM model. Chem Eng Sci 97:162–175

    Article  Google Scholar 

  46. Guo Z, Zhao T (2002) Lattice Boltzmann model for incompressible fows through porous media. Phys Rev E 66:036304

    Article  Google Scholar 

  47. Guo Y, Morgan JK (2004) Influence of normal stress and grain shape on granular friction: results of discrete element simulations. J Geophys Res 109:B12305

    Article  Google Scholar 

  48. Harrison SM, Cleary PW (2014) Towards modelling of fluid flow and food breakage by the teeth in the oral cavity using smoothed particle hydrodynamics (SPH). Eur Food Res Technol 238:185–215

    Article  Google Scholar 

  49. Hazzard JF, Mair K (2003) The importance of the third dimension in granular shear. Geophys Res Lett 30(13):1708

    Article  Google Scholar 

  50. Healy D, Jones RR, Holdsworth RE (2006) Three-dimensional brittle shear fracturing by tensile crack interaction. Nature 439:64–67

    Article  Google Scholar 

  51. Ikari MJ, Saffer DM, Marone C (2009) Frictional and hydrologic properties of clay-rich fault gouge. J Geophys Res 114:B05409

    Article  Google Scholar 

  52. Jeong N (2010) Advanced study about permeability for micro-porous structures using the Lattice Boltzmann method. Transp Porous Media 83:271–288

    Article  Google Scholar 

  53. Jeong N, Choi DH, Lin CL (2006) Prediction of Darcy-Forchheimer drag for micro-porous structures of complex geometry using the lattice Boltzmann method. J Micromech Microeng 16:2240–2250

    Article  Google Scholar 

  54. Karrech A, Regenauer-Lieb K, Poulet T (2011) Continuum damage mechanics for the lithosphere. J Geophys Res B Solid Earth 116:B04205

    Article  Google Scholar 

  55. Karrech A, Schrank C, Freij-Ayoub R, Regenauer-Lieb K (2014) A multi-scaling approach to predict hydraulic damage of poromaterials. Int J Mech Sci 78:1–7

    Article  Google Scholar 

  56. Knipe RJ, Jones G Fisher QJ (1998) Faulting, fault sealing and fluid flow in hydrocarbon reservoirs: an introduction, vol 147. Geological Society, London, Special Publications, pp vii–xxi

  57. Kuwahara F, Nakayama A, Koyama H (1994) Numerical modeling of heat and fluid flow in a porous medium. In: Proceedings of the 10th international heat transfer conference, vol.5, pp 309–314

  58. Larson RE, Higdon JJL (1989) A periodic grain consolidation model of porous media. Phys Fluids A 1:38–46

    Article  MATH  Google Scholar 

  59. Lee SL, Yang JH (1997) Modeling of Darcy–Forchheimer drag for fluid flow across a bank of circular cylinders. Int J Heat Mass Transf 40:3149–3155

    Article  MATH  Google Scholar 

  60. Lemiale V, Mead S, Cleary P (2012) Numerical Modelling of Landslide Events Using a Combination of Continuum and Discrete Methods. In: Ninth international conference on computational fluid dynamics in the minerals and process industries, Melbourne, Australia

  61. Lemiale V, Karantgis L, Broadbridge P (2014a) Smoothed Particle Hydrodynamics applied to the modelling of landslides. Appl Mech Mater 553:519–524

    Article  Google Scholar 

  62. Lemiale V, King P, Rudman M, Prakash M, Cleary PW, Jahedi M, Gulizia S (2014b) Temperature and strain rate effects in cold spray investigated by Smoothed Particle Hydrodynamics. Surf Coati Technol 254:121–130

    Article  Google Scholar 

  63. Lieou CKC, Elbanna AE, Carlson JM (2014) Grain fragmentation in sheared granular flow: weakening effects, energy dissipation, and strain localization. Phys Rev E. doi:10.1103/PhysRevE.89.022203

  64. Lin CL, Miller JD, Garcia C (2005) Saturated flow characteristics in column leaching as described by LB simulation. Miner Eng 18:1045–1051

    Article  Google Scholar 

  65. Liu S, Afacan A, Masliyah J (1994) Steady incompressible laminar flow in porous media. Chem Eng Sci 49:3565–3586

    Article  Google Scholar 

  66. Liu J, Pereira GG, Regenauer-Lieb K (2014) From characterisation of pore structures to simulations of pore-scale fluid flow and upscaling of permeability using microtomography: A case study of heterogeneous carbonates. J Geochem Explor 144:84–96

    Article  Google Scholar 

  67. Lubarda V, Mastilovic S, Knap J (1996) Brittle–ductile transition in porous rocks by cap model. J Eng Mech 122(7):633–642

    Article  Google Scholar 

  68. Lyakhovsky V, Sagy A, Boneh Y, Reches Z (2014) Fault wear by damage evolution during steady-state slip. Pure Appl Geophys 171:3143–3157

    Article  Google Scholar 

  69. Lyakhovsky V, Ben Zion Y (2014) A Continuum damage-breakage faulting model and solid-granular transitions. Pure Appl Geophys 171:3099–3123

    Article  Google Scholar 

  70. Ma GW, Wang QS, Yi XW, Wang XJ (2014) A modified SPH method for dynamic failure simulation of heterogeneous material, Math Probl Eng 2014:808359(1-14)

  71. Macdonald IF, El-Sayed MS, Mow K, Dullien FAL (1979) Flow through porous media-the Ergun equation revisited. Ind Eng Chem Fundam 18:199–208

    Article  Google Scholar 

  72. Mair K, Abe S (2008) 3D numerical simulations of fault gouge evolution during shear: grain size reduction and strain localization. Earth Planet Sci Lett 274:72–81

    Article  Google Scholar 

  73. Menendez B, Zhu W, Wong T-F (1996) Micromechanics of brittle faulting and cataclastic flow in Berea sandstone. J Struct Geol 18:1–16

    Article  Google Scholar 

  74. Monaghan JJ (1992) Smoothed particle hydrodynamics. Ann Rev Astron Astrophy. 30:543–574

    Article  MathSciNet  Google Scholar 

  75. Monaghan JJ (2005) Smoothed particle hydrodynamics. Rep Prog Phys 68:1703–1759

    Article  MathSciNet  MATH  Google Scholar 

  76. Mora P, Place D (1993) A lattice solid model for the nonlinear dynamics of earthquakes. Int J Mod Phys C 4(06):1059–1074

    Article  Google Scholar 

  77. Morgan JK (1999) Numerical simulations of granular shear zones using the distinct element method: 2. Effects of particle size distribution and interparticle friction on mechanical behavior. J Geophys Res 104:2721–2732

    Article  Google Scholar 

  78. Nakayama A, Kuwahara F, Kawamura Y, Koyama H (1995) Three-dimensional numerical simulation of flow through a microscopic porous structure. Proc ASME/JSME Therm Eng Conf 3:313–318

    Google Scholar 

  79. Narvaez A, Yazdchi K, Luding S, Harting J (2013) From creeping to inertial flow in porous media: a lattice Boltzmann-finite element study. J Stat Mech Theory Exp P02038. doi:10.1088/1742-5468/2013/02/P02038

  80. Ngyuen GD, Einav I (2009) The energetic of cataclasis based on breakage mechanics. Pure Appl Geophys 166:1693–1724

    Article  Google Scholar 

  81. O’Sullivan C (2011) Particle-based discrete element modeling: geomechanics perspective. Int J Geomech 11:449–464

    Article  MathSciNet  Google Scholar 

  82. Pan CX, Luo LS, Miller CT (2006) An evaluation of lattice Boltzmann schemes for porous medium flow simulation. Comput Fluids 35:898–909

    Article  MATH  Google Scholar 

  83. Pereira GG (1999) Numerical pore-scale modelling of three-phase flow: comparisons between simulations and experiment. Phys Rev E 59:4229–4242

    Article  Google Scholar 

  84. Pereira GG, Dupuy PM, Cleary PW, Delaney GW (2012) Comparison of permeability of model porous media between SPH and LB. Prog Comput Fluid Dyn 12:176–186

    Article  Google Scholar 

  85. Pereira GG, Prakash M, Cleary PW (2011) SPH modelling of fluid flow at the grain level in a porous medium. Appl Math Model 35:1666–1675

    Article  MathSciNet  MATH  Google Scholar 

  86. Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41:1329–1364

    Article  Google Scholar 

  87. Prakash M, Cleary PW (2015) Modelling highly deformable metal extrusion using SPH. Comput Part Mech 2:19–38

    Article  Google Scholar 

  88. Pramanik R, Deb D (2013) Failure process of brittle rock using smoothed particle hydrodynamics. J Eng Mech 139(11):1551–1565

    Article  Google Scholar 

  89. Pramanik R, Deb D (2015) SPH procedures for modeling intersecting discontinuities in geomaterial. Int J Numer Anal Methods Geomech 39:343–367

    Article  Google Scholar 

  90. Ramsay JG (1980) Shear zone geometry: a review. J Struct Geol 2(1—-2):83–99

    Article  Google Scholar 

  91. Regenauer-Lieb K, Yuen DA (2003) Modeling shear zones in geological and planetary sciences: solid- and fluid-thermal-mechanical approaches. Earth-Sci Rev 63:295–349

    Article  Google Scholar 

  92. Rutquist J (2012) The geomechanics of CO\(_2\) storage in deep sedimentary formations. Geotech Geol Eng 30:525–551

    Article  Google Scholar 

  93. Succi S (2001) The lattice Boltzmann equation for fluid dynamics and beyond. Oxford University Press, Oxford

  94. Wibberley C, Yielding G, Di Toro G (2008) Recent advances in the understanding of fault zone internal structure: a review, Geol Soc London, Special Publications 299:5–33

  95. Wilkins JL (1964) Calculation of elastic-plastic flow. In: Alders B et al (eds) Methods of computational physics. Academic Press, New York, pp 211–263

    Google Scholar 

  96. Wong T-F, Baud P (2012) The brittle–ductile transition in porous rock: a review. J Struct Geol 44:25–53

    Article  Google Scholar 

  97. Wong T-F, David C, Zhu W (1997) The transition from brittle faulting to cataclastic flow in porous sandstones: mechanical deformation. J Geophys Res Solid Earth 102(B2):3009–3025

    Article  Google Scholar 

Download references

Acknowledgments

We thank Flávia Falcão, Melissa Nogueira and Cláudio Lima for advice and comments, and Petrobras for funding of this research.

Author information

Authors and Affiliations

  1. CSIRO, Private Bag 10, Clayton South, 3168, Australia

    Paul W. Cleary, Gerald G. Pereira & Vincent Lemiale

  2. CSIRO, 26 Dick Perry Avenue, Kensington, WA, 6151, Australia

    Claudio Delle Piane & M. Ben Clennell

Authors
  1. Paul W. Cleary
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gerald G. Pereira
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vincent Lemiale
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Claudio Delle Piane
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. M. Ben Clennell
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Paul W. Cleary.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cleary, P.W., Pereira, G.G., Lemiale, V. et al. Multiscale model for predicting shear zone structure and permeability in deforming rock. Comp. Part. Mech. 3, 179–199 (2016). https://doi.org/10.1007/s40571-015-0073-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40571-015-0073-4

Keywords

Search

Navigation