Skip to main content
Log in

A multiscale DEM-LBM analysis on permeability evolutions inside a dilatant shear band

  • Research Paper
  • Published:
Acta Geotechnica Aims and scope Submit manuscript

Abstract

This paper presents a multiscale analysis of a dilatant shear band using a three-dimensional discrete element method and a lattice Boltzmann/finite element hybrid scheme. In particular, three-dimensional simple shear tests are conducted via the discrete element method. A spatial homogenization is performed to recover the macroscopic stress from the micro-mechanical force chains. The pore geometries of the shear band and host matrix are quantitatively evaluated through morphology analyses and lattice Boltzmann/finite element flow simulations. Results from the discrete element simulations imply that grain sliding and rotation occur predominately with the shear band. These granular motions lead to dilation of pore space inside the shear band and increases in local permeability. While considerable anisotropy in the contact fabric is observed with the shear band, anisotropy of the permeability is, at most, modest in the assemblies composed of spherical grains.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

References

  1. Andò E, Hall SA, Viggiani G, Desrues J, Bésuelle P (2012) Grain-scale experimental investigation of localised deformation in sand: a discrete particle tracking approach. Acta Geotech 7:1–13

    Article  Google Scholar 

  2. Antonellini M, Pollard DD (1995) Distinct element modeling of deformation bands in sandstone. J Struct Geol 17:1165–1182

    Article  Google Scholar 

  3. Aydin A, Borja RI, Eichhubl P (2005) Geological and mathematical framework for failure modes in granular rock. J Struct Geol 29:1831–1842

    Google Scholar 

  4. Bear J (1972) Dynamics of fluids in porous media. Elsevier Publishing Company, New York

    MATH  Google Scholar 

  5. Bésuelle P, Rudnicki JW (2004) Localization: shear bands and compaction bands. International Geophysics Series, vol 89, pp 219–321

  6. Bésuelle P, Desrues J, Raynaud S (2000) Experimental characterisation of the localisation phenomenon inside a vosges sandstone in a triaxial cell. Int J Rock Mech Min Sci 37(8):1223–1237

    Article  Google Scholar 

  7. Borja RI, Song X, Rechenmacher AL, Abedi S, Wu W (2013) Shear band in sand with spatially varying density. J Mech Phys Solids 61(1):219–234

    Article  Google Scholar 

  8. Boutt DF, Cook BK, Williams JR (2011) A coupled fluid-solid model for problems in geomechanics: application to sand production. Int J Num Anal Methods Geomech 35(9):997–1018

    Article  MATH  Google Scholar 

  9. Casagrande A (1936) Characteristics of cohensionless soils affecting the stability of slops and earth fills. J Boston Soc Civil Eng 23:13–32

    Google Scholar 

  10. Chen C, Packman AI, Gaillard JF (2008) Using X-ray micro-tomography and pore-scale modeling to quantify sediment mixing and fluid flow in a developing streambed. Geophys Res Lett 35(14)

  11. Chupin O, Rechenmacher AL, Abedi S (2012) Finite strain analysis of nonuniform deformation inside shear bands in sands. Int J Num Anal Methods Geomech 36(14):1651–1666

    Article  Google Scholar 

  12. Cundall PA (1988) Computer simulations of dense sphere assemblies. In: M Satake, JT Jenkins (eds) Micromechanics of granular materials, Elsevier Science Pub. B.V., Amsterdam, pp 113–123

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

    Article  Google Scholar 

  14. El Shamy U, Zeghal M (2005) Coupled continuum-discrete model for saturated granular soils. J Eng Mech 131(4):413–426

    Article  Google Scholar 

  15. Feng YT, Han K, Owen DRJ (2007) Coupled lattice Boltzmann method and discrete element modelling of particle transport in turbulent fluid flows: computational issues. Int J Num Anal Methods Geomech 72(9):1111–1134

    MathSciNet  MATH  Google Scholar 

  16. Hall S, Bornert M, Desrues J, Pannier Y, Lenoir N, Viggiani G, Bésuelle P (2010) Discrete and continuum analysis of localized deformation in sand using x-ray ct and volumetric digital image correlation. Géotechnique 60:315–322

    Article  Google Scholar 

  17. Hilfer R, Manwart C (2001) Permeability and conductivity for reconstruction models of porous media. Phys Rev E 64

  18. Houlsby GT (2009) Potential particles: a method for modelling non-circular particles in DEM. Comput Geotech 36(6):953–959

    Article  Google Scholar 

  19. Irmay S (1954) On the hydraulic conductivity of unsaturated soils. Trans Am Geophys Union 35:463–468

    Article  Google Scholar 

  20. Jensen JL (1991) Use of geometric average for effective permeability estimation. Math Geol 23(6):833–840

    Article  Google Scholar 

  21. Johnson KL (1985) Contact mechanics, Cambridge University Press, Cambridge

  22. Johnson DL, Koplik J, Schwartz LM (1986) New pore-size parameter characterizing transport in porous media. Phys Rev Lett 57:2564–2567

    Article  Google Scholar 

  23. Kuhn MR (2005) Scaling in granular materials. In: García-Rojo R, Herrmann HJ, McNamara S (eds) Powders and grains 2005. A.A. Balkema, Leiden, pp 115–122

  24. Kuhn MR (2011) Implementation of the Jäger contact model for discrete element simulations. Chem Eng. 88(1):66–82

    MATH  Google Scholar 

  25. Kuhn MR, Bagi K (2004) Contact rolling and deformation in granular media. Int J Solids Struct 41:5793–5820

    Article  MATH  Google Scholar 

  26. Legland D, Kiêu K, Devaux M-F (2011) Computation of Minkowski measures on 2d and 3d binary images. Image Anal Stereol 26(2):1854–5165

    Google Scholar 

  27. Lenoir N, Andrade JE, Sun WC, Rudnicki JW (2010) Permeability measurements in sandstones using x-ray ct and lattice Boltzmann calculations inside and outside of compaction bands. Adv Comput Tomogr Geomater. GEOX2010, ISTE & Wiley, pp 279–286

  28. Lindquist WB, Vankatarangan A, Dunsmuir J, Wong T-F (2000) Pore and throat size distributions measured from synchrotron x-ray tomographic images of fontainebleau sandstone. J Geophys Res 105:21509–21527

    Article  Google Scholar 

  29. Louis L, Baud P, Wong T-F (2007) Characterization of pore-space heterogeneity in sandstone by x-ray computed tomography. Geol Soc Lond Special Publ 284(1):127–146

    Article  Google Scholar 

  30. Mitchell JK, Soga K (2005) Fundamentals of soil behavior, 3rd edn. Wiley, New Jersey

  31. Oda M, Nemat-Nasser S, Mehrabadi MM (1982) A statistical study of fabric in a random assembly of spherical granules. Int J Num Anal Methods Geomech 6:77–94

    Article  MathSciNet  MATH  Google Scholar 

  32. Rechenmacher AL, Abedi S, Chupin O, Orlando AD (2011) Characterization of mesoscale instabilities in localized granular shear using digital image correlation. Acta Geotech 6:205–217

    Article  Google Scholar 

  33. Rudnicki JW (2004) Shear and compaction band formation on an elliptic yield cap. J Geophys Res 109:B3

    Article  Google Scholar 

  34. Rudnicki JW, Rice JR (1975) Conditions for the localization of deformation in pressure-sensitive dilatant materials. J Mech Phys Solids 23:371–394

    Article  Google Scholar 

  35. Satake M (1982) Fabric tensor in granular materials. In Vermeer PA, and Luger HJ (eds) Proceedings of IUTAM symposium on deformation and failure of granular materials. A.A. Balkema, Rotterdam, pp 63–68

  36. Scheidegger AE (1960) The physics of flow through porous media. University of Toronto Press, Toronto

    MATH  Google Scholar 

  37. Schneider CA, Rashand WS, Eliceiri KW (2012) Nih image to imagej: 25 years of image analysis. Nat Methods 9:671–675

    Article  Google Scholar 

  38. Succi S (2001) The lattice Boltzmann equation. Oxford University Press, Oxford

    MATH  Google Scholar 

  39. Sun WC, Andrade JE, Rudnicki JW (2011a) Multiscale method for characterization of porous microstructures and their impact on macroscopic effective permeability. Int J Num Methods Eng 88:1260–1279

    Article  MathSciNet  MATH  Google Scholar 

  40. Sun WC, Andrade JE, Rudnicki JW, Eichhubl E (2011b) Connecting microstructural attributes and permeability from 3d tomographic images of in situ shear-enhanced compaction bands using multiscale computations. Geophys Res Lett 38:L10302

    Article  Google Scholar 

  41. Talon L, Bauer D, Gland N, Youssef S, Auradou H, Ginzburg I (2012) Assessment of the two relaxation time lattice-Boltzmann scheme to simulate stokes flow in porous media. Water Resourc Res 48:W04526

    Article  Google Scholar 

  42. Thornton C (2000) Numerical simulations of deviatoric shear deformation of granular media. Géotechnique 50(1):43–53

    Article  Google Scholar 

  43. Thornton C, Randall CW (1988) Applications of theoretical contact mechanics to solid particle system simulation. In Satake M, Jenkins JT (eds) Micromechanics of granular materials, Elsevier Science Pub. B.V., Amsterdam, pp 133–142

  44. Wawersik WR et al (2008) Terrestrial sequestration of CO2: an assessment of research needs. Adv Geophys 43:97–117

    Article  Google Scholar 

  45. White JA, Borja RI, Fredrich JT (2006) Calculating the effective permeability of sandstone with multiscale lattice Boltzmann/finite element simulations. Acta Geotech 1:195–209

    Article  Google Scholar 

Download references

Acknowledgments

The authors gratefully acknowledge the support provided by the Geosciences Research Program of the U. S. Department of Energy under Grant No. DE-FG02-08ER15980 to Northwestern University. We also thank Professor Teng-fong Wong for fruitful discussion. We thank Professor Ronaldo I Borja and the anonymous reviewer for helpful suggestions that improved the paper.

Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to WaiChing Sun.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sun, W., Kuhn, M.R. & Rudnicki, J.W. A multiscale DEM-LBM analysis on permeability evolutions inside a dilatant shear band. Acta Geotech. 8, 465–480 (2013). https://doi.org/10.1007/s11440-013-0210-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11440-013-0210-2

Keywords

Navigation