Acta Geotechnica

, Volume 10, Issue 4, pp 399–419 | Cite as

Stress-induced anisotropy in granular materials: fabric, stiffness, and permeability

Research Paper

Abstract

The loading of a granular material induces anisotropies of the particle arrangement (fabric) and of the material’s strength, incremental stiffness, and permeability. Thirteen measures of fabric anisotropy are developed, which are arranged in four categories: as preferred orientations of the particle bodies, the particle surfaces, the contact normals, and the void space. Anisotropy of the voids is described through image analysis and with Minkowski tensors. The thirteen measures of anisotropy change during loading, as determined with three-dimensional discrete element simulations of biaxial plane strain compression with constant mean stress. Assemblies with four different particle shapes were simulated. The measures of contact orientation are the most responsive to loading, and they change greatly at small strains, whereas the other measures lag the loading process and continue to change beyond the state of peak stress and even after the deviatoric stress has nearly reached a steady state. The paper implements a methodology for characterizing the incremental stiffness of a granular assembly during biaxial loading, with orthotropic loading increments that preserve the principal axes of the fabric and stiffness tensors. The linear part of the hypoplastic tangential stiffness is monitored with oedometric loading increments. This stiffness increases in the direction of the initial compressive loading but decreases in the direction of extension. Anisotropy of this stiffness is closely correlated with a particular measure of the contact fabric. Permeabilities are measured in three directions with lattice Boltzmann methods at various stages of loading and for assemblies with four particle shapes. Effective permeability is negatively correlated with the directional mean free path and is positively correlated with pore width, indicating that the anisotropy of effective permeability induced by loading is produced by changes in the directional hydraulic radius.

Keywords

Anisotropic permeability Discrete element method Fabric Granular material Stress-induced anisotropy 

References

  1. 1.
    Adler PM (1992) Porous media: geometry and transports. Butterworth-Heinemann, BostonGoogle Scholar
  2. 2.
    Andò E, Viggiani G, Hall SA, Desrues J (2013) Experimental micro-mechanics of granular media studied by X-ray tomography: recent results and challenges. Géotech Lett 3:142–146CrossRefGoogle Scholar
  3. 3.
    Antony SJ, Kuhn MR (2004) Influence of particle shape on granular contact signatures and shear strength: new insights from simulations. Int J Solids Struct Granul Mech 41(21):5863–5870CrossRefGoogle Scholar
  4. 4.
    Arns CH, Bauget F, Limaye A, Arthur Sakellariou TJ, Senden APS, Sok RM, Pinczewski WV, Bakke S, Berge LI et al (2005) Pore-scale characterization of carbonates using X-ray microtomography. SPE J Richardson 10(4):475CrossRefGoogle Scholar
  5. 5.
    Arthur JRF, Chua KS, Dunstan T (1977) Induced anisotropy in a sand. Géotechnique 27(1):13–30CrossRefGoogle Scholar
  6. 6.
    Arthur JRF, Menzies BK (1972) Inherent anisotropy in a sand. Géotechnique 22(1):115–128CrossRefGoogle Scholar
  7. 7.
    Azéma E, Radjaï F, Peyroux R, Saussine G (2007) Force transmission in a packing of pentagonal particles. Phys Rev E 76:011301CrossRefGoogle Scholar
  8. 8.
    Bardet JP (1994) Numerical simulations of the incremental responses of idealized granular materials. Int J Plast 10(8):879–908CrossRefGoogle Scholar
  9. 9.
    Bathurst RJ, Rothenburg L (1990) Observations on stress–force–fabric relationships in idealized granular materials. Mech Mater 9:65–80 fabric, DEM, circlesCrossRefGoogle Scholar
  10. 10.
    Bear J (2013) Dynamics of fluids in porous media. Courier Corporation, ChelmsfordGoogle Scholar
  11. 11.
    Calvetti F, Combe G, Lanier J (1997) Experimental micromechanical analysis of a 2D granular material: relation between structure evolution and loading path. Mech Cohesive Frict Mater 2(2):121–163CrossRefGoogle Scholar
  12. 12.
    Calvetti F, Viggiani G, Tamagnini C (2003) A numerical investigation of the incremental behavior of granular soils. Rivista Italiana di Geotecnica 3:11–29Google Scholar
  13. 13.
    Chapuis RP, Gill DE, Baass K (1989) Laboratory permeability tests on sand: influence of the compaction method on anisotropy. Can Geotech J 26(4):614–622CrossRefGoogle Scholar
  14. 14.
    Chen Y-C, Hung H-Y (1991) Evolution of shear modulus and fabric during shearing deformation. Soils Found 31(4):148–160CrossRefGoogle Scholar
  15. 15.
    Darve F (1990) The expression of rheological laws in incremental form and the main classes of constitutive equations. In: Darve F (ed) Geomaterials: constitutive equations and modelling. Elsevier, London, pp 123–147Google Scholar
  16. 16.
    Darve F, Roguiez X (1999) Constitutive relations for soils: new challenges. Rivista Italiana di Geotecnica 4:9–35Google Scholar
  17. 17.
    DeHoff RT, Aigeltinger EH, Craig KR (1972) Experimental determination of the topological properties of three-dimensional microstructures. J Microsc 95(1):69–91CrossRefGoogle Scholar
  18. 18.
    Dobry R, Ladd RS, Yokel FY, Chung RM, Powell D (1982) Prediction of pore water pressure buildup and liquefaction of sands during earthquakes by the cyclic strain method. NBS Building Science Series 138, Natl. Bureau of StandardsGoogle Scholar
  19. 19.
    Fredrich JT, Menéndez B, Wong TF (1995) Imaging the pore structure of geomaterials. Science 268(5208):276–279CrossRefGoogle Scholar
  20. 20.
    Guo N, Zhao J (2013) The signature of shear-induced anisotropy in granular media. Comput Geotech 47:1–15MathSciNetCrossRefGoogle Scholar
  21. 21.
    Hall SA, Muir Wood D, Ibraim E, Viggiani G (2010) Localised deformation patterning in 2D granular materials revealed by digital image correlation. Granul Matter 12(1):1–14CrossRefGoogle Scholar
  22. 22.
    Hilpert M, Glantz R, Miller CT (2003) Calibration of a pore-network model by a pore-morphological analysis. Transp Porous Media 51(3):267–285CrossRefGoogle Scholar
  23. 23.
    Hoque E, Tatsuoka F (1998) Anisotropy in elastic deformation of granular materials. Soils Found 38(1):163–179CrossRefGoogle Scholar
  24. 24.
    Ishibashi I, Chen Y-C, Chen M-T (1991) Anisotropic behavior of Ottawa sand in comparison with glass spheres. Soils Found 31(1):145–155CrossRefGoogle Scholar
  25. 25.
    Kanatani K (1988) Stereological estimation of microstructures in materials. In: Satake M, Jenkins JT (eds) Micromechanics of granular materials. Elsevier, Amsterdam, pp 1–10Google Scholar
  26. 26.
    Konishi J, Oda M, Nemat-Nasser S (1982) Inherent anisotropy and shear strength of assembly of oval cross-sectional rods. In: Vermeer PA, Luger HJ (eds) Deformation and failure of granular materials. A.A. Balkema Pub, Rotterdam, pp 403–412Google Scholar
  27. 27.
    Koutsourelakis PS, Deodatis G (2006) Simulation of multidimensional binary random fields with application to modeling of two-phase random media. J Eng Mech 132(6):619–631CrossRefGoogle Scholar
  28. 28.
    Kruyt NP (2012) Micromechanical study of fabric evolution in quasi-static deformation of granular materials. Mech Mater 44:120–129CrossRefGoogle Scholar
  29. 29.
    Kruyt NP, Rothenburg L (2009) Plasticity of granular materials: a structural-mechanics view. In: AIP conference proceedings vol 1145, p 1073Google Scholar
  30. 30.
    Kuhn MR (2002) OVAL and OVALPLOT: programs for analyzing dense particle assemblies with the Discrete Element Method. http://faculty.up.edu/kuhn/oval/oval.html
  31. 31.
    Kuhn MR (2003) Smooth convex three-dimensional particle for the discrete element method. J Eng Mech 129(5):539–547CrossRefGoogle Scholar
  32. 32.
    Kuhn MR (2010) Micro-mechanics of fabric and failure in granular materials. Mech Mater 42(9):827–840CrossRefGoogle Scholar
  33. 33.
    Kuhn MR, Renken H, Mixsell A, Kramer S (2014) Investigation of cyclic liquefaction with discrete element simulations. J Geotech Geoenviron Eng 140(12):04014075CrossRefGoogle Scholar
  34. 34.
    Kuo C-Y, Frost JD, Chameau J-LA (1998) Image analysis determination of stereology based fabric tensors. Géotechnique 48(4):515–525CrossRefGoogle Scholar
  35. 35.
    Kwiecien MJ, Macdonald IF, Dullien FAL (1990) Three-dimensional reconstruction of porous media from serial section data. J Microsc 159(3):343–359CrossRefGoogle Scholar
  36. 36.
    Li X, Dafalias Y (2002) Constitutive modeling of inherently anisotropic sand behavior. J Geotech Geoenviron Eng 128(10):868–880CrossRefGoogle Scholar
  37. 37.
    Liang Z, Ioannidis MA, Chatzis I (2000) Geometric and topological analysis of three-dimensional porous media: pore space partitioning based on morphological skeletonization. J Colloid Interface Sci 221(1):13–24CrossRefGoogle Scholar
  38. 38.
    Lindquist WB, Lee S-M, Coker DA, Jones KW, Spanne P (1996) Medial axis analysis of void structure in three-dimensional tomographic images of porous media. J Geophys Res Solid Earth (1978–2012) 101(B4):8297–8310CrossRefGoogle Scholar
  39. 39.
    Magoariec H, Danescu A, Cambou B (2008) Nonlocal orientational distribution of contact forces in granular samples containing elongated particles. Acta Geotech 3(1):49–60CrossRefGoogle Scholar
  40. 40.
    Majmudar TS, Bhehringer RP (2005) Contact force measurements and stress-induced anisotropy in granular materials. Nature 435(1079):1079–1082CrossRefGoogle Scholar
  41. 41.
    Michielsen K, De Raedt H (2001) Integral-geometry morphological image analysis. Phys Rep 347(6):461–538MathSciNetCrossRefGoogle Scholar
  42. 42.
    Mitchell JK, Soga K (2005) Fundamentals of soil behavior, 3rd edn. Wiley, New YorkGoogle Scholar
  43. 43.
    Ng T-T (2001) Fabric evolution of ellipsoidal arrays with different particle shapes. J Eng Mech 127(10):994–999CrossRefGoogle Scholar
  44. 44.
    Oda M (1972) Initial fabrics and their relations to mechanical properties of granular material. Soils Found 12(1):17–36CrossRefGoogle Scholar
  45. 45.
    Oda M (1972) The mechanism of fabric changes during compressional deformation of sand. Soils Found 12(2):1–18CrossRefGoogle Scholar
  46. 46.
    Oda M, Kazama H (1998) Microstructure of shear bands and its relation to the mechanisms of dilatancy and failure of dense granular soils. Géotechnique 48(4):465–481CrossRefGoogle Scholar
  47. 47.
    Oda M, Nemat-Nasser S, Konishi J (1985) Stress-induced anisotropy in granular masses. Soils Found 25(3):85–97CrossRefGoogle Scholar
  48. 48.
    Ouadfel H, Rothenburg L (1999) An algorithm for detecting inter-ellipsoid contacts. Comput Geotech 24(4):245–263CrossRefGoogle Scholar
  49. 49.
    Ouadfel H, Rothenburg L (2001) Stress–force–fabric relationship for assemblies of ellipsoids. Mech Mater 33(4):201–221CrossRefGoogle Scholar
  50. 50.
    Peña AA, García-Rojo R, Herrmann HJ (2007) Influence of particle shape on sheared dense granular media. Granul Matter 9:279–291CrossRefGoogle Scholar
  51. 51.
    Pietruszczak S, Mroz Z (2001) On failure criteria for anisotropic cohesive–frictional materials. Int J Numer Anal Methods Geomech 25(5):509–524CrossRefGoogle Scholar
  52. 52.
    Prasad PB, Jernot JP (1991) Topological description of the densification of a granular medium. J Microsc 163(2):211–220CrossRefGoogle Scholar
  53. 53.
    Radjai F, Wolf DE, Jean M, Moreau J-J (1998) Bimodal character of stress transmission in granular packings. Phys Rev Lett 80(1):61–64CrossRefGoogle Scholar
  54. 54.
    Reeves PC, Celia MA (1996) A functional relationship between capillary pressure, saturation, and interfacial area as revealed by a pore-scale network model. Water Resour Res 32(8):2345–2358CrossRefGoogle Scholar
  55. 55.
    Rothenburg L, Bathurst RJ (1989) Analytical study of induced anisotropy in idealized granular materials. Géotechnique 39(4):601–614CrossRefGoogle Scholar
  56. 56.
    Rothenburg L, Bathurst RJ (1992) Micromechanical features of granular assemblies with planar elliptical particles. Géotechnique 42(1):79–95CrossRefGoogle Scholar
  57. 57.
    Santamarina JC, Cascante G (1996) Stress anisotropy and wave propagation: a micromechanical view. Can Geotech J 33(5):770–782CrossRefGoogle Scholar
  58. 58.
    Satake M (1982) Fabric tensor in granular materials. In: Vermeer PA, Luger HJ (eds) Proceedings of IUTAM symposium on deformation and failure of granular materials. A.A. Balkema, Rotterdam, pp 63–68Google Scholar
  59. 59.
    Schröder-Turk GE, Mickel W, Kapfer SC, Klatt MA, Schaller FM, Hoffmann MJF, Kleppmann N, Armstrong P, Inayat A, Hug D, Reichelsdorfer M, Peukert W, Schwieger W, Mecke K (2011) Minkowski tensor shape analysis of cellular, granular and porous structures. Adv Mater 23(22–23):2535–2553CrossRefGoogle Scholar
  60. 60.
    Schröder-Turk GE, Mickel W, Kapfer SC, Schaller FM, Breidenbach B, Hug D, Mecke K (2010) Minkowski tensors of anisotropic spatial structure. arXiv preprint arXiv:1009.2340
  61. 61.
    Serra J (1982) Image analysis and mathematical morphology. Academic Press, LondonGoogle Scholar
  62. 62.
    Sun WC (2015) A stabilized finite element formulation for monolithic thermo-hydro-mechanical simulations at finite strain. Int J Numer Methods Eng. doi:10.1002/nme.4910 Google Scholar
  63. 63.
    Sun WC, Andrade JE, Rudnicki JW (2011) Multiscale method for characterization of porous microstructures and their impact on macroscopic effective permeability. Int J Numer Meth Eng 88(12):1260–1279MathSciNetCrossRefGoogle Scholar
  64. 64.
    Sun WC, Andrade JE, Rudnicki JW, Eichhubl P (2011) Connecting microstructural attributes and permeability from 3D tomographic images of in situ shear-enhanced compaction bands using multiscale computations. Geophys Res Lett 38(10):L10302Google Scholar
  65. 65.
    Sun WC, Chen Q, Ostien JT (2014) Modeling the hydro-mechanical responses of strip and circular punch loadings on water-saturated collapsible geomaterials. Acta Geotech 9(5):903–934CrossRefGoogle Scholar
  66. 66.
    Sun WC, Kuhn MR, Rudnicki JW (2013) A multiscale DEM-LBM analysis on permeability evolutions inside a dilatant shear band. Acta Geotech 8(5):465–480CrossRefGoogle Scholar
  67. 67.
    Sun WC, Ostien JT, Salinger AG (2013) A stabilized assumed deformation gradient finite element formulation for strongly coupled poromechanical simulations at finite strain. Int J Numer Anal Meth Geomech 37(16):2755–2788Google Scholar
  68. 68.
    Tatsuoka F, Nakamura S, Huang C-C, Tani K (1990) Strength anisotropy and shear band direction in plane strain tests of sand. Soils Found 30(1):35–54CrossRefGoogle Scholar
  69. 69.
    Thornton C (1990) induced anisotropy and energy dissipation in particulate material—results from computer-simulated experiments. In: Boehler JP (ed) Yielding, damage, and failure of anisotropic solids. Mechanical Engineering Pub, London, pp 113–130Google Scholar
  70. 70.
    Thornton C, Antony SJ (1998) Quasi-static deformation of particulate media. Philos Trans R Soc Lond A 356(1747):2763–2782CrossRefGoogle Scholar
  71. 71.
    Thornton C, Zhang L (2010) On the evolution of stress and microstructure during general 3D deviatoric straining of granular media. Géotechnique 60(5):333–341CrossRefGoogle Scholar
  72. 72.
    Vogel HJ (1997) Morphological determination of pore connectivity as a function of pore size using serial sections. Eur J Soil Sci 48(3):365–377CrossRefGoogle Scholar
  73. 73.
    Wang Y, Mok C (2008) Mechanisms of small-strain shear-modulus anisotropy in soils. J Geotech Geoenviron Eng 134(10):1516–1530CrossRefGoogle Scholar
  74. 74.
    White JA, Borja RI, Fredrich JT (2006) Calculating the effective permeability of sandstone with multiscale lattice Boltzmann/finite element simulations. Acta Geotech 1(4):195–209CrossRefGoogle Scholar
  75. 75.
    Wong RCK (2003) A model for strain-induced permeability anisotropy in deformable granular media. Can Geotech J 40(1):95–106CrossRefGoogle Scholar
  76. 76.
    Zaretskiy Y, Geiger S, Sorbie K, Förster M (2010) Efficient flow and transport simulations in reconstructed 3D pore geometries. Adv Water Resour 33(12):1508–1516CrossRefGoogle Scholar
  77. 77.
    Zhao J, Guo N (2013) A new definition on critical state of granular media accounting for fabric anisotropy. AIP Conf Proc 1542:229–232CrossRefGoogle Scholar
  78. 78.
    Zhu W, Montési LGJ, Wong T (2007) A probabilistic damage model of stress-induced permeability anisotropy during cataclastic flow. J Geophys Res 112(B10):B10207CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Civil Engineering, Donald P. Shiley School of EngineeringUniversity of PortlandPortlandUSA
  2. 2.Department of Civil Engineering and Engineering Mechanics, The Fu Foundation School of Engineering and Applied ScienceColumbia University in the City of New YorkNew YorkUSA

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