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

Acta Geotechnica - Tập 10 - Trang 399-419 - 2015
Matthew R. Kuhn1, WaiChing Sun2, Qi Wang2
1Department of Civil Engineering, Donald P. Shiley School of Engineering, University of Portland, Portland, USA
2Department of Civil Engineering and Engineering Mechanics, The Fu Foundation School of Engineering and Applied Science, Columbia University in the City of New York, New York, USA

Tóm tắt

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.

Tài liệu tham khảo

Adler PM (1992) Porous media: geometry and transports. Butterworth-Heinemann, Boston 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 3:142–146 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):5863–5870 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):475 Arthur JRF, Chua KS, Dunstan T (1977) Induced anisotropy in a sand. Géotechnique 27(1):13–30 Arthur JRF, Menzies BK (1972) Inherent anisotropy in a sand. Géotechnique 22(1):115–128 Azéma E, Radjaï F, Peyroux R, Saussine G (2007) Force transmission in a packing of pentagonal particles. Phys Rev E 76:011301 Bardet JP (1994) Numerical simulations of the incremental responses of idealized granular materials. Int J Plast 10(8):879–908 Bathurst RJ, Rothenburg L (1990) Observations on stress–force–fabric relationships in idealized granular materials. Mech Mater 9:65–80 fabric, DEM, circles Bear J (2013) Dynamics of fluids in porous media. Courier Corporation, Chelmsford 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):121–163 Calvetti F, Viggiani G, Tamagnini C (2003) A numerical investigation of the incremental behavior of granular soils. Rivista Italiana di Geotecnica 3:11–29 Chapuis RP, Gill DE, Baass K (1989) Laboratory permeability tests on sand: influence of the compaction method on anisotropy. Can Geotech J 26(4):614–622 Chen Y-C, Hung H-Y (1991) Evolution of shear modulus and fabric during shearing deformation. Soils Found 31(4):148–160 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 123–147 Darve F, Roguiez X (1999) Constitutive relations for soils: new challenges. Rivista Italiana di Geotecnica 4:9–35 DeHoff RT, Aigeltinger EH, Craig KR (1972) Experimental determination of the topological properties of three-dimensional microstructures. J Microsc 95(1):69–91 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 Standards Fredrich JT, Menéndez B, Wong TF (1995) Imaging the pore structure of geomaterials. Science 268(5208):276–279 Guo N, Zhao J (2013) The signature of shear-induced anisotropy in granular media. Comput Geotech 47:1–15 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):1–14 Hilpert M, Glantz R, Miller CT (2003) Calibration of a pore-network model by a pore-morphological analysis. Transp Porous Media 51(3):267–285 Hoque E, Tatsuoka F (1998) Anisotropy in elastic deformation of granular materials. Soils Found 38(1):163–179 Ishibashi I, Chen Y-C, Chen M-T (1991) Anisotropic behavior of Ottawa sand in comparison with glass spheres. Soils Found 31(1):145–155 Kanatani K (1988) Stereological estimation of microstructures in materials. In: Satake M, Jenkins JT (eds) Micromechanics of granular materials. Elsevier, Amsterdam, pp 1–10 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 403–412 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):619–631 Kruyt NP (2012) Micromechanical study of fabric evolution in quasi-static deformation of granular materials. Mech Mater 44:120–129 Kruyt NP, Rothenburg L (2009) Plasticity of granular materials: a structural-mechanics view. In: AIP conference proceedings vol 1145, p 1073 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 Kuhn MR (2003) Smooth convex three-dimensional particle for the discrete element method. J Eng Mech 129(5):539–547 Kuhn MR (2010) Micro-mechanics of fabric and failure in granular materials. Mech Mater 42(9):827–840 Kuhn MR, Renken H, Mixsell A, Kramer S (2014) Investigation of cyclic liquefaction with discrete element simulations. J Geotech Geoenviron Eng 140(12):04014075 Kuo C-Y, Frost JD, Chameau J-LA (1998) Image analysis determination of stereology based fabric tensors. Géotechnique 48(4):515–525 Kwiecien MJ, Macdonald IF, Dullien FAL (1990) Three-dimensional reconstruction of porous media from serial section data. J Microsc 159(3):343–359 Li X, Dafalias Y (2002) Constitutive modeling of inherently anisotropic sand behavior. J Geotech Geoenviron Eng 128(10):868–880 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):13–24 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):8297–8310 Magoariec H, Danescu A, Cambou B (2008) Nonlocal orientational distribution of contact forces in granular samples containing elongated particles. Acta Geotech 3(1):49–60 Majmudar TS, Bhehringer RP (2005) Contact force measurements and stress-induced anisotropy in granular materials. Nature 435(1079):1079–1082 Michielsen K, De Raedt H (2001) Integral-geometry morphological image analysis. Phys Rep 347(6):461–538 Mitchell JK, Soga K (2005) Fundamentals of soil behavior, 3rd edn. Wiley, New York Ng T-T (2001) Fabric evolution of ellipsoidal arrays with different particle shapes. J Eng Mech 127(10):994–999 Oda M (1972) Initial fabrics and their relations to mechanical properties of granular material. Soils Found 12(1):17–36 Oda M (1972) The mechanism of fabric changes during compressional deformation of sand. Soils Found 12(2):1–18 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):465–481 Oda M, Nemat-Nasser S, Konishi J (1985) Stress-induced anisotropy in granular masses. Soils Found 25(3):85–97 Ouadfel H, Rothenburg L (1999) An algorithm for detecting inter-ellipsoid contacts. Comput Geotech 24(4):245–263 Ouadfel H, Rothenburg L (2001) Stress–force–fabric relationship for assemblies of ellipsoids. Mech Mater 33(4):201–221 Peña AA, García-Rojo R, Herrmann HJ (2007) Influence of particle shape on sheared dense granular media. Granul Matter 9:279–291 Pietruszczak S, Mroz Z (2001) On failure criteria for anisotropic cohesive–frictional materials. Int J Numer Anal Methods Geomech 25(5):509–524 Prasad PB, Jernot JP (1991) Topological description of the densification of a granular medium. J Microsc 163(2):211–220 Radjai F, Wolf DE, Jean M, Moreau J-J (1998) Bimodal character of stress transmission in granular packings. Phys Rev Lett 80(1):61–64 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):2345–2358 Rothenburg L, Bathurst RJ (1989) Analytical study of induced anisotropy in idealized granular materials. Géotechnique 39(4):601–614 Rothenburg L, Bathurst RJ (1992) Micromechanical features of granular assemblies with planar elliptical particles. Géotechnique 42(1):79–95 Santamarina JC, Cascante G (1996) Stress anisotropy and wave propagation: a micromechanical view. Can Geotech J 33(5):770–782 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 63–68 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):2535–2553 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 Serra J (1982) Image analysis and mathematical morphology. Academic Press, London 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 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):1260–1279 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):L10302 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):903–934 Sun WC, Kuhn MR, Rudnicki JW (2013) A multiscale DEM-LBM analysis on permeability evolutions inside a dilatant shear band. Acta Geotech 8(5):465–480 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):2755–2788 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):35–54 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 113–130 Thornton C, Antony SJ (1998) Quasi-static deformation of particulate media. Philos Trans R Soc Lond A 356(1747):2763–2782 Thornton C, Zhang L (2010) On the evolution of stress and microstructure during general 3D deviatoric straining of granular media. Géotechnique 60(5):333–341 Vogel HJ (1997) Morphological determination of pore connectivity as a function of pore size using serial sections. Eur J Soil Sci 48(3):365–377 Wang Y, Mok C (2008) Mechanisms of small-strain shear-modulus anisotropy in soils. J Geotech Geoenviron Eng 134(10):1516–1530 White JA, Borja RI, Fredrich JT (2006) Calculating the effective permeability of sandstone with multiscale lattice Boltzmann/finite element simulations. Acta Geotech 1(4):195–209 Wong RCK (2003) A model for strain-induced permeability anisotropy in deformable granular media. Can Geotech J 40(1):95–106 Zaretskiy Y, Geiger S, Sorbie K, Förster M (2010) Efficient flow and transport simulations in reconstructed 3D pore geometries. Adv Water Resour 33(12):1508–1516 Zhao J, Guo N (2013) A new definition on critical state of granular media accounting for fabric anisotropy. AIP Conf Proc 1542:229–232 Zhu W, Montési LGJ, Wong T (2007) A probabilistic damage model of stress-induced permeability anisotropy during cataclastic flow. J Geophys Res 112(B10):B10207