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

Acta Geotechnica - Tập 8 - Trang 465-480 - 2013
WaiChing Sun1, Matthew R. Kuhn2, John W. Rudnicki3
1Mechanics of Materials, Sandia National Laboratories, Livermore, USA
2Department of Civil Engineering, Donald P. Shiley School of Engineering, University of Portland, Portland, USA
3Department of Civil and Environmental Engineering, Technology Institute A333, Northwestern University, Evanston, USA

Tóm tắt

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.

Tài liệu tham khảo

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 Antonellini M, Pollard DD (1995) Distinct element modeling of deformation bands in sandstone. J Struct Geol 17:1165–1182 Aydin A, Borja RI, Eichhubl P (2005) Geological and mathematical framework for failure modes in granular rock. J Struct Geol 29:1831–1842 Bear J (1972) Dynamics of fluids in porous media. Elsevier Publishing Company, New York Bésuelle P, Rudnicki JW (2004) Localization: shear bands and compaction bands. International Geophysics Series, vol 89, pp 219–321 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 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 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 Casagrande A (1936) Characteristics of cohensionless soils affecting the stability of slops and earth fills. J Boston Soc Civil Eng 23:13–32 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) 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 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 Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Géotechnique 29:47–65 El Shamy U, Zeghal M (2005) Coupled continuum-discrete model for saturated granular soils. J Eng Mech 131(4):413–426 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 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 Hilfer R, Manwart C (2001) Permeability and conductivity for reconstruction models of porous media. Phys Rev E 64 Houlsby GT (2009) Potential particles: a method for modelling non-circular particles in DEM. Comput Geotech 36(6):953–959 Irmay S (1954) On the hydraulic conductivity of unsaturated soils. Trans Am Geophys Union 35:463–468 Jensen JL (1991) Use of geometric average for effective permeability estimation. Math Geol 23(6):833–840 Johnson KL (1985) Contact mechanics, Cambridge University Press, Cambridge Johnson DL, Koplik J, Schwartz LM (1986) New pore-size parameter characterizing transport in porous media. Phys Rev Lett 57:2564–2567 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 Kuhn MR (2011) Implementation of the Jäger contact model for discrete element simulations. Chem Eng. 88(1):66–82 Kuhn MR, Bagi K (2004) Contact rolling and deformation in granular media. Int J Solids Struct 41:5793–5820 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 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 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 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 Mitchell JK, Soga K (2005) Fundamentals of soil behavior, 3rd edn. Wiley, New Jersey 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 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 Rudnicki JW (2004) Shear and compaction band formation on an elliptic yield cap. J Geophys Res 109:B3 Rudnicki JW, Rice JR (1975) Conditions for the localization of deformation in pressure-sensitive dilatant materials. J Mech Phys Solids 23:371–394 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 Scheidegger AE (1960) The physics of flow through porous media. University of Toronto Press, Toronto Schneider CA, Rashand WS, Eliceiri KW (2012) Nih image to imagej: 25 years of image analysis. Nat Methods 9:671–675 Succi S (2001) The lattice Boltzmann equation. Oxford University Press, Oxford 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 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 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 Thornton C (2000) Numerical simulations of deviatoric shear deformation of granular media. Géotechnique 50(1):43–53 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 Wawersik WR et al (2008) Terrestrial sequestration of CO2: an assessment of research needs. Adv Geophys 43:97–117 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