Constitutive modelling of granular materials using a contact normal-based fabric tensor

Anandarajah A (2008) Critical state of granular materials based on the sliding-rolling theory. J Geotech Geoenviron Eng 134(1):125–135 Anandarajah A, Dafalias YF (1986) Bounding surface plasticity III: application to anisotropic cohesive soils. J Eng Mech 112(12):1292–1318 Arthur JRF, Menzies BK (1972) Inherent anisotropy in a sand. Géotechnique 22(1):115–128 Been K, Jefferies M (2004) Stress-dilatancy in very loose sand. Can Geotech J 41:972–989 Been K, Jefferies MG, Hachey J (1991) The critical state of sands. Géotechnique 41(3):365–381 Collins IF (2003) A systematic procedure for constructing critical state models in three dimensions. Int J Solids Struct 40:4379–4397 Collins IF, Houlsby GT (1997) Application of thermomechanical principles to the modelling of geotechnical materials. Proc R Soc Lond Ser A 453:1975–2001 Dafalias YF (1986) Bounding surface plasticity. I: mathematical foundation and hypoplasticity. J Eng Mech 112(9):966–987 Dafalias YF (2016) Must critical state theory be revisited to include fabric effects? Acta Geotech 11(3):479–491. https://doi.org/10.1007/s11440-016-0441-0 Dafalias YF, Taiebat M (2013) Anatomy of rotational hardening in clay plasticity. Géotechnique 63:1–13 Darve F, Nicot F (2005) On flow rule in granular media:phenomenological and mutli-scale views (Part II). Int J Numer Anal Meth Geomech 29:1141–1432 Fonseca J, O’Sullivan C, Coop MR, Lee PD (2013) Quantifying the evolution of soil fabric during shearing using directional parameters. Géotechnique 63(6):487–499 Fu P, Dafalias YF (2011) Fabric evolution within shear bands of granular materials and its relation to critical state theory. Int J Numer Anal Meth Geomech 35(18):1918–1948 Gao Z, Zhao J, Li XS, Dafalias YF (2014) A critical state sand plasticity model accounting for fabric evolution. Int J Numer Anal Meth Geomech 38(4):370–390 Gutierrez M, Wang J (2009) Non-coaxial version of Rowe’s stress-dilatancy relation. Granular Matter 11:129–137 Gutierrez M, Ishihara K, Twohata I (1993) Model for the deformation of sand during rotation of principal stress directions. Soils Found 33(3):105–117 Hardin BO, Richard FE (1963) Elastic wave velocities in granular materials. J Geotech Eng ASCE 89(SM1):33–65 Hashiguchi K (2000) Fundamentals in constitutive equations:continuity and smoothness conditions and loading criterion. Soils Found 40(4):155–161 Hashiguchi K (2001) Description of inherent/induced anisotropy of soils: rotational hardening rule with objectivity. Soils Found 41(6):139–145 Hashiguchi K, Chen ZP (1998) Elastoplastic constitutive equations of soils with the subloading surface and the rotational hardening. Int J Numer Anal Meth Geomech 22:197–227 Hu N (2015) On fabric tensor-based constitutive modelling of granular materials: theory and numerical implementation (Ph.D. thesis). The University of Nottingham, UK Huang X, Hanley KJ, O’Sullivan C, Kwok CY, Wadee MA (2014) DEM analysis of the influence of the intermediate stress ratio on the critical-state behaviour of granular materials. Granular Matter 16(5):641–655. https://doi.org/10.1007/s10035-014-0520-6 Kanatani K (1984) Stereological determination of structural anisotropy. Int J Eng Sci 22(5):531–546 Kolymbas D (1991) An outline of hypoplasticity. Arch Appl Mech 61(3):143–151 Kruyt NP (2012) Micromechanical study of fabric evolution in quasi-static deformation of granular materials. Mech Mater 2012:120–129 Kuhn MR (2010) Micro-mechanics of fabric and failure in granular materials. Mech Mater 42:827–840 Lade PV, Yamamuro JA, Gutta SK (2009) Rotational kinematic hardening model for three-dimensional stress reversals in sand. Int J Numer Anal Meth Geomech 33:967–991 Li XS (2002) A sand model with state-dependent dilatancy. Géotechnique 52(3):173–186 Li XS, Dafalias YF (2000) Dilatancy for cohesionless soils. Géotechnique 50(4):449–460 Li XS, Dafalias YF (2002) Constitutive modelling of inherently anisotropic 973 sand behaviour. J Geotech Geoenviron Eng 128(10):868–880 Li XS, Dafalias YF (2004) A constitutive framework for anisotropic sand including non-proportional loading. Géotechnique 54(1):41–55 Li XS, Dafalias YF (2012) Anisotropic critical state theory: role of fabric. J Eng Mech 138(3):263–275 Li X, Li XS (2009) Mirco-macro quantification of the internal structure of granular materials. J Eng Mech 135(7):641–656 Li X, Yu HS (2010) Numerical investigation of granular material under rotational shear. Géotechnique 60(5):381–394 Li X, Yu HS (2013) On the stress-force-fabric relationship for granular materials. Int J Solids Struct 50:1285–1302 Li X, Yu HS (2013) Particle-scale insight into deformation noncoaxiality of granular materials. Int J Geomech 15(4):04014061. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000338 Loukidis D, Salgado R (2009) Modeling sand response using two-surface plasticity. Comput Geotech 36:166–186 Manzari MT, Nour MA (1997) On implicit integration of bounding surface plasticity models. Comput Struct 63(3):385–395 Matsuoka H, Nakai T (1974) Stress deformation and strength characteristics of soil under three different principal stresses. Proc Jpn Soc Civ Eng 232:59–70 Mirua S, Toki F (1984) Elastoplastic stress-strain relationship for loose sands with anisotropic fabric under three-dimensional stress conditions. Soils Found 24(2):43–57 Miura K, Miura S, Toki S (1986) Deformation behaviour of anisotropic dense sand under principal stress axes rotation. Soils Found 26(6):577–585 Nemat-Nasser S (2000) A micromechanically-based constitutive model for frictional deformation of granular materials. J Mech Phys Solids 48:1541–1563 Nemat-Nasser S, Zhang J (2002) Constitutive relations for cohesionless frictional granular materials. Int J Plast 18:531–547 Nguyen H, Rahman M, Fourie A (2016) Undrained behaviour of granular material and the role of fabric in isotropic and K0 consolidations: DEM approach. Geotechnique 67(2):153–167 Nova R, Wood DM (1979) A constitutive model for sand in triaxial compression. Int J Numer Anal Meth Geomech 3(3):255–278. https://doi.org/10.1002/nag.1610030305 Oda M (1972) Deformation mechanism of sand in triaxial compression tests. Soils Found 12(4):45–63 Oda M (1972) Initial fabrics and their relations to mechanical properties of granular material. Soils Found 12(1):17–36 Oda M, Konishi J (1974) Microscopic deformation mechanism of granular material in simple shear. Soils Found 14 (4) Oda M, Konishi J, Nemat-Nasser S (1980) Some experimentally based fundamental results on mechanical behaviour of granular materials. Géotechnique 30(4):479–495 Oda M, Nemat-Nasser S, Konishi J (1985) Stress-induced anisotropy in granular masses. Soils Found 25(3):85–97 Okochi Y, Tatsuoka F (1984) Some factors affecting K0-values of sands in triaxial cell. Soils Found 24(3):52–62 Ouadfel H, Rothenburg L (2001) ‘Stress-force-fabric’ relationship for assemblies of ellipsoids. Mech Mater 33:201–221 Papadimitriou AG, Dafalias YF, Yoshimine M (2005) Plasticity modeling of the effect of sample preparation method on sand response. Soils Found 45(2):109–123 Pestana J, Whittle A (1999) Formulation of a unified constitutive model for clays and sands. Int J Numer Anal Meth Geomech 23:1215–1243 Potts DM, Gens A (1984) The effect of the plastic potential in boundary value problems involving plane strain deformation. Int J Numer Anal Meth Geomech 8(3):259–286. https://doi.org/10.1002/nag.1610080305 Pradhan BS, Tatsuoka F, Horii N (1988) Strength and deformation characteristics of sand in torsional simple shear. Soils Found 28(3):131–148 Pradhan BS, Tatsuoka F, Yasuhiko S (1989) Experimental stress-dilatancy relations of sand subjected to cyclic loading. Soils Found 29(1):45–64 Reynolds O (1885) On the dilatancy of media composed of rigid particles in contact with experimental illustrations. Phil Mag 20:469–482 Roscoe KH (1970) The influence of strains in soil mechanics. Géotechnique 20 (129-170) Rothenburg L, Bathurst RJ (1989) Analytical study of induced anisotropy in idealized granular materials. Géotechnique 39:601–614 Rothenburg L, Kruyt NP (2004) Critical state and evolution of coordination number in simulated granular materials. Int J Solids Struct 41:5763–5774 Rowe PW (1962) The stress-dilatancy relation for static equilibrium of an assembly of particles in contact. Proc R Soc Lond Ser A 269:500–527 Schofield A, Wroth CP (1968) Critical state soil mechanics. McGraw-Hill, London Sekiguchi H (1977) Induced anisotropy and time dependency in clays. In Murayama, S; Schofield, AN (eds) Proceeding 9th intemational conference on soil mechanics and foundation engineering, specialty session 9. Tokyo, pp 229–238 Sheng DC, Sloan SW, Yu HS (2000) Aspects of finite element implementation of critical state models. Comput Mech 26:185–196 Shi J, Guo P (2018) Fabric evolution of granular materials along imposed stress paths. Acta Geotech 13(6):1341–1354 Taiebat M, Dafalias YF (2008) SANISAND: simple anisotropic sand plasticity model. Int J Numer Anal Meth Geomech 32:915–948 Tatsuoka F (1999) Small strain behaviour of granular materials. In: Oda M, Iwashita K (eds) Mechanics of granular materials: an introduction. Balkema Publishers, Rotterdam, pp 299–308 Thornton C (2000) Numerical simulation of deviatoric shear deformation of granular media. Géotechnique 50(1):43–53 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 Tordesillas A, Muthuswamy M (2009) On the modeling of confined buckling of force chains. J Mech Phys Solids 57:706–727 Uthayakumar M, Vaid YP (1998) Static liquefaction of sands under multiaxial loading. Can Geotech J 35:273–283 Vairaktaris E, Theocharis AI, Dafalias YF (2018) Correlation of fabric tensors for granular materials using 2D DEM. Acta Geotech. https://doi.org/10.1007/s11440-018-0755-1 Verdugo R, Ishihara K (1996) The steady state of sandy soils. Soils Found 36(2):81–91 Wan RG, Guo PJ (2004) Stress dilatancy and fabric dependencies on sand behaviour. J Eng Mech 130(6):635–645 Wheeler SJ, Näätänen A, Karstunen M, Lojander M (2003) An anisotropic elastoplastic model for soft clays. Can Geotech J 40:403–418 Wong RKS, Arthur JRF (1985) Induced and inherent anisotropy in sand. Géotechnique 35(4):471–481 Wood DM (1990) Soil behaviour and critical state soil mechanics. Cambridge University Press, Cambridge Xie YD, Yang ZX, Barreto D, Jiang MD (2017) The influence of particle geometry and the intermediate stress ratio on the shear behavior of granular materials. Granular Matter 19(2):35 Yang LT (2013) Experimental study of soil anisotropy using hollow cylinder testing (PhD thesis), The University of Nottingham, UK Yang DS (2014) Microscopic study of granular material behaviour under general stress paths (Ph.D. thesis). The University of Nottingham, UK Yang ZX, Wu Y (2016) Critical state for anisotropic granular materials: a discrete element perspective. Int J Geomech 04016054-1-15. https://doi.org/10.1061/(asce)GM.1943-5622.0000720 Yang ZX, Li XS, Yang J (2008) Quantifying and modelling fabric anisotropy of granular soils. Géotechnique 58(4):237–248. https://doi.org/10.1680/geot.2008.58.4.237 Yang LT, Li X, Yu HS, Wanatowski D (2016) A laboratory study of anisotropic geomaterials incorporating recent micromechanical understanding. Acta Geotech 11(5):1111–1129. https://doi.org/10.1007/s11440-015-0423-7 Yang ZX, Xu T, Chen Y (2018) Unified modeling of the influence of consolidation conditions on monotonic soil response considering fabric evolution. J Eng Mech 144(8):04018073 Yimsiri S, Soga K (2010) DEM analysis of soil fabric effects on behaviour of sand. Géotechnique 60(6):483–495 Yimsiri S, Soga K (2011) Effects of soil fabric on behaviours of granular soils: microscopic modeling. Comput Geotech 38:861–874 Yoshimine M, Ishihara K, Vargas W (1998) Effects of principal stress direction and intermediate principal stress on undrained shear behavior of sand. Soils Found 38(3):179–188 Yu HS (1998) CASM: a unified state parameter model for clay and sand. Int J Numer Anal Meth Geomech 22:621–653 Yu HS (2006) Plasticity and geotechnics. Springer, London Yu HS, Kong CD, Wang J, Zhang G (2005) Experimental evaluation and extension of a simple critical state model for sand. Granular Matter 7:213–225 Yu HS, Khong C, Wang J (2007) A unified plasticity model for cyclic behaviour of clay and sand. Mech Res Commun 34:97–114 Yuan R, Yu HS, Yang DS, Hu N (2019) On a fabric evolution law incorporating the effects of b-value. Comput Geotech 105:142–154 Zhang L, Thornton L (2007) A numerical examination of the direct shear test. Géotechnique 57(4):343–354. https://doi.org/10.1680/geot.2007.57.4.343 Zhao J, Guo N (2013) Unique critical state characteristics in granular media considering fabric anisotropy. Géotechnique 63(8):695–704 Zhu H, Mehrabadi MM, Massoudi M (2006) Incorporating the effect of fabric in the dilatant double shearing model for planar deformation of granular materials. Int J Plast 22:628–653 Zhu H, Mehrabadi MM, Massoudi M (2006) Three-dimensional constitutive relations for granular materials based on the dilatant double shearing mechanism and the concept of fabric. Int J Plast 22:826–857 Zigler H (1959) A modification of Prager’s hardening rule. Appl Mech Phys 17:55–60