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Hypoplastic modeling of anisotropic sand behavior accounting for fabric evolution under monotonic and cyclic loading

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Abstract

A unified hypoplastic model is formulated by incorporating the anisotropic critical state theory to describe the fabric effect in sand under both monotonic and cyclic loading conditions. An evolving deviatoric fabric tensor that characterizes the internal microstructure of sand is introduced into the hypoplastic model in conjunction with the intergranular strain concept. A scalar-valued fabric anisotropic variable indicating the interplay between the fabric and the loading direction is employed to account for the impact of fabric anisotropy on both the dilatancy and shear strength of sand. The model is demonstrated to be capable of simulating the anisotropic behavior of sand, using a single set of parameters under both monotonic and cyclic loading conditions, as evidenced by the satisfactory match with experimental results from various sources. In particular, by considering the influence of fabric evolution on the dilatancy of sand, the model adequately accounts for the fabric change effect and accurately captures the deviatoric strain accumulation, cyclic mobility, and the flow liquefaction phenomenon under cyclic loading condition.

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References

  1. Abelev A, Lade PV (2004) Characterization of failure in cross-anisotropic soils. J Eng Mech 130(5):599–606

    Google Scholar 

  2. Atkinson JH, Richardson D, Stallebrass S (1990) Effect of recent stress history on the stiffness of overconsolidated soil. Géotechnique 40(4):1–540

    Google Scholar 

  3. Azami A, Pietruszczak S, Guo P (2010) Bearing capacity of shallow foundations in transversely isotropic granular media. Int J Numer Anal Methods Geomech 34:771–793

    MATH  Google Scholar 

  4. Bauer E (1996) Calibration of a comprehensive hypoplastic model for granular materials. Soils Found 36(1):13–26

    Google Scholar 

  5. Bauer E, Huang W, Wu W (2004) Investigations of shear banding in an anisotropic hypoplastic material. Int J Solids Struct 41:5903–5919

    MATH  Google Scholar 

  6. Been K, Jefferies MG (1985) A state parameter for sands. Géotechnique 35(2):99–112

    Google Scholar 

  7. Dafalias YF, Manzari MT (2004) Simple plasticity sand model accounting for fabric change effects. J Eng Mech 130(6):622–634

    Google Scholar 

  8. Dafalias YF, Papadimitriou AG, Li XS (2004) Sand plasticity model accounting for inherent fabric anisotropy. J Eng Mech 130(11):1319–1333

    Google Scholar 

  9. Dafalias YF, Popov EP (1975) A model of nonlinearly hardening materials for complex loading. Acta Mech 21(3):173–192

    MATH  Google Scholar 

  10. Fonseca J, O’Sullivan C, Coop MR (2013) Quantifying the evolution of soil fabric during shearing using directional parameters. Géotechnique 63(6):487–499

    Google Scholar 

  11. Fuentes W, Wichtmann T, Gil M, Lascarro C (2019) ISA-hypoplasticity accounting for cyclic mobility effects for liquefaction analysis. Acta Geotech 15:1513–1531

    Google Scholar 

  12. Gao ZW, Zhao JD (2015) Constitutive modeling of anisotropic sand behavior in monotonic and cyclic loading. J Eng Mech 141(8):04015017

    Google Scholar 

  13. Gao ZW, Zhao JD, Li XS, Dafalias YF (2014) A critical state sand plasticity model accounting for fabric evolution. Int J Numer Anal Methods Geomech 38(4):370–390

    Google Scholar 

  14. Gudehus G (1996) A comprehensive constitutive equation for granular materials. Soils Found 36(1):1–12

    Google Scholar 

  15. Herle I, Gudehus G (1999) Determination of parameters of a hypoplastic constitutive model from properties of grain assemblies. Mech Cohesive Frict Mater 4(5):461–486

    Google Scholar 

  16. Ishihara K, Tatsuoka F, Yasuda S (1975) Undrained deformation and liquefaction of sand under cyclic stresses. Soils Found 15(1):29–44

    Google Scholar 

  17. Ishihara K, Yamazaki F (1980) Cyclic simple shear tests on saturated sand in multi-directional loading. Soils Found 20(1):45–59

    Google Scholar 

  18. Iwan WD (1967) On a class of models for the yielding behavior of continuous and composite systems. J Appl Mech 34(3):612–617

    Google Scholar 

  19. Jardine RJ, Symes MJ, Burland JB (1984) The measurement of soil stiffness in the triaxial apparatus. Géotechnique 34:323–340

    Google Scholar 

  20. Kimura T, Kusakabe O, Saitoh K (1985) Geotechnical model tests of bearing capacity problems in a centrifuge. Géotechnique 35(1):33–45

    Google Scholar 

  21. Kirkgard MM, Lade PV (1993) Anisotropic three-dimensional behavior of a normally consolidated clay. Can Geotech J 30(4):848–858

    Google Scholar 

  22. Kolymbas D (1991) An outline of hypoplasticity. Arch Appl Mech 3(61):143–151

    MATH  Google Scholar 

  23. Krieg RD (1975) A practical two-surface plasticity theory. J Appl Mech 42:641–646

    Google Scholar 

  24. Kuhn MR, Renken HE, Mixsell AD, Kramer SL (2014) Investigation of cyclic liquefaction with discrete element simulations. J Geotech Geoenviron Eng 140(12):04014075

    Google Scholar 

  25. Li X, Li XS (2009) Micro–macro quantification of the internal structure of granular materials. J Eng Mech 135(7):641–656

    Google Scholar 

  26. Li XS (2002) A sand model with state-dependent dilatancy. Géotechnique 52(3):173–186

    Google Scholar 

  27. Li XS, Dafalias YF (2002) Constitutive modeling of inherently anisotropic sand behavior. J Geotech Geoenviron Eng 128(10):868–880

    Google Scholar 

  28. Li XS, Dafalias YF (2012) Anisotropic critical state theory: role of fabric. J Eng Mech 138(3):263–275

    Google Scholar 

  29. Li XS, Dafalias YF (2000) Dilatancy for cohesionless soils. Géotechnique 50(4):449–460

    Google Scholar 

  30. Manzari MT, Dafalias YF (1997) A two-surface critical plasticity model for sand. Géotechnique 47(2):255–272

    Google Scholar 

  31. Masson S, Martinez J (2001) Micromechanical analysis of the shear behavior of a granular material. J Eng Mech 127(10):1007–1016

    Google Scholar 

  32. Mroz Z (1967) On the description of anisotropic work hardening. J Mech Phys Solids 15:163–175

    Google Scholar 

  33. Mroz Z, Norris VA, Zienkiewicz OC (1978) An anisotropic hardening model for soils and its application to cyclic loading. Int J Numer Anal Methods Geomech 2:203–221

    MATH  Google Scholar 

  34. Nakata Y, Hyodo M, Murata H, Yasufuku N (1998) Flow deformation of sands subjected to principal stress rotation. Soils Found 38(2):115–128

    Google Scholar 

  35. Nemat-Nasser S (1980) On behavior of granular material in simple shear. Soils Found 20(3):59–73

    Google Scholar 

  36. Nemat-Nasser S, Tobita Y (1982) Influence of fabric on liquefaction and densification potential of cohesionless sand. Mech Mater 1:43–62

    Google Scholar 

  37. Niemunis A, Herle I (1997) Hypoplastic model for cohesionless soils with elastic strain range. Mech Cohesive Frict Mater 2(4):279–299

    Google Scholar 

  38. Oda M (1984) Distribution of directional data and fabric tensors. Int J Eng Sci 22(2):49–164

    MathSciNet  Google Scholar 

  39. Oda M (1972) The mechanism of fabric changes during compressional deformation of sand. Soils Found 12(2):1–18

    Google Scholar 

  40. Oda M, Kawamoto K, Suzuki K, Fujimori H, Sato M (2001) Microstructural interpretation on reliquefaction of saturated granular soils under cyclic loading. J Geotech Geoenviron Eng 127(5):416–423

    Google Scholar 

  41. Oda M, Koishikawa I (1979) Effect of strength anisotropy on bearing capacity of shallow footing in a dense sand. Soils Found 19(3):15–28

    Google Scholar 

  42. Oda M, Koishikawa I, Higuchi T (1978) Experimental study of anisotropic shear strength of sand by plane strain test. Soils Found 18(1):25–38

    Google Scholar 

  43. Pan K, Xu TT, Liao D, Yang ZX (2020) Failure mechanisms of sand under asymmetrical cyclic loading conditions: experimental observation and constitutive modelling. Géotechnique. https://doi.org/10.1680/jgeot.20.P.004

    Article  Google Scholar 

  44. 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

    Google Scholar 

  45. Petalas AL, Dafalias YF, Papadimitriou AG (2018) SANISAND-FN: an evolving fabric-based sand model accounting for stress principal axes rotation. Int J Numer Anal Methods Geomech 43(1):97–123

    Google Scholar 

  46. Prevost JH (1977) Mathematical modeling of monotonic and cyclic undrained clay behavior. Int J Numer Anal Methods Geomech 1(2):195–216

    MATH  Google Scholar 

  47. Qiu G, Henke S, Grabe J (2011) Application of a coupled Eulerian–Lagrangian approach on geomechanical problems involving large deformations. Comput Geotech 38(1):30–39

    Google Scholar 

  48. Roscoe KH, Schofield A, Wroth CP (1958) On the yielding of soils. Géotechnique 8(1):22–53

    Google Scholar 

  49. Schofield AN, Wroth CP (1968) Critical state soil mechanics. McGraw-Hill, London

    Google Scholar 

  50. Sitharam TG (2003) Discrete element modelling of cyclic behaviour of granular materials. Geotech Geol Eng 21(4):297–329

    Google Scholar 

  51. Soroush A, Ferdowsi B (2011) Three dimensional discrete element modeling of granular media under cyclic constant volume loading: a micromechanical perspective. Powder Technol 212(1):1–16

    Google Scholar 

  52. Sriskandakumar S (2004) Cyclic loading response of Fraser River sand for validation of numerical models simulating centrifuge tests. M.S. thesis. University of British Columbia, Vancouver, BC, Canada

  53. Tejchman J, Bauer E, Wu W (2007) Effect of fabric anisotropy on shear localization in sand during plane strain compression. Acta Mech 189:23–51

    MATH  Google Scholar 

  54. Theocharis AI, Vairaktaris E, Dafalias YF, Papadimitriou AG (2019) Necessary and sufficient conditions for reaching and maintaining critical state. Acta Geotech 43(12):2041–2055

    Google Scholar 

  55. Theocharis AI, Vairaktaris E, Dafalias YF, Papadimitriou AG (2017) Proof of incompleteness of critical state theory in granular mechanics and its remedy. J Eng Mech 143(2):04016117

    Google Scholar 

  56. Uthayakumar M, Vaid YP (1998) Static liquefaction of sands under multiaxial loading. Can Geotech J 35:273–283

    Google Scholar 

  57. Vaid YP, Chern JC, Tumi H (1985) Confining pressure, grain angularity, and liquefaction. J Geotech Geoenviron Eng 111(10):1229–1235

    Google Scholar 

  58. von Wolffersdorff PA (1996) A hypoplastic relation for granular materials with a predefined limit state surface. Mech Cohesive Frict Mater 1(3):251–271

    Google Scholar 

  59. Wang G, Xie YN (2014) Modified bounding surface hypoplasticity model for sands under cyclic loading. J Eng Mech 140(1):91–101

    Google Scholar 

  60. Wang R, Fu PC, Zhang JM, Dafalias YF (2016) Dem study of fabric features governing undrained post-liquefaction shear deformation of sand. Acta Geotech 11(6):1321–1337

    Google Scholar 

  61. Wang S, Wu W (2020) A simple hypoplastic model for overconsolidated clays. Acta Geotech. https://doi.org/10.1007/s11440-020-01000-z

    Article  Google Scholar 

  62. Wang S, Wu W, Peng C, He XZ, Cui DS (2018) Numerical integration and FE implementation of a hypoplastic constitutive model. Acta Geotech 13(6):1265–1281

    Google Scholar 

  63. Wang S, Wu W, Yin ZY, Peng C, He XZ (2018) Modelling the time-dependent behavior of granular material with hypoplasticity. Int J Numer Anal Methods Geomech 42(12):1331–1345

    Google Scholar 

  64. Wang ZL, Dafalias YF, Shen CK (1990) Bounding surface hypoplasticity model for sand. J Eng Mech 116(5):983–1001

    Google Scholar 

  65. Wichtmann T, Triantafyllidis T (2016) An experimental database for the development, calibration and verification of constitutive models for sand with focus to cyclic loading: part I—tests with monotonic loading and stress cycles. Acta Geotech 11:739–761

    Google Scholar 

  66. Wichtmann T, Triantafyllidis T (2016) An experimental database for the development, calibration and verification of constitutive models for sand with focus to cyclic loading: part II—tests with strain cycles and combined loading. Acta Geotech 11:763–774

    Google Scholar 

  67. Woo SI, Salgado R (2015) Bounding surface modeling of sand with consideration of fabric and its evolution during monotonic shearing. Int J Solids Struct 63:277–288

    Google Scholar 

  68. Wu W (1998) Rational approach to anisotropy of sand. Int J Numer Anal Methods Geomech 22(11):921–940

    MATH  Google Scholar 

  69. Wu W, Bauer E (1994) A simple hypoplastic constitutive model for sand. Int J Numer Anal Methods Geomech 18(12):833–862

    MATH  Google Scholar 

  70. Wu W, Kolymbas D (1990) Numerical testing of the stability criterion for hypoplastic constitutive equations. Mech Mate 9(3):245–253

    Google Scholar 

  71. Wu W, Bauer E, Kolymbas D (1996) Hypoplastic constitutive model with critical state for granular materials. Mech Mater 23(1):143–163

    Google Scholar 

  72. Xu GF, Peng C, Wu W, Qi JL (2017) Combined constitutive model for creep and steady flow rate of frozen soil in an unconfined condition. Can Geotech J 54(7):907–914

    Google Scholar 

  73. Yang ZX, Li XS, Yang J (2008) Quantifying and modelling fabric anisotropy of granular soils. Géotechnique 58(4):237–248

    Google Scholar 

  74. Yang ZX, Liao D, Xu TT (2019) A hypoplastic model for granular soils incorporating anisotropic critical state theory. Int J Numer Anal Methods Geomech 44(6):723–748

    Google Scholar 

  75. Yang ZX, Wu Y (2017) Critical state for anisotropic granular materials: a discrete element perspective. Int J Geomech 17(2):81–92

    Google Scholar 

  76. Yang ZX, Xu TT, Chen YN (2018) Unified modeling of the influence of consolidation conditions on monotonic soil response considering fabric evolution. J Eng Mech 144(8):04018073

    Google Scholar 

  77. Yang ZX, Zhao CF, Xu CJ, Wilkinson SP, Cai YQ, Pan K (2016) Modelling the engineering behaviour of fibrous peat formed due to rapid anthropogenic terrestrialization in Hangzhou, China. Eng Geol 215:2–35

    Google Scholar 

  78. 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

    Google Scholar 

  79. Zhao JD, Guo N (2013) Unique critical state characteristics in granular media considering fabric anisotropy. Géotechnique 63(8):695–704

    Google Scholar 

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Acknowledgements

The research described in the paper was funded by the National Key R&D program of China under Grant 2016YFC0800200 and the Natural Science Foundation of China under Grant Nos. 51825803 and 52020105003.

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  1. Department of Civil Engineering, Zhejiang University, Hangzhou, 310058, China

    D. Liao & Z. X. Yang

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Liao, D., Yang, Z.X. Hypoplastic modeling of anisotropic sand behavior accounting for fabric evolution under monotonic and cyclic loading. Acta Geotech. 16, 2003–2029 (2021). https://doi.org/10.1007/s11440-020-01127-z

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