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Evolution of granular media under constant-volume multidirectional cyclic shearing

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Abstract

By means of the three-dimensional discrete element method, we study the long-time evolution toward liquefaction state in granular materials composed of spherical particles under multidirectional cyclic shearing at constant volume. Extensive simulations were carried out along 1-D linear, 2-D linear, circular/oval, and 8-like shear paths, and the evolution of the system was analyzed in terms of pore pressure, shear strain, and granular texture. The macroscopic stress path and stress–strain response agree well with laboratory experiments. We find that the liquefaction resistance, i.e., the number of cycles necessary to reach the liquefaction state, is generally lower under multidirectional loading as compared to unidirectional loading. As the transient vanishing of mean stress does not occur for all stress paths, we introduce a shear strain-based liquefaction criterion that can be consistently applied to all strain paths. The granular texture is monitored through the coordination number, particle connectivity, force and fabric anisotropies, and friction mobilization. In particular, a particle-void descriptor, named centroid distance, is found to be closely related to the shear strain accumulation. We show that the force anisotropy tensors become almost proportional to the deviatoric stress tensor more quickly than the fabric anisotropy tensor, which takes most of the pre-liquefaction period to follow the external loading. The relationship between deviatoric stress ratio and the force and fabric anisotropies, known to hold in monotonic triaxial loading, also holds with high accuracy in the studied multidirectional cyclic shearing paths; the contributing weights of the anisotropies level off in the post-liquefaction period and do not depend on the shear path.

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References

  1. Alonso-Marroquin F, Herrmann HJ (2004) Ratcheting of granular materials. Phys Rev Lett 92(5)

  2. Alonso-Marroquin F, Luding S, Herrmann HJ, Vardoulakis I (2005) Role of anisotropy in the elastoplastic response of a polygonal packing. Phys Rev E 71(5)

  3. Azéma E, Radjaï F (2012) Force chains and contact network topology in sheared packings of elongated particles. Phys Rev E 85(3)

  4. Bi D, Zhang J, Chakraborty B, Behringer RP (2011) Jamming by shear. Nature 480(7377):355–358

    Article  Google Scholar 

  5. Bonilla RRO (2004) Numerical simulations of undrained granular media. Ph.D. thesis, University of Waterloo, University of Waterloo Waterloo, Canada

  6. Boulanger RW, Seed RB (1995) Liquefaction of sand under bidirectional monotonic and cyclic loading. J Geotech Eng 121(12):870–878

    Article  Google Scholar 

  7. Boulanger RW, Seed RB, Chan CK, Seed HB, Sousa J (1991) Liquefaction behavior of saturated sands under uni-directional and bi-directional monotonic and cyclic simple shear loading. Tech. Rep. 2, University of California, Berkeley, The address of the publisher. UCB/GT/91-08

  8. Cantor D, Azéma E, Sornay P, Radjaï F (2018) Rheology and structure of polydisperse three-dimensional packings of spheres. Phys Rev E 98(5)

  9. Carlton BD, Kaynia AM (2016) Comparison of the seismic response of offshore slopes using 1, 2, or 3 ground motion components. Offshore Technol Conf. Houston, TX, pp 1–12

    Google Scholar 

  10. Cerna-Diaz A, Olson SM, Numanoglu OA, Hashash YMA, Bhaumik L, Rutherford CJ, Weaver T (2017) Free-field cyclic response of dense sands in dynamic centrifuge tests with 1D and 2D shaking. In: Geotechnical Frontiers 2017, pp. 121–130. American Society of Civil Engineers

  11. Chiaro G, Koseki J, Sato T (2012) Effects of initial static shear on liquefaction and large deformation properties of loose saturated Toyoura sand in undrained cyclic torsional shear tests. Soils Found 52(3):498–510

    Article  Google Scholar 

  12. Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Géotechnique 29(1):47–65

    Article  Google Scholar 

  13. Dyvik R, Lacasse S, Berre T, Raadim B (1987) Comparison of truly undrained and constant volume direct simple shear tests. Géotechnique 37(1):3–10

    Article  Google Scholar 

  14. El Shafee O, Abdoun TH, Zeghal M (2017) Centrifuge modelling and analysis of site liquefaction subjected to biaxial dynamic excitations. Géotechnique 67(3):260–271

    Article  Google Scholar 

  15. Estrada N, Azéma E, Radjaï F, Taboada A (2011) Identification of rolling resistance as a shape parameter in sheared granular media. Phys Rev E 84(1)

  16. Evans TM, Zhang L (2019) A numerical study of particle friction and initial state effects on the liquefaction of granular assemblies. Soil Dynamics and Earthquake Engineering 126

  17. Ghaboussi J, Dikmen SU (1981) Liquefaction analysis for multidirectional shaking. J Geotech Eng Div 107(5):605–627

    Article  Google Scholar 

  18. Gong G, Thornton C, Chan AHC (2012) DEM simulations of undrained triaxial behavior of granular material. J Eng Mech 138(6):560–566

    Google Scholar 

  19. Guo N, Zhao J (2013) The signature of shear-induced anisotropy in granular media. Comput Geotech 47:1–15

    Article  MathSciNet  Google Scholar 

  20. Hall SA, Bornert M, Desrues J, Pannier Y, Lenoir N, Viggiani G, Bésuelle P (2010) Discrete and continuum analysis of localised deformation in sand using x-ray \(\mu \)ct and volumetric digital image correlation. Géotechnique 60(5):315–322

    Article  Google Scholar 

  21. Huang X, Hanley KJ, Zhang Z, Kwok C, Xu M (2019) Jamming analysis on the behaviours of liquefied sand and virgin sand subject to monotonic undrained shearing. Comput Geotech 111:112–125

    Article  Google Scholar 

  22. Huang X, Hanley KJ, Zhang Z, Kwok CY (2019) Structural degradation of sands during cyclic liquefaction: insight from DEM simulations. Comput Geotech 114

  23. Huang X, Kwok CY, Hanley KJ, Zhang Z (2018) Dem analysis of the onset of flow deformation of sands: linking monotonic and cyclic undrained behaviours. Acta Geotech 13(5):1061–1074

    Article  Google Scholar 

  24. Hyodo M, Murata H, Yasufuku N, Fujii T (1991) Undrained cyclic shear strength and residual shear strain of saturated sand by cyclic triaxial tests. Soils Found 31(3):60–76

    Article  Google Scholar 

  25. Idriss IM, Boulanger RW (2006) Semi-empirical procedures for evaluating liquefaction potential during earthquakes. Soil Dyn Earthq Eng 26(2–4):115–130

    Article  Google Scholar 

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

    Article  Google Scholar 

  27. Jiang M, Zhang A, Li T (2019) Distinct element analysis of the microstructure evolution in granular soils under cyclic loading. Granular Matter 21(2):39

    Article  Google Scholar 

  28. Kammerer AM, Pestana JM, Seed RB (2002) Undrained response of monterey 0/30 sand under multidirectional cyclic simple shear loading conditions. Geotechnical Engineering Report UCB/GT/02-01, University of California, Berkeley

  29. Kammerer AM, Pestana JM, Seed RB (2005) Behavior of monterey 0/30 sand under multidirectional loading conditions. In: Geomechanics: testing, modeling, and simulation, pp. 154–173. American Society of Civil Engineers

  30. Kanatani KI (1984) Distribution of directional data and fabric tensors. Int J Eng Sci 22(2):149–164

    Article  MathSciNet  MATH  Google Scholar 

  31. Kruyt NP (2010) Micromechanical study of plasticity of granular materials. Comptes rendus mécanique 338(10–11):596–603

    Article  MATH  Google Scholar 

  32. Kuhn MR (2017) Granular geomechanics. Elsevier

  33. Kuhn MR, Daouadji A (2019) Stress fluctuations during monotonic loading of dense three-dimensional granular materials. Granular Matter 21(1):10

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  36. Luding S (2008) Cohesive, frictional powders: contact models for tension. Granular Matter 10(4):235–246

    Article  MathSciNet  MATH  Google Scholar 

  37. Majmudar TS, Behringer RP (2005) Contact force measurements and stress-induced anisotropy in granular materials. Nature 435(7045):1079–1082

    Article  Google Scholar 

  38. Martin EL, Thornton C, Utili S (2020) Micromechanical investigation of liquefaction of granular media by cyclic 3D DEM tests. Géotechnique 70(10):906–915

    Article  Google Scholar 

  39. Matsuda H, Hendrawan AP, Ishikura R, Kawahara S (2011) Effective stress change and post-earthquake settlement properties of granular materials subjected to multi-directional cyclic simple shear. Soils Found 51(5):873–884

    Article  Google Scholar 

  40. MiDi GDR (2004) On dense granular flows. Eur Phys J E 14(4):341–365

    Article  Google Scholar 

  41. Morimoto T, Otsubo M, Koseki J (2021) Microscopic investigation into liquefaction resistance of pre-sheared sand: effects of particle shape and initial anisotropy. Soils Found

  42. Mutabaruka P (2013) Numerical modeling of immersed granular media: initiation and propagation of avalanches in a fluid. Ph.D. thesis, Université Montpellier II-Science and Technology of Languedoc, Montpellier, France

  43. Mutabaruka P, Taiebat M, Pellenq RJM, Radjaï F (2019) Effects of size polydispersity on random close-packed configurations of spherical particles. Phys Rev E 100(4)

  44. Ng TT, Dobry R (1994) Numerical simulations of monotonic and cyclic loading of granular soil. J Geotech Eng 120(2):388–403

    Article  Google Scholar 

  45. Nguyen DH, Azéma E, Sornay P, Radjaï F (2015) Effects of shape and size polydispersity on strength properties of granular materials. Phys Rev E 91(3)

  46. Oda M (1982) Fabric tensor for discontinuous geological materials. Soils Found 22(4):96–108

    Article  Google Scholar 

  47. O’Sullivan C (2011) Particulate discrete element modelling: a geomechanics perspective. CRC Press

  48. Ouadfel H, Rothenburg L (2001) ‘Stress-force-fabric’ relationship for assemblies of ellipsoids. Mech Mater 33(4):201–221

    Article  Google Scholar 

  49. Pouragha M, Wan R (2016) Onset of structural evolution in granular materials as a redundancy problem. Granular Matter 18(3):38

    Article  Google Scholar 

  50. Pyke RM, Seed RB, Chan CK (1975) Settlement of sands under multidirectional shaking. J Geotech Eng Div 101(4):379–398

    Article  Google Scholar 

  51. Radjaï F, Dubois F (2011) Discrete-element modeling of granular materials. Wiley-Iste, UK

    Google Scholar 

  52. Radjai F, Richefeu V (2009) Bond anisotropy and cohesion of wet granular materials. Philos Trans R Soc A: Math Phys Eng Sci 367(1909):5123–5138

    Article  Google Scholar 

  53. Rahman MM, Nguyen HBK, Fourie AB, Kuhn MR (2021) Critical state soil mechanics for cyclic liquefaction and postliquefaction behavior: DEM study. J Geotech Geoenviron Eng 147(2):04020166

    Article  Google Scholar 

  54. Reyes A, Adinata J, Taiebat M (2019) Impact of bidirectional seismic shearing on the volumetric response of sand deposits. Soil Dyn Earthq Eng 125

  55. Rothenburg L, Bathurst RJ (1989) Analytical study of induced anisotropy in idealized granular materials. Géotechnique 39(4):601–614

    Article  Google Scholar 

  56. Satake M (1982) Fabric tensor in granular materials. In: Vermeer PA, Lager HJ (eds) Deformation and failure of granular materials. Balkema, Rotterdan, pp 63–68

    Google Scholar 

  57. Schwager T, Pöschel T (2007) Coefficient of restitution and linear-dashpot model revisited. Granular Matter 9(6):465–469

    Article  Google Scholar 

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

    Article  Google Scholar 

  59. Sitharam TG, Vinod JS, Ravishankar BV (2009) Post-liquefaction undrained monotonic behaviour of sands: experiments and dem simulations. Géotechnique 59(9):739–749

    Article  Google Scholar 

  60. 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

    Article  Google Scholar 

  61. Su D, Li XS (2008) Impact of multidirectional shaking on liquefaction potential of level sand deposits. Géotechnique 58(4):259–267

    Article  Google Scholar 

  62. Sun M (2019) The effects of multidirectional loading on soil liquefaction. Ph.D. thesis, University of Cambridge

  63. Thornton C (2000) Numerical simulations of deviatoric shear deformation of granular media. Géotechnique 50(1):43–53

    Article  Google Scholar 

  64. Thornton C (2015) Granular dynamics, contact mechanics and particle system simulations. Springer, Berlin

    Book  Google Scholar 

  65. Vaid YP, Chern JC (1983) Effects of static shear on resistance to liquefaction. Soils Found 23(1):47–60

    Article  Google Scholar 

  66. Vaid YP, Stedman JD, Sivathayalan S (2001) Confining stress and static shear effects in cyclic liquefaction. Can Geotech J 38(3):580–591

    Article  Google Scholar 

  67. Voivret C, Radjaï F, Delenne JY, Youssoufi MSE (2007) Space-filling properties of polydisperse granular media. Phys Rev E 76(2)

  68. Wang G, Wei J (2016) Microstructure evolution of granular soils in cyclic mobility and post-liquefaction process. Granular Matter 18(3):51

    Article  Google Scholar 

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

    Article  Google Scholar 

  70. Wang R, Fu P, Zhang JM, Dafalias YF (2019) Fabric characteristics and processes influencing the liquefaction and re-liquefaction of sand. Soil Dyn Earthq Eng 125

  71. Wei J (2017) Discrete element analysis of fabric evolution in cyclic liquefaction of granular soils. Ph.D. thesis, The Hong Kong University of Science and Technology, Hong Kong

  72. Wei J, Huang D, Wang G (2018) Microscale descriptors for particle-void distribution and jamming transition in pre-and post-liquefaction of granular soils. J Eng Mech 144(8):04018067

    Google Scholar 

  73. Wei J, Huang D, Wang G (2020) Fabric evolution of granular soils under multidirectional cyclic loading. Acta Geotechnica pp 1–15

  74. Wei J, Wang G (2017) Discrete-element method analysis of initial fabric effects on pre-and post-liquefaction behavior of sands. Géotech Lett 7(2):161–166

    Article  Google Scholar 

  75. 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(4):739–761

    Article  Google Scholar 

  76. Yang J, Sze HY (2011) Cyclic behaviour and resistance of saturated sand under non-symmetrical loading conditions. Géotechnique 61(1):59–73

    Article  Google Scholar 

  77. Yang M, Seidalinov G, Taiebat M (2019) Multidirectional cyclic shearing of clays and sands: Evaluation of two bounding surface plasticity models. Soil Dyn Earthq Eng 124:230–258

    Article  Google Scholar 

  78. Yang M, Taiebat M, Vaid YP (2016) Bidirectional monotonic and cyclic shear testing of soils: state of knowledge. In: 69th Canadian geotechnical conference. Vancouver, BC, Canada. Paper ID: 4198, 8 pages

  79. Zeghal M, El-Shafee O, Abdoun T (2018) Analysis of soil liquefaction using centrifuge tests of a site subjected to biaxial shaking. Soil Dyn Earthq Eng 114:229–241

    Article  Google Scholar 

  80. Zhang L, Evans TM (2020) Investigation of initial static shear stress effects on liquefaction resistance using discrete element method simulations. Int J Geomech 20(7):04020087

    Article  Google Scholar 

  81. Zhou W, Liu J, Ma G, Chang X (2017) Three-dimensional DEM investigation of critical state and dilatancy behaviors of granular materials. Acta Geotech 12(3):527–540

    Article  Google Scholar 

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Acknowledgements

Financial support for this study was provided by the Natural Sciences and Engineering Research Council of Canada (NSERC). M. Yang and M. Taiebat would like to thank Professor Y. Vaid for the insightful discussions that led to Fig. 9.

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Authors and Affiliations

  1. Department of Civil Engineering, University of British Columbia, Vancouver, Canada

    Ming Yang & Mahdi Taiebat

  2. CNRS-University of Montpellier, LMGC, Montpellier, France

    Farhang Radjaï

  3. IFREMER, DYNECO/DHYSED, Plouzané, France

    Patrick Mutabaruka

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  1. Ming Yang
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Yang, M., Taiebat, M., Mutabaruka, P. et al. Evolution of granular media under constant-volume multidirectional cyclic shearing. Acta Geotech. 17, 779–802 (2022). https://doi.org/10.1007/s11440-021-01239-0

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