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Granular Matter

, 21:37 | Cite as

Two-dimensional discrete element simulation of the mechanical behavior and strain localization of anisotropic dense sands

  • Xilin LüEmail author
  • Sheng Zeng
  • Liuchi Li
  • Jiangu Qian
  • Maosong Huang
Original Paper
  • 68 Downloads

Abstract

This paper presents a microscopic investigation on the effects of initial anisotropy, drainage condition, and consolidation state on the mechanical behavior and strain localization of dense sands. Discrete element simulations with non-spherical clumps were carried out to simulate drained and undrained biaxial tests of isotropically and K0 consolidated anisotropic sands. In drained tests, the stress–strain relationship shows an initial hardening and subsequent softening behavior, and the peak shear stress decreases as the bedding plane angle increases. K0 consolidation has slight influence on the peak friction angle and does not affect the friction angle at zero dilatancy. In undrained tests, softening behavior occurs when the bedding plane angle is small, while for higher bedding plane angle, the strengthening response takes over. As the bedding plane angle increases, the peak friction angle decreases initially but increases afterwards. The relative displacement and rotation angle of clumps as well as the void ratio distribution within the specimen indicate the appearance of shear band. Shear bands leads to the inhomogeneous deformation field within specimens. Excessive dilation inside of shear band is produced, and it may induce re-contraction behavior under drained condition and may re-increase the pore water pressure under undrained condition. The appearance of shear band reduces the peak shear strength, and the specimen with a low bedding angle results in a larger reduction of shear strength than that from the specimen with a high bedding angle. Particle rotation mode and force chain network change along with the formation of a shear band. As the longest axis of clumped particle varies from vertical to parallel with respect to the loading direction, the majority of particle contacts inside of shear band changes from multi-point mode to single contact mode. The obtained shear band width and inclination angle were computed, and their variations with bedding angle were obtained.

Keywords

Shear band Dense sand Anisotropy Discrete element simulation Undrained shear 

Notes

Acknowledgments

The financial supports by National Key Research and Development Program (through Grant No. 2016YFC0800200), National Science Foundation of China (NSFC through Grant No. 41672270), and Shanghai Pujiang Project (through Grant No. 17PJD040) are gratefully acknowledged. We are grateful to anonymous reviewers for their valuable suggestions and comments to improve the quality of the paper.

Compliance with ethical standards

Conflict of interest

We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

References

  1. 1.
    Gutierrez, M.: Effects of constitutive parameters on strain localization in sands. Int. J. Numer. Anal. Meth. Geomech. 35(2), 161–178 (2011)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Nicot, F., Darve, F., Dat, V.K.: Huynh: bifurcation and second-order work in geomaterials. Int. J. Numer. Anal. Meth. Geomech. 31(8), 1007–1032 (2007)CrossRefGoogle Scholar
  3. 3.
    Rudnicki, W., Rice, J.R.: Conditions for the localization of deformation in pressure-sensitive dilatant materials. J. Mech. Phys. Solids 23, 371–394 (1975)ADSCrossRefGoogle Scholar
  4. 4.
    Wang, Q., Lade, P.V.: Shear banding in true triaxial tests and its effect on failure in sand. J. Eng. Mech. ASCE 127(8), 754–761 (2001)CrossRefGoogle Scholar
  5. 5.
    Lade, P.V.: Assessment of test data for selection of 3-D failure criterion for sand. Int. J. Numer. Anal. Meth. Geomech. 30(4), 307–333 (2006)CrossRefGoogle Scholar
  6. 6.
    Sibille, L., Hadda, N., Nicot, F., Tordesillas, A., Darve, F.: Granular plasticity, a contribution from discrete mechanics. J. Mech. Phys. Solid 75, 119–139 (2015)ADSCrossRefGoogle Scholar
  7. 7.
    Daouadji, A., Hicher, P.Y., Jrad, M., Sukumaran, B., Belouettar, S.: Experimental and numerical investigation of diffuse instability in granular materials using a microstructural model under various loading paths. Géotechnique 63(5), 368–381 (2013)CrossRefGoogle Scholar
  8. 8.
    Symrs, M.J.P.R., Gens, A., Hight, D.W.: Undrained anisotropy and principal stress rotation in saturated sand. Géotechnique 34(1), 11–27 (1984)CrossRefGoogle Scholar
  9. 9.
    Vardoulakis, I.: Deformation of water-saturated sand I. Uniform undrained deformation and shear banding. Géotechnique 46(3), 441–456 (1996)CrossRefGoogle Scholar
  10. 10.
    Sivathayalan, S., Logeswaran, P.: Behaviour of sands under generalized drainage boundary conditions. Can. Geotech. J. 44(2), 138–150 (2007)CrossRefGoogle Scholar
  11. 11.
    Mukherjee, M., Gupta, A., Prashant, A.: Instability analysis of sand under undrained biaxial loading with rigid and flexible boundary. Int. J. Geomech. 17(1), 04016042 (2017)CrossRefGoogle Scholar
  12. 12.
    Lü, X., Huang, M., Qian, J.: Prediction of plane strain undrained diffuse instability and strain localization with non-coaxial plasticity. Soils Found. 54(6), 1070–1080 (2014)CrossRefGoogle Scholar
  13. 13.
    Lü, X., Huang, M.: Static liquefaction of sands under isotropically and K0-consolidated undrained triaxial conditions. J. Geotech. Geoenviron. Eng. ASCE 141(1), 04014087 (2015)CrossRefGoogle Scholar
  14. 14.
    Guo, P.J.: Undrained shear band in water saturated granular media: a critical revisiting with numerical examples. Int. J. Numer. Anal. Meth. Geomech. 37(4), 353–373 (2013)CrossRefGoogle Scholar
  15. 15.
    Liu, G., Rong, G., Peng, J., Zhou, C.: Numerical simulation on undrained triaxial behavior of saturated soil by a fluid coupled-DEM model. Eng. Geol. 193(4), 256–266 (2015)CrossRefGoogle Scholar
  16. 16.
    Sitharam, T.G., Vinod, J.S., Ravishankar, B.V.: Evaluation of undrained response from drained triaxial shear tests: DEM simulations and experiments. Géotechnique 58(7), 605–608 (2008)CrossRefGoogle Scholar
  17. 17.
    Sibille, L., Donzé, F.V., Nicot, F., Chareyre, B., Darve, F.: From bifurcation to failure in a granular material: a DEM analysis. Acta Geotech. 3(1), 15–24 (2008)CrossRefGoogle Scholar
  18. 18.
    Yang, Z.X., Yang, J., Wang, L.Z.: Micro-scale modeling of anisotropy effects on undrained behavior of granular soils. Granular Matter 15(5), 557–572 (2013)CrossRefGoogle Scholar
  19. 19.
    Nguyen, H.B.K., Rahman, M.M., Fourie, A.B.: Undrained behaviour of granular material and the role of fabric in isotropic and K0 consolidations: DEM approach. Géotechnique 67(2), 153–167 (2016)CrossRefGoogle Scholar
  20. 20.
    Wang, R., Fu, P., Tong, Z., Zhang J., Dafalias, Y.F.: Strength anisotropy of granular material consisting of perfectly round particles. Int. J. Numer. Anal. Meth. Geomech. 41(17), 1758–1778 (2017)CrossRefGoogle Scholar
  21. 21.
    Guo, P.: Critical length of force chains and shear band thickness in dense granular materials. Acta Geotech. 7, 41–55 (2012)CrossRefGoogle Scholar
  22. 22.
    Iwashita, K., Oda, M.: Micro-deformation mechanism of shear banding process based on modified distinct element method. Powder Technol. 109(1), 192–205 (2000)CrossRefGoogle Scholar
  23. 23.
    Wang R., Fu P., Zhang J.-M., Dafalias Y.F. (2019) Deformation of granular material under continuous rotation of stress principal axes. Int. J. Geomech. (2019).  https://doi.org/10.1061/(ASCE)GM.1943-5622.0001383 CrossRefGoogle Scholar
  24. 24.
    Shan, T., Zhao, J.D.: A coupled CFD-DEM analysis of granular flow impacting on a water reservoir. Acta Mech. 225, 2449–2470 (2014)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Guo, N., Zhao, J.D.: Parallel hierarchical multiscale modelling of hydro-mechanical problems for saturated granular soils. Comput. Methods Appl. Mech. Eng. 305, 37–61 (2016)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    Johnson, D.H., Vahedifard, F., Jelinek, B., Peters, J.F.: Micromechanics of undrained response of dilative granular media using a coupled DEM-LBM model: a case of biaxial test. Comput. Geotech. 20, 103–112 (2017)CrossRefGoogle Scholar
  27. 27.
    Xu, M., Song, E., Jiang, H., Hong, J.: DEM simulation of the undrained shear behavior of sand containing dissociated gas hydrate. Granular Matter 18(4), 79 (2016)CrossRefGoogle Scholar
  28. 28.
    Wang, G., Wei, J.: Microstructure evolution of granular soils in cyclic mobility and post-liquefaction process. Granular Matter 18(3), 51 (2016)CrossRefGoogle Scholar
  29. 29.
    Huang, M., Lü, X., Qian, J.: Non-coaxial elasto-plasticity model and bifurcation prediction of shear banding in sands. Int. J. Numer. Anal. Meth. Geomech. 34(9), 906–919 (2010)zbMATHGoogle Scholar
  30. 30.
    Lü, X., Bardet, J.P., Huang, M.: Spectral analysis of nonlocal regularization in two-dimensional finite element models. Int. J. Numer. Anal. Meth. Geomech. 36(2), 219–235 (2012)CrossRefGoogle Scholar
  31. 31.
    Lü, X., Zeng, S., Qian, J., Huang, M.: Investigation of the shear strength of cross-anisotropic sand using discrete element simulation. Géotech. Lett. 7(3), 1–7 (2017)ADSCrossRefGoogle Scholar
  32. 32.
    Abelev, A.V., Lade, P.V.: Characterization of failure in cross-anisotropic soils. J. Eng. Mech. 130(5), 599–606 (2004)CrossRefGoogle Scholar
  33. 33.
    Oda, M., Takemura, T., Takahashi, M.: Microstructure in shear band observed by microfocus X-ray computed tomography. Géotechnique 55(4), 333–335 (2005)CrossRefGoogle Scholar
  34. 34.
    Sibille, L., Froiio, F.: A numerical photogrammetry technique for measuring microscale kinematics and fabric in Schneebeli materials. Granular Matter 9, 183–193 (2007)CrossRefGoogle Scholar
  35. 35.
    Alshibli, K.A., Hasan, A.: Spatial variation of void ratio and shear band thickness in sand using X-ray computed tomography. Géotechnique 58(4), 249–257 (2008)CrossRefGoogle Scholar
  36. 36.
    Takano, D., Nicolas, L., Otani, J., Hall Stephen, A.: Localised deformation in a wide-grained sand under triaxial compression revealed by X-ray tomography and digital image correlation. Soils Found. 55(4), 906–915 (2015)CrossRefGoogle Scholar
  37. 37.
    Li, X., Yu, H.S., Li, X.S.: Macro–micro relations in granular mechanics. Int. J. Solids Struct. 46(25), 4331–4341 (2009)CrossRefGoogle Scholar
  38. 38.
    Jiang, M., Konrad, J.M., Leroueil, S.: An efficient technique for generating homogeneous specimens for DEM studies. Comput. Geotech. 30(7), 579–597 (2003)CrossRefGoogle Scholar
  39. 39.
    Jiang, M., Jun, S., Li, L., Zhou, C., Cui, L.: Investigation of influence of particle characteristics on the non-coaxiality of anisotropic granular materials using DEM. Int. J. Numer. Anal. Meth. Geomech. 41(2), 198–222 (2017)CrossRefGoogle Scholar
  40. 40.
    Hosn, R.A., Sibille, L., Benahmed, N., Chareyre, B.: Discrete numerical modeling of loose soil with spherical particles and interparticle rolling friction. Granular Matter 19(1), 4 (2017)CrossRefGoogle Scholar
  41. 41.
    Zhao, J., Guo, N.: The interplay between anisotropy and strain localisation in granular soils: a multiscale insight. Géotechnique 65(8), 642–656 (2015)CrossRefGoogle Scholar
  42. 42.
    Seyedi Hosseininia, E.: Investigating the micromechanical evolutions within inherently anisotropic granular materials using discrete element method. Granul. Matter 14(4), 483–503 (2012)CrossRefGoogle Scholar
  43. 43.
    Bolton, M.D.: The strength and dilatancy of sands. Géotechnique 37(2), 219–226 (1987)CrossRefGoogle Scholar
  44. 44.
    Schanz, T., Vermeer, P.A.: Angles of friction and dilatancy of sand. Géotechnique 46(1), 145–151 (1996)CrossRefGoogle Scholar
  45. 45.
    Mooney, M.A., Finno, R.J., Viggiane, M.G.: A unique critical state for sand? J. Geotech. Geoenviron. ASCE 124(11), 1100–1108 (1998)CrossRefGoogle Scholar
  46. 46.
    Lade, P.V., Rodriguez, N.M., Van, D., Eugene, J.: Effects of principal stress directions on 3D failure conditions in cross-anisotropic sand. J. Geotech. Geoenviron. Eng. ASCE 140(2), 04013001 (2014)CrossRefGoogle Scholar
  47. 47.
    Igwe, O.: The combined effect of particle size distribution and relative density on the large strain behavior of sandy soils. Geotech. Geol. Eng. 36, 1037–1048 (2018)Google Scholar
  48. 48.
    Druckrey, A.M., Alshibli K.A.: 3D particle-scale displacement gradient to uncover the onset of shear bands in sand. In: Proceedings of the 11th International Workshop on Bifurcation and Degradation in Geomaterials, Dedicated to Hans, Cyprus, pp. 39–46 (2017)Google Scholar
  49. 49.
    Bardet, J.P., Proubet, J.: A numerical investigation of the structure of persistent shear bands in granular media. Géotechnique 41(4), 599–613 (1991)CrossRefGoogle Scholar
  50. 50.
    Esin, M., Dyskin, A.V., Pasternak, E.: The effect of rotational degrees of freedom on the formation of deformation patterns in granular materials using digital image correlation. In: Proceedings of the 10th International Workshop on Bifurcation and Degradation in Geomaterials, Hong Kong, pp. 127–133 (2015)Google Scholar
  51. 51.
    Ikeda, K., Yamakawa, Y., Desrues, J., Murota, K.: Bifurcations to diversify geometrical patterns of shear bands on granular material. Phys. Rev. Lett. 100(19), 198001 (2008)ADSCrossRefGoogle Scholar
  52. 52.
    Ikeda, K., Sasaki, H., Ichimura, T.: Diffuse mode bifurcation of soil causing convection-like shear investigated by group-theoretic image analysis. J. Mech. Phys. Solids 54(2), 310–339 (2006)ADSMathSciNetCrossRefGoogle Scholar
  53. 53.
    Alshibli, K.A., Sture, S.: Sand shear band thickness measurements by digital imaging techniques. J. Comput. Civ. Eng. 13(2), 103–109 (1999)CrossRefGoogle Scholar
  54. 54.
    Oda, M., Kazama, H.: Microstructure of shear bands and its relation to the mechanisms of dilatancy and failure of dense granular soils. Géotechnique 48(4), 465–481 (1998)CrossRefGoogle Scholar
  55. 55.
    Bardet, J.P.: Orientation of shear bands in frictional soils. J. Eng. Mech. ASCE 117(7), 1466–1485 (1991)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Geotechnical EngineeringTongji UniversityShanghaiChina
  2. 2.Key Laboratory of Geotechnical and Underground Engineering of Ministry of EducationTongji UniversityShanghaiChina
  3. 3.Department of Mechanical and Civil EngineeringCalifornia Institute of TechnologyPasadenaUSA

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