Skip to main content
SpringerLink
Log in

Investigation of Instabilities in Granular Media and Their Numerical Simulation

  • Brief Communication
  • Published:
Indian Geotechnical Journal Aims and scope Submit manuscript

Abstract

The inception of instabilities in sand across different “length-scales,” viz., continuum, discrete, and laboratory element tests, has been highlighted in this study. With instability onset, the material behavior no longer remains “single element” in the sense of continuum mechanics, and due care is required while calibrating different constitutive relationships for use in various numerical simulations. A laboratory “element” test can instead be viewed as a boundary value problem at the instability onset. The post-instability response of a soil specimen represents the “system-response” with the evolution of inhomogeneities being primarily influenced by the boundary conditions among various other factors. Instability onset in drained and undrained biaxial tests has been explored by adopting the bifurcation framework with the aid of a generalized nonassociative elastoplastic material model. For the locally drained globally undrained scenario within a continuum numerical framework, instability onset is found to be influenced by the refinement of mesh discretization. Signatures of rate-dependent localized behavior of sand specimens are also commented on from numerical simulations of drained biaxial tests. To address the “pathological mesh dependence” of classical continuum modeling, we resort to a micromechanical discrete granular framework that considers the actual particle morphology. The numerical predictions match reasonably well with the flexible boundary plane strain experiments. The inherent grain fabric arrangement is found to be the triggering mechanism behind the localized strain accumulation at multiple zones. The influence of loading boundary conditions and various signatures of local nonuniformities is also explored with the aid of image analysis in plane strain and triaxial tests.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

References

  1. Bardet J (1990) A comprehensive review of strain localization in elastoplastic soils. Comput Geotech 10(3):163–188

    Article  Google Scholar 

  2. Bigoni D (2012) Nonlinear solid mechanics: bifurcation theory and material instability. Cambridge University Press, Cambridge

    Book  Google Scholar 

  3. Mukherjee M, Gupta A, Prashant A (2017) Instability analysis of sand under undrained biaxial loading with rigid and flexible boundary. Int J Geomech 17(1):04016042

    Article  Google Scholar 

  4. Mukherjee, M. (2016). Instabilities and rate-dependency in mechanical behavior of sand, Doctoral dissertation, Indian Institute of Technology Kanpur

  5. Bhattacharya D, Prashant A (2020) Effect of loading boundary conditions in plane strain mechanical response and local deformations in sand specimens. J Geotech Geoenviron Eng 146(9):04020086

    Article  Google Scholar 

  6. Mitchell JK, Soga K (2005) Fundamentals of soil behavior. Wiley, New York

    Google Scholar 

  7. Han C, Drescher A (1993) Shear bands in biaxial tests on dry coarse sand. Soils Found 33(1):118–132

    Article  Google Scholar 

  8. Desai CS (2016) Disturbed state concept as unified constitutive modeling approach. J Rock Mech Geotech Engi 8(3):277–293

    Article  Google Scholar 

  9. Muir Wood D (2007) The magic of sands—the 20th Bjerrum Lecture presented in Oslo, 25 November 2005. Can Geotech J 44(11):1329–1350

    Article  Google Scholar 

  10. Muir Wood D (2012) Heterogeneity and soil element testing. Ge’otechnique Letters 2:101–106

    Article  Google Scholar 

  11. Vardoulakis I (1981) Bifurcation analysis of the plane rectilinear deformation on dry sand samples. Int J Solids Struct 17(11):1085–1101

    Article  Google Scholar 

  12. Han C, Vardoulakis I (1991) Plane-strain compression experiments on water saturated fine-grained sand. Ge’otechnique 41(1):49–78

    Article  Google Scholar 

  13. Yamamuro JA, Lade PV (1997) Static liquefaction of very loose sands. Can Geotech J 34(6):905–917

    Article  Google Scholar 

  14. Borja RI (2002) Bifurcation of elastoplastic solids to shear band mode at finite strain. Comput Methods Appl Mech Eng 191(46):5287–5314

    Article  MathSciNet  Google Scholar 

  15. Lade PV (2002) Instability, shear banding, and failure in granular materials. Int J Solids Struct 39(13–14):3337–3357

    Article  Google Scholar 

  16. Alshibli KA, Batiste SN, Sture S (2003) Strain localization in sand: plane strain versus triaxial compression. J Geotech Geoenviron Eng 129(6):483–494

    Article  Google Scholar 

  17. Desrues J, Viggiani G (2004) Strain localization in sand: an overview of the experimental results obtained in grenoble using stereophotogrammetry. Int J Numer Anal Methods Geomech 28(4):279–321

    Article  Google Scholar 

  18. Andrade JE, Borja RI (2007) Modeling deformation banding in dense and loose fluid-saturated sands. Finite Elem Anal Des 43(5):361–383

    Article  MathSciNet  Google Scholar 

  19. Andò E, Viggiani G, Hall SA, Desrues J (2013) Experimental micro-mechanics of granular media studied by X-ray tomography: recent results and challenges. Géotechnique Letters 3(3):142–146

    Article  Google Scholar 

  20. Kawamoto R, Andò E, Viggiani G, Andrade JE (2018) All you need is shape: predicting shear banding in sand with LS-DEM. J Mech Phys Solids 111:375–392

    Article  Google Scholar 

  21. Gajo A, Muir Wood D (1999) A kinematic hardening constitutive model for sands: the multiaxial formulation. Int J Numer Anal Meth Geomech 23(9):925–965

    Article  Google Scholar 

  22. Wood DM (2004) Geotechnical modelling. CRC Press, Florida

    Book  Google Scholar 

  23. Vardoulakis I (1985) Stability and bifurcation of undrained, plane rectilinear deformations on water-saturated granular soils. Int J Numer Anal Meth Geomech 9:399–414

    Article  Google Scholar 

  24. Bardet JP (1991) Analytical solutions for the plane-strain bifurcation of compressible solids. J Appl Mech 58:651–657

    Article  Google Scholar 

  25. Bardet JP, Shiv A (1995) Plane-strain instability of saturated porous media. J Eng Mech 121:717–724

    Article  Google Scholar 

  26. Rice, J. R. (1976). The localization of plastic deformation, In: Proceedings of the 14th International Congress on Theoretical and Applied Mechanics, Vol. 1, North-Holland Publishing, Amsterdam, Netherlands, 207–220

  27. Mukherjee M, Gupta A, Prashant A (2016) Drained instability analysis of sand under biaxial loading using a 3D material model. Comput Geotech 79:130–145

    Article  Google Scholar 

  28. Shuttle D, Smith I (1988) Numerical simulation of shear band formation in soils. Int J Numer Anal Meth Geomech 12(6):611–626

    Article  Google Scholar 

  29. Borja RI, Regueiro RA (2001) Strain localization in frictional materials exhibiting displacement jumps. Comput Methods Appl Mech Eng 190(20–21):2555–2580

    Article  Google Scholar 

  30. Bhattacharya D, Mukherjee M, Prashant A (2020) Perturbation intensity and mesh convergence in coupled undrained instability analysis in sands under biaxial loading. Int J Geomech 20(7):04020081

    Article  Google Scholar 

  31. Mukherjee M, Gupta A, Prashant A (2020) A rate-dependent model for sand to predict constitutive response and instability onset. Acta Geotech. https://doi.org/10.1007/s11440-020-00988-8

    Article  Google Scholar 

  32. Perzyna P (1963) The constitutive equations for rate sensitive plastic materials. Quarter Appl Math 20:321–332

    Article  MathSciNet  Google Scholar 

  33. Needleman A (1988) Material rate dependence and mesh sensitivity in localization problems. Comput Methods Appl Mech Eng 67:69–85

    Article  Google Scholar 

  34. Bhattacharya D, Kawamoto R, Karapiperis K, Andrade JE, Prashant A (2020) Mechanical behaviour of granular media in flexible boundary plane strain conditions: experiment and level-set discrete element modelling. Acta Geotech. https://doi.org/10.1007/s11440-020-00996-8

    Article  Google Scholar 

  35. Bagi K (2006) Analysis of microstructural strain tensors for granular assemblies. Int J Solids Struct 43(10):3166–3184

    Article  Google Scholar 

  36. Bhattacharya, D. (2019). Instabilities in granular media with flexible boundaries. Doctoral dissertation, Indian Institute of Technology Gandhinagar

  37. Stanier SA, Blaber J, Take AW, White D (2015) Improved image-based deformation measurement for geotechnical applications. Can Geotech J 53(5):727–739

    Article  Google Scholar 

  38. Andrade JE, Avila CF, Hall SA, Lenoir N, Viggiani G (2011) Multiscale modeling and characterization of granular matter: from grain kinematics to continuum mechanics. J Mech Phys Solids 59(2):237–250

    Article  Google Scholar 

  39. Ai SG, Feng SJ (2020) Multiscale modeling for analyzing slip weakening at material interfaces. Comput Geotech 118:103348

    Article  Google Scholar 

  40. Zhao S, Zhao J, Lai Y (2020) Multiscale modeling of thermo-mechanical responses of granular materials: a hierarchical continuum–discrete coupling approach. Comput Methods Appl Mech Eng 367:113100

    Article  MathSciNet  Google Scholar 

  41. Yang Y, Misra A (2012) Micromechanics based second gradient continuum theory for shear band modeling in cohesive granular materials following damage elasticity. Int J Solids Struct 49(18):2500–2514

    Article  Google Scholar 

  42. Placidi L, Barchiesi E, Misra A (2018) A strain gradient variational approach to damage: a comparison with damage gradient models and numerical results. Math Mech Complex Syst 6(2):77–100

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Indian Institute of Technology Gandhinagar, Palaj, Gandhinagar, 382355, Gujarat, India

    Debayan Bhattacharya & Amit Prashant

  2. Indian Institute of Technology Mandi, Mandi, 175005, Himachal Pradesh, India

    Mousumi Mukherjee

Authors
  1. Debayan Bhattacharya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mousumi Mukherjee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Amit Prashant
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Amit Prashant.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bhattacharya, D., Mukherjee, M. & Prashant, A. Investigation of Instabilities in Granular Media and Their Numerical Simulation. Indian Geotech J 51, 552–566 (2021). https://doi.org/10.1007/s40098-021-00524-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40098-021-00524-9

Keywords

Search

Navigation