Journal of Engineering Mathematics

, Volume 52, Issue 1, pp 11–34 | Cite as

The incremental response of soils. An investigation using a discrete-element model

Article

Abstract

The incremental stress-strain relation of dense packings of polygons is investigated by using molecular-dynamics simulations. The comparison of the simulation results to the continuous theories is performed using explicit expressions for the averaged stress and strain over a representative volume element. The discussion of the incremental response raises two important questions of soil deformation: Is the incrementally nonlinear theory appropriate to describe the soil mechanical response? Does a purely elastic regime exist in the deformation of granular materials? In both cases the answer will be “no”. The question of stability is also discussed in terms of the Hill condition of stability for non-associated materials. It is contended that the incremental response of soils should be revisited from micromechanical considerations. A micromechanical approach assisted by discrete element simulations is briefly outlined.

Keywords

elastoplasticity granular materials hypoplasticity incremental response 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Landau, L.D., Lifshitz, E.M. 1986Theory of Elasticity, Volume 7 of Course of Theoretical PhysicsPergamon PressMoscow362Google Scholar
  2. 2.
    Vermeer, P.A. 1998

    Non-associated plasticity for soils, concrete and rock

    Herrmann, H.J.Hovi, J.-P.Luding, S. eds. Physics of Dry Granular Media - NATO ASI Series E350Kluwer Academic PublishersDordrecht163193
    Google Scholar
  3. 3.
    Roscoe, K.H., Burland, J.B. 1968

    On the generalized stress-strain behavior of ‘wet’ clay

    Heyman, J.Leckie, F.A. eds. Engineering PlasticityCambridge University PressCambridge535609
    Google Scholar
  4. 4.
    Gudehus, G., Darve, F., Vardoulakis, I. 1984Constitutive Relations of SoilsBalkemaRotterdam512Google Scholar
  5. 5.
    Cundall, P.A., Strack, O.D.L. 1979A discrete numerical model for granular assemblagesGéotechnique294765Google Scholar
  6. 6.
    Bagi, K. 1996Stress and strain in granular assembliesMech. Mater22165177Google Scholar
  7. 7.
    Cundall, P.A., Drescher, A., Strack, O.D.L. 1982

    Numerical experiments on granular assemblies; measurements and observations

    Vermeer, P.Luger, H. eds. IUTAM Conference on Deformation and Failure of Granular MaterialsBalkema-RotterdamDelf355370
    Google Scholar
  8. 8.
    Goldenberg, C., Goldhirsch, I. 2002Force chains, microelasticity, and macroelasticityPhys. Rev. Lett89084302Google Scholar
  9. 9.
    Bagi, K. 1999Microstructural stress tensor of granular assemblies with volume forcesJ. Appl. Mech66934936Google Scholar
  10. 10.
    Lätzel M. (2002). From Discontinuous Models Towards A Continuum Description Of Granular Media. PhD thesis. Universität Stuttgart, 172 ppGoogle Scholar
  11. 11.
    Bardet, J.P. 1994Numerical simulations of the incremental responses of idealized granular materialsInt. J. Plasticity10879908Google Scholar
  12. 12.
    Kishino, Y. 2003On the incremental nonlinearity observed in a numerical model for granular mediaItal. Geotech. J3312Google Scholar
  13. 13.
    Calvetti, F., Viggiani, G., Tamagnini, C. 2003

    Micromechanical inspection of constitutive modeling

    Pande., Pietruszczak.,  eds. Constitutive Modeling and Analysis of Boundary Value Problems in Geotechnical EngineeringHevelius EdizioniBenevento187216
    Google Scholar
  14. 14.
    Oda, M., Iwashita, K. 2000Study on couple stress and shear band development in granular media based on numerical simulation analysesInt. J. Engng. Sci3817131740Google Scholar
  15. 15.
    Vardoulakis, I., Sulem, J. 1995Bifurcation Analysis in GeomechanicsBlakie Academic & ProfessionalLondon462Google Scholar
  16. 16.
    Bathurst, R.J., Rothenburg, L. 1988Micromechanical aspects of isotropic granular assemblies with linear contact interactionsJ. Appl. Mech551723Google Scholar
  17. 17.
    Darve, F., Laouafa, F. 2000Instabilities in granular materials and application to landslidesMech. of Cohes. Frict. Mater5627652Google Scholar
  18. 18.
    Gudehus, G. 1979A comparison of some constitutive laws for soils under radially symmetric loading and unloadingCan. Geotech. J20502516Google Scholar
  19. 19.
    Drucker, D.C., Prager, W. 1952Soil mechanics and plastic analysis of limit designQ. Appl. Math10157165Google Scholar
  20. 20.
    Nova, R., Wood, D. 1979A constitutive model for sand in triaxial compressionInt. J. Num. Anal. Meth. Geomech3277299Google Scholar
  21. 21.
    Roscoe, K.H. 1970The influence of the strains in soil mechanicsGeotechnique20129170Google Scholar
  22. 22.
    Poorooshasb, H.B., Holubec, I., Sherbourne, A.N. 1967Yielding and flow of sand in triaxial compressionCan. Geotech. J4277398Google Scholar
  23. 23.
    Wood, D.M. 1982Soil Mechanics-transient and cyclic loadsJohn Wiley and Sons Ltd.Chichester420Google Scholar
  24. 24.
    Tatsouka, F., Ishihara, K. 1974Yielding of sand in triaxial compressionSoils Found146376Google Scholar
  25. 25.
    Dafalias, Y.F., Popov, E.P. 1975A model of non-linearly hardening material for complex loadingActa Mech21173192Google Scholar
  26. 26.
    Kolymbas, D. 1991An outline of hypoplasticityArch. Appl. Mech61143151Google Scholar
  27. 27.
    Darve, F., Flavigny, E., Meghachou, M. 1995Yield surfaces and principle of superposition: revisit through incrementally non-linear constitutive relationsInt. J. Plast11927942Google Scholar
  28. 28.
    Chambon, R., Desrues, J., Hammad, W., Charlier, R., CLo, E 1994a new rate type constitutive model for geomaterials. Theoretical basis nd implementationInt. J. Anal. Meth. Geomech18253278Google Scholar
  29. 29.
    Wu, W., Bauer, E., Kolymbas, D. 1996Hypoplastic constitutive model with critical state for granular materialsMech. Mater234569Google Scholar
  30. 30.
    Herle, I., Gudehus, G. 1999Determination of parameters of a hypoplastic constitutive model from properties of grain assembliesMech. Cohes.-Frictl. Matls4461486Google Scholar
  31. 31.
    Kolymbas, D. 1993Modern Approaches to PlasticityElsevierHorton489Google Scholar
  32. 32.
    Kun, F., Herrmann, H.J. 1999Transition from damage to fragmentation in collision of solidsPhys. Rev. E5926232632Google Scholar
  33. 33.
    Moukarzel, C., Herrmann, H.J. 1992A vectorizable random latticeJ. Statist. Phys68911923Google Scholar
  34. 34.
    Okabe, A., Boots, B., Sugihara, K. 1992Spatial TessellationsConcepts and Applications of Voronoi Diagrams. Wiley Series in probability and Mathematical Statistics. John Wiley & SonsChichester532Google Scholar
  35. 35.
    Tillemans, H.J., Herrmann, H.J. 1995Simulating deformations of granular solids under shearPhysica A217261288Google Scholar
  36. 36.
    Allen, M.P., Tildesley, D.J. 1987Computer Simulation of LiquidsOxford University PressOxford385Google Scholar
  37. 37.
    Buckingham, E. 1914On physically similar systems: Illustrations of the use of dimensional equationsPhys. Rev4345376Google Scholar
  38. 38.
    Marcher, T., Vermeer, P.A. 2001

    Macromodeling of softening in non-cohesive soils

    Vermeer, P.A.Diebels, S.Ehlers, W.Herrmann, H.J.Luding, S.Ramm, E. eds. Continuous and Discontinuous Modeling of Cohesive Frictional MaterialsSpringerBerlin89110
    Google Scholar
  39. 39.
    Desrues J. (1984). Localisation de la Deformation Plastique dans les Materieux Granulaires. PhD thesis, University of GrenobleGoogle Scholar
  40. 40.
    Alonso-Marroquin, F., Herrmann, H.J. 2002Calculation of the incremental stress-strain relation of a polygonal packingPhys. Rev. E66021301Google Scholar
  41. 41.
    F. Alonso-Marroquin and H.J. Herrmann, Ratcheting of granular materials. Phys. Rev. Lett. 92 (2004) 054301.Google Scholar
  42. 42.
    Dafalias, Y.F. 1986Bounding surface plasticity. I: Mathematical foundation and hypoplasticityJ. Engng. Mech112966987Google Scholar
  43. 43.
    Vermeer, P.A. 1984

    A five-constant model unifying well-established concepts

    Gudehus, G.Darve, F.Vardoulakis, I. eds. Constitutive Relations of SoilsBalkemaRotterdam175197
    Google Scholar
  44. 44.
    Hill, R. 1958A general theory of uniqueness and stability in elastic-plastic solidsJ. Geotech. Eng6239249Google Scholar
  45. 45.
    Astrom, J.A., Herrmann, H.J., Timonen, J. 2000Granular packings and fault zonesPhys. Rev. Lett8446384641Google Scholar
  46. 46.
    Alonso-Marroquin, F., Herrmann, H.J., Vardoulakis, I. 2002

    Micromechanical investigation of soil plasticity: An investigation using a discrete model of polygonal particles

    Vermeer, P.A.Ehlers, W.Herrmann, H.J.Ramm, E. eds. Modeling of Cohesive-Frictional MaterialsBalkemaRotterdam4567
    Google Scholar
  47. 47.
    Mühlhaus, H.-B., Vardoulakis, I. 1987The thickness of shear bands in granular materialsGéotechnique37271283Google Scholar
  48. 48.
    Alonso-Marroquin F., McNamara S., Herrmann H.J. (2003). Micromechanische Untersuchung des granulares Ratchetings. Antrag an die Deutsche Forschungsgemeinschaft, Universität StuttgartGoogle Scholar
  49. 49.
    McDowell, G.R., Bolton, M.D., Robertson, D. 1996The fractal crushing of granular materialsJ. Mech. Phys. Solids4420792102Google Scholar
  50. 50.
    Bolton, M.D. 2002

    The role of micro-mechanics in soil mechanics

    Hyodo, M.Nakata, Y. eds. International Workshop on Soil CrushabilityYamaguchi UniversityJapan166178
    Google Scholar
  51. 51.
    Thornton, C., Barnes, D.J. 1986Computer simulated deformation of compact granular assembliesActa Mech644561Google Scholar
  52. 52.
    Luding, S. 2004Micro-macro transition for anisotropic, frictional granular packingsInt. J. Sol. Struct4158215836Google Scholar
  53. 53.
    Madadi, M., Tsoungui, O., Lätzel, M., Luding, S. 2004On the fabric tensor of polydisperse granular media in 2DInt. J. Sol. Struct4125632580Google Scholar
  54. 54.
    Radjai, F., Jean, M., Moreau, J.J., Roux, S. 1996Force distribution in dense two-dimensional granular systemsPhys. Rev. Lett77274277Google Scholar
  55. 55.
    Bagi, K. 2003Statistical analysis of contact force components in random granular assembliesGranular Matter54554Google Scholar
  56. 56.
    Jaeger, H.M., Nagel, S.R., Behringer, R.P. 1996Granular solids, liquids and gasesRev. Mod. Phys6812591273Google Scholar
  57. 57.
    Coppersmith, D. 1996Model for force fluctuations in bead packsPhys. Rev. E5346734685Google Scholar
  58. 58.
    Roux, S., Radjai, F. 2001

    On the state variables of the granular materials

    Aref, H.Philips, J.W. eds. Mechanics of a New MilleniumKluwerDordrecht181196
    Google Scholar
  59. 59.
    Luding, S. 2004

    Micro-macro models for anisotropic granular media

    Vermeer, P.A.Ehlers, W.Herrmann, H.J.Ramm, E. eds. Modeling of Cohesive-Frictional MaterialsBalkemaRotterdam195205
    Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Institute of Computer PhysicsUniversity of StuttgartStuttgartGermany

Personalised recommendations