Granular Matter

, Volume 7, Issue 2–3, pp 109–118 | Cite as

Shakedown of unbound granular material



Compacted unbounded granular materials are extensively used as sub-layer in pavement design. Most pavement design guides assume that they are responsible for the degradation and deformation of the roads and railways that they support. Biaxial tests are usually employed to investigate the elasto-plastic response of these materials to cyclic loading. A particularly interesting question is whether a limit load exists, below which the excitations shake down, in the sense that the material does not accumulate further deformations. We have carried out a detailed study of the elasto-plastic behavior of a simple model of unbound granular matter submitted to cyclic loading. The dissipated energy throughout the simulation has been used for the characterization of the different regimes of responses.


Shakedown Ratcheting Unbound granular material Simulation Resilient behavior 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Allen, J.J.: Resilient response of granular materials subjected to time-dependent lateral stresses. Transp. Res. Rec. 510, 1–14 (1974)Google Scholar
  2. 2.
    Alonso-Marroquin, F., Herrmann, H.J.: Ratcheting of granular materials. Phys. Rev. Lett. 92, 054301 (2004), cond-mat/0403065Google Scholar
  3. 3.
    Austroads, AP 17/92 -Pavement Design - A Guide to the Structural Design of Road Pavements. Austroads, Haymarket, Australia, 1992Google Scholar
  4. 4.
    Collins, I.F., Boulbibane, M.: Geomechanical analysis of unbound pavements based on sahekdown theory. J. Geot. Geoenv. Eng. 126, 50–59 (2000)Google Scholar
  5. 5.
    Cundall, P.A.: Numerical experiments on localization in frictional materials. Ingenieur-Archiv 59, 148–159 (1989)Google Scholar
  6. 6.
    Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular assemblies. Géotechnique 29(1), 47–65 (1979)Google Scholar
  7. 7.
    Drucker, D.C., Prager, W.: Soil mechanics and plastic analysis of limit design. Q. Appl. Math. 10(2), 157–165 (1952)Google Scholar
  8. 8.
    Koiter, W.T.: General theorems for elastic-plastic Solids. volume 1, pp. 165–221, North-Holland, Amsterdam (1960)Google Scholar
  9. 9.
    König, J.A.: Shakedown of elasto-plastic structures. Elsevier-PWN, Warszawa (1987)Google Scholar
  10. 10.
    Kun, F., Herrmann, H.J.: A study of fragmentation processes using a discrete element method. Comput. Methods Appl. Mech. Eng. 138, 3–18 (1996)Google Scholar
  11. 11.
    Lekarp, F., Dawson, A.: Modelling permanent deformation behaviour of unbound granular materials. Construction and Building Materials 12(1), 9–18 (1998)Google Scholar
  12. 12.
    Lekarp, F., Dawson, A., Isacsson, U.: Permanent strain response of unbound aggregates. J. Transp. Eng. 126(1), 76–82 (2000)Google Scholar
  13. 13.
    Lekarp, F., Isacsson, U., Dawson, A.: Resilient response of unbound aggregates. J. Transp. Eng. 126(1), 66–75 (2000)Google Scholar
  14. 14.
    Luding, S.: Collisions & contacts between two particles. In: Herrmann, H.J., Hovi, J.-P., Luding, S. (eds.), Physics of dry granular media - NATO ASI Series E350, pp. 285, Dordrecht, 1998 Kluwer Academic PublishersGoogle Scholar
  15. 15.
    McNamara, S., Herrmann, H.J.: Measurement of indeterminacy in packings of perfectly rigid spheres. Phys. Rev. E. 70, 061303 (2004)Google Scholar
  16. 16.
    Melan, E.: Theorie statisch unbestimmter Systeme aus ideal–plastischem Baustoff. Sitzungsberichte der Akademie der Wissenschaften in Wien, IIa 145, 195–218 (1936)Google Scholar
  17. 17.
    Sharp, R.W., Booker, J.R.: Shakedown of pavements under moving surface loads. J. Trans. Eng. 110, 1–14 (1984)Google Scholar
  18. 18.
    Taciroglu, E., Hjelmstad, D.: Simple nonlinear model for elastic response of cohesionless granular materials. J. Eng. Mech. 128, 969–978 (2002)Google Scholar
  19. 19.
    Tillemans, H.-J., Herrmann, H.J.: Simulating deformations of granular solids under shear. Physica A 217, 261–288 (1995)Google Scholar
  20. 20.
    Werkmeister, S., Dawson, A.R., Wellner, F.: Permanent deformation behavior of granular materials and the shakedown theory. Jnl. Trans. Res. Board 1757, 75–81 (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Institute for Computer Applications 1StuttgartGermany

Personalised recommendations