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Effect of Material Stiffness Variation on Shakedown Solutions of Soils Under Moving Loads

  • Shu Liu
  • Juan Wang
  • Dariusz Wanatowski
  • Hai-Sui Yu
Conference paper
Part of the Sustainable Civil Infrastructures book series (SUCI)

Abstract

Shakedown limits of pavements and railway foundations can be calculated based on shakedown theorems. These values can be used to guide the thickness designs of pavement and railway constructions considering material plastic properties. However, most existing shakedown analyses were carried out by assuming a unique stiffness value for each material. This paper mainly concentrates on the influence of stiffness variation on the shakedown limits of pavements and railway foundations under moving loads. Finite element models as well as a user-defined material subroutine UMAT are first developed to obtain the elastic responses of soils considering a linearly increasing stiffness modulus with depth. Then, based on the lower-bound shakedown theorem, shakedown solutions are obtained by searching for the most critical self-equilibrated residual stress field. It is found that for a single-layered structure, the rise of a stiffness changing ratio will give a larger shakedown limit; and the increase is more pronounced when the friction angle is relatively high. For multi-layered pavement and railway systems, neglecting the stiffness variation may overestimate the capacity of the structures.

References

  1. Boulbibane, M., Weichert, D.: Application of shakedown theory to soils with non-associated flow rules. Mech. Res. Commun. 24(5), 513–519 (1997)CrossRefGoogle Scholar
  2. Brown, S.F., Yu, H.S., Juspi, H., Wang, J.: Validation experiments for lower-bound shakedown theory applied to layered pavement systems. Géotechnique 62(10), 923–932 (2012)CrossRefGoogle Scholar
  3. Collins, I.F., Cliffe, P.F.: Shakedown in frictional materials under moving surface loads. Int. J. Numer. Anal. Meth. Geomech. 11(4), 409–420 (1987)CrossRefGoogle Scholar
  4. Hammam, A.H., Eliwa, M.: Comparison between results of dynamic and static moduli of soil determined by different methods. HBRC J. 9(2), 144–149 (2013)CrossRefGoogle Scholar
  5. Krabbenhøft, K., et al.: Shakedown of a cohesive-frictional half-space subjected to rolling and sliding contact. Int. J. Solids Struct. 44(11–12), 3998–4008 (2007)CrossRefGoogle Scholar
  6. Larew, H.G., Leonards, G.A.: A strength criterion for repeated loads. Highway Res. Board Proc. 41, 529–556 (1962)Google Scholar
  7. Lekarp, F., Dawson, A.: Modelling permanent deformation behaviour of unbound granular materials. Constr. Build. Mater. 12(1), 9–18 (1998)CrossRefGoogle Scholar
  8. Li, H.X., Yu, H.S.: A nonlinear programming approach to kinematic shakedown analysis of frictional materials. Int. J. Solids Struct. 43(21), 6594–6614 (2006)CrossRefGoogle Scholar
  9. Liu, S., et al.: Shakedown solutions for pavements with materials following associated and non-associated plastic flow rules. Comput. Geotech. 78, 218–266 (2016)CrossRefGoogle Scholar
  10. Raad, L., et al.: Stability of multilayer systems under repeated loads. Transp. Res. Rec. 1207, 181–186 (1988)Google Scholar
  11. Rowe, R.K., Booker, J.R.: The behaviour of footings resting on a non-homogeneous soil mass with a crust. Part II. Circular footings. Can. Geotech. J. 18(18), 265–279 (1980)Google Scholar
  12. Rowe, R.K., Booker, J.R.: The elastic displacements of single and multiple underream anchors in a Gibson soil. Geotechnique 31(1), 125–142 (1981)CrossRefGoogle Scholar
  13. Sharp, R.W., Booker, J.R.: Shakedown of pavements under moving surface loads. J. Transp. Eng. ASCE 110, 1–14 (1984)CrossRefGoogle Scholar
  14. Vesic, A.B.: Bending of beams resting on isotropic elastic solid. J. Eng. Mech. 87(2), 35–54 (1961)Google Scholar
  15. Wang, J., Yu, H.S.: Shakedown analysis and design of layered road pavements under three-dimensional moving surface loads. Road Mater. Pavem. Des. 14, 703–722 (2013a)CrossRefGoogle Scholar
  16. Wang, J., Yu, H.S.: Residual stresses and shakedown in cohesive-Frictional half-space under moving surface loads. Geomech. Geoeng. 8(1), 1–14 (2013b)CrossRefGoogle Scholar
  17. Wang, J., Yu, H.S.: Three-dimensional shakedown solutions for anisotropic cohesive-frictional materials under moving surface loads. Int. J. Numer. Anal. Meth. Geomech. 38(4), 331–348 (2014)CrossRefGoogle Scholar
  18. Werkmeister, S., et al.: Pavement design model for unbound granular materials. Jo. Transp. Eng. 130(5), 665–674 (2004)CrossRefGoogle Scholar
  19. Yu, H.S., Hossain, M.Z.: Lower bound shakedown analysis of layered pavements using discontinuous stress fields. Comput. Methods Appl. Mech. Eng. 167(3–4), 209–222 (1998)CrossRefGoogle Scholar
  20. Yu, H.S., Wang, J.: Three-dimensional shakedown solutions for cohesive-frictional materials under moving surface loads. Int. J. Solids Struct. 49(26), 3797–3807 (2012)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Shu Liu
    • 1
  • Juan Wang
    • 1
  • Dariusz Wanatowski
    • 2
  • Hai-Sui Yu
    • 2
  1. 1.Ningbo Nottingham New Materials Institute, University of Nottingham Ningbo ChinaNingboChina
  2. 2.Faculty of Engineering, School of Civil EngineeringUniversity of LeedsLeedsUK

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