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

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


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.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Shu Liu
    • 1
  • Juan Wang
    • 1
    Email author
  • 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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