Three-Dimensional Shakedown Solutions for Cross-Anisotropic Cohesive-Frictional Materials Under Moving Loads

  • Hai-Sui Yu
  • Juan WangEmail author
  • Shu Liu


Based on Melan’s lower-bound shakedown theorem, shakedown analysis of cross-anisotropic cohesive-frictional materials under three-dimensional moving Hertz loads is presented. The material behaviour is characterised by a generalised Mohr-Coulomb criterion. By means of a critical self-equilibrated residual stress field, rigorous lower-bound shakedown solutions can be obtained through a simple optimisation procedure. Influences of both elastic anisotropy and plastic anisotropy are investigated. And shakedown solutions for a two-layered pavement system with cross-anisotropic materials are also presented. Results imply that pavement design based on the isotropic assumption may result in unsafe design against rutting.


Shakedown Layered pavements Cross-anisotropic Mohr-Coulomb criterion 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Faculty of Engineering, Nottingham Centre for GeomechanicsThe University of NottinghamNottinghamUK
  2. 2.Department of Civil EngineeringThe University of NottinghamNingboChina

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