Three-dimensional shakedown solutions for cohesive-frictional materials under moving surface loads

Hai Sui Yu, Juan Wang

Research output: Journal PublicationArticlepeer-review

75 Citations (Scopus)


Pavement and railtrack design is of huge importance to society and yet the theoretical basis for most current design methods is still very simplistic and crude (Brown, 1996; Yu, 2006). This paper is part of a concerted effort at the Nottingham Centre for Geomechanics to develop improved theoretical foundations for pavement and railtrack design. It is mainly concerned with the development of rigorous lower-bound solutions for shakedown of cohesive-frictional materials under three-dimensional moving traffic loads. Compared with previous studies, two important aspects are taken into account. First, this paper considers a more general case of elliptical contact area between traffic and material surface, as most previous lower-bound studies considered the traffic load is applied through an infinite long roller. Secondly, by introducing a critical self-equilibrated residual stress field, this shakedown problem is reduced to a formulation in terms of a load parameter only. By using a simple optimisation procedure, the maximum load parameter leads to a lower-bound shakedown limit to this problem. Results for the special case of circular contact area are also presented in analytical form, which can then be readily applied for practical design.

Original languageEnglish
Pages (from-to)3797-3807
Number of pages11
JournalInternational Journal of Solids and Structures
Issue number26
Publication statusPublished - 15 Dec 2012
Externally publishedYes


  • Cohesive-frictional materials
  • Elliptical contact area
  • Lower-bound
  • Moving loads
  • Shakedown

ASJC Scopus subject areas

  • Modelling and Simulation
  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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