Acta Mechanica Sinica

, Volume 32, Issue 1, pp 112–124 | Cite as

Modelling long-term deformation of granular soils incorporating the concept of fractional calculus

  • Yifei Sun
  • Yang XiaoEmail author
  • Changjie Zheng
  • Khairul Fikry Hanif
Research Paper


Many constitutive models exist to characterise the cyclic behaviour of granular soils but can only simulate deformations for very limited cycles. Fractional derivatives have been regarded as one potential instrument for modelling memory-dependent phenomena. In this paper, the physical connection between the fractional derivative order and the fractal dimension of granular soils is investigated in detail. Then a modified elasto-plastic constitutive model is proposed for evaluating the long-term deformation of granular soils under cyclic loading by incorporating the concept of factional calculus. To describe the flow direction of granular soils under cyclic loading, a cyclic flow potential considering particle breakage is used. Test results of several types of granular soils are used to validate the model performance.

Graphical abstract


Constitutive model Fractional order Fractional calculus Long-term deformation 



The authors would like to thank Professor W. Chen and Dr. Xiaodi Zhang in the Department of Engineering Mechanics, Hohai University, for their kind instruction and continuous inspiration on several fundamentals of the fractional calculus during the undergraduate period. The authors would also like to thank Mr. Rodger Paton at University of Wollongong for his technical assistance in computer programing. The financial supports provided by the Fundamental Research Funds (Grant 106112015CDJXY200008) is appreciated.


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Yifei Sun
    • 1
  • Yang Xiao
    • 2
    Email author
  • Changjie Zheng
    • 3
  • Khairul Fikry Hanif
    • 4
  1. 1.Faculty of Engineering and Information SciencesUniversity of WollongongWollongongAustralia
  2. 2.College of Civil EngineeringChongqing UniversityChongqingChina
  3. 3.ARC Centre of Excellence for Geotechnical Science and EngineeringUniversity of NewcastleNewcastleAustralia
  4. 4.Faculty of Engineering, Computing and MathematicsUniversity of Western AustraliaPerthAustralia

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