International Journal of Civil Engineering

, Volume 17, Issue 2, pp 171–179 | Cite as

Non-associative Fractional-Order Bounding-Surface Model for Granular Soils Considering State Dependence

  • Yifei SunEmail author
  • Yufeng Gao
  • Yang Shen
Technical note


The constitutive behaviour of granular soil is usually non-associative and depends on the soil density and pressure. To simulate such dependence of the non-associative stress–strain response on material state, two distinct yielding and plastic potential surfaces were usually suggested in the traditional elastoplastic models, which, however, made the model to become complex. To solve this problem, a simple fractional-order plasticity model without using any plastic potential functions was proposed before. However, the model did not consider the dependence of deformation on the density and pressure of soil, which could make the model incompatible with the critical-state soil mechanics. In contrast to the previous study, a state-dependent non-associative bounding-surface model within the framework of critical-state soil mechanics is proposed in this study. The plastic flow direction is obtained using a state-dependent fractional-order differentiation of the bounding surface. To demonstrate the capability of the model, drained and undrained triaxial test results of different granular soils under a variety of initial states are simulated, from which good agreement between the model predictions and the test results is observed.


Factional calculus Plastic flow Granular soil Constitutive model 



The authors would like to thank Prof. Wen Chen in the Department of Engineering Mechanics, Hohai University, for his invaluable inspiration on fractional calculus. The financial support provided by the Fundamental Research Funds for the Central Universities (Grant No. 2017B05214), the National Natural Science Foundation of China (Grant No. 41630638), the National Key Basic Research Program of China (“973” Program) (Grant No. 2015CB057901), and the Priority Academic Program Development of Jiangsu Higher Education Institutions are also appreciated.


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Copyright information

© Iran University of Science and Technology 2017

Authors and Affiliations

  1. 1.Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Jiangsu Research Centre for Geotechnical Engineering TechnologyHohai UniversityNanjingChina
  2. 2.Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, College of Civil and Transportation EngineeringHohai UniversityNanjingChina

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