Advantages and limitations of an α-plasticity model for sand

  • Yifei Sun
  • Wojciech Sumelka
  • Yufeng GaoEmail author
Research Paper


The stress–strain response of sand was observed to depend on its material state, i.e., pressure and density. Successful modelling of such state-dependent response of sand relied on the correct representation of its state-dependent stress–dilatancy behaviour. In this study, an improved fractional-order \(\left( \alpha \right)\) plasticity model for sands with a wide range of initial void ratios and pressures is proposed, based on a state-dependent fractional-order plastic flow rule and a modified yielding surface. Potential positive performances and negative limitations of the proposed approach in terms of the critical state of sand are discussed, based on the simulations of a series of drained and undrained triaxial tests of different sands. It can be found that unlike previous fractional models, the developed model can reasonably simulate the key features, e.g., strain softening/hardening, volumetric dilation/contraction, liquefaction, quasi-steady-state flow as well as steady-state flow, of sand for a wide range of initial states. However, due to typical forms of the critical-state lines being used, negative performances of the fractional approach could occur when simulating the undrained behaviour of very loose sand and the drained behaviour of very dense sand.


Fractional derivative Liquefaction Plasticity Sand State-dependent dilatancy 



The first author would like to appreciate Prof. Wen Chen for his lifelong inspiration. The financial support provided by the National Key R&D Program of China (2016YFC0800205) National Natural Science Foundation of China (Grant Nos. 41630638, 51890912, 51808191), the National Key Basic Research Program of China (“973” Program) (Grant No. 2015CB057901) and the Humboldt Research Foundation, Germany, is appreciated. The second author also acknowledges the support of the National Science Centre, Poland, under Grant No. 2017/27/B/ST8/00351.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Civil and Environmental EngineeringRuhr-Universität BochumBochumGermany
  2. 2.Institute of Structural EngineeringPoznan University of TechnologyPoznanPoland
  3. 3.Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, College of Civil and Transportation EngineeringHohai UniversityNanjingChina

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