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Fractional viscoplastic model for soils under compression

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Abstract

Soils in the field are often subjected to time-dependent compression, where the induced shear strength and deformation could be different upon different loading rates. To capture the rate-dependent stress–strain behaviour of soils under compression, a stress-fractional viscoplastic model is developed in this study, based on Perzyna’s overstress theory. The viscoplastic flow direction of soil is modelled with a unit tensor obtained by performing fractional derivatives on the yielding surface. With the increase in the fractional order, the predicted compressive shear strength varies, and a transition from pure strain hardening to strain hardening and softening is observed. Additionally, as the strain rate increases, the predicted shear strength increases, which agrees well with the corresponding experimental observations. Further validation against a series of oedometer and triaxial test results under different strain-rate loads indicates that the fractional-order viscoplastic model can efficiently capture the rate-dependent behaviour of soils.

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Acknowledgements

The invaluable inspiration from Prof. Wen Chen is highly appreciated. The financial support provided by the National Natural Science Foundation of China (Grant Nos. 41630638, 51808191), the National Key Basic Research Program of China (“973” Program) (Grant No. 2015CB057901), and the Humboldt Foundation is also 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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Authors and Affiliations

  1. Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nan**g, 210098, China

    Yifei Sun

  2. Faculty of Civil and Environmental Engineering, Ruhr-Universität Bochum, 44801, Bochum, Germany

    Yifei Sun

  3. Faculty of Civil and Environmental Engineering, Poznan University of Technology, Piotrowo 5, 60-965, Poznan, Poland

    Wojciech Sumelka

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  1. Yifei Sun
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Correspondence to Yifei Sun.

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Sun, Y., Sumelka, W. Fractional viscoplastic model for soils under compression. Acta Mech 230, 3365–3377 (2019). https://doi.org/10.1007/s00707-019-02466-z

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