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A hypoplastic model for crushable sand under a wide range of stress levels

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Abstract

Depending on the characteristics of soil particles and external load, natural soils often undergo particle breakage which may significantly influence their mechanical behavior. In this study, a hypoplastic model is proposed to describe the sand behavior over a wide range of stress levels, especially those sufficient to cause particle breakage. The characterized void ratios and granulate hardness of the model are related to the plastic work to reflect the impact of particle breakage on the strength and deformation properties of sand. The influence of confining pressure on the extent of particle breakage is properly considered. The model is demonstrated to be capable of simulating the response of crushable sand under various test conditions. The simulation results of the original hypoplastic model are also presented, which indicates that neglecting the particle breakage may cause unreasonable predictions at high stress state.

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Data availability

The codes for implementing the hypoplastic model in this study are available upon reasonable request.

Abbreviations

σ, ε :

Stress tensor and strain tensor

\({\varvec{\mathcal{L}}}\), N :

Linear term and nonlinear term of the hypoplastic model

p, p 0 :

Mean normal stress and its initial value

p a :

Atmospheric pressure

q :

Deviatoric stress

η :

Stress ratio

ε v, ε q :

Volumetric strain and deviatoric strain

ε a :

Axial strain

f s, f d :

Stiffness factor and barotropy factor

h s , h s0 :

Granular hardness and its initial value

φ c :

Critical friction angle

B :

Hypoplastic flow direction

\(W_{{\text{p}}}\), \(\dot{W}_{{\text{p}}}\) :

Plastic work and its rate

e , e 0 :

Void ratio and its initial value

e i, e d, e c :

Upper bound, lower bound, and critical state void ratios

e i 0, e d0, e c0 :

Values of ei, ed, ec at p = 0 kPa

\(\Delta e_{i0} , \, \Delta e_{d0} , \, \Delta e_{c0}\) :

Variations of ei0, ed0, ec0 Caused by the particle breakage

e max, e min :

Maximum and minimum void ratios

\(\varepsilon_{v}^{f}\) :

Volumetric strain at failure

E 5% :

Ratio of deviatoric stress to axial strain at \(\varepsilon_{a}^{{}} = 5\%\)

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Acknowledgements

The authors are grateful to the Chongqing Natural Science Key Program (Grant Nos. cstc2020jcyj-zdxmX0019) and National Natural Science Foundation of China (Grant Nos. 42241109) for the financial support.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hong Kong, China

    Dong Liao

  2. State Key Laboratory of Water Resources Engineering and Management, Wuhan University, Wuhan, 430072, China

    Shun Wang

  3. Department of Civil Engineering, The University of Hong Kong, Hong Kong, China

    Chenyang Zhang

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  1. Dong Liao
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Correspondence to Chenyang Zhang.

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Liao, D., Wang, S. & Zhang, C. A hypoplastic model for crushable sand under a wide range of stress levels. Acta Geotech. (2024). https://doi.org/10.1007/s11440-024-02230-1

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