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An updated critical state model by incorporating inertial effects for granular material in solid–fluid transition regime

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Abstract

The open question of granular solid–fluid transition plays an important role in both modeling natural hazards and industrial particulate process. The well-developed critical state plasticity theory for granular solids and \(\mu (I)\) theory for granular liquids are limited in terms of solving this problem. Therefore, as a first study, an updated critical state model was mathematically formulated and proposed for granular material in the solid–fluid regime for its friction and dilatancy behavior. The proposed model is consistent with classical critical state plasticity theory for granular solids and \(\mu (I)\) theory for granular liquids. The introduction of two indices in the updated critical state model extends the validity domain in modeling friction and dilatancy behavior in granular materials. The updated critical state model successfully predicted the critical states in q-p-I space and \(\phi_{{\text{s}}}\)-p-I space from 96 discrete element method (DEM) simulations of triaxial loading cases with different initial porosities and confining stresses at various loading rates from slow to fast where the inertial number is from 10–4 to 0.2. The proposed critical state theory is believed to provide a new approach toward developing a visco-elasto-plastic framework for granular material in solid–fluid transition regime.

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Acknowledgements

The authors gratefully acknowledge the financial support received by the National Natural Sciences Foundation of China (No.12172057, 12032005, 12132018), National Key R&D Program of China (2018YFC1505504), and “Beijing Institute of Technology Research Fund Program for Young Scholars”. We also appreciate the comments and suggestions by the two anonymous reviewers which much improved the quality of this paper. We thank Liwen Bianji (Edanz) (www.liwenbianji.cn) for editing the English text of a draft of this manuscript.

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  1. Department of Mechanics, School of Aerospace Engineering, Beijing Institute of Technology, Beijing, 100081, China

    Xiaoliang Wang, Ge Li & Qingquan Liu

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  1. Xiaoliang Wang
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Correspondence to Qingquan Liu.

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Wang, X., Li, G. & Liu, Q. An updated critical state model by incorporating inertial effects for granular material in solid–fluid transition regime. Granular Matter 24, 38 (2022). https://doi.org/10.1007/s10035-021-01202-6

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