Comptes Rendus
Short paper
Fractional stress-dilatancy equation based on critical state lines with arbitrary form
Comptes Rendus. Mécanique, Volume 349 (2021) no. 1, pp. 167-178.

The original state-dependent fractional stress-dilatancy (FSD) equation for soils is developed based on the critical state lines (CSLs) with linear form. However, experimental evidences showed that the CSLs of soil in the p q and ep planes could be both nonlinear as well due to significant material degradation. This note aims to propose a unified FSD equation for soils with arbitrary types of CSLs. Detailed derivations are provided. To validate the proposed FSD equation, a series of triaxial test results of ballast and rockfill are simulated.

Published online:
DOI: 10.5802/crmeca.78
Keywords: Fractional derivative, Fractional plasticity, Stress-dilatancy, Sand, Rockfill, State dependence

Yifei Sun 1, 2; Jiancheng Zhang 3

1 Faculty of Civil and Environmental Engineering, Ruhr Universität Bochum, 44780 Bochum, Germany
2 Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, China
3 School of Naval Architecture and Civil Engineering, Jiangsu University of Science and Technology, Zhangjiagang 215600, Jiangsu, China
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
     author = {Yifei Sun and Jiancheng Zhang},
     title = {Fractional stress-dilatancy equation based on critical state lines with arbitrary form},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {167--178},
     publisher = {Acad\'emie des sciences, Paris},
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     year = {2021},
     doi = {10.5802/crmeca.78},
     language = {en},
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PB  - Académie des sciences, Paris
DO  - 10.5802/crmeca.78
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Yifei Sun; Jiancheng Zhang. Fractional stress-dilatancy equation based on critical state lines with arbitrary form. Comptes Rendus. Mécanique, Volume 349 (2021) no. 1, pp. 167-178. doi : 10.5802/crmeca.78.

[1] Y. P. Yao; D. A. Sun; T. Luo A critical state model for sands dependent on stress and density, Int. J. Numer. Anal. Methods Geomech., Volume 28 (2004), pp. 323-337 | DOI | Zbl

[2] X. S. Shi; J. Yin; J. Zhao Elastic visco-plastic model for binary sand-clay mixtures with applications to one-dimensional finite strain consolidation analysis, J. Eng. Mech., Volume 145 (2019), 04019059

[3] K. Been; M. G. Jefferies A state parameter for sands, Géotechnique, Volume 35 (1985), pp. 99-112 | DOI

[4] K. Been; M. Jefferies; J. Hachey The critical state of sands, Géotechnique, Volume 41 (1991), pp. 365-381 | DOI

[5] M. Tafili; T. Triantafyllidis State-dependent dilatancy of soils: experimental evidence and constitutive modeling, Recent Developments of Soil Mechanics and Geotechnics in Theory and Practice (T. Triantafyllidis, ed.), Springer International Publishing, Cham, 2020, pp. 54-84 | DOI

[6] D. Yin; H. Wu; C. Cheng; Y. Chen Fractional order constitutive model of geomaterials under the condition of triaxial test, Int. J. Numer. Anal. Methods Geomech., Volume 37 (2013), pp. 961-972 | DOI

[7] Y. Xiao; Z. Sun; A. M. Stuedlein; C. Wang; Z. Wu; Z. Zhang Bounding surface plasticity model for stress–strain and grain-crushing behaviors of rockfill materials, Geosci. Front., Volume 11 (2020), pp. 495-510 | DOI

[8] S. Jocković; M. Vukićević Bounding surface model for overconsolidated clays with new state parameter formulation of hardening rule, Comput. Geotech., Volume 83 (2017), pp. 16-29 | DOI

[9] Y. Sun; Y. Gao; Y. Shen Mathematical aspect of the state-dependent stress-dilatancy of granular soil under triaxial loading, Géotechnique, Volume 69 (2019), pp. 158-165 | DOI

[10] Y. Sun; W. Sumelka State-dependent fractional plasticity model for the true triaxial behaviour of granular soil, Arch. Mech., Volume 71 (2019), pp. 23-47 | MR | Zbl

[11] F. Yu Influence of particle breakage on behavior of coral sands in triaxial tests, Int. J. Geomech., Volume 19 (2019), 04019131

[12] M. Liu; Y. Zhang; H. Zhu 3D elastoplastic model for crushable soils with explicit formulation of particle crushing, J. Eng. Mech., Volume 143 (2017), 04017140

[13] B. Indraratna; Q. Sun; S. Nimbalkar Observed and predicted behaviour of rail ballast under monotonic loading capturing particle breakage, Can. Geotech. J., Volume 52 (2014), pp. 73-86 | DOI

[14] Y. Lai; M. Liao; K. Hu A constitutive model of frozen saline sandy soil based on energy dissipation theory, Int. J. Plast., Volume 78 (2016), pp. 84-113 | DOI

[15] A. Schofield; P. Wroth Critical State Soil Mechanics, McGraw-Hill London, New York, USA, 1968

[16] D. Lu; J. Liang; X. Du; C. Ma; Z. Gao Fractional elastoplastic constitutive model for soils based on a novel 3D fractional plastic flow rule, Comput. Geotech., Volume 105 (2019), pp. 277-290 | DOI

[17] V. Bandini; M. R. Coop The influence of particle breakage on the location of the critical state line of sands, Soils Found., Volume 51 (2011), pp. 591-600 | DOI

[18] Y. Xiao; H. Liu; Y. Chen; J. Jiang; W. Zhang State-dependent constitutive model for rockfill materials, Int. J. Geomech., Volume 15 (2014), 04014075

[19] D. Sarkar; M. Goudarzy; D. König An interpretation of the influence of particle shape on the mechanical behavior of granular material, Granul. Matter, Volume 21 (2019), p. 53 | DOI

[20] Y. Sun; B. Indraratna; S. Nimbalkar Three-dimensional characterisation of particle size and shape for ballast, Geotech. Lett., Volume 4 (2014), pp. 197-202 | DOI

[21] Y. Sun; C. Zheng Breakage and shape analysis of ballast aggregates with different size distributions, Particuology, Volume 35 (2017), pp. 84-92 | DOI

[22] M. Caputo Linear models of dissipation whose Q is almost frequency independent-II, Geophys. J. Int., Volume 13 (1967), pp. 529-539 | DOI

[23] H. Sun; Y. Zhang; D. Baleanu; W. Chen; Y. Chen A new collection of real world applications of fractional calculus in science and engineering, Commun. Nonlinear Sci. Numer. Simul., Volume 64 (2018), pp. 213-231 | DOI | Zbl

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