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 ${p}^{\prime}$–$q$ and $e$–${p}^{\prime}$ 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.

Revised:

Accepted:

Published online:

Yifei Sun ^{1, 2};
Jiancheng Zhang ^{3}

@article{CRMECA_2021__349_1_167_0, 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}, volume = {349}, number = {1}, year = {2021}, doi = {10.5802/crmeca.78}, language = {en}, }

TY - JOUR AU - Yifei Sun AU - Jiancheng Zhang TI - Fractional stress-dilatancy equation based on critical state lines with arbitrary form JO - Comptes Rendus. Mécanique PY - 2021 SP - 167 EP - 178 VL - 349 IS - 1 PB - Académie des sciences, Paris DO - 10.5802/crmeca.78 LA - en ID - CRMECA_2021__349_1_167_0 ER -

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. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.78/

[1] 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] 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] A state parameter for sands, Géotechnique, Volume 35 (1985), pp. 99-112 | DOI

[4] The critical state of sands, Géotechnique, Volume 41 (1991), pp. 365-381 | DOI

[5] 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] 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] Bounding surface plasticity model for stress–strain and grain-crushing behaviors of rockfill materials, Geosci. Front., Volume 11 (2020), pp. 495-510 | DOI

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

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

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

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

[12] 3D elastoplastic model for crushable soils with explicit formulation of particle crushing, J. Eng. Mech., Volume 143 (2017), 04017140

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

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

[15] Critical State Soil Mechanics, McGraw-Hill London, New York, USA, 1968

[16] 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] 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] State-dependent constitutive model for rockfill materials, Int. J. Geomech., Volume 15 (2014), 04014075

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

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

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

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

[23] 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

*Cited by Sources: *

Comments - Policy