Acta Mechanica Solida Sinica

, Volume 30, Issue 5, pp 507–519 | Cite as

Development and application of state-dependent fractional plasticity in modeling the non-associated behavior of granular aggregates

  • Yifei Sun
  • Shunxiang Song
  • Yang Xiao
  • Jiancheng Zhang


To characterize the constitutive behavior of granular aggregates, a non-associated plasticity model with two different yield and plastic potential surfaces was usually used. However, in this paper, a state-dependent fractional elastoplastic model is proposed by only performing the first- and fractional-order differentiations of the yield function. The non-associated plastic flow is obtained without using any plastic potential functions. The state dependence is considered by correlating the fractional order with a state parameter. The model is then validated by simulating a series of test results of different granular aggregates, including sand, ballast and rockfill, under a variety of loading conditions.


Fractional plasticity Granular aggregates Non-associated flow 


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  1. 1.
    Y. Xiao, H. Liu, Y. Chen, J. Jiang, Strength and deformation of rockfill material based on large-scale triaxial compression tests. I: influences of density and pressure, J. Geotech. Geoenviron. Eng. 140 (12) (2014) 04014070.Google Scholar
  2. 2.
    Y. Xiao, H. Liu, Y. Chen, J. Jiang, Strength and deformation of rockfill material based on large-scale triaxial compression tests. II: Influence of particle breakage, J. Geotech. Geoenviron. Eng. 140 (12) (2014) 04014071.Google Scholar
  3. 3.
    G. McDowell, M. Bolton, D. Robertson, The fractal crushing of granular materials, J. Mech. Phys. Solids 44 (12) (1996) 2079–2101.CrossRefGoogle Scholar
  4. 4.
    G. Ma, W. Zhou, T.-T. Ng, Y.-G. Cheng, X.-L. Chang, Microscopic modeling of the creep behavior of rockfills with a delayed particle breakage model, Acta Geotech. 10 (4) (2015) 481–496.CrossRefGoogle Scholar
  5. 5.
    I. Einav, Breakage mechanics—Part II: modelling granular materials, J. Mech. Phys. Solids 55 (6) (2007) 1298–1320.MathSciNetzbMATHGoogle Scholar
  6. 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. Meth. Geomech. 37 (8) (2013) 961–972.Google Scholar
  7. 7.
    A. Schofield, P. Wroth, Critical State Soil Mechanics, McGraw-Hill, London, 1968.Google Scholar
  8. 8.
    G. Mortara, A constitutive framework for the elastoplastic modelling of geomaterials, Int. J. Solids Struct. 63 (0) (2015) 139–152.Google Scholar
  9. 9.
    Y.P. Yao, H. Yamamoto, N.D. Wang, Constitutive model considering sand crushing, Soils Found. 48 (4) (2008) 603–608.CrossRefGoogle Scholar
  10. 10.
    A. Varadarajan, K. Sharma, S. Abbas, A. Dhawan, Constitutive model for rockfill materials and determination of material constants, Int. J. Geomech. 6 (4) (2006) 226–237.CrossRefGoogle Scholar
  11. 11.
    H.B. Liu, D.G. Zou, J.M. Liu, Constitutive modeling of dense gravelly soils subjected to cyclic loading, Int. J. Numer. Anal. Meth. Geomech. 38 (14) (2014) 1503–1518.CrossRefGoogle Scholar
  12. 12.
    G. McDowell, A simple non-associated flow model for sand, Granular Matter 4 (2) (2002) 65–69.CrossRefGoogle Scholar
  13. 13.
    Y. Sun, H. Liu, G. Yang, Y. Xiao, Formulation of cross-anisotropic failure criterion for soils, Water Sci. Eng. 6 (4) (2013) 456–468.Google Scholar
  14. 14.
    S. Tsutsumi, K. Kaneko, Constitutive response of idealized granular media under the principal stress axes rotation, Int. J. Plast. 24 (11) (2008) 1967–1989.CrossRefGoogle Scholar
  15. 15.
    W. Sumelka, M. Nowak, Non-normality and induced plastic anisotropy under fractional plastic flow rule: a numerical study, Int. J. Numer. Anal. Meth. Geomech. 40 (5) (2015) 651–675.Google Scholar
  16. 16.
    I. Podlubny, Fractional Differential Equations: an Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and Some of their Applications, Academic press, San Diego, California, 1998.zbMATHGoogle Scholar
  17. 17.
    B.M. Vinagre, I. Podlubny, A. Hernandez, V. Feliu, Some approximations of fractional order operators used in control theory and applications, Fract. Calculus Appl. Anal. 3 (3) (2000) 231–248.MathSciNetzbMATHGoogle Scholar
  18. 18.
    K. Been, M.G. Jefferies, A state parameter for sands, Géotechnique 22 (6) (1985) 99–112.Google Scholar
  19. 19.
    X. Li, Y. Wang, Linear representation of steady-state line for sand, J. Geotech. Geoenviron. Eng. 124 (12) (1998) 1215–1217.CrossRefGoogle Scholar
  20. 20.
    Y. Sun, Y. Shen, Constitutive model of granular soils using fractional order plastic flow rule, Int. J. Geomech. 17 (8) (2017) 04017025.CrossRefGoogle Scholar
  21. 21.
    Y. Sun, Y. Xiao, Fractional order plasticity model for granular soils subjected to monotonic triaxial compression, Int. J. Solids Struct. 118–119 (2017) 224–234.CrossRefGoogle Scholar
  22. 22.
    X. Li, Y. Dafalias, Dilatancy for cohesionless soils, Géotechnique 50 (4) (2000) 449–460.CrossRefGoogle Scholar
  23. 23.
    Z.-Y. Yin, C.S. Chang, Stress–dilatancy behavior for sand under loading and unloading conditions, Int. J. Numer. Anal. Meth. Geomech. 37 (8) (2013) 855–870.Google Scholar
  24. 24.
    Y. Xiao, H. Liu, H. Liu, Y. Chen, W. Zhang, Strength and dilatancy behaviors of dense modeled rockfill material in general stress space, Int. J. Geomech. 16 (5) (2016) 10.1061/(ASCE)GM.1943-5622.0000645(04016015).CrossRefGoogle Scholar
  25. 25.
    X. Kong, J. Liu, D. Zou, H. Liu, Stress-dilatancy relationship of Zipingpu gravel under cyclic loading in triaxial stress states, Int. J. Geomech. 16 (4) (2016) 10.1061/(ASCE)GM.1943-5622.0000584(04016001).CrossRefGoogle Scholar
  26. 26.
    T. Wichtmann, A. Niemunis, T. Triantafyllidis, Flow rule in a high-cycle accumulation model backed by cyclic test data of 22 sands, Acta Geotech. 9 (4) (2014) 695–709.CrossRefGoogle Scholar
  27. 27.
    T. Wichtmann, H. Rondón, A. Niemunis, T. Triantafyllidis, A. Lizcano, Prediction of permanent deformations in pavements using a high-cycle accumulation model, J. Geotech. Geoenviron. Eng. 136 (5) (2010) 728–740.CrossRefGoogle Scholar
  28. 28.
    Y. Xiao, H. Liu, Y. Chen, J. Jiang, W. Zhang, State-dependent constitutive model for rockfill materials, Int. J. Geomech. 15 (5) (2014) 04014075.Google Scholar
  29. 29.
    Y. Xiao, H. Liu, Elastoplastic constitutive model for rockfill materials considering particle breakage, Int. J. Geomech. 17 (1) (2016) 10.1061/(ASCE)GM.1943-5622.0000681(04016041).Google Scholar
  30. 30.
    K.L. Lee, H.B. Seed, Drained strength characteristics of sands, J. Soil Mech. Found. Div. 93 (6) (1967) 117–141.Google Scholar
  31. 31.
    R. Verdugo, K. Ishihara, The steady state of sandy soils, Soils Found. 36 (2) (1996) 81–91.CrossRefGoogle Scholar
  32. 32.
    B. Aursudkij, G.R. McDowell, A.C. Collop, Cyclic loading of railway ballast under triaxial conditions and in a railway test facility, Granular Matter 11 (6) (2009) 391–401.CrossRefGoogle Scholar
  33. 33.
    W. Salim, B. Indraratna, A new elastoplastic constitutive model for coarse granular aggregates incorporating particle breakage, Can. Geotech. J. 41 (4) (2004) 657–671.CrossRefGoogle Scholar
  34. 34.
    Z. Fu, S. Chen, C. Peng, Modeling cyclic behavior of rockfill materials in a framework of generalized plasticity, Int. J. Geomech. 14 (2) (2014) 191–204.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2017

Authors and Affiliations

  1. 1.Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, College of Civil and Transportation EngineeringHohai UniversityNanjingChina
  2. 2.College of Civil and Transportation EngineeringHohai UniversityNanjingChina
  3. 3.State Key Laboratory of Coal Mine Disaster Dynamics and Control, School of Civil EngineeringChongqing UniversityChongqingChina
  4. 4.School of Naval Architecture and Civil EngineeringJiangsu University of Science and TechnologyJiangsuChina

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