Skip to main content
SpringerLink
Log in

Bounding surface plasticity for sand using fractional flow rule and modified critical state line

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

Bounding surface plasticity has been widely used for capturing the stress–strain behaviour of geomaterials. However, it may require multiple sets of model parameters for constitutive modelling of sands with a wide range of initial states, because of the distinct critical state characteristics under low and high densities or pressures in the \(e-\ln {p}'\) plane. In this study, an enhanced bounding surface plasticity approach for sand with a wide range of initial material states is developed. A fractional plastic flow rule and a modified critical state line are suggested, which ensures that without using any predefined state indices, the developed model can consider the state-dependent dilatancy and hardening behaviours of sand subjected to low and high pressures/densities. The approach is validated by simulating the well-documented test results of Toyoura sand and Sacramento River sand. For comparison, the original state-dependent dilatancy approach in Li and Dafalias (Géotechnique 50(4):449–460, 2000. https://doi.org/10.1680/geot.2000.50.4.449) is also adopted and implemented. It is found that the two approaches can reasonably capture the typical stress–strain behaviour, e.g. hardening/contraction, softening/dilation, liquefaction, quasi-steady state flow, and non-flow, of sands with different initial material states, by using a single set of model parameters. However, compared to the current work, Li and Dafalias (2000) model relied on a predefined state parameter, for capturing the state-dependent behaviour of sand under a wide range of initial states

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. Been, K., Jefferies, M.G.: A state parameter for sands. Géotechnique 35(2), 99–112 (1985). https://doi.org/10.1016/0148-9062(85)90263-3

    Article  Google Scholar 

  2. Coop, M.R.: The mechanics of uncemented carbonate sands. Géotechnique 40(4), 607–626 (1990). https://doi.org/10.1680/geot.1990.40.4.607

    Article  Google Scholar 

  3. Muir Wood, D., Belkheir, K., Liu, D.: Strain softening and state parameter for sand modelling. Géotechnique 44(2), 335–339 (1994)

    Article  Google Scholar 

  4. Lu, D., Liang, J., Du, X., Ma, C., Gao, Z.: Fractional elastoplastic constitutive model for soils based on a novel 3D fractional plastic flow rule. Comput. Geotech. 105, 277–290 (2019). https://doi.org/10.1016/j.compgeo.2018.10.004

    Article  Google Scholar 

  5. Yao, Y., Wang, N.: Transformed stress method for generalizing soil constitutive models. J. Eng. Mech. 140(3), 614–629 (2014). https://doi.org/10.1061/(ASCE)EM.1943-7889.0000685

    Article  Google Scholar 

  6. Yao, Y.P., Sun, D.A., Luo, T.: A critical state model for sands dependent on stress and density. Int. J. Numer. Anal. Methods Geomech. 28(4), 323–337 (2004). https://doi.org/10.1002/nag.340

    Article  MATH  Google Scholar 

  7. Russell, A.R., Khalili, N.: A bounding surface plasticity model for sands exhibiting particle crushing. Can. Geotech. J. 41(6), 1179–1192 (2004)

    Article  Google Scholar 

  8. Liu, H.B., Zou, D.G.: Associated generalized plasticity framework for modeling gravelly soils considering particle breakage. J. Eng. Mech. 139(5), 606–615 (2013). https://doi.org/10.1061/(ASCE)EM.1943-7889.0000513

    Article  Google Scholar 

  9. Dafalias, Y.F.: Bounding surface plasticity. I: mathematical foundation and hypoplasticity. J. Eng. Mech. 112(9), 966–987 (1986). https://doi.org/10.1061/(ASCE)0733-9399(1986)112:9(966)

    Article  Google Scholar 

  10. Jocković, S., Vukićević, M.: Bounding surface model for overconsolidated clays with new state parameter formulation of hardening rule. Comput. Geotech. 83, 16–29 (2017). https://doi.org/10.1016/j.compgeo.2016.10.013

    Article  Google Scholar 

  11. Xiao, Y., Liu, H., Chen, Y., Jiang, J.: Bounding surface plasticity model incorporating the state pressure index for rockfill materials. J. Eng. Mech. 140(11), 04014087 (2014). https://doi.org/10.1061/(ASCE)EM.1943-7889.0000802

    Article  Google Scholar 

  12. Bardet, J.P.: Bounding surface plasticity model for sands. J. Eng. Mech. 112(11), 1198–1217 (1986). https://doi.org/10.1061/(ASCE)0733-9399(1986)112:11(1198)

    Article  Google Scholar 

  13. Sun, Y., Sumelka, W.: State-dependent fractional plasticity model for the true triaxial behaviour of granular soil. Arch. Mech. 71(1), 23–47 (2019). https://doi.org/10.24423/aom.3084

    Article  MathSciNet  MATH  Google Scholar 

  14. Yu, F.: Particle breakage and the critical state of sands. Géotechnique 67(8), 713–719 (2017). https://doi.org/10.1680/jgeot.15.P.250

    Article  Google Scholar 

  15. Pastor, M., Zienkiewicz, O.C., Chan, A.H.C.: Generalized plasticity and the modelling of soil behaviour. Int. J. Numer. Anal. Methods Geomech. 14(3), 151–190 (1990). https://doi.org/10.1002/nag.1610140302

    Article  MATH  Google Scholar 

  16. Li, X., Wang, Y.: Linear representation of steady-state line for sand. J. Geotech. Geoenviron. Eng. 124(12), 1215–1217 (1998). https://doi.org/10.1061/(ASCE)1090-0241(1998)124:12(1215)

    Article  Google Scholar 

  17. Cen, W.J., Luo, J.R., Bauer, E., Zhang, W.D.: Generalized plasticity model for sand with enhanced state parameters. J. Eng. Mech. 144(12), 04018108 (2018). https://doi.org/10.1061/(ASCE)EM.1943-7889.0001534

    Article  Google Scholar 

  18. Wang, Z.L., Dafalias, Y.F., Shen, C.K.: Bounding surface hypoplasticity model for sand. J. Eng. Mech. 116(5), 983–1001 (1990)

    Article  Google Scholar 

  19. Schofield, A., Wroth, P.: Critical State Soil Mechanics. McGraw-Hill London, New York (1968)

    Google Scholar 

  20. Kan, M., Taiebat, H., Khalili, N.: Simplified mapping rule for bounding surface simulation of complex loading paths in granular materials. Int. J. Geomech. 14(2), 239–253 (2014). https://doi.org/10.1061/(ASCE)GM.1943-5622.0000307

    Article  Google Scholar 

  21. Sun, Y., Gao, Y., Zhu, Q.: Fractional order plasticity modelling of state-dependent behaviour of granular soils without using plastic potential. Int. J. Plast. 102, 53–69 (2018). https://doi.org/10.1016/j.ijplas.2017.12.001

    Article  Google Scholar 

  22. Sun, Y., Shen, Y.: Constitutive model of granular soils using fractional order plastic flow rule. Int. J. Geomech. 17(8), 04017025 (2017). https://doi.org/10.1061/(ASCE)GM.1943-5622.0000904

    Article  Google Scholar 

  23. Sun, Y., Xiao, Y.: Fractional order model for granular soils under drained cyclic loading. Int. J. Numer. Anal. Methods Geomech. 41(4), 555–577 (2017). https://doi.org/10.1002/nag.2570

    Article  Google Scholar 

  24. Li, X., Dafalias, Y.: Dilatancy for cohesionless soils. Géotechnique 50(4), 449–460 (2000). https://doi.org/10.1680/geot.2000.50.4.449

    Article  Google Scholar 

  25. Ishihara, K.: Liquefaction and flow failure during earthquakes. Geotechnique 43(3), 351–451 (1993). https://doi.org/10.1680/geot.1993.43.3.351

    Article  Google Scholar 

  26. Verdugo, R., Ishihara, K.: The steady state of sandy soils. Soils Found. 36(2), 81–91 (1996). https://doi.org/10.3208/sandf.36.2_81

    Article  Google Scholar 

  27. Lee, K.L., Seed, H.B.: Drained strength characteristics of sands. J. Soil Mech. Found. Div. ASCE 93(6), 117–141 (1967)

    Google Scholar 

  28. Seed, H.B., Lee, K.L.: Undrained strength characteristics of cohesionless soils. J. Soil Mech. Found. Div. ASCE 93(SM6), 333–360 (1967)

    Google Scholar 

  29. Matsuoka, H., Yao, Y., Sun, D.: The cam-clay models revised by the SMP criterion. Soils Found. 39(1), 81–95 (1999). https://doi.org/10.3208/sandf.39.81

    Article  Google Scholar 

  30. Sun, Y., Gao, Y., Song, S., Chen, C.: Three-dimensional state-dependent fractional plasticity model for soils. Int. J. Geomech. 20(2), 04019161 (2020). https://doi.org/10.1061/(ASCE)GM.1943-5622.0001557

    Article  Google Scholar 

  31. Sheng, D., Yao, Y., Carter, J.P.: A volume-stress model for sands under isotropic and critical stress states. Can. Geotech. J. 45(11), 1639–1645 (2008). https://doi.org/10.1139/T08-085

    Article  Google Scholar 

  32. Daouadji, A., Hicher, P.Y.: An enhanced constitutive model for crushable granular materials. Int. J. Numer. Anal. Methods Geomech. 34(6), 555–580 (2010)

    Article  Google Scholar 

  33. Shi, X.S., Yin, J., Zhao, J.: Elastic visco-plastic model for binary sand-clay mixtures with applications to one-dimensional finite strain consolidation analysis. J. Eng. Mech. 145(8), 04019059 (2019). https://doi.org/10.1061/(ASCE)EM.1943-7889.0001623

    Article  Google Scholar 

  34. Shi, X.S., Nie, J., Zhao, J., Gao, Y.: A homogenization equation for the small strain stiffness of gap-graded granular materials. Comput. Geotech. 121, 103440 (2020). https://doi.org/10.1016/j.compgeo.2020.103440

    Article  Google Scholar 

  35. Shi, X.S., Zhao, J.: Practical estimation of compression behavior of clayey/silty sands using equivalent void-ratio concept. J. Geotech. Geoenviron. Eng. 146(6), 04020046 (2020). https://doi.org/10.1061/(ASCE)GT.1943-5606.0002267

    Article  Google Scholar 

  36. Hardin, B.O., Richart, J.F.E.: Elastic wave velocities in granular soils. J. Soil Mech. Found. Div. ASCE 89(1), 33–66 (1963)

    Google Scholar 

  37. Indraratna, B., Sun, Q., Nimbalkar, S.: Observed and predicted behaviour of rail ballast under monotonic loading capturing particle breakage. Can. Geotech. J. 52(1), 73–86 (2014)

    Article  Google Scholar 

  38. Manzari, M.T., Dafalias, Y.F.: A critical state two-surface plasticity model for sands. Géotechnique 47(2), 255–272 (1997)

    Article  Google Scholar 

  39. Salim, W., Indraratna, B.: A new elastoplastic constitutive model for coarse granular aggregates incorporating particle breakage. Can. Geotech. J. 41(4), 657–671 (2004)

    Article  Google Scholar 

  40. Tatsuoka, F., Ishihara, K.: Yielding of sand in triaxial compression. Soils Found. 14(2), 63–76 (1974). https://doi.org/10.3208/sandf1972.14.2_63

    Article  Google Scholar 

  41. Xiao, H., Lee, F.H., Chin, K.G.: Yielding of cement-treated marine clay. Soils Found. 54(3), 488–501 (2014). https://doi.org/10.1016/j.sandf.2014.04.021

    Article  Google Scholar 

  42. Javanmardi, Y., Imam, S.M.R., Pastor, M., Manzanal, D.: A reference state curve to define the state of soils over a wide range of pressures and densities. Géotechnique 68(2), 95–106 (2018). https://doi.org/10.1680/jgeot.16.P.136

    Article  Google Scholar 

  43. Sumelka, W.: Fractional viscoplasticity. Mech. Res. Commun. 56, 31–36 (2014). https://doi.org/10.1016/j.mechrescom.2013.11.005

    Article  Google Scholar 

  44. Sumelka, W., Nowak, M.: Non-normality and induced plastic anisotropy under fractional plastic flow rule: a numerical study. Int. J. Numer. Anal. Methods Geomech. 40(5), 651–675 (2016). https://doi.org/10.1002/nag.2421

    Article  Google Scholar 

Download references

Acknowledgements

The first author would like to thank Prof. Wen Chen for his lifelong inspiration. The financial support provided by the National Natural Science Foundation of China (Grant Nos. 51890912, 41630638), the Alexander Von Humboldt Foundation, Germany, and the National Science Centre, Poland (Grant No. 2017/27/B/ST8/00351), is appreciated.

Author information

Authors and Affiliations

  1. Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing, 210098, China

    Yifei Sun

  2. Faculty of Civil and Environmental Engineering, Ruhr-Universität Bochum, 44801, Bochum, Germany

    Yifei Sun

  3. Institute of Structural Analysis, Poznan University of Technology, Piotrowo 5, 60-965, Poznan, Poland

    Wojciech Sumelka

  4. Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, College of Civil and Transportation Engineering, Hohai University, Nanjing, 210098, China

    Yufeng Gao

Authors
  1. Yifei Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wojciech Sumelka
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yufeng Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yufeng Gao.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sun, Y., Sumelka, W. & Gao, Y. Bounding surface plasticity for sand using fractional flow rule and modified critical state line. Arch Appl Mech 90, 2561–2577 (2020). https://doi.org/10.1007/s00419-020-01737-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-020-01737-9

Keywords

Search

Navigation