Advertisement

A 3D elastic-plastic-viscous constitutive model for soils considering the stress path dependency

  • DeChun Lu
  • JinBo Miao
  • XiuLi DuEmail author
  • Yu Tian
  • YangPing Yao
Article
  • 10 Downloads

Abstract

In order to consider the stress path dependency of soils, this paper decomposes any arbitrary stress path into several infinitesimal stress paths. Then the infinitesimal stress path is further transformed into the superposition of two parts, i.e., a constant stress ratio part and a constant mean stress part, which are sufficiently close to the real stress path. The plastic strain increments under the transformed paths are determined separately, and then the plastic strain under any path is obtained. Based on the instantaneous loading line of normally consolidated soil, a reference state line is proposed to determine the overconsolidation ratio and creep time of soil. The overconsolidation ratio is introduced into the viscous flow rule to obtain the viscous strain increment. The stress-strain-time relationship for triaxial compression condition is extended to 3D stress condition by the transformed stress method. The proposed model adopts only seven material parameters and each of them has a clear physical meaning. Comparisons with test results demonstrate that the model can not only reasonably predict the plastic strain under typical stress paths of excavation, but adequately capture the time-dependent behaviours of soils, including creep, stress relaxation and strain rate effect.

Keywords

soils elastic-plastic-viscous constitutive model stress path dependency reference state line creep stress relaxation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

References

  1. 1.
    Liingaard M, Augustesen A, Lade P V. Characterization of models for time-dependent behavior of soils. Int J GeoMech, 2004, 4: 157–177CrossRefGoogle Scholar
  2. 2.
    Yao Y P, Kong L M, Zhou A N, et al. Time-dependent unified hardening model: Three-dimensional elastoviscoplastic constitutive model for clays. J Eng Mech, 2015, 141: 04014162CrossRefGoogle Scholar
  3. 3.
    Qiao Y, Ferrari A, Laloui L, et al. Nonstationary flow surface theory for modeling the viscoplastic behaviors of soils. Comput Geotech, 2016, 76: 105–119CrossRefGoogle Scholar
  4. 4.
    Wang Z, Wong R C K. Strain-dependent and stress-dependent creep model for a till subject to triaxial compression. Int J Geomech, 2016, 16: 04015084CrossRefGoogle Scholar
  5. 5.
    Feng W Q, Lalit B, Yin Z Y, et al. Long-term non-linear creep and swelling behavior of Hong Kong marine deposits in oedometer condition. Comput Geotech, 2017, 84: 1–15CrossRefGoogle Scholar
  6. 6.
    Yuan Y, Whittle A J. A novel elasto-viscoplastic formulation for compression behaviour of clays. Géotechnique, 2018, 68: 1044–1055CrossRefGoogle Scholar
  7. 7.
    Zhou H W, Wang C P, Han B B, et al. A creep constitutive model for salt rock based on fractional derivatives. Int J Rock Mech Min Sci, 2011, 48: 116–121CrossRefGoogle Scholar
  8. 8.
    Ma B, Muhunthan B, Xie X. Stress history effects on 1-D consolidation of soft soils: A rheological model. Int J Numer Anal Meth Geomech, 2013, 37: 2671–2689CrossRefGoogle Scholar
  9. 9.
    Madaschi A, Gajo A. A one-dimensional viscoelastic and viscoplastic constitutive approach to modeling the delayed behavior of clay and organic soils. Acta Geotech, 2017, 12: 827–847CrossRefGoogle Scholar
  10. 10.
    Di Prisco C, Imposimato S, Vardoulakis I. Mechanical modelling of drained creep triaxial tests on loose sand. Géotechnique, 2000, 50: 73–82CrossRefGoogle Scholar
  11. 11.
    Tong X, Tuan C Y. Viscoplastic cap model for soils under high strain rate loading. J Geotech Geoenviron Eng, 2007, 133: 206–214CrossRefGoogle Scholar
  12. 12.
    Yin Z Y, Chang C S, Karstunen M, et al. An anisotropic elasticviscoplastic model for soft clays. Int J Solids Struct, 2010, 47: 665–677zbMATHCrossRefGoogle Scholar
  13. 13.
    Yin Z Y, Karstunen M, Hicher P Y. Evaluation of the influence of elasto-viscoplastic scaling functions on modelling time-dependent behaviour of natural clays. Soils Found, 2010, 50: 203–214CrossRefGoogle Scholar
  14. 14.
    Yin Z Y, Karstunen M, Chang C S, et al. Modeling time-dependent behavior of soft sensitive clay. J Geotech Geoenviron Eng, 2011, 137: 1103–1113CrossRefGoogle Scholar
  15. 15.
    Desai C S, Sane S, Jenson J. Constitutive modeling including creep- and rate-dependent behavior and testing of glacial tills for prediction of motion of glaciers. Int J Geomech, 2011, 11: 465–476CrossRefGoogle Scholar
  16. 16.
    Maranha J R, Pereira C, Vieira A. A viscoplastic subloading soil model for rate-dependent cyclic anisotropic structured behaviour. Int J Numer Anal Meth Geomech, 2016, 40: 1531–1555CrossRefGoogle Scholar
  17. 17.
    Wang S, Wu W, Yin Z Y, et al. Modelling the time-dependent behaviour of granular material with hypoplasticity. Int J Numer Anal Methods Geomech, 2018, 42: 1331–1345CrossRefGoogle Scholar
  18. 18.
    Zhu J G. Experimental study and elastic visco-plastic modelling of the time dependent behavior of Hong Kong marine deposits. Dissertation for the Doctoral Degree. Hong Kong: Hong Kong Polytechnic University, 2000Google Scholar
  19. 19.
    Cuvilliez S, Djouadi I, Raude S, et al. An elastoviscoplastic constitutive model for geomaterials: Application to hydromechanical modelling of claystone response to drift excavation. Comput Geotech, 2017, 85: 321–340CrossRefGoogle Scholar
  20. 20.
    Jiang J, Ling H I, Kaliakin V N, et al. Evaluation of an anisotropic elastoplastic-viscoplastic bounding surface model for clays. Acta Geotech, 2017, 12: 335–348CrossRefGoogle Scholar
  21. 21.
    Leoni M, Karstunen M, Vermeer P A. Anisotropic creep model for soft soils. Géotechnique, 2008, 58: 215–226CrossRefGoogle Scholar
  22. 22.
    Rezania M, Taiebat M, Poletti E. A viscoplastic SANICLAY model for natural soft soils. Comput Geotech, 2016, 73: 128–141CrossRefGoogle Scholar
  23. 23.
    Islam M N, Gnanendran C T. Elastic-viscoplastic model for clays: Development, validation, and application. J Eng Mech, 2017, 143: 04017121CrossRefGoogle Scholar
  24. 24.
    Bodas Freitas T M, Potts D M, Zdravkovic L. A time dependent constitutive model for soils with isotach viscosity. Comput Geotech, 2011, 38: 809–820CrossRefGoogle Scholar
  25. 25.
    Kong Y, Xu M, Song E. An elastic-viscoplastic double-yield-surface model for coarse-grained soils considering particle breakage. Comput Geotech, 2017, 85: 59–70CrossRefGoogle Scholar
  26. 26.
    Schanz T, Vermeer P A, Bonnier P G. The hardening soil model: Formulation and verification. In: Proceedings of International Symptom Beyond 2000 in Computational Geotechnics-10 Years of Plaxis International. Rotterdam, 1999. 1–16Google Scholar
  27. 27.
    Debernardi D, Barla G. New viscoplastic model for design analysis of tunnels in squeezing conditions. Rock Mech Rock Eng, 2009, 42: 259–288CrossRefGoogle Scholar
  28. 28.
    Sekiguchi H. Theory of undrained creep rupture of normally consolidated clay based on elasto-viscoplasticity. Soils Found, 1984, 24: 129–147CrossRefGoogle Scholar
  29. 29.
    Cassiani G, Brovelli A, Hueckel T. A strain-rate-dependent modified Cam-Clay model for the simulation of soil/rock compaction. Geo-Mech Energy Environ, 2017, 11: 42–51CrossRefGoogle Scholar
  30. 30.
    Yin Z Y, Hicher P Y. Identifying parameters controlling soil delayed behaviour from laboratory and in situ pressuremeter testing. Int J Numer Anal Meth Geomech, 2008, 32: 1515–1535zbMATHCrossRefGoogle Scholar
  31. 31.
    Qu G, Hinchberger S D, Lo K Y. Evaluation of the viscous behaviour of clay using generalised overstress viscoplastic theory. Géotechnique, 2010, 60: 777–789CrossRefGoogle Scholar
  32. 32.
    Yin J H, Zhu J G, Graham J. A new elastic viscoplastic model for time-dependent behaviour of normally and overconsolidated clays: Theory and verification. Can Geotech J, 2002, 39: 157–173CrossRefGoogle Scholar
  33. 33.
    Kelln C, Sharma J, Hughes D, et al. An improved elastic-viscoplastic soil model. Can Geotech J, 2008, 45: 1356–1376CrossRefGoogle Scholar
  34. 34.
    Nakai T. An isotropic hardening elastoplastic model for sand considering the stress path dependency in three-dimensional stresses.. Soils Found, 1989, 29: 119–137CrossRefGoogle Scholar
  35. 35.
    Yao Y P, Sun D A, Matsuoka H. A unified constitutive model for both clay and sand with hardening parameter independent on stress path. Comput Geotech, 2008, 35: 210–222CrossRefGoogle Scholar
  36. 36.
    Lu D C. A constitutive model for soils considering complex stress paths based on the generalized nonlinear strength theory (in Chinese). Dissertation for the Doctoral Degree. Beijing: Beihang University, 2006Google Scholar
  37. 37.
    Xiao Y, Liu H, Chen Y, et al. Bounding surface plasticity model incorporating the state pressure index for rockfill materials. J Eng Mech, 2004, 140: 04014087CrossRefGoogle Scholar
  38. 38.
    Xiao Y, Liu H. Elastoplastic constitutive model for rockfill materials considering particle breakage. Int J Geomech, 2017, 17: 04016041CrossRefGoogle Scholar
  39. 39.
    Yao Y, Lu D, Zhou A, et al. Generalized non-linear strength theory and transformed stress space. Sci China Ser E-Tech Sci, 2004, 47: 691–709zbMATHCrossRefGoogle Scholar
  40. 40.
    Šuklje L. The analysis of the consolidation process by the isotaches method. In: Proceedings of the 4th International Conference on Soil Mechanics and Foundation Engineering. London, 1957. 200–206Google Scholar
  41. 41.
    Leroueil S. Šuklje memorial lecture: The isotache approach. Where are we 50 years after its development by Professor Šuklje? In: Proceedings of the 13th Danube-European Conference on Geotechnical Engineering. Ljubljana, 2006. 55–88Google Scholar
  42. 42.
    Bjerrum L. Engineering geology of Norwegian normally-consolidated marine clays as related to settlements of buildings. Géotechnique, 1967, 17: 83–118CrossRefGoogle Scholar
  43. 43.
    Tatsuoka F, Di Benedetto H, Enomoto T, et al. Various viscosity types of geomaterials in shear and their mathematical expression. Soils Found, 2008, 48: 41–60CrossRefGoogle Scholar
  44. 44.
    Yin Z Y, Jin Y F, Shen J S, et al. Optimization techniques for identifying soil parameters in geotechnical engineering: Comparative study and enhancement. Int J Numer Anal Methods Geomech, 2018, 42: 70–94CrossRefGoogle Scholar
  45. 45.
    Jin Y F, Yin Z Y, Zhou W H, et al. A single-objective EPR based model for creep index of soft clays considering L2 regularization. Eng Geol, 2019, 248: 242–255CrossRefGoogle Scholar
  46. 46.
    Nakai T, Hinokio M. A simple elastoplastic model for normally and over consolidated soils with unified material parameters. Soils Found, 2004, 44: 53–70CrossRefGoogle Scholar
  47. 47.
    Nakai T, Matsuoka H. A generalized elastoplastic constitutive model for clay in three-dimensional stresses. Soils Found, 1986, 26: 81–98CrossRefGoogle Scholar
  48. 48.
    Kiyota T, Tatsuoka F. Viscous property of loose sand in triaxial compression, extension and cyclic loading. Soils Found, 2006, 46: 665–684CrossRefGoogle Scholar
  49. 49.
    Yin Z Y, Yin J H, Huang H W. Rate-dependent and long-term yield stress and strength of soft Wenzhou marine clay: Experiments and modeling. Mar Georesources Geotech, 2015, 33: 79–91CrossRefGoogle Scholar
  50. 50.
    Lacerda W A. Stress-relaxation and creep effects on soil deformation. Dissertation for the Doctoral Degree. Berkeley: University of California, 1976Google Scholar
  51. 51.
    Lu D C, Miao J B, Du X L, et al. A new method of developing elastic-plastic-viscous constitutive model for clays. Sci China Tech Sci, 2019, 62: doi:  https://doi.org/10.1007/s11431-018-9469-9

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • DeChun Lu
    • 1
  • JinBo Miao
    • 1
  • XiuLi Du
    • 1
    Email author
  • Yu Tian
    • 1
  • YangPing Yao
    • 2
  1. 1.Key Laboratory of Urban Security and Disaster Engineering of Ministry of EducationBeijing University of TechnologyBeijingChina
  2. 2.School of Transportation Science and EngineeringBeihang UniversityBeijingChina

Personalised recommendations