Skip to main content

Advertisement

SpringerLink
Log in

Elastoplastic constitutive model for frozen sands based on framework of homogenization theory

  • Research Paper
  • Published:
Acta Geotechnica Aims and scope Submit manuscript

Abstract

In this paper, the stress–strain responses of frozen sands and an elastoplastic constitutive model based on the homogenization theory of heterogeneous materials are presented. In the model, frozen soils are conceptualized as binary-medium materials consisting of bonded blocks and weak bands, and their mechanical behavior is described with elastic–brittle and elastoplastic constitutive models, respectively. By introducing two groups of parameters (i.e., the breakage ratio (λv and λs) and strain concentration coefficient (cv and cs) related to the spherical and deviatoric stress components), the proposed model incorporates the breakage process of ice crystals and nonuniform strain distributions between the matrix (bonded elements) and inclusions (frictional elements) of the heterogeneous frozen soil samples. Moreover, an elasticity-based model and a double hardening constitutive model are employed to simulate the mechanical properties of the bonded elements and the characteristics of the frictional elements, respectively. To provide appropriate and quantitative predictions with the binary-medium constitutive model proposed here, triaxial compression tests are performed on the frozen and unfrozen sands to determine the individual parameters at confining pressures of 300–1800 kPa. The model validations demonstrate that the predictions agree well with the available laboratory results.

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
Fig. 15

Similar content being viewed by others

References

  1. Zhou YW, Guo DX, Qiu GQ (2000) Geocryology in China. Science Press, Beijing

    Google Scholar 

  2. Lai YM, Xu XT, Dong YH (2013) Present situation and prospect of mechanical research on frozen soils in China. Cold Reg Sci Technol 87:6–18

    Article  Google Scholar 

  3. Parameswaran VR (1985) Effect of alternating stress on the creep of frozen soils. Mech Mater 4:109–119

    Article  Google Scholar 

  4. Parameswaran VR (1987) Extended failure time in the creep of frozen soils. Mech Mater 6:233–243

    Article  Google Scholar 

  5. Tsytovich NA (1985) The mechanics of frozen ground (trans: Zhang CQ, Zhu YL). Science Press, Beijing

  6. French HM (1996) The periglacial environment, 2nd edn. Essex, London

    Google Scholar 

  7. Zhu ZW, Kang GZ, Ma Y (2016) Temperature damage and constitutive model of frozen soil under dynamic loading. Mech Mater 102:108–116

    Article  Google Scholar 

  8. Liu EL, Lai YM, Wong H, Feng JL (2018) An elasto-plastic model for saturated freezing soils based on thermo-poromechanics. Int J Plast 107:246–285

    Article  Google Scholar 

  9. Zhao YH, Weng GJ (1996) Plasticity of a two-phase composite with partially debonded inclusions. Int J Plast 12:781–804

    Article  MATH  Google Scholar 

  10. Zhao YH, Weng GJ (1997) Transversely isotropic moduli of two partially debonded composites. Int J Solids Struct 34:493–507

    Article  MATH  Google Scholar 

  11. Zhu QZ, Shao JF, Mainguy M (2010) A micromechanics-based elasto-plastic damage model for granular materials at low confining pressure. Int J Plast 26:586–602

    Article  MATH  Google Scholar 

  12. Zhou MM, Meschke G (2014) Strength homogenization of matrix-inclusion composites using the linear comparison composite approach. Int J Solids Struct 51:259–273

    Article  Google Scholar 

  13. Nguyen L, Fatahi B (2016) Behaviour of clay treated with cement & fibre while capturing cementation degradation and fibre failure-C3F Model. Int J Plast 81:168–195

    Article  Google Scholar 

  14. Dejaloud H, Jafarian Y (2017) A micromechanical-based constitutive model for fibrous fine-grained composite soils. Int J Plast 89:150–172

    Article  Google Scholar 

  15. Zhou MM, Meschke G (2018) A multiscale homogenization model for strength predictions of fully and partially frozen soils. Acta Geotech 13:175–193

    Article  Google Scholar 

  16. Lai YM, Jin L, Chang XX (2009) Yield criterion and elasto-plastic damage constitutive model for frozen sandy soil. Int J Plast 25:1177–1205

    Article  MATH  Google Scholar 

  17. Lai YM, Yang YG, Chang XX (2010) Strength criterion and elasto-plastic constitutive model of frozen silt in generalized plastic mechanics. Int J Plast 26:1461–1484

    Article  MATH  Google Scholar 

  18. Lai YM, Xu XT, Yu WB (2014) An experimental investigation of the mechanical behavior and a hyperplastic constitutive model of frozen loess. Int J Eng Sci 84:29–53

    Article  Google Scholar 

  19. Ghoreishian A, Grimstad SA, Kadivar G (2016) Constitutive model for rate-independent behavior of saturated frozen soils. Can Geotech J 53:1646–1657

    Article  Google Scholar 

  20. Lai YM, Liao MK, Hu K (2016) A constitutive model of frozen saline sandy soil based on energy dissipation theory. Int J Plast 78:84–113

    Article  Google Scholar 

  21. Xu GF, Wu W, Qi JL (2016) Modeling the viscous behavior of frozen soil with hypoplasticity. Int J Numer Anal Meth Geomech 40:2061–2075

    Article  Google Scholar 

  22. Zhou ZW, Ma W, Zhang SJ (2016) Multiaxial creep of frozen loess. Mech Mater 95:172–191

    Article  Google Scholar 

  23. Loria AF, Frigo B, Chiaia B (2017) A non-linear constitutive model for describing the mechanical behaviour of frozen ground and permafrost. Cold Reg Sci Technol 133:63–69

    Article  Google Scholar 

  24. Roscoe KH, Schofield AN, Thurairajah A (1963) Yielding of clays in states wetter than critical. Geotechnique 13:211–240

    Article  Google Scholar 

  25. Lade PV, Duncan JM (1975) Elasto-plastic stress-strain theory for cohesionless soil. J Geotech Geoenviron Eng 101:1037–1053

    Google Scholar 

  26. Lade PV (1977) Elasto-plastic stress–strain theory for cohesionless soil with curved yield surfaces. Int J Solids Struct 13:1019–1035

    Article  MATH  Google Scholar 

  27. Zheng YR, Kong L (2005) Generalized plastic mechanics and its application. Eng Sci 7:21–36

    Article  Google Scholar 

  28. Yao YP, Sun DA, Matsuoka H (2008) A unified constitutive model for both clay and sand with hardening parameter independent on stress path. Comput Geotech 35:210–222

    Article  Google Scholar 

  29. Yao YP, Hou W, Zhou AN (2009) UH model: three dimensional unified hardening model for overconsolidated clays. Geotechnique 59:451–469

    Article  Google Scholar 

  30. Yao YP, Zhou AN (2013) Non-isothermal unified hardening model: a thermo-elasto-plastic model for clays. Geotechnique 63:1328–1345

    Article  Google Scholar 

  31. Nguyen L, Fatahi B, Khabbaz H (2014) A constitutive model for cemented clays capturing cementation degradation. Int J Plast 56:1–18

    Article  Google Scholar 

  32. Hashiguchi K (1980) Constitutive equations of elasto-plastic materials with elastic-plastic transition. J Appl Mech 47:266–272

    Article  MATH  Google Scholar 

  33. Hashiguchi K, Ozaki S (2008) Constitutive equation for friction with transition from static to kinetic friction and recovery of static friction. Int J Plast 24:2102–2124

    Article  MATH  Google Scholar 

  34. Nakai T, Hinokio M (2004) A simple elasto-plastic model for normally and over consolidated soils with unified material parameters. Soils Found 44:53–70

    Article  Google Scholar 

  35. Liu MD, Carter JP (2002) A structured Cam-clay model. Can Geotech J 39:1313–1332

    Article  Google Scholar 

  36. Desai CS (2015) Constitutive modeling of materials and contacts using the disturbed state concept: part 1–Background and analysis. Comput Struct 146:214–233

    Article  Google Scholar 

  37. Desai CS (2015) Constitutive modeling of materials and contacts using the disturbed state concept: part 2–Validations at specimen and boundary value problem levels. Comput Struct 146:234–251

    Article  Google Scholar 

  38. Liu MD, Carter JP, Desai CS (2003) Modeling compression behavior of structured geomaterials. Int J Geomech 3(2):191–204

    Article  Google Scholar 

  39. Yin ZY, Chang CS, Hicher PY, Karstunen M (2009) Micromechanical analysis of kinematic hardening in natural clay. Int J Plast 25:1413–1435

    Article  MATH  Google Scholar 

  40. Gao Z, Zhao J (2012) Constitutive modeling of artificially cemented sand by considering fabric anisotropy. Comput Geotech 41:57–69

    Article  Google Scholar 

  41. Shen WQ, Shao JF (2016) An incremental micro-macro model for porous geomaterials with double porosity and inclusion. Int J Plast 83:37–54

    Article  Google Scholar 

  42. Liu EL, Lai YM, Liao MK, Liu XY (2016) Fatigue and damage properties of frozen silty sand samples subjected to cyclic triaxial loading. Can Geotech J 53:1939–1951

    Article  Google Scholar 

  43. Ma W, Wu ZW, Zhang LX (1999) Analyses of process on the strength decrease in frozen soils under high confining pressures. Cold Reg Sci Technol 29:1–7

    Article  Google Scholar 

  44. Shen ZJ (2002) Breakage mechanics and double-medium model for geological materials. Hydro- Sci Eng 4:1–6 (in Chinese)

    Google Scholar 

  45. Shen ZJ, Hu ZQ (2003) Binary medium model for loess. J Hydraul Eng 7:1–6 (in Chinese)

    Google Scholar 

  46. Shen ZJ (2006) Progress in binary medium modeling of geological materials. In: Wu W, Yu HS (eds) Trends in geomechanics. Springer, Berlin, pp 77–99

    Chapter  Google Scholar 

  47. Liu EL, Yu HS, Zhou C, Nie Q, Luo KT (2017) A binary-medium constitutive model for artificially structured soils based on the disturbed state concept and homogenization theory. Int J Geomech 17:04016154

    Article  Google Scholar 

  48. Liu EL (2005) Binary medium model for structured soils. J Hydraul Eng 36:391–395

    Google Scholar 

  49. Liu EL, Zhang JH (2013) Binary medium model for rock sample. Constitutive modeling of geomaterials. Springer, Berlin, Heidelberg, pp 341–347

    Book  Google Scholar 

  50. Liu EL, Luo KT, Zhang SY (2013) Binary medium model for structured soils with initial stress-induced anisotropy. Rock Soil Mech 34:3103–3109 (in Chinese)

    Google Scholar 

  51. Liu Z, Yu X (2011) Coupled thermo-hydro-mechanical model for porous materials under frost action: theory and implementation. Acta Geotech 6(2):51–65

    Article  MathSciNet  Google Scholar 

  52. Xu XT, Wang YB, Yin ZH, Zhang HW (2017) Effect of temperature and strain rate on mechanical characteristics and constitutive model of frozen Helin loess. Cold Reg Sci Technol 136:44–51

    Article  Google Scholar 

  53. Xu XT, Li QL, Xu GF (2019) Investigation on the behavior of frozen silty clay subjected to monotonic and cyclic triaxial loading. Acta Geotech. https://doi.org/10.1007/s11440-019-00826-6

    Article  Google Scholar 

  54. Chang D, Lai YM, Yu F (2019) An elastoplastic constitutive model for frozen saline coarse sandy soil undergoing particle breakage. Acta Geotech. https://doi.org/10.1007/s11440-019-00775-0

    Article  Google Scholar 

  55. Xu GF, Wu W, Qi JL (2016) An extended hypoplastic constitutive model for frozen sand. Soils Found 56(4):704–711

    Article  Google Scholar 

  56. Cai C, Ma W, Zhou Z et al (2019) Laboratory investigation on strengthening behavior of frozen China standard sand. Acta Geotech 14:179–192

    Article  Google Scholar 

  57. Wang JG, Leung CF, Ichikawa Y (2002) A simplified homogenization method for composite soils. Comput Geotech 29:477–500

    Article  Google Scholar 

  58. Shen ZJ (1995) A double hardening model for clays. Rock Soil Mech 16:1–8 (in Chinese)

    Google Scholar 

  59. Liu EL, Xing HL (2009) A double hardening thermos-mechanical constitutive model for overconsolidated clays. Acta Geotech 4:1–6

    Article  Google Scholar 

  60. Liu EL (2010) Breakage and deformation mechanisms of crushable granular materials. Comput Geotech 37:723–730

    Article  Google Scholar 

  61. Lemaitre J, Chaboche JL (1970) Mechanics of solid materials. Cambridge University Press, London

    MATH  Google Scholar 

  62. Lu DC, Du XL, Wang G, Zhou A et al (2016) A three-dimensional elastoplastic constitutive model for concrete. Comput Struct 163:41–55

    Article  Google Scholar 

Download references

Acknowledgements

The authors appreciate the editor and reviewers very much for their comments in revising the paper. This research was supported by National Natural Science Foundation of China (41771066), the 100-Talent Program of the Chinese Academy of Sciences (Granted to Dr. Enlong Liu), and Key Research Program of Frontier Sciences of Chinese Academy of Sciences (QYZDY-SSW-DQC015).

Author information

Authors and Affiliations

  1. State Key Laboratory of Frozen Soil Engineering, Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou, 730000, China

    De Zhang & Enlong Liu

  2. University of Chinese Academy of Sciences, Beijing, 100049, China

    De Zhang

  3. State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource and Hydropower, Sichuan University, Chengdu, 610065, China

    Enlong Liu

  4. Institute of Disaster Management and Reconstruction, Sichuan University, Chengdu, 610207, China

    Ji Huang

Authors
  1. De Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Enlong Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ji Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Enlong Liu.

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

Zhang, D., Liu, E. & Huang, J. Elastoplastic constitutive model for frozen sands based on framework of homogenization theory. Acta Geotech. 15, 1831–1845 (2020). https://doi.org/10.1007/s11440-019-00897-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11440-019-00897-5

Keywords

Search

Navigation