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Micromechanics-based binary-medium constitutive model for frozen soil considering the influence of coarse-grained contents and freeze–thaw cycles

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Abstract

In cold regions, the deformation characteristics of frozen soils with different coarse-grained contents change significantly under the freeze–thaw (F-T) cycles. A series of cryogenic triaxial compression tests were conducted to investigate the deformation characteristics of frozen soil at −10 °C experiencing freeze–thaw cycles. The results indicated that the stress–strain response is nonlinear, elastoplastic accompanied by strain hardening, and volumetric compaction followed by dilatancy for a given coarse-grained content and F-T cycle. To reveal the aforementioned mechanisms, a micromechanics-based binary-medium constitutive model combining the breakage mechanics for geomaterials theory and the homogenization method is proposed. The following salient features of the proposed model in terms of micro–meso–macro scales are summarized: (i) The frozen soil is idealized as a representative volume element (RVE) at the macroscale, which is composed of elastic bonded elements and elastoplastic frictional elements at the mesoscale. The meso–macro upscaling process for frozen soil is described as the binary-medium constitutive. Furthermore, the Mori–Tanaka method is employed to describe the non-uniform deformation between macro-RVE and mesoscale bonded elements in frozen soil. (ii) At the microscale, the micro–meso upscaling process of the bonded elements is performed by employing the homogenization method which allows for considering the ice cementation breakage and the influence of coarse-grained contents. Meanwhile, for the frictional element, considering the microplastic deformation is related to the frictional sliding mechanism, a Drucker–Prager yield criterion and a non-associate flow rule based on the homogenization approach are proposed. Finally, the developed micromechanics-based binary-medium constitutive model can describe the deformation mechanism of frozen soil from both micro- to meso-scale and from meso- to macro-scale simultaneously, and the deformation of frozen soil with different coarse-grained contents under different F-T cycles is well predicted.

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Data availability

The data used to support the findings of this study are available from the corresponding author upon request.

References

  1. Amato G, Ando E, Lyu C et al (2022) A glimpse into rapid freezing processes in clay with x-ray tomography. Acta Geotech 17:327–338

    Google Scholar 

  2. Bignonnet F, Dormieux L, Kondo D (2016) A micro-mechanical model for the plasticity of porous granular media and link with the Cam clay model. Int J Plast 79:259–274

    Google Scholar 

  3. Bikong C, Hoxha D, Shao JF (2015) A micro-macro model for time-dependent behavior of clayey rocks due to anisotropic propagation of microcracks. Int J Plast 69:73–88

    Google Scholar 

  4. Christ M, Kim YC, Park JB (2009) The influence of temperature and cycles on acoustic and mechanical properties of frozen soils. KSCE J Civ Eng 13(3):153–159

    Google Scholar 

  5. Deprez M, Kock DT, Schutter DG et al (2020) A review on freeze-thaw action and weathering of rocks. Earth Sci Rev 203:103143

    Google Scholar 

  6. Du HM, Ma W, Zhang SJ et al (2016) Strength properties of ice-rich frozen silty sands under uniaxial compression for a wide range of strain rates and moisture contents. Cold Reg Sci Technol 123:107–113

    Google Scholar 

  7. Eshelby JD (1957) The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc Royal Soc London Series A Math Phys Sci 241(1226):376–396

    MathSciNet  MATH  Google Scholar 

  8. Fish J, Yu Q, Shek K (1999) Computational damage mechanics for composite materials based on mathematical homogenization. Int J Numer Meth Eng 45(11):1657–1679

    MATH  Google Scholar 

  9. Ghoreishian ASA, Grimstad G, Kadivar M et al (2016) Constitutive model for rate-independent behavior of saturated frozen soils. Can Geotech J 53(10):1646–1657

    Google Scholar 

  10. Guéry AAC, Cormery F, Shao JF et al (2008) A micromechanical model of elastoplastic and damage behavior of a cohesive geomaterial. Int J Solids Struct 45(5):1406–1429

    MATH  Google Scholar 

  11. Hazirbaba K (2019) Effects of freeze-thaw on settlement of fine grained soil subjected to cyclic loading. Cold Reg Sci Technol 160:222–229

    Google Scholar 

  12. He P, Zhu YL, Cheng GD (2000) Constitutive models of frozen soil. Can Geotech J 37(4):811–816

    Google Scholar 

  13. Hill RA (1965) Self-consistent mechanics of composite materials. J Mech Phys Solids 13(4):213–222

    Google Scholar 

  14. Huang Y, Hwang KC, Hu KX et al (1995) A unified energy approach to a class of micromechanics models for composite materials. Acta Mech Sin 11(1):59–75

    Google Scholar 

  15. Kennedy FE, Schulson EM, Jones DE (2000) The friction of ice on ice at low sliding velocities. Philos Mag A 80(5):1093–1110

    Google Scholar 

  16. Kotov PI, Stanilovskaya JYV (2021) Predicting changes in the mechanical properties of frozen saline soils. Eur J Environ Civ En 1–13.

  17. 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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  20. Li B, Zhu ZW, Ning JG et al (2022) Viscoelastic-plastic constitutive model with damage of frozen soil under impact loading and freeze-thaw loading. Int J Mech Sci 214:106890

    Google Scholar 

  21. Li Z, Riska K (2002) Index for estimating physical and mechanical parameters of model ice. J Cold Reg Eng 16(2):72–82

    Google Scholar 

  22. Li ZQ, Hu F, Qi SW et al (2020) Strain-softening failure mode after the post-peak as a unique mechanism of ruptures in a frozen soil-rock mixture. Eng Geol 274:105725

    Google Scholar 

  23. Liu EL, Lai YM (2020) Thermo-poromechanics-based viscoplastic damage constitutive model for saturated frozen soil. Int J Plast 128:102683

    Google Scholar 

  24. Liu EL, Lai YM, Wong H et al (2018) An elastoplastic model for saturated freezing soils based on thermo-poromechanics. Int J Plast 107:246–285

    Google Scholar 

  25. Liu JK, Lv P, Cui YH et al (2014) Experimental study on direct shear behavior of frozen soil-concrete interface. Cold Reg Sci Technol 104:1–6

    Google Scholar 

  26. Liu XY, Liu EL, Zhang D et al (2019) Study on effect of coarse-grained content on the mechanical properties of frozen mixed soils. Cold Reg Sci Technol 158:237–251

    Google Scholar 

  27. Loria AFR, 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

    Google Scholar 

  28. Maghous S, Dormieux L, Barthelemy JF (2009) Micromechanical approach to the strength properties of frictional geomaterials. Eur J Mech-A/Solids 28(1):179–188

    MathSciNet  MATH  Google Scholar 

  29. Matsuoka N, Murton J (2008) Frost weathering: recent advances and future directions. Permafrost Periglac 19:195–210

    Google Scholar 

  30. Mori T, Tanaka K (1973) Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall 21(5):571–574

    Google Scholar 

  31. Nassr A, Esmaeili-Falak M, Katebi H et al (2018) A new approach to modeling the behavior of frozen soils. Eng Geol 246:82–90

    Google Scholar 

  32. Oksanen P, Keinonen J (1982) The mechanism of friction of ice. Wear 78(3):315–324

    Google Scholar 

  33. Qi J, Wang S, Yu F (2013) A review on creep of frozen soils. In: Yang Q, Zhang JM, Zheng H, Yao Y (Eds.), Constitutive Modeling of Geomaterials. Verlag Berlin Heidelberg, pp 129–133.

  34. Qi JL, Ma W, Song C (2008) Influence of freeze–thaw on engineering properties of a silty soil. Cold Reg Sci Technol 53(3):397–404

    Google Scholar 

  35. Razbegin VN, Vyalov SS, Maksimyak RV et al (1996) Mechanical properties of frozen soils. Soil Mech Found Eng 33(2):35–45

    Google Scholar 

  36. Shen MD, Zhou ZW, Zhang SJ (2021) Effect of stress path on mechanical behaviours of frozen subgrade soil. Road Mater Pavement 1–30.

  37. Shen WQ, Kondo D, Dormieux L et al (2013) A closed-form three scale model for ductile rock with a plastically compressible porous matrix. Mech Mater 59:73–86

    Google Scholar 

  38. Shen WQ, Shao JF, Kondo D et al (2012) A micro–macro model for clayey rocks with a plastic compressible porous matrix. Int J Plast 36:64–85

    Google Scholar 

  39. Shen ZJ (2006) Progress in binary medium modeling of geological materials. Modern trends in geomechancis, Wu W and Yu HS eds., Springer, Berlin 77–99.

  40. Sun K, Annan Z (2021) A multisurface elastoplastic model for frozen soil. Acta Geotech 16:3401–3424

    Google Scholar 

  41. Ting JM, Torrence MR, Ladd CC (1983) Mechanisms of strength for frozen sand. J Geotech Eng 109(10):1286–1302

    Google Scholar 

  42. Tounsi H, Rouabhi A, Jahangir E et al (2020) Mechanical behavior of frozen metapelite: laboratory investigation and constitutive modeling. Cold Reg Sci Technol 175:103058

    Google Scholar 

  43. Tsubakihara Y, Kishida H, Nishiyama T (1993) Friction between cohesive soils and steel. Soils Found 33(2):145–156

    Google Scholar 

  44. Tsytovich NA, Swinzow E, Tschebotarioff G (1975) The mechanics of frozen ground. McGraw-Hill, New York

    Google Scholar 

  45. Wang P, Liu EL, Zhi B (2021) An elastic-plastic model for frozen soil from micro to macro scale. Appl Math Model 91:125–148

    MathSciNet  MATH  Google Scholar 

  46. Wang P, Liu EL, Zhi B et al. (2023) A rate-dependent constitutive model for saturated frozen soil considering local breakage mechanism. J Rock Mech Geotech.

  47. Wang P, Liu EL, Zhi B et al (2022) Creep characteristic and unified macro-meso creep model for saturated frozen soil under constant/variable temperature conditions. Acta Geotech 17:5299–5319

    Google Scholar 

  48. Wang SN, Zhu Y, Ma W et al (2021) Effects of rock block and confining pressure on dynamic characteristics of soil-rock mixtures. Eng Geol 280:105963

    Google Scholar 

  49. Yang YG, Feng G, Lai YM et al (2016) Experimental and theoretical investigations on the mechanical behavior of frozen silt. Cold Reg Sci Technol 130:59–65

    Google Scholar 

  50. Yang YG, Lai YM, Chang XX (2010) Laboratory and theoretical investigations on the deformation and strength behaviors of artificial frozen soil. Cold Reg Sci Technol 64:39–45

    Google Scholar 

  51. Yang YH, Wei ZA, Yin GZ et al (2016) Uniaxial compression test of frozen tailings. Cold Reg Sci Technol 129:60–68

    Google Scholar 

  52. Yang ZH, Still B, Ge XX (2015) Mechanical properties of seasonally frozen and permafrost soils at high strain rate. Cold Reg Sci Technol 113:12–19

    Google Scholar 

  53. Yu Q, Zhang ZX, Shen ZY (1993) Instaneous-state deformation and strength behavior of frozen soil. J Glaciol Geocryol 15(2):258–265 ((In Chinese))

    Google Scholar 

  54. Zhang D, Li QM, Liu EL et al (2019) Dynamic properties of frozen silty soils with different coarse-grained contents subjected to cyclic triaxial loading. Cold Reg Sci Technol 157:64–85

    Google Scholar 

  55. Zhang D, Liu EL, Huang J (2020) Elastoplastic constitutive model for frozen sands based on framework of homogenization theory. Acta Geotech 15:1831–1845

    Google Scholar 

  56. Zhang FL, Zhu ZW, Ma W et al (2021) A unified viscoplastic model and strain rate–temperature equivalence of frozen soil under impact loading. J Mech Phys Solids 152:104413

    MathSciNet  Google Scholar 

  57. Zhang YG, Liu SH, Lu Y et al (2021) Experimental study of the mechanical behavior of frozen clay-gravel composite. Cold Reg Sci Technol 189:103340

    Google Scholar 

  58. Zhang Z, Ma W, Qi JL (2013) Structure evolution and mechanism of engineering properties change of soils under effect of freeze-thaw cycle. J Jinlin Univ (Earth Sci Ed) 43(6):1904–1914

    Google Scholar 

  59. Zhao LY, Lai YM, Shao JF et al (2021) Friction-damage coupled models and macroscopic strength criteria for ice-saturated frozen silt with crack asperity variation by a micromechanical approach. Eng Geol 294:106405

    Google Scholar 

  60. Zhao LY, Shao JF, Zhu QZ et al (2019) Homogenization of rock-like materials with plastic matrix based on an incremental variational principle. Int J Plast 123:145–164

    Google Scholar 

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

    Google Scholar 

  62. Zhou ZW, Ma W, Zhang SJ et al (2020) Experimental investigation of the path-dependent strength and deformation behaviours of frozen loess. Eng Geol 265:105449

    Google Scholar 

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Acknowledgements

This study is supported by the funding of the Autonomous Research Topic of the State Key Laboratory of Frozen Soil Engineering, Chinese Academy of Sciences (No. SKLFSE-ZQ-202206) and the funding of the National Natural Science Foundation of China (NSFC) (Grant No. 41771066).

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Authors and Affiliations

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

    Dan Wang, Enlong Liu, Chengsong Yang, Pan Wang & Bingtang Song

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

    Dan Wang

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

    Enlong Liu

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  1. Dan Wang
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  4. Pan Wang
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  5. Bingtang Song
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Contributions

WD contributed to methodology, investigation, test, model, data curation, writing-original draft. LEL contributed to conceptualization, supervision, funding acquisition, writing—review and editing. YCS contributed to supervision, data curation, writing—review and editing. WP contributed to investigation, data curation. SBT contributed to investigation, test.

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Correspondence to Enlong Liu.

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Wang, D., Liu, E., Yang, C. et al. Micromechanics-based binary-medium constitutive model for frozen soil considering the influence of coarse-grained contents and freeze–thaw cycles. Acta Geotech. 18, 3977–3996 (2023). https://doi.org/10.1007/s11440-023-01831-6

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