Skip to main content
SpringerLink
Log in

A creep model for frozen soil based on the fractional Kelvin–Voigt's model

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

Abstract

A creep model based on Kelvin–Voigt fractional-order derivative model (KVFD) with less parameters and clearer physical description is established to obtain viscous-elastic property of frozen soil using spherical indentation tests (SITs), uniaxial creep tests and triaxial creep tests. Mechanical parameters identification principal (MPIP) is presented to verify fractional-order derivative Kelvin, Maxwell, Merchant and Burgers models have unique solution of mechanical parameters. MPIP is utilized to prove cascaded model of more than two fractional-order derivative Kelvin elements and Maxwell elements bring variable solutions of parameters in following conditions: (1) More than two cascaded fractional-order derivative Kelvin elements have same fractional-order and relaxation time; (2) More than two fractional-order derivative Maxwell elements are included in cascaded model. Experimental data of SITs reveal discrepancy of deformation curve also leads to diverse solutions of parameters and discrepancy of relaxation modulus. Discrepancy of relaxation modulus decreases with the decrease in deformation discrepancy. Relaxation modulus predicted by the proposed model is closer to Hertz’s solution but higher than those given by Roman’s solution after 5 h of loading. Validation of test data in SITs, uniaxial and triaxial creep tests demonstrates that the proposed model agrees well with the available laboratory results of frozen sand.

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

Similar content being viewed by others

References

  1. Bezukhov NI (1961) Fundamentals of elasticity, plasticity, and creep theory, VysshayaShkola, Moscow (in Russian).

  2. Cheng YT, Cheng CM (2005) General relationship between contact stiffness, contact depth, and mechanical properties for indentation in linear viscoelastic solids using axisymmetric indenters of arbitrary profiles. Appl Phys Lett 87:111914

    Article  Google Scholar 

  3. Demirci N, Tonuk E (2014) Non-integer viscoelastic constitutive law to model soft biological tissues to in-vivo indentation. Acta Bioeng Biomech 16:13–21

    Google Scholar 

  4. Fang JH, Chen X, Xu AH, Zhang Z (2018) The experimental study of the influence of freeze-thaw cycles on the physical and mechanic properties of Qinghai-Tibet red clay. J Glaciol Geocryol 40(1):62–69 (in Chinese)

    Google Scholar 

  5. Fukada S, Fang B, Shigeno A (2011) Experimental analysis and simulation of nonlinear microscopic behavior of ball screw mechanism for ultra-precision positioning. Precis Eng-J Int Soc Precis Eng Nanotechnol 35(4):650–668

    Google Scholar 

  6. Hertz H (1882) On the contact of elastic solids. Reine Angew Math 92:156–171

    Article  MathSciNet  Google Scholar 

  7. Hou F, Li QM, Liu EL, Zhou C, Liao MK, Luo HW, Liu XY (2016) A fractional creep constitutive model for frozen soil in consideration of the strengthening and weakening effects. Adv Mater Sci Eng. https://doi.org/10.1155/2016/5740292

    Article  Google Scholar 

  8. Huang G, Lu H (2007) Measurements of two independent viscoelastic functions by nano indentation. Exp Mech 47:87–98

    Article  Google Scholar 

  9. Huang FY, Mao F (2015) Fractional derivative Burgers creep model of frozen sand soil by genetic algorithm. Anhui Archit 22(6):99–102 ((In Chinese))

    MathSciNet  Google Scholar 

  10. Huang CJ, Zhang Z, Jin HJ, Feng WJ, Jin DD, Andrey M (2020) Nonlinear Kelvin model solution of frozen soil relaxation modulus and experimental study based on spherical template indenter. J Glaciol Geocryol 42(2):550–561 (in Chinese)

    Google Scholar 

  11. Huang CJ, Zhang Z, Jin HJ, Li XY, Chen X, Feng WJ (2020) Comparison of modulus equations of frozen soil based on spherical template indenter. Cold Reg Sci Technol. https://doi.org/10.1016/j.coldregions.2019.102911

    Article  Google Scholar 

  12. Hui LI (2015) Accelerating simulated annealing fractional order derivative Kelvin creep model of artificial frozen soil. AER-Adv Eng Res 12:1479–1485

    Google Scholar 

  13. Intrigila B, Melatti I, Tofani A, Macchiarelli G (2007) Computational models of myocardial endomysial collagen arrangement. Comput Methods Prog Biomed 86(3):232–244

    Article  Google Scholar 

  14. Jaeger A, Lackner R, Stangl K (2007) Microscale characterization of bitumen back-analysis of viscoelastic properties by means of nanoindentation. Int J Mater Res 98:404–413

    Article  Google Scholar 

  15. Kolesnikov YV, Morozov EM (1989) Contact fracture mechanics. Nauka, Moscow (in Russian)

  16. Kozhevnikov IF, Duhamel D, Yin HP, Feng ZQ (2010) A new algorithm for solving the multi-indentation problem of rigid bodies of arbitrary shapes on a viscoelastic half-space. Int J Mech Sci 52(3):399–409

    Article  Google Scholar 

  17. Laboratory methods for determining the strength and strain characteristics: GOST 12248–96[S]. Moscow: Ministry of Construction and Housing of the Russian Federation, 1991

  18. Lee EH, Radok JRM (1960) The contact problem for viscoelastic bodies. J Appl Mech 27:438–444

    Article  MathSciNet  Google Scholar 

  19. Li K, Cheng H (2013) Experimental research on frozen soil mechanical performance in tunnel restoration project of subway. J Anhui Univ Sci Technol (Nat Sci) 33(2):67–70 (in Chinese)

    Google Scholar 

  20. Li J, Tang YQ, Feng W (2020) Creep behavior of soft clay subjected to artificial freeze–thaw from multiple-scale perspectives. Acta Geotech 15:2849–2864. https://doi.org/10.1007/s11440-020-00980-2

    Article  Google Scholar 

  21. Li DW, Zhang CC, Ding GS, Zhang H, Chen JH, Cui H, Pei WS, Wang SF, An LS, Li P, Yuan C (2018) Fractional derivative-based creep constitutive model of deep artificial frozen soil. Cold Reg Sci Technol 170:102942

    Article  Google Scholar 

  22. Liao MK, Lai YM, Liu EL, Wan XS (2016) A fractional order creep constitutive model of warm frozen silt. Acta Geotech 12(2):377–389

    Article  Google Scholar 

  23. Liu XL, Li DJ, Han C et al (2021) A Caputo variable-order fractional damage creep model for sandstone considering effect of relaxation time. Acta Geotech. https://doi.org/10.1007/s11440-021-01230-9

    Article  Google Scholar 

  24. Martynova E (2016) Determination of the properties of viscoelastic materials using spherical nanoindentation. Mech Time-Depend Mater 20(1):85–93

    Article  Google Scholar 

  25. Qian WC (1956) Elastic mechanics theory. Chinese Science Press, Beijing (in Chinese)

    Google Scholar 

  26. Roman LT, Veretekhina ÉG (2004) Determination of deformation characteristics of permafrost from impression of a spherical plate. Soil Mech Found Eng 41(2):60–64

    Article  Google Scholar 

  27. Shahsavari R, Ulm FJ (2009) Indentation analysis of fractional viscoelastic solids. J Mech Mater Struct 4:523–550

    Article  Google Scholar 

  28. Standard for engineering classification of soil: GB/T 50145-2007[S]. Beijing: Ministry of Water Sources of the People’s Republic of China, 2007 (in Chinese)

  29. Wang ZZ, Mu SY, Niu YH, Chen LJ, Liu J, Liu XD (2008) Predictions of elastic constants and strength of transverse isotropic frozen soil. Rock Soil Mech 29(11):475–480 ((in Chinese))

    Google Scholar 

  30. Wu ZW, Ma W (1993) Strength and creep of frozen soil. Press of Lanzhou University, Lanzhou (in Chinese)

    Google Scholar 

  31. Yang YG, Feng G, Lai YM, Zhang XX (2014) Tri-axial creep characteristic and fractional order constitutive model of frozen silt. Electron J Geotech Eng 19:3757–3768

    Google Scholar 

  32. Yang WH (1966) The contact problem for fiscoelastic bodies. J Appl Mech 395–401

  33. Yu TL, Zhang LY, Lei JQ, San SD (2010) Discussion on compression strength of ice when flowing ice blocks having dynamic pressure effect on bridge piers in Spring. J China Foreign Highw 3:168–172 (in Chinese)

    Google Scholar 

  34. Zhang Z, Ma W, Zhang ZQ, Li B, Yao XL (2012) Application of spherical indentation spherical indentation to long-term strength tests for frozen soil. Rock Soil Mech 33(11):3516–3520 (in Chinese)

    Google Scholar 

  35. Zhang HM, Wang Y, Insana MF (2016) Ramp-hold relaxation solutions for the KVFD model applied to soft viscoelastic media. Meas Sci Technol 27(2):025702

    Article  Google Scholar 

  36. Zhang HM, Zhang QZ, Ruan LT, Duan JB, Wan MX, Insana MF (2018) Modeling ramp-hold indentation measurements based on Kelvin-Voigt fractional derivative model. Meas Sci Technol 29(3):035701

    Article  Google Scholar 

  37. Zhang L, Zhou HW, Wang XY et al (2021) A triaxial creep model for deep coal considering temperature effect based on fractional derivative. Acta Geotech. https://doi.org/10.1007/s11440-021-01302-w

    Article  Google Scholar 

  38. Zhou FX, Wang LY, Liu HB (2021) A fractional elasto-viscoplastic model for describing creep behavior of soft soil. Acta Geotech 16:67–76. https://doi.org/10.1007/s11440-020-01008-5

    Article  Google Scholar 

  39. Zhou H, Zhang YC, Zhang Z, Feng WJ, Zhou B, Wu JJ (2014) Changing rule of long-term strength of frozen loess cohesion under impact of freeze-thaw cycle. Rock Soil Mech 35(8):2241–2246+2254 (in Chinese)

    Google Scholar 

  40. Zhou FX, Wang LY, Liu ZY, Zhao WC (2021) A viscoelastic-viscoplastic mechanical model of time-dependent materials based on variable-order fractional derivative. Mech Time-Depend Mater

  41. Zhou H (2015) The change rule of frozen loess long-term strength under freeze-thaw cycle. LanZhou city of China, master degree paper of Lanzhou university, 29–38 (in Chinese)

  42. Zhu ZY, Luo F, Zhang YZ, Zhang DJ, He JL (2019) A creep model for frozen sand of Qinghai-Tibet based on Nishihara model. Cold Reg Sci Technol 167:102843

    Article  Google Scholar 

Download references

Acknowledgements

This research was supported by National Natural Science Foundation of China (41771078, 41871061), the Science and Technology Project of Yalong River Hydropower Development Company (LHKA-G201906), and the Cooperation and Exchange Project between NSFC and RFBR (42011530083).

Author information

Authors and Affiliations

  1. School of Civil Engineering/Institute of Cold Regions Engineering, Science and Technology/Northeast-China, Observatory and Research-Station of Permafrost Geo-Environment-Ministry of Education/Coordinated Innovation Center for Permafrost Environment, Road Construction and Maintenance in Northeast-China, Northeast Forestry University, Harbin, 150040, People’s Republic of China

    Ze Zhang & Huijun Jin

  2. School of Astronautics, Harbin Institute of Technology, Harbin, 150090, China

    Canjie Huang

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

    Ze Zhang, Canjie Huang, Huijun Jin, Wenjie Feng & Doudou Jin

  4. Civil Engineering College, Harbin Institute of Technology, Harbin, 150090, China

    Canjie Huang

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

    Doudou Jin

  6. Yalong River Hydropower Development Company, LTD, Beijing, 610051, China

    Guike Zhang

Authors
  1. Ze Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Canjie Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Huijun Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wenjie Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Doudou Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Guike Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Canjie Huang.

Ethics declarations

Conflict of interest

The authors declare there is no conflict of interests regarding the publications of this study.

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, Z., Huang, C., Jin, H. et al. A creep model for frozen soil based on the fractional Kelvin–Voigt's model. Acta Geotech. 17, 4377–4393 (2022). https://doi.org/10.1007/s11440-021-01390-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11440-021-01390-8

Keywords

Search

Navigation