Skip to main content

Advertisement

SpringerLink
Log in

A fractional order creep constitutive model of warm frozen silt

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

Abstract

A series of triaxial creep tests were conducted on warm frozen silts extracted from Qinghai–Tibet Plateau at temperature of −1.5 °C under confining pressures of 0.5, 1.0, and 2.0 MPa, respectively. The applied test stress levels were 30, 50, 60, and 70% of triaxial shear strength, respectively. The test results indicate that the creep strain increases with the increase in applied stress level and there is a stress threshold, based on which the test results can be classified into two types of creep strain curves. The creep strain curve only includes primary and secondary creep stages when the stress level is less than the threshold value. When the stress level exceeds the threshold value, the creep strain velocity gradually increases and the specimen quickly fails in tertiary creep stage. Based on the creep test results, a fractional order rheological element model is established for warm frozen silt, which is also generalized from uniaxial stress state to the three-dimensional stress state. From the analysis on the features of the stress threshold, a creep strength criterion is also proposed simultaneously. Comparing the calculated results of the warm frozen silt with the tested ones, it is found that the predicted results of the proposed model are in good agreement with the test results. In the proposed fractional order model, the relationship between the damage factor and time is established to describe the damage degree of the specimen. Compared with the existing creep constitutive model of frozen soil, the proposed fractional order model has advantages of fewer model parameters, higher simulation precision and wider applicability in analyzing the mechanical properties of warm frozen silt.

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

Similar content being viewed by others

References

  1. Arenson LU, Springman SM (2005) Mathematical descriptions for the behaviour of ice-rich frozen soils at temperature close to 0 °C. Can Geotech J 42(2):431–442

    Article  Google Scholar 

  2. Arenson LU, Springman SM, Sego DC (2007) The rheology of frozen soils. Appl Rheol 17:1–14

    Google Scholar 

  3. Cheng GD (2003) Construction of Qinghai–Tibetan railway with cooled roadbed. China Railw Sci 24(3):1–4

    Article  Google Scholar 

  4. Darabi MK, Abu Al-Rub RK, Masad EA, Huang CV, Dallas NL (2011) A thermo viscoelastic viscoplastic viscodamage constitutive model for asphaltic materials. Int J Solids Struct 48(1):191–207

    Article  MATH  Google Scholar 

  5. Enelund M, Mahler L, Runesson K, Josefson BL (1999) Formulation and integration of the standard linear viscoelastic solid with fractional order rate laws. Int J Solids Struct 36(16):2417–2442

    Article  MATH  Google Scholar 

  6. Fabrizio M (2014) Fractional rheological models for thermomechanical systems dissipation and free energies. Fract Calc Appl Anal 1(17):207–223

    MathSciNet  MATH  Google Scholar 

  7. Fish AM (1991) Strength of frozen soil under a combined stress. In: 6th International Symposium on Ground Freeging, pp 135–145

  8. Katsuki D, Gutierrez M (2011) Viscoelastic damage model for asphalt concrete. Acta Geotech 6:231–241

    Article  Google Scholar 

  9. Kiryakova V, Al-Sauabi B (1999) Explicit solutions to hyper-Bessel integral equations of second kind. Comput Math Appl 37:75–86

    Article  MathSciNet  MATH  Google Scholar 

  10. Kutergin VN, Kal’bergenov RG (2012) Influence of salinity on rheologic and strength properties of frozen soils in yamal. Soil Mech Found Eng 49(6):105–111

    Article  Google Scholar 

  11. Lai YM, Li JB, Li QZ (2012) Study on damage statistical constitutive model and stochastic simulation for warm ice-rich frozen silt. Cold Reg Sci Technol 71:102–110

    Article  Google Scholar 

  12. Lai YM, Jin L, Chang XX (2009) Yield criterion and elasto–plastic damage constitutive model for frozen sandy soil. Int J Plast 25(6):1177–1205

    Article  MATH  Google Scholar 

  13. Lai YM, Yang YG, Chang XX, Li SY (2010) Strength criterion and elastoplastic constitutive model of frozen silt in generalized plastic mechanics. Int J Plast 26(10):1461–1484

    Article  MATH  Google Scholar 

  14. Li DW, Fan JH, Wang RH (2011) Research on visco-elastic–plastic creep model of artificially frozen soil under high confining pressures. Cold Reg Sci Technol 65:219–225

    Article  Google Scholar 

  15. Ma XJ, Zhang JM, Chang XX, Zheng B (2007) Experimental study on creep of warm and ice-rich frozen soil. Chin J Geotech Eng 29(6):848–852

    Google Scholar 

  16. Madurapperuma MAKM, Puswewala UGA (2008) Numerical implementation of a constitutive model for soil creep. J Mech Mater Struct 12:1857–1874

    Article  Google Scholar 

  17. Marklund E, Eitzenberger J, Varna J (2008) Nonlinear viscoelastic viscoplastic material model including stiffness degradation for hemp/lignin composites. Compos Sci Technol 68(9):2156–2162

    Article  Google Scholar 

  18. Qin YH, Zhang JM, Zheng B, Ma XJ (2009) Experimental study for the compressible behavior of warm and ice-rich frozen soil under the embankment of Qinghai–Tibet Railroad. Cold Reg Sci Technol 57:148–153

    Article  Google Scholar 

  19. Schiessel H, Metzler R, Blumen A, Nonnenmacher TF (1995) Generalized viscoelastic models: their fractional equations with solutions. J Phys A Math Theor 28:6567–6584

    MATH  Google Scholar 

  20. Sumelka W (2014) Fractional viscoplasticity. Mech Res Commun 56:31–36

    Article  MATH  Google Scholar 

  21. Sun J (2007) Rock rheological mechanics and its advance in engineering applications. Chin J Rock Mech Eng 6(26):1081–1107

    Google Scholar 

  22. Wang SH, Qi JL, Yao XL (2011) Stress relaxation characteristics of warm frozen clay under triaxial conditions. Cold Reg Sci Technol 69:112–117

    Google Scholar 

  23. Wu ZW, Ma W (1994) Strength and creep of frozen soil. Lanzhou University Press, Lanzhou, pp 20–26

    Google Scholar 

  24. Wu ZW, Ma W (1994) Strength characteristic of frozen soil. J Glaciol Geocryol 16(1):15–20

    Google Scholar 

  25. Xu Z, Chen W (2013) A fractional-order model on new experiments of linear viscoelastic creep of Hami Melon. Comput Math Appl 66:677–681

    Article  MathSciNet  Google Scholar 

  26. Yang YG, Lai YM, Chang XX (2010) Experimental and theoretical studies on the creep behavior of warm ice-rich frozen sand. Cold Reg Sci Technol 63:61–67

    Article  Google Scholar 

  27. Yin DS, Wu H, Cheng C, Chen YQ (2013) Fractional order constitutive model of geomaterials under the condition of triaxial test. Int J Numer Anal Meth Geomech 37:961–972

    Article  Google Scholar 

  28. Yu YJ, Tian XG, Lu TJ (2013) On fractional order generalized thermoelasticity with micromodeling. Acta Mech 224:2911–2927

    Article  MathSciNet  MATH  Google Scholar 

  29. Zheng B, Zhang JM, Ma XJ (2009) Study on Compression deformation of warm and ice-enriched frozen soil. Chin J Rock Mech Eng 28(Supp. 1):3063–3068

    Google Scholar 

  30. Zhao X, Yang HT, He YQ (2014) Identification of constitutive parameters for fractional viscoelasticity. Commun Nonlinear Sci Numer Simul 19:311–322

    Article  MathSciNet  MATH  Google Scholar 

  31. Zhao XD, Zhou GQ (2013) Experimental study on the creep behavior of frozen clay with thermal gradient. Cold Reg Sci Technol 86:127–132

    Article  Google Scholar 

  32. Zhou HW, Wang CP, Han BB, Duan ZQ (2011) A creep constitutive model for salt rock based on fractional derivatives. Int J Rock Mech Min Sci 48:116–121

    Article  Google Scholar 

  33. Zhou HW, Wang CP, Mishnaevsky L, Duan ZQ, Ding JY (2013) A fractional derivative approach to full creep regions in salt rock. Mech Time-Depend Mater 17:413–425

    Article  Google Scholar 

Download references

Acknowledgments

This research was supported by National Key Basic Research Program of China (973 Program No. 2012CB026102), National Natural Science Foundation of China (41230630, 51204161), the Western Project Program of the Chinese Academy of Sciences (KZCX2-XB3-19), the foundation of State Key Laboratory of Frozen Soil Engineering (SKLFSE-ZY-03), and CAS Pioneer Hundred Talents Program.

Author information

Authors and Affiliations

  1. State Key Laboratory of Frozen Soil Engineering, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Lanzhou, 730000, China

    Mengke Liao, Yuanming Lai, Enlong Liu & Xusheng Wan

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

    Mengke Liao & Xusheng Wan

  3. School of Civil Engineering, Lanzhou Jiaotong University, Lanzhou, 730070, China

    Yuanming Lai

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

    Enlong Liu

Authors
  1. Mengke Liao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuanming Lai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Enlong Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xusheng Wan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuanming Lai.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liao, M., Lai, Y., Liu, E. et al. A fractional order creep constitutive model of warm frozen silt. Acta Geotech. 12, 377–389 (2017). https://doi.org/10.1007/s11440-016-0466-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11440-016-0466-4

Keywords

Search

Navigation