Geotechnical and Geological Engineering

, Volume 36, Issue 5, pp 2985–2993 | Cite as

Nonlinear Variation Parameters Creep Model of Rock and Parametric Inversion

  • Liu Yang
  • Zhi-da Li
Original paper


Traditional Nishihara model is a linear constant parameters model, and it is difficult to describe nonlinear accelerated creep characteristics of rock with this model. Therefore, an improved Nishihara model is proposed in the way of replacing, cascading elements and substituting parameters in the original model. Firstly, fractional differential elements are used to replace viscous elements in the traditional Nishihara model; then a viscous plastic element with assumption exponential relationship between the rock nonlinear rheological deformation and time power function is cascaded; finally, the viscosity coefficient of the traditional model is rewritten to a variable parameter related to stress and time, thus obtaining the nonlinear variation parameters creep model of rock. The improved model is verified with data from creep test to frozen soft rock during Cretaceous period, which shows that this model can describe the rock nonlinear accelerated creep characteristics more accurately and more comprehensively.


Fractional calculus Viscosity Viscoplasticity Accelerated creep Variable parameter 


  1. Boukharov GN, Chanda MW, Boukharov NG (1995) The three processes of brittle crystalline rock creep. Int J Rock Mech Min Sci Geomech Abstr 32(4):325–335CrossRefGoogle Scholar
  2. Cao SG, Bian J, Li P (2002) Rheologic constitutive relationship of rocks and a modified model. Chin J Rock Mech Eng 21(5):632–634Google Scholar
  3. Chen YJ, Pan CL, Cao P et al (2003) A new mechanical model for soft rock rheology. Rock Soil Mech 24(2):209–214Google Scholar
  4. He ZL, Zhu ZD, Zhu ML et al (2016) An unsteady creep constitutive model based on fractional order derivatives. Rock Soil Mech 37(3):737–744Google Scholar
  5. Li DW, Wang RH, Fan JH (2011) Nonlinear rheological model for frozen soft rock during Cretaceous period. Chin J Geotech Eng 33(3):398–403Google Scholar
  6. Liu BG, Cui SD (2010) Experimental study of creep damage of mudstone. Chin J Rock Mech Eng 29(10):2127–2133Google Scholar
  7. Tang H, Zhao FS, Duan Z et al (2014) The improved Nishihara mode of loess based on fractional calculus. Hydrogeol Eng Geol 5(41):50–55Google Scholar
  8. Wang LG, He F, Liu XF et al (2004) Nonlinear creep model and stability analysis of rock. Chin J Rock Mech Eng 23(10):1640–1642Google Scholar
  9. Welch SWJ, Rorrer RAL, Duren JRG (1999) Application of time-based fractional calculus methods to viscoelastic creep and stress relaxation of materials. Mech Time Depend Mater 3:279–303CrossRefGoogle Scholar
  10. Xie HP, Chen ZH et al (2003) Rock mechanics. Science Press, Beijing (in Chinese) Google Scholar
  11. Xu WY, Yang SQ, Chu WJ (2006) Nonlinear viscoelasto-plastic rheological model (Hohai model) of rock and its engineering application. Chin J Rock Mech Eng 25(3):433–447Google Scholar
  12. Xu GW, He C, Hu XY et al (2015) A modified Nishihara model based on fractional calculus theory and its parameter intelligent identification. Rock Soil Mech Z2(36):132–138Google Scholar
  13. Yan Y, Wang SJ, Wang EZ (2010) Creep equation of variable parameters based on Nishihara model. Rock Soil Mech 31(10):3025–3035Google Scholar
  14. Yang SQ, Ni HM, Yu SH (2007) A kind of nonlinear rheological model for rocks. J Hohai Univ (Nat Sci) 35(4):388–392Google Scholar
  15. Zeng J (2016) Based on the theory of fractional order calculus mudstone creep damage constitutive model. Zhongzhou Coal 1:57–60Google Scholar
  16. Zhou HW, Wang CP, Han BB et al (2011) A creep constitutive model for salt rock based on fractional derivatives. Int J Rock Mech Min Sci 48(1):116–121CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of TransportationWuhan University of TechnologyWuhanChina

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