Creep Parameter Determination and Model Establishment Considering Stress and Time Effects

  • Wenbo Liu
  • Shuguang ZhangEmail author
Original Paper


In order to better study the creep properties of rock under different stress and time, the creep test was taken from the surrounding rock of the roadway. First, a model that describes the whole process of rock creep was introduced so that it could correspond to the various stages of creep. Then, a new method for determining creep parameters was proposed. The calculated creep parameters were processed by combining the stress difference and the time product, and the relationship between the creep parameters and the overstress difference and time product was analyzed. A creep model considering stress and time effects was obtained. Finally, the model was verified by the experimental data and calculation results, and the rationality and correctness of the method for determining the parameters of the creep model were analyzed. The results shown that the special point of creep curve and the definition of creep deformation were combined with the model equation and experimental data to determine the creep parameters under different stress and time. The improved creep model could better describe the creep damage process of rock under different stress states, and provided a new idea for establishing the unsteady creep model and determining the model parameters. The product of E2 controlled the limit of viscoelastic deformation gradually decreased with the product of time and overstress difference. The shear viscoelastic coefficient η1 gradually decreased as the product of time and overstress difference increases. The product of η2 controlling the steady creep rate decreased with time and the overstress difference. The higher the stress level, the greater the steady creep rate, but the overall stable creep rate was less than the accelerated creep rate. The nonlinear viscous coefficient η3 mainly controled the accelerated creep deformation of rock and gradually decreased with the increase of stress and time. The trend of creep parameters as a whole indicated that stress and time had certain degrading effects on rock creep parameters.


Stress state Time Creep phase Determination of creep parameters Creep rate 



The authors would like to acknowledge the editor and the reviewers for their constructive criticism on the earlier version of this paper and for offering valuable suggestions that contributed to the paper’s improvement. This study was supported by the National Natural Science Foundation of China (51274109).

Compliance with Ethical Standards

Conflict of interest

The authors declare no conflict of interest.


  1. Anno (1998) Time-dependent behaviour of deep level tabular excavations in hard rock. Rock Mech Rock Eng 32(2):123–155Google Scholar
  2. Cui S (2010) Study on time effect of rock mechanical parameters and unsteady rheological constitutive model”. Beijing Jiaotong University, BeijingGoogle Scholar
  3. Cyr ED, Mohsen M, Raja KM, Inal K (2015) A three dimensional (3D) thermo-elasto-viscoplastic constitutive model for FCC polycrystals. Int J Plast 70(7):166–190CrossRefGoogle Scholar
  4. Desayi P, Nandakumar N (1995) A semi-empirical approach to Predict shear strength of ferrocement. Cem Concr Compos 17(3):207–218CrossRefGoogle Scholar
  5. Fahimifar A, Karami M (2015) Modifications to an elasto-visco-plastic constitutive model for prediction of creep deformation of rock samples. Soils Found 55(6):1364–1371CrossRefGoogle Scholar
  6. Jia SP, Zhang LW, Wu BS (2018) A coupled hydro-mechanical creep damage model for clayey rock and its application to nuclear waste repository. Tunn Undergr Space Technol 74:230–246CrossRefGoogle Scholar
  7. Liu BG, Cui SD (2011) Improvement of single specimen method for determination of rock strength parameters. China Civ Eng J 44(S1):162–165Google Scholar
  8. Liu HZ, Xie HQ, He JD (2016) Nonlinear creep damage constitutive model for soft rocks. Mech Time Depend Mater 21(1):1–24Google Scholar
  9. Pramthawee P, Jongpradist P, Sukkarak R (2017) Integration of creep into a modified hardening soil model for time-dependent analysis of a high rockfill dam. Comput Geotech 91(11):104–116CrossRefGoogle Scholar
  10. Qi YJ, Jiang QH, Wang ZJ (2012) 3D creep constitutive equation of modified Nishihara model and its parameters identification. Chin J Rock Mech Eng 31(2):347–355Google Scholar
  11. Shlyannikov V, Tumanov A (2018) Creep damage and stress intensity factor assessment for plane multi-axial and three-dimensional problems. Int J Solids Struct 15:166–183CrossRefGoogle Scholar
  12. Singh S, Chandan KL, Kl Gopi (2018) Estimation of creep parameters of rock salt from uniaxial compression tests. Int J Rock Mech Min Sci 107(6):243–248CrossRefGoogle Scholar
  13. Tang H, Wang DP, Huang RQ (2017) A new rock creep model based on variable-order fractional derivatives and continuum damage mechanics. Bull Eng Geol Environ 7(1):1–9Google Scholar
  14. Tao M, Li X, Li D (2013) Rock failure induced by dynamic unloading under 3D stress state. Theor Appl Fract Mech 65(6):47–54CrossRefGoogle Scholar
  15. Wang R, Zhuo Z, Zhou HW (2017) A fractal derivative constitutive model for three stages in granite creep. Results Phys 7:2632–2638CrossRefGoogle Scholar
  16. Winkel BV, Gerstle KH, Ko HY (1972) Analysis of time-dependent deformations of openings in salt media. Int J Rock Mech Min Sci 9(2):249–260CrossRefGoogle Scholar
  17. Xiong YL, Ye GL, Zhu HH (2017) A unified thermo-elasto-viscoplastic model for soft rock. Int J Rock Mech Min Sci 93(3):1–12CrossRefGoogle Scholar
  18. Yang SQ, Xu P, Xu T (2015) Nonlinear visco-elastic and accelerating creep model for coal under conventional triaxial compression. Geomech Geophys Geo-Energy Geo-Resour 1:109–120CrossRefGoogle Scholar
  19. Yao XL, Qi JL, Zhang JM (2018) A one-dimensional creep model for frozen soils taking temperature as an independent variable. Soils Found 58(6):627–640CrossRefGoogle Scholar
  20. Zhao Y, Wang Y, Wang W (2017) Modeling of non-linear rheological behavior of hard rock using triaxial rheological experiment. Int J Rock Mech Min Sci 93(3):66–75CrossRefGoogle Scholar
  21. Zhou CB, Wan ZJ, Zhang Y (2012) Creep characteristics and constitutive model of gas coal mass under high temperature and triaxial stress. J China Coal Soc 12:2020–2025Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Liaoning Technical UniversityFuxinChina
  2. 2.Guilin University of Technology, Guangxi Key Laboratory of Geomechanics and Geotechnical EngineeringGuilinChina

Personalised recommendations