A novel constitutive modelling approach measured under simulated freeze–thaw cycles for the rock failure

Abstract

In this study, we derived a computational modelling relation between the model parameters and characteristic parameters of rock deformation and failure via total differentials. We construct a damage model of rock under simulated freeze–thaw cycles and loading based on continuum damage mechanics theory that considers the influence of confining pressure and the random characteristics of rock material defects. This model reflects the variation in regulation between the internal mechanism of freeze–thaw damage and selected physical variables, making it more adaptable. We further analyze the evolution of microdamage and induced material mechanical properties of the rock using our proposed model, producing a total damage evolution curve under freeze–thaw cycles and loading that reflects the closure, initiation, propagation and coalescence of internal microcracks, as well as the subsequent appearance of macrocracks and rock failure. As the number of freeze–thaw cycles increases, rock damage intensifies, as demonstrated by the material’s deteriorating micromechanical properties. However, in later stages of deformation, both the strain and plasticity of the rock increase. With increasing confining pressure, rock damage and the damage accumulation rate, peak damage evolution ratio and descending segment after the peak decrease which manifest in the enhanced resistance of the rock to failure and increased macroscopic plastic deformation. Finally, we perform triaxial compression tests of rock under freeze–thaw cycles to validate our model. The macroscopic rock deformation and failure predicted by our model’s damage characteristics analysis are consistent with our experimental result.

This is a preview of subscription content, access via your institution.

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Abbreviations

σ :

Nominal stress vector

C :

Elastic matrix

ε :

Nominal strain vector

D :

Damage

F :

Infinitesimal intensity

D :

Loading damage

E n :

Elastic modulus after n freeze–thaw cycles

D m :

Total damage

μ :

Poisson’s ratio

I 1 :

First invariant of the stress tensor

J 2 :

Second invariant of stress deviation

α 0 :

Parameter related to rock mechanics characteristics

σ *1 :

Effective axial stress

σ *3 :

Effective lateral stress

σ 1 :

Nominal axial stress

σ 3 :

Lateral nominal stress

φ :

Internal friction angle

σ cn :

Peak stress at an appropriate confining pressure

ε cn :

Corresponding strain

References

  1. 1.

    Hilbich C, Hauck C, Hoelzle M, Scherler M, Schudel L, Völksch I, Vonder Mühll D, Mäusbacher R (2008) Monitoring mountain permafrost evolution using electrical resistivity tomography: a 7-year study of seasonal, annual, and long-term variations at Schilthorn, Swiss Alps. J Geophys Res Earth Surf 113:1–12

    Article  Google Scholar 

  2. 2.

    Cheng GD, Ma W (2003) A research review of international permafrost engineering——5th international symposium on permafrost engineering. J Glaciol Geocryol 25(3):303–308

    Google Scholar 

  3. 3.

    Wang P, Xu J, Liu S, Wang H, Liu S (2016) Static and dynamic mechanical properties of sedimentary rock after freeze–thaw or thermal shock weathering. Eng Geol 210:148–157

    Article  Google Scholar 

  4. 4.

    Quansheng LIU, Shibing H, Yongshui K (2015) Advance and review on freezing–thawing damage of fractured rock. Chin J Rock Mech Eng 34(3):452–471

    Google Scholar 

  5. 5.

    Tan X, Chen W, Yang J, Cao J (2011) Laboratory investigations on the mechanical properties degradation of granite under freeze–thaw cycles. Cold Reg Sci Technol 68(3):130–138

    Article  Google Scholar 

  6. 6.

    Takarli M, Prince W, Siddique R (2008) Damage in granite under heating/cooling cycles and water freeze–thaw condition. Int J Rock Mech Min Sci 45(7):1164–1175

    Article  Google Scholar 

  7. 7.

    Zhou K, Bin LI, Li J, Deng H, Feng BIN (2015) Microscopic damage and dynamic mechanical properties of rock under freeze–thaw environment. Trans Nonferrous Met Soc China 25(4):1254–1261

    Article  Google Scholar 

  8. 8.

    Nicholson DT, Nicholson FH (2000) Physical deterioration of sedimentary rocks subjected to experimental freeze–thaw weathering. Earth Surf Process Landf J Br Geomorphol Res Gr 25(12):1295–1307

    Article  Google Scholar 

  9. 9.

    Park J, Hyun C-U, Park H-D (2015) Changes in microstructure and physical properties of rocks caused by artificial freeze–thaw action. Bull Eng Geol Environ 74(2):555–565

    Article  Google Scholar 

  10. 10.

    Prick A (1995) Dilatometrical behaviour of porous calcareous rock samples subjected to freeze–thaw cycles. CATENA 25(1–4):7–20

    Article  Google Scholar 

  11. 11.

    Ge X, Ren J, Pu Y, Ma W, Zhu Y (2001) Primary study of CT real-time testing of fatigue meso-damage propagation law of rock. Chin J Geotech Eng Ed 23(2):191–195

    Google Scholar 

  12. 12.

    Walbert C, Eslami J, Beaucour A-L, Bourges A, Noumowe A (2015) Evolution of the mechanical behaviour of limestone subjected to freeze–thaw cycles. Environ Earth Sci 74(7):6339–6351

    Article  Google Scholar 

  13. 13.

    Yavuz H, Altindag R, Sarac S, Ugur I, Sengun N (2006) Estimating the index properties of deteriorated carbonate rocks due to freeze–thaw and thermal shock weathering. Int J Rock Mech Min Sci 43(5):767–775

    Article  Google Scholar 

  14. 14.

    Ince I, Fener M (2016) A prediction model for uniaxial compressive strength of deteriorated pyroclastic rocks due to freeze–thaw cycle. J Afr Earth Sci 120:134–140

    Article  Google Scholar 

  15. 15.

    Liu Q, Huang S, Kang Y, Liu X (2015) A prediction model for uniaxial compressive strength of deteriorated rocks due to freeze–thaw. Cold Reg Sci Technol 120:96–107

    Article  Google Scholar 

  16. 16.

    Momeni A, Abdilor Y, Khanlari GR, Heidari M, Sepahi AA (2016) The effect of freeze–thaw cycles on physical and mechanical properties of granitoid hard rocks. Bull Eng Geol Environ 75(4):1649–1656

    Article  Google Scholar 

  17. 17.

    Zhang H-M, Yang G-S (2013) Experimental study of damage deterioration and mechanical properties for freezing thawing rock. J China Coal Soc 38(10):1756–1762

    MathSciNet  Google Scholar 

  18. 18.

    Sabatakakis N, Koukis G, Tsiambaos G, Papanakli S (2008) Index properties and strength variation controlled by microstructure for sedimentary rocks. Eng Geol 97(1–2):80–90

    Article  Google Scholar 

  19. 19.

    Zhang H-M, Yang G-S (2011) Freeze-thaw cycling and mechanical experiment and damage propagation characteristics of rock. J China Univ Min Technol 40:140–145

    Google Scholar 

  20. 20.

    De Kock T et al (2015) A pore-scale study of fracture dynamics in rock using X-ray micro-CT under ambient freeze–thaw cycling. Environ Sci Technol 49(5):2867–2874

    Article  Google Scholar 

  21. 21.

    Huimei Z, Gengshe Y (2010) Research on damage model of rock under coupling action of freeze-thaw and load. Chin J Rock Mech Eng 29(3):471–476

    Google Scholar 

  22. 22.

    Wang D, Ma W, Niu Y, Chang X, Wen Z (2007) Effects of cyclic freezing and thawing on mechanical properties of Qinghai-Tibet clay. Cold Reg Sci Technol 48(1):34–43

    Article  Google Scholar 

  23. 23.

    Luo X, Jiang N, Fan X, Mei N, Luo H (2015) Effects of freeze–thaw on the determination and application of parameters of slope rock mass in cold regions. Cold Reg Sci Technol 110:32–37

    Article  Google Scholar 

  24. 24.

    Ya-ni LU, Xin-ping LI, Xing-hong WU (2014) Fracture coalescence mechanism of single flaw rock specimen due to freeze–thaw under triaxial compression. Rock Soil Mech 35(6):1579–1584

    Google Scholar 

  25. 25.

    Qu D, Li D, Li X, Yi LUO, Xu K (2018) Damage evolution mechanism and constitutive model of freeze–thaw yellow sandstone in acidic environment. Cold Reg Sci Technol 155:174–183

    Article  Google Scholar 

  26. 26.

    Li B, Mao J, Nawa T, Han T (2017) Mesoscopic damage model of concrete subjected to freeze–thaw cycles using mercury intrusion porosimetry and differential scanning calorimetry (MIP-DSC). Constr Build Mater 147:79–90

    Article  Google Scholar 

  27. 27.

    Liu Q, Xu G, Liu X (2008) Experimental and theoretical study on freeze-thawing damage propagation of saturated rocks. Int J Mod Phys B 22(09n11):1853–1858

    Article  Google Scholar 

  28. 28.

    Huang S, Liu Q, Cheng A, Liu Y (2018) A statistical damage constitutive model under freeze–thaw and loading for rock and its engineering application. Cold Reg Sci Technol 145:142–150

    Article  Google Scholar 

  29. 29.

    Chen W, Tan X, Yu H, Yuan KK, Li SC (2011) Advance and review on thermo-hydromechanical characteristics of rock mass under condition of low temperature and freeze–thaw cycles. Chin J Rock Mech Eng 30(7):1318–1336

    Google Scholar 

  30. 30.

    Bayram F (2012) Predicting mechanical strength loss of natural stones after freeze–thaw in cold regions. Cold Reg Sci Technol 83:98–102

    Article  Google Scholar 

  31. 31.

    Chen YL, Dai MX, Liu ML, Wu D, Wang P (2013) Experimental investigation on freezing damage characteristics of granite with initial damage. Chin Q Mech 34(1):74–80

    Article  Google Scholar 

  32. 32.

    Xi-dong YAN, Hong-yan LIU, Chuang-feng X, Chao L, Dong-hui W (2015) Constitutive model research on freezing–thawing damage of rock based on deformation and propagation of microcracks. Rock Soil Mech 36(12):3489–3499

    Google Scholar 

  33. 33.

    Lemaitre J (2012) A course on damage mechanics. Springer Science & Business Media, New York

    Google Scholar 

  34. 34.

    Cao W-G, Zhao M-H, Tang X-J (2003) Study on simulation of statistical damage in the full process of rock failure. Chin J Geotech Eng Ed 25(2):184–187

    Google Scholar 

Download references

Acknowledgements

The authors are grateful for financial support from the National Natural Science Foundation of China (Nos. 11172232, 51774231, 11872299, 41772333); The Project Supported by Natural Science Basic Research Plan in Shaanxi Province of China (2018JQ4026); Future Scientists Program of “Double First Rate” of China University of Mining and Technology (2019WLKXJ076).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Chao Yuan.

Ethics declarations

Conflict of interest

The authors that they have declare no conflict of interest.

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

Verify currency and authenticity via CrossMark

Cite this article

Zhang, H., Yuan, C., Yang, G. et al. A novel constitutive modelling approach measured under simulated freeze–thaw cycles for the rock failure. Engineering with Computers 37, 779–792 (2021). https://doi.org/10.1007/s00366-019-00856-4

Download citation

Keywords

  • Freeze–thaw cycle
  • Rock failure
  • Constitutive model
  • Confining pressure