Skip to main content

Advertisement

Log in

A micro-mechanics-based elastoplastic friction-damage model for brittle rocks and its application in deformation analysis of the left bank slope of Jinping I hydropower station

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

Abstract

This study develops a micro-mechanics-based elastoplastic damage model within the framework of irreversible thermodynamics. In the model, damage is related to growth of micro-cracks, while plastic deformation is induced by frictional sliding along those cracks. The damage criterion and functions of thermodynamic force are used to describe the damage evolution of rocks and determine whether they are damaged. Time-dependent deformation of rock is also taken into account by considering subcritical growth of micro-cracks. For engineering application, the proposed model is implemented in the standard finite element code Abaqus as a user-defined material model (UMAT) by using a specific local integration algorithm. The accuracy of the proposed model is assessed by comparing numerical results with experimental data in conventional triaxial compression tests and triaxial creep tests. The proposed model is then used for simulating the displacement field, damage and plastic zones of the left bank high slope. The predicted results are in a good consistency with field monitored data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

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
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

References

  1. Bieniawski ZT (1967) Mechanism of brittle fracture of rock. Parts 1–3. Int J Rock Mech Min Sci Geomech Abstr 4(4):395–406

    Article  Google Scholar 

  2. Chen W, Konietzky H (2014) Simulation of heterogeneity, creep, damage and lifetime for loaded brittle rocks. Tectonophysics 633:164–175

    Article  Google Scholar 

  3. Chiarelli A-S, Shao J-F, Hoteit N (2003) Modeling of elastoplastic damage behavior of a claystone. Int J Plast 19(1):23–45

    Article  MATH  Google Scholar 

  4. Clausen J, Damkilde L, Andersen L (2007) An efficient return algorithm for non-associated plasticity with linear yield criteria in principal stress space. Comput Struct 85(23):1795–1807

    Article  Google Scholar 

  5. Dormieux L, Kondo D, Ulm FJ (2006) Microporomechanics. Wiley

  6. Gambarotta L, Lagomarsino S (1993) A microcrack damage model for brittle materials. Int J Solids Struct 30(2):177–198

    Article  MATH  Google Scholar 

  7. Gao F, Stead D, Elmo D (2016) Numerical simulation of microstructure of brittle rock using a grain-breakable distinct element grain-based model. Comput Geotech 78:203–217

    Article  Google Scholar 

  8. Ghazvinian E, Diederichs M, Quey R (2014) 3d random voronoi grain-based models for simulation of brittle rock damage and fabric-guided micro-fracturing. J Rock Mech Geotech Eng 6(6):506–521

    Article  Google Scholar 

  9. Grassl P, Jirásek M (2006) Damage-plastic model for concrete failure. Int J Solids Struct 43(22):7166–7196

    Article  MATH  Google Scholar 

  10. Hoek E, Bieniawski ZT (1984) Brittle fracture propagation in rock under compression. Int J Fract 26(4):276–294

    Article  Google Scholar 

  11. Holcomb DJ, Costin LS (1986) Damage in brittle materials: experimental methods. Resear report, Sandia National Labs., Albuquerque, NM (USA). Geomechanics Div

  12. Hu K, Zhu QZ, Chen L, Shao JF, Liu J (2018) A micromechanics-based elastoplastic damage model for rocks with a brittle–ductile transition in mechanical response. Rock Mech Rock Eng 51(6):1729–1737

    Article  Google Scholar 

  13. Huang R, Lin F, Yan M (2010) Deformation mechanism and stability evaluation for the left abutment slope of Jinping I hydropower station. Bull Eng Geol Environ 69(3):365–372

    Article  Google Scholar 

  14. Huining XU, Zhong Z, Jin XU, Ren H, Ming N, Lu W, Zheng H, Yang J (2013) Experimental study of weakening effect of high water head on weak rock masses from Jinping I hydropower station. Chin J Rock Mech Eng 32:4207–4214

    Google Scholar 

  15. Kachanov M (1992) Effective elastic properties of cracked solids: Critical review of some basic concepts. Applied Mechanics Reviews 45(8):304–335

    Article  Google Scholar 

  16. Krajcinovic D (1996) Damage mechanics, vol 41. Elsevier, Amsterdam

    MATH  Google Scholar 

  17. Labuz JF, Dai ST, Papamichos E (1996) Plane-strain compression of rock-like materials. Int J Rock Mech Min Sci Geomech Abstr 33(6):573–584

    Article  Google Scholar 

  18. Li X, Konietzky H (2015) Numerical simulation schemes for time-dependent crack growth in hard brittle rock. Acta Geotech 10(4):513–531

    Article  Google Scholar 

  19. Li X, Konietzky H, Li XB, Wang Y (2019) Failure pattern of brittle rock governed by initial microcrack characteristics. Acta Geotech 14:1437–1457

    Article  Google Scholar 

  20. Liu ZB, Shao JF (2017) Strength behavior, creep failure and permeability change of a tight marble under triaxial compression. Rock Mech Rock Eng 50(3):1–13

    Google Scholar 

  21. Lockner D, Byerlee J, Kuksenko V, Ponomarev A, Sidorin A (1992) Observations of quasistatic fault growth from acoustic emissions. In: International geophysics, Vol 51. Elsevier, pp 3–31

  22. Lubliner J, Oliver J, Oller S, Onate E (1989) A plastic-damage model for concrete. Int J Solids Struct 25(3):299–326

    Article  Google Scholar 

  23. Martin CD (1993) The strength of massive Lac du bonnet granite around underground openings, PhD thesis, Department of Civil & Geological Engineering, University of Manitoba, Winnipeg, Manitoba

  24. Molladavoodi H, Mortazavi A (2011) A damage-based numerical analysis of brittle rocks failure mechanism. Finite Elem Anal Des 47(9):991–1003

    Article  Google Scholar 

  25. Nguyen CT, Nguyen GD, Das A, Bui HH (2017) Constitutive modelling of progressive localised failure in porous sandstones under shearing at high confining pressures. Int J Rock Mech Min Sci 93:179–195

    Article  Google Scholar 

  26. Paterson MS, Wong TF (2005) Experimental rock deformation—the brittle field, vol 43, no 326, pp 317–317

  27. Peng Q, Chen MX (2012) An efficient return mapping algorithm for general isotropic elastoplasticity in principal space. Comput Struct 92(3):173–184

    Article  Google Scholar 

  28. Pietruszczak S, Lydzba D, Shao JF (2004) Description of creep in inherently anisotropic frictional materials. J Eng Mech 130(6):681–690

    Article  Google Scholar 

  29. Qi S, Wu F, Yan F, Lan H (2004) Mechanism of deep cracks in the left bank slope of jinping first stage hydropower station. Eng Geol 73(1–2):129–144

    Article  Google Scholar 

  30. Qi S, Wu F, Zhou Y, Song Y, Gong M (2010) Influence of deep seated discontinuities on the left slope of Jinping I hydropower station and its stability analysis. Bull Eng Geol Environ 69(3):333–342

    Article  Google Scholar 

  31. Simo JC (1992) Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory. Comput Methods Appl Mech Eng 99(1):61–112

    Article  MathSciNet  MATH  Google Scholar 

  32. Walton G, Hedayat A, Kim E et al (2017) Post-yield strength and dilatancy evolution across the brittle–ductile transition in Indiana limestone. Rock Mech Rock Eng 50(7):1691–1710

    Article  Google Scholar 

  33. Wang F, Konietzky H, Fruhwirt T, Dai YJ (2020) Laboratory testing and numerical simulation of properties and thermal-induced cracking of eibenstock granite at elevated temperatures. Acta Geotech. https://doi.org/10.1007/s11440-020-00926-8

    Article  Google Scholar 

  34. Wawersik WR, Brace WF (1971) Post-failure behavior of a granite and diabase. Rock Mech 3(2):61–85

    Article  Google Scholar 

  35. Wong T (1982) Micromechanics of faulting in westerly granite. Int J Rock Mech Min Sci 19:49–62

    Article  Google Scholar 

  36. Xu NW, Tang CA, Li LC, Zhou Z, Sha C, Liang ZZ, Yang JY (2011) Microseismic monitoring and stability analysis of the left bank slope in Jinping first stage hydropower station in Southwestern China. Int J Rock Mech Min Sci 48(6):950–963

    Article  Google Scholar 

  37. Xu T, Zhou G, Heap MJ, Yang S, Konietzky H, Baud P (2018) The modeling of time-dependent deformation and fracturing of brittle rocks under varying confining and pore pressures. Rock Mech Rock Eng 51(10):3241–3263

    Article  Google Scholar 

  38. Zhao LY, Shao JF, Zhu QZ (2018a) Analysis of localized cracking in quasi-brittle materials with a micro-mechanics based friction-damage approach. J Mech Phys Solids 119:163–187

    Article  MathSciNet  Google Scholar 

  39. Zhao LY, Zhu QZ, Shao JF (2018b) A micromechanics-based plastic damage model for quasi-brittle materials under a large range of compressive stress. Int J Plast 100:156–176

    Article  Google Scholar 

  40. Zhong D-H, Li M-C, Song L-G, Wang G (2006) Enhanced nurbs modeling and visualization for large 3d geoengineering applications: an example from the Jinping first-level hydropower engineering project, China. Comput Geosci 32(9):1270–1282

    Article  Google Scholar 

  41. Zhu QZ (2016) Strength prediction of dry and saturated brittle rocks by unilateral damage-friction coupling analyses. Comput Geotech 73:16–23

    Article  Google Scholar 

  42. Zhu QZ, Shao JF (2015) A refined micromechanical damage-friction model with strength prediction for rock-like materials under compression. Int J Solids Struct 60:75–83

    Article  Google Scholar 

  43. Zhu QZ, Zhao LY, Shao JF (2016) Analytical and numerical analysis of frictional damage in quasi brittle materials. J Mech Phys Solids 92:137–163

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This study was jointly supported by the National Key RD Program of China (Grant No. 2017YFC1501100); the National Natural Science Foundation of China (Grant No. 51679068); the Fundamental Research Funds for the Central Universities (Grant No. 2018B656X14); and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant No. KYCX18_0556). Hu Kun is grateful to the China Scholarship Council for providing him a scholarship during his stay in France.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jian-Fu Shao.

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

Hu, K., Shao, JF., Zhu, QZ. et al. A micro-mechanics-based elastoplastic friction-damage model for brittle rocks and its application in deformation analysis of the left bank slope of Jinping I hydropower station. Acta Geotech. 15, 3443–3460 (2020). https://doi.org/10.1007/s11440-020-00977-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11440-020-00977-x

Keywords

Navigation