Skip to main content
SpringerLink
Log in

Numerical analysis of the brittle–ductile transition of deeply buried marble using a discrete approach

  • Published:
Computational Particle Mechanics Aims and scope Submit manuscript

Abstract

In high geostress areas, rocks tend to experience plastic deformation processes and show ductility. Therefore, the study of the mechanical properties of rocks, especially the post-peak behavior, is crucial for underground geotechnical engineering. For this reason, the macroscopic mechanical property of marble is studied by using the PFC/PBM numerical method. An improved numerical marble sample with random properties is used by setting different contact strengths following a bimodal Weibull distribution. Thereafter, on the basis of an improved boundary servo mechanism, the brittle–ductile transition appearing in laboratory tests on marble is successfully realized by the discrete approach, and a servo velocity threshold function of axial loading speed and confining pressure is obtained. Furthermore, the marble model and servo method are applied in the excavation of typical underground caverns. The effects of constrained velocity and geostress level on the surrounding rock failure model of the cavern are described and analyzed. In addition, mechanism of the excavation failure under high geostress is discussed.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Bouchaud JP, Cates ME, Claudin P (1995) Stress distribution in granular media and nonlinear wave equation. J De Phys I 5(6):639–656. https://doi.org/10.1051/jp1:1995157

    Article  Google Scholar 

  2. Burman BC (1980) A discrete numerical-model for granular assemblies. Géotechnique 30(3):331–334

    Article  Google Scholar 

  3. Cao WG, Zhao H, Li X, Zhang YJ (2010) Statistical damage model with strain softening and hardening for rocks under the influence of voids and volume changes. Can Geotech J 47(8):857–871(15). https://doi.org/10.1139/T09-148

    Article  Google Scholar 

  4. Cho N, Martin CD, Sego DC (2007) A clumped particle model for rock. Int J Rock Mech Min Sci 44(7):997–1010. https://doi.org/10.1038/201450d0

    Article  Google Scholar 

  5. Cundall PA, Hart RD (1992) Numerical modelling of discontinua. Eng Comput 9(2):101–113. https://doi.org/10.1108/eb023851

    Article  Google Scholar 

  6. Cundall PA, Potyondy DO (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41(8):1329–1364

    Article  Google Scholar 

  7. Cundall PA, Carranza-Torres C, Hart R (2003) A new constitutive model based on the hoek-brown criterion. In: the 3rd international symposium on FLAC and FLAC3D numerical modelling in Geomechanics, pp 17–25

  8. Duan K, Kwok CY, Ma X (2017) Dem simulations of sandstone under true triaxial compressive tests. Acta Geotech 12(3):495–510. https://doi.org/10.1007/s11440-016-0480-6

    Article  Google Scholar 

  9. Hsiao FY, Kao HC (2015) Modeling the post-peak strength degradation on tunnel stability. In: the 3rd international symposium on FLAC and FLAC3D numerical modelling in Geomechanics

  10. 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. https://doi.org/10.1007/s00603-018-1427-z

    Article  Google Scholar 

  11. Inc ICG (2018) PFC2D-particle flow code in 2 dimensions, user’s manual

  12. Johnson NL, Kotz S, Balakrishnan N (1994) Continuous Univariate Distributions. JOHN WILEY and SONS, INC, New Jersey

    MATH  Google Scholar 

  13. Lee H, Jeon S (2011) An experimental and numerical study of fracture coalescence in pre-cracked specimens under uniaxial compression. Int J Solids Struct 48(6):979–999. https://doi.org/10.1016/j.ijsolstr.2010.12.001

    Article  MATH  Google Scholar 

  14. Li Y, Oh J, Mitra R, Hebblewhite B (2016) A constitutive model for a laboratory rock joint with multi-scale asperity degradation. Comput Geotech 72:143–151. https://doi.org/10.1016/j.compgeo.2015.10.008

    Article  Google Scholar 

  15. Lin Q, Ping C, Wang P (2018) Study of post-peak strain softening mechanical behaviour of rock material based on hoek-brown criterion. Adv Civil Eng. https://doi.org/10.1155/2018/6190376

    Article  Google Scholar 

  16. Liu D, Liu C, Kang Y, Guo B, Jiang Y (2017) Mechanical behavior of benxi formation limestone under triaxial compression: a new post-peak constitutive model and experimental validation. Bull Eng Geol Environ 77:1701–1715. https://doi.org/10.1007/s10064-017-1193-2

    Article  Google Scholar 

  17. Meng F, Zhou H, Zhang C, Xu R, lu J (2014) Evaluation methodology of brittleness of rock based on post-peak stress-strain curves. Rock Mech Rock Eng 48(5):1787–1805. https://doi.org/10.1007/s00603-014-0694-6

    Article  Google Scholar 

  18. Nguyen GD, Nguyen CT, Bui HH, Nguyen VP (2016) Constitutive modelling of compaction localisation in porous sandstones. Int J Rock Mech Min Sci 83:57–72. https://doi.org/10.1016/j.ijrmms.2015.12.018

    Article  Google Scholar 

  19. Paterson MS, Wong T (2005) Experimental Rock Deformation-the Brittle Field. Springer-Verlag, Berlin Heidelberg

    Google Scholar 

  20. Pourhosseini O, Shabanimashcool M (2014) Development of an elasto-plastic constitutive model for intact rocks. Int J Rock Mech Min Sci 66(66):1–12. https://doi.org/10.1016/j.ijrmms.2013.11.010

    Article  Google Scholar 

  21. Shi C, Yang W, Yang J, Chen X (2019) Calibration of micro-scaled mechanical parameters of granite based on a bonded-particle model with 2d particle fow code.pdf. Granul Matter 21(2):21–38. https://doi.org/10.1007/s10035-019-0889-3

    Article  Google Scholar 

  22. Tang C (1997) Numerical simulation of progressive rock failure and associated seismicity. Int J Rock Mech Min Sci 34(2):249–261. https://doi.org/10.1016/S0148-9062(96)00039-3

    Article  Google Scholar 

  23. Tang CA, Liu H, Lee P, Tsui Y, Tham L (2000) Numerical studies of the influence of microstructure on rock failure in uniaxial compression - part I: effect of heterogeneity. Int J Rock Mech Min ences 37(4):555–569. https://doi.org/10.1016/S1365-1609(99)00121-5

    Article  Google Scholar 

  24. Vajdova V, Zhu W, Chen TMN, Wong TF (2010) Micromechanics of brittle faulting and cataclastic flow in tavel limestone. J Struct Geol 32(8):1158–1169. https://doi.org/10.1016/j.jsg.2010.07.007

    Article  Google Scholar 

  25. Wu X, Jiang Y, Guan Z (2018) A modified strain-softening model with multi-post-peak behaviours and its application in circular tunnel. Eng Geol p S0013795216305336, https://doi.org/10.1016/j.enggeo.2018.03.031

  26. Yang SQ, Yin PF, Huang YH, Cheng JL (2019) Strength, deformability and x-ray micro-ct observations of transversely isotropic composite rock under different confining pressures. Eng Fract Mech. https://doi.org/10.1016/j.engfracmech.2019.04.030

    Article  Google Scholar 

  27. Zhang C, Chu W, Liu N, Zhu Y, Hou J (2011) Laboratory tests and numerical simulations of brittle marble and squeezing schist at jinping ii hydropower station, china. J Rock Mech Geotech Eng 3(1):30–38. https://doi.org/10.3724/SP.J.1235.2011.00030

    Article  Google Scholar 

  28. Zhang XP, Wong LNY (2012) Cracking processes in rock-like material containing a single flaw under uniaxial compression: A numerical study based on parallel bonded-particle model approach. Rock Mech Rock Eng 45(5):711–737. https://doi.org/10.1007/s00603-011-0176-z

    Article  Google Scholar 

  29. Zhang XP, Wong LNY (2014) Choosing a proper loading rate for bonded-particle model of intact rock. Int J Fract 189(2):163–179. https://doi.org/10.1007/s10704-014-9968-y

    Article  Google Scholar 

  30. Zhang Y, Liu Z, Shi C, Shao J (2018a) Three-dimensional reconstruction of block shape irregularity and its effects on block impacts using an energy-based approach. Rock Mech Rock Eng 51(4):1173–1191. https://doi.org/10.1007/s00603-017-1385-x

    Article  Google Scholar 

  31. Zhang Y, Shao J, Liu Z, Shi C, De Saxcé G (2018b) Effects of confining pressure and loading path on deformation and strength of cohesive granular materials: a three-dimensional dem analysis. Acta Geotech 14:443–460. https://doi.org/10.1007/s11440-018-0671-4

    Article  Google Scholar 

  32. Zhang YH, Wong LNY (2018) A review of numerical techniques approaching microstructures of crystalline rocks. Comput Geosci 115:167–187. https://doi.org/10.1016/j.cageo.2018.03.012

    Article  Google Scholar 

  33. Zhou CY, Zhu FX (2010) An elasto-plastic damage constitutive model with double yield surfaces for saturated soft rock. Int J Rock Mech Min Sci 47(3):385–395. https://doi.org/10.1016/j.ijrmms.2010.01.002

    Article  Google Scholar 

Download references

Acknowledgements

The work presented in this paper was financially supported by the National Natural Science Foundation of China (Grants Nos. 41831278, 51679071), the National Key R&D Program of China (2018YFC1508501) and the Natural Science Foundation of Jiangsu Province (Grant No. BK20171434).

Author information

Authors and Affiliations

  1. Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing, China

    Yiping Zhang, Chong Shi, Yulong Zhang, Junxiong Yang & Xiao Chen

  2. Research Institute of Geotechnical Engineering, Hohai University, Nanjing, 210098, Jiangsu, China

    Yiping Zhang, Chong Shi, Yulong Zhang, Junxiong Yang & Xiao Chen

Authors
  1. Yiping Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chong Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yulong Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Junxiong Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xiao Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yiping Zhang.

Ethics declarations

Conflict of interest

The authors declare that they have 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

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, Y., Shi, C., Zhang, Y. et al. Numerical analysis of the brittle–ductile transition of deeply buried marble using a discrete approach. Comp. Part. Mech. 8, 893–904 (2021). https://doi.org/10.1007/s40571-020-00375-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40571-020-00375-w

Keywords

Search

Navigation