Skip to main content
SpringerLink
Log in

Numerical Study of the Fracturing Process in Marble and Plaster Hollow Plate Specimens Subjected to Uniaxial Compression

  • Original Paper
  • Published:
Rock Mechanics and Rock Engineering Aims and scope Submit manuscript

Abstract

Physical models of plaster, calcitic and dolomitic marbles from greek quarries with a single pre-existing cylindrical hole of various diameters, subjected in uniaxial compression are simulated numerically with a bonded particle model by employing the two- and the three-dimensional versions of the Particle Flow Code. The linear parallel bond model is employed for the plaster’s simulation, and respectively the flat-joint model for the marbles. The calibration procedure and results are presented, as well as the simulation results of the hollow specimens. The micro-cracking, the fracturing process and the sequence of their appearance during the numerical tests of the hollow plates are in good agreement with the laboratory tested physical models. Each fracture pattern is similar to the one of the physical models. Also, the regions of micro-cracking in the numerical models is quite similar to the regions of intense deformation observed from digital image correlation analysis on the respective physical models. The followed methodology for the determination of the phenomena’s onset is presented as well. A comparison between the peak strength and the required applied axial stress for the primary fracture and spalling initiation of the numerical and the physical models is presented along with the accompanied scale effect. Additional numerical investigation is performed, quantifying the stress distribution along and normal to the primary fracture’s path during the numerical test. The current study reveals the potential of the bonded particle model to reliably simulate laboratory and field structures, at least for the studied materials.

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.

Institutional subscriptions

Fig. 1

(modified after Carter (1992) and Martin (1993))

Fig. 2

(modified after Itasca Consulting Group Inc 2014)

Fig. 3

(modified after Itasca Consulting Group Inc. 2014)

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
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30

Similar content being viewed by others

References

  • Carter BZ (1992) Physical and numerical modeling of fracture in rock: with special emphasis on the potash mines of saskatchewan. PhD Thesis

  • Chatzipanagis I, Vougioukas D (2004) The significance of the lithostratigrafhic position and the tectonic deformation for the location and the exploitation of the dolomitic marbles of Falacron Mountain. In: Proceedings of the 10th International Congress, pp 63–71

  • Fakhimi A, Carvalho F, Ishida T, Labuz JF (2002) Simulation of failure around a circular opening in rock. Int J Rock Mech Mining Sci 39(4):507–515. https://doi.org/10.1016/S1365-1609(02)00041-2

    Article  Google Scholar 

  • Itasca Consulting Group Inc. (2014) PFC 5.0 Documentation

  • Lajtai EZ (1972) Effect of tensile stress gradient on brittle fracture initiation. Int J Rock Mech Min Sci 9:569–578

    Article  Google Scholar 

  • Lotidis MA (2014) The approach of synthetic rock mass for the numerical simulation of the brittle rocks’ failure around underground openings. MEng Thesis, School of Mining and Metallurgical Engineering, National Technical University of Athens, Athens, Greece

  • Lotidis MA, Nomikos PP, Sofianos AI (2015) A numerical investigation of rock fracture around cavities in compression. In: Eurock 2015: future development of rock mechanics, 7–10 October, pp 719–724

  • Lotidis MA, Nomikos PP, Sofianos AI (2016) Bonded particles models of rock plates with circular cavities in uniaxial and biaxial compression. Chall J Struct Mech 2(4):205–211. https://doi.org/10.20528/cjsmec.2016.11.026

    Article  Google Scholar 

  • Lotidis MA, Nomikos PP, Sofianos AI (2017) Numerical simulation of granite plates containing a cylindrical opening in compression. Procedia Eng 191:242–247. https://doi.org/10.1016/j.proeng.2017.05.177

    Article  Google Scholar 

  • Lotidis MA, Nomikos PP, Sofianos AI (2019) Laboratory study of the fracturing process in marble and plaster hollow plates subjected to uniaxial compression by combined acoustic emission and digital image correlation techniques (under revision)

  • Martin CD (1993) The strength of massive lac du bonnet granite around underground openings. PhD Thesis, June

  • Mas Ivars D, Pierce ME, Darcel C et al (2011) The synthetic rock mass approach for jointed rock mass modelling. Int J Rock Mech Mining Sci 48(2):219–244. https://doi.org/10.1016/j.ijrmms.2010.11.014

    Article  Google Scholar 

  • Murrell SAF (1964) The theory of the propagation of elliptical Griffith cracks under various conditions of plane strain or plane stress: Part I. Br J Appl Phys 15:1195–1210. https://doi.org/10.1088/0508-3443/15/10/308

    Article  Google Scholar 

  • Papanastasiou PC, Vardoulakis IG (1989) Bifurcation analysis of deep boreholes: II. Scale effect. Int J Numer Anal Methods Geomech 13(2):183–198. https://doi.org/10.1002/nag.1610130206

    Article  Google Scholar 

  • Potyondy DO (2010) A grain-based model for rock: approaching the true microstructure. In: Proceedings of Rock Mechanics in the Nordic Countries, Kongsberg, Norway, 9–12 June, pp 225–234

  • Potyondy DO (2011) Parallel-bond refinements to match macroproperties of hard rock. Continuum and distinct element numerical modeling in geomechanics 2011. In: Proceedings of Second International FLAC/DEM Symposium, Melbourne, Australia, 14–16 February, pp 459–465

  • Potyondy DO (2012) A flat-jointed bonded-particle material for hard rock. In: Proceedings of the 46th US Rock Mechanics Symposium, Chicago, Illinois, 24–27 June

  • Potyondy DO (2012) PFC2D Flat-joint contact model. Technical memorandum ICG7138-L, 26 July

  • Potyondy DO (2013) PFC3D flat-joint contact model (version 1). Technical memorandum ICG7234-L, 25 June

  • Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Mining Sci 41(8):1329–1364. https://doi.org/10.1016/j.ijrmms.2004.09.011

    Article  Google Scholar 

  • Zhang X-P, 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 

Download references

Author information

Authors and Affiliations

  1. Tunnelling Laboratory, School of Mining and Metallurgical Engineering, National Technical University of Athens, 9 Iroon Polytechneiou str., Zografou, 15780, Athens, Greece

    Michail A. Lotidis, Pavlos P. Nomikos & Alexandros I. Sofianos

Authors
  1. Michail A. Lotidis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pavlos P. Nomikos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alexandros I. Sofianos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michail A. Lotidis.

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

Lotidis, M.A., Nomikos, P.P. & Sofianos, A.I. Numerical Study of the Fracturing Process in Marble and Plaster Hollow Plate Specimens Subjected to Uniaxial Compression. Rock Mech Rock Eng 52, 4361–4386 (2019). https://doi.org/10.1007/s00603-019-01884-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00603-019-01884-8

Keywords

Search

Navigation