Skip to main content

Advertisement

Log in

A Laboratory-Testing-Based Study on the Strength, Deformability, and Dilatancy of Carbonate Rocks at Low Confinement

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

Abstract

A servo-controlled testing setup was used to investigate the stress–strain behaviour of three carbonate rocks into the post-failure region. A series of uniaxial and triaxial tests on Indiana limestone, Carrara marble, and Toral de Los Vados limestone have been performed, gathering information on the evolution of the strength parameters and stiffness of these rocks, as well as on their post-yield dilatational properties. The Carrara marble was found to be extremely ductile, even under uniaxial conditions, whereas the Indiana limestone and Toral de Los Vados limestone were more brittle. The Indiana limestone, which was the weakest rock tested, showed a notable transition to more ductile failure modes, even at modest confinements on the order of 10 MPa; this transition was reflected in the volumetric strain evolution of the rock in the form of a transition of the dilation angle towards lower, less variable values. All of the rocks tested were found to be consistent with a cohesion-weakening-friction-strengthening model for yield, with the peak friction angle of both the Carrara marble and Indiana limestone being attained after peak strength. The evolution of stiffness was also considered as a function of accumulated plastic strain. Each rock decreased in stiffness significantly following the onset of yield, and eventually reached a near-constant residual stiffness on the order of 50 % of the initial elastic stiffness.

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.

Institutional subscriptions

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

Similar content being viewed by others

References

  • Alejano LR, Alonso E (2005) Considerations of the dilatancy angle in rocks and rock masses. Int J Rock Mech Min Sci 42:481–507

    Article  Google Scholar 

  • Alonso E, Alejano LR, Varas F, Fdez-Manin G, Carranza-Torres C (2003) Ground reaction curves for tunnels in strain-softening rock masses. Int J Numer Anal Meth Geomech 27:1153–1185

    Article  Google Scholar 

  • Archambault G, Roleau A, Daigneault R, Flamand R (1993) Progressive failure of rock masses by a self-similar anastomosing process of rupture at all scales and its scale effects on their shear strength. The Second International Workshop on Scale Effects in Rock Masses, Lisbon, pp 133–141

  • Arzúa J, Alejano LR (2013) Dilation in granite according to servo-controlled strength tests. Int J Rock Mech Min Sci 61:43–56

    Google Scholar 

  • Arzúa J, Alejano LR, Walton G (2014) Strength and dilation of jointed granite specimens in servo-controlled triaxial tests. Int J Rock Mech Min Sci 69:93–104

  • Besuelle P, Rudnicki JW (2004) Localization: Shear bands and compaction bands. Mechanics of fluid-saturated rocks. Elsevier, Boston, pp 219–321

    Google Scholar 

  • Brace WF, Paulding BW, Scholz C (1966) Dilatancy in the fracture of crystalline rocks. J Geophys Res 71(16):3939–3953

    Article  Google Scholar 

  • Cargill JS, Shakoor A (1990) Evaluation of empirical methods for measuring the uniaxial compressive strength of rock. Int J Rock Mech Min Sci Geomech Abstr 27(6):495–503

    Article  Google Scholar 

  • Chandler NA (2013) Quantifying long-term strength and rock damage properties from plots of shear strain versus volume strain. Int J Rock Mech Min Sci 59:105–110

    Google Scholar 

  • Cipullo A, White W, Lee IK (1985) Computer controlled volumetric strain measurements in metadolerite. Bull Eng Geol Environ 32(1):55–65

    Google Scholar 

  • Corkum AG, Lorig LJ, DeGagne DO (2012) Continuum representation of brittle rock failure bulking-induced displacements around tunnels. In: 46th ARMA Rock Mechanics/Geomechanis Symposium, Chicago, Illinois

  • Crouch SL (1970) Experimental determination of volumetric strain in failed rock. Int J Rock Mech Min Sci Geomech Abstr 7(4):231–241

    Google Scholar 

  • Diederichs MS (1999) Instability of hard rockmasses: the role of tensile damage and relaxation (Unpublished PhD). University of Waterloo, Waterloo

  • Diederichs MS (2003) Rock fracture and collapse under low confinement conditions. Rock Mech Rock Eng 36:339–381

    Article  Google Scholar 

  • Diederichs MS, Martin CD (2010) Measurement of spalling parameters from laboratory testing. In: Zhao, Labiouse, Dudt, Mathier (eds) Rock mechanics in civil and environmental engineering. Taylor & Francis Group, London

  • Diederichs MS, Kaiser PK, Eberhardt E (2004) Damage initiation and propagation in hard rock during tunnelling and the influence of near-face stress rotation. Int J Rock Mech Min Sci 41:785–812

    Article  Google Scholar 

  • Diederichs M, Damjanac B, Jensen M, Lam T, Martin D, McCreath D (2013) Ultra-long-term geomechanics design for a deep geological repository in sedimentary rock. In: 47th US Rock Mechanics/Geomechanics Symposium, San Francisco

  • Dunham RJ (1962) Classification of carbonate rocks according to depositional texture. Am Assoc Pet Geol Mem 1:108–121

    Google Scholar 

  • Edmond JM, Paterson MS (1972) Volume changes during the deformation of rocks at high pressures. Int J Rock Mech Min Sci 9:161–182

    Article  Google Scholar 

  • Elliot GM, Brown ET (1985) Yield of a soft, high porosity rock. Geotechnique 35(4):413–423

    Article  Google Scholar 

  • Farmer I (1983) Engineering behaviour of rocks, 2nd edn. Chapman and Hall, New York

    Book  Google Scholar 

  • Fredrich JT, Evans B, Wong T (1989) Micromechanics of the brittle to plastic transition in Carrara marble. J Geophys Res 94:4129–4145

    Article  Google Scholar 

  • Fredrich JT, Evans B, Wong T (1990) Effect of grain size on brittle and semibrittle strength: implications for micromechanical modelling of failure in compression. J Geophys Res 95:10907–10920

    Article  Google Scholar 

  • Griggs DT, Turner FJ, Heard HC (1960) Deformation of rocks at 500 to 800 degrees C. Geol Soc Am Mem 79:39–104

    Article  Google Scholar 

  • Hajiabdolmajid V, Kaiser PK, Martin CD (2002) Modelling brittle failure of rock. Int J Rock Mech Min Sci 39:431–741

    Article  Google Scholar 

  • Hart DJ, Wang HF (1995) Laboratory measurements of a complete set of poroelastic moduli for Berea sandstone and Indiana limestone. J Geophys Res 100:17741–17751

    Article  Google Scholar 

  • Hill JR (2013) Indiana limestone. Retrieved 08/01/2013 from http://igs.indiana.edu/MineralResources/Limestone.cfm

  • Hoagland RG, Hahn GT, Rosenfield AR (1973) Influence of microstructure on fracture propagation in rock. Rock Mech 5:77–106

    Article  Google Scholar 

  • Hoek E, Carranza-Torres C, Corkum B (2002) Hoek-brown failure criterion—2002 edition. N Am Rock Mech Soc Meet:267–273

  • Howarth DF, Rowlands JC (1987) Quantitative assessment of rock texture and correlation with drillability and strength properties. Rock Mech Rock Eng 20:57–85

    Article  Google Scholar 

  • Hudson JA, Brown ET, Fairhurst C (1971) Optimizing the control of rock failure in servo-controlled laboratory tests. Rock Mech 3(4):217–224

    Article  Google Scholar 

  • Itasca Consulting Group (2011) FLAC Version 7.0—theory and Background (5th edn), Minneapolis, Minnesota

  • Ji Y, Baud P, Wong T (2012) Characterization of pore geometry of indiana limestone in relation to mechanical compaction. Oil Gas Sci Technol 67(5):753–775

    Article  Google Scholar 

  • Labuz JF, Biolzi L (1991) Class I vs. class II stability: a demonstration of size effect. Int J Rock Mech Min Sci 28:199–205

    Article  Google Scholar 

  • Lajtai EZ (1998) Microscopic fracture processes in a granite. Rock Mech Rock Eng 31(4):237–250

    Article  Google Scholar 

  • Loew S, Ziegler H, Keller F (2000) ALPTRANSIT: Engineering geology of the world’s longest tunnel system. In: GeoEng2000, an International Conference on Geotechnical and Geological Engineering, Melbourne, vol 1, pp 927–937

  • Martin CD (1997) Seventeenth Canadian geotechnical colloquium: the effect of cohesion loss and stress path on brittle rock strength. Can Geotech J 34:698–725

    Article  Google Scholar 

  • Martin CD, Chandler NA (1994) The progressive fracture of lac du bonnet granite. Int J Rock Mech Min Sci Geomech Abstr 31:643–659

    Article  Google Scholar 

  • Medhurst TP (1996) Estimation of the in situ and deformability of coal for engineering design, Ph.D. Thesis, University of Queensland

  • Medhurst TP, Brown ET (1998) A study of the mechanical behaviour of coal for pillar design. Int J Rock Mech Min Sci 35(8):1087–1105

    Article  Google Scholar 

  • Mogi K (1966) Pressure dependence of rock strength and transition from brittle fracture to ductile flow. Bull Earthq Res Inst 44:215–232

    Google Scholar 

  • Nuclear Waste Management Organization (NWMO) (2013) About the DGR. Retrieved 08/01/2013, from http://www.nwmo.ca/dgr

  • Olsson WA (1974) Grain size dependence of yield stress in marble. J Geophys Res 79(32):4859–4862

    Article  Google Scholar 

  • Ord A (1991) Deformation of rock: a pressure-sensitive, dilatant material. Pure appl Geophys 137:337–366

    Article  Google Scholar 

  • Peck L, Barton CC, Gordon RB (1985) Microstructure and the resistance of rock to tensile fracture. J Geophys Res 90:1533–1546

    Google Scholar 

  • Price AM, Farmer IW (1979) Application of yield models to rock. Int J Rock Mech Min Sci Geomech Abstr 16:157–159

    Article  Google Scholar 

  • Ramamurthy T (2001) Shear strength response of some geological materials in triaxial compression. Int J Rock Mech Min Sci 38:683–697

    Article  Google Scholar 

  • Read HE, Hegemeier GA (1984) Strain softening of rock, soil and concrete—a review article. Mech Materials 3:271–294

    Article  Google Scholar 

  • Riedel JJ, Labuz JF (2007) Propagation of a shear band in sandstone. Int J Numer Anal Meth Geomech 31:1281–1299

    Article  Google Scholar 

  • Robinson RH (1959) The effect of pore and confining pressure on the failure process in sedimentary rocks. Colorado Sch Mines Q 54:177–199

    Google Scholar 

  • Rummel F, Fairhurst C (1970) Determination of the post-failure behaviour of brittle rock using a servo-controlled testing machine. Rock Mech Rock Eng 2(4):189–204

    Article  Google Scholar 

  • Schmertmann JH, Osterberg JO (1960) An experimental study of the development of cohesion and friction with axial strain in saturated cohesive soils. In: Research Conference on Shear Strength of Cohesive Soils, Boulder, CO, pp 643–694

  • Schmidt RA, Huddle CW (1977) Effect of confining pressure on fracture toughness of indiana limestone. Int J Rock Mech Min Sci Geomech Abstr 14:289–293

    Article  Google Scholar 

  • Singh AB (1997) Study of rock fracture by permeability method. J Geotech Geoenviron Eng 123(7):601–608

    Article  Google Scholar 

  • Sture S, Ko HY (1978) Strain-softening of brittle geologic materials. Int J Numer Anal Meth Geomech 2:237–253

    Article  Google Scholar 

  • Turner FJ, Griggs DT, Heard HC (1954) Experimental deformation of calcite crystals. Geol Soc Am Bull 65:883–934

    Article  Google Scholar 

  • Vajdova V, Baud P, Wong T (2004) Compaction, dilatancy, and failure in porous carbonate rocks. J Geophys Res 109

  • Varas F, Alonso E, Alejano LR, Fdez.-Manin G (2005) Study of bifurcation in the problem of unloading a circular excavation in a strain-softening material. Tunn Undergr Space Technol 20:311–322

    Article  Google Scholar 

  • Vardoulakis I, Sulem J (1995) Birfurcation analysis in geomechanics. Blackie, Glasgow

    Google Scholar 

  • Vermeer PA, de Borst R (1984) Non-associated plasticity for soils, concrete, and rock. Heron 29(3)

  • Walton G, Diederichs MS, Arzúa J (2014) A detailed look at pre-peak dilatancy in a granite—determining “plastic” strains from laboratory test data. Eurock 2014, Vigo, Spain

  • Wawersik WR (1975) Technique and apparatus for strain measurements on rock in constant confining pressure experiments. Rock Mech 7(4):231–241

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Wawersik WR, Fairhurst C (1970) A study of brittle rock fracture in laboratory compression experiments. Int J Rock Mech Min Sci 7(5):561–564

    Article  Google Scholar 

  • Zhao XG, Cai M (2010) A mobilized dilation angle model for rocks. Int J Rock Mech Min Sci 47:368–384

    Article  Google Scholar 

  • Zhao XG, Cai M, Cai M (2010) Considerations of rock dilation on modeling failure and deformation of hard rocks—a case study of the mine-by test tunnel in Canada. J Rock Mech Geotech Eng 2:338–349

    Google Scholar 

  • Zheng Z, Cook NGW, Myer LR (1989) Stress induced microcrack geometry at failure in unconfined and confined axial compressive tests. US Rock Mech Symp 30:749–756

    Google Scholar 

Download references

Acknowledgments

The authors would like to acknowledge the significant contributions of the Natural Resources Canada CANMET laboratory in Ottawa in preparing the Indiana Limestone samples for testing. We would also like to thank the Nuclear Waste Management Organization of Canada and the Spanish Ministry of Science and Technology for their financial support, without which this work would not have been possible.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to L. R. Alejano.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Walton, G., Arzúa, J., Alejano, L.R. et al. A Laboratory-Testing-Based Study on the Strength, Deformability, and Dilatancy of Carbonate Rocks at Low Confinement. Rock Mech Rock Eng 48, 941–958 (2015). https://doi.org/10.1007/s00603-014-0631-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00603-014-0631-8

Keywords

Navigation