Abstract
The mechanical behavior of low porosity carbonate rocks is investigated by a series of conventional triaxial compression tests performed at room temperature, at various confining pressures up to 70 MPa and at a constant strain rate of 5 × 10 −5 s−1. Aiming at an improvement of the accuracy and quality of the constant mi of the non-linear Hoek–Brown criterion for jointed rock, four dense, high strength and low-porosity carbonate rocks were tested in conventional triaxial testing, under confining pressures over the entire brittle field, from σ3 = 0 to the brittle-ductile transition. Intact, fresh and dry specimens from limestones and two marbles were tested using a standard NX Hoek triaxial cell. The results indicate that the average brittle-ductile transition pressure and the value of mi determined by the experimental data over the entire brittle field, were approximately twice as high for limestones as for marbles. With the inclusion of the results from five well-known carbonate rocks published by other researchers, it was found that, for the total number of nine carbonate rocks, the ratio of the critical principal stress ratio at the transition (σ1/σ3) was equal to 5.84 irrespective of rock type, transition pressure, grain size, and mi value. Moreover, the transition pressure decreases logarithmically with the average rock grain size and the ratio of the transition pressure to the unconfined compressive strength σci.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Baud P, Schubnel A, Wong T-f (2000) Dilatancy, compaction and failure mode in Solnhofen limestone. J Geophys Res 105:19289–19303. https://doi.org/10.1029/2000JB900133
Bernabe Y, Brace WF (1990) Deformation and fracture of Berea sandstone: the brittle/ductile transition in rocks: American Geophysical Union. Geophys Monographs 56:91–101
Besuelle P, Desrues J, Raynaud S (2000) Experimental characterisation of the localisation phenomenon inside a vosges sandstone in a triaxial cell. Int J Rock Mech Min Sci 37(8):1223–1237
Bewick RP, Kaiser PK, Valley B (2011) Interpretation of triaxial testing data for estimation of the hoek-brown strength parameter mi. Paper ARMA 11–347. 45th US Rock Mechanics/Geomechanics Symposium, San Francisco, CA, June 26–29, 2011
Brace WF (1964) Brittle fracture of rocks. In: Judd WR (ed) State of stress in the earth’s crust. American Elsevier, New York, pp 111–80
Brantut N, Heap MJ, Baud P, Meredith PG (2014) Mechanisms of time-dependent deformation in porous limestone. J Geophys Res: Solid Earth 119(7):5444–5463. https://doi.org/10.1002/2014JB011186
Byerlee JD (1968) The brittle-ductile transition in rock. J Geophys Res 73:4741–4750. https://doi.org/10.1029/JB073i014p04741
Cai M (2010) Practical estimates of tensile strength and hoek-brown strength parameter mi of brittle rocks. Rock Mech Rock Eng 43:167–184. https://doi.org/10.1007/s00603-009-0053-1
Carter TG, JL Carvalho (2020) Suggested Tensile Test Data Interpretation for Estimating Hoek-Brown mi. Paper presented at the 54th U.S. Rock Mechanics/Geomechanics Symposium, physical event cancelled, June 2020
Carter TG (2019) A Suggested Visual Approach for estimating Hoek-Brown mi for Different Rock Types.14th ISRM Congr. on Rock Mech. & Rock Eng'rg, Sept. 13–18, 2019, Foz do Iguassu, Brazil, ISBN 978–0–367–42284–4 Paper#14356, 13pp
Carter TG (2021) Towards improved definition of the hoek-brown constant mi for numerical modelling, Rocscience International Conference 2021
Carter TG, Marinos V (2020) Putting geological focus back into rock engineering design. Rock Mech Rock Eng 53:4487–4508. https://doi.org/10.1007/s00603-020-02177-1
David C, Menendez B, Zhu W, Wong T-F (2001) Mechanical compaction, microstructures and permeability evolution in sandstones. Phys Chem Earth (A) 26:45–51. https://doi.org/10.1016/S1464-1895(01)00021-7
Dunham RJ (1962) Classification of carbonate rocks according to depositional texture. Amer Assoc Petrol Geol Mem 1:108–121
Fredrich JT, Evans B, Wong TF (1989) Micromechanics of the brittle to plastic transition in carrara marble. J Geophys Res 94:4129–4145. https://doi.org/10.1029/JB094iB04p04129
Fredrich JT, Evans B, Wong TF (1990) Effect of grain size on brittle and semibrittle strength: Implications for micromechanical modelling of failure in compression. J Geophys Res 95(B7):10907–10920. https://doi.org/10.1029/JB095iB07p10907
Friedman M, Logan JM (1973) Lüders’ bands in experimentally deformed sandstone and limestone. GSA Bull 84(4):1465–1476. https://doi.org/10.1130/0016-7606(1973)84%3c1465:LBIEDS%3e2.0.CO;2
Folk RL (1959) Practical petrographic classification of limestones. Amer Assoc Petrol Geol Bull 43:1–38. https://doi.org/10.1306/0BDA5C36-16BD-11D7-8645000102C1865D
Garland J, Neilson J, Laubach SE, Whidden KJ (2012) Advances in carbonate exploration and reservoir analysis. Geol Soc, London, Spec Publ 370:1–15. https://doi.org/10.1144/SP370.15
Gerogiannopoulos NG (1977) A critical state approach to rock mechanics. Ph.D. thesis, Imperial College London. http://hdl.handle.net/10044/1/7741
Hadizadeh J, Rutter EH (1983) The low temperature brittle-ductile transition in a quartzite and the occurrence of cataclastic flow in nature. Geol Rundsch 72:493–509. https://doi.org/10.1007/BF01822079
Heard ΗC (1960) Transition from brittle fracture to ductile flow in solenhofen limestone as a function of temperature, confining pressure and interstitial fluid pressure, in Rock Deformation, edited by D.T Griggs and J.Handin, Mem. Geol. Soc. Am., 79, 193-226
Hoek E (1983) Strength of jointed rock masses twenty-third rankine lecture. Géotechnique33 3:185–244. https://doi.org/10.1680/geot.1983.33.3.187
Hoek, E. (2007) Practical rock engineering. http://www.rocscience.com
Hoek E, Brown ET (1980a) Underground Excavations in Rock, p. 527. London, Inst. Min. Metall
Hoek E, Brown ET (1980) Empirical strength criterion for rock masses. J Geotech Eng Div Proc Am Soc Civil Engrs 106(GT9):1013–1035. https://doi.org/10.1061/AJGEB6.0001029
Hoek E, Brown ET (1997) Practical estimates of rock mass strength. Int J Rock Mech Min 34(8):1165–1186. https://doi.org/10.1016/S1365-1609(97)80069-X
Hoek E, Brown ET (2019) The hoek-brown failure criterion and GSI –2018 edition. J Rock Mech Geotech Eng 11:445–463. https://doi.org/10.1016/j.jrmge.2018.08.001
Hoek E, Franklin JA (1968) A simple triaxial cell for field and laboratory testing of rock. Trans Instn Min Metall 77:A22-26
Hoek E, Martin CD (2014) Fracture initiation and propagation in intact rock - a review. J Rock Mech Geotech Eng 6(4):278–300. https://doi.org/10.1016/j.jrmge.2014.06.001
Hoek E, Wood D, Shah S (1992) A modified Hoek–Brown criterion for jointed rock masses. Rock Characterization, Proceedings ISRM Symposium, Eurock ’92, Hudson (editor), British Geotechnical Society, London, pp. 209–214
Hugman RHH, Friedman M (1979) Effects of texture and composition on mechanical behavior of experimentally deformed carbonate rocks. Am Assoc Pet Geol Bull 63:1478–1489. https://doi.org/10.1306/2F9185C7-16CE-11D7-8645000102C1865D
ISRM (2012). Suggested methods for rock failure criteria. Rock Mech Rock Eng 45(6) 971–1022
Jaeger JC, Cook NGW (1979) Fundamentals of rock mechanics, 3rd edn. Chapman & Hall, London
Lebedev M, Zhang Y, Sarmadivaleh M, Barifcani A, Al-Khdheeawi E, Iglauer S (2017) Carbon geosequestration in limestone: Pore-scale dissolution and geomechanical weakening. Int J Greenhouse Gas Control 66:106–119
Liu Z, Shao J (2017) Strength behavior, creep failure and permeability change of a tight marble under baud triaxial compression. Rock Mech Rock Eng 50:529–541. https://doi.org/10.1007/s00603-016-1134-6
Maher SW, Walters JP (1960) The marble industry of tennessee: tennessee division of geology. Inf Circ 9:25
Mair K, Elphick SC, Main IG (2002) Influence of confining pressure on the mechanical and structural evolution of laboratory deformation band. Geophys Res Lett. https://doi.org/10.1029/2001GL013964
Marinos P, E Hoek (2000) GSI: A Geologically Friendly Tool for Rock Mass Strength Estimation. In Proceedings of International Conference on Geotechnical & Geological Engineering (GeoEng 2000), Technomic publ., 1422–1442, Melbourne
Mogi K (1966) Pressure dependence of rock strength and transition from brittle fracture to ductile flow. Bull Earthq Res Inst 44:215–232
Mogi K (2007) Experimental rock mechanics. Taylor and Francis, London, UK
Murell SAF (1965) The effect of triaxial stress systems on the strength of rocks at atmospheric temperatures. Geophys J Roy Astron Soc 10(3):231–281. https://doi.org/10.1111/j.1365-246X.1965.tb03155.x
Paterson MS, Wong T.-F (2005) Experimental Rock Deformation – The Brittle Field, 2nd ed. 348 pp
Regnet JB, David C, Robion P, Menéndez B (2019) Microstructures and physical properties in carbonate rocks: a comprehensive review. Mar Pet Geol 103:366–376. https://doi.org/10.1016/j.marpetgeo.2019.02.022
Renner J, F Rummel (1996) The effect of experimental and microstructural parameters on the transition from brittle failure to cataclastic flow of carbonate rocks, Tectonophysics 258:151–169. https://doi.org/10.1016/0040-1951(95)00192-1
Richards LR, Read, SAL (2011) A comparison of methods for determining mi the Hoek-Brown parameter for intact rock material. In Proceedings 45th US Rock Mechs / Geomechanics Symposium, San Francisco, USA, 26-29 June 2011, eds. A. Iannacchione et al., Paper ARMA / USRMS 11-246
Rocscience (2015) RocData, version 5.0, Rocscience Inc, Toronto, www.rocscience.com
Sabatakakis N, Tsiambaos G, Ktena S, Bouboukas S (2018) The effect of microstructure on mi strength parameter variation of common rock types. Bull Eng Geol Environ 77(4):1673–1688. https://doi.org/10.1007/s10064-017-1059-7
Schlumberger (2019) Technical challenges-carbonate reservoirs. https://www.slb.com/technical-challenges/carbonates. Accessed 11 April 2021
Sharma G, Mohanty KK (2013) Wettability alteration in high-temperature and high-salinity carbonate reservoirs. SPE J 18:646–655. https://doi.org/10.2118/147306-PA
Shimada M, Cho A, Yukutake H (1983) Fracture strength of dry silicate rocks at high confining pressures and activity of acoustic emission. Tectonophysics 96:159–172. https://doi.org/10.1016/0040-1951(83)90248-2
Vajdova V, Baud P, Wu L, Wong TF (2012) Micromechanics of inelastic compaction in two allochemical limestones. J Struct Geol 43:100–117. https://doi.org/10.1016/j.jsg.2012.07.006
Walton G, Arzúa J, Alejano LR et al (2015) A laboratory-testing-based study on the strength, deformability, and dilatancy of carbonate rocks at low confinement. Rock Mech Rock Eng 48:941–958. https://doi.org/10.1007/s00603-014-0631-8
Walton G, Hedayat A, Kim E, Labrie D (2017) Post-yield strength and dilatancy evolution across the brittle–ductile transition in Indiana limestone Rock Mech Rock Eng 50(7):1691–1710
Wawersik WR, Fairhurst C (1970) A study of brittle rock fracture in laboratory compression experiments. Int J Rock Mech Min Sci Geomech Abstr 7(5):561–575. https://doi.org/10.1016/0148-9062(70)90007-0
Wong T-f, Baud P, Klein E (2001) Localized failure modes in a compactant porous rock. Geophys Res Lett 28:2521–2524. https://doi.org/10.1029/2001GL012960
Wong T-F, Baud P (2012) The brittle-ductile transition in porous rock: a review. J Struct Geol 44:25–53. https://doi.org/10.1016/j.jsg.2012.07.010
Wong TF, David C, Zhu WC (1997) The transition from brittle faulting to cataclastic flow in porous sandstones: mechanical deformation. J Geophys Res 102(B2):3009–3025. https://doi.org/10.1029/96JB03281
Xeidakis GS, Samaras IS (1996) A contribution to the study of some greek marbles. Bull Int Assoc Eng Geol 53:121. https://doi.org/10.1007/BF02594948
Zhang CS, Chu WJ, Liu N, Zhu YS, 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
ZhangY M, Lebedev A, Al-Yaseri H, Yu LN, Nwidee M, Sarmadivaleh A, Barifcani SI (2018) Morphological evaluation of heterogeneous oolitic limestone under pressure and fluid flow using x-ray microtomography. J Appl Geophys 150:172–181. https://doi.org/10.1016/j.jappgeo.2018.01.026
Zhu W, Baud P, Wong TF (2010) Micromechanics of cataclastic pore collapse in limestone. J Geophys Res 115:B04405. https://doi.org/10.1029/2009JB006610
Zhu GQ, Feng XT, Zhou YY et al (2019) Experimental study to design an analog material for jinping marble with high strength, high brittleness and high unit weight and ductility. Rock Mech Rock Eng 52:2279–2292. https://doi.org/10.1007/s00603-018-1710-z
Zuo JP, Liu H, Li H (2015) A theoretical derivation of the Hoek-Brown failure criterion for rock materials. J Rock Mech Geotech Eng 7(4):361–366. https://doi.org/10.1016/j.jrmge.2015.03.008
Acknowledgements
This research is co-financed by Greece and the European Union (European Social Fund- ESF) through the Operational Programme «Human Resources Development, Education and Lifelong Learning» in the context of the project “Strengthening Human Resources Research Potential via Doctorate Research” (MIS-5000432), implemented by the State Scholarships Foundation (ΙΚΥ).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors 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
About this article
Cite this article
Tsikrikis, A., Papaliangas, T. & Marinos, V. Brittle-Ductile Transition and Hoek–Brown mi Constant of Low-Porosity Carbonate Rocks. Geotech Geol Eng 40, 1833–1849 (2022). https://doi.org/10.1007/s10706-021-01995-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10706-021-01995-6