Hoek–Brown Strength Criterion for Actively Confined Concrete
Publication: Journal of Materials in Civil Engineering
Volume 21, Issue 3
Abstract
The application of the Hoek–Brown empirical strength criterion to actively confined concrete is investigated. A large database of experimental results on hydraulically and triaxially confined concrete is reviewed and analyzed. The normalized two-parameter Hoek–Brown criterion provides a simpler and more robust fit than theoretical and empirical models previously proposed in the literature for actively confined concrete. The Hoek–Brown curved failure surface is used to predict the failure angles that are experimentally observed in the brittle mode. A residual stress lower bound is proposed based on the brittle fracture mechanism. The analysis of this residual stress lower bound allows the formal identification of the transition between the brittle and the ductile failure modes in confined concrete. The modeling results are compared with the available published data and good agreement is found between the experimental observations and the predictions of the model. Recommendations for the integration of the Hoek–Brown model in the concrete design equations are also provided.
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Acknowledgments
The writers wish to acknowledge the support of the Research Council at the Lebanese American University.
References
Abercombie, R. E., and Rice, J. R. (2005). “Can observations of earthquake scaling constrain slip weakening.” Geophys. J. Int., 162(2), 406–424.
Ansari, F., and Li, Q. (1998). “High-strength concrete subjected to triaxial compression.” ACI Mater. J., 95(6), 747–755.
Balan, T. A., Spacone, E., and Kwon, M. (2001). “A 3D hypoplastic model for cyclic analysis of concrete structures.” Eng. Struct., 23(4), 333–342.
Balmer, G. G. (1949). “Shearing strength of concrete under high triaxial stress-computation of Mohr’s envelope as a curve.” Structural Research Laboratory Rep. No. SP-23, U.S. Bureau of Reclamation, Denver.
Bellotti, R., and Rossi, P. (1991). “Cylinder tests: Experimental technique and results.” Mater. Struct., 24(1), 45–51.
Benz, T., Schwab, R., Kauther, R. A., and Vermeer, P. A. (2008). “A Hoek-Brown criterion with intrinsic material strength factorization.” Int. J. Rock Mech. Min. Sci., 45(2), 210–222.
Biggoni, D., and Piccolroaz, A. (2004). “Yield criteria for quasibrittle and frictional materials.” Int. J. Solids Struct., 41(11–12), 2855–2878.
Böker, R. (1915). “Die Mechanik der bleibenden Formänderung in Kristallinisch aufgebauten Körpern.” Mitteinlungen über Forschungsarbeiten auf dem Gebiete Des Ingenieurwesens, Vol. 175, Association of German Engineers, Berlin, 1–51 .
Candappa, D. C., Sanjayan, J. G., and Setunge, S. (2001). “Complete triaxial stress-strain curves of high-strength concrete.” J. Mater. Civ. Eng., 13(3), 209–215.
Considère, A. (1902a). “Etude théorique de la résistance à la compression du Béton Fretté.” Comptes Rendus de l’Académite des Sciences, Vol. 25, Académie des Sciences, Paris, 365–368.
Considère, A. (1902b). “Résistance à la compression du Béton Armé et du Béton Fretté.” Le génie civil [Experimental researches on reinforced concrete], L. S. Moisseiff, translator, McGraw-Hill, New York.
Edelbro, C. (2003). “Rock mass strength, A review.” Technical Rep., Dept. of Civil Engineering, Div. of Rock Mechanics, Lulea Univ. of Technology, Lulea, Sweden.
Elwi, A. A., and Murray, D. W. (1979). “A 3D hypoelastic concrete constitutive relationship.” J. Engrg. Mech. Div., 105(4), 623–642.
Etse, G., and Willam, K. (1994). “Fracture energy formulation for inelastic behavior of plain concrete.” J. Eng. Mech., 120(9), 1983–2009.
Fujikake, K., Mindess, S., and Xu, H. (2004). “Analytical model for concrete confined with fiber reinforced polymer composite.” J. Compos. Constr., 8(4), 341–351.
Gabet, T., Malecot, Y., and Daudeville, L. (2006). “Ultimate strength of plain concrete under extreme combined stresses: Triaxial and proportional stress paths.” Revue Européenne de Génie Civil [European J. Environmental and Civil Engineering], 10(3), 1–15.
Gardner, N. (1969). “Triaxial behavior of concrete.” ACI J., 66(15), 136–146.
Goodman, R. E. (1989). Introduction to rock mechanics, 2nd Ed., Wiley, New York.
Gould, N. C., and Harmon, T. G. (2000). “Design limit states for composite-confined concrete columns.” Proc., Symp. on Engineering Mechanics, ASCE, Reston, Va.
Hammons, M. I., and Neeley, B. D. (1993). “Triaxial characterization of high-strength Portland cement concrete.” Transportation Research Record. 1382, Transportation Research Board, Washington, D.C., 73–77.
Harmon, T. G., Ramakrishnan, S., and Wang, E. H. (1998). “Confined concrete subjected to uniaxioal monotonic loading.” J. Eng. Mech., 124(12), 1303–1309.
Hoek, E. (1983). “Strength of jointed rock masses.” Geotechnique, 33(3), 187–223.
Hoek, E., and Brown, E. T. (1980). “Empirical strength criterion for rock masses.” J. Geotech. Engrg. Div., 109(9), 1013–1035.
Hoek, E., and Brown, E. T. (1997). “Practical estimates of rock mass strength.” Int. J. Rock Mech. Min. Sci., 34(8), 1165–1186.
Hoek, E., Caranza-Torres, C. T., and Corkum, B. (2002). “Hoek-Brown failure criterion-2002 edition.” Proc., North American Rock Mechanics Society (NARMS-TAC 2002), H. R. W. Bawden, J. Curran, and M. Telsenicki, eds., Mining Innovation and Technology, Toronto, 267–273, ⟨www.rocscience.com⟩.
Hoek, E., and Franklin, J. A. (1968). “Simple triaxial cell for field or laboratory testing of rock.” Trans. Inst. Min. Metall., Sect. C, 77, A22–A26.
Imran, I., and Pantazopoulou, S. J. (1996). “Experimental study of plain concrete under triaxial stress.” ACI Mater. J., 93(6), 589–601.
Jaeger, J. C. (1960). “Shear failure of anisotropic rocks.” Geol. Mag., 97(1), 65–72.
Jamet, P., Millard, A., and Nahas, G. (1984). “Triaxial behaviour of a micro-concrete complete stress-strain curves for confining pressures ranging from .” Proc., RILEM-CEB Symp. Concrete under Multiaxial Conditions, Vol. 1, INSA, Toulouse, France, 1227–1241.
Kotsovos, M. D. (1979). “A mathematical description of the strength properties of concrete under generalized stress.” Mag. Concrete Res., 31(8), 151–158.
Lahlou, K., Aitcin, P. C., and Chaallal, O. (1992). “Behavior of high-strength concrete under confined stresses.” Cem. Concr. Compos., 14(3), 185–193.
Mander, J. B., Priestley, M. J. N., and Park, R. (1988). “Theoretical stress-strain model for confined concrete.” J. Struct. Eng., 114(8), 1804–1826.
Matlab. (2002). The language of technical computing, version 6.5, The MathWorks Inc., Natick, Mass., ⟨http://www.mathworks.com/⟩.
McLamore, R., and Gray, K. E. (1967). “The mechanical behavior of anisotropic sedimentary rocks.” J. Eng. Ind., 89(B), 62–76.
Mills, L. L., and Zimmerman, R. M. (1970). “Compressive strength of plain concrete under multiaxial loading conditions.” ACI J., 67(10), 802–807.
Mogi, K. (1966). “Pressure dependence of rock strength and transition from brittle fracture to ductile flow.” Bull. Earthquake Res. Inst., Univ. Tokyo, 44, 215–232.
Montoya, E., Vecchio, F. J., and Sheikh, S. A. (2006). “Compression field modeling of confined concrete: Constitutive models.” J. Mater. Civ. Eng., 18(4), 510–517.
Newman, J. B. (1979). Concrete under complex stress. Developments in technology I, E. F. Lydon, ed., Applied Science Publishers Ltd., London.
Orowan, E. (1960). “Mechanism of seismic faulting.” Rock deformation: Geological Society of America Memoir 79, D. Griggs and J. Handin, eds., The Geological Society of America, Boulder, Colo., 323–345.
Ottosen, N. S. (1977). “A failure criterion of concrete.” J. Engrg. Mech. Div., 103(4), 527–535.
Pantazopoulou, S. J., and Mills, R. H. (1995). “Microstructural aspects of the mechanical response of plain concrete.” ACI Mater. J., 92(6), 605–616.
Pramono, E., and Willam, K. (1989). “Fracture energy-based plasticity formulation of plain concrete.” J. Eng. Mech., 115(6), 1183–1203.
Rice, J. R. (1980). “The mechanics of earthquake rupture.” Physics of the earth’s interior, Proc., Int. School of Physics “E. Fermi,” Course 78, 1979, A. M. Dziewonski and E. Boschi, eds., Italcam Physical Society/North Holland, Amsterdam, The Netherlands.
Richart, F. E., Brandtzaeg, A., and Brown, R. L. (1928). “A study of the failure of concrete under combined compressive stresses.” Engineering Experiment Station Bulletin No., 128, Univ. of Illinois, Urbana, Ill., 6–102.
Romano, M. (1969). “On Leon’s criteria.” Meccanica, 4(1), 48–66.
Rutland, C., and Wang, M. L. (1997). “The effects of confinement on the failure orientation in cementitious materials experimental observations.” Cem. Concr. Compos., 19(2), 149–160.
Schickert, G., and Winkler, H. (1977). “Results of tests concerning strength and strain of concrete subjected to multiaxial compressive stresses.” Deutscher Ausschuss für Stahlbeton (German Committee for Reinforced Concrete), Issue 277, Ernst & Sohn, Berlin.
Schwartz, A. E. (1964). “Failure of rock in the triaxial shear test.” Proc., 6th Symp. on Rock Mechanics, University of Missouri at Rolla Press, Rolla, Mo., 109–151.
Seow, P. E. C., and Swaddiwudhipong, S. (2005). “Failure surface for concrete under multiaxial load—A unified approach.” J. Mater. Civ. Eng., 17(2), 219–228.
Setunge, S., Attard, M. M., and Darvall, P. (1992). “Ultimate strength criterion for very high-strength concrete subjected to triaxial loadings.” Research Rep. No. 1/92, Dept. of Civil Engineering, Monash Univ., Victoria 3800, Australia.
Setunge, S., Attard, M. M., and Darvall, P. (1993). “Ultimate strength of confined very high-strength concrete.” ACI Struct. J., 90(6), 632–641.
Sfer, D., Carol, I., Gettu, R., and Etse, G. (2002). “Study of the behavior of concrete under triaxial compression.” J. Eng. Mech., 128(2), 156–163.
Smith, S. S., Kaspar, J. W., Gerstle, K. H., and Sture, S. (1989). “Concrete over the top, or: Is there life after peak?.” ACI Mater. J., 86(5), 491–497.
Sture, S., and Ko, H. Y. (1978). “Strain-softening of brittle geologic materials.” Int. J. Numer. Analyt. Meth. Geomech., 2(3), 237–253.
Tabbara, M. R., and Karam, G. N. (2007). “Modeling the strength of concrete cylinders confined with FRP wraps using the Hoek-Brown strength criterion.” Proc., 8th Int. Symp. on Fiber Reinforced Polymer Reinforcement for Concrete Structures, FRPRCS-8, University of Patras Press, Patras, Greece.
Terzaghi, K. (1945). “Stress conditions for the failure of saturated concrete and rocks.” American Society for Testing and Materials Proc., Vol. 45, and Harvard Soil Mechanics Series, 27, ASTM, Philadelphia, 777–801.
Torrenti, J. M. (1986). “Some remarks upon concrete softening.” Mater. Struct., 19(113), 391–394.
Torrenti, J. M., Desrues, J., Benaija, E. H., and Boulay, C. (1991). “Stereophotogrammetry and localization in concrete under compression.” J. Eng. Mech., 117(7), 1455–1465.
Ucar, R. (1986). “Determination of shear failure envelope in rock masses.” J. Geotech. Engrg., 112(3), 303–315.
Van Geel, E. (1998). “Concrete behaviour in multiaxial compression: Experimental research.” Bouwstenen Nr. 48, Technische Universiteit Eindhoven, Faculteit Bouwkunde Publisher, Eindhoven, The Netherlands.
Van Mier, J. G. M., and Vonk, R. A. (1991). “Fracture of concrete under multiaxial stress—Recent developments.” Mater. Struct., 24(1), 61–65.
Von Kármán, T. (1911). “Festigkeitsversuhe unter allseitigem Druck.” Zeitschrift des Vereines Deutscher Ingenieure, Vol. 55, Association of German Engineers, 1749–1757.
Willam, K. J., and Warnke, E. P. (1974). “Constitutive model for the triaxial behaviour of concrete.” Proc., Seminar on Concrete Structures Subjected to Triaxial Stresses, ISMES, Bergamo, Italy.
Xie, J., Elwi, A. E., and MacGregor, J. C. (1995). “Mechanical properties of three high-strength concretes containing silica fume.” ACI Mater. J., 92(2), 135–145.
Yu, M. H. (2002). “Advances in strength theories for materials under complex stress state in the 20th century.” Appl. Mech. Rev., 55(3), 169–218.
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Published In
Journal of Materials in Civil Engineering
Volume 21 • Issue 3 • March 2009
Pages: 110 - 118
Copyright
© 2009 ASCE.
History
Received: Apr 20, 2007
Accepted: Oct 15, 2008
Published online: Mar 1, 2009
Published in print: Mar 2009
Notes
Note. Associate Editor: Zhishen Wu
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