Simplified Analytical Model for Interfacial Bond Strength of Deformed Steel Rebars Embedded in Pre-cracked Concrete
Publication: Journal of Structural Engineering
Volume 146, Issue 8
Abstract
Although extensive bond models have been developed for use in the numerical simulation of uncracked reinforced concrete, no simplified method exists providing satisfactory accuracy and efficiency for pre-cracked concrete. This paper intends, therefore, to explain bond failure mechanisms in pre-cracked concrete—as compared to intact concrete—using a simplified theoretical model. The main bond failure mechanisms considered in this study involve: (1) crushing a wedge-shaped concrete block using reinforcing bar ribs, and (2) tearing off the concrete between two adjacent ribs. Based on these scenarios, analytical expressions are derived to predict the average bond strength for uncracked concrete, in which the bearing angle, the rib face angle, the rib height, the rib spacing, and the friction coefficient between surfaces are the key parameters. A modified version of this model is proposed to predict the maximum bond strength of rebars embedded in pre-cracked concrete by introducing a reduction factor of surrounding confinement caused by the pre-cracking phenomenon. An experimental program was also conducted to validate the proposed models. Experimental results emphasize the crucial impact of the pre-cracking phenomenon on both the bond strength and the failure pattern. Analysis results show that the bearing angle and surrounding confinement by concrete cover are crucial parameters controlling bond failure of rebars in pre-cracked concrete. The results also indicate that as the crack width corresponding to the low confinement increases, rib sliding is expected to occur as an illustration of weak interfacial strength. The proposed bond mechanism models are also in good agreement with the experimental observations.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
The authors would like to thank the technical staff of ETS Montreal for support in the experiments.
References
ACI (American Concrete Institute). 2014. Building code requirements for reinforced concrete. ACI 318. Farmington Hills, MI: ACI.
Arslan, G. 2004. “Mesh size effect on load carrying capacity of the reinforced concrete beams without stirrups by using drucker-prager cracking concrete fracture criteria.” Sigma J. Eng. Nat. Sci. 22 (3): 34–42.
Baltay, P., and A. Gjelsvik. 1990. “Coefficient of friction for steel on concrete at high normal stress.” J. Mater. Civ. Eng. 2 (1): 46–49. https://doi.org/10.1061/(ASCE)0899-1561(1990)2:1(46).
Belarbi, A., and T. T. C. Hsu. 1991. Constitutive laws of reinforced concrete in biaxial tension-compression. Houston: Univ. of Houston.
Brantschen, F. 2016. Influence of bond and anchorage conditions of the shear reinforcement on the punching strength of RC slabs. Ph.D. thesis, School of Architecture, Civil and Environmental Engineering.
Brantschen, F., D. Faria, M. Fernández Ruiz, and A. Muttoni. 2016. “Bond behaviour of straight, hooked, U-shaped and headed bars in cracked concrete.” Struct. Concr. 17 (5): 799–810. https://doi.org/10.1002/suco.201500199.
Cairns, J., and R. B. Abdullah. 1996. “Bond strength of black and epoxy-coated reinforcement-a theoretical approach.” Mater. J. 93 (4): 362–369. https://doi.org/10.14359/9823.
Cairns, J., and K. Jones. 1995. “Influence of rib geometry on strength of lapped joints: an experimental and analytical study.” Mag. Concr. Res. 47 (172): 253–262. https://doi.org/10.1680/macr.1995.47.172.253.
Cela, J. J. L. 1998. “Analysis of reinforced concrete structures subjected to dynamic loads with a viscoplastic Drucker–Prager model.” Appl. Math. Modell. 22 (7): 495–515. https://doi.org/10.1016/S0307-904X(98)10050-1.
Cervenka, V. 1985. “Constitutive model for cracked reinforced concrete.” J. Proc. 82 (6): 877–882. https://doi.org/10.14359/10409.
Choi, O. C., H. Choi, and G. Hong. 2010. “Bearing angle model for bond of reinforcing bars to concrete.” In Fracture mechanics of concrete and concrete structures, 807–810. Seoul: Korea Concrete Institute.
Choi, O. C., and W. S. Lee. 2002. “Interfacial bond analysis of deformed bars to concrete.” Struct. J. 99 (6): 750–756. https://doi.org/10.14359/12339.
Choi, O. C., and S. Yang. 2010. “Bond analysis model of deformed bars to concrete.” In Fracture mechanics of concrete and concrete structures-assessment, durability, monitoring and retrofitting of concrete structures, edited by B. H. Oh et al. Seoul: Korea Concrete Institute.
CSA (Canadian Standards Association). 2009. Carbon steel bars for concrete reinforcement. CAN/CSA-G30. 18-09. Mississauga, ON, Canada: CSA.
Darwin, D., and E. K. Graham. 1993. Effect of deformation height and spacing on bond strength of reinforcing bars. Lawrence, KS: Univ. of Kansas Center for Research.
Dawood, N., and H. Marzouk. 2012. “Cracking and tension stiffening of high-strength concrete panels.” ACI Struct. J. 109 (1): 21–30. https://doi.org/10.14359/51683490.
Dehestani, M., A. Asadi, and S. Mousavi. 2017. “On discrete element method for rebar-concrete interaction.” Constr. Build. Mater. 151 (Oct): 220–227. https://doi.org/10.1016/j.conbuildmat.2017.06.086.
Desnerck, P., J. M. Lees, and C. T. Morley. 2015. “Bond behaviour of reinforcing bars in cracked concrete.” Constr. Build. Mater. 94 (Sep): 126–136. https://doi.org/10.1016/j.conbuildmat.2015.06.043.
Einpaul, J., F. Brantschen, M. Fernández Ruiz, and A. Muttoni. 2016. “Performance of punching shear reinforcement under gravity loading: Influence of type and detailing.” ACI Struct. J. 113 (4): 827–838. https://doi.org/10.14359/51688630.
Eligehausen, R., E. P. Popov, and V. V. Bertero. 1982. “Local bond stress-slip relationships of deformed bars under generalized excitations.” In Vol. 4 of Proc., 7th European Conf. on Earthquake Engineering, 69–80. Athens, Greece: Technical Chamber of Greece. https://doi.org/10.18419/opus-415.
Esfahani, M. R., and B. V. Rangan. 1998. “Bond between normal strength and high-strength concrete (HSC) and reinforcing bars in splices in beams.” Struct. J. 95 (3): 272–280. https://doi.org/10.14359/545.
Feng, Q., P. Visintin, and D. J. Oehlers. 2016. “Deterioration of bond–slip due to corrosion of steel reinforcement in reinforced concrete.” Mag. Concr. Res. 68 (15): 768–781. https://doi.org/10.1680/jmacr.15.00217.
Fernández Ruiz, M., E. Hars, and A. Muttoni. 2005. Bond mechanics in structural concrete. Theoretical model and experimental results. Lausanne, Switzerland: Ecole Polytechnique Federale de Lausanne.
fib (Fédération Internationale du Béton). 2000. “Bond of reinforcement in concrete.”. Lausanne, Switzerland: fib.
Gambarova, P. G., G. P. Rosati, and B. Zasso. 1989. “Steel-to-concrete bond after concrete splitting: Test results.” Mater. Struct. 22 (1): 35. https://doi.org/10.1007/BF02472693.
Guizani, L., O. Chaallal, and S. S. Mousavi. 2017. “Local bond stress-slip model for reinforced concrete joints and anchorages with moderate confinement.” Can. J. Civ. Eng. 44 (3): 201–211. https://doi.org/10.1139/cjce-2015-0333.
Hadidi, R., and M. A. Saadeghvaziri. 2005. “Transverse cracking of concrete bridge decks: State-of-the-art.” J. Bridge Eng. 10 (5): 503–510. https://doi.org/10.1061/(ASCE)1084-0702(2005)10:5(503).
Han, J., S. Wang, Y. Chen, and C. Cao. 2018. “Analytical derivation of rib bearing angle of reinforcing bar subject to axial loading.” Mag. Concr. Res. 71 (4): 175–183. https://doi.org/10.1680/jmacr.17.00329.
Harajli, M. 2009. “Bond stress–slip model for steel bars in unconfined or steel, FRC, or FRP confined concrete under cyclic loading.” J. Struct. Eng. 135 (5): 509–518. https://doi.org/10.1061/(ASCE)0733-9445(2009)135:5(509).
Hong, S., and S. K. Park. 2012. “Uniaxial bond stress-slip relationship of reinforcing bars in concrete.” In Adv. Mater. Sci. Eng.2012 (1): 12. https://doi.org/10.1155/2012/328570.
Idda, K. 1999. Verbundverhalten von Betonrippenstählen bei Querzug. Ph.D. thesis, Universität Fridericiana zu Karlsruhe (TH), Institut fuer Massivbau und Baustofftechnologie.
Jiang, C., Y.-F. Wu, and M.-J. Dai. 2018. “Degradation of steel-to-concrete bond due to corrosion.” Constr. Build. Mater. 158 (Jan): 1073–1080. https://doi.org/10.1016/j.conbuildmat.2017.09.142.
Joergensen, H. B., and L. C. Hoang. 2015. “Strength of loop connections between precast bridge decks loaded in combined tension and bending.” Struct. Eng. Int. 25 (1): 71–80. https://doi.org/10.2749/101686614X14043795570697.
Khalaf, J., Z. Huang, and M. Fan. 2016. “Analysis of bond-slip between concrete and steel bar in fire.” Comput. Struct. 162 (Jan): 1–15. https://doi.org/10.1016/j.compstruc.2015.09.011.
Kollegger, J., and G. Mehlhorn. 1990. “Experimentelle Untersuchungen zur Bestimmung der Druckfestigkeit des gerissenen Stahlbetons bei einer Querzugbeanspruchung.” [In German.] Deutscher Ausschuß für Stahlbeton. Berlin: Wilhelm Ernst & Sohn.
Lin, H., Y. Zhao, J. Ožbolt, and H.-W. Reinhardt. 2017. “Bond strength evaluation of corroded steel bars via the surface crack width induced by reinforcement corrosion.” Eng. Struct. 152 (Dec): 506–522. https://doi.org/10.1016/j.engstruct.2017.08.051.
Lindorf, A., L. Lemnitzer, and M. Curbach. 2009. “Experimental investigations on bond behaviour of reinforced concrete under transverse tension and repeated loading.” Eng. Struct. 31 (7): 1469–1476. https://doi.org/10.1016/j.engstruct.2009.02.025.
Lindorf, C. 2011. “Bond fatigue in reinforced concrete under transverse tension.” Ph.D. thesis, Faculty of Civil Engineering, Dresden Univ.
Lutz, L. A., and P. Gergely. 1967. “Mechanics of bond and slip of deformed bars in concrete.” ACI J. 64 (11): 711–721.
Lutz, L. A., P. Gergely, and G. Winter. 1966. The mechanics of bond and slip of deformed reinforcing bars in concrete. Ithaca, NY: Cornell Univ.
Mahrenholtz, C. 2012. Seismic bond model for concrete reinforcement and the application to column-to-foundation connections. Ph.D. thesis, Univ. of Stuttgart.
Mahrenholtz, C., and R. Eligehausen. 2017. “Cyclic tests on concrete reinforcement for development of seismic bond model.” ACI Mater. J. 114 (4): 571–579. https://doi.org/10.14359/51689777.
Matsumoto, K., T. Wang, D. Hayashi, and K. Nagai. 2016. “Investigation on the pull-out behavior of deformed bars in cracked reinforced concrete.” J. Adv. Concr. Technol. 14 (9): 573–589. https://doi.org/10.3151/jact.14.573.
Menzel, C. A. 1939. “Some factors influencing results of pull-out bond tests.” J. Proc. 35 (6): 517–542. https://doi.org/10.14359/8507.
Metelli, G., and G. A. Plizzari. 2014. “Influence of the relative rib area on bond behaviour.” Mag. Concr. Res. 66 (6): 277–294. https://doi.org/10.1680/macr.13.00198.
Mikame, A., K. Uchida, and H. Noguchi. 1991. “A study of compressive deterioration of cracked concrete.” In Proc., Int. Workshop on Finite Element Analysis of Reinforced Concrete. New York: Columbia Univ.
Montoya, E., F. Vecchio, and S. Sheikh. 2001. “Compression field modeling of confined concrete.” Struct. Eng. Mech. 12 (3): 231–248. https://doi.org/10.12989/sem.2001.12.3.231.
Mousavi, S., M. Dehestani, and K. Mousavi. 2017. “Bond strength and development length of steel bar in unconfined self-consolidating concrete.” Eng. Struct. 131 (Jan): 587–598. https://doi.org/10.1016/j.engstruct.2016.10.029.
Mousavi, S. S., L. Guizani, and C. M. Ouellet-Plamondon. 2019. “On bond-slip response and development length of steel bars in pre-cracked concrete.” Constr. Build. Mater. 199 (Jan): 560–573. https://doi.org/10.1016/j.conbuildmat.2018.12.039.
Murata, J., and T. Kawai. 1984. “Studys on bond strength of deformed bars by pull-out tests.” Doboku Gakkai Ronbunshu 1984 (348): 113–122. https://doi.org/10.2208/jscej.1984.348_113.
Murcia-Delso, J., and P. Benson Shing. 2014. “Bond-slip model for detailed finite-element analysis of reinforced concrete structures.” J. Struct. Eng. 141 (4): 04014125. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001070.
Petersen, L., L. Lohaus, and M. A. Polak. 2007. “Influence of freezing-and-thawing damage on behavior of reinforced concrete elements.” ACI Mater. J. 104 (4): 369–378. https://doi.org/10.14359/18826.
Purainer, R. 2005. “Last-und Verformungsverhalten von Stahlbetonflächen-tragwerken unter zweiaxialer Zugbeanspruchung.” [In German.] Ph.D. thesis, Universität der Bundeswehr München.
Rabbat, B., and H. Russell. 1985. “Friction coefficient of steel on concrete or grout.” J. Struct. Eng. 111 (3): 505–515. https://doi.org/10.1061/(ASCE)0733-9445(1985)111:3(505).
Rehm, G. 1957. “The fundamental law of bond.” In Proc., RILEM-Symp. on Bond and Crack Formation in Reinforced Concrete, 491–498. Stockholm, Sweden: Tekniska Hogskolans Rotaprinttrychkeri.
Saadeghvaziri, M. A., and R. Hadidi. 2005. “Transverse cracking of concrete bridge decks: Effects of design factors.” J. Bridge Eng. 10 (5): 511–519. https://doi.org/10.1061/(ASCE)1084-0702(2005)10:5(511).
Shirai, N., and H. Noguchi. 1989. “Compressive deterioration of cracked concrete.” In Structural design, analysis and testing, 1–10. Reston, VA: ASCE.
Skorobogatov, S., and A. Edwards. 1979. “The influence of the geometry of deformed steel bars on their bond strength in concrete.” Proc. Inst. Civ. Eng. 67 (2): 327–339. https://doi.org/10.1680/iicep.1979.2460.
Soretz, S., and H. Holzenbein. 1979. “Influence of rib dimensions of reinforcing bars on bond and bendability.” ACI J. Proc. 76 (1): 111–128. https://doi.org/10.14359/6939.
Turk, K., S. Caliskan, and M. S. Yildirim. 2005. “Influence of loading condition and reinforcement size on the concrete/reinforcement bond strength.” Struct. Eng. Mech. 19 (3): 337–346. https://doi.org/10.12989/sem.2005.19.3.337.
Vecchio, F. J., and M. P. Collins. 1993. “Compression response of cracked reinforced concrete.” J. Struct. Eng. 119 (12): 3590–3610. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:12(3590).
Walker, P., M. Batayneh, and P. Regan. 1997. “Bond strength tests on deformed reinforcement in normal weight concrete.” Mater. Struct. 30 (7): 424. https://doi.org/10.1007/BF02498566.
Wang, Z.-H., L. Li, Y.-X. Zhang, and W.-T. Wang. 2019. “Bond-slip model considering freeze-thaw damage effect of concrete and its application.” Eng. Struct. 201: 109831. https://doi.org/10.1016/j.engstruct.2019.109831.
Wu, C., and G. Chen. 2015. “Unified model of local bond between deformed steel rebar and concrete: Indentation analogy theory and validation.” J. Eng. Mech. 141 (10): 04015038. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000945.
Wu, C., G. Chen, J. S. Volz, R. K. Brow, and M. L. Koenigstein. 2012. “Local bond strength of vitreous enamel coated rebar to concrete.” Constr. Build. Mater. 35: 428–439. https://doi.org/10.1016/j.conbuildmat.2012.04.067.
Wu, Y.-F., and X.-M. Zhao. 2012. “Unified bond stress–slip model for reinforced concrete.” J. Struct. Eng. 139 (11): 1951–1962. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000747.
Zhao, W., and B. Zhu. 2017. “Basic parameters test and 3D modeling of bond between high-strength concrete and ribbed steel bar after elevated temperatures.” Struct. Concr. 18 (5): 653–667. https://doi.org/10.1002/suco.201600005.
Zhao, W., and B. Zhu. 2018. “Theoretical model for the bond–slip relationship between ribbed steel bars and confined concrete.” Struct. Concr. 19 (2): 548–558. https://doi.org/10.1002/suco.201700008.
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Published In
Journal of Structural Engineering
Volume 146 • Issue 8 • August 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Jun 18, 2019
Accepted: Jan 30, 2020
Published online: May 19, 2020
Published in print: Aug 1, 2020
Discussion open until: Oct 19, 2020
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