Assessment of the Behavior of FRP-Strengthened RC Slabs Using a Discrete Crack Model
Publication: Journal of Composites for Construction
Volume 22, Issue 6
Abstract
This paper presents a new discrete crack model that can simulate the complex behavior of fiber-reinforced polymer (FRP)-strengthened reinforced concrete (RC) slabs. The model approximates the kinematics of crack openings by a rigid body movement that can be easily embedded in regular finite elements. As such, concrete cracking and its interaction with the FRP can be automatically accounted for in finite element simulations. The proposed technique includes all relevant material nonlinearities related with concrete, steel, and FRP, as well the debonding at interfaces. The model is validated against experimental results on one-way simply supported slabs before assessing in detail the relevance of the discrete simulation of cracks for the analysis of the behavior of the strengthened structure. The numerical model provides important insights on the bond mechanism that cannot be easily determined otherwise. For example, the debond failure is shown to be composed of a critical local stable debonding length that is then followed by global debonding which triggers a rapid loss of strength provided by the FRP. The model also provides the stable bond length from parametric analysis of the optimal strengthening layout. Overall, the model correctly predicts the composite behavior and strength of the FRP-strengthened structure, confirming experimental observations, and expanding the current capabilities of existing analytical and numerical models.
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Acknowledgments
The authors would like to acknowledge the support from the Australian Research Council through its Future Fellowship (FT140100130), Discovery Early Career Researcher Award (DE150101703), Discovery Project (DP140100529) and Linkage Project (LP130100482), and from the Faculty of Engineering and Information Technologies, The University of Sydney, under the Faculty Research Cluster Program. Acknowledgment is also extended to FCT (Portuguese Foundation for Science and Technology), through ISISE, under Project UID/ECI/04029/2013.
References
Alfaiate, J., and L. J. Sluys. 2004. “On the use of embedded discontinuities in the framework of a discrete crack approach.” In Proc. WCCM VI. Beijing: Tsinghua University Press & Springer-Verlag.
Ali-Ahmad, M. K., K. V. Subramaniam, and M. Ghosn. 2007. “Analysis of scaling and instability in FRP-concrete shear debonding for beam-strengthening applications.” J. Eng. Mech. 133 (1): 58–65. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:1(58).
Areias, P. M. A., D. Dias-da-Costa, J. Alfaiate, and E. N. B. S. Júlio. 2009. “Arbitrary bi-dimensional finite strain cohesive crack propagation.” Comput. Mech. 45 (1): 61–75. https://doi.org/10.1007/s00466-009-0418-z.
Bazant, Z. P., and B. H. Oh. 1983. “Crack band theory of concrete.” Mater. Sruct. 16 (3): 155–177. https://doi.org/10.1007/BF02486267.
Bilotta, A., C. Faella, E. Martinelli, and E. Nigro. 2012. “Indirect identification method of bilinear interface laws for FRP bonded on a concrete substrate.” J. Compos. Constr. 16 (2): 171–184. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000253.
Bocca, P., A. Carpinteri, and S. Valente. 1991. “Mixed mode fracture of concrete.” Int. J. Solids Struct. 27 (9): 1139–1153. https://doi.org/10.1016/0020-7683(91)90115-V.
Borst, R. D., J. J. C. Remmers, A. Needleman, and M.-A. Abellan. 2004. “Discrete vs smeared crack models for concrete fracture: Bridging the gap.” Int. J. Numer. Anal. Methods Geomech. 28 (78): 583–607. https://doi.org/10.1002/nag.374.
Carloni, C., and K. V. Subramaniam. 2010. “Direct determination of cohesive stress transfer during debonding of FRP from concrete.” Compos. Struct. 93 (1): 184–192. https://doi.org/10.1016/j.compstruct.2010.05.024.
Chen, G. M., J. G. Teng, and J. F. Chen. 2011. “Finite-element modeling of intermediate crack debonding in FRP-plated RC beams.” J. Compos. Constr. 15 (3): 339–353. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000157.
Chen, J. F., and J. G. Teng. 2001. “Anchorage strength models for FRP and steel plates bonded to concrete.” J. Struct. Eng. 127 (7): 784–791. https://doi.org/10.1061/(ASCE)0733-9445(2001)127:7(784).
Chong, K. T., S. Foster, and R. I. Gilbert. 2008. “Time-dependent modelling of RC structures using the cracked membrane model and solidification theory.” Comput. Struct. 86 (11–12): 1305–1317. https://doi.org/10.1016/j.compstruc.2007.08.005.
Coronado, C. A., and M. M. Lopez. 2007. “Damage approach for the prediction of debonding failure on concrete elements strengthened with FRP.” J. Compos. Constr. 11 (4): 391–400. https://doi.org/10.1061/(ASCE)1090-0268(2007)11:4(391).
Coronado, C. A., and M. M. Lopez. 2010. “Numerical modeling of concrete-FRP debonding using a crack band approach.” J. Compos. Constr. 14 (1): 11–21. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000044.
De Lorenzis, L., and G. Zavarise. 2008. “Modeling of mixed-mode debonding in the peel test applied to superficial reinforcements.” Int. J. Solids Struct. 45 (20): 5419–5436. https://doi.org/10.1016/j.ijsolstr.2008.05.024.
De Lorenzis, L., and G. Zavarise. 2010. “Debonding analysis of thin plates from curved substrates.” Eng. Fract. Mech. 77 (16): 3310–3328. https://doi.org/10.1016/j.engfracmech.2010.08.013.
Dias-da-Costa, D., J. Alfaiate, L. J. Sluys, P. Areias, and E. N. B. S. Júlio. 2013. “An embedded formulation with conforming finite elements to capture strong discontinuities.” Int. J. Numer. Methods Eng. 93 (2): 224–244. https://doi.org/10.1002/nme.4393.
Dias-da-Costa, D., J. Alfaiate, L. J. Sluys, and E. N. B. S. Júlio. 2009. “A discrete strong discontinuity approach.” Eng. Fract. Mech. 76 (9): 1176–1201. https://doi.org/10.1016/j.engfracmech.2009.01.011.
Dias-da-Costa, D., J. Alfaiate, L. J. Sluys, and E. N. B. S. Júlio. 2010. “A comparative study on the modelling of discontinuous fracture by means of enriched nodal and element techniques and interface elements.” Int. J. Fract. 161 (1): 97–119. https://doi.org/10.1007/s10704-009-9432-6.
Ebead, U. A., and K. W. Neale. 2007. “Mechanics of fibre-reinforced polymer-concrete interfaces.” Can. J. Civ. Eng. 34 (3): 367–377. https://doi.org/10.1139/l06-107.
Faella, C., E. Martinelli, and E. Nigro. 2009. “Direct versus indirect method for identifying FRP-to-concrete interface relationships.” J. Compos. Constr. 13 (3): 226–233. https://doi.org/10.1061/(ASCE)1090-0268(2009)13:3(226).
Ferracuti, B., M. Savoia, and C. Mazzotti. 2006. “A numerical model for FRP-concrete delamination.” Compos. Part B 37 (4–5): 356–364. https://doi.org/10.1016/j.compositesb.2005.08.002.
Ferracuti, B., M. Savoia, and C. Mazzotti. 2007. “Interface law for FRP-concrete delamination.” Compos. Struct. 80 (4): 523–531. https://doi.org/10.1016/j.compstruct.2006.07.001.
fib. 2013. Model code for concrete structures 2010. Berlin: Wiley-VCH.
Graça-e-Costa, R., J. Alfaiate, D. Dias-da-Costa, and L. J. Sluys. 2012. “A non-iterative approach for the modelling of quasi-brittle materials.” Int. J. Fract. 178 (1–2): 281–298. https://doi.org/10.1007/s10704-012-9768-1.
Gray, W. G., and P. C. Y. Lee. 1977. “On the theorems for local volume averaging of multiphase systems.” Int. J. Multiphase Flow 3 (4): 333–340. https://doi.org/10.1016/0301-9322(77)90013-1.
Gutiérrez, M. A. 2004. “Energy release control for numerical simulations of failure in quasi-brittle solids.” Commun. Numer. Methods Eng. 20 (1): 19–29. https://doi.org/10.1002/cnm.649.
Hadigheh, S. A., and R. J. Gravina. 2016. “Generalization of the interface law for different FRP processing techniques in FRP-to-concrete bonded interfaces.” Composites Part B 91: 399–407. https://doi.org/10.1016/j.compositesb.2016.01.015.
Hadigheh, S. A., R. J. Gravina, and S. Setunge. 2015. “Identification of the interfacial fracture mechanism in the FRP laminated substrates using a modified single lap shear test set-up.” Eng. Fract. Mech. 134: 317–329. https://doi.org/10.1016/j.engfracmech.2014.12.001.
Hamed, E., and M. A. Bradford. 2012. “Flexural time-dependent cracking and post-cracking behaviour of FRP strengthened concrete beams.” Int. J. Solids Struct. 49 (13): 1595–1607. https://doi.org/10.1016/j.ijsolstr.2012.03.001.
Hillerborg, A., M. Modeer, and P. E. Petersson. 1976. “Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements.” Cem. Concr. Res. 6 (6): 773–781. https://doi.org/10.1016/0008-8846(76)90007-7.
Hollaway, L. C., and J. G. Teng. 2008. Strengthening and rehabilitation of civil infrastructures using fibre-reinforced polymer (FRP) composites. Cambridge, UK: Woodhead Publishing Limited.
Holzenkämpfer, P. 1994. “Ingenieurmodelle des verbunds geklebter bewehrung für betonbauteile.” Ph.D. thesis, Institut für Baustoffe, Massivbau und Brandschutz, Technische Universität Braunschweig.
Ingraffea, A. R., W. H. Gerstk, P. Gergely, and V. Saouma. 1984. “Fracture mechanics of bond in reinforced concrete.” J. Struct. Eng. 110 (4): 871–890. https://doi.org/10.1061/(ASCE)0733-9445(1984)110:4(871).
Khomwan, N., S. J. Foster, and S. T. Smith. 2010. “FE modeling of FRP-repaired planar concrete elements subjected to monotonic and cyclic loading.” J. Compos. Constr. 14 (6): 720–729. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000126.
Lee, Y. J., T. E. Boothby, C. E. Bakis, and A. Nanni. 1999. “Slip modulus of FRP sheets bonded to concrete.” J. Compos. Constr. 3 (4): 161–167. https://doi.org/10.1061/(ASCE)1090-0268(1999)3:4(161).
Lu, X. Z., J. J. Jiang, J. G. Teng, and L. P. Ye. 2006. “Finite element simulation of debonding in FRP-to-concrete bonded joints.” Constr. Build. Mater. 20 (6): 412–424. https://doi.org/10.1016/j.conbuildmat.2005.01.033.
Lu, X. Z., J. G. Teng, L. P. Ye, and J. J. Jiang. 2005. “Bond-slip models for FRP sheets/plates bonded to concrete.” Eng. Struct. 27 (6): 920–937. https://doi.org/10.1016/j.engstruct.2005.01.014.
Malvern, L. E. 1969. Introduction to the mechanics of a continuous medium. Englewood Cliffs, NJ: Prentice-Hall International.
Manzoli, O. L., and P. B. Shing. 2006. “A general technique to embed non-uniform discontinuities into standard solid finite elements.” Comput. Struct. 84 (10–11): 742–757. https://doi.org/10.1016/j.compstruc.2005.10.009.
Neto, P., J. Alfaiate, J. R. Almeida, and E. B. Pires. 2004. “The influence of mode II fracture on concrete strengthened with CFRP.” Comput. Struct. 82 (17–19): 1495–1502. https://doi.org/10.1016/j.compstruc.2004.03.045.
Neto, P., J. Alfaiate, D. Dias-da-Costa, and J. Vinagre. 2016. “Mixed-mode fracture and load misalignment on the assessment of FRP-concrete bond connections.” Compos. Struct. 135: 49–60. https://doi.org/10.1016/j.compstruct.2015.08.139.
Neubauer, U., and F. Rostásy. 1997. “Design aspects of concrete structures strengthened with externally bonded CFRP plates.” In Proc., 7th Int. Conf. on Structural Faults and Repairs, 109–118. Edinburgh, UK: Engineering Technics Press.
Oehlers, D. J., and R. Seracino. 2004. Design of FRP and steel plated RC structures: Retrofitting beams and slabs for strength, stiffness and ductility. Amsterdam, Netherlands: Elsevier.
Oliver, J., A. E. Huespe, and P. J. Sanchez. 2006. “A comparative study on finite elements for capturing strong discontinuities: E-FEM vs. X-FEM.” Comput. Methods Appl. Mech. Eng. 195 (37–40): 4732–4752. https://doi.org/10.1016/j.cma.2005.09.020.
Pellegrino, C., and C. Modena. 2009. “Influence of FRP axial rigidity on FRP-concrete bond behaviour: An analytical study.” Adv. Struct. Eng. 12 (5): 639–649. https://doi.org/10.1260/136943309789867854.
Pham, H. B., R. Al-Mahaidi, and V. Saouma. 2006. “Modelling of CFRP-concrete bond using smeared and discrete cracks.” Compos. Struct. 75 (1–4): 145–150. https://doi.org/10.1016/j.compstruct.2006.04.039.
Rabinovich, O., and Y. Frostig. 2000. “Closed-form high-order analysis of RC beams strengthened with FRP strips.” J. Compos. Constr. 4 (2): 65–74. https://doi.org/10.1061/(ASCE)1090-0268(2000)4:2(65).
Rabinovitch, O., and Y. Frostig. 2003. “Experiments and analytical comparison of RC beams strengthened with CFRP composites.” Composites Part B 34 (8): 663–677. https://doi.org/10.1016/S1359-8368(03)00090-8.
Rots, J. G. 1988. “Computational modeling of concrete fracture.” Ph.D. thesis, Civil Engineering and Geosciences, Delft Univ. of Technology.
Rots, J. G. 1991. “Smeared and discrete representations of localized fracture.” Int. J. Fract. 51 (1): 45–59. https://doi.org/10.1007/BF00020852.
Rots, J. G., and S. Invernizzi. 2004. “Regularized sequentially linear saw-tooth softening model.” Int. J. Numer. Anal. Methods Geomech. 28 (78): 821–856. https://doi.org/10.1002/nag.371.
Savoia, M., B. Ferracuti, and L. Vincenzi. 2009. “Inverse analysis for the calibration of FRP-concrete interface law.” Adv. Struct. Eng. 12 (5): 613–625. https://doi.org/10.1260/136943309789867845.
Smith, S. T., S. Hu, S. J. Kim, and R. Seracino. 2011. “FRP-strengthened RC slabs anchored with FRP anchors.” Eng. Struct. 33 (4): 1075–1087. https://doi.org/10.1016/j.engstruct.2010.11.018.
Smith, S. T., H. Zhang, and Z. Wang. 2013. “Influence of FRP anchors on the strength and ductility of FRP-strengthened RC slabs.” Constr. Build. Mater. 49: 998–1012. https://doi.org/10.1016/j.conbuildmat.2013.02.006.
Sun, R., E. Sevillano, and R. Perera. 2015. “A discrete spectral model for intermediate crack debonding in FRP-strengthened RC beams.” Compos. Part B 69: 562–575. https://doi.org/10.1016/j.compositesb.2014.10.017.
Täljsten, B. 1994. “Plate bonding: Strengthening of existing concrete structures with epoxy bonded plates of steel or fibre reinforced plastics.” Ph.D. thesis, Division of Structural Engineering, Luleå Univ. of Technology.
Verhoosel, C. V., J. J. C. Remmers, and M. A. Gutiérrez. 2009. “A dissipation-based arc-length method for robust simulation of brittle and ductile failure.” Int. J. Numer. Methods Eng. 77 (9): 1290–1321. https://doi.org/10.1002/nme.2447.
Wang, J. 2006. “Cohesive zone model of intermediate crack-induced debonding of FRP-plated concrete beam.” Int. J. Solids Struct. 43 (21): 6630–6648. https://doi.org/10.1016/j.ijsolstr.2006.01.013.
Wang, J. L. 2007. “Cohesive-bridging zone model of FRP-concrete interface debonding.” Eng. Fract. Mech. 74 (17): 2643–2658. https://doi.org/10.1016/j.engfracmech.2007.02.013.
Wu, Y. F., Z. Q. Zhou, Q. D. Yang, and W. Q. Chen. 2010. “On shear bond strength of FRP-concrete structures.” Eng. Struct. 32 (3): 897–905. https://doi.org/10.1016/j.engstruct.2009.12.017.
Wu, Z. S., H. Yuan, and H. D. Niu. 2002. “Stress transfer and fracture propagation in different kinds of adhesive joints.” J. Eng. Mech. 128 (5): 562–573. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:5(562).
Yuan, H., Z. S. Wu, and H. Yoshizawa. 2001. “Theoretical solutions on interfacial stress transfer of externally bonded steel/composite laminates.” J. Struct. Mech. Earthquake Eng. 18 (1): 27–39.
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Journal of Composites for Construction
Volume 22 • Issue 6 • December 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: Aug 10, 2017
Accepted: May 9, 2018
Published online: Aug 20, 2018
Published in print: Dec 1, 2018
Discussion open until: Jan 20, 2019
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