TECHNICAL PAPERS
Jul 18, 2009

Stiffness Degradation and Time to Cracking of Cover Concrete in Reinforced Concrete Structures Subject to Corrosion

Publication: Journal of Engineering Mechanics
Volume 136, Issue 2

Abstract

Corrosion-induced cracks in reinforced concrete (RC) structures degrade the stiffness of the cover concrete. The stiffness degradation is mainly caused by the softening in the stress-strain relation in the cracked concrete. Limited efforts have been made to model the cracking and the corresponding effects on the cover concrete, despite of its importance in assessing and modeling the behavior of RC structures. This paper proposes a stiffness degradation factor to model the stiffness degradation of the cover concrete subject to cracking. The proposed factor is computed in terms of the cracking strain corresponding to the maximum opening of the concrete cracks based on an energy principle applied to a fractured RC structure. The time to cracking of the cover concrete is then determined as the time from the corrosion initiation needed by the crack front to reach the outer surface of the cover concrete. The proposed stiffness degradation factor and the method to compute the time to cracking are illustrated through two numerical examples. The times to cracking of the cover concrete that are predicted using the proposed method are in agreement with the measured values from laboratory experiments.

Get full access to this article

View all available purchase options and get full access to this article.

Acknowledgments

The writers thank Dr. Pillai for helpful discussions and suggestions and the Zachry Department of Civil Engineering at UNSPECIFIEDTexas A&M University, College Station, Texas, for its financial support.

References

Ahmed, S. F. U., Maalej, M., and Mihashi, H. (2007). “Cover cracking of reinforced concrete beams due to corrosion of steel.” ACI Mater. J., 104(2), 153–161.
Aliabadi, M. H. (1997). “Boundary element formulations in fracture mechanics.” Appl. Mech. Rev., 50(2), 83–96.
Aliabadi, M. H., and Saleh, A. L. (2002). “Fracture mechanics analysis of cracking in plain and reinforced concrete using the boundary element method.” Eng. Fract. Mech., 69(2), 267–280.
Aligizaki, K. K. (1999). “Modeling of concrete cracking due to corrosion of embedded reinforcement.” Ph.D. thesis, Pennsylvania State Univ., University Park, Pa.
Alonso, C., Andrade, C., Rodriguez, J., and Diez, J. M. (1998). “Factors controlling cracking of concrete affected by reinforcement corrosion.” Mater. Struct., 31(7), 435–441.
Andrade, C., Alonso, C., and Molina, F. J. (1993). “Cover cracking as a function of bar corrosion. Part 1: Experimental test.” Mater. Struct., 26, 453–464.
Barenblatt, G. I. (1962). “The mathematical theory of equilibrium cracks in brittle fracture.” Adv. Appl. Mech., 7, 55–129.
Bažant, Z. P. (1979a). “Physical model for steel corrosion in concrete sea structures–theory.” J. Struct. Div., 105(6), 1137–1153.
Bažant, Z. P. (1979b). “Physical model for steel corrosion in concrete sea structures—Applications.” J. Struct. Div., 105(6), 1155–1165.
Bažant, Z. P., and Li, Y. -N. (1995). “Stability of cohesive crack model. Part I: Energy principles.” J. Appl. Mech., 62(9), 959–964.
Bažant, Z. P., and Oh, B. H. (1984). “Deformation of progressively cracking reinforced concrete beams.” ACI J., 81(3), 268–278.
Bažant, Z. P., and Planas, J. (1998). Fracture and size effect in concrete and other quasibrittle materials, CRC, Boca Raton, Fla.
Bhargava, K., Ghosh, A. K., Mori, Y., and Ramanujam, S. (2006). “Model for cover cracking due to rebar corrosion in RC structures.” Eng. Struct., 28(8), 1093–1109.
Cabrera, J. G. (1996). “Deterioration of concrete due to reinforcement steel corrosion.” Cem. Concr. Compos., 18(1), 47–59.
Cady, P. D., and Weyers, R. E. (1983). “Chloride penetration and the deterioration of concrete bridge decks.” Cem., Concr., Aggregates, 5(2), 81–87.
Cairns, J., Du, Y., and Law, D. (2008). “Structural performance of corrosion-damaged concrete beams.” Mag. Concrete Res., 60(5), 359–370.
Capozucca, R. (2008). “Detection of damage due to corrosion in prestressed RC beams by static and dynamic tests.” Constr. Build. Mater., 22(5), 738–746.
Choe, D., Gardoni, P., Rosowsky, D., and Haukaas, T. (2008). “Probabilistic capacity models and fragility estimates for corroding reinforced concrete columns.” Reliab. Eng. Syst. Saf., 93(3), 383–393.
Choe, D., Gardoni, P., Rosowsky, D., and Haukaas, T. (2009). “Seismic fragility estimates for reinforced concrete bridges subject to corrosion.” Struct. Safety, 31(4), 275–283.
El Maaddawy, T., and Soudki, K. (2007). “A model for prediction of time from corrosion initiation to corrosion cracking.” Cem. Concr. Compos., 29(3), 168–175.
Fett, T., and Munz, D. (1997). Stress intensity factors and weight functions, CMP, Southampton, U.K.
Floegl, H., and Mang, M. (1982). “Tension stiffening concept based on bond slip.” J. Struct. Div., 108(12), 2681–2701.
Frankel, G. S. (1998). “Pitting corrosion of metals.” J. Electrochem. Soc., 145(6), 2186–2198.
Frankel, G. S., and Sridhar, N. (2008). “Understanding localized corrosion.” Mater. Today, 11(10), 38–44.
Gulikers, J. (2003). “Problems encountered in the detection of reinforcement corrosion in concrete tunnel linings—Theoretical considerations.” Mater. Corros., 54(6), 454–459.
Guo, Y. H., and Padovan, J. (1994). “Moving template analysis of crack growth. II: Multiple crack extension and benchmarking.” Eng. Fract. Mech., 48(3), 427–444.
Hillerborg, A., Modeer, M., and Petersson, P. E. (1976). “Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements.” Cem. Concr. Res., 6(6), 773–782.
Ingraffea, A. R., Gerstle, W. H., Gergely, P., and Saouma, V. (1984). “Fracture mechanics of bond in reinforced concrete.” J. Struct. Eng., 110(4), 871–890.
Kaesche, K. (2003). Corrosion of metals: Physicochemical principles and current problems, Springer, New York.
Klisinski, M., Runesson, K., and Sture, S. (1991). “Finite element with inner softening band.” J. Eng. Mech., 117(3), 575–587.
Leung, C. K. Y. (1997). “Modeling of concrete cracking induced by steel corrosion.” Brittle Matrix Composites 5, A. M. Brandt, V. C. Li, and H. Marshall, eds., Woodhead, Cambridge, U.K., 340–349.
Leung, C. K. Y. (2001). “Modeling of concrete cracking induced by steel expansion.” J. Mater. Civil Eng., 13(3), 169–175.
Li, C. Q., Melchers, R. E., and Zheng, J. J. (2006). “Analytical model for corrosion-induced crack width in reinforced concrete structures.” ACI Struct. J., 103(4), 479–487.
Liu, Y. (1996). “Modeling the time-to-corrosion cracking of the cover concrete in chloride contaminated reinforced concrete structures.” Ph.D. dissertation, Virginia Tech, Blacksburg, Va.
Liu, Y., and Weyers, R. E. (1998). “Modeling the time-to-corrosion cracking in chloride contaminated reinforced concrete structures.” ACI Mater. J., 95(6), 675–681.
Macdonald, D. D. (1992). “Point defect model for the passive state.” J. Electrochem. Soc., 139(12), 3434–3449.
Macdonald, D. D. (1999). “Passivity-the key to our metals-based civilization.” Pure Appl. Chem., 71(6), 951–978.
Mangat, P. S., and Elgarf, M. S. (1999). “Bond characteristics of corroding reinforcement in concrete beams.” Mater. Struct., 32(2), 89–97.
Maruyama, K., Takaoka, Y., Shimizu, K., and Nakada, Y. (1989). “Cracking behavior of concrete due to corrosion of reinforcing bars.” Trans. Jpn. Concr. Inst., 11, 163–170.
Molina, F. J., Alonso, C., and Andrade, C. (1993). “Cover cracking as a function of rebar corrosion. Part 2: Numerical model.” Mater. Struct., 26(9), 532–548.
Morinaga, S. (1988). “Prediction of service lives of reinforced concrete buildings based on rate of corrosion of reinforcing steel.” Rep. No. 23, Shimizu Corp., Japan, 82.
Mosalam, K. M., and Paulino, G. H. (1997). “Evolutionary characteristic length method for smeared cracking finite element models.” Finite Elem. Anal. Design, 27(1), 99–108.
Noghabai, K., (1999). “Discrete versus smeared versus element-embedded crack models on ring problem.” J. Eng. Mech., 125(3), 307–315.
Ohtsu, M., and Yosimura, S. (1997). “Analysis of crack propagation and crack initiation due to corrosion of reinforcement.” Constr. Build. Mater., 11(7–8), 437–442.
Padovan, J., and Guo, Y. H. (1994). “Moving template analysis of crack growth. I: Procedure development.” Eng. Fract. Mech., 48(3), 405–425.
Padovan, J., and Jae, J. (1997). “FE modelling of expansive oxide induced fracture of rebar reinforced concrete.” Eng. Fract. Mech., 56(6), 797–812.
Pagitsas, M., Diamantopoulou, A., and Sazou, D. (2001). “Distinction between general and pitting corrosion based on the nonlinear dynamical response of passive iron surfaces perturbed chemically by halides.” Electrochem. Commun., 3(7), 330–335.
Pantazopoulou, S. J., and Papouli, K. D. (2001). “Modeling cover-cracking due to reinforcement corrosion in RC structures.” J. Eng. Mech., 127(4), 342–351.
Rasheeduzzafar, Al-Saadoun, S. S., and Al-Gahtani, A. S. (1992). “Corrosion cracking in relation to bar diameter, cover, and concrete quality.” J. Mater. Civ. Eng., 4(4), 327–342.
Raupach, M., and Schiessl, P. (1997). “Monitoring system for the penetration of chlorides, carbonation and the corrosion risk for the reinforcement.” Constr. Build. Mater., 11(4), 207–214.
Rodriguez, J., Ortega, L. M., Casal, J., and Diez, J. M. (1996). “Corrosion of reinforcement and service life of concrete structures.” Proc., 7th Int. Conf. on Durability of Building Materials and Components, Vol. 1, C. Sjöström, ed., E & FN Spon, London, 117–126.
Rots, J. G. (1988). “Computational modeling of concrete fracture.” Ph.D. dissertation, Delft Univ. of Technology, Delft, The Netherlands.
Scanlon, A. (1975). “Time dependent deflections of reinforced concrete slabs.” Ph.D. dissertation, Univ. of Alberta, Edmonton, Alta.
Stewart, M. (2004). “Spatial variability of pitting corrosion and its influence on structural fragility and reliability of RC beams in flexure.” Struct. Safety, 26(4), 453–470.
Stewart, M., and Rosowsky, D. (1998). “Structural safety and serviceability of concrete bridges subject to corrosion.” J. Infrastruct. Syst, 4(4), 146–155.
Tada, H., Paris, P. C., and Irwin, G. R. (2000). The stress analysis of cracks handbook, ASME, New York.
Tastani, S., and Pantazopoulou, S. J. (2005). “Recovery of seismic resistance in corrosion-damaged reinforced concrete through FRP jacketing.” Int. J. Mater. Prod. Technol., 23(3/4), 389–415.
Torres, L., Lopez-Almansa, F., and Bozzo, L. M. (2004). “Tension-stiffening model for cracked flexural concrete members.” J. Struct. Eng., 130(8), 1242–1251.
Torres-Acosta, A. A. (1999) “Cracking induced by localized corrosion of reinforcement in chloride contaminated concrete.” Ph.D. dissertation, Dept. of Civil and Environmental Engineering, Univ. of South Florida, Tampa, Fla.
Torres-Acosta, A. A., Fabela-Gallegos, M. J., Munoz-Noval, A., Vazquez-Vega, D., Hernandez-Jimenez, J. R., and Martinez-Madrid, M. (2004). “Influence of corrosion on the structural stiffness of reinforced concrete beams.” Corrosion (Houston), 60(9), 962–872.
Uddin, F. A. K. M., Shigeishi, M., and Ohtsu, M. (2006). “Fracture mechanics of corrosion cracking in concrete by acoustic emission.” Meccanica, 41(4), 425–442.
Val, D. V., Chernin, L., and Stewart, M. G. (2009). “Experimental and numerical investigation of corrosion-induced cover cracking in reinforced concrete structures.” J. Struct. Eng., 135(4), 376–385.
Vidal, T., Castel, A., and François, R. (2007). “Corrosion process and structural performance of a 17 year old reinforced concrete beam stored in chloride environment.” Cem. Concr. Res., 37(11), 1551–1561.
Vu, K. A. T., and Stewart, M. G. (2000). “Structural reliability of concrete bridges including improved chloride-induced corrosion models.” Struct. Safety, 22(4), 313–333.
Vu, K. A. T., Stewart, M. G., and Mullard, J. (2005). “Corrosion-induced cracking: Experimental data and predictive models.” ACI Struct. J., 102(5), 719–726.
Wang, X. H., and Liu, X. L. (2004). “Modelling effects of corrosion on cover cracking and bond in reinforced concrete.” Mag. Concrete Res., 56(4), 191–199.
Williamson, S. J., and Clark, L. A. (2000). “Pressure required to cause cover cracking of concrete due to reinforcement corrosion.” Mag. Concrete Res., 52(6), 455–467.
Wu, X. R., and Carlsson, A. J. (1991). Weight functions and stress intensity factor solutions, Pergamon, Oxford
Wu, Z., Yoshikawa, H., and Tanabe, T. (1991). “Tension-stiffness model for cracked reinforced concrete.” J. Struct. Eng., 117(3), 715–732.
Zhao, Y. X., and Jin, W. L. (2006). “Modeling the amount of steel corrosion at the cracking of concrete cover.” Adv. Struct. Eng., 9(5), 687–696.

Information & Authors

Information

Published In

Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 136Issue 2February 2010
Pages: 209 - 219

History

Received: Oct 15, 2008
Accepted: Jul 16, 2009
Published online: Jul 18, 2009
Published in print: Feb 2010

Permissions

Request permissions for this article.

Authors

Affiliations

Jinquan Zhong, S.M.ASCE
Doctoral Student, Zachry Dept. of Civil Engineering, Texas A&M Univ., College Station, TX 77843-3136.
Paolo Gardoni, M.ASCE [email protected]
Associate Professor, Zachry Dept. of Civil Engineering, Texas A&M Univ., College Station, TX 77843-3136 (corresponding author). E-mail: [email protected]
David Rosowsky, F.ASCE
Professor, A.P. and Florence Wiley Chair, Zachry Dept. of Civil Engineering, Texas A&M Univ., College Station, TX 77843-3136.

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share