Keywords: finite element, bond loss, concrete beam, reinforcement, strength.

Corrosion of reinforcement is the principle cause of deterioration of concrete structures. It not only decreases the cross sectional area of reinforcement, which affects both strength and ductility of bars [1], but also leads to cracking and eventual spalling of concrete [2]. In addition, corrosion also deteriorates the bond between concrete and reinforcement [3]. As a consequence, both safety and serviceability of corrosion-damaged structures are impaired.

This paper reports the analytical results of reinforced concrete beam using a finite element (FE) method package, DIANA, to investigate the effect of bond loss alone, on the behaviour of concrete beams.

The reinforced concrete beams physically tested by Rodriguez et al. [4] were idealised as a two-dimensional model and analysed under a plane stress assumption. The FE model comprised three kinds of elements. The eight node quadrilateral plane stress element CQ16M was used to idealise both beam concrete and the two steel plates positioned at beam support and loading point. The three node straight truss element CL6TR was employed to model both longitudinal and transverse reinforcement. The six node interface element CL12I was utilised to simulate the bond behaviour and was inserted between the reinforcement elements CL6TR and concrete ones CQ16M.

The Von Mises model with strain hardening plasticity theory was used to simulate the non-linear behaviour both of the reinforcement and the compression concrete. A smeared multidirectional crack model with tension softening was employed to idealise the non-linear behaviour of tension concrete. Cracking of tension concrete was assumed to initiate in a direction normal to the maximum principal stress once the limiting strength of concrete is exceeded.

The local bond-slip model used to simulate interaction behaviour between concrete and reinforcement was mainly based on the bond model proposed in the CEB Model Code 1990 [5]. The maximum bond strength for non-corroded bars was taken as 1.9 times of concrete tensile strength, i.e. . The deterioration of bond strength was simulated by applying a residual strength coefficient to the bond stress in the local bond-slip model in order to obtain a reduced bond value , while the corresponding slip is assumed to be the same as those of non-corroded beams. The geometric dimensions and material properties of concrete and reinforcement were taken either from measurements reported by Rodriguez et al. [4], or from default recommendations given in the DIANA User Manual [6].

A comparison of the analytical results using the FE model with full bond strength with the experimental results of non-corroded concrete beams reported by Rodriguez et al. [4] indicates that the developed FE model was able to give reasonable results and therefore it is used to assess the potential influence of loss of bond alone, as a consequence of reinforcement corrosion, by using residual strength coefficients on the maximum bond strength in the local bond-slip model of 0.5, 0.4 and 0.3, respectively, in the ultimate bond strength throughout the whole length of the longitudinal tension reinforcement only, where a direct comparison between the FE computations and experimental results cannot be made. Such an analysis aims at revealing how bond loss may affect residual strength and ductility of concrete beams.

The analytical results using the FE beam model indicate that the bond loss alone had no significant effect on initial stiffness of the beams. If the residual bond strength were not less than 50% and 60% of the full bond strengths for Beam I and Beam II, respectively, the bond loss has little influence on their mechanical behaviour.

However, when the residual bond strength is reduced below 50% and 60% of the full bond strengths, bond loss decreases ultimate strength and ductility of reinforced concrete beams and may transform a ductile flexural failure with substantial post-yield deflection into a brittle failure with very small defection. In addition, the behaviour of concrete beams with a high reinforcement ratio is more sensitive to the bond loss than those with a low reinforcement ratio.

1

Du Y.G., Clark L.A., and Chan A.H.C., "Residual Capacity of Corroded Reinforcing Bars", Magazine of Concrete Research, Vol.57, No. 7, April, 2005. doi:10.1680/macr.57.3.135.60482

2

Du Y.G., Chan A.H.C. and Clark L.A. "Finite Element Analysis of Corrosion Cracking of Concrete Beams", International Journal of Computers & Structures (in press), 2006.

3

Cairns J., Du Y.G. and Law D.W. "Residual Bond Strength of Corroded Plain Round Bars", Magazine of Concrete Research, Vol.58, No. 4, May, 2006. doi:10.1680/macr.2006.58.4.221

4

Rodriguez J., Ortega L.M., Casal J. "Load Carrying Capacity of Concrete Structures with Corroded Reinforcement", Proceedings of the 6th International Conference on Structural Faults and Repair, London, UK, Edinburgh: Engineering Technics. Press, July 1995.

5

CEB_FIP Model Code 1990, Comite Euro-International du Beton, CEB-FIP, 1993.

6

DIANA User's Manual, Non-linear Analysis, TNO Building and Construction Research

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