Keywords: smeared crack model, reinforced concrete, monotonic, cyclic loading, RC bridge pier.

This paper presents a study of different smeared crack models for reinforced concrete bridge piers under cyclic loading. An existing multi-smeared crack model and a new plastic-damage-contact model, named Craft, which were implemented in the finite element (FE) program LUSAS, are used in this investigation. At first the two models are verified through comparisons with experimental results for various cases of reinforced concrete (RC) structures under monotonic loading. Then the models are used to predict the behaviour of a RC bridge pier under cyclic loading. Some comments are also made to the use of the models subject to earthquake-like cyclic loading.

This paper focuses on the performance of two plasticity-based smeared crack models, namely the Multi-crack model [1] and Craft model [2], which were implemented into the FE program LUSAS, for the analysis of RC bridge piers under cyclic loading. The theoretical background of the models is briefly described and then they are verified by analysing various cases of concrete and RC structures under monotonic loading. The models are then used for the analysis of RC bridge piers under cyclic loading. Emphasis is particularly placed on evaluating the ability of the models to capture the cyclic behaviour in order to go to the next stage of the research programme, i.e. analysing RC bridge piers under artificially generated earthquakes.

In the case of validation of the models under monotonic loading, there are two examples presented in this paper. The first example is the analysis of an unreinforced concrete rectangular beam experiment conducted by Carpinteri [3]. In the finite element modelling, the results of two different meshes are presented. The comparison between the numerical and experimental results shows that both the Multi-crack and Craft models agree well with the experimental result and also, the analytical result [4]. The second example is the analysis of a rectangular reinforced concrete beam tested by Bresler and Scordelis [5]. The numerical results of the two models show a good correlation between the experimental and numerical results in terms of the load and the central deflection of the testing beam. In addition, the load-central deflection curve obtained from the analytical solution (detailed in reference [4]) is plotted and it confirms that the results of the three methods are reasonably close to each other.

In the case of the validation of the models under cyclic loading, an analysis of a RC bridge pier which was tested under a pseudo-dynamic condition during the PREC8 project [6] is presented. Regarding the comparison between numerical and experimental results, it is concluded that, the Multi-crack model is, in general, not capable of capturing the cyclic behaviour of RC bridge piers. The chief flaw with the model is that unloading behaviour in concrete is linear elastic, which is unrealistic for concrete. However, it is still capable of reproducing the reasonable magnitudes of the peak load and displacement at zero loads. Therefore, the model should be used with care if used for analysis of structures under cyclic loading as the damping and unloading stiffness have been overestimated. Refinement of the model would be required for using this model if is to be used for cyclic loading.

The result of the plastic-damage-contact model, Craft, is generally in good agreement with experimental results of the RC bridge pier under cyclic loading. This is because the model takes into account most of non-linear effects of concrete and reinforced concrete under cyclic loading. However, as the peak load at each cycle is slightly too high compared with experiment, slight modifications to the material properties will be checked and also, the consideration of bond slip between concrete and steel reinforcement may be necessary.

Based on these investigations, the Craft model is suggested to use for further analyses of RC bridge piers under cyclic and earthquake-like cyclic loading.

1

LUSAS, "User Manual", FEA Ltd, England, 2001.

2

A.D. Jefferson, "Craft, A Plastic-Damage-Contact Model for Concrete, I. Model Theory and Thermodynamics", International Journal of Solids and Structures, 40(22), 5973-5999, 2003. doi:10.1016/S0020-7683(03)00390-1

3

A. Carpinteri, "Minimum Reinforcement in Reinforced Concrete Beams", RILEM TC 90-FMA, CODE WORK, Cardiff, 20-22 September 1989, UK, 1989.

4

V.B. Nguyen, and A.H.C. Chan, "A New Analytical Solution for Cracked Reinforced Concrete Beams", Computers and Structures, 2006 (In preparation)

5

B. Bresler, and A.C. Scordelis, "Shear Strength of Reinforced Concrete Beams", ACI Journal, 60(1), 51-72, 1963.

6

A.V. Pinto, "Pseudo-Dynamic and Shaking Table Tests on R.C. Bridges", PREC8 Report, LNEC Lisbon, Portugal, 1996.

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