Keywords: bond-slip, concrete-rebar interface, damage, damaged reinforced concrete element, finite element, reinforced concrete.

In the finite element analysis of reinforced concrete, the most widely used approach is to model the concrete, reinforcement bars (rebars) and concrete-rebar interface separately, whereby the bond-slip on the interface is modeled using bond-link elements or dimensionless contact elements. Hence, in most cases, many elements are needed for accurate results to be obtained especially when 3-dimensional analysis is carried out. In cases of complicated arrangement of rebars, as it is in the common engineering applications, the modeling will be a laborious job. Further more, according to experimental observations, there are interactions between concrete cracking and bond deterioration which are difficult to take into account using this type of concrete- interface-rebar meshing.

In this paper, effort has been made to integrate concrete, rebar and concrete-rebar interface into a reinforced concrete element. The degradation of the material (concrete, rebar and concrete-rebar interface) behaviors is described using continuum damage mechanics, so the element is named as damaged reinforced concrete (DRC) element. The DRC element consists of a 2-node rod element for the rebar, a 4-node interface element for the concrete-rebar interface and a 10-node brick element for the concrete. The tension mode of the rebar and the slip mode of the interface are considered in the rod element and the interface element, respectively. The 10-node concrete element is developed from an 8-node isoparametric element, with an additional displacement mode introduced to account for the shear deformation induced by bond stress from the concrete-rebar interface. As a result of these deformation modes, 3 damages are defined in reference[1], i.e. the bond damage of the interface due to the slip; the non-local damage of concrete due to the displacement modes of the 8-node isoparametric element; and the local damage in the concrete around the rebar due to the additional displacement mode and wedge action of the deformed rebar. The zone where local damage occurred is thus called the affected zone, and for simplification, , , and , are all assumed to be scalars.

Of the three kinds of damages, the local damage , and the bond damage , are closely related, and both of them can be attributed to the wedge action of the rebars. Hence, for simplification, the local damage , is assumed to be proportional to the bond damage , , i.e.

where , is a parameter that needs to be calibrated in the DRC element. Thus, in the DRC element, the local damage , is treated as one aspect of interaction between the concrete cracking and the bond deterioration. The other aspect of interaction considered in the DRC element is the bond weakening due to concrete cracking, which has been reported in reference[2], and another parameter is introduced to account for it.

In the DRC element, the material performances of the concrete, rebar and the concrete-rebar interface are all modeled using damage mechanics, and these descriptions by damage scalars made it easier to consider the interaction between the concrete weakening and the bond deterioration. The yielding of the steel bar is also described using a damage scalar, so that the effect of rebar yielding on the bond behavior can be taken into account.

In the DRC element, the evolution equations of the non-local damage , is obtained from fitting a linear softening phase of stress-strain curve, and the damage scalar , is used to simulate the behavior of an ideal elastic-plastic rebar. A translated Weibull cumulative distribution function is used as the evolution rule of the bond damage ,, and the distribution parameters are expressed using the material parameters in the bond- slip curve. The parameters considering the interaction between the concrete weakening and the bond deterioration, and , are determined according to the experimental observations of other researchers[2,3].

Finally, the limitations of the DRC element and the further work are also discussed.

1

Y. Liu, "Computational experiment of composite structural element using damage mechanics", First Year's Report, Nanyang Technological University, Singapore, 1999.

2

K. Maekawa, J. Qureshi, "Computational model for reinforcing bar embedded in concrete under combined axial pullout and transverse displacement", Concrete Library of JSCE, Japen, 1997.

3

S. Hayashi, S. Kokusho, "Fundamental study of bond between deformed bar and concrete", Proc. Of AIJ, Oct, 1982.

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