Keywords: bond slip, RC structures, FEM method, design tool for engineering practice, sample analysis.

The paper presents a numerical model for bond between reinforcing bars and concrete. It is based on one-dimensional geometry of reinforcing bars, but it considers interface surface properties, and the same physical models can be applied as in the case of the full surface interface. Any bond-slip relationship can be implemented within the model. Example analysis of a shear failure of beams is presented and the effect of bond on the beam response is demonstrated.

Bond between steel reinforcing bars and concrete is an important part of the reinforced concrete mechanical system. Due to its significance for practical design, bond was investigated by many researchers and technical committees, e.g. Report FIB 2000 [1]. This effort resulted in numerous empirical formulas and complex code provisions for bar anchoring length and reinforcement detailing. This knowledge is mainly utilized in practical design, but it can also serve as a basis for constitutive models in numerical analysis. However, in most numerical nonlinear analyses of reinforced concrete structures in engineering practice a perfect bond between concrete and reinforcement bars is assumed.

Although this is usually appropriate, there are cases, in which the effect of bond slip cannot be neglected. Currently, there exist various methods to account for this phenomenon. Recently various researchers proposed approaches based on detailed three-dimensional analysis of interaction between concrete and bars using 3D models of concrete and reinforcement with two-dimensional interfaces between them. Such an approach was chosen by Lundgren [2], who developed an interface bond model based on plasticity theory with fully three-dimensional features. The advantage of this approach is that the interfacial behaviour can be described using established material modelling methods such as for instance plasticity. Debonding as well as dilatancy and other bond characteristics can be very well modelled by this approach. However, for practical analysis of reinforced concrete structures this approach is not very appealing due to its extremely large computational capacity requirements. Also the development of appropriate numerical models is not straightforward and not supported by existing automatic mesh generation tools.

In the presented model the engineering strain in a reinforcement bar is calculated by , where and are respectively total and slip element displacement and is length of the bar. The added slip displacement field is eliminated by the equilibrium condition for reinforcement bar with prescribed bond, which reads , where , , and is stress in the bar, bar perimeter and bar cross sectional area, respectively. The states a rule for cohesion stress. Such a function is usually obtained from a laboratory pullout experiment. This method is relatively simple and efficient. It involves an additional iterative loop to calculate bar's element slips , (that is placed within evaluation FE nodal forces). It poses a good compromise between the solution accuracy and computational demands and hence, it is applicable for analyses from wide engineering practice.

The behaviour of the proposed approach is demonstrated on analyses of laboratory experiments, such as a shear failure of a beam as well as on the analysis of post- tensioned hollow-core slabs, where bond between smooth pre-stressing bars and concrete plays an essential role in determining the load-carrying capacity of the system, e.g. Figure 1.

1

FIB2000, "Bond of Reinforcement in Concrete - State-of-art Report Task Group Bond Models", FIB Bulletin, 10, 2000.

2

K. Lundgren, "Three-Dimensional Modelling of Bond in Reinforced Concrete", Thesis, Department of Civil Eng., Chalmers University of Technology, 1999.

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