Keywords: bond modelling, nonlinear analysis, pullout tests, bond-zone, interface elements, bond-link springs, DIANA finite element package.

This paper presents a comparison between two well-known bond-slip modelling techniques in finite elements (FE). The first is the "bond-link" method, or springs as preferred by many scholars, proposed by Ngo and Scordelis [1] and adopted by many FE codes such as ABAQUSRand ANSYSR. The second is the "bond-zone" method, developed by De Groot et al. [2], that relies on "interface elements". The bond-zone method is adopted by DIANARFE code.

Simple FE models were built using the bond-zone approach in DIANARto compare with similar models in the literature that used the bond-link approach. These simple models represent different testing configurations (pullout and tension tests), different reinforcement materials (FRP and steel), and partial and full embedment lengths.

Results from the pullout models showed that the bond-link approach yielded somewhat higher values of bond stress along the embedment. Load vs. Slip curves for pre-pullout loading were similar for both bond-link and bond-zone models and accordingly, the higher bond stress values indicate over-estimation of bond stiffness at spring points as a result of concentrating the bond strength of a length equal to the spring spacing in one place. This also led to the final pullout failure load being slightly higher than in bond-zone models, although the total available bond strength is thought to be similar.

The tension test model confirmed the same tendency for bond stresses to be higher in the bond-link method for the same value of external loading. This led to a higher axial stress build-up rate in concrete and accordingly might affect the value of external loading at which cracks propagate. Also, transmitting reinforcement stress to concrete through a few predefined gates (springs) will lead to stress concentration at these gates, and may provide guidance as to where the cracks should form hence, affecting the crack spacing.

Partial embedment pullout models showed that the rate of decrease of bond stress (as a result of increased embedment) is higher for short embedment lengths than long ones. The bond-zone models also revealed that slip plays a major role in dictating the bond stress values at the loaded-end of short embedment lengths and that this role diminishes after a certain embedment length threshold is exceeded. However, this was not the case at the unloaded-end where slip and bar stress seemed to equally affect the values of bond stress.

The overall modelling results suggest that the bond-zone method presents a better and more natural distribution of bond strength and accordingly is expected to be closer to reality. Bond-zone three-dimensional models required fewer input parameters, which results in fewer variables especially when it comes to selecting interface-element thickness normal-to-the-bar and in the third dimension out-of-plane.

1

D. Ngo, A.C. Scordelis, "Finite-element analysis of reinforced concrete beams", ACI Structural Journal 64(3), 152-163, 1976.

2

A.K. De Groot, G.M.A. Kusters, T. Monnier, "Numerical modelling of bond-slip behaviour", Heron, MT, Conc. Mech. 26(1B), 6-38, 1981.

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