Simulation of the degraded (steel - concrete) bond strength due to corrosion via modeling pull out tests

Steel corrosion is recognised as major degradation factor of structural capacity and durability of reinforced concrete (RC) structures, especially in marine environment. RC structures with corroded reinforcement present reduced performance due to loss of the cross-sectional area of reinforcement, cracks in concrete and loss of bond between steel and the surrounding concrete. In the present study, simulation of the degraded bond strength on corroded RC elements was elaborated developing a three-dimensional (3D) model through finite element analysis (FEA) in ABAQUS, taking into account the recommendations of fib Model Code 2010. As a basis for the model validation, an existing experimental study on the effect of corrosion and stirrups spacing on bond behavior was considered. In the abovementioned study the bond mechanism of two groups of corroded RC specimens in confined (stirrups Φ8/120mm) and unconfined (without stirrups) conditions were examined upon the completion of eccentric pull-out tests. In order to model the complex conditions of the corroded steel-concrete interface, the cohesive behavior was adopted by appropriately modificated parameters, for each corrosion level. The bond-slip curves extracted from the developed model were shown to be in a good agreement with the relevant experimental results. In particular, the bond strength of confined RC specimens deviates at about 10% among the analytical and experimental outcomes, for both uncorroded and corroded conditions up to 8.3% corrosion level. In case of the unconfined specimens, the bond strength prediction was satisfactory up to 5% corrosion level, whereas for greater corrosion level, large deviation was observed. Regarding the prediction of the relative slip between steel and concrete, further investigation is required as the development of slip is influenced by a plethora of factors.


Introduction
Since the turn of the past century, reinforced concrete (RC) has dominated as the most popular construction and infrastructure material worldwide, as it is characterized by high mechanical performance, low production costs and easy handling.The basic prerequisite for the satisfactory operation and mechanical performance of reinforced concrete is the cooperation of its two materials, concrete and steel reinforcement, through the mechanism of bond between them.As the steel reinforcing bars take up the tensile forces in RC cross-sections, stresses are developed, which appear as components parallel and perpendicular to the steel -concrete interface.The stress that is parallel to the reinforcing bar is referred to as bond stress.The radial tension stress generated perpendicular to the contact surface is represented by shear stress in the XY plane of the concrete [1].The bond mechanism, expressed in terms of bond strength (stress) and relative slip (displacement), reflects the cooperation of the two materials and affect the overall structural response of reinforced concrete members, their deformation and torsional capacity.
However, corrosion of steel reinforcement consists a major degradation factor of bond mechanism and subsequently of the bearing capacity of RC members, since corrosion products influence negatively the steel -concrete interface conditions, allowing the development of relative slip between them and reducing the bond strength.In the presence of corrosive environment, volume expansion of steel reinforcement due to corrosion results in generating splitting stresses in the concrete which in turn affects the bond between concrete and steel (Figure 1).At extensive corroded steel reinforcement, the increased volume of corrosion oxides generates expansive stresses, which gradually increase leading to concrete cracking development and subsequently spalling of concrete cover [2][3][4][5].In this framework, the present work simulated the degraded bond strength due to steel corrosion through modeling pull out tests on corroded RC specimens based on previous experimental study of Koulouris and Apostolopoulos [3].A three-dimensional (3D) model was developed, using finite element analysis (FE) in ABAQUS to simulate the degradation of bond strength of corroded structural components, taking into account the recommendations of fib Model Code 2010.Focusing the study on the RC members of old existing structures, which are characterised as slightly confined or unconfined, the effect of stirrups spacing on bond behavior was considered in the simulation of the degraded bond strength.Thus, adopting the aforementioned experimental study, RC specimens with Φ8/120mm transverse reinforcement (slightly confined) and without stirrups (unconfined) were developed for the analytical model, which was subjected to tensile pull-out tests of the main eccentrically placed corroded bar.

Model geometry
Taking into consideration the specimens' geometry from the study of Koulouris and Apostolopoulos [6], the dimensions of the model were 200mm x 240 mm x 310mm, as depicted in Figure 2a and 2b.In detail, based on the abovementioned study, two categories of specimens were studied, namely specimens without stirrups (Figure 2a) and specimens with stirrups Φ8/120 mm (Figure 2b).The FE model for the controlled specimen was created considering a basic perfect connection, in which concrete and steel reinforcement were connected to surrounding interface nodes (Figure 2c).

Modelling of materials
In ABAQUS, the Kent & Park model [7] was adopted for both unconfined and confined concrete (Figure 3a), where the compressive stress of unconfined concrete for class C20/25 was considered equal to 28 MPa.As for steel reinforcement, a bilinear σ-ε model was adopted based on the Rasmunseen model [8], which takes into account the elasto-plastic behavior of steel (Figure 3b).

Modelling deteriorated Bond-Slip behavior
To simulate bond-slip behavior in ABAQUS, a mechanical model based on traction-separation law was used, which allows the bond between the two surfaces (steel and concrete) to be expressed as a linear elastic relationship between traction (t) (bond stress) and separation (δ) (slip).In this study, the thickness of the interface was assumed negligible, although this is not the actual situation.Hence, surface-based cohesive behavior was adopted, since it provides a simplified way to model cohesive connections with negligibly small interface thicknesses using the traction-separation constitutive model.To implement traction-separation in the model, 3 elastic stiffness coefficients, a damage initiation displacement δinit and an evolution displacement δevol further of which there is no contact were determined.An elastic constitutive matrix represents the elastic behavior, which relates the shear and normal stresses to the shear and normal separations across the interface.The constitutive relation for elastic part is either uncoupled or coupled.Due to uncertainties about the coupled behavior, uncoupled constitutive relation has been chosen and coefficients Knn, Kss, and Ktt were determined, as follows: where τmax is calculated according to Model Code 2010 [9].In order to calculate δinit is determined via Model Code's equation for local bond : as for τb,max in the presence or absence of stirrups we have the following piecewise function, where fcm is the mean compressive strength of concrete:

Modelling of corrosion
The damage occurred in concrete due to corrosion in FE model can be represented, as proposed by Wang and Liu [10] via a quantitative general assessment of the induced damage in concrete with the aim of the subsequent effect on the concrete-steel bond.Cracks that occur due to corrosion in concrete affect the mechanical behavior of the structural member and reduce its load-bearing capacity.In that manner, the degradation of the mechanical properties of the surrounding to the corroded reinforcing bar concrete up to the radius of the crack front Ri, [11,12] is set appropriately in each case to simulate the different corrosion damage, as shown in Figure 6.Furthermore, to account for the different corrosion levels among the specimens and, hence, the reduced capacity on bond strength, a reduction factor R, was used to the above calculated τmax based on Model Code (Table 1), to simulate the effect of corrosion on bond mechanism.It is worth mentioning that corrosion damage was considered uniform.
Table 1.The magnitude of the reduction in residual bond strength for corroded reinforcement [9].In figure 8, in case of unconfined specimens, without stirrups, the prediction of bond strength through the Abaqus model is validated for corrosion level up to 5%.Then for greater corrosion level, deviation is presented for the prediction of bond strength.This observation comes in agreement with available experimental data in literature, where large scatter of the degraded bond strength is recorded.

Conclusions
In the current study, a comparison between experimental pull-out tests and analytical model via Abaqus was carried out.From the current results, the following outcomes were obtained: 1.The Abaqus model demonstrated sufficient convergence in respect to the experimental results for the bond strength, for both cases of unconfined (without stirrups) and slightly confined (stirrups Φ8/120 mm) specimens.However, there is no good agreement for the slip at bond strength, especially for unconfined specimens.

Figure 1 .
Figure 1.Cracking development and spalling of concrete cover due to corrosion of steel reinforcement [6].

Figure 2 .
Figure 2. Typical geometry of two categories of experimental specimens: (a) without stirrups, (b) with stirrups Φ8/120 mm and (c) representation of model's geometry.

Figure 4 .
Figure 4. (a) Uncoupled Traction-Separation Law Matrix and b) Bilinear Curve, elastic part and damage evolution.

Figure 6 .
Figure 6.Assigning material properties based on the different Crack Front Ri for Specimens with no stirrup confinement.a) Reference Specimen b) Test Specimen with 0.97% mass loss c) Test Specimen with 2.05% mass loss d) Test Specimen with 4.12% mass loss.