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									NUMERICAL MODELLING OF BOND BETWEEN CONCRETE AND
CORRODED REINFORCEMENT
Leon Chernin and Dimitri V. Val

School of the Built Environment, Heriot-Watt University, Edinburgh EH14 4AS, UK




Abstract
   Corrosion of reinforcing steel is the main cause of deterioration of reinforced concrete
structures. It causes cracking and eventually spalling of the concrete cover, reduction of cross-
sectional area of reinforcing steel and damage to bond between concrete and reinforcement.
The paper concentrates on the last issue, i.e., corrosion-induced degradation of the bond in RC
structures. It starts with a brief overview of existing analytical and numerical models of the
corrosion-induced degradation of the interface between steel and concrete caused by corrosion
A new model describing the influence of steel corrosion on the interaction at the steel-
concrete interface is then developed based on available experimental data. In the paper only
plain reinforcing bars are considered, for which bond depends on two mechanisms – adhesion
and friction. The model takes into account the effect of corrosion on these mechanisms and
also accounts for the effects of creep and drying shrinkage. Thermal analogy is used for
simulations of corrosion and drying shrinkage of concrete. The model in an axisymmetric
formulation is implemented into a finite-element (FE) numerical model and then calibrated
using experimental data from pull-out tests. Finally, the model is used to simulate pull-out
tests of corroded plain round bars. Results of the FE simulations are presented and compared
with test results.


1. INTRODUCTION
   One of the most important factors governing strength and serviceability of reinforced
concrete structures is bond, which provides the transfer of tensile forces between the
reinforcement and the surrounding concrete. Loss of the bond (i.e., slip between the
reinforcement and the concrete) along a partial length in the mid-span of a RC element does
not usually lead to the element failure, however, it will cause stress redistribution resulting in
concrete cracking, reduction of the element stiffness and an increase in the element deflection.
Damage to the bond is mainly caused by corrosion of reinforcing steel.
   The paper presents an investigation of corrosion-induced degradation of the bond of steel-
concrete interface. Existing analytical and numerical models describing this process are




                                                                                         Page 1
critically reviewed. A new model describing the influence of steel corrosion on the interaction
at the steel-concrete interface is developed based on available experimental data [1-3]. The
bond is modelled taking into account two mechanisms – adhesion and friction, and their
deterioration induced by corrosion. The model in an axisymmetric formulation is
implemented into the FE commercial code – ABAQUS, using a user defined subroutine [4]; it
is calibrated against the experimental data reported by Cairns et al. [5]. Effects of creep and
drying shrinkage are also accounted in the FE analysis. Thermal analogy method is used for
simulations of both reinforcing bar corrosion and drying shrinkage of concrete. Finally, the
model is used to simulate pull-out tests of corroded plain round bars. Results of the FE
simulations are presented and compared with test results. A good agreement between the test
results and those of FE analysis is obtained.

2. CORRODED REINFORCING BAR/CONCRETE INTERFACE: AN OVERVIEW
   Adhesion (or interfacial cohesion) and friction are two factors (in absence of mechanical
interlocking between bar ribs and concrete lugs) controlling the bond of steel-concrete
interface. Loss of steel at the rebar surface caused by corrosion increases the surface
roughness, which leads to an increase in friction at the interface [1, 6]. However, rebar slip
can cause smoothing of the interface and, consequently, decrease friction between the two
materials. Corrosion products developing at the steel-concrete interface together with growing
interfacial pressure cause binding of concrete and reinforcing steel together that initially
increases the strength of adhesion [2]. Subsequent thickening of the rust layer eventually
results in gradual deterioration of the adhesion [3].
   Influence of corrosion on interfacial friction was taken into account in a number of
analytical models [7-9]. Friction is incorporated into existing numerical models only
implicitly as a part of interfacial resistance with neglecting corrosion-induced influence [10-
13]. Adhesion is usually neglected in modelling the bond between steel and concrete [8, 9,
14]. Only the analytical model suggested by Coronelli [7] includes deterioration of adhesion
due to corrosion. However, tests carried out by Williamson and Clark [2] showed that
corrosion products could cause binding of concrete and reinforcing steel together. For
example, steel-concrete “fusion” led in the tests to increase of the bond strength between plain
reinforcing bars and concrete even after splitting of concrete cover.

3. MODELLING A CORRODED REINFORCING BAR/CONCRETE INTERFACE
   In the present study a model of shear response of corroded steel-concrete interface is
developed on the basis of available experimental results [1-3]. The shear resistance of the
corroded steel-concrete interface, fb,fr, is described by the Coulomb model with the cohesion
term, fcoh, representing adhesion as
fb , fr ( s, x, icorr )  f coh ( s, x, icorr )   ( s, x)  f n ( x)                       (1)

where fn is the normal stress on the interface,  the coefficient of friction, s slip of the
reinforcing bar, x the corrosion penetration, and icorr the corrosion current density. fcoh is
formulated as a product of two functions: fcoh,s and fcoh,x. The former represents the influence
of the rebar slip, s, while the latter takes into account the influence of the level of corrosion
(expressed in terms of x) and the rate of rust production (expressed in terms of the corrosion
current density, icorr), i.e.,




                                                                                        Page 2
f coh ( s, x, icorr )  f coh , s ( s )  f coh , x ( x, f coh ,icorr (icorr ))                                                     (2)
where fcoh,icorr is the component of interfacial cohesion depending on the rate of rust
production. The functions fcoh,s, fcoh,x and fcoh,icorr are shown in Figure 1, where sc1 is the rebar
slip at the beginning of cohesion deterioration, sc2 the rebar slip at the total loss of interfacial
cohesion, xc1 the corrosion penetration corresponding to fcoh,icorr, xc2 the critical corrosion
penetration corresponding to elimination of interfacial cohesion, c0 the initial cohesion of
steel-concrete interface; kicorr and cicorr are an empirical coefficient and icorr,c is the corrosion
rates at the start of fcoh,icorr decrease.

         fcoh,s (MPa)                                                                   fcoh,x (MPa)
                                                                       fcoh,icorr

 1.0



                                                                                  c0
                                                  s (mm)                                                                          x (mm)
               sc1                       sc2                                                            xc1                xc2

                        (a)                                                                              (b)

                                                 fcoh,icorr (MPa)

                                  fcoh,max                                        fcoh,icorr=cicor exp[–kicorricorr]




                                                                                                          icorr (A/cm2)
                                                          icorr,c
                                                                              (c)
           Figure 1: Components of interfacial cohesion: (a) fcoh,s, (b) fcoh,x and (c) fcoh,icorr.

   The influence of corrosion on frictional characteristics of the steel-concrete interface is
modelled by varying the coefficient of friction, μ, in the range between 0.3 and 0.6 in
accordance with Xu [1]. The relationship between a component of μ representing corrosion
influence, i.e., x, and corrosion penetration, x, is presented in Figure 2(a), where xµ is the
corrosion penetration corresponding to a high level of roughness of steel surface.
Additionally, the decrease of friction (i.e., component s) caused by smoothing of the steel-
concrete interface, which develops with slip, s, is accounted in the form presented in Figure




                                                                                                                                 Page 3
2(b), where s,max is the initial (maximum) coefficient of friction before rebar slip develops;
s,res is the residual coefficient of friction corresponding to high values of rebar slip; and sµ1
and sµ2 are the slip displacements at the start and the end of degradation of s, respectively;
and ks is the coefficient describing reduction of the coefficient of friction due to the rebar
slip. The proposed relationship between s and s assumes that smoothing of the corroded
steel-concrete interface does not develop immediately with the rebar slip but after a certain
slip – sµ1. Additionally, s,res cannot be less than the coefficient of friction of an uncorroded
steel-concrete interface, i.e., 0.3 (see Figure 2(b)). Finally, values of the coefficient of friction
are completely governed by s, i.e.,  ≡ s.
           x                                               s          s,max≡x
                                                                        s,res=max{ksx; 0.3}
     0.6
                                                  s,max

                                                   s,res
     0.3
                                  x (mm)                                                  s (mm)
                      xµ                                         sµ1        sµ2

                    (a)                                                 (b)
                           Figure 2: (a) x versus x and (b) s versus s.

4. MODEL CALIBRATION AND IMPLEMENTATION INTO A FE ANALYSIS
   The presented model of a corroded steel-concrete interface cannot be calibrated against the
results of pull-out tests with corroding deformed reinforcement, because it is difficult to
separate contribution of mechanical interlock between concrete lugs and bar ribs from the
contribution of friction and chemical adhesion to the interfacial resistance. Therefore, the
model is calibrated using the results of pull-out tests with plain 16 mm diameter reinforcing
bars carried out by Cairns et al. [5] (see Figure 3). The test specimens Y1-Y6 were designed
in accordance with RILEM recommendations for pull-out test [15]. The concrete had the
following characteristics: the compressive strength fc = 38.4 MPa, the tensile strength fct =
3.43 MPa, the modulus of elasticity Ec = 33700 MPa. Before the pull-out test all the
specimens (except of a control one – Y6) were subjected to accelerated corrosion under
impressed current. The level of corrosion was kept sufficiently low to avoid corrosion-
induced cracking of concrete. The specimen Y4 was cracked, and, therefore, it was excluded
from the analysis. The specimens Y1-Y3 were cured during 139 days while the specimen Y5
only during 67 days. The influence of creep on the modulus of elasticity of the concrete and
strains developed in the concrete due to its drying shrinkage are calculated using
recommendations of Model Code 1990 [16].
   Comparison between results of the corroded specimens Y1-Y5 and of the uncorroded
specimen Y6 (Figure 3) shows that corrosion increases significantly the pull-out force and,
consequently, the bond strength. It can be attributed to a change of contact conditions at the
steel-concrete interface. In addition, all the diagrams presented in Figure 3 show a similar




                                                                                           Page 4
                                             tendency – an initial sharp increase in the
                                             pull-out force at low values of the slip which
    60  Y3                                   is followed by its reduction along with
                                             increasing slip until it becomes almost
                                             constant while the slip continues to grow. It
Pull-Out Force (kN)




            Y1                               is logical to assume that the peak points of
    40 Y2                                    the diagrams correspond to the stage where
                                             the interfacial cohesion (adhesion) and
         Y5
                                             friction are maximal. Afterwards the slip
                                             developing at the interface causes
    20                                       deterioration of the interfacial cohesion and
                                             smoothing of the interface accompanied by
        Y6
                                             friction degradation. Eventually only the
                                             frictional component contributes to the pull-
     0                                       out force, i.e., almost horizontal parts of the
       0           3            6         9  diagrams at high values of the slip represent
                 Free End Slip (mm)          pure frictional response of the smoothed
                                             steel-concrete interface. The mentioned
       Figure 3: RILEM pull-out test [5].
                                             assumptions were used in calibration of the
parameters of the interfacial model (see Figures 1 and 2). The results of calibration are
presented in Table 1.
Table 1: Values of the model parameters
               xc1    xc2 x  c0 cicorr kicorr fcoh,max icorr,c    sc1 sc2 ks s1 s2
              0.12    0.5 0.1 1.0                6.0    27.0      0.01 1.0     1.0 5.0
                                  230 0.1346                               0.7
              mm      mm mm MPa                 MPa A/cm2        mm mm        mm mm

   The axisymmetric FE model (presented in Figrue 3) is then developed in the FE
commercial code ABAQUS for simulation of the pull-out tests performed by Cairns et al. [5].
The described model of the corroded steel-concrete interface is incorporated into ABAQUS
using a user defined subroutine. Thermal analogy is used for modelling two volumetric
processes: the expansion of corrosion products and the drying shrinkage of concrete. The
expansion of corrosion products is modelled by volumetric expansion of a reinforcing bar
caused by its heating. Orthotropic volumetric expansion of a reinforcing bar is chosen in order
to prevent the rebar elongation, which is achieved by setting the coefficient of thermal
expansion in the direction of the rebar axis equal to zero. The drying shrinkage of concrete is
accounted in the FE analysis by isotropic volume contraction created by cooling of the
concrete. Values of the volume contraction are calculated in accordance with
recommendations of CEB-FIP Model Code 1990 [16] in terms of shrinkage strains. In the FE
analyses the thermal strains created by concrete cooling are made equal to those caused by
shrinkage.




                                                                                      Page 5
                                                                                 Boundary
                                                                                 Conditions
                           Concrete



                                                                                  Displacement
                         Line of
                       Symmetry

                                   Contact Interface       Rebar

                       Figure 4: Axisymmetric FE model for simulation of a RILEM pull-out test.

5. SIMULATION OF PULL-OUT TEST WITH A CORRODED PLANE ROUND BAR
   Results of the FE analysis of the control non-corroded specimen Y6 are presented in Figure
5. Comparison of the test results with those of the FE simulation shows a good agreement in
the prediction of the peak value of the pull-out force. However, reduction of the pull-out force
after the peak in the FE analysis occurs at a faster rate than in the tests. The slow rate of the
decrease of the pull-out force in the test can possibly be attributed to the decrease of friction
    10                                            that occurs because of smoothing of the steel-
                          experimental results    concrete interface caused by the rebar slip.
                          numerical results       This friction decrease was neglected in the FE
     8                          Specimen Y6       simulation of the uncorroded specimen Y6.
 Pull-Out Force (kN)




                                                     Results of the FE simulation of the
     6                                            corroded specimens Y1-Y5 are shown in
                                                  Figure 6. As can be seen, a reasonably good
                                                  agreement between the FE analysis results
     4                                            and the test results has been obtained for the
                                                  corroded specimens. The main differences
                                                  between the results are: (i) the decrease of the
     2
                                                  pull-out force has a non-linear shape while the
                                                  developed interfacial model assumes a
     0                                            piecewise linear relationship; (ii) the peak
       0            2           4             6   value of the pull-out force in several FE
                 Free End Slip (mm)               results is reached at lower values of the slip
     Figure 5: FE simulation of the control       than in the tests (see Figures 6(a) and 6(c)).
           uncorroded specimen Y6.




                                                                                                  Page 6
                                                                                            60
                                           experimental results                                              experimental results
                      60                   numerical results                                                 numerical results
                                                    Specimen Y1                                                    Specimen Y2
Pull-Out Force (kN)




                                                                      Pull-Out Force (kN)
                                                                                            40
                      40



                                                                                            20
                      20




                       0                                                                     0
                           0          2             4             6                              0     2           4            6
                                 Free End Slip (mm)                                                  Free End Slip (mm)
                                          (a)                                                              (b)
                                                                                            40
                                           experimental results                                              experimental results
                      60                   numerical results                                                 numerical results
                                                    Specimen Y3                                                    Specimen Y5
Pull-Out Force (kN)




                                                                      Pull-Out Force (kN)




                                                                                            30


                      40
                                                                                            20


                      20
                                                                                            10



                       0                                                                     0
                           0      2             4         6                                      0     3           6            9
                                 Free End Slip (mm)                                                  Free End Slip (mm)
                                          (c)                                                              (d)
                                 Figure 6: FE simulations of the corroded specimens Y1-Y5.

CONCLUSIONS
                      A critical overview of existing analytical and numerical models describing the
                       corrosion-induced deterioration of steel-concrete interface has then been presented.
                      A new model which accounts for the influence of corrosion on cohesion (adhesion) and
                       friction between reinforcing steel and concrete has then been proposed. The model has




                                                                                                                          Page 7
      been calibrated using results of the RILEM type pull-out tests, in which specimens with
      plain reinforcing bars were subjected to accelerated corrosion before being loaded.
     The model has then been incorporated into the FE commercial code ABAQUS using a
      user defined subroutine. It has been explained that for modelling the pull-out behaviour
      of plain reinforcing bars it is essential to take into account drying shrinkage of concrete.
      Thermal analogy has been used to simulate expansion of corrosion products and drying
      shrinkage of concrete.
     FE analysis of pull-out tests with corroded reinforcing bars embedded in concrete cubes
      has been carried out using an axisymmetric formulation. A reasonably good agreement
      between the numerical and test results has been obtained. Possible causes of deviation
      of the numerical results from the experimental ones have been discussed.

REFERENCE
[1] Xu, Y., 'Experimental study of bond-anchorage properties for deformed bars in concrete'
     Proceedings of International Conference Bond in Concrete from Research to Practice, Riga,
     Latvia, 1992 1/9-1/17.
[2] Williamson, S.J. and Clark, L.A., 'Effect of Corrosion and Load on Reinforcement Bond
     Strength', Str. Eng. Int. 2 (2002) 117-122.
[3] Cairns, J., Du, Y. and Law, D., 'Influence of corrosion on the friction characteristics of the
     steel/concrete interface', Constr. Build. Mat. 21 (2007) 190–197.
[4] ABAQUS, Abaqus Version 6.7 Documentation, (Hibbitt, Karlsson & Sorensen, Inc., Pawtuchet,
     RI, USA, 2007).
[5] Cairns, J., Du, Y. and Law, D., 'Residual bond strength of corroded plain round bars', Mag. Con.
     Res. 58 (4) (2006) 221-231.
[6] Lundgren, K., 'Bond between ribbed bars and concrete. Part 2: The effect of corrosion', Mag.
     Conc. Res. 57 (7) (2005) 383-395.
[7] Coronelli, D., 'Corrosion cracking and bond strength modeling for corroded bars in reinforced
     concrete', ACI Str. J. 99 (3) (2002) 267-276.
[8] Bhargava, K., Ghosh, A.K., Mori, Y., and Ramanujam, S., 'Corrosion-induced bond strength
     degradation in reinforced concrete – Analytical and empirical models', Nucl. Eng. Des. 237
     (2007) 1140-1157.
[9] Xu, G., Wei, J., Tan, T. and Liu, Q., 'Modeling bond strength of corroded plain bar reinforcement
     in concrete', Str. Con. 3 (8) (2007) 133-138.
[10] Lundgren, K., 'Modelling the effect of corrosion on bond in reinforced concrete', Mag. Con. Res.
     54 (3) (2002) 165-173.
[11] Pregartner, T., Cairns, J. and Ožbolt, J., 'Modelling effect of corrosion on bond strength of plain
     bar reinforcement', Str. Con. 5 (3) (2004) 113-120.
[12] Amleh, L. and Ghosh, A., 'Modeling the effect of corrosion on bond strength at the steel –concrete
     interface with finite-element analysis', Canad. J. Civ. Eng. 33 (2006) 673–682.
[13] Berto, L., Simioni, P. and Saetta, A., 'Numerical modelling of bond behaviour in RC structures
     affected by reinforcement corrosion', Eng. Str. 30 (5) (2007) 1375-1385.
[14] Wang, X.H., and Liu, X.L., 'Modelling effects of corrosion on cover cracking and bond in
     reinforced concrete', Mag. Con. Res. 56 (4) (2004) 191-199.
[15] RILEM/CEB/FIP, 'Bond test for reinforcing steel: 2. Pullout Test', Recommendation RC 6, 1978.
[16] CEB-FIP Model Code 1990, CEB Bulletin d’Information 213/214. Comité Euro-International du
     Béton, Lausanne, Switzerland 1993.




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