UDK 620.193:624.012.45:519.61/.64	ISSN 1580-2949
Original scientific article/Izvirni znanstveni članek	MTAEC9, 48(3)395(2014)
EFFECT OF REBAR CORROSION ON THE BEHAVIOR OF A REINFORCED CONCRETE BEAM USING MODELING AND EXPERIMENTAL RESULTS
VPLIV KOROZIJE BETONSKEGA ŽELEZA NA ARMIRANOBETONSKI STEBER Z UPORABO MODELIRANJA IN EKSPERIMENTALNIH REZULTATOV
Ali Ghods, Mohammad Reza Sohrabi, Mahmoud Miri
University of Sistan and Baluchestan, Faculty of Engineering, Department of Civil Engineering, P.O. Box 9816745563-162, Zahedan, Iran
ali.ghods@pgs.usb.ac.ir
Prejem rokopisa - received: 2013-07-21; sprejem za objavo - accepted for publication: 2013-09-13
Reinforcement corrosion in concrete may cause adverse effects, such as the area reduction of rebars, concrete cracking, a reduction of the bond strength and a change in the bond-slip behavior between concrete and rebars. All these effects will finally lead to the inappropriate performance of concrete structures. In this paper a corroded reinforced concrete beam, whose experimental results are available, is modeled based on the finite-element method using ANSYS. The results are then compared with the available and confirmed results. A reduction of the reinforcement area and a change in the bond strength between the concrete and the reinforcement are seen in the model. The effect of reinforcement corrosion on the force-displacement curve and the modeled beam are also studied and compared with the results from reinforced concrete made in the laboratory. It was observed that with an increase of the reinforcement corrosion rate, the load-carrying capacity of the concrete beam and the bond strength decreases. In addition, the area under the load-displacement curve of the concrete beam decreases with the increase of the reinforcement corrosion.
Keywords: corrosion, beam, modeling, force-displacement
Korozija armature v betonu lahko vpliva škodljivo, tako kot zmanjšanje prereza betonskega železa, pokanje betona, zmanjšanje sile vezanja in sprememba vedenja vezave in drsenja med betonom in armaturo; vse to privede do neprimernih lastnosti betonske konstrukcije. V tem članku je bil modeliran z uporabo metode končnih elementov in ANSYS korodiran betonski steber s poznanimi eksperimentalnimi podatki. Rezultati so bili primerjani z razpoložljivimi in preverjenimi rezultati. Iz modela je razvidno zmanjšanje področja utrditve in sprememba v sili vezanja med betonom in armaturo. Preučevan je bil tudi vpliv korozije armature na krivuljo sila - raztezek in modeliran steber ter primerjan z laboratorijskimi rezultati pri armiranem betonu. Ugotovljeno je, da se z naraščanjem hitrosti korozije armature zmanjšujeta nosilnost betonskega stebra in sila vezanja. Področje pod krivuljo obremenitev - raztezek armiranega betonskega stebra se zmanjšuje z večanjem korozije armature.
Ključne besede: korozija, steber, modeliranje, sila - raztezek
1 INTRODUCTION	rebar, which intensifies the factor of cohesive friction.4
During the next stage, longitudinal cracks reduce the Reinforcement corrosion is one of the major factors	confinement of corrosion products, which in turn reduces in the deterioration of reinforced concrete structures,	the bond strength. The more the corrosion proceeds, the such as bridges, parking and coastal structures. This phe-	more the bond-strength reduction will emerge. nomenon may lead to area reduction of rebars, cracking,	Similar to any other engineering issue, studies con-concrete scaling, reduction of bond strength and change	cerning corrosion were conducted through three general in the bond-slip behavior between concrete and rebars.	methods, including experimental, analytical, and numeriAll of these factors will eventually lead to the adverse	cal simulation. A few studies have been carried out using function of concrete structures.	numerical studies and applying some known finite-ele-The area reduction of rebars is the most evident result	ment software aiming to study the effects of reinforce-of rebar corrosion. Although carbonate corrosion in con-	ment corrosion in concrete. For instance, Berra et al.7 crete occurs uniformly, chloride corrosion usually causes	investigated the effect of corrosion on the bond deteri-local corrosion known as 'pitting'.1 It causes a consider-	oration between concrete and rebar using ABAQUS. able area reduction of rebars, which sometimes occurs	Lundgren8 used DIANA finite-element software for the without any noticeable signs.2-4	numerical simulation of the experimental creation of Some parts of the earlier literature focused on the	cracks, caused by corrosion, and corroded rebar pullout bond reduction between concrete and rebar and its effect	tests. Saether and Sand9 also modeled a corroded rein-on the strength of beams and reinforced concrete slabs.5 6	forced concrete beam, for which the experimental results In fact, the reduction of the bond strength between the	were available. Meanwhile, they used DIANA and ob-concrete and the rebar occurs in two stages. During the	tained similar results with the created sample. Most of early stage, corrosion products gather on the rebar sur-	the earlier finite-element models were two-dimensio-face and increase its diameter. This phenomenon in-	nal.10 An attempt is made in the current research to creases the radial stresses between the concrete and the	present a 3D model using ANSYS for a beam, for which
the experimental results are available. The results obtained from the finite-element analysis of this beam are compared with the available ones. After verification of the model, a parametric study is carried out on the beam. It means that the load-displacement curve is drawn at different percentages of the corrosion and variations in the load-carrying capacity of the beam are studied. They are then compared with the load-displacement curve of the beams made in the laboratory. Finally, the reinforcement slip in the concrete is studied for various percentages of the corrosion using the model.
2 ELEMENTS USED IN ANSYS
2.1	Element for concrete
The SOLID65 element is a 3D element with eight nodes and three degrees of freedom (transmission on y, z directions) in each node. The element is capable of modeling the fissures and breaks of concrete.11,12 A major aspect of the element is the nonlinear performance of its materials. Reinforcement can be defined in this element as well; of course, the reinforcements are defined individually here. Multi-linear isotropic hardening under the von Mises fracture criteria is used in this element. Generally, five coefficients are used to determine its smooth break, which include one-axis tensile strength, one-axis compressive strength, two-axis compressive strength, and one- and two-axis compressive strength under a specific confining pressure. Moreover, the shear transmission coefficients can also be applied as the inputs for open and close cracks. Figure 1 exhibits the geometrical specifications of the SOLID64 element.
2.2	Element for Reinforcement
All the tensional and compressive reinforcements and stirrups are modeled in this study using the LINK8 ele-
Figure 1: Geometry and specifications of the SOLID65 element Slika 1: Geometrija in podrobnosti elementa SOLID65
ment. This element is a 3D element, only with tensional and/or compressive axial forces.11,12 The element has two nodes with three degrees of freedom in each node, including transmission for the .., y, z directions. The input of this element is the cross-section. Figure 2 presents the specifications for this element.
2.3 Element for cohesion
The COMBIN39 element is applied for modeling the cohesion between the concrete and the rebar. This element is a uni-directional element capable of determining the force-displacement nonlinearity equation.11,13 In addition, it has axial and torsional capability in one-, two-and three-dimensional analyses. Its axial option, which is used here, has a maximum of three degrees of freedom in each node. This element can have zero length, i.e., the start and end nodes can be defined as on each other. Figure 3 exhibits a sample of the load-displacement diagram of the element.
3 CONTROL BEAM OF MODELING
3.1 The Beam Tested by Rodriguez et al.
Here, we discuss one of the reinforced concrete beams with corroded rebars tested by Rodriguez et al.14 The test series of Rodriguez et al.14 include 31 beams with various details of reinforcement, different shear reinforcement and a range of corrosion percentages. Figure 4 shows the geometry and specifications of the beam reinforcement for modeling is this paper.
As shown in the figure, this beam has both tensional and compressive reinforcement and stirrups. In the beams tested by Rodriguez et al.,14 the concrete had a compressive strength of between 48 MPa and 55 MPa. In order to accelerate the corrosion in the rebars, 3 % of calcium chloride (by mass of cement) was added to the concrete mix design. A compressive strength ranging from 31 MPa to 37 MPa was recorded for the concrete with the calcium chloride. The beams were cured under humid conditions for 28 d. Then a current of about 0.1 mA/cm2 was applied to create an accelerated corrosion during the aging of the specimens, ranging from 100 d to 200 d.
Figure 2: Geometry and specifications of the LINK8 element Slika 2: Geometrija in podrobnosti elementa LINK8
Figure 3: Geometry and specifications of the COMBIN39 element Slika 3: Geometrija in podrobnosti elementa COMBIN39
Figure 4: Geometry and specifications of the beam for modeling1 Slika 4: Geometrija in podrobnosti stebra za modeliranje14
It should be noted that due to the presence of stirrups, the corrosion was not uniformly distributed along the longitudinal rebars and the corrosion rate for the ten-sional and compressive rebars and stirrups was different in each beam. After the completion of the accelerated corrosion process, the beams were exposed to a four-point bending test. Table 1 lists the complete characteristics of the beams for modeling. The non-corroded and corroded beams tested by Rodriguez et al.14 are shown by Rod.01 and Rod.02 respectively in the remainder of the paper
Table 1: Specifications of the beams for modeling14 Tabela 1: Podrobnosti za modeliranje stebra14
Parameter
One-axis compressive strength of concrete
One-axis tensile strength
Percentage of reinforcement
Concrete elasticity modulus
Steel elasticity modulus
Steel elastoplastic tangent modulus
Tensile steel
Compres-sive steel
Stirrup
Area reduction percentage due to corrosion
fc/MPa
ft/MPa
p/%
£c/MPa
Es/GPa
Esr/MPa
%
%
(%)
Beam with Corrosion
Rod.02
31.4
2.8
0..5
28300
206
824
13 9
12 58
23.15
Beam without
Corrosion
Rod.01
.50
3..5
0..5
32200
206
824
electric current and to measure the corrosion in the concrete. The ends of the wires were taken out of the concrete. To protect the wires from corrosion and humidity, their ends were covered by an appropriated cohesive material before conducting the test. After 28 d of curing, the beam was placed in a distilled water basin containing 3 % of calcium chloride (by mass of distilled water). Then a negative current was applied in the basin to analyze salt to chlorine. To create the corrosion, a maximum 100 mA/cm2 DC current was applied using wires. The other conditions are almost the same as those mentioned for the Rod.02 beam in Table 1. Hereinafter, these specimens are shown by Gh.03. Figure 5 shows an image of these samples.
5 MODELING OF BEAMS BY CORROSION
5.1 Reinforcement Model
Uniform corrosion does not have a considerable effect on the stress-strain properties of the reinforcements and it is convenient to model it by reducing the cross-section of the steel rebars. Pitting corrosion may cause a significant reduction in the mechanical behavior of the steel reinforcement due to the local concentration of stress. Generally, if a reinforcement rebar initially has a diameter of ^q, its diameter will be reduced due to the corrosion. The remaining cross-section of the tension rebar affected by uniform corrosion can be calculated from Eq. (1):9
Jl((Pn - ax)2

nip R
(1)
4 LABORATORY-MADE REINFORCED CONCRETE BEAM
Six reinforced concrete beams were made by the authors, using the same dimensions and reinforcement conditions as used by Rodriguez et al.14 Three beams were tested for a further validation of the modeled beam and evaluating the effect of the corrosion on the behavior of the reinforced concrete under test. A concrete mixer was used for concreting and the modularity of the beams. In addition, after pouring the concrete into the mold, it was compacted using a 1.. cm diameter rod. The beams were extracted from the mold after 24 h and cured using sacks for 28 d. Two-layer pressure-resistance and humidity-resistance string wires were used to create an
Where pR is the remaining diameter of the reinforcement, a is a coefficient dependent on the type of corrosion and x shows the penetration rate of the corrosion.9
Figure 5: Reinforced concrete beams made by the authors (Gh.03) Slika 5: Armiranobetonski steber, ki so ga izdelali avtorji (Gh.03)
Figure 6: Remaining cross-section of the corroded rebar Slika 6: Preostali prerez korodiranih palic v armaturi
For uniform corrosion it is assumed that the coefficient a is equal to 2. For pitting corrosion the cross-section becomes irregular and the area reduction may be considerably greater than the uniform corrosion (Figure 6). The above relation can be used for estimating the reinforcement cross-section in the pitting corrosion by introducing the circular cross-sectional diameter as ^r. In this condition, the a coefficient is considered within the range of 4 to 8.9
In this study it is assumed that the corrosion is uniform. Therefore, no reduction is considered for the mechanical properties of the steel and only the area reduction is considered for the corroded reinforcements in the calculations. The stress-strain relation of the steel, in tension, was considered as an elastoplastic material with a linear hardness, which is shown in Figure 7.
5.2 Concrete Model
Cracked concrete, due to the corrosion under the effect of compressive stresses, shows a lower performance when compared with the un-cracked concrete. In this condition, the reduced compressive strength is used for the beams whose compression rebars are affected by corrosion. The amount of reduced compressive strength is suggested by Eq. (2):15
Figure 7: Stress-strain curve for rebars in tension
Slika 7: Krivulja napetost - raztezek pri natezni obremenitvi palice iz
armature
fD -■ Jc -|
fc
1 + k
(2)
In this equation, fcD is the compressive strength of the cracked concrete, fc is the specified compressive strength of the un-cracked concrete, k is a coefficient equal to 0.1 (k = 0.1), Cco is the strain of the concrete under the maximum load, and ei is the lateral strain caused by the crack, which is a function of the corroded reinforcements number, the volume expansion of the corrosion products on the rebar, and the average amount of corrosion influence.
In modeling reinforcement beam by ANSYS, it is necessary to define the stress-strain curve for concrete. This relation depends on several factors. The most common forms are used here. One simple model to introduce a concrete stress-strain relation is the application of an idealized elastoplastic relation, which is shown in Figure 8a. Another model, which is more realistic, is the parabolic model, like that shown in Figure 8b. In both models, the tensional behavior of the concrete is shown by a two-linear estimation in which the tensile stress increases up to the tensile strength ft and then it is followed by a softening behavior.
5.3 Bonding Model
Before the development of cracks in the concrete, low rates of corrosion may increase the bond strength between the reinforcement and the concrete. The bond strength starts decreasing with the formation of corrosive cracks, which normally occur along the reinforcement. There are numerous experimental results on corrosive reinforcements. However, the presence and development of corrosion products were proved to be the main parameter in weakening the bond strength between the corroded reinforcement and the concrete. Various relations have been offered for the bond strength. In the present study, the following relation is used for the bond strength. This relation considers the effects of both the concrete and the stirrups:16
r
"max - R •
055 + 0.24
VfT+0191
■-b yj
Ast /vt
v^ S d b
(3)
R - A+
Figure 8: Different types of stress-strain curves for concrete Slika 8: Različne krivulje napetost - raztezek za beton
1
f
Figure 9: Diagram of the relation proposed for the bond-slip strength17
Slika 9: Diagram predlagane odvisnosti trdnosti za vezavo - drsenje17
Where is the reduced bond strength, c is the thickness of concrete cover, db is the reinforcement diameter, fc is the specified compressive strength of concrete, Ast is the area of shear reinforcement, fyt is the yield strength of the stirrups, s s is the stirrup spacing, and R is a factor that considers the reduction of the bond strength in which A1 and A2 are coefficients reflecting the rate of corrosion in an accelerated corrosion process. For corrosion process of 0.09 mA/cm2, the values of these coefficients were determined as Ai = 1.104, A2 = -0.024. Finally, X is the corrosion rate, which is stated as a percentage of the rebar mass loss.
The advantage of this model for the bond strength between the concrete and the rebar is that it is capable of modeling the increase of the bond strength at low rates of corrosion. Obviously, this depends on the corrosion rate.
Studies show that the relation between the bond strength and the slip is controlled by the corrosion rate in longitudinal rebars and the rate of corrosion products. A modified relation was proposed for bond-slip rule by Harajli et al.,17 which is shown in Figure 9.
In this diagram S2 = 0.35c0, where C0 is the distance between the rebar ribs, which is assumed to be 8 mm. Other specifications of the diagram are defined in the following relations:17
u = u
au
^ = s,
s = Se (1'03)ln( u max/u 1) + s ln ''max
VUmax /
(4)
(5)
(6)
In these relations S1 = 0.15C0, U1 = 2.57(/c)0.5, a = 0.7, and the sc for plain and steel-reinforced concrete is 0.15 and 0.4, respectively.17
In this research the above diagram is used for modeling the bond stress between concrete and rebar. Of course, the element applied for bond modeling is COMBIN39. As explained in Section 2, this element needs a force-displacement curve. Therefore, the following equation is introduced for this purpose:17
Figure 10: Force-slip diagram for the COMBIN39 element where the tension reinforcements are located
Slika 10: Diagram sila - zdrs za element COMBIN39 pri natezni obremenitvi armature
In this relation, F (s) is the shear force between the reinforcement and the concrete, u(s) is the bond strength, d is the reinforcement diameter, and l is the distance between two adjacent COMBIN39 elements (Figure 10).
For instance, the relation between the force-slip for the corroded tension reinforcements is as follows, which is in fact the same force-slip diagram of COMBIN39 element where the tension reinforcements are located.
This diagram is obtained assuming a reduction of the reinforcement mass by 10 percent (x = 10 %). The corresponding force-slip diagrams for different percentages of reduction of the reinforcement mass are shown in Figure 11.
5.4 The Model Created using ANSYS
As explained in the earlier sections, a finite-element model of the control beam tested by Rodriguez et al.14 was made using ANSYS (Figure 12).
Because of the symmetrical condition, half of the beam was considered during modeling. It should be noted that it is a complicated task to make a precise model for a corroded reinforced beam. This is due to the fact that the corrosion rate along longitudinal rebars, caused by stirrups, is not constant. In addition, the average rate of corrosion in each beam for tensile and com-
F( s) = u( s)ndl
(7)
Figure 11: Force-slip diagram for COMBIN39 for different percentages of corrosion
Slika 11: Diagram sila - zdrs za element COMBIN39 pri različnih deležih korozije
s
^ s1 >
> U1 .
Figure 12: Supports and loading conditions for the control beam Slika 12: Podpore in obremenitev kontrolnega stebra
pressive reinforcements and stirrups is different. However, in the beam selected for modeling, the average rates of corrosion in the tensile and compressive reinforcements are almost equal.14 As shown in Table 1, the rates of corrosion in tensile and compressive reinforcements are 13.9 % and 12.6 %, respectively. It is noteworthy that in the finite-element model made here, changes to the reinforcement area were considered as mentioned in Section 1-4 and the changes of the bond stress were taken in to account, according to the remarks of Section 3-4 (Figures 13 and 14).
Finally, the load was applied to the model incrementally. Attempts were made to choose smaller incremental steps of load to obtain a better convergence. The load could be increased as long as it was not be possible to increase it any more due to the model instability, using the Newton-Raphson method for the non-linear analysis.
In order to observe the sensitivity of the meshing size as a result of the existing model it is also investigated with mesh seeds of 100, 200 and 300 in each direction. After that the results were compared and it has clear that the differences were negligible; therefore, a mesh size of
100 was used in the ANSYS because of the speed and comfort.
6 MODELED BEAM RESULTS vs. EXPERIMENTAL RESULTS
Here, we continue the discussion by comparing the load-displacement curve at the mid-span of the modeled and the experimental beam. Figure 15 compares the results of the numerical analysis of the corrosion-free Rod.01 modeled beam with its experimental results. It is clear that the numerical modeling has a favorable precision, especially for estimating the factored load.
Figure 15: Numerical and experimental results of the load-displacement curves for the Rod.01 beam
Slika 15: Numericni in eksperimentalni rezultati obtežbe - raztezka pri stebru Rod.01
Figure 13: Modeled reinforcements Slika 13: Modelirana armaturna mreža
Figure 14: Control beam model on ANSYS Slika 14: ANSYS-model kontrolnega stebra
Figure 16: Numerical and experimental results of load-displacement curves for the Rod.02 beam (with corrosion)
Slika 16: Numericni in eksperimentalni rezultati obtežbe - raztezka pri stebru Rod.02 (s korozijo)
Figure 17: Numerical results of the load-displacement for the corroded and non-corroded model beam
Slika 17: Numericni rezultati obtežbe - raztezka za modelni steber s korozijo in brez nje
Figure 19: Results of load-displacement for different rates of corrosion in the model beam and Gh.03
Slika 19: Rezultati obtežbe - raztezka pri različnih stopnjah korozije pri modelnem stebru Gh.03
Figure 16 also shows the mid-span load-displacement relationships for the Rod.02 modeled beam and its experimental results, which are affected by the reinforcement corrosion. Comparing the results indicates a favorable precision between the results of the modeled beam by the authors and Rodriguez's experimental results. The corroded beam in the model estimates the factored load with an error close to 9 % more than the Rod.02 beam. With respect to the specific complexities of the model and the approximations used in modeling, the numerical result has a favorable precision.
Figure 17 shows the results of the load-displacement for the corroded and non-corroded beams, obtained from the modeling, in a diagram.
It should be noted that the finite-element model underestimates the results of the non-corroded beam and overestimates the results of the corroded beam. Therefore, the difference of the load-carrying capacity between the corroded and non-corroded beams is underestimated as compared with the experimental results.
The results of the load-carrying capacity at different percentages of corrosion for the modeled beams and those created by the authors (Gh.03) are explained subsequently. Four-point loading is used, as shown in Figure 18, to achieve the load-carrying capacity of the beams in the laboratory. It should be noted that the parameter here introduced as an index to show the corrosion
rate has the same percentage of mass for the reinforcements earlier introduced as the parameter x in the previous sections. Figure 19 shows the amounts of load-displacement in (3, 10, and 20) % corrosion in the created beams (Gh.03) and the modeled beams.
Figure 19 shows that the increase of the corrosion rate reduces the ultimate load-carrying capacity and the ultimate displacement. In addition, the length of the nonlinear area in the beam increases with lower rates of corrosion. Failure of the beams with a high rate of reinforcement corrosion will probably tend to approach a brittle fracture; of course, such a question requires a separate study. It means that their fracture mechanism can be studied through examining the formation of cracks and their positions at the time of the beam fracture with different rates of corrosion. The very good precision of the offered model can be observed by examining the results obtained from the force-displacement curve in the modeled and experimental beams. The differences among the precisions may be due to the variations in the rate of corrosion along the longitudinal rebars related to the existence of stirrups. In this figure, the results of the numerical analysis of the model are overestimated as compared with the experimental ones.
Figure 18: Four-point loading for corroded beam Slika 18: Stiritočkovna obremenitev stebra s korozijo
Figure 20: Rate of reinforcement slip in proportion to concrete for different rates of corrosion
Slika 20: Razmerje drsenja armature in betona pri različnih stopnjah korozije
With respect to the favorable precision of the modeled beam, the rate of reinforcement slip in proportion to concrete can be studied. In fact, it is the same displacement in the nonlinear spring element, which is placed for modeling the bonding strength between the concrete and the reinforcement. Figure 20 shows the rate of reinforcement slip in proportion to the concrete along the beam. The diagram is drawn for different rates of corrosions.
The figure shows that the rate of slip increases with the increase of the rate of corrosion in the reinforcement. In fact, according to Figure 11, with an increase of the rate of corrosion, the concrete-reinforcement bond strength decreases. This leads to an increase of the slip. As Figure 20 shows, the place with maximum slip in a beam with 20 % corrosion approaches the center of the beam.
7 CONCLUSION
A reinforced concrete beam with reinforcement corrosion was modeled in this paper. The area reduction of the reinforcement and the bond-strength reduction was observed between the concrete and the reinforcement. The results obtained from the finite-element analysis of this beam were compared with those achieved by Rod-riguez.14 It was shown that there was a good agreement between the load-displacement diagram and the experimental work.
The reinforcement corrosion rate in the model was altered as a parameter, and its effect on the load-carrying capacity was studied. The results were then compared with those experienced by the authors.
It was revealed that with an increase of the reinforcement corrosion rate, the load-carrying capacity of the concrete beam decreases.
The area under the load-displacement curve of the concrete beam decreases with the increase of the reinforcement corrosion. This may be an indication for the reduction of the concrete beam's ductility. Therefore, it can be expected that the concrete beam will become more brittle with an increase of the corrosion.
By comparing the results obtained from the model with the beams made by the authors, very good precision of the model is realized. The difference may be due to the lack of uniform corrosion of the longitudinal rebars caused by stirrups, and the use of different methods for accelerating the corrosion by the authors and Rodriguez
et al.14
It was observed that the bond strength reduces with an increase of the corrosion rate. This leads to an increase of reinforcement slip in reinforced concrete beams.
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