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1 INTRODUCTION

This work starts from an overview of previous works about Finite Element Method (FEM) analysis and modeling of corrosion penetration (Lignola et al. 2009). FEM analysis were aimed at demonstrat-ing the possibility to use the “single bar” simulation results for more complex Reinforced Concrete (RC) members. A refined model was proposed to evaluate the non linear development of stresses inside con-crete when reinforcement bars start to corrode. Two mechanical analytical multi-layer models were de-fined: the former one simulates the effects of corro-sion to the initiation of the crack, while the other one simulates the propagation of the crack until it reach-es the external surface of concrete cover. They both allow to discuss the influence that concrete and steel main parameters have on cracking process of RC members, considering the reduction of the bar sec-tion due to corrosion.

The reduction of the reinforcement's diameter can cause its detachment from concrete when bar diame-ter reduction is equal to rib height, hrib, of bars. Oxide volumetric expansion influences bond be-tween concrete and bar. Firstly, it increases bond due to increasing of internal lateral pressure, second-ly, it reduces due to concrete cracking. The aim of this paper is to evaluate the corrosion process effects

on bond development in RC structures. Solving a four-layers non-linear system it is possible to calcu-late the corrosion penetration, x, causing concrete in-itiation and propagation of cracking. Theoretical plots will show influence that corrosion process has on bond development.

2 BACKGROUND

2.1 Choice of modeling parameters Concrete is assumed elastic in compression due to the reduced stresses while it is fully nonlinear in ten-sion. A bilinear curve is assumed for concrete in ten-sion, having an elastic branch up to peak tensile strain εct followed by a softening linear branch to ze-ro stress at ultimate strain εu. To relate crack open-ing, wc, to ultimate strain, εu, a characteristic length, h, for concrete equal to 3dMAX was assumed, where dMAX is the maximum aggregate dimension; in fact, its value influences the fracture energy. Concrete modeling has been performed according to first complete draft of Model Code 2010 (MC10). Consi-dered diameters of the bars are Φ10, simulating stir-rups, Φ16 and Φ20; concrete cover and strength class are selected according to the exposure class XC1, XC2 and XC4 according to first complete draft

Transverse stress on corroded steel reinforcement bars in concrete

A. Bossio, M. Montuori, F. Bellucci, G.P. Lignola, A. Prota, E. Cosenza & G. Manfredi Federico II, Naples, Italy

ABSTRACT: Degradation of Reinforced Concrete (RC) Structures is a main economical problem, affecting emerging and industrialized countries. Some studies report that it costs 3÷4% of the Gross Domestic Product (GDP). The reinforcement corrosion is a major cause of degradation for structures and infrastructures throughout the world leading to their premature deterioration before their design life was attained. Different types of attack affects structures, in different ways and times and the worst consequences are: (i) reduction of the cross section of the reinforcement and thus reduction of strength capacity, (ii) formation of corrosion products that lead to loss of bond with the concrete, (iii) appearance of cracks in the concrete cover and con-sequent detachment thus leading to aesthetic and further durability issues. These problems require an interdis-ciplinary approach involving both material science and structural design competencies. Focusing on the bond behavior, the aim of this paper is to evaluate how internal lateral pressure, caused by corrosion products ex-pansion until concrete cover spalling, influences the bond between concrete and steel. A detailed analysis is proposed on the effect of corrosion both on the mechanical interlock and on the transverse pressure influen-cing relevant bond properties of steel reinforcement bars in concrete structures. Main theoretical results are supported by experimental laboratory tests on this key topic.

Bond in Concrete 2012 – General Aspects of Bond J. W. Cairns, G. Metelli and G. A. Plizzari (eds)

2012 Publisher creations, ISBN: 978 - 88 - 907078 - 1 - 0

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of Model Code 2010, too. Creep effect and type of aggregate used in concrete mixture are considered in order to evaluate the influence of Young’s modulus of concrete on corrosion behavior of RC members. FEM analysis and analytical model have been sum-marized below to evaluate corrosion penetration ac-cording to different parameters.

2.2 FEM analysis FEM analysis (Lignola et al. 2009) have been aimed to compare “single bar” (typical of laboratory spe-cimens) with real “multi-bar” RC members’ beha-vior. FEM simulations were performed for both “single bar” and “real member” schemes, stressing the influence of concrete classes, diameters and clear distances of bars and concrete cover on concrete cracking. Starting from a single bar scheme sur-rounded by a concrete axisymmetric cylinder, the case of real reinforced concrete elements was dis-cussed and simple rules were proposed to correlate the simple scheme to the real case. A hundred para-metric comparative FEM analyses showed that un-derestimation of the simplified scheme is almost negligible only if, in “single bar” models, concrete cover equal to min(cc;ic/2) is adopted. Maximum un-derestimation of the model was found equal to about 10% thus still comparable to usual uncertainty on concrete tensile strength (see Figure 1).

-10 %

0 %

10 %

20 %

30 %

40 %

50 %

20 30 40

D1 2 C =20m m D12 C=3 0mm

D1 6 C =20m m D16 C=3 0mm

D2 0 C =20m m D20 C=3 0mm

ic (mm )

a)

-10%

0%

10%

20%

30%

40%

50%

20 30 40

D12 C=20mm D12 C=30mm

D16 C=20mm D16 C=30mm

D20 C=20mm D20 C=30mm

ic (mm)

b)

Figure 1. Scatter of tensile stresses: considering, in single bar model, a concrete cover equal to: a) cc; b) min (cc;ic/2)

2.3 Initiation of cracking A refined model was then proposed to evaluate the non linear development of stresses inside concrete cover when cross section of bar starts to reduce due to corrosion. Formation of oxide layer, in fact, is re-lated to the reduction of cross section of bars (Fig. 2a). The relationship between initiation of cracking and reduction of section was provided. (Bossio et al. 2011).

Reduction of cross section of bar due to corrosion at cracking initiation depends on the amount of oxide formed. Set the value of Young’s modulus of oxide, Eo, the dependency from volumetric expan-sion factor of oxide, n, is very high and the bar re-duction, leading to crack initiation, increases as n decreases. As bar and concrete radii increase, the bar reduction at crack initiation increases, too. It can be showed that, from a mechanical point of view, the dependence on concrete net cover (R4-R0) is re-duced, even if, from an electrochemical point of view, a greater concrete cover slows down the pene-tration of aggressive agents and consequently the process of initiation of bar corrosion, because net cover provides a higher protection to bars.

2.4 Propagation of cracking When internal lateral pressure firstly reaches maxi-mum tensile strength of concrete, cracking process starts. The relationships between the cracking devel-opment (mechanical) and the reduction of the steel section (electrochemical) were provided in Bossio et al. (2011).

The mechanical analytical model was based on a nonlinear system of equations of equilibrium (bar-oxide-concrete) and compatibility (boundaries of four layers).

Considering a four-layers (bar, oxide, cracked concrete and uncracked concrete) non-linear system, propagation of cracking still depends on the same parameters of initiation of crack case, but it is some-how different. Oxide production increases slightly as Eo decreases, for a given crack propagation.

Parameters like as type or dimension of aggre-gates (influencing fracture energy and Young’s modulus, respectively) and creep effect, dramatically influence the corrosion process and crack propaga-tion, that can be all simulated by means of the four-layers analytical model (Fig. 2b).

Set an exposure class and a corrosion level, the model allows, inter alia, evaluating the value of mean compressive internal stress, fl, and its effects on bond behavior.

Main results have been summarized in Figure 3.

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R0

R4

R1 x

R2

S1steel=S1oxide

S2concrete=S2oxide-y

y

OXIDE

STEEL

UNCRACKEDCONCRETE

R0

R4

R1 x

R2

S1steel=S1oxide

y

R3

S2crackedconcrete=S2oxide-y

S3concrete

OXIDE

CRACKEDCONCRETE

STEEL

UNCRACKEDCONCRETE

a) b)

Figure 2. Geometric scheme for analytical modeling of crack: (a) initiation, (b) propagation.

0% 50% 100%

0

5

10

0.00%

0.15%

0.30%

7 25 42

Crack Propagation

x [μ

m]

Sect

ion

Los

t

R3 [mm] Figure 3. Section lost vs increasing of cracked concrete front R3.

3 THREE DIFFERENT MODELS TO EVALUATE BOND INCREASES

To study corrosion effects on bond, previous analyt-ical model has been applied considering three differ-ent bond theories. Bond is the term used to denote the interaction and transfer of force between rein-forcement and concrete.

It is possible to consider corrosion effects on bond behavior considering the development of ulti-mate bond stress, τb,f, and maximum bond stress, τ0, ratio; considering τ0 = 1.25 × fco

0.5 according to MC10, and fco = mean concrete cylindrical com-pressive strength.

Following paragraphs, synthetically, summarize equations to evaluate ultimate bond stress and max-imum bond stress ratio, Ωp,tr. The symbol fl represents internal lateral pressure developed by oxide expansion.

0.0

1.0

2.0

0.0 10.0 20.0

Ωp,

trM

C20

10

fl [N/mm2] Figure 4 Ωp,trMC10 ratio vs internal pressure, fl.

3.1 First complete draft of Model Code 2010 Referring to MC10 §6, it is proposed equation:

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⋅

−−==Ωco

l

fffb

trMCp 1.02.0

tanh10

,10, τ

τ (1)

Figure 4 shows the Ωp,trMC2010 ratio calculated for different concrete strength classes.

3.2 Simple Friction Model A Simple Friction Model (SFM) was considered, too. The value of Ωp,trSFM is calculated according to:

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅+==Ω

01

0

,, τ

μτ

τlffb

trSFMp (2)

fco =12 N/mm2

fco =80 N/mm2

464

where µ = friction coefficient of rusted steel = 0.3 as suggested by Coronelli (2002).

0.0

1.0

2.0

3.0

0.0 15.0 30.0

Ωp.

tr

fl [N/mm2]

MC10SFMEC2

Figure 5. Ωp,tr ratios vs internal pressure, fl, in case of con-crete strength class C25/30.

3.3 Eurocode 2 Referring to Eurocode 2 (EC2) §5.2.2 the value of Ωp,trEC2, is calculated according to:

4.10

,

4.011

2, ≤−== ⎟⎟⎠

⎞⎜⎜⎝

⎛⋅−

Ωlf

fbtrECp τ

τ (3)

Figure 5 shows the Ωp,trMC10 ratio related to EC2 and to SFM, calculated for a concrete strength class C25/30.

3.4 Corrosion simulation Oxide expansion inside the groove occupied by

the bar, generates an internal pressure of bar on con-crete leading to bond increase. Operating on safe side it is possible to say that crack opening determi-nates the loss of lateral pressure thus bond capacity reaches the original value (Fig. 6 vertical decreasing curve). Then bond capacity decreases consistently up to a value of displacement between bar and con-crete, generated by bar reduction and oxide expan-sion, equal to height of bar ribs, hrib, (Fig. 7). So one of main consequences of reduction of bar cross section is disengagement.

Conditions of uniform attack are considered, as caused by the artificial corrosion processes used in experimental programs to reproduce the effects of carbonation (uniform attack in field conditions). Solving the four-layers analytical model it is possi-ble to determinate the bar reduction value inducing complete concrete cover cracking and the corres-ponding value of internal lateral pressure, fl, which in turns yields to variations of bond performances.

3.4.1 Concrete exposure class effect Exposure classes are considered to simulate different scenarios. Concrete strength and cover according to table 1, were used, corresponding to the minimum allowable values (MC10).

0.50

1.00

1.50

0 10 20 30 40 50

Ωp,

tr

x [µm]

MC10SFMEC2

Figure 6. Different Ωp,tr ratios vs bar reduction, x.

Con

cret

eO

xide

Bar

S

x

Initial Bar Configuration

2concrete

hrib

Figure 7. Oxide-steel-concrete configuration at disengagement. Table 1. Concrete main parameters according to MC10. Concrete exposure class

Concrete cover Concrete strength class

- mm N/mm2

XC1 20 C20/25XC2 20 C25/30XC4 30 C30/37

Considering XC1 exposure class parameters and a Φ16 bar diameter, Figure 8 shows the value of fl [N/mm2] related to bar reduction, x, and to Ωp,tr ratios.

The graph shows that as bar reduction, x, in-creases, internal lateral pressure, fl, increases, too.

At higher level of bar reduction, x, the reduction of thickness of uncracked concrete circular crown yields to a reduction of stiffness thus to a reduction of lateral pressure, fl. Internal lateral pressure value, fl, is deeply related to bond capacity improvement. However it is preferable to relate directly bond im-provement Ωp,tr with bar reduction, x, as shown in Figure 9.

Other concrete exposure classes are considered also to evaluate bond behavior. Figure 10 and Fig-ure 11 show results for XC2 and XC4 exposure classes, respectively.

3.4.2 Bar diameter effect To consider effect of bar diameter on bond behavior, different bar diameters are considered, using the same concrete exposure class parameters. It is shown that bar diameter has not a great influence on bar reduction, x.

C20/25 R0= 8 mm n=2.5 R4-R0=20 mm

465

0.00

1.00

2.00

Ω p,tr

MC10SFMEC2

0.00

4.00

8.00

0.0 4.5 9.0

x [µm

]

fl [N/mm2]

Figure 8. Ωp,tr ratios and bar reduction, x, vs internal lateral pressure fl – concrete exposure class XC1.

As seen in Figure 12, the lower is bar diameter, the greater is Ωp,tr ratio even if bar reduction, x, is similar.

3.4.3 Creep effect Corrosion is a medium-term problem affecting RC members, so it is important to consider creep effect on bond development. In fact, creep leads to con-crete Young’s modulus, Ec, decreases. In particular assuming a creep reduction factor 1/(1+ϕ), in-creasing ϕ with time and sustained load, the higher is the creep factor, the lower is the Young’s modulus of concrete. Figure 13 shows creep effect on development of bar reduction vs internal lateral pressure, in case of XC2 class, ϕ16 bar diameter, concrete cover equal to 20 mm and concrete strength class C25/30. Maximum fl is similar, however corresponds to different x values. In the case of XC4 class the bar reduction, x, is higher than in other cases. This is due to a greater concrete net cover value and to a higher strength of concrete.

3.4.4 Concrete Strength effect Concrete strength class has effect on crack initiation but it is negligible on crack propagation (Bossio 2011). Figure 15 shows concrete strength class ef-fect on bond behavior. The greater is concrete strength class the greater is Ωp,trEC2 ratio to reach concrete cover cracking. It is possible to notice how C40/50 strength class is deeply affected by 1.4 limi-tation imposed by Eurocode 2 (Eq. 1 § 3.1).

0.40

1.00

1.60

0.0 6.0 12.0

Ωp,

tr

x [µm]

MC10

SFM

EC2

Figure 9. Ωp,tr ratios vs bar reduction, x, – class XC1.

0.40

1.00

1.60

0.0 6.0 12.0

Ωp,

tr

x [µm]

MC10SFMEC2

Figure 10. Ωp,tr ratios vs bar reduction, x – class XC2.

0.40

1.00

1.60

0.0 6.0 12.0

Ωp,

tr

x [µm]

MC10SFMEC2

Figure 11. Ωp,tr ratios vs bar reduction, x – class XC4.

3.4.5 Concrete cover effect An important parameter to consider in RC structures design is concrete cover, cc. It is a significant pro-tection of bars in concrete from corrosion. Some plots are shown in Figures 16 a, b, c to underline in-fluence that concrete cover has on bond develop-ment in case of thickness equal to 20 mm, 30 mm or 40 mm. Bar diameter considered is ϕ16, and con-crete strength class C25/30.

Figure 16a shows that concrete cover has a great effect on bar reduction, x.

466

Bar reduction, x, has a negligible effect on max-imum value of Ωp,tMC2010, even if the greater is net concrete cover, the greater is bar reduction to reach complete cover crack and higher is the value of in-ternal lateral pressure as shown in table 2.

0.40

1.00

1.60

0.0 6.0 12.0

Ω p,tr

EC2

x [µm]

ϕ10 bars

ϕ16 bars

ϕ20 bars

Figure 12. Ωp,trEC2 vs bar reduction, x, – class XC4 – bar diame-ter comparison – EC2.

0.00

7.00

14.00

0.0 3.0 6.0

x [µm

]

fl [N/mm2]

ϕ=0ϕ=0.5ϕ=1ϕ=2ϕ=3

Figure 13. Bar reduction, x, vs internal lateral pressure fl – Creep effect on bond development.

0.40

1.00

1.60

0.0 7.0 14.0

Ω p,tr

MC

10

x [µm]

ϕ=0

ϕ=0.5

ϕ=1

ϕ=2

ϕ=3

Figure 14. Ωp,trMC10 vs bar reduction, x, – creep effect according to MC10.

Considering SFM Figure 16b shows results about concrete cover effect on Ωp,trSFM (trend is similar to MC10).

Figure 16c shows that in case of greater concrete cover the value of Ωp,trEC2 ratio reaches the limita-tion imposed by EC2 when bar reduction, x is equal to 6.160 µm. Table 2 shows, numerically, concrete cover effect on bar reduction and internal lateral pressure, fl, values.

The greater is creep reduction factor, the greater is the bar reduction leading to crack internal lateral

pressure value; conversely Ωp,tr decreases for a given x at higher creep values.

0.40

1.00

1.60

0.0 7.0 14.0

Ωp,

trEC

2

x [µm]

C20/25C25/30C30/37C40/50

Figure 15. Ωp,trEC2 vs bar reduction, x, – concrete class compar-ison according to EC2.

0.20

1.00

1.80

0.0 7.0 14.0

Ω p,tr

MC1

0

x [µm]

cc=20 mmcc=30 mmcc=40 mm

Figure 16a. Ωp,trMC10 vs bar reduction, x, – concrete cover, cc, comparison according to MC10.

0.20

1.00

1.80

0.0 7.0 14.0

Ω p,tr

SFM

x [µm]

cc=20 mm

cc=30 mm

cc=40 mm

Figure 16b. Ωp,trSFM vs bar reduction, x, – concrete cover, cc, comparison according to SFM.

0.20

1.00

1.80

0.0 7.0 14.0

Ω p,tr

EC2

x [µm]

cc=20 mmcc=30 mmcc=40 mm

Figure 16c. Ωp,trEC2 vs bar reduction, x, – concrete cover, cc, comparison according to EC2.

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Table 2. Bar reduction, x, internal lateral pressure, fl, and Ωp,tr ratios values

x fl Ωp,trMC10 Ωp,trSFM Ωp,trEC2

µm N/mm2 - - -0.000 0.000 1.000 1.000 1.0001.370 2.623 1.207 1.131 1.1171.831 3.413 1.266 1.171 1.1583.653 5.552 1.417 1.278 1.2855.627 6.871 1.500 1.344 1.3797.414 7.432 1.533 1.372 1.4008.800 7.402 1.531 1.370 1.400

10.018 6.642 1.486 1.332 1.362

x fl Ωp,trMC10 Ωp,trSFM Ωp,trEC2 x fl Ωp,trMC10 Ωp,trSFM Ωp,trEC2

µm N/mm2 - - - µm N/mm2 - - -0.000 0.000 1.000 1.000 1.000 0.000 0.000 1.000 1.000 1.0001.339 2.423 1.191 1.121 1.107 1.384 2.717 1.214 1.136 1.1221.761 3.105 1.243 1.155 1.142 6.160 7.693 1.548 1.385 1.4003.293 4.729 1.361 1.236 1.233 8.469 8.681 1.601 1.434 1.4004.719 5.429 1.409 1.271 1.277 10.482 9.029 1.618 1.451 1.4005.309 5.503 1.414 1.275 1.282 12.026 8.875 1.611 1.444 1.4005.797 5.439 1.410 1.272 1.278 13.054 8.372 1.585 1.419 1.4006.210 5.252 1.397 1.263 1.266 13.723 7.251 1.523 1.363 1.400

ϕ16 bars - cc=20 mm

ϕ16 bars - cc=30 mm

ϕ16 bars - cc=40 mm

0.00

7.00

14.00

0.0 5.0 10.0

x [µ

m]

fl [N/mm2]

cc=20 mmcc=30 mmcc=40 mm

0.4

1

1.6

0 8 16

Ωp,

trE

C2

x [µm]

n=2n=2.5n=3n=4n=5n=6

Figure 17. Ωp,trEC2 vs bar reduction, x, – oxide volumetric ex-pansion factor, n, effect, according to EC2.

3.4.5 Oxide Volumetric expansion factor effect Bar oxidation generates voluminous oxides. Their volumetric expansion is usually summarized using volumetric expansion factor, n. It can be reportedly taken between 2 and 6 depending on the type of cor-rosion products formed (Pedeferri & Bertolini 2000).

Figure 17 shows oxide volumetric expansion factor, n, effect on bond behavior in case of con-crete cover equal to 30 mm, ϕ16 bar diameter and C25/30 concrete strength class.

The greater is volumetric expansion factor, the lower is bar reduction to reach complete concrete cover cracking. It is noticed that it has negligible ef-fects on bond development, but has a great effect on percentage of cross bar section lost.

0.4

1.0

1.6

0.0 3.5 7.0

Ωp,

trE

C2

x [µm]

Eo=130 MPaEo=1000 MPaEo=210,000MPa

Figure 18. Ωp,trEC2 vs bar reduction, x – oxide Young’s mod-ulus, Eo, effect, according to EC2.

3.4.6 Oxide Young’s modulus effect Because of uncertainty about oxide Young’s mod-ulus, Eo, value, in Figure 18 it is shown its effect on bond behavior in the case of class XC2 and bar di-ameter equal to ϕ16. Considered values are: 130 MPa (Carè et al. 2008), 1000 MPa and 210,000 MPa (to consider oxide as stiff as steel bar).

It is clearly shown that it has a negligible effect on Ωp,tr ratio, probably because the oxide layer is thinner than other layers.

4 CONCLUSION

This work is a part of a wider study aiming to evalu-

468

ate main concrete and steel parameters effect on cor-roded RC Structures.

The scope of present paper is to evaluate the ef-fect of seven parameters on bond behavior. Some concrete exposure classes are considered and corro-sion process is simulated using a non-linear analyti-cal model. Three bond theories are considered to have comparative results. Corrosion simulation has been done using different concrete and steel parame-ters to evaluate their effects on RC corroded ele-ments’ bond capacity.

On safe side it is possible to assume that volume-tric expansion of corrosion products generates, firstly, a bond increasing; secondly, after crack opening, it decreases instantly to initial value. Then, due to concrete deterioration, it decreases to zero.

Considering different concrete exposure classes it can be noticed that lateral internal pressure, fl, is deeply related to bar reduction, x. Considering the same exposure class, predictions have a similar trend: bar reduction, x, is deeply depending on ex-posure class due to different concrete cover values.

Considering the bar diameter it can be noticed that it has a negligible effect on bond behavior, but the thinner it is, the greater is the bar reduction, x, to crack opening and the greater is the bond increase.

Creep effect is very remarkable. In fact, the greater is creep reduction factor, the greater is the bar reduction leading to lateral pressure value at crack opening.

Considering concrete strength class it has a neg-ligible effect on bond behavior. Internal lateral pres-sure, is the same, while bar reduction value changes.

Concrete cover has a negligible effect on Ωp,tr ratio, but it has an almost linear effect on bar reduc-tion, x. Considering a cc=40 mm, bar reduction value is double than cc=20 mm case. In fact, con-crete cover provides greater protection against ag-gressive agents penetration. Moreover the different bond theories seem to be almost similar, except of EC2, that is deeply affected by 1.4 limitation that gives a threshold of bond increasing.

Oxide volumetric expansion factor, n, is surely one of the most important parameter to consider in a corrosion process simulation. The lower it is, the greater is bar reduction leading to concrete cover complete crack. Conversely oxide Young’s modulus, Eo, has negligible effect on bond behavior.

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Pedeferri P. & Bertolini L. 2000. La durabilità del calcestruzzo armato Milano: McGraw-Hill.