EFFECT OF STEEL CORROSION LEVEL ON FLEXURAL

BEHAVIOR OF REINFORCED CONCRETE BEAM

1Kitjapat PHUVORAVAN

1Lecturer, Faculty of Engineering, Kasetsart University, Bangkok, Thailand,

fengkpp@ku.ac.th

Abstract: Corrosion of main steel reinforcement is one of the major factors in flexural

capacity reduction of reinforced concrete (RC) beam. Steel corrosion reduces the cross

section area as well as the continuity of the surface of steel. Such reductions lower the tension

strength of steel and decrease the bond strength due to a slip between steel and the

surrounding concrete, and, consequently deteriorate the member strength. This paper presents

the effect of steel corrosion level on flexural behavior of RC beams by performing nonlinear

finite element analysis. Concrete was modeled as three dimensional solid elements while all

steel reinforcement was represented by truss elements having nonlinear property for both

materials. Nonlinear springs were used to model bonding between steel and concrete. The

results showed that for corrosion of reinforcement in the middle portion of RC beam,

percentage reduction in moment capacity is approximately the same as percentage of

corrosion level. However, for corrosion of reinforcement for the whole length of RC beam,

the percentage reduction in moment capacity is significantly greater than percentage of

corrosion level.

Key Words: steel corrosion, reinforced concrete beam, finite element, flexural behavior

1. INTRODUCTION

Reinforced concrete has been used as essential materials in main load-carrying system of

various structures in several countries. Reinforced concrete is recognized to be durable and

capable of withstanding a variety of environment conditions. Nevertheless, failures of

structures still do occur as a result of premature steel reinforcement corrosion. The corrosion

of rebar in reinforced concrete, shown in Figure 1, deteriorates the strength of such a

structure. The effects of corrosion is even more pronounced in flexural reinforced concrete

member as nearly all of tension force is exerted on steel reinforcement.

The corrosion of steel rebar in an RC beam reduces cross-sectional steel area and creates

local discontinuities of the steel surface. The tensile capacity of the steel is reduced in

proportion directly to the loss of the steel area. Moreover, the loss of the steel surface causes

a loss of the bond between the steel and the surrounded concrete. All of these actions

contribute to the loss of stiffness and ductility of the beam and, thus, reduce the ultimate

strength of the beam. A previous study (Al-Sulaimani et al., 1990) shows that corrosion up to

about 1.5% does not affect the ultimate capacity while 4.5% of corrosion could reduce the

ultimate load to an extent of 12%. In general, the corrosion level can be determined from the

percentage of weight loss.

The effects of steel area reduction and the loss in bond strength due to corrosion are not

easily accounted for by means of conventional design codes. This paper presents the effect of

steel corrosion level on flexural behavior of RC beams by performing nonlinear finite

element analysis, which has been verified with experimental results. The objective is to

investigate the effect of steel corrosion level and the location of corrosion in main

reinforcement on the load carrying capacity of the beams. The results from this research lead

to the preliminary evaluation of the remaining flexural strength for RC beam under corroded

condition.

Figure 1. Corrosion of Reinforcing Steel in Reinforced Concrete Beam

2. FINITE ELEMENT ANALYSIS FOR CORROSION

Three-dimensional finite element analysis (FEA) was employed to investigate the effect of

steel corrosion on flexural strength of RC beams. The adopted finite element model was

verified by Phuvoravan and Amatavirakul (2009) to capture the major behaviors of steel

corrosion. The bond-slip between the steel and the concrete was represented by non-linear

spring. The spring having no dimension connected the nodes of steel elements and concrete

elements. The load exerted on the springs and the deformation of the springs which

characterized the load-deformation pattern was obtained by converting the maximum bond

stress into force. Figure 2 shows the details of the spring connecting a concrete node to a

node of steel element. The connected nodes are coincident nodes thus giving no dimension to

the spring.

Figure 2. Details of the FE Model

2.1 Material Models

Reinforced concrete flexural member nonlinearly responses to the applied load according to

properties of both concrete and steel. Thus, modeling of material properties of concrete,

reinforcing steel, and bond behavior plays an important role in the accuracy of the analyses.

2.1.1 Concrete

The nonlinear relationship between stress and strain in compression zone can be derived from

Equation 1. Such a relationship is shown in Figure 3. The tensile strength of concrete was

taken as 10% of the compressive strength. The modulus of elasticity of concrete is

determined from Equation 2 and a value of 0.18 was set for Poisson’s ratio.

2

0

1

+

=

ε

ε

εcEf (1)

where c

c

E

f '

0

2=ε

ε

fEc =

f : stress at any strain ε

0ε : strain at ultimate compressive strength

'

cf : compressive strength (psi)

cE : modulus of elasticity (psi) which is related to compressive strength by:

'000,57 cc fE = (2)

2.1.2 Steel

The stress-strain relationship of the steel reinforcement shown in Figure 4 was considered to

be elastic perfectly plastic-i.e. before yielding stage the relationship is linearly elastic and

becomes plastic stage after yielding.

Figure 3. Concrete Stress-Strain Curve Figure 4. Steel Stress-Strain Curve

2.2 Effects of Corrosion in Finite Element Model

The effects of reinforcement corrosion deteriorate the strength of concrete structures as

previously discussed. In modeling the flexural behavior of reinforced concrete beams of this

study, the two most important factors to be considered were the reduction of cross-sectional

steel area and the bond strength between steel and concrete.

2.2.1 Reduction of Cross-sectional Area

The reduction of steel area is proportional to the degree of corrosion and can be simply

evaluated from Equation 3.

)1( Pc XAA −= (3)

where cA : cross-sectional area of corroded steel

A : cross-sectional area of virgin steel

PX : corrosion level

2.2.2 Reduction of Bond Strength

The loss of cross-sectional steel area and the concrete cracks developed around the corroded

steel contribute to a slip between the steel and the concrete and, thereby, reduce the bond

strength of reinforced concrete. The maximum bond stress of non corroded reinforced

concrete beam can be determined from Equation 4. In this condition, the maximum bond

stress consists of the bond strength contributed by concrete, τconc , and stirrups, τst (Kemp and

Wilhelm, 1979).

4434421444 3444 21stconc

bs

ytt

c

b

cv

ds

fAf

d

c

ττ

τ

+

+= 191.024.055.0 '

max (4)

where vmaxτ : maximum bond stress for normal beam

cc : concrete covering

bd : diameter of tensile steel

tA : cross-sectional area of stirrup

ytf : yield strength of stirrup

ss : spacing of stirrup

For corroded reinforced concrete beam, the maximum bond stress can be obtained by

applying a reduction factor to the bond strength contributed by concrete, τconc . The value of

the reduction factor, R, is co-related to the corrosion level, Xp, as in Equation 5. This

Equation was empirically proposed (Bhargava et al., 2007) from an extensive study on

corrosion-induced bond strength degradation in RC. The equation is valid when Xp is greater

than 1.5 % and the reduction factor becomes unity when Xp is less than 1.5%.

PXeR

198.0346.1

−= (5)

where R : normalized bond strength

PX : corrosion level

3. EXPERIMENTAL BEAM DATA

The results of experimental study (Maaddawy et al., 2005) were chosen to investigate the

corrosion effect in this paper. Two main case studies are RC beam with reinforcement

corrosion in the middle portion, and RC beam with reinforcement corrosion for the whole

length.

Figure 5. Beam Reinforcement Details for Case Study no. 1

Figure 6. Four-Point Bending Test Setup for Case Study no. 1

For the first case study, corrosion was restricted to the tensile steel placed in the middle 1400

mm of the beams. The corrosion induced was divided into four levels, i.e., 0%, 8.9%, 14.2%,

and 22.2% corrosion. Each beam was 3200 mm long with a cross section of 152×254 mm as

shown in Figure 5. Two DB16mm deformed steel bars with a yield stress of 450 N/mm2 and

two 8-mm plain bars with a yield stress of 340 N/mm2 were placed in the tension zone and

compression zone, respectively. The 28-day compressive strength of concrete had an average

value of 40 MPa. Four-point bending test as shown in Figure 6 with a shear span of 1000 mm

is set up to investigate the flexural behavior.

Figure 7. Beam Reinforcement Details for Case Study no. 2

For the second case study, corrosion was activated on bottom main reinforcement for the

whole length of RC beam. The corrosion induced was divided into three levels, i.e., 0%,

8.8%, and 14% corrosion. Each beam was 1100 mm long with a cross section of 150×150

mm as shown in Figure 7. Two DB12mm deformed steel bars and two RB8mm plain bars

Portion of Corroded ReinforcementPortion of Corroded Reinforcement

were placed in the tension zone and compression zone, respectively. The 28-day compressive

strength of concrete had an average value of 36 MPa for 0% and 8.8% corrosion, and 44 MPa

for 14% corrosion. Four-point bending test as shown in Figure 8 with a shear span of 200 mm

is set up to investigate the flexural behavior.

Figure 8. Four-Point Bending Test Setup for Case Study no. 2

4. FINITE ELEMENT MODELING

Due to the symmetry of the specimen and the applied loads, only a quarter of the beams were

modeled in order to reduce the computational time. The convergence test was performed in

order to determine the appropriate number of elements for each case study. The element

dimension is selected so that the element is not in poor shape to avoid numerical error. For

case study no. 1, the model utilized a total number of 1551 elements. Concrete portion is

modeled using 1260 three-dimensional solid elements, while main steel reinforcement and

steel stirrup are modeled using 250 truss elements. The bond continuity between concrete and

steel is modeling using 41 nonlinear spring elements.

For case study no. 2, the model consisted of a total number of 588 finite elements. Concrete

portion is modeled using 468 three-dimensional solid elements, while main steel

reinforcement and steel stirrup are modeled using 96 truss elements. The bond continuity

between concrete and steel is modeling using 24 nonlinear spring elements.

The bond stress versus slip relationship used in the analysis is shown in Figure 9 for case

study no. 1 and 2, respectively. The relationship is based mainly on corrosion level and other

important parameters as discussed earlier.

Figure 9. The Adopted Bond Stress versus Slip relationship for Case Study no. 1 and 2

0

1

2

3

4

5

6

7

0 2 4 6 8 10

Slip (mm)

Bon

d stress (M

Pa)

0%

8.8%

14%

0

1

2

3

4

5

6

7

0 2 4 6 8 10 12

Slip (mm)

Bon

d stress (M

Pa)

0%

8.9%

14.2%

22.2%

5. ANALYTICAL RESULTS

Comparisons of the results obtained from the FEA and the laboratory test results are shown in

Figure 10 and Figure 13 for case study no. 1 and 2, respectively. The relationship between

applied loads and mid-span deflection derived by FEA give a good agreement comparing to

the results obtained from the structural tests. Finite element model by the use of spring

element to model bond-slip is able to excellently represent the corroded condition of

reinforcement. Furthermore, concrete stress distribution, reinforcement force, and bond force

can be investigated under various load levels in FEA.

Figure 10. Load-Deflection Curve for Case Study no. 1 (No Corrosion & 8.9% Corrosion)

A typical line showing the relationship of load and deflection could be divided into three

regions. The first region shows a linear relationship until reaching the first crack in tension

zone of the beam after which the line exhibits a non-linear pattern due to the crushing of

concrete. The final region starts at the point where the tensile steel reaches its yield stress.

The deflection at mid span increases rapidly though the load is gradually applied.

For case study no.1 where corrosion of reinforcement in the middle portion of RC beam, the

study showed that bond-slip contributed relatively smaller effect than did the reduction of the

cross-sectional steel area. When the degree of corrosion increased, the ultimate load and the

yield load decreased accordingly. Figure 11 shows progressive cracking at first crack state

and at the ultimate load capacity for 8.9% steel corrosion. Immediately after first crack at the

middle portion of the beam, additional flexural cracks occur at interval within constant

moment region. At the ultimate load capacity, diagonal tensile crack occurs at the shear

region near support, and the compressive crushing occurs at the top fiber of the beam. Figure

12 shows reinforcement force and bond force under various load levels for 8.9% corrosion. It

can be seen that steel force reaches its maximum yielding force when the load level is at

ultimate load carrying capacity, and thus, the beam fails by steel yielding.

Load

Diagonal tensile cracks

Compressive

cracksLoad

Diagonal tensile cracks

Compressive

cracksLoad

Flexural cracksFirst crack

Load

Flexural cracksFirst crack

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

0 20 40 60 80 100

Midspan deflection (mm)

Load (N)

Maaddawy (2005)

FEM0

10000

20000

30000

40000

50000

60000

70000

80000

0 20 40 60 80 100

Midspan deflection (mm)

Load (N)

Maaddawy (2005)

FEM

Figure 11. Progressive Cracking at First Crack and at Ultimate Load Capacity

(Case Study no.1, 8.9% Corrosion)

Figure 12. Reinforcement Force and Bond Force under Various Load Levels

(Case Study no. 1, 8.9% Corrosion)

It should be noted from Table 1 that, as the level of corrosion increased by 8.9%, the ultimate

moment decreased in the order of 9.17% and the loss of the ultimate flexural moment could

be as great as 22.65% when the corrosion level reached 22.2%. It is evident that the loss of

the ultimate moment is predominantly attributed by the steel mass loss.

Table 1. Flexural Ultimate Moment for Case Study no. 1 and 2, respectively.

Corrosion

level

Reduction in

Moment (%)

0

8.9

14.2

22.2

-

9.17

14.1

22.65

Corrosion

level

Reduction in

Moment (%)

0

8.8

14.0

-

24.45

37.88

For case study no. 2 where corrosion of reinforcement for the whole length of RC beam,

bond-slip behavior plays a important role in the flexural behavior of the beam. When the

degree of corrosion increased, the ultimate load and the yield load decreased rapidly. Figure

14 shows progressive cracking at first crack state and at the ultimate load capacity for 8.8%

steel corrosion. At first cracking state, flexural cracking is concentrated at the middle bottom

portion of the beam. At the ultimate load capacity, diagonal tensile crack occurs at the shear

region near support, the compressive crushing occurs at the top fiber of the beam, and

cracking spreads throughout the beam. Figure 15 shows reinforcement force and bond force

under various load levels for 8.8% corrosion. It can be seen that, at the ultimate load level,

bond force reaches its maximum bond capacity, and thus, the beam fails by bond failure.

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

0 5 10 15 20 25

Midspan deflection (mm)

Loa

d (N

)

Azher (2005)

FEM0

10000

20000

30000

40000

50000

60000

70000

80000

0 5 10 15 20 25

Midspan deflection (mm)

Load (N)

Azher (2005)

FEM

0

20000

40000

60000

80000

100000

0 10 20 30 40

Element from the left of beam

Force in Steel (N

)

10000

13165

13166

20000

30000

40000

50000

60000

70000

71633

yielding82350

0

20000

40000

60000

80000

100000

0 10 20 30 40

Element from the left of beam

Force in Steel (N

)

10000

13165

13166

20000

30000

40000

50000

60000

70000

71633

yielding82350

-3000

-1500

0

1500

3000

4500

6000

0 10 20 30 40

Element from the left of beam

Force in Spring (N)

10000

13165

13166

20000

30000

40000

50000

60000

70000

71633

Figure 13. Load-Deflection Curve for Case Study no. 2 (No Corrosion & 8.8% Corrosion)

Figure 14. Progressive Cracking at First Crack and at Ultimate Load Capacity

(Case Study no.2, 8.8% Corrosion)

From Table 1, the level of corrosion increased by 8.8%, the ultimate moment decreased by

24.45% and the loss of the ultimate flexural moment could be as great as 37.88% when the

corrosion level reached 14%. It can be seen that the loss of the ultimate moment is not only

depend on the amount of the steel mass loss, but also the bond loss due to corrosion.

Figure 15. Reinforcement Force and Bond Force under Various Load Levels

(Case Study no. 2, 8.8% Corrosion)

6. CONCLUSION

Finite element analyses could be used to realistically predict the flexural behavior of

reinforced concrete beams having various reinforcement corrosion levels. Modeling the bond

strength by applying the non-linear spring element makes it possible to capture the crucial

behavior of the flexural capacity of the RC beam with corroded reinforcement. It is also

concluded that, for corrosion of reinforcement in the middle portion of RC beam, percentage

reduction in moment capacity is approximately the same as percentage of corrosion level;

while, for corrosion of reinforcement for the whole length of RC beam, the percentage

reduction in moment capacity is significantly greater than percentage of corrosion level.

Load

First crack

Load

First crack

LoadDiagonal tensile cracks

Compressive

cracks LoadDiagonal tensile cracks

Compressive

cracks

0

10000

20000

30000

40000

50000

60000

70000

0 5 10 15 20

Element from the left of beam

Force in Steel (N

)

10000

12101

12102

20000

30000

40000

50000

60000

68494

yielding

60770

0

10000

20000

30000

40000

50000

60000

70000

0 5 10 15 20

Element from the left of beam

Force in Steel (N

)

10000

12101

12102

20000

30000

40000

50000

60000

68494

yielding

60770

0

500

1000

1500

2000

2500

0 5 10 15 20

Element from the left of beam

Force in Spring (N

)

10000

12101

12102

20000

30000

40000

50000

60000

68494

bond failure

2088

2350

0

500

1000

1500

2000

2500

0 5 10 15 20

Element from the left of beam

Force in Spring (N

)

10000

12101

12102

20000

30000

40000

50000

60000

68494

bond failure

2088

2350

REFERENCES

Al-Sulaimani, G. J., Kaleemullah, M., Basunbul, I. A., and Rasheeduzzafar (1990) Influence

of Corrosion and Cracking on Bond Behaviour and Strength of Reinforced Concrete

Members, ACI Structural Journal, Vol.87, No.2, 220-231.

Bhargava, K., Ghosh, A.K., Mori, Y., and Ramanujam, S. (2007) Corrosion-induced Bond

Strength Degradation in Reinforced Concrete-Analytical and Empirical Models, Nuclear

Engineering and Design, Vol. 237, 1140-1157.

Kemp, E.L., and Wilhelm, W.J. (1979) Investigation of the Parameters Influencing Bond

Cracking, ACI Structural Journal, Vol.76, No.1, 47-71.

Maaddawy, T.E., Soudki, K., Topper, T. (2005) Long-Term Performance of Corrosion-

Damaged Reinforced Concrete Beams, ACI Structural Journal, Vol.102, No.5, 649-656.

Phuvoravan, K., and Amatavirakul, T. (2009) Finite Element Analysis of Reinforced

Concrete Beam under Corroded Condition, Proceeding to the 6th Regional Symposium on

Infrastructure Development (RSID), Bangkok, Thailand, January 12-13, 2009, STR37.