Finite Element Analysis of Finite Element Analysis of Reinforced Concrete Beam Reinforced Concrete Beam under Corroded Conditionunder Corroded Condition

Kitjapat Kitjapat PhuvoravanPhuvoravan, Ph.D., , Ph.D., P.E.P.E.

Lecturer, Civil Engineering Department, Lecturer, Civil Engineering Department, KasetsartKasetsart UniversityUniversity

ThanyathornThanyathorn AmatavirakulAmatavirakulStructural Engineer, Structural Engineer, QbicQbic Engineers and Engineers and

Architects Co., Ltd.Architects Co., Ltd.

JSPSJSPS DOST 3DOST 3rdrd I t ti l S iI t ti l S i

PRESENTATION OUTLINEPRESENTATION OUTLINE

1. Introduction & Corrosion of Reinforcement2. Bond Stress-Slip Relationship3. Influence of Corrosion in Bonding 4. Finite Element Modeling5. Verification of Spring Element6. Finite Element Results7. Conclusion

1. Introduction & Corrosion of 1. Introduction & Corrosion of ReinforcementReinforcement

1. Introduction & Corrosion of 1. Introduction & Corrosion of ReinforcementReinforcement

Research ObjectiveResearch Objective

To study the flexural behavior of RC beam under corrosion

To study the finite element modeling technique in predicting the flexural behavior of RC beam under corrosion

To evaluate the reduced moment resisting capacity of RC beam under corrosion

1. Introduction & Corrosion of 1. Introduction & Corrosion of ReinforcementReinforcement

In general, “Passivation Film” from cement hydration process causes concrete to have high alkalinity (pH = 12-13.8). (Lambert, 2002)

This 10 nanometer thickness film coats the reinforcement from corrosion. As long as the film is not damaged, reinforcement will not be corroded. (Phares et al., 2006)

The passivation film can be damaged by:1. Carbonation 2 Chloride

Effect of CorrosionEffect of Corrosion

Effect of Corrosion in RC

Loss in Bonding between Concrete and Reinforcement

Cracking and Spalling of Concrete Cover

Area Reduction and Mechanical Property Reduction

BondingBondingConcreteConcreteReinforcemReinforcementent

Reduction in Load-Resisting Capacity

2. Bond Stress2. Bond Stress--Slip Relationship Slip Relationship

Pullout Test

Slip

L

dLFπ

τ =

Where = Bond Stress

= Tensile Force

= Reinforcement Diameter

= Embedded Length

τ

F

d

L

F

Mathematical Model of Bond Mathematical Model of Bond Stress versus SlipStress versus Slip

Eligehausen(1983)

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10 12 14 16

Slip (mm)

Bond

stress

(Mpa

)

Equation of Eligehausen. (1983)

Eligehausen. (1983)

Mathematical Model of Bond Stress Mathematical Model of Bond Stress versus Slipversus Slip

5.0'21 )/(748.0 dcfcuu == ττ

5.0' )/(234.0 dcfcfu =τ

5.0'1 )30/)(4/20( cfd−=τ

)1/1ln()/1(5.0'1 )30/( ττα u

cu ef=∆

0.32 =∆ u

du 6.03 =∆

(MPa)(MPa)

(MPa)

(mm)(mm)(mm)

4.0=α

Effect of Bond Slip in Finite Element Effect of Bond Slip in Finite Element ModelModel

0

20000

40000

60000

80000

100000

0 4 8 12 16 20 24

Midspan deflection (mm)

Load

(N)

Azher (2005)Prefect BondBond-Slip

3. Influence of Corrosion in 3. Influence of Corrosion in BondingBonding

Reduction in Reinforcement Area

)1( WAAc ∆−=

Where = Reinforcement Area after Corrosion

= Reinforcement Area before Corrosion

= Weight Loss Percentage of Reinforcement

cA

A

W∆

3. Influence of Corrosion in 3. Influence of Corrosion in BondingBonding

Source: Almusallam et al (1996)

LEVEL OF CORROSION0.87

%1.50%0%4.27%

7.80%

6.70%

Reduction in Maximum Bond

Stress between Concrete and Reinforcement

3. Influence of Corrosion in 3. Influence of Corrosion in BondingBonding

Source: Bhargava et al., (2007)

XpeR 117.0192.1 −=

Where = Normalized bond strength

= Corrosion Level (%)

R

PX

Proposed Model for Bond StressProposed Model for Bond Stress--Slip Slip under Corrosionunder Corrosion

ucc R 121 )( τττ ×==

fufc R ττ ×= )(

(MPa)(MPa)

uc 11 ∆=∆

uc 22 ∆=∆

uc 33 ∆=∆

(mm)(mm)(mm)

Bond StressBond Stress--Slip in UseSlip in Use

0

1

2

3

4

5

6

7

0 2 4 6 8 10 12

Slip (mm)

Bond

stress

(MPa

)

0%

8.9%

14.2%

22.2%

0

1

2

3

4

5

6

7

0 2 4 6 8 10Slip (mm)

Bond

stress

(MPa

)

0%

8.8%

14%

Case Study No.1

Case Study No.2

Case Study No.1Case Study No.1

Units in mm.

Portion of Corroded Reinforcement

Beam with Corroded Reinforcement in thee Portion of Beam (Maaddawy et al., 2005)

4.4. Finite Element ModelingFinite Element Modeling

Case Study No.1Case Study No.1

400Control beam

408.9CN-504014.2CN-1104022.2CN-210

Concrete Concrete Strength Strength

(MPa)(MPa)

CorrosioCorrosion Leveln Level

(%)(%)BeamBeam

4 Levels of Corrosion

Case Study No.2Case Study No.2

Portion of Corroded Reinforcement

Beam with Corroded Reinforcement for the e Length of Beam (Maaddawy et al., 2005)

Case Study No.2Case Study No.2

360Control Beam

368.8BT-14414BT-2

Concrete Concrete Strength Strength

((MPaMPa))

CorrosioCorrosion Level n Level

(%)(%)BeamBeam

3 Levels of Corrosion

Material Properties:Material Properties:

Concrete: Compressive Uniaxial Stress-Strain Relationship(Desayi and Krishman, 1964)

2

0

1 ⎟⎟⎠

⎞⎜⎜⎝

⎛+

=

εε

εcEf

c

c

Ef '

02

=ε

εfEc =

Where = Stress at any strain, psi

= Strain at stress

f

ε

0ε

'000,57 cc fE =

Steel: Elastic-Perfectly Plastic Model

4.4. Finite Element ModelingFinite Element Modeling

Element Types: Concrete & Element Types: Concrete & ReinforcementReinforcement

Concrete:8-Node 3D Solid Element

Reinforcement:2-Node Truss El t

4.4. Finite Element ModelingFinite Element Modeling

Element Types: BondElement Types: Bond--SlipSlip

2-Node Nonlinear Spring Element

Reinforcement Node

Concrete Node

4.4. Finite Element ModelingFinite Element Modeling

(Case Study No.1)(Case Study No.1)

Concrete: 1260 Solid Elements Longitudinal Reinforcement: 82 Truss ElementsStirrup: 168 Truss ElementsBond: 41 Spring Elements

Stirrup

Main Reinforcem

ent

4.4. Finite Element ModelingFinite Element Modeling

(Case Study No.2)(Case Study No.2)

Concrete: 468 Solid ElementsLongitudinal Reinforcement: 48 Truss ElementsStirrup: 48 Truss ElementsBond: 24 Spring Elements

Stirrup

Main Reinforcem

ent

4.4. Finite Element ModelingFinite Element Modeling

Finite Element Modeling of BondFinite Element Modeling of Bond--Slip Slip BehaviorBehavior

4.4. Finite Element ModelingFinite Element Modeling

Boundary ConditionsBoundary Conditions

Symmetry Condition

Symmetry Condition

Simply Support Condition

Bottom View

4.4. Finite Element ModelingFinite Element Modeling

Boundary Conditions and LoadingsBoundary Conditions and Loadings

Roller support

Loading

Symmetry Condition

4.4. Finite Element ModelingFinite Element Modeling

5. Verification of Spring Element5. Verification of Spring Element

Concrete Strength = 24.7 MPaReinforcement Diameter = 12.7 mmReinf. Yield Stress = 315 MPa

PullPull--out out TestTest

Finite Element Model for PullFinite Element Model for Pull--out Testout Test

P

End Slip

3.5D

6.35 mm

12.7 mm

Reinforcement

5. Verification of Spring Element5. Verification of Spring Element

Relationship between Bond StressRelationship between Bond Stress--Slip and Input ForceSlip and Input Force--Displacement for Displacement for Spring ElementSpring Element

TestTestF

L

dLFπ

τ = ModModelel

dLF τπ=

L

Concrete

Reinforcement

Comparison of Bond StressComparison of Bond Stress--End Slip End Slip between Experimental and Finite between Experimental and Finite Element ResultsElement Results

0

2

4

6

8

0 0.2 0.4 0.6 0.8 1

End slip (mm)

Bond

stress

(MPa

)

Lee et al. (2002)FEM

6. Finite Element Analysis 6. Finite Element Analysis ResultsResults

6.1 Case Study No.16.1 Case Study No.1RC Beam with Corroded RC Beam with Corroded

Reinforcement in the Middle Reinforcement in the Middle Portion of BeamPortion of Beam

Flexural Behavior of RC BeamFlexural Behavior of RC Beam

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

0 20 40 60 80 100Midspan deflection (mm)

Load

(N)

Maaddawy (2005)FEM

0

10000

20000

30000

40000

50000

60000

70000

80000

0 20 40 60 80 100

Midspan deflection (mm)

Load

(N)

Maaddawy (2005)FEM

0

10000

20000

30000

40000

50000

60000

70000

80000

0 20 40 60 80 100

Midspan deflection (mm)

Load

(N)

Maaddawy (2005)FEM

0

10000

20000

30000

40000

50000

60000

70000

0 20 40 60 80 100

Midspan deflection (mm)

Load

(N)

Maaddawy (2005)

FEM

0% Corrosion

Level

8.9% Corrosion

Level

14.2%i

22.2%

Stress Distribution in Beam St ess st but o eaSectionSection

0

127

254

-45 -35 -25 -15 -5 5Stress (MPa)

Secti

on (m

m)1000013442134432000030000400005000060000700007500079035

0

127

254

-45 -35 -25 -15 -5 5

Stress (MPa)

Secti

on (m

m)

10000131651316620000300004000050000600007000071633

0

127

254

-45 -35 -25 -15 -5 5Stress (MPa)

Secti

on (m

m)

10000130201302120000300004000050000600006500068018

0

127

254

-45 -35 -25 -15 -5 5Stress (MPa)

Secti

on (m

m)

10000

12757

12758

20000

30000

40000

50000

60000

61125

0% Corrosion

Level

8.9% Corrosion

Level

14.2%i

22.2%

Progressive Cracking (0% Progressive Cracking (0% Corrosion)Corrosion)

First crack

Load

Load

Load

Diagonal tensile cracks

Compressive cracks

Load

Flexural cracks

Progressive Cracking (8.9% Progressive Cracking (8.9% Corrosion)Corrosion)

Load

Diagonal tensile cracks

Compressive

cracks

First crack

Load

Flexural cracks

Load

First crack

Reinforcement Force and Bond Force Reinforcement Force and Bond Force under Various Load Levelsunder Various Load Levels

-3000

-1500

0

1500

3000

4500

6000

0 10 20 30 40

Element from the left of beam

Force

in Sp

ring (

N)

10000134421344320000300004000050000600007000079035

0

20000

40000

60000

80000

100000

0 10 20 30 40Element from the left of beam

Force

in St

eel (N

)

10000134421344320000300004000050000600007000079035

0% Corrosio

n

Bond Force

90450yielding

Reinforcement Force

Reinforcement Force and Bond Force Reinforcement Force and Bond Force under Various Load Levelsunder Various Load Levels

8.9% Corrosion

-3000

-1500

0

1500

3000

4500

6000

0 10 20 30 40

Element from the left of beam

Force

in Sp

ring (

N)

10000131651316620000300004000050000600007000071633

0

20000

40000

60000

80000

100000

0 10 20 30 40Element from the left of beam

Force

in St

eel (N

)

10000131651316620000300004000050000600007000071633

yielding82350

Bond Force

Reinforcement Force

Reinforcement Stress and Bond Reinforcement Stress and Bond StressStress

-5000

0

5000

10000

15000

20000

25000

0 4 8 12 16 20 24 28 32 36 40

Element from the left of beam

Forc

e (N)

แรงในเหล็กเสริม

แรงยึดเหนี่ยว

Load

Bond Stress

Steel Stress Steel

ForceBond Force

Moment CapacityMoment Capacity

61,125

68,018

71,663

79,035

Ultimate Ultimate loadload

FEM (N)FEM (N)

30,562

34,009

35,816

39,517

Max. Max. MomentMoment

((kNkN--mm)mm)

22.7522.2

13.9414.2

9.378.9

-0

Reduce Reduce MomentMoment

(%)(%)

CorrosioCorrosionn

(%)(%)

6. Finite Element Analysis 6. Finite Element Analysis ResultsResults

6.2 Case Study No.26.2 Case Study No.2RC Beam with Corroded RC Beam with Corroded

Reinforcement for the Whole Reinforcement for the Whole Length of BeamLength of Beam

Flexural Behavior of RC BeamFlexural Behavior of RC Beam

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

0 5 10 15 20 25Midspan deflection (mm)

Load

(N)

Azher (2005)FEM

0

10000

20000

30000

40000

50000

60000

70000

80000

0 5 10 15 20 25

Midspan deflection (mm)

Load

(N)

Azher (2005)FEM

0

10000

20000

30000

40000

50000

60000

70000

0 5 10 15 20

Midspan deflection (mm)

Load

(N)

Azher (2005)

FEM

0% Corrosion

Level

8.8% 14%

Stress Distribution in Beam Stress Distribution in Beam SectionSection

0

75

150

-40 -30 -20 -10 0 10

Stress (MPa)

Secti

on (m

m)

100001221812219200004000060000800009000090611

0

75

150

-40 -30 -20 -10 0 10Stress (MPa)

Secti

on (m

m)

100001210112102200003000040000500006000068494

0

75

150

-50 -40 -30 -20 -10 0 10

Stress (MPa)

Secti

on (m

m)

100001329513296200003000040000500005500056320

0% Corrosion

Level

8.8% 14%

Load

Load

Load

Load

Compressive

cracks

Diagonal tensile cracks

Progressive Cracking (0% Progressive Cracking (0% Corrosion)Corrosion)

Load

Load

Load

Diagonal tensile cracks

Compressive

cracks

First crack

Load

og ess e C ac gg g (8 8%(Corrosion)Corrosion)

0

10000

20000

30000

40000

50000

60000

70000

0 5 10 15 20

Element from the left of beam

Force

in St

eel (N

)

10000

12218

12219

20000

40000

60000

80000

90000

90661

yielding66670

-1000

0

1000

2000

3000

4000

5000

6000

0 5 10 15 20

Element from the left of beam

Force

in Sp

ring (

N)

10000

12218

12219

20000

40000

60000

80000

90000

90661

bond failure4900

5513

under Various Load Levelsunder Various Load Levels

0% Corrosio

n

Bond Force

Reinforcement Force

0

500

1000

1500

2000

2500

0 5 10 15 20

Element from the left of beam

Force

in Sp

ring (

N)

10000

12101

12102

20000

30000

40000

50000

60000

68494

0

10000

20000

30000

40000

50000

60000

70000

0 5 10 15 20

Element from the left of beam

Force

in St

eel (N

)

10000

12101

12102

20000

30000

40000

50000

60000

68494

yielding60770

bond failure

2088

2350

Reinforcement Force and Bond Force Reinforcement Force and Bond Force under Various Load Levelsunder Various Load Levels

8.8% Corrosion

Bond Force

Reinforcement Force

0

450

900

1350

1800

0 5 10 15 20

Element from the left of beam

Force

in Sp

ring (

N)

10000

13295

13296

20000

30000

40000

50000

56320

0

10000

20000

30000

40000

50000

60000

70000

0 5 10 15 20

Element from the left of beam

Force

in ste

el (N)

10000

13295

13296

20000

30000

40000

50000

56320

yielding57230

bond failure

1495

1683

Reinforcement Force and Bond Force Reinforcement Force and Bond Force under Various Load Levelsunder Various Load Levels

14% Corrosion

Bond Force

Reinforcement Force

Moment CapacityMoment Capacity

56,320

68,494

90,661

Ultimate Ultimate loadload

FEM (N)FEM (N)

9,856

11,986

15,865

Max. Max. MomentMoment

((kNkN--mm)mm)

37.8814

24.458.8

-0

Reduce Reduce MomentMoment

(%)(%)

ระดับสนิมระดับสนิม(%)(%)

7. Conclusion7. ConclusionProposed finite element model is able to predict the flexural behavior of RC beam under corroded conditions

Finite element model is able to determine the ultimate load carrying capacity close to the experimental results

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

diti f i f t

7. Conclusion 7. Conclusion (cont(cont’’d)d)

Finite element model can capture the concrete stress distribution, reinforcement force, and bond force under various load levels

Corrosion of reinforcement in the middle portion of RC beam results in yielding failure of reinforcement at the ultimate load capacity

Corrosion of reinforcement for the whole length of RC beam results in bond failure at

Questions ?