1

Corrosion Induced Cracking: Analytical and Non-Linear Fracture

mechanics Modelling

OSTRAVA

10-02-2005

Institute of Structural Mechanics

Faculty of Civil Engineering

University of Technology, Brno

Florentina Pernica, Drahomír Novák

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Introduction• The aim: to develop NLFM computational model

for the corrosion induced cracking and compare the results with one obtained from analytical model.

• Computational model that was prepared using software ATENA 2D.

• Analytical model for corrosion induced cracking in RC structures.

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Analytical model for corrosion

• The deterioration mechanism: corrosion of reinforcement.

• Two processes may lead to depassivation of steel:

- carbonatio of concrete - chloride ingress.

• An analytical model for corrosion induced cracking in RC structures has been derived based on the concepts of fracture mechanics and smeared cracks.

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Analytical model

ef

t

αc

αc

sc E

πbf

b/aνa/bν

tπdw

2

11

4

c

sefr

ν(t)ab(t)ab

)d(D

tdEaσP

22

22

0

1

2

2

5

Analytical model

0

2

4

6

8

10

12

14

16

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7

Crack Width (mm)

Pres

sure

(MPa

)0

0,1

0,2

0,3

0,4

0,5

0,6

0 2 4 6 8 10

Time (year)

Cra

ck W

idth

(m

m)

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10

Time (year)

Pres

sure

(MPa

)

6

• Was done using software ATENA 2D based on non-linear fracture mechanics.

• Was developed mainly for the realistic simulation of RC structures, realistic modelling of cracking in quasi-brittle materials.

• The corrosion problem was solved as 2D plane stain.

The computational model

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Modelling of the entire concrete circle: mesh, boundaries conditions and applying shrinkage

Evolution of cracks at peak load

Alternative 1

Concrete E(Gpa)

ft

(MPa)

fc

(MPa)

Gf

(MN/m)3D

NonLinCementitious 2 

3.032E+04 

2.3 

 -23

 

 4E-05

 

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Alternative 2

1

2

Concrete E(Gpa)

ft

(MPa)

fc

(MPa)

Gf

(MN/m)3D

NonLinCementitious 2 

3.032E+04 

2.3 

 -23

 

 4E-05

 

0

2

4

6

8

10

12

14

16

18

20

0 0,2 0,4 0,6 0,8

Crack width (mm)

Str

ess

(MP

a)

ATENA 2D Ft=2 MPa

ATENA 2D Ft=2,31 MPA

Analytical model

Quarter of concrete circle1- the values of stress were taken2-the values of crack width were measured

Graphs stress vs. crack width

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Alternative 3

Concrete E(Gpa)

ft

(MPa)

fc

(MPa)

Gf

(MN/m)

3D NonLinCementitious 2

 3.032E+04

 

 2.3

 

 -23

 

 4E-05

 

3D NonLinCementitious 2

weaker

 2.5E+04

 1.8

 -18

 1.5e-05

1

Evolution of cracks in first steps Evolution of cracks at peak load 0

2

4

6

8

10

12

0 0,1 0,2 0,3 0,4 0,5 0,6

Crack width (mm)

Str

ess

(MP

a)

Atena 2D

Analytical model

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Conclusions

• FEM computational model was developed.

• The trends of stress vs. crack width curves of both experimental and numerical results were similar.

• The differences: due to insufficient previous material parameters calibration and due to comparing linear with non-linear solution.