Transcript Corrosion Induced Cracking: Analytical and Non-Linear Fracture mechanics Modelling OSTRAVA

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.
• Analytical model for corrosion
induced cracking in RC structures.
• Computational model that was
prepared using software ATENA
2D.
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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
wc 
4πd s t 
1  νc a/b  α  1  νc b/a  α
P1  σ r a  
2πbf t

Eef
2 Eef d s t 
 b 2  a 2(t)

(D  2d 0 )

ν
c 
 b 2  a 2(t)



4
16
0,5
14
12
Pressure (MPa)
0,6
0,4
0,3
0,2
0,1
10
8
6
4
2
0
0
0
2
4
6
8
0
10
2
4
6
8
10
Time (year)
Time (year)
16
14
12
Pressure (MPa)
Crack Width (mm)
Analytical model
10
8
6
4
2
0
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
Crack Width (mm)
5
The computational model
• 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.
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Alternative 1
Modelling of the entire concrete
circle: mesh, boundaries conditions
and applying shrinkage
Concrete
3D
NonLinCementitious 2
Evolution of cracks at peak load
E
(Gpa)
ft
(MPa)
fc
(MPa)
Gf
(MN/m)
3.032E+04
2.3
-23
4E-05
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Alternative 2
2
20
18
16
ATENA 2D Ft=2 MPa
Stress (MPa)
14
ATENA 2D Ft=2,31 MPA
12
10
Analytical model
8
6
4
2
1
0
0
0,2
0,4
0,6
0,8
Crack width (mm)
Quarter of concrete circle
1- the values of stress were taken
2-the values of crack width were measured
Concrete
3D
NonLinCementitious 2
Graphs stress vs. crack width
E
(Gpa)
ft
(MPa)
fc
(MPa)
Gf
(MN/m)
3.032E+04
2.3
-23
4E-05
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Alternative 3
12
10
Stress (MPa)
8
Atena 2D
6
Analytical model
4
2
1
0
Evolution of cracks
in0,1first0,2steps0,3
0
Concrete
0,4
Crack width (mm)
Evolution
of cracks at peak load
0,6
0,5
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
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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.
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