Simulation of damage due to

frizzflowerUrban and Civil

Nov 29, 2013 (3 years and 8 months ago)

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Msc. eng. Magdalena German

Faculty of Civil Engineering

Cracow University of Technology


Budapest, 24.09.2011

Simulation of damage due to
corrosion in RC cross
-
section

Presentation scheme


Outline of the phenomenon


Calculation procedure and corrosion initiation results


Damage simulation


Example


Results


Conclusions


Outline of the phenomenon



Chloride corrosion
is one of the main causes of
deterioration of the reinforced concrete elements



Endangered structures:


Bridges and roads under the deicing programmes


Marine constructions


Industrial constructions

Outline of the phenomenon



Corrosion results in:


Longitudinal cracking of the
element


Concrete spalling


Loss of bond between steel
and concrete


General failure of the
element

Outline of the phenomenon


Chloride corrosion phenomena is described using
Tuutti’s model:

Initiation phase

Propagation phase

time

stress

Chloride treshold concentration

Outline of the phenomenon


Highly alkaline porous solution (pH=13) sustains passive
layer on reinforcement surface, however with time pH
reduces due to carbonation of concrete


During the initiation phase chlorides permeate into concrete
eventually breaking the passive layer


Initiation phase ends when chloride concentration around
the reinforcement reaches chloride threshold value (approx.
0.4% of cement mass)

Cl
-

pH=13

Cl
-

pH>9

Cl
-

pH<9

Outline of the phenomenon


Due to depassivation corrosion cell is formed, where:


Reinforcement bar is conductor


Porous solution is electrolite


Cathodic reaction (constant oxygen supply)


Anodic reaction


Rust production



OH
-

anode

cathode

Fe
2+

O
2

e
-

Porous solution as
eletrolyte

Steel rebar as
conductor





e
Fe
Fe
2





OH
e
O
H
O
4
4
2
2
2
2
2
)
(
2
OH
Fe
OH
Fe




Outline of the phenomenon


Density of rust is less than density of steel consumed
in corrosion process


Volumetric expansion of corrosion products occurs


Internal pressure is generated causing cracking of
surrounding concrete

d

d
rust

Time
increase

with

a step=1
day

Calculation

of
electical

field
potential

due

to
chloride

ions

flux
.

Calculation

of
free

chloride

concentration

C
f


C
f
> 0.35%
cem. mass

N
o

Boundary

conditions

for
chloride

and
oxygen

concentrations

Yes

Calculation

of
oxygen

concentration

Calculation

of
corrosion

current

Calculation

of mass of
corrosion

products
M
r

Calculation

of
pressure

caused

by
volumetric

expansion


SIMULATION
OF DAMAGE

Calculation procedure


Corrosion initiation phase results


Chloride concentration


Corrosion current density

SIMULATION OF DAMAGE

Pressure and stress generation


In previous studies concrete around the reinforcement
is modelled as thick
-
walled cylinder, in which
circumferential stress is expressed by:





It is a simplified model

using linear theory of elasticity


Cracking of the concrete ring

is calculated using analytical procedures.
























2
2
2
2
2
2
1
2
2
2
r
d
c
d
d
c
p
d
c

d/
2

p

Plastic damage model in Abaqus FEA


Stress
-
strain relation (E
0



init. el. stiffness tensor;
w



scalar degradation
damage):



Damage variable
k



the only necessary state variable:



The total stress



Plastic strain for plastic potential defined in the effective stress space:



Evolution of damage is based on evaluation of dissipated fracture energy
required to generate microcracks


Two damage variables (tensile and compressive) are defined
independently, each is fractionized into the effective
-
stress response and
stiffness degradation response

Smeared cracking model in Abaqus FEA


Fixed crack when crack
detection surface is reached


„Damaged” elasticity model
of cracked continuum


Tension softening/stiffening
and fracture energy concept


Shear retention (shear
modulus linearly reduced)


Compressive behaviour
elastic


plastic

Figure

source
:
Abaqus

manual

Example


Dimensions of cross
-
section


350
mm x
600
mm


Concrete cover


50
mm


Boundary conditions:

U
1
=
0
at one node

U
2
=
0
along upper edge


Load


uniformly distributed pressure
representing action of expanding
corrosion products on concrete


Calculatios are performed for meshes
with element size
15
,
10
and
5
mm

Example


The analysis is made for half
-
section configuration


A comparison of two cross
-
sections loaded with the
unit pressure has shown that little difference in results
is caused by using half
-
section configuration

Material properties


DAMAGE PLASTICITY



SMEARED CRACKING

j

5
°

e

0.1

f
b0
/f
c0

1.16

K

0.666

COMPRESSIVE BEHAVIOR

Yield stress

Inelastic strain

25MPa

0

35MPa

0.002

TENSILE BEHAVIOR

Yield stress

Fracture energy

1.8MPa

0.08

Compression

stress

Plastic strain

25MPa

0

35MPa

0.002

TENSION STIFFENING


/

c

e
-
e
c

1

0

0

0.002

FAILURE RATIOS

Ratio

1

1.16

Ratio

2

0.072

Ratio

3

1.28

Ratio

4

0.333

SHEAR RETENTION

r
close

1

e
max

0.2

Strain progress, el. size 15mm


Damage

plasticity

model

Smeared

cracking model


Stress progress, el. size 15mm

Damage

plasticity

model

Smeared

cracking model

Strain
-
stress diagrams, el. size 15mm


Damage

plasticity

model

Strain
-
stress diagrams, el. size
15
mm


Smeared

cracking model


Strain progress, el. size 10mm


Damage

plasticity

model

Smeared

cracking model


Stress progress, el. size
10
mm

Damage

plasticity

model

Smeared

cracking model

Strain
-
stress diagrams, el. size 10mm

Damage

plasticity

model


Strain
-
stress diagrams, el. size
10
mm

Smeared

cracking model



Strain progress, el. size 5mm


Damage

plasticity

model

Smeared

cracking model


Stress progress, el. size
5
mm

Damage

plasticity

model

Smeared

cracking model

Strain
-
stress diagrams, el. size 5mm


Damage

plasticity

model

Strain
-
stress diagrams, el. size 5mm


Smeared

cracking model


Conclusions


Results of FE simulation depend on mesh density
. Size of
mesh defines the shape of damage



Simulation shows that concrete is
more likely

to crack
between the rebars
, when cover is still uncracked.



It suggest that, concrete
can be

uncracked at the surface,
but
there is loss of bonding between concrete and steel. It
can be significant when element is additionally loaded.



Both used models give similar results, however there are
differences between values of particular features

Future work


Eliminate differences between two models



Problem of steel
-
concrete interface



Problem of modeling rust volumetric expansion


concrete

concrete

Steel changing volume

concrete

concrete

Rust changing volume

steel

concrete

displacement

steel

concrete

Rust changing volume

displacement