# Simulation of damage due to

Urban and Civil

Nov 29, 2013 (4 years and 7 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