Simulation of damage due to
corrosion in RC cross-section
Msc. eng. Magdalena German
Faculty of Civil Engineering
Cracow University of Technology
Budapest, 24.09.2011
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:
stress Initiation phase Propagation phase
Chloride treshold concentration
time
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)
pH=13 pH>9 pH 0.35%
cem. mass
Calculation of corrosion current
Calculation of oxygen concentration
Calculation of mass of corrosion products Mr
Calculation of pressure caused by volumetric expansion
SIMULATION
OF DAMAGE
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:
d 2 p
2
c d 2 2
1
2
c d 2 d 2
2
r 2
p
d/2 c
It is a simplified model
using linear theory of elasticity
Cracking of the concrete ring
is calculated using analytical procedures.
Plastic damage model in Abaqus FEA
Stress-strain relation (E0 – 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 –
350mm x 600mm
Concrete cover – 50mm
Boundary conditions:
U1=0 at one node
U2=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 5mm
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
Compression stress Plastic strain
j 5° 25MPa 0
e 0.1 35MPa 0.002
fb0/fc0 1.16 TENSION STIFFENING
K 0.666 /c e-ec
1 0
COMPRESSIVE BEHAVIOR
0 0.002
Yield stress Inelastic strain
FAILURE RATIOS
25MPa 0 Ratio 1 1.16
35MPa 0.002 Ratio 2 0.072
TENSILE BEHAVIOR Ratio 3 1.28
Yield stress Fracture energy Ratio 4 0.333
1.8MPa 0.08 SHEAR RETENTION
rclose 1
emax 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 15mm
Smeared cracking model
Strain progress, el. size 10mm
Damage plasticity model
Smeared cracking model
Stress progress, el. size 10mm
Damage plasticity model
Smeared cracking model
Strain-stress diagrams, el. size 10mm
Damage plasticity model
Strain-stress diagrams, el. size 10mm
Smeared cracking model
Strain progress, el. size 5mm
Damage plasticity model
Smeared cracking model
Stress progress, el. size 5mm
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 concrete
Rust changing volume displacement
Steel changing volume steel steel
displacement
Rust changing volume
concrete concrete concrete