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:
Propagation phase
Initiation phase
Chloride treshold concentration
stress
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>9
pH=13
Cl-
Cl-
pH<9
Cl-
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)
O2  2H 2O  4e  4OH

O2

Anodic reaction
Fe  Fe 2  e 
OH-
Fe2+
cathode
Rust production
Fe  2OH  Fe(OH ) 2
2

anode
Porous solution as
eletrolyte
e-
Steel rebar as
conductor
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
drust
d
Calculation procedure
Boundary conditions for chloride and oxygen concentrations
Time increase with a step=1 day
Calculation of electical field potential due to chloride ions flux.
Calculation of free chloride concentration Cf
No
Cf > 0.35%
cem. mass
Yes
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

c  d 2  d 2
2

2
 c  d 22 
1 

2 
2
r


p
 It is a simplified model
using linear theory of elasticity
 Cracking of the concrete ring
is calculated using analytical procedures.
d/2
c
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
5°
j
0.1
e
fb0/fc0
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
 SMEARED CRACKING
Compression stress
Plastic strain
25MPa
0
35MPa
0.002
TENSION STIFFENING
/c
e-ec
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
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
Steel changing volume
concrete
concrete
Rust changing volume
displacement
steel
steel
Rust changing volume
concrete
concrete
displacement
concrete