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 schemeOutline of the phenomenonCalculation procedure and corrosion initiation resultsDamage simulationExampleResultsConclusions

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 constructionsIndustrial constructions

Outline of the phenomenon

Corrosion results in:Longitudinal cracking of the

elementConcrete spallingLoss of bond between steel

and concreteGeneral failure of the

element

Outline of the phenomenonChloride corrosion phenomena is described using

Tuutti’s model:

Initiation phase Propagation phase

time

stress

Chl

orid

e tr

esho

ld c

once

ntra

tion

Outline of the phenomenonHighly 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 phenomenonDue to depassivation corrosion cell is formed, where:

Reinforcement bar is conductorPorous solution is electrolite

Cathodic reaction (constant oxygen supply)

Anodic reaction

Rust production

OH-

anode

cathodeFe2+

O2

e-

Porous solution as eletrolyte

Steel rebar as conductor

eFeFe 2

OHeOHO 442 22

2

2 )(2 OHFeOHFe

Outline of the phenomenonDensity of rust is less than density of steel consumed

in corrosion processVolumetric expansion of corrosion products occursInternal pressure is generated causing cracking of

surrounding concrete

d

drust

Time increase with a step=1 dayTime increase with a step=1 day

Calculation of electical field potential due to chloride ions flux.Calculation of electical field potential due to chloride ions flux.

Calculation of free chloride concentration Cf Calculation of free chloride concentration Cf

Cf > 0.35% cem. mass

No

Boundary conditions for chloride and oxygen concentrations

Boundary conditions for chloride and oxygen concentrations

Yes

Calculation of oxygen concentrationCalculation of oxygen concentration

Calculation of corrosion currentCalculation of corrosion current

Calculation of mass of corrosion products MrCalculation of mass of corrosion products Mr

Calculation of pressure caused by volumetric expansion 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 generationIn 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

22

2 21

22

2

r

dc

ddc

pd

cd/2

p

Plastic damage model in Abaqus FEA Stress-strain relation (E0 – init. el. stiffness tensor; – scalar degradation

damage):

Damage variable – 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

ExampleDimensions of cross-section –

350mm x 600mmConcrete cover – 50mmBoundary 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

ExampleThe analysis is made for half-section configurationA 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

5° 0.1fb0/fc0 1.16K 0.666COMPRESSIVE BEHAVIOR

Yield stress Inelastic strain25MPa 035MPa 0.002

TENSILE BEHAVIORYield stress Fracture energy1.8MPa 0.08

Compression stress Plastic strain25MPa 035MPa 0.002

TENSION STIFFENING/c -c

1 00 0.002

FAILURE RATIOSRatio 1 1.16Ratio 2 0.072Ratio 3 1.28Ratio 4 0.333

SHEAR RETENTIONclose 1max 0.2

Strain progress, el. size 15mmDamage plasticity model

Smeared cracking model

Stress progress, el. size 15mmDamage 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 10mmDamage plasticity model

Smeared cracking model

Stress progress, el. size 10mmDamage 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 5mmDamage plasticity model

Smeared cracking model

Stress progress, el. size 5mmDamage plasticity model

Smeared cracking model

Strain-stress diagrams, el. size 5mm

Damage plasticity model

Strain-stress diagrams, el. size 5mm

Smeared cracking model

ConclusionsResults 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 workEliminate 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 volumedisplacement