Msc. eng. Magdalena German Faculty of Civil Engineering Cracow University of Technology Budapest, 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+ O2O2 e-e- Porous solution as eletrolyte 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 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 Calculation of free chloride concentration C f C f > 0.35% cem. mass NoNo 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. c d/2 p

Plastic damage model in Abaqus FEA Stress-strain relation (E 0 – 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

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  5°  0.1 f b0 /f c K0.666 COMPRESSIVE BEHAVIOR Yield stressInelastic strain 25MPa0 35MPa0.002 TENSILE BEHAVIOR Yield stressFracture energy 1.8MPa0.08 Compression stressPlastic strain 25MPa0 35MPa0.002 TENSION STIFFENING /c/c -c-c FAILURE RATIOS Ratio Ratio Ratio Ratio SHEAR RETENTION  close 1  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 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 Rust changing volume steel concrete displacement steel concrete Rust changing volume displacement