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Computer Aided Material Science

Computer Aided Material Science. Tutors. dr hab. inż. Robert Filipek, prof. AGH Lecture , Group 5 dr Krzysztof Szyszkiewicz-Warzecha Groups : 1, 2, 3 mgr inż. Jakub Stec Groups : 4, 6. Chloride induced corrosion of reinforcing steel in concrete. Reinforcement corrosion in concrete.

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Computer Aided Material Science

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  1. Computer Aided Material Science

  2. Tutors • dr hab. inż. Robert Filipek, prof. AGH Lecture, Group 5 • dr Krzysztof Szyszkiewicz-Warzecha Groups: 1, 2, 3 • mgr inż. Jakub Stec Groups: 4, 6

  3. Chloride induced corrosion of reinforcing steel in concrete

  4. Reinforcement corrosion in concrete 12.5 < pH < 13.5 Steel in a passive state

  5. Reinforcement corrosion in concrete pH < 11.8 Steel in an active state: chlorides, carbonization, …

  6. Chloride induced pitting corrosion N.Silva - Chloride Induced Corrosion of Reinforcement Steel in Concrete. Threshold Values and Ion Distributions at the Concrete-Steel Interface. PhD thesis.

  7. Reinforcement corrosion in concrete Corroded viaduct at the Marywilskast. in Warsaw

  8. Simple diffusion model of chloride ingress

  9. Simple diffusion model of chloride ingress Steel rebar Cement-based material Solution + Cl + - + + Cl - Cl Cl + + - + + + + Cl + + - Cl - - + Cl Cl + + + + + + Cl - Cl - + - Cl + + + + + Cl Cl - + Cl t = 0

  10. Simple diffusion model of chloride ingress Steel rebar Cement-based material Solution z + Cl + - + + Cl - Cl Cl Cl + + - + + + + Cl + + - Cl Cl - - + Cl Cl + + + + + + Cl Cl - Cl Cl - + - Cl + + + + + Cl Cl - + Cl x t > 0 y

  11. Simple diffusion model of chloride ingress in 1D – geometry Steel rebar Cement-based material Solution x x = 0 x = L Thickness of the cement based material: L = 5 cm

  12. Simple diffusion model of chloride ingress in 1D – equations Cement-based material Steel rebar Solution No reaction: Mass balance equation:

  13. Simple diffusion model of chloride ingress in 1D – equations Cement-based material Steel rebar Solution Mass balance equation in 1D:

  14. Simple diffusion model of chloride ingress in 1D – equations Cement-based material Steel rebar Solution Flux by Fick’s I law: D–diffusion coefficient

  15. Simple diffusion model of chloride ingress in 1D – equations Cement-based material Steel rebar Solution Fick’s II law

  16. Simple diffusion model of chloride ingress in 1D – boundary conditions Cement-based material Steel rebar Solution Interface Solution/Cement-based material – chloride source Dirichlet boundary condition:

  17. Simple diffusion model of chloride ingress in 1D – boundary conditions Cement-based material Steel rebar Solution Interface Cement-based material/Steel rebar Neumann boundary condition: Chlorides accumulate on the surface of steel rebar

  18. Simple diffusion model of chloride ingress in 1D – initial conditions Cement-based material Steel rebar Solution No chlorides in cement-based material at t=0:

  19. Simple diffusion model of chloride ingress in 1D Task 1 Calculate the chloride concentration profile in the cement-based materials after 1 year.

  20. Data

  21. Simple diffusion model of chloride ingress in 1D Task 2 Knowing that threshold chloride concentration (cth) is 0.2% estimate the time after which corrosion of steel rebar starts.

  22. Simple diffusion model of chloride ingress Model simplifications: • One phase continuous cement-based material; • No reactions; • Chloride ingress independent of other ions diffusion.

  23. Diffusion and reaction model of chloride ingress In the pores of concrete we can see free and bound chlorides - - + - Cement-based material - - - - - + + + + + + + - - - - - - + + - - + - - - + - - - - - + - + - - Cl (free) - - + - + + + + - - - + - - - + Cl(bound) - - - - - + + + - - + - - cations +

  24. Chloride binding Chloride binding can take place in two ways: • chemical reaction (with calcium aluminate hydrates), • physical adsorption (on the surface of the C-S-H gel). Freundlich isotherm

  25. Diffusion and reaction model of chloride ingress – fluxes and reactions Two components: free (f) and bound chloride (b): Cl (free) - Cl(bound) -

  26. Diffusion and reaction model of chloride ingress – final equations To take into account the porous nature of the concrete sample we must include the porosity coefficient, , into the model equations. Cl (free) - Cl(bound) - Equations in the expanded form (fluxes and reactions inserted explicitly):

  27. Diffusion and reaction model of chloride ingress - boundary conditions Cement-based material Steel rebar Solution Boundary conditions for the bound chlorides are not required!

  28. Diffusion and reaction model of chloride ingress– initial conditions Cement-based material Steel rebar Solution No free and bound chlorides in cement-based material at t=0:

  29. Diffusion and reaction model of chloride ingress Task 1 Calculate the concentration profiles of: free, bound and total chloride in the cement-based materials after 1 year.

  30. Data

  31. Diffusion and reaction model of chloride ingress Task 2 Knowing that threshold chloride concentration (cth) is 0.2% estimate the time after which corrosion of steel rebar starts.

  32. Diffusion and reaction model of chloride ingress Task 3 Calculate the amount of: free, bound and total chlorides in the cement-based material

  33. Optimization

  34. Prediction of unknowns Mathematical modeling Model parameters; Initial, boundary conditions Physical laws; Constitutive equations e.g. concentration, potential, temperature fields

  35. Prediction of Mathematical modeling Initialand boundary conditions Physical laws; Constitutive equations Model parameters Unknowns

  36. Prediction of model parameters The inverse problem Known experimental data, Initial, boundary conditions Physical laws; Constitutive equations e.g. transport parameters, shape (geometry), etc. e.g. measured concentration, temperature fields, etc.

  37. The inverse problem • Goal: determination the physical parameters of any mathematical model by comparing its prediction with experimental data • Idea: define the proper goal function • Realization: optimize the goal function to obtain best fitting of model to experimental results

  38. Goalfunction

  39. Goalfunction or

  40. Goalfunction

  41. Simple diffusion model Boundary conditions: Initial conditions:

  42. Measured chloride profiles

  43. Measured data

  44. Simple diffusion model – inverse problem Task 1 Determine the diffusion coefficient based on the measured chloride concentration profiles.

  45. Simple diffusion model – inverse problem

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