Deterioration Models and Service Life Planning (Part 3)

1. Deterioration Models and Service Life Planning (Part 3) Rak-43.3301 Repair Methods of Structures I (4 cr) Esko Sistonen

3. Service Life Design Basics • Establishing Life Expectancy • Identifying • –Environmental Exposure Conditions • – Deterioration Mechanisms • – Material Resistance to Deterioration • Establishing Mathematical Modeling Parameters to Predict Deterioration • Setting Acceptable Damage Limits

4. Indicative Values for Design Service Life – fib Bulletin 34

5. Service Life DesignedStructures Rostam, S., Service Life Design - The European Approach. ACI Concrete International, No. 7, 15 (1993)24-32. Great Belt Bridge, Denmark (100 a) Confederation Bridge, Canada (100 a) San Francisco – Oakland Bay Bridge (150 a)

6. SiteExposureConditions Aggressivity of Environment – Seawater – De-icing agents – Chemicalattack Temperature / Humidity – Freeze / thaw cycles – Wet / Dry cycles – Tropical (every +10 ºC doubles rate of corrosion) http://www.icdc2012.com/

7. Member Exposure Conditions Marine • Submerged, tidal, splash, atmosphericzones Geographic Orientation • N-S-E-W, seaward, landward SurfaceOrientation • Ponding, condensation, protection from wetting, corners

8. Exposure Classes – EN-206-1 European Standard EN 206

9. Possible degradation mechanisms acting on concrete exposed to sea water (Malhorta 2000).

10. ReinforcedConcrete – Chloride Induced Corrosion (Seawater, de de-icing salts) – Carbonation Induced Corrosion (Normal CO2 from atmosphere)

11. Structural Steel – Corrosion after Breakdown of Protective Coating Systems http://bridges.transportation.org/Documents/DesignforServiceLife.pdf

12. Deterioration Models / Limit States Tuutti, K. 1982. Corrosion of steel in concrete. Stockholm. Swedish Cement and Concrete Research Institute. CBI Research 4:82. 304 p.

13. The increase of the probability of failure. Illustrative presentation (Melchers 1999).

14. The service life of hot-dip galvanised reinforcement bars tL = t0 + t1 + t2, where tL is the service life of a reinforced concrete structure [a], t0 is the initiation time [a], t1 is the propagation time for the zinc coating [a], and t2 is the propagation time for an ordinary steel reinforcement bar [a].

15. The principle used in calculating the service life of hot-dip galvanised reinforcement bars. The final limit state for the service life is the time after which the corrosion products spall the concrete cover, or the maximum allowed corrosion depth is reached.

16. In general, deterioration phenomena comply with the simple mathematical model where s is the deterioration depth or grade, k is the coefficient, t is the deterioration time [a], and n is the exponent of time [ - ]. 

17. As k is assumed to be constant the first derivate of Equation gives for the rate of deterioration where r is the deterioration rate, k is the coefficient, t is the deterioration time [a], and n is the exponent of time [ - ].

18. The service life of a reinforced concrete structure can be expressed as follows: where tL is the service life of a reinforced concrete structure [a], smax is the maximum deterioration depth or grade allowed, k is the coefficient, and n is the exponent of time [ - ].

19. The initiation time of corrosion in carbonated uncracked concrete can be expressed as follows: where t0 is the initiation time [a], c is the thickness of the concrete cover [mm], and ccarb is the coefficient of carbonation [mm/(a)½].

20. The initiation time of corrosion in chloride-contaminated uncracked concrete can be expressed as follows: where t0 is the initiation time [a], c is the thickness of the concrete cover [mm], and kcl is the coefficient of the critical chloride content [mm/(a)½].

21. The initiation time of corrosion at crack in carbonated concrete can be expressed as: where t0 is the initiation time [a], c is the thickness of the concrete cover [mm], w is the crack width [mm], ccarb is the coefficient of carbonation [mm/(a)½], De is the diffusion coefficient of the concrete with respect to carbon dioxide [mm2/a], and Dcr is the diffusion coefficient of the crack with respect to carbon dioxide [mm2/a].

22. An approximate estimate of the carbonation depth from the equation at a crack can be presented as follows: where dcr is the carbonation depth at a crack [mm], w is the crack width [mm], and t is the time [a].

23. Corrosion of steel can be assumed to initiate a crack when the top of the carbonated zone reaches the steel. Thus, the initiation time of corrosion is obtained: where t0 is the initiation time [a], c is the thickness of the concrete cover [mm], and w is the crack width [mm].

24. The initiation time of corrosion at crack in chloride-contaminated concrete can be expressed as: where t0 is the initiation time [a], c is the thickness of the concrete cover [mm], w is the crack width [mm], kcl is the coefficient of the critical chloride content [mm/(a)½], Ccris the critical chloride content [wt%CEM], C1 is the surface chloride content [wt%CEM], Dc is the chloride diffusion coefficient of the concrete [mm2/a], and Dccr is the diffusion coefficient of the crack with respect to chloride ions [mm2/a].

25. In the case of uniform rate of corrosion for the zinc coating, the propagation time for the zinc coating in uncracked and cracked carbonated or chloride-contaminated concrete can be expressed as follows: where t1 is the propagation time for the zinc coating [a], d is the thickness of zinc coating [mm], and r1 is the rate of corrosion [mm/a].

26. In the case of decreasing rate of corrosion for the zinc coating, the propagation time for the zinc coating in uncracked and cracked carbonated or chloride-contaminated concrete can be expressed as follows: where t1 is the propagation time for the zinc coating [a], d is the thickness of zinc coating [mm], and k1 is the coefficient of the rate of corrosion [mm/(a)1/2].

27. The corrosion depth during the propagation time, where the corrosion products spall the concrete cover, is calculated as follows: where s is the corrosion depth [mm], c is the thickness of the concrete cover [mm], and Ø is the diameter of the reinforcement bar [mm].

28. In the case of uniform rate of corrosion for an ordinary steel reinforcement bar, the propagation time for an ordinary steel reinforcement bar in uncracked carbonated or chloride-contaminated concrete can be expressed as follows: where t2 is the propagation time for an ordinary steel reinforcement bar [a], c is the thickness of the concrete cover [mm], rs is the rate of corrosion [mm/a], and Ø is the diameter of the reinforcement bar [mm].

29. In the case of decreasing rate of corrosion for an ordinary steel reinforcement bar, the propagation time for an ordinary steel reinforcement bar in uncracked carbonated or chloride-contaminated concrete can be expressed as follows: where t2 is the propagation time for an ordinary steel reinforcement bar [a], c is the thickness of the concrete cover [mm], ks is the coefficient of the rate of corrosion [mm/(a)1/2], and Ø is the diameter of the reinforcement bar [mm].

30. In the case of uniform rate of corrosion for an ordinary steel reinforcement bar, the propagation time for an ordinary steel reinforcement bar in cracked carbonated or chloride-contaminated concrete can be expressed as follows: where t2 is the propagation time for an ordinary steel reinforcement bar [a], smax is the maximum permitted corrosion depth of a reinforcement [mm], and r2 is the rate of corrosion [mm/a].

31. In the case of decreasing rate of corrosion for an ordinary steel reinforcement bar, the propagation time for an ordinary steel reinforcement bar in cracked carbonated or chloride-contaminated concrete can be expressed as follows: where t2 is the propagation time for an ordinary steel reinforcement bar [a], smax is the maximum permitted corrosion depth of a reinforcement [mm], and k2 is the coefficient of the rate of corrosion [mm/(a)1/2].

32. Deterministic formulae used in calculation of the service life of hot-dip galvanised reinforcement bars. The symbol m(tL) represents the mean service life value.

33. The equivalent value for the rate of corrosion: where rs is the uniform rate of corrosion [mm/a], ks is the coefficient of the rate of corrosion [mm/(a)1/2], and t2 is the propagation time [a].

34. The rate of corrosion rs as a function of the coefficient of the rate of corrosion ks and propagation time t2.

35. Corrosion depth s as a function of the thickness of the concrete cover c and reinforcement bar diameter Ø.

36. The initiation time in chloride-contaminated uncracked concrete is calculated as follows: where t0 is the initiation time [a], Dc is the chloride diffusion coefficient of the concrete [mm2/a], c is the thickness of the concrete cover [mm], Ccris the critical chloride content [wt%CEM], and C1 is the surface chloride content [wt%CEM].

37. the coefficient of the critical chloride content is calculated as follows: where kcl is the coefficient of the critical chloride content [mm/(a)½], Dc is the chloride diffusion coefficient of concrete [mm2/a], Ccris the critical chloride content [wt%CEM], and C1 is the surface chloride content [wt%CEM].

38. The critical water-soluble chloride content with different reinforcement bar types (Ccr) in uncarbonated concrete.

39. The coefficient of the critical chloride content kcl as a function of the chloride diffusion coefficient of concrete Dc, the critical chloride content Ccr, concrete strength fcm, and the surface chloride content C1.

40. Corrosion parameters (basic values).

41. Corrosion parameters (carbonated uncracked concrete).

42. Corrosion parameters (carbonated cracked concrete).

43. Corrosion parameters (chloride-contaminated uncracked concrete).

44. Corrosion parameters (chloride contaminated cracked concrete).

45. The standard deviation of the service life can be estimated with the formula: where s(tL) is the standard deviation of the service life [a], s(xi) is the standard deviation of variable xi [ - ], ∂µ(tL)/∂xi is the partial derivate of the service life for variable xi [ - ], µ(xi) is the mean value of the service life for variable xi [ - ], ni is the coefficient of variation for factor i [ - ], and n is the number of variables [ - ].

46. The relative significance of parameters in the deterministic service life formula (influence on maximum error) can be determined with: where RI(xi) is the relative significance of factor i [ - ], and µ(tL) is the mean value of service life [ - ].

47. The number of variable combinations in sensitive analysis can be calculated as follows: where SK is the number of variable combinations [ - ], n is the number of variables [ - ], and k is a summing term [ - ].

48. The standard deviation and mean value of the lognormal distribution function can be calculated with: where s(Y) is the standard deviation of the lognormal distribution function [ - ], s(tL) is the standard deviation of the service life [a], m(tL) is the mean value of the service life [a], and m(Y) is the mean value of the lognormal distribution function [ - ].

49. The lognormal density and cumulative distribution function as time is expressed with: where t is the time [a], and [.]is the (0,1)-normal cumulative distribution function.

50. The target service life expressed with the probability of damage is as follows: where tLtarg is the target service life [a], m(Y) is the mean value of the lognormal distribution function [a], s(Y) is the standard deviation of the lognormal distribution function [a], and b is the test parameter for the (0,1)-normal cumulative distribution function ø [ - ].