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

6. Site Exposure Conditions Aggressivity of Environment – Sea water – De-icing agents – Chemical attack 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, atmospheric zones Geographic Orientation N-S-E-W, seaward, landward Surface Orientation 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. Reinforced Concrete – Chloride Induced Corrosion (Seawater, de de-icing salts) – Carbonation Induced Corrosion (Normal CO 2 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 t L = t 0 + t 1 + t 2, where t L is the service life of a reinforced concrete structure [a], t 0 is the initiation time [a], t 1 is the propagation time for the zinc coating [a], and t 2 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 sis the deterioration depth or grade, kis the coefficient, tis the deterioration time [a], and nis the exponent of time [ - ].

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

18. The service life of a reinforced concrete structure can be expressed as follows: where t L is the service life of a reinforced concrete structure [a], s max is the maximum deterioration depth or grade allowed, kis the coefficient, and nis the exponent of time [ - ].

19. The initiation time of corrosion in carbonated uncracked concrete can be expressed as follows: where t 0 is the initiation time [a], cis the thickness of the concrete cover [mm], and c carb 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 t 0 is the initiation time [a], cis the thickness of the concrete cover [mm], and k cl 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 t 0 is the initiation time [a], cis the thickness of the concrete cover [mm], wis the crack width [mm], c carb is the coefficient of carbonation [mm/(a) ½ ], D e is the diffusion coefficient of the concrete with respect to carbon dioxide [mm 2 /a], and D cr is the diffusion coefficient of the crack with respect to carbon dioxide [mm 2 /a].

22. An approximate estimate of the carbonation depth from the equation at a crack can be presented as follows: where d cr is the carbonation depth at a crack [mm], wis the crack width [mm], and tis 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 t 0 is the initiation time [a], cis the thickness of the concrete cover [mm], and wis the crack width [mm].

24. The initiation time of corrosion at crack in chloride- contaminated concrete can be expressed as: where t 0 is the initiation time [a], cis the thickness of the concrete cover [mm], wis the crack width [mm], k cl is the coefficient of the critical chloride content [mm/(a) ½ ], C cr is the critical chloride content [wt% CEM ], C 1 is the surface chloride content [wt% CEM ], D c is the chloride diffusion coefficient of the concrete [mm 2 /a], and D ccr is the diffusion coefficient of the crack with respect to chloride ions [mm 2 /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 t 1 is the propagation time for the zinc coating [a], dis the thickness of zinc coating [mm], and r 1 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 t 1 is the propagation time for the zinc coating [a], dis the thickness of zinc coating [mm], and k 1 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 sis the corrosion depth [mm], cis the thickness of the concrete cover [mm], and Øis 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 t 2 is the propagation time for an ordinary steel reinforcement bar [a], cis the thickness of the concrete cover [mm], r s is the rate of corrosion [mm/a], and Øis 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 t 2 is the propagation time for an ordinary steel reinforcement bar [a], cis the thickness of the concrete cover [mm], k s is the coefficient of the rate of corrosion [mm/(a) 1/2 ], and Øis 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 t 2 is the propagation time for an ordinary steel reinforcement bar [a], s max is the maximum permitted corrosion depth of a reinforcement [mm], and r 2 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 t 2 is the propagation time for an ordinary steel reinforcement bar [a], s max is the maximum permitted corrosion depth of a reinforcement [mm], and k 2 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(t L ) represents the mean service life value.

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

34. The rate of corrosion r s as a function of the coefficient of the rate of corrosion k s and propagation time t 2.

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 t 0 is the initiation time [a], D c is the chloride diffusion coefficient of the concrete [mm 2 /a], cis the thickness of the concrete cover [mm], C cr is the critical chloride content [wt% CEM ], and C 1 is the surface chloride content [wt% CEM ].

37. the coefficient of the critical chloride content is calculated as follows: where k cl is the coefficient of the critical chloride content [mm/(a) ½ ], D c is the chloride diffusion coefficient of concrete [mm 2 /a], C cr is the critical chloride content [wt% CEM ], and C 1 is the surface chloride content [wt% CEM ].

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

39. The coefficient of the critical chloride content k cl as a function of the chloride diffusion coefficient of concrete D c, the critical chloride content C cr, concrete strength f cm, and the surface chloride content C 1.

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  (t L )is the standard deviation of the service life [a],  (x i )is the standard deviation of variable x i [ - ], ∂µ(t L )/∂x i is the partial derivate of the service life for variable x i [ - ], µ(x i )is the mean value of the service life for variable x i [ - ], i is the coefficient of variation for factor i [ - ], and nis 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(x i )is the relative significance of factor i [ - ], and µ(t L )is the mean value of service life [ - ].

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

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

49. The lognormal density and cumulative distribution function as time is expressed with: where tis 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 t Ltarg is the target service life [a],  (Y)is the mean value of the lognormal distribution function [a],  (Y)is the standard deviation of the lognormal distribution function [a], and  is the test parameter for the (0,1)-normal cumulative distribution function ø [ - ].

51. The standard deviation and mean value of the Weibull distribution function can be calculated with: where  is the shape parameter in Weibull distribution [ - ], is the scale parameter in Weibull distribution [ - ], and tis the time [a].

52. The standard deviation and mean value of the Weibull distribution function can be calculated with: where  (t L )is the mean value of the service life [a],  (t L )is the standard deviation of the service life [a], and  is the Gamma function.

53. The coefficient of carbonation c carb as a function of the target service life and the rate of corrosion of a hot-dip galvanised reinforcement bar r 1 with a 5% probability of damage.

54. The relative significance of corrosion parameters as a function of the rate of corrosion of an ordinary steel reinforcement bar r s in carbonated uncracked concrete.

55. The coefficient of the rate of corrosion of an ordinary steel reinforcement bar k s as a function of the target service life and the coefficient of the rate of corrosion of a hot-dip galvanised reinforcement bar k 1 with a 5% probability of damage.

56. The relative significance of corrosion parameters as a function of the coefficient of the rate of corrosion of the ordinary steel reinforcement bar k s in carbonated uncracked concrete.

57. Zinc coating thickness d as a function of the target service life and the thickness of the concrete cover c with a 5% probability of damage.

58. Rate of corrosion of an ordinary steel reinforcement bar r 2 as a function of the target service life and rate of corrosion of a hot-dip galvanised reinforcement bar r 1 with a 5% probability of damage.

59. The coefficient of the critical content of chloride k cl as a function of the target service life and the rate of corrosion of a hot-dip galvanised reinforcement bar r 1 with a 5% probability of damage.

60. The coefficient of the critical chloride content k cl as a function of the target service life and the coefficient of the rate of corrosion of an ordinary steel reinforcement bar k s with a 5% probability of damage.

61. Corrosion parameters used in Monte Carlo simulation Carbonated uncracked concrete (decreasing rate of corrosion).

62. Distribution of corrosion parameters

63. Probability density and cumulative distribution function: a fit of Gamma distribution [p = 0.34]). The horizontal axes indicate the time that has passed (in years).

64. Mean value of the service life and fit of Gamma distribution with a 5% and 10% probability of damage

65. Corrosion parameters used in Monte Carlo simulation Chloride-contaminated uncracked concrete (uniform rate of corrosion)

66. Distribution of corrosion parameters

67. Probability density and cumulative distribution function: a fit of Gamma distribution [p = 0.57]). The horizontal axes indicate the time that has passed (in years).

68. Mean value of the service life and a fit of Gamma distribution with a 5% and 10% probability of damage.

69. Service life based on steel corrosion, carbonation of uncracked concrete, initiation time t 0, propagation time for zinc coating t 1, propagation time for ordinary steel reinforcement bar t 2, and target service life t Ltarg : Weibull and lognormal distribution.

70. Target service life with Weibull and lognormal distribution probability function (probability of damage 5%).

71. Most suitable distribution types (beam specimen: hot-dip galvanised steel reinforcement bar).

72. Rate of corrosion of the hot-dip galvanised reinforcement beam specimens after five years of exposure in tap water for all values (left) (n = 216 pc/Gamma distribution) and extreme values (right) (n = 27 pc/Extreme value distribution (Type 1)).

73. Corrosion potential of the hot-dip galvanised reinforcement beam specimens after five years of exposure in tap water for all values (left) (n = 215 pc/Gamma distribution) and extreme values (right) (n = 27 pc/Extreme value distribution (Type 1)).

74. The resistivity of concrete of the hot-dip galvanised reinforcement beam specimens after five years of exposure in tap water for all values (left) (n = 216 pc/Gamma distribution) and extreme values (right) (n = 27 pc/Extreme value distribution (Type 1)).

75. Effect of interaction between chloride diffusion and carbonation on service life by changing values of deterioration parameters in individual service life calculation formula.

77. Lucano, J., Miltenberger, M. Predicting Diffusion Coefficients from Concrete Mixture Proportions. http://www.itl.nist.gov/ Log Normal and Normal distribution function

78. Concrete cover measurements Pentti, M. The Accuracy of the Extent-of-Corrosion Estimate Based on the Sampling of Carbonation and Cover Depths of Reinforced Concrete Facade Panels.