Deterioration Models and Service Life Planning (Part 3)

Rak-43.3301 Repair Methods of Structures I (4 cr)

Esko Sistonen

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

Indicative Values for Design Service Life – fib Bulletin 34

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.

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/

Member Exposure Conditions

Marine • Submerged, tidal, splash, atmospheric zonesGeographic Orientation • N-S-E-W, seaward, landward Surface Orientation • Ponding, condensation, protection from

wetting, corners

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

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

Reinforced Concrete

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

Structural Steel

– Corrosion after Breakdown of Protective Coating Systems

http://bridges.transportation.org/Documents/DesignforServiceLife.pdf

Deterioration Models / Limit States

Tuutti, K. 1982. Corrosion of steel in concrete. Stockholm. Swedish Cement andConcrete Research Institute. CBI Research 4:82. 304 p.

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

The service life of hot-dip galvanised reinforcement bars

tL = t0 + t1 + t2,

wheretL 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].

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.

In general, deterioration phenomena comply with the simple mathematical

model

wheres is the deterioration depth or grade,k is the coefficient,t is the deterioration time [a], andn is the exponent of time [ - ]. 

As k is assumed to be constant the first derivate of Equation gives for the rate of deterioration

wherer is the deterioration rate,k is the coefficient,t is the deterioration time [a], andn is the exponent of time [ - ].

The service life of a reinforced concrete structure can be expressed as follows:

wheretL is the service life of a reinforced concrete structure [a],smax is the maximum deterioration depth or grade allowed,k is the coefficient, andn is the exponent of time [ - ].

The initiation time of corrosion in carbonated uncracked concrete can be expressed as follows:

wheret0 is the initiation time [a],c is the thickness of the concrete cover [mm], andccarb is the coefficient of carbonation [mm/(a)½].

The initiation time of corrosion in chloride-contaminated uncracked concrete can be

expressed as follows:

wheret0 is the initiation time [a],c is the thickness of the concrete cover [mm], andkcl is the coefficient of the critical chloride content [mm/(a)½].

The initiation time of corrosion at crack in carbonated concrete can be expressed as:

wheret0 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], andDcr is the diffusion coefficient of the crack with respect to

carbon dioxide [mm2/a].

An approximate estimate of the carbonation depth from the equation at a crack can be

presented as follows:

wheredcr is the carbonation depth at a crack [mm],w is the crack width [mm], andt is the time [a].

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:

wheret0 is the initiation time [a],c is the thickness of the concrete cover [mm], andw is the crack width [mm].

The initiation time of corrosion at crack in chloride-contaminated concrete can be expressed as:

wheret0 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],Ccr is 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], andDccr is the diffusion coefficient of the crack with respect to

chloride ions [mm2/a].

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:

wheret1 is the propagation time for the zinc coating [a],d is the thickness of zinc coating [mm], andr1 is the rate of corrosion [mm/a].

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:

wheret1 is the propagation time for the zinc coating [a],d is the thickness of zinc coating [mm], andk1 is the coefficient of the rate of corrosion [mm/(a)1/2].

The corrosion depth during the propagation time, where the corrosion products spall the

concrete cover, is calculated as follows:

wheres is the corrosion depth [mm],c is the thickness of the concrete cover [mm], andØ is the diameter of the reinforcement bar [mm].

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:

wheret2 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], andØ is the diameter of the reinforcement bar [mm].

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:

wheret2 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], andØ is the diameter of the reinforcement bar [mm].

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:

wheret2 is the propagation time for an ordinary steel reinforcement bar [a],smax is the maximum permitted corrosion depth of a

reinforcement [mm], andr2 is the rate of corrosion [mm/a].

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:

wheret2 is the propagation time for an ordinary steel reinforcement bar [a],smax is the maximum permitted corrosion depth of a

reinforcement [mm], andk2 is the coefficient of the rate of corrosion [mm/(a)1/2].

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.

The equivalent value for the rate of corrosion:

wherers is the uniform rate of corrosion [mm/a],ks is the coefficient of the rate of corrosion [mm/(a)1/2], andt2 is the propagation time [a].

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

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

The initiation time in chloride-contaminated uncracked concrete is calculated as follows:

wheret0 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],Ccr is the critical chloride content [wt%CEM], andC1 is the surface chloride content [wt%CEM].

the coefficient of the critical chloride content is calculated as follows:

wherekcl is the coefficient of the critical chloride content

[mm/(a)½],Dc is the chloride diffusion coefficient of concrete [mm2/a],Ccr is the critical chloride content [wt%CEM], andC1 is the surface chloride content [wt%CEM].

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

concrete.

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.

Corrosion parameters (basic values).

Corrosion parameters (carbonated uncracked concrete).

Corrosion parameters (carbonated cracked concrete).

Corrosion parameters (chloride-contaminated uncracked concrete).

Corrosion parameters (chloride contaminated cracked concrete).

The standard deviation of the service life can be estimated with the formula:

n

1i

2

ii

Ln

1i

2

ii

LL

2 )(xx

)t()σ(x

x

)t()(tσ

i

wheres(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 x i [ - ],

µ(xi) is the mean value of the service life for variable x i [ - ],

ni is the coefficient of variation for factor i [ - ], and

n is the number of variables [ - ].

The relative significance of parameters in the deterministic service life formula (influence on

maximum error) can be determined with:

%100

)(xx

)t(

)(xx

)t(

%100

)σ(xx

)t(

)σ(xx

)t(

)RI(xn

1iii

i

L

iii

L

n

1ii

i

L

ii

L

i

whereRI(xi) is the relative significance of factor i

[ - ], andµ(tL) is the mean value of service life [ - ].

The number of variable combinations in sensitive analysis can be calculated as follows:

1n

1kK

knSwhereSK is the number of variable combinations [ - ],

n is the number of variables [ - ], andk is a summing term [ - ].

The standard deviation and mean value of the lognormal distribution function can be calculated with:

2

L

L2

tμ

tσ1lnYσ

Yσ2

1tμ lnYμ 2

L

wheres(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 [ - ].

The lognormal density and cumulative distribution function as time is expressed with:

2

2Yμ tln

Yσ2

1

eσ(Y)π2t

1tf

L

L

tσ

)μ(tlntΦF(t)

wheret is the time [a], and[.] is the (0,1)-normal cumulative distribution function.

The target service life expressed with the probability of damage is as follows:

σ(Y)][β

μ(Y)

Ltarg e

et

σ(Y)ln(t)-μ(Y)

wheretLtarg 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 [ - ].

The standard deviation and mean value of the Weibull distribution function can be calculated with:

αtλ1αW etλλαf t

)(e1)( ttF

wherea is the shape parameter in Weibull distribution [ - ],l is the scale parameter in Weibull distribution [ - ],

andt is the time [a].

The standard deviation and mean value of the Weibull distribution function can be calculated with:

α

11Γ

λ

1)μ(t L

2

2L 1α

1Γ

α

21Γ

λ

1)σ(t

wherem(tL) is the mean value of the service life [a],

s(tL) is the standard deviation of the service life [a],

andG is the Gamma function.

The coefficient of carbonation ccarb as a function of the target service life and the rate of corrosion of a hot-dip galvanised

reinforcement bar r1 with a 5% probability of damage.

The relative significance of corrosion parameters as a function of the rate of corrosion of an ordinary steel reinforcement bar

rs in carbonated uncracked concrete.

The coefficient of the rate of corrosion of an ordinary steel reinforcement bar ks as a function of the target service life and the

coefficient of the rate of corrosion of a hot-dip galvanised reinforcement bar k1 with a 5% probability of damage.

The relative significance of corrosion parameters as a function of the coefficient of the rate of corrosion of the ordinary steel reinforcement

bar ks in carbonated uncracked concrete.

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.

Rate of corrosion of an ordinary steel reinforcement bar r2 as a function of the target service life and rate of

corrosion of a hot-dip galvanised reinforcement bar r1 with a 5% probability of damage.

The coefficient of the critical content of chloride kcl as a function of the target service life and the rate of corrosion of

a hot-dip galvanised reinforcement bar r1 with a 5% probability of damage.

The coefficient of the critical chloride content kcl as a function of the target service life and the coefficient of the rate of corrosion of an ordinary steel reinforcement

bar ks with a 5% probability of damage.

Corrosion parameters used in Monte Carlo simulation Carbonated uncracked concrete (decreasing rate of

corrosion).

Distribution of corrosion parameters

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).

22

1

2

ø

80

k

c

k

d

c

ct

scarbL

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

damage

22

1

2

ø

80

k

c

k

d

c

ct

scarbL

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

corrosion)

Distribution of corrosion parameters

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).

ø

80

1

2

r

c

r

d

k

ct

sclL

Mean value of the service life and a fit of Gamma distribution with a 5% and 10%

probability of damage.

ø

80

1

2

r

c

r

d

k

ct

sclL

Service life based on steel corrosion, carbonation of uncracked concrete, initiation time t0, propagation time for zinc coating t1, propagation time for ordinary steel reinforcement bar t2, and

target service life tLtarg: Weibull and lognormal distribution.

Target service life with Weibull and lognormal distribution probability function (probability of

damage 5%).

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

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)).

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)).

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)).

Effect of interaction between chloride diffusion and carbonation on service life by changing values of deterioration parameters in

individual service life calculation formula. Service life based on steel corrosion: Chloride diffusion of uncracked concrete

Log-normal distribution function (probability of damage 5%)

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

0 10 20 30 40 50 60 70 80 90 100Target service life tLtarg [ a ]

Co

eff

icie

nt

of

cri

tic

al

ch

lori

de

co

nte

nt

k cl

[mm

/a0.

5 ]

ks = 20 µm/(a)½

ks = 30 µm/(a)½

ks = 40 µm/(a)½

ks = 50 µm/(a)½

ks = 60 µm/(a)½

ks = 70 µm/(a)½

ks = 80 µm/(a)½

ks = 90 µm/(a)½

ks = 100 µm/(a)½

ks = 110 µm/(a)½

[ ]ee

)Y(

)Y(

argLtt s

2

s

2

clL øk

c80

k

ct

c = 30 mm ( = 0,25)f = 12 mm ( = 0,15)ks = variable ( = 0,4)

kcl = variable ( = 0,15)

Lucano, J., Miltenberger, M. Predicting Diffusion Coefficients from Concrete Mixture Proportions.

http://www.itl.nist.gov/

Log Normal and Normal distribution function

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.