»The future model for chloride ingress is based on
observations from 20 years of natural exposure
By
Jens Mejer Frederiksen
Managing Engineer
B.Sc. Civ.Eng. (hon)
»Chloride ingress in concrete, Problem
• Too fast chloride ingress in concrete will cause too
early corrosion on the steel reinforcement
• Chloride can be transported in the moist parts of
the concrete pores/defects in many different ways:
• Diffusion
• Due to convection (moisture movements)
• Migration due to an electrical field
• Chloride can react or interact with the binder in
concrete
• Therefore, to define a general model for chloride
ingress into concrete is pretty complicated
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2
» Today’s agenda
• Problem
• Methodology
o Experimental
Ø Exposure
Ø Specimens
Ø Analysis, tendencies
o Models
Ø Fick’s 2nd Law
Ø Solutions
Ø Constitutive formulas
Ø Misuse of models – on obtained data
Ø Misuse of models – in predictions
o Optimisation
• Results
o A tool for design/specification of concrete
» Today’s agenda
• Problem
• Methodology
o Experimental
Ø Exposure
Ø Specimens
Ø Analysis, tendencies
o Models
Ø Fick’s 2nd Law
Ø Solutions
Ø Constitutive formulas
Ø Misuse of models – on obtained data
Ø Misuse of models – in predictions
o Optimisation
• Results
o A tool for design/specification of concrete
»Chloride ingress in concrete, Problem
• The most important problem at
today’s lecture is the short time
available for this topic/presentation!
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»Chloride ingress in concrete, Problem
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Source: Betonhåndbogen, Chapter 19.3
(http://www.betonhaandbogen.dk/bogen-i-kapitler)
»
Prediction of the service life
is in many cases closely related to
Prediction of time to corrosion initiation
Mosquée
Hassan II,
Casablanca
The Great
Belt Link
Constructed
(Constructed:
1987-1993)
No requirements!
Repaired (!!):
2005-2008
1987-1998
Requirement
100 years
New Port
Tanger
Med. I
Constructed
2004-2007
Requirement
100 years
»Kyösti Tuutti’s service life phases
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»Kyösti Tuutti’s service life phases
Structural integrity
Initiation phase
Acceptable level of deterioration
Service life
Time
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»Chloride ingress in concrete
Protection against too fast chloride
ingress was in focus for the durability
design of the Great Belt Link,
Denmark, 1987
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Source: Betonhåndbogen, Chapter 19.3
(http://www.betonhaandbogen.dk/bogen-i-kapitler)
»Chloride ingress in concrete
Protection against too fast chloride
ingress was also in focus for the
durability design of the breakwater
structures of the new harbours in
Tangier, Morocco, 2004
… and a lot of other
major and minor projects
around the world
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»Chloride ingress in concrete
• Since approx. 1988 the way to measure chloride
content of concrete has been agreed
internationally (the common standards are older,
but in practice a number of alternative methods
were introduced and influenced the “de facto
standard”).
• Since approx. 1991 the way to measure calcium
content of concrete has been agreed
internationally.
• Therefore, nowadays chloride ingress can be
observed pretty easy and with a correct result.
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» Today’s agenda
• Problem
• Methodology
o Experimental
Ø Exposure
Ø Specimens
Ø Analysis, tendencies
o Models
Ø Fick’s 2nd Law
Ø Solutions
Ø Constitutive formulas
Ø Misuse of models – on obtained data
Ø Misuse of models – in predictions
o Optimisation
• Results
o A tool for design/specification of concrete
»Chloride ingress in concrete
• It is well-known that we can learn a lot from laboratory
experiments
• But it is also well-known that data from the laboratory
are difficult to use in natural exposure conditions
• The main problem when we are trying to gather
information about chloride ingress in various
environments and for various types of concrete is the
lack of a good homogenous set of data
• This was foreseen by a group of swedes in the early
1990’s - the exposure station in Träslövsläge was
formed
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»Träslövsläge Marine exposure station
under the supervision of SP in Borås
Specimens
Concrete panels
(1000 ´ 700 ´ 100 mm)
Exposure:
• Marine atmospheric zone
• Marine splash zone
• Marine submerged zone (14 ± 4 g chloride/l)
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Träslövsläge
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» Natural exposure in Träslövsläge
•ATM
•SPL
•SUB
» Natural exposure in Träslövsläge
• 40 types of concrete
• Profiles measured at 1 to 5
different exposure times
• In total more than 200
chloride and calcium
profiles
• More than 1000 points on
profiles
•ATM
•SPL
•SUB
Measured chloride profiles
» Today’s agenda
• Problem
• Methodology
o Experimental
Ø Exposure
Ø Specimens
Ø Analysis, tendencies
o Models
Ø Fick’s 2nd Law
Ø Solutions
Ø Constitutive formulas
Ø Misuse of models – on obtained data
Ø Misuse of models – in predictions
o Optimisation
• Results
o A tool for design/specification of concrete
» Fick’s 2nd law
– the error function solution
2
ì ¶C
¶ C
= D 2 , x > 0, t > 0
ï
¶x
ï ¶t
ïC (0, t ) = C , t > 0, (constant )
s
í
ïC ( x ,0) = 0, x > 0
ï
ï lim C ( x , t ) = 0, t > tex
î x ®+¥
The simple error function solution
Two parameters
constant in time
Time
Cs = Csa = constant for all t
Diffusivity (D)
Boundary
condition (Cs)
æ x ö
C ( x, t ) = Ci + (Cs - Ci )erfcç
÷
è 2 Dt ø
constant in time
Time
D = Da = constant for all t
Measured chloride profiles
Da is decreasing
Fitted parameters from chloride
profiles - Da is decreasing
Fitted parameters from chloride
profiles - Da is decreasing
Applied model – three parameters
constant in time
Diffusivity (D)
Boundary
condition (Cs)
æ
ö
0
.
5
x
÷
C ( x, t ) = Ci + (Csa - Ci )erfcç
ç (t - t ) D (t - t ) ÷
ex
a
ex ø
è
Time
decreasing
in time
Time
D changed into Da
An average over the exposure time
æ tex ö
Da (t ) = Daex ç ÷
è t ø
a
Measured chloride profiles
Another problem:
Csa is increasing!
Fitted parameters from chloride profiles
Csa is increasing
Fitted parameters from chloride profiles
Csa is increasing
»Poor correlation for constant Da and Csa from 10
years of exposure to 20 years
Plot of
• K0,1 for 10 years
of exposure
vs.
• K0,1 for 20 years
of exposure
K Cr
-1 æç
C - Ci
= 2 × Da × erfc ç r
è C sa - C i
ö
÷× 1
÷
ø
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» Fick’s 2nd law
– Leif Mejlbro’s solution
2
ì ¶C
¶ C
= D 2 , x > 0, t > 0
ï
¶x
ï ¶t
ï
p
íC (0, t ) = t , t > 0, p > -1 (constant )
ïC ( x ,0) = 0, x > 0
ï
ï lim C ( x , t ) = 0, t > tex
îx ® +¥
» Fick’s 2nd law
– Leif Mejlbro’s solution
C ( x , t ) = C i + (C sa (t - tex ) - C i ) ´ Yp (
0.5 x
(t - tex )Da (t - t ex )
Ψp is a new function – called “Mejlbro’s Psi
function”, and is simply the error function
complement (erfc) made general, i.e.
Ψp=0(z) = erfc(z) = 1-erf(z)
)
increasing in time
Time
Diffusivity (D)
Boundary
condition (Cs)
The Mejlbro-Poulsen Model
decreasing
in time
Time
C ( x , t ) = C i + (C sa (t - tex ) - C i ) ´ Yp (
0.5 x
(t - tex ) Da (t - tex )
)
The Mejlbro-Poulsen Model
has four parameters
0.5 x
C ( x, t ) = Ci + (C sa (t - tex ) - Ci ) ´ Yp (
)
(t - t ex ) Da (t - tex )
a
C sa
æ
ö
t
æ
ö
ex
= C i + S ´ ç (t - t ex ) ´ D aex ´ ç ÷ ÷
ç
t ø ÷
è
è
ø
p
S = S p /(tex Daex ) p
æ t ex
Da (t ) = Dach (t ) » Dav (t ) = Dav,ex çç
è t
a
ö
÷÷
ø
»Constitutive models are based on laboratory
results – HETEK 1995
» Constitutive formulas – 17 coefficients!
( c)
eqv wL
D
=
W + k air ,D × L
C + FA × k FA, D + MS × k MS , D
» Constitutive formulas – 17 coefficients!
( c)
eqv wL
D
=
W + k air ,D × L
C + FA × k FA, D + MS × k MS , D
( ( c) )
D1 = B × eqv wL
D100
æ 1 ö
= D1 ç
÷
è 100 ø
N
D
× k D1, env[mm2/year]
a
[mm2/year]
a = k a ,env
» Constitutive formulas – 17 coefficients!
( c)
eqv wL
D
=
W + k air ,D × L
C + FA × k FA, D + MS × k MS , D
( ( c) )
D1 = B × eqv wL
D100
æ 1 ö
= D1 ç
÷
è 100 ø
N
D
× k D1, env[mm2/year]
a
[mm2/year]
C1 = ( A × eqv (w / c )C + k air ,C × L ) × k C1 ,env
C100 = C1 × kC100 ,env
eqv( w / c ) C =
a = k a ,env
[% mass binder]
[% mass binder]
W
C + FA × k FA,C + MS × k MS ,C
» Today’s agenda
• Problem
• Methodology
o Experimental
Ø Exposure
Ø Specimens
Ø Analysis, tendencies
o Models
Ø Fick’s 2nd Law
Ø Solutions
Ø Constitutive formulas
Ø Misuse of models – on obtained data
Ø Misuse of models – in predictions
o Optimisation
• Results
o A tool for design/specification of concrete
» The optimised coefficient for the
constitutive equations
Coefficients in transport Coefficients in binding
1. B = 771 [mm²/year]
1. A = 5.3 [% mass binder]
2. N = 1.19
2. kair,C = 0.11
3. kair,D = 0.04 [kg/%]
3. kFA,C = -1.33
4. kFA,D = 5.3
4. kMS,C = -0.49
5. kMS,D = 10.7
5. kC1,ATM = 0.56
6. kD1,ATM = 0.15
6. kC1,SUB = 1.1
7. kD1,SUB = 0.54
7. kC100,ATM = 1.1
8. ka,ATM = 0.42
8. kC100,SUB = 2.1
9. ka,SUB = 0.44
» The resulting optimisation
» How well can we estimate 20 years data
with a model based on 10 years data?
» How well can we estimate 20 years data
with a model based on 10 years data?
»Poor correlation for constant Da and Csa from 10
years of exposure to 20 years
Plot of
• K0,1 for 10 years
of exposure
vs.
• K0,1 for 20 years
of exposure
K Cr
-1 æç
C - Ci
= 2 × Da × erfc ç r
è C sa - C i
ö
÷× 1
÷
ø
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» Today’s agenda
• Problem
• Methodology
o Experimental
Ø Exposure
Ø Specimens
Ø Analysis, tendencies
o Models
Ø Fick’s 2nd Law
Ø Solutions
Ø Constitutive formulas
Ø Misuse of models – on obtained data
Ø Misuse of models – in predictions
o Optimisation
• Results
o A tool for design/specification of concrete
» A tool for design/specification of
concrete
• With the found coefficients the chloride ingress into a variety of
concretes made with CEM I + Silica Fume + Fly ash – with or
without air entraining can be calculated.
• We do however miss good and reliable data for chloride
threshold values in order to make the service life design.
• Also the expected requirements for acceptance testing of the
concrete’s chloride ingress parameters can be an output – not
included yet
» Concluding remarks –
and further studies
• The set of data from Träslövsläge is probably the most
comprehensive set of data we have
• The data set do have limitations (e.g. small and thin specimens,
concrete with fly ash has a limited presence, lack of corrosion
data – though some do exist)
• If we want to have a tool for desktop design of chloride resistant
concrete the data set forms a good basis for further development
• The optimisation procedure applied here is simplistic – much
better, but more complicated tools are available, e.g. for
covariance analysis – not included yet
• Data from the road environment do exist and ought to be given
the same type of attention – not included yet
»Thanks for your attention
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