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Probabilistic Assessment of Corrosion Riskdue to Concrete Carbonation

Frédéric DupratAlain Sellier

Materials and Durability of Constructions LaboratoryINSA / UPS - Toulouse - France

Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005Introduction

Carbonation modeling

Probabilistic approach

Results




Results

CO2

CO2

CO2

CO2 pressure on external edges for most of concrete structures

CO2 ingress:carbonation

CO2

CO2

CO2




Results



Precipitation of calcite

CO2

CO2

CO2




Results




Dissolution of calciumfixed by cement hydrates

OHCaCOOH

COCa(OH) 232

22

CO2

CO2

CO2




Results





Decrease of pHin pore solution





Decrease of pHin pore solution

Favourable conditions to initiation and development of corrosion

CO2

CO2

CO2




Results

c

g2CO

D




Results

Physical parameters: - diffusion coefficient - concrete cover thickness

Predictingmodel

Mean values

Given date:depassivation

no depassivation

g2CO

D




Results


Predictingmodel


no depassivation

Mean values

Random incertainties

c

c

(c)

Laws of probability


g2CO

D

Predictingmodel


no depassivation

Mean values

Random incertainties

Laws of probability


Given date:probability of depassivation

e




Results

Diffusion term Capacity term

��g g2 2

g g2 2CO CO

CO φ 1-Sr div D grad CO μt

Concentration

Porosity

Saturation

Diffusion

Sink term : precipitation of calcite




Results

gCO2 Strongly non-linear term

Numerical instability around the carbonation

front

Change of variable

Agressivespecies

CO2g

Dissolved species

CaS

Probabilistic Assessment of Corrosion Risk due to Carbonation Baltimore January 5-7 2005


��g g2 2

g g2 2CO CO


Introduction



Results

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0 500 1000 1500 2000 2500

CO2g (mol/m3)

CaS (mol/m3)


Strongly non-linear term

Numerical instability around the carbonation

front

Change of variable


��g g2 2

g g2 2CO CO


Introduction



Results

Agressivespecies

CO2g

Dissolved species

CaS

( ) ( )

1

��

g2s

eq

g g2 2s g

2 sCOCas s s

a D

CO COφ 1-SrCaφ 1-Sr CO div D grad Ca

t Ca Ca Ca

All consumed CO2 reacts with CaS in hydrates

10-3< (a) <10-2

negligible (Deq) non-linear



��g g2 2

g g2 2CO CO


Introduction



Results

S

S

g2

COS Cagrad

Ca

CODdiv

t

Cag2



Introduction



Results

G

CaSm

CaSM

Deqm

DeqM

Deq CaS

SCa

Deq(CaS)

L

Conservation of flowSCa

*eq

L

0 eq D

L

xD

dx

SM

Sm

Ca

Ca Seq

S

SmSM*eq

CaD

dCa

CaCaD

CaS(G)

Deq*


S

S

g2

COS Cagrad

Ca

CODdiv

t

Cag2

Diffusion term

Introduction



Results

airCO0COCO g2

g2

g2

DtrDD

Influence of cracking

Reference diffusion

Tortuousity, connectivity of cracks

Tension volumic strain

Gazeous diffusion

Magnifying the diffusion coefficient




Results




Results

Equivalent CaS diffusion coefficient field

Mechanical strain field

Loading and mechanical properties

Magnified CO2 diffusion coefficient field

Physical properties: CO2 diffusion coefficients

tortuousity, saturation degree

Initial condition:CaS=2500 mol/m3

Initial equivalent CaS diffusion coefficient field

Boundary condition:CaS=0 along the edges

t=t0

Solid calcium field: CaS

Convergencefor CaS field ?

no t=tf ?

yes

t=t +t

no

Start

Endyes

Practical application: reinforced concrete beam

6 m 25 cm

5.2 kN/m

55 cm

Eb 35000 MPa

0COg2

D

airCOg2

D10-8 m2/s

1.39.10-5 m2/s 0.5 0.15Sr 0.3

Carbonation profiles

1month 5 years 20 years 35 years 50 years




Results

Carbonation depth

Zone saineCas=2500mol/m3

(b) Zone carbonatée Cas <<2500mol/m3(a) ½ section centrale de la poutre

A

A

B

B

(c) Evolution du profil en calcium noncarbonaté entre les points A et B enfonction du temps

Position de l’armature

Carbonated zoneCaS<< 2500 mol/m3

Non-carbonated zoneCaS= 2500 mol/m3

A

BA B

Non-carbonated CaS profiles between

A and B

Eb 35000 MPa

0COg2

D

airCOg2

D10-8 m2/s

1.39.10-5 m2/s 0.5 0.15Sr 0.3



0.0

0.5

1.0

1.5

2.0

2.5

0 10 20 30 40 50

Time (year)

Car

bona

ted

dept

h (c

m)

Introduction



Results

6 m

5.2 kN/m

25 cm

55 cm




Results

• Diffusion coefficient• Tortuousity / Connectivity• Concrete Young's modulus• Loading• Cover thickness

G(U) = 0

u1

u2

Concrete cover cAB

P*

O

Carbonation depth dAB

Finite elementanalysis

FailureG(U) < 0[ cAB < dAB ] A

B

A

BPerformanceG(U) > 0[ cAB > dAB ]

(k)(k)

(k)(k)(k)(k)T1)(k

UGgrad

UG UU




ResultsReliability index = min(UTU)1/2 with G(U)=0

Rackwitz-Fiessler's algorithm

• Significant computational cost

• Very much time consuming

• Non-guaranteed convergence

Non-linear FEM

1 G(U) computation at T=60 years 12 minutes CPU time

Gradient not accurately estimated

Direct approach




Results

N

1i

1N

1i

N

1ijjiij

2iii

N

1iii0 UUaUaUaaUQ

Response surface approach

Reliability index = min(UTU)1/2 with Q(U)=0

(k)(k)

(k)(k)(k)(k)T1)(k

UQgrad

UQ UU

Quadratic response surfacewith mixed terms

• a0, ai, aii, aij determined by least square method

• (N+1)(N+2)/2 numerical observations

1 "center point"2N axial points

1N

1iiN out-of-axes points

star shape experimental design

• Successive experimental designs are necessary




Results

N

1i

1N

1i

N

1ijjiij

2iii

N

1iii0 UUaUaUaaUQ



(k)(k)

(k)(k)(k)(k)T1)(k

UQgrad

UQ UU

u1

u2

ED(1)

Q(U)(1)=0P*

G(U)=0

P*(1)

P*

G(U)=0




Results

N

1i

1N

1i

N

1ijjiij

2iii

N

1iii0 UUaUaUaaUQ



(k)(k)

(k)(k)(k)(k)T1)(k

UQgrad

UQ UU

u1

u2

ED(2)Q(U)(2)=0

P*(2)




Results

P*(m)

#1 Previous P*(m) outside the ED(m)

ED(m+1) "recentered" on P*(m)

ED(m)

P0

u1

u2

Building the experimental design

P*

G(U)=0




Results

u1

u2


ED(m+1)

|1||2|



+

i

m*m

m*m

0i U

UQ

UQgrad

1ΔΔ

i| 0.25

0 = N½

+

U*(m)

P*

G(U)=0




Results

u1

u2


Q(U)(m)=0

Q(U)(m)<0

Q(U)(m)>0



+

i

m m

m m

0i U

UQ

UQgrad

1ΔΔ

i| 0.25

0 = N½

+

ED(m+1)

2

U(m)

P*

G(U)=0




Results

u1

u2


#2 Previous P*(m) inside the ED(m)

ED(m)

P*(m)

P0

P1

P2P0

P*

G(U)=0

Retained points:

cos(P0Pi,P0P*(m)) > 0




Results

u1

u2


Retained points:



ED(m+1)

P*(m)

P2

Complementary points:

symmetrical transformed / P*(m)P*

G(U)=0




Results

u1

u2


Retained points:



ED(m+1)

P*(m)



G(U)=0Bringing the transformed points

closer to P*(m)

P2




Results

u1

u2


Retained points:



ED(m+1)

P*(m)




closer to P*(m)




Results

u1

u2


Retained points:



ED(m+1)




closer to P*(m)

P0





Results

Start

First experimental design ED(0)

RF algorithm: P*(0)

ED(m)ED(0) ; P*(m)P*(0)

P*(m) inside

the ED(m) ?

Finite elementanlysis

RF algorithm: P*(m+1)

| P*(m+1) P*(m) | < 0.15

End

Building the ED(m+1)

with procedure #2

yes

Building the ED(m+1)

with procedure #1

no

Reliability index yes

ED(m)ED(m+1)

P*(m)P*(m+1)

no




Results


Material properties:• Concrete strength• Reference diffusion coefficient• Turtuousity factor

Concrete probes of low scale

Variance reduction

Concrete probes of similar scale

No change




Results



Distribution Mean CoV

Lognormal 35 MPa 0.1

Concrete probes of similar scale

No change




Results




Lognormal 35 MPa 0.1Lognormal 10-8 m2/s 0.8 Uniform 0.5 0.46[0.1 to 0.9]




Results




Lognormal 35 MPa 0.1Lognormal 10-8 m2/s 0.8 Uniform 0.5 0.46[0.1 to 0.9]Loading parameter:

• Live load E1max 1.04 kN/m2 0.38

Geometrical parameter:• Concrete cover thickness Lognormal 2 cm 0.2




Results


Efficiency of the adaptative RSM

Features Iteration 1 Iteration 2 Iteration 3New experimental points 21 21 1

Designpoint

U1 (diffusion of CO2)U2 (tortuousity)U3 (concrete strength)U4 (concrete cover)U5 (live load)

5.51795.306 10-2

-1.366 10-4

-2.95753.595 10-2

4.84167.734 10-2

-4.478 10-4

-2.08927.531 10-2

4.80968.518 10-2

-4.978 10-4

-2.01298.372 10-2

Reliability index 6.2608 5.2737 5.2145Iterations in -search algorithm 6 4 3

T=2 years

Features Iteration 1 Iteration 2New experimental points 21 21

Designpoint

U1 (diffusion of CO2)U2 (tortuousity)U3 (concrete strength)U4 (concrete cover)U5 (live load)

1.19540.2712

-2.094 10-3

-0.79053.533 10-2

1.22910.2552

-1.790 10-3

-0.71442.995 10-2

Reliability index 1.4590 1.4447Iterations in -search algorithm 4 3

T=30 years




Results


Variation of the reliability with time

0

1

2

3

4

5

6

0 10 20 30 40 50 60Time (years)

Re

liab

ility

ind

ex

SLS

• Significant decrease of the reliability index

• Reliability index lower than threshold value recommended by Eurocodes after T=30 years




Results


Variation of the sensitivity factors with time

• Diffusion coefficient and cover thickness for T < 35 years

• Tortuousity factor and loading play a role for T > 35 years

0.00.10.2

0.30.40.50.60.7

0.80.91.0

0 10 20 30 40 50 60

Diffusion Cover thickness Tortuousity Load

Time (years)

Se

nsi

tivity

fa

cto

r

http:// probabilistic assessment of corrosion risk due to concrete carbonation frédéric duprat...

Documents

carbonation slide

carbonation baltimore

depassivation slide

concrete structures

development of corrosion

france slide

external edges

pore solution slide