Bruno CAPRA , Alain SELLIER, Jonathan MAI-NHU, …...(Petre Lazar 2001) • Engineering models:...

Effects of carbonation on the lifetime of concrete structures and updating by concrete structures and updating by

Bayesian networks

Bruno CAPRA, Alain SELLIER,

Jonathan MAI-NHU, Patrick ROUGEAU

SSCS 2012, Mai 29 – June 1, Aix-en-Provence, France

OXAND S.A., France

DECISION MAKING: INTEGRATION OF KNOWLEDGE

Where, how and when to act ?

Con

stru

ctio

n

End

of i

ncub

atio

n

Incubation100 %

Prediction

History

Risk %

Updating

10µµµµm

Material analysis

Risk Management and Updating

t0

tit

? ?

Con

stru

ctio

n

End

of i

ncub

atio

n

t0 t

it

? ?

Time

Prediction

TTimeemps

Residual kinetics

Perte de la source froide

Débit Q < 0,4 * Qnom

Temp. RRI > 45°C

ou

Data Acquisition

Simulations

Data Treatment

2

SSCS 2012, May 29 – June 1, Aix-en-Provence, France

Dam

MonitoringStructural Analysis

Défaut de débit sur voie A

Défaut de débit sur voie B

Eclatement local

Fuites

Tassement de terrrain

Séisme Surpressions Poids propre

Mauvaise conception mécanique

Détérioration de la capacité

portante

Corrosion interne

généralisée

Corrosion externe en zone

singulière

Idem

Idem Idem

Risk Analysis

Quantification

Simulations

Risk management associated to ageing

MONITORING

Risk analysis

Quantification of main failure modes

ACQUISITIONOF FIELD DATA

SIMULATION

main failure modes

Prediction

DATA BASEUpdating

3


Decision factor evaluation

Predictive maintenanceCost estimationOptimisation of maintenance decision

DECISION

UPDATING:better management of

uncertainty

Factory: 3 machines : M1, M2, M3Production: white and red parts

(Color C: discrete variable)

BAYESIAN APPROACHBasic principles 1

1

1

1

2 3 3

2

2

2

3

3

3

3

3 3

(Color C: discrete variable)

Probabilities to have white or red parts: P(C=white)= ½P(C=red)= ½

- Conditional probabilities :P(C=red|M1) = 1 P(C=red|M2) = ½

M1 M2 M3

Probability

0.5

Red White

4


P(C=red|M2) = ½P(C=red|M3) = ¼

- A priori : origin of the partP(M1) = P(M2) = ¼ P(M3) = ½ 3

1 2

0.5

0.25

Probability

- A priori: origin of the part

P(M1) = P(M2) = ¼ P(M3) = ½

BAYESIAN APPROACHBasic principles

31 2

0.5

0.25

Probability

PriorP(M1) = P(M2) = ¼ P(M3) = ½

- Observation : red piece picked

- Bayes’ theorem:

∑== ii

i UPUiBP

UPUiBP

BP

UPUiBPBUP

)()(

)()(

)(

)()()(

Red

Observation

Updatingprocess

Obs.

5


- A posteriori:

P(M1|red) = ½ P(M2|red) = P(M3|red) = ¼

∑==

ii

i UPUiBPBPBUP

)()()()(

12 3

Probability

0.5

0.25

process

Posterior

Compressive strengthPdf

Updating of a continuous parameter

Example with Normal distributions

1. A priori law: N(40, 10)

2. Observation:N(35, 7)

Compressive strength

0,04

0,06

0,08Pdf

6


3. A posteriori:N(36.6, 5.7)

0

0,02

0 20 40 60Rc (Mpa)

Bayesian approach

Prior(expert, existing

Likelihood(observations, tests, (expert, existing

knowledge, feedback…)(observations, tests,

feedback…)

Updating (Bayes)

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Posterior (better uncertainty control)

Bayesian networks

- Simple updating :

evolution of one single parameter

=> Bayes’ theorem

(analytical solution for some cases)

- Degradation modeling function of

numerous uncertain parameters

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numerous uncertain parameters

=> Bayesian networks

(numerical simulation)

Life time of concrete structure

Concrete structure Concrete degradation vs time

9


Life time assessment: important stake for structure owner

Carbonation of concrete

10


(Thierry 2006)

Strongly depends on transport properties of concrete (diffusivity, porosity)

pH

Corrosion of steel in concreteDiagramme de Pourbaix du système Fe-H 20 à 25°C

Sound concrete(ph=13,5 ; E=-200 mV)

Carbonation

Carbonated concrete(ph=7 ; E=-400 mV)

CORROSION

Volume increase of steel oxydation products

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oxydation products

Mechanical stresses leading to concrete cracking

Corrosion risk for concrete structures

Carbonation depthX = f(Rc, RH, t,…) Concrete wall: X = f(Rc, RH, t,…)

d: concrete cover

Environment: relative humidity

Concrete wall: mean compressive strength Rc

Steel reinforcement

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relative humidityRH

reinforcement

Limit state: failure when x ≥ d (corrosion starts)

( ) tRckRHfx )(γ=

Carbonatation models for concrete

(Petre Lazar 2001)

• Engineering models:

with: - RH: relative humidity- Rc: compressive strength of concrete- γ: exposition coefficient to CO2- t: time

and:

( )

−=

++−=

06.01

365)(

2.04833.35833.3 2

Rck

RHRHRHf

13


Carbonation rate mainly depends on Rc: influence of cement type ?

−= 06.01.2

365)(Rc

Rck

Carbonation rate related to the amount of cement hydrates likely to be carbonated(C-S-H but also Portlandite, Ettringite and Aluminates) and CO2 pressure

Carbonatation models for concrete

• Engineering models related to physical parameters:

(C-S-H but also Portlandite, Ettringite and Aluminates) and CO2 pressure

(Hyvert et al 2010, Mai-Nhu et al 2012)

+

+

+

=

1020

2

011

0

1.1

1.2

)(

2

QP

P

n

C

P

PCRT

tPQQ

Derr

txn

atm

p

n

atm

ref

CO

cϕ

β

14


( )

( )2032,013

2exp

1

0mod1

0

28,

2

2

2,2710.44,6

21

cmf

KhanKhan

c

ref

CO

èle

CO

e

tP

RTx

Q

D

Q

D

err−−

=

=Where:

Prior estimation of carbonation depth

• APPLET’s French national project:

• Life time of structures, variabilities and uncertainties related to concretecharacteristics

• Compressive strength (CEM I + silica fume): mean value at 28 days : 58.3 MPa• Compressive strength (CEM I + silica fume): mean value at 28 days : 58.3 MPastandard dev : 4.3 MPa (CV=7.3 %)

• Accelerated carbonation test (CO2 pp = 50%)

Uncertainties:

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Concrete compres. strength: LogN (58,3 MPa; 4,3 MPa)

Model error:LogN (1,11 MPa; 0,52 MPa)

Experimental data


Carbonation tests at different times (CO pp = 50%)

Age Carbonation depth (mm)Mean value (mm)

Standard deviation

(mm)

Coefficient of

variation

28 j 5,2 6 5,2 2 3,8 4,8 6,2 6 2,2 2 4,34 1,72 39,5 %

90 j 6,5 8,2 5,7 2,7 6 5,5 7,2 6,8 4,3 4,5 5,74 1,59 27,8 %

Carbonation tests at different times (CO2 pp = 50%)

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Strong variability: 30 to 40% !

Posterior estimation of carbonation depth


•Experimental data are used to update the prior estimation of carbonation depth

Model/experimental data:

• 28 days: underestimationof carbonation depth

• 90 days: overestimation of carbonation depth

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carbonation depth

• uncertainty � then � (CV from 30 to 40 % )


• Evolution of uncertainty

• First updating at 28 days: pdf of carbonation depth

Before first updating (27 days)

After first updating (28 days)

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• Evolution of uncertainty

• Second updating at 90 days: pdf of carbonation depth

After second updating (90 days)

Before second updating (89 days)

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Updating of the random variables

Random variableCompressive strength

(MPa)Model error

Initial data

Lognormal law:

Mean: 58,3

Standard deviation: 4,3

Lognormal law:

Mean : 1,10

Stand. Dev.: 0,5

Prior simulated(Monte Carlo)

(400 000 drawings)

Mean: 58,2

Stand. Dev.: 4,2

Mean: 1,10

Stand. Dev. 0,5

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(400 000 drawings)

28 days updatingMean: 52,6

Stand. Dev.: 6,4

Mean: 1,35

Stand. Dev.: 0,7

90 days updatingMean: 51,5

Stand. Dev.: 5,2

Mean: 0,95

Stand. Dev.: 0,5

Updating of the random variables

• Updating of compressive strength probability density function

First updating (28 days)

Prior estimation

Second updating (90 days)

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Software: SIMEO MC2

MCMC method

(Markov Chains Monte Carlo)

– Markov Chain

– Métropolis-Hastings – Métropolis-Hastings algorythm with Gibbs sampling

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CONCLUSIONS

In the field of infrastructure risk based management, Bayesian networks allow :Bayesian networks allow :

- the use of field data for updating(especially where few data are available)

- the use of heterogeneous information(expert, feedback, tests,…)

- user control of confidence- a better control of uncertainty for ageing processes

But :

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But :- the method is more complicated than classical reliability approaches (convergence) and must be applied with care- does not prevent from non representative models

Thank you for your attention

Bruno CAPRA, Jean LE DROGO, Valentin WOLFF

Thank you for your attention

OXAND France, Netherland, Switzerland, UK, Canada

[email protected]@oxand.com

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Bruno CAPRA, Jean LE DROGO, Valentin WOLFF

OXAND S.A., France

[email protected]

Bruno CAPRA , Alain SELLIER, Jonathan MAI-NHU, …...(Petre Lazar 2001) • Engineering models:...

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