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Durability Assessment of Large SurfacesUsing Standard Reliability Methods

M. Sykora & M. HolickyCzech Technical University in Prague

IntroductionMeasurements

Simplified deterioration modelExample

Conclusions

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Cooling tower and its maintenance

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Steel retaining walls

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Site measurementsLocal distribution of a carbonation depth

0 12 24

0

0.1

Relative Frequency

n = 74m= 11.05 mmv = 0.31a = 0.59

LognormalGammaNormal

Carbonation Depth [mm]

spatial variation (environmental actions,material properties)?→ discretisation techniques→ simplified approach based on “independent” elementary surfaces

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Simplified deterioration model- division into zones (similar exposures – splash/upper parts of piers)

- within zones homogeneous random fields W (material properties, concrete cover) + hyperparameters X (single value for whole structure)

- discretization of the zone into N elementary surfaces (random field variables independent)

fib Bulletin 59 Condition control and assessment of reinforced concrete structures

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Simplified deterioration model

Pf(t) = P{ndeg(t) / N ≥ alim} = EX(t){1 - Fbinom[Nalim, N, pf(W|x(t))]}

- For steel structures the size of an elementary surface may correspond to a size of inspected areas (e.g. 3 m)

- Concrete, chloride ingress ~ 0,5-2 m

The limiting deterioration level alim = 0,1-0,2

alim = 0,15 accepted in the example

pf(∙) is the failure probability of an elementary surface

FORM/SORM

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Example – carbonation of concretefib Model Code for Service Life Design

Type Variable Symbol Distrib. Unit X VX

Random Concrete cover R Beta mm R 0.35

fields Inverse carbon. resistance

RNAC,0-1 Gamma

(mm2/y.) / (kg/m3)

2e4 0.5

Relative humid. RHreal Beta - 0.71 0.18 Hyper- CO2 concentr. Cs normal kg/m3 8.2e-4 0.12 parameters Model uncert. KS LN - 1 0.1

elementary surface: pf(t,mR|kS,x) = P[R(mR) − kS S(t,W|x) < 0]

Measurements

no trend?

2

s1

NAC,0c

5.2

5ref

5real

wsreal1

NAC,0

wSR

c 0767.0

71

12,,,

btowpb

tcR

t

rh

rhtbcrhtRS

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Variation of Pf(t) with tR = 25 mm, alim = 0.15

0 20 40 60 80 1000

0.1

0.2

0.3

0.4

0.5

time t

Pf(t)

N = 100

N = 20

N = 1

N = 100no correlation

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Probabilistic optimization of the concrete cover

• The total cost

Ctot = C0 + C1 μR + E[Cf]

• Expected consequences

• Annual discount rate q

t qP

PCC

d11

Ef

fff

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Variation of optimum reliability index bopt with Nq = 0.03, t = 40 years, and Cf / C1 = 100 and 1 000

0

1

2

3

N

bopt(R,opt)

100 1000 1.104 1.10510

Cf / C1 = 100

Cf / C1 = 1 000

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Conclusions• Structural durability may be affected by spatial variability

particularly for large surfaces.

• Presented model seems to require lower computational demands compared to random field techniques (to be proved by upcoming studies).

• This model is expected to be an effective tool for optimisation studies.

• Numerical example of concrete carbonation reveals that the failure probability somewhat increases with a size of surface.

• The optimum concrete cover and reliability index can be considered independent of the size of the surface area.

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Miroslav Sykora and Milan Holicky miroslav.sykora@klok.cvut.cz

Durability Assessment of Large SurfacesUsing Standard Reliability Methods

Thank you for your attention.