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Sykora & Holicky - Durability Assessment of Large Surfaces… 1
Durability Assessment of Large SurfacesUsing Standard Reliability Methods
M. Sykora & M. HolickyCzech Technical University in Prague
IntroductionMeasurements
Simplified deterioration modelExample
Conclusions
Sykora & Holicky - Durability Assessment of Large Surfaces… 2
Cooling tower and its maintenance
Sykora & Holicky - Durability Assessment of Large Surfaces… 3
Steel retaining walls
Sykora & Holicky - Durability Assessment of Large Surfaces… 4
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
Sykora & Holicky - Durability Assessment of Large Surfaces… 5
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
Sykora & Holicky - Durability Assessment of Large Surfaces… 6
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
Sykora & Holicky - Durability Assessment of Large Surfaces… 7
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
Sykora & Holicky - Durability Assessment of Large Surfaces… 8
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
Sykora & Holicky - Durability Assessment of Large Surfaces… 9
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
Sykora & Holicky - Durability Assessment of Large Surfaces… 10
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
Sykora & Holicky - Durability Assessment of Large Surfaces… 11
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.
Sykora & Holicky - Durability Assessment of Large Surfaces… 12
Miroslav Sykora and Milan Holicky [email protected]
Durability Assessment of Large SurfacesUsing Standard Reliability Methods
Thank you for your attention.