Utility of Spatially Variable Damage Performance

Utility of Spatially Variable Damage Performance Indicators for Improved Safety and Maintenance Decisions for Deteriorating Infrastructure Mark G. Stewart John A. Mullard Brendan J. Drake Centre for Infrastructure Performance and Reliability School of Engineering The University of Newcastle, Australia

1

Scope of Talk z z z

Why model spatial variability? Random field modelling Spatially variable damage performance indicators: – More information to decision-makers – Damage performance indicators: • structural reliability • likelihood and extent of damage

– Examples: • Structural reliability of RC beams subject to pitting corrosion • Corrosion damage and time to first maintenance for RC bridge decks • Life-cycle performance of maintenance strategies

Brief overview of applications and utility to decision-making 2

Introduction z

Material deterioration is not homogeneous – pitting (localised) corrosion – cover cracking, spalling and other corrosion damage

z

Spatial and temporal variability: – – – – –

material properties dimensions, orientation exposure to aggressive agents loading maintenance and repair

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... Introduction

z

Spatial variability often not considered: – spatial data not reported in literature • quantifying spatial variability more difficult

– closer inspection of data reveals more spatial variability • what is the appropriate scale to model spatial variability?

– CPU for time-dependent reliability analysis already high • why model increased complexity?

... will consider spatial variability of pitting corrosion and corrosion damage on time-dependent structural reliabilities and maintenance actions - RC structures 4

Random Field Modelling z

Characterised by: – mean – standard deviation – correlation function

existing reliability studies

• triangular, Gaussian, etc. ⎛ 2 ⎛τ ⎛ ⎞ τ y x ⎜ Gaussian : ρ(τ) = exp −⎜ ⎟ − ⎜⎜ ⎜ ⎝ dx ⎠ ⎝ dy ⎝ where d = θ π

???

2 ⎞ ⎛ τ ⎞2 ⎞ ⎟ −⎜ z ⎟ ⎟ ⎟ ⎝d ⎠ ⎟ z ⎠ ⎠

– scale of fluctuation θ =

∫

θx=0.5 m, θy=0.75 m

+∞ −∞

ρ(τ)dτ 5

1. RC Beam - Pitting Corrosion element j j=1

j=2

j=m

n reinforcing bars

δ L

– – – – – –

Gumbel distribution of max pitting per element pit occurs in middle of element δ=100 mm corrosion reduces yield strength four point bending RC Office Floor Beam (Y16 rebars)

b

a

Do 6

... 1. RC Beam - Pitting Corrosion

z

Spatial analysis: – Critical limit state for series system:

G t i (X) = min(M j (t i ) − S j (t i )) j=1,m

• Mj(ti) = resistance at element j at time ti – deterioration process will reduce Mi with time

• Sj(ti) = load effect at element j at time ti

z

Non-spatial analysis – Mid-span limit state only

G t i (X) = M mid (t i ) − Speak (t i ) 7

... 1. RC Beam - Pitting Corrosion

z

Cumulative pf

p f (0,t L ) = 1− Pr [G t 1 (X) > 0 ∩ G t 2 (X) > 0 ∩ .....∩ G t k (X) > 0]

z

t1 < t 2 < .... < t k ≤ t L

Updated pf for next t years – conditional on T years of service proven performance pf (t | T) =

pf (T + t)− pf (T) 1− pf (T)

• assessing safety of existing structures 8

... Results: Distribution of Spatial Position of Governing Limit State Bending Moment Diagram (γ=20%) 0.07

peak actions j=32-47

0.05

t

Proportion of min[G (X)]

0.06

0.04

0.03

0.02

0.01

0 2

6 10 14 18 22 26 30 34 38 42 46 50 54 58 62 66 70 74 78 80

Element j

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... Results: Structural Reliabilities 0.01 No Deterioration Spatial Analysis Non-Spatial Analysis

Probability of Failure

0.001 0.0001

β =3.8 T

p (0,t)

-5

10

f

p (1|t)

10-6

f

10-7 10-8 0

10

20

30

40

50

Time t (years)

pf for spatial analysis = 250% higher than non-spatial pf βT=3.8: spatial = ‘unsafe’ after 31 years non-spatial = ‘unsafe’ after 34 years ∴ non-spatial is non-conservative

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2. Corrosion Damage and Time to First Maintenance (Stewart and Mullard, 2006)

z

Corrosion Damage – corrosion-induced cracking of concrete cover – patch repair when extent of damage (d)=Xrepair=1%

z

Need to predict likelihood and extent of damage

Cover Cracking

– Random field modelling of deterioration – Spatial time-dependent reliability analysis

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... 2. Corrosion Damage and Time to First Maintenance z

Spatial time-dependent reliability analysis – – – –

RC bridge deck (900 m2), 50 mm cover, w/c=0.5, Y16 rebars Corrosion occurs from exposure to coastal sea-spray Damage limit state (1 mm crack width) Spatial variability: – concrete cover – concrete compressive strength – surface chloride concentration

correlation length θx=θy=2.0 m

– 2D random field model • Δ=0.5 m, k=3,600 elements

– Probability that at least x% of a concrete surface has cracked • (Pr(d(t) ≥x%)

– Likelihood of time to first maintenance = Pr(d(t)≥Xrepair%).

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... Results: Probability Contours for Pr(d(t)≥Xrepair%) 0.5 12.5

A=900 m

2

0.05

7.5

0.95

repair

Repair Threshold X %

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5 X

repair

2.5

X

repair

=2.5% =1%

0 0

10

20

30

40

50

60

70

80

90

100 110 120

Time t (years) Xrepair=1%: Xrepair=2.5%:

90% chance of damage b/w 21-47 years defer first maintenance by 9 years 13

3. Life-Cycle Performance and CostEffectiveness of Maintenance Strategies (Stewart, 2006)

z

Comparison of risks (costs) against benefits – Optimal solution = minimisation of life-cycle costs M

LCC(T) = C D + C C + CQA + CIN (T) + C MR (T) + ∑ pfi (T)CSFi i =1

• • • • •

design and construction present value costs (CD, CC) cost of improved durability - increased cover, f’c,... (CQA) costs of inspections, maintenance and repairs (CIN) probability of “failure” (pf) cost of failure (CSF) LCC (T) = C D + C C + C QA + C IN (T) + C MR ( T) + E SF ( T)

• expected cost of damage during service life T (ESF)

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... 3. Cost-Effectiveness of Maintenance Strategies Repair Cost CF(x)

Netherlands data:

€ 2,000/m2

Co= €5,000 CR= €2,000/m2

€ 5,000 0%

100%

Extent of Damage (x%)

predict extent of damage ??? = fn (time, deterioration, design, etc.) Predict probability that the extent of damage (d) is known –Pr(d(t)=x%)

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... 3. Cost-Effectiveness of Maintenance Strategies

z

Repair threshold = damage to Xrepair% of surface – eg. damage area of Xrepair=1% indicates need for first repair – but at time of inspection damage maybe > Xrepair% • eg. time b/w inspection ↑, observed damage (x%) ↑

z

Repair strategy (patching) assumes – severe cracking (1 mm) always detected when inspected – repair immediately after Xrepair% cracking discovered – repair returns patched area to ‘as new’ condition – 100% repair efficiency (not realistic) – other surfaces will continue to deteriorate

– severe cracking may re-occur during service life – multiple repairs may be needed

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... 3. Cost-Effectiveness of Maintenance Strategies Extent of damage d(t)

deterioration of original + repaired concrete first repair d(t1) Xrepair

Xrepair% d(t1-Δt)