updating failure probability - uliege · 3 message objective fatigue assessment diagram can be used...

UPDATING FAILURE PROBABILITY

OF A WELDED JOINT IN OWT SUBSTRUCTURES

Q. Mai1 J.D. Sørensen2 P. Rigo1

1Department of ArGEnCoUniversity of Liege

2Department of Civil Engineering

Aalborg University

OMAE Conference - Busan, 2016

2Motivation

ReduceO&M Costs

RBIUpdate Pf

(insp.)Limit StateFunction

Q. Mai | FAD in Updating Failure Probability

3

Message Objective

Fatigue Assessment Diagram can be used to update the failure

probability of an existing OWT substructure when new informa-

tion about either loading, structural responses or inspections isavailable.


4Outline

Fatigue Assessment Diagram

Updating Probability of Failure

Results


5Outline



Results


6


Lr0 0.2 0.4 0.6 0.8 1 1.2 1.4

Kr

0

0.2

0.4

0.6

0.8

1

✓Lr

=sref

sY

; Kr

=KI

Kmat

◆

Unsafe

Figure: Level 2A Fatigue Assessment Diagram

BS-7910, 2005. Guide to Methods for Assessing the Acceptability of Flaws in Metallic Structures.British Standard Institution (BSi).


6


Lr0 0.2 0.4 0.6 0.8 1 1.2 1.4

Kr

0

0.2

0.4

0.6

0.8

1

Lr ,max

=sY

+sU

2sY

✓Lr

=sref

sY

; Kr

=KI

Kmat

◆

Unsafe




6


Lr0 0.2 0.4 0.6 0.8 1 1.2 1.4

Kr

0

0.2

0.4

0.6

0.8

1

✓Lr

=sref

sY

; Kr

=KI

Kmat

◆

Unsafe




6


Lr0 0.2 0.4 0.6 0.8 1 1.2 1.4

Kr

0

0.2

0.4

0.6

0.8

1

✓Lr

=sref

sY

; Kr

=KI

Kmat

◆

Safe

Unsafe




6


Lr0 0.2 0.4 0.6 0.8 1 1.2 1.4

Kr

0

0.2

0.4

0.6

0.8

1

✓Lr

=sref

sY

; Kr

=KI

Kmat

◆

Unsafe




7Outline



Results


8Uncertainties

Variable Value

n No. of cycle/year 1⇥107

t Steel thickness [mm] 65

R Outer radius [mm] 79.5

L Joint length [mm] 100

hs Bend. to memb. ratio 0.81

�Ktr

Transition SIF range 196

m1 Paris law, 1st line 5.10

m2 Paris law, 2nd line 2.88

Ca

/Cc

C ratio for a and c 0.9

Variable Distr. Mean CoV

S Stress range [MPa] W k=0.8 N(µ,s)

sY

Yield strength [MPa] LN 368.75 0.07

sU

Ultimate strength [MPa] LN 750 0.04

�Kth

SIF range threshold LN 160 0.4

Kmat

Fracture toughness 3p W - -

C1 Paris law, 1st line LN 4.8⇥10�18 1.7

C2 Paris law, 2nd line LN 5.86⇥10�13 0.6

a0 Initial crack depth LN 0.15 0.66

a0/c0 Initial aspect ratio LN 0.6 0.40

Bscf

Uncertainty in SCF LN 1 0.05

Bsif

Uncertainty in SIF LN 1 0.05


9

Updating method

Uncertainties

Kmat

�Kth

FM

sY

sU �s

a0,c0 SIF SCF

Limit State Function

POD

DecisionsCrack Growth Simulation

UpdatedPf


9

Updating method

Kmat

�Kth

FM

sY

sU �s

a0,c0 SIF SCF


POD


UpdatedPf


9

Updating method

Kmat

�Kth

FM

sY

sU �s

a0,c0 SIF SCF

Limit State Function Pf

UpdatingPf

POD

Decisions

Yeter, B., Garbatov, Y., and Soares, C. G.,2015. “Fatigue Reliability of an Offshore WindTurbine Supporting Structure Accounting for

Inspection and Repair”.

Crack Growth SimulationUpdated

Pf


9

Updating method

Kmat

�Kth

FM

sY

sU �s

a0,c0 SIF SCF


POD


UpdatedPf


10Crack Growth Simulation

Crack depth a and crack length 2c are coupled during thesimulation.

8><

>:

da

dN= C

a

(�Ka

)m �Ka

��Kth

dc

dN= C

c

(�Kc

)m �Kc

��Kth

(1)

�Ka

= SYa

ppa (2)

�Kc

= SYc

ppa (3)


11Crack Growth Simulation

Life time

Sem

icrack

lengthC

Cd

i

Inspection i

Figure: Crack growth in combination with inspections


12Outline



Results


13

ResultsCrack Propagation

Year0 2 4 6 8 10 12 14 16 18 20

Cra

ck d

epth

[mm

]

0

1

2

3

4

5

6

7

8

9

Figure: Crack propagation


14

ResultsNo Crack Detected

Year0 2 4 6 8 10 12 14 16 18 20

Prob

abilit

y#10-3

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5Annual Failure Probability

No crack detectedNo inspection

Figure: Annual POF


15

ResultsCrack Detected & Repaired

Year0 2 4 6 8 10 12 14 16 18 20

Prob

abilit

y#10-3

0

0.5

1

1.5

2

2.5

3

3.5Annual Failure Probability

Normal RepairPerfect Repair

Figure: Annual POF


16

Summary

Fatigue Assessment Diagram can be used to update the failure

probability of an existing OWT substructure when new informa-

tion about either loading, structural responses or inspections isavailable.

I OutlookI Reduction of uncertainty related to stress-ranges given new

information about loading and structural responseI Improved modelling of crack growth after reaching the wall

thickness.


17

Acknowledgement

This research is funded by the National Fund for Scientific Researchin Belgium — F.R.I.A - F.N.R.S.

About me:Quang MAI

University of Liège, [email protected]


mailto:[email protected]

updating failure probability - uliege · 3 message objective fatigue assessment diagram can be used...

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