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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.
Q. Mai | FAD in Updating Failure Probability
4Outline
Fatigue Assessment Diagram
Updating Probability of Failure
Results
Q. Mai | FAD in Updating Failure Probability
5Outline
Fatigue Assessment Diagram
Updating Probability of Failure
Results
Q. Mai | FAD in Updating Failure Probability
6
Fatigue Assessment Diagram
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).
Q. Mai | FAD in Updating Failure Probability
6
Fatigue Assessment Diagram
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
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).
Q. Mai | FAD in Updating Failure Probability
6
Fatigue Assessment Diagram
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).
Q. Mai | FAD in Updating Failure Probability
6
Fatigue Assessment Diagram
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
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).
Q. Mai | FAD in Updating Failure Probability
6
Fatigue Assessment Diagram
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).
Q. Mai | FAD in Updating Failure Probability
7Outline
Fatigue Assessment Diagram
Updating Probability of Failure
Results
Q. Mai | FAD in Updating Failure Probability
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
Q. Mai | FAD in Updating Failure Probability
9
Updating method
Uncertainties
Kmat
�Kth
FM
sY
sU �s
a0,c0 SIF SCF
Limit State Function
POD
DecisionsCrack Growth Simulation
UpdatedPf
Q. Mai | FAD in Updating Failure Probability
9
Updating method
Kmat
�Kth
FM
sY
sU �s
a0,c0 SIF SCF
Limit State Function
POD
DecisionsCrack Growth Simulation
UpdatedPf
Q. Mai | FAD in Updating Failure Probability
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
Q. Mai | FAD in Updating Failure Probability
9
Updating method
Kmat
�Kth
FM
sY
sU �s
a0,c0 SIF SCF
Limit State Function
POD
DecisionsCrack Growth Simulation
UpdatedPf
Q. Mai | FAD in Updating Failure Probability
9
Updating method
Kmat
�Kth
FM
sY
sU �s
a0,c0 SIF SCF
Limit State Function
POD
DecisionsCrack Growth Simulation
UpdatedPf
Q. Mai | FAD in Updating Failure Probability
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)
Q. Mai | FAD in Updating Failure Probability
11Crack Growth Simulation
Life time
Sem
icrack
lengthC
Cd
i
Inspection i
Figure: Crack growth in combination with inspections
Q. Mai | FAD in Updating Failure Probability
11Crack Growth Simulation
Life time
Sem
icrack
lengthC
Cd
i
Inspection i
Figure: Crack growth in combination with inspections
Q. Mai | FAD in Updating Failure Probability
11Crack Growth Simulation
Life time
Sem
icrack
lengthC
Cd
i
Inspection i
Figure: Crack growth in combination with inspections
Q. Mai | FAD in Updating Failure Probability
12Outline
Fatigue Assessment Diagram
Updating Probability of Failure
Results
Q. Mai | FAD in Updating Failure Probability
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
Q. Mai | FAD in Updating Failure Probability
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
Q. Mai | FAD in Updating Failure Probability
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
Q. Mai | FAD in Updating Failure Probability
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.
Q. Mai | FAD in Updating Failure Probability
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, Belgiumaq.mai@ulg.ac.be
Q. Mai | FAD in Updating Failure Probability
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