UPDATING FAILURE PROBABILITY OF A WELDED JOINT IN OWT SUBSTRUCTURES Q. Mai 1 J.D. Sørensen 2 P. Rigo 1 1 Department of ArGEnCo University of Liege 2 Department of Civil Engineering Aalborg University OMAE Conference - Busan, 2016
Motivation 2 Update Pf Limit State Reduce RBI (insp.) O&M Costs Function Q. Mai | FAD in Updating Failure Probability
Message Objective 3 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 is available. Q. Mai | FAD in Updating Failure Probability
Outline 4 Fatigue Assessment Diagram Updating Probability of Failure Results Q. Mai | FAD in Updating Failure Probability
Outline 5 Fatigue Assessment Diagram Updating Probability of Failure Results Q. Mai | FAD in Updating Failure Probability
Fatigue Assessment Diagram 6 1 0.8 0.6 Kr 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Lr 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).
Fatigue Assessment Diagram 6 1 0.8 0.6 Kr 0.4 L r , max = σ Y + σ U 0.2 2 σ Y 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Lr 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).
Fatigue Assessment Diagram 6 1 0.8 ✓ K I ◆ 0.6 L r = σ ref ; K r = K mat Kr σ Y 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Lr 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).
Fatigue Assessment Diagram 6 1 0.8 ✓ K I ◆ 0.6 L r = σ ref ; K r = K mat Kr σ Y 0.4 0.2 Safe 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Lr 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).
Fatigue Assessment Diagram 6 1 Unsafe 0.8 ✓ K I ◆ 0.6 L r = σ ref ; K r = K mat Kr σ Y 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Lr 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
Outline 7 Fatigue Assessment Diagram Updating Probability of Failure Results Q. Mai | FAD in Updating Failure Probability
Uncertainties 8 Variable Distr. Mean CoV Variable Value S Stress range [ MPa ] W k=0.8 N ( µ , σ ) Yield strength [ MPa ] LN 368.75 0.07 σ Y 1 × 10 7 No. of cycle/year ν Ultimate strength [ MPa ] LN 750 0.04 σ U t Steel thickness [mm] 65 ∆ K th SIF range threshold LN 160 0.4 R Outer radius [mm] 79.5 K mat Fracture toughness 3p W - - L Joint length [mm] 100 Paris law, 1 st line 4 . 8 × 10 − 18 C 1 LN 1 . 7 Bend. to memb. ratio 0.81 η σ Paris law, 2 nd line C 2 LN 5 . 86 × 10 − 13 0.6 ∆ K tr Transition SIF range 196 a 0 Initial crack depth LN 0.15 0.66 Paris law, 1 st line m 1 5.10 a 0 / c 0 Initial aspect ratio LN 0.6 0.40 Paris law, 2 nd line m 2 2.88 B scf Uncertainty in SCF LN 1 0.05 C a / C c C ratio for a and c 0.9 Uncertainty in SIF LN 1 0.05 B sif Q. Mai | FAD in Updating Failure Probability
Updating method 9 Uncertainties
Updating method 9 a 0 , c 0 SIF SCF σ Y σ U ∆ σ K mat ∆ K th FM
Updating method 9 a 0 , c 0 SIF SCF σ Y σ U ∆ σ Limit State Function Pf K mat ∆ K th FM POD Yeter, B., Garbatov, Y., and Soares, C. G., Updating 2015. “Fatigue Reliability of an O ff shore Wind Turbine Supporting Structure Accounting for Pf Inspection and Repair”. Decisions
Updating method 9 a 0 , c 0 SIF SCF σ Y σ U ∆ σ Limit State Function K mat ∆ K th FM POD Crack Growth Simulation Decisions
Updating method 9 a 0 , c 0 SIF SCF σ Y σ U ∆ σ Limit State Function K mat ∆ K th FM POD Updated Crack Growth Simulation Pf Decisions Q. Mai | FAD in Updating Failure Probability
Crack Growth Simulation 10 Crack depth a and crack length 2 c are coupled during the simulation. 8 da dN = C a ( ∆ K a ) m ∆ K a ≥ ∆ K th > < (1) dc dN = C c ( ∆ K c ) m ∆ K c ≥ ∆ K th > : √ π a ∆ K a = SY a (2) √ π a ∆ K c = SY c (3) Q. Mai | FAD in Updating Failure Probability
Crack Growth Simulation 11 Semi crack length C Life time Figure: Crack growth in combination with inspections
Crack Growth Simulation 11 Semi crack length C C d i Inspection i Life time Figure: Crack growth in combination with inspections
Crack Growth Simulation 11 Semi crack length C C d i Inspection i Life time Figure: Crack growth in combination with inspections Q. Mai | FAD in Updating Failure Probability
Outline 12 Fatigue Assessment Diagram Updating Probability of Failure Results Q. Mai | FAD in Updating Failure Probability
Results Crack Propagation 13 9 8 7 Crack depth [mm] 6 5 4 3 2 1 0 0 2 4 6 8 10 12 14 16 18 20 Year Figure: Crack propagation Q. Mai | FAD in Updating Failure Probability
Results No Crack Detected 14 # 10 -3 Annual Failure Probability 5 No crack detected 4.5 No inspection 4 3.5 Probability 3 2.5 2 1.5 1 0.5 0 0 2 4 6 8 10 12 14 16 18 20 Year Figure: Annual POF Q. Mai | FAD in Updating Failure Probability
Results Crack Detected & Repaired 15 # 10 -3 Annual Failure Probability 3.5 Normal Repair Perfect Repair 3 2.5 Probability 2 1.5 1 0.5 0 0 2 4 6 8 10 12 14 16 18 20 Year Figure: Annual POF Q. Mai | FAD in Updating Failure Probability
Summary 16 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 is available. I Outlook I Reduction of uncertainty related to stress-ranges given new information about loading and structural response I Improved modelling of crack growth after reaching the wall thickness. Q. Mai | FAD in Updating Failure Probability
Acknowledgement 17 This research is funded by the National Fund for Scientific Research in Belgium — F.R.I.A - F.N.R.S. About me: Quang MAI University of Liège, Belgium aq.mai@ulg.ac.be Q. Mai | FAD in Updating Failure Probability
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