fatigue of offshore structures: applications and research issues

Fatigue of Offshore Structures:Applications and Research Issues

Steve Wintersteinstevewinterstein@alum.mit.edu

Fatigue Under Random LoadsMean Damage Rate:

where S = stress range; c and m material properties Welded steels: m = 2 - 4; Composites: m = 6 - 12

Fatigue Under Random LoadsMean Damage Rate:

where S = stress range; c and m material properties Welded steels: m = 2 - 4; Composites: m = 6 - 12

Fatigue Under Random LoadsMean Damage Rate:

where S = stress range; c and m material properties Welded steels: m = 2 - 4; Composites: m = 6 - 12

Assumes:Stresses Gaussian, narrow-band

Fatigue Under Random LoadsMean Damage Rate:

where S = stress range; c and m material properties Welded steels: m = 2 - 4; Composites: m = 6 - 12

Assumes:Stresses Gaussian, narrow-band

Common errors: Assume Gaussian, narrow-band

Bandwidth & Non-Gaussian EffectsDamage Rate: E[DT] = CBW * CNG * E[DT | Rayleigh]

CBW, CNG = corrections for bandwidth, non-Gaussian effects

Bandwidth & Non-Gaussian EffectsDamage Rate: E[DT] = CBW * CNG * E[DT | Rayleigh]

CBW, CNG = corrections for bandwidth, non-Gaussian effects

Bandwidth Corrections:• Unimodal spectra: Wirsching (1980s)• Bimodal spectra: Jiao and Moan (1990s)• Arbitrary spectra: Simulation (2000s: becoming cheaper)

Bandwidth & Non-Gaussian EffectsDamage Rate: E[DT] = CBW * CNG * E[DT | Rayleigh]

CBW, CNG = corrections for bandwidth, non-Gaussian effects

Bandwidth Corrections:• Unimodal spectra: Wirsching (1980s)• Bimodal spectra: Jiao and Moan (1990s)• Arbitrary spectra: Simulation (2000s: becoming cheaper)• Typically: CBW < 1

Bandwidth & Non-Gaussian EffectsDamage Rate: E[DT] = CBW * CNG * E[DT | Rayleigh]

CBW, CNG = corrections for bandwidth, non-Gaussian effects

Bandwidth Corrections:• Unimodal spectra: Wirsching (1980s)• Bimodal spectra: Jiao and Moan (1990s)• Arbitrary spectra: Simulation (2000s: becoming cheaper)• Typically: CBW < 1

Non-Gaussian Corrections:• Nonlinear transfer functions from hydrodynamics• Moment-based models (Hermite) & simulation or closed-form estimates of CNG

Bandwidth & Non-Gaussian EffectsDamage Rate: E[DT] = CBW * CNG * E[DT | Rayleigh]

CBW, CNG = corrections for bandwidth, non-Gaussian effects

Bandwidth Corrections:• Unimodal spectra: Wirsching (1980s)• Bimodal spectra: Jiao and Moan (1990s)• Arbitrary spectra: Simulation (2000s: becoming cheaper)• Typically: CBW < 1

Non-Gaussian Corrections:• Nonlinear transfer functions from hydrodynamics• Moment-based models (Hermite) & simulation or closed-form estimates of CNG

• Typically: CNG > 1

Can We Even Predict RMS stresses?

Container Ships: Yes (Without Springing)

Can We Even Predict RMS stresses?

Container Ships: Yes (Without Springing)

TLP Tendons: Yes (With Springing)

Can We Even Predict RMS stresses?

Container Ships: Yes (Without Springing)

TLP Tendons: Yes (With Springing)

VIV of Risers: No

Can We Even Predict RMS stresses?

Container Ships: Yes (Without Springing)

TLP Tendons: Yes (With Springing)

VIV of Risers: No

FPSOs: ??

Ship Fatigue: Theory vs Data

Observed Damage (horizontal scale): predicted from measured strains by inferring stresses, fatigue damage. Predicted Damage (vertical scale): linear model based on observed HS

Ref: W. Mao et al, “The Effect of Whipping/Springing on Fatigue Damage and Extreme Response of Ship Structures,” Paper 20124, OMAE 2010, Shanghai.

TLP Tendon Fatigue: 1st-order vs Combined Loads

Water Depth: 300m

One of earliest TLPs (installed 1992)

Ref: “Volterra Models of Ocean Structures: Extremes and Fatigue Reliability,” J.Eng.Mech.,1994

TLP Tendon Fatigue: 1st-order vs Combined Loads

Damage contributionof various Tp

Large damage at Tp = 7s due tofrequency of seastates

Large damage at Tp = 12s due togeometry of platform

Larger non-Gauss effects if TPITCH = 3.5s(resonance when Tp = 7s)

Ref: “Volterra Models of Ocean Structures: Extremes and Fatigue Reliability,” J.Eng.Mech.,1994

VIV: Theory (Shear7) vs Data

Ref: M. Tognarelli et al, “Reliability-Based Factors of Safety for VIV Fatigue Using Field Measurements,” Paper 21001, OMAE 2010, Shanghai.

VIV Factor:

m=3.3,s=1.4

Median:a50=27

LRFD Fatigue Design

LRFD Fatigue Design

LRFD Fatigue Design

LRFD Fatigue Design

Finally: Combined Damage on an FPSO

•High-cycle (low amplitude) loads due to waves… DFAST

•Low-cycle (high amplitude) loads due to other source (e.g., FPSO loading/unloading) -->

DSLOW

•How to combine DFAST and DSLOW?

SRSS: Largest safe region; least conservative

Proposed Combination “Rules”DTOT = [ DSLOW K + DFAST K ] 1/K

•K = 1/m Lotsberg (2005): Effectively adds stress amplitudes

•K= 2/m: Random vibration approach; adds variances

•K = 1: “Linear” damage accumulation

•K = 2: SRSS applied to damage (not rms levels)

Notes: Less conservative rule as K increases; m = S-N slope: Damage = c Sm; D1/m = c’ S

Combined Fatigue:

DNV Approach

Merci beaucoup!

Extra background slides follow…

The Snorre Tension-Leg Platform

Water depth: 300m

One of earliest TLPs (installed 1992)

How important are TN=2.5s cycles?• Important when TWAVE = 2.5s … but this condition has small wave heights

• Important when TWAVE = 5.0s … due to second-order nonlinearity (springing)

• Non-Gaussian effects when TWAVE = 5.0s:

Answer: The Fatiguing

Bookkeeping

Likelihood ofvarious (Hs,Tp)

Answer: The Fatiguing

Bookkeeping

Likelihood ofvarious (Hs,Tp)

Damage contributionof various (Hs,Tp)

Answer: The Fatiguing

Bookkeeping

Likelihood ofvarious (Hs,Tp)

Damage contributionof various Tp

Results:

Damage contributionof various Tp

Large damage at Tp = 7s due tofrequency of seastates

Large damage at Tp = 12s due togeometry of platform

Larger non-Gauss effects if TPITCH = 3.5s(resonance when Tp = 7s)