083 moan structural reliability
TRANSCRIPT
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T.Moan MARE WINT Sept.20131
Structural reliability and risk analysis
of «offshore structures»By Torgeir Moan, CeSOS and Department of Marine Technology, NTNU
T.Moan MARE WINT Sept.20132
List of content Introduction
- Facilities
- Regulatory framework
- Accident/failure experiences
- Safety Management
Structural Reliability Analysis- Introduction
- Estimation of failure probability of components
- Uncertainties in Load effect (S) and Resistance (R)
- System reliability- Time variant Reliability
- Summary of Reliability methods
- Practical use of Structural Reliability Analysis
- Guidelines for Reliability Analysis
Reliability -base-Calibration of codes for new applications
- Relation between prob. Of failure and safert factors
- Reliability based Calibration of safety factors
Fatigue reliability
- Background
- Fatigue life models (based on SN- and Fracture Mechanics)
- Reliability updating approaches
T.Moan MARE WINT Sept.20133
List of content - continued
Fatigue reliability - continued- Inspection scheduling
- Calibration of fatigue design criteria
- Fatigue reliability of gear components
Quantitative r isk assessment- Risk Analysis Framework
- Internal and external hazards
- ALS design check
- Ship Collision risk
- Accidental Actions on wind turbines
T.Moan MARE WINT Sept.20134Wind turbines vs other marine structures
Facilities for wind vs oil and gas technology
• Number of units – one of
a kind versus mass
production.
• Safety issues:
No hydro carbons and
people on board wind
turbines
• The wind energy sector is
a “ marginal business”
• Return are more sensitiveto IMMR (O&M) costs
(access)
Integrating
knowledge
4Introduction
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Regulatory framework - general
5
to avoid:
• Fatalities or injury
• Environmental damage
• Property damage
Regulatory regime (depends on economy; accident potential):
Regulatory principles
- Goal-setting viz. prescriptive
- Probabilistic viz. deterministic
- First principles viz.
purely experientialOverall stabilit y Strength Escapeways/lifeboats
Offshore oil and gas Wind turbines
- National regulatory
bodies;
- Industry: API, NORSOK,
- Classification soc.
- ISO/IMO
- National Regulatory
bodies
- Classification societies ??
- IEC
Introduction
T.Moan MARE WINT Sept.20136
Introduction
Experiences
Oil and gas platforms- significance of the oil and gas industry to the world econmy
- need for technology development for deeper water, challenging
natural and industrial environment,…
- ageing facilities
Wind turbines
CeSOS NTNU
Gathering of experiences – development of procedures/methods/data
Failure - and accident data
Safety management procedure- safety criteria, (limit states) – including accidental limit state
- risk and reliability analysis of design, inspection/monitoring
Methods (hydrodynamics, structural analysis)
Data (strength data for tubular joints)
5
T.Moan MARE WINT Sept.20137
A Case of structural fai lure - due to ” natural hazards” ?
Severe damage caused by
hurricane Lilli in the Gulf of
Mexico
Technical-physical causes:Observation: Wave forces exceeded the
structural resistance
Human – organizational factors:
Design
- Inadequate wave conditions or load calculation
or strength formulation or safety factors
Fabrication deficiencies
due to
- inadequate state of art in offshore
engineeringor,
- errors and omission during
design or fabrication!
CeSOS NTNU
6Introduction
T.Moan MARE WINT Sept.20138
a) Alexander L. Kielland – fatigue
failure, progressive failure and
capsizing, North Sea, 1980
c) Piper Alpha fire and explosion,
NorthSea, 1988
b) Ocean Ranger, flooding and capsizing,
New Foundland, 1982.
(Model during survival testing)
d) P - 36 explosion, flooding and
capsizing, Brazil, 2001
Lessons learnt from total losses of platformsIntroduction
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0
2
4
6
8
10
12
14
16
18
20
B l o w o u t
C o l i s i o n / c o n t a c t
D r o p p e d o b j e c t
E x p l o s i o n F i r e
G r o u n d i n g
S p i l l / r e l e a s e
S t r u c t u r a l d a m a g e
C a p s i z e / f o u n d e r i n g / l i s t
Mobile
Fixed
(World wide in the period 1980-95, Source: WOAD 1996)
Accident experiences for mobi le drill ing and
fixed production platforms(Number of accidents per 1000 platform years)
Operational errors
Design or
Fabricationerrors
CeSOS NTNU
7Introduction
T.Moan MARE WINT Sept.201310
In-service experiences with cracks infixed offshore platforms (See Vårdal, Moan et al, 1997...)
Data basis
- 30 North Sea platforms, with a service time of 5 to 25 years
- 3411 inspections on jackets
- 690 observations of cracks
The predicted frequency of crack occurrence was found
to be 3 times larger than the observed frequency; i.e.
conservative prediction methods
On the other hand:
- Cracks which are not predicted, do occur.
Hence, 13 % of observed fatigue cracks occurred in jointswith characteristic fatigue life exceeding 800 years; due to
- abnormal fabrication defects
(initial crack size ≥ 0.1 mm !)
- inadequate inspection
CeSOS NTNU
8Introduction
T.Moan MARE WINT Sept.201311
Failure Rates and Down Times of Wind Turbines
Availability- 96 - 98 % on land
- 80 % for early wind
farms offshore
-Need for robust design,(reliable and few
components) &
smart maintenance,
but also improved
accessibility
- Larger turbine size?
( > 5 - 20 MW)
Courtesy:
Fraunhofer
- Predict,
monitor and
measure degradation
(Courtesy: Fraunhofer)
Introduction
T.Moan MARE WINT Sept.201312
Risk Control Measures
Cause of failure Safety measure
Inadequate design check to
account for normal variability
−Increase safety factors or use
lower Rc and higher Sc
Human error and omission
─ Design
─ Fabrication
─ Operation
Unknown phenomena
In general:
-improve the quality of the initial job.-implement proper QA/QC
−possible ALS design check
− ALS design check
R&D
Introduction
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Safety management (ISO 2394, ISO19900, etc)
ULS
FLS: D = Σni/Ni ≤ Dallowable ALS
• Measures to maintain acceptable risk
- Life Cycle Approach
design, fabrication and operational criteria
- QA/QC of engineering design process
- QA/QC of the as-fabricated structure
- QA/QC during operation
(structural inspection )
- Event control of accidental events
- Evacuation and Escape
CeSOS NTNU
n ro uc on
T.Moan MARE WINT Sept.201314
Safety with respect to- Fatalities
- Environmental damage
- Property damage
Floatability / stability
Structural strength of the hull
Strength of (possible)mooring system
Escapeways and
lifeboatstationes etc for evacuation
Regulatory requirements:
- National Regulatory bodies;
(MMS, HSE, NPD
- Industry : API, NORSOK,…
- Class societies/IACS
- IMO/ISO/(CEN)
OR
model
tests
Introduction
T.Moan MARE WINT Sept.201315
Safety cri teria for design and reassessment(with focus o n structural failure modes) ISO
Limit states Physical appearance
of failure mode
Remarks
Ultimate (ULS)
- Ultimate strength of
structure, mooring or
possible foundation
Component design check
Fatigue (FLS)
- Failure of welded joints
due to repetitive loads
Component design check
depending on residual
system strength and
access for inspection
Accidental co llapse ( ALS)
- Ultimate capacity1) of
damaged structure with
“credible” damage
Platethick-
ness
Collapsed
cylinder
Jack-up collapsed
Fatigue
crack
CeSOS NTNU
10Introduction
T.Moan MARE WINT Sept.201316
Accidental Col lapse Limit State for
Structures (NPD, 1984)
• Estimate the damage due to accidental loads (A) at
an annual exceedance probability of 10-4
- and likely fabrication errors
• Check survival of the structure with damage
under functional (F) and environmental loads (E) -
at an annual exceedance probability of 10-2.
• Load & resistance factors equal to 1.0E
P,F
P,F
A
CeSOS NTNU
11Introduction
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Ocean
environment
Analysis for demonstrating compliance with
design criteriaFunctional loads
- dead loads
- -pay loads
Accidental
loads
Piper Alpha
Responseanalysis- dynamic v.s.quasi-static/quasi-dynamic
Sea loads
Designcriteria
Loadeffects
Collapseresistance
SN-curve/fracturemechanics
Ultimate
globalresistance
Extreme
moment (M)andaxialforce (N)
Localstressrangehistory
Extremeglobalforce
Designcheck
ULS:
FLS:
ALS :
Damaged
structure
Analysis of damage
Industrial
and
Operational
Conditions
CeSOS NTNU
Defined probability level
12Introduction
T.Moan MARE WINT Sept.201318
Risk and reliability assessment
Definition• Reliability:
Probability of a component/system to perform a required function
• Risk:
Expected loss (probability times consequences)Recognised in the oil and gas industry
- calibration of LFRD design approaches (1970s, 1980s)
- RBI (Risk/Reliability Based Inspection)
(methods in 1980s-; industry adoption in 1990s-)
rational mechanics methods for design of structures, foundations loads and resistances are subjected to uncertainties
- normal variability and uncertainty; gross errors
design is decision under uncertainty :
- rational treatment of uncertainty (range, mean+st.dev. etc)- implying probabilistic methods
especially in connection with new technology, no standards
CeSOS NTNU
ALARP
principle
13Introduction
T.Moan MARE WINT Sept.201319
Estimation of Failure Probability of components A s imple example: The probability of failure , Pf , for
a time-invariant reliability problem, is
- R is the resistance
- S is the loading
The main issues in the following will be to
- describe the R and S as random variables- derive the expression for the Pf and generalise it for more
complex problems
Notional
probaility,
not true, actuarial
[ ] [ ]
[ ] ( )f
P P R S 0 P ln R lnS 0
.... P R ' S' 0 '
= − ≤ = − ≤ =
= − ≤ = Φ −β
22
ln
2121ln
21
21ln
S R
S
R
S R
R
S
S
R
V V V V
V
V
≈
⎟
⎠
⎞
⎜
⎝
⎛
⎠
⎞
⎜
⎝
⎛
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
⋅
=
μ
μ
μ
μ
β
where Φ ( ) is the standard normal density function
φ(u)
( ) ( )u
u t dtφ
−∞
Φ = ∫
T.Moan MARE WINT Sept.201320
β Pf Pf β
1
2
2.5
3
3.5
4
4.5
5
5.5
6
1.59 ·10-1
2.27·10-2
6.21·10-3
1.35·10-3
2.33·10-4
3.17·10-5
3.40 ·10-6
2.90 ·10-7
1.90·10-8
1.00·10-9
10-1
10-2
10-3
10-4
10-5
10-6
10-7
10-8
10-9
10-10
1.29
2.32
3.09
3.72
4.27
4.75
5.20
5.61
6.00
6.36
Relation between Pf and β
1.2 1.4( ) 10 β β −Φ − ≈= f P A rough approximation:
Estimation of Failure Probability
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General methods to determine PfThe probability of failure , Pf , for
a time-invariant reliability problem, is
( ) ( )
( ) 0
0 ( )
≤
⎡ ⎤= ≤ = = Φ −⎣ ⎦ ∫∫ f g
P P g f d β x
x
x x x
- g(x) is the limit state function, i.e. g(x) = R - S
- X is the set of n random variables
- f x(x) in the joint probability density of the vector X.
- Pf is determined by calculating the integral byMC simulation or FORM/SORM methods
(Avoid FOSM methods etc)
Main issue: Modelling load effects and
resistance in terms of: f x(x)
Notional
probaility,
not true, actuarial
Estimation of Failure Probability
T.Moan MARE WINT Sept.201322
General formulation for two variables An approach which represents a first step towards a general formulation can be based on
Volume: f RS(r,s)drds is per definition the
probability that s and r lies in the interval
(s, s+ds) and (r, r+dr), respectively
Formulation of failure probability , which can be generalized
NOTE:
The probability density function for independent variables is )()( s f r f S R
⋅
Estimation of Failure Probability
T.Moan MARE WINT Sept.201323
FORM/ SORM
Instead of integrating the probability density in the domain of physical variable
R and S, the integral may be transformed into a domain of independentstandard normal variables, u1 and u2. This is done here for the simpleproblem where
Transformation of variables
Transformtion of failure function
1
2
R
R
S
S
RU
S U
μ
σ
μ
σ
− ⎫= ⎪⎪⎬
− ⎪=⎪⎭
[ ] [ ] [ ]P P R S P R S 0 P M 0f = ≤ = − ≤ = ≤
( )2, R R R N μ σ = ( )2,S S S N μ σ =
'
1 2( ) ( ) R R S S M R S U U σ μ σ μ = − = + − +
1
( ) ( )
( ( ))−
Φ =
= Φ x
x
u F x
x F u
In general transformation of (independent variables)
x into variables u is :
Estimation of Failure Probability
T.Moan MARE WINT Sept.201324
( )d cfr. previous definitionμ − μ
= → βσ + σ
R S
2 2
R S
1 2' '
'
1 2 1 2 1 2 1 2
( 0) ( 0)
0 ( ) ( ). ( ) ( ) f U U M M
P P M f u u du du u u du duφ φ β ≤ ≤
⎡ ⎤= ≤ = = = Φ −
⎣ ⎦ ∫∫ ∫∫
Distance d:
Failure p robability
The same answer as before.
The advantage of this method is when multiple variables are needed.
R,S space U-space
Estimation of Failure Probability
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Monte Carlo simulation
Instead of using integration, the failure probability may be determined by
using Monte Carlo simulation and interpreting probability as relative
frequency.
This approach is described in the following for the simple case specified by:
with independent variables R and S given by probability density function f R(r)
and f S(s), respectively.
pf may be determined as follows:
1) Generate n sample of pair (R,S) from f R(r) and f S(s), respectively
[ ]0= ≤
= − f p P M
R S
( )
( )
( )
( )
1 1
2 2
3 3
n n
ˆ ˆ r , s
ˆ ˆ r , s
ˆ ˆ r , s
ˆ ˆ r , s
Estimation of Failure Probability
T.Moan MARE WINT Sept.201326
Samples for a variable X with a distribution function FX(x) or
a density f X(x) may be generated by , where pi is a
sample of a variable which is uniformly distributed in the interval
[0,1]. can then be obtained by using tables of random number
or standard subroutines in computers.
2) Determine for all pairs.
3) Determine no. of cases (k) where - which correspond to failure.
Then
This estimate is accurate for large n. to determine a pf of (10-4-10-6)requires an n of the order (10-5-10-7)
{ }iˆ x( )1−=i X iˆ ˆ x F v
iˆ v
= −i i iˆ ˆ ˆ r s
0
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System reliability System failure may imply fatalities
A system may
- fail due to overload or fatigue failures (at
multiple crack initiation sites), but may have- reserve capacity beyond first component
failure
Simplified system model for frame type
structures:
Pf,SYS = P[FSYS]
= P[FSYS(U)] + Σ P[FSYS(U)| Fi] P [Fi]
- P [Fi] probability of fatigue failure
- P[FSYS(U)|Fi] conditional probability of ultimate failure
[ ] ( )( )(...)1 1
0= =
⎡ ⎤= = ≤⎢ ⎥
⎣ ⎦∪∩ j N k
FSYS i
i j
P P FSYS P g
P[FSYS(U)]=P[Rsys - Ssys 0)]
Estimation of Failure Probability
T.Moan MARE WINT Sept.201330
Illustration of calculation of failure probability for a time-
variant load and resistance
Estimation of Failure Probability
T.Moan MARE WINT Sept.201331
Failure probability in time period, T:
Example:
Wave loads (due to inertia forces) in North Sea:
(ratio of loads prop. to ratio
of wave heights)
VS = 0.30 for both cases (incl. statistical + model uncertainty)
Resistance
μR = 100, VR = 0.10
For lognormal variables
[ ]= ≤ max f P P R S
( ) )100(8.01 maxmax yearsS year S ⋅≈
)100(8.0
)1( yearsSmax year Smaxμ μ
⋅
μ s yearsmax( )100 50= 40)1max( = year sμ
( ) β ′−Φ= f P ln
22
S R
S
R
V V +≈′
μ β
18.2)100( =′ years β 246.1100: E years P f
89.2)1( =′ year β 393.11: E year P f
7~3
1093.1
21046.1
)1(
)100(
⋅
⋅
=
year P
years P
f
f
What is the probability of
failure in 20 years compared
to the failure prob. in 1 year ?
T.Moan MARE WINT Sept.201332
Structural Reliabili ty Analysis Procedure- Aim: Estimate Pf
- Formulate the reliability problem (time invariant problems)
- Define failure function: g( ) ≤ 0
- Define properties of random variables xi
(type of distribution, mean value, st. dev.)
- Calculate
- Failure probability, Pf (reliability index, β)
by appropriate method (FORM/SORM,
Monte Carlo simulation)
- Sensitivity of Pf (β) to parameter, θ
- Time variant reliability
- Systems reliability
- Uncertainty modelling
- random variables
- stochastic process
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Uncertainties in Load effects (S) and Resistance
(R): Classification of uncertainties according to
their “nature”
Normal Uncertainties or, Variability
─ Fundamental (natural) Variability
Example - Wave elevation/
- Loading/
- Load effects
─ Lack of Knowledge
e.g. - model uncertainty
- statistical uncertainty (due to limited data)
⇓
Wave
elevation
(loads) time
T.Moan MARE WINT Sept.201334
Characterisation of a random variable, X
- Mean, μx
- ; or
- probability density function (f X(x) /distribution (FX(x))
Fundamental uncertainty in wave elevation and corresponding wave-induced loads and load effects by stochastic methods
Model uncertainty, X of a method:
Estimate by obtaining a sample of:
─ Predicted value (for a given set of parameters: PV
─ True value (e.g. based on obs. or accurate analyses): TV
Model uncertainty for observation i:
Xi = TVi/PViEstablish statistics for X by a sample {Xi}n
NOTES:
- Gross Errors are not considered in SRA as such
- Unknown phenomena that can cause failures, cannot be treated with
probabilistic methods simply because they are unknown !
x
xCOV μ
σ =
ValueMean
Dev. Stand.
T.Moan MARE WINT Sept.201335
Uncertainties according to their
physical source – associated with wave loads
- wave height, period, current velocity
(including variability, limited amount of data, etc.)
- wave theory
- drag and mass coefficient
Wave height: H100(100 year wave height)
Mean uncertainty ~ 1.0
Wave load model based on regular wave – relating to API/ISO
Mean uncertainty ~ 0.9 - 1.1 (1.0)
COV ~ 0.25 - 0.35
Total uncertainty may be estimated by:
F = ψ .c’.Hα
where ψ is the model uncertainty and the uncertainty in wave
height is represented by H.
⎩⎨⎧
−
−==
GoM
Sea NorthCOV
H
H
20.015.0
15.010.0
μ
σ
T.Moan MARE WINT Sept.201336
Estimation of uncertainties of extreme loads on jackets
(simplified approach)
Design Wave Approach
• Kinematics : Stokes 5th order theory
particle velocity particle acceleration
• Wave loading
API (ISO) procedure will be referred to here
18m
→ F
c=18 m
H=30m
70m
1F C v v C D aD M2 4
c H (approximation by regression fit)
π= ×ρ × × + × × ×
α≈ ×
2
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Estimate of uncertainty in the global wave load on jackets
– base shear force of the Magnus and Tern jackets:
i) predicted(F
)measured(iF
μ
σ
Model uncertainty =
Mean = 1.06
COV = ≡ 25%
The Magnus platform
CeSOS NTNU
Keulegan-Carpenter number
ISO 19900load analysis procedure
21
T.Moan MARE WINT Sept.201338
Modelling of uncertainty in ult imate strength of beam-column
X A - parameter uncertainty in cross-section area
Xfy - parameter uncertainty in yield strength f YXR- model uncertainty = Rtrue/Rpred:
Mean :
CoV :
Model uncertainty of ECCS method for strength of tubular columns
N N
fy A Rc pred
ynom
y
nom
Rnom ynom
pred y
u
R y
pred y
u
uu
X X X R
f
f
A
A X A f
f
f A X f
f
f A f N R
⋅
⎟
⎠
⎞
⎜
⎝
⎛
⎟
⎠
⎞
⎜
⎝
⎛
⋅
⎟
⎠
⎞
⎜
⎝
⎛
=
⎟
⎠
⎞
⎜
⎝
⎛
=
)(
R X1.00+0.10 for 0 2.0μ = λ < λ ≤
⎩
<
≤
=
0.26.0 for 08.0
6.0 for 05.0
λ λ
λ R X
V
Slenderness, λ
u
y pred
f
f
⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠
T.Moan MARE WINT Sept.201339 T.Moan MARE WINT Sept.201340
0
2
4
6
0 2 4 60
2
4
6
0 2 4 6
β LN
β M
β LN
β M
cov (S) cov (S)
0.2
0.4
0.2
0.4
cov (R) = 0.1, cov (S)-variable cov (R) = 0.2, cov (S)-variable
β LN : lognormal R and S β M : R lognormal and S lognormal
Tail sensitivity
(not analytical !)
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Relation between reliability measure, (Pf ) and
Safety Factors (γR , γS ) in ULS design check
( )2 2
1 .2 1 .4
2 2
ln
ln /( )
....... ( ) ( ) 10 ;
β
μ μ
β
−
≈ Φ −⎡ ⎤⎣ ⎦+
= Φ − = Φ − ≈+
= ≤ R S f R S
R R S S
R S
(B γ γ /B )
V V
V V
P P R S
Resistance R
Load effect S
- Rc ; Sc - characteristic resistance and load effect
- γR ; γS - partial safety factors
Reliability analysis:
R and S modelled as random variables;
e.g. by lognormal distributions
Semi-probabilistic design code:
c R S cR /γ γ S≥
Goal: Implied Pf ≅ Pft
pdf
R,S
μ - denotes mean valueσ - denotes st. deviationV = σ/μ – coefficient of variationΦ(-β) = standard cumulative normal distr.
R R C B Rμ = S S C B S μ =
μ μ R R S S V ); ,V )( (
≥ < R S
;B B 1 1
14
0.85 0.7 log β ≈ − f P
T.Moan MARE WINT Sept.201342
Reliability - based ULS requirements
R — resistance
D, L, E — load effects due to• permanent
• live load effects
• environmental
Reliability-based code calibrations:
Offshore oil and gas
- NPD/DNV; API/LRFD;
- Conoco studies of TLPs ;
Wind turbines
-IEC
RC/γR > γDDC + γLLC + γEEC Goal: The Implied
Pf = P(R>D+L+E)≅
Pft
Pf depends upon the
systematic and random
uncertainties in
R; D, L, and E
Design equation
CeSOS NTNU
β
βT
WSD
LRFD
Load ratio, Ec/(Lc+Ec)
15
T.Moan MARE WINT Sept.201343
• Initial and modified inspection/
monitoring plan
- method, frequency
Safety against fatigue or other degradation
failure is achieved by design, inspection and repair
• Design criteria: FLS
ALS
.... 0.1 1.0
= ≤
= −
∑ i allowablei
n D D
N
Brace
wall
Ground
Chordwall
CeSOS NTNU
NDE diver inspection or LBB
• Repair (grinding, welding,..steel…)
16
See Overview by Moan, in J. Structures and Infrastructureengineering, Vol.1, No.1 March 2005, pp. 33-62
T.Moan MARE WINT Sept.201344
In-service Experiences
Fatigue behaviour
Fatigue depends on local geometry
- Cracks start to grow at ”hot spot”
points, with high stress concentration
- Initial crack depth of 0.1 mm
- driven by cyclic tensile stresses
Cracks can be detected and repaired.
- Mean detectable crack depth:
NDE: 1-2 mm
Close visual inspection: 10-20 mm
Fracture or ductile tearing under given
extreme stress
Total loss if the structure lacks residualstrength after a member failure
Tubular
joints
Time
S t r e s s , σ S
Fatigue failure:
- through thickness
crack
- member failure
- visible crack
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T.Moan MARE WINT Sept.201345
Experiences with cracks infixed offshore platforms (See Vårdal, Moan et al, 1997...)
Data basis
- 30 North Sea platforms, with a service time of 5 to 25 years
- 3411 inspections on jackets- 690 observations of cracks
The predicted frequency of crack occurrence was found
to be 3 times larger than the observed frequency
On the other hand:
- Cracks which are not predicted, do occur.
Hence, 13 % of observed fatigue cracks occurred in joints
with characteristic fatigue life exceeding 800 years; due to
- abnormal fabrication defects (initial crack size ≥ 0.1 mm !)- inadequate inspection
T.Moan MARE WINT Sept.201346
In-service experiences: Comparison of fatigue life
predicted by old and new method
T.Moan MARE WINT Sept.201347
In-service experiences:
Corrosion
• affects ultimate and
fatigue strength
- plate thinning effect
- crack growth rate
• no or damaged coating
or cathodic protection
• corrosion rate for
general corrosion:
0.1 – 1.0 mm/year;
Splash zone:
• Corrosive environment /
difficult access
T.Moan MARE WINT Sept.201348
• Fatigue loading
- Weibull distribution of stress ranges
(with shape and scale parameters B and A)
• Fatigue resistance
- SN approach- Fracture mechanics model:
a - crack depth
N - number of cycles
c, m - material parameters
• Deterministic vs . probabilistic approach
- Reliability model
Time
S t r e s s , σ S
Stress,σ
f x(x)f x(x)
xcx
Prob. density
Fatigue life models
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T.Moan MARE WINT Sept.201349
Fatigue failure expressed by SN – formulation
Load effect (stress range), S
– Fs(s) = 1 – exp(-(s/A)B)
– Total number of cycles in period, N0
Resistance, SN formulation (simplified)
N = KS-m
K, m: material, local geometry dependent
Cumulative damage:
where sref = A(lnNref )1/m
often Nref = N0(108 in 20 years – e.g. or wave loads)
( ) Γ ⎛ ⎞= = = + =⎜ ⎟⎝ ⎠
∑ m m mi 0 0 0 eqi
n N N N m D E S A 1 S
N K K B K
T.Moan MARE WINT Sept.201350
Fatigue reliability baed on SN formulationConsider
failure probability in a given (service time) period:
Assume
m, B, No deterministic
so, k and Δ lognormal distribution
( ) ( )
m
i o o
m B
i o
n N s mDB N K ln N
= = Γ +∑ 1
[ ]f P P D= ≥ Δ
( )
( )( )
o
f
m B
o
m
o o
s K
P
K ln Nm N s
B
V m V V
X X
where the notation is the modal value of
Δ
= Φ −β
ΔΓ +
β =+ +
i
2 2 2
1
T.Moan MARE WINT Sept.201351
1E-05
1E-04
1E-03
1E-02
1E-01
1E+00
0 5 10 15 20Time
F a
i l u r e
p r o b a b i l i t y
Cumulative failure probability
•Probability of failure in interval t +Δt , given ithas survived up to t
•Suitable for time-dependent problems
•i.e. implicitly accounts for degradation of
structure!
Reliability model (cont…)
Hazard rate, h R(t )
Implied reliability
Ca
se
Δ
allow
able
Service
life
P f
Annual
hazard
rate h( t)
1 1 10 –1 10 –2
2 0.33 10 –2 2*10 –3
1E-05
1E-04
1E-03
1E-02
1E-01
1E+00
0 5 10 15 20Time
F a
i l u r e
p r o b a b i l i t y
Annual hazard rate
Cumulative failure probability
( )( )
1 ( ) R
t h t
F t =
−
F (t ) – distribution of time to failure
f (t ) – probability density function
If F (t ) is the fatigue P f accumulated up to t
and f (t ) the “instantaneous” Pf evaluated at t ,
Then
h R(t ) = Annual hazard rate or annual fai lure probabil ity for fat igueT.Moan MARE WINT Sept.201352
Reliability level as a function of uncertainty level
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1 2 3 4 5 6 7 8 9 10
Fat igue de sign factor
F a i l u r e
p r o b a b i l i t y
Cumulative failure probability
Cumulative, stdv(lnA )=0.15
Cumulative, stdv(lnA )=0.3
Ann ual fa ilure pro bability
Ann ual, std v(lnA )=0.15
Ann ual, std v(lnA )=0.3
Fs(s) = 1 – exp(-(s/A)B)
.... 0.1 1.01/
= ≤
= −=
∑ i allowablei
allowable
n D D
N
FDF D
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T.Moan MARE WINT Sept.201353
Fracture mechanics model
Basic model
Fatigue failure event:
g(x) = acr – a(C, m, lnA, B) ≤ 0
C, m - material parameters
lnA, B - load effect (stress) parameters
NO, Δ - deterministic
Reliability calculation by FORM/SORM or
Monte Carlo Simulation
[ ]f g( ) 0
p P g( ) 0 f (x)dx ( )≤
= ≤ = = Φ −β∫∫x
x
T.Moan MARE WINT Sept.201354
Reliabili ty model (cont…)
P r o b a b i l i t y
d e n s i t y ,
f A ( a )
Plate thickness a(t ) – crack depth
Time in-service
Calculated probability of through thickness crack(without updating)
aupd (t i)
a0t i
a(t i)
P r e d i c
t e d m e a
n c r a c
k s i z e
P r o b a b i l i t y
d e n s i t y ,
f A ( a )
Plate thickness a(t ) – crack depth
Time in-service
Calculated probability of through thickness crack(without updating)
aupd (t i)
a0t i
a(t i)
P r e d i c
t e d m e a
n c r a c
k s i z e
[ ]( ) 0 f P P M t = ≤
Fatigue failure probability, P f
( ) ( ) f t a a t = −
Often used
β – reliability index
Φ – standard normal distribution
( ) f P β = Φ −
Predicted
crack size
Final crack size
(plate thickness)1
1 2 2 1 2
0( ) (1 )2m m m m mma t a C S Y N π
− −⎡ ⎤= + −⎣ ⎦
For special case: Y (a)=constant
T.Moan MARE WINT Sept.201355
Inspection quality (POD curves)• Non-destructive examination
• Magnetic Particle Inspection
• Eddy Current (EC)
• Visual inspection (within 0.5m
distance), depending upon access
to crack site
• (Fujimoto et al., 1996, 1997)
based on trading vessels)ACFM in air
Depth (mm)
(length based on
a/2c=0.2)
Method Tubular joint in
sea water
Butt
weld in
air
ACFM (Alternate
Current Field
Measurement)
0.70
(3.5)
0.21
(1.05)
Magnetic
Particle Insp.
0.89
(4.45)
Not
reported
Eddie Current2.08
(10.4)
0.32
(1.6)
In-service MPI &EC (Moan et al,
1997)
1.95(9.75)
T.Moan MARE WINT Sept.201356
Failure probabilityPf (t) = P[ac – a(t) ≤ 0 ]
ac = critical crack size
Updating of failure probability based on
Inspection ( Madsen, Moan, Skjong,Sørensen, ….): :
Example: no crack is detected:
Pf,up (t) = P[ac – a(t) ≤ 0 | aD – a(t) ≥ 0]
= P[F |IE] = P[F IE]/ P[IE]
ac = critical crack size
aD = detectable crack size
where F AD (a) = POD(a)
• Known outcomes in-service
vs uncertain outcomes at the design stage• Updating late in the service life has larger
influence
Reliability based inspection planning w.r.t. fatigue
Mean detectable
crack depth of 1.5 mm
Pf
CeSOS NTNU
17
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T.Moan MARE WINT Sept.201357
Target level, pfsysT for global failure and p fT (βT)for fatigue reliability of a specific joint
P [Fi] P [FSYS(U)|Fi] = pfsysT
Fatiguefailureprobabilityin theservice life
Conditionalannualultimatefailureprobability
Target
Level forglobal failure ofthe structure;Depending onthe potential of - Fatalities- Pollution- Property loss
P [FSYS(U)|Fi] = Φ(-βFSYS|Fi)
Φ(-βT) = P [Fi] = pfsysT / P [FSYS(U)|Fi] =
βTGlobal failure model
of jacket with
member (i) removedT.Moan MARE WINT Sept.201358
Inspection sceduling for a welded joint
based upon no detection of crack during inspection
0 4 8 12 16 20
Inspection at time t=8with no crack detection
Noinspection
R e l i a b i l i t y l e v e l , β
Time (years)
1st inspection 2nd inspection
Target levelfor a given joint
In-service scheduling of inspections
to maintain a target reliability level
Extension of method:- consideration of other inspection events;
- effect of corrosion etc
- many welded joints , i.e. system of joints
; depending on the
consequences of failure
1 .2 1 .4( ) 10
0.85 0.7 log
β
β
−Φ − ≈
≈ −
= f f P
P
CeSOS NTNU
18
βT
T.Moan MARE WINT Sept.201359
Contribution to cumulative fatigue damage ofwind loads, wave loads and interaction of windand wave loads
Tubular
Joints
Characteristic fatigue damage
Raw
data
Weibull
model
General-
ized
gamma
model
Leg1-
Joint20.0881 0.0859 0.0952
Leg1-
Joint30.2713 0.2714 0.2862
Sur12-
Joint10.2142 0.2069 0.2213
Leg2-
Joint20.0876 0.0836 0.0889
Characteristic fatigue damage
for different model
Long term fatigue analysis of multi-planar tubular joints
In an offshore jacket wind turbine
Two-parameter Weibull model:
Fs(s) = 1 – exp(-(s/A)B)
T.Moan MARE WINT Sept.201360
Fatigue reliability results:
Reliability index for welded joints in
jacket as a function of time. No
inspection and repair. .0.1corr R =
Reliability index for welded joints in
jacket as a function of time. ,
years, mm, mm, and
mm.
0.1corr
R =5 pt t =0.11
Ra =
00.11a = 2.0
Da =
Fatigue reliability analysis of multi-planar welded
tubular joints considering corrosion and inspection
(Source: W.B.Dong et al., diff.papers)
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T.Moan MARE WINT Sept.201361
Reliability - based calibration of FLS requirements
Design criterion :
FDF - depends upon:
• consequence of failure
• inspection quality
Criterion:
( ) ( ) fsysT P FSYS FF i P FF i P ⎡ ⎤ ⎡ ⎤⋅ ≤⎣ ⎦⎣ ⎦
FailureConsequence
Noinspection
Inspectionin splashzone
Inspectioninside/topside
Static determ. 10 (10) 5 (3) 3 (2)
Fulfills ALSwith onemember failed
4 (3) 2 (2) 1 (1)
0 2 4 6 8 10 12 14 16 18 20
6
5
4
3
2
1
with
inspection
no
inspection
Δd = 0.1
Δd = 0.2
Δd = 0.3
Time after installation t [year]
R e l i a b i l i t y i n d
e x β
∑ =Δ≤= FDF/1 N
nD d
i
i
T.Moan MARE WINT Sept.201362
Main purpose:
(1) Check the effects of gearboxon the Torque calculation;
(2) Check the effects of globalmodel on the contact forcecalculation.
Time domain based simulation model of 750 kW
land-based wind turbine Comparison between coupled and decoupled analysis method:
T.Moan MARE WINT Sept.201363
• Model for crack propagation:
Linear elastic fracture mechanics (LEFM) model
is used:
( ) _ m
II eff da C K dN
= ⋅ Δ
, :C m material parameters, which can be
determined by experiments;
:a half crack length;
: N cycle numbers;
_ : II eff K Δ effective Mode II (shear) stressintensity factor range ; dependent on
Hardness ; microstructure; friction;
crack closure
- Subsurface initiated pitting.
Gear contact fatigue analysis of a wind
turbine drive train under dynamic conditions
(a) Contact model of two gear flanks and
(b) Equivalent model of two cylinders(Glodez, et al.,1997)
Schematic of crack propagation
T.Moan MARE WINT Sept.201364
Reliability-based gear contact fatigue analysis-
a frame work
Reliability as a function of time
Uncertainties:
- loading: contact
pressure
- Model uncertaintiesin aerodynamic loads,
global and local struct.analysis
planet gear
-
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T.Moan MARE WINT Sept.201365
Summary of reliability methods
Simple formulae (“lognormal format”)
─ Convenient as reference. Note: used in API Code Calibration
FORM/SORM
─ Very efficient
─ Approximate and need to be validated
Monte Carlo method
─ Basic method yields “exact” solution if the sample n is largeenough (time consuming)
─ Improved efficiency by
• Importance sampling (but caution is required)
Combined FORM and MC
─ Estimate approximate solution by FORM
─ Improve solution by MC, focused on the most important area
T.Moan MARE WINT Sept.201366
Practical use of Structural Reliability Analysis
Choice of method (simple explicit method based on lognormal
variables - FORM/MC)
Estimate uncertainties
─ Focus on the most important variables/ uncertainties
─ Introduce variable to represent uncertainty of the “mechanics”
model
─ Effect of probabilistic model (e.g. pdf)
Calculate reliability
─ Check relative importance/ influence of variables and possiblyimprove uncertainty measures
Estimation of target level
T.Moan MARE WINT Sept.201367
Case-by-case Structural Reliability Analysis
Reliability-based design
• New types of structures
• New use
Design and inspection planning
• Integrated design and inspection planning
Requalification
• New use
• New information
• Damage/subsidence
• Extension of service life
T.Moan MARE WINT Sept.201368
Guidelines for Structural Reliability Analysis
Content
– Methods
– Uncertainty modelling
– Target levels
Issued guidelines
– Det norske Veritas
– Norwegian Geotechnical Intitute
Criticism
– Important to develop such guidelines by an authorized committee
– The target reliability level should be defined by close calibration to
acceptable design/ operation practice and properly defined reliability
methodology.
Risk Assessment in Offshore Safety
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T.Moan MARE WINT Sept.201369
Risk Assessment in Offshore Safety
ManagementWith respect to
• Fatalities
• Environmental
damage
• Property damage
Offshore structures are designed according to approaches which are:
- Goal-based; rather than prescriptive- Probabilistic; rather than deterministic
- First principles; not purely experiental
- Integrated total; not separately (i.e. system consideration)
- Balance of safety elements; not hardware only
Critical
eventFault tree
Event tree
NPD Guidelines for
Quantitative Risk Analysis(1981)
NPD’s Accidental Collapse
Limit State (ALS) (1984)
UK Safety Case (1992)
T.Moan MARE WINT Sept.201370RISK ANALYSISRISK ANALYSISRISK ANALYSIS
RISK ESTIMATIONRISK ESTIMATIONRISK ESTIMATION
Risk Analysis PlanningRisk Analysis Planning
System DefinitionSystem Definition
Hazard IdentificationHazard Identification
Risk PictureRisk Picture
RiskReducingMeasures
RiskReducingMeasures
Frequency
Analysis
Consequence
Analysis
Risk Acceptance
Criteria
Risk Acceptance
Criteria
Acceptable Acceptable
Unacceptable
Tolerable
Critical
eventFault tree Event tree
Risk analysis framework (oil and gas industry)• Empirical data: Accumulated no. of platform years world wide:
fixed p latforms: ~ 150 000
mobi le units: ~ 15 000
• Theoretical analysis (Fault tree/event tree)
T.Moan MARE WINT Sept.201371
Internal hazards:
Blade pitch and control system faults
• Blade seize: imbalance loads
• Shutdown loads: impulse from aerodynamic braking can lead to pitch vibrations
• What about sensor faults?
• Does changing the shutdown pitch rate help?
• Possible instability for TLPWTs (idling with one blade pitched – Jonkman andMatha, 2010)
Wilkinson et al., 2011
P i t c h s y s t e m
-200 -150 -100 -50 0 50 100 150 200-1.5
-1
-0.5
0
0.5
1
1.5x 10
4
T o w e r
T o p B M Y , k N m
TLP, EC 5
time - TF, s
B
C
Shut downturbine quickly
Faultoccurs
Continueoperating withfaulted blade
T.Moan MARE WINT Sept.201372
External hazards: Accidental Loads
1Explosion loads(pressure, duration - impulse)
scenarios
explosion mechanics
probabilistic issues⇒ characteristic loads for design2 Fire loads
(thermal action, duration, size)
3 Ship impact loads(impact energy, -geometry)
4 Dropped objects
5 Accidental ballast
6 Unintended pressure
7 Abnormal Environmental loads8 Environmental loads on platform
in abnormal floating position
A id t l C l l Li i t St t
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T.Moan MARE WINT Sept.201373
Accidental Col lapse Limit State
relating to structural strength (NPD,1984, later NORSOK)
• Estimate the damage due toaccidental event (damage, D or action, A) at an
annual probability of 10-4
- apply risk analysis to establishdesign accidental loads
• Survival check of the damaged structure as a whole,considering P, F and environmental actions ( E )
at a probability of 10-2
Target annual probability of total loss:
10-5 for each type of hazard
P, F
A
P, F
A
P, FP, F
E
A
T.Moan MARE WINT Sept.201374
Estimating the Accidental Event
Theory based on:
- accidental events originate from a small fault and develop in a sequence of
increasingly more serious events, culminating in the final event,
- it is often reasonably well known how a system will respond to a certain event.
Damage or accidental load with annual probability of occurrence: P = 10-4
Need homogeneous empi rical data of the order 2/p = 20 000 years
to estimate events by empirical approach
Accumulated plat form years world wide:
- fixed platforms: ~ 180 000
- mobile units: ~ 20 000
- FPSO: ~ 2 000
Account of all measures to reduce the probabil ity and c ons equences of the hazards
T.Moan MARE WINT Sept.201375
Ship collisions
Types and scenarios
– according to
type of ships and their function:
• offshore site related ships
(supply vessels, offshore tankers,…)
• floating structures (storage
vessels, drilling units, crane
barges..)
• external ships (merchant, fishing..)Oseberg BSubmarine U27
but not submarinesT.Moan MARE WINT Sept.201376
Risk reduction
- ship collision risk
• reduce risk by
reducing the prob.
(traffic control) and/or the
consequences of collision
• Design for collision events
- Min collision: Supply vessel
5000 tons displacement
and a speed of 2 m/s;
i.e. 11, 14 MJ
(to be increased!)
- collision events with trading vessels
(with a probability of exceedance of
10- 4 ) site specific events identified by
risk analysis
Collisions do occur.
Frequency of Impact by Passing Vessels
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T.Moan MARE WINT Sept.201377
– annual impact frequency for a given
platform in a given location – annual number of vessels with a size (j) in
route (i)
– probability that vessel of size (I) in
navigation group (k) in route (i) is on
collision course
Frequency of Impact by Passing Vessels
∑ ∑∑= ==
⋅=n
1i
4
1k
jk ,FR ijk ,CC
5
1 j
ijC PP NP
CP
ij N
ijk ,CCP
jk ,FR P
Probability density
of ship position
ij,CCP
platform
C e n t r e l i n e
– probability that a vessel with a size (j) in
navigation group (k) does not succeed in
avoiding the platform
T.Moan MARE WINT Sept.201378
Calculation of impact damage
External mechanics
The fraction of the kinetic energy to be
absorbed as deformation energy(structural damage) is determined by
means of:
Conservation of momentum
Conservation of energy
Internal mechanics
Energy dissipated by vessel
and offshore structure
Equal force level
Area under force-def. curvedws dwi
R iRs
Ship FPSO
Es,sEs,i
External mechanics
Internal mechanics
Measure of damage:
Indentation depth
T.Moan MARE WINT Sept.201379
Ultimate global collapse analysis of platforms
Non-linear analysis to assess
the resistance of
- intact and damaged structures
by accounting for
geometrical imperfection,
residual stresses
local buckling, fracture,
rupture in joints
nonlinear geometrical and
material effects
Nonlinear FEM-General purpose (ABAQUS….)
-Special purpose (USFOS…)
28
T.Moan MARE WINT Sept.201380
Residual global ultimate strength after damage
(due to collison, dropped objects, ” fatigue failure” )
Residual st rength
of damaged
North Sea jacket.Linear pile-soil model
Ultimate strength
Broad side loading
Brace261
Brace363
Brace463
Ultimate strengthFult / FH100
2.73 2.73 2.73
Residual strength
Fult(d) / Fult
1.0 0.76 1.0
7 0 m 5 6
m
main structure
deck
(261)
(363)
(463)
Broad-side and end view.
Deck model indicated by dashed line
(261)
(363)
(463)
(455)(456)
collision
dropped
object
29
Framework for Risk based Design against
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T.Moan MARE WINT Sept.201381
Framework for Risk-based Design against
Accidental actions
][]|[]|[)( )(
,
)( i
jk
k j
i
jk FSYS A P A D P D FSYS P i P ∑ ⋅⋅=
probability of damagedsystem failure under
relevant F&E actions
probability of damage, D
given A jk(i) (decreased
by designing againstlarge A j
(i))
probability of accidentalaction at location (j)
and intensity (k)
(i)
jk P A⎡ ⎤⎣ ⎦ is determined by risk analysis while the other probabilities
are determined by structural reliability analysis.
[ ]P FSYS | D Is determined by due consideration of relevant action andtheir correlation with the haazard causing the damage
For each type of
accidental action
T.Moan MARE WINT Sept.201382
Accidental act ions for wind turbines
IEC 61400-1
• “External” ALS actions may need to be considered
Ship collision:• Maximum size of service vessel and limiting operational conditions to
be specified by designer:
• • Vessel speed not less than 0.5 m/s• • Kinetic energy based on
• – 40% added mass sideway
• – 10% added mass bow/stern
• • Impact energy < 1 MJ (small)• • Max. force may be assumed 5 MN - includes dynamic amplification
IEC 6400-3
T.Moan MARE WINT Sept.201383
2.3 Standard directives for
approval practice
Number 4: The structures shall be
designed and configured in such
a way that –in the event of collision
with a ship, the hull of the ship shall
be damaged as little as possible.
Design Collision Event
•A single-hull Suezmax tanker with 160,000 tdw
•The ship is drifting sideways at 2 m/s•Ship displacement ≈ 190,000 tons
•Kinetic energy (40% added mass) = 530 MNm
T.Moan MARE WINT Sept.201384
Mass of 5 MW turbine 450 tons
•Drop height 60 m•Energy 275 MJ
•Nacelle may fall through the tank!
Suezmax tanker collision
Al tenative jacket
failure modes(Source: J.Amdahl, Tekna seminar, NTNU, January 2012)
Collapse mode is favourable –
nacelle drops into sea
•Upper weak soil
layers beneficial
30
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T.Moan MARE WINT Sept.201385
Concluding remarks
Experiences regarding
- failures and accidents and
- life cycle safety managementfor oil and gas installations can serve as a basis for structures
in other offshore industries, notably wind turbines,
- when the differences between
the oil and gas and the other industriesare recognised
In particular
- normal uncertainty and variability in structural
performance as well as possible “gross errors” in fabricationand operation should be properly considered in the decision
process
CeSOS NTNU
Thank you! T.Moan MARE WINT Sept.201386
Selected references – which include more complete reference listsDesign codes: ISO 2394 (Reliability of structures); ISO 19900- (Offshore structures)
Emami, M.R., and Moan, T.: “Ductility demand of simplified pile-soil-jacket system under extreme sea wavesand earthquakes”, Third European Conf. on Structural Dynamics, Balkema Publ. G. Augusti et al.(eds.) Rotterdam, 1996, pp. 1029 – 1038.
Moan, T. and Amdahl, J.: “Catastrophic Failure Modes of Marine Structures”, in Structural Failure,
Wierzbiecki, T. (Ed.), John Wiley & Sons, Inc., New York, 1989.Moan, T., Vårdal, O.T., Hellevig, N.C. and Skjoldli, K. “Initial Crack Dept. and POD Values inferred from in-service Observations of Cracks in North Sea Jackets”, J. OMAE, Vol. 122, August 2000, pp. 157-162.
Moan, T. and Amdahl, J.: “ Nonlinear Analysis for Ultimate and Accidental Limit State. Design andRequalification of Offshore Platforms” WCCM V. Fifth World Congress on Computational Mechanics(Eds.: H.A. Mang, F.G. Rammerstorfer, J. Eberhardsteiner) July 7-12, 2002, Vienna, Austria.
Moan, T. “Reliability-based management of inspection, maintenance and repair of offshore structures”.Structure and Infrastructure Engineering. Vol.1, No.1, 2005, pp. 33-62.
Moan, T. Reliability of aged offshore structures. In: "Condition Assessment of Aged Structures", 2008, Ed.Paik, J. K. and Melchers R. E., Woodhead Publishing.
Moan, T. Development of accidental collapse limit state criteria for offshore structures. J. Structural Safety,2009, Vol. 31, No. 2, pp. 124-135.
Vinnem, J.E.: “Offshore Risk Assessment”, Kluwer Academic Publishers, Doordrecht, 1999.