Jacket application

TECHNICAL REPORT

JOINT INDUSTRY PROJECT
GUIDELINE FOR OFFSHORE STRUCTURAL
RELIABILITY ANALYSIS:
APPLICATION TO JACKET PLATFORMS

REPORT NO. 95-3203

DET NORSKE VERITAS

DET NORSKE VERITAS

TECHNICAL REPORT
Date of first issue: Organisational unit: DET NORSKE VERITAS AS
5 September 1996 Struct. Reliability & Marine Techn. Division Nordic Countries
Approved by: Veritasveien 1
N-1322 HØVIK,Norway
Øistein Hagen Tel. (+47) 67 57 99 00
Principal Engineer Fax. (+47) 67 57 74 74
Org. No: NO 945 748 931 MVA
Client: Client ref.: Project No.:
Joint Industry Project Rolf Skjong 22210110

Summary:
A guideline for offshore structural reliability analysis of jacket structures is presented. The
guideline comprises experience and knowledge on application of probabilistic methods to
structural design, and provides advice on probabilistic modelling and structural reliability
analysis of jacket structures.
The characteristic features for jacket structures are outlined and a description of the analysis
steps required for assessing the response in jacket structures exposed to environmental actions
is given.
Model uncertainties associated with the response analysis of jacket structures are discussed
and recommendations are given for how to account for these uncertainties in the reliability
analysis.
Important limit state functions that should be considered in a Level-III reliability analysis of
jacket structural components are defined and discussed.
The experience gained from two case studies involving probabilistic response analyses of
jacket structures, a fatigue failure limit state (FLS) and a total collapse limit state (ULS), are
summarised.
This report should be read in conjunction with the reports:
• Guideline for Offshore Structural Reliability Analysis - General, DNV Report no. 95-2018
• Guideline for Offshore Structural Reliability Analysis - Examples for Jacket Platforms, DNV
Report no. 95-3204.

Report No.: Subject Group:
95-3203 P12 Indexing terms
Report title:
structural reliability
Guideline for Offshore Structural Reliability
Analysis: jacket platforms
Application to Jacket Platforms environmental loads
capacity
Work carried out by:
Gudfinnur Sigurdsson, Espen Cramer, No distribution without permission from the
Inge Lotsberg, Bent Berge Client or responsible organisational unit
Work verified by:
Øistein Hagen Limited distribution within Det Norske Veritas

Date of this revision: Rev.No.: Number of pages:
Unrestricted distribution
05.09.96 01 80
DET NORSKE VERITAS, Head Office: Veritasvn 1, N-1322 HØVIK, Norway Org. NO 945 748 931 MVA

DET NORSKE VERITAS

TECHNICAL REPORT

DET NORSKE VERITAS, Head Office: Veritasvn 1, N-1322 HØVIK, Norway Org. NO 945 748 931 MVA

Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 5
DNV Report No. 95-3203 Introduction

Table of Contents
1. INTRODUCTION ...................................................................................................................................................7
1.1 OBJECTIVE ...............................................................................................................................................................7
1.2 DEFINITION OF A JACKET ..........................................................................................................................................7
1.2.1 General ............................................................................................................................................................7
1.2.2 Types of Jackets ...............................................................................................................................................8
1.2.3 Structural Design Parameters .........................................................................................................................8
1.2.4 Jacket Design Analysis ....................................................................................................................................9
1.3 ARRANGEMENT OF THE REPORT ............................................................................................................................... 9
2. RESPONSE TO ENVIRONMENTAL ACTIONS .............................................................................................11
2.1 CLASSES OF RESPONSE ...........................................................................................................................................11
2.2 ENVIRONMENTAL LOADS AND RESPONSE ..............................................................................................................12
2.2.1 Environmental Parameters............................................................................................................................12
2.2.2 Combination of Environmental Parameters ..................................................................................................12
2.2.3 Simulation of Wave Loads .............................................................................................................................13
2.2.4 Extreme Response Effects (ULS) ...................................................................................................................14
2.2.5 Fatigue (FLS) ................................................................................................................................................14
3. UNCERTAINTY MODELLING - TARGET RELIABILITY ..........................................................................16
3.1 GENERAL ...............................................................................................................................................................16
3.2 UNCERTAINTY MODELLING ....................................................................................................................................16
3.2.1 Overview........................................................................................................................................................16
3.2.2 Types of Uncertainty......................................................................................................................................16
3.2.3 Uncertainty Implementation ..........................................................................................................................17
3.3 TARGET RELIABILITY .............................................................................................................................................17
3.3.1 General ..........................................................................................................................................................17
3.3.2 Selection of Target Reliability Level..............................................................................................................18
4. DISCUSSION OF LIMIT STATES.....................................................................................................................20
4.1 INTRODUCTION .......................................................................................................................................................20
4.2 BUCKLING FAILURE OF MEMBERS (ULS)...............................................................................................................22
4.2.1 Local Buckling of Members ...........................................................................................................................22
4.2.2 Global Buckling of Members .........................................................................................................................23
4.2.2.1 Background .............................................................................................................................................................. 23
4.2.2.2 Limit State Function................................................................................................................................................. 25
4.2.3 Buckling of Members Subjected to External Pressure...................................................................................26
4.2.3.1 Background .............................................................................................................................................................. 26
4.2.3.2 Limit State Function................................................................................................................................................. 28
4.3 JOINT FAILURE (ULS) ............................................................................................................................................28
4.3.1 Background....................................................................................................................................................28
4.3.2 Limit State Function ......................................................................................................................................32
4.4 FATIGUE FAILURE AT HOT-SPOT OF WELDED CONNECTIONS (FLS) .......................................................................33
4.4.1 General ..........................................................................................................................................................33
4.4.1.1 Overview.................................................................................................................................................................. 33
4.4.1.2 System Aspects ........................................................................................................................................................ 34
4.4.2 SN-Fatigue Approach ....................................................................................................................................35
4.4.2.1 General..................................................................................................................................................................... 35
4.4.2.2 SN-Fatigue Modelling.............................................................................................................................................. 36
4.4.2.3 Uncertainty in SN-curves ......................................................................................................................................... 37
4.4.2.4 Fatigue Damage Model ............................................................................................................................................ 37
4.4.2.5 Limit State Formulation ........................................................................................................................................... 39
4.4.3 The FM-Approach for Fatigue Assessment ...................................................................................................39
4.4.3.1 General..................................................................................................................................................................... 39
4.4.3.2 Crack Growth Rate................................................................................................................................................... 40
4.4.3.3 Crack Size over Time ............................................................................................................................................... 41
4.4.3.4 Fatigue Quality......................................................................................................................................................... 43
4.4.3.5 Fatigue Crack Growth Material Parameters ............................................................................................................. 43

Sigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to Jacket
Platforms”, DNV Report 95-3203


4.4.3.6 Limit State Formulation / Failure Criteria................................................................................................................ 44
4.4.4 Load and Response Modelling ......................................................................................................................45
4.4.4.1 General..................................................................................................................................................................... 45
4.4.4.2 Sea State Description ............................................................................................................................................... 45
4.4.4.3 Global Structural Analysis ....................................................................................................................................... 50
4.4.4.4 Local Stress Calculation........................................................................................................................................... 52
4.4.5 Stress Range Distribution ..............................................................................................................................54
4.4.6 Formulation of Inspection Results.................................................................................................................57
4.4.7 Event Margins with Inspections Results:.......................................................................................................59
4.5 TOTAL STRUCTURAL COLLAPSE (ULS) ...................................................................................................................61
4.5.1 General ..........................................................................................................................................................61
4.5.2 Limit State Formulation.................................................................................................................................62
4.5.3 Distribution of the Annual Maximum Loading (Base-Shear) ........................................................................67
5. SUMMARY OF APPLICATION EXAMPLES .................................................................................................70
5.1 SUMMARY OF FATIGUE FAILURE LIMIT STATE - FLS EXAMPLE .............................................................................70
5.1.1 Modelling Approach ......................................................................................................................................70
5.1.2 Discussion of Results .....................................................................................................................................71
5.2 SUMMARY OF TOTAL COLLAPSE LIMIT STATE - ULS EXAMPLE.............................................................................72
5.2.1 Modelling Approach ......................................................................................................................................72
5.2.2 Discussion of Results .....................................................................................................................................73
6. REFERENCES ......................................................................................................................................................75



1. INTRODUCTION
1.1 Objective
The objective of the application part of the project Guideline for Offshore Structural Reliability
Analysis for the structure types jacket, TLP and jack-up, is to give
• an overview of the characteristics of that structure's response to environmental actions,
• a detailed guidance on the reliability analysis of that structure with respect to several
important modes of failure,
• examples of reliability analyses applied to selected failure modes for that structure type.
The guidelines are intended for the application of Level III reliability analysis (DNV 1992b) to
the structure type; i.e. in which the joint probability distribution of the uncertain parameters is
used to compute the probability of failure. This is usually a fairly demanding type of analysis,
and is primarily expected to be applied in structural reassessment, in service inspection planning,
code development/calibration and for detailed design verification of major load bearing
components of the structure. Hence, the guidelines prepared in this project concentrate on the
requirements for these types of analyses, and do not make any attempt to embrace all aspects of
the decision process. However, within these limitations, our aim is to cover significant aspects of
the structural of reliability analysis.

1.2 Definition of a Jacket
1.2.1 General
Fixed steel offshore structures are often called “jackets”. The name jacket originates from the
early days of the offshore industry when a trussed structure, jacket, was placed over the piles to
provide lateral stiffness to withstand wave, current and wind forces.
Jackets have been installed in water depths ranging from 0 to 400 metres, and in conceptual
designs greater water depths have been considered. The steel weight and thus the cost increases
rapidly with water depth, therefore alternative platform solutions are often chosen for large water
depths. Jackets have been designed to support topside weights of up to about 50000 tonnes, and
it is feasible to design jackets for even larger topside weights.
The performance of jackets in hostile ocean environment has generally been good, although local
fatigue damages have occurred in the earlier platforms. There have been very few total failures,
and then only with the oldest platforms.



1.2.2 Types of Jackets
A jacket may be used to support a large number of facilities, and depending on the purpose
(drilling, production, utility, etc.) and ocean environment (water depth, waves, current, wind,
earthquake, etc., it may be a simple or a very complex structure. Figure 1.2 shows a jacket
designed to support drilling and production facilities.
Depending on the configuration, the jackets are classified (depending on the mode of installation)
as:
- Self floater jacket
- Barge launched jacket
- Lift installed jacket

In early days the self floating jacket, which was floated out to the installation site and upended,
was quite popular because it required a minimum of offshore installation equipment. The barge
launched mode of installation has been most common as long as only “smaller” lifting vessels
were available. During the last ten years many platforms weighing less than 10.000 tonnes have
been lift installed, thus minimising the need for temporary installation aids.
Most often jackets have piled foundations, but lately jackets have also been designed with plated
foundations, which reduce installation time. Among the piled jackets it is distinguished between
those with piles in the legs, template type jacket, and those with piles arranged as skirts and
clusters, tower type jackets.

1.2.3 Structural Design Parameters
The jacket design is governed by the following:
- Functional requirements, i.e., support of topside, well conductors, risers, etc.
- Water depth
- Foundation soil conditions
- Environmental conditions, i.e., wave, current, wind, temperature, earthquake, etc.

Important items to be considered in an economical jacket design are:
- Jacket configuration
- Foundation (piled, plated, etc.)
- Type of installation (barge launch or lift installed)
- Use of high strength steel
- Use of cast nodes to improve fatigue performance.



1.2.4 Jacket Design Analysis
Shallow water depth jackets are generally designed with adequate strength based on a static
analysis where the wave loads are applied statistically on the structure. In addition a deterministic
fatigue analysis and earthquake analysis (if required) are carried out. The jacket is in addition
designed for the temporary installation phases. The natural period of the jacket is calculated to
establish the need for wave dynamic analysis.
Deep water jackets often exhibit dynamically amplified response when subjected to wave forces.
The reason is that these platforms have a longer fundamental period of vibration (closer to the
wave periods) than the shallow water platforms. These platforms need to be designed based on
both static and dynamic (stochastic) wave analyses. For the fatigue investigation a stochastic
dynamic fatigue analysis may be more suited than a deterministic fatigue analysis. Earthquake
analysis is carried out as required, and the jacket is designed for the temporary installation
phases.
As mentioned above deep water platforms may be dynamically sensitive to wave forces. The
frequency distribution of the random waves becomes a significant wave design parameter and the
selection of wave spectra for design analyses is therefore extremely important. Due to the long
fundamental period of vibration of the platform the fatigue behaviour may become one of the
critical design considerations.

1.3 Arrangement of the Report
The response of Jacket structures to environmental loads are described in section 2, together with
methods for computation of the resulting load effects. The model uncertainties associated with
the computation of these load effects and the selection of target reliability are discussed in
section 3. Important limit states are described in chapter 4, where also the stochastic modelling of
these failure modes are discussed. Section 5 provides a summary of two reliability analyses,
respectively for ultimate limit state and fatigue limit state for selected components in the Jacket
structure. The details of these analyses are presented in a separate report, Guideline for Offshore
Structural Reliability Analysis - Example for Jacket Platforms (DNV 1995b).
The present report is based on the general guidelines set out in the Guideline for Reliability
Analysis of Marine Structures - General, DNV (1995a). Companion applications are also
available for jack-ups and TLP structures.



Figure 1.2 Jacket designed to support drilling and production facilities


DNV Report No. 95-3203 Response to Environmental Actions

2. RESPONSE TO ENVIRONMENTAL ACTIONS
2.1 Classes of Response
An important task in the reliability evaluation of an offshore structure is identification and
modelling of all significant loads and load combinations which the structure is exposed to during
the service life.
The following Load Categories are defined for design and reassessment of jacket structures:
• Permanent Loads (P)
• Live Loads (variable functional loads) (L)
• Environmental Loads (E)
• Deformation Loads (D)
• Accidental Loads (A)

This section mainly considers environmental loads and load effects related to jacket structures.
For structural engineering purposes, these environmental loads may be characterised mainly by
over-water wind loads, by surface wave loads and by current loads that exist during severe storm
conditions.
In the North Sea, the surface waves during storm conditions are of major importance in the
design of Jacket structures for deep water environments, where the wind loads only represent a
contribution of less that 5% of the total environmental loading. However, in the Gulf of Mexico
the wind loads are of major importance, having wind speeds during hurricane conditions
exceeding 50 m/s. Currents at a particular site can also contribute significantly to the total Jacket
loading, where current generally refers to the motion of water that arises from sources other than
surface waves. E.g., tidal currents arise from the astronomical forces exerted on the water by the
moon and sun, wind-drift currents arise from the drag of local wind on the water surface and
ocean currents arise from the drag of large-scale wind systems on the ocean.
During storm conditions, current velocities at the surface of more than 1 m/s are not uncommon,
giving rise to more than 10% of the total induced environmental force.
The following sections give a more detailed description of environmental loads and responses on
jacket structures. Regarding the other load categories, reference is made to DNV (1995a).



2.2 Environmental Loads and Response
2.2.1 Environmental Parameters
The parameters describing the environmental conditions shall be based on observations from, or
in the vicinity of the actual location and on general knowledge about the environmental
conditions in the area. This is e.g. reflected in The Norwegian Petroleum Directorate, Guidelines
for Loads and Load Effects (NPD (1996)) where it is stated that in designing, the recording of
wave data should have a duration of at least 10 years (if wave loads are of major importance).
The main environmental parameters governing jacket design are:
• wave height (H), wave period (T) and wave direction
• current velocity, current direction and current profile
• steady wind velocity, wind direction and wind profile
• water level variations (tidal, storm surge and potentially field subsidence)

Further details and descriptions of these parameters may be found in the General Guideline,
Section 5 Loads. The above parameters are usually sufficient for jacket design in relatively
shallow waters with no structural dynamic effects present.
However, if the fundamental eigenperiods of the jacket system are at a level which may cause
resonance phenomena, additional environmental parameters are needed in the design. For such
circumstances the wave spectrum needs to be defined for different sea states, and the relative
occurrence rate of significant wave height (Hs) and zero up crossing period (Tz) (or spectral peak
period (Tp)) needs to be established. The wave spectra are usually of a single peak type (PM, or
JONSWAP), however double peak spectra may also be applicable for some areas.
Other environmental parameters which need to be evaluated in jacket design are:
• ice and snow
• marine growth (thickness, weight and variation with water depth)
• temperature (sea/air)
• earthquake

2.2.2 Combination of Environmental Parameters
Traditionally jacket design is performed by assuming wind, waves and current acting in the same
direction. The assigned probability level for each of the environmental parameters when
combining them may vary depending on the applicable code.
The NPD Guideline for Load and Load Effects (NPD (1996)) presents a combination of
environmental loads which has been extensively used the last decade, see Table 2.1. More
detailed procedures for assessing the combined environmental loading will normally be accepted
in design provided sufficient data and documentation are available. In this context one should be
aware of that jacket design is usually governed by the wave loads.
If simultaneous time series of environmental parameters exists, long term joint environmental
models may be used. Alternatively, the environmental parameters may be approximated by
marginal distributions as reflected in Table 2.1. For further details, see DNV (1995a) Section 5.


Table 2.1 Combination of environmental loads with expected mean values (m) and annual
probability of exceedance 10-2 (ULS) and 10-4 (PLS), NPD (1996).
Limit State Wind Waves Current Ice Snow Earth- Sea
quake level
10-2 10-2 10-1 - - - 10-2
Ultimate 10-1 10-1 10-2 - - - 10-2
Limit State 10-1 10-1 10-1 10-2 - - m
(ULS) - - - - 10-2 - m
- - - - - 10-2 m
Progressive 10-4 10-2 10-1 - - - m*
Limit State 10-2 10-4 10-1 - - - m*
(PLS) 10-1 10-1 10-4 - - - m*
- - - - - 10-4 m

2.2.3 Simulation of Wave Loads
The Morris’s equation has been widely applied in the design of jacket structures in the last
decades for assessing the wave induced loading. This is not a complete and consistent
formulation which fully simulates the wave loads. The Morris’s equation has, however, proved to
give reasonable reliable results by careful selection of the drag (Cd) and inertia (Cm) coefficients
in combination with an appropriate wave theory.
The jackets are usually made up of tubulars with outer diameters varying typically from 0.3m up
to 6.0m (bottle legs). For deterministic static in-place analysis, a drag coefficient in the range 0.7-
0.8 together with an inertia coefficient of 2.0 are often used in design. Anodes are usually
included in the modelling by increasing the drag coefficient with 8-12% depending on the
amount of anodes required.
Stokes’ 5th order wave theory is the most commonly applied wave theory in design of jackets.
The higher Stokes theory has a good analytical validity in deep water, whereas the fit to the
boundary conditions in shallow water is relatively poor. This theory is suitable as it describes the
wave kinematics above the mean water level and give information about the crest height which
in turn is needed in e.g. air gap calculations.
First order wave theory may also be used when the procedure for extrapolating the wave profile
above (and below) the mean water level is carefully selected. The “Stream” function gives a good
analytical validity over a wide range of wave conditions and is to be used in relatively shallow
waters. This theory also has a set of free parameters that can be adjusted to achieve the best fit to
the dynamic free boundary conditions. For very shallow waters Cnoidal & Solitary Wave may be
applicable. Other wave theories exists (e.g. New-Wave, Tromans et al. (1991)), however, the
experience with use is limited.
The energy distribution around the dominating wave direction is usually described by a cosine
distribution where the level of spreading is defined by the exponent in the cosine function,
typically varying from 2 - 8. For extreme load conditions, it is usually not recommended to
include wave spreading. This is e.g. reflected in NPD Guideline for Loads and Load Effects
(NPD (1996)) where it is recommended not to include wave spreading for significant wave
heights above 10 meters if it gives reduced load effect. This recommendation is based on actual
measurements/recordings in the North Sea. It has also been proposed to set the cosine exponent



in the wave spreading function equal to the significant wave height (in meters). This implies
more or less long-crested waves for significant wave heights above 10 meters.

2.2.4 Extreme Response Effects (ULS)
For extreme load conditions a jacket is usually considered drag dominated. This is, however,
dependent on the wave conditions and the dimensions of the tubulars. For relatively deep water
jackets the drag dominance is shifted towards the inertia regime due to large diameter tubulars at
the lower jacket levels. For fatigue calculations the inertia regime is also having a higher
influence due to the importance of the intermediate wave heights in the fatigue damage
contribution.
In relatively shallow waters with low fundamental periods of the jacket, static deterministic
analyses will generally be sufficient. If the dynamic amplification is low (e.g. less than 5-10%),
the dynamic effects can be simulated by dynamic amplification factors (DAF) in combination
with static analyses. For extreme load analyses the dynamic amplification will be low, whereas
for fatigue analyses the degree of amplification will be higher and more important.
A spectral approach is required if the dynamic effects are dominant. For extreme load analysis
the level of dynamic amplification is limited due to the period spacing between jacket
eigenperiods and extreme wave periods. These aspects are further commented below for fatigue.
Concerning linear vs. non-linear structural analyses, there are examples of jackets in water depths
of 150 -200m and fundamental eigenperiods beyond 3 seconds where non-linear effects related to
wave loads are found to be very important. These non-linear effects are typically surface effects,
non-linear wave-current interaction and the non-linear drag forces. This implies that linearised
stochastic dynamic analyses may underestimate the response significantly if the dynamics are
dominating.
Design wave analyses are usually considered conservative, but this depends, however, on the
actual selection of design parameters in the analysis. For relatively deep water jackets it has been
found that time domain simulations commonly give higher responses than what may be
determined by single design wave analysis.

2.2.5 Fatigue (FLS)
Depending on the level of dynamic amplification, either a long-term distribution of single wave
heights (H) and associated wave periods (T), or a scatter diagram ( H s − Tp or H s − Tz ), is
needed in the fatigue assessment. As stated earlier, it is a requirement for the fatigue analysis that
the long-term environmental distributions have been established based on relevant measurements
and subsequent statistical post-processing. Long-term single wave height distributions are usually
limited to 10 - 20 H/T combinations whereas a scatter diagram may consist of up to 200 short
term sea states.
The wave induced stress range response needs to be determined for the fatigue analysis. Different
approaches may here be applied for assessing the stress range response. Usually different waves
(H/T combinations) are stepped “through” the structure with a step interval of 10-15 degrees and
from these curves the stress ranges are determined. Special considerations may be required for
elements in the splash zone as these elements are intermittent in and out of the water as the
waves are passing.



The shape of the wave spectra has an influence on the response results. This is especially the case
when the fundamental eigenperiod of the jacket system is high and there is little damping in the
dynamic system such that resonance will occur. A dynamic system like this will e.g. give
significantly higher responses at resonance with a Jonswap spectrum compared to a PM
spectrum.
A linearisation of the drag forces is needed for dynamic analyses. Different methods exist for
performing this type of linearisation. One approach is to linearise with respect to a characteristic
wave height for each wave period. Members with intermittent submergence need to be treated
separately. The response results are strongly dependent on the chosen linearisation wave heights,
and especial attention should be made in the linearisation evaluation in order not to achieve over-
conservative results. Another and more consistent linearisation procedure is to apply the wave
energy spectrum, by assuming the ocean waves and the corresponding fluid kinematics to be
Gaussian processes.
Slamming on horizontal members in the splash zone needs to be taken into account in the FLS
design. Different approaches may be applied to determine the dynamic response and the number
of oscillations due to wave slamming. However, usually this effect is minimised by carefully
placing the horizontal levels of the jacket outside the splash zone.


DNV Report No. 95-3203 Uncertainty Modelling - Target Reliability

3. UNCERTAINTY MODELLING - TARGET RELIABILITY
3.1 General
There is a close connection between the uncertainty modelling and the target reliability level, as
the obtained reliability against e.g. fatigue failure or ultimate collapse in a reliability analysis is
dependent on the chosen uncertainty modelling, especially with respect to the implementation of
modelling uncertainties.

3.2 Uncertainty Modelling
3.2.1 Overview
This section provides general guidance in respect to uncertainty modelling as appropriate to the
ultimate and fatigue limit state modelling for jacket structures. In Section 4, the proposed models
accounting for the uncertainties related to the FLS and ULS analyses of jacket platforms are
described in detail.
For further guidance, see also Guideline for Offshore Structural Reliability Analysis - General
(DNV 1995a), Section 5, and the applied uncertainty modelling in Guideline for Offshore
Structural Reliability Analysis - Examples for Jacket Platforms (DNV 1995b).
In DNV Classification Notes 30.6, Structural Reliability Analysis of Marine Structures (DNV
1992b), a general description of the uncertainty modelling for marine structures is presented.

3.2.2 Types of Uncertainty
Uncertainties associated with an engineering problem and its physical representation in an
analysis have various sources which may be grouped as follows:
• physical uncertainty, also known as intrinsic or inherent uncertainty, is a natural randomness
of a quantity, such as the uncertainty in the yield stress of steel as caused by a production
variability, or the variability in wave and wind loading.
• measurement uncertainty is uncertainty caused by imperfect instruments and sample
disturbance when observing a quantity by some equipment.
• statistical uncertainty is uncertainty due to limited information such as a limited number of
observations of a quantity.
• model uncertainty is uncertainty due to imperfections and idealisations made in physical
model formulations for load and resistance as well as in choices of probability distribution
types for representation of uncertainties.
This grouping of uncertainty sources is usually adequate. However, one shall be aware that other
types of uncertainties may be present, such as uncertainties related to human errors. Transitions
between the quoted different uncertainty types may exist.



3.2.3 Uncertainty Implementation
Uncertainties are represented in reliability analyses by modelling the governing variables as
random variables. The corresponding probability distributions can be defined based on statistical
analyses of available observations of the individual variables, yielding information on their mean
values, standard deviations, correlation with other variables, and in some cases also their
distribution types.
Variables for which uncertainties are judged to be important, e.g. by experience or by sensitivity
study, shall be represented as random variables in a reliability analysis. Their respective
probability distributions shall be documented as far as possible, based on theoretical
considerations and statistical analysis of available background data.
Dependency among variables may be important appear and shall be assessed and accounted for
when necessary. Correlation coefficients can be estimated by statistical analyses.
Model uncertainties in a physical model for representation of load and/or resistance quantities
can be described by stochastic modelling factors, defined as the ratio between the true quantity
and the quantity as predicted by the model for multiplicative correction factors. A mean value not
equal to 1.0 for the stochastic modelling factor expresses a bias in the model, and the standard
deviation expresses the variability of the predictions by the model. An adequate assessment of a
model uncertainty factor may be available from sets of field measurements and predictions.
Subjective choices of the distribution of a model uncertainty factor will, however, often be
necessary. The importance of a model uncertainty may vary from case to case and should be
studied by interpretation of parameter sensitivities.

3.3 Target Reliability
3.3.1 General
Target reliabilities have to be met in design in order to ensure that certain safety levels are
achieved. A reliability analysis can be used to verify that such a target reliability is achieved for a
structure or structural element. A difficulty in this context is that the uncertainties included in a
structural reliability analysis will deviate from those encountered in real life. This is because;
• the reliability analysis does not include gross errors which may occur in real life
• the reliability analysis, due to lack of knowledge, includes statistical uncertainty and model
uncertainty in addition to the physical uncertainty (epistemic) which is present in real life
• the reliability analysis may include uncertainty in the probabilistic model due to distribution
tail assumptions
This means that a reliability index calculated by a reliability analysis is an operational or nominal
value, dependent on the analysis model and the distribution assumptions, rather than a true
reliability value which may be given a frequency interpretation. Calculated reliabilities can
therefore usually not be directly compared with required target reliability values, unless the latter
are based on similar assumptions with respect to analysis models and probability distributions.
This is a limitation which implies that target reliability indices cannot, normally, be specified on
a general basis, but only case by case for individual applications.
For a more detailed discussion of the subject of determining the target reliability level, reference
is given to the DNV (1995a).



3.3.2 Selection of Target Reliability Level
Target reliabilities depend on the consequence and nature of failure, and to the extent possible,
should be calibrated against well established cases that are known to have adequate safety. In
cases where well established structures are not available for the calibration of target reliabilities,
such target reliabilities may be derived by comparison of safety levels established for similar
existing structural design solutions or through decision analysis techniques.
By carrying out a reliability analysis of a structure satisfying a specified code using a given
probabilistic model, the implicit required reliability level in this code will be obtained, which
may be applied as the target reliability level. The advantage with this approach compared to
applying a predefined reliability level, is that the same probabilistic approach is applied in the
definition of the inherent reliability of the code specified structure and the considered structure,
reducing the influence of the applied uncertainty modelling in the determination of the target
reliability level.
The use of codes could with advantages be applied e.g. in the determination of the minimum
acceptable reliability level, below which structural inspections for jacket structures exposed to
fatigue degradation are required. In the NPD, Act, regulations and provisions for the petroleum
activities (NPD 1996), it is stated that for structural details with no access for inspection or
repair, the design factors specified in Table 3.1 are to be applied in the design, dependent on the
consequence of failure of the detail. This could be interpreted as that a structural detail does not
need to be inspected prior to one 10th, or one 3rd, of the fatigue design life for substantial and no
substantial failure consequence, respectively. The reliability levels at these time periods (one
tenth, or one third of the design life) then consequently also correspond to the target reliability
level for which a structural inspection is required according to the code.

Table 3.1 Design fatigue factors when no access for inspection or repair exist
Damage No access or in
Consequence the splash zone
Substantial 10
consequence
No substantial 3
consequence

In general, acceptable structural probabilities of failure, specified as minimum values of target
reliabilities, depend on the consequence and nature of failure. The evaluation of the consequence
of failure comprises an evaluation with regard to human injury, environmental impact and
economical loss, whereas the nature or class of failure considers the type of structural failure.
Required minimal reliability levels make sense only together with a specification of a reference
period. The reference period should reflect the nature of the failure and is generally equal to the
anticipated lifetime of the structure, or simply one year. As a general statement it might be
argued that an annual target failure probability should be used when human life is at stake while
lifetime target failure probabilities applies if the consequence is material cost only.
The economical aspect will mainly depend on the economical consequence of the failure due to
repair cost, missing income and/or demand in the repair period. When the failure consequence
regards economic loss, minimum target structural failure probabilities may be specified by the



operator based on requirements from national authorities and company design philosophy and/or
risk attitude. The safety level may therefore in general vary between the individual structures.
The direct consequence of failure for the environment could be included in the target safety level
related to economical consequences.
A major accident is likely to have a negative influence on the reputation of the company, both
towards the government and towards the society in general. The consequence of this effect is
difficult to quantify. It is probably related to the company philosophy or may simply be
considered as a part of the economical consequence.
The consequence of failure related to human injury will in large extent depend on the type of
failure and operational condition for the platform. E.g., in DNV CN 30.6 (DNV 1992b), the
criterion concerning human injury is to be formulated as the annual probability of failure (defined
as total collapse of the platform) shall not exceed 10-6 for no warning and serious consequences.
The target reliability level may also be based upon the proposed values presented in Table 3.2,
taken from DNV Classification Notes 30.6 (DNV 1992b). When predefined reliability levels are
applied as target values, care must, however, be made in the uncertainty modelling in order to
account for the same level of uncertainty as is reflected in the predefined target reliability level.
The target reliabilities, specified in Table 3.2., are therefore closely connected with the proposed
uncertainty modelling described in the Classification Notes.

Table 3.2 Values of acceptable annual failure probability and target reliability index
Class of Failure Less Serious Serious
Consequence Consequence
I. Redundant structure PF = 10-3 PF = 10-4
β = 3.09 β = 3.71
II. Significant warning prior to PF = 10-4 PF = 10-5
occurrence of failure in a non-
β = 3.71 β = 4.26
redundant structure
III.No warning before the PF = 10-5 PF = 10-6
occurrence of failure in a non-
β = 4.26 β = 4.75
redundant structure


DNV Report No. 95-3203 Discussion of Limit States

4. DISCUSSION OF LIMIT STATES
4.1 Introduction
The objective for all structural designs is to build structures which fulfil proper requirements
with respect to functionality, safety and economy. These three aspects are closely connected and
an iterative process is necessary to achieve the most optimal design. Current design practice is
based on partial safety factors and control against several limit states. A structure, or a structural
component, is considered not to satisfy the design requirements if one or more of the limit states
are exceeded. Four main categories of limit state are defined in the NPD regulations (NPD 1996):
• Ultimate Limit State (ULS) which is defined on the basis of danger of failure, large inelastic
displacement or strains, comparable to failure, free drifting, capsizing and sinking.
• Fatigue Limit State (FLS) which is defined on the basis of danger of fatigue due to the effect
of cyclic loading.
• Progressive Collapse Limit State (PLS) which is defined on the basis of danger of failure, free
drifting, capsizing or sinking of the structure when subjected to abnormal effects.
• Serviceability Limit State (SLS) which is defined on the basis of criteria applicable to
functional capability, or durability properties under normal conditions.

Only the fatigue limit state and the ultimate limit state will be discussed further in this report.
The Ultimate Limit State for a structure can be considered as the collapse of the structure. This
limit state is difficult to describe through simple design equations, and therefore the design is
normally performed at a component level where the capacity of the single joints and members
between the joints are analysed/designed separately. Alternatively, the capacity for the Ultimate
Limit State can be assessed by non-linear analysis. At present non-linear analyses are performed
for reassessment and requalification purposes, but is not considered to be practical at a design
stage. Also guidelines on how to perform such analyses are lacking. Therefore limit state
functions for reliability analysis of jacket structures will in general also be based on design
equations for single components.
The ULS limit state functions required for design of jacket structures are:
• Capacity of members between the joints with respect to yielding and buckling. This includes
both local buckling and global bending buckling of the member, section 4.2.1-2. The local
capacity is further affected by external pressure which may interact with global member
buckling, section 4.2.3.
• Capacity of joints, section 4.3

Traditional ULS design are based on load effects determined by elastic frame analyses.
It should be noted that the design equations in the design standards are based on characteristic
values which are defined at some fracture value or lower bound value. For reliability analyses the
limit states are based on the actual values, accounting for uncertainties, where the load and
material coefficients are not included in the equations for the limit state functions.



The Progressive Collapse Limit State is used to design the platforms for accidental events having
a probability of occurrence larger than 10-4. Accidental events such as explosion, fire and ship
impacts are considered. The accidental events are defined from Quantitative Risk Analyses, see
Section 2 of Guideline for Offshore Structural Reliability - General (1995a). Possible damage to
the structure is calculated based on an elasto-plastic analysis, and the structure is then analysed
with that damage for a given environmental loading. This analysis is similar to that of an
Ultimate Limit State analysis, but with different load and material coefficients in the design
equation according to the NPD regulations, (NPD 1996).
The Serviceability Limit State is used for control of deflections and accelerations of the topside
structures, but is hardly used for the design of jacket structures.
The potential application areas for structural reliability analyses of jacket structures are within
detailed design verification and for in-service inspection planning. For important components,
the failure modes comprise;
• Jacket members (legs and braces) (ULS):
* Buckling of members:
- Local buckling of members
- Global buckling of members
- Buckling of members subjected to external pressure
* Total structural collapse due to environmental loading (e.g. wave and current loading on
the jacket and wind loading on the superstructure)
• Tubular joints (ULS):
* Joint failure
• Tubular joints and connections (FLS):
* Fatigue at hot-spots in welded connections
In the following sections the above component failure modes due to buckling failure of members,
joint failure and fatigue failure are discussed, and examples for models which may be applied in
a reliability analysis are given. Furthermore, a simplified limit state for system failure defined as
total structural collapse due to environmental loading is discussed, where the total structure is
considered as a single component.



4.2 Buckling Failure of Members (ULS)
4.2.1 Local Buckling of Members
The susceptibility to local buckling of tubular members is a function of member geometry and
yield strength. The behaviour of a tubular subjected to a bending moment is shown in Figure 4.1.
As the capacity behaviour is dependent on the geometry and material characteristics, it is
convenient to define the tubulars in section classes (Eurocode 3 (1993)) as illustrated in Table
4.1

Table 4.1 Requirements to section classes in Eurocode 3
Section Class I Section Class II Section Class III Section Class IV
d/t ≤ 11750/fy 11750/fy ≤ d/t ≤ 16450/fy 16450/fy ≤ d/t ≤ 21150/fy 21150/fy ≤ d/t
fy = yield strength (MPa) d = diameter t = thickness

The section classes are defined as follows:
Class I : cross-sections are those which can form a plastic hinge with the rotation capacity
required for plastic analysis.
Class II: cross-sections are those which can develop their plastic moment resistance, but have
limited rotation capacity.
Class III: cross-sections are those in which the calculated stress in the extreme compression
fibre of the steel member can reach its yield strength, but local buckling is liable to
prevent development of the plastic moment resistance.
Class IV: cross-sections are those in which it is necessary to make explicit allowances for the
effects of local buckling when determining their moment resistance or compression
resistance. Tubulars belonging to this section class may also be defined as a shell
structure.
These section classes are not defined for conditions with external pressure, and tests or numerical
analyses must be carried out for documentation. This is controlled under section 4.2.3.

Θ

Figure 4.1 Tubular capacity in bending for different section class dependent on degree of
deformation Θ.



4.2.2 Global Buckling of Members
4.2.2.1 Background
The procedure for design of tubulars subjected to a bending moment according to the NPD
regulations is based on linear elastic analysis as if all tubulars were belonging to section class III.
(Reference is made to Eurocode 3 (1993) with respect to requirements to section classes which
for tubulars are shown in Table 4.1). This procedure is considered to be sufficient for tubulars
subjected to external pressure.
The procedure for design of tubulars in air is considered conservative for section classes I and II
as yielding of the section is allowed (by definition of section class). A higher capacity accounting
for the plastic section modules is directly achieved through a non-linear analysis. The increase in
the bending capacity by going from elastic to plastic section modules is a factor of 4/π=1.27.
The effect of plastic section modulus is more directly incorporated in the API design equations
than that of NPD although it is opened for plastic design also in the NPD regulations.
Other items related to buckling of tubular members are:
- effective buckling lengths
- buckling curves
- effect of external pressure.

In a design analysis it is common to assume a buckling length that is representative for typical
member configurations as X-braces, K-frames, single braces, jacket legs and piles. The effective
buckling length is dependent on the joint flexibilities and for X-braces also on the amount of
tension force in the crossing element. It is also a matter of discussion whether the buckling length
should be measured from centreline to centreline of jacket legs which can be argued for in the
case of a combined collapse of the braces and the legs, or if the buckling length should be
associated with the face to face length between the legs which may be argued for considering
buckling of a single brace. The effective buckling length may be derived from analytical
considerations. However, the effective buckling lengths derived from theoretical considerations
are longer than the buckling lengths obtained from tests of frame structures loaded until collapse.
It should be noted that the basis for the buckling curves in the different codes is different. The
API buckling curve is derived as a lower bound value for low slenderness while it is equal to the
Euler stress for high slenderness values which may be considered as an upper bound value for
that region. Another definition of a buckling curve is used in the AISC (1986). The background
for the buckling curves used in design of steel structures in European design standards is based
on work carried out within the European Convention for Constructional Steelwork which is
presented in Manual on Stability of Steel Structures (1976). The design curves are presented by
their characteristic values which are defined as mean values minus two standard deviations along
the slenderness axis. The test results are assumed normal distributed.
It is also noted that the requirements to allowable fabrication eccentricity are different associated
with the various buckling curves. For the European buckling curves, a straightness deviation at
the middle of the column equal 0.0015 times the column length is allowed, while for API and
AISC the corresponding numbers are 0.0010 and 0.00067, respectively.
Different buckling curves used for design of tubular members are shown in Figure 4.2.



The design equation for global member buckling in the NPD regulations (NPD 1996) reads
fy
σ c + Bσ b + Bσ b ≤
*

γm
where

N
σc = = design axial compressive stress
A
N = axial force

A = section area
1
B = bending amplification factor =
N
1−
NE
N E = Euler buckling load
fy fk
σb = σc ( − 1)(1 −
*
)
fk γ m fE
NE
fE =
A
f k = characteristic buckling strength derived from the buckling curve

Buckling stress
1.2
ECCS,NPD,DNV
API LRFD
1 API WSD/AISC
Euler
0.8

0.6

0.4

0.2

0
0 0.5 1 1.5 2 2.5 3 3.5
Reduced slenderness

Figure 4.2 Different buckling curves used for design of tubular members



4.2.2.2 Limit State Function
The limit state function for global buckling of members can be formulated as

G = f y − ( σ c + Bσ b + Bσ b )
*

where
f y = yield strength

N
σc = = design axial com pressive stress
A
N = axial force
A = section area
1
B = bending amplification factor =
N
1−
NE
N E = Euler buckling load
fy f
σb = σc ( − 1)(1 − k )
*

fk fE
NE
fE =
A
f k = buckling strength derived from the buckling curve



4.2.3 Buckling of Members Subjected to External Pressure
4.2.3.1 Background
The capacity of tubulars subjected to axial force, bending and external pressure may be designed
based on the guidelines on design and analysis provided by the Norwegian Petroleum Directorate
(NPD 1996) with additional guidance by Lotsberg (1993), or by a design procedure presented by
Loh (1990). In the following the design procedure given by NPD and Lotsberg is given. It should
be noted that it is only the effective axial force that contributes to the axial stresses that enhance
buckling, see Figure 4.3. The axial stress resulting from the external pressure do contribute in the
equation for the von Mises stress considering yielding, but does not contribute to the axial force
that gives global buckling stress.

Figure 4.3 Illustration of effective axial force to be used for global buckling. (The total
stress is governing for the local structural behaviour in terms of yielding
and local buckling)

The equation for global buckling is modified to account for the effect of external pressure as
follows:

B + B 2 − 4 AC
σ ac =
2A
where
f y2
A = 1+ 2
f ea



2 f y2
B=( − 1)σ p
f ea f ep

f y2 σ 2
C= σ2 + − f y2
p
p 2
f ep

fea = elastic buckling stress with respect to axial force

π 2E æ tö
2

f ea =k ç ÷
12(1 − ν 2 ) è l ø

0123l 4 (1 − ν 2 )
.
k = 1+
r
r 2 t 2 (1 + )
150t
fep = elastic buckling stress in hoop direction with respect to external pressure

2
ætö
f ep = 0.25ç ÷
è rø

σp = stress in hoop direction due to external pressure

The equation for global buckling is then modified as follows
σ ac − σ axp
σ c + Bσ * + Bσ b ≤
b
γm
where σaxp = axial stress in the tubular due to end cap pressure = σp/2.
For other notations see section 4.2.2. Note that σc now is derived as the effective axial stress
(without including the end cap stress resulting from external pressure).
An example of the difference between the effective axial stress and the total stress in a tubular
member as function of the water depth is shown in Figure 4.4. It is noted that the difference is
small for water depths below say 100 metres, but that it becomes significant for deep-water
structures.



4.2.3.2 Limit State Function
The limit state function for global buckling of members subjected to external pressure can be
formulated as,
G = σ ac − σ axp − (σ c + B σ * + B σ b )
b

with notation as given in section 4.2.1.

200
Effective stress
180
Total stress
160

140
Allowable stress

120

100

80

60

40

20

0
0 200 400 600 800 1000
Waterdepth in m

Figure 4.4 Axial stress in the tubular as function of water depth and external pressure
at global member buckling

4.3 Joint Failure (ULS)
4.3.1 Background
A number of design equations have been established for the static strength of tubular joints. The
equations in API (1991) and NPD (1996) show a similar shape although the coefficients are
different as also might be expected as the API RP2A is based on allowable stresses, while the
NPD has based the design on the partial coefficient method since 1977. The following work is
based on the NPD regulations, but only small modifications would be required to revert to
another standard such as that of API or HSE.

It should be mentioned that work on joint capacities is being carried out within the development
of a new ISO standard on design of steel offshore structures. This work should be considered as
basis for limit state functions when it is available.

The following symbols are used:



T = Chord wall thickness
t = Brace wall thickness
R = Outer radius of chord
r = Outer radius of brace
θ = Angle between chord and considered brace
D = Outer diameter of chord
d = Outer diameter of brace
a = gap (clear distance) between considered brace and nearest load-carrying brace measured
along chord outer surface
β = r/R
γ = R/T
g = a/D
fy = Yield strength
Qf = See Table 4.3
Qg = See Table 4.2
Qu = See Table 4.2
Qβ = See Table 4.2
N = Axial force in brace
MIP = In-plane bending moment
MOP = Out-of-plane bending moment
Nk = Axial load capacity of brace(as governed by the chord strength)
MIPK = In-plane bending moment capacity of brace(as governed by the chord strength)
MOPK = Out-of-plane bending moment capacity of brace(as governed by the chord strength)
σax = Axial stress in chord
σIP = In-plane bending stress in chord
σax = Out-of-plane bending stress in chord



Table 4.2 Values for Qu (Characteristic values)
Type of joint and geometry Type of load in brace member
Axial In-plane bending Out-of-plane
bending
T&Y 2.5 +19β
X (2.7 +13β)Qβ 5.0γ0.5β 3.2/(1-0.81β)
K 0.90(2 +21β)Qg

ì 0.3
ï β(1 − 0.833β ) for β > 0.6
ï
Qβ = í
ï .
10 for β ≤ 0.6
ï
î

ì18 − 01a / T
. . for γ ≤ 20
ï
Qg = í
ï 18 − 4 g for γ > 20
î .

but in no case shall Qg be taken less than 1.0.

Table 4.3 Values of Qf
Loading Qf
Axial 1.0-0.03γA2
In-plane bending 1.0-0.045γA2
Out-of-plane bending 1.0-0.021γA2

where
σ ax + σ 2 + σ 2
2

A = 2 IP OP

0.64 f y2

The characteristic capacity of the brace subjected to axial force is determined by
fyT 2
Nk = Qu Q f
sin θ



The characteristic capacity of the brace subjected to in-plane moments is determined by
df y T 2
M IPk = Qu Q f
sin θ

The characteristic capacity of the brace subjected to out-of-plane moments is determined by
df y T 2
M OPk = Qu Q f
sin θ

2
N æ M IP ö M 1
+ç
çM ÷ ÷ + OP ≤
N k è IPk ø M OPk γ m

where γm is a material coefficient =1.15.

Figure 4.5 Simple Tubular Joint



Figure 4.6 Force displacement relationship for a tubular joint

4.3.2 Limit State Function
The limit state function for the static capacity of tubular joints can be formulated as
2 2
N æ M IP ö M N æ M IP ö M
G = 1− ( +ç
çM ÷ ÷ + OP ) or G = − log( +ç ÷ + OP )
N k è IPk ø M OPk N k è M IPk ø M OPk

where the equations given above are used to calculate Nk, MIPk and MOPk with Qu from Table 4.4
and A as given below.
Table 4.4 Values for Qu based on 50 per cent fractiles (median values)
Axial In-plane bending Out-plane bend.
T&Y 2.8 +21β
X (3.0 +14.6β)Qβ 5.6γ0.5β 3.6/(1-0.81β)
K (2.6 +27β)Qg

The parameter A for calculation of Qf in Table 4.4 is obtained as:

σ ax + σ 2 + σ 2
2

A2 = IP OP

f y2



The CoV values in Table 4.5 for Qu may be used for the reliability analysis based on the
presented limit state functions. Qu is normal distributed. For CoV for yield strength, see DNV
(1995a).

Table 4.5 Values for CoV for Qu
Axial In-plane bending Out-plane bend.
T&Y 0.10
X 0.10 0.10 0.10
K 0.20

4.4 Fatigue Failure at Hot-spot of Welded Connections (FLS)
4.4.1 General
4.4.1.1 Overview
Jacket structures of all types are generally subjected to cyclic loading from wind, current,
earthquakes and waves, which cause time-varying stress effects in the structure. The
environmental quantities are of random nature and may be more or less correlated to each other
through the generating and driving mechanisms. Waves and earthquake loads are generally
considered to be the most important sources for structural excitations. However, earthquake
loads are only taken into account in the analysis of structures close to, or within tectonic areas,
and will not be included here. Wind and current loads represent an insignificant contribution to
the fatigue loading and may be ignored in the fatigue analysis of jacket structures.
A fatigue analysis of offshore structures can in general terms be described as a calculation
procedure, starting with the environment (waves) creating stress ranges at the hot-spot regions
and ending with the fatigue damage estimation. The link between the waves and the fatigue
damage estimate is formed by mathematical models for the wave forces, the structural behaviour
and the material behaviour. The probabilistic fatigue analysis may be divided into four main
steps:
1) Probabilistic modelling of the environmental sea states (short- and long-term modelling)
2) Probabilistic modelling of the wave loading
3) Structural response analysis (global and local)
4) Stochastic modelling of fatigue damage accumulation.
The above steps are covered in DNV (1995a). In the following, it will be focused on the
application to jacket structures.
In addition to the above steps, the analysis includes a stochastic modelling of the fatigue capacity
and the probabilistic evaluation, i.e. the probabilistic derivation of the likelihood of the event that
the accumulated fatigue damage exceeds the defined critical fatigue strength level.



In order to carry out a realistic fatigue evaluation of a jacket structure, it is necessary to introduce
some simplifying assumptions in the modelling. These assumptions consist of:
• For a short term period (a few hours) the sea surface can be considered as a realisation of a
zero-mean stationary Gaussian process. The sea surface elevation is (completely)
characterised by the frequency spectrum, which for a given direction of wave propagation, can
be described by two parameters, the significant wave height HS and some characteristic
period like the spectral peak period TP or the zero-mean up-crossing period TZ .
• The long term probability distribution of the sea state parameters ( HS − TP or HS − TZ
diagram) is known.
• Applying frequency domain approach for assessing the structural response, the wave loading
on structural members must be linearised and the structural stress response must be assumed
to be a linear function of the loading, i.e. the structural and material models are linear.
• The relationship between the sectional forces and the local hot-spot stresses (SCFs) is known,
where an empirical parameter description is most common.

Fatigue is the process of damage accumulation in a material undergoing fluctuation stresses and
strains caused by time-varying loading. Fatigue failure occurs when the accumulated damage is
exceeding a critical level. The fatigue process experienced by most offshore structures is high-
cycle fatigue, i.e. the fluctuating nominal stress levels are below the yield strength and the
number of cycles to failure is larger than 10 4 . Fatigue damage in welded structures is likely to
occur at the welded joints due to the stress concentration at areas of geometric discontinuity.
Notches and initial defects caused by the welding processes may also occur in this area.
Traditional fatigue design of jackets is based on the SN-fatigue approach where fatigue failure is
assumed to occur when the crack has propagated through the thickness of the member. However,
at a design stage without any observed cracks in the structure, the estimated fatigue damage
based on fracture mechanics is normally less reliable than that derived from SN data due to the
difficulties involved in assessing the initial crack size. Applying the SN-approach, the fatigue
damage is measured in degree of damage, D , from an initial value 0 to ∆ , where ∆ is defined
as the fatigue damage accumulation resulting in failure, depending on the detail considered and
the selected SN-curve.
When performing a reliability updating on the basis of structural inspections for cracks, the
inspection outcome can not be used directly to update the degree of damage accumulation unless
the fracture mechanics approach is applied. In order to also be able to perform reliability
updating when the SN approach is applied, a procedure for establishing a relationship between
these two fatigue approaches is proposed in the following.

4.4.1.2 System Aspects
Jacket structures are typically redundant with respect to brace failures and a total structural
collapse will not occur before several members have failed. After a member has failed due to e.g.
fatigue, the applied loading will be transferred by the remaining members, i.e. a redistribution of
the load through the structure occurs. In the damaged structure, each remaining member has
already some accumulated fatigue damage, and due to the redistribution of the stresses in the
structure the rate of damage accumulation will change. By accounting for the changes due to
failure in other members, the total damage at a section can by formulated mathematically. Once


the time to failure for each individual section in a sequence is defined, the sequence event is
defined as the intersection of a set of section failure events for which the time to failure for each
individual section is less than the lifetime of the structure.
Usually, there will be many alternative sequences leading to collapse, and the total structural
failure is the event that one of these collapse sequences occurs.
A system reliability approach is required when the probability of total structure failure
accounting for the progressive nature of collapse is to be estimated. One of the difficulties with
such an approach is that for typical structures there are a very large number of sequences leading
to failure, and that it is not feasible to include all of these in the analysis. Usually, however, only
few of the failure sequences have significant contributions to the total failure probability.
Therefore, in most structural reliability analyses, a search technique can be used to identify
important failure sequences and the system failure event is approximated as the union of
important sequences.

4.4.2 SN-Fatigue Approach
4.4.2.1 General
The fatigue life of a joint may in general be characterised by three time intervals:
Tinitial The crack initiation period or first discernible surface cracking.
Tth The total time until the crack has propagated through the thickness.
Tsec The total time until gross loss of structural stiffness with extensive through thickness
cracking (defined as section failure).

Based on inspections for fatigue cracks in the joints, a fatigue reliability updating based on the
outcome of the inspections can be carried out applying Bayesian updating. The inspection results
can for the SN-approach not be used directly to update the estimated accumulated fatigue
damage. However, if a relationship between the damage accumulator D in the SN-approach and
the crack size was available, it would be possible to utilise the inspection results for reliability
updating.
No guidelines or established procedures are available for establishing the relationship between
the accumulated fatigue damage from the SN-approach and the crack size. This relationship may,
however, be obtained by calibrating the parameters describing the crack propagation in the
fracture mechanics approach. In the following the parameters are calibrated by fitting the
probability of having a through thickness crack as a function of time obtained from the fracture
mechanics approach to the results obtained from the SN-approach, applying e.g. least-squares
fitting.
It should be noted that calibrating the through thickness cracking to a SN-curve is in general
inconsistent, as the crack initiation period included in the SN-approach is not incorporated in the
fracture mechanics formulation. This may lead to unconservative results in the reliability
updating based on the outcome of inspections.
More consistent results may be obtained by applying only the SN-curve for the crack
propagation period (if available) in the calibration of the fracture mechanics material parameters,
i.e. a SN-curve describing the number of load cycles it takes for an already initialised crack to



propagate through the thickness. This approach assumes there exists a model available to
estimate the crack initiation time and that the time period until inspection is greater than the
crack initiation time.
However, very limited information is available for describing the crack initiation time and the
SN-curves for the crack propagation period. The calibration of the fracture mechanics parameters
is therefore in the present study based on SN-curves where the crack initiation period is included
in the modelling of the fatigue capacity applying the SN approach. It should in this connection
also be noted that for welded details, the crack initiation period is relatively small compared to
the whole fatigue life.
4.4.2.2 SN-Fatigue Modelling
SN-data are experimental data giving the number of cycles N of stress range S resulting in fatigue
failure. These data are defined by SN-curves for different structural details.
The design SN-curves are based on a statistical analysis of experimental data. They are given as
linear or piece-wise linear relations between log10S and log10N. A design curve is defined as the
mean curve, minus two standard deviations of log10N obtained from the data fitting. The standard
deviation is computed based on the assumption of a fixed and known slope.
The design SN-curves are thus of the form

log 10 N = log 10 a − 2σ log10 N − m log 10 S

or
−m
N = K ⋅S , S > S0
where
N number of cycles to failure for stress range S
a a constant relating to the mean SN-curve
σ log10 N the standard deviation of log10N

m the inverse slope of the SN-curve
S0 stress range level for which change in slope occurs, i.e. for bilinear SN-
curve or endurance limit for single slope SN-curve
log10 K log 10 a − 2σ log10 N

The bilinear SN-curve is defined as,
ì K S −m ; S > S0
ï − −
N =í K S 0 m = K 2 S 0 m2
ï K S − m2 ; S ≤ S0
î 2
where m2 is the inverse slope of the SN-curve ( ∞ for endurance limit at S 0 ).
The numerical values for the relevant parameters are summarised in table 7.10 in DNV (1995a).
For tubular joints, the T-curve (DNV 1984) is recommended for modelling the fatigue capacity.



In air, the T-curve has m=3, which changes to m2 =5 at N = N 0 = 10 7 . For cathodically protected
structures in seawater the T-curve has m=3 and a cut-off value at N = N 0 = 2 ⋅ 108 . Knowing N 0
and K, the stress range level S 0 can be obtained by
1
æ Kö m
S0 = ç ÷
è N0 ø
The fatigue strength of welded joints is dependent on the plate thickness, t, with decreasing
fatigue strength with increasing thickness. The design T-curve is used when the thickness t in a
tubular joint is less than 32 mm. For the thickness t ≥ 32 mm a modification of the T-curve is
performed, and the modified T-curve becomes,
m æ t ö
log10 N = log10 K − ⋅ log10 ç ÷ − m ⋅ log10 S S > S0
4 è 32 ø
or
− m/ 4 −m
N = ( t / 32 ) ⋅K ⋅S S > S0

− m/ 4
The factor ( t / 32 ) is denoted the thickness-effect factor.

4.4.2.3 Uncertainty in SN-curves
The uncertainties associated with describing the fatigue capacity through empirical SN-curves
are accounted for by considering a stochastic SN-relation. This may be done by treating the
parameters in the deterministic linear or bilinear SN-relation as random variables. I.e. by
modelling the inverse slope m as deterministic and fitting the log10N test data from the fatigue
tests to the Normal distribution. The uncertainty modelling of the SN-curve can then be obtained
by modelling K as a Log-Normal distributed stochastic variable. E.g., for the T-curve with
cathodic protection in seawater, where the inverse sloop m is modelled as deterministic and K is
modelled as Log-Normal distributed, the stochastic modelling of the SN-curve is defined by the
following properties:
E[ K ] = 539 ⋅ 1012
. Std [ K ] = 335 ⋅ 1012
.
m = m1 = 3 N ≤ N0
m = m2 = ∞ N > N0
The importance of modelling the cut-off level N 0 as stochastic should also be evaluated. For
stochastic modelling of N 0 the Normal distribution should be selected, e.g. with

E[ N 0 ] = 2 ⋅ 108 CoV [ N 0 ] = 010
.

4.4.2.4 Fatigue Damage Model
The accumulated fatigue damage is computed from the representative stress distribution and the
SN-capacity model. The accumulated damage depends on the number and magnitude of the


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