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- 1. TECHNICAL REPORTJOINT INDUSTRY PROJECT GUIDELINE FOR OFFSHORE STRUCTURAL RELIABILITY ANALYSIS: APPLICATION TO JACKET PLATFORMS REPORT NO. 95-3203 DET NORSKE VERITAS
- 2. TECHNICAL REPORTJOINT INDUSTRY PROJECT GUIDELINE FOR OFFSHORE STRUCTURAL RELIABILITY ANALYSIS: APPLICATION TO JACKET PLATFORMS REPORT NO. 95-3203 DET NORSKE VERITAS
- 3. DET NORSKE VERITASTECHNICAL 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 80DET NORSKE VERITAS, Head Office: Veritasvn 1, N-1322 HØVIK, Norway Org. NO 945 748 931 MVA
- 4. DET NORSKE VERITASTECHNICAL REPORTDET NORSKE VERITAS, Head Office: Veritasvn 1, N-1322 HØVIK, Norway Org. NO 945 748 931 MVA
- 5. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 5DNV Report No. 95-3203 IntroductionTable of Contents1. INTRODUCTION ...................................................................................................................................................71.1 OBJECTIVE ...............................................................................................................................................................71.2 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 ....................................................................................................................................91.3 ARRANGEMENT OF THE REPORT ............................................................................................................................... 92. RESPONSE TO ENVIRONMENTAL ACTIONS .............................................................................................112.1 CLASSES OF RESPONSE ...........................................................................................................................................112.2 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) ................................................................................................................................................143. UNCERTAINTY MODELLING - TARGET RELIABILITY ..........................................................................163.1 GENERAL ...............................................................................................................................................................163.2 UNCERTAINTY MODELLING ....................................................................................................................................16 3.2.1 Overview........................................................................................................................................................16 3.2.2 Types of Uncertainty......................................................................................................................................16 3.2.3 Uncertainty Implementation ..........................................................................................................................173.3 TARGET RELIABILITY .............................................................................................................................................17 3.3.1 General ..........................................................................................................................................................17 3.3.2 Selection of Target Reliability Level..............................................................................................................184. DISCUSSION OF LIMIT STATES.....................................................................................................................204.1 INTRODUCTION .......................................................................................................................................................204.2 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................................................................................................................................................. 284.3 JOINT FAILURE (ULS) ............................................................................................................................................28 4.3.1 Background....................................................................................................................................................28 4.3.2 Limit State Function ......................................................................................................................................324.4 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 ............................................................................................................. 43Sigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 6. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 6DNV Report No. 95-3203 Introduction 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:.......................................................................................................594.5 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) ........................................................................675. SUMMARY OF APPLICATION EXAMPLES .................................................................................................705.1 SUMMARY OF FATIGUE FAILURE LIMIT STATE - FLS EXAMPLE .............................................................................70 5.1.1 Modelling Approach ......................................................................................................................................70 5.1.2 Discussion of Results .....................................................................................................................................715.2 SUMMARY OF TOTAL COLLAPSE LIMIT STATE - ULS EXAMPLE.............................................................................72 5.2.1 Modelling Approach ......................................................................................................................................72 5.2.2 Discussion of Results .....................................................................................................................................736. REFERENCES ......................................................................................................................................................75Sigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 7. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 7DNV Report No. 95-3203 Introduction1. INTRODUCTION1.1 ObjectiveThe objective of the application part of the project Guideline for Offshore Structural ReliabilityAnalysis for the structure types jacket, TLP and jack-up, is to give• an overview of the characteristics of that structures 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) tothe structure type; i.e. in which the joint probability distribution of the uncertain parameters isused 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 bearingcomponents of the structure. Hence, the guidelines prepared in this project concentrate on therequirements for these types of analyses, and do not make any attempt to embrace all aspects ofthe decision process. However, within these limitations, our aim is to cover significant aspects ofthe structural of reliability analysis.1.2 Definition of a Jacket1.2.1 GeneralFixed steel offshore structures are often called “jackets”. The name jacket originates from theearly days of the offshore industry when a trussed structure, jacket, was placed over the piles toprovide lateral stiffness to withstand wave, current and wind forces.Jackets have been installed in water depths ranging from 0 to 400 metres, and in conceptualdesigns greater water depths have been considered. The steel weight and thus the cost increasesrapidly with water depth, therefore alternative platform solutions are often chosen for large waterdepths. Jackets have been designed to support topside weights of up to about 50000 tonnes, andit is feasible to design jackets for even larger topside weights.The performance of jackets in hostile ocean environment has generally been good, although localfatigue damages have occurred in the earlier platforms. There have been very few total failures,and then only with the oldest platforms.Sigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 8. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 8DNV Report No. 95-3203 Introduction1.2.2 Types of JacketsA 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 jacketdesigned 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 jacketIn 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 bargelaunched mode of installation has been most common as long as only “smaller” lifting vesselswere available. During the last ten years many platforms weighing less than 10.000 tonnes havebeen lift installed, thus minimising the need for temporary installation aids.Most often jackets have piled foundations, but lately jackets have also been designed with platedfoundations, which reduce installation time. Among the piled jackets it is distinguished betweenthose with piles in the legs, template type jacket, and those with piles arranged as skirts andclusters, tower type jackets.1.2.3 Structural Design ParametersThe 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.Sigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 9. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 9DNV Report No. 95-3203 Introduction1.2.4 Jacket Design AnalysisShallow water depth jackets are generally designed with adequate strength based on a staticanalysis where the wave loads are applied statistically on the structure. In addition a deterministicfatigue analysis and earthquake analysis (if required) are carried out. The jacket is in additiondesigned for the temporary installation phases. The natural period of the jacket is calculated toestablish 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 thewave periods) than the shallow water platforms. These platforms need to be designed based onboth static and dynamic (stochastic) wave analyses. For the fatigue investigation a stochasticdynamic fatigue analysis may be more suited than a deterministic fatigue analysis. Earthquakeanalysis is carried out as required, and the jacket is designed for the temporary installationphases.As mentioned above deep water platforms may be dynamically sensitive to wave forces. Thefrequency distribution of the random waves becomes a significant wave design parameter and theselection of wave spectra for design analyses is therefore extremely important. Due to the longfundamental period of vibration of the platform the fatigue behaviour may become one of thecritical design considerations.1.3 Arrangement of the ReportThe response of Jacket structures to environmental loads are described in section 2, together withmethods for computation of the resulting load effects. The model uncertainties associated withthe computation of these load effects and the selection of target reliability are discussed insection 3. Important limit states are described in chapter 4, where also the stochastic modelling ofthese 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 Jacketstructure. The details of these analyses are presented in a separate report, Guideline for OffshoreStructural Reliability Analysis - Example for Jacket Platforms (DNV 1995b).The present report is based on the general guidelines set out in the Guideline for ReliabilityAnalysis of Marine Structures - General, DNV (1995a). Companion applications are alsoavailable for jack-ups and TLP structures.Sigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 10. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 10DNV Report No. 95-3203 IntroductionFigure 1.2 Jacket designed to support drilling and production facilitiesSigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 11. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 11DNV Report No. 95-3203 Response to Environmental Actions2. RESPONSE TO ENVIRONMENTAL ACTIONS2.1 Classes of ResponseAn important task in the reliability evaluation of an offshore structure is identification andmodelling of all significant loads and load combinations which the structure is exposed to duringthe 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 byover-water wind loads, by surface wave loads and by current loads that exist during severe stormconditions.In the North Sea, the surface waves during storm conditions are of major importance in thedesign of Jacket structures for deep water environments, where the wind loads only represent acontribution of less that 5% of the total environmental loading. However, in the Gulf of Mexicothe wind loads are of major importance, having wind speeds during hurricane conditionsexceeding 50 m/s. Currents at a particular site can also contribute significantly to the total Jacketloading, where current generally refers to the motion of water that arises from sources other thansurface waves. E.g., tidal currents arise from the astronomical forces exerted on the water by themoon and sun, wind-drift currents arise from the drag of local wind on the water surface andocean 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 onjacket structures. Regarding the other load categories, reference is made to DNV (1995a).Sigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 12. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 12DNV Report No. 95-3203 Response to Environmental Actions2.2 Environmental Loads and Response2.2.1 Environmental ParametersThe parameters describing the environmental conditions shall be based on observations from, orin the vicinity of the actual location and on general knowledge about the environmentalconditions in the area. This is e.g. reflected in The Norwegian Petroleum Directorate, Guidelinesfor Loads and Load Effects (NPD (1996)) where it is stated that in designing, the recording ofwave 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 relativelyshallow waters with no structural dynamic effects present.However, if the fundamental eigenperiods of the jacket system are at a level which may causeresonance phenomena, additional environmental parameters are needed in the design. For suchcircumstances the wave spectrum needs to be defined for different sea states, and the relativeoccurrence rate of significant wave height (Hs) and zero up crossing period (Tz) (or spectral peakperiod (Tp)) needs to be established. The wave spectra are usually of a single peak type (PM, orJONSWAP), 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)• earthquake2.2.2 Combination of Environmental ParametersTraditionally jacket design is performed by assuming wind, waves and current acting in the samedirection. The assigned probability level for each of the environmental parameters whencombining them may vary depending on the applicable code.The NPD Guideline for Load and Load Effects (NPD (1996)) presents a combination ofenvironmental loads which has been extensively used the last decade, see Table 2.1. Moredetailed procedures for assessing the combined environmental loading will normally be acceptedin design provided sufficient data and documentation are available. In this context one should beaware of that jacket design is usually governed by the wave loads.If simultaneous time series of environmental parameters exists, long term joint environmentalmodels may be used. Alternatively, the environmental parameters may be approximated bymarginal distributions as reflected in Table 2.1. For further details, see DNV (1995a) Section 5.Sigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 13. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 13DNV Report No. 95-3203 Response to Environmental ActionsTable 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 - - - 10-2Limit State 10-1 10-1 10-1 10-2 - - m (ULS) - - - - 10-2 - m - - - - - 10-2 mProgressive 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 m2.2.3 Simulation of Wave LoadsThe Morris’s equation has been widely applied in the design of jacket structures in the lastdecades for assessing the wave induced loading. This is not a complete and consistentformulation which fully simulates the wave loads. The Morris’s equation has, however, proved togive reasonable reliable results by careful selection of the drag (Cd) and inertia (Cm) coefficientsin combination with an appropriate wave theory.The jackets are usually made up of tubulars with outer diameters varying typically from 0.3m upto 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 usuallyincluded in the modelling by increasing the drag coefficient with 8-12% depending on theamount 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 theboundary conditions in shallow water is relatively poor. This theory is suitable as it describes thewave kinematics above the mean water level and give information about the crest height whichin turn is needed in e.g. air gap calculations.First order wave theory may also be used when the procedure for extrapolating the wave profileabove (and below) the mean water level is carefully selected. The “Stream” function gives a goodanalytical validity over a wide range of wave conditions and is to be used in relatively shallowwaters. This theory also has a set of free parameters that can be adjusted to achieve the best fit tothe dynamic free boundary conditions. For very shallow waters Cnoidal & Solitary Wave may beapplicable. Other wave theories exists (e.g. New-Wave, Tromans et al. (1991)), however, theexperience with use is limited.The energy distribution around the dominating wave direction is usually described by a cosinedistribution 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 toinclude 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 waveheights above 10 meters if it gives reduced load effect. This recommendation is based on actualmeasurements/recordings in the North Sea. It has also been proposed to set the cosine exponentSigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 14. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 14DNV Report No. 95-3203 Response to Environmental Actionsin the wave spreading function equal to the significant wave height (in meters). This impliesmore 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 waterjackets the drag dominance is shifted towards the inertia regime due to large diameter tubulars atthe lower jacket levels. For fatigue calculations the inertia regime is also having a higherinfluence due to the importance of the intermediate wave heights in the fatigue damagecontribution.In relatively shallow waters with low fundamental periods of the jacket, static deterministicanalyses 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 combinationwith static analyses. For extreme load analyses the dynamic amplification will be low, whereasfor 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 analysisthe level of dynamic amplification is limited due to the period spacing between jacketeigenperiods 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 depthsof 150 -200m and fundamental eigenperiods beyond 3 seconds where non-linear effects related towave 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 linearisedstochastic dynamic analyses may underestimate the response significantly if the dynamics aredominating.Design wave analyses are usually considered conservative, but this depends, however, on theactual selection of design parameters in the analysis. For relatively deep water jackets it has beenfound that time domain simulations commonly give higher responses than what may bedetermined by single design wave analysis.2.2.5 Fatigue (FLS)Depending on the level of dynamic amplification, either a long-term distribution of single waveheights (H) and associated wave periods (T), or a scatter diagram ( H s − Tp or H s − Tz ), isneeded in the fatigue assessment. As stated earlier, it is a requirement for the fatigue analysis thatthe long-term environmental distributions have been established based on relevant measurementsand subsequent statistical post-processing. Long-term single wave height distributions are usuallylimited to 10 - 20 H/T combinations whereas a scatter diagram may consist of up to 200 shortterm sea states.The wave induced stress range response needs to be determined for the fatigue analysis. Differentapproaches 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 andfrom these curves the stress ranges are determined. Special considerations may be required forelements in the splash zone as these elements are intermittent in and out of the water as thewaves are passing.Sigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 15. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 15DNV Report No. 95-3203 Response to Environmental ActionsThe shape of the wave spectra has an influence on the response results. This is especially the casewhen the fundamental eigenperiod of the jacket system is high and there is little damping in thedynamic system such that resonance will occur. A dynamic system like this will e.g. givesignificantly higher responses at resonance with a Jonswap spectrum compared to a PMspectrum.A linearisation of the drag forces is needed for dynamic analyses. Different methods exist forperforming this type of linearisation. One approach is to linearise with respect to a characteristicwave height for each wave period. Members with intermittent submergence need to be treatedseparately. 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 waveenergy spectrum, by assuming the ocean waves and the corresponding fluid kinematics to beGaussian processes.Slamming on horizontal members in the splash zone needs to be taken into account in the FLSdesign. Different approaches may be applied to determine the dynamic response and the numberof oscillations due to wave slamming. However, usually this effect is minimised by carefullyplacing the horizontal levels of the jacket outside the splash zone.Sigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 16. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 16DNV Report No. 95-3203 Uncertainty Modelling - Target Reliability3. UNCERTAINTY MODELLING - TARGET RELIABILITY3.1 GeneralThere is a close connection between the uncertainty modelling and the target reliability level, asthe obtained reliability against e.g. fatigue failure or ultimate collapse in a reliability analysis isdependent on the chosen uncertainty modelling, especially with respect to the implementation ofmodelling uncertainties.3.2 Uncertainty Modelling3.2.1 OverviewThis section provides general guidance in respect to uncertainty modelling as appropriate to theultimate and fatigue limit state modelling for jacket structures. In Section 4, the proposed modelsaccounting for the uncertainties related to the FLS and ULS analyses of jacket platforms aredescribed 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 OffshoreStructural Reliability Analysis - Examples for Jacket Platforms (DNV 1995b).In DNV Classification Notes 30.6, Structural Reliability Analysis of Marine Structures (DNV1992b), a general description of the uncertainty modelling for marine structures is presented.3.2.2 Types of UncertaintyUncertainties associated with an engineering problem and its physical representation in ananalysis 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 othertypes of uncertainties may be present, such as uncertainties related to human errors. Transitionsbetween the quoted different uncertainty types may exist.Sigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 17. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 17DNV Report No. 95-3203 Uncertainty Modelling - Target Reliability3.2.3 Uncertainty ImplementationUncertainties are represented in reliability analyses by modelling the governing variables asrandom variables. The corresponding probability distributions can be defined based on statisticalanalyses of available observations of the individual variables, yielding information on their meanvalues, standard deviations, correlation with other variables, and in some cases also theirdistribution types.Variables for which uncertainties are judged to be important, e.g. by experience or by sensitivitystudy, shall be represented as random variables in a reliability analysis. Their respectiveprobability distributions shall be documented as far as possible, based on theoreticalconsiderations and statistical analysis of available background data.Dependency among variables may be important appear and shall be assessed and accounted forwhen necessary. Correlation coefficients can be estimated by statistical analyses.Model uncertainties in a physical model for representation of load and/or resistance quantitiescan be described by stochastic modelling factors, defined as the ratio between the true quantityand the quantity as predicted by the model for multiplicative correction factors. A mean value notequal to 1.0 for the stochastic modelling factor expresses a bias in the model, and the standarddeviation expresses the variability of the predictions by the model. An adequate assessment of amodel 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 benecessary. The importance of a model uncertainty may vary from case to case and should bestudied by interpretation of parameter sensitivities.3.3 Target Reliability3.3.1 GeneralTarget reliabilities have to be met in design in order to ensure that certain safety levels areachieved. A reliability analysis can be used to verify that such a target reliability is achieved for astructure or structural element. A difficulty in this context is that the uncertainties included in astructural 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 assumptionsThis means that a reliability index calculated by a reliability analysis is an operational or nominalvalue, dependent on the analysis model and the distribution assumptions, rather than a truereliability value which may be given a frequency interpretation. Calculated reliabilities cantherefore usually not be directly compared with required target reliability values, unless the latterare 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 ona general basis, but only case by case for individual applications.For a more detailed discussion of the subject of determining the target reliability level, referenceis given to the DNV (1995a).Sigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 18. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 18DNV Report No. 95-3203 Uncertainty Modelling - Target Reliability3.3.2 Selection of Target Reliability LevelTarget 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. Incases 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 similarexisting structural design solutions or through decision analysis techniques.By carrying out a reliability analysis of a structure satisfying a specified code using a givenprobabilistic model, the implicit required reliability level in this code will be obtained, whichmay be applied as the target reliability level. The advantage with this approach compared toapplying a predefined reliability level, is that the same probabilistic approach is applied in thedefinition 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 targetreliability level.The use of codes could with advantages be applied e.g. in the determination of the minimumacceptable reliability level, below which structural inspections for jacket structures exposed tofatigue degradation are required. In the NPD, Act, regulations and provisions for the petroleumactivities (NPD 1996), it is stated that for structural details with no access for inspection orrepair, the design factors specified in Table 3.1 are to be applied in the design, dependent on theconsequence of failure of the detail. This could be interpreted as that a structural detail does notneed to be inspected prior to one 10th, or one 3rd, of the fatigue design life for substantial and nosubstantial failure consequence, respectively. The reliability levels at these time periods (onetenth, or one third of the design life) then consequently also correspond to the target reliabilitylevel for which a structural inspection is required according to the code.Table 3.1 Design fatigue factors when no access for inspection or repair existDamage No access or inConsequence the splash zoneSubstantial 10consequenceNo substantial 3consequenceIn general, acceptable structural probabilities of failure, specified as minimum values of targetreliabilities, depend on the consequence and nature of failure. The evaluation of the consequenceof failure comprises an evaluation with regard to human injury, environmental impact andeconomical 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 referenceperiod. The reference period should reflect the nature of the failure and is generally equal to theanticipated lifetime of the structure, or simply one year. As a general statement it might beargued that an annual target failure probability should be used when human life is at stake whilelifetime 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 torepair cost, missing income and/or demand in the repair period. When the failure consequenceregards economic loss, minimum target structural failure probabilities may be specified by theSigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 19. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 19DNV Report No. 95-3203 Uncertainty Modelling - Target Reliabilityoperator based on requirements from national authorities and company design philosophy and/orrisk 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 levelrelated to economical consequences.A major accident is likely to have a negative influence on the reputation of the company, bothtowards the government and towards the society in general. The consequence of this effect isdifficult to quantify. It is probably related to the company philosophy or may simply beconsidered as a part of the economical consequence.The consequence of failure related to human injury will in large extent depend on the type offailure and operational condition for the platform. E.g., in DNV CN 30.6 (DNV 1992b), thecriterion concerning human injury is to be formulated as the annual probability of failure (definedas 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 areapplied as target values, care must, however, be made in the uncertainty modelling in order toaccount 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 proposeduncertainty 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 ConsequenceI. Redundant structure PF = 10-3 PF = 10-4 β = 3.09 β = 3.71II. Significant warning prior to PF = 10-4 PF = 10-5 occurrence of failure in a non- β = 3.71 β = 4.26 redundant structureIII.No warning before the PF = 10-5 PF = 10-6 occurrence of failure in a non- β = 4.26 β = 4.75 redundant structureSigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 20. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 20DNV Report No. 95-3203 Discussion of Limit States4. DISCUSSION OF LIMIT STATES4.1 IntroductionThe objective for all structural designs is to build structures which fulfil proper requirementswith respect to functionality, safety and economy. These three aspects are closely connected andan iterative process is necessary to achieve the most optimal design. Current design practice isbased on partial safety factors and control against several limit states. A structure, or a structuralcomponent, is considered not to satisfy the design requirements if one or more of the limit statesare 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. Thislimit state is difficult to describe through simple design equations, and therefore the design isnormally performed at a component level where the capacity of the single joints and membersbetween the joints are analysed/designed separately. Alternatively, the capacity for the UltimateLimit State can be assessed by non-linear analysis. At present non-linear analyses are performedfor reassessment and requalification purposes, but is not considered to be practical at a designstage. Also guidelines on how to perform such analyses are lacking. Therefore limit statefunctions for reliability analysis of jacket structures will in general also be based on designequations 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 4.3Traditional 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 characteristicvalues which are defined at some fracture value or lower bound value. For reliability analyses thelimit states are based on the actual values, accounting for uncertainties, where the load andmaterial coefficients are not included in the equations for the limit state functions.Sigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 21. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 21DNV Report No. 95-3203 Discussion of Limit StatesThe Progressive Collapse Limit State is used to design the platforms for accidental events havinga probability of occurrence larger than 10-4. Accidental events such as explosion, fire and shipimpacts are considered. The accidental events are defined from Quantitative Risk Analyses, seeSection 2 of Guideline for Offshore Structural Reliability - General (1995a). Possible damage tothe structure is calculated based on an elasto-plastic analysis, and the structure is then analysedwith that damage for a given environmental loading. This analysis is similar to that of anUltimate Limit State analysis, but with different load and material coefficients in the designequation according to the NPD regulations, (NPD 1996).The Serviceability Limit State is used for control of deflections and accelerations of the topsidestructures, but is hardly used for the design of jacket structures.The potential application areas for structural reliability analyses of jacket structures are withindetailed 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 connectionsIn 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 ina reliability analysis are given. Furthermore, a simplified limit state for system failure defined astotal structural collapse due to environmental loading is discussed, where the total structure isconsidered as a single component.Sigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 22. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 22DNV Report No. 95-3203 Discussion of Limit States4.2 Buckling Failure of Members (ULS)4.2.1 Local Buckling of MembersThe susceptibility to local buckling of tubular members is a function of member geometry andyield 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 isconvenient to define the tubulars in section classes (Eurocode 3 (1993)) as illustrated in Table4.1Table 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 = thicknessThe 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 numericalanalyses must be carried out for documentation. This is controlled under section 4.2.3. ΘFigure 4.1 Tubular capacity in bending for different section class dependent on degree of deformation Θ.Sigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 23. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 23DNV Report No. 95-3203 Discussion of Limit States4.2.2 Global Buckling of Members4.2.2.1 BackgroundThe procedure for design of tubulars subjected to a bending moment according to the NPDregulations 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 whichfor tubulars are shown in Table 4.1). This procedure is considered to be sufficient for tubularssubjected to external pressure.The procedure for design of tubulars in air is considered conservative for section classes I and IIas yielding of the section is allowed (by definition of section class). A higher capacity accountingfor the plastic section modules is directly achieved through a non-linear analysis. The increase inthe 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 equationsthan 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 typicalmember configurations as X-braces, K-frames, single braces, jacket legs and piles. The effectivebuckling length is dependent on the joint flexibilities and for X-braces also on the amount oftension force in the crossing element. It is also a matter of discussion whether the buckling lengthshould be measured from centreline to centreline of jacket legs which can be argued for in thecase of a combined collapse of the braces and the legs, or if the buckling length should beassociated with the face to face length between the legs which may be argued for consideringbuckling of a single brace. The effective buckling length may be derived from analyticalconsiderations. However, the effective buckling lengths derived from theoretical considerationsare 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. TheAPI buckling curve is derived as a lower bound value for low slenderness while it is equal to theEuler stress for high slenderness values which may be considered as an upper bound value forthat region. Another definition of a buckling curve is used in the AISC (1986). The backgroundfor the buckling curves used in design of steel structures in European design standards is basedon work carried out within the European Convention for Constructional Steelwork which ispresented in Manual on Stability of Steel Structures (1976). The design curves are presented bytheir characteristic values which are defined as mean values minus two standard deviations alongthe slenderness axis. The test results are assumed normal distributed.It is also noted that the requirements to allowable fabrication eccentricity are different associatedwith the various buckling curves. For the European buckling curves, a straightness deviation atthe middle of the column equal 0.0015 times the column length is allowed, while for API andAISC 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.Sigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 24. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 24DNV Report No. 95-3203 Discussion of Limit StatesThe design equation for global member buckling in the NPD regulations (NPD 1996) reads fyσ c + Bσ b + Bσ b ≤ * γmwhere Nσc = = design axial compressive stress AN = axial forceA = section area 1B = bending amplification factor = N 1− NEN E = Euler buckling load fy fkσb = σc ( − 1)(1 − * ) fk γ m fE NE fE = A f k = characteristic buckling strength derived from the buckling curveBuckling 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 slendernessFigure 4.2 Different buckling curves used for design of tubular membersSigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 25. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 25DNV Report No. 95-3203 Discussion of Limit States4.2.2.2 Limit State FunctionThe limit state function for global buckling of members can be formulated asG = f y − ( σ c + Bσ b + Bσ b ) *where f y = yield strength Nσc = = design axial com pressive stress AN = axial forceA = section area 1B = bending amplification factor = N 1− NEN E = Euler buckling load fy fσb = σc ( − 1)(1 − k ) * fk fE NEfE = Af k = buckling strength derived from the buckling curveSigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 26. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 26DNV Report No. 95-3203 Discussion of Limit States4.2.3 Buckling of Members Subjected to External Pressure4.2.3.1 BackgroundThe capacity of tubulars subjected to axial force, bending and external pressure may be designedbased 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 byLoh (1990). In the following the design procedure given by NPD and Lotsberg is given. It shouldbe noted that it is only the effective axial force that contributes to the axial stresses that enhancebuckling, see Figure 4.3. The axial stress resulting from the external pressure do contribute in theequation for the von Mises stress considering yielding, but does not contribute to the axial forcethat 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 asfollows: B + B 2 − 4 AC σ ac = 2Awhere f y2 A = 1+ 2 f eaSigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 27. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 27DNV Report No. 95-3203 Discussion of Limit States 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 pressureThe equation for global buckling is then modified as follows σ ac − σ axpσ c + Bσ * + Bσ b ≤ b γmwhere 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 tubularmember as function of the water depth is shown in Figure 4.4. It is noted that the difference issmall for water depths below say 100 metres, but that it becomes significant for deep-waterstructures.Sigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 28. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 28DNV Report No. 95-3203 Discussion of Limit States4.2.3.2 Limit State FunctionThe limit state function for global buckling of members subjected to external pressure can beformulated as,G = σ ac − σ axp − (σ c + B σ * + B σ b ) bwith 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 mFigure 4.4 Axial stress in the tubular as function of water depth and external pressure at global member buckling4.3 Joint Failure (ULS)4.3.1 BackgroundA number of design equations have been established for the static strength of tubular joints. Theequations in API (1991) and NPD (1996) show a similar shape although the coefficients aredifferent as also might be expected as the API RP2A is based on allowable stresses, while theNPD has based the design on the partial coefficient method since 1977. The following work isbased on the NPD regulations, but only small modifications would be required to revert toanother standard such as that of API or HSE.It should be mentioned that work on joint capacities is being carried out within the developmentof a new ISO standard on design of steel offshore structures. This work should be considered asbasis for limit state functions when it is available.The following symbols are used:Sigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 29. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 29DNV Report No. 95-3203 Discussion of Limit StatesT = Chord wall thicknesst = Brace wall thicknessR = Outer radius of chordr = Outer radius of braceθ = Angle between chord and considered braceD = Outer diameter of chordd = Outer diameter of bracea = gap (clear distance) between considered brace and nearest load-carrying brace measuredalong chord outer surfaceβ = r/Rγ = R/Tg = a/Dfy = Yield strengthQf = See Table 4.3Qg = See Table 4.2Qu = See Table 4.2Qβ = See Table 4.2N = Axial force in braceMIP = In-plane bending momentMOP = Out-of-plane bending momentNk = 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 chordσIP = In-plane bending stress in chordσax = Out-of-plane bending stress in chordSigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 30. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 30DNV Report No. 95-3203 Discussion of Limit StatesTable 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 bendingT&Y 2.5 +19βX (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 ïQβ = í ï . 10 for β ≤ 0.6 ï î ì18 − 01a / T . . for γ ≤ 20 ïQg = 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 QfLoading QfAxial 1.0-0.03γA2In-plane bending 1.0-0.045γA2Out-of-plane bending 1.0-0.021γA2where σ ax + σ 2 + σ 2 2A = 2 IP OP 0.64 f y2The characteristic capacity of the brace subjected to axial force is determined by fyT 2Nk = Qu Q f sin θSigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 31. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 31DNV Report No. 95-3203 Discussion of Limit StatesThe characteristic capacity of the brace subjected to in-plane moments is determined by df y T 2M IPk = Qu Q f sin θThe characteristic capacity of the brace subjected to out-of-plane moments is determined by df y T 2M 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 mwhere γm is a material coefficient =1.15.Figure 4.5 Simple Tubular JointSigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 32. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 32DNV Report No. 95-3203 Discussion of Limit StatesFigure 4.6 Force displacement relationship for a tubular joint4.3.2 Limit State FunctionThe 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 MG = 1− ( +ç çM ÷ ÷ + OP ) or G = − log( +ç ÷ + OP ) N k è IPk ø M OPk N k è M IPk ø M OPkwhere the equations given above are used to calculate Nk, MIPk and MOPk with Qu from Table 4.4and A as given below.Table 4.4 Values for Qu based on 50 per cent fractiles (median values)Type of joint and geometry Type of load in brace member Axial In-plane bending Out-plane bend.T&Y 2.8 +21βX (3.0 +14.6β)Qβ 5.6γ0.5β 3.6/(1-0.81β)K (2.6 +27β)QgThe parameter A for calculation of Qf in Table 4.4 is obtained as: σ ax + σ 2 + σ 2 2A2 = IP OP f y2Sigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 33. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 33DNV Report No. 95-3203 Discussion of Limit StatesThe CoV values in Table 4.5 for Qu may be used for the reliability analysis based on thepresented limit state functions. Qu is normal distributed. For CoV for yield strength, see DNV(1995a).Table 4.5 Values for CoV for QuType of joint and geometry Type of load in brace member Axial In-plane bending Out-plane bend.T&Y 0.10X 0.10 0.10 0.10K 0.204.4 Fatigue Failure at Hot-spot of Welded Connections (FLS)4.4.1 General4.4.1.1 OverviewJacket 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. Theenvironmental quantities are of random nature and may be more or less correlated to each otherthrough the generating and driving mechanisms. Waves and earthquake loads are generallyconsidered to be the most important sources for structural excitations. However, earthquakeloads 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 tothe 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 calculationprocedure, starting with the environment (waves) creating stress ranges at the hot-spot regionsand ending with the fatigue damage estimation. The link between the waves and the fatiguedamage estimate is formed by mathematical models for the wave forces, the structural behaviourand the material behaviour. The probabilistic fatigue analysis may be divided into four mainsteps: 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 theapplication to jacket structures.In addition to the above steps, the analysis includes a stochastic modelling of the fatigue capacityand the probabilistic evaluation, i.e. the probabilistic derivation of the likelihood of the event thatthe accumulated fatigue damage exceeds the defined critical fatigue strength level.Sigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 34. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 34DNV Report No. 95-3203 Discussion of Limit StatesIn order to carry out a realistic fatigue evaluation of a jacket structure, it is necessary to introducesome 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 andstrains caused by time-varying loading. Fatigue failure occurs when the accumulated damage isexceeding 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 thenumber of cycles to failure is larger than 10 4 . Fatigue damage in welded structures is likely tooccur 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 isassumed 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 damagebased on fracture mechanics is normally less reliable than that derived from SN data due to thedifficulties involved in assessing the initial crack size. Applying the SN-approach, the fatiguedamage is measured in degree of damage, D , from an initial value 0 to ∆ , where ∆ is definedas the fatigue damage accumulation resulting in failure, depending on the detail considered andthe selected SN-curve.When performing a reliability updating on the basis of structural inspections for cracks, theinspection outcome can not be used directly to update the degree of damage accumulation unlessthe fracture mechanics approach is applied. In order to also be able to perform reliabilityupdating when the SN approach is applied, a procedure for establishing a relationship betweenthese two fatigue approaches is proposed in the following.4.4.1.2 System AspectsJacket structures are typically redundant with respect to brace failures and a total structuralcollapse 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 ofthe load through the structure occurs. In the damaged structure, each remaining member hasalready some accumulated fatigue damage, and due to the redistribution of the stresses in thestructure the rate of damage accumulation will change. By accounting for the changes due tofailure in other members, the total damage at a section can by formulated mathematically. OnceSigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 35. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 35DNV Report No. 95-3203 Discussion of Limit Statesthe time to failure for each individual section in a sequence is defined, the sequence event isdefined as the intersection of a set of section failure events for which the time to failure for eachindividual section is less than the lifetime of the structure.Usually, there will be many alternative sequences leading to collapse, and the total structuralfailure is the event that one of these collapse sequences occurs.A system reliability approach is required when the probability of total structure failureaccounting for the progressive nature of collapse is to be estimated. One of the difficulties withsuch an approach is that for typical structures there are a very large number of sequences leadingto failure, and that it is not feasible to include all of these in the analysis. Usually, however, onlyfew 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 identifyimportant failure sequences and the system failure event is approximated as the union ofimportant sequences.4.4.2 SN-Fatigue Approach4.4.2.1 GeneralThe 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 theoutcome of the inspections can be carried out applying Bayesian updating. The inspection resultscan for the SN-approach not be used directly to update the estimated accumulated fatiguedamage. However, if a relationship between the damage accumulator D in the SN-approach andthe crack size was available, it would be possible to utilise the inspection results for reliabilityupdating.No guidelines or established procedures are available for establishing the relationship betweenthe 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 thefracture mechanics approach. In the following the parameters are calibrated by fitting theprobability of having a through thickness crack as a function of time obtained from the fracturemechanics approach to the results obtained from the SN-approach, applying e.g. least-squaresfitting.It should be noted that calibrating the through thickness cracking to a SN-curve is in generalinconsistent, as the crack initiation period included in the SN-approach is not incorporated in thefracture mechanics formulation. This may lead to unconservative results in the reliabilityupdating based on the outcome of inspections.More consistent results may be obtained by applying only the SN-curve for the crackpropagation 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 toSigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203
- 36. Guideline for Offshore Structural Reliability: Application to Jacket Plattforms Page No. 36DNV Report No. 95-3203 Discussion of Limit Statespropagate through the thickness. This approach assumes there exists a model available toestimate the crack initiation time and that the time period until inspection is greater than thecrack initiation time.However, very limited information is available for describing the crack initiation time and theSN-curves for the crack propagation period. The calibration of the fracture mechanics parametersis therefore in the present study based on SN-curves where the crack initiation period is includedin the modelling of the fatigue capacity applying the SN approach. It should in this connectionalso be noted that for welded details, the crack initiation period is relatively small compared tothe whole fatigue life.4.4.2.2 SN-Fatigue ModellingSN-data are experimental data giving the number of cycles N of stress range S resulting in fatiguefailure. 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 aslinear or piece-wise linear relations between log10S and log10N. A design curve is defined as themean curve, minus two standard deviations of log10N obtained from the data fitting. The standarddeviation 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 Sor −m N = K ⋅S , S > S0whereN number of cycles to failure for stress range Sa a constant relating to the mean SN-curveσ log10 N the standard deviation of log10Nm the inverse slope of the SN-curveS0 stress range level for which change in slope occurs, i.e. for bilinear SN- curve or endurance limit for single slope SN-curvelog10 K log 10 a − 2σ log10 NThe 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 2where 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.Sigurdsson,G; E. Cramer;I. Lotsberg, B.Berge “Guideline for Offshore Structural Reliability Analysis- Application to JacketPlatforms”, DNV Report 95-3203

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