PETRONAS TECHNICAL STANDARDS

DESIGN AND ENGINEERING PRACTICE

REPORT (SM)

PRACTICE FOR THE DYNAMIC

ANALYSIS OF FIXED OFFSHORE

PLATFORMS FOR EXTREME STORM

CONDITIONS

PTS 20.061

JANUARY 1987

PREFACE

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Report EP 87-0170

Title : PRACTICE FOR THE DYNAMIC ANALYSIS OF FIXED OFFSHORE PLATFORMS FORE EXTREME STROM CONDITIONS

By : EPD / 112

Date : May 1987

This report presents the currently held technical opinion regarding the subject of the above title, and isendorsed as a Practice by SIPM-EP.

SIPM-EP/11, as custodian, will either update/revise the document as appropriate or withdraw itsstatus as an endorsed Practice. Any questions relating indicator is given below.

Reporter : Name : I.M. Hines Signature

Reference indicator : EPD / 112

Date : January 1987

Reviewer : Name : G. Moeyes Signature

Reference indicator : EPD / 112

Date : January 1987

Custodian : Name : J.H. Vugts Signature

Reference indicator : EPD / 11

Date : January 1987

LIST OF CONTENTS

SUMMARY

1. INTRODUCTION

2. APPROACHES TO DYNAMIC ANALYSIS

2.1 Some fundamental problems

2.2 Random time domain simulations

2.3 Frequency domain solutions and spectral methods

2.4 Applications and tools

3. RECENT EXTREME EVENT ANALYSIS CASE HISTORIES

3.1 Introduction

3.2 Concept screening using frequency domain tools

3.2.1 Background

3.2.2 Estimation of short-term cyclic loading components

3.2.3 Static loading components due to wind current and self-weight

3.2.4 Overall assessment

3.3 Member sizing for the extreme storm including dynamics

3.3.1 Background

3.3.2 Pseudo-dynamic design procedures

3.3.3 Assessment

4. RECOMMENDATIONS

4.1 Some general conclusions and a short-term recommended approach

4.2 Longer term developments

4.3 Final comments

5. REFERENCES

FIGURES

APPENDIX A - Static plus mass inertia 'Pseudo dynamic' analysis procedure

SUMMARY

This document provides a review of the existing experience and procedures available within theindustry in general, and PETRONAS in particular, for the prediction of the extreme storm dynamicresponse of conventional, bottom supported offshore platforms. The report focuses upon the analysisand design requirements for steel spaceframe towers or jacket structures.

Advantages and disadvantages of the various methods are discussed with respect to their applicationin different stages of the design process, and recommendations for the most useful techniques atpresent are made. Further developments are proposed, with particular reference to the computingfacilities available in PETRONAS.

1. INTRODUCTION

Over the past ten years or so the fixed platform concept has slowly been pushed into deeper andmore hostile environments. Designers of conventional, deepwater fixed platforms have had to copewith the increased flexibility of these structures and to develop analysis and design procedures whichaccount for the resulting dynamic amplification of the applied loading which is associated with themass inertia forces. In these structures the influence of structural dynamic response is evident both interms of the amplification of the extreme storm design loadings and the increase of cyclic fatiguedamage associated with dynamic response to less severe, but more frequently occurring, everydaysea states. The extent of dynamic response is associated with the relationships between thestructure's fundamental modes and the frequency content of the applied loading. Design and analysisprocedures for deepwater structures which respond dynamically must account for the random natureof the excitation and the response in an appropriate manner.

At the present time, there are relatively few structures which have been designed using dynamic,structural analysis tools. Even for those structures where dynamic response has been considered,there are often major differences in the methods used; at present there is little in the way of a singlecommon approach. As a result, available experience is very limited and the state of the art is stillunder continuous development.

This document provides a review of the existing experience and procedures available within theindustry in general, and PETRONAS in particular, for the prediction of the extreme storm dynamicresponse of conventional, bottom supported offshore platforms. The report focuses upon the analysisand design requirements and experiences for steel spaceframe towers or jacket structures; thesestructures have provided the initial stimulus for work in this area. However, much of the generaldiscussion on analysis philosophy and analytical methods is also applicable to inertia dominatedcompliant structures which may represent a future generation of deepwater bottom supportedplatforms.

The first section of the report summarises some fundamental problems which need to be faced whenevaluating dynamic response for extreme storm conditions and presents the various options which arecurrently available. This is followed by a review of some recent analysis experiences which will beused to highlight the benefits and the deficiencies of some of the various options. A recommendedprocedure is then outlined to provide an approach which is considered to be suitable for analysis anddesign requirements for the foreseeable (short term) future. The main emphasis here is on aprocedure which can most readily fit within the framework of existing design codes of practicedeveloped for shallow water structures (e.g. API or DNV), thus enabling an otherwise conventionaldesign to be carried out. Finally, some recommendations for future development work in this area areoutlined. These try to anticipate the outcome of ongoing, longer-term efforts geared to thedevelopment of a design approach which is better suited to the probabilistic nature of the randomwave environment.

2. APPROACHES TO DYNAMIC ANALYSIS

2.1 Some fundamental problems

In formulating analysis and design procedures capable of predicting the response of a flexibledeepwater platform under the influence of extreme storm environmental loading, a number of inter-related problem areas need to be addressed:

i) The geometry, stiffness, mass and damping characteristics of the structure and its foundation.

ii) Adequate numerical procedures capable of solving the dynamic response equations with therequired accuracy.

iii) The magnitude and spatial distribution of the wave and current loadings and their relationship tothe structure's natural frequencies.

iv) Procedures to represent and analyse the force mechanisms, and the interaction between thestructure and the surrounding fluid.

v) An analysis and design framework within which to combine the results of dynamic responsepredictions with those of the other load conditions which occur throughout the platform life.

Of these problem areas, and accepting the difficulties associated with an adequate representation ofthe damping mechanisms and the foundation, the first area probably poses the least difficulty, andcan be dealt with adequately using presently available modelling and analysis techniques. As a resultit will not be considered further here. The second area has been addressed in detail in Reference 1and the conclusions and recommendations of this study do not need to be repeated. It suffices to saythat adequate dynamic analysis methods do exist which are compatible with all levels of the designcycle; from preliminary concept screening to detailed member design and fatigue analysis.

The third, fourth and fifth areas remain more problematic and these will form the basis for much of thediscussion which follows.

It is now widely recognised that the offshore environment represents a true random process. Despitethis, most offshore structures have been, and are still being designed using regular wave(deterministic) static analysis procedures. This approach is well supported by many years ofsatisfactory service in which relatively few structural failures have occurred for shallow waterstructures which are relatively stiff and respond quasi-statically to the ocean environment. In thecontext of the overall design procedure used, the deterministic design wave approach has served theindustry rather well.

Early, first generation dynamic analyses for deepwater offshore structures were also based upondeterministic procedures (e.g. preliminary analyses of Shell Oil's Cognac platform, Reference 2). Thedynamic response was evaluated using time domain numerical simulations of the platform responsewhen loaded by an infinite train of periodic design waves of fixed height and period.

Whilst this approach represents a plausible and practical extension to existing design practice, itsuffers from a number of fundamental flaws:

i) Using this procedure, design sea state energy isassociated with a single discrete wavefrequency. As a result, the frequency content of the applied loading is also artificially lumped at anumber of specific frequencies; in the first instance, at the frequency of the deterministic wavebut this component may also be supplemented by one or more higher harmonic contributions.The higher harmonics originate from several sources: from the non-linear velocity squared dragforces associated with the Morison force formulation, both with or without current; from the use ofnon-linear wave theories (such as Stokes 5th); or from free surface loading effects associatedwith the changing position and shape of the wave surface. Realistic relationships between thefrequency content of the applied loading and the structure's natural frequency (or frequencies)are, therefore, not represented correctly.

ii) The non-linear elements in the procedure referred to above introduce higher harmoniccomponents at discrete multiples of the fundamental wave frequency which may be tuned to thestructure's natural frequencies and, therefore, can excite the platform in a resonant mode,causing substantially larger (and artificial) dynamic amplification effects.

These problems are highlighted in Figure 2.1, taken from Reference 2, which shows results of sometime domain dynamic analyses of a single degree-of- freedom structure when subjected to regularStokes 5th design waves and an equivalent random sea with the same probability of occurrence. Thesingle degree-of- freedom model was first loaded with the total force time history of the regulardeterministic Stokes 5th wave used for the design of the Cognac platform. Simulations were thenmade using the random wave force history as developed from the corresponding storm wavespectrum.

The figure shows the resulting dynamic amplification factor of base shear as a function of thestructure natural period. The Stokes 5th wave used has a period of 11.5 seconds and the SDOFsystem is seen to resonate with the second harmonic of the Stokes wave at 5.75 seconds and withthe third harmonic at 3.8 seconds. The fundamental harmonic resonance (at 11.5 seconds) is notshown, since it is outside the structure period range of interest.

Conversely the random simulation results (obtained by averaging the results of 20 separatesimulations) show a much smoother variation with the structure period. This is much morerepresentative of the actual broader band frequency content of a real sea, even in design stormconditions.

As a result of the shortcomings illustrated in the above discussion, dynamic analysis using periodicregular wave loading is considered to be unreliable. Methods which account for the actualrelationships between the frequency content of random seas and the fundamental mode naturalfrequencies of the structure are required.

Two possible types of solution enable the random nature of the environment to be represented. Theseare the stochastic approach, usually based upon linearised, frequency domain spectral analysistechniques, or the use of random time domain simulations. Both approaches are discussed briefly inthe following sections, where attention is focused upon the basic features of the problem formulationand the treatment of non-linear effects.

2.2 Random time domain simulations

For a multi-member, steel space frame offshore platform the principal sources of non-linearity resultfrom the wave loading (usually predicted using the Morison equation) soil characteristics anddamping. The non-linearity within the velocity squared drag component of the Morison equation, isfurther complicated by the influence of free surface inundation effects. Further uncertainty surroundsquestions about how, and under what circumstances, the relative motion of the structure mayinfluence both the applied loading and the system damping.

Accepting the basic Morison force formulation, it is now considered that solutions based upon randomtime domain solutions represent the most realistic representation of the response of an offshoreplatform in a real sea. The procedure involves a number of discrete steps which are shownschematically in Figure 2.2 and summarised here:

i) Develop time histories of wave surface elevation and water particle kinematics either frommeasured wave data or using inverse Fourier transformations from specified storm wave spectra.This information is used to develop time histories of the applied hydrodynamic loading.

ii) Using the applied loading history perform- numerical time domain integration of the equations ofmotion in order to develop timehistories of the structural response include all the non-linearcomponents of both the loading and the dynamic system.

iii) Statistical analysis of the resulting time histories.

These solutions are able to incorporate system non- linearities, such as those outlined above,explicitly without the need for simplification or linearisation of the components. This is achieved at apenalty of computational cost which depends upon the length and number of simulations required andthe size and complexity of the platform model. The method carries an additional penalty in terms ofthe difficulties associated with the interpretation and application of the results. In modelling therandom environment it is assumed that the wave surface elevation is a stationary, ergodic, Gaussianprocess. As a result of system non-linearities, the response is certainly non- Gaussian but it is alsopossible that it may not be stationary in a statistical sense as well. Therefore, a single realisation ofthe non-linear structural response only represents one of a theoretically infinite number of suchrealisations. In order to develop confidence in the short term statistical characteristics of the responseit is necessary to carry out a number of such simulations. Information on the extreme values, whichrepresent the tails of the peak response distributions, can only be obtained reliably by performing avery large number of simulations, or by performing extrapolations based upon existing or assumedextreme value distributions, e.g. the Weibull distribution.

2.3 Frequency domain solutions and spectral methods

For loading and response problems that can be appropriately linearised, conventional spectralanalysis procedures provide a convenient and efficient means to incorporate the random waveenvironment. In this context a linear spectral analysis (Reference 3) is now well established as thefinal design, state of the art industry standard for examination of the potential for cyclic fatiguedamage. The frequency domain spectral approach, as shown schematically in Figure 2.3, can alsoreadily incorporate the influence of structural dynamic response.

Simplified, first order screening tools have been developed within SIPM during the past fewyears, as a means to carry out a preliminary examination of the fatigue behaviour of steel spaceframestructures (References 4, 5). The procedures retain the fundamental benefits of a dynamic, spectralfatigue analysis, without incurring the high cost associated with a detailed 3-D analysis. These toolshave proved to be invaluable in preliminary concept screening studies; some recent applications aredocumented in References 4 and 6.

For the prediction of extreme responses the linearised spectral method has a number of obviouslimitations. These are associated with the difficulty of incorporating the non-linear effects and also, aswith the time domain approach, in the extrapolation of short term statistics to predict the peakresponse levels. As stated previously, due to non-linearities in the system, the resulting response isactually non- Gaussian. The fact that the linearisation procedures adopted in the problem formulationmake the response as modelled truly Gaussian, does not change this basic characteristic of theresponse. In this sense the linear model does not reflect the actual situation. In design stormconditions the influence of non-linear drag components and free surface effects are more significantthan in the fatigue environment. The choice of the linearisation procedure is, therefore, of criticalimportance.

Procedures based upon a sea state dependent, statistical linearisation of the drag loading, asdeveloped by Borgman (Reference 7) and implemented by Malhotra and Penzien (Reference 8), areconsidered to be the most consistent of those available at the present time. However, these methodsdo not enable the influence of variations in the free surface wetted area to be taken into account. Freesurface effects are known to be of major importance in defining both the local and global forcedistributions on the structure during extreme event conditions (Reference 9). Furthermore, most of theexisting applications of the Borgman approach (e.g. in SIPM's FREERISE program, Reference 10)are restricted to first order expansions of the original Morison drag force formulation. The fulllinearised wave force expansion contains higher order terms which require convolutions of the wavevelocity spectra. This introduces higher order components in the wave force spectrum in the vicinity ofthree times the principal wave frequency of the storm. These terms are relatively unimportant forstructures which respond quasi-statically. However, they may be significant for flexible structureswhich respond dynamically since these higher harmonic components may coincide with thefundamental mode natural frequencies and could excite the structure in a resonant manner.

A non-linear spectral formulation which incorporates these terms, and which includes the influence ofcurrent, is described by Eatock Taylor and Rajagopalan in References 11, 12, 13. These paperscontain results of some analyses for a flexible, multi-member, steel spaceframe structure. Linear andnon-linear spectral formulations are compared with random time domain simulations in terms of theresulting second order response statistics (e.g. standard deviations of response). These resultsdemonstrate the significant influence of the higher harmonic components and indicate that the non-linear stochastic approach may represent a suitable alternative to random time domain simulations forthe prediction of short term statistics. This approach is discussed further in section 4.2.

Hybrid time/frequency domain analysis has been proposed by Kan and Petroukas (Reference 24) asa method for overcoming some of the limitations of the linearised spectral approach. The method stillrelies upon the use of a transfer function and spectral analysis techniques to determine the short termstatistical responses. However, in this case, the transfer functions are determined from a randomwave, time domain analysis, with transformation into the frequency domain being achieved via Foulertransforms. The procedure used is outlined in Figure 2.4. The hybrid approach, was originallyproposed as a means to include non-linear effects within the scope of a spectral fatigue analysis, butapplications for the extreme storm condition also appear feasible.

As with random time domain solutions, difficulties remain, however, in predicting the extremeresponse levels experienced during the design storm condition. These are the values which areultimately required in order to perform actual structural sizing operations which are consistent withexisting design practice. In order to facilitate predictions of the peak response values using the resultsfrom a linearised frequency domain analysis, use. has been made of the probabilistic description ofMorison type wave force loading when acting on a single vertical pile (References 14 and 15). For alinear Gaussian model the Most Probable Maximum (MPM) value is approximately 3.7 times theStandard Deviation (SD) value, assuming 1000 peaks which corresponds approximately to a three-hour storm. However, if the process is non-linear and hence non-Gaussian (i.e. as a result of dragloading) the ratio of the MPM and SD of wave force may be significantly higher (as high as 8.6 in atotally drag dominant, non-Gaussian system). For most practical situations a mixture of linear andnon-linear contributions are evident in the loading and the actual MPM/SD ratio will be somewherewithin this range. It should further be noted that the mix and, therefore, the degree of non-Gaussianitywill vary from one location in the structure to another and from one response variable to the next.

Using this information, some approximate methods have been proposed, to enable solutions to beobtained in the frequency domain. These are engineering approximations to enable the most probablemaximum loading and response values to be estimated for situations (and response parameters)other than the single vertical pile, waves only problem (i.e. no current) for which the distributions wereoriginally developed. This is achieved by making assumptions regarding the nature of the peakdistributions. It is postulated that the probabilistic descriptions of the response variables in theamplitude domain may be directly related to those of the Morison wave force formulation for a singlevertical pile. This implies that the probability distributions derived for the Morison wave forceformulation for a single vertical pile, are also applicable to other response parameters (e.g. memberforces and stresses) and to more complex structures comprising a large number of individual, spatiallydistributed and non-vertical loading elements. It must be stressed that these procedures remainengineering postulates which attempt to incorporate the effects of the non-Gaussian nature of theresponse on the resulting statistical distributions. It is almost certain that such postulates are not valid.However, at present there is no theoretical or experimental evidence available to resolve the matterand by lack of a better model the approach described above is pragmatically adopted. They doprovide a practical framework for the interpretation of the frequency domain results, however, there isclearly very little experience with the consequences of applying these methods in order to performdesign member sizing.

2.4 Applications and tools

Examination of extreme storm dynamic response may be required at a number of different stagesduring the development of a platform concept and using different levels of sophistication and detail.The tools need to be related to the needs of the analysis or design phase and there is obviously aclear distinction between the requirements for concept screening exercises, for design development,for design verification in accordance with existing design codes, or for ultimate strength analyseswhich fall outside the regular codes of practice.

Concept screening exercises, and parameter or feasibility studies are most usefully performed usingsimplified models which concentrate on the overall response characteristics of the structure, i.e.natural frequencies and mode shapes, global responses such as base shear and overturningmoments together with associated dynamic amplification factors. Fundamental mode responsecharacteristics can be adequately represented using relatively simple, lumped parameter stickmodels. These models enable sensitivity studies to be performed quickly and at very low costcompared to equivalent full 3D models. They can also be coupled to waveload generation routines ineither the time domain (e.g. the MARIANTO program, Reference 16) or the frequency domain (e.g.the FREERISE package, Reference 10). These programs predict dynamic and static level shear forceand overturning moment distributions, thereby enabling the development of level dynamicamplification factors based upon the short term response statistics for random wave storm loadingconditions.

The packages referred to above are unable to predict individual member loadings which have to beestimated separately using the level shear and moment response characteristics. This shortcomingprompted the development of a concept screening tool for simple steel spaceframe structures (theTRUSSFRAME program see References 4, 5) which operates in the frequency domain. It makes useof dynamic response characteristics from a stick model, base shear and overturning moment transferfunctions, and a simplified pin jointed (truss frame) description of the structure to estimate individualaxial stress transfer functions for leg and brace elements. The calculations are performed assumingresponse to be dominated by overall frame action; i.e. local loading and response effects are ignored.The package was originally developed with fatigue screening in mind, but in principal it can also beapplied to extreme event response predictions. Such an application is described in section 3.2.

Requirements for design tools are somewhat more demanding than those of concept screening toolsfor parametric exercises. Design tools must translate the results of the dynamic response predictionsinto the absolute requirements in terms of member sizes and total steel weight. The influence ofdynamic response in the extreme storm must be combined with the effects of the other storm loadingson the platform (i.e. topsides loading, self-weight, buoyancy, wind loads, etc.) both in terms of theirglobal and local effects. It is also suggested that provided the effects of structure flexibility areconsidered from an early stage in concept development, dynamic components of the extreme stormloading are unlikely to govern the bulk of the steel in the structure, even in the deepest ofwaterdepths. This is in contrast to fatigue loading conditions where resonant dynamic behaviour mayin some cases be fully controlling. Other in-place loadings such as self weight, quasi-static waveforces, and also those associated with the fabrication, load out, launch, hydrostatic forces, etc. alsoimpact steel weight significantly. Collectively, these loads are likely to have a more important role intotal weight growth than the dynamic loads taken in isolation; e.g. in the Cognac platform, theinfluence of dynamic loads increased the total steel weight by an estimated 25% and this includescontributions from fatigue. This relatively low weight growth resulted from a strong awareness ofdynamic response effects and careful attention to the inter- relationships between platform dynamiccharacteristics, wave loading and dynamic response.

These experiences demonstrate the importance of a reliable assessment of dynamic response andthe need to incorporate these effects at a very early stage in the design development. However, theyalso suggest the need for a balanced approach to the design. The procedures used must incorporatethe key features of the dynamic response problem, but they must also fit within the framework of anintegrated design approach, which also recognises the significance of the other load conditions in aconsistent manner.

Full 3-D, random wave, time domain analysis tools are now available (e.g. Shell Oil's DYNAL IIIpackage, Reference 17) which enable the random wave environment and dynamic responseinfluences to be represented explicitly for any design storm condition and for large structures. Thesepackages are able to generate corresponding time histories of individual member loadings. However,these tools are computationally expensive for large structures and furthermore a single randomsimulation results in only one of an infinite number of possible response histories, each including onepossible extreme for each individual response. Selecting appropriate values for design member sizingis, therefore, complicated by the requirement for an appropriate procedure to deal with the extremeresponse statistics and a consistent design framework within which to apply these. In the first instanceit appears preferable and logical to try to relate a design procedure incorporating random waveloading and dynamic response effects to that of the existing approach for shallower water offshoreplatforms which have been designed in accordance with deterministic procedures. However, use ofthe Morison formulation within the framework of the linear random directional wave model implies theuse of different wave force coefficients to those which are normally applied for deterministic waveanalyses (see Reference 18). Resulting force levels from the random wave model may also be higherwith corresponding increases in individual member loading.

Given this situation, it is questionable whether it is appropriate to apply the individual member forcesobtained from a detailed, random wave analyses within the context of the existing codes of practicesuch as the API code. Design tools should recognise that the industry, and the codes of practicecommonly applied (API, DNV), incorporate safety factors which are intended for use with a specificset of load and strength definitions and which combine to produce an overall level of safety andreliability. To date, these methods have evolved an accepted approach which is based uponexperience using the regular wave, deterministic design philosophy for structures which respond

quasi-statically. Safety factors in the working stress philosophy account for many items that theengineer does not consider explicitly during each design; e.g. at present these codes do not considerthe influence of structural dynamics other than via an overall factor of safety.

If the random nature of the wave environment and the subsequent dynamic response areincorporated explicitly, then it appears logical that some fundamental revisions to the existing codes ofpractice may be necessary. Ultimately, the overall quality and realism of the deterministic and randomwave model approaches need to be compared and any appropriate code revisions should incorporatesafety factors which produce a consistent level of overall safety and reliability. Such revisions arepresently being considered within the context of the API's proposed Load and Resistance FactorDesign (LRFD, Reference 19). This is attempting to develop probability based design guidelines foroffshore structures and to rationalise the overall safety for fixed platforms including those whichrespond dynamically. The approach is based upon use of partial safety factors in which theuncertainties in the individual component load and strength elements are quantified. Such an explicitrepresentation allows for a more consistent adjustment of the safety factors in the event ofimprovements in the understanding, and hence the representation of any single element of the wholedesign process. On this basis, explicit representation of the random nature of the wave environmentand the dynamic response may justify a reduction in the safety factors associated with theseindividual components. The first draft proposal for the LRFD design code employing the partial factorphilosophy was submitted to the industry for comment during the latter part of 1986.

Given the present state of flux in the LRFD approach, the observed discrepancies in load levelspredicted by the random and deterministic wave force models and the difficulties of generating andinterpreting the random wave design event loads for a large structure, a number of simple dynamicanalysis procedures have been developed to cope with the design requirements of the first generationof deepwater platforms. These are an attempt to represent the key features of global dynamicresponse behaviour within the context of established deterministic wave design practice. The linkbetween the random dynamic response and the quasi-static design event forces is achieved bymaking use of global dynamic amplification factors. These amplification factors are developed usingrandom dynamic analyses which preserve the relative frequency content of the wave environmentand the structure's natural modes.

In the simplest approach, quasi-static design event wave forces are determined with the use of aconventional deterministic wave force analysis. The resulting cyclic component of the applied loadingis then factored by a constant, global dynamic amplification factor which has been determined from anappropriate random wave analysis. The member analysis and design are then performed in adeterministic manner using the existing design codes. This approach has the disadvantage that theapplied dynamic loading is assumed to have the same distribution over the height of the structure asthe quasi-static wave forces.

A refinement to this procedure is the use of a separate inertia force loadset which is intended torepresent the distribution of mass inertia forces over the height of the structure in a more consistentmanner. A set of mass inertia forces are developed in accordance with the mass distribution and thenatural mode shape(s) over the height of the structure. These forces are applied at the main planlevels in proportion to the mass distribution, in order to achieve target dynamic level shear and/oroverturning moment values. The resulting mass inertia force distribution is then treated as a normalstatic extra loadset and combined with the deterministic design wave loads in order to generate globallevel shear and overturning loads which are consistent with the required dynamic amplification effects.The procedure and the key assumptions involved will be described in more detail in section 3.3.

The use of either of the above approaches eliminates the difficulties associated with use of theindividual member forces from a random wave analysis in an absolute sense. Random wave analysesin either the frequency or time domain are used to determine the appropriate global (level shear andmoment) dynamic amplification factors. These amplification factors can in principle be generated forany response variable. However, the DAF's are applied within the framework of a deterministic waveanalysis, which is limited to designing individual members for the forces which correspond to the peakglobal forces such as the maximum base shear and overturning moment. As a result it is consistent tolimit the random analyses and the prediction of the associated DAF's to those of the global responsesonly. In this case, it is both technically feasible and economic to use simplified random, time domainanalysis tools (e.g. the DYNSCRN program, Reference 20) to simulate global response parameterswhich can be used to evaluate the required dynamic amplification factors.

3. RECENT EXTREME EVENT ANALYSIS CASE HISTORIES

3.1 Introduction

In the previous section some general features of extreme event analysis and design problems werediscussed and the available tools introduced. This section contains some case histories whichillustrate the practical application of the general methods, procedures and computer programs whichhave been used within PETRONAS to examine extreme event dynamic analysis and designproblems.

3.2 Concept screening using frequency domain tools

3.2.1 Background

In May 1984 SIPM EP/23.1 embarked on an engineering study to examine the in-place behaviour of anumber of steel spaceframe structures within the context of the Troll field development. The studywas essentially a concept screening exercise in which a large number of different structural conceptswere developed and compared on the basis of their in-situ behaviour, and with particular emphasis onfatigue performance. This emphasis reflected the results of a number of earlier, deepwater, fixedplatform studies which indicated the potentially controlling influence of cyclic fatigue damage fordeepwater structures in a North Sea environment. Recognising the influence of structural dynamics,and with the fatigue analysis objectives clearly in mind, it was decided to use simplified, frequencydomain concept screening tools throughout the study (i.e. the TRUSSFRAME and FREERISEprograms References 5, 10). Previous studies had shown these to yield reliable assessments of cyclicfatigue damage due to frame action resulting from global static and dynamic loading. A more limitedevaluation of the extreme event loading and response was also carried out as part of the study. Thecyclic components of extreme event loading were also estimated making use of the same frequencydomain analysis tools. The case history of how this extreme event analysis was performed is aninteresting 'how it was done story' which is documented in full detail in section 9 of Reference 6. Thekey features of the procedure will be repeated here for completeness but the main objective in thepresent discussion is to highlight the strengths and weaknesses of the approach within the context ofthe discussion contained in section 2.

In order to estimate the total combined loading in the extreme storm condition it is necessary toconsider the combined effects of the cyclic loading in the design storm and the effects of mean staticloads arising from wind, current and structure self weight forces.

3.2.2 Estimation of short term cyclic loading components

The short term responses under the design storm condition (i.e. standard deviations of base shear,overturning moment and individual leg and brace axial forces) were developed using theTRUSSFRAME program (Reference 5). Basic input for TRUSSFRAME comprised the following items.

i) Transfer functions of global wave force excitation (base shear and overturning moment) for theprescribed storm condition, including the influence of steady current. These were established forthe three principal wave directions; two orthogonal primary axes and a single worst case diagonaldirection which was intended to maximise leg loads. A simplified, distributed vertical memberwave force idealisation of the structure was used. This was achieved using the computerprogram FREERISE (Reference 10) which incorporates a first order statistical linearisation of thedrag forces using the approach developed by Borgman (Reference 7).

ii) The fundamental mode dynamic characteristics of the structure in each of the principalorthogonal directions. This includes the mass distribution of the structure, natural frequenciesand mode shapes for the fundamental modes and the corresponding generalised masses in thenatural modes considered. This information was generated using simple stick beam modelrepresentations of the structure within the FREERISE computer program. For the forcedresponse calculations performed using the mode acceleration method) a percentage of criticalmodal damping must also be supplied.

iii) A geometrical description of the structur expressed in terms of a 2-D pin jointed truss frame. Thedescription defines the number of bays and leg members in each truss, the main frame leg andbrace geometry and the leg and brace member sizes.

An overview of the method used in the TRUSSFRAME program is shown in Figure 3.1. Full details ofthe method are contained in References 4 and 5.

The TRUSSFRAME analysis generates axial stress transfer functions due to overall frame actionresponses for brace and leg members. These can be processed using the appropriate design stormspectra to estimate the short term statistics of response (standard deviation values, etc.) usingconventional spectral analysis techniques. The TRUSSFRAME method was originally developed withfatigue analysis in mind and in this respect suffers from a number of limitations when applied forextreme storm conditions, which are as follows:

i) Free surface wave force effects cannot be included directly and must be estimated separatelyafterwards. This is not a major concern for fatigue analysis but these effects may be significantfor the design storm condition.

ii) At each wave frequency the applied wave force is represented by a point load. This results in theshear force and overturning moment distributions shown in Figure 3.1. The approximation is quiteacceptable for the dynamic fatigue problem where the short wave, higher frequency loading inthe region of the resonant frequency usually controls. However, it results in load distributionswhich are inappropriate for the extreme storm condition where the low frequency contributionsare important and results in overestimates of the applied loading in the bays of the structuredirectly below the centre of application of the point load. Furthermore, the point loadapproximation yields incomplete transfer functions for members in the higher bays. At lowfrequencies the point of application of the applied force is sufficiently far below the surface to bebelow the upper bay levels. As a result the truss frame solution cannot be applied to estimate themember load and stress levels above the location at which the point load is applied. Finally, sincethe applied loading only represents global forces the approximation ignores any additional effectsdue to direct wave loading on members (see (iv) below). A fuller description of these limitations inthe context of the extreme storm analysis is contained in sections 8.5 and 9.5.1 of Reference 6.

iii) The approach is limited to a 2-D frame only. For a non-symmetric structure, separate analysesare required for each orthogonal direction. Oblique wave directions, which are usually controllingfor outer leg members cannot be handled directly, other than for a symmetric structure havingidentical normal mode characteristics in each of the two principal planes. This problem is evenmore acute for a non-symmetric structure having different natural mode characteristics in each ofthe principal orthogonal planes. It requires separate FREERISE and TRUSSFRAME models foreach direction and necessitates external combination and manipulation of the results for theprincipal orthogonal directions, in order to generate appropriate response transfer functions forthe leg and brace members under diagonal loading conditions.

iv) Member loads are based only on frame action with no influence from local loading effects. Fixedend moments are also ignored in line with the pin jointed truss assumptions.

v) The basic pin jointed truss equations are only applicable to certain structural geometries. Braceconfiguration must be of a simple X-brace type. The equations are also only valid for structureswhich have supports beneath each of the legs. As such the method is unsuitable for the cornercluster pile type of structure having interior trusses (e.g. for launch) and with no direct reactionpoints under the interior legs (see Figure 3.1).

The TRUSSFRAME program generates the short term axial stress responses for leg and bracemembers. Design level most probable maximum stresses were extrapolated assuming the peak forcedistributions of the Morison force on a single vertical pile as described in section 2.2. This wasachieved by making use of the standard deviations of the drag only and inertia only components ofloading on the platform (see Reference 15), as predicted from a FREERISE, vertical member waveforce model of each structure. The influence of free surface effects was estimated in a crude mannerbased upon the changes in the wave surface elevation during the passage of the deterministic designwave.

3.2.3 Static loading components due to wind, current and self-weight

The influence of wind and current forces were also evaluated using the TRUSSFRAME program usingsimple point loads. The wind loads were estimated by hand whilst current loads were determinedseparately using the FREERISE wave force model. Resulting stress level predictions are, therefore,subject to some of the same approximations and difficulties discussed in section 3.2.2.

The influence of topside loading, structure weight and buoyancy were also estimated. Simplifiedmethods and hand calculations were employed to evaluate the submerged weight distributions andthe resulting frame action influences on the foundation and the leg and brace axial stress levels. Forthe Troll structures the influence of these components was found to represent up to 50% of themaximum combined leg stress and up to 30% of the maximum axial brace stress for the design stormcondition. Whilst these values reflect the particularly demanding topsides requirements of the Trollfield it should be emphasised that these relative contributions are not unusually high for deepwaterstructures.

3.2.4 Overall assessment

The use of the above procedure for extreme event analysis required use of a large number ofsimplifying assumptions and the application of a variety of separate analysis programs with transfer ormanual manipulation of data between the various steps. A number of structure specific 'fixes' werealso applied to the TRUSSFRAME program to enable the basic stress transfer functions to bedeveloped for the asymmetric structures having more than four legs. Whilst all these manipulationswere and are possible, and have the advantage of increasing understanding of the basic load andresponse phenomena, the fragmented nature of the analysis is costly in terms of the inconvenienceand the associated time required for implementation. The procedures used are also difficult to workinto a general analysis framework which retains the simplicity, and hence the attraction, of the originalTRUSSFRAME approach but which also includes the important features of the extreme eventdynamic analysis problem. Limitations in the point load applied force distribution assumed inTRUSSFRAME imply that the method cannot be applied over the full height of the structure. For theTroll structures in 340 metres waterdepth, full transfer functions, including the important low frequencybranch, were only generated over approximately the bottom 170 metres of the structure, i.e. the lowerhalf in this case. These difficulties need to be considered in the light of the comments made regardingthe potential influence of structural dynamics on total steel weight and the requirement to size theentire structure in an acceptable manner, and not just the lower bay members for which theTRUSSFRAME method remains appropriate for extreme storm conditions.

On the basis of these experiences it is necessary to conclude that the existing frequency domain toolsare not well suited to extreme event design assessments which are to be used for detailed membersizing operations. They are, however, suitable for parametric evaluations which are restricted toexamination of the global response characteristics of the structure. Isolated members in the lowerbays of the structure can be examined in somewhat more detail and can provide insight into theoverall frame action response.

The FREERISE and TRUSSFRAME programs both offer the potential to develop the forced responsecharacteristics of lumped parameter stick models. For such applications it is the author's opinion thatthe FREERISE option is the most attractive of the two. The reasons for this personal preference arethat the FREERISE program includes a more accurate definition of the applied loading over the heightof the structure and that the forced response is developed within a single model, without the need fora lot of data transfer between separate programs. Wave force excitation transfer functions, includingcurrent and the frequency characteristics resulting from the spatial separation of waveloadingelements, are combined with the dynamic characteristics within a single model. Level shear andmoment distributions are also determined over the full height of the structure. If required these maythen be used to estimate individual leg and brace stresses by hand, without the need to run aseparate TRUSSFRAME analysis. It should be emphasised that these reservations are geared to thespecific requirements of extreme event analysis; the attractiveness and benefits of the application ofTRUSSFRAME for fatigue analysis have already been mentioned and are fully documented inReferences 4, 21.

3.3 Member sizing for the extreme storm including dynamics

3.3.1 Background

The tools outlined in section 3.2 are not readily employed within the framework of a completestructure design. As described in section 2.4 ultimate weapons based upon the use of randomdirectional wave models are also insufficiently mature or lack the design code framework for directapplication. In these circumstances it is necessary to resort to the more approximate methodsdescribed in section 2.4 which are largely based upon the regular wave deterministic approach butwhich attempt to deal with the mass inertia forces from dynamic response in a reasonable manner.These methods have been applied successfully to the detailed design of Shell Oil's existing Cognacand Eureka structures in the Gulf of Mexico (References 2 and 18) and for the forthcoming Bullwinkleplatform for 1400 ft waterdepth. The same approach was used in a design study for a deepwaterstructure in the northern North Sea, performed by Earl & Wright, London, within the context of a JointIndustry Project (Reference 21).

The method will be illustrated with reference to a recent application within SIPM for theconceptual design of a slimline structure for 200 m waterdepth (Reference 22). This structure hadfundamental mode periods in the range of 4.2 to 4.9 seconds and dynamic response in the extremestorm was expected to be significant.

3.3.2 Pseudo-dynamic design procedures

Global dynamic response effects were determined by performing forced response analyses for thedesign storm, including current, using a simplified stick model frequency domain analysis. This wasdone using the FREERISE program which incorporates a distributed vertical member wave forcemodel of the structure, thereby enabling spatial separation effects in the wave force transfer functionsto be incorporated. The FREERISE models were used to establish dynamic amplification factors ofbase shear and overturning moment based upon the standard deviations of the global responses; i.e.the ratios of the standard deviations of the dynamic and static base shears and overturning moments.Wave forces under a regular (deterministic) design wave were established for the wave crest positioncorresponding to maximum base shear as in a conventional design wave analysis. This establishedthe target design level static loading. A set of mass inertia forces were created in order to develop therequired dynamic amplification of base shear and overturning moment. This inertia loadset reflects themass distribution and the natural mode shape(s) over the height of the structure and represents theadditional base shear and overturning moment components necessary to achieve the requireddynamic amplification of these quantities. These were established by making use of the fundamentalbending modes and lumped mass distribution of the structure. The inertia loadsets were developed inproportion to the lumped mass and mode shape distributions over the height of the structure for theend-on and broadside wave directions. The inertia loads were applied as additional static loadsetswithin an otherwise conventional, deterministic, storm wave structural analysis. For oblique directionsthe components of the diagonal wave loading were determined in each of the end-on and broadsidedirections. They are assumed to excite the orthogonal fundamental modes simultaneously (in-phase)and the appropriate inertia loadsets were generated accordingly. The basic steps in the method aredescribed in more detail in Appendix A.

Since the inertial loadsets are proportional to the fundamental bending modes of the structure in eachof the principal directions, the approach is a reasonable representation of the extreme wave dynamicresponse. Apart from the basic dependence upon the quasi-static design level forces, the method isbased upon two principal assumptions.

i) That the mass inertia forces resulting from dynamic response are in-phase with the appliedloading.

ii) That the mass inertia forces from each of the modes used are in-phase with each other.

The first assumption appears reasonable given that the structure's fundamental mode naturalfrequencies are much higher than, and well separated from those of the predominant wave energy.Resulting dynamic response is not resonant in nature and dynamic forces correspond to the massinertia forces associated with the motion of the structure when excited at frequencies lower than thoseof the fundamental modes. This assumption was also checked within the framework of the Trollspaceframe structure studies as described in section 9.4.2 of Reference 6 and found to be veryreasonable.

The dynamic response contributions of most fixed offshore platforms are dominated by thefundamental models). In this case the second assumption is also reasonable and will enable localloads to be represented reliably. As the influence of the second mode increases, the aboveapproximation (and hence the individual member forces) becomes more inaccurate due to relativephase differences between the inertia forces in the selected modes, which are not constant over theheight of the structure.

3.3.3 Assessment

The method described above incorporates several approximations but also has a number of practicalbenefits resulting from the fact that it fits within the umbrella of existing static design analysis. Themethod enables inertia force effects to be combined with other important global and local loadings(self weight, topsides etc.) in order to develop the detailed member force picture for design codechecking. On this basis it provides a true design tool rather than an analysis option.

In the applications considered to date in PETRONAS, the global dynamic amplification factors havebeen developed using a frequency domain approach and are based upon the standard deviations ofthe base shear and overturning moment response levels. The DAF's can also be developed in thetime domain (for random wave loading) using either MARIANTO (Reference 16) or the DYNSCRNprogram as developed by SOC (Reference 20) and now available in KSEPL. The MARIANTOprogram is a true, single member stick model, originally developed for the analysis of risers; therefore,it is unable to incorporate the effects of spatially distributed waveforce elements. The DYNSCRNprogram incorporates a distributed, vertical member wave force model (similar to FREERISE) which isdefined in terms of a series of lumped volumes and areas which are loaded using the random wavekinematics model. A modal analysis with static response correction is used to perform the timedomain dynamic analysis. However, the costly stiffness analysis is avoided by making use of modalresponse coefficients which are determined from a 'once only' modal analysis of the full structure. TheDYNSCRN program has been used by SOC for all recent deepwater designs and has the advantageof an explicit representation of non-linear effects due to drag loading and free surface variations. InReference 18, Larrabee describes some experience with the package during the analysis of theEureka structure. It was found that dynamic amplification factors based upon the standard deviationsof response obtained from a linear (or linearised) Gaussian model were conservative when comparedto the results of time domain simulation analyses, particularly for the higher load and response levels.He suggests that for the extreme event condition the DAF's should preferably be based upon theresults of random time simulations and should be related to the probabilities of exceedence of peakdynamic and static forces, i.e.

plevelyprobabilitatresponseStaticplevelyprobabilitatresponseDynamic

DAF =

In this definition a maximum dynamic response is not necessarily coupled to a maximum static eventin the same response time history. The method proposed, obviously suffers from some of theproblems (discussed previously) associated with determining the peak response, particularly at lowprobability levels, and the need for a significant number of simulations. Given this, and the apparentconservatism in the alternative estimate from the standard deviation values approach, DAF's basedupon standard deviations of response appear to offer a suitable basis for estimating global dynamiceffects in the short term. However, a more rigorous examination of the probability based definition isrequired, to identify whether the conclusions in Reference 18 are applicable in a more general sense.In this case the peak response definition may offer potential for reductions in the DAF and hence thetotal steelweight.

4. RECOMMENDATIONS

4.1 Some general conclusions and a short term recommended approach

Drawing upon the experiences documented in the previous sections, it is possible to draw a numberof general conclusions and to recommend a short term course of action for examining the extremeevent dynamic responses of deepwater fixed platforms. These recommendations assume continueduse of the presently available dynamic analysis tools and programs:

i) Dynamic response analyses using a regular wave deterministic model are inappropriate, dueto the artificial lumping of excitation energy at a single wave frequency and due to thepossible introduction of higher order wave force components associated with the selection ofa particular wave theory.

ii) Frequency domain tools, coupled to stick type dynamic models, provide an efficient means topredict the global response characteristics of dynamically sensitive structures. Such tools area valuable asset during early concept screening exercises, or for carrying out parameterstudies.

However, existing tools such as FREERISE and TRUSSFRAME do not provide a practicalmeans for design event member sizing operations since they are unable to reflect theinfluence of significant free surface effects, are unable to incorporate the influence of theother platform loadings such as self weight forces directly, ignore the effects of direct waveloading on members and do not include design code check facilities.

iii) Time domain simulations in random waves represent the ultimate analysis weapon becauseof their ability to include an explicit definition of all loading and response non-linearities. Thesemethods are expensive to develop and to use. However, their most significant drawback is arelative lack of experience in both their application and with an appropriate statisticaltreatment of the design member force time histories. At the present time, these difficultiesprevent use of the full 3-D random analysis tool in an absolute sense within the framework ofthe existing design codes. To avoid these problems random time domain analyses arepresently being employed in a relative sense to compare static and dynamic responsepredictions for the evaluation of global response dynamic amplification factors.

iv) For in-place design and code checking of conventional bottom supported fixed platforms a'pseudo-dynamic' analysis, founded upon the existing deterministic, design wave approach,represents a good short term engineering compromise. The effects of mass inertia forcesshould be represented using an additional static loadset which is developed to meet targetdynamic amplification factors for global responses. This procedure is considered appropriatefor structures having fundamental mode natural frequencies which are much higher than thepeak frequency of the design storm event (say, the ratio of the natural frequencies and thefrequency of the peak storm energy should be greater than 2.5 to 3.0). The responses of suchstructures remain essentially stiffness dominated and the basic assumptions are satisfied.

Since the method relies upon a reliable estimate of the global dynamic amplification factorsfor the design storm this is most correctly achieved using simplified random time domaintools. However, stick model frequency domain tools may provide reasonable estimates whichare sufficiently accurate for preliminary design purposes.

The pseudo-dynamic method can be employed economically during the preliminary membersizing and concept development phase, by making use of plane frame 2-D models. Theseinclude most of the geometrical and the local and global loading characteristics of the full 3-Dstructure but enable all in-place loadings to be represented and a stiffness analysis to becompleted. This facilitates complete member design at much reduced cost.

v) For in-place design and code checking of structures having a fundamental natural frequencywhich is (much) closer to or even lower than the peak frequency of the design storm event the'pseudo dynamic' analysis method is most probably inadequate. Compliant bottom supportedstructures may, for example, fall in this category. There is little or no experience with suchanalyses within PETRONAS but under these conditions it is probably necessary to perform afull 3-D dynamic analysis or a random environment, including direct loading on members and

all static platform loadings. Time domain simulations are obviously preferred but linearisedfrequency domain assessments may provide reliable estimates and may be acceptable ifappropriate tools for the former approach are not available.

A few additional comments are also appropriate in a more general sense. In designing a deepwaterplatform it is imperative that the influence of dynamic response is recognised at an early stage in thedesign development process. The relationship between the frequency content of the applied loadingand the natural modes of vibration of the structure are the key elements in defining the dynamicresponse. In this respect the transfer function of the applied wave loading and the expected range ofnatural periods for different foundation conditions provide useful information to guide the designer.Attempts should be made to reduce the wave force excitation in the vicinity of the expected range ofthe fundamental mode natural frequencies. This may be achieved by a careful selection of thegeometry of the structural members and appurtenances in and close to the free surface. Optimisationexercises have been shown to have a dramatic influence on the fatigue performance of dynamicallysensitive deepwater structures (see Reference 6). The results of such an optimisation are lessdramatic for the extreme storm condition, since amplification of the low frequency loading, which is notmarkedly influenced by spatial separation effects, contributes significantly. However, such anoptimisation is still beneficial in reducing the total dynamic loading and hence steel weight of thestructure, see the discussion in section 9.4.2 of Reference 6.

4.2 Longer term developments

Most of the dynamic response investigations carried out in PETRONAS to date have been performedusing simplified, first order frequency domain tools. This choice is easily justified given theiravailability, low cost, and ease of use. Furthermore, the need for detailed design of a deepwaterstructure has so far not arisen with PETRONAS.

Until quite recently, more accurate random time domain or non-linear frequency domain analysis toolssimply did not exist, were prohibitively expensive, or insufficiently well developed to enable theirwidespread application. This situation is changing and any future development work should reflectthis.

Given the potential impact of non-linear components in the extreme storm condition, it is nowaccepted that models which reflect these features explicitly are required. A two pronged approach issuggested which should enable some experience with time domain tools to be obtained, whilstdevelopment work proceeds with alternative frequency domain options.

In the author's opinion a prerequisite for future development work examining the extreme eventproblem is a random time domain simulation program. The simplified DYNSCRN dynamic analysisprogram is now under evaluation in KSEPL. This program provides an opportunity to develop somefirst hand experience with a random time domain simulation program without the need to developthese facilities from scratch first. It is suggested that the random time domain approach shouldprovide the reference baseline for future development work and comparisons, simply because it is themost explicit model presently available and because the tools already exist.

Some experience is necessary in order to establish the potential of the DYNAL/DYNSCRN tools andto be able to anticipate the usual unwritten difficulties associated with using any new program. In thefirst instance a comparison with the use and the results of an existing structure seems mostappropriate. An extreme event dynamic analysis is planned for a jack-up unit, but this work will becarried out by KSEPL. Given this situation, some in-house analysis seems essential and acomparison study for one of the Troll structures previously examined in the frequency domain wouldseem an ideal candidate. In order to do this, the program needs to be accessible from withinPETRONAS offices and this problem needs to be addressed first and foremost. Comparisons of theglobal DAF's obtained from the frequency and time domain models will require a substantial effort butwill provide some essential 'hands-on' user experience and highlight any practical problems with theprograms. Once this experience has been gained, effort could be directed towards the problemsassociated with predicting the peak force levels from the resulting simulation time histories. A logicalfirst step would be to try to fit an existing peak value distribution (such as Weibull) to the data resultingfrom one or more simulations and to compare these results with extrapolations made from thefrequency domain solutions.

Some other developments based upon frequency domain approaches are also considered valuable.These are particularly important if a design or analysis approach based upon the so-called long-termprediction method, i.e. geared to probability of exceedence of structure responses rather thanenvironmental criteria (Reference 15), is to be pursued to its logical conclusion.

As mentioned in section 2.3 higher order terms present in the original Borgman drag forcelinearisation are presently neglected in the FREERISE implementation. These may be significant forflexible structures. Eatock Taylor has published several papers (References 10, 11, 12) whichdescribe frequency domain dynamic analysis tools for 2-D plane frames which include these effects.The value of these methods and perhaps even the tools themselves, needs to be examined in moredetail than has been possible during the production of this document. For the case of constant waveforce coefficients the Bendat and Piersol wave loading model, which was developed with funding fromEP/23.1 (Reference 23), produces the same wave force spectrum as the higher order Borgmanmodel. The Bendat and Piersol model thus represents a more general wave force formulation, whichdegenerates to the Borgman model for the constant drag coefficient case. During the final stages ofthe deepwater platform JIP (Reference 21) the Bendat and Piersol model was coupled to a distributedvertical member wave force representation of the structure to enable wave forces generated usingrandom simulations and deterministic waves to be compared (see Reference 25). If this model weregeneralised to include the wave loading distribution on an arbitrary multi-member structure andcoupled to a dynamic structural analysis program (such as NASTRAN, SESAM80 or a similarcapability), such a tool might offer an economical and attractive alternative in the frequency domain.The outstanding difficulties associated with non-linear free surface phenomena would still need to beaddressed separately, but comparisons with time domain solutions would enable quantification oftheir significance and a means to calibrate the frequency domain model.

In the first instance it is proposed that the feasibility of incorporating the higher order contributions inthe frequency domain FREERISE program should be investigated. This could be achieved bygeneralising the existing first order expansion, or coupling the Bendat and Piersol model to theprogram. Results should then be compared with time domain simulations. If this proves feasible andpromising, the next logical step would be to examine the potential for incorporating these waveloading routines in a true distributed member spaceframe model assuming a 2-D representation.Clearly, availability of the wave force routines is only part of the problem since these need to becoupled to an appropriate dynamic analysis capability. A means to incorporate the free surface effectswould also be required and ultimately a facility to account for other static load components would alsobe needed to complete the picture. All these potential developments need to be reviewed within thecontext of PETRONAS longer term plans for an integrated design and analysis tool which isintended to be built around a single structural analysis kernel.

4.3 Final comments

The objective of this report was to review existing methods and tools which are available to examinethe extreme event dynamic response of bottom supported offshore platforms. Most of the materialpresented is based upon experience gained during the course of a number of conventional fixedplatform studies in which we have been involved over the past few years. In this context it obviouslyrepresents a subjective assessment which is influenced by the personal experiences which resultedfrom actually carrying out a number of different analyses and also observing the methods used byother factions of the industry. An attempt has been made to look outside our present experience andto anticipate some of the potential development work which may enable weight and cost savings inany future deepwater fixed platforms. Finally. this note has assembled a collection of some of themost relevant references which should provide a useful bibliography for a general introduction to theproblems and as a basis for future development activity in this area.

5. REFERENCES

1) I.M. HinesA COMPARISON OF MODAL SUPERPOSITION AND DIREC SOLUTION TECHNIQUESFOR THE DYNAMIC ANALYSIS OF OFFSHORE STRUCTURESSIPM report EP-52648, September 1980.

2) J.A. RuhlEXTREME WAVE DYNAMICS OF THE COGNAC PLATFORMPaper 708, Shell Offshore Engineering Conference,February 1978.

3) J.H. Vugts and R.K. KinraPROBABILISTIC FATIGUE ANALYSIS OF FIXED OFFSHORE STRUCTURES OTC 2608,1976.

4) J.H. VugtsOFFSHORE STRUCTURES ENGINEERINGChapter 7, SIPM report EP-60690, August 1984.

5) J.W. v.d. GraafTRUSSFRAME ANALYSIS PROGRAMUsers input guide, Version 1, SIPM Internal Note, May 1984.

6) A COMPARISON OF THE IN-PLACE BEHAVIOUR OF STEEL SPACE FRAMESTRUCTURES FOR THE TROLL FIELD (BLOCK 31/2) FOR A/S NORSKE SHELLVolume 2, SIPM EP/23.1, SIPM EF report EP-62400, August 1985.

7) L.E. BorgmanOCEAN WAVE SIMULATION FOR ENGINEERING DESIGNJournal of ASCE 95 (WW4), p. 557-583, 1969.

8) A.K. Malhotra and J. PenzienNON-DETERMINISTIC ANALYSIS OF OFFSHORE STRUCTURESJournal of ASCE 96 (EM6), 985-1003, 1970.

9) R.D. Larrabee

MEASURED AND PREDICTED COGNAC PLATFORM RESPONS DURING HURRICANEFREDERICSIPM report EP-55873, June 1982.

10) J.W. v.d. GraafFREERISE - FREQUENCY DOMAIN RISER ANALYSIS PROGRAMUsers guide, SIPM report EP-57703-2, May 1983.

11) R. Eatock Taylor and A. RajagopalanLOAD SPECTRA FOR SLENDER OFFSHORE STRUCTURES IN WAVES AND CURRENTEarthquake engineering and structural dynamics, Vol. 11, p. 831-842, 1983.

12) R. Eatock Taylor and A. RajagopalanDYNAMICS OF OFFSHORE STRUCTURES; Part 1 - Perturbation analysis, Journal of soundand vibration, 82(3). p. 401-431, 1982.

13) A. Rajagopalan and R. Eatock TaylorDYNAMICS OF OFFSHORE STRUCTURES; Part 2 - Stochastic averaging, Journal of soundand vibration, 83(3). p. 417-431, 1982.

14) M.P. HarperANALYSIS OF A MULTI-BORE PRODUCTION RISER IN A NORTHERN NORTH SEAENVIRONMENTSIPM EP report EP-51647, November 1979.

15) R.B. lnglis and J.G.L. Pijftrs

UNIFIED PROBABILISTIC APPROACH TO PREDICTING THE RESPONSE OF OFFSHORESTRUCTURES INCLUDING THE EXTREME RESPONSESIPM EP report EP-61300, October 1984.

16) L. ter Haar and P.H.J. VerbeekMARIANTO - MARINE RISER ANALYSIS TOOLKSPEL report RKGR.84.043, April 1984.

17) L.D. Ruthven (Shell Oil Co.)DYNAL III - A COMPUTER PROGRAM FOR THE DYNAMIC ANALYSIS OF OFFSHORESTRUCTURESUsers guide, interim report, SIPM EP report EP-59963, 1984.

18) R.D. LarrabeeEXTREME EVENT WAVE DYNAMICS OF PLATFORM EUREKA(Shell Oil Co.) BRC 28-81, July 1981.

19) F. MosesDEVELOPMENT OF PRELIMINARY LOAD AND RESISTANCE DESIGN DOCUMENT FORFIXED OFFSHORE PLATFORMSAPI PRAC PROJECT 85-22 Final report, January 1986.

20) R.D. Larrabee and K.R. Lucas (Shell Oil Co.)COMPUTER PROGRAM DYNSCRN - SIMULATED PLATFORM DYNAMICS IN RANDOMSEAS,Theory and users manual, BRC 25-80, September 1980.

21) Earl and Wright, LondonDEEPWATER FIXED PLATFORM JIPPhase 2 Final report, SIPM EP report EP-62998, May1985.

22) I.M. Hines, I.J. Bradshaw, A.C.M. v.d. StapFEASIBILITY STUDY FOR A SLIMLINE LIFT INSTALLED PLATFORM FOR 200 METRENORTHERN NORTH SEA WATERDEPTHSIPM report EP-86-0088, September 1986.

23 A.G. Bouquet and J.H. VugtsA NON-LINEAR FREQUENCY DOMAIN DESCRIPTION OF WAVE FORCES ON ANELEMENT OF A VERTICAL PILE IN RANDOM SEASSIPM report EP-5937, April 1984.

24) D.K.Y. Kan and C. PetrauskasHYBRID TIME-FREQUENCY DOMAIN FATIGUE ANALYSIS FOR DEEPWATERPLATFORMSOTC 3965, OIC Conference 1981.

25) Earl & Wright, London, A.G. BouquetDEEPWATER FIXED PLATFORM JIPPhase 2, Task 15 Report, May 1985.

LIST OF FIGURES

Figure number Figure Title

2.1 Comparisons of a single degree of freedom system dynamic response usingrandom and deterministic models

2.2 Schematic of random time domain simulation analysis

2.3 Schematic of the spectral analysis procedure

3.1 overview of the method used in the TRUSSFRAME program

Fig. 2.1 Comparisons of dynamic response of a single degree - of - freedom system to deterministic and random waves

Fig. 2.2: Schematic of random time domain simulation analysis

Fig. 2.3: Schematic of frequency domain spectral analysis

Fig. 2.4: Schematic of hybrid time/frequency domain analysis

Fig. 3.1: Overview of the procedure used in the TRUSSFRAME program.

APPENDIX A - STATIC PLUS MASS INERTIA 'PSEUDO DYNAMIC' ANALYSIS PROCEDURE

A.1 Introduction

This appendix describes a simplified dynamic structural analysis procedure suitable for the analysis ofconventional bottom supported fixed structures, under the influence of environmental loading and selfweight forces. The basis for the procedure was first developed by Shell Oil Co. during thedesign of the Cognac platform, see Reference 2. It has been refined somewhat, resulting in theprocedure documented here; since then, this procedure has been applied during the detailed designof several other deepwater fixed platforms (see References 18, 21).

As discussed in section 2.4 of the main text the need for a simplified dynamic analysis procedureresults from the requirement to design a structure rather than simply analyse its dynamic response.Sophisticated time or frequency domain dynamic analysis tools are now available for predicting theresponse of a fixed bottom supported structure to random wave loading (see References 10, 17, 20).It is hoped that these will subsequently become feasible design tools rather than analysis options.However, existing experience with such tools is rather limited and problems remain with reliablepredictions of the extreme member force statistics and with their application within the framework ofexisting design codes. Given this background, a simplified approach is desirable as a short termalternative to the implementation of true random wave analysis design tools The simplified approachshould incorporate the essential features of the platform dynamic response, but also fit within theframework of existing codes of practice which are presently based upon the use of conventionaldeterministic wave design procedures. A regular deterministic, quasi-static analysis which is modifiedto include the effects of mass inertia forces provides such an option and will be outlined in the nextsection.

A.2 Outline of the procedure

The simplified 'pseudo dynamic analysis' described here is essentially a static analysis using a totalapplied load which matches predetermined global dynamic force levels. Platform design is usuallybased upon the instant of time corresponding to the maximum global platform loading rather thanthose of the individual member maxima. On this basis the quasi-static loading from environmentalforces is supplemented by additional static loadsets which are developed so as to matchpredetermined dynamic base shear and overturning moment values.

The procedure consists of the following basic steps:

i) Establish the cyclic quasi-static base shear (CBS) and overturning moment (COM)corresponding to the specified design wave height, period and current for each orthogonaldirection, using a regular design wave method.

ii) Establish the influence of dynamic response in terms of the increases in the cycliccomponents of loading due to mass inertia force amplification effects. The effects of dynamicresponse should preferably be determined using appropriate random wave dynamic analysistools in either the time or frequency domain (e.g. references 5, 20). The dynamic componentsare evaluated in terms of the resulting dynamic amplification factors of cyclic base shear andoverturning moment (DAFS, DAFM). The DAF's are determined from the ratios of the shortterm response statistics, I.e. standard deviations of static and dynamic base shear andoverturning moment or on the basis of equal probabilities of occurrence of peak static anddynamic responses as discussed in section 3.3.3 and Reference 18.

The resulting dynamic mass inertia shear force and moment components are then as follows:

INERTIAL SHEAR = (DAFS - I) *CBS (A1)

INERTIAL MOMENT = (DAFM - 1)*COM (A2)

If appropriate dynamic models are not available with which to determine the appropriateDAF'S, these can be estimated on the basis of experience with previous structures. At thevery early stages of design they may simply be guestimated.

(iii) For each of the principal orthogonal directions, generate a mass inertia loadset, in terms of aseries of lateral point loads acting at each plan level over the height of the structure. Themass inertia loadsets are proportional to the fundamental bending modes of the structure ineach principal direction.

So that:

V1 = Mφ1 (A1)

V2 = Mφ2 (A2)

Where: Vi = vector of lateral modal forces in mode i

M = system mass matrix

φi = mode shape for ith mode

Assuming full participation of each mode the resulting inertial base shear and overturningmoments for mode i, are obtained by summing the contributions from each level as follows:

INERTIAL SHEAR : jijV mn,1j

i φΣ==

(A5)

In mode i

INERTIAL MOMENT : jjijM mhn,1j

i φΣ==

(A6)

In mode i

Where:

j = plan level subscriptn = total number of lumped massesi = mode numbermj = lumped mass at level jhj = height above base to level jφij = mode shape amplitude for mode i at level j

vi) The dynamic components of the base shear and overturning moment are then developedfrom the sum of the modal contributions. Inertial responses in each mode are proportional tothe product of the mass and the mode shapes as shown in Figure A.1. The contributionsfrom each mode are a function of the modal participation factor αi which depend upon thecharacteristics of the loading and the mode shape.

The proportionality (or participation) coefficients αi for each mode are determined by solvingthe following equations, assuming two modes being relevant.

INERTIAL SHEAR = jj2n,1j

2jj1n,1J

1 mm φΣα+φΣα==

(A7)

INERTIAL MOMENT = jjj2n,1j

2jjj1n,1j

1 mhmh φΣα+φΣα==

(A8)

See figure A.1.

v) Once the proportionality coefficients (α1, α2) are established, the mass inertia force loadsetsfor each mode and for each principal direction can be obtained by multiplying the mass inertialoadsets developed in step (iii) above by the appropriate modal participation (α) values, seeFigure A 1. These can be applied to the structure as static extra loadsets which supplementall the other environmental and self weight loads. The mass inertia loadset is combined with aregular wave deterministic analysis to design the structure in the same manner as forconventional shallow water structures which do not experience dynamic response.

The loadsets used to design the structure are shown in Figure A.1. The above proceduremust be applied to both principal wave approach directions requiring the development ofinertial loadsets for end-on and broadside loadcases using the appropriate mode shapes andmass distributions, and participation.

For oblique wave directions some further approximations are necessary. Firstly total dynamicand static force components must be determined in the direction of the wave approach anglein order to establish the dynamic force contribution or the required dynamic amplificationfactor for the oblique direction. The components of the total quasi-static applied loading ineach of the principal directions must also be established. This information can then be used toestimate the appropriate mass inertia loadsets for each principal direction. A simultaneouslinear combination of the inertia loadsets in both principal directions is used in order toachieve the target dynamic amplification for the diagonal direction.

The above relationships match the required base shear and overturning moment using twoproportionality constants α1, α2, and two modes. Level shears and moments at any two otherlocations tan also be matched in a similar manner. If the dynamic response components areto be matched at more than two levels (say n) then n modes and n proportionality constantsmust be used resulting in a set of n equations similar to A7, A8 above.

.

Figure A1: Development of inertia force loadsets used in pseudo-dynamic analysis