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
PETRONAS Technical Standards (PTS) publications reflect the views, at the time of publication, of PETRONAS OPUs/Divisions. They are based on the experience acquired during the involvement with the design, construction, operation and maintenance of processing units and facilities. Where appropriate they are based on, or reference is made to, national and international standards and codes of practice. The objective is to set the recommended standard for good technical practice to be applied by PETRONAS' OPUs in oil and gas production facilities, refineries, gas processing plants, chemical plants, marketing facilities or any other such facility, and thereby to achieve maximum technical and economic benefit from standardisation. The information set forth in these publications is provided to users for their consideration and decision to implement. This is of particular importance where PTS may not cover every requirement or diversity of condition at each locality. The system of PTS is expected to be sufficiently flexible to allow individual operating units to adapt the information set forth in PTS to their own environment and requirements. When Contractors or Manufacturers/Suppliers use PTS they shall be solely responsible for the quality of work and the attainment of the required design and engineering standards. In particular, for those requirements not specifically covered, the Principal will expect them to follow those design and engineering practices which will achieve the same level of integrity as reflected in the PTS. If in doubt, the Contractor or Manufacturer/Supplier shall, without detracting from his own responsibility, consult the Principal or its technical advisor. The right to use PTS rests with three categories of users : 1) 2) 3)
PETRONAS and its affiliates. Other parties who are authorised to use PTS subject to appropriate contractual arrangements. Contractors/subcontractors and Manufacturers/Suppliers under a contract with users referred to under 1) and 2) which requires that tenders for projects, materials supplied or - generally - work performed on behalf of the said users comply with the relevant standards.
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Report EP 87-0170 Title
: PRACTICE FOR THE DYNAMIC ANALYSIS OF FIXED OFFSHORE PLATFORMS FOR E 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 is endorsed as a Practice by SIPM-EP. SIPM-EP/11, as custodian, will either update/revise the document as appropriate or withdraw its status as an endorsed Practice. Any questions relating indicator is given below.
Reporter
:
Reviewer :
Custodian :
Name
:
I.M. Hines
Reference indicator
:
EPD / 112
Date
:
January 1987
Name
:
G. Moeyes
Reference indicator
:
EPD / 112
Date
: January 1987
Name
:
J.H. Vugts
Reference indicator
:
EPD / 11
Date
:
January 1987
Signature
Signature
Signature
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
3.3
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
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 the industry in general, and PETRONAS in particular, for the prediction of the extreme storm dynamic response of conventional, bottom supported offshore platforms. The report focuses upon the analysis and design requirements for steel spaceframe towers or jacket structures. Advantages and disadvantages of the various methods are discussed with respect to their application in different stages of the design process, and recommendations for the most useful techniques at present are made. Further developments are proposed, with particular reference to the computing facilities available in PETRONAS.
1.
INTRODUCTION
Over the past ten years or so the fixed platform concept has slowly been pushed into deeper and more hostile environments. Designers of conventional, deepwater fixed platforms have had to cope with the increased flexibility of these structures and to develop analysis and design procedures which account for the resulting dynamic amplification of the applied loading which is associated with the mass inertia forces. In these structures the influence of structural dynamic response is evident both in terms of the amplification of the extreme storm design loadings and the increase of cyclic fatigue damage associated with dynamic response to less severe, but more frequently occurring, everyday sea states. The extent of dynamic response is associated with the relationships between the structure's fundamental modes and the frequency content of the applied loading. Design and analysis procedures for deepwater structures which respond dynamically must account for the random nature of 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 single common approach. As a result, available experience is very limited and the state of the art is still under continuous development. This document provides a review of the existing experience and procedures available within the industry in general, and PETRONAS in particular, for the prediction of the extreme storm dynamic response of conventional, bottom supported offshore platforms. The report focuses upon the analysis and design requirements and experiences for steel spaceframe towers or jacket structures; these structures have provided the initial stimulus for work in this area. However, much of the general discussion on analysis philosophy and analytical methods is also applicable to inertia dominated compliant structures which may represent a future generation of deepwater bottom supported platforms. The first section of the report summarises some fundamental problems which need to be faced when evaluating dynamic response for extreme storm conditions and presents the various options which are currently available. This is followed by a review of some recent analysis experiences which will be used to highlight the benefits and the deficiencies of some of the various options. A recommended procedure is then outlined to provide an approach which is considered to be suitable for analysis and design requirements for the foreseeable (short term) future. The main emphasis here is on a procedure which can most readily fit within the framework of existing design codes of practice developed for shallow water structures (e.g. API or DNV), thus enabling an otherwise conventional design to be carried out. Finally, some recommendations for future development work in this area are outlined. These try to anticipate the outcome of ongoing, longer-term efforts geared to the development of a design approach which is better suited to the probabilistic nature of the random wave environment.
2.
APPROACHES TO DYNAMIC ANALYSIS
2.1
Some fundamental problems
In formulating analysis and design procedures capable of predicting the response of a flexible deepwater platform under the influence of extreme storm environmental loading, a number of interrelated 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 the required accuracy.
iii)
The magnitude and spatial distribution of the wave and current loadings and their relationship to the structure's natural frequencies.
iv)
Procedures to represent and analyse the force mechanisms, and the interaction between the structure and the surrounding fluid.
v)
An analysis and design framework within which to combine the results of dynamic response predictions 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 of the damping mechanisms and the foundation, the first area probably poses the least difficulty, and can be dealt with adequately using presently available modelling and analysis techniques. As a result it will not be considered further here. The second area has been addressed in detail in Reference 1 and the conclusions and recommendations of this study do not need to be repeated. It suffices to say that adequate dynamic analysis methods do exist which are compatible with all levels of the design cycle; 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 the discussion which follows. It is now widely recognised that the offshore environment represents a true random process. Despite this, 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 of satisfactory service in which relatively few structural failures have occurred for shallow water structures which are relatively stiff and respond quasi-statically to the ocean environment. In the context of the overall design procedure used, the deterministic design wave approach has served the industry rather well. Early, first generation dynamic analyses for deepwater offshore structures were also based upon deterministic procedures (e.g. preliminary analyses of Shell Oil's Cognac platform, Reference 2). The dynamic response was evaluated using time domain numerical simulations of the platform response when 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, it suffers from a number of fundamental flaws: i)
Using this procedure, design sea state energy isassociated with a single discrete wave frequency. As a result, the frequency content of the applied loading is also artificially lumped at a number of specific frequencies; in the first instance, at the frequency of the deterministic wave but 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 drag forces associated with the Morison force formulation, both with or without current; from the use of non-linear wave theories (such as Stokes 5th); or from free surface loading effects associated with the changing position and shape of the wave surface. Realistic relationships between the frequency 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 harmonic components at discrete multiples of the fundamental wave frequency which may be tuned to the structure'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 some time domain dynamic analyses of a single degree-of- freedom structure when subjected to regular Stokes 5th design waves and an equivalent random sea with the same probability of occurrence. The single degree-of- freedom model was first loaded with the total force time history of the regular deterministic Stokes 5th wave used for the design of the Cognac platform. Simulations were then made using the random wave force history as developed from the corresponding storm wave spectrum. The figure shows the resulting dynamic amplification factor of base shear as a function of the structure natural period. The Stokes 5th wave used has a period of 11.5 seconds and the SDOF system is seen to resonate with the second harmonic of the Stokes wave at 5.75 seconds and with the third harmonic at 3.8 seconds. The fundamental harmonic resonance (at 11.5 seconds) is not shown, since it is outside the structure period range of interest.
Conversely the random simulation results (obtained by averaging the results of 20 separate simulations) show a much smoother variation with the structure period. This is much more representative of the actual broader band frequency content of a real sea, even in design storm conditions. As a result of the shortcomings illustrated in the above discussion, dynamic analysis using periodic regular wave loading is considered to be unreliable. Methods which account for the actual relationships between the frequency content of random seas and the fundamental mode natural frequencies of the structure are required. Two possible types of solution enable the random nature of the environment to be represented. These are the stochastic approach, usually based upon linearised, frequency domain spectral analysis techniques, or the use of random time domain simulations. Both approaches are discussed briefly in the following sections, where attention is focused upon the basic features of the problem formulation and 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 result from the wave loading (usually predicted using the Morison equation) soil characteristics and damping. The non-linearity within the velocity squared drag component of the Morison equation, is further complicated by the influence of free surface inundation effects. Further uncertainty surrounds questions about how, and under what circumstances, the relative motion of the structure may influence both the applied loading and the system damping. Accepting the basic Morison force formulation, it is now considered that solutions based upon random time domain solutions represent the most realistic representation of the response of an offshore platform in a real sea. The procedure involves a number of discrete steps which are shown schematically in Figure 2.2 and summarised here: i)
Develop time histories of wave surface elevation and water particle kinematics either from measured 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 of motion in order to develop timehistories of the structural response include all the non-linear components 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 a penalty of computational cost which depends upon the length and number of simulations required and the size and complexity of the platform model. The method carries an additional penalty in terms of the difficulties associated with the interpretation and application of the results. In modelling the random environment it is assumed that the wave surface elevation is a stationary, ergodic, Gaussian process. As a result of system non-linearities, the response is certainly non- Gaussian but it is also possible that it may not be stationary in a statistical sense as well. Therefore, a single realisation of the non-linear structural response only represents one of a theoretically infinite number of such realisations. In order to develop confidence in the short term statistical characteristics of the response it is necessary to carry out a number of such simulations. Information on the extreme values, which represent the tails of the peak response distributions, can only be obtained reliably by performing a very large number of simulations, or by performing extrapolations based upon existing or assumed extreme 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 spectral analysis procedures provide a convenient and efficient means to incorporate the random wave environment. In this context a linear spectral analysis (Reference 3) is now well established as the final design, state of the art industry standard for examination of the potential for cyclic fatigue damage. The frequency domain spectral approach, as shown schematically in Figure 2.3, can also readily incorporate the influence of structural dynamic response. Simplified, first order screening tools have been developed within SIPM during the past few years, as a means to carry out a preliminary examination of the fatigue behaviour of steel spaceframe structures (References 4, 5). The procedures retain the fundamental benefits of a dynamic, spectral fatigue analysis, without incurring the high cost associated with a detailed 3-D analysis. These tools have proved to be invaluable in preliminary concept screening studies; some recent applications are documented in References 4 and 6. For the prediction of extreme responses the linearised spectral method has a number of obvious limitations. These are associated with the difficulty of incorporating the non-linear effects and also, as with the time domain approach, in the extrapolation of short term statistics to predict the peak response levels. As stated previously, due to non-linearities in the system, the resulting response is actually non- Gaussian. The fact that the linearisation procedures adopted in the problem formulation make the response as modelled truly Gaussian, does not change this basic characteristic of the response. In this sense the linear model does not reflect the actual situation. In design storm conditions the influence of non-linear drag components and free surface effects are more significant than in the fatigue environment. The choice of the linearisation procedure is, therefore, of critical importance. Procedures based upon a sea state dependent, statistical linearisation of the drag loading, as developed by Borgman (Reference 7) and implemented by Malhotra and Penzien (Reference 8), are considered to be the most consistent of those available at the present time. However, these methods do not enable the influence of variations in the free surface wetted area to be taken into account. Free surface effects are known to be of major importance in defining both the local and global force distributions on the structure during extreme event conditions (Reference 9). Furthermore, most of the existing 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 full linearised wave force expansion contains higher order terms which require convolutions of the wave velocity spectra. This introduces higher order components in the wave force spectrum in the vicinity of three times the principal wave frequency of the storm. These terms are relatively unimportant for structures which respond quasi-statically. However, they may be significant for flexible structures which respond dynamically since these higher harmonic components may coincide with the fundamental 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 of current, is described by Eatock Taylor and Rajagopalan in References 11, 12, 13. These papers contain results of some analyses for a flexible, multi-member, steel spaceframe structure. Linear and non-linear spectral formulations are compared with random time domain simulations in terms of the resulting second order response statistics (e.g. standard deviations of response). These results demonstrate the significant influence of the higher harmonic components and indicate that the nonlinear stochastic approach may represent a suitable alternative to random time domain simulations for the 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) as a method for overcoming some of the limitations of the linearised spectral approach. The method still relies upon the use of a transfer function and spectral analysis techniques to determine the short term statistical responses. However, in this case, the transfer functions are determined from a random wave, time domain analysis, with transformation into the frequency domain being achieved via Fouler transforms. The procedure used is outlined in Figure 2.4. The hybrid approach, was originally proposed as a means to include non-linear effects within the scope of a spectral fatigue analysis, but applications for the extreme storm condition also appear feasible.
As with random time domain solutions, difficulties remain, however, in predicting the extreme response levels experienced during the design storm condition. These are the values which are ultimately required in order to perform actual structural sizing operations which are consistent with existing design practice. In order to facilitate predictions of the peak response values using the results from a linearised frequency domain analysis, use. has been made of the probabilistic description of Morison type wave force loading when acting on a single vertical pile (References 14 and 15). For a linear Gaussian model the Most Probable Maximum (MPM) value is approximately 3.7 times the Standard Deviation (SD) value, assuming 1000 peaks which corresponds approximately to a threehour storm. However, if the process is non-linear and hence non-Gaussian (i.e. as a result of drag loading) the ratio of the MPM and SD of wave force may be significantly higher (as high as 8.6 in a totally drag dominant, non-Gaussian system). For most practical situations a mixture of linear and non-linear contributions are evident in the loading and the actual MPM/SD ratio will be somewhere within this range. It should further be noted that the mix and, therefore, the degree of non-Gaussianity will 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 be obtained in the frequency domain. These are engineering approximations to enable the most probable maximum 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 were originally developed. This is achieved by making assumptions regarding the nature of the peak distributions. It is postulated that the probabilistic descriptions of the response variables in the amplitude domain may be directly related to those of the Morison wave force formulation for a single vertical pile. This implies that the probability distributions derived for the Morison wave force formulation for a single vertical pile, are also applicable to other response parameters (e.g. member forces and stresses) and to more complex structures comprising a large number of individual, spatially distributed and non-vertical loading elements. It must be stressed that these procedures remain engineering postulates which attempt to incorporate the effects of the non-Gaussian nature of the response 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 matter and by lack of a better model the approach described above is pragmatically adopted. They do provide a practical framework for the interpretation of the frequency domain results, however, there is clearly very little experience with the consequences of applying these methods in order to perform design member sizing.
2.4
Applications and tools
Examination of extreme storm dynamic response may be required at a number of different stages during 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 a clear distinction between the requirements for concept screening exercises, for design development, for design verification in accordance with existing design codes, or for ultimate strength analyses which fall outside the regular codes of practice. Concept screening exercises, and parameter or feasibility studies are most usefully performed using simplified 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 overturning moments together with associated dynamic amplification factors. Fundamental mode response characteristics can be adequately represented using relatively simple, lumped parameter stick models. These models enable sensitivity studies to be performed quickly and at very low cost compared to equivalent full 3D models. They can also be coupled to waveload generation routines in either 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 force and overturning moment distributions, thereby enabling the development of level dynamic amplification factors based upon the short term response statistics for random wave storm loading conditions.
The packages referred to above are unable to predict individual member loadings which have to be estimated separately using the level shear and moment response characteristics. This shortcoming prompted the development of a concept screening tool for simple steel spaceframe structures (the TRUSSFRAME program see References 4, 5) which operates in the frequency domain. It makes use of dynamic response characteristics from a stick model, base shear and overturning moment transfer functions, and a simplified pin jointed (truss frame) description of the structure to estimate individual axial stress transfer functions for leg and brace elements. The calculations are performed assuming response 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 be applied 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 tools for parametric exercises. Design tools must translate the results of the dynamic response predictions into the absolute requirements in terms of member sizes and total steel weight. The influence of dynamic response in the extreme storm must be combined with the effects of the other storm loadings on the platform (i.e. topsides loading, self-weight, buoyancy, wind loads, etc.) both in terms of their global and local effects. It is also suggested that provided the effects of structure flexibility are considered from an early stage in concept development, dynamic components of the extreme storm loading are unlikely to govern the bulk of the steel in the structure, even in the deepest of waterdepths. This is in contrast to fatigue loading conditions where resonant dynamic behaviour may in some cases be fully controlling. Other in-place loadings such as self weight, quasi-static wave forces, and also those associated with the fabrication, load out, launch, hydrostatic forces, etc. also impact steel weight significantly. Collectively, these loads are likely to have a more important role in total weight growth than the dynamic loads taken in isolation; e.g. in the Cognac platform, the influence of dynamic loads increased the total steel weight by an estimated 25% and this includes contributions from fatigue. This relatively low weight growth resulted from a strong awareness of dynamic response effects and careful attention to the inter- relationships between platform dynamic characteristics, wave loading and dynamic response. These experiences demonstrate the importance of a reliable assessment of dynamic response and the need to incorporate these effects at a very early stage in the design development. However, they also suggest the need for a balanced approach to the design. The procedures used must incorporate the key features of the dynamic response problem, but they must also fit within the framework of an integrated design approach, which also recognises the significance of the other load conditions in a consistent manner. Full 3-D, random wave, time domain analysis tools are now available (e.g. Shell Oil's DYNAL III package, Reference 17) which enable the random wave environment and dynamic response influences to be represented explicitly for any design storm condition and for large structures. These packages are able to generate corresponding time histories of individual member loadings. However, these tools are computationally expensive for large structures and furthermore a single random simulation results in only one of an infinite number of possible response histories, each including one possible extreme for each individual response. Selecting appropriate values for design member sizing is, therefore, complicated by the requirement for an appropriate procedure to deal with the extreme response statistics and a consistent design framework within which to apply these. In the first instance it appears preferable and logical to try to relate a design procedure incorporating random wave loading and dynamic response effects to that of the existing approach for shallower water offshore platforms which have been designed in accordance with deterministic procedures. However, use of the Morison formulation within the framework of the linear random directional wave model implies the use of different wave force coefficients to those which are normally applied for deterministic wave analyses (see Reference 18). Resulting force levels from the random wave model may also be higher with corresponding increases in individual member loading. Given this situation, it is questionable whether it is appropriate to apply the individual member forces obtained from a detailed, random wave analyses within the context of the existing codes of practice such as the API code. Design tools should recognise that the industry, and the codes of practice commonly applied (API, DNV), incorporate safety factors which are intended for use with a specific set of load and strength definitions and which combine to produce an overall level of safety and reliability. To date, these methods have evolved an accepted approach which is based upon experience 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 the engineer does not consider explicitly during each design; e.g. at present these codes do not consider the 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 are incorporated explicitly, then it appears logical that some fundamental revisions to the existing codes of practice may be necessary. Ultimately, the overall quality and realism of the deterministic and random wave model approaches need to be compared and any appropriate code revisions should incorporate safety factors which produce a consistent level of overall safety and reliability. Such revisions are presently being considered within the context of the API's proposed Load and Resistance Factor Design (LRFD, Reference 19). This is attempting to develop probability based design guidelines for offshore structures and to rationalise the overall safety for fixed platforms including those which respond dynamically. The approach is based upon use of partial safety factors in which the uncertainties in the individual component load and strength elements are quantified. Such an explicit representation allows for a more consistent adjustment of the safety factors in the event of improvements in the understanding, and hence the representation of any single element of the whole design process. On this basis, explicit representation of the random nature of the wave environment and the dynamic response may justify a reduction in the safety factors associated with these individual components. The first draft proposal for the LRFD design code employing the partial factor philosophy 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 levels predicted by the random and deterministic wave force models and the difficulties of generating and interpreting the random wave design event loads for a large structure, a number of simple dynamic analysis procedures have been developed to cope with the design requirements of the first generation of deepwater platforms. These are an attempt to represent the key features of global dynamic response behaviour within the context of established deterministic wave design practice. The link between the random dynamic response and the quasi-static design event forces is achieved by making use of global dynamic amplification factors. These amplification factors are developed using random dynamic analyses which preserve the relative frequency content of the wave environment and the structure's natural modes. In the simplest approach, quasi-static design event wave forces are determined with the use of a conventional deterministic wave force analysis. The resulting cyclic component of the applied loading is then factored by a constant, global dynamic amplification factor which has been determined from an appropriate random wave analysis. The member analysis and design are then performed in a deterministic manner using the existing design codes. This approach has the disadvantage that the applied dynamic loading is assumed to have the same distribution over the height of the structure as the quasi-static wave forces. A refinement to this procedure is the use of a separate inertia force loadset which is intended to represent the distribution of mass inertia forces over the height of the structure in a more consistent manner. A set of mass inertia forces are developed in accordance with the mass distribution and the natural mode shape(s) over the height of the structure. These forces are applied at the main plan levels in proportion to the mass distribution, in order to achieve target dynamic level shear and/or overturning moment values. The resulting mass inertia force distribution is then treated as a normal static extra loadset and combined with the deterministic design wave loads in order to generate global level 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 the individual member forces from a random wave analysis in an absolute sense. Random wave analyses in either the frequency or time domain are used to determine the appropriate global (level shear and moment) dynamic amplification factors. These amplification factors can in principle be generated for any response variable. However, the DAF's are applied within the framework of a deterministic wave analysis, which is limited to designing individual members for the forces which correspond to the peak global forces such as the maximum base shear and overturning moment. As a result it is consistent to limit the random analyses and the prediction of the associated DAF's to those of the global responses only. In this case, it is both technically feasible and economic to use simplified random, time domain analysis tools (e.g. the DYNSCRN program, Reference 20) to simulate global response parameters which 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 were discussed and the available tools introduced. This section contains some case histories which illustrate the practical application of the general methods, procedures and computer programs which have been used within PETRONAS to examine extreme event dynamic analysis and design problems.
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 a number of steel spaceframe structures within the context of the Troll field development. The study was essentially a concept screening exercise in which a large number of different structural concepts were developed and compared on the basis of their in-situ behaviour, and with particular emphasis on fatigue performance. This emphasis reflected the results of a number of earlier, deepwater, fixed platform studies which indicated the potentially controlling influence of cyclic fatigue damage for deepwater 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, frequency domain concept screening tools throughout the study (i.e. the TRUSSFRAME and FREERISE programs References 5, 10). Previous studies had shown these to yield reliable assessments of cyclic fatigue damage due to frame action resulting from global static and dynamic loading. A more limited evaluation of the extreme event loading and response was also carried out as part of the study. The cyclic components of extreme event loading were also estimated making use of the same frequency domain analysis tools. The case history of how this extreme event analysis was performed is an interesting 'how it was done story' which is documented in full detail in section 9 of Reference 6. The key features of the procedure will be repeated here for completeness but the main objective in the present discussion is to highlight the strengths and weaknesses of the approach within the context of the discussion contained in section 2. In order to estimate the total combined loading in the extreme storm condition it is necessary to consider the combined effects of the cyclic loading in the design storm and the effects of mean static loads 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 the TRUSSFRAME 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 the prescribed storm condition, including the influence of steady current. These were established for the three principal wave directions; two orthogonal primary axes and a single worst case diagonal direction which was intended to maximise leg loads. A simplified, distributed vertical member wave force idealisation of the structure was used. This was achieved using the computer program FREERISE (Reference 10) which incorporates a first order statistical linearisation of the drag forces using the approach developed by Borgman (Reference 7).
ii)
The fundamental mode dynamic characteristics of the structure in each of the principal orthogonal directions. This includes the mass distribution of the structure, natural frequencies and mode shapes for the fundamental modes and the corresponding generalised masses in the natural modes considered. This information was generated using simple stick beam model representations of the structure within the FREERISE computer program. For the forced response calculations performed using the mode acceleration method) a percentage of critical modal damping must also be supplied.
iii)
A geometrical description of the structur expressed in terms of a 2-D pin jointed truss frame. The description defines the number of bays and leg members in each truss, the main frame leg and brace 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 of the method are contained in References 4 and 5. The TRUSSFRAME analysis generates axial stress transfer functions due to overall frame action responses for brace and leg members. These can be processed using the appropriate design storm spectra to estimate the short term statistics of response (standard deviation values, etc.) using conventional spectral analysis techniques. The TRUSSFRAME method was originally developed with fatigue analysis in mind and in this respect suffers from a number of limitations when applied for extreme storm conditions, which are as follows: i)
Free surface wave force effects cannot be included directly and must be estimated separately afterwards. This is not a major concern for fatigue analysis but these effects may be significant for the design storm condition.
ii)
At each wave frequency the applied wave force is represented by a point load. This results in the shear force and overturning moment distributions shown in Figure 3.1. The approximation is quite acceptable for the dynamic fatigue problem where the short wave, higher frequency loading in the region of the resonant frequency usually controls. However, it results in load distributions which are inappropriate for the extreme storm condition where the low frequency contributions are important and results in overestimates of the applied loading in the bays of the structure directly below the centre of application of the point load. Furthermore, the point load approximation yields incomplete transfer functions for members in the higher bays. At low frequencies the point of application of the applied force is sufficiently far below the surface to be below the upper bay levels. As a result the truss frame solution cannot be applied to estimate the member load and stress levels above the location at which the point load is applied. Finally, since the applied loading only represents global forces the approximation ignores any additional effects due to direct wave loading on members (see (iv) below). A fuller description of these limitations in the 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 analyses are required for each orthogonal direction. Oblique wave directions, which are usually controlling for outer leg members cannot be handled directly, other than for a symmetric structure having identical normal mode characteristics in each of the two principal planes. This problem is even more acute for a non-symmetric structure having different natural mode characteristics in each of the principal orthogonal planes. It requires separate FREERISE and TRUSSFRAME models for each direction and necessitates external combination and manipulation of the results for the principal orthogonal directions, in order to generate appropriate response transfer functions for the leg and brace members under diagonal loading conditions.
iv)
Member loads are based only on frame action with no influence from local loading effects. Fixed end 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. Brace configuration must be of a simple X-brace type. The equations are also only valid for structures which have supports beneath each of the legs. As such the method is unsuitable for the corner cluster pile type of structure having interior trusses (e.g. for launch) and with no direct reaction points under the interior legs (see Figure 3.1).
The TRUSSFRAME program generates the short term axial stress responses for leg and brace members. Design level most probable maximum stresses were extrapolated assuming the peak force distributions of the Morison force on a single vertical pile as described in section 2.2. This was achieved by making use of the standard deviations of the drag only and inertia only components of loading on the platform (see Reference 15), as predicted from a FREERISE, vertical member wave force model of each structure. The influence of free surface effects was estimated in a crude manner based upon the changes in the wave surface elevation during the passage of the deterministic design wave.
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 using simple point loads. The wind loads were estimated by hand whilst current loads were determined separately 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. Simplified methods and hand calculations were employed to evaluate the submerged weight distributions and the resulting frame action influences on the foundation and the leg and brace axial stress levels. For the Troll structures the influence of these components was found to represent up to 50% of the maximum combined leg stress and up to 30% of the maximum axial brace stress for the design storm condition. Whilst these values reflect the particularly demanding topsides requirements of the Troll field it should be emphasised that these relative contributions are not unusually high for deepwater structures.
3.2.4
Overall assessment
The use of the above procedure for extreme event analysis required use of a large number of simplifying assumptions and the application of a variety of separate analysis programs with transfer or manual manipulation of data between the various steps. A number of structure specific 'fixes' were also applied to the TRUSSFRAME program to enable the basic stress transfer functions to be developed for the asymmetric structures having more than four legs. Whilst all these manipulations were and are possible, and have the advantage of increasing understanding of the basic load and response phenomena, the fragmented nature of the analysis is costly in terms of the inconvenience and the associated time required for implementation. The procedures used are also difficult to work into a general analysis framework which retains the simplicity, and hence the attraction, of the original TRUSSFRAME approach but which also includes the important features of the extreme event dynamic analysis problem. Limitations in the point load applied force distribution assumed in TRUSSFRAME imply that the method cannot be applied over the full height of the structure. For the Troll structures in 340 metres waterdepth, full transfer functions, including the important low frequency branch, were only generated over approximately the bottom 170 metres of the structure, i.e. the lower half in this case. These difficulties need to be considered in the light of the comments made regarding the potential influence of structural dynamics on total steel weight and the requirement to size the entire structure in an acceptable manner, and not just the lower bay members for which the TRUSSFRAME method remains appropriate for extreme storm conditions. On the basis of these experiences it is necessary to conclude that the existing frequency domain tools are not well suited to extreme event design assessments which are to be used for detailed member sizing operations. They are, however, suitable for parametric evaluations which are restricted to examination of the global response characteristics of the structure. Isolated members in the lower bays of the structure can be examined in somewhat more detail and can provide insight into the overall frame action response. The FREERISE and TRUSSFRAME programs both offer the potential to develop the forced response characteristics of lumped parameter stick models. For such applications it is the author's opinion that the FREERISE option is the most attractive of the two. The reasons for this personal preference are that the FREERISE program includes a more accurate definition of the applied loading over the height of the structure and that the forced response is developed within a single model, without the need for a lot of data transfer between separate programs. Wave force excitation transfer functions, including current and the frequency characteristics resulting from the spatial separation of waveloading elements, are combined with the dynamic characteristics within a single model. Level shear and moment distributions are also determined over the full height of the structure. If required these may then be used to estimate individual leg and brace stresses by hand, without the need to run a separate TRUSSFRAME analysis. It should be emphasised that these reservations are geared to the specific requirements of extreme event analysis; the attractiveness and benefits of the application of TRUSSFRAME for fatigue analysis have already been mentioned and are fully documented in References 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 complete structure design. As described in section 2.4 ultimate weapons based upon the use of random directional wave models are also insufficiently mature or lack the design code framework for direct application. In these circumstances it is necessary to resort to the more approximate methods described in section 2.4 which are largely based upon the regular wave deterministic approach but which 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 Cognac and Eureka structures in the Gulf of Mexico (References 2 and 18) and for the forthcoming Bullwinkle platform for 1400 ft waterdepth. The same approach was used in a design study for a deepwater structure in the northern North Sea, performed by Earl & Wright, London, within the context of a Joint Industry Project (Reference 21). The method will be illustrated with reference to a recent application within SIPM for the conceptual design of a slimline structure for 200 m waterdepth (Reference 22). This structure had fundamental mode periods in the range of 4.2 to 4.9 seconds and dynamic response in the extreme storm was expected to be significant.
3.3.2
Pseudo-dynamic design procedures
Global dynamic response effects were determined by performing forced response analyses for the design storm, including current, using a simplified stick model frequency domain analysis. This was done using the FREERISE program which incorporates a distributed vertical member wave force model of the structure, thereby enabling spatial separation effects in the wave force transfer functions to be incorporated. The FREERISE models were used to establish dynamic amplification factors of base 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 position corresponding to maximum base shear as in a conventional design wave analysis. This established the target design level static loading. A set of mass inertia forces were created in order to develop the required dynamic amplification of base shear and overturning moment. This inertia loadset reflects the mass distribution and the natural mode shape(s) over the height of the structure and represents the additional base shear and overturning moment components necessary to achieve the required dynamic amplification of these quantities. These were established by making use of the fundamental bending modes and lumped mass distribution of the structure. The inertia loadsets were developed in proportion to the lumped mass and mode shape distributions over the height of the structure for the end-on and broadside wave directions. The inertia loads were applied as additional static loadsets within an otherwise conventional, deterministic, storm wave structural analysis. For oblique directions the components of the diagonal wave loading were determined in each of the end-on and broadside directions. 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 are described in more detail in Appendix A. Since the inertial loadsets are proportional to the fundamental bending modes of the structure in each of the principal directions, the approach is a reasonable representation of the extreme wave dynamic response. Apart from the basic dependence upon the quasi-static design level forces, the method is based upon two principal assumptions. i)
That the mass inertia forces resulting from dynamic response are in-phase with the applied loading.
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 natural frequencies 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 mass inertia forces associated with the motion of the structure when excited at frequencies lower than those of the fundamental modes. This assumption was also checked within the framework of the Troll spaceframe structure studies as described in section 9.4.2 of Reference 6 and found to be very reasonable. The dynamic response contributions of most fixed offshore platforms are dominated by the fundamental models). In this case the second assumption is also reasonable and will enable local loads to be represented reliably. As the influence of the second mode increases, the above approximation (and hence the individual member forces) becomes more inaccurate due to relative phase differences between the inertia forces in the selected modes, which are not constant over the height of the structure.
3.3.3
Assessment
The method described above incorporates several approximations but also has a number of practical benefits resulting from the fact that it fits within the umbrella of existing static design analysis. The method 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 code checking. 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 have been developed using a frequency domain approach and are based upon the standard deviations of the base shear and overturning moment response levels. The DAF's can also be developed in the time domain (for random wave loading) using either MARIANTO (Reference 16) or the DYNSCRN program as developed by SOC (Reference 20) and now available in KSEPL. The MARIANTO program 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 DYNSCRN program incorporates a distributed, vertical member wave force model (similar to FREERISE) which is defined in terms of a series of lumped volumes and areas which are loaded using the random wave kinematics model. A modal analysis with static response correction is used to perform the time domain dynamic analysis. However, the costly stiffness analysis is avoided by making use of modal response coefficients which are determined from a 'once only' modal analysis of the full structure. The DYNSCRN program has been used by SOC for all recent deepwater designs and has the advantage of an explicit representation of non-linear effects due to drag loading and free surface variations. In Reference 18, Larrabee describes some experience with the package during the analysis of the Eureka structure. It was found that dynamic amplification factors based upon the standard deviations of response obtained from a linear (or linearised) Gaussian model were conservative when compared to 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 the results of random time simulations and should be related to the probabilities of exceedence of peak dynamic and static forces, i.e. DAF =
Dynamic response at probability level p Static response at probability level p
In this definition a maximum dynamic response is not necessarily coupled to a maximum static event in the same response time history. The method proposed, obviously suffers from some of the problems (discussed previously) associated with determining the peak response, particularly at low probability levels, and the need for a significant number of simulations. Given this, and the apparent conservatism in the alternative estimate from the standard deviation values approach, DAF's based upon standard deviations of response appear to offer a suitable basis for estimating global dynamic effects in the short term. However, a more rigorous examination of the probability based definition is required, 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 the total 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 number of general conclusions and to recommend a short term course of action for examining the extreme event dynamic responses of deepwater fixed platforms. These recommendations assume continued use of the presently available dynamic analysis tools and programs: i)
Dynamic response analyses using a regular wave deterministic model are inappropriate, due to the artificial lumping of excitation energy at a single wave frequency and due to the possible introduction of higher order wave force components associated with the selection of a particular wave theory.
ii)
Frequency domain tools, coupled to stick type dynamic models, provide an efficient means to predict the global response characteristics of dynamically sensitive structures. Such tools are a valuable asset during early concept screening exercises, or for carrying out parameter studies. However, existing tools such as FREERISE and TRUSSFRAME do not provide a practical means for design event member sizing operations since they are unable to reflect the influence of significant free surface effects, are unable to incorporate the influence of the other platform loadings such as self weight forces directly, ignore the effects of direct wave loading on members and do not include design code check facilities.
iii)
Time domain simulations in random waves represent the ultimate analysis weapon because of their ability to include an explicit definition of all loading and response non-linearities. These methods are expensive to develop and to use. However, their most significant drawback is a relative lack of experience in both their application and with an appropriate statistical treatment of the design member force time histories. At the present time, these difficulties prevent use of the full 3-D random analysis tool in an absolute sense within the framework of the existing design codes. To avoid these problems random time domain analyses are presently being employed in a relative sense to compare static and dynamic response predictions 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 forces should be represented using an additional static loadset which is developed to meet target dynamic amplification factors for global responses. This procedure is considered appropriate for structures having fundamental mode natural frequencies which are much higher than the peak frequency of the design storm event (say, the ratio of the natural frequencies and the frequency of the peak storm energy should be greater than 2.5 to 3.0). The responses of such structures remain essentially stiffness dominated and the basic assumptions are satisfied. Since the method relies upon a reliable estimate of the global dynamic amplification factors for the design storm this is most correctly achieved using simplified random time domain tools. However, stick model frequency domain tools may provide reasonable estimates which are sufficiently accurate for preliminary design purposes. The pseudo-dynamic method can be employed economically during the preliminary member sizing and concept development phase, by making use of plane frame 2-D models. These include most of the geometrical and the local and global loading characteristics of the full 3-D structure but enable all in-place loadings to be represented and a stiffness analysis to be completed. This facilitates complete member design at much reduced cost.
v)
For in-place design and code checking of structures having a fundamental natural frequency which 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 supported structures may, for example, fall in this category. There is little or no experience with such analyses within PETRONAS but under these conditions it is probably necessary to perform a full 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 linearised frequency domain assessments may provide reliable estimates and may be acceptable if appropriate tools for the former approach are not available. A few additional comments are also appropriate in a more general sense. In designing a deepwater platform it is imperative that the influence of dynamic response is recognised at an early stage in the design development process. The relationship between the frequency content of the applied loading and the natural modes of vibration of the structure are the key elements in defining the dynamic response. In this respect the transfer function of the applied wave loading and the expected range of natural 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 of the fundamental mode natural frequencies. This may be achieved by a careful selection of the geometry of the structural members and appurtenances in and close to the free surface. Optimisation exercises have been shown to have a dramatic influence on the fatigue performance of dynamically sensitive deepwater structures (see Reference 6). The results of such an optimisation are less dramatic for the extreme storm condition, since amplification of the low frequency loading, which is not markedly influenced by spatial separation effects, contributes significantly. However, such an optimisation is still beneficial in reducing the total dynamic loading and hence steel weight of the structure, 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 performed using simplified, first order frequency domain tools. This choice is easily justified given their availability, low cost, and ease of use. Furthermore, the need for detailed design of a deepwater structure has so far not arisen with PETRONAS. Until quite recently, more accurate random time domain or non-linear frequency domain analysis tools simply did not exist, were prohibitively expensive, or insufficiently well developed to enable their widespread application. This situation is changing and any future development work should reflect this. Given the potential impact of non-linear components in the extreme storm condition, it is now accepted that models which reflect these features explicitly are required. A two pronged approach is suggested which should enable some experience with time domain tools to be obtained, whilst development work proceeds with alternative frequency domain options. In the author's opinion a prerequisite for future development work examining the extreme event problem is a random time domain simulation program. The simplified DYNSCRN dynamic analysis program is now under evaluation in KSEPL. This program provides an opportunity to develop some first hand experience with a random time domain simulation program without the need to develop these facilities from scratch first. It is suggested that the random time domain approach should provide the reference baseline for future development work and comparisons, simply because it is the most 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 and to be able to anticipate the usual unwritten difficulties associated with using any new program. In the first instance a comparison with the use and the results of an existing structure seems most appropriate. An extreme event dynamic analysis is planned for a jack-up unit, but this work will be carried out by KSEPL. Given this situation, some in-house analysis seems essential and a comparison study for one of the Troll structures previously examined in the frequency domain would seem an ideal candidate. In order to do this, the program needs to be accessible from within PETRONAS offices and this problem needs to be addressed first and foremost. Comparisons of the global DAF's obtained from the frequency and time domain models will require a substantial effort but will provide some essential 'hands-on' user experience and highlight any practical problems with the programs. Once this experience has been gained, effort could be directed towards the problems associated with predicting the peak force levels from the resulting simulation time histories. A logical first step would be to try to fit an existing peak value distribution (such as Weibull) to the data resulting from one or more simulations and to compare these results with extrapolations made from the frequency 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-term prediction method, i.e. geared to probability of exceedence of structure responses rather than environmental 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 force linearisation are presently neglected in the FREERISE implementation. These may be significant for flexible structures. Eatock Taylor has published several papers (References 10, 11, 12) which describe 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 more detail than has been possible during the production of this document. For the case of constant wave force coefficients the Bendat and Piersol wave loading model, which was developed with funding from EP/23.1 (Reference 23), produces the same wave force spectrum as the higher order Borgman model. The Bendat and Piersol model thus represents a more general wave force formulation, which degenerates to the Borgman model for the constant drag coefficient case. During the final stages of the deepwater platform JIP (Reference 21) the Bendat and Piersol model was coupled to a distributed vertical member wave force representation of the structure to enable wave forces generated using random simulations and deterministic waves to be compared (see Reference 25). If this model were generalised to include the wave loading distribution on an arbitrary multi-member structure and coupled to a dynamic structural analysis program (such as NASTRAN, SESAM80 or a similar capability), 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 be addressed separately, but comparisons with time domain solutions would enable quantification of their 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 in the frequency domain FREERISE program should be investigated. This could be achieved by generalising the existing first order expansion, or coupling the Bendat and Piersol model to the program. Results should then be compared with time domain simulations. If this proves feasible and promising, the next logical step would be to examine the potential for incorporating these wave loading 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 be coupled to an appropriate dynamic analysis capability. A means to incorporate the free surface effects would also be required and ultimately a facility to account for other static load components would also be needed to complete the picture. All these potential developments need to be reviewed within the context of PETRONAS longer term plans for an integrated design and analysis tool which is intended 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 examine the extreme event dynamic response of bottom supported offshore platforms. Most of the material presented is based upon experience gained during the course of a number of conventional fixed platform studies in which we have been involved over the past few years. In this context it obviously represents a subjective assessment which is influenced by the personal experiences which resulted from actually carrying out a number of different analyses and also observing the methods used by other factions of the industry. An attempt has been made to look outside our present experience and to anticipate some of the potential development work which may enable weight and cost savings in any future deepwater fixed platforms. Finally. this note has assembled a collection of some of the most relevant references which should provide a useful bibliography for a general introduction to the problems and as a basis for future development activity in this area.
5.
REFERENCES
1)
I.M. Hines A COMPARISON OF MODAL SUPERPOSITION AND DIREC SOLUTION TECHNIQUES FOR THE DYNAMIC ANALYSIS OF OFFSHORE STRUCTURES SIPM report EP-52648, September 1980.
2)
J.A. Ruhl EXTREME WAVE DYNAMICS OF THE COGNAC PLATFORM Paper 708, Shell Offshore Engineering Conference,February 1978.
3)
J.H. Vugts and R.K. Kinra PROBABILISTIC FATIGUE ANALYSIS OF FIXED OFFSHORE STRUCTURES OTC 2608, 1976.
4)
J.H. Vugts OFFSHORE STRUCTURES ENGINEERING Chapter 7, SIPM report EP-60690, August 1984.
5)
J.W. v.d. Graaf TRUSSFRAME ANALYSIS PROGRAM Users input guide, Version 1, SIPM Internal Note, May 1984.
6)
A COMPARISON OF THE IN-PLACE BEHAVIOUR OF STEEL SPACE FRAME STRUCTURES FOR THE TROLL FIELD (BLOCK 31/2) FOR A/S NORSKE SHELL Volume 2, SIPM EP/23.1, SIPM EF report EP-62400, August 1985.
7)
L.E. Borgman OCEAN WAVE SIMULATION FOR ENGINEERING DESIGN Journal of ASCE 95 (WW4), p. 557-583, 1969.
8)
A.K. Malhotra and J. Penzien NON-DETERMINISTIC ANALYSIS OF OFFSHORE STRUCTURES Journal of ASCE 96 (EM6), 985-1003, 1970.
9)
R.D. Larrabee MEASURED AND PREDICTED COGNAC PLATFORM RESPONS DURING HURRICANE FREDERIC SIPM report EP-55873, June 1982.
10)
J.W. v.d. Graaf FREERISE - FREQUENCY DOMAIN RISER ANALYSIS PROGRAM Users guide, SIPM report EP-57703-2, May 1983.
11)
R. Eatock Taylor and A. Rajagopalan LOAD SPECTRA FOR SLENDER OFFSHORE STRUCTURES IN WAVES AND CURRENT Earthquake engineering and structural dynamics, Vol. 11, p. 831-842, 1983.
12)
R. Eatock Taylor and A. Rajagopalan DYNAMICS OF OFFSHORE STRUCTURES; Part 1 - Perturbation analysis, Journal of sound and vibration, 82(3). p. 401-431, 1982.
13)
A. Rajagopalan and R. Eatock Taylor DYNAMICS OF OFFSHORE STRUCTURES; Part 2 - Stochastic averaging, Journal of sound and vibration, 83(3). p. 417-431, 1982.
14)
M.P. Harper ANALYSIS OF A MULTI-BORE PRODUCTION RISER IN A NORTHERN NORTH SEA ENVIRONMENT SIPM EP report EP-51647, November 1979.
15)
R.B. lnglis and J.G.L. Pijftrs UNIFIED PROBABILISTIC APPROACH TO PREDICTING THE RESPONSE OF OFFSHORE STRUCTURES INCLUDING THE EXTREME RESPONSE SIPM EP report EP-61300, October 1984.
16)
L. ter Haar and P.H.J. Verbeek MARIANTO - MARINE RISER ANALYSIS TOOL KSPEL report RKGR.84.043, April 1984.
17)
L.D. Ruthven (Shell Oil Co.) DYNAL III - A COMPUTER PROGRAM FOR THE DYNAMIC ANALYSIS OF OFFSHORE STRUCTURES Users guide, interim report, SIPM EP report EP-59963, 1984.
18)
R.D. Larrabee EXTREME EVENT WAVE DYNAMICS OF PLATFORM EUREKA (Shell Oil Co.) BRC 28-81, July 1981.
19)
F. Moses DEVELOPMENT OF PRELIMINARY LOAD AND RESISTANCE DESIGN DOCUMENT FOR FIXED OFFSHORE PLATFORMS API 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 RANDOM SEAS, Theory and users manual, BRC 25-80, September 1980.
21)
Earl and Wright, London DEEPWATER FIXED PLATFORM JIP Phase 2 Final report, SIPM EP report EP-62998, May1985.
22)
I.M. Hines, I.J. Bradshaw, A.C.M. v.d. Stap FEASIBILITY STUDY FOR A SLIMLINE LIFT INSTALLED PLATFORM FOR 200 METRE NORTHERN NORTH SEA WATERDEPTH SIPM report EP-86-0088, September 1986.
23
A.G. Bouquet and J.H. Vugts A NON-LINEAR FREQUENCY DOMAIN DESCRIPTION OF WAVE FORCES ON AN ELEMENT OF A VERTICAL PILE IN RANDOM SEAS SIPM report EP-5937, April 1984.
24)
D.K.Y. Kan and C. Petrauskas HYBRID TIME-FREQUENCY DOMAIN PLATFORMS OTC 3965, OIC Conference 1981.
25)
Earl & Wright, London, A.G. Bouquet DEEPWATER FIXED PLATFORM JIP Phase 2, Task 15 Report, May 1985.
FATIGUE
ANALYSIS
FOR
DEEPWATER
LIST OF FIGURES
Figure number
Figure Title
2.1
Comparisons of a single degree of freedom system dynamic response using random 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 of conventional bottom supported fixed structures, under the influence of environmental loading and self weight forces. The basis for the procedure was first developed by Shell Oil Co. during the design of the Cognac platform, see Reference 2. It has been refined somewhat, resulting in the procedure documented here; since then, this procedure has been applied during the detailed design of 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 procedure results 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 the response 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 reliable predictions of the extreme member force statistics and with their application within the framework of existing design codes. Given this background, a simplified approach is desirable as a short term alternative to the implementation of true random wave analysis design tools The simplified approach should incorporate the essential features of the platform dynamic response, but also fit within the framework of existing codes of practice which are presently based upon the use of conventional deterministic wave design procedures. A regular deterministic, quasi-static analysis which is modified to include the effects of mass inertia forces provides such an option and will be outlined in the next section. A.2
Outline of the procedure
The simplified 'pseudo dynamic analysis' described here is essentially a static analysis using a total applied load which matches predetermined global dynamic force levels. Platform design is usually based upon the instant of time corresponding to the maximum global platform loading rather than those of the individual member maxima. On this basis the quasi-static loading from environmental forces is supplemented by additional static loadsets which are developed so as to match predetermined 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 orthogonal direction, using a regular design wave method.
ii)
Establish the influence of dynamic response in terms of the increases in the cyclic components of loading due to mass inertia force amplification effects. The effects of dynamic response should preferably be determined using appropriate random wave dynamic analysis tools in either the time or frequency domain (e.g. references 5, 20). The dynamic components are evaluated in terms of the resulting dynamic amplification factors of cyclic base shear and overturning moment (DAFS, DAFM). The DAF's are determined from the ratios of the short term response statistics, I.e. standard deviations of static and dynamic base shear and overturning moment or on the basis of equal probabilities of occurrence of peak static and dynamic 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 appropriate DAF'S, these can be estimated on the basis of experience with previous structures. At the very 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 a series of lateral point loads acting at each plan level over the height of the structure. The mass inertia loadsets are proportional to the fundamental bending modes of the structure in each 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 overturning moments for mode i, are obtained by summing the contributions from each level as follows: INERTIAL SHEAR
:
Vi =
:
Mi =
Σ
φ ij m j
(A5)
Σ
φ ij h j m j
(A6)
j = 1, n
In mode i
INERTIAL MOMENT
j = 1, n
In mode i Where: j n i mj hj φij vi)
= = = = = =
plan level subscript total number of lumped masses mode number lumped mass at level j height above base to level j mode shape amplitude for mode i at level j
The dynamic components of the base shear and overturning moment are then developed from the sum of the modal contributions. Inertial responses in each mode are proportional to the product of the mass and the mode shapes as shown in Figure A.1. The contributions from each mode are a function of the modal participation factor αi which depend upon the characteristics of the loading and the mode shape. The proportionality (or participation) coefficients αi for each mode are determined by solving the following equations, assuming two modes being relevant.
INERTIAL SHEAR
=
α1
INERTIAL MOMENT
=
α1
See figure A.1.
Σ
J = 1, n
Σ
j = 1, n
φ1j m j + α 2
Σ
j = 1, n
φ1j h j m j + α 2
Σ
φ2j m j
j = 1, n
φ2j h j m j
(A7)
(A8)
v)
Once the proportionality coefficients (α1, α2) are established, the mass inertia force loadsets for each mode and for each principal direction can be obtained by multiplying the mass inertia loadsets developed in step (iii) above by the appropriate modal participation (α) values, see Figure A 1. These can be applied to the structure as static extra loadsets which supplement all the other environmental and self weight loads. The mass inertia loadset is combined with a regular wave deterministic analysis to design the structure in the same manner as for conventional shallow water structures which do not experience dynamic response. The loadsets used to design the structure are shown in Figure A.1. The above procedure must be applied to both principal wave approach directions requiring the development of inertial loadsets for end-on and broadside loadcases using the appropriate mode shapes and mass distributions, and participation. For oblique wave directions some further approximations are necessary. Firstly total dynamic and static force components must be determined in the direction of the wave approach angle in order to establish the dynamic force contribution or the required dynamic amplification factor for the oblique direction. The components of the total quasi-static applied loading in each of the principal directions must also be established. This information can then be used to estimate the appropriate mass inertia loadsets for each principal direction. A simultaneous linear combination of the inertia loadsets in both principal directions is used in order to achieve the target dynamic amplification for the diagonal direction. The above relationships match the required base shear and overturning moment using two proportionality constants α1, α2, and two modes. Level shears and moments at any two other locations tan also be matched in a similar manner. If the dynamic response components are to be matched at more than two levels (say n) then n modes and n proportionality constants must 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
