• Share
  • Email
  • Embed
  • Like
  • Save
  • Private Content
Download
 

Download

on

  • 1,179 views

 

Statistics

Views

Total Views
1,179
Views on SlideShare
1,179
Embed Views
0

Actions

Likes
0
Downloads
58
Comments
0

0 Embeds 0

No embeds

Accessibility

Categories

Upload Details

Uploaded via as Adobe PDF

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

    Download Download Document Transcript

    • Guidelines for Offshore Structural Reliability Page No. 1-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072 LIST OF CONTENTSSection Title Page1.0 INTRODUCTION 31.1 Objective 31.2 Jack-ups in General 31.3 Modes of Operation 31.4 Important Structural Design Parameters 41.5 Arrangement of Report 62.0 RESPONSE 72.1 General 72.2 Jack-up Response in the Floating Mode 72.3 Jack-up Response in the Elevated Mode of Operation 102.3.1 Time Domain Analysis 112.3.2 Methods of Evaluating Response 122.3.3 Static Load Components 142.3.4 Sea Loadings 142.3.5 Wind Loadings 152.3.6 Foundations 163.0 UNCERTAINTY MODELLING 193.1 General 193.2 Loading Uncertainty Modelling 193.2.1 Aleatory Uncertainty 193.2.2 Epistemic Uncertainty 203.3 Response Uncertainty Modelling 213.3.1 Analysis Uncertainty 213.3.2 Damping 213.3.3 Foundation 223.4 Resistance Uncertainty Modelling 244.0 LIMIT STATES 254.1 General 254.1.1 Limit States Appropriate to Jack-up Structures 254.2 The Ultimate Limit State 274.2.1 Leg Strength 274.2.2 Foundation Bearing Failure 304.2.3 Holding System 304.2.4 Global Deflections 324.2.5 Global Leg Buckling 324.2.6 Overturning Stability 324.3 Literature Study 335.0 SUMMARY OF APPLICATION EXAMPLES 345.1 General 345.2 Overview of Analytical Procedure 345.3 Structural Reliability Example 365.4 Foundation Reliability Example 38
    • Guidelines for Offshore Structural Reliability Page No. 2-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072Section Title Page6.0 RECOMMENDATIONS FOR FURTHER WORK 416.1 General 416.2 Elevated Condition 416.3 Floating / Installation Phase Conditions 427.0 REFERENCES 44
    • Guidelines for Offshore Structural Reliability Page No. 3-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-00721.0 INTRODUCTION1.1 ObjectiveThe objective of this report is to document offshore structural reliability guidelinesappropriate to self-elevating unit structures (hereafter referred to as ‘jack-ups’). With thisintention the following items are addressed ;- characteristic responses- modes of failure and related reliability analysis characteristics and parameters- typical examples of reliability analysis.The guidelines are intended for application of Level III structural reliability where the jointprobability distribution of uncertain parameters is used to compute a probability of failure.1.2 Jack-ups in GeneralThe term ‘Jack-up’ covers a large variety of offshore structures from small liftboat structures,Stewart (1991), to large deepwater designs, e.g. Bærheim (1993). The purpose of the jack-updesign is to provide a mobile, self-installing, stable working platform at an offshore (or off-land) location. The jack-up platform itself may be designed to serve any function such as, forexample ; tender assist, accommodation, drilling or production.Thus, the term jack-up may represent a structure that has a mass of a few hundred tonnes andis capable of elevating not more than a few metres above the still water surface, to a structurethat has a mass of over 20,000 tonnes and is capable of operating in water depths in excess of100 metres.· It is evident, for the above stated reasons, that statistics representing jack-up structures should be treated with a good deal of suspicion as they may not be representative for the type of structure required to be considered.· These guidelines are intended to deal primarily with conventional design, larger size jack-ups, namely those intended to operate in waterdepths in excess of, say, 50 metres. A typical arrangement of such a unit is shown in Figure 1.1 below, Bærheim (1993).1.3 Modes of OperationA jack-up generally arrives on location in the self-floating mode. The transportation of thejack-up to the site may, however, have been undertaken as a wet, or dry (piggy-back) tow, or,may have been undertaken by the use of self-propulsion. Once on location installation willtake place, which will typically involve elevating the hull structure to a predetermined heightabove the water surface, preloading, and then elevating to an operational height.Characteristically the jack-up will then remain on location for a period of 2-4 months, beforejacking down, raising the legs to the transit mode condition, and transferring to the nextlocation.· This short-term contracting of jack-up units has historically resulted in that, within its life cycle, the jack-up rarely operates to its maximum design environmental criteria.· There is a current tendency to design jack-up units for extended period operation at specific sites, Bærheim (1993), Scot Kobus (1989), e.g. as work-over or production units.
    • Guidelines for Offshore Structural Reliability Page No. 4-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072 Such units may been designed to operate in extreme environmental conditions, at relatively large waterdepths for a period in excess of 20 years.Figure 1.1 : Arrangement of a Typical Harsh Environment Jack-up1.4 Important Structural Design ParametersJack-up designs varying from being monotower structures (single leg designs) to multiple legdesigns, e.g. up to six legs, although units with sixteen legs are not unknown, Boswell(1986). The supporting leg structures may be a framework design, or, may be plate profiledesign.· The conventional jack-up design has three vertical legs, each leg normally being constructed of a triangular or square framework.Jack-up basic design involves numerous choices and variables. Typically the most importantvariables may be listed as stated below.Support FootingThe legs of a jack-up are connected to structure necessary to transfer the loadings from theleg to the seafloor. This structure normally has the intended purpose to provide vertical
    • Guidelines for Offshore Structural Reliability Page No. 5-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072support and moment restraint at the base of the legs. The structural arrangement of suchfooting may take the following listed forms;-gravity based (steel or concrete),-piled-continuous foundation support, e.g. mat foundations-individual leg footings, e.g. spudcans (with or without skirts).LegsThe legs of a jack-up unit are normally vertical, however, slant leg designs also exist. Designvariables for jack-up legs may involve the following listed considerations ;-number of legs-global orientation and positioning of the legs-frame structure or plate structure-cross section shape and properties-number of chords per leg-configuration of bracings-cross-sectional shape of chords-unopposed, or opposed pinion racks-type of nodes (e.g. welded or non-welded (e.g. forged) nodes)-choice of grade of material, i.e. utilisation of extra high strength steelMethod of transferring loading from (and to) the deckbox to the legsThe method of transferring the loadings from (and to) the deckbox to the legs is critical todesign of the jack-up. Typical design are ;-utilisation and design of guides (e.g. with respect to ; number, positioning, flexibility, supporting length and plane(s), gaps, etc.)-utilisation of braking system in gearing units-support of braking units (e.g. fixed or floating systems)-utilisation of chocking systems-utilisation of holding and jacking pins and the support afforded by such.DeckboxThe deckbox is normally designed from stiffened panel elements. The shape of the deckstructure may vary considerably from being triangular in basic format to rectangular and evenoctagonal. The corners of the deckbox may be square or they may be rounded. Units intendedfor drilling are normally provided with a cantilever at the aft end of the deckbox, however,even this solution is not without exception and units with drilling derricks positioned in themiddle of the deckbox structure are not unknown.There are a large number of solutions available to the designer of a jack-up unit and, althoughseries units have been built, there exist today an extremely large number of unique jack-updesigns.
    • Guidelines for Offshore Structural Reliability Page No. 6-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-00721.5 Arrangement of ReportResponse of jack-up structures is described in Section 2, together with relevant methods forcomputation of the resulting load effects. Model uncertainties associated with thecomputation of these load effects are discussed in Section 3. Important limit states togetherwith stochastic modelling of failure modes are described in Section 4. Section 5 provides asummary of two example reliability analyses undertaken for the ultimate limit state, DNV(1996b). Recommendations for further work are given in Section 6.Note :This report should be read in conjunction with the following listed documentation ;- “Guideline for Offshore Structural Reliability Analysis -General”, DNV Technical Report no.95-2018, DNV (1996a)- “Guideline for Offshore Structural Reliability Analysis- Examples for Jack-ups”, DNV Technical Report no.95-0072, DNV (1996b)Companion application guidelines are also documented covering for jacket and TLPstructures.
    • Guidelines for Offshore Structural Reliability Page No. 7-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-00722.0 RESPONSE2.1 GeneralJack-up units are normally designed to function in several different operational modes. Thesemodes may be characterised as follows ;-transit-installation-retrieval-operational (including survival) condition.Response of a jack-up in the floating mode of operation is, obviously, far different from thatof the jack-up in the as-installed, elevated condition. Both of these modes are critical to thesafe operation of a jack-up unit as each mode of operation may impose its own limitingdesign criteria on certain parts of the structure.To provide relevant guidance with respect to the stochastic properties and probabilisticanalytical procedures for both of these modes of operation, is considered to be too large anundertaking to be handled by this example guidance note.· This section is therefore mainly concerned with jack-ups in the elevated mode of operation whilst it deals only in general terms with jack-ups in the floating mode. 2.2 Jack-up Response in the Floating ModeA jack-up unit may transfer from one location to another by a number of methods. For ‘field’moves a jack-up would, normally, transfer in the self-floating mode utilising either its ownpropulsion system, or, be ‘wet’ towed to the new location. For ‘ocean’ tows, on the otherhand, it is common practice to transfer by means of a dry-tow.Three major sources of accident have been identified in respect to a jack-up in the transitcondition, Standing and Rowe (1993), namely those due to;-1- Wave damage to the unit structure leading to penetration of watertight boundaries.-2- Damage to the structure as a result of shifting cargo (usually caused by direct wave impact, excessive motions and/or inadequate seafastenings).-3- Structural damage in the vicinity of the leg support structures.In the jack-up installation phase there are normally two main areas of concern, these being ;-1- Impact loadings upon contact with the seabed.-2- Foundation failure (i.e. punch-through) during preloading.Impact loadings occur when the jack-up unit is operating in the floating mode, whilstfoundation failure is a condition occurring when the jack-up is normally elevated above thestill water surface.The retrieval phase of a jack-up has not traditionally been considered as providingdimensioning load conditions. However, when a leg is held fast at the seabed, e.g. due tolarge penetrations, there may be large loadings imposed upon the jack-up structure. Suchloadings may result from the action of waves, current, wind, deballasting and jacking uploadings.Few model tests, or full-scale measurements, have been undertaken for jack-ups in thefloating mode. Indeed, recent record searches and enquiries with model basins to establish
    • Guidelines for Offshore Structural Reliability Page No. 8-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072relevant model test data, Standing and Rowe (1993), have only been able to identify sixrelevant model tests in total, with published papers on only two of these cases, Fernandes(1985, 1986). These experiments include free decay tests to provide estimates of dampingand natural periods, measurements in heave, roll and pitch motions in regular and irregularwaves at zero speed, and measurements of resistance, heave, roll and pitch in regular andirregular waves at 6 knots tow speed. A number of the tests were repeated with the legs raisedor lowered various distances. Some full scale results were also published.Comparisons with linear wave theory, based upon potential flow assumptions, predict rolland pitch responses in regular wave sea states very well at frequencies away from resonance,but may tend to overpredict the responses at the natural period (dependent upon dampingassumptions). The results from the published jack-up model test data seem to be consistentwith findings from ships and barges, i.e. that roll response at resonance is overestimatedunless due account is taken of the increased damping resulting from viscous effects.Generally, levels of measured and predicted heave motions in regular waves agreedreasonably well although there may be marked differences in the shapes of the curves.Measurements in regular waves at 6 knots showed a considerable increase in the pitchdamping, compared with similar results at zero speed, with reduced response at the naturalperiod. Heave response was similar to that at zero speed.· Conventional wave diffraction theory will, in general, predict motion responses of a jack- up unit with a reasonable degree of accuracy. If non-linear loading effects e.g. water on deck (‘green seas’), slamming, damping (especially at and around resonance periods), non-zero transit speed etc. are significant, then it is necessary to utilise time-domain simulation and/or model test data.· The use of strip theory or Morison formulation to compute the total sea loadings on a jack-up in transit will normally be inappropriate.· In connection with the prediction of motion responses, notwithstanding account taken of relevant non-linear loading effects, it seems reasonable to refer to ship or barge related reliability data (e.g. Frieze (1991), Lotsberg (1991), Wang and Moan (1993)).· When evaluating leg strength at critical connections, transfer functions for element forces and moments (or stresses) may be calculated directly from the rig’s motions analysis. A model similar to that shown in Figure 2.1 may, typically, be utilised for such purpose.· Generally, the following loads will be necessary to consider in respect to any ultimate strength analysis of a jack-up in the transit condition ; -static load components -inertia load components (as a result of motion) -wind load components.· If any significant structural non-linearities are present in the system then such non- linearities should be accounted for in the model. One such non-linearity that may be significant is the modelling of any gaps between jackhouse guides and chords.· Reliability analysis of seafastening arrangements is documented, DNV (1992). The generalities of this documented example and the procedure utilised may also be applied to seafastenings for a jack-up unit under transit. If direct wave impact on the item held by the seafastening is a possible designing load, then such loading and associated load uncertainty should additionally be included within the analysis.
    • Guidelines for Offshore Structural Reliability Page No. 9-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072Figure 2.1 : Typical Hydrodynamic/Structural Model of a Jack-up in the Transit Condition.
    • Guidelines for Offshore Structural Reliability Page No. 10-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-00722.3 Jack-up Response in the Elevated Mode of OperationResponse of jack-up structures in the elevated condition has previously been extensivelystudied, Ahilan (1993), with relevant analytical methodology being described in detail in theJack-up Recommended Practice, SNAME (1993).The response of jack-up structures, when subjected to random sea excitation, is found to benon-Guassian in nature. Due to the non-linearities in the structural system the extremeresponses are generally found to be larger than the extremes of a corresponding Gaussianprocess, Karunakaran (1993).Relevant, non-linear effects that may be significant in respect to response of jack-upstructures are given as ;- non-linear loading components (e.g. drag force loadings)- bottom restraint (non-linear foundation characteristics)- damping (e.g. due to the motions of the jack-up structure, there may be significant hydrodynamic damping as a result of the relative velocity of the water particles and the leg member)- dynamics of the structure (as the natural period of the structure is typically relatively high, e.g. 5-8 seconds, there may be significant wave energy available to excite the structural system and hence relatively large inertial forces may result)- second order effects (such effects may significantly influence the response in the considered structure)- non-linearites of structural interfaces (e.g. gaps between the leg structure and guides)· For reliability analysis, in order to account for the non-linearities in jack-up loading and response, it is considered necessary that explicit time domain analysis, utilising stochastic sea simulation, is undertaken.· Foundation modelling assumptions have been shown to be an important aspect in respect to the resulting response from analytical models of jack-up units, Manuel et al. (1993). Hence, unless it can be demonstrated that the effects are not significant, non-linear characteristics in the foundation system should be explicitly modelled when undertaking analyses in connection with reliability studies.· Guidance provided in the guideline example for jacket structures, DNV (1996c), in respect to the fatigue limit state covers the state-of-the-art knowledge with respect to fatigue reliability analysis. Response in respect to the fatigue limit state is therefore not explicitly covered in this section. Due to the non-linear characteristics of jack-up loading and response, frequency domain solution techniques are however not recommended unless, either it can be demonstrated that such effects are insignificant, or, due account has been taken of such effects.
    • Guidelines for Offshore Structural Reliability Page No. 11-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-00722.3.1 Time Domain AnalysisTwo general methods may be utilised in time domain analysis. These two methods being ; -use of simple, single degree of freedom (SDOF) models, and, -use of multi-degree of freedom models.In both cases however the following general guidance may be given for the analysis, SNAME(1993) ;1. The generated random sea should consist of superposition of, at least, 200 regular wave components utilising divisions of equal energy of the wave spectrum.2. In order to obtain sufficiently stable response statistics, simulation time for a single simulation should generally not be less than 60 minutes.3. The integration time step should not normally be taken greater than the smaller of the following ; - one twentieth of the zero up-crossing period of the wave spectrum - one twentieth of the jack-up natural period.4. When evaluating the response of the jack-up, the transient effects at the start of the analysis should be removed. At least the smallest of 100 seconds, or 200 time steps should be removed in this connection.5. The method of evaluating the response (e.g. the Most Probable Maximum (MPM) response) should be compatible with the simulation time and sea qualification procedure adopted for the analysis. -Further guidance in connection with this item is provided in the Commentaries to the Jack-up Recommended Practice, SNAME (1993).The asymmetry of crest heights and troughs, accounted for by higher order wave theories, isnot reproduced in methods based upon random wave simulation techniques. Linear wavetheory, Sarpkaya (1981), utilised in random wave simulation, accounts for particle kinematicsupto the still water surface and ‘kinematic stretching’ is undertaken to compute thekinematics to the instantaneous free surface. It is recommended, Gudmestad and Karunakaran(1994), that Wheeler stretching, Wheeler (1969), is utilised in this connection.The extent of wave asymmetry is a function of waterdepth. For waterdepths less than 25metres, in extreme environmental conditions, irregular wave simulation is normallyconsidered to be inappropriate and regular wave analysis should be considered. Forwaterdepths greater than 25 meters wave asymmetry may be accounted for by the formulationgiven in equation 2.1 below, SNAME (1993). Hs = ( 1 + 0.5 e (-d/25) ) Hsrp (2.1)Where :Hs : adjusted significant wave height to account for wave kinematics (metres)Hsrp : significant wave height (metres)d : waterdepth (metres)
    • Guidelines for Offshore Structural Reliability Page No. 12-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072As time domain analyses are usually fairly resource demanding procedures, it is normalpractice to utilise simplified structural modelling techniques (see Figure 2.2)· A full description of the methodology and procedure utilised in creating both a simplified hydrodynamic and simplified structural model for a jack-up is included in DNV( Feb 1992) and SNAME (1993).Figure 2.2 : Typical Simplified Model of a Jack-up Structure.2.3.2 Methods of Evaluating Response· Reliability analysis of jack-up structures will generally be undertaken based upon the following considerations ; -1- Site specific environmental and foundational data should be utilised. -2- Directional and seasonal data may be utilised. In order to reduce the amount of analytical work involved, wind, wave and current load components may however normally be assumed to be coincident. -3- The selected (governing) environmental load direction may be initially identified by evaluation of relevant deterministic, ‘quasi-static’ response analyses of the jack- up structure under consideration. The standard procedure of treating wind, waves, currents and seawater level separately and combining the independent extremes as if these extremes occur simultaneously, is conservative. In most cases however, jack- up environmental loading is wave dominated and the assumption of simultaneity of the extremes of the environmental parameters is found to be satisfactory.
    • Guidelines for Offshore Structural Reliability Page No. 13-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072The probability of failure is estimated during a reference period significantly longer than theanalysed, simulated time period. An extrapolation procedure for determining the extremevalues for the reliability analysis is therefore required when several environmental variablesare to be combined.· The reference period for extreme environmental data is normally selected as being equal to the one year return period such that the results may be directly compared with annual target reliabilities.· For jack-ups, the two most appropriate procedures for estimation of extreme load events would seem to be ; -1- By use of long term statistics of independent sea states -2- By use of conditional extreme event analysis.These procedures are described in detail in Chapter 6 to the guidelines, DNV (1996a). Forconventional jack-up structures, in general, the long term response is controlled by theextreme sea states and, as such, both of these procedures are normally acceptable. Anexample of the estimation of extreme load events by use of long term statistics ofindependent sea states is provided in the jack-up examples guidelines DNV (1996b).Karunakaran (1993) documents that the short term extreme storm response is marginallyhigher than the long term response if the long term response is controlled by extreme seastates. If however the long term response is controlled by resonance sea states, the short termextreme storm response is about 10% lower than the long term response for those casestudies considered.Response from time history simulations may be characterised by the normalised statisticalmoments ; mx, sx, sx’, g3, g4, which are the mean, standard deviation, standard deviation of thetime derivative, skewness and kurtosis of the response respectively. A limit state may then bedefined from the statistical moments of the response and the estimated reliability thusobtained by the resulting response surface, DNV (1996b).· Response surface techniques are considered to provide the most appropriate methodology in the estimation of the reliability of jack-up structures for extreme load events.In order to model how the statistical moments change with realisations of the basic variables,the derivatives of these moments may be estimated by finite differences of the variables atone estimation point. As the limit state functions are highly non-linear this technique willonly give satisfactory results if a good fit is obtained around the design point.Generally, reliability analyses of jack-up structures may be undertaken by use of first andsecond order solution methods (FORM/SORM), Madsen (1986). -See also DNV (1996a),Chapters 2 and 3, for further guidance concerning utilisation of reliability methods.
    • Guidelines for Offshore Structural Reliability Page No. 14-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-00722.3.3 Static Loading ComponentsPrevious jack-up reliability analyses, Karunakaran (1993), Løseth et al. (1990), haveidentified that response uncertainty is not significantly affected by the choice of the staticmass model. This is further demonstrated in the example documented in DNV (1996b).· Permanent loads and variable loads are generally lumped together. For structural assessment the upper bound of this sum is normally conservatively modelled. For overturning assessment the mean variable load is combined with the permanent load.2.3.4 Sea LoadingsSea loadings on conventional jack-up structures are calculated utilising Morison’s equation,Sarpkaya (1981) ; pD 2 1 Fn ( r , t ) = r Cma n ( r , t ) + rDCd v n ( r , t ) v n ( r , t ) (2.2) 4 2Wave and current velocity components in the Morison equation are obtained by combiningthe vectorial sum of the wave particle velocity and the current velocity normal to the memberaxis. (When relative motions are involved, eqn 2.2 may be modified to reflect such motionsin the terms an(r,t) and vn(r,t)).Epistemic uncertainties related to Morison’s equation are documented in Section 3.Wave LoadingsThe basic stochastic sea description is defined by use of a wave energy spectrum. The choiceof the analytical wave spectrum and associated spectral parameters should reflect the widthand shape of the spectra and significant wave height for the site being considered. Generally,either the Pierson-Moskowitz or the Jonswap spectra will be appropriate. See DNV (1996a),Section 5.· Due to the possibility of inducing greater dynamic response at lower wave periods than that necessarily associated with storm maximum significant wave height, a range of periods and associated significant wave heights should normally be investigated.· The simulated storm length is normally to be taken as 3 hours, SNAME (1993) or 6 hours, NPD (1992).
    • Guidelines for Offshore Structural Reliability Page No. 15-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072For the extreme load event it is normally, conservatively assumed that a long crested seasimulation is undertaken, NPD (1992), however, in accordance with SNAME (1993) thefollowing directionality function F(a) may be utilised ; F(a) = C. cos2na for -p/2 £ a £ p/2 (2.3)where ;n : 2.0 for fatigue analysis 4.0 for extreme analysis p /2C : constant chosen such that : å -p / 2 F (a )da = 10 .Current Loadings· Current velocity should include all relevant components, DNV (1996). Normally, however, it is acceptable to divide the total current into two components, namely, that of wind and wave generated current, V(w,w) and that of residual (e.g. tidal) current, Vr. The first of these two current components may be assumed to be fully correlated with the significant wave height, whilst the latter current component, Vr, is assumed to be completely independent of the other environmental characteristics. See DNV (1996a), Section 5.1.3.2, for a full description of this procedure.Unless site specific data indicate otherwise the current profile should be described accordingto the procedure documented in SNAME (1993).2.3.5 Wind LoadingsSingh (1989) has found a number of inconsistencies in existing wind loading calculationprocedures. Based upon this finding it has been concluded that wind tunnel measurementsappear to provide the only viable method for accurately estimating loads on complex offshorestructures.· For jack-up structures, if it is not possible to utilise model test data, either by direct testing, or from scaling of geosim models, then, assuming that wave loading is the dominating load effect, it is normally acceptable to base such loading on simplified, direct calculation methods.SNAME (1993) documents an acceptable procedure for the calculation of wind loadings,where the wind loading, Fwi , is calculated as a static load contribution by use of the equation; Fwi = ½ r Vref² Ch Cs Aw (2.4)wherer : density of airVref : the 1 minute sustained wind velocity at 10 meters above sea levelCh : height coefficientCs : shape coefficientAw : projected area of the block consideredIn locations where wind loading may be the dominating load effect (e.g. due to cyclones etc.)this load effect should be specially considered.
    • Guidelines for Offshore Structural Reliability Page No. 16-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-00722.3.6 FoundationsThe uncertainty in jack-up response is greatly influenced by the uncertainties in the soilcharacteristics that determine the resistance of the foundation to the forces imposed by thejack-up structure. Ronold (1990) showed that, for a jack-up, the total uncertainty governingthe safety against foundation failure is dominated by the uncertainty in the loading. Nadim etal. (1994), on the other hand, showed that the response of a jack-up structure subjected to acombination of static and cyclic loads is just as much influenced by the uncertainties in theloads as by the uncertainties in the soil resistance. The significant discrepancy between theseresults is due to the different assumptions made with respect to the uncertainties in thevariables. One should therefore be careful in generalising the results obtained for a specificsite to other environmental and soil conditions.For traditional jack-up foundation solutions, the stability and performance of a jack-upfoundation is primarily determined by the installation procedure for the unit. This operationinvolves elevating the hull and pumping water ballast into the preload tanks, causing thespudcans to penetrate into soil and thereby increasing their bearing capacity.· The geotechnical areas of concern for jack-up foundations are: -Prediction of footing penetration during preloading. -Jack-up foundation capacity under various load combinations after preloading. -Foundation stiffness characteristics under the design storm.The recent trend in using jack-up structures in deeper waters and on a more permanent basishas resulted in another type of foundation solution, namely spud-cans equipped with skirts.The installation of skirted footings is normally achieved by suction, not preloading. Theskirted footings not only provide more predictable capacity, they also increase the footingfixity significantly. The procedure for estimating the capacity of the individual footings isbased upon analytical procedures similar to that undertaken for foundation of gravity basedstructures. For jack-up foundation systems, however, it is important to look at the completefoundation ‘system’ because at loads close to failure, significant re-distribution of reactionsamong the footings may take place. (Refer to the foundation example in DNV (1996c) formore information in respect to this item.)It is evident from statistics, Sharples et al. (1989), Arnesen et al. (1988), that punch-throughduring preloading is the most frequently encountered foundation problem for jack-ups.Punch-through occurs when a weak soil layer is encountered beneath a strong surficial soillayer.· The only way to avoid punch-through is to undertake a thorough site investigation at the jack-up location prior to installation in order to identify the potentially problematic weak soil layers.The total amount of preload used in the installation is often used as a checking parameter forthe spudcan capacity to withstand extreme loads. The so-called “100% preload check”requires that the foundation reaction during preloading on any leg should be equal to, orgreater than, the maximum vertical reaction arising from gravity loads and 100% ofenvironmental loads. The preload defines the static foundation capacity under pure verticalloading immediately after installation. Under the design storm the footing is subjected tosimultaneous action of vertical and horizontal loads, and overturning moment. The storminduced loads are cyclic with a short duration and the supporting soil may have a higherreference static shear strength than right after installation due to consolidation under the jack-
    • Guidelines for Offshore Structural Reliability Page No. 17-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072up weight. On the other hand, for equal degrees of consolidation, the vertical capacity of afooting will be greater during pure vertical loading than during a combination of vertical,horizontal and moment loadings.Having regard to the oversimplification of the l00% preload check, SNAME (1993) suggestsa phased method with three steps, increasing in the order of complexity, for the evaluation offoundation capacity, as follows :Step 1. Preload CheckThe foundation capacity check is based on the preloading capability - assuming pinnedfootings.Step 2. Bearing Capacity CheckBearing capacity check based on resultant loading on the footing under the design storm.Step 3. Displacement CheckThe displacement check requires the calculation of displacements associated with anoverload situation arising from Step 2.Any higher level check need only be performed if the lower level checks fail to meet thefoundation acceptance criteria.It is difficult to quantify the uncertainties associated with the “preload check” approach.Nadim and Lacasse (1992) developed a procedure for reliability analysis of the foundationbearing capacity of jack-ups. The procedure, which may be categorised as a Step 2 approach,is based on a prior calculation of the bearing capacity under different load combinations(interaction diagram) and updating the interaction diagram from the measured verticalpreload. The bearing capacity calculations are performed probabilistically using the FORMapproximation. The procedure developed by Nadim and Lacasse (1992) was used by Nadimet al. (1994) to study the reliability of a jack-up at a dense sand site in the North Sea.An important result of the FORM analyses is the correlation between the foundation capacityunder a given combination of horizontal and vertical loads (and overturning moment ifspudcan fixity is significant) and the foundation capacity under pure vertical loading. Thedegree of correlation determines the significance of the measured preload on reducing theuncertainty associated with foundation capacity for a given load combination.· For a given loading combination (vertical, horizontal and moment), the lognormal distribution function appears to provide a good fit to the foundation capacity, Nadim and Lacasse (1992).· The properties of the volume of soil under the footing fluctuate spatially and can be represented by a random field. The effects of this are accounted for by spatial averaging, Vanmarcke (1977, 1984), and by using stochastic interpolation techniques, Matheron (1963), if enough data exist.· Otherwise, the uncertainties in the soil parameters are based on the statistics of the available data. Mean and standard deviation are calculated by ordinary statistical methods, e.g. Ang and Tang (1975). Usually the probability distribution function used to represent geological processes follows a normal or lognormal law. More often than not however, and especially in the case of jack-up structures, there are not enough data
    • Guidelines for Offshore Structural Reliability Page No. 18-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072 available, and the designer needs to use correlations or normalised properties as a function of the type of soil to establish consistent soil profiles.See also DNV (1996a), Section 7.3.As an example the undrained shear strength of soft sedimentary clay normalised to the in-situoverburden stress is about 0.23 ± 0.03 for a horizontal failure mode; the friction angle of sandcan be selected on the basis of its relative density and an in-situ penetration test.
    • Guidelines for Offshore Structural Reliability Page No. 19-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-00723.0 UNCERTAINTY MODELLING3.1 GeneralThis section provides general guidance in respect to uncertainty modelling as appropriate tothe extreme load event for a jack-up structure.3.2 LoadingUncertaintyModellingUncertainty in the load process may be attributed to either aleatory uncertainty (inherentvariability and natural randomness of a quantity) or epistemic uncertainty (uncertainty owingto limited knowledge). In respect to jack-up reliability analysis, guidance appropriate to themost significant of the uncertain variables associated with the load process is given below.3.2.1 Aleatory UncertaintyTables 3.1 to 3.3 below document a summary of recommended distributions for selectedstochastic variables. It should be noted however that site specific evaluation of environmentalvariables may dictate use of variable distributions other than those recommended in the tablesbelow. For further guidance see also DNV (1996a), Chapter 5.Description DistributionRandomness of storm extremes PoissonWaterdepth (D) Uniform (tidal effects), or, Normal (storm surge effects - conditional on Hs)Marine Growth LognormalTable 3.1 : General Environmental Variable DistributionsDescription DistributionSignificant wave height (Hs) 3-parameter Weibull/LognormalZero up-crossing period (Tz) Lognormal (conditional on Hs)Spectral peak period (Tp) Lognormal (conditional on Hs)Joint distribution (Hs,Tz) or (Hs,Tp) 3-parameter Weibull for Hs and Lognormal for Tz or Tp (conditional on Hs)Tidal current speed (Vt) UniformWind generated current speed (Vw) Normal (conditional on U10m)Average wind speed (U10m) Weibull (conditional on Hs)Table 3.2 : Long Term Analysis Variable Distributions
    • Guidelines for Offshore Structural Reliability Page No. 20-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072Description DistributionSignificant wave height (Hs) Gumbel *1, 2Total current speed (Vc) Gumbel *1, 2Average wind speed (U10m) Gumbel *1, 2Table 3.3 : Extreme Analysis Variable DistributionsKEY :*1 : Normally it is sufficient to consider the extreme dominating variable being either ; -the significant wave height, -the current, or, -the wind speed, in combination with this extreme distribution the remaining two variables are assigned the distribution according to Table 3.2.*2 : Instead of a Gumbel distribution, a Weibull distribution (see the long term analysis variables in table 3.2), raised to the power of the number of considered seastates in one year, NSea, may be utilised in practice. (See DNV (1996a), Section 6.7.)3.2.2 Epistemic Uncertainty· The following listed time independent, basic load variables have been identified as being possible significant contributors to the overall reliability of a jack-up structures, Løseth (1990), Karunakaran (1993), Dalane (1993) ; -Drag coefficient -Inertia coefficient -Marine growth -Mass of structure.Guidance to selection of distribution type and distribution parameters for random modeluncertainty factors associated with these basic load variables is given in Table 3.4 below.Basic Variable Name Distribution m1 C.o.V.Drag coefficient 2 (CD) Lognormal 1.0 0.2 3Inertia coefficient (CI) Lognormal 1.0 0.1Marine growth 4 Lognormal 1.0 0.2Mass of structure 5 Lognormal 1.0 0.14Table 3.4 : Load Model Uncertainty VariablesKEY :1: The absolute value of the distribution variables are given relative to the value applied in the structural analysis.2: The selection of appropriate drag coefficients for the structural analysis are stated in SNAME (1993).3: For extreme value jack-up analysis, without loss of any generality, it is normally considered acceptable to select the inertia coefficient as a fixed quantitiy. An inertia coefficient of 1.8 may be utilised.4: The selection of the appropriate value for the marine growth should be evaluated based upon a site specific evaluation, e.g. NPD (1992).5: See also section 2.3.3
    • Guidelines for Offshore Structural Reliability Page No. 21-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-00723.3 Response Uncertainty Modelling· Significant contributions to response model uncertainty may be attributed to the following causes, Nadim (1994), Løseth (1990), Karunakaran (1993); -Analytical uncertainty -Damping ratio -Foundation stiffness3.3.1 Analysis UncertaintyAnalytical uncertainty accounts for the model uncertainty resulting from the statisticalaccuracy of a single analytical simulation (i.e. the variability resulting from differentengineers, utilising different software, undertaking exactly the same analysis). With respectto jack-up response analysis this uncertainty is documented in DNV (1996a), Chapter 6.Guidance to selection of distribution type and distribution parameters for random analyticaluncertainty factors is given in Table 3.5 below.Basic Variable Name Distribution m C.o.V.Analytical uncertainty Lognormal 1.0 0.18Table 3.5 : Analytical Model Uncertainty Variables3.3.2 DampingDamping model uncertainty may vary depending upon the procedure adopted for includingdamping within the response analysis, Langen (1979). Relative velocity, hydrodynamicdamping should generally not be used if Eqn. 3.1 below is not satisfied, SNAME (1993). uTn/Di ³ 20 (3.1)whereu : water particle velocityTn : first natural period in surge/swayDi : diameter of leg chord· For extreme response analysis, in general, hydrodynamic damping may normally be explicitly accounted for by use of the relative velocity formulation in Morison’s equation.· A value for total global damping may be obtained by summation of those appropriate damping component percentages stated in Table 3.6, SNAME (1993).
    • Guidelines for Offshore Structural Reliability Page No. 22-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072Damping Source Global Damping (% of critical damping)Structure, holding system etc. 2%Foundation 2% or 0% 1Hydrodynamic 3% or 0% 2Table 3.6 : Table of Recommend Critical DampingKEY :1: Where a non-linear foundation model is adopted the hysteresis foundation damping will be accounted for directly and should not be included in the global damping.2: In cases where the Morison, relative velocity formulation is utilised the hydrodynamic damping will be accounted for directly and should not be included in the global damping.Guidance to selection of distribution type and distribution parameters for random dampinguncertainty factor associated with the response basic variables is given in Table 3.7 below.Basic Variable Name Distribution m1 C.o.V.Damping ratio Lognormal 1.0 0.25Table 3.7 : Damping Model Uncertainty VariablesKEY :1: The absolute value of the distribution variables are given relative to the value applied in the structural analysis.3.3.3 FoundationFor geotechnical analysis, model uncertainty is difficult to assess as there are few comparablefull scale prototypes that have actually gone to failure and where there was enoughknowledge about the site conditions and the load characteristics to enable calculation of theuncertainty.· Therefore to evaluate model uncertainty, comparisons of relevant scaled model tests with deterministic calculations, expert opinions and information from literature, in addition to any field observations that are available for similar structures on comparable soil conditions, are normally utilised.Using "traditional" analysis methods to undertake the bearing capacity analysis of thespudcan of a jack-up foundation results in large model uncertainties, as was documented byEndley et al. (1981). They compared, for 70 case studies on soft clays and 15 case studies onlayered profiles consisting of soft clay over stiff clay, predicted rig footing penetration withobserved penetrations. The comparisons suggest a model uncertainty with mean value 1.0and standard deviation 0.33, as based on the 70 cases studied. The observed data rangedbetween 0.4 and 1.55 times the predicted values.McClelland et al. (1982) undertook similar comparisons for jack-ups on uniform clay profilesand for jack-ups on layered profiles. In this study the standard deviation was about 0.20 to0.25 about a mean of 1.0.
    • Guidelines for Offshore Structural Reliability Page No. 23-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072The “traditional" methods of analysis are the so-called "bearing capacity formulas” which donot account for strength anisotropy, cyclic loading, soil layering, nor variation of soilproperties with depth or laterally. The model uncertainty values quoted above are valid for afailure mode under vertical loading only.In the method proposed by Nadim and Lacasse (1992), a more rigorous bearing capacityapproach than the "traditional" approach is used. The analysis uses a limiting equilibriummethod of slices. Effects of anisotropy and cycling loading, the uncertainty in the calculationmodel for both vertical and horizontal (moment) loading and combined static and cyclicloading are included. The uncertainty in this calculation model was studied in detail withseries of model tests at different scales.On the basis of the work carried-out by Andersen and his co-workers, Andersen et al. (1988),(l989), (1992), (1993), Dyvik et al. (1989), (1993), model uncertainty for bearing capacity ofa footing in clay may be mean 1.00, standard deviation 0.05 for failure under static loadingonly, and mean 1.05, standard deviation 0.15 for failure under combined static and cyclicloading. For footings installed in sand, much less information exists, and tentative values maybe mean 1.00, standard deviation 0.20 to 0.25, based on engineering judgement and theresults of recent centrifuge model tests, Andersen et al. (1994). The model uncertainty mayvary according to the failure surface. It should be noted that the mean of model uncertaintyfactor for most offshore foundations (e.g. piles in sand and clay, shallow foundations onsand) is greater than 1.0, i.e. the analytical models tend to be conservative. The methodsdeveloped for shallow foundations on clay, however, have been fine-tuned and calibratedagainst large-scale tests in the past 20 years, and much of the inherent conservatism in themethods has been removed.Little information exists on the model uncertainty associated with the foundationdisplacement of a jack-up structure (see step 3 in section 2.3.6) and the model uncertainty canonly be guessed for those cases. A model uncertainty with a coefficient of variation of at least50 % is expected.Guidance to selection of distributions associated with the foundation parameters is given inTable 3.8 below. Reference should also be made to DNV (1996a), Section 7.3.Description Distribution*1Rotational stiffness LognormalHorizontal stiffness LognormalVertical stiffness LognormalTable 3.8 : Foundation Parameter DistributionsKEY :*1 : See also section 2.3.6
    • Guidelines for Offshore Structural Reliability Page No. 24-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-00723.4 Resistance Uncertainty ModellingThe level of reliability of jack-up structures is “load driven”, Ronold (1990), Dalane (1993),that is to say that the importance of the uncertainties in the loading is much greater than theimportance of the uncertainties in the capacities. As a consequence of this it is most likelythat a structural failure event will result from the load being high, rather than the strengthcapacity being low.· Uncertainties associated with resistance are dependent upon the resistance model included in the limit state under consideration. Modelling of the uncertainly parameters associated with the resistance model should be relevant to the formulation of the resistance model utilised in the limit state. See section 4.0 for further guidance.· General resistance uncertainty information is given in DNV (1996a), Chapter 7.· A realistic analysis of the ultimate (‘push-over’) capacity of a jack-up structure can in many cases only be performed by using advanced non-linear finite element software, e.g. USFOS (1996).
    • Guidelines for Offshore Structural Reliability Page No. 25-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-00724.0 LIMIT STATES4.1 GeneralLimit states are formulations of physical criteria beyond which the structure no longersatisfies the design performance requirements. Limit state categorisation is generally definedas follows, ISO 13819, Part 1, ISO (1995) ;a). The ultimate limit states that generally correspond to the maximum resistance to applied actions.b.) The serviceability limit states that correspond to the criteria governing normal functional use.c.) The fatigue limit states that correspond to the accumulated effect of repeated actions.d.) The accidental damage limit states that correspond to the situation where damage to components has occurred due to an accidental event.Some code of practices, e.g. Eurocode 3 (1992), however, defines only two limit states, thesebeing ; the Ultimate Limit State, and the Serviceability Limit State. In such cases the statesprior to structural collapse which, for simplicity are considered in place of the collapse itself,are also classified and treated as the ultimate limit state.4.1.1 Limit States Appropriate to Jack-up StructuresServiceability Limit State (SLS)· For steel structures, the serviceability limit state is not normally a designing criterion and is therefore not further discussed within this section.Fatigue Limit State (FLS)· The fatigue limit state is a relevant limit state to consider for jack-up structures. Both for long term site engagements and for the transit condition, the fatigue limit state may be designing.· The guidance provided in the guideline example for jacket structures, DNV (1996c), in respect to the fatigue limit state, although utilising frequency domain solution techniques, covers the state-of-the-art knowledge with respect to fatigue reliability analysis of jack- up structures. The fatigue limit state is therefore not explicitly covered in this section and reference should be made to DNV (1996c) for appropriate guidance concerning the fatigue limit state.Ultimate Limit State (ULS)ISO 13819, Part 1, ISO (1995), lists the following examples of ultimate limit states ;a.) loss of static equilibrium of the structure, or of a part of the structure, considered as a rigid body (e.g. overturning or capsizing),b.) failure of critical components of the structure caused by exceeding the ultimate strength ( in some cases reduced by repeated actions) or the ultimate deformation of the components,
    • Guidelines for Offshore Structural Reliability Page No. 26-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072c.) transformation of the structure into a mechanism (collapse or excessive deformation),d.) loss of structural stability (buckling etc.),e.) loss of station keeping (free drifting), andf.) sinking.· The ultimate limit state for jack-up structures is difficult to describe through simple design equations. Additionally, general guidelines on how to perform structural system collapse analyses are lacking, hence limit state functions for reliability analysis of jack- up structures are general based on design equations for single components.For a jack-up in the elevated mode of operation the following listed ultimate limit states maybe considered as designing ;Component Level-leg local structural strength-hull local structural strength-foundation capacity (local)-holding system loadings· The following listed limit states may therefore be considered as being relevant component limits states for reliability analyses ; -1- Leg element yield -2- Leg element buckling -3- Leg joint capacity -4- Foundation bearing failure -5- Holding system capacitySystem (Global) Level-leg global structural strength-hull global structural strength-overturning stability-horizontal deflections-foundation capacity.Accidental Damage Limit State (ALS)The accidental damage limit state check ensures that local damage or flooding does not leadto complete loss of integrity or performance of the structure.· The intention of this limit state is to ensure that the structure can tolerate the damage due to specified accidental events and subsequently maintain integrity for a sufficient period under specified environmental conditions to enable evacuations to take place. The accidental events and the consequences of such events are normally based upon Quantitative Risk Analyses (QRA). For further details on QRA reference should be made to DNV (1996a), Chapter 2.4.2 The Ultimate Limit State
    • Guidelines for Offshore Structural Reliability Page No. 27-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072This subsection describes in more detail Ultimate Limit State criteria documented insubsection 4.1.1.4.2.1 Leg StrengthGeneralAs previously mentioned, (see Section 3.4), reliability of a jack-up structure in the ultimatelimit state condition is found to be ‘load driven’, i.e. the importance of the uncertaintiesassociated with the loading dominates. When describing the uncertain quantities associatedwith the limit state it is generally therefore not necessary to breakdown the individualuncertainties associated with, for example, a buckling resistance code formulation, and codecriteria may be utilised with generalised randomisation parameters.· Suitable strength resistance criteria, may be found in a wide variety of structural codes and standards. The following references may be recommended ; -AISC (1984) -API (1993) -DNV (1995) -Eurocode 3 (1992) -NPD (1990) -SNAME (1993)When utilising standard codes and Practices the following issues should be considered ;(i) The formulations contained in these codes may only be applicable within certain limits (e.g. R/t ratio between given limits). It should therefore be ensured that the resistance formulation utilised in the limit state is satisfactory for the structure under consideration.(ii) The resistance formulations contained within these codes are based upon analytical approximations to the physical behaviour where characteristic values are defined at some fractile value or lower bound value. For reliability analysis the capacity formulation in the limit states should be based on the 50 percent fractile (median) values. The basis for buckling curves in different codes and standards are different. The API buckling curve, API (1993) is derived as a lower bound value for low slenderness while it is equal to the Euler stress for high slenderness values, which may be considered as an upper bound value in that region. Another definition of a buckling curve is used in AISC (1984). The background for the buckling curves used in design of steel structures in European design standards is based on work carried out within the European Convention for Constructional Steelwork which is presented in The Manual on Stability of Steel Structures, ECCS (1976). The design curves are presented by their characteristic values which are defined as mean values minus two standard deviations along the slenderness axis. The test results are assumed normal distributed.(iii) Effective buckling lengths are dependent upon joint flexibilities. Buckling lengths may normally be measured in relation to centreline to centreline for chords, whilst, face to face lengths are normally acceptable for the braces. X-brace buckling lengths depend upon the amount of tension loading in the crossing member. The effective lengths may be derived from analytical considerations. The effective buckling
    • Guidelines for Offshore Structural Reliability Page No. 28-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072 lengths derived from tests of frame structures until collapse are generally shorter than those derived from theoretical calculations.(iv) Different allowable requirements to fabrication tolerances (eccentricity) are associated with the various buckling curves. For European buckling curves a straightness deviation at the middle of the column equal to 0.0015 times the column length is allowed, while for API (1993) and AISC (1984) the corresponding numbers are 0.0010 and 0.00067 respectively.For conventional design jack-up structural elements the effect of external pressure may,normally be disregarded.The susceptibility of local buckling of tubular members is a function of the member geometryand yield strength. For jack-up structures, it may normally be assumed that leg elements arestocky, beam elements. Yield strength control is implicitly covered by the buckling limit statefor members in compression, whilst, for tension members, the limit state is given by, forexample, eqn. 5.1, NPD (1990), NS3472 (1984). G = fy - [ s a + s by + s bz ]2 + 3[ t xy + t xz + t t ]2 (5.1)where fy = material yield strength sa = axial stress componentt t = torsional shear stress componentsby , sbz = bending stress componentst xy , t xz = plain shear stress componentsThe capacity criterion stated in SNAME (1993) is an example of an expression applicable todescribe resistance of jack-up elements subjected to compressive loadings. Such formulationmay be described in the limit state format as ; 1 h h Pu 8 éì M uex ü ì M uey ü ù h ï ï ú G = 1 - X bias [ + êí ý +í ý ] (5.2) Pn 9 êî M nx þ ï M ny ï ú î þ û ëWhere ; Pu is the chord axial load Pn is the chord nominal axial strength in compression M uex is the chord local effective applied bending moment about the local x-axis M uey is the chord local effective applied bending moments about the local y-axis M nx is the chord local nominal bending strength about the local x-axis M ny is the chord local nominal bending strength about the local y-axis h is the exponent for biaxial bending.
    • Guidelines for Offshore Structural Reliability Page No. 29-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072A full description of limiting criteria, the parameters utilised in Equation 5.2, and themethodology utilised in calculating the specific values of these terms are documented inSNAME (1993), Section 8.1.4.The SNAME (1993) formulation for buckling resistance is based upon AISC (1978). Theuncertainty parameters stated in Galambos (1988) may therefore be utilised in describing theuncertainty parameters including Xbias.Joint CapacityJoint capacity design equations have been established for the static strength of tubular joints.The equations in API (1993) and NPD (1990) show a similar shape although the coefficientsare different as also might be expected as the API (1993) are based on allowable stresses andNPD (1990) has based the design on the partial coefficient method.Jack-up brace/chord connections are, however, normally non-standard, due to the rackstructure inclusion in the chord section. Static strength capacity formulation for standardtubular/tubular connections may give erroneous results for brace/chord connections.Work on joint capacities is currently being performed in development of a new ISO standardon design of steel offshore structures. This work should be considered as basis for limit statefunctions when it is available.As an example limit state Eqn 5.3 documents the static strength of tubular joints formulationbased on the NPD guidelines, NPD (1990) and the limit state function for the static capacityof tubular joints can then be formulated, NPD(1990) as ; 2 N æ M IP ö M G = 1 - X bias [ +ç ÷ + OP ] N k è M IPk ø M OPk (5.3)whereXbias = bias (See DNV (1996a), Chapter 7.2) N = brace axial force Nk = characteristic capacity of the brace subjected to axial force M IP = brace in-plane moment M IPk = characteristic capacity of the brace subjected to in-plane moments M OP = brace out-of-plane moment M OPk = characteristic capacity of the brace subjected to out-of-plane momentsA detailed description of this limit state is given in DNV (1996c).
    • Guidelines for Offshore Structural Reliability Page No. 30-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-00724.2.2 Foundation Bearing FailureThe limit state function for the ultimate limit state of foundation bearing capacity is definedas : G = R - L, where R and L are respectively the lengths of resistance and load vectors asshown in Fig 4.1. The origin of the vectors on the vertical axis, Pw, is the static load on thefooting due to submerged weight of the jack-up. The end point of vector L, point A, is the co-ordinate in the load space under the design storm. The end point of vector R, point B, is thefoundation bearing capacity along the load path Pw®A.For the limit state function, G, the lengths of resistance, R, and load vectors, L, are defined asfollows ; L= (Vex - Pw ) 2 + ( Hex ) 2 + ( Mex / r ) 2 (5.4) R= (Vcy , f - Pw ) 2 + ( Hcy , f ) 2 + ( Mcy , f / r ) 2 (5.5)Vex = Vertical load on footing under the extreme load combinationHex = Lateral load on footing under the extreme load combinationMex = Moment load on footing under the extreme load combinationVcy,f = Vertical capacity of footing along the path defined by load vector starting at (Pw,0,0) in direction of (Vex, Hex, Mex)Hcy,f = Lateral capacity of footing along the path defined by load vector starting at (Pw,0,0) in direction of (Vex, Hmax, Mex)Mcy,f = Moment capacity of footing along the path defined by load vector starting at (Pw,0,0) in direction of (Vex, Hmax, Mex)Pw = Mean vertical load on footing during the storm (mainly due to submerged weight of jack-up)r = Radius of footing (reference length used for normalising the moment)The values of Vcy,f, Hcy,f, and Mcy,f are obtained by extending the load vector starting at(Pw,0,0) in the direction of (Vex, Hex, Mex) until it intersects the bearing capacity interactiondiagram as shown on Fig. 4.1a.L and R are the lengths of the extreme load and resistance vectors shown on Fig. 4.1b.4.2.3 Holding SystemThe limit state function for the ultimate limit state of holding system capacity is defined as :G = R - S, where R is the ultimate holding capacity of the jacking system and S is theresponse loading. The ultimate capacity of the holding system is usually obtained by detailedfinite element analysis (F.E.M. analysis) in combination with relevant prototype testing.
    • Guidelines for Offshore Structural Reliability Page No. 31-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072Figure 4.1 : Definition of Limit State Function for a Footing on Clay with Moment Fixity.
    • Guidelines for Offshore Structural Reliability Page No. 32-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-00724.2.4 Global DeflectionsThe limit state function for the ultimate limit state of global deflections is defined as : G = R- S, where R is a stated value (some prescribed threshold), e.g. chosen from considerations inrespect to proximity to another offshore installation, and S is the response displacement.4.2.5 Global Leg StrengthThe structural behaviour beyond first member failure depends not only on the ability of thestructure to redistribute the load, but also on the post-failure behaviour of the system, e.g. theductility of the individual members and joints.For a balanced structure, i.e. where all members, in a linear analysis, have the sameutilisation at the time of first member failure, the first member to fail and the system effectsfor overload capacity beyond the first member failure are determined by randomness inmember capacity.As the uncertainty in the structural capacity is much less than that in the loading, Dalane(1993), and the structure is not balanced, there will normally be only a few failure modes thatwill dominate. The identification of such members is however, complicated by simplicitiesmade in the analysis e.g. at the interfaces between the hull and the leg structures, and at thefoundation interfaces.There has been little previous workings undertaken concerning jack-up collapse analysisrelated to reliability analysis, however, by referring to jacket experience, it is considered thatthe collapse capacity may be directly related to the global overturning moment. This impliesthat the collapse capacity can be represented by a single random variable. The loading mayalso be represented by a single random variable, and, as such, the limit state function for theultimate limit state of global leg strength capacity may be defined as : G = R - S, where R isthe strength capacity of the leg (i.e. the overturning moment) and S is the loading.Guidelines related to the total collapse of jacket structures are given in (1995c). Suchguidelines may form the basis for considerations relevant for the collapse (‘push-over’)analysis of a jack-up structure.4.2.6 Overturning StabilityJack-up overturning stability criteria are documented in various publications, e.g. SNAME(1993), DNV (Feb 1992). An example of this limit state is given by SNAME (1993) as ; G = ( MD + ML + MS ) - ( ME + MDN ) (5.6)MD = the stabilising moment due to weight of structure and non-varying loads (at the displaced position)ML = the stabilising moment due to the variable loads(at the displaced position)MS = the stabilising moment due to the seabed foundation fixityME = the overturning moment due to the extreme environmental load conditionMDN = the dynamic overturning momentWhen considering the moments in connection with this limit state it is important to ensurethat the axis of rotation of the system is fully considered.
    • Guidelines for Offshore Structural Reliability Page No. 33-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-00724.3 Literature StudyFrom a literature review it may be concluded that there have, in the past, been few publicpapers issued concerning structural reliability of jack-up units.From an extensive documentation review the following listed reliability studies have beenidentified in respect to jack-up structures ;General Structural Reliability Papers ;1.) Løseth, R., Mo, O., and Lotsberg, I, (1990)2.) Leira, B.J., and Karunakaran, D. (1991)3.) Mo.O., et.al. (1991)4.) Ahilan, R.V. et.al. (1992)5.) Gudmestad, O.T., et.al. (1992)6.) Karunakaran, D., et.al. (1993)7.) Ahilan, R.V., Baker, M.J., and Snell, R.O., (1993)8.) Dalane J.I.(1993)The majority of the papers referred to above may be considered as providing informationconcerning general reliability.Løseth et.al. (1990) and Karunakaran et al.(1993) document the global limit state criteria ofmaximum axial force and base shear in one leg. Karunakaran et al.(1993) also documentsconsiderations with respect to deck displacement and foundation limit states. Ahilan etal.(1992), (1993) covers reliability code calibration studies undertaken in connection withSNAME (1993). Mo et al. (1991) and Dalane (1993) document structural leg strengthcapacity considerations.Foundation Reliability Papers ;1.) Ronold, K.O., (1990)2.) Nadim, F., Lacasse, S., (1992)3.) Nadim, F., Haver, S., and Mo, O. (1994)
    • Guidelines for Offshore Structural Reliability Page No. 34-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-00725.0 SUMMARY OF APPLICATION EXAMPLES5.1 GeneralThis section documents a summary of the reliability analyses undertaken to analyse theresponse of a jack-up structure in a typical North Sea environment at a waterdepth of 81metres as documented in DNV (1996b). In order to assess change in reliability as a functionof time, the reliability examples are undertaken for a jack-up exposed to multi-year operationat the same location. The following listed time dependent effects have been considered in theanalyses ;- Soil ConsolidationThe foundation rotational stiffness was increased by a factor of 2.5 to account for soilconsolidation.- Drag CoefficientDrag coefficients were increased by a factor of 15% to account for the change in drag due toincreased roughness.- Marine GrowthMarine growth diameter thickness’ according to the values recommended by the NPD (1992)were applied.- Deckbox MassThe total mass of the rig was assumed to have increased by a factor of 10% to account forweight growth in the deckbox.Two limit states have been considered covering the structural strength of the jack-up leg andthe foundation capacity. In both of these cases the effects on reliability of long term operationat the specific site have been evaluated.The reliability analyses documented in DNV (1996b) have been undertaken by themethodology generally known as ‘Long Term Statistics by Independent Seastates’, Bjerageret al. (1988), and were based upon response resulting from time domain simulations inirregular seastates.Report DNV (1996b) fully documents the following items ;- introduction to the problem stating assumptions and provisions- theory of the models for representation of the problem- a description of the limit state formulation and the formulation itself- probabilistic and deterministic modelling descriptions- the reliability analysis procedures- results of the analysis, including reliability indices, failure probabilities, uncertainty importance factors, and parametric sensitivity factors- discussion and conclusions.5.2 Overview of Analytical ProcedureUtilising site specific criteria, detailed deterministic and simplified dynamic, non-linearanalyses were undertaken in order to determine appropriate jack-up response statistics.
    • Guidelines for Offshore Structural Reliability Page No. 35-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072Long term statistics were established by use of PROTIM (1989). PROBAN (1989) wasutilised to solve the probabilities of failure of the limit state functions.For the foundation example a probabilistic bearing capacity model was established in order toaccount for the different combinations of force and moment at the foundation footing.An overview of this procedure is shown schematically in figure 5.1. DESIGN CRITERIA ESTABLISH CRITICAL PARAMETERS ; -Load Direction DETAILED MODEL -Design Criteria WAJAC -Element ANALYSES (Deterministic Sea) -Foundation soil springs ESTABLISH THE RESPONSE STATISTICS ; SIMPLIFIED MODEL FENRIS -Force and moment for the ANALYSES FENSEA most critically loaded (Stochastic Sea) structural element -Force and moment for the most utilized footing PROBAN PROTIM STRUCTURAL RELIABILITY OUTPUT : The annual probability ESTABLISH of failure for the most critically PROBABILISTIC BEARING loaded structural element. CAPACITY MODEL for the (Determined by establishing the long term statistics considering different combinations of independent seastates) force and moment on most utilized footing ESTABLISH FOUNDATION RELIABILITY DISTRIBUTIONS OF OUTPUT : The annual ANNUAL EXTREMES for probability of failure for the force and moment on most most utilized footing. utilized footingFigure 5.1 : Overview of Analytical Procedure
    • Guidelines for Offshore Structural Reliability Page No. 36-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-00725.3 Structural Reliability ExampleThis example documents an ultimate limit state reliability analysis undertaken for a jack-upstructure exposed to multi-year operation. The foundation description ‘unconsolidated soil’ isintended to reflect a cohesive soil condition (e.g. clay) at the time of the initial placement ofthe jack-up unit. The ‘consolidated soil’ condition is a condition where, at the same location,after a given period of operation, say 10 years, the foundation is considered to have settledand consolidated. Failure probability of leg, chord buckling provided the measure of thechange in reliability with time.An overview of the analytical methodology adopted in the reliability analysis is shown infigure 5.1.The main results from the undertaken reliability analysis are presented in table 5.1. Table 5.2presents results from the sensitivity evaluation, where the mean and standard deviation havebeen increased by 10% over those values utilised in the undertaken reliability analysis.SORM Reliability index - Unconsolidated Soil : b = 4.35 - Consolidated Soil : b = 4.41Variable Unconsolidated Soil Consolidated Soil Importance Factor Importance FactorSignificant Wave Height, Hs 56% 44%Randomness of Storm Extreme, Uaux 16% 15%Drag Coefficient, CD 11% 15%Critical Stress, Fcr 9% 10%Heading, q 3% 1%Wave Spreading, n 2% 4%Foundation Rotational Stiffness, Kr 2% 9%Tidal current, VT <1% 1%Damping <1% 1%Deckbox Mass <1% <1%Table 5.1 : Structural Reliability Importance Factors Unconsolidated Soil Consolidated Soil Condition
    • Guidelines for Offshore Structural Reliability Page No. 37-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072 Condition Variable Mean / Lower CoV / Upper Mean / CoV / Upper Bound Bound Lower Bound Bound Environment N/A -0.3138 N/A -0.2611 Rotational Stiffness, Kr 0.0202 -0.0038 0.0286 -0.0227 Vertical Stiffness, Kv -0.0063 0.0002 0 0 Lateral Stiffness, Kh -0.0008 0 0 0 Drag Coefficient, CD -0.1686 -0.0379 -0.1847 0.0497 Tidal current, VT -0.0340 0.0007 -0.0316 0.0005 Marine Growth -0.0025 0.0001 -0.0186 0.0001 Damping -0.0090 0.0003 -0.0369 -0.0013 Deckbox Mass 0.0193 -0.0007 0.0600 -0.0043 Wave Spreading, n -0.0037 -0.0377 -0.0048 -0.0764 Waterdepth, D 0.0074 0.0075 0.0322 0.0315 Spectral Peak Parameter, g -0.0008 -0.0040 -0.0019 -0.0134 Heading, q -0.0424 -0.1728 -0.0260 -0.0637 Yield Strength, fy 0.0054 0 0 0 Critical Stress, Fcr 0.2525 -0.0421 0.2643 -0.0467 Duration, D -0.0195 N/A -0.0197 N/A No. of Seastates, Nsea -0.0214 N/A -0.0214 N/ATable 5.2 : Sensitivity Analysis of Results (Db for a 10% increase in the meanvalue and CoV for selected variables)Key :N/A : Not applicableThe reliability levels resulting from the example seem to be relatively high for a jack-up unitwhen compared to other relevant studies for jack-up units, e.g. SNAME (1993). The mainreason for this is that the jack-up chord element under investigation in the example, althoughbeing the most heavily loaded structural element, is not loaded up to the allowabledeterministic capacity of the element in the designing storm condition. The conditionanalysed was however based upon an actual loading situation for the jack-up unit. Thisexample would therefore tend to confirm the in-service experience that jack-up unitsgenerally operate at reasonably high levels of reliability in respect to structural strength dueto the fact that, in the normal mode of operation, the jack-up is not utilised to the maximumcapability of the jack-up unit in respect to the leg strength ultimate limit state condition. Forjack-up units designed to operate as production units over a longer period of time at a singlelocation, where the jack-up is designed and optimised for site specific criteria, such aconclusion can not however be made from the investigation performed in the example.Over the period of time considered, the reliability of the jack-up is found to remain fairlyconstant in the example presented. It would appear that the time varying negative effects ofincreased static and environmentally induced loadings are offset by the effects of soilconsolidation. In the case represented in the example study, consolidation of the foundationhas lead to an increased bottom restraining condition. Other soil conditions may howeverlead to degradation of the foundation restraint. In all cases site specific data should beutilised as the basis for evaluating the long term effects of the foundation.
    • Guidelines for Offshore Structural Reliability Page No. 38-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072 5.4 Foundation Reliability ExampleThe foundation reliability example documented in DNV (1996b) demonstrates ultimate limitstate analyses undertaken for the stability of the most utilised footing for unconsolidated andconsolidated soil conditions. Each leg of the jack-up considered in the presented case studywas supported by a 20 m diameter footing with 6 m skirts. The site consisted of 2 clay layers:a soft clay layer down to 5 m depth and a stiff, overconsolidated clay layer underneath. Themechanical model for evaluating the capacity of skirted footings in clay was assumed welldeveloped and the modelling uncertainty relatively small.The limit state function for the ultimate limit state of bearing capacity for the most utilisedfooting was defined as G = R - L, where R and L were respectively the lengths of theresistance and load vectors as shown on Fig. 4.1.The distribution of the resistances was estimated by specifying a deterministic load on thefoundation and evaluating the probability of failure using FORM. By varying the load, theprobability of failure at different load levels was computed. The results showed that alognormal distribution provides an excellent fit for the static foundation capacity.The CoVs and distributions of the foundation resistance parameters used in the analyses aregiven in Table 5.3 (see Section 4.2.2 and Fig. 4.1 for definitions). VARIABLE Distribution Mean CoV Unconsolidated clay (all layers) Vpre Lognormal 212 MN 12% Hs,max Lognormal 40 MN 13% Ms,max Lognormal 640 MNm 14% Consolidated clay (all layers) Vpre Lognormal 253 MN 12% Hs,max Lognormal 51 MN 13% Ms,max Lognormal 777 MNm 14% Other variables (same for consolidated and unconsolidated conditions) F1 Normal 1.06 3% F2 Normal 0.72 3% F3 Normal 0.78 3%Table 5.3 : Foundation Resistance ParametersThe extreme loads on the most utilised footing were computed by PROBAN (1989). Table5.4 shows the load parameters used in the foundation reliability calculations. The CoV of Pwwas assumed to be identical to the CoV of the deck mass.
    • Guidelines for Offshore Structural Reliability Page No. 39-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072 VARIABLE Distribution Mean CoV Unconsolidated Soil Condition Vex - Pw Gumbel 5.0 MN 111% Hex Gumbel 4.9 MN 54% Mex Gumbel 169.5 MNm 82% Pw Lognormal 71.6 MN 14% Consolidated Soil Condition Vex - Pw Gumbel 5.3 MN 118% Hex Gumbel 6.4 MN 49% Mex Gumbel 323.9 MNm 51% Pw Lognormal 78.7 MN 14%Table 5.4 : Extreme Loads on Most Utilised FootingWhen the effects of load redistribution among the footings were neglected, the computedfoundation safety indices were respectively 1.85 and 1.45 for the unconsolidated andconsolidated soil conditions. The reason for these low values was that when the possibility ofload redistribution among the jack-up legs was not taken into account, the failure mode of themost utilised leg was governed by the large overturning moment for both soil conditions.This failure mode, however, is not realistic for a 3-leg jack-up structure because for thewhole foundation system consisting of the 3 footings, it is more optimal to resist the externaloverturning moment by axial forces, rather than by local moments at each footing. Withtraditional spud cans, the moment fixity is completely lost when the bearing capacity isreached. However, with skirted spud cans, the moment acting on the most utilised footing atfailure may be 60 to 80% of the moment capacity.The main results from the foundation reliability analyses, after accounting for theredistribution of reactions among the 3 footings and reduction of fixity of the most utilisedfooting at large loads, are summarised in Table 5.5.FORM Reliability index - Unconsolidated Soil : b = 4.11 - Consolidated Soil : b = 4.22 Variable Unconsolidated Soil Consolidated Soil Importance Factor Importance Factor Static Sliding Capacity, HSmax 11% 13% Cyclic Loading Factor, F2 1% 1% Extreme Base Shear, Hex 88% 86% All other parameters <1% <1%Table 5.5 : Results for Most Utilised Footing with Load Redistribution
    • Guidelines for Offshore Structural Reliability Page No. 40-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072There is a lack of documentation concerning the reliability of jack-up foundation ultimatelimit state conditions. For the example application, it was considered appropriate to comparethe computed safety indices with those in Table 2.7 of the Reliability Guidelines DNV(1996a). This table presents target annual failure probability and corresponding reliabilityindices. Once the effects of optimal utilisation of the foundation system (i.e. redistributionof reactions among the 3 footings when the loads approach the foundation capacity) areconsidered, the foundation failure development may be considered as being ductile with noreserve capacity. The failure consequence is considered as being somewhere between notserious and serious. Therefore an annual target failure probability of 10-4 to 10-5 (b = 3.71 to4.26) is appropriate. The safety indices of b = 4.11 for the unconsolidated soil condition andb = 4.22 for the consolidated soil condition would therefore appear to be satisfactory.
    • Guidelines for Offshore Structural Reliability Page No. 41-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-00726.0 RECOMMENDATIONS FOR FURTHER WORK6.1 GeneralFrom the literature review study undertaken and documented in section 4.3, it is clear thatthere have been very few reliability analyses undertaken for jack-up structures.· This section discusses recommendations for further workings in connection with identification of the reliability of jack-up structures.6.2 Elevated ConditionJack-up structures have traditionally been used in shallow waters. There is a current tendencyto utilise jack-ups in deeper waters, in harsh environment conditions, for extended periods ofoperations.· The uncertainty weightings for these two scenarios are different and the safety implicit in current jack-up design procedures may not necessarily be appropriate, Gudmestad (1990), Dalane (1993).Jack-up structures, as compared to jacket structures, have a number of unique characteristics,which add to the complexity of the problem being considered. (e.g., See sections 1.4 and 2.3).With respect to limit state formulation, the most important of these characteristics may beconsidered as ;(i) The non-linearities in the system generally preclude the use of linear analytical procedures(see section 2.3).(ii) Jack-up chord sections normally include a rack construction. This means that traditionalformulation for stress concentration factors and joint static capacity (e.g. punching shear) aregenerally not appropriate.· Results from reliability studies undertaken for traditional jacket type offshore structures are, generally, not ‘transferable’ to jack-up structures.The stiffness characteristics (fixity) of spudcan footings are complicated and strongly non-linear. Jostad et al. (1994) show that while spudcans might have significant moment fixityunder operational loads, the moment fixity disappears as the loads approach foundationcapacity. The footing stiffness affects the dynamic characteristics of the jack-up, which inturn influence the loads on the spudcans. So far, there have been no systematic studies of theeffects of the uncertainties in the spudcan stiffness characteristics on the jack-up response.Conclusions :-1- The implicit probability of failure of jack-ups by use of dedicated jack-up codes and standards should be evaluated for their applicability to deep water, harsh environment operations for extended periods.-2- Jack-up system capacity due to accidental damage load events should be evaluated. The robustness of the jack-up structure should then be compared to that of a jacket structure. (The U.K., H.S.E. is currently engaged in such a project and the findings from these workings should be considered in this connection.)
    • Guidelines for Offshore Structural Reliability Page No. 42-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072-3- Traditional, frequency domain (linear analysis) based fatigue reliability should be compared with that reliability achieved utilising time domain (non-linear) analysis in order to identify, for a jack-up structures, the importance of the non-linear effects for the fatigue limit state.-4- Reliability considering the following foundation related criteria is recommended to be investigated ; -system effects -response as related to the uncertainty and non-linearity in foundational support.6.3 Floating / Installation Phase ConditionsOf the 250 jack-up casualties reported during the period 1979 to 1991, some 50% of the totallosses, or major incidents occurred during towage, Standing and Rowe (1993).Standing and Rowe (1993) document the following listed items as being the major source ofaccident in respect to a jack-up in the transit condition ;(i) Wave damage to the unit structure leading to penetration of watertight boundaries.(ii) Damage to the structure as a result of shifting cargo (usually caused by direct wave impact, excessive motions and/or inadequate seafastenings).(ii) Structural damage in the vicinity of the leg support structures.· There does not appear to have been any reliability studies undertaken for jack-ups in the transit condition.During the installation phase, there are normally two main areas of concern, these being;impact loadings upon contact with the seabed, and, foundation failure (i.e. punch-through)during preloading.Sharples et al (1989) summarised the causes for jack-up mishaps in a 10 year period. Out of226 “accidents", over 50 were attributed to “soils”. The causes for unsatisfactory foundationperformance were distributed as follows:Punch-through of footings 70%Failure due to storm loading 16%Scour around footings 5%Other causes 9%Based on a survey of major accidents between 1980 and 1987, Arnesen et al. (1988) came tosimilar conclusions.· It is evident from the above statistics that punch-through during preloading is the most frequently-encountered foundation problem for jack-ups.· The physics of the impact loading problem are extremely complicated and the uncertainties in the process are not well documented. Additionally, regulation requirements for the installation condition are considered to be vague and incomplete.
    • Guidelines for Offshore Structural Reliability Page No. 43-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072Conclusions :-1- Reliability analysis for the transit condition would appear to be necessary, not least, in order to understand the importance of uncertainties associated with the process and to identify areas where further workings are required.-2- Reliability investigations in the installation phase should be considered for the following listed loading conditions ; -preloading -impact loading.
    • Guidelines for Offshore Structural Reliability Page No. 44-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-00727.0 REFERENCESAhilan, R.V. et.al.(1992), ‘Reliability Based Development of Jackup Assessment Criteria’,Tenth Structures Congress (ASCE), San Antonio, 1992.Ahilan, R.V., Baker, M.J., and Snell, R.O.(1993), ‘Development of Jackup assessmentCriteria using Probabilistic Methods’, OTC 7305, Houston, 1993AISC(1984),’Specification for the Design, Fabrication and Erection of Structural Steel forBuildings’, American Institute of Steel Construction, Eighth Edition, Oct.1984.Andersen, K.H. and Lauritzsen, R.(1988), ‘Bearing Capacity for foundation with CyclicLoads,’, ASCE. Jorn. of Geotechnical Engineering. V 114, No 5, pp. 516-555Andersen, K H., Lauritzsen, R., Dyvik, R., and Aas, P.M.(1988), ‘Cyclic Bearing CapacityAnalysis for Gravity Platforms; Calculation Procedure, Verification by Model Tests, andApplication for the Gullfaks C Platform.’, Proc. BOSS88 Conf. Trondheim, Norway. V 1,pp. 311-325Andersen, K.H., Dyvik, R., Lauritzsen, R., Heien, D., Hårvik L., and Amundsen, T., (1989),‘Model Tests of Gravity Platforms. II: Interpretation.’ ASCE. Jorn. of GeotechnicalEngineering. V 115, No 11, pp. 1550-l568.Andersen, K.H., Dyvik, R., and Schrøder, K.(1992), ‘Pull-Out Capacity Analyses of SuctionAnchors for Tension Leg Platforms.’, Proc. BOSS92 Conf. London, U.K. V 2, pp. 1311-1322.Andersen, K.H., Dyvik, R., Schrøder, K., Hansteen, O.E., and Bysvecn, S.(1993). ‘FieldTests of Anchors in clay II: Predictions and Interpretation.’, ASCE Jorn. of GeotechnicalEngineering. V 119, No 10, pp. 1532-l549.Andersen, K.H, Allard, A. and Hermstad J.(1994), ‘Centrifuge Model Tests of A GravityPlatform on Very Dense Sand; II. Interpretation.’, Proc. BOSS94 Conf. Cambridge, Mass.USA. Vol. 1, pp. 255-252.Ang, A.H.S. and Tang, W.H.,(1975), ‘Probability Concepts in Engineering Planning andDesign. Volume I - Basic Principles.’, John Wiley and Sons, Inc., New York, 409p.Arnesen, K., Dahlberg, R., Kjeøy, H., and Carlsen, C.A.,(1988), ‘Soil -Structural InteractionAspects for Jackup Platforms’, BOSS’88 Conf. Trondheim, Norway, June 1988.API(1993), ‘Recommended Practice for Planning, Design and Constructing Fixed OffshorePlatforms -Load and Resistance Factor Design’, API Recommended Practice 2A-LRFD (RP2A-LRFD), First Edition, July 1993.Bjerager, P., Løseth, R., Winterstein, S., and Cornell, A., (1988) ‘Reliability Method forMarine Structures Under Multiple Environmental Load Processes’, Proceeding of 5thInternational Conf. on Behaviour of Offshore Structures, Vol.3, Trondheim, Norway, June1988, pp1239-1253.Boswell(1986), ‘The Jackup Drilling Platform’, Edited by L.F.Boswell, City University,London. Collins Publication, 1986
    • Guidelines for Offshore Structural Reliability Page No. 45-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072Bærheim M.(1993), ‘Structural Effects of Foundation Fixity on a Large Jackup’, Proc. TheJackup Platform, 4th Int.Conf., 1993Dalane, J.I.(1993), ‘System reliability in Design and Maintenance of Fixed OffshoreStructures’, Dr.Ing. Thesis, NTH, May 1993.DNV(1992),‘Structural Reliability Analysis of Marine Structures’, DNV Classification NoteNo. 30.6, Example 4.5, July 1992DNV (Feb. 1992), ‘Strength Analysis of Main Structures of Self-elevating Units’,Classification Note no. 31.5, Feb. 1992.DNV(1995), ‘Buckling Strength Analysis’, Det Norske Veritas Classification Note no. 30.1,July 1995.DNV(1996), ‘Rules for Classification of Mobile Offshore Units’, Det Norske Veritas, Part 3Chapter 1, ‘Structural Design General’, January 1996DNV(1996a) “Guideline for Offshore Structural Reliability Analysis - General”, DNVTechnical Report no.95-2018, Dated: May 1996DNV(1996b),‘Guidelines for Offshore Structural Reliability - Examples for Jackups’, DNVTechnical Report no.95-0072, Dated: February 1996DNV(1996c),‘Guidelines for Offshore Structural Reliability Applications to JacketPlatforms’, DNVI Technical Report no.95-3203, Dated: Draft Format May 1996.Dyvik, R., Andersen, K.H., Madshus, C., and Amundsen, T., ( 1989). ‘Model Tests ofGravity Platforms I: Description.’, ASCE. Jorn. of Geotechnical Engineering. V 115, No 10,pp. 1532-1549.Dyvik, R., Andersen, K.H., Hansen, S.B., and Christophersen, H.P. (1993). ‘Field Tests ofAnchors in Clay I: Description.’, ASCE Jorn. of Geotechnical Engineering. V 119, No 10 pp.1515-1531.ECCS(1976), ‘Manual on Stability of Steel Structures’, Second Edition, June 1976Endley, S.N., Rapoport, V., Thompson, V.J., and Baglioni, V.P.(1981). ‘Predictions of Jack-Up Rig Footing Penetration’, 13th Offshore Technology Conference, Houston, Texas, USA,Paper OTC 4144, Vol. 4, pp.285-296Eurocode 3(1992): ‘Design of Steel Structures -Part 1.1: General Rules and Rules forBuildings’, CEN, April 1992.Fernandes, A.C.(1985), ‘Analysis of a Jackup Platform by Model Testing’, Proc. of the 5thInt. Sym. on Offshore Engineering, Vol.5, 1985Fernandes, AC, et.al.(1986), ‘Dynamic Behaviour of a Jackup Platform in Waves’, Proc. ofthe 21st American Towing Tank Conf., 1986
    • Guidelines for Offshore Structural Reliability Page No. 46-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072Frieze, P.A., et al.(1991), ‘Report of ISSC Committee V.1 Applied Design’, 11th ISSC,Wuxi, China, Elsevier Applied Science, London 1991Galambos, V. (1988), Guide to Stability Design Criteria for Metal Structures, Fourth Edition,John Wiley & SonsGudmestad, O.T.(1990), ‘Refined Modelling of Hydrodynamic Loads on DynamicallySensitive Structures’, Integrity of Offshore Structures-4, Elsevier Applied SciencePublication, pp19-37, July 1990.Gudmestad, O.T., et.al.(1992), ‘Nonlinear Dynamic Response Analysis of DynamicallySensitive Offshore Structures’, OMEA, 1992.Gudmestad, O.T., and Karunakaran, D.(1994), ‘Wave Kinematics Models for Calculation ofwave Loads on Truss Structures’, OTC 7421, Houston 1994.ISO(1995), International Standard ISO/DIS 13819-1, ‘Petroleum and Natural Gas Industries -Offshore Structures’, Part 1 : General Requirements, 1995Jones, D.E., Hoyle, M.J.R., and Bennett, W.T.(1993), ‘The Joint Industry Development of aRecommended Practice for the Site-Specific Assessment of Mobile Jackup Units’ OTC 7306,Houston, 1993Jostad, H.P., Nadim, F., and Andersen, K.H.,(1994). ‘A Computational Model for Fixity ofSpud Cans on Stiff Clay.’, Proc. BOSS’94, Conf. Cambridge, Mass., USA, Vol.1 pp 151-171.Karunakaran, D.N.(1993), ‘Nonlinear Dynamic response and Reliability Analysis of Drag-dominated Offshore Platforms’, Dr.Ing. Thesis, NTH, Nov. 1993Karunakaran, D., et.al.(1993), ‘Prediction of Extreme Dynamic Response of a Jackup usingNonlinear Time Domain Simulations’, OMEA, 1993.Keaveny, J., Nadim, F., and Lacasse, S.(1989). ‘Autocorrelation Functions for OffshoreGeotechnical Data.’, Proc 5th ICOSSAR. San Francisco, Cal. USA. pp. 263-270Langen, I.; and Sigbjørnsson, R.(1979), ‘Dynamisk Analyse av Konstruksjoner’, TapirPublications, 1979.Leira, B.J., and Karunakaran, D.(1991), ‘Site Dependent Reliability of a Mobile JackupPlatform’, OMAE, 1991.Lotsberg, I., et. al.(1991), ‘Probabilistic Design of a Ship Type Floating Production Vessel’,OMAE Conf., Stavanger, ASME, New York 1991Løseth, R., Bjerager, P.(1989), ‘ Reliability of Offshore Structures with Uncertain Propertiesunder Multiple Load Processes’, OTC 5969, Houston 1989Løseth, R., Mo, O., and Lotsberg, I.(1990), ‘Probabilistic Analysis of a Jackup Platform withRespect to the Ultimate Limit State’, Euroms-90, EOMS, Trondheim 1990.Madsen , H.O., Krenk, S., and Lind, N.C.(1986), ‘Methods of Structural Safety’, Prentice-Hall Inc., Englewood Cliffs, NJ, 1986.
    • Guidelines for Offshore Structural Reliability Page No. 47-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072Manuel, L., Cornell, C.A. (1993), ‘Sensitivity of the Dynamic Response of a Jack-up Rig toSupport Modelling and Morison Force Assumptions’, Proc. of the 12th Int. Conf. onOffshore Mech. and Arctic Eng., ASME, Vol2, Jan. 1993.Matheron, G. (1985), ‘Principles of Geostatistics.’, Economic Geology, Vol. 58, pp. 1246-1266.McClelland, B., Young, A.G., and Remmes B.D.,(1982). ‘Avoiding Jack-Up Rig FoundationFailures.’, Geotechnical Engineering, V 13, No 2, pp. 151-188.Mo, O., Lotsberg, I., Løseth, R.M., (1991) ‘Response Analysis of Jackup Platforms’, Inter.Society of Offshore and Polar Eng. (ISOPE), 1991, Vol.1.Nadim, F., and Lacasse, S. (1992). ‘Probabilistic Bearing Capacity Analysis of Jack-UpStructures.’, Canadian Geotechnical Journal. v 29. No 4. pp. 580-588.Nadim, F., Haver, S., and Mo, O.,(1994). ‘Effects of Load uncertainty on Performance ofJack-Up Foundation.’, Proc. 6th ICOSSAR. Innsbruck, Austria.NPD(1990), ‘Guidelines on Design and Analysis of Steel Structures’, Norwegian PetroleumDirectorate, 3rd January 1990.NPD(1992), ‘Guidelines concerning Loads and Load Effects to Regulations concerningLoadbearing Structures in the Petroleum Activities’, Issued by the Norwegian Directorate,7th Feb. 1992.NS 3472(1984), Norwegian Standard NS 3472 E, ‘Steel Structures, Design Rules’, June1984.PROBAN (1989) Proban Theory Manual, Det Norske Veritas Research A.S.Report no. 89-2023, 22nd December 1989.PROTIM (1989) ‘Theoretical and Users Manual for PROTIM -Probabilistic Analysis ofTime Domain Simulation Results’, Det Norske Veritas Research A.S.Report no. 89-2038, 21st December 1989.Ronold, K.O.(1990), ‘Long Term Reliability of a Jackup Foundation’, Proc. 3rd IFIPWorking Conf. on Reliability and Optimisation of Structural Systems, Berkeley, California,1990.Sarpkaya, T.; and Isaacson, M.(1981), ‘Mechanics of Wave Forces on Offshore Structures’Van Norstrand Reinhold Publication, 1981.Sesam(1993), ‘Integrated System for Structural Design and Analysis’, Sesam User’s Manual,Sesam System DNV Sesam A.S., 1st January 1993.Scot Kobus L.C., et al.(1989), ‘Jackup Conversion for Production’, Marine StructuresDesign, Construction and Safety, Vol.2, 1989.
    • Guidelines for Offshore Structural Reliability Page No. 48-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Report No. 95-0072Sharples, B.P.M., Trickey, J.C., and Bennet, W.T.(1989), ‘Risk Analysis of Jack-Up Rigs.’,Proc. 2nd Intern. Conf. Jack-Up Drilling Platform, Design, Construction and Operation.(Ed.L.F. Boswell and C.A. DMello). Elsevier Applied Science, London, UK pp. 101-123.Singh, S.(1989), ‘Uncertainties in the Estimation of Fluid Loading on Offshore Structureswith Special emphasis on Wind Forces’, Trans. Inst. Marine Engineers, Vol 101, Part 6,1989.SNAME(1993), ‘Site Specific Assessment of Mobile Jackup Units, Guideline,Recommended Practice, and Commentaries’, S.N.A.M.E., Techn. & Research Bulletin 5-5,1993Standing, R.G. and Rowe, S.J.(1993), ‘Stability and Seakeeping Review for Jackups inTransit’, Proc. of the 4th Int. Conf. on the Jackup Platform, 1993Stewart W.P. et al.(1991),‘Observed Storm Stability of Jackup Boats (Liftboats)’, OTC 6611,1991USFOS (1996), ‘USFOS -A Computer Program for Progressive Collapse Analysis of SteelOffshore Structures”, SINTEF Report no. STF71 F88039, Dated 1996-01-01Vanmarcke, E.H. (1977). ‘Probabilistic Modelling of Soil Profiles.’, ASCE. Journ. ofGeotechnical Engineering. V 103, No 11, pp. 1227-1246.Vanmarcke, E.H. (1984). ‘Random Fields.’, MIT Press. Cambridge, Mass, USA. 382p.Wang, X., and Moan, T.(1993), ‘Reliability Analysis of Production Ships’, Proc. ISOPEConf., Osaka, 1993Wheeler, J. D.(1969), ‘Method for Calculating Forces Produced by Irregular Waves’, OTC1006, 1969