JACKUP EXAMPLE - LIST OF CONTENTS - DNV

Guidelines for Offshore Structural Reliability Page No. 1-DNV Application to Jackup Structures------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Report No. 95-0072

LIST OF CONTENTS

Section Title Page

1.0 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 6

2.0 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 16

3.0 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 24

4.0 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 33

5.0 SUMMARY OF APPLICATION EXAMPLES 345.1 General 345.2 Overview of Analytical Procedure 345.3 Structural Reliability Example 365.4 Foundation Reliability Example 38


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Section Title Page

6.0 RECOMMENDATIONS FOR FURTHER WORK 416.1 General 416.2 Elevated Condition 416.3 Floating / Installation Phase Conditions 42

7.0 REFERENCES 44


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1.0 INTRODUCTION

1.1 Objective

The 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 General

The 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 structuresshould be treated with a good deal of suspicion as they may not be representative for thetype of structure required to be considered.

� These guidelines are intended to deal primarily with conventional design, larger sizejack-ups, namely those intended to operate in waterdepths in excess of, say, 50 metres. Atypical arrangement of such a unit is shown in Figure 1.1 below, Bærheim (1993).

1.3 Modes of Operation

A 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 lifecycle, 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 atspecific sites, Bærheim (1993), Scot Kobus (1989), e.g. as work-over or production units.


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Such units may been designed to operate in extreme environmental conditions, atrelatively large waterdepths for a period in excess of 20 years.

Figure 1.1 : Arrangement of a Typical Harsh Environment Jack-up

1.4 Important Structural Design Parameters

Jack-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 beingconstructed 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


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support 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 steel

Method 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.


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1.5 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.


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2.0 RESPONSE

2.1 General

Jack-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 ofoperation whilst it deals only in general terms with jack-ups in the floating mode.

2.2 Jack-up Response in the Floating Mode

A 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


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relevant 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 ondeck (‘green seas’), slamming, damping (especially at and around resonance periods),non-zero transit speed etc. are significant, then it is necessary to utilise time-domainsimulation and/or model test data.

� The use of strip theory or Morison formulation to compute the total sea loadings on ajack-up in transit will normally be inappropriate.

� In connection with the prediction of motion responses, notwithstanding account taken ofrelevant non-linear loading effects, it seems reasonable to refer to ship or barge relatedreliability data (e.g. Frieze (1991), Lotsberg (1991), Wang and Moan (1993)).

� When evaluating leg strength at critical connections, transfer functions for element forcesand moments (or stresses) may be calculated directly from the rig’s motions analysis. Amodel 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 ultimatestrength 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 besignificant is the modelling of any gaps between jackhouse guides and chords.

� Reliability analysis of seafastening arrangements is documented, DNV (1992). Thegeneralities of this documented example and the procedure utilised may also be appliedto seafastenings for a jack-up unit under transit. If direct wave impact on the item held bythe seafastening is a possible designing load, then such loading and associated loaduncertainty should additionally be included within the analysis.


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Figure 2.1 : Typical Hydrodynamic/Structural Model of a Jack-up in the Transit Condition.


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2.3 Jack-up Response in the Elevated Mode of Operation

Response 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 andthe leg member)

- dynamics of the structure (as the natural period of the structure is typically relativelyhigh, e.g. 5-8 seconds, there may be significant wave energy available to excite thestructural system and hence relatively large inertial forces may result)

- second order effects (such effects may significantly influence the response in theconsidered 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 andresponse, it is considered necessary that explicit time domain analysis, utilisingstochastic 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-linearcharacteristics in the foundation system should be explicitly modelled when undertakinganalyses in connection with reliability studies.

� Guidance provided in the guideline example for jacket structures, DNV (1996c), inrespect to the fatigue limit state covers the state-of-the-art knowledge with respect tofatigue reliability analysis. Response in respect to the fatigue limit state is therefore notexplicitly covered in this section. Due to the non-linear characteristics of jack-up loadingand response, frequency domain solution techniques are however not recommendedunless, either it can be demonstrated that such effects are insignificant, or, due accounthas been taken of such effects.


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2.3.1 Time Domain Analysis

Two 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 regularwave components utilising divisions of equal energy of the wave spectrum.

2. In order to obtain sufficiently stable response statistics, simulation time for a singlesimulation should generally not be less than 60 minutes.

3. The integration time step should not normally be taken greater than the smaller of thefollowing ;- 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 theanalysis should be removed. At least the smallest of 100 seconds, or 200 time stepsshould 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 qualificationprocedure adopted for the analysis. -Further guidance in connection with this item isprovided 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)


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As 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 simplifiedhydrodynamic and simplified structural model for a jack-up is included in DNV( Feb1992) 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 thefollowing 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 ofanalytical work involved, wind, wave and current load components may howevernormally be assumed to be coincident.

-3- The selected (governing) environmental load direction may be initially identifiedby 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 ifthese extremes occur simultaneously, is conservative. In most cases however, jack-up environmental loading is wave dominated and the assumption of simultaneity ofthe extremes of the environmental parameters is found to be satisfactory.


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The 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 annualtarget reliabilities.

� For jack-ups, the two most appropriate procedures for estimation of extreme load eventswould 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 ; �x, �x, �x’, �3, �4, 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 methodologyin 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.


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2.3.3 Static Loading Components

Previous 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 structuralassessment the upper bound of this sum is normally conservatively modelled. Foroverturning assessment the mean variable load is combined with the permanent load.

2.3.4 Sea Loadings

Sea loadings on conventional jack-up structures are calculated utilising Morison’s equation,Sarpkaya (1981) ;

F r t D C a r t DC v r t v r tn m n d n n( , ) ( , ) ( , ) ( , )� ��

�

2

412

(2.2)

Wave 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 Loadings

The 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 thanthat necessarily associated with storm maximum significant wave height, a range ofperiods and associated significant wave heights should normally be investigated.

� The simulated storm length is normally to be taken as 3 hours, SNAME (1993) or 6hours, NPD (1992).


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For 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(�) may be utilised ;

F(�) = C. cos2n� for -�/2 � � � �/2 (2.3)

where ;n : 2.0 for fatigue analysis

4.0 for extreme analysis

C : constant chosen such that : �

� ��

�

� �/

/ ( ) .2

2 10F dCurrent 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 ofwind and wave generated current, V(w,w) and that of residual (e.g. tidal) current, Vr. Thefirst of these two current components may be assumed to be fully correlated with thesignificant wave height, whilst the latter current component, Vr, is assumed to becompletely 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 Loadings

Singh (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 directtesting, or from scaling of geosim models, then, assuming that wave loading is thedominating 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 � Vref² Ch Cs Aw (2.4)

where� : density of airVref : the 1 minute sustained wind velocity at 10 meters above sea levelCh : height coefficientCs : shape coefficientAw : projected area of the block considered

In locations where wind loading may be the dominating load effect (e.g. due to cyclones etc.)this load effect should be specially considered.


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2.3.6 Foundations

The 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 thejack-up location prior to installation in order to identify the potentially problematic weaksoil 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-


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up 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 lognormaldistribution function appears to provide a good fit to the foundation capacity, Nadim andLacasse (1992).

� The properties of the volume of soil under the footing fluctuate spatially and can berepresented 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 theavailable data. Mean and standard deviation are calculated by ordinary statisticalmethods, e.g. Ang and Tang (1975). Usually the probability distribution function used torepresent geological processes follows a normal or lognormal law. More often than nothowever, and especially in the case of jack-up structures, there are not enough data


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available, and the designer needs to use correlations or normalised properties as afunction 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.


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3.0 UNCERTAINTY MODELLING

3.1 General

This section provides general guidance in respect to uncertainty modelling as appropriate tothe extreme load event for a jack-up structure.

3.2 Loading Uncertainty Modelling

Uncertainty 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 Uncertainty

Tables 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 - conditionalon Hs)

Marine Growth Lognormal

Table 3.1 : General Environmental Variable Distributions

Description 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


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Description DistributionSignificant wave height (Hs) Gumbel *1, 2

Total current speed (Vc) Gumbel *1, 2

Average wind speed (U10m) Gumbel *1, 2

Table 3.3 : Extreme Analysis Variable Distributions

KEY :

*1 : Normally it is sufficient to consider the extreme dominating variable being either ; -the significant wave height, -thecurrent, or, -the wind speed, in combination with this extreme distribution the remaining two variables are assignedthe 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 tothe 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 beingpossible 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 � 1 C.o.V.

Drag coefficient 2 (CD) Lognormal 1.0 0.2Inertia coefficient 3 (CI) Lognormal 1.0 0.1Marine growth 4 Lognormal 1.0 0.2Mass of structure 5 Lognormal 1.0 0.14

Table 3.4 : Load Model Uncertainty Variables

KEY :

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


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3.3 Response Uncertainty Modelling

� Significant contributions to response model uncertainty may be attributed to thefollowing causes, Nadim (1994), Løseth (1990), Karunakaran (1993);

-Analytical uncertainty -Damping ratio-Foundation stiffness

3.3.1 Analysis Uncertainty

Analytical 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 � C.o.V.Analytical uncertainty Lognormal 1.0 0.18

Table 3.5 : Analytical Model Uncertainty Variables

3.3.2 Damping

Damping 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 20 (3.1)

where u : water particle velocity Tn : first natural period in surge/swayDi : diameter of leg chord

� For extreme response analysis, in general, hydrodynamic damping may normally beexplicitly accounted for by use of the relative velocity formulation in Morison’sequation.

� A value for total global damping may be obtained by summation of those appropriatedamping component percentages stated in Table 3.6, SNAME (1993).


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Damping Source Global Damping (% of critical damping)

Structure, holding system etc. 2%Foundation 2% or 0% 1

Hydrodynamic 3% or 0% 2

Table 3.6 : Table of Recommend Critical Damping

KEY :

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 � 1 C.o.V.Damping ratio Lognormal 1.0 0.25

Table 3.7 : Damping Model Uncertainty Variables

KEY :

1 : The absolute value of the distribution variables are given relative to the value applied in the structural analysis.

3.3.3 Foundation

For 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 withdeterministic calculations, expert opinions and information from literature, in addition toany field observations that are available for similar structures on comparable soilconditions, 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.


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The “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*1

Rotational stiffness LognormalHorizontal stiffness LognormalVertical stiffness Lognormal

Table 3.8 : Foundation Parameter Distributions

KEY :

*1 : See also section 2.3.6


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3.4 Resistance Uncertainty Modelling

The 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 modelincluded in the limit state under consideration. Modelling of the uncertainly parametersassociated with the resistance model should be relevant to the formulation of theresistance 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 inmany cases only be performed by using advanced non-linear finite element software, e.g.USFOS (1996).


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4.0 LIMIT STATES

4.1 General

Limit 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 toapplied actions.

b.) The serviceability limit states that correspond to the criteria governing normalfunctional 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 tocomponents 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 Structures

Serviceability 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 bedesigning.

� The guidance provided in the guideline example for jacket structures, DNV (1996c), inrespect 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 andreference should be made to DNV (1996c) for appropriate guidance concerning thefatigue 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 arigid body (e.g. overturning or capsizing),

b.) failure of critical components of the structure caused by exceeding the ultimatestrength ( in some cases reduced by repeated actions) or the ultimate deformation ofthe components,


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c.) 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), and

f.) sinking.

� The ultimate limit state for jack-up structures is difficult to describe through simpledesign equations. Additionally, general guidelines on how to perform structural systemcollapse 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 relevantcomponent limits states for reliability analyses ;

-1- Leg element yield-2- Leg element buckling-3- Leg joint capacity-4- Foundation bearing failure-5- Holding system capacity

System (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 dueto specified accidental events and subsequently maintain integrity for a sufficient periodunder specified environmental conditions to enable evacuations to take place. Theaccidental events and the consequences of such events are normally based uponQuantitative Risk Analyses (QRA). For further details on QRA reference should be madeto DNV (1996a), Chapter 2.

4.2 The Ultimate Limit State


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This subsection describes in more detail Ultimate Limit State criteria documented insubsection 4.1.1.

4.2.1 Leg Strength

GeneralAs 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 codesand 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 certainlimits (e.g. R/t ratio between given limits). It should therefore be ensured that theresistance formulation utilised in the limit state is satisfactory for the structure underconsideration.

(ii) The resistance formulations contained within these codes are based upon analyticalapproximations to the physical behaviour where characteristic values are defined atsome fractile value or lower bound value. For reliability analysis the capacityformulation 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 APIbuckling curve, API (1993) is derived as a lower bound value for low slendernesswhile it is equal to the Euler stress for high slenderness values, which may beconsidered as an upper bound value in that region. Another definition of a bucklingcurve is used in AISC (1984). The background for the buckling curves used in designof steel structures in European design standards is based on work carried out withinthe European Convention for Constructional Steelwork which is presented in TheManual on Stability of Steel Structures, ECCS (1976). The design curves arepresented by their characteristic values which are defined as mean values minus twostandard deviations along the slenderness axis. The test results are assumed normaldistributed.

(iii) Effective buckling lengths are dependent upon joint flexibilities. Buckling lengthsmay 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 lengthsdepend upon the amount of tension loading in the crossing member. The effectivelengths may be derived from analytical considerations. The effective buckling


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lengths derived from tests of frame structures until collapse are generally shorter thanthose derived from theoretical calculations.

(iv) Different allowable requirements to fabrication tolerances (eccentricity) areassociated with the various buckling curves. For European buckling curves astraightness deviation at the middle of the column equal to 0.0015 times the columnlength is allowed, while for API (1993) and AISC (1984) the corresponding numbersare 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 f y a by bz xy xz t� � � � � � ��

2 23 (5.1)

where

fy = material yield strength �a = axial stress component

t� = torsional shear stress component �by , �bz = bending stress components

xy� , xz� = plain shear stress components

The 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 ;

� �G X PP

MM

MMbias

u

n

uex

nx

uey

ny

� � ��

��

��

�

��

�

�

�

�

��

1 89

1� � �

(5.2)

Where ;Pu is the chord axial loadPn is the chord nominal axial strength in compressionMuex is the chord local effective applied bending moment about the local x-axisMuey is the chord local effective applied bending moments about the local y-axisMnx is the chord local nominal bending strength about the local x-axisMny is the chord local nominal bending strength about the local y-axis� is the exponent for biaxial bending.


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A 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 Capacity

Joint 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 ;

� �G X NN

MM

MMbias

k

IP

IPk

OP

OPk

� � ��

��

�

� �1

2

(5.3)

where

Xbias = bias (See DNV (1996a), Chapter 7.2) N = brace axial forceNk = characteristic capacity of the brace subjected to axial forceMIP = brace in-plane momentMIPk = characteristic capacity of the brace subjected to in-plane momentsMOP = brace out-of-plane momentMOPk = characteristic capacity of the brace subjected to out-of-plane moments

A detailed description of this limit state is given in DNV (1996c).


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4.2.2 Foundation Bearing Failure

The 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 = ( ) ( ) ( / )V P H M rex w ex ex� � �2 2 2 (5.4)

R = ( ) ( ) ( / ), , ,V P H M rcy f w cy f cy f� � �2 2 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 System

The 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.


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Figure 4.1 : Definition of Limit State Function for a Footing on Clay with Moment Fixity.


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4.2.4 Global Deflections

The 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 Strength

The 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 Stability

Jack-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 moment

When considering the moments in connection with this limit state it is important to ensurethat the axis of rotation of the system is fully considered.


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4.3 Literature Study

From 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)


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5.0 SUMMARY OF APPLICATION EXAMPLES

5.1 General

This 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 Consolidation The 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 Growth Marine growth diameter thickness’ according to the values recommended by the NPD (1992)were applied.

- Deckbox Mass The 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 Procedure

Utilising site specific criteria, detailed deterministic and simplified dynamic, non-linearanalyses were undertaken in order to determine appropriate jack-up response statistics.


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Long 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.

Figure 5.1 : Overview of Analytical Procedure

DETAILED MODELANALYSES(Deterministic Sea)

WAJAC

ESTABLISH CRITICALPARAMETERS ;-Load Direction-Design Criteria-Element-Foundation soil springs

DESIGNCRITERIA

SIMPLIFIED MODELANALYSES(Stochastic Sea)

FENRISFENSEA

ESTABLISH THERESPONSE STATISTICS ;-Force and moment for themost critically loadedstructural element-Force and moment for themost utilized footing

PROTIMPROBAN

STRUCTURAL RELIABILITYOUTPUT : The annual probabilityof failure for the most criticallyloaded structural element.(Determined by establishing the longterm statistics consideringindependent seastates)

ESTABLISHPROBABILISTIC BEARINGCAPACITY MODEL for thedifferent combinations offorce and moment on mostutilized footing

ESTABLISHDISTRIBUTIONS OFANNUAL EXTREMES forforce and moment on mostutilized footing

FOUNDATION RELIABILITYOUTPUT : The annualprobability of failure for themost utilized footing.


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5.3 Structural Reliability Example

This 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 : � = 4.35 - Consolidated Soil : � = 4.41

Variable Unconsolidated SoilImportance Factor

Consolidated SoilImportance Factor

Significant Wave Height, Hs 56% 44%Randomness of Storm Extreme, Uaux 16% 15%Drag Coefficient, CD 11% 15%Critical Stress, Fcr 9% 10%Heading, � 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


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ConditionVariable Mean / Lower

BoundCoV / Upper

BoundMean /

Lower BoundCoV / Upper

BoundEnvironment N/A -0.3138 N/A -0.2611Rotational Stiffness, Kr 0.0202 -0.0038 0.0286 -0.0227Vertical Stiffness, Kv -0.0063 0.0002 0 0Lateral Stiffness, Kh -0.0008 0 0 0Drag Coefficient, CD -0.1686 -0.0379 -0.1847 0.0497Tidal current, VT -0.0340 0.0007 -0.0316 0.0005Marine Growth -0.0025 0.0001 -0.0186 0.0001Damping -0.0090 0.0003 -0.0369 -0.0013Deckbox Mass 0.0193 -0.0007 0.0600 -0.0043Wave Spreading, n -0.0037 -0.0377 -0.0048 -0.0764Waterdepth, D 0.0074 0.0075 0.0322 0.0315Spectral Peak Parameter, � -0.0008 -0.0040 -0.0019 -0.0134Heading, � -0.0424 -0.1728 -0.0260 -0.0637Yield Strength, fy 0.0054 0 0 0Critical Stress, Fcr 0.2525 -0.0421 0.2643 -0.0467Duration, D -0.0195 N/A -0.0197 N/ANo. of Seastates, Nsea -0.0214 N/A -0.0214 N/A

Table 5.2 : Sensitivity Analysis of Results (�� for a 10% increase in the meanvalue

and CoV for selected variables)

Key :N/A : Not applicable

The 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.


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5.4 Foundation Reliability Example

The foundation reliability example documented in DNV (1996b) demonstrates ultimate limitstate analyses undertaken for the stability of the most utilised footing for 'unconsolidated' and'consolidated' 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 CoV's 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 CoVUnconsolidated 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 Parameters

The 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.


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VARIABLE Distribution Mean CoVUnconsolidated 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 ConditionVex - 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 Footing

When 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 : � = 4.11 - Consolidated Soil : � = 4.22

Variable Unconsolidated SoilImportance Factor

Consolidated SoilImportance 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


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There 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 (� = 3.71 to4.26) is appropriate. The safety indices of � = 4.11 for the unconsolidated soil condition and� = 4.22 for the consolidated soil condition would therefore appear to be satisfactory.


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6.0 RECOMMENDATIONS FOR FURTHER WORK

6.1 General

From 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 withidentification of the reliability of jack-up structures.

6.2 Elevated Condition

Jack-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 incurrent 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 structuresare, 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 andstandards should be evaluated for their applicability to deep water, harshenvironment 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 jacketstructure. (The U.K., H.S.E. is currently engaged in such a project and the findingsfrom these workings should be considered in this connection.)


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-3- Traditional, frequency domain (linear analysis) based fatigue reliability should becompared with that reliability achieved utilising time domain (non-linear) analysis inorder to identify, for a jack-up structures, the importance of the non-linear effects forthe fatigue limit state.

-4- Reliability considering the following foundation related criteria is recommended tobe investigated ;-system effects-response as related to the uncertainty and non-linearity in foundational support.

6.3 Floating / Installation Phase Conditions

Of 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 thetransit 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 mostfrequently-encountered foundation problem for jack-ups.

� The physics of the impact loading problem are extremely complicated and theuncertainties in the process are not well documented. Additionally, regulationrequirements for the installation condition are considered to be vague and incomplete.


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Conclusions :

-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 processand to identify areas where further workings are required.

-2- Reliability investigations in the installation phase should be considered for thefollowing listed loading conditions ;-preloading-impact loading.


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7.0 REFERENCES

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