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Guidelines for Offshore Structural Reliability Page No. 1
-DNV Application to Jackup Structures
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Report No. 95-0072

LIST OF CONTENTS

Section Title Page

1.0 INTRODUCTION 3
1.1 Objective 3
1.2 Jack-ups in General 3
1.3 Modes of Operation 3
1.4 Important Structural Design Parameters 4
1.5 Arrangement of Report 6

2.0 RESPONSE 7
2.1 General 7
2.2 Jack-up Response in the Floating Mode 7
2.3 Jack-up Response in the Elevated Mode of Operation 10
2.3.1 Time Domain Analysis 11
2.3.2 Methods of Evaluating Response 12
2.3.3 Static Load Components 14
2.3.4 Sea Loadings 14
2.3.5 Wind Loadings 15
2.3.6 Foundations 16

3.0 UNCERTAINTY MODELLING 19
3.1 General 19
3.2 Loading Uncertainty Modelling 19
3.2.1 Aleatory Uncertainty 19
3.2.2 Epistemic Uncertainty 20
3.3 Response Uncertainty Modelling 21
3.3.1 Analysis Uncertainty 21
3.3.2 Damping 21
3.3.3 Foundation 22
3.4 Resistance Uncertainty Modelling 24

4.0 LIMIT STATES 25
4.1 General 25
4.1.1 Limit States Appropriate to Jack-up Structures 25
4.2 The Ultimate Limit State 27
4.2.1 Leg Strength 27
4.2.2 Foundation Bearing Failure 30
4.2.3 Holding System 30
4.2.4 Global Deflections 32
4.2.5 Global Leg Buckling 32
4.2.6 Overturning Stability 32
4.3 Literature Study 33

5.0 SUMMARY OF APPLICATION EXAMPLES 34
5.1 General 34
5.2 Overview of Analytical Procedure 34
5.3 Structural Reliability Example 36
5.4 Foundation Reliability Example 38

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Section Title Page

6.0 RECOMMENDATIONS FOR FURTHER WORK 41
6.1 General 41
6.2 Elevated Condition 41
6.3 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 guidelines
appropriate to self-elevating unit structures (hereafter referred to as ‘jack-ups’). With this
intention 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 joint
probability 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-up
design 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, for
example ; tender assist, accommodation, drilling or production.

Thus, the term jack-up may represent a structure that has a mass of a few hundred tonnes and
is capable of elevating not more than a few metres above the still water surface, to a structure
that has a mass of over 20,000 tonnes and is capable of operating in water depths in excess of
100 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 Operation

A jack-up generally arrives on location in the self-floating mode. The transportation of the
jack-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 will
take place, which will typically involve elevating the hull structure to a predetermined height
above 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, before
jacking down, raising the legs to the transit mode condition, and transferring to the next
location.

· 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.

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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-up

1.4 Important Structural Design Parameters

Jack-up designs varying from being monotower structures (single leg designs) to multiple leg
designs, 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 profile
design.

· 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 important
variables may be listed as stated below.

Support Footing
The legs of a jack-up are connected to structure necessary to transfer the loadings from the
leg 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 such
footing 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).

Legs
The legs of a jack-up unit are normally vertical, however, slant leg designs also exist. Design
variables 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 legs
The method of transferring the loadings from (and to) the deckbox to the legs is critical to
design 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.

Deckbox
The deckbox is normally designed from stiffened panel elements. The shape of the deck
structure may vary considerably from being triangular in basic format to rectangular and even
octagonal. The corners of the deckbox may be square or they may be rounded. Units intended
for 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 the
middle of the deckbox structure are not unknown.

There are a large number of solutions available to the designer of a jack-up unit and, although
series units have been built, there exist today an extremely large number of unique jack-up
designs.

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1.5 Arrangement of Report
Response of jack-up structures is described in Section 2, together with relevant methods for
computation of the resulting load effects. Model uncertainties associated with the
computation of these load effects are discussed in Section 3. Important limit states together
with stochastic modelling of failure modes are described in Section 4. Section 5 provides a
summary 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 TLP
structures.

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2.0 RESPONSE

2.1 General

Jack-up units are normally designed to function in several different operational modes. These
modes 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 that
of the jack-up in the as-installed, elevated condition. Both of these modes are critical to the
safe operation of a jack-up unit as each mode of operation may impose its own limiting
design criteria on certain parts of the structure.

To provide relevant guidance with respect to the stochastic properties and probabilistic
analytical procedures for both of these modes of operation, is considered to be too large an
undertaking 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 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 own
propulsion system, or, be ‘wet’ towed to the new location. For ‘ocean’ tows, on the other
hand, 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 transit
condition, 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, whilst
foundation failure is a condition occurring when the jack-up is normally elevated above the
still water surface.

The retrieval phase of a jack-up has not traditionally been considered as providing
dimensioning load conditions. However, when a leg is held fast at the seabed, e.g. due to
large penetrations, there may be large loadings imposed upon the jack-up structure. Such
loadings may result from the action of waves, current, wind, deballasting and jacking up
loadings.

Few model tests, or full-scale measurements, have been undertaken for jack-ups in the
floating 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 six
relevant 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 damping
and natural periods, measurements in heave, roll and pitch motions in regular and irregular
waves at zero speed, and measurements of resistance, heave, roll and pitch in regular and
irregular waves at 6 knots tow speed. A number of the tests were repeated with the legs raised
or lowered various distances. Some full scale results were also published.

Comparisons with linear wave theory, based upon potential flow assumptions, predict roll
and 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 damping
assumptions). The results from the published jack-up model test data seem to be consistent
with findings from ships and barges, i.e. that roll response at resonance is overestimated
unless due account is taken of the increased damping resulting from viscous effects.
Generally, levels of measured and predicted heave motions in regular waves agreed
reasonably 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 pitch
damping, compared with similar results at zero speed, with reduced response at the natural
period. 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.

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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 extensively
studied, Ahilan (1993), with relevant analytical methodology being described in detail in the
Jack-up Recommended Practice, SNAME (1993).

The response of jack-up structures, when subjected to random sea excitation, is found to be
non-Guassian in nature. Due to the non-linearities in the structural system the extreme
responses are generally found to be larger than the extremes of a corresponding Gaussian
process, Karunakaran (1993).

Relevant, non-linear effects that may be significant in respect to response of jack-up
structures 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.

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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 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, is
not reproduced in methods based upon random wave simulation techniques. Linear wave
theory, Sarpkaya (1981), utilised in random wave simulation, accounts for particle kinematics
upto the still water surface and ‘kinematic stretching’ is undertaken to compute the
kinematics 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 25
metres, in extreme environmental conditions, irregular wave simulation is normally
considered to be inappropriate and regular wave analysis should be considered. For
waterdepths greater than 25 meters wave asymmetry may be accounted for by the formulation
given 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 normal
practice 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.

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The probability of failure is estimated during a reference period significantly longer than the
analysed, simulated time period. An extrapolation procedure for determining the extreme
values for the reliability analysis is therefore required when several environmental variables
are 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). For
conventional jack-up structures, in general, the long term response is controlled by the
extreme sea states and, as such, both of these procedures are normally acceptable. An
example of the estimation of extreme load events by use of long term statistics of
independent sea states is provided in the jack-up examples guidelines DNV (1996b).

Karunakaran (1993) documents that the short term extreme storm response is marginally
higher than the long term response if the long term response is controlled by extreme sea
states. If however the long term response is controlled by resonance sea states, the short term
extreme storm response is about 10% lower than the long term response for those case
studies considered.

Response from time history simulations may be characterised by the normalised statistical
moments ; mx, sx, sx’, g3, g4, which are the mean, standard deviation, standard deviation of the
time derivative, skewness and kurtosis of the response respectively. A limit state may then be
defined from the statistical moments of the response and the estimated reliability thus
obtained 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 at
one estimation point. As the limit state functions are highly non-linear this technique will
only 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 and
second 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), have
identified that response uncertainty is not significantly affected by the choice of the static
mass 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 Loadings

Sea 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 2

Wave and current velocity components in the Morison equation are obtained by combining
the vectorial sum of the wave particle velocity and the current velocity normal to the member
axis. (When relative motions are involved, eqn 2.2 may be modified to reflect such motions
in 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 choice
of the analytical wave spectrum and associated spectral parameters should reflect the width
and 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).

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For the extreme load event it is normally, conservatively assumed that a long crested sea
simulation is undertaken, NPD (1992), however, in accordance with SNAME (1993) the
following 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 /2
C : 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 according
to the procedure documented in SNAME (1993).

2.3.5 Wind Loadings

Singh (1989) has found a number of inconsistencies in existing wind loading calculation
procedures. Based upon this finding it has been concluded that wind tunnel measurements
appear to provide the only viable method for accurately estimating loads on complex offshore
structures.

· 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)

where
r : density of air
Vref : the 1 minute sustained wind velocity at 10 meters above sea level
Ch : height coefficient
Cs : shape coefficient
Aw : 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 soil
characteristics that determine the resistance of the foundation to the forces imposed by the
jack-up structure. Ronold (1990) showed that, for a jack-up, the total uncertainty governing
the safety against foundation failure is dominated by the uncertainty in the loading. Nadim et
al. (1994), on the other hand, showed that the response of a jack-up structure subjected to a
combination of static and cyclic loads is just as much influenced by the uncertainties in the
loads as by the uncertainties in the soil resistance. The significant discrepancy between these
results is due to the different assumptions made with respect to the uncertainties in the
variables. One should therefore be careful in generalising the results obtained for a specific
site to other environmental and soil conditions.

For traditional jack-up foundation solutions, the stability and performance of a jack-up
foundation is primarily determined by the installation procedure for the unit. This operation
involves elevating the hull and pumping water ballast into the preload tanks, causing the
spudcans 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 basis
has 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. The
skirted footings not only provide more predictable capacity, they also increase the footing
fixity significantly. The procedure for estimating the capacity of the individual footings is
based upon analytical procedures similar to that undertaken for foundation of gravity based
structures. For jack-up foundation systems, however, it is important to look at the complete
foundation ‘system’ because at loads close to failure, significant re-distribution of reactions
among the footings may take place. (Refer to the foundation example in DNV (1996c) for
more information in respect to this item.)

It is evident from statistics, Sharples et al. (1989), Arnesen et al. (1988), that punch-through
during 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 soil
layer.

· 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 for
the 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, or
greater than, the maximum vertical reaction arising from gravity loads and 100% of
environmental loads. The preload defines the static foundation capacity under pure vertical
loading immediately after installation. Under the design storm the footing is subjected to
simultaneous action of vertical and horizontal loads, and overturning moment. The storm
induced loads are cyclic with a short duration and the supporting soil may have a higher
reference 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 a
footing 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) suggests
a phased method with three steps, increasing in the order of complexity, for the evaluation of
foundation capacity, as follows :

Step 1. Preload Check
The foundation capacity check is based on the preloading capability - assuming pinned
footings.

Step 2. Bearing Capacity Check
Bearing capacity check based on resultant loading on the footing under the design storm.

Step 3. Displacement Check
The displacement check requires the calculation of displacements associated with an
overload situation arising from Step 2.

Any higher level check need only be performed if the lower level checks fail to meet the
foundation 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 foundation
bearing 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 vertical
preload. The bearing capacity calculations are performed probabilistically using the FORM
approximation. The procedure developed by Nadim and Lacasse (1992) was used by Nadim
et 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 capacity
under a given combination of horizontal and vertical loads (and overturning moment if
spudcan fixity is significant) and the foundation capacity under pure vertical loading. The
degree of correlation determines the significance of the measured preload on reducing the
uncertainty 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

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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-situ
overburden stress is about 0.23 ± 0.03 for a horizontal failure mode; the friction angle of sand
can 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 to
the extreme load event for a jack-up structure.

3.2 LoadingUncertaintyModelling

Uncertainty in the load process may be attributed to either aleatory uncertainty (inherent
variability and natural randomness of a quantity) or epistemic uncertainty (uncertainty owing
to limited knowledge). In respect to jack-up reliability analysis, guidance appropriate to the
most 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 selected
stochastic variables. It should be noted however that site specific evaluation of environmental
variables may dictate use of variable distributions other than those recommended in the tables
below. For further guidance see also DNV (1996a), Chapter 5.

Description Distribution
Randomness of storm extremes Poisson
Waterdepth (D) Uniform (tidal effects), or,
Normal (storm surge effects - conditional
on Hs)
Marine Growth Lognormal

Table 3.1 : General Environmental Variable Distributions

Significant wave height (Hs) 3-parameter Weibull/Lognormal
Zero 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) Uniform
Wind 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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Significant 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, -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 model
uncertainty 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
3
Inertia coefficient (CI) Lognormal 1.0 0.1
Marine growth 4 Lognormal 1.0 0.2
Mass 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 the
following 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 statistical
accuracy of a single analytical simulation (i.e. the variability resulting from different
engineers, utilising different software, undertaking exactly the same analysis). With respect
to jack-up response analysis this uncertainty is documented in DNV (1996a), Chapter 6.

Guidance to selection of distribution type and distribution parameters for random analytical
uncertainty factors is given in Table 3.5 below.

Basic Variable Name Distribution m 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 including
damping within the response analysis, Langen (1979). Relative velocity, hydrodynamic
damping should generally not be used if Eqn. 3.1 below is not satisfied, SNAME (1993).

uTn/Di ³ 20 (3.1)

where
u : water particle velocity
Tn : first natural period in surge/sway
Di : 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).

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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 damping
uncertainty 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 0.25

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 comparable
full scale prototypes that have actually gone to failure and where there was enough
knowledge about the site conditions and the load characteristics to enable calculation of the
uncertainty.

· 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 the
spudcan of a jack-up foundation results in large model uncertainties, as was documented by
Endley et al. (1981). They compared, for 70 case studies on soft clays and 15 case studies on
layered profiles consisting of soft clay over stiff clay, predicted rig footing penetration with
observed penetrations. The comparisons suggest a model uncertainty with mean value 1.0
and standard deviation 0.33, as based on the 70 cases studied. The observed data ranged
between 0.4 and 1.55 times the predicted values.

McClelland et al. (1982) undertook similar comparisons for jack-ups on uniform clay profiles
and for jack-ups on layered profiles. In this study the standard deviation was about 0.20 to
0.25 about a mean of 1.0.

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Report No. 95-0072

The “traditional" methods of analysis are the so-called "bearing capacity formulas” which do
not account for strength anisotropy, cyclic loading, soil layering, nor variation of soil
properties with depth or laterally. The model uncertainty values quoted above are valid for a
failure mode under vertical loading only.

In the method proposed by Nadim and Lacasse (1992), a more rigorous bearing capacity
approach than the "traditional" approach is used. The analysis uses a limiting equilibrium
method of slices. Effects of anisotropy and cycling loading, the uncertainty in the calculation
model for both vertical and horizontal (moment) loading and combined static and cyclic
loading are included. The uncertainty in this calculation model was studied in detail with
series 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 of
a footing in clay may be mean 1.00, standard deviation 0.05 for failure under static loading
only, and mean 1.05, standard deviation 0.15 for failure under combined static and cyclic
loading. For footings installed in sand, much less information exists, and tentative values may
be mean 1.00, standard deviation 0.20 to 0.25, based on engineering judgement and the
results of recent centrifuge model tests, Andersen et al. (1994). The model uncertainty may
vary according to the failure surface. It should be noted that the mean of model uncertainty
factor for most offshore foundations (e.g. piles in sand and clay, shallow foundations on
sand) is greater than 1.0, i.e. the analytical models tend to be conservative. The methods
developed for shallow foundations on clay, however, have been fine-tuned and calibrated
against large-scale tests in the past 20 years, and much of the inherent conservatism in the
methods has been removed.

Little information exists on the model uncertainty associated with the foundation
displacement of a jack-up structure (see step 3 in section 2.3.6) and the model uncertainty can
only be guessed for those cases. A model uncertainty with a coefficient of variation of at least
50 % is expected.

Guidance to selection of distributions associated with the foundation parameters is given in
Table 3.8 below. Reference should also be made to DNV (1996a), Section 7.3.

Description Distribution*1
Rotational stiffness Lognormal
Horizontal stiffness Lognormal
Vertical stiffness Lognormal

Table 3.8 : Foundation Parameter Distributions
KEY :

*1 : See also section 2.3.6

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