Guidelines for Offshore Structural Reliability
-DNV Application to Jackup Structures
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Report No. 95-0072
LIST OF CONTENTS
Section
Title
Page
1.0
1.1
1.2
1.3
1.4
1.5
INTRODUCTION
Objective
Jack-ups in General
Modes of Operation
Important Structural Design Parameters
Arrangement of Report
3
3
3
3
4
6
2.0
2.1
2.2
2.3
2.3.1
2.3.2
2.3.3
2.3.4
2.3.5
2.3.6
RESPONSE
General
Jack-up Response in the Floating Mode
Jack-up Response in the Elevated Mode of Operation
Time Domain Analysis
Methods of Evaluating Response
Static Load Components
Sea Loadings
14
Wind Loadings
Foundations
7
7
7
10
11
12
14
3.0
3.1
3.2
3.2.1
3.2.2
3.3
3.3.1
3.3.2
3.3.3
3.4
UNCERTAINTY MODELLING
General
Loading Uncertainty Modelling
Aleatory Uncertainty
Epistemic Uncertainty
Response Uncertainty Modelling
Analysis Uncertainty
Damping
Foundation
Resistance Uncertainty Modelling
19
19
19
19
20
21
21
22
24
4.0
4.1
4.1.1
4.2
4.2.1
4.2.2
4.2.3
4.2.4
4.2.5
4.2.6
4.3
LIMIT STATES
General
Limit States Appropriate to Jack-up Structures
The Ultimate Limit State
Leg Strength
Foundation Bearing Failure
Holding System
Global Deflections
Global Leg Buckling
Overturning Stability
Literature Study
25
25
25
27
27
30
30
32
32
32
33
5.0
5.1
5.2
5.3
5.4
SUMMARY OF APPLICATION EXAMPLES
General
Overview of Analytical Procedure
Structural Reliability Example
Foundation Reliability Example
34
34
34
36
38
15
16
21
Guidelines for Offshore Structural Reliability
-DNV Application to Jackup Structures
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Report No. 95-0072
Section
Title
Page
6.0
6.1
6.2
6.3
RECOMMENDATIONS FOR FURTHER WORK
General
Elevated Condition
Floating / Installation Phase Conditions
41
41
41
42
7.0
REFERENCES
44
Guidelines for Offshore Structural Reliability
-DNV Application to Jackup Structures
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Report No. 95-0072
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 offland) 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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-DNV Application to Jackup Structures
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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
1.4
: Arrangement of a Typical Harsh Environment Jack-up
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
Guidelines for Offshore Structural Reliability
-DNV Application to Jackup Structures
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Report No. 95-0072
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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-DNV Application to Jackup Structures
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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.
Guidelines for Offshore Structural Reliability
-DNV Application to Jackup Structures
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Report No. 95-0072
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;
-1Wave damage to the unit structure leading to penetration of watertight boundaries.
-2Damage to the structure as a result of shifting cargo (usually caused by direct wave
impact, excessive motions and/or inadequate seafastenings).
-3Structural 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 ;
-1Impact loadings upon contact with the seabed.
-2Foundation 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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-DNV Application to Jackup Structures
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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 jackup 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 nonlinearities 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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-DNV Application to Jackup Structures
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Figure 2.1
: Typical Hydrodynamic/Structural Model of a Jack-up in the
Transit Condition.
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-DNV Application to Jackup Structures
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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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-DNV Application to Jackup Structures
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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
Where :
Hs
: adjusted significant wave height to account for wave kinematics (metres)
Hsrp
: significant wave height (metres)
d
: waterdepth (metres)
(2.1)
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-DNV Application to Jackup Structures
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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
2.3.2
·
: Typical Simplified Model of a Jack-up Structure.
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 jackup 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, jackup 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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-DNV Application to Jackup Structures
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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 ;
-1By use of long term statistics of independent sea states
-2By 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) ;
1
pD 2
Fn ( r , t ) = r
Cma n ( r , t ) + rDCd v n ( r , t ) v n ( r , t )
4
2
(2.2)
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
C
: constant chosen such that :
Current Loadings
·
p /2
å
-p / 2
F (a )da = 10
.
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
where
r
Vref
Ch
Cs
Aw
(2.4)
: density of air
: the 1 minute sustained wind velocity at 10 meters above sea level
: height coefficient
: shape coefficient
: 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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-DNV Application to Jackup Structures
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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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-DNV Application to Jackup Structures
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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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-DNV Application to Jackup Structures
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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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-DNV Application to Jackup Structures
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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
Randomness of storm extremes
Waterdepth (D)
Marine Growth
Table 3.1
: General Environmental Variable Distributions
Description
Significant wave height (Hs)
Zero up-crossing period (Tz)
Spectral peak period (Tp)
Joint distribution (Hs,Tz) or (Hs,Tp)
Tidal current speed (Vt)
Wind generated current speed (Vw)
Average wind speed (U10m)
Table 3.2
Distribution
Poisson
Uniform (tidal effects), or,
Normal (storm surge effects - conditional
on Hs)
Lognormal
Distribution
3-parameter Weibull/Lognormal
Lognormal (conditional on Hs)
Lognormal (conditional on Hs)
3-parameter Weibull for Hs and Lognormal
for Tz or Tp (conditional on Hs)
Uniform
Normal (conditional on U10m)
Weibull (conditional on Hs)
: Long Term Analysis Variable Distributions
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-DNV Application to Jackup Structures
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Description
Significant wave height (Hs)
Total current speed (Vc)
Average wind speed (U10m)
Table 3.3
Distribution
Gumbel *1, 2
Gumbel *1, 2
Gumbel *1, 2
: 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
Drag coefficient 2
(CD)
3
Inertia coefficient
(CI)
Marine growth 4
Mass of structure 5
Table 3.4
Distribution
Lognormal
Lognormal
Lognormal
Lognormal
m1
1.0
1.0
1.0
1.0
C.o.V.
0.2
0.1
0.2
0.14
: 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
4:
The selection of the appropriate value for the marine growth should be evaluated based upon a site specific
inertia coefficient as a fixed quantitiy. An inertia coefficient of 1.8 may be utilised.
evaluation, e.g. NPD (1992).
5:
See also section 2.3.3
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-DNV Application to Jackup Structures
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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
Analytical uncertainty
Table 3.5
3.3.2
Distribution
Lognormal
m
1.0
C.o.V.
0.18
: Analytical Model Uncertainty Variables
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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-DNV Application to Jackup Structures
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Damping Source
Structure, holding system etc.
Foundation
Hydrodynamic
Table 3.6
Global Damping
(% of critical damping)
2%
2% or 0% 1
3% or 0% 2
: 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
Damping ratio
Table 3.7
Distribution
Lognormal
m1
1.0
C.o.V.
0.25
: 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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-DNV Application to Jackup Structures
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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
Rotational stiffness
Horizontal stiffness
Vertical stiffness
Table 3.8
: Foundation Parameter Distributions
KEY :
*1 :
See also section 2.3.6
Distribution*1
Lognormal
Lognormal
Lognormal
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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 the
importance of the uncertainties in the capacities. As a consequence of this it is most likely
that a structural failure event will result from the load being high, rather than the strength
capacity being low.
·
Uncertainties associated with resistance are dependent upon the resistance model
included in the limit state under consideration. Modelling of the uncertainly parameters
associated with the resistance model should be relevant to the formulation of the
resistance model utilised in the limit state. See section 4.0 for further guidance.
·
General resistance uncertainty information is given in DNV (1996a), Chapter 7.
·
A realistic analysis of the ultimate (‘push-over’) capacity of a jack-up structure can in
many cases only be performed by using advanced non-linear finite element software, e.g.
USFOS (1996).
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-DNV Application to Jackup Structures
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4.0
LIMIT STATES
4.1
General
Limit states are formulations of physical criteria beyond which the structure no longer
satisfies the design performance requirements. Limit state categorisation is generally defined
as follows, ISO 13819, Part 1, ISO (1995) ;
a).
The ultimate limit states that generally correspond to the maximum resistance to
applied actions.
b.)
The serviceability limit states that correspond to the criteria governing normal
functional use.
c.)
The fatigue limit states that correspond to the accumulated effect of repeated actions.
d.)
The accidental damage limit states that correspond to the situation where damage to
components has occurred due to an accidental event.
Some code of practices, e.g. Eurocode 3 (1992), however, defines only two limit states, these
being ; the Ultimate Limit State, and the Serviceability Limit State. In such cases the states
prior 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 be
designing.
·
The guidance provided in the guideline example for jacket structures, DNV (1996c), in
respect to the fatigue limit state, although utilising frequency domain solution techniques,
covers the state-of-the-art knowledge with respect to fatigue reliability analysis of jackup structures. The fatigue limit state is therefore not explicitly covered in this section and
reference should be made to DNV (1996c) for appropriate guidance concerning the
fatigue limit state.
Ultimate Limit State (ULS)
ISO 13819, Part 1, ISO (1995), lists the following examples of ultimate limit states ;
a.)
loss of static equilibrium of the structure, or of a part of the structure, considered as a
rigid body (e.g. overturning or capsizing),
b.)
failure of critical components of the structure caused by exceeding the ultimate
strength ( in some cases reduced by repeated actions) or the ultimate deformation of
the components,
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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 simple
design equations. Additionally, general guidelines on how to perform structural system
collapse analyses are lacking, hence limit state functions for reliability analysis of jackup 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 may
be considered as designing ;
Component Level
-leg local structural strength
-hull local structural strength
-foundation capacity (local)
-holding system loadings
·
The following listed limit states may therefore be considered as being relevant
component limits states for reliability analyses ;
-1Leg element yield
-2Leg element buckling
-3Leg joint capacity
-4Foundation bearing failure
-5Holding 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 lead
to complete loss of integrity or performance of the structure.
·
4.2
The intention of this limit state is to ensure that the structure can tolerate the damage due
to specified accidental events and subsequently maintain integrity for a sufficient period
under specified environmental conditions to enable evacuations to take place. The
accidental events and the consequences of such events are normally based upon
Quantitative Risk Analyses (QRA). For further details on QRA reference should be made
to DNV (1996a), Chapter 2.
The Ultimate Limit State
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This subsection describes in more detail Ultimate Limit State criteria documented in
subsection 4.1.1.
4.2.1
Leg Strength
General
As previously mentioned, (see Section 3.4), reliability of a jack-up structure in the ultimate
limit state condition is found to be ‘load driven’, i.e. the importance of the uncertainties
associated with the loading dominates. When describing the uncertain quantities associated
with the limit state it is generally therefore not necessary to breakdown the individual
uncertainties associated with, for example, a buckling resistance code formulation, and code
criteria may be utilised with generalised randomisation parameters.
·
Suitable strength resistance criteria, may be found in a wide variety of structural codes
and standards. The following references may be recommended ;
-AISC (1984)
-API (1993)
-DNV (1995)
-Eurocode 3 (1992)
-NPD (1990)
-SNAME (1993)
When utilising standard codes and Practices the following issues should be considered ;
(i)
The formulations contained in these codes may only be applicable within certain
limits (e.g. R/t ratio between given limits). It should therefore be ensured that the
resistance formulation utilised in the limit state is satisfactory for the structure under
consideration.
(ii)
The resistance formulations contained within these codes are based upon analytical
approximations to the physical behaviour where characteristic values are defined at
some fractile value or lower bound value. For reliability analysis the capacity
formulation in the limit states should be based on the 50 percent fractile (median)
values.
The basis for buckling curves in different codes and standards are different. The API
buckling curve, API (1993) is derived as a lower bound value for low slenderness
while it is equal to the Euler stress for high slenderness values, which may be
considered as an upper bound value in that region. Another definition of a buckling
curve is used in AISC (1984). The background for the buckling curves used in design
of steel structures in European design standards is based on work carried out within
the European Convention for Constructional Steelwork which is presented in The
Manual on Stability of Steel Structures, ECCS (1976). The design curves are
presented by their characteristic values which are defined as mean values minus two
standard deviations along the slenderness axis. The test results are assumed normal
distributed.
(iii)
Effective buckling lengths are dependent upon joint flexibilities. Buckling lengths
may normally be measured in relation to centreline to centreline for chords, whilst,
face to face lengths are normally acceptable for the braces. X-brace buckling lengths
depend upon the amount of tension loading in the crossing member. The effective
lengths may be derived from analytical considerations. The effective buckling
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lengths derived from tests of frame structures until collapse are generally shorter than
those derived from theoretical calculations.
(iv)
Different allowable requirements to fabrication tolerances (eccentricity) are
associated with the various buckling curves. For European buckling curves a
straightness deviation at the middle of the column equal to 0.0015 times the column
length is allowed, while for API (1993) and AISC (1984) the corresponding numbers
are 0.0010 and 0.00067 respectively.
For conventional design jack-up structural elements the effect of external pressure may,
normally be disregarded.
The susceptibility of local buckling of tubular members is a function of the member geometry
and yield strength. For jack-up structures, it may normally be assumed that leg elements are
stocky, beam elements. Yield strength control is implicitly covered by the buckling limit state
for members in compression, whilst, for tension members, the limit state is given by, for
example, eqn. 5.1, NPD (1990), NS3472 (1984).
G = fy -
[ s a + s by + s bz ]2 + 3[ t xy + t xz + t t ]2
(5.1)
where
fy
sa
t
= material yield strength
= axial stress component
= torsional shear stress component
t
sby , sbz
t xy , t xz
= bending stress components
= plain shear stress components
The capacity criterion stated in SNAME (1993) is an example of an expression applicable to
describe resistance of jack-up elements subjected to compressive loadings. Such formulation
may be described in the limit state format as ;
1
G = 1 - X bias [
h h
h
Pu 8 éêì M uex ü ïì M uey ïü ùú
+ í
ý +í
ý
Pn 9 êî M nx þ ïî M ny ïþ ú
û
ë
]
Where ;
Pu
Pn
M uex
M uey
M nx
M ny
h
is the chord axial load
is the chord nominal axial strength in compression
is the chord local effective applied bending moment about the local x-axis
is the chord local effective applied bending moments about the local y-axis
is the chord local nominal bending strength about the local x-axis
is the chord local nominal bending strength about the local y-axis
is the exponent for biaxial bending.
(5.2)
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A full description of limiting criteria, the parameters utilised in Equation 5.2, and the
methodology utilised in calculating the specific values of these terms are documented in
SNAME (1993), Section 8.1.4.
The SNAME (1993) formulation for buckling resistance is based upon AISC (1978). The
uncertainty parameters stated in Galambos (1988) may therefore be utilised in describing the
uncertainty 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 coefficients
are different as also might be expected as the API (1993) are based on allowable stresses and
NPD (1990) has based the design on the partial coefficient method.
Jack-up brace/chord connections are, however, normally non-standard, due to the rack
structure inclusion in the chord section. Static strength capacity formulation for standard
tubular/tubular connections may give erroneous results for brace/chord connections.
Work on joint capacities is currently being performed in development of a new ISO standard
on design of steel offshore structures. This work should be considered as basis for limit state
functions when it is available.
As an example limit state Eqn 5.3 documents the static strength of tubular joints formulation
based on the NPD guidelines, NPD (1990) and the limit state function for the static capacity
of tubular joints can then be formulated, NPD(1990) as ;
G = 1 - X bias [
2
N æ M IP ö
M
+ç
÷ + OP
N k è M IPk ø
M OPk
]
where
Xbias
N
Nk
M IP
M IPk
M OP
M OPk
= bias (See DNV (1996a), Chapter 7.2)
= brace axial force
= characteristic capacity of the brace subjected to axial force
= brace in-plane moment
= characteristic capacity of the brace subjected to in-plane moments
= brace out-of-plane moment
= characteristic capacity of the brace subjected to out-of-plane moments
A detailed description of this limit state is given in DNV (1996c).
(5.3)
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4.2.2
Foundation Bearing Failure
The limit state function for the ultimate limit state of foundation bearing capacity is defined
as : G = R - L, where R and L are respectively the lengths of resistance and load vectors as
shown in Fig 4.1. The origin of the vectors on the vertical axis, Pw, is the static load on the
footing due to submerged weight of the jack-up. The end point of vector L, point A, is the coordinate in the load space under the design storm. The end point of vector R, point B, is the
foundation 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 as
follows ;
(Vex - Pw ) 2 + ( Hex ) 2 + ( Mex / r ) 2
(5.4)
(Vcy , f - Pw ) 2 + ( Hcy , f ) 2 + ( Mcy , f / r ) 2
(5.5)
L=
R=
Vex
Hex
Mex
Vcy,f
=
=
=
=
Hcy,f
=
Mcy,f
=
Pw
=
r
=
Vertical load on footing under the extreme load combination
Lateral load on footing under the extreme load combination
Moment load on footing under the extreme load combination
Vertical capacity of footing along the path defined by load vector
starting at (Pw,0,0) in direction of (Vex, Hex, Mex)
Lateral capacity of footing along the path defined by load vector
starting at (Pw,0,0) in direction of (Vex, Hmax, Mex)
Moment capacity of footing along the path defined by load vector
starting at (Pw,0,0) in direction of (Vex, Hmax, Mex)
Mean vertical load on footing during the storm (mainly due to
submerged weight of jack-up)
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 interaction
diagram 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 the
response loading. The ultimate capacity of the holding system is usually obtained by detailed
finite element analysis (F.E.M. analysis) in combination with relevant prototype testing.
Guidelines for Offshore Structural Reliability
-DNV Application to Jackup Structures
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Report No. 95-0072
Figure 4.1 :
Definition of Limit State Function for a Footing on Clay with Moment
Fixity.
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-DNV Application to Jackup Structures
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Report No. 95-0072
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 in
respect 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 the
structure to redistribute the load, but also on the post-failure behaviour of the system, e.g. the
ductility of the individual members and joints.
For a balanced structure, i.e. where all members, in a linear analysis, have the same
utilisation at the time of first member failure, the first member to fail and the system effects
for overload capacity beyond the first member failure are determined by randomness in
member 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 that
will dominate. The identification of such members is however, complicated by simplicities
made in the analysis e.g. at the interfaces between the hull and the leg structures, and at the
foundation interfaces.
There has been little previous workings undertaken concerning jack-up collapse analysis
related to reliability analysis, however, by referring to jacket experience, it is considered that
the collapse capacity may be directly related to the global overturning moment. This implies
that the collapse capacity can be represented by a single random variable. The loading may
also be represented by a single random variable, and, as such, the limit state function for the
ultimate limit state of global leg strength capacity may be defined as : G = R - S, where R is
the 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). Such
guidelines 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 )
MD
ML
MS
ME
MDN
(5.6)
= the stabilising moment due to weight of structure and non-varying loads
(at the displaced position)
= the stabilising moment due to the variable loads(at the displaced position)
= the stabilising moment due to the seabed foundation fixity
= the overturning moment due to the extreme environmental load condition
= the dynamic overturning moment
When considering the moments in connection with this limit state it is important to ensure
that the axis of rotation of the system is fully considered.
Guidelines for Offshore Structural Reliability
-DNV Application to Jackup Structures
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Report No. 95-0072
4.3
Literature Study
From a literature review it may be concluded that there have, in the past, been few public
papers issued concerning structural reliability of jack-up units.
From an extensive documentation review the following listed reliability studies have been
identified in respect to jack-up structures ;
General Structural Reliability Papers ;
1.)
2.)
3.)
4.)
5.)
6.)
7.)
8.)
Løseth, R., Mo, O., and Lotsberg, I, (1990)
Leira, B.J., and Karunakaran, D. (1991)
Mo.O., et.al. (1991)
Ahilan, R.V. et.al. (1992)
Gudmestad, O.T., et.al. (1992)
Karunakaran, D., et.al. (1993)
Ahilan, R.V., Baker, M.J., and Snell, R.O., (1993)
Dalane J.I.(1993)
The majority of the papers referred to above may be considered as providing information
concerning general reliability.
Løseth et.al. (1990) and Karunakaran et al.(1993) document the global limit state criteria of
maximum axial force and base shear in one leg. Karunakaran et al.(1993) also documents
considerations with respect to deck displacement and foundation limit states. Ahilan et
al.(1992), (1993) covers reliability code calibration studies undertaken in connection with
SNAME (1993). Mo et al. (1991) and Dalane (1993) document structural leg strength
capacity considerations.
Foundation Reliability Papers ;
1.)
2.)
3.)
Ronold, K.O., (1990)
Nadim, F., Lacasse, S., (1992)
Nadim, F., Haver, S., and Mo, O. (1994)
Guidelines for Offshore Structural Reliability
-DNV Application to Jackup Structures
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Report No. 95-0072
5.0
SUMMARY OF APPLICATION EXAMPLES
5.1
General
This section documents a summary of the reliability analyses undertaken to analyse the
response of a jack-up structure in a typical North Sea environment at a waterdepth of 81
metres as documented in DNV (1996b). In order to assess change in reliability as a function
of time, the reliability examples are undertaken for a jack-up exposed to multi-year operation
at the same location. The following listed time dependent effects have been considered in the
analyses ;
- Soil Consolidation
The foundation rotational stiffness was increased by a factor of 2.5 to account for soil
consolidation.
- Drag Coefficient
Drag coefficients were increased by a factor of 15% to account for the change in drag due to
increased 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 for
weight growth in the deckbox.
Two limit states have been considered covering the structural strength of the jack-up leg and
the foundation capacity. In both of these cases the effects on reliability of long term operation
at the specific site have been evaluated.
The reliability analyses documented in DNV (1996b) have been undertaken by the
methodology generally known as ‘Long Term Statistics by Independent Seastates’, Bjerager
et al. (1988), and were based upon response resulting from time domain simulations in
irregular 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-linear
analyses were undertaken in order to determine appropriate jack-up response statistics.
Guidelines for Offshore Structural Reliability
-DNV Application to Jackup Structures
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Report No. 95-0072
Long term statistics were established by use of PROTIM (1989). PROBAN (1989) was
utilised to solve the probabilities of failure of the limit state functions.
For the foundation example a probabilistic bearing capacity model was established in order to
account for the different combinations of force and moment at the foundation footing.
An overview of this procedure is shown schematically in figure 5.1.
DESIGN
CRITERIA
DETAILED MODEL
ANALYSES
(Deterministic Sea)
SIMPLIFIED MODEL
ANALYSES
(Stochastic Sea)
WAJAC
FENRIS
FENSEA
PROBAN
STRUCTURAL RELIABILITY
OUTPUT : The annual probability
of failure for the most critically
loaded structural element.
(Determined by establishing the long
term statistics considering
independent seastates)
FOUNDATION RELIABILITY
OUTPUT : The annual
probability of failure for the
most utilized footing.
Figure 5.1
: Overview of Analytical Procedure
ESTABLISH CRITICAL
PARAMETERS ;
-Load Direction
-Design Criteria
-Element
-Foundation soil springs
ESTABLISH THE
RESPONSE STATISTICS ;
-Force and moment for the
most critically loaded
structural element
-Force and moment for the
most utilized footing
PROTIM
ESTABLISH
PROBABILISTIC BEARING
CAPACITY MODEL for the
different combinations of
force and moment on most
utilized footing
ESTABLISH
DISTRIBUTIONS OF
ANNUAL EXTREMES for
force and moment on most
utilized footing
Guidelines for Offshore Structural Reliability
-DNV Application to Jackup Structures
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Report No. 95-0072
5.3
Structural Reliability Example
This example documents an ultimate limit state reliability analysis undertaken for a jack-up
structure exposed to multi-year operation. The foundation description ‘unconsolidated soil’ is
intended to reflect a cohesive soil condition (e.g. clay) at the time of the initial placement of
the 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 settled
and consolidated. Failure probability of leg, chord buckling provided the measure of the
change in reliability with time.
An overview of the analytical methodology adopted in the reliability analysis is shown in
figure 5.1.
The main results from the undertaken reliability analysis are presented in table 5.1. Table 5.2
presents results from the sensitivity evaluation, where the mean and standard deviation have
been increased by 10% over those values utilised in the undertaken reliability analysis.
SORM Reliability index - Unconsolidated Soil : b = 4.35
- Consolidated Soil : b = 4.41
Variable
Significant Wave Height, Hs
Randomness of Storm Extreme, Uaux
Drag Coefficient, CD
Critical Stress, Fcr
Heading, q
Wave Spreading, n
Foundation Rotational Stiffness, Kr
Tidal current, VT
Damping
Deckbox Mass
Table 5.1
Unconsolidated Soil
Importance Factor
56%
16%
11%
9%
3%
2%
2%
<1%
<1%
<1%
Consolidated Soil
Importance Factor
44%
15%
15%
10%
1%
4%
9%
1%
1%
<1%
: Structural Reliability Importance Factors
Unconsolidated
Soil Consolidated Soil Condition
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-DNV Application to Jackup Structures
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Report No. 95-0072
Variable
Environment
Rotational Stiffness, Kr
Vertical Stiffness, Kv
Lateral Stiffness, Kh
Drag Coefficient, CD
Tidal current, VT
Marine Growth
Damping
Deckbox Mass
Wave Spreading, n
Waterdepth, D
Spectral Peak Parameter, g
Heading, q
Yield Strength, fy
Critical Stress, Fcr
Duration, D
No. of Seastates, Nsea
Table 5.2
value
Condition
Mean / Lower
Bound
N/A
0.0202
-0.0063
-0.0008
-0.1686
-0.0340
-0.0025
-0.0090
0.0193
-0.0037
0.0074
-0.0008
-0.0424
0.0054
0.2525
-0.0195
-0.0214
CoV / Upper
Bound
-0.3138
-0.0038
0.0002
0
-0.0379
0.0007
0.0001
0.0003
-0.0007
-0.0377
0.0075
-0.0040
-0.1728
0
-0.0421
N/A
N/A
Mean /
Lower Bound
N/A
0.0286
0
0
-0.1847
-0.0316
-0.0186
-0.0369
0.0600
-0.0048
0.0322
-0.0019
-0.0260
0
0.2643
-0.0197
-0.0214
CoV / Upper
Bound
-0.2611
-0.0227
0
0
0.0497
0.0005
0.0001
-0.0013
-0.0043
-0.0764
0.0315
-0.0134
-0.0637
0
-0.0467
N/A
N/A
: Sensitivity Analysis of Results (Db for a 10% increase in the mean
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 unit
when compared to other relevant studies for jack-up units, e.g. SNAME (1993). The main
reason for this is that the jack-up chord element under investigation in the example, although
being the most heavily loaded structural element, is not loaded up to the allowable
deterministic capacity of the element in the designing storm condition. The condition
analysed was however based upon an actual loading situation for the jack-up unit. This
example would therefore tend to confirm the in-service experience that jack-up units
generally operate at reasonably high levels of reliability in respect to structural strength due
to the fact that, in the normal mode of operation, the jack-up is not utilised to the maximum
capability of the jack-up unit in respect to the leg strength ultimate limit state condition. For
jack-up units designed to operate as production units over a longer period of time at a single
location, where the jack-up is designed and optimised for site specific criteria, such a
conclusion 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 fairly
constant in the example presented. It would appear that the time varying negative effects of
increased static and environmentally induced loadings are offset by the effects of soil
consolidation. In the case represented in the example study, consolidation of the foundation
has lead to an increased bottom restraining condition. Other soil conditions may however
lead to degradation of the foundation restraint. In all cases site specific data should be
utilised as the basis for evaluating the long term effects of the foundation.
Guidelines for Offshore Structural Reliability
-DNV Application to Jackup Structures
Page No. 38
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Report No. 95-0072
5.4
Foundation Reliability Example
The foundation reliability example documented in DNV (1996b) demonstrates ultimate limit
state 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 study
was 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. The
mechanical model for evaluating the capacity of skirted footings in clay was assumed well
developed and the modelling uncertainty relatively small.
The limit state function for the ultimate limit state of bearing capacity for the most utilised
footing was defined as G = R - L, where R and L were respectively the lengths of the
resistance and load vectors as shown on Fig. 4.1.
The distribution of the resistances was estimated by specifying a deterministic load on the
foundation and evaluating the probability of failure using FORM. By varying the load, the
probability of failure at different load levels was computed. The results showed that a
lognormal distribution provides an excellent fit for the static foundation capacity.
The CoV's and distributions of the foundation resistance parameters used in the analyses are
given in Table 5.3 (see Section 4.2.2 and Fig. 4.1 for definitions).
VARIABLE
Distribution
Mean
CoV
Unconsolidated clay (all layers)
Vpre
Lognormal
212 MN
12%
Hs,max
Lognormal
40 MN
13%
Ms,max
Lognormal
640 MNm
14%
Consolidated clay (all layers)
Vpre
Lognormal
253 MN
12%
Hs,max
Lognormal
51 MN
13%
Ms,max
Lognormal
777 MNm
14%
Other variables (same for consolidated and unconsolidated conditions)
F1
Normal
1.06
3%
F2
Normal
0.72
3%
F3
Normal
0.78
3%
Table 5.3
: Foundation Resistance Parameters
The extreme loads on the most utilised footing were computed by PROBAN (1989). Table
5.4 shows the load parameters used in the foundation reliability calculations. The CoV of Pw
was assumed to be identical to the CoV of the deck mass.
Guidelines for Offshore Structural Reliability
-DNV Application to Jackup Structures
Page No. 39
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Report No. 95-0072
VARIABLE
Vex - Pw
Hex
Mex
Pw
Vex - Pw
Hex
Mex
Pw
Table 5.4
Distribution
Mean
Unconsolidated Soil Condition
Gumbel
5.0 MN
Gumbel
4.9 MN
Gumbel
169.5 MNm
Lognormal
71.6 MN
Consolidated Soil Condition
Gumbel
5.3 MN
Gumbel
6.4 MN
Gumbel
323.9 MNm
Lognormal
78.7 MN
CoV
111%
54%
82%
14%
118%
49%
51%
14%
: Extreme Loads on Most Utilised Footing
When the effects of load redistribution among the footings were neglected, the computed
foundation safety indices were respectively 1.85 and 1.45 for the unconsolidated and
consolidated soil conditions. The reason for these low values was that when the possibility of
load redistribution among the jack-up legs was not taken into account, the failure mode of the
most 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 the
whole foundation system consisting of the 3 footings, it is more optimal to resist the external
overturning moment by axial forces, rather than by local moments at each footing. With
traditional spud cans, the moment fixity is completely lost when the bearing capacity is
reached. However, with skirted spud cans, the moment acting on the most utilised footing at
failure may be 60 to 80% of the moment capacity.
The main results from the foundation reliability analyses, after accounting for the
redistribution of reactions among the 3 footings and reduction of fixity of the most utilised
footing at large loads, are summarised in Table 5.5.
FORM Reliability index - Unconsolidated Soil : b = 4.11
- Consolidated Soil : b = 4.22
Variable
Static Sliding Capacity, HSmax
Cyclic Loading Factor, F2
Extreme Base Shear, Hex
All other parameters
Table 5.5
Unconsolidated Soil
Importance Factor
11%
1%
88%
<1%
Consolidated Soil
Importance Factor
13%
1%
86%
<1%
: Results for Most Utilised Footing with Load Redistribution
Guidelines for Offshore Structural Reliability
-DNV Application to Jackup Structures
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Report No. 95-0072
There is a lack of documentation concerning the reliability of jack-up foundation ultimate
limit state conditions. For the example application, it was considered appropriate to compare
the computed safety indices with those in Table 2.7 of the Reliability Guidelines DNV
(1996a). This table presents target annual failure probability and corresponding reliability
indices. Once the effects of optimal utilisation of the foundation 'system' (i.e. redistribution
of reactions among the 3 footings when the loads approach the foundation capacity) are
considered, the foundation failure development may be considered as being 'ductile with no
reserve capacity'. The failure consequence is considered as being somewhere between 'not
serious' and 'serious'. Therefore an annual target failure probability of 10-4 to 10-5 (b = 3.71 to
4.26) is appropriate. The safety indices of b = 4.11 for the unconsolidated soil condition and
b = 4.22 for the consolidated soil condition would therefore appear to be satisfactory.
Guidelines for Offshore Structural Reliability
-DNV Application to Jackup Structures
Page No. 41
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Report No. 95-0072
6.0
RECOMMENDATIONS FOR FURTHER WORK
6.1
General
From the literature review study undertaken and documented in section 4.3, it is clear that
there have been very few reliability analyses undertaken for jack-up structures.
·
6.2
This section discusses recommendations for further workings in connection with
identification of the reliability of jack-up structures.
Elevated Condition
Jack-up structures have traditionally been used in shallow waters. There is a current tendency
to utilise jack-ups in deeper waters, in harsh environment conditions, for extended periods of
operations.
·
The uncertainty weightings for these two scenarios are different and the safety implicit in
current jack-up design procedures may not necessarily be appropriate, Gudmestad
(1990), Dalane (1993).
Jack-up structures, as compared to jacket structures, have a number of unique characteristics,
which add to the complexity of the problem being considered. (e.g., See sections 1.4 and 2.3).
With respect to limit state formulation, the most important of these characteristics may be
considered 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 traditional
formulation for stress concentration factors and joint static capacity (e.g. punching shear) are
generally not appropriate.
·
Results from reliability studies undertaken for traditional jacket type offshore structures
are, generally, not ‘transferable’ to jack-up structures.
The stiffness characteristics (fixity) of spudcan footings are complicated and strongly nonlinear. Jostad et al. (1994) show that while spudcans might have significant moment fixity
under operational loads, the moment fixity disappears as the loads approach foundation
capacity. The footing stiffness affects the dynamic characteristics of the jack-up, which in
turn influence the loads on the spudcans. So far, there have been no systematic studies of the
effects of the uncertainties in the spudcan stiffness characteristics on the jack-up response.
Conclusions :
-1-
The implicit probability of failure of jack-ups by use of dedicated jack-up codes and
standards should be evaluated for their applicability to deep water, harsh
environment operations for extended periods.
-2-
Jack-up system capacity due to accidental damage load events should be evaluated.
The robustness of the jack-up structure should then be compared to that of a jacket
structure. (The U.K., H.S.E. is currently engaged in such a project and the findings
from these workings should be considered in this connection.)
Guidelines for Offshore Structural Reliability
-DNV Application to Jackup Structures
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Report No. 95-0072
-3-
Traditional, frequency domain (linear analysis) based fatigue reliability should be
compared with that reliability achieved utilising time domain (non-linear) analysis in
order to identify, for a jack-up structures, the importance of the non-linear effects for
the fatigue limit state.
-4-
Reliability considering the following foundation related criteria is recommended to
be investigated ;
-system effects
-response as related to the uncertainty and non-linearity in foundational support.
6.3
Floating / Installation Phase Conditions
Of the 250 jack-up casualties reported during the period 1979 to 1991, some 50% of the total
losses, or major incidents occurred during towage, Standing and Rowe (1993).
Standing and Rowe (1993) document the following listed items as being the major source of
accident in respect to a jack-up in the transit condition ;
(i)
Wave damage to the unit structure leading to penetration of watertight boundaries.
(ii)
Damage to the structure as a result of shifting cargo (usually caused by direct wave
impact, excessive motions and/or inadequate seafastenings).
(ii)
Structural damage in the vicinity of the leg support structures.
·
There does not appear to have been any reliability studies undertaken for jack-ups in the
transit condition.
During the installation phase, there are normally two main areas of concern, these being;
impact loadings upon contact with the seabed, and, foundation failure (i.e. punch-through)
during preloading.
Sharples et al (1989) summarised the causes for jack-up mishaps in a 10 year period. Out of
226 “accidents", over 50 were attributed to “soils”. The causes for unsatisfactory foundation
performance 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 to
similar conclusions.
·
It is evident from the above statistics that punch-through during preloading is the most
frequently-encountered foundation problem for jack-ups.
·
The physics of the impact loading problem are extremely complicated and the
uncertainties in the process are not well documented. Additionally, regulation
requirements for the installation condition are considered to be vague and incomplete.
Guidelines for Offshore Structural Reliability
-DNV Application to Jackup Structures
Page No. 43
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Report No. 95-0072
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 process
and to identify areas where further workings are required.
-2-
Reliability investigations in the installation phase should be considered for the
following listed loading conditions ;
-preloading
-impact loading.
Guidelines for Offshore Structural Reliability
-DNV Application to Jackup Structures
Page No. 44
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Report No. 95-0072
7.0
REFERENCES
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AISC(1984),’Specification for the Design, Fabrication and Erection of Structural Steel for
Buildings’, American Institute of Steel Construction, Eighth Edition, Oct.1984.
Andersen, K.H. and Lauritzsen, R.(1988), ‘Bearing Capacity for foundation with Cyclic
Loads,’, ASCE. Jorn. of Geotechnical Engineering. V 114, No 5, pp. 516-555
Andersen, K H., Lauritzsen, R., Dyvik, R., and Aas, P.M.(1988), ‘Cyclic Bearing Capacity
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Andersen, K.H., Dyvik, R., Lauritzsen, R., Heien, D., Hårvik L., and Amundsen, T., (1989),
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Engineering. V 115, No 11, pp. 1550-l568.
Andersen, K.H., Dyvik, R., and Schrøder, K.(1992), ‘Pull-Out Capacity Analyses of Suction
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Andersen, K.H., Dyvik, R., Schrøder, K., Hansteen, O.E., and Bysvecn, S.(1993). ‘Field
Tests of Anchors in clay II: Predictions and Interpretation.’, ASCE Jorn. of Geotechnical
Engineering. V 119, No 10, pp. 1532-l549.
Andersen, K.H, Allard, A. and Hermstad J.(1994), ‘Centrifuge Model Tests of A Gravity
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USA. Vol. 1, pp. 255-252.
Ang, A.H.S. and Tang, W.H.,(1975), ‘Probability Concepts in Engineering Planning and
Design. Volume I - Basic Principles.’, John Wiley and Sons, Inc., New York, 409p.
Arnesen, K., Dahlberg, R., Kjeøy, H., and Carlsen, C.A.,(1988), ‘Soil -Structural Interaction
Aspects for Jackup Platforms’, BOSS’88 Conf. Trondheim, Norway, June 1988.
API(1993), ‘Recommended Practice for Planning, Design and Constructing Fixed Offshore
Platforms -Load and Resistance Factor Design’, API Recommended Practice 2A-LRFD (RP
2A-LRFD), First Edition, July 1993.
Bjerager, P., Løseth, R., Winterstein, S., and Cornell, A., (1988) ‘Reliability Method for
Marine Structures Under Multiple Environmental Load Processes’, Proceeding of 5th
International Conf. on Behaviour of Offshore Structures, Vol.3, Trondheim, Norway, June
1988, pp1239-1253.
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