RESEARCH REPORT 037 Impact of changes to T&R 5-5A on HSE

HSE
Health & Safety
Executive
Impact of changes to T&R 5-5A on
jack-up system reliability levels
Prepared by Global Maritime
for the Health and Safety Executive 2003
RESEARCH REPORT 037
HSE
Health & Safety
Executive
Impact of changes to T&R 5-5A on
jack-up system reliability levels
A C Morandi MEng, PhD, CEng, MRINA, MSNAME
American Global Maritime
Marine, Offshore and Engineering Consultants
11767 Katy Freeway
Suite 660
Houston
Texas 77079
USA
The Guideline and Recommended Practice for jack-up site specific assessment contained in
theSNAME T&R Bulletin 5-5A attempted, amongst other objectives, to create a unified, industryaccepted practice that could evolve to form the basis for an ISO standard. Technology continues to
evolve and several modifications to the document have been proposed which can provide the impetus
needed to fully meet such an important goal.
The present work aims to develop a robust methodology to provide quantified guidance relating to the
impact on reliability of changes to T&R 5-5A being presently considered by the industry. This will
facilitate the industry consensus necessary for such changes to be fully incorporated into jack-up site
assessment.
Phase 1 of the work is covered in this report. A review of previous pushover and reliability analyses is
given and areas where modeling improvements are recommended were identified. Factors that affect
jack-up system reliability were identified and a premise for performing reliability analyses of jack-ups
utilizing state-of-the-art modeling is outlined. Two rig/location cases were selected that were as close to
the T&R 5-5A calibration cases as possible and the impact of proposed changes to T&R 5-5A on unity
checks was evaluated based on such cases.
This report and the work it describes were funded by the Health and Safety Executive (HSE). Its
contents, including any opinions and/or conclusions expressed, are those of the authors alone and do
not necessarily reflect HSE policy.
HSE BOOKS
© Crown copyright 2003
First published 2003
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ii
CONTENTS
SECTION
PAGE NO.
EXECUTIVE SUMMARY
v
1.
INTRODUCTION
1
1.1
BACKGROUND AND OBJECTIVES
1
1.2
OUTLINE OF THE REPORT
2
2.
RELIABILITY OF JACK-UPS
3
2.1
WHAT IS RELIABILITY?
3
2.2
GENERAL APPROACH TO RELIABILITY OF JACK-UPS
5
2.3
FACTORS AFFECTING JACK-UP BEHAVIOR
7
3.
ENVIRONMENTAL LAODING AND RESPONSE
11 3.1
INTRODUCTION
11
3.2
ENVIRONMENTAL LOADING
11
3.3
DYNAMIC RESPONSE
16
4.
FOUNDATION BEHAVIOR
19
4.1
JACK-UP FOUNDATION ASSESSMENT
19
4.2
STEP 3 METHOD FOR SAND
22
4.3
STEP 3 METHOD FOR CLAY
25
4.4
FIELD AND TEST DATA
25
4.5
STATISTICAL MODELING
29
-iii-
5.
RIG DATA
31
5.1
HULL ELEVATED WEIGHT AND COG
31
5.2
LEG AND SPUDCAN WEIGHT AND COG
31 5.3
DIMENSIONS OF LEG STRUCTURE
31
5.4
LEG-HULL CONNECTION AND HULL STIFFNESS
32 5.5
CHOCK / PINION STRENGTH
32
5.6
LEG STRENGTH
32
5.7
SHAPE IMPERFECTIONS
33
6.
JACK-UP PUSHOVER AND RELIABILITY ANALYSIS
35 6.1
PROJECTS SURVEYED
35
6.2
SUMMARY OF RESULTS
36
6.3
REVIEW OF INDIVIDUAL PROJECTS
41
7.
PROCEDURE FOR RELIABILITY ANALYSIS
49
7.1
LIMIT STATES
49
7.2
STEP-BY-STEP PROCEDURE
50
8.
IMPACT OF CHANGES TO T&R 5-5A
55 8.1
PROPOSED CHANGES AND CASES ANALYSED
55 8.2
SUMMARY OF RESULTS OBTAINED
59
9.
CONCLUSIONS
63
10.
REFERENCES
65
APPENDIX 1 - GLOSSARY OF STRUCTURAL RELIABILITY ANALYSIS AND
RELATED TERMS
-iv-
EXECUTIVE SUMMARY
The present project aims to develop a robust methodology to provide quantified guidance
relating to the impact on reliability of changes to the SNAME T&R Bulletin 5-5A
Recommended Practice for site assessment of jack-ups being presently considered by the
industry. This will facilitate the industry consensus necessary for such changes to be fully
incorporated into jack-up site assessment. Phase 1 of the work is covered in this report.
As modeling improved over the past decade the estimated reliabilities increased substantially
relative to those initially estimated in the calibration of T&R 5-5A. In addition, field experience
with jack-up rigs operating in water depths exceeding 90m has also significantly expanded. Both
factors permit changes to T&R 5-5A to be examined in a more confident manner.
A review of previous pushover and reliability analyses is given and areas where modeling
improvements are recommended were identified. Appendix 1 includes a glossary explaining key
terms used in reliability assessment to facilitate discussion within the industry. High levels of
jack-up system reliability were identified based on structural strength, assuming stable
foundations and sufficient air gap. It is expected that such positive results will be maintained
when foundation failure is included by adopting less biased, state-of-the-art foundation models.
Factors that affect jack-up system reliability were identified and a premise for performing
reliability analyses of jack-ups utilizing state-of-the-art modeling is outlined. The premise was
independently reviewed by Prof. Robert Bea of University of California at Berkeley.
Two rig / location cases were selected that were as close to the T&R 5-5A calibration cases as
possible and the impact of proposed changes to T&R 5-5A on unity checks was evaluated based
on such cases. The analyses were focused on proposed improvements in the modeling of
foundation fixity and an expansion of the rig’s operational envelope was observed for Case 1
(Mod V in 97m Water Depth) but not so much for Case 2 (116-C in 65m Water Depth).
Phase 2 (to be funded on a joint industry basis) will apply the premise here developed in order to
assess the impact of proposed changes to T&R 5-5A on jack-up system reliability levels.
-v-
-vi-
1. INTRODUCTION
1.1 BACKGROUND AND OBJECTIVES
The present scope of work was agreed between the UK Health and Safety Executive (HSE) and
Global Maritime (GM). Its principal aim is to develop and implement a robust methodology to
provide quantified guidance relating to the impact on reliability of the changes to SNAME T&R
Bulletin 5-5A1 being presently considered by the industry.
T&R 5-5A was developed nearly ten years ago when jack-up units were moving into North Sea
locations for operations in deeper water, stiff soils and in a harsh environment where evacuation
of personnel may not be an option. This was, at the time, relatively new compared to the
traditional operations jack-ups performed in the Gulf of Mexico.
The assessment criteria in T&R 5-5A was subject to a calibration2 where a load and resistance
factor design (LRFD) approach was taken based on notional reliability estimates. This was also a
relatively new approach within the industry, following shortly after the development of API RP
2A – LRFD3 for fixed structures.
On the operational side, Hunt4 notes that jack-up drilling in water depths of 90m or more was
previously considered a challenge, but over the last ten years a number of these units have
successfully completed drilling programs in such water depths in the North Sea:
x
Global Santa Fe Galaxy I, Shearwater, 90m, 1995
x
Global Santa Fe Galaxy III, S. Everest, 90m, 2000
x
Global Santa Fe Monarch, Mungo & Marnock, 91m, 1998
x
Global Santa Fe Monitor, Erskine, 90m, 1996
x
Maersk Endurer, Shearwater, 90m, 1997
x
Maersk Giant, Yme, 93m, on location for 5.5 years
x
Maersk Galant, Huldra, 125m, 2000
The same paper4 indicates that jack-ups are being considered for North Sea operations in 400ft
(120m) water depth. Jack-ups have also been successfully deployed in water depths exceeding
90m in the Gulf of Mexico and worldwide locations.
On the technical side, significant advances have been made in the prediction of jack-up response,
system strength and reliability. Notional reliabilities estimated in the calibration2 of T&R 5-5A
suggested relatively high probabilities of failure due to environmental overload in some cases
with annual probability of failure for exemplary rigs (assumed as operating near their limits all
year) in the range of 7x10-4 (E = 3.2) to 8x10-2 (E = 1.4). The average probabilities of failure for
the exemplary rigs were of 0.5x10-2 (E = 2.6) to 1.4x10-2 (E = 2.2). The relatively limited number
-1-
of jack-ups operating near their limits and the inexistence of a clear record of failures and of
‘remarkable survivals’ does not permit a confident verification of such values. However, new
technology allowed several sources of conservatism in those simplified analyses to be removed
and a better appreciation of the risks associated with environmental overload has evolved.
On the economic side, the continued success of the oil industry in the North Sea in the coming
years will depend strongly on the application of improved technology to achieve more efficient
operations but maintaining high safety levels.
A prima facie case exists for examining improvements to T&R 5-5A that may allow an expansion
of the operational envelope of jack-ups while maintaining adequate safety levels. A step in this
direction has been taken with the reduction in load factor5 from 1.25 to 1.15 when using 50-year
extremes of wave, wind and current (or the adoption of 100-year joint probabilities with a load
factor of 1.25 which appears to give similar results in the North Sea). An increase of 6% in
allowable water depth relatively to the Revision 1 of T&R 5-5A was identified for a specific case
in a recent HSE-funded study6.
Further improvements of T&R 5-5A are being proposed by the industry and reliability based
techniques provide a useful framework for examining the impact of such changes on safety
levels. The principal aim of this project is to develop a robust methodology for performing
reliability analyses of jack-ups utilizing state-of-the-art modeling aiming at providing robust
quantified estimates of reliability levels associated with proposed changes to T&R 5-5A.
1.2 OUTLINE OF THE REPORT
The project covers the following main tasks:
x A review of pushover and reliability analysis of jack-ups.
x An analysis premise outlining a methodology to be adopted in jack-up reliability analysis
utilizing state-of-the-art models.
x Determination of the impact of the proposed changes to T&R 5-5A on the limits of operation
of two rig/location cases (close to the exemplary rigs in the T&R 5-5A calibration). In Phase
2 of the project (to be funded on a joint industry basis) one of such cases is to be selected for
implementing the proposed reliability analysis methodology.
Section 2 of the report summarizes the main aspects to be considered when evaluating system
reliability of jack-ups. Section 3 covers environmental loading and response including both quasi­
static and dynamic effects. Section 4 covers foundation behavior for both soft clay and stiff sand
soils. Section 5 covers rig data and structural strength. Section 6 summarizes a survey and a
critical review of jack-up pushover and reliability analyses carried out by the industry in recent
years. Section 7 outlines an analysis procedure for estimating jack-up reliability levels. Section 8
summarizes the results obtained concerning the limits of operation of the two rig/location cases.
Section 9 gives conclusions and recommendations.
-2-
2. RELIABILITY OF JACK-UPS
2.1 WHAT IS RELIABILITY?
The term reliability has different interpretations within the offshore industry. For example,
reliability of components (number of failures per year) is catalogued in several databases. Risk
assessment methods (HAZID, HAZOP, FMEA, etc.) look into the potential failure scenarios
arising from initiating events and their consequences. Structural reliability analysis (SRA) is
related to but distinct from the above and has generally applied a quantified probabilistic
framework to evaluate the probability of failure of an initially intact structure given the design
safety margins (or safety factors).
The International Maritime Organization (IMO) risk based approach as recommended by Formal
Safety Assessments (FSAs), for example, consists of five interlinked steps: 1) Hazard
identification, 2) Risk analysis, 3) Identification of risk control options, 4) Cost-benefit
assessment of the risk control options, and 5) Recommendations to decision makers. When
performing FSA for ship and offshore structures it is beneficial to apply structural reliability
analysis in the risk assessment (Step 2) and the cost-benefit assessment (Step 4). The failure paths
and criticality of structural components based on results from SRA are also a useful input to Step
3 and to Step 5.
SRA estimates of a simplified nature have been utilized in several applications such as in the
calibration of load and resistance factor design (LRFD) practices. The SRA results obtained as
part of such process are often referred to as notional reliability estimates. The term notional
reliability (or the very fact that the number has only notional value as in the calibration of T&R 5­
5A) often raises questions amongst practicing engineers about the validity of utilizing SRA.
The deviation between results obtained from such LRFD practices and those of existing practices
may also be a matter that needs careful consideration and often draws criticism towards the
application of reliability based approaches.
It is often difficult to make comparisons between calculated reliabilities and actuarial reliability
values (based on observed rates of failure). The differences between calculated reliability and
actuarial reliability arise due to the different uncertainties involved:
x
Type I (or aleatory) uncertainty which is associated with the natural randomness of
physical phenomena. It is also known as inherent uncertainty and cannot be reduced with
additional information.
x
Type II (or epistemic) uncertainty arises from limitations in knowledge including, for
example, measurement uncertainty, statistical uncertainty and modeling uncertainty. It
can be reduced with additional information.
x
Type III uncertainty is associated with human and organizational factors.
-3-
It is not feasible to obtain measurements, statistical analysis or mechanical / structural modeling
totally free from Type II uncertainty. It is possible (and necessary) to represent such uncertainties
in terms of their associated bias and variability but the accuracy of such representation depends
on the existing knowledge. So the calculated reliabilities will tend to be impacted by our
knowledge limitations.
Historically SRA has focused on well defined loading and failure conditions such as member
failure under extreme storm loading or fatigue of welded connections and generally does not
include Type III uncertainties. By contrast the actuarial reliability as expressed by statistics of
failure will highlight Type III uncertainties as human and organizational malfunctions can result
in blowouts, collisions, fires or explosions. In Boon et.al.7 five cases of damage to pinions in the
elevating system are discussed but again none were related to an overload due to insufficient
design safety factors.
Recorded rates of failure are also impacted by uncertainties in the characterization of the failure
and its initiating events. In jack-up operations, for example, most incidents can be termed
structural failure as something broke in some way but most reported incidents can be attributed to
human and organizational factors, resulting from a combination of errors or omissions by the
designer, builder and / or operator.
The key to improve calculated reliabilities is to reduce Type II uncertainties until their impact is
small compared to those of Type I uncertainties. SRA will then emulate the actuarial reliability of
a system in an error-free environment. In order for such estimates to remain a robust
representation it is necessary to minimize the system ‘fragility’ (its sensitivity to human and
organizational factors). The concerns discussed above are progressively being resolved as the
application of SRA matures, more realistic risk levels are estimated and engineers become more
familiar with the techniques involved.
SRA introduces features many practicing engineers are not familiar with, but it is essentially a
more rational way of covering some of the same issues designers attempt to address when using
the traditional working stress design (WSD) method:
x
Possible unfavorable deviations between the nominal design loads / load effects and those
potentially experienced by the structure in the field.
x
Possible unfavorable deviations between the as-built structure and the nominal material
properties, component strength and fabrication tolerances assumed in design.
x
Uncertainties related to the above.
x
Possible deviations between novel design concepts (and potentially different limit states),
fabrication methods and installation procedures relative to established practices.
x
The reduced probability that space and time variant loads will be focused in time and
space as assumed in design.
x
Consequences of failure (brittle vs. ductile failure, system effects beyond first component
failure, manned vs. unmanned structures, reduced exposure, etc.).
x
Criticality, accessibility, inspectability and durability (components that need to be more
carefully detailed, monitored, inspected and maintained).
-4-
There are several operational issues that are perhaps unique to jack-ups such as those associated
with punch-through, footprint interaction or incidents during wet tow but the issue of safety
factors used in jack-up site assessment criteria relates mostly to risks associated with
environmental overload for the intact unit in its elevated condition. It is in this type of application
(determination of design / assessment safety factors) that SRA can be of most benefit and this will
be the focus of this report.
2.2 GENERAL APPROACH TO RELIABILITY OF JACK-UPS
Structural reliability has formed the basis for the calibration of LRFD practices for the design of
fixed structures such as API RP 2A – LRFD3 and the North West European Regional Annex to
ISO 19902 presently under development8.
An important observation is that air gap exceedance and foundation failures have not been dealt
with in a direct manner in such calibrations. An important reason for the latter is the significant
conservative bias in existing prediction models for foundation behavior and failure which may
lead to predicted risk levels that are perhaps unrealistically high as discussed by Efthymiou9 and
by Bea10. Bias is defined as the ratio of the true value of a random variable to the predicted or
nominal value.
The ‘separation’ between structural and foundation failure in fixed structures is a helpful strategy
for calibration but it should be noted that when a more accurate foundation model is included,
system failure may occur not due to a sequence of structural component failures but due to a
progressive loss of foundation stiffness and excessive deck displacements. The concept of
ductility spectra shown in Figure 1 is more realistic and expresses the structural capacity as the
necessary structural ductility to accommodate an extreme event.
Figure 1 – Ductility Spectrum for Fixed Platform11
-5-
In Figure 1, ductility is defined as the ratio of the global structural displacement at the final
plastic structural failure relative to the global structural displacement at first component failure. In
simple terms, the structure is able to accommodate an overload in excess to that predicted by a
‘static’ pushover analysis by dissipating energy in the form of inertial forces and plastic straining.
In addition, energy will be dissipated by increased damping in the foundations.
Omission of the transient, dynamic non-linear effects on the loading and response of the structure
is a common simplification adopted in SRA. This may be an implicit conservative bias in the
static pushover analysis not explicitly accounted for as it will depend on the type of structure, soil
conditions, etc. It can be noted in Figure 1 that because the jacket structure is now softening due
to yield, dynamic effects may play a more important part in the response.
A ductility spectrum for jack-ups is shown in Figure 2 in terms of hull sway. The dotted line at
3m hull sway corresponds to failure in a ‘static’ pushover (overload ratio of 1.0).
Figure 2 – Ductility Spectrum for Jack-up12
Ductility may allow loading levels that are 20% higher (overload ratio of 1.2) to be
accommodated but this margin is highly dependent on dynamics as could be expected for the case
of a jack-up. The hull sway for overload ratio of 1.0 (static pushover) is not so dependent on the
natural period but very large values of sway were predicted for the higher overload ratios
depending on the natural period.
The separation between structural and foundation failure in analysis is much harder to justify
when looking at the reliability of jack-ups because of the important interaction between structure
and foundation. This puts a premium on the future application of realistic foundation models
when evaluating jack-up reliability.
-6-
According to Bea13, loss of air gap may have contributed to jack-up failures during hurricanes
(such as Hilda). However it is unclear how site assessment, preloading and air gap practices at the
time correlate to those presently adopted by the industry. This subject will not be covered in
detail in this report. Also according to Bea13, a large part of such failures may correspond to mat­
supported units which will not be covered in this report. It is noted that for independent leg units,
different models have been applied to evaluate the impact of wave loads in the hull14, 15 and this is
an issue under discussion by the jack-up industry16 and being covered by a separate HSE
project17.
2.3 FACTORS AFFECTING JACK-UP BEHAVIOR
The following factors tend to have an impact on the physics of jack-up response and failure.
x
Rig data
o Hull elevated weight and Longitudinal Centre of Gravity (LCG)
o Leg and spudcan weight and buoyancy
o Leg structure
o Leg-hull connection
x
Environmental Conditions
o Water depth
o Wave height, peak periods, directionality, spreading
o Wind velocity, gustiness, profile, directionality
o Current velocity, profile, directionality
o Tide and surge
x
Environmental ‘Load Recipe’:
o Leg drag coefficient
o Wind areas
o Wave kinematics
o Current blockage
o Marine growth
x
Dynamic Extreme Response
o Long-term random dynamic response
o Non-Gaussian effects
-7-
o Rogue waves
o Mass and added mass
o Damping ƒ
Structural (viscous)
ƒ
Hydrodynamic (fluid-structure relative velocity)
ƒ
Soil (viscous, hysteretic, radiation)
o Natural period: cancellation / reinforcement
o Sea spectra
x
Spudcan - Soil Interaction
o Soil Properties (sand /clay)
o Preload and penetration
o Foundation behavior within soil yield surface
ƒ
Stiffness (vertical, horizontal and fixity)
ƒ
Coupling effects
ƒ
Spudcan embedment
ƒ
Backflow
o Soil yield surface
ƒ
Bearing capacity under leeward leg
ƒ
Sliding capacity under windward leg
o Foundation behavior beyond the yield surface
ƒ Additional penetration under leeward leg
ƒ Suction effects under windward leg. The suction force under the footing
may be as significant as the bearing capacity but is highly dependent on
soil type.
o Spudcan shape and roughness
o Cyclic degradation
o Strain rate effects
o Scour / erosion
o Layered soils (squeezing, punch-through)
-8-
x
Structural / Mechanical Resistance
o Material properties
ƒ
Yield strength
ƒ
Young’s modulus ƒ
Ductility / Strain hardening
ƒ
Cyclic degradation
ƒ
Strain rate effects
o
Leg inclination
o
Chock / pinion capacity
In performing a reliability analysis appropriate variables need to be defined for quantified
predictions to be made. In principle, probability density functions need to be defined to cover
both the Type I and Type II uncertainties associated with such variables. It is noted that the
response surface method permits several of these variables to be covered by a global response
parameter such as base shear and overturning moment. The response surface method18, 19 is an
effective procedure to avoid the complexity associated with treating joint occurrences of random
environmental variables.
Previous reliability analyses2, 20-24, have dealt with several of these variables and published results
provide us with some guidance on the most significant ones. There is very little information on
dE / dP (rate of change of the Safety Index E with the mean value P of a variable) which could
provide information on the impact of Bias in predicting a given variable.
However there is sufficient information on sensitivity factors D from first order reliability method
(FORM) analyses providing useful information regarding the impact of the Type I and Type II
uncertainties of a given parameter on the overall reliability levels.
Although results tend to vary, the different publications (discussed in Section 6) consistently
point to uncertainties in the following variables as having the most significant impact on
reliability levels:
x
Significant wave height (Hs) of extreme seastates: D in the range of 20% to 70%
x
Variability of extreme crest (or rig response) in a seastate: D in the range of 15% to 25%
x
Environmental ‘load recipe’: D in the range of 5% to 30%
x
Resistance: D in the range of 9% to 50%
The different publications (see Section 6) consistently point to uncertainties in the following
variables as not having a significant impact on reliability levels (D of 5%-6% or less):
-9-
x
Spectral peak period
x
Spectral peak enhancement factor
x
Current velocity
x
Wind velocity
x
Tide and surge
x
Lightship
x
Variable load
It is worthwhile noting that in most references20-24 uncertainties related to adopted foundation
fixity levels were accounted for and showed no significant impact on the overall reliability levels
even when a coefficient of variation (CoV) of 25% was adopted. It is noted that the stiffness of
the soil at high load levels is fundamentally dictated by the soil yield surface. The vertical
capacity in the yield surface is tested on site by preloading the unit and the moment capacity is
related to the vertical capacity and to the spudcan diameter and is in a sense also tested. The soil
uncertainties will have more of an impact on the horizontal capacity - this capacity is not very
important for bearing failure under the leeward leg but may be more important for sliding of the
windward leg.
It appears that it is the bias in modeling (such as using pinned condition as opposed to a
displacement foundation fixity model) and therefore in the predicted mean value that impacts the
results rather than the variability and uncertainty in the soil properties.
-10-
3. ENVIRONMENTAL LOADING AND RESPONSE
3.1 INTRODUCTION
A vital part of SRA is to generate probability distributions of extreme loads considering the
following environmental conditions:
x
Water levels
x
Wave height, peak periods, directionality, spreading
x
Wind velocity, gustiness, profile, directionality
x
Current velocity, profile, directionality
There is a vast body of published work dealing with this topic, particularly in connection with
fixed platforms. A comprehensive review is beyond the scope of the present work and this report
will summarize only the key aspects and latest developments that are likely to impact jack-up
reliability.
The fundamental objective here is to establish long-term distributions for the rig global response
in terms of base shear and overturning moment. Several different areas need to be addressed:
x Short-term statistics of ocean surface elevation (within a seastate or storm)
x Long-term statistics of ocean surface elevation (with an annual probability of exceedance
of 10-4 or less)
x Long-term joint environmental models for surface elevation, periods, current, wind,
spreading, etc.
x Kinematics of extreme waves and fluid-structure interaction forces
x Long-term statistics of response for dynamically sensitive structures
x Analysis of uncertainties associated with the above
3.2 ENVIRONMENTAL LOADING
Wave and response processes are not necessarily stationary over long periods of time such as
those of interest in SRA. In other words the statistics vary with time. However, the water surface
elevation can be considered stationary within a timescale of 20 minutes to a few hours. In broad
terms the complete long term description of environmental or load statistics is usually a
combination of short timescale models and long timescale models.
-11-
The shorter periods of stationarity are controlled by the significant wave height Hs and a measure
of periodicity (such as the peak spectral period Tp or the zero-upcrossing period Tz) while a long
term formulation gives the probability distribution of Hs, Tp or Tz.
A reference for the short-term statistics of ocean surface elevation known to most naval architects
is the paper by Ochi25. In simple terms, for a fully developed, wind generated sea (no swell and
no coastal effects) the paper formulates point-in-time water surface elevation as a stationary,
narrow-banded Gaussian process. The peaks of this process (such as the crests), assumed as
statistically independent, are then represented by a Rayleigh distribution and the maximum in N
peaks (N crests) by a ‘powered’ Rayleigh distribution.
Over the last 30 years several improvements have been developed, some of which are
summarized by Guedes Soares26. Explicit reference is made here to the work of Forristal27-29.
Results of direct assistance to designers are given based on a combination of theory, physical
experiments and numerical experiments. For example, crest height is related to significant wave
height as a function of wave steepness and water depth, including the effects of second-order
interaction between spectral components and directional spreading. Figure 3 shows results in
terms of the ratio between crest height and significant wave height at the 1/1000 probability level
(most probable maximum in three hour storm).
Figure 3 – Crest Height normalized by Hs27
-12-
A Weibull distribution is used to fit numerical results for 3-hour seastates as follows:
P (Kc > K) = Exp [- (K / D3Hs)E3]
(1)
Where P (Kc > K) is the probability that the crest height Kc will exceed a given value K in a
seastate with significant wave height Hs. The following non-dimensional parameters are given:
Steepness ratio S1 = (2SHs) / (g T12)
Ursell number Ur = Hs /
k12
d
(2)
3
(3)
D3 = 0.3536 + 0.2568 S1 + 0.08 Ur
(4)
E3 = 2 – 1.7912 S1 – 0.5302 Ur + 0.284 Ur2
(5)
Here T1 is the mean wave period calculated from the ratio of the first two moments of the wave
spectrum (effectively an alternative to Tp or Tz), g is gravity, k1 is the wavenumber for a
frequency of 1/T1 and d is the water depth.
Moving to the longer timescales, most wave databases provide information of the scatter diagram
at a point and sometimes include directionality. A bi-variate distribution of Hs, Tp can be
constructed from a conditional distribution of Tp and a marginal distribution of Hs. For example,
Weibull or Gumbel distributions can be fit to extreme values of Hs and distributions of wave
period conditional on Hs can be adequately modeled by a log-normal distribution.
A similar approach is taken for other environmental conditions such as water levels, current
velocity and wind velocity in that a conditional distribution is defined for each of these
parameters and used together with the marginal distribution of Hs.
A significant development in the North Sea has been the development of the NEXT hindcast
database which is the product of studies performed by Oceanweather Inc. as part of a joint
industry project (JIP) to extend and enhance the NESS (North European Storm Study) hindcast
database. In very broad terms, hindcasting produces a series of wind, wave and current
information that allows the estimate of the statistics of a broad range of environmental, loading
and response parameters.
Tromans and Vanderschuren have recently completed work30-32 where long term statistics of
extreme environmental load were derived from NEXT in support to the fixed platform JIP8
‘North West European Regional Annex to ISO 19902’.
A starting point of the work is the use of entire storms as independent events much as used in the
Gulf of Mexico. This is different from the conventional North Sea approach to obtaining long­
term marginal distributions of Hs by fitting cumulative distributions to the significant wave
heights of successive seastates, neglecting both the correlation between successive seastates and
the uncertainty in the extreme wave of a seastate.
The short time statistics are conditional on and defined by the most probable extreme response.
Figure 4 shows results for base shear (X) normalized by the most probable maximum base shear
in each storm (Xmp). Adopting this normalization, the envelope of the distributions for all storms
in the time series do not depart much from the average. Such distributions attempt to capture the
Type I uncertainties (natural variability) associated with the extreme value of response in a
seastate.
-13-
Figure 4 – Probability Distribution of the Extreme Response in a Storm –
Base Shear at Inde Platform30
The largest storms from a directional sector are then used to fit a probability distribution for the
Xmp values. Such distributions attempt to capture Type I uncertainties (natural variability)
associated with the long term response.
Since the method is formulated in terms of response it is sufficiently general to capture the most
probable maximum surface elevation or global loading or structural response thus lending itself to
the derivation of long-term response statistics including joint probabilities.
For example, recent results33 suggest that for a Central North Sea location, crest height values
including the latest NEXT data and joint probabilities for tide and surge would lead to a total
height of 19m for a 10,000-year return period. As a comparison, conventional practice based on
HSE’s guidance notes would suggest 100-year independent crest, tide and surge values adding to
18.5m. The difference in approaches is significant, particularly in terms of air gap requirements.
The work by Tromans and Vanderschuren30 suggests the following distribution for the
normalized annual probability of exceedance of global loading:
Q (L / L100) = Exp [- (L / L100 – 0.350) / 0.141]
(6)
where L is the quasi-static load for a given return period normalized by the 100-year value L100.
Based on equation 6, the ratio of global loading for a 10,000-year return period to the global
loading for a 100-year return period is 1.65.
Such a ratio is in reasonable agreement with in-house data for various locations in the North Sea
as shown in Figure 5.
-14-
Figure 5 – Variation of Base Shear with Return Period (North Sea)
As discussed above, the results implied by equation 6 include Type I uncertainties due to both
short and long term natural variability of global loading. The paper does not explicitly quantify
such uncertainties but it suggests that results from NEXT for the whole of the North Sea tend to
converge towards those previously obtained with NESS for the Northern North Sea. Based on
previous publications9, it is deducted that a total global force CoV of 21.5% applies at the 100­
year level just for Type I uncertainties, approximately composed of 15% due to short term natural
variability and 15% due to long term natural variability.
Now turning to Type II (modeling) uncertainties, environmental variables corresponding to return
periods of 50, 100 or 10,000-years need to be evaluated on the basis of time series of data
extending over a relatively short time period of, for example, 5 to 30 years. The uncertainties
associated with such estimates are an important issue.
In addition, when looking at force estimates further uncertainties arise due to:
x
Leg drag and inertia coefficient
x
Wind areas
x
Wave kinematics
x
Current blockage
x
Marine growth
-15-
Tromans and Vanderschuren30 give an alternative equation that includes Type II uncertainties in
the hindcast and other aspects of the method (fitting of probability distributions, modeling of
short term uncertainty in the extreme of a storm, estimating of the arrival rate of storms):
Q (L / L100) = Exp [- (L / L100 – 0.327) / 0.146]
(7)
The same paper proposes that, in addition, the environmental design load at the 100-year level
arising from the ISO standard (or API RP 2A LRFD) that is part of equations 6 and 7 is subject to
9% conservative bias and a CoV of 16.5% (Type II uncertainties of 15% due to extrapolation of
wave height data and 9% due to the load ‘recipe’) and that such uncertainty should be modeled by
an additional modeling uncertainty variable with a normal distribution truncated at +- 1.5
standard deviations (as values beyond such truncation limit would be filtered out during the
design process). Comments by Tromans34 indicate that an overall global loading CoV of at least
30% will result.
It is noted that the CoV values proposed by Tromans and Vanderschuren30 are relatively low in
comparison to others suggested within the industry13,35.
The approach taken above was strongly influenced by comparisons between measurements and
predictions on a seastate-by-seastate basis rather than on a wave-by-wave basis. The latter is
related to the wave force peak associated with the largest wave height at a particular point and
involves greater uncertainty than the former which is related to the largest wave force occurring
in a particular seastate which is the parameter of interest in reliability analysis. It is also pointed
out34 that uncertainties in the individual components of the wave load recipe tend to be averaged
when looking at the results of the recipe as a whole.
3.3 DYNAMIC RESPONSE
There is again a vast literature covering this aspect of jack-up behavior but this report will
concentrate on the most relevant recent work. Extensive investigations on the long term non­
linear response of dynamically sensitive jack-ups were reported in several publications by
Karunakaran and co-authors36-41.
This work provided a very comprehensive verification of design methods for estimating dynamic
amplification factor (DAF) values as compared to a probabilistic approach accounting for the
effect of non–linearities in the long term response of jack-ups rigs.
Such non-linearities arise in the environmental loading due to drag loading as well as nonGaussian behavior of the sea surface elevation, the structural response due to p-' effects and the
soil-structure interaction due to non-linear soil properties and hysteretic behavior.
In simple terms, a Gaussian (normally-distributed) response will result from a linear system
subject to a Gaussian input. A non-linear system will tend to display non-Gaussian response even
for Gaussian input which means that a given value of response may be more likely to be exceeded
than would be estimated from a normal distribution, see Figure 6.
-16-
Figure 6 – Typical Normalized Statistics of Response to a 3-Hour Seastate
In jack-up site assessment this effect is incorporated by assuming that the water surface elevation
at a given point follows a narrow-banded normal distribution (Gaussian process). This is used as
an input to random dynamic simulations of jack-up response including non-linear behavior. The
statistics of response (base shear and overturning moment) from such simulations are then post­
processed to determine the most probable maximum extreme (MPME) value in a reference
seastate.
The MPME can be expressed as:
(8)
MPME = P + Cr V
Here P denotes the mean value and V denotes the standard deviation of a given response R. Cr is
the drag-inertia parameter which indicates the degree of non-gaussianity in the response.
By conducting the simulation with and without dynamics, the MPME values can be inferred for
the quasi-static response only and for the total response including dynamics and DAF values can
be derived.
Typical results in terms of base shear and overturning moment for a jack-up structure are shown
in Figure 6 (based on in-house data) which gives the probability distribution (in the vertical axis)
for the rig response (in the horizontal axis, normalized by the mean and standard deviation) to a
three-hour storm. The log-log plot is used so that a Weibull distribution plots as a straight line.
-17-
At the MPME probability level (1-1/Np, where Np is the number of peaks) the drag-inertia
parameter Cr for water surface elevation approaches a value of 3.7 indicating that the input
seastate had indeed Gaussian behavior.
The drag-inertia parameter for the quasi-static base shear and overturning moment tends to
exceed 8.0, typical of highly non-Gaussian response due to drag-dominated loading (fluid forces
are proportional to the square of the fluid velocity). In such a case, there is a higher probability of
exceeding a given response – or smaller Ln(-Ln(1-Probability)) – than would be given by
Gaussian response behavior. The inertial component of response for such a lightly damped
system tends to have a more linear nature and the total response including quasi-static and inertial
components is re-normalized (Cr = 4.9) as it tends to converge back to a normal distribution.
An important consequence is that, everything else held constant, the same load factor will lead to
a higher reliability for an inertia-dominated structure (such as a gravity based structure or a
floating vessel) than for a drag-dominated structure (such as a jacket platform). Jack-ups tend to
fall somewhere in between these two cases depending on the water depth, with inertial loads
becoming more important in deeper water. Another interpretation is that a smaller load factor is
needed for an inertia-dominated structure in order to achieve a given level of reliability.
Typical site assessment DAF values include simplifications such as assuming Gaussian water
surface elevation as mentioned above (which is not strictly true), assuming a damping ‘recipe’
covering structure, soils and fluid (T&R 5-5A recommends a 7% ‘blanket’ value of modal
damping when neglecting fluid-structure interaction or a 4% value when accounting for this
effect with the relative form of the Morison equation) and adopting different ways of modeling
the spudcan-soil non-linear behavior.
The radiation damping component of soil-structure interaction can be very important but is not
straightforward to quantify or validate against test and field data as it may depend on the soil type
and the level of loading. Such a component of damping is mostly neglected in assessment or
incorporated in the 2% total damping assigned to the foundation.
The work reported by Karunakaran and co-authors36-41 included a combination of analytical,
model test and field instrumentation results explicitly accounting for the most significant non­
linearities and providing robust evidence that presently used design assumptions are on the
conservative side. The above discussion indicates that the variability associated with the dynamic
response is actually less significant than that associated with the quasi-static drag loading.
-18-
4. FOUNDATION BEHAVIOR
4.1 JACK-UP FOUNDATION ASSESSMENT
Foundation behavior has a significant impact on the safety and operational capability of a jack-up
unit. The fundamental issues to be recognized in jack-up foundation assessment are as follows:
x A safety margin should exist between the loading in the footing and a representative soil
resistance value, see Figure 7.
x Unless there is potential for punch-through, foundations do not buckle as, for example,
steel members in compression. Foundation limit states need to be defined in terms of
plastic softening that may lead to a structural or mechanical failure preventing personnel
evacuation or preventing the rig from jacking down and moving off location.
x It follows that the failure envelope FVH in Figure 7 is actually a function of spudcan
displacements. The two more fundamental mechanisms for excessive displacements in
the foundations are:
o Bearing failure under the leeward leg footing
o Sliding of the windward leg footing
x The boundary conditions (fixity) provided by the spudcan-soil interaction have a very
significant effect on the forces in the structure and in the footing itself as it impacts
footing reactions, the bending moment distribution along the leg, the dynamic
amplification and the p-' effects.
Figure 7 – Foundation Check to T&R 5-5A
-19-
The loading on the footing is basically comprised of a combination of vertical reaction V,
horizontal reaction H and moment M. For simplicity Figure 7 shows only vertical and horizontal
loads but the concepts can be easily extended to include moment. The vertical leg reaction is a
random variable that fluctuates around its mean value given by the mean gravity loads (dead and
variable) and by zero horizontal load (Points A and C in Figure 7).
Under the leeward leg both vertical and horizontal reactions tend to increase with increasing
environmental loading (Path A – B in Figure 7). The bearing capacity FVH of the soil is given by a
vertical foundation capacity that depends on the horizontal reaction H.
Under the windward leg the horizontal reaction tends to increase and the vertical reaction tends to
decrease with increasing environmental loading (Path C – D in Figure 7) and the potential for
sliding needs to be investigated. Figure 7 shows the sliding capacity line FH for sand as controlled
purely by frictional effects (V*tanG, where G is the steel-soil friction angle). Passive pressure
resistance will also contribute to the resistance against sliding, particularly if the footing has
protrusions such as a tip of conical, cruciform or other geometry.
In a working stress design (WSD) format the safety margin is provided by a safety factor while in
a load and resistance factor design (LRFD) format such as that in T&R 5-5A a load factors JE and
resistance factors ØVH and ØHfc are adopted as shown in Figure 7.
The selection of appropriate values for the safety factor (or load and resistance factors) is by no
means a simple task. According to Bea13, onshore foundation design tends to adopt safety factors
of the order of 1.5 (referenced to 100-year storm conditions or 475 years for earthquakes). The
safety factor against jacket piled foundations within API RP 2A is also of the order of 1.5 for both
the WSD and LRFD versions.
However, the particularities of jack-up foundations need to be recognized. Although a
documented industry-wide standard for jack-up assessment was not available prior to T&R 5-5A,
it is well understood that historically jack-ups have been assessed in terms of safety against
bearing failure based on a preload check where the vertical reaction under the leeward leg (V50)
due to 50-year independent extremes of wind, wave, current and water levels, calculated based on
neglecting both dynamics and spudcan fixity, was required to be just under the vertical reaction
during preload Vo with a safety factor of 1.0 (V50 < Vo). This represents a safety factor of 1.0
against leg differential settlement thus accepting some level of settlement under the assessment
storm due to potential variability in loads and soil properties. This has been acceptable under the
tacit assumption that the true limit state is excessive deformation that could prevent evacuation of
personnel or prevent the unit from jacking down and moving off location.
Safety against sliding was implicitly covered by the overturning checks, again for 50-year
independent extremes of wind, wave, current and water levels. Historically sliding under the
windward leg has been assessed in terms of a safety factor of 1.1 against exceedance of the rig
righting moment by the environmental overturning moment, under the tacit assumption that the
rig would be able to jack down after the assessment event as its inertia would prevent structural or
mechanical overload.
T&R 5-5A explicitly requires inclusion of dynamics but also permits inclusion of fixity. Strict
load and resistance factors against any settlement under the assessment event are prescribed as
follows:
-20-
JE: 1.15 to 50-year extremes of wave, wind and current or 1.25 to 100-year joint probabilities ØP: 0.90 (preload check) ØVH: 0.85 (bearing capacity, fully embedded spudcan) ØHfc: 0.64 (sliding, clay, undrained), 0.80 (sliding, sand, drained) In evaluating footing loads three levels of foundation assessment are distinguished with
increasing order of complexity and model refinement as shown in Figure 8.
Figure 8 –T&R 5-5A Foundation Assessment Procedure42
Step 1 and Step 2a assume pinned conditions at the foundation in a structural analysis. The effects
of dynamics need to be included but any beneficial effects of fixity or load re-distribution
between the spudcans are neglected. Load and resistance factors are prescribed. Assuming the
100-year vertical reaction to be 50% due to gravity and 50% due to environmental effects than a
total safety factor of around 1.25 (Step 1) to 1.32 (Step 2a) is required against additional
settlement of the legs beyond the preload penetration. As far as sliding is concerned a total safety
factor of around 1.25 / 0.8 = 1.56 (sand) to 1.25 / 0.64 = 1.95 (clay) is required.
The results obtained in Steps 1 and 2a tend to significantly depart from historical practice.
The fundamental issue here is that T&R 5-5A applies resistance factors to the ‘load resistance’
(the load at which the structure fails) as opposed to the ‘displacement resistance’ (the
displacement at which the structure fails). The former may be well suited for a brittle type of
failure (such a brace under compression) but may not be well suited for a progressive softening
behavior as in jack-up foundations.
It is noted that, from a strictly statistical point of view, the limited population of jack-ups operated
near their limits may not permit a verification of actuarial reliability at the low failure probability
-21-
levels expected for manned structures. However there has been no well documented evidence that
the historical design criteria led to any premature failures.
Step 2b allows the use of non-linear rotational and of linear translational foundation stiffness but
the resulting load combination needs to stay within a soil yield surface:
16 *(V/VLo)2 *(1- V/VLo)*abs(1- V/VLo) – (H/HLo)2 – (M/MLo)2 = 0 (9)
Step 2b may lead to less conservative results than Steps 1 and 2a if the vertical and horizontal
capacities remain within the yield surface. However, as most rigs were designed to have preload
capacity consistent with the historical criteria, it follows that the vertical reaction tends to
approach the preload capacity and the yield surface once the rig approaches the limits given in the
MOM and no beneficial effects from fixity are actually realized.
The most advanced and least conservative way of assessing foundations to Step 2b includes the
following developments:
x Assume different stiffness values in the three spudcans. Van Langen42 developed a
hardening plasticity model consistent with Step 2b and demonstrated the additional
benefit that can be realized relative to pinned conditions as loading is shed from the
leeward to the windward legs.
x A recent IADC sponsored project43 has proposed modifications to the stiffness values
used in the evaluation of dynamic amplification factor (DAF) values to more closely
match the results of instrumentation programs.
Steps 1, 2a and 2b all limit the load combinations in the spudcan to values that lead to minimal
additional settlement beyond the penetration under preload.
Step 3 permits consideration of additional displacements beyond the initial penetration under
preload and may allow for expanded capacity, particularly for stiff soils as commonly found in
the North Sea. A Step 3 methodology should be adopted in reliability analysis where the ultimate
strength of the unit is being considered but this is not currently formulated in T&R 5-5A. The
next sections outline how a Step 3 methodology would be applied to sand and to clay soils.
4.2 STEP 3 METHOD FOR SAND
As discussed above the sliding safety margin under the windward leg of a jack-up tends to
decrease with decreased vertical load and also decrease with increased horizontal load. This
unfavorable combination is exactly what takes place under the windward leg of a jack-up as
global loading increases so the load combination under the windward leg may approximate the
soil sliding failure surface. This situation may be worsened by p-' effects and in stiff sand
conditions where there is a tendency for smaller penetrations and the spudcan may not have been
fully seated after preloading.
The potential migration of base shear to the leeward legs following sliding of the windward leg
would in principle increase the stresses in the leeward legs in what is sometimes referred to as the
Hambly failure mode44 after the late Edmund Hambly.
-22-
In addition, sand suction effects are likely to be much less significant in preventing uplift of the
windward spudcan. However, it is noted the inertia of the rig is expected to prevent such uplift
from occurring under the passage of an extreme environmental event.
Under the leeward legs, on the other hand, the increased vertical reaction will penetrate the
spudcan further and potentially increase the area of contact with the soil. This effect increases the
vertical bearing capacity proportionally to the cube of the increase in diameter as indicated, for
example, by T&R 5-5A.
In addition, the yield surface appropriate to the initial penetration in the seabed depends on the
preload reaction Vo causing that penetration. When the vertical leg reaction Vr is increased
beyond Vo, yielding occurs and a new yield surface develops through the new (and higher) Vr.
This is one of the main effects a Step 3 method aims to capture.
In a stiff soil such as in Figure 9 it is expected that significant additional soil capacity in terms of
vertical load and fixity may be mobilized with a limited amount of additional penetration. In
Figure 9, Vass is the vertical leg reaction in assessment, V10,000 and H10,000 are the vertical and
horizontal leg reactions due to the 10,000-year event. The additional leg settlement is found by
the combined yield surface.
Figure 9 – Foundation behavior in North Sea Stiff Soil
Field experience also indicates that significant forces need to be applied in order to fully seat
spudcans in the strong soils of the North Sea.
A Step 3 method was formulated and tested and results are illustrated in the Cambridge centrifuge
model tests45, Figure 10, where significant fixity was observed in the leeward legs after sliding of
-23-
the windward legs. The vertical load capacity in equation 9 was made to depend on the plastic
vertical displacements of the footing.
Figure 10 – Cambridge Centrifuge Test Data45, Dense Sands
It is observed that modeling pore water drainage in centrifuge tests can be a complex task
because, under ultimate load conditions, part of the leeward leg spudcan may separate from the
soil surface and the consequent pore water pumping effects may not be accurately modeled. Such
effects can be mitigated, for example, by conducting the tests with a viscous oil to model the pore
water pressure and drainage effects more accurately. Care must be taken in centrifuge testing,
particularly when cyclic loading a foundation on sand. Figure 10 is nevertheless useful in
demonstrating the potential benefits of applying a Step 3 method.
In summary, for stiff sand soils, the resulting soil-structural interaction under high levels of
loading will be a balance between the loss of stiffness under the windward leg and the plastic
stiffness under the leeward legs.
-24-
4.3 STEP 3 METHOD FOR CLAY
In soft clay soils there is a tendency for larger penetrations to be observed under preload. The
larger penetrations tend to make sliding of the windward leg much less of an issue as there is a
greater contact area between the soil and the spudcan (and sometimes the leg itself in case of
backflow). In addition the weight of the column of soil above the spudcan will provide a greater
constraint against lateral soil movement thus increasing the lateral resistance component of the
sliding capacity. Also suction effects are expected to be higher leading to tension stresses that
reduce the possibility of windward spudcan uplift.
In a clay soil as global loading is increased, the windward vertical leg reaction reduces and higher
values of horizontal load / moment may be accommodated within the soil yield surface than
would be the case for a stiff sand soil. However, under the leeward legs, the plastic soil
deformations may lead to large differential settlement. Spudcan fixity values will remain for load
combinations that exceed the yield surface given by T&R 5-5A but the settlement of the legs
needs to be carefully considered.
It follows that for soft clay soils the assumption of pinned conditions at the spudcans will usually
lead to conservative results, provided that the plastic displacements of the leeward legs do not
lead to excessive leg differential settlement. A Step 3 method for clay was formulated by Oxford
University47.
4.4 FIELD AND TEST DATA
Significant spudcan fixity has been observed in various instrumentation programs48-52. A common
approach used in such programs is to derive response spectra for parameters such as hull surge,
sway and yaw from measured data captured with accelerometers in suitable positions in the rig.
The spectral peak corresponding to the resonant response can be identified and the associated
period gives an indication of the natural period of the unit.
Fixity values that match the natural period evaluated from a Finite Element (FE) model with the
natural period evaluated from the measured responses can then be determined. The underlying
assumption is that various other parameters such as leg, hull and leg-to-hull stiffness as well as
the rig mass and added mass and the vertical and horizontal soil stiffness values can be reflected
in a FE model with sufficient accuracy. The most widely used definition of ‘dynamic’ fixity is:
F1 (%) = (fm2 - fp2) / (ff2 – fp2)
(10)
where fm is the measured natural frequency, ff is the natural frequency for fully fixed (clamped)
footings and fp is the natural frequency for pinned footings.
Major instrumentation programs have been reported in the North Sea including 32 storms
reported in the paper by Nelson et.al.48 for 8 rig / locations as well as 10 storms reported in the
paper by Hunt et.al.51 for 1 rig / location (Endurer at Shearwater) and reported52 in more detail in
HSE’s OTR Report 2001/035.
-25-
Figure 11 shows the measured wave heights normalized to the site specific values for different
return periods. The values reported by Nelson et al48 are understood to be maximum wave heights
normalized by the corresponding value according to the HSE guidance Notes. The values by Hunt
et al51 are based on significant wave heights normalized by the Shearwater design values.
Figure 11 – Measured Wave Heights48-52
The results reported by Hunt et.al.51 are significant as the maximum recorded seastate did
approach the 50-year return period storm quite closely (94% of the 50-year significant wave
height).
Figure 12 illustrates the potential softening of the foundations based on the three most severe
seastates observed based on information in the relevant papers. The curve also suggests that a
dynamic fixity of at least 25% could be easily justified at usual site assessment load levels.
Extrapolation to the 10,000-year level is of course not so straightforward but the trend for
softening with increasing storm intensity is nowhere near the severe reductions proposed by T&R
5-5A Step 2b (in the bottom part of the curve in Figure 12).
-26-
1
Magellan @ Joanne
Monitor @ Joule
Endurer @ Shearwater
0.9
0.8
Measured
Dynamic Fixity
0.7
0.6
0.5
0.4
0.3
fr = 0.66
0.2
T&R 5-5A
0.1
10,000-year
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Normalized Wave Height
1
1.1 1.2 1.3 1.4
(50-year)
Figure 12 – Foundation Softening with increasing Load Levels48-52
The most striking feature of the measurement results is shown in Figure 13 which compares the
dynamic fixity given by the measurements with that given by T&R 5-5A. It can be seen that the
largest departure between T&R 5-5A and measurements actually occurs for Endurer at
Shearwater, the case where the most severe storms were observed. While the measured fixity in
this case seems broadly in line with cases report by Nelson et.al.48, the fixity predicted by Step 2b
quickly drops towards pinned conditions as the 50-year event is approached – a common feature
of assessments to T&R 5-5A.
-27-
Figure 13 – Dynamic Fixity from Instrumentation Programs48-52
The reason for such behavior is illustrated by the centrifuge test data partially funded for Mod V
footings given in Temperton et.al.49 and summarized in Figure 14. As load combinations
approach the yield surface, T&R 5-5A Step 2b converges to pinned conditions. However, fixity
values for load combinations that exceed the yield surface (failure ratio of 1.0) can be clearly
observed and it is in this range that Step 2b departs more severely from the data. In Figure 14 Krot
is fixity, Vo is preload capacity and D is spudcan diameter.
Figure 14 – Centrifuge (Mod V) Test Data49
-28-
4.5 STATISTICAL MODELING
Several aspects of foundation design are difficult to quantify unless a significant amount of site or
laboratory data is obtained and carefully analyzed. Therefore a simplified, cautious and safe
approach is usually taken by geotechnical engineers in design and assessment. For example,
suction effects may develop in the jack-up soil-spudcan interaction leading to soil tensile stresses
that will increase the foundation capability to resist moment loads thus leading to greater fixity.
However, the magnitude of such effects will depend on many aspects (soil permeability, limited
drainage flow path lengths in sands, etc.) so a seasoned geotechnical engineer will tend not to
explicitly consider this aspect unless, for example, skirts are fitted to the footing.
However, in SRA the bias associated with conservative predictions needs to be incorporated for
realistic risk levels to be evaluated and this is particularly true for jack-ups.
The issue of conservative bias has been previously discussed in this report. In reliability analysis
such effects need to be quantified in some form for reasonably confident risk levels to be
estimated. More reasonable piled foundation failure risk levels are obtained when bias is
explicitly accounted for in reliability analysis as described by Bea10:
Boring:
1.2 – 1.3
Sampling:
1.5 – 2.0
Testing:
1.5 – 2.0
Strength Characterization:
1.5 – 2.0
Loading – Extreme Wave:
1.5 – 2.0
Loading – Earthquake:
2.0 – 2.5
Analysis:
1.2 – 1.3
Age:
1.5 – 1.8
The paper10 states that if rudimentary methods were used to perform the soil boring (sea water, no
heave compensation), sampling (wireline, driven small diameter samplers), testing (unconfined
compression) and characterization (lower bound to available data) then the overall bias could be
expected to be in the range of 2 or more. Such factors are therefore specific to the location and
sampling procedures adopted and therefore not simple to include in a reliability-based calibration.
Unfortunately such a detailed investigation is not as yet available for jack-ups under storm loads.
Some relevant information is found for shallow foundations such as those of gravity-based
structures under earthquake conditions in another paper by Bea53. Factors of a similar nature to
the above are listed and in addition a bias factor of 1.7 is given for ‘static’ sliding resistance.
As far as jack-ups are concerned and referring to Figure 7, both V and H are subject to Type I and
Type II uncertainties in the rig condition (hull elevated weight, leg weight and buoyancy) and in
the random environmental loading and response discussed in Section 3. Both FVH and FH are
subject to Type I and Type II uncertainties due to variability in soil properties and due to
modeling uncertainties.
-29-
Another important feature of jack-ups is that the yield surface in equation 9 is mostly a function
of the vertical soil capacity and of the spudcan geometry, except for the horizontal capacity for
clay. Test results47,54 indicate limited variability of the individual terms in the yield surface given
in equation 9. Tests45,47,54 also indicate close correlation between hardening plasticity models and
test results beyond the yield surface.
Although the above refers strictly to laboratory tests, the process of preloading effectively
minimizes (or truncates) the bias as well as Type I and Type II uncertainties in the static vertical
capacity as well as in the other capacity terms which are a function of the vertical capacity. A
departure between in situ static soil properties and those assumed in calculations will result in
greater or smaller penetration but the vertical capacity will be controlled at least for values under
the preload capacity.
It is then proposed that mean values of static capacity, additional penetration and fixity should be
predicted by a Step 3 method as outlined in sections 4.2 and 4.3 with a bias of 1.0 and CoV of
10%. The Step 3 methods should provide static fixity levels beyond those of Step 2b and closer to
the field and test data. Beyond the static values, bias and uncertainties due to strain rate effects
(which tend to increase capacity) and cyclic effects (which tends to reduce capacity) need to be
considered and it is suggested that work carried out by Bea53 is adopted here as a starting point.
It is recognized that some rig designs have been more thoroughly investigated in the field and by
test data. Figure 15 shows a comparison between the field measurements for the Mod V and Mod
VI rigs (Monitor, Magellan and Galaxy-1) and a lower bound to the centrifuge test data of Figure
14 (based on the Mod V). The centrifuge test data takes the investigation to high load levels
(beyond the 50-year event) which are unlikely to be experienced in the field but the trends are
roughly the same as for the field measured data. The simplified requirement of Krot / (Vo D) = 30
is consistently less conservative than T&R 5-5A Step 2b and more conservative than the
measurements and therefore could be used as an applicable value for the above rigs in lieu of a
full Step 3 analysis.
Figure 15 – Lower Bound to (Mod V) Centrifuge Test Data48-50
-30-
5. RIG DATA
5.1 HULL ELEVATED WEIGHT AND LCG
Past reliability analyses of fixed platforms tended to adopt a mean value based on the nominal
design value as well as bias of 1.0 for both dead and variable loads and CoV values of the order
of 6% and 10% for dead and live loads respectively.
In jack-ups the hull elevated weight comprising lightship and variable load is specified in the
marine operations manual (MOM) and is an input to the site assessment of the rig. Deadweight
surveys may be conducted after fabrication and after major upgrades and the results are
independently verified and approved by a recognized classification society (RCS). The total hull
elevated weight is closely monitored and the MOM also tends to specify a severe storm mode of
operation where the position of the longitudinal centre of gravity (LCG) is sometimes required to
coincide with the LCG of the legs within a tight tolerance.
It is not expected that uncertainties in hull elevated weight will significantly contribute to the
system probability of failure. A normal distribution is proposed, with the mean value based on the
elevated weight used in the site specific assessment, bias of 1.0 and CoV of 5%.
5.2 LEG AND SPUDCAN WEIGHT AND BUOYANCY
Design and assessment values of leg and spudcan weight and buoyancy are estimated mostly by
calculation with the shipyard providing some degree of verification after fabrication by weighing
typical bays and comparing to the calculated values. The leg weight estimates are independently
verified by a RCS. It is not expected that uncertainties in leg weight and buoyancy will
significantly contribute to the system probability of failure in the elevated condition. A normal
distribution is proposed, with the mean value based on the elevated weight used in the site
specific assessment, bias of 1.0 and CoV of 10%.
5.3 DIMENSIONS OF LEG STRUCTURE
Reliability analyses of fixed platforms tend to adopt a bias of 1.0 for tubular member dimensions
(diameter, thickness and length) with CoV values of around 2% or less. It is not expected that
such minimal variability will significantly contribute to the system probability of failure.
-31-
5.4 LEG-HULL CONNECTION STIFFNESS / HULL STIFFNESS
Leg-hull connection is one of the most challenging aspects of jack-up analysis and the values
used are estimated based on calculation and are therefore subject to some variability.
For rigs with rack chocks, the leg-hull connection stiffness is much larger than the leg stiffness
and the transfer of bending moment between leg and hull tends to occur via coupled vertical
reactions at the chocks. The stiffness values used in design or site assessment are often subject to
independent verification but large differences can be found depending on modeling assumptions.
However, it is the chock stiffness (vertical component in particular) that will affect the results in a
more substantial manner. In-house data suggests calculated values for chock vertical stiffness
may differ by a factor of around 2 but the influence on leg loads is limited. A recent study43 of
jack-up fixity proposed that overall leg-hull connection stiffness is likely to vary by a factor of 2
but the impact on results in terms of natural period is not significant for a rig with rack chocks
(less than 1%). It follows that such variability should not affect the results substantially.
A different picture emerges for a rig without rack chocks. Based on in-house experience natural
periods may differ by some 10% depending on modeling assumptions. In the HSE study22-24 on
‘reliability of jack-ups vs. jackets’, pushover analyses results differed by 8% due to different
modeling of guide clearance and pinion backlash. Here it is recommended that independently
verified and validated values are used in any analysis and these are available in-house for designs
such as LeTourneau’s 116-C. Similar considerations apply to hull stiffness.
5.5 CHOCK / PINION STRENGTH
Chock strength and pinion slippage loads are usually evaluated by rig designers, either from test
data or FE analysis. Such information is not usually in the public domain although third parties
may obtain such data from rig owners under appropriate confidentiality agreements. The main
purpose of such tests or calculations is to confirm the rig elevated ratings and these are reviewed
by a RCS.
Since the aim is not necessarily to test such components to failure, it is expected that the strength
values will be somewhat biased on the conservative side. In lieu of a more thorough review of
designer’s test data it is proposed that the ultimate loads from test data are adopted here and no
safe side bias is considered.
5.6 LEG STRENGTH
Leg ultimate strength is to be evaluated based on pushover analyses with a well tested program
such as SACS, USFOS or ABAQUS. Care is to be taken to capture member buckling lengths, the
effect of shape imperfections (see Section 5.7), elasto-plastic member buckling and post-buckling
load re-distribution. Members are to be sub-divided in a sufficient number of segments along
-32-
their length and stress integration points in their cross section. The stiffness matrix needs to be
updated to capture geometrical and material non-linearity. A bias of 1.0 and CoV of 10% were
assumed for the structural resistance modeling in the fixed platform JIP8 ‘Calibrate Load Factors
for the North West European Regional Annex to ISO 19902’.
Mills intentionally produce steel that have yield strength exceeding the nominal value so they do
not have to reject more than perhaps 5% of the steel tested. In addition steel is tested at a much
lower load rate than would be encountered in an extreme storm event so the tests tend to
underestimate the actual material resistance. A bias of 1.15 and a CoV of 10% are proposed
relative to the design yield strength. Material records for a typical rig suggested typical values of
yield and tensile strength at least 22% above the nominal design value and minimum recorded
values at least 17% above the nominal design value.
5.7 SHAPE IMPERFECTIONS (INCLUDING LEG INCLINATION)
T&R 5-5A recommends leg inclination to be assumed in the worst possible shape and in the most
critical leg relative to wave, wind and current loads which are also assumed co-linear. This
usually increases the leg strength unity checks by some 6%.
In a collapse analysis, the initial out-of-straightness of members can also have a significant effect
in reducing the calculated strength (up to 20% - 30%) if assumed in the most critical members
and exactly in line with the co-linear wave, wind and current.
Although leg inclination (as well as other shape imperfections) tends to occur they will not be
necessarily in the worst possible shape and leg in line with the environment and its effect should
not be expected to affect the underlying reliability in a substantial manner.
-33-
-34-
6. JACK-UP PUSHOVER AND RELIABILITY ANALYSIS
6.1 PROJECTS SURVEYED
A survey was carried out of published results in conferences such as the Offshore Technology
Conference (OTC), Offshore Mechanics and Arctic Engineering (OMAE), International Offshore
and Polar Engineering (ISOPE), Behavior of Offshore Structures (BOSS) and City University
Jack-up Conference as well as HSE’s OTO reports and other sources. Some recent in-house data
by GM is also referenced although the specific rig details are omitted to preserve confidentiality.
Several major investigations into jack-up behavior directly relevant to the North Sea have been
carried out by the industry in the last ten years as discussed below:
1. Long term non-linear response of dynamically sensitive jack-ups, reported in several
publications by Karunakaran and co-authors36-41.
2. Calibration of partial factors for jack-ups, reported initially by Loseth and Hauge20 and
more recently by Mo and Orbeck-Nilssen55.
3. Variability in load and strength for a jack-up structure, reported by Dalane et. al.21.
4. Failure probability of a jack-up in the Central North Sea, reported by van de Graaf,
Tromans and co-authors56.
5. Ultimate capacity of jack-ups considering foundation behavior, reported by Amdahl and
co-authors12,57.
6. Reliability of fixed and jack-up structures, reported by Morandi and co-authors22-24.
7. Non-linear analysis of jack-up structures subject to random waves, Oxford University
PhD Thesis by M. Cassidy (supervised by G. Houlsby)58.
8. Improvement of the North Sea Annex to T&R 5-5A, reported by Morandi and coauthors59-60.
9. Reliability aspects of proposed changes to SNAME 5-5A, by P. Marshall44.
10. Pushover analysis of jack-up rigs in the North Sea, reported by Morandi and co-authors14.
11. Effect of wave-in-deck loads on jack-ups, reported by Harworth and co-authors15.
12. Other GM in-house results of pushover analyses for jack-ups in the North Sea, not yet
reported in the open literature.
These will be referred to as projects in the remainder of the report and a brief description of the
rig designs investigated is given in Table 1.
-35-
Table 1 – Rig Designs in Survey
Project
Rig Design
1
MSC CJ62
(West Epsilon)
Not Given
MSC CJ62
(Inferred)
Mod V
(Inferred)
Not Given
2
3
4
5
6
10
11
12
Gorilla IV
(Modified)
Mod VI
(GSF Galaxy I)
Maersk Endurer
(Modified)
Not Given
Leg
Layout
Triangular
Triangular
Triangular
Triangular
Square
Triangular
Triangular
Triangular
Chords
Split Tube Chord
X-Bracing
Split Tube Chord
X-Bracing
Split Tube Chord
X-Bracing
Split Tube Chord
X-Bracing
Tear Drop Chord
K-Bracing
Split Tube Chord
X-Bracing
Split Tube Chord
K-Bracing
Split Tube Chord
X-Bracing
Leg-Hull
Connection
Chocks
Hull Weight
(tonnes)
16,900
Chocks
16,000
-
Chocks
11,600
Chocks
Pinions
23,365
‘funct. load’
12,963
Chocks
18,271
Pinions
12,500
Chocks
10,923
It can be seen that a fairly representative sample was found with the various projects focusing on
the deep water / harsh environment rigs. In some cases the rig design considered was not
explicitly mentioned and was inferred from the information in the paper as indicated in Table 1.
Although two cases of rigs without chocks were found (based on Rowan Gorilla IV and Maersk
Endurer) the majority of the cases corresponded to rigs with chocks as well as triangular legs with
split tubular chords and X-braces. This is a common design feature of many of the deep water /
harsh environment rigs presently in the market such as Mod V, Mod VI, CJ62 and Super Gorilla,
Figures 16 to 18. In addition, the Super Gorilla has horizontal braces crossing the X-braces and
the pinions actually hold the hull elevated weight while the chocks hold the storm loading.
6.2 SUMMARY OF RESULTS
In total, 20 rig / location cases were identified as shown in Table 2. A wide range of locations was
covered but with a focus on the deep water parts of the North Sea (UK and Norwegian Sectors). It
can be seen that the industry’s experience with this type of analysis for jack-ups has significantly
expanded in recent years.
-36-
Figure 16 – Plot of a Finite Element Model of a Mod V Design Rig
-37-
Figure 17 – Plot of a Finite Element Model of a Mod VI Design Rig
-38-
Figure 18 – Plot of a Finite Element Model of a Super Gorilla Design Rig
-39-
Table 2 – Summary of Results
Proj.
Rig Design
Case
1
Water
Depth (m)
107
(Sleipner Vest)
83.7
Foundation
1
2
2
MSC CJ62
(West Epsilon)
-
3
3
4
3
5
4
7
8
5
5
9
6
10
10
11
10
12
10
13
10
14
10
15
10
16
10
17
10
18
19
20
12
12
12
Skirted
Penet.
(m)
-
RSR
(100-y JP)
-
Meets NS
Annex ?
Yes
Stiff Soil
-
-
Yes
MSC CJ62
(Inferred)
MSC CJ62
(Inferred)
Mod V
(Inferred)
Not Given
Not Given
108
(Ekofisk)
108
(Statfjord)
92
Skirted
-
2.67
Yes
Skirted
-
2.43
Yes
Pinned
Shallow
2.24*
105
105
Pinned
Sand
Shallow
Shallow
2.90
2.85
No
(inferred)
Yes
Yes
Gorilla IV
(Modified)
Mod VI
(GSF Galaxy I)
Mod VI
(GSF Galaxy I)
Mod VI
(GSF Galaxy I)
Mod VI
(GSF Galaxy I)
Mod VI
(GSF Galaxy I)
Mod VI
(GSF Galaxy I)
Mod VI
(GSF Galaxy I)
Mod VI
(GSF Galaxy I)
Not Given
Not Given
Not Given
88
(ETAP)
120
(Case A)
120
(Case A)
95
(ETAP)
95
(ETAP)
90
(Shearwater)
90
(Shearwater)
118
(Skene)
118
(Skene)
95
90
90
Pinned
7.7
2.7 – 2.9**
Yes
Pinned
8
2.56
Marginal
Clay / Sand
8
Exceeds 3
Yes
Pinned
1
Exceeds 3
Yes
Clay / Sand
1
Exceeds 3
Yes
Pinned
7
Exceeds 3
Yes
Clay / Sand
7
Exceeds 3
Yes
Pinned
4.8
2.35
No
Clay / Sand
4.8
Exceeds 3
Yes
Pinned
Pinned
Clay
0.8
4
4
2.10
2.30
Exceeds 3
No
No
Yes
* Increase of 10% applied as nominal yield strength was originally used
** Increase of 10% applied to account for joint probabilities
-40-
Most projects considered a ‘baseline’ pinned condition case as well as a separate case where an
attempt was made to model the spudcan-soil interaction in more detail. Given the previous
discussion on bias in modeling, Table 2 is focused on results obtained for structural system failure
precluding foundation failure and loss of air gap.
The various projects do not necessarily report the assessment unity checks for the rigs in a
detailed manner but, given the deep waters, all cases are expected to be reasonably near the limits
of operation of the rigs as given by Bulletin 5-5A in at least one of the assessment criteria and
most cases are expected to be near the limits of operation from the point of view of leg stresses.
Based on the information available a rough estimate is made in Table 2 of whether the unit would
meet the North Sea Annex of Bulletin 5-5A or not. All analyses in Table 2 were based on
validated software – either SACS or USFOS.
The reserve strength ratio (RSR) in Table 2 is defined as the ratio between ultimate system
strength and design strength. The design strength was taken here as the global loading
corresponding to the ‘true’ 100-year load (as given by joint probabilities) augmented by the
associated dynamic amplification factor (DAF) values.
According to recent North Sea data30, the ratio between ‘true’ 10,000-year and the ‘true’ 100-year
drag loading is between 1.64 – 1.66 accounting for modeling uncertainty. The DAF values tend to
reduce for the increased return periods, at least for a constant level of fixity. Based on in-house
data (some of which was published in Project 10), assuming a lower bound approach to fixity and
assuming the uncertainties associated with structural capacity to be negligible compared to those
of the environmental loading, an RSR as defined above with values of 1.55 – 1.60 would suffice
for the rigs to survive a 10,000-year event. The striking feature of Table 2 is that all cases
considerably exceeded such RSR values.
6.3 REVIEW OF THE INDIVIDUAL PROJECTS
1. Long term non-linear response of dynamically sensitive jack-up.
This project (or series of projects) provided a very comprehensive verification of design methods
for estimating dynamic amplification factor (DAF) values as compared to a probabilistic
approach accounting for the effect of non–linearities in the long term response of jack-up rigs.
The work in Project 1 has not attempted to quantify system strength or reliability but forms a
useful background to future activities in this project as discussed in Section 3.3.
2. Calibration of partial factors for jack-ups
The work covers component reliability estimates for calibrating partial safety factors which are
mentioned in a recent description55 of DnV Offshore 2000. As shown in Figure 19, component­
based annual probability of failure values for the recommended load factor of 1.2 fell in the range
of 10-4 to 10-7 depending on the degree of inertial loading. For a rig in the limit of the code
assuming high damping (8%), the response is more drag-dominated and the load factor leads to
the lower bound component reliability. For a rig in the limit of the code assuming low damping
(1%), the response is more inertia-dominated and the same load factor leads to the upper bound
component reliability.
-41-
Figure 19 – Component Reliability based on Mo & Ørbeck-Nilssen55
3. Variability in load and strength for a jack-up structure
The work investigated the system reliability of jack-ups for operation in 108m water depth at
Ekofisk and Statfjord and the effect of variability in the system strength on the total failure
probability.
The RSR results in Table 2 refer to the baseline 100-year loading which includes DAF values.
The previous observations on the reduction of DAF with increased return period apply here so the
results are expected to be conservative. The paper indicates that ‘true’ 100-year loading as given
by joint probabilities was 30% - 40% lower than design values given by independent extremes (in
this case 100-year wave with 10-year current).
The RSR values were fairly high, probably owing to high fixity due to the use of skirts. However,
the system failure probability values were of 3.4x10-4 and 1.3x10-4 per annum for Ekofisk and
Statfjord respectively which are somewhat high compared to other similar analyses. It is believed
that the single degree of freedom modeling of dynamics and the high uncertainty assumed for
drag loading (base shear coefficient of variation of 45% - 52%) are probably more conservative
than would be presently adopted in a state-of-the-art analysis.
-42-
4. Failure probability of a jack-up in the Central North Sea
The work investigated the long term response of a jack-up based on joint probabilities using a
generic load model and extreme load statistics, with the rig capacity estimated by pushover
analysis. The ‘true’ 100-year environmental load was determined to be 6.5 MN as opposed to a
value of 10 MN for a conventional site assessment load, indicating a reduction of 35% similar to
that indicated in Project 3.
The paper provides a useful outline of what such an analysis should cover, although a few areas
would be better modeled using present state-of-the-art knowledge.
Constant and high DAF values were adopted (1.53 for base shear and 2.47 for overturning
moment), independently of return period. Such high baseline DAF values would be typical of
pinned conditions and it is apparent that no fixity was included in the study. In addition the DAF
values for longer return periods would reduce substantially and this is acknowledged by the
authors.
Steel mills intentionally produce steels that have yield strengths exceeding the nominal value so
they do not have to reject more than perhaps 5% of the steel tested. In addition steel is tested at a
much lower load rate than would be encountered in an extreme storm event thus underestimating
the actual material resistance. The paper adopted nominal values of yield strength which are
effectively a lower bound on the true yield strength and this is acknowledged by the authors.
Two foundation models were considered. First the rig was assumed as pinned at the spudcans.
Then a ‘less-than-pinned’ condition was analyzed with sliding of the windward leg and pinned
conditions in the leeward legs.
As discussed in 4.2, for stiff sand soils, the end result will be a balance between the loss of
stiffness under the windward leg and the plastic stiffness under the leeward legs. As discussed in
4.4 significant fixity may be present beyond the T&R 5-5A soil yield surface. It follows that the
‘less-than-pinned’ condition under the windward leg in combination with pinned conditions under
the leeward legs and the results obtained are expected to be conservative, perhaps by a substantial
amount. Project 4 utilized the USFOS spudcan model which is consistent with Step 2b of T&R 5­
5A (such as discussed by Von Langen42) and does not, as yet, utilize the beneficial effects of a
Step 3 model discussed in Section 4.2 and illustrated in Figure 10.
Project 4 is very useful in that the rig was close to its operating limits as inferred form the results
given in the paper. The annual failure probabilities (and considering all the qualifications above)
were relatively low: 1.3x10-7 for the leg collapse with stable foundations (but pinned conditions in
all legs), 1.8x10-6 for overturning and 2.5x10-5 for leeward leg failure following sliding of the
windward leg.
It is also noted that ‘overturning’ here means that the vertical reaction in the windward leg will be
instantaneously canceled. However, that does not mean the rig would overturn. Time domain
analyses suggest that it takes about 1 – 1.5 sec for the peak overturning moment to reduce below
the righting moment. During this period of time the accelerations induced on the rig may be
minimal as the rig has a very large inertia in relation to the instantaneous center of rotation in the
leeward legs (the rig inertia is about 1000 times the difference between peak overturning moment
and righting moment). The problem needs to be treated in the time-domain using representative
storm segments and accounting for initial conditions. The limit state needs to be defined based on
-43-
the base shear transferred to the leeward legs during the 1 – 1.5 sec period when the righting
moment is exceeded, including a realistic model of the foundation behavior.
5. Ultimate capacity of jack-ups considering foundation behavior
The work addressed the issue of sliding in a more advanced manner than the previous project
with a hardening plasticity model for the foundations and also included a time-domain collapse
analysis. The RSR for pinned conditions was of the order of 2.9 as shown in Table 2. A similar
reserve in strength was obtained from a full time-domain collapse analysis. More recent results
for another jack-up case suggest a RSR of 2.1 following static sliding of the windward leg and
13% increase in capacity when performing the analysis in the time-domain. Unfortunately only
scant details on these analyses were found.
6. Reliability of fixed and jack-up structures
The work looked at jack-up component and system reliability using a pinned condition approach
as well as a hardening plasticity foundation model for a soft clay location. In such locations there
is a tendency for larger penetrations to be observed and in this case values of 7 to 7.7 m were
predicted.
As discussed in 4.3, for soft clay soils the assumption of pinned conditions at the spudcans will
usually lead to conservative results, provided that the plastic displacements of the leeward legs do
not lead to excessive leg differential settlement.
The minimum component reliability estimated in Project 6 was 5x10-4 over 20-years (lifetime
risk). Relating the annual risk to the lifetime risk is simple if each year is considered as a
statistically independent event (no correlation of trials from year to year). For small probability of
failure the corresponding annual probability of failure would be 5x10-4 /20 = 2.5x10-5.
However, many variables are independent of the environmental load such as the resistance so
there will be a correlation of risk from year to year. A simple approach is to assume full
correlation and therefore the annual probability of failure equal to the lifetime probability of
failure but this may be quite conservative.
The correct value is calculable but in summary the minimum component reliability based on
pinned conditions was estimated to range from 5x10-4 (conservative) to 2.5x10-5 per annum. The
corresponding values including the fixity implied by the soil hardening plasticity model and
assuming no foundation failure were in the range of 2.4x10-6 to 1.2x10-7. Such structural
component reliability levels are reasonably in line with those estimated in Project 2.
The system lifetime reliability for pinned conditions and neglecting foundation failure was of
4.5x10-5 leading to annual probability of failure in the range of 4.5x10-5 to 2.2x10-6. The same
pinned conditions DAF was used in both the site assessment and the pushover analyses and this is
expected to be fairly conservative (DAF should reduce for increased return periods).
Relatively high risk levels were found when estimating foundation system reliability. The lifetime
system reliability was estimated as 4.8x10-2 so the annual system reliability would be in the range
of 4.8x10-2 to 2.4x10-3. The low reliability levels were dominated by early foundation failure as
discussed below.
Figure 20 gives the load-penetration curve for two cases in the location used in this project
(Kittiwake). The soil has a deep (19m) layer of soft clay with nearly constant undrained shear
-44-
strength so any gains of total vertical capacity are due to spudcan embedment. Stronger material
is found below this soft layer.
Penetration (m)
Vertical Load (MN)
0
-1
-2 0
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
-13
-14
-15
-16
-17
-18
-19
-20
-21
-22
25
50
75 100 125 150 175 200 225 250 275 300
Jack-up 1
Jack-up 2
Figure 20 – Leg Differential Settlement, Kittiwake Location
For the preload capacity and spudcan bearing area of ‘Jack-up 1’ (considered in Project 6) the
base of the spudcan did not entirely clear the soft material. Loads corresponding to higher return
periods (such as 10,000-years) may lead to large differential settlement and this was captured by
the pushover analysis which indicated limited reserve strength due to leg collapse following
bearing capacity failure of the soil under the leeward leg. It is noted that the Bulletin 5-5A unity
check was fully met in this case. However, this result is particular to this rig in this type of soil
and should not be generalized. In fact, clay soils tend to show an increase of undrained shear
strength with depth.
‘Jack-up 2’ (higher preload capacity and lower spudcan bearing area) in the same location by
contrast clears the soft material and penetrates down to the stronger region leading to a safer
situation14.
7. Non-linear analysis of jack-up structures subject to random waves
The work implemented NewWave theory for predicting environmental loads and a hardening
plasticity model to represent the foundations in order to estimate the long term response (hull
displacement) of a jack-up. It has not attempted at estimating reliability levels and will not be
discussed further in this report, although it serves as a useful future reference.
-45-
8. Improvement of the North Sea Annex to T&R 5-5A
This work was sponsored by the Jack-up Committee of the International Association of Drilling
Contractors (IJUC) and looked on reliability and calibration aspects of Bulletin 5-5A. No new
results are presented but a first summary of the industry’s pushover analysis results is given
therein which is enhanced here. This work will not be discussed further in this report, although it
serves as a useful reference.
9. Reliability aspects of proposed changes to SNAME 5-5A
The work reviewed pushover analysis and reliability analysis results for jack-ups and developed a
useful and coherent framework for such results in terms of a consensus risk band for jack-ups.
10. Pushover analysis of jack-up rigs in the North Sea
The work investigated the system strength of the Galaxy I jack-up unit in the North Sea
considering different locations with layered soils, Figures 21 and 22. The main objective of the
project was to verify that a jack-up rig had sufficient reserve strength to accommodate the
passage of a crest with a return period of 10,000-years with the associated current and wind
reflecting joint probabilities. Unbiased values of yield strength were adopted. All cases were near
the limits of operation of the rig as given by a site assessment to Bulletin 5-5A although not
necessarily due to structural strength.
The methodology adopted improvements relative to the previous projects. The traditional ‘North
Sea’ approach of factoring up a reference wave load pattern was not used. Instead the analyses
were based on increasing the crest height and more accurately capturing the consequent change in
kinematics, fluid loading and dynamic response.
Pinned conditions were assumed as well as fixity based on retaining a reasonably conservative
value of fixity (based on the test and field data previously discussed) under high load levels
beyond the Bulletin 5-5A yield surface. In all cases the structure had considerable reserve
strength beyond a 10,000-year event and was also seen to survive such event when foundation
failure was included.
The results for leg differential settlement under the leeward leg are particularly interesting. Figure
21 shows that the load and resistance factors adopted in the assessment (100-year environment)
ensure that the vertical reaction under the leeward leg for the 10,000-year event does not exceed
the preload value. However, as shown in Figure 22, the T&R 5-5A unity check may be
substantially exceeded and yet the additional settlement under the 10,000-year event would be
minimal.
Such results, together with those obtained in Project 6 suggest that the load factors in Bulletin 5­
5A need to be carefully considered for each type of soil. The case in Project 6 meets 5-5A quite
comfortably but leads to a potentially unfavorable situation. Some of the cases in Project 10 do
not meet such criteria but lead to a more favorable situation – in these cases the safety factor (and
actually a substantial amount of fixity) can be found in the slope of the soil resistance vs. depth
curve and the criteria in Bulletin 5-5A is overly conservative.
-46-
Figure 21 – Leg Differential Settlement, Shearwater
Figure 22 – Leg Differential Settlement, Case A
Another important finding is that overturning moment is a more relevant global parameter to
describe the ultimate capacity of rigs with chocks. This happens as overturning moment has a
-47-
central impact on chord loads which control leg strength for this type of rig design. It is noted that
all previous system reliability analyses were based on base shear as the global parameter.
11. Effect of wave-in-deck loads on jack-ups
The work primarily investigated the effect of loss of air gap on jack-up system strength. The rig
was found to survive a 10,000-year event without loss of air gap for fixity referred to as SNAME
T&R 5-5A fixity. Due to the modeling assumptions contained in such study it was not possible to
clearly correlate the results obtained to a RSR relative to 100-year joint probabilities as in Table
2, even for the cases that excluded loss of air gap. However, the work was useful as an input to
sensitivity studies on the potential impact of loss of air gap on system strength and is described in
an OTR report61 and in a conference paper15.
12. Other Global Maritime in-house results of pushover analyses for jack-ups in the North Sea
These results correspond to methodology similar to that adopted in Project 10 but adopting some
cases where the rig actually fails Bulletin 5-5A.
-48-
7. PROCEDURE FOR RELIABILITY ANALYSIS
7.1 LIMIT STATES
Four different limit states are defined:
x
Structural Strength. The initiating event is failure of a structural component and the
potential consequence may be leg structural failure, depending on the reserve strength of
the unit. This check verifies that there is no weakness in the structural components.
x
Leg-Hull Connection Strength. The initiating event here is failure of the chocks and the
potential consequence is a failure of the leg-hull connection system. This check verifies
that there is no weakness in the leg-hull connection system.
x
Leg Differential Settlement. The initiating event here is the increase in vertical load in the
leeward leg due to the environmental overturning moment leading to excessive settlement
of the leeward leg in relation to the windward legs, Figure 23. The potential
consequences are ‘punch-through type’ failure of the leg and the hull being excessively
out of level. This check verifies that the soil has sufficient bearing capacity.
x
Leg Sliding. The initiating event here is the reduction in the vertical force in the
windward leg due to the environmental overturning moment leading to sliding of such
leg, Figure 24. The potential consequence here is structural failure of the leeward legs
due to re-distribution of the leg shear load.
Figure 23 – Bearing Failure under the Leeward Leg
-49-
Figure 24 – Sliding of the Windward Leg
7.2 STEP-BY-STEP PROCEDURE
A summary of the probabilistic modeling discussed in the previous sections is given in Table 3.
In principle the system reliability could be estimated by developing appropriate response surfaces
for each of the limit states and evaluating probabilities of failure using, for example, Monte Carlo
simulation. Statistical correlation between basic random variables as well as between failure
modes can be included.
This may require an excessive amount of computations as convergence in the statistics of jack-up
dynamic response to extreme seastates can be time consuming. Because of the large number of
environmental combinations to be investigated plus the large number of variables to be
potentially included in the response surface, such an approach does not appear to be feasible.
The following alternatives are proposed:
x Formulate the limit states in terms of overturning moment (OTM). OTM tends be a more
consistent measure of global capacity of jack-ups than base shear based on previous
analyses14.
x For each directional sector and limit state, adopt separate probability density functions
(PDF) for the extreme response and for the resistance.
x The PDF for extreme response is to be determined based on quasi-static loads, dynamic
inertial loads and foundation fixity that vary with return period (the N-year return period
value has a 10-N probability of exceedance).
-50-
x
The PDF for the resistance is to be based on a response surface including the vertical soil
capacity (which controls the soil yield surface), the soil yield surface modeling
uncertainty and the collapse analysis modeling uncertainty.
x
Include in the response surfaces only those variables previously identified as having a
key impact in the overall reliability levels: significant wave height, uncertainty in the
extreme value of response, load recipe and resistance.
x
Adopt a FORM approach to evaluate the annual failure probability. Assume the variables
in the response surfaces as independent and uncorrelated.
x
Assume high correlation between the purely structural system failure paths. Failure paths
dictated by foundation failure are addressed by defining different limit states as in 7.1.
Correlation between limit states are to be accounted for based on the scalar product of the
design points from the FORM analyses.
x
For directional sectors where sliding is not an issue, evaluate system strength based on
quasi-static collapse analysis as in previous work14 (with appropriate scaling of crests,
DAF, kinematics, etc.). For other sectors perform dynamic collapse analysis.
x
In the dynamic analysis use industry standard methods as those in T&R 5-5A. Account
for drag-dominated and inertia dominated behavior. Fixity values are to be decided
depending on load level based on field, test data and Step 3 analyses. However, Step 3
methods will not be directly used in the dynamic analysis. The water surface elevation in
such storms may include the effects of both directional spreading and second order
interaction between spectral components. A constrained simulation approach to the
simulations may be adopted to minimize computational effort.
x
Verify that overall CoV of quasi-static loading agrees with values discussed in 3.2 (of the
order of 25 -30%). Verify that ratio L / L100 agrees with values discussed in 3.2. Verify
that the ratio of crest height to Hs agrees with values discussed in 3.2. Verify that mean
100-year joint probability loading agrees with the North Sea Annex of T&R 5-5A.
x
Adopt a Step 3 foundation model in the collapse analyses. Capacity terms would be a
function of the vertical capacity tested in the field (up to the preload level) by preloading.
The step-by-step procedure below is proposed:
Step 1: Create a detailed FE model of the rig for quasi-static large deflection analyses as well as a
simplified FE model for time-domain analyses. Calibrate the simplified model against the
detailed model.
-51-
Step 2: Establish marginal distributions of Hs and distributions of Tp conditional on Hs. Define the
Hs - Tp contour for increasing return periods such as 100-years, 10,000-years, etc., Figure 25. The
methodology to be used is based on inverse-FORM and contours are to be inflated to incorporate
Type II environmental uncertainties (see discussion by Winterstein et.al.62 and by BittnerGregersen et.al.63).
Figure 25 – Typical Environmental Contours for the North Sea64
Step 3: Apply the same approach as in Step 2 to derive a combination of wave, wind and current
representative of the extreme 100-year return period response OTMQS100. In principle,
distributions for current and wind conditional on Hs would need to be established, and a response
surface for quasi-static overturning moment as a function of Hs, Tp, current and wind would need
to be derived. However, it is proposed that existing in-house joint probability values for selected
locations are used.
Step 4: The statistics of the response of the rig (OTM) to seastates of different return periods (and
therefore annual probability of exceedance) are determined based on random simulations along
the environmental contours of Hs – Tp and using the simplified FE model. G
Step 5: Define the fractile H of the statistics in Step 4 (dynamics excluded) that matches the
OTMQS100 value in Step 3. Define the corresponding value including dynamics OTMDYN100 based
on the same fractile H. Repeat for increasing return periods and define the distribution for the
annual probability of exceedance of overturning moment values (inclusive of Type II
uncertainties). Note that, for example, the 10,000-year return period value corresponds to an
annual probability of exceedance of 10-4. This procedure effectively defines different DAFs for
different return periods capturing variations in fixity and drag-inertia behavior. It is tacitly
assumed that a reasonably accurate representation of dynamics can be obtained if a correct level
of the quasi-static loading is applied to the system64.G
-52-
Step 6: Define a probability distribution for the resistance using the response surface method.
Step 7: Determine the probability of failure with a FORM procedure and from the probability
distributions in Step 5 and in Step 6.
Table 3 – Summary of Probabilistic Modeling
Variable
Distribution
Mean
Bias
CoV (%)
Hull Elevated Weight
Leg Weight / Buoyancy
Structural Dimensions
Leg-Hull Stiffness
Hull Stiffness
Shape Imperfections
System Strength Model
Steel Yield Strength
Steel Young’s Modulus
Steel Strain Hardening
Normal
Normal
Normal
Deterministic
Deterministic
Not included
Log-Normal
Log-Normal
Normal
Not included
As per MOM
As per MOM
As per Drawings
FE Model
FE Model
Collapse Analysis
Nominal Design
Nominal Design
-
1.0
1.0
1.0
1.0
1.0
1.0
1.15
1.0
-
5
10
2
0
0
10
10
2
-
Significant Wave Height
Extreme Response
Site Specific
Site Specific
1.0
1.0
Deterministic
Deterministic
Log-Normal
Deterministic
1.0
1.0
1.0
1.0
Site Specific
Time-Domain
Analysis
0
0
Condit. on Hs
0
Yes
Yes
Water Levels - Surge
Water Levels – Tide
Spectral Peak Period
Spectral Peak
Enhancement
Spreading
Current – Tidal
Current – Wind Driven
Wind Velocity
Load Recipe
Site Specific
Time-Domain
Analysis
Site Specific
Site Specific
Condit. on Hs
Site Specific
Spectra
T&R 5-5A
Site Specific
Condit. on Hs
Condit. on Hs
T&R 5-5A
1.0
1.0
1.0
1.0
0.91
0
0
Condit. on Hs
Condit. on Hs
16.5
No
No
No
No
Yes
5% (Vr d Vo)
10% (Vr > Vo)
10%
Yes
Yes
Yes
Yes
Deterministic
Deterministic
Normal
Weibull
Truncated
Normal
Horizontal Soil Stiffness
Vertical Soil Stiffness
Horizontal Stiffness
Vertical Soil Capacity Vr
Function of Vr
Function of Vr
Function of Vr
Normal
Preload
1.0
Total Soil Capacity
Normal
Yield Surface
1.0
-53-
Variable
in Limit
State ?
No
No
No
No
No
No
Yes
No
No
No
No
No
No
No
Yes
-54-
8. IMPACT OF CHANGES TO T&R 5-5A
8.1 PROPOSED CHANGES AND CASES ANALYZED
Several modifications to T&R 5-5A (Rev. 1, 1997) have been proposed which can be broadly
grouped as follows:
x Reductions in the level of loading applied in the assessment:
o Reduction in wave kinematics due to spreading and spatial coherence effects.
Results obtained65 for a 116-C design rig suggested significant reduction in
kinematics for a Gulf of Mexico environment but more limited reductions for a
North Sea environment. The North Sea results did not deviate substantially from
the current wave height reduction in T&R 5-5A. The work65 has been
substantially reviewed and well accepted but, at the time of this report, there has
been no industry consensus on implementing such change. In any case, it does
not appear to affect the North Sea in a substantial manner.
o Adoption of joint probabilities for environmental data. Joint probabilities at the
100-year return period level are proposed in the North Sea Annex together with a
load factor of 1.25. At the time of this report there has been no industry
consensus on implementing 50-year joint probability data.
o Reduction in load factors. T&R 5-5A is introducing a load factor reduced to 1.15,
when using 50-year independent extremes for the environmental data.
o Working Stress Design (WSD) version. This is not just a modification of loading
levels but will be included in this group. At the time of this report there has been
no industry consensus on implementing such change.
x Modifications in stiffness leading to a reduction in response:
o Evaluate DAF based on a fixed percentage of the initial soil stiffness rather than
on a fixity degraded according to the Step 2b soil yield surface. Such
modification was originally included in the North Sea Annex and will be
implemented in the next revision of T&R 5-5A.
o Adopt soil initial stiffness in line with field and test data43.
o Allow soil fixity beyond the Step 2b yield surface to be included in the
assessment unity checks, again more in line with field and test data.
x Increases in the resistance values used in the assessment:
-55-
o Adoption of a revised chord column buckling curve. Generally understood to be
valid but not as yet fully developed.
o Less conservative preload resistance factors. At the time of this report there has
been no industry consensus on implementing such change.
These all effectively represent a relaxation of the criteria established in T&R 5-5A (Rev. 1, 1997)
and would have the beneficial effect of expanding the operational limits of the rigs. In addition,
such changes could also bridge the gap between the operational limits implied by the population
of safe (or exemplary) rigs adopted in the calibration and the reduced operational limits that
derive from T&R 5-5A (Rev. 1, 1997). However, all of these changes involve some increase in
risk (albeit small when looked in isolation) and their joint effect is yet to be quantified.
Table 4 summarizes the combinations of such changes considered in the present work. The focus
was on the modeling of foundation stiffness as this seems to be the area where there is more
industry consensus. Improved foundation models are generally considered as improvements in
knowledge leading to a reduction in modeling uncertainty.
Table 4 – Calculation Methodologies in Assessment
Methodology Environment
Load Factor
Fixity in DAF
Initial Soil
Fixity Kro
Degraded Soil
Fixity Kr
Baseline (0)
50-y Extrs.
1.25
Pinned
Pinned
Pinned
1
50-y Extrs.
1.15
Pinned
Pinned
Pinned
2
50-y Extrs.
1.15
80% of Kro
Field Data43
Step 2b
3
100-y JP
1.25
80% of Kro
Field Data43
Step 2b
4
50-y Extrs.
1.15
80% of Kro
Field Data43
Step 3
The following comments apply to Table 4:
x
The baseline case is considered to be representative of Revision 1 of T&R 5-5A (1997)
for the two rig / location cases considered here which are close to the operational limits of
the rigs in terms of preload capacity. The soil yield surface given in Step 2b within T&R
5-5A tends to converge to a pinned condition in such cases. In Revision 1 of T&R 5-5A,
the fixity allowed in evaluating the dynamic amplification factors was limited by the soil
yield surface via a secant stiffness procedure with a fixity ‘knock-down’ factor of 2. The
fixity allowed in evaluating the unity checks had also to conform to the soil yield surface.
x
Assessment 1 is representative of the changes agreed by the SNAME OC-7 Panel in
Halifax, October 2000: reducing the environmental load factor to 1.15.
-56-
x Assessments 2 and 3 incorporate the use of a constant value of fixity (80% of the initial
stiffness) in evaluating the DAF and a degrading value of fixity that conforms to the Step
2b soil yield surface when evaluating the unity checks. Such an approach was first
proposed in the North Sea Annex and will be incorporated in the next revision of T&R 5­
5A. In addition, initial soil stiffness values were adopted based on the recommendations
of recent work43 that brings the initial fixity values closer to field and test data.
x Assessment 4 looks into different values of fixity for the different footings and for the
different headings as well as the impact of a limited (0.1m) differential leg settlement as
could be allowed in a Step 3 foundation modeling.
A re-examination5 of the calibration of T&R 5-5A indicated that some of the exemplary rig /
location cases considered therein would actually fail a site assessment to Revision 1 (1997) of
such document. This applied to two cases in particular:
x Case 1 - Mod V at 97m Water Depth
x Case 2 - 116-C at 65m Water Depth
The analyses reported here considered cases that were as close to the above calibration cases as
possible but utilizing realistic site specific data as well as up to date rig data. Relevant rig and
environmental data used are summarized in Tables 5 to 7.
Table 5 – Main Rig Parameters
Case 1
Case 2
Leg Length (m)
151.3
104.6
Hull Lightship Weight (tonnes)
8,743
5,308
Variable Load (tonnes)
2,189
1,968
Leg & Spudcan Dry Weight (tonnes) – 3 Legs
4,392
2,672
Leg Equivalent Axial Area (m2)
0.446
0.346
Leg Equivalent Shear Area (m2)
0.03
0.058
Leg Equivalent Inertia (m4)
10.56
5.898
Leg/Hull Vertical Stiffness (tonnes/m)
9.48E6
2.23E5
Leg/Hull Rotational Stiffness (t-m/rad)
2.36E8
8.53E6
Wind Areas (m2)
1,633 – 2,221
1,146
-57-
Table 6 – Environmental Data for Case 1
50-year Extremes
100-year Joint Probab.
WD incl. surge & tide (m)
97.57
97.57
Hmax (m)
23.6
24.6
Tass (sec)
15.5
15.1
Tp (sec)
15.56
16.0
Airgap (m)
22.86
22.86
Wind (m/s)
35.6 (1-min)
35 (1-hour)
Elevation from seafloor (m)
Current (m/s)
Current (m/s)
0.0
0.45
0.17
10.0
0.60
0.23
25.0
0.66
0.25
67.57
0.66
0.25
77.57
0.69
0.27
87.57
0.74
0.29
92.57
0.83
0.32
95.57
0.83
0.32
The environmental data for Case 1 corresponds to the Central North Sea: the 50-year extremes
are based on ETAP and the 100-year joint probability data is based on NEXT.
The soil conditions correspond to Mungo (3.3m layer of soft to stiff clay over a 5.4m layer of
very dense sand, penetration of 1.9m), also in the Central North Sea. Modeling of the soil
conditions for Mungo according to T&R 5-5A Revision 1 (1997) is detailed in the literature66 and
was re-examined here in view of the more recent work43 on fixity. It was noted in Section 1.1 that
the Mod V operated successfully at Mungo & Marnock in a water depth of 91m.
-58-
Table 7 – Environmental Data for Case 2
50-year Extremes
WD incl. surge & tide (m)
67.00
Hmax (m)
15.6
Tass (sec)
12.2
Tp (sec)
12.7
Airgap (m)
17.9
1-minute Wind (m/s)
35.6
Elevation from seafloor (m)
Current (m/s)
0.0
0.41
15.0
0.52
65.7
0.52
67.0
0.90
The environmental and soil data for Case 2 were extracted from the calibration2 of T&R 5-5A
(based on the Beatrice location) and re-examined here again in view of the more recent work on
fixity. The soil consists of 15m of medium to dense sand and the penetration was of 2.5m.
8.2 SUMMARY OF RESULTS OBTAINED
Table 8 summarizes the results obtained for Cases 1 and 2 according to the baseline methodology
in Table 4 and in terms of unity checks for leg strength, overturning and preload. Table 8 also
compares such results with the corresponding results estimated for the exemplary rigs in the re­
examination5 of the calibration of T&R 5-5A. It can be seen that the unity check values of Case 1
and Case 2 are not the same as those in the calibration cases due to differences in rig / location
data but the conclusions in terms of pass / fail are the same for all cases and assessment criteria.
Leg Strength
Table 8 – Comparison of Unity Check Values
Case 1
Calibration:
Case 2
Mod V @ 97m
1.26
1.15
0.98
Calibration:
116-C @ 65m
0.86
Overturning
1.06
1.02
0.78
0.91
Preload
1.11
1.18
1.18
1.21
-59-
Figure 26 gives the results for Case 1 considering all the methodologies in Table 4 and in terms of
unity check for leg strength, preload, overturning and sliding.
1.8
1.6
Unity Check
1.4
1.2
1
0.8
0.6
Strength
0.4
Overturning
Preload
Sliding
0.2
0
0
1
2
3
4
Methodology in Table 4
Figure 26 – Summary of Results for Case 1
The following is noted in Figure 26:
x The different methodologies progressively reduce the unity checks and for Methodology
4 the rig would pass all of the unity checks. It is noted that a relatively high preload
capacity was used under the assumption that a staged preloading procedure would be
employed where each leg is preloaded individually.
x The results for Methodology 2 (50-year extremes with a load factor of 1.15) and for
Methodology 3 (100-year joint probabilities with a load factor of 1.25) were very similar
for this case, except for sliding.
x Sliding is the controlling criteria for this case and is very sensitive to the different
methodologies as both the soil horizontal capacity and horizontal loading at the footing
are affected.
The corresponding results for Case 2 are given in Figure 27. Given the similarity between results
of Methodologies 2 and 3 noticed for the Mod V, only results for Methodology 2 were computed
in detail.
-60-
1.4
Unity Check
1.2
1
0.8
0.6
Strength
0.4
Preload
Overturning
0.2
Sliding
0
0
1
2
3
4
Methodology in Table 4
Figure 27 – Summary of Results for Case 2
The following is noted in Figure 27:
x Again the different methodologies progressively reduce the unity checks. However, the
reduction is much less pronounced in this case. This is attributed to the fact that the unit
has a higher preload unity check from the start (baseline case) and this limits the benefits
from the improved fixity models adopted in the various methodologies.
x In this case the rig would not pass the preload unity check. Differently from Case 1, the
‘standard’ preload capacity usually quoted in the 116-C MOM was adopted assuming all
legs would be preloaded at the same time.
-61-
-62-
9. CONCLUSIONS
Historical criteria for jack-up foundation assessment prescribed essentially a safety factor of 1.0
against leg differential settlement thus accepting some level of settlement under the assessment
storm due to potential variability in loads and soil properties. This has been historically
acceptable under the tacit assumption that the true limit state is not exceedance of the preload
capacity but actually an excessive deformation that could prevent evacuation of personnel or
prevent the unit from jacking down and moving off location.
T&R 5-5A essentially prescribes strict load and resistance factors against any settlement under
the assessment event with a total safety factor against settlement that is close to (but smaller
than) the values used against failure of onshore foundations and offshore jacket piled foundations.
Field experience indicates that significant forces need to be applied in order to fully seat spudcans
in the strong soils of the North Sea and such load and resistance factors may not be necessary in
many situations (as shown in Figure 22). However care must be taken in certain situations where
the footings penetrate to and are held over a relatively weak layer of soil and a potential punch­
through mechanism may develop under storm conditions (as shown in Figure 20).
The fundamental issue here is that T&R 5-5A applies resistance factors to the ‘load resistance’
(the load at which the structure fails) as opposed to the ‘displacement resistance’ (the
displacement at which the structure fails). The former may be well suited for a brittle type of
failure (such a brace under compression) but may not be well suited for a progressive softening
behavior as in jack-up foundations.
Historically sliding under the windward leg has been assessed in terms of a safety factor of 1.1
against exceedance of the rig righting moment by the environmental overturning moment, under
the tacit assumption that the rig would be able to jack down after the assessment event as its
inertia would prevent structural or mechanical overload. T&R 5-5A prescribes a substantially
higher safety factor against such an event. In addition, T&R 5-5A prescribes load and resistance
factors against sliding that are substantially higher than the values used against failure of onshore
foundations or offshore jacket piled foundations.
Finally historical design procedures ignored dynamics but also the beneficial effects of fixity.
T&R 5-5A attempts to include both effects but its current modeling of fixity (Steps 1, 2a and 2b)
seems to be overly conservative.
Several modifications to T&R 5-5A are being proposed which all effectively represent a
relaxation of the criteria established in T&R 5-5A (Rev. 1, 1997). The two rig location cases
considered in this report concentrated on improvements in the modeling of foundation fixity for
evaluating dynamic amplification as well as the unity checks. An expansion of the rig’s
operational envelope was observed for Case 1 (Mod V in 97m Water Depth) but not so much for
Case 2 (116-C in 65m Water Depth). The more favorable results for Case 1 are due to the
adoption of a relatively high preload capacity under the assumption that a staged preloading
procedure would be employed where each leg is preloaded individually.
-63-
Given the background to the current debate, a robust reliability analysis methodology can give a
positive contribution to obtaining an industry wide consensus on a way forward.
A step-by-step procedure has been proposed for performing system reliability analysis for jack­
ups using state-of-the-art techniques, with emphasis in the following areas:
x
x
x
Environmental loading
Dynamic response
Foundation behavior
A review of test and field data concerning fixity was conducted and showed that relevant
information now exists at load levels approaching assessment levels (field data) or even
exceeding such levels (test data) at least for selected rig designs. In evaluating the ultimate
capacity of the rig it is proposed that a Step 3 model of the foundation should be adopted in order
to obtain more realistic fixity levels.
-64-
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-65-
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29. Forristal , G.Z.: ‘Short term crest statistics’. Air Gap Workshop, organized by BOMEL on
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31. Tromans, P.S., Vanderschuren, L.: ‘Response based design conditions in the North Sea p
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offshore structures’. Ocean Engineering, 19, pp. 161-181, 1992.
33. Legget, I.: ‘Metocean data for jack-up assessments’. International Conference - The Jack-up
Platform, Eds. C. D’Mello, L.F. Boswell and B. McKinley. London, 2001.
34. Joint Industry Project, ‘Calibrate environmental load factors for the NW European regional
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35. Wu, S.: ’ISO Extreme Environmental Load Factor Calibration JIP - Review Comments by
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36. Karunakaran, D.N., Leira, B.J., Spidsøe, N., ‘Effect of nonlinear behavior on long term
response of a dynamically sensitive jack-up platform’. The Jack-up Platform, Ed. L. Boswell, C.
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37. Karunakaran, D.N., Spidsøe, N., Gudmestad, O., ‘Non-linear dynamic behavior of jack-up
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38. Karunakaran, D.N., Spidsøe, N., ‘Verification of methods for simulation of nonlinear
dynamic response of jack-up platforms’. Proceedings The Jack-up Platform, Ed. L. Boswell, C.
D’Mello, , London, 1995.
39. Karunakaran, D.N., Spidsøe, N., ‘Effects of non-gaussian waves to the dynamic response of
jack-up platforms’. Proceedings The Jack-up Platform, Ed. L. Boswell, C. D’Mello, , London,
1995.
40. Karunakaran, D.N., Spidsøe, N., Bærheim, M., ‘Full-scale measurements from a large
deepwater jack-up platform’. Proceedings The Jack-up Platform, Ed. L. Boswell, C. D’Mello, ,
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41. Karunakaran, D., Haver, S., Bærheim, M., Spidsøe, N., ‘Dynamic behavior of Kvitebjorn
jacket in North Sea’. Proceedings Offshore Mechanics and Arctic Engineering, OMAE’01, Rio
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42. Van Langen, H., Hospers, B.: ‘Theoretical model for determining behaviour of spudcans’.
Paper OTC 7302. Offshore Technology Conference, 1993.
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equations with field data’. Report L19073/NDE/MJRH prepared for the IADC Jack-up
Committee.
44. Marshall, P., ‘Reliability aspects of proposed changes to SNAME 5-5A’, Proceedings The
Jack-up Platform, Ed. C. D’Mello, L. Boswell, B. McKinley, London, 2001.
45. Van Langen, H., Wong, P.C., Dean, E.T.R., ‘Jack-up foundation load-displacement
assessment’. Proceedings The Jack-up Platform, Ed. L. Boswell, C. D’Mello, W. Supple, London,
1997.
46. Cassidy, M.J., Houlsby, G.T.: ‘On the modeling of foundations for jack-up units on sand’.
Paper OTC 10995. Offshore Technology Conference, 1999.
47. Martin, C., Houlsby, G.T.: ‘Jack-up units in clay: Structural analysis with realistic modeling
of spudcan behaviour’. Paper OTC 10996. Offshore Technology Conference, 1999.
48. Nelson, K., Smith, N.P., Hoyle, M., Stonor, R., Versavel, T., ‘Jack-up response measurements
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49. Temperton, I., ‘Centrifuge modeling of spudcan foundations under combined loads’.
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50. Springett, C.N., Temperton, I., Stonor, R.W.P., ‘Measured spudcan fixity: analysis of
instrumentation data from three North Sea jack-up and correlation to site assessment procedures’.
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51. Hunt, R.J., Dier, A.F., Howarth, M.W., Jones, W.: ‘Further interpretation of North Sea jack­
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52. Health and Safety Executive: ‘Interpretation of full-scale monitoring data from a jack-up rig’.
Offshore Technology Report 2001/035, prepared by MSL Engineering, 2001.
53. Bea, R.G., Craig, M.J.K., Gudmestad, O.T., Karthieghian, V., Pradayana, G., ‘Developments
in proposed guidelines for design of offshore platforms to resist earthquakes’. Paper OTC 11069.
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55. Mo, O., Ørbeck-Nielssen, K., ‘Jack-up design according to DNV Offshore 2000’. Proc. The
Jack-up Platform, Ed. C. D’Mello, L. Boswell, B. McKinley, London, 2001.
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behaviour’, Proc. Behaviour of Offshore Structures, BOSS’94, Massachussets, 1994.
58. Cassidy, M.J., ‘Non-linear analysis of jack-up structures subjected to random waves’. PhD
Thesis, Oxford University, 1999.
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60. Morandi, A.C., Smith, I., Virk, G.S., ‘Reliability of jack-ups under extreme storm conditions’.
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parameters for extreme response: inverse FORM with omission factors’. Proc. ICOSSAR’93,
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63. Bitner-Gregersen, E.: ‘Extreme wave steepness estimated from environmental contour plots
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65. Noble Denton Europe: ‘The effect of new developments in wave modeling on jack-up loads’.
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APPENDIX 1 GLOSSARY OF STRUCTURAL RELIABILITY ANALYSIS AND RELATED TERMS
This glossary has been prepared as an Appendix to report GMH-3068-1160, Rev.2.
The definitions here were made as consistent as possible with ‘General Principles on Reliability
for Structures’ (ISO 2394:1986 and draft revision dated 1996). The definitions obtained directly
from this document are indicated as (ISO).
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GENERAL
Action. An assembly of concentrated or distributed mechanical forces acting on a structure
(direct actions) or the cause of deformations imposed to the structure or constrained in it
(indirect action). (ISO). Types of action relevant to offshore structures:
Permanent action. Action which is likely to act continuously throughout a given
reference period and for which variations in magnitude with time are small
compared with the mean value or the variation of which is only in one sense and
can lead to some limiting value. (ISO)
Variable action. Action for which the variation in magnitude with time cannot be
neglected compared with the mean value. (ISO)
Accidental action. Action that is unlikely to occur with a significant value on a given
structure over a given reference period. (ISO)
Fixed action. Action that has a fixed distribution on a structure such that its magnitude
and direction are determined unambiguously for the whole structure when
determined at one point of the structure. (ISO)
Free action. Action that may have an arbitrary spatial distribution over the structure
within given limits. (ISO)
Static action. Action which will not cause significant acceleration of the structure or
structural elements. (ISO)
Dynamic action. Action which may cause significant acceleration of the structure or
structural elements. (ISO)
Bounded action. Action that has a limiting value that cannot be exceeded and which is
exactly or approximately known. (ISO)
Unbounded action. Action that has no limiting value. (ISO)
Action effect. Effect such as member forces, stress, deformation, displacement, motion, etc. of a
single action or combination of actions on the structure.
Failure. Insufficient load bearing capacity or inadequate serviceability of a structure or structural
element. (ISO). An event causing an undesirable or adverse condition, such as a
deterioration of functional capability to such an extent that the safety of the unit,
personnel or environment is significantly reduced.
Life cycle. The total period of time during which the planning, execution and use of a
construction works takes place. The life cycle begins with identification of needs and
ends with demolition. (ISO)
Load combination. The design values of the different actions considered simultaneously in the
verification of the reliability of a structure for a specific limit state. (ISO)
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Models. A simplified mathematical description of experimental setup simulating actions,
material properties, the behavior or a structure, etc. (ISO)
Redundancy. The ability of a component or system to maintain or restore its function after an
initial failure has occurred. Redundancy can be achieved for instance by installation of
more units or elements to restrain the loads, or by alternative means for performing a
function.
Reference period. A chosen period of time during which specified requirements are to be
fulfilled.
Reliability class. A class of structures or structural elements for which a particular specified
degree of reliability is required. (ISO)
Resistance. Capability of a structure or part of a structure to resist action effects.
Robustness (or structural insensitivity). The ability of a structural system to limit the
consequences of the loss of integrity of one or more of its structural components (due to
fatigue, impact, fire and blast, human errors or other causes) to an extent not
disproportionate to the original cause. (ISO)
Serviceability. A condition in which a structure is considered to perform its design function
satisfactorily. (ISO)
Structure. Organized combination of connected parts designed to provide some measure of
rigidity and resistance against various actions. (ISO)
Structural element. Physically distinguishable part of a structure such as a column, beam, plate.
(ISO). Also referred to as a structural component. Typical elements are members (such
as tubular members) and joints.
Structural form. General structural type such as jacket, jack-up, etc.
Structural Integrity Management (SIM). Inspection, maintenance and repair procedures
aiming at maintaining the integrity of structural components at adequate levels
Structural system. The load-bearing elements of a building or civil engineering works and the
way in which these elements function together. (ISO)
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DESIGN (AND ASSESSMENT)
Assessment. The total set of activities performed in order to find out if the reliability of a
structure is acceptable or not. (ISO).
Characteristic value. A (representative) value chosen insofar as it can be fixed on statistical
bases, so that it can be considered to have a prescribed probability of being exceeded
towards unfavorable values during a reference period. (ISO). Characteristic value is a
design nominal value derived on a statistical basis.
Characteristic value of action. Representative value of an action (such as a load), determined
on a statistical basis, to be used in the determination of design action effects.
Characteristic value of action effects. Effects (member forces, stresses, etc.) of a single
characteristic action or combination of characteristic actions.
Characteristic value of a geometrical quantity. A quantity usually corresponding to
dimensions specified by the designer based on fabrication tolerances.
Characteristic value of a material property. A priori specified fractile of the statistical
distribution of the material property in the supply produced within the scope of the
relevant material standard. (ISO). For example, adopting the 5% fractile for yield
strength in design meaning the adoption of a value of yield strength with a 95%
probability of being exceeded.
Characteristic value of resistance. Representative value of resistance to be used in the design of
a structure or structural element. Usually evaluated on the basis of characteristic material
properties.
Consequence-based criteria. Assessment criteria based on acceptable risk levels (probability of
failure times consequence).
Design value of an action Fd. The value obtained by multiplying the characteristic action value
by the partial factor ȖF. (ISO). ȖF is the load factor.
Design value of a material property. Value obtained by dividing the characteristic value by a
partial factor IM or, in special circumstances, by direct assignment. (ISO). IM is the
material factor.
Partial Safety Factor (in the context of design / assessment). Factor by which the
characteristic value of a variable is modified to give the design value. The following are
the most commonly used PSFs:
(Partial) Load Factor. Partial safety factors by which the characteristic values of load or
load effect are multiplied to obtain the design load or load effect.
(Partial) Material Factor. Partial safety factor by which the characteristic material
strength is divided to obtain the design material strength.
(Partial) Resistance Factor. Partial safety factor by which the characteristic value of
resistance is divided to obtain the design resistance.
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BASIC PROBABILISTIC TERMS AND DEFINITIONS
Central Moment of Order n, mn.
mn
n
³ (x - E(x))
f(x)dx
Coefficient of Kurtosis O4
O4
m3
V4
Indicates the ‘flatness’ of a PDF. Flatter distributions have high Kurtosis. A normal
distribution has a kurtosis equal to 3.
Coefficient of Skewness O3 .
O3
m3
V3
Indicates the level of asymmetry in how a particular parameter is dispersed about the
mean value. Positive skewness indicates that the probability of a value greater than the
mean by a certain margin occurring is higher than the probability of a value smaller
than the mean value by the same margin occurring. The normal distribution is
symmetric and therefore has zero skewness.
Coefficient of Variation COV
COV
V
E ( x)
Confidence Level. Probability that a fixed, unknown quantity lies within a confidence interval
estimated from observations of the quantity in an experiment. In a large number of
experiments, the estimated interval will contain the unknown quantity a fraction of the
time about equal to the confidence level. Confidence level is synonymous with
confidence probability and reflects that, owing to sampling and testing error, we cannot
with certainty make a statement about the value of the sought-after unknown quantity.
Correlation Coefficient of x and y, Ux,y:
U x, y
Rx, y
V xV y
Covariance Between x and y, Rx,y: Rx,y=M(x,y)1,1-E(x)E(y)
Cumulative Probability Function F(x). The probability distribution function of the random
variable X. It is related to the PDF f(x) by:
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x
F ( x)
³ f ( x)dx
f
Exceedance Probability Function Q(x): Q(x) = 1-F(x)
Mean P. The average value of a parameter. If the parameter is described by a probability density
function f(x) then the mean (or expected value E(x)) is given by P = E(x) = M1 = M1(x)
(Joint) Moment of Order i,j ...about zero M(x)i,j…:
M ( x)i, j...
i i
1 2
³ ³ x x ... f ( x)dx
Probability Concepts:
Bayesian interpretation of probability. Probabilistic framework used as an aid in
decision making by expressing a subjective interpretation of limited information.
Frequentist interpretation of probability. Probabilistic framework related to the
frequency of occurrence of outcomes of random experiments.
Objective probability. See frequentist interpretation of probability.
Subjective probability. See Bayesian probability.
PDF - Probability Density Function f(x). It is the continuous equivalent of a histogram and
gives the frequency of occurrence of a particular value of the random variable X. More
formally, f(x)dx gives the probability that a realization of a continuous random variable
x falls in the interval [x, x+dx]. The basic variables used in reliability analysis require
appropriate PDFs. The most commonly used in SRA of offshore structures are discussed
below.
Normal Distribution. If some variable is the sum of a large number of independent
variables, a normal distribution is appropriate. The normal distribution is often
applied to describe approximately linear physical phenomena as well as additive
independent errors. Normal distributions are convenient to manipulate and are
widely used in SRA.
Lognormal Distribution. If some variable is the product of a large number of
independent variables, a lognormal distribution is appropriate. Lognormal
distributions are convenient to manipulate and are widely used in SRA.
Rayleigh Distribution. The square root of the sum of squares of two independent
standard normal variables is a Rayleigh variable. The Rayleigh distribution thus
describes the amplitudes of a linear Gaussian process, since each spectral
component consists of a sine and a cosine term. The Rayleigh distribution is
derived based on an assumption that the considered process is narrow banded.
This assumption leads to conservative results when applying the Rayleigh
distribution to broad-banded processes.
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Gumbel (or Fisher–Tippet I) Distribution. The Gumbel Distribution is also called the
Type I asymtotic extreme value distribution of largest values. It is used to model
the extreme values of variables that have a tail of exponential form. It is applied
to representation of extreme environmental conditions and extreme
environmental loads, and is also used in response analysis.
Weibull (or Fisher–Tippet III) Distribution. The Weibull distribution is used to fit
empirical data, especially long term values. The three-parameter Weibull
distribution gives better possibilities to fit empirical data but also make
estimating the parameters more difficult.
Hermite Transformation Model. The Hermite Transformation Model is applied to data
that show weakly non-normal behavior. The mathematical model is based on the
first four statistical moments.
(Joint) Probability Density Function, f(x1,…xn). The concept above can be generalized to a
multivariate problem. Here the probability that a realization of a random variable xi in a
set of n random variables falls within an interval [xi, xi + dxi] at the same time as the
realization of another variable xj in the same set falls within an interval [xj, xj + dxj], and
so on for the remaining n-2 variables, is given by f(x1,..,xn)dx1…dxn.
Random (Stochastic) Process. It describes a physical quantity that is a function of time X(t) in
the sense that the value of X at any instant in time t is an outcome of a random variable.
Actions are often modeled as stochastic variables that are both functions of time and
location. When such functions are time-dependent, they are denoted as stochastic
processes. When they are functions of location, they are denoted as random fields.
Random (Stochastic) Variable. A variable which takes on a value from a set of possible
realizations according to a probability function or a probability density function.
Root Mean Square RMS. This is the square root of the mean of the sum of the squares of a
parameter.
RMS2 = V2 + P2
The standard deviation and the root mean square coincide when the mean is zero.
Statistical Moment of Order k about zero Mk:
x
Mk
M k (x)
³x
k
f ( x)dx
f
Standard Deviation V. Indicates the dispersion of the parameter about its mean value.
m2
V
Variance V2
V2
m2
M 2 M 12
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STRUCTURAL RELIABILITY ANALYSIS
Actuarial reliability. Reliability estimate of an objective or frequentist nature derived
from realistic observed rates of failure, thus allowing actuarial risk and
consequence assessments to be performed.
Aleatory uncertainty. Represents the natural randomness of a variable and is also
known as inherent uncertainty. Aleatory uncertainty is variability that cannot be
reduced. For example, soil undrained shear strength, water surface elevation.
Basic Variables. A set of the most relevant variables that influence failure / non-failure
of a structural component or system. Treated as random variables entering the
limit-state equation. Basic variables include those accounting for model
uncertainties in the limit-state equation itself.
Bayesian Probability. Probabilistic framework used as an aid in decision making by
expressing a subjective interpretation of limited information.
Bias. The ratio of measured (‘real’) value to the predicted value of a variable. Bias
greater that 1.0 implies under-prediction.
Design Point. The most probable combination of the basic variables leading to failure,
i.e., the point on the limit-state surface with the highest joint probability density.
In the standardized normal space, it is the point in the surface defined by the
limit state equation that is closest to the origin.
Design situations. A set of physical conditions representing a certain time interval for
which the design shall demonstrate the relevant limit states are not exceeded.
Element reliability. The reliability of a single structural element which has one single
dominating failure mode. (ISO). Also referred to as component reliability.
Epistemic (Model) Uncertainties. Uncertainty arising from a lack of knowledge,
including measurement uncertainty, statistical uncertainty and modeling
uncertainty. It can be reduced with additional information or improved
measurement and/or testing.
FORM - First-Order Reliability Method. Reliability method where the limit-state
equation is approximated by an expansion around the design point where only
the first order terms are retained. In the standardized normal space, the surface
defined by the limit state equation is approximated by a hyper-plane (linear
surface) at the design point.
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Frequentist probability. Probabilistic framework related to the frequency of occurrence
of outcomes of random experiments.
Limit State. State that defines the limit between a desirable situation (no failure) from an
undesirable situation (failure). It can be viewed as a generalization of the
concept of safety margin to multiple variables and failure modes.
The following are limit states common to marine structures:
ULS = Ultimate limit state (ISO)
FLS = Fatigue limit state
PLS = Progressive collapse limit state
SLS = Serviceability limit state (ISO)
Limit State Equation. Mathematical expression of a limit state. It is usually a function
of the basic probabilistic variables that is negative for failure and positive for
non-failure.
Limit State Surface. The surface in the standardized normal space defined by the limit
state equation. It separates the region defined by the combination of basic
variables that leads to failure from the region defined by the combination of
variables that does not lead to failure.
Notional reliability. Reliability estimate of a subjective or Bayesian nature derived from
first engineering principles rather than observed rates of failure. Used in practice
for offshore installations because their successful structural safety record leads
to very scarce structural failure events being recorded.
Partial Safety Factors (in the context of SRA). Multipliers that convert nominal values
of the basic variables into the values that such variables have at the design point
in a multi-variate SRA. By applying the appropriate partial safety factors to each
variable in each design situation, it is theoretically possible to obtain structures
with precisely the same reliability. However such values are uniquely defined
for each combination of structure / load condition / failure mode / etc. Reliability
based codes then attempt to reach a balance between a practical set of factors
and a minimum spread of reliability around a target value.
Probability of failure. Probability of attaining a non-desirable situation (exceedance of
limit state or failure).
Reliability. Ability of a component or a system to perform its required function without
failure during a specified time interval. In a multi-variate problem it is the
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probability density integrated over the safe states in the space spanned by the
basic variables.
Reliability method. A mathematical technique used to evaluate the probability of failure.
Response surface. A simplified mathematical approximation of a more complex limit
state equation, ‘designed ‘ to be accurate in the region of maximum probability
of failure content such as the design point.
Risk. A function of the probability and of the consequences of failure.
Safety Index E (Cornell). A scalar measure of safety incorporating the main statistical
properties of the safety margin:
E = PM / VM
PM and VM are, respectively, the mean and standard deviation of the safety
margin M. If M is normally distributed then the following applies:
pf = )(-E), where )() is the standard normal distribution
If the variability in the parameters is increased then E will decrease. Also E is
directly proportional to the difference between the mean values of resistance
and action.
Safety Index E (Hasofer-Lind). Extension of Cornell’s safety index to a multi-variate
problem where the safety margin has been generalized in terms of a limit state. It
represents the distance between the design point and the origin in a standardized
normal space.
Safety Margin M. The margin between resistance R (capacity) and action A (demand).
M=R-A
Sensitivity factors Di. Indicate how sensitive the safety index is to a particular variable i.
In a multi-variate SRA it is defined by the cosine of the angle between the safety
index vector and the variable axis. The sum of the squares of the sensitivity
factors of all variables equals unity.
Sensitivity measures. Parameters describing the variation in failure probability
associated with the variation of the statistical properties of the basic variables
(mean value, standard deviation, etc.).
SORM - Second-Order Reliability Method. Reliability method where the limit-state
equation is approximated using first and second order terms. In the standardized
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normal space, the surface defined by the limit state equation is approximated by
a quadratic surface at the design point.
Standardized Normal Space. A space of normally distributed random variables with
zero mean values, unit standard deviations, and zero correlation coefficients.
Mathematical N-dimensional space where the N basic variables affecting the
limit state equation are standardized by subtracting the mean value and dividing
by the standard deviation.
Structural Reliability Analysis (SRA). A set of mathematical procedures for evaluating
failure probabilities of structural components / systems given relevant limit state
equations containing basic variables described in a probabilistic manner. In a
wider sense, SRA explicitly recognizes that structures operate not in a simple
deterministic environment but in a complex environment involving quantities
with significant degrees of variability and where limitations exist on the
knowledge of the behavior of the structure.
System reliability. The reliability of a structural element which has more than one
relevant failure mode or the reliability of a system of more than one structural
element. (ISO).
Type I uncertainty. See aleatory uncertainty.
Type II uncertainty. See epistemic uncertainty.
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