Document 1778587

HSE
Health & Safety
Executive
Sensitivity of jack-up reliability
to wave-in-deck calculation
Prepared by MSL Engineering Ltd
for the Health and Safety Executive 2003
RESEARCH REPORT 019
HSE
Health & Safety
Executive
Sensitivity of jack-up reliability
to wave-in-deck calculation
MSL Engineering Limited
Platinum Blue House
1 st Floor
18 The Avenue
Egham
Surrey
TW20 9AB
This document represents a study undertaken by MSL Engineering Limited for the Health and Safety
Executive (HSE) to determine the effects of air gap erosion and subsequent hull inundation on a typical
Jack-Up structure.
A wave-in-deck loading model was developed (“The MSL Model”) and a sensitivity study was
performed to assess the important factors affecting the loads generated during inundation. In addition,
a typical Jack-Up structure was modelled using the USFOS structural analysis package in order to
determine the dynamic response of a Jack-Up to storm loading where inundation occurs. The effects of
response to previous waves, foundation modelling complexity and hull inundation levels were assessed
by performing a number of short duration time-domain analyses.
This report and the work it describes were funded by the 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
ISBN 0 7176 2177 4
All rights reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted in
any form or by any means (electronic, mechanical,
photocopying, recording or otherwise) without the prior
written permission of the copyright owner.
Applications for reproduction should be made in writing to: Licensing Division, Her Majesty's Stationery Office, St Clements House, 2-16 Colegate, Norwich NR3 1BQ or by e-mail to [email protected]
ii
FOREWORD
This document represents a study undertaken by MSL Engineering Limited for the Health and
Safety Executive to determine the effects of air gap erosion and subsequent hull inundation on
a typical Jack-Up structure.
A wave-in-deck loading model was developed (“The MSL Model”) and a sensitivity study
was performed to assess the important factors affecting the loads generated during inundation.
In addition, a typical Jack-Up structure was modelled using the USFOS structural analysis
package in order to determine the dynamic response of a Jack-Up to storm loading where
inundation occurs. The effects of response to previous waves, foundation modelling
complexity and hull inundation levels were assessed by performing a number of short
duration time-domain analyses.
iii
iv
CONTENTS
Page No
FOREWORD ...............................................................................................................III
CONTENTS ................................................................................................................V
1.
SUMMARY..................................................................................................... 1
2.
INTRODUCTION............................................................................................ 3
3.
MSL WAVE-IN-DECK MODEL...................................................................... 5
3.1
Introduction ......................................................................................... 5
3.2
Derivation of Wave-in-Deck Loads........................................................ 5
3.3
Model Implementation .......................................................................... 6
3.4
Wave Aeration ..................................................................................... 7
3.5
Wave Spreading ................................................................................... 7
4.
ENVIRONMENTAL DATA............................................................................. 9
4.1
Site Assessment.................................................................................... 9
4.2
10,000-Year Storm Conditions .............................................................. 9
4.3
Environmental Load Totals ...................................................................10
5.
RESULTS OF WAVE-IN-DECK PARAMETRIC STUDY................................ 11
5.1
Typical Results..................................................................................... 11
5.2
Effect of Increasing Wave Inundation on Wave-in-Deck Loads ............... 11
Effect of Different Wave Theories on Wave-in-Deck Loads .....................12
5.3
5.4
Effect of Wave Aeration on Wave-in-Deck Loads ...................................13
6.
DYNAMIC MODELLING ............................................................................... 15
6.1
Introduction ......................................................................................... 15
6.2
Structural Model................................................................................... 16
6.3
USFOS Hull Model .............................................................................. 18
6.4
Inclusion of Relative Velocity Terms ..................................................... 19
6.5
Foundation Modelling........................................................................... 19
6.6
Application of Pre-Wave Condit ion ....................................................... 21
7.
RESULTS OF DYNAMIC ANALYSES............................................................ 23
7.1
Effect of Inclusion of Wave-in-Deck Loads on Structural Response,
Linear Foundations ............................................................................... 23
7.2
Effect of Modified Morison’s Equation to include Relative Velocity ........ 23
7.3
Effect of Increasing Hull Inundation on Structural Response
(Linear Foundations)............................................................................. 24
7.4
Effect of Wave Theory on Structural Response....................................... 24
7.5
Effect of Response to Previous Wave on Extreme Wave Response .......... 24
7.6
Effect of Foundation Fixity on Structural Response ................................ 25
8.
CONCLUSIONS.............................................................................................. 27
9.
REFERENCES................................................................................................. 29
v
vi
1. SUMMARY
A wave -in-deck model (“The MSL model”) has been developed to assess the importance of
the loads caused by possible wave inundation on the hulls of Jack-Up structures. The MSL
method allows the use of higher order wave theories such as Stream Function and Stokes 5th
Order theories, and allows an aeration profile for the wave to be inputted.
A sensitivity study was performed using the MSL wave-in-deck model (in MathCAD format)
to assess the importance of a number of variables on the wave-in-deck loads generated, such
as degree of hull inundation, aeration level at the top of the wave and wave theory used.
Dynamic pushover analyses were performed on a detailed non-linear model of a typical JackUp structure using the USFOS structural analysis package. The hull structure was modelled
such that it attracted the wave-in-deck loads in accordance with the MSL model. The
pushover analyses were based on a 10,000-year wave. A sensitivity study was performed to
investigate the effects that hull inundation, foundation modelling, wave theory and structural
response to a preceding wave have on dynamic response to the extreme wave.
It has been found that wave-in-deck loads cause a significant increase in environmental
loading once inundation occurs. The horizontal loading at the front face of the hull leads to a
large increase in global overturning moment once inundation occurs. A key finding is that the
upward wave-in-deck loading (principally caused by buoyancy of the hull) leads to a large
decrease in vertical loading on the windward legs, with leg tension possible for inundations of
2m. The reduced vertical foundation load tends to decrease the moment capacity of the
spudcan foundation, leading to greater leg/hull moments and global displacements.
1
2
2. INTRODUCTION
In April 2001, MSL presented the findings of a study entitled “Assessment of the Effect of
Wave-in-Deck Loads on a Typical Jack-Up” (1,2) at the ISO North Sea Annex Committee
Meeting and the SNAME Panel 4 Meeting. This study contained the following:
1. A wave-in-deck model, developed by MSL and referred to as the MSL model,
implemented within an Excel Spreadsheet, based on linear wave theory.
2. Static pushover analyses for deck inundation levels ranging from 0.5m to 4m. The wavein-deck loads used in the pushover analyses (performed using the SACS structural
analysis package (3)) were calculated using the software developed in item (1).
The principal finding of this previous study was that the step change in environmental loading
once inundation occurs is likely to have a large consequence on structural integrity. Leg lift­
off, due primarily to the large buoyancy loads predicted in the MSL model, was identified as a
potential failure mechanism.
The discussions that took place at the ISO and SNAME meetings, and subsequently at a
meeting between HSE, Shell and MSL identified the following areas in which the previous
study could be refined:
1. Wave Model
One of the principal findings of the previous study was that the vertical loads (mainly
buoyancy) generated during wave inundation are considerable. However, this conclusion
was reached using Airy waves, which were used to allow the wave-in-deck model to be
implemented within an Excel spreadsheet. It was agreed that the effect of higher order
waves (for example Stream function and Stokes 5th Order) on wave-in-deck loads should
be investigated.
2. Wave Aeration
During the ISO/SNAME discussions, it was suggested that the top region of the extreme
wave may be highly aerated, hence giving lower buoyancy and horizontal wave loads,
and in turn a reduced tendency for leg lift-off to occur.
3. Water Particle Velocity
It was suggested that the calculated velocity (from higher order wave theorie s) should be
reduced to more accurately capture the wave-in-deck loads, and the sensitivity of the
loads to this reduction should be investigated.
4. Foundation Modelling
The model used in the previous study used linear foundations. It was suggested that the
structure would be more accurately modelled using non-linear foundation springs.
5. Dynamic Response to Wave-in-deck loads
The response of a Jack-Up unit to wave loading is comprised of a static and dynamic
component. The dynamic component is normally significant as the natural period of the
structure is often close to the period of the extreme wave. When a site assessment is
3
performed using methods recommended in SNAME 5-5A (4), the usual approach is to
apply a Dynamic Amplification Factor (DAF) to the wave loads to represent the worst
likely inertia loading on the structure. However, the dynamic response of the structure to
wave-in-deck loads may be different to the dynamic response to wave loads on the legs.
There are three areas where differences may arise: a) the phasing of wave-in-deck loads
may be different to the wave loads on the legs, b) the duration of the wave-in-deck loads
will be shorter than the duration of the wave loads on the legs, and c) the vertical
buoyancy loads may excite a higher order response mode than the global structural sway
mode. The previous MSL study predicted that leg lift-off was a possible failure mode.
This conclusion was reached assuming that the structure would react statically to wavein-deck loads, and that the DAFs for wave loading on the legs remain valid when used in
conjunction with wave-in-deck loads. It was suggested that the dynamic response of a
Jack-Up structure to wave-in-deck loads may more accurately be assessed by performing
pushover analyses in the time domain.
In order to incorporate the above items the present study has performed the following:
1. The existing Excel wave-in-deck model was converted to MathCAD format. The
MathCAD program was updated so that:
• Wave surface profile and velocity fields could be imported from a 3rd party wave
processor. The wave processors used were SACS Seastate and ASAS-WAVE (5).
• A fluid density profile with depth below the free surface may be defined, thereby
accounting for wave aeration
• A reduction in horizontal particle velocity, dependent on depth below the free surface,
may be defined.
2. The static model used in the first study (mounted in SACS) was converted for the USFOS
analysis package. USFOS is a non-linear analysis program that has the capability of
performing time-domain analyses, giving the dynamic response of the structure to the
applied loads. The following refinements were made to the structural model:
• Use of non-linear pinions
• Use of non-linear foundations (including uncoupled and coupled springs)
• Wave-in-deck loads calculated within the structural model by using appropriate non­
structural elements such that the loads were accurately captured in the time domain
• Relative fluid velocities included in formulation of Morison’s equation
Sensitivity studies were performed on both the MathCAD wave-in-deck model and the time
domain analyses to assess the relative importance of the items discussed above.
The remainder of this report is structured as follows: Section 2 describes the MSL wave-indeck loading model and Section 3 details the environmental data used in the project. Section 4
contains the results of the sensitivity study performed on wave-in-deck load generation using
the MSL wave-in-deck software. Section 5 contains details of the USFOS structural model
used for dynamic simulations of wave-in-deck response, and Section 6 summarises the results
of the dynamic analyses. Section 7 contains the conclusions reached from this study.
4
3. MSL WAVE-IN-DECK MODEL
3.1 Introduction
A previously performed literature survey
broadly fall within two categories, namely:
(6)
identified that existing wave-in-deck models
• A global or silhouette approach, which provides global loads based on an exposed area of
deck to the wave
• A detailed component approach, where loads on individual components are summed to
give a global force.
The detailed component approach (e.g. Kaplan model (7)) is often used for topsides structures
on fixed platforms, where the loads generated on individual members (e.g. beams, columns,
items of equipment) may be calculated individually and combined to give a global force. In
the case of the solid hull structures found on Jack-Ups, the global/silhouette approach is
considered more suitable and has been adapted for use in the MSL wave-in-deck model.
It may be noted that API RP 2A Section 17 (8) presents a simple method for predicting the
global wave/current forces on platform decks. In the API model the load is evaluated based on
calculating the drag force from a wave incident on the projected area of the deck. This method
only produces front horizontal loads without explicit consideration of inertial, impact or
pressure gradient effects. Wave phasing is also neglected.
3.2 Derivation of Wave-in-Deck Loads
The MSL model considers both horizontal and vertical loads generated when deck inundation
occurs, and is summarised in Figure 1. The horizontal load is derived assuming that the wave
is effectively “sliced off” by the hull, with its momentum completely destroyed in the process.
The vertical load includes the buoyancy of the hull as well as the hydrodynamic force induced
by the vertical velocity of the wave particles as the wave passes under the base of the hull.
Buoyancy loads are determined by calculating the weight of the displaced volume of water
(i.e. the 'shaved off' region of the wave).
Reference may be made to Figure 2 for the following derivations.
Horizontal load:
The horizontal load at the front face of the hull is derived from momentum considerations:
&u
Fh = m
(1)
& = horizontal mass flow rate at the front face
where m
u = horizontal particle velocity including current ( = u + u c )
and hence it may be shown that by integrating the wave load over the wetted height of the
front face of the hull that:
h x=0
Fh =
� rb (u + u ) F(h
2
x=0
c
x= 0
- z hull)dz
z hull
(2)
5
where r = fluid density
b = the width of the hull
h = wave surface profile measured from seabed
z = vertical distance from seabed
F = Heaviside function; F(a) = 1 for a > 0, 0 otherwise
Note that in the case of an aerated wave, the fluid density may be a function of vertical
distance from the free surface.
Vertical Hydrodynamic Load:
The vertical hydrodynamic load on the underside of the hull may be deduced using similar
considerations as above, and integrating the vertical load over the submerged area of the hull:
l
Fv = � rbv 2F (h x= 0 - zhull )dx
(3)
0
where v = vertical particle velocity
l = hull length in the direction of the wave
Buoyancy Load:
The buoyancy load is assumed to be equal to the weight of the volume of water displaced by
the hull:
l
Fb = � rgb(h - zhull )F(h - z hull )dx
(4)
0
Note that the position of the resultants for both vertical hydrodynamic load and buoyancy load
are a function of time.
3.3 Model Implementation
The original MSL wave-in-deck model utilised linear waves (i.e. Airy waves). In linear wave
theory, the surface profile of the wave, horizontal velocities and vertical velocities may be
described using relatively simple equations (9), and are more easily incorporated into a
spreadsheet format. Higher order wave theories, such as Stokes 5th order theory and Stream
Function waves are much more difficult to directly incorporate within a spreadsheet.
Higher order wave theories were included in the updated MSL model by utilising existing
wave generation programs to create surface profiles and velocity fields. Two different
programs were used to do this, depending on the wave theory used:
(i)
(ii)
SACS SEASTATE: Used for Stokes 5th order and Stream Function theories
ASAS-WAVE: Used for Shell NewWave
The output from these programs was then formatted so that it was in the form of a time
history of surface elevations, and velocity fields for horizontal and vertical particle velocities.
Increments of 10 degrees were used, giving a total of 36 time steps for the full wave cycle.
Interpolation between the values generated by ASAS/SACS was used within the MathCAD
program to enable smooth, integrable functions of surface profile with time and horizontal
6
and vertical velocity with time and depth. This allowed wave-in-deck loads to be calculated
over the period of hull inundation.
3.4 Wave Aeration
The degree of aeration at the top of the wave will have an effect on the wave -in-deck loads
generated, acting to reduce buoyancy loads as well as reducing horizontal and vertical
hydrodynamic loads. However, the instantaneous quasi-hydrodynamic load at a given point
will only be proportional to the density of the water at that point. The very dramatic decreases
in short duration wave slam loads due to an aerated wave front (10) is due to a large increase in
water compressibility, and should not be confused with the longer duration quasi-hydrostatic
loads being generated in the present situation.
Most of the research that has been performed on wave aeration has been concentrated in the
surf zone, where the highly turbulent wave action leads to high degrees of aeration (11). In
open water situations, wave aeration is likely to be caused by high winds acting on the crest of
the wave, as well as some local wave spilling. The aeration levels occurring in open water are
likely to be much lower than those measured in the surf zone. In addition, the depth to which
this aeration exists is likely to be small, with bubbles probably only penetrating the upper
zone of the wave.
In order to investigate the sensitivity wave-in-deck loads to aeration at the wave crest,
aeration levels of 0, 10%, 20% and 30% at the free surface were used. The distribution of
aeration with distance from the free surface was adapted from work presented by Bea (12).
Aeration was assumed to act to a depth of one velocity head (using the horizontal crest
particle velocity), defined with by following equation:
ø
Ø
� 100gd �
k
�
r = r unaerated Œ(1 - k ) + log ��
+
51
œ
2 Ł uc2 �ł
ß
º
(5)
For the extreme waves used in this study, one velocity head is approximately 2.5m. The
aeration profiles derived from Equation 5 are shown in Figure 3. Values of the variable k
were chosen to give the desired aeration at the free surface.
3.5 Wave Spreading
In the SNAME 5-5A Recommended Practice, the reduction in wave loads caused by wave
spreading is accounted for by reducing the deterministic wave height from 1.86Hs to 1.60Hs,
where Hs is the significant wave height. This reduction may alternatively be modelled by
applying a “wave kinematics factor” to the horizontal particle velocities of the wave. A wave
kinematics factor of 0.84 was used in this study whilst keeping the deterministic wave height
as 1.86Hs, hence ensuring that a realistic crest elevation was used in the wave-in-deck
calculations and that the wave loads on the legs were reduced to a more representative value.
The 0.84 factor was used when generating wave-in-deck loads as well as wave loads on the
legs.
7
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4. ENVIRONMENTAL DATA
4.1 Site Assessment
In the original study (1) , a simple site assessment was performed on the Jack-Up to determine
the maximum member utilisation using an environmental load partial safety factor of 1.15 and
an LAT of 96.6m. The SACS structural analysis package was used to perform the assessment.
It should be noted that the site assessment was limited to the extreme in-place condition only.
The following conditions were applied to the structure for the site assessment, and are
representative of conditions in the Central North Sea (Table 1):
Table 1
Environmental Conditions for Site Assessment
LAT
96.6m
Hs
12.4m (50-year value)
Peak period
15.3sec
Hmax
23.1m (=1.86Hs)
Current
0.67m/s
1-minute mean wind speed
40.1m/s
The maximum member utilisation found using the above environmental conditions was 1.0,
indicating that the Jack-Up, in the state analysed, is highly utilised. The site assessment was
performed using a yield stress of 607N/mm2 . This was increased to 690 N/mm2 for the
pushover analyses to represent a mean value.
4.2 10,000-Year Storm Conditions
In the present study, the 10,000-year wave was used to generate wave-in-deck loads and
perform structural analyses in the time domain. The 10,000-year wave height and period were
used as the survival of such a wave is required if a target failure rate of 10-4 is to be achieved.
However, the deck inundation levels used in this study are not directly related to a given
return period, and have not been determined from site-specific conditions.
The 10,000-year wave used is as follows (Table 2):
Table 2
10,000-year Environmental Conditions
Hmax
31.2m
Tmax
17.7sec
Current
0.67m/s
1-minute mean wind speed
40.1m/s
Values determined using
SNAME 5-5A methodology
Note: 50-year values used
It may be noted that individual 10,000-year extreme values of current and wind were not
applied in conjunction with the 10,000-year wave conditions.
9
4.3 Environmental Load Totals
The following load totals (see Table 3) resulting from the applied 10,000-year environmental
conditions were determined from the original SACS model, and were subsequently replicated
using the USFOS model:
Table 3
Environmental Loads (excluding wave -in-deck loads)
Item
Maximum Base Shear
Maximum Overturning Moment
Wind Base Shear
Wind Overturning Moment
Maximum Value
Time of Occurrence
*
29MN
+0.4s
1590MNm
+0.8s
3.2MN
-
430MNm
-
* time of zero seconds refers to the moment at which the top of the wave is in-line with
the face of the hull
10
5. RESULTS OF WAVE-IN-DECK PARAMETRIC STUDY
5.1 Typical Results
A graphical representation of the wave passing through the structure may be found in Figure
4. Figure 5 shows typical results from the MathCAD wave-in-deck software. In this case, a
stream function wave was used with a deck inundation of 3m. The following points may be
made from Figures 4 and 5:
1. The duration of the horizontal wave-in-deck load is around 2.5 seconds, and is at a
maximum when the wave crest is in line with the front face of the hull (t=0 seconds).
2. The peak horizontal wave-in-deck load is 135MN. This is slightly out of phase with the
peak base shear from wave loading on the legs (the phase difference is around 0.5
seconds).
3. For an inundation of 3m, the maximum horizontal wave-in-deck load makes up around
30% of the total base shear at t=0.
4. The vertical loading on the hull is dominated by buoyancy loads. The peak buoyancy of
71MN occurs approximately 1 second after the peak horizontal wave-in-deck load.
5. The duration of the vertical loading is around 4 seconds for an inundation of 3m.
6. The maximum wave-in-deck overturning moment (which includes horizontal and vertical
loading effects) occurs at t=0 seconds.
7. The overturning wave-in-deck moment becomes negative at around 1.25 seconds after the
time of peak horizontal wave-in-deck loading. At this point the centre of buoyancy has
passed the plan centroid of the three legs, and the horizontal load is almost zero.
8. The maximum wave-in-deck overturning moment makes up around 55% of the total wave
load.
Note that the overturning moment was defined as the moment about a horizontal line at the
mudline perpendicular to the direction of the applied wave and passing through the plan
centroid of the 3 legs. Figure 6 shows base shear and overturning moment time-histories for
wave and current on the legs (with no wave-in-deck loads) and wave and current on the
structure (including wave-in-deck loads).
5.2 Effect of Increasing Wave Inundation on Wave-in-Deck Loads
The effect of increasing wave inundation on the wave-in-deck loads generated (using a
Stream Function wave) are shown in Figures 7 to 10.
Figure 7 shows horizontal loads for increasing inundation levels. The magnitude of the
maximum horizontal wave-in-deck load is approximately proportional to the maximum
inundation level, as the velocity profile is roughly constant at the very crest of the wave. The
duration of loading increases from 1.4 seconds (1m inundation) to 2.8 seconds (4m
inundation).
Figure 8 shows the buoyancy loads generated for increasing inundation levels. The maximum
buoyancy loads generated dur ing inundation increases from 14MN for 1m inundation (0.5
11
seconds after the peak wave-in-deck base shear) to 102MN for 4m inundation (occurring 1.1
seconds after the peak wave -in-deck base shear). The buoyancy values compare with a total
dead load of 161MN for the structure. As the wave passes through the Jack-Up, the centre of
action of the buoyancy load moves from providing a positive overturning moment on the hull
to a negative overturning moment (Figure 9).
Figure 10 shows the effect of inundation leve l on total wave-in-deck overturning moment.
The maximum total overturning moment increases from 717MNm (1m inundation) to
2980MNm (4m inundation). The duration of the loading also increases as the maximum
inundation increases, with the positive phase of the overturning moment increasing from
around 1.8 seconds (1m inundation) to 2.7 seconds (4m inundation). The time period between
maximum positive and negative overturning moment is relatively insensitive to inundation
level, being primarily a function of wave celerity.
5.3 Effect of Different Wave Theories on Wave-in-Deck Loads
As stated previously, the MSL wave-in-deck model was updated so that higher order waves,
such as Stream Function and Stokes 5th Order theories could be incorporated. The surface
profile of the wave will affect the magnitude, duration and phasing of buoyancy loads. The
horizontal velocities at the top of the wave will directly affect the horizontal loads generated.
Figure 11 shows a comparison of wave surface profiles. It can be seen that the Airy wave
gives a less peaked profile than the other waves, and hence would be expected to give greater
wave-in-deck loading durations. In addition, for a given inundation level, a larger volume of
water will be displaced by the hull during the inundation process, and hence the hull will
attract larger buoyancy loads for Airy waves. It should be noted that the still water level of the
waves were adjusted to give the same extreme crest elevation.
The Stream function and Stokes 5th order theory produce very similar profiles. The shape of
the NewWave profile is similar to that of the Stream/Stokes 5th profiles at the crest of the
wave, and would therefore be expected to provide similar load durations and buoyancy levels.
Figure 12 shows the distribution of horizontal particle velocity with elevation for the four
wave theories assessed. It may be seen that the horizontal velocities predicted by linear wave
theory are between 5% and 10% less than those predicted by both Stokes 5th order and
Stream function (this agrees with work presented by Barltrop (9)). The NewWave formulation
gives somewhat higher horizontal velocities near the surface of the wave.
Figure 13 shows the effect of using different wave theories on wave-in-deck loads. The Airy
wave underestimates the horizontal wave-in-deck loading compare to the higher order wave
theories by around 12%, as a result of the lower particle velocities predicted. However, the
Airy wave overestimates buoyancy loading on the hull by around 20% due to its sinusoidal
surface profile. It may be seen from the bottom graph of Figure 13 that the two effects
described above have conflicting contributions to overturning moment, with Airy waves
being a reasonably good approximation of combined overturning moment for inundations up
to 2m.
It may be noted that the wave-in-deck loads determined are relatively insensitive to the
method of current stretching adopted. Horizontal wave-in-deck loads are dependent on the
horizontal particle velocities at the top of the wave, and hence the stretching profile used to
extrapolate surface velocities down from the crest to the mean water level will not to have a
significant effect on calculated load for inundation levels up to 5m.
12
5.4 Effect of Wave Aeration on Wave-in-Deck Loads
Figure 14 shows the effect of aeration at the wave crest on wave-in-deck loads. The aeration
profile described in Equation 5 was used. It may be seen that a relatively high surface aeration
of 30% reduces the wave-in-deck buoyancy, base shear and overturning moment by around
20%.
13
14
6. DYNAMIC MODELLING
6.1 Introduction
The dynamic response of a Jack-Up unit to wave loading, even when no inundation of the hull
occurs, is complex. The effects of random waves, dynamic amplification, drag dominated (i.e.
non-linear) loading, non-linear structural response, global P-delta moment and relative fluid
velocities mean that the calculation of extreme structural response must be performed with
care. The step change in loading that occurs with hull inundation makes the response even
more complex, with the nature of the true response being far from obvious.
Where no inundation occurs, the dynamic amplification of static response to extreme loading
may be assessed by following the methods described within SNAME 5-5A. A simple and
commonly used method is to determine a DAF based on a Single Degree of Freedom (SDOF)
model. The DAF is calculated by comparing the global sway period of the structure with the
period of the extreme wave. A dynamic loadset is then applied statically to the model to
represent this inertia loading. The SDOF method assumes that structural response is
dependent on one loading regime with a given period, and on one modal response to that
loading.
However, when inundation of the hull occurs, the loading and response regime become much
more complex. The items listed below will affect the true extreme response:
(i) The duration of horizontal wave-in-deck loads:
It was seen in Section 5.1 that the duration of horizontal wave loads is generally in the
region of 1 to 3 seconds. This compares with a natural period in the sway mode of
between 5 seconds (fixed foundations) and 12 seconds (pinned foundations) for the
present structure. It is likely that the dynamic amplification factor for this type of loading
alone will be less than 1.0 for pinned foundations, but may be greater than 1.0 for stiff
foundations.
(ii) The duration of vertical wave-in-deck loads:
The duration of the vertical wave loads (mainly buoyancy loads) is in the region of 1 to 4
seconds. However, the period of the structural mode likely to be excited by these loads is
less than 2.0 seconds for this structure (including vertical foundation flexibility),
suggesting that the structure may react statically to vertical loading.
(iii) Load phasing
It was seen in Section 5.1 that the greatest wave-in-deck overturning moment generally
occurs at the time when the top of the wave is in line with the front face of the hull. This
is in the region of 0.5 seconds before the peak wave-on-leg loading occurs. In addition,
the wave-in-deck overturning moment becomes negative at a time when the wave load on
the legs is near or at its maximum value. This negative overturning moment is likely to
have a moderating effect on the maximum horizontal structural response.
(iv) Relative particle velocity:
The predicted horizontal displacement of the Jack-Up under extreme load conditions is
considerable, with displacements in the order of 3-5m being possible. For example, a
wave period of 17.7 seconds causing a 5m displacement gives a peak horizontal velocity
of around 1.8 m/s (assuming sinusoidal response). Given that the particle velocity at the
crest is around 7 m/s, the incorporation of relative velocities will have a significant effect
for extreme wave conditions.
15
(v) Foundation conditions:
The degree of foundation fixity assumed at the spudcan has a profound effect on the
predicted structural response of a Jack-Up unit. Increased foundation fixity leads to lower
bending moments at the leg/hull connection as well as a reduced sway natural period. A
reduction in the natural period will reduce the DAF for the wave loads on the legs and
probably increase the DAF for horizontal wave-in-deck loads.
The inclusion of uncoupled non-linear foundations (i.e. separate non-linear springs in the
horizontal, vertical and rotational directions) makes the structural response more
complex, as the bending moment distribution down the legs and the natural period of the
structure will vary during the wave cycle.
Perhaps the best method for modelling foundation fixity during a wave cycle is to apply
coupled non-linear springs to the base of the legs. This means, for example, that the
rotational fixity provided by the spudcan is dependent on the vertical load applied to it at
that time. The USFOS analysis package (13) contains a “SPUDCAN” element to
specifically include these effects, whose formulation is based on work by Van Langen (14).
(vi) Initial conditions prior to the extreme wave:
The structural displacements, velocities and accelerations prior to the extreme wave
loading on the structure will significantly affect the response to the extreme wave itself.
The most rigorous analysis method to assess their effects would be to run a number of 3­
hour simulations of the storm conditions causing the 10,000-year wave in the time
domain. Statistical methods (such as those detailed in SNAME 5-5A) could then be used
to determine the worst likely response in a 3-hour period. It should be noted that it is this
extreme response that a dynamic amplification factor applied to quasi-static wave loads is
meant to represent. Such lengthy time history analyses is beyond the scope of the present
study, even if pertinent data for such storms existed. However, the importance of the
initial structural conditions prior to the main wave may be made by applying a “pre­
wave” to the structure, with the main wave occurring at some time later. The pre-wave is
applied to give the structure a set of initial displacements, velocities and accelerations.
This approach is described in more detail in Section 6.6.
A detailed structural model of a typical Jack-Up was created in USFOS by converting and
updating the SACS model used in the original MSL wave-in-deck study. The model was
created to allow the investigation of the above effects and to model dynamic structural
response to wave-in-deck loading as accurately as possible.
6.2 Structural Model
6.2.1
Introduction
The modelled Jack-Up is a 3-legged structure with a maximum elevated weight of 12500t
(Figure 15). The total weight of the modelled platform is 16500t. The legs are triangular,
consisting of 3 tubular chords spaced at 12.2m and braced at bays of 6.96m with a K-bracing
arrangement. The combined weight of the legs and the spudcans (excluding buoyancy) is
1275t. At the bottom of each leg is a spudcan, with a plated tank section immediately above
extending to a height of 23m. The overall height of each leg is 146m, and are spaced
approximately 55m apart. The connection between the leg and hull consists of a set of pinions
and rigid horizontal guides at the bottom of the hull and at the top of the yoke frame.
In plan, the hull structure is approximately triangular, with a side length of approximately
72m (Figure 2). The four pyramid structures shown in Figure 2 are used only to apply the
vertical topsides loads to give the correct vertical centre of gravity.
16
The following comparisons of key results were performed to ensure the conversion from the
original SACS model to USFOS format was successful:
•
•
•
•
Dead loading
Base shear and overturning moment for the extreme wave
Mode shapes and their associated periods
Static pushover response.
A comparison of the results from the two models is shown in Table 4. Static pushover
analyses were performed on both models. Ultimate structural capacity and global force­
displacement curves were found to agree closely.
Table 4
Comparison of SACS and USFOS finite element models
Results for:
SACS
USFOS
Dead weight
16500t
16500t
29.5MN
29.6MN
Overturning moment
1660MNm
1720MNm
Sway natural period
11.1 seconds
11.4 seconds
Base Shear
USFOS is a dedicated non-linear, dynamic analysis package, specifically written for the
offshore industry. The following enhancements to the original SACS model were made in
converting to USFOS:
•
•
•
•
Use of uncoupled and coupled non-linear foundations
Modelling of non-linear pinions, allowing load redistribution at the leg/hull connection
Analyses performed in the time domain
Relative fluid particle velocities included in Morison’s equation.
6.2.2
Leg modelling
All major structural members in the legs were explicitly modelled. The leg model was
sufficiently detailed to ensure representative loads resulting from wave and current would be
generated.
The main chord members of a Jack-Up may have different section properties across the major
and minor axes, caused by rack teeth and any additional strengthening to the tubular that may
be present. For the purposes of the present study, the chord members were modelled as
equivalent tubulars, whose diameter and wall thickness were chosen to give the average
plastic modulus and the cross-sectional area of the combined section. It is these properties that
have the most effect on the global structural stiffness and the plastic axial and bending
capacity of the legs. The tank plating at the base of each leg was represented by truss
members to give a suitable stiffness. Brace offsets were not modelled.
The hydrodynamic loads for rack post members were generated assuming the original chord
diameter of 850mm and modified values of Cd and Cm based on recommendations contained
in SNAME 5-5A. Averaged values of Cd for the three chords in each leg were used for
simplicity. The following values of Cd and Cm were used (Table 5).
17
Table 5
Hydrodynamic Coefficients Applied to Chord Members
Element
Cd
Cm
Rough rack post
1.66
1.8
Smooth rack post
1.45
2.0
Rough brace member
1.0
1.8
Smooth brace member
0.65
2.0
Tank region at base of leg
8.9*
89.1*
* coefficients applied to individual members of 850mm diameter
6.2.2
Leg/Hull Connection
The guides and pinions forming the connection between the legs and the hull were
represented by spring elements within USFOS. The guides and the pinions were attached to
the yoke frame, which was modelled to give a representative structural stiffness. The
following guide and pinion stiffnesses were modelled (Table 6):
Table 6
Guide and Pinion Stiffnesses
Element
Stiffness
Upper guide
86.0 x 103 t/m
Lower guide
500 x 103 t/m
75.0 x 103 t/m (vertical)
Pinions
35.1 x 103 t/m (horizontal)
The gaps that exist between the guides and the chord members and in the pinion mechanism
were not modelled in this study.
The pinion members were modelled as bi-linear springs. Pinion slippage (yielding) was
assumed to occur at an ultimate capacity of 12.3MN, with additional displacement assumed to
give no extra load capacity. It may be noted that during the short duration time-domain
analyses performed in this study, although some pinion slippage was noted, the displacements
of the pinion springs were not excessive.
6.3 USFOS Hull Model
The hull was modelled using plate elements. The plate thicknesses were chosen to reflect the
true stiffness of the bulkhead stiffnesses including local stiffeners. Plate thicknesses and
stiffener geometries were taken directly from available drawings of the jack-up structure. The
plate elements were assumed to behave elastically under all applied loads.
Non-structural elements were added to the plated hull model to allow the automatic
generation of wave-in-deck loads during time-domain analyses, as illustrated in Figure 16.
Two sets of elements were defined:
(i) Buoyancy elements:
These were defined as vertical members extending from the base to the top of the hull.
Each member was partitioned into 99 sections to allow the accurate calculation of hull
buoyancy as the wave crest passed through the hull. A cross-sectional area was assigned
18
to each member appropriate to the hull plan area around it. The sum of these member
areas equalled the plan area of the hull, taking due account of the voids in the hull around
the le g sections. The dummy members were assigned zero drag and inertia coefficients.
The areas of the members were then increased by 10% to account for vertical
hydrodynamic loads predicted by the MathCAD model.
(ii) Drag elements:
Additional vertical dummy elements were added to the side of the hull facing the
incoming waves. Each member extended over the full height of the hull. Appropriate
values of the product of Cd and member diameter were chosen to give a suitable value of
effective frontal area. Member buoyancy and the inertia coefficients were set to zero.
The USFOS wave -in-deck model was validated by applying a Stokes 5th order wave statically
to the USFOS model and comparing the reported loads with those predicted from the
MathCAD analyses reported in Section 5. A comparison of the two methods is shown in
Figure 17. There is excellent agreement between the two methods (both in terms of the
magnitude of the loads generated and the relative phasing of vertical and horizontal load
components), with no need for correction factors to be applied. It should be noted that for the
validation, the hull leg was prevented from moving vertically and horizontally, hence
removing the effects of relative fluid velocities and displacements.
6.4 Inclusion of Relative Velocity Terms
The potentially large structural displacements of a Jack-Up in extreme storm loadings
suggests that the velocity of the structure during the wave cycle may be significant when
compared to the wave particle velocities. Morison’s equation may be extended to include a
relative velocity term:
Fdrag = 0.5 rCD D un - r&n (un - r&n )
(6)
where u n is the combined particle velocity from wave and current normal to the member
considered
r&n is the velocity of the considered member normal to its axis in the direction of the
combined particle velocity
The inclusion of a relative velocity term introduces a fluid damping effect. Relative velocities
were included within the load formulation in the USFOS model except where noted.
6.5 Foundation Modelling
6.5.1
Linear Foundations
Three sets of linear foundations were used in the present study (Table 7):
19
Table 7
Linear spring stiffnesses
Spring stiffness
Rotational
(kNm/rad)
Horizontal
(kN/m)
Vertical (kN/m)
SNAME 5-5A “extreme”
4.96 x 106
75.5 x 103
130 x 103
Fatigue spring
124 x 106
579 x 103
2.48 x 106
20 x 106
316 x 103
412 x 103
SPUDCAN* initial stiffness
* The SPUDCAN linear springs were derived using the USFOS in-built spudcan model. Section
6.5.2 below contains further details of the spring derivation.
The SNAME 5-5A “extreme” fixity was determined using the SNAME recipe. The fatigue
spring fixity is close to the “measured” values inferred from measured natural periods of a
similar Jack-Up (15).
6.5.2
Coupled Non-Linear Springs
A ‘SPUDCAN’ element is included within USFOS which was specifically developed to
represent the foundation fixity conditions provided by preloaded spudcans. The element is
derived from the stiffness formulation presented by van Langen, which is consistent with
SNAME 5-5A Recommended Practice and is based on hardening plasticity theory.
The USFOS SPUDCAN element creates a set of coupled springs that represent foundation
stiffnesses in the horizontal, vertical and rotational directions. The rotational and horizontal
stiffness are dependent on the vertical load on the element at that time, and hence the
foundation stiffness is modified continuously throughout the dynamic analyses.
The parameters used for the SPUDCAN element are shown in Table 8, and are typical of data
in the Central North Sea.
Table 8
Input Parameters for USFOS spudcan element
Soil type
Clay
Effective spudcan diameter
16.19m
Undrained shear strength
50kN/m2
Shear modulus
5.39 x 103 kN/m2
Embedment depth
5m
Preload
175 x 103 kN*
* artificially high value, chosen to allow the analysis to continue beyond the 50-year preload value
of 101.3 x 103 kN.
The spudcan element provides a linear section to the load-displacement relationship, beyond
which a ‘plastic’ displacement region exists. Typical load-displacement curves (for horizontal
and moment loading) are shown in Figures 18 and 19.
The relationship between vertical load and moment capacity (both ultimate moment capacity
and the moment at first yield) and vertical load and sliding capacity are shown in Figures 20
and 21. It may be seen that the ultimate moment capacity is broadly in line with the average
ultimate moment capacity determined by Noble Denton (16) following the SNAME 5-5A
20
methodology using similar soil parameters. The moment capacity reduces from a maximum
of 285MNm at a vertical load of 100MN to zero when no vertical load is applied. The sliding
capacity reduces from a maximum of 12.3MN at a vertical load of 100MN to zero when no
vertical load is applied.
Table 7 above shows the initial foundation stiffnesses derived from the USFOS model.
Comparison with the “extreme” and “fatigue” stiffnesses derived by Noble Denton show good
agreement.
As was noted in Table 8, an artificially high value of preload was applied to the SPUDCAN
element (175MN instead of around 100MN). This was required as the element is only
formulated up to the preload vertical load, with larger loads causing the analysis to stop. The
increased preload gave larger moment capacities than would otherwise have been predicted.
6.5.3
Non-Linear Foundations
In order to investigate the importance of the coupling effect of the foundation springs (see
Section 6.5.2) on structural response, and to determine whether uncoupled non-linear springs
would give simila r results, non-linear springs were developed based on the foundation
stiffnesses derived from the USFOS SPUDCAN element. The force-displacement curves
were based on the results from the SPUDCAN element at a vertical load of 80MN. The linear
springs were based on the initial stiffness of the SPUDCAN element.
6.6 Application of Pre-Wave Condition
In order to model the possible contribution of the structural response to a preceding wave on
the response to the main wave, the following methodology was used:
1. Apply 50-year deterministic wave statically to the structure to create a wave loadset
2. In the dynamic model, apply the 50-year loadset gradually to the structure
3. Suddenly release the load, which then makes the structure oscillate at its natural (i.e.
sway) period
4. Apply the 10,000-year wave at a time Dt after releasing the 50-year load.
By varying the value of Dt over a range equal to the sway natural period of the structure the
full envelope of maximum response to the extreme wave may be determined.
21
22
7. RESULTS OF DYNAMIC ANALYSES
7.1 Effect of Inclusion of Wave-in-Deck Loads on Structural Response, Linear
Foundations
Three analyses were performed to assess the significance of the following wave-in-deck loads
for global response:
Run number
Vertical wave-in-deck loads
Horizontal wave-in-deck loads
1
�
�
2
x
�
3
x
x
The above runs were performed with an inundation of 3m and linear ‘extreme’ foundation
springs.
The horizontal displacements at deck level are shown in Figure 22. It can be seen that the
inclusion of wave-in-deck loads has slightly increased the maximum horizontal displacement.
It may also be seen that, in this case, the inclusion of buoyancy loads has acted to reduce the
maximum displacement as compared to the wave-in-deck model with no buoyancy taken into
account. The buoyancy reduces structural displacement (for the linear foundation case) for
two reasons: firstly, the large upward load acts to stiffen the structure, and secondly, the
buoyancy creates a negative overturning moment at the same time as the peak wave-on-legs
base shear.
The effect of including wave-in-deck loads on vertical foundation reactions is shown in
Figure 23. For the windward leg, the inclusion of wave-in-deck loads, including buoyancy,
reduced the vertical reaction significantly between the times of 6 and 10 seconds (i.e. during
the time when the hull is inundated). The decrease in vertical load on the two windward legs
is approximately equal to the buoyancy predicted by the MSL MathCAD model (69MN
compared to 71MN predicted in Section 5) and hence indicates that the structure reacts
statically to vertical loading. The large decrease in vertical load does not occur for the wavein-deck model with buoyancy effects ignored, although there is a slight decrease in loading
due to the increased overturning moment caused by the horizontal wave-in-deck component.
In the case of the leeward leg, it may be seen that the wave-in-deck buoyancy has a
moderating effect on the maximum vertical reaction, especially when the wave has passed the
centroid of the hull and is hence causing a negative overturning moment. The wave-in-deck
case with buoyancy loads ignored leads to an overestimate of vertical loading on the leeward
leg, as the additional overturning moment from horizontal wave-in-deck loads is included but
the relieving moment due to eccentric buoyancy is not.
7.2 Effect of Modified Morison’s Equation to include Relative Velocity
Figures 24 and 25 shows the effect of ignoring relative velocity terms on structural response,
using linear “extreme” foundation springs and an inundation of 3m. The inclusion of relative
velocity effectively introduces a damping term into the response. It should be noted that the
reductions in maximum response and maximum/minimum leg reactions may not be as
marked for cases where stiffer foundation conditions are assumed, as the structural velocities
will be smaller.
23
7.3 Effect of Increasing Hull Inundation on Structural Response (Linear
Foundations)
The effect of increasing hull inundation on horizontal structural displacement is shown in
Figure 26. Inundation levels up to 3m were investigated. SNAME 5-5A extreme fixity levels
(Section 6.5) were used. No pre-wave was applied. It may be seen that the amount of hull
inundation does not greatly affect the horizontal displacement of the structure. Although the
horizontal wave-in-deck loads are significant (approximately 30% of the total base shear),
they are slightly out of phase with the wave loading on the legs. In addition, the presence of
large upward vertical loads due to hull buoyancy acts to stiffen the structure in the global
sway mode, and the negative overturning moment identified in Section 5.2 also reduces the
extreme response.
The effect of increasing hull inundation on the vertical reaction on the leeward leg is shown in
Figure 27. Increasing inundation has little effect on the maximum reaction, as at the time at
which it occurs (t=10 seconds) the hull is no longer inundated.
Figure 28 shows the vertical load on one of the windward legs for differing inundation levels.
Between 6 and 10 seconds, the time during which hull inundation occurs, the load reduces
significantly due to hull buoyancy. At an inundation level of 3m, the minimum vertical load is
reduced to 3.8MN as compared to 24.8MN with no inundation. Once the inundation phase is
complete, the vertical load on the windward legs returns to a similar value as the no
inundation case.
It should be noted that the simulations described above did not take the effects of a preceding
wave into account.
7.4 Effect of Wave Theory on Structural Response
In Section 5, the MSL wave-in-deck model predicted that Airy waves overestimate vertical
wave-in-deck loads by around 20% as compared to higher order wave theories such as Stream
Function and Stokes 5th order theory. In order to assess the implications of the use of Airy
waves on structural response, an Airy wave was applied to the USFOS model and the results
compared with those of a Stream Function wave for 3m inundation. Figure 29 shows the
vertical loads on the windward and leeward legs for the two wave types. It may be seen from
the upper graph that the Airy wave produces a longer duration of reduced vertical reaction as
well as a lower minimum value. For this case (i.e. 3m inundation), negative vertical spudcan
loads are predicted. The lower part of Figure 29 demonstrates that the maximum vertical load
on the leeward leg is around 10% higher for the Airy wave case as compared to the Stream
Function wave.
7.5 Effect of Response to Previous Wave on Extreme Wave Response
Twelve separate analyses were performed using the methodology outlined in Section 6.6,
using a range of values of Dt between 1 and 12 seconds. This represents the full duration of
the global sway mode, implying that the full enve lope of structural response, including the
maximum response, has been captured. An inundation level of 3m and ‘extreme’ linear
foundation springs were used.
Figure 30 shows the horizontal displacements for the twelve analyses performed. The
difference between the highest and lowest maximum displacements is relatively small,
indicating that the ‘pre-wave’ conditions have a relatively small effect on the final maximum
horizontal response. The maximum displacement case occurred where the main wave struck
the hull when the structure had a large displacement in the opposite sense than the direction of
24
wave attack - i.e. at this phase angle the structure has its largest acceleration in the direction
of wave attack.
Figure 31 shows the envelope of vertical reactions on the windward leg for a range of Dt
values. It may be seen that the minimum foundation reaction is –1.9MN, as compared to the
mean minimum vertical load value of +1.8MN. It appears from this result that an assessment
of the likely conditions before the extreme wave strikes the hull may be important, especially
where leg tension/lift-off is a possibility.
7.6 Effect of Foundation Fixity on Structural Response
7.6.1
Introduction
In order to assess the importance of the method of foundation modelling on structural
response the following modelling approaches were used and the results compared:
•
•
•
Linear springs (3 different rotational stiffnesses used)
Non-linear uncoupled springs
Non-linear coupled springs
Details of the above are contained in the following sections.
7.6.2
Linear Foundations
The results of analyses using the three linear foundation stiffnesses detailed in Table 5 above
are shown in Figure 32. Each analysis was performed with a hull inundation of 2.8m. It is
clear that the foundation stiffness has a large effect on structural response – the maximum
horizontal displacement is approximately three times greater for the “extreme” foundation
stiffness compared to the “fatigue” stiffness. However, foundation stiffness does not appear to
have a very large effect on the minimum vertical load in the case of the windward legs, with
the sudden decrease in reaction due to buoyancy effects being largely independent of the
foundation conditions. The differences in minimum vertical reaction are principally due to
additional “P-delta” moment due to differences in horizontal displacement.
7.6.3
Non-Linear Foundation Springs
The effect of the foundation modelling method on structural response was investigated by
using three modelling methods: linear, non-linear and coupled non-linear springs. All three
foundation models had the same initial stiffnesses in the horizontal, vertical and rotational
directions.
The effect of the type of foundation modelling used on horizontal displacement is illustrated
in Figure 33. It may be seen that the maximum displacement is highly dependent on the
foundation modelling method used (Table 9):
Table 9
Effect of Foundation Modelling Method on Structural Response
Foundation model
Maximum
displacement (m)
Increase on linear
case
Linear springs
3.35
-
Non-linear uncoupled springs
3.98
+19%
Coupled springs (USFOS spudcan element)
5.01
+50%
25
Modelling the foundations as coupled non-linear springs represents the most accurate
approach available for representing the true response of the foundations. It may be seen that it
is this modelling approach that gives the largest response to extreme wave loading.
Figure 34 shows the vertical loads and moments at the base of a windward leg during a wave
cycle. The maximum ultimate moment capacity occurs at a vertical load of around 100MN. It
may be seen that in all cases, the vertical load on the windward leg foundation is below
100MN, and hence the foundation moment capacity reduces as the applied vertical load
reduces. In the case of the linear spring model, the applied moment exceeds the capacity of
the foundation, with a maximum moment of 508MNm. The point of maximum moment
occurs at a time where the vertical load is relatively low, hence giving a small moment
capacity of 120MNm. The low vertical load on the windward legs is due to the global
overturning moment on the structure in combination with large buoyancy loads caused by hull
inundation.
For non-linear coupled springs, the moment at the foundation is limited by the ultimate
capacity of the foundation (in this case about 260MNm based on an axial load of 80MN). As
the springs are uncoupled, the moment capacity is independent of vertical load, and hence
during the period of low vertical leg loading (i.e. during hull inundation) the foundation is
outside the predicted failure surface.
In the case of the coupled non-linear springs, it may be seen from Figure 34 that the loads on
the foundation remain within the moment failure surface. This has a particularly large effect
when the vertical loads are at a minimum (i.e. during hull inundation) where the moment is
limited to less than 80MNm.
The effect the method of foundation modelling has on the moment at the base of the
windward leg is demonstrated in Figure 35. The moment is limited to below 150MNm
between 5 and 10 seconds for the spudcan element case, whereas the moment in the linear and
the uncoupled non-linear foundation models exceed this value during this time. This leads to a
reduction in global stiffness for the spudcan element case compared to the linear and
uncouple d non-linear foundation models, hence leading to greater displacements (Figure 33).
Figure 36 shows the phasing of vertical foundation loads for the leeward and windward legs
(spudcan foundation case). The upper and lower limits for the vertical load are taken from
Figure 21, and signify where the horizontal foundation capacity is significantly reduced from
the maximum capacity of 12MN. It may be seen from Figure 36 that the windward leg
reaction is almost always greater than the lower threshold value. In this case, there is no
significant shear redistribution from the windward legs to the leeward leg. However, if the
vertical load was reduced by a slightly larger amount, leg sliding would be predicted, which
would in turn lead to a significantly higher shear load on the leeward leg.
Figure 37 shows the phasing of the horizontal and vertical loads on the leeward leg. It may be
seen that the maximum vertical load occurs around 2 seconds after the peak horizontal load,
and hence in this case the loads on the leeward leg foundation remain well within the failure
envelope shown in Figure 21. This implies that leg sliding caused by excessively large
vertical loads is not predicted for the leeward leg.
26
8. CONCLUSIONS
The following conclusions have been made as a result of the analyses presented in this report:
• Wave inundation causes a significant step change in environmental loading.
• The vertical loads generated during hull inundation are considerable, and are principally
due to buoyancy effects. For example, an inundation of 3m caused a vertical load
equivalent to 40% of the structural dead weight.
• The use of Airy waves (as compared to higher order wave theories such as Stream
Function and Stokes 5th Order) is likely to underestimate horizontal loading and peak
overturning moment whilst overestimating vertical loads.
• Aeration at the top of the wave is unlikely to significantly affect wave-in-deck loading.
• The Jack-Up unit analysed reacted statically to vertical wave-in-deck loading. This is
likely to be the case for most types of Jack-Up.
• The vertical loads on the windward legs reduce to almost zero for inundations of between
2m and 3m.
• The response to the extreme wave is not highly dependent on the effects of the preceding
wave, hence suggesting that the DAF to be used in conjunction with an extreme wave
(with hull inundation) should be relatively low.
• Where linear foundations are used, the horizontal displacement is highly dependent on the
level of fixity assumed.
• The use of coupled non-linear foundations increases horizontal response and reduces the
moments at the bottom of the windward legs. This will in turn increase the moments at
the leg/hull connections.
27
28
9. REFERENCES
1. MSL Engineering Ltd. 'Assessment of the Effect of Wave-in-Deck Loads on a Typic al
Jack-Up'. HSE Offshore Technology Report OTO 2001 034, June 2001.
2. Howarth, M., Dier, A. and Jones, W. “A Study of Jack-Up Hull Inundation under
Extreme Waves”, Eighth International Conference on the Jack-Up Platform, City
University, 2001.
3. SACS Release 5 User Manual. Engineering Dynamics, Inc. 1999.
4. “Site Specific Assessment of Mobile Jack-Up Units, TR 5-5A”, Society of Naval
Architects and Marine Engineers (SNAME), Jersey City, 1997.
5. ASAS-WAVE User Manual - “Wave Loader for Offshore Structures”, Version 13, 2001.
6. BOMEL and Offshore Design. “Review of Wave-in-Deck Load Assessment Procedures”,
Offshore Technology Report No. OTO 97 073.
7. Kaplan, P., Murray, J.J. and Y, W.C. “Theoretical Analysis of Wave Impact Forces on
Platform Deck Structures”. Offshore Mechanics and Arctic Engineering Conference,
Copenhagen, June 1995.
8. API Recommended Practice 2A-WSD, Twenty-first Edition, December 2000.
9. Barltrop N. and Adams A. “Dynamics of Fixed Marine Structures”, MTD / ButterworthHeinemann, 1991
10. Howarth M et. al. "Scale effects of wave impact pressures on Cob armour units" 25th
International Conference on Coastal Engineering, September 1996, Orlando, publn.
ASCE, New York
11. Crawford, A. J., Bullock, G. N., Hewson, P. J. and Bird, P. A. D. 1998. Wave impact
pressures and aeration at a breakwater. Ocean Wave Measurement and Analysis.
American Society of Civil Engineers, Vol.2, pp 1366 -1379.
12. Bea R, Iverson R and Xu T. "Wave-in-deck Forces on Offshore Platforms", Journal of
Offshore Mechanics and Arctic Engineering. Volume 123, Number 1, February 2001.
13. USFOS Version 7-7 User’s Manual, Sintef Group, 2000.
14. Van Langen, H and Hospers, B. “Theoretical Model for Determining Rotational
Behaviour of Spud Cans”, Offshore Technology Conference 7302, 1993.
15. MSL Engineering Limited. “Interpretation of Full-Scale Monitoring Data from a Jack-Up
Rig”, HSE Offshore Technology Report No. 2001 035.
16. “Maersk Endurer Mobile Jack-Up Drilling Unit. Shearwater Site-Specific Assessment
Studies”. Noble Denton Report No. L17726/NDE/GAH, 1997.
29
wave
direction
top of wave
assumed to
be sliced off
horizontal wavein-deck load
air
gap
SWL
wave +
current
load on
legs
buoyancy
+ vertical
wave
loads
50­
year
crest
sea bed
Figure 1
MSL Wave-in-Deck Model
30
80m
72m
b(x)
x
PLAN
surface profile
h(x,t)
v(z,x,t)
PARTICLE
VELOCITY
u(z,x,t)
z hull
z
ELEVATION
Figure 2
MSL Wave-in-Deck Model - Nomenclature
31
aeration,%
0
5
10
15
20
25
30
0
depth / velocity head
0.2
0.4
0.6
0.8
k=0.685
k=1 (Bob Bea)
k=1.369
k=2.054
1
1.2
Figure 3
Aeration Profiles for Wave-in-Deck Load Calculation
32
35
Stage 2: Top of crest at hull front
face - t = 0 sec
Stage 1: Just prior to wave
in deck loading - t = -1.25s
1. Maximum horizontal wave-indeck loading
2. Buoyancy loads acts to give an
additional positive overturning
moment
3. Wave loading on legs yet to
reach a maximum value
Structure has initial
displacement, velocity and
accelerations from response
to previous waves
Stage 3: t = 1.25s to 3.25s
1. Maximum wave loading on legs has
occurred shortly before stage 2. Zero
horizontal wave-in-deck loading
3. Buoyancy load providing a negative
overturning moment (i.e. a 'righting'
moment)
Figure 4
Graphical Representation of Wave Cycle
33
Horizontal Load
14E+6
12E+6
Force (N)
10E+6
8E+6
6E+6
4E+6
2E+6
000E+0
-2
-1
0
1
2
3
4
5
time (s)
Vertical Load
80E+6
70E+6
buoyancy
60E+6
hydrodynamic
Force (N)
50E+6
40E+6
30E+6
20E+6
10E+6
000E+0
-2
-1
0
1
2
3
4
5
3
4
5
time (s)
Total Overturning Moment
3E+9
2E+9
Moment (Nm)
2E+9
1E+9
500E+6
000E+0
-2
-1
0
1
2
-500E+6
-1E+9
time (s)
Figure 5
Typical Wave-in-Deck Loads Generated using MSL Model
34
50E+6
legs + wave-in-deck
legs only
40E+6
base shear (N)
30E+6
20E+6
10E+6
000E+0
-2
-1
0
1
2
3
4
5
-10E+6
time (s)
5E+9
legs + wave-in-deck
legs only
overturning moment (Nm)
4E+9
3E+9
2E+9
1E+9
000E+0
-2
-1
0
1
2
3
4
time (s)
Figure 6
Wave-in-Deck Loads + Wave Loads on Legs, Inundation = 3m
35
5
20E+6
1m
2m
Load (N)
15E+6
3m
4m
10E+6
5E+6
000E+0
-2
-1
0
1
2
3
4
time (s)
Figure 7
Effect of Inundation on Horizontal Wave-in-Deck Load
120E+6
1m
100E+6
2m
3m
Load (N)
80E+6
4m
60E+6
40E+6
20E+6
000E+0
-2
-1
0
1
2
time (s)
Figure 8
Effect of Inundation on Buoyancy
36
3
4
3.0E+09
1m
2m
3m
Overturning moment (Nm)
2.0E+09
4m
1.0E+09
0.0E+00
-2
-1
0
1
2
3
4
-1.0E+09
time (s)
Figure 9
Effect of Inundation on Overturning Moment due to Vertical Wave-in-Deck Loads
3.0E+09
1m
2m
3m
Overturning moment (Nm)
2.0E+09
4m
1.0E+09
0.0E+00
-2
-1
0
1
2
3
4
-1.0E+09
time (s)
Figure 10
Effect of Inundation on Total Overturning Moment due to Wave-in-Deck Loads
37
130
120
elevation (m)
110
100
90
80
70
Airy (linear)
60
Stream function
Stokes 5th order
50
Shell NewWave
40
0
2
4
6
8
10
12
14
16
18
time (s)
Figure 11
Surface profiles of 4 types of deterministic wave
120
100
elevation (m)
80
60
40
Airy (linear)
Stokes 5th order
Stream function
20
Shell NewWave
0
0
1
2
3
4
5
6
7
8
9
horizontal particle velocity (m/s)
Figure 12
Horizontal particle velocity profiles of 4 types of deterministic wave
38
10
Maximum Horizontal Loads
30E+6
Stream
Load (N)
25E+6
Stokes
Airy
20E+6
NewWave
15E+6
10E+6
5E+6
000E+0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
3
3.5
4
4.5
3.5
4
4.5
inundation (m)
Maximum Vertical Loads
140E+6
Stream
120E+6
Stokes
Airy
NewWave
80E+6
60E+6
40E+6
20E+6
000E+0
0
0.5
1
1.5
2
2.5
inundation (m)
Maximum Combined Overturning Moment
5E+9
overturning moment (Nm)
Load (N)
100E+6
Stream
4E+9
Stokes
Airy
3E+9
NewWave
2E+9
1E+9
000E+0
0
0.5
1
1.5
2
2.5
3
inundation (m)
Figure 13
Effect of Wave The ory on Wave-in-Deck Loads
39
1
0.8
Load
0.6
0.4
Buoyancy
0.2
Horizontal
Peak OTM
0
0
5
10
15
20
25
aeration at free surface (%)
Figure 14
Effect of Wave Aeration on Wave-in-Deck Loads
40
30
35
Figure 15
USFOS Structural Model
41
Wave
direction
Elevation of Front Face of Hull
1a
2a
Vertical drag dummy members
at the hull front face
3a
8a 9a
Each member split into
99 subdivisions
4a
10a
11a
Drag Members at front face:
Cd x D chosen to give correct
horizontal load. Buoyancy set to
zero.
5a
16a
12a
17a
6a
21a
22a
18a
19a
20a
13a
14a
7a
Drag dummy
member
15
21b
22b
18b
19b
20b
13b
7b
14b
6b
5b
10b
11b
4b
8b
1b
Each member split into
99 subdivisions
12b
17b
16b
2b
3b
Vertical buoyancy dummy
member at the centre of
each zone
Buoyancy dummy
member
Hull Plan
Figure 16
USFOS Wave-in-Deck Model
42
Buoyancy members:
Diameter chosen to give correct
area and hence buoyancy load
Cd set to zero.
Horizontal Load
1.2E+07
USFOS
1.0E+07
MathCAD
Force (N)
8.0E+06
6.0E+06
4.0E+06
2.0E+06
0.0E+00
-2
-1
0
1
2
3
4
5
time (s)
Buoyancy Load
5.0E+07
USFOS
4.0E+07
MathCad
Force (N)
3.0E+07
2.0E+07
1.0E+07
0.0E+00
-2
-1
0
1
2
3
time (s)
Figure 17
Validation of USFOS Wave-in-Deck Model
43
4
5
300E+6
250E+6
moment (Nm)
200E+6
150E+6
100E+6
USFOS element
50E+6
Yield Moment
Ultimate Moment
000E+0
0
0.005
0.01
0.015
0.02
0.025
0.03
rotation (radians)
Figure 18
Typical SPUDCAN Moment-Rotation Relationship
140E+6
120E+6
horizontal load (N)
100E+6
80E+6
60E+6
40E+6
20E+6
000E+0
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
horizontal displacement (m)
Figure 19
Typical USFOS SPUDCAN Horizontal Load-Displacement Relationship
44
0.1
vertical load (MN)
200
180
yield moment
160
ultimate moment
ND ultimate capacity
140
120
100
80
60
40
20
0
0
50
100
150
200
250
300
moment (MNm)
Figure 20
Vertical Load vs. Moment Capacity, USFOS SPUDCAN Element
200
180
160
vertical load (MN)
140
120
100
80
60
yield load
40
ND ultimate capacity
20
0
0
2
4
6
8
horizontal load (MN)
10
12
Figure 21
Vertical Load vs. Sliding Capacity, USFOS SPUDCAN Element
45
14
'Extreme' Linear Foundation Springs
8
full wave-in-deck model
wave-in-deck model (no buoyancy)
6
hull displacement (m)
no wave-in-deck loads
4
2
0
0
2
4
6
8
10
12
14
16
-2
-4
-6
time (s)
Figure 22
Effect of Inclusion of Wave-in-Deck Loads on Displacement
46
18
20
Windward Leg Load
100E+6
vertical leg load (N)
80E+6
60E+6
40E+6
full wave-in-deck model
20E+6
wave-in-deck model (no buoyancy)
no wave-in-deck loads
000E+0
0
2
4
6
8
10
12
14
16
18
20
time (s)
Leeward Leg Load
160E+6
full wave-in-deck model
140E+6
wave-in-deck model (no buoyancy)
no wave-in-deck loads
vertical leg load (N)
120E+6
100E+6
80E+6
60E+6
40E+6
20E+6
000E+0
0
2
4
6
8
10
12
14
16
18
-20E+6
time (s)
Figure 23
Effect of the Inclusion of Wave-in-Deck loads on Vertical Foundation Loads
47
20
3m Inundation, "Extreme" Springs
8
horizontal displacement (m)
6
4
2
0
0
5
10
15
-2
-4
relative velocity terms
included
-6
relative velocity terms
ignored
-8
time (s)
Figure 24
Effect of Relative Velocity on Structural Response
48
20
Windward Leg
150E+6
relative velocity ignored
vertical load (N)
125E+6
relative velocity included
100E+6
75E+6
50E+6
25E+6
000E+0
0
2
4
6
8
10
12
14
16
18
20
time (s)
Leeward Leg
200E+6
relative velocity ignored
vertical load (N)
150E+6
relative velocity included
100E+6
50E+6
000E+0
0
5
10
15
-50E+6
time (s)
Figure 25
Effect of Relative Velocity on Vertical Foundation Reactions
49
20
"Extreme" Linear Foundation Springs
6
horizontal displacement (m)
5
4
no inundation
1m inundation
3
2m inundation
2
3m inundation
1
0
-1
0
2
4
6
8
10
12
14
16
18
20
-2
-3
-4
-5
time (s)
Figure 26
Effect of Increasing Inundation on Horizontal Displacement
"Extreme" Linear Foundation Springs
140E+6
120E+6
no inundation
vertical load (N)
100E+6
1m inundation
2m inundation
3m inundation
80E+6
60E+6
40E+6
20E+6
000E+0
0
2
4
6
8
10
time (s)
12
14
16
Figure 27
Effect of Increasing Inundation on Leeward Leg Reaction
50
18
20
90E+6
80E+6
70E+6
vertical load (N)
60E+6
50E+6
40E+6
30E+6
Hull Buoyancy
20E+6
0m inundation
1m inundation
2m inundation
10E+6
3m inundation
00E+0
0
2
4
6
8
10
12
14
16
time (s)
Figure 28
Effect of Increasing Inundation on Reaction of Windward Legs
51
18
20
windward leg
100E+6
vertical load (N)
80E+6
60E+6
40E+6
20E+6
stream function
Airy
000E+0
0
5
10
15
20
-20E+6
time (s)
leeward leg
140E+6
120E+6
stream function
Airy
vertical load (N)
100E+6
80E+6
60E+6
40E+6
20E+6
000E+0
0
5
10
15
time (s)
Figure 29
Comparison of Foundation Loads, Stream Function and Airy waves
52
20
"Extreme" Linear Springs, Inundation = 3m
8
envelope of maximum response
6
horizontal displacement (m)
4
2
0
0
5
10
15
20
-2
-4
-6
time (s)
Figure 30
Effect of Preceding Wave on Horizontal Displacement
53
25
"Extreme " Linear Foundation Springs, Inundation = 3m
90E+6
80E+6
70E+6
vertical reaction (N)
60E+6
50E+6
40E+6
30E+6
20E+6
10E+6
000E+0
2
4
6
8
10
12
14
16
18
-10E+6
time (s)
Figure 31
Effect of Preceding Wave on Windward Leg Vertical Reaction
54
20
22
24
Horizontal Displacement
8
6
'Extreme' foundation springs
USFOS initial stiffness
'Fatigue' foundation springs
displacement (m)
4
2
0
0
2
4
6
8
10
12
14
16
18
20
-2
-4
-6
time (s)
Windward Leg
90E+6
80E+6
vertical reaction (N)
70E+6
60E+6
50E+6
40E+6
30E+6
20E+6
'Fatigue' foundation springs
'USFOS' initial stiffness
10E+6
'Extreme' foundation springs
000E+0
0
2
4
6
8
10
12
14
16
time (s)
Figure 32
Effect of Different Linear Foundation Stiffnesses on Response
55
18
20
horizontal displacement (m)
5
linear springs
non-linear springs
4
spudcan elements
3
2
1
0
0
5
10
15
20
-1
-2
time (s)
Figure 33
Comparison of Horizontal Displacement for Different Foundation Models
56
200E+6
foundation failure
surface
linear springs
150E+6
non-linear
uncoupled springs
vertical load (N)
spudcan element
100E+6
initial position
50E+6
-400E+6
-200E+6
000E+0
000E+0
200E+6
400E+6
moment (Nm)
Figure 34
Comparison of Windward Leg Foundation Behaviour for Different Foundation Models
57
600E+6
600E+6
SPUDCAN elements
linear springs
non-linear uncoupled springs
foundation moment (Nm)
400E+6
200E+6
000E+0
0
2
4
6
8
10
12
14
-200E+6
-400E+6
time (s)
Figure 35
Windward Leg Foundation Moments for Different Foundation Models
58
16
18
20
140E+6
windward leg
leeward leg
120E+6
horizontal foundation capacity signifcantly reduced above this line
vertical load (N)
100E+6
80E+6
60E+6
40E+6
20E+6
horizontal foundation capacity signifcantly reduced below this line
000E+0
0
2
4
6
8
10
time (s)
Figure 36
Phasing of Vertical Foundation Loads
59
12
14
16
18
140E+6
25E+6
vertical load
horizontal load
20E+6
100E+6
15E+6
80E+6
60E+6
10E+6
40E+6
5E+6
20E+6
000E+0
000E+0
0
2
4
6
8
10
12
time (s)
Figure 37
Phasing of Foundation Loads, Leeward Leg
Printed and published by the Health and Safety Executive
C1.25
04/03
14
16
18
horizontal load (N)
vertical load (N)
120E+6
ISBN 0-7176-2177-4
CRR 019
£25.00
9 780717
621774