Stress redistribution in platform substructures effect on structural reliability

HSE
Health & Safety
Executive
Stress redistribution in platform substructures
due to primary member damage and its
effect on structural reliability
Prepared by EQE International Limited for the
Health and Safety Executive 2004
RESEARCH REPORT 245
HSE
Health & Safety
Executive
Stress redistribution in platform substructures
due to primary member damage and its
effect on structural reliability
A Nelson, (Senior Engineer)
D J Sanderson, (Senior Engineer)
S D Thurlbeck, (Principal Engineer)
EQE International Limited
EQE House
The Beacons
Warrington Road
Birchwood
Cheshire
WA3 6WJ
An investigation has been conducted to establish the damage tolerance of five different bracing
configurations that have been applied to a generic jacket structure. The investigations have provided
an insight into how the different bracing configurations are able to accommodate a fully severed
member and the impact that this has on the load distribution, ultimate strength and ultimately the
predicted structural reliability. In performing this study a total of 406 FE analyses have been carried
out.
The baseline structure was based upon a wellhead platform jacket comprising of three bays that is
currently operational and stands in approximately 45m of water in the Southern North Sea. The five
bracing configurations were each applied to this structure and the members were sized using an elastic
limit design process, using consistent slenderness ratios between corresponding members in each of
the bracing configurations.
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 2004
First published 2004
ISBN 0 7176 2870 1
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
CONTENTS
Executive Summary ...................................................................................................v 1.0
INTRODUCTION .................................................................................................1 1.1
1.2
Background..........................................................................................................1 Scope of Work .....................................................................................................1 2.0
MODEL DESCRIPTION ......................................................................................3 2.1
2.2
2.3
2.4
2.5
Baseline Structure ...............................................................................................3 Generic Structure.................................................................................................3 Bracing Configurations ........................................................................................5 Material ................................................................................................................5 Load Application ..................................................................................................7 3.0
STRESS REDISTRIBUTION STUDY..................................................................9 3.1
3.2
3.3
Background..........................................................................................................9 Results and Discussions......................................................................................9 Stress Redistribution Study Summary ...............................................................13 4.0
CRACKED MEMBER STUDY...........................................................................15 4.1
4.2
4.3
4.4
4.5
Background........................................................................................................15 Modifications to Single Diagonal Braced Jacket Model .....................................15 Results ...............................................................................................................15 Discussion .........................................................................................................16 Cracked Member Study Summary.....................................................................16 5.0
ULTIMATE STRENGTH ANALYSIS.................................................................19 5.1
5.2
5.3
Background........................................................................................................19 Results and Discussions....................................................................................19 Ultimate Strength Study Summary.....................................................................21 6.0
RELIABILITY STUDY........................................................................................23
6.1
6.2
6.3
6.4
6.5
Background........................................................................................................23 Reliability Assessment .......................................................................................23 Results ...............................................................................................................26 Discussion .........................................................................................................27 Reliability Study Summary .................................................................................28 7.0
CONCLUSIONS ................................................................................................31 8.0
RECOMMENDATIONS .....................................................................................33 9.0
REFERENCES ..................................................................................................35 iii
Appendix A
Model Description ...........................................................................57 Appendix B
Stress Redistribution Study .........................................................113 Appendix C
Joint Utilisation Value Distribution Plots ....................................141 Appendix D
Joint Group Utilisation Value Plots..............................................147 Appendix E
Ultimate Strength Study................................................................153 iv
EXECUTIVE SUMMARY An investigation has been conducted to establish the damage tolerance of five different
bracing configurations that have been applied to a generic jacket structure. The
investigations have provided an insight into how the different bracing configurations are
able to accommodate a fully severed member and the impact that this has on the load
distribution, ultimate strength and ultimately the predicted structural reliability. In
performing this study a total of 406 FE analyses have been carried out.
The baseline structure was based upon a wellhead platform jacket comprising of three bays
that is currently operational and stands in approximately 45m of water in the Southern
North Sea. The five bracing configurations were each applied to this structure and the
members were sized using an elastic limit design process, using consistent slenderness
ratios between corresponding members in each of the bracing configurations.
The investigations have yielded the following results:
x Severance of a member in a highly redundant structure leads to local stress
redistribution that is generally confined to the frame in which the member has been
severed when the frame is parallel to the storm direction. Typically those joints that
lie in the same frame, but on the contiguous diagonals that do not contain the severed
member, are significantly affected.
x Severance of a member in one of the low redundancy structures leads to a more global
stress redistribution, with the majority of joints throughout the structure seeing an
increase in load.
x Introduction of a cracked member into a Single Diagonal braced structure had limited
effect, with only localised increases in load. Increases in load were observed in those
joint groups that the cracked member intersected. In particular an increase in load was
observed in the cracked member’s joints with the jacket legs that has been attributed to
the increased bending of the member as a result of the eccentricity of the neutral axis
local to the cracked region.
x The ultimate strength study demonstrated:
-
That severance of a lower bay tensile member had the greatest consequence on
ultimate strength. This identifies these members as having a higher criticality in
the context of primary bracing integrity.
-
Highly redundant structures to be highly damage tolerant.
-
That the single diagonal braced structure provides a high strength structure
comparable to the X-braced but not as damage tolerant.
-
That K-braced and inverted K-braced structures have the lowest ultimate strengths
with the K-brace structured being the least tolerant to damage.
-
That the introduction of a second severed member into the inverted K-braced
structure resulted in a drastic reduction in its ultimate strength.
x Stress redistribution causes an acceleration in the rate of fatigue damage at
neighbouring members when damage occurs. This causes an increase in the
probability of failure of the neighbouring members and an associated increase in
overall platform collapse due to multiple-member failure. This effect has been
v
demonstrated for two multiple-member failure cases; one on the X-braced structure
and one on the inverted K braced structure.
x The reliability study showed that high redundancy structures are more reliable for two
major reasons:
-
They are stronger when damaged (i.e. more damage tolerant) and hence can resist
more extreme (i.e. infrequent) storms.
-
Stress redistribution effects are more limited and hence the acceleration of fatigue
damage (and associated increase in probability of failure) to neighbouring
members is less onerous.
It is considered that the work described in this report and its associated appendices
provides the first steps towards developing a reliability based performance measure for
jackets. The report has provided evidence of the types of jackets that carry the largest risk
of structural failure.
vi
1. INTRODUCTION
1.1 BACKGROUND
Flooded Member Detection (FMD) is an increasingly common inspection technique that is
applied to offshore steel jackets. It requires significant damage to be present in a member
before it detects a problem with that member. Owing to the harsh loading environment that
jacket structures are exposed to in the North Sea, the time period between crack initiation and
the severing of a member is relatively short. This, combined with a desire on the part of the
asset managers to lengthen inspection intervals, could result in a jacket being exposed to a
severed member for a significant duration. It is therefore necessary to understand the impact
on structural integrity of the structure upon failure of a member and hence the impact on the
jacket’s predicted structural reliability, to support the justification for a proposed FMD
inspection scheme.
The purpose of this study is to build upon the work detailed in Reference 1 carried out as part
of the Joint Industry Project on the reliability of FMD as a tool for integrity assurance of steel
jackets (HSE Project N° P3513). It aims to investigate the effects of damaged members on
the load distribution within jacket structures and the associated impact on structural
reliability.
1.2 SCOPE OF WORK
The redistribution of load following the failure of a member is dependent upon the
redundancy of the structure. For this reason five bracing configurations that were perceived
to possess varying degrees of redundancy have been considered as part of this study. These
are as follows:
x X-braced.
x Diamond braced.
x K-braced.
x Inverted K-braced
x Single diagonal braced.
These five bracing configurations were applied to a generic jacket that comprised of the
jacket’s legs, conductors, horizontal plane framing, piles and topsides, thus effectively
creating five different jackets. All dimensions and topside loads for this generic jacket were
initially taken to be those of an actual platform, located in the Southern North Sea, standing in
approximately 45 metres of water. The sizing of the bracing members was based on an
elastic design process using the methods outlined in Reference 2.
It was essential that the study considered three-dimensional effects introduced into the jacket
structures as a result of the stress redistribution. Loss of a member on one face of a platform
can induce non-planar effects such as torsion into the jacket’s structure. To reduce the
amount of analyses, each face of the jacket was designed to be symmetrical such that wave
attack directions that need to be analysed would be reduced to just one quadrant of the
compass (due to corner symmetry), i.e. North, North East and East. The size of the models,
combined with the single wave attack direction, enabled a significant number of studies to be
conducted.
1
All models were developed in ABAQUS (Reference 3).
EQE’s in-house software, developed for ABAQUS, allows normal design, and non-linear
pushover analyses to be undertaken using the same model. It also permits shell sub-models to
be introduced into the beam models to enable the introduction of through-thickness
circumferential cracks into the analyses.
2
2. MODEL DESCRIPTION
2.1 BASELINE STRUCTURE
In order to provide a systematic investigation into the influence of different bracing
configurations that are common place in the construction of offshore installations,
particularly in the North Sea, a generic structure was developed that consisted of the
jacket’s legs, horizontal plane framing, conductors, piles and a topside weight. This
generic structure was based upon a current jacket that is located in the Southern sector of
the North Sea, and is illustrated in
Figure 1. It is an inverted K-braced, four-legged wellhead platform, and stands in
approximately 45m of water. This jacket is referred to as the ‘baseline jacket’.
A brief description of the jacket models used in this study is provided below. A more detailed
description of the model and its development along with the applied loads and material model
used in the studies is provided in Reference 2.
2.2 GENERIC STRUCTURE
2.2.1
Topsides
The topsides’ weight was based upon that of the baseline jacket that weighs 1200 tonnes, and
was represented in the generic structure as a single mass element. The location of this mass
element was 5 metres above the topsides’ stab-in points, at the geometric centre of the
jacket’s plan view. The topsides’ mass element was tied into the structure at the stab-in
points using beam type ‘multi-point constraints’ which effectively formed a rigid link
between the topsides’ mass element and the stab-in points.
2.2.2
Piles
The piles of the baseline structure were used to determine the number, type and characteristics
of the generic structure’s piles. Where the piles were sleeved an effective cross-section was
derived that provided a comparable bending restraint to that of the composite cross section.
The cross-sectional dimensions of the baseline structure’s piles were modified during the
model development phase of the work to increase their combined bending and axial load
capacity, thus promoting structural failure in the structure’s framing. The resultant cross­
sectional dimensions of the generic structure’s piles are as follows:
Sleeved Piles: Outer diameter = 2.2967 m
Wall thickness = 0.1075 m
Pile:
Outer Diameter = 2.1948 m
Wall thickness = 0.0780 m
The effective point of fixity for the piles was assumed to be 20 m below the mud-line.
No account was taken of the additional restraint on the piles offered by the soil interaction.
This was deemed acceptable on the basis that the jacket was being developed to investigate
3
the structural behaviour of differing bracing configurations and not the failure of the
structure’s foundations during extreme storm events.
2.2.3
Legs
All four of the structure’s legs were modelled with identical cross-sectional properties
that were slightly modified from those of the baseline structure.
Figure 2 illustrates the variation in cross-sectional dimensions along the length of the legs.
The batter applied to the structure was in line with the baseline structure and was as follows:
North direction = 6.185°
East direction = 1.606°
2.2.4
Conductors and Guides
The generic structure contained a total of 18 conductors (6 rows of 3) consistent with
the number on the baseline structure. (
Figure 1 depicts the first row of conductors.) The modelling of the conductors was
simplified using tubular beam elements with an outer diameter of 0.685m and a wall thickness
of 0.030m. They were tied into the conductor guide framing using multi-point constraints that
have been configured to allow axial sliding but prevent planar motion relative to the framing
structure.
The conductors were fully restrained at a depth of 10 metres below the mud line.
2.2.5
Levels
The generic structure comprised of four levels consistent with the baseline structure that are
referred to as:
Mud line
(43.5 m below LAT)
Level 1
(26 m below LAT)
Level 2
(8.5 m below LAT)
Level 3
(10 m above LAT)
Further details of the framing at each of these levels are provided in Reference 2.
2.2.6
Tubular Joints
Within the jacket structure all tubular joints were modelled as rigid connections; i.e. joint
flexibility ignored.
4
2.2.7
Joint Groups
For the purpose of this study individual tubular joints between chords and braces were
grouped together to form joint groups. Each joint group within a given structure was assigned
a unique identifier, details of which are contained in Reference 2.
2.3 BRACING CONFIGURATIONS
Five different bracing configurations were applied to the generic structure. These were as
follows:
x X-braced
x Diamond braced
x K-braced
x Inverted K-braced
x Single diagonal braced
Figure 3 illustrates the five bracing configurations.
Sizing of the bracing members was conducted by assessing the joint and member utilisation
values resulting from the structures’ exposure to the 100 year storm event for each of the three
directions considered as part of this study. Utilisation values were calculated in accordance
with the guidelines detailed in References 4 and 5. The members were sized to give
utilisation values of less than unity, with consistent slenderness ratios between corresponding
members in the each bracing configuration.
Within each bay of each structure the bracing members were of the same cross-section. Table
1 provides details of the bracing members’ cross-section dimensions for each of the five
bracing configurations.
Table 1 Bracing members’ cross-section dimensions
Bracing
configuration
Member dimensions in each bay (mm)
Upper bay
Middle bay
Lower bay
X-braced
700 x 55
750 x 55
850 x 40
Diamond braced
550 x 35
600 x 40
700 x 45
Inverted K-braced
800 x 40
850 x 40
950 x 45
K-braced
800 x 40
850 x 40
950 x 45
Single diagonal
braced
1100 x 70
1200 x 55
1350 x 45
2.4 MATERIAL
The material model used in the studies was based upon a typical structural steel, Grade
355EM, which is commonly used in the fabrication of offshore jacket structures in the North
Sea.
The steel has the following material properties:
5
Density:
7820kgm-3
Elastic Modulus:
206.8GPa
Poisson’s Ratio:
0.29
Table 2 details the steel’s plastic properties.
For the Stress Redistribution Study and the buckling analysis the material was assumed to be
linear elastic. For the non-linear pushover analysis the elasto-plastic material model was
applied.
6
Table 2 Plastic material properties
True Stress
True Strain
355.0
0.000
461.5
0.06780
537.7
0.12744
612.3
0.21708
681.8
0.33675
709.7
0.39662
797.1
0.63620
814.9
0.69612
847.4
0.81596
890.0
0.99576
2.5 LOAD APPLICATION
2.5.1
Gravity and Buoyancy Loading
Gravity and buoyancy loads were applied to each of the five structures to effectively pre­
stress the structures. The contribution of each structural member to the overall jacket’s
buoyancy was calculated using the fluid to structure load interaction within the ABAQUS FE
software, i.e. ABAQUS AQUA. Further details on the use of ABAQUS AQUA in this study
are provided in Reference 2.
2.5.2
Environmental Loading
The loading applied in each of the studies conducted as part of this work was based upon the
100 year storm wave, current and wind loading as defined for the baseline jacket’s location.
The 100 year wind load was applied as a simplified point load applied at the geometric centre
of the four stab-in points and had a magnitude of 4.664kN.
The 100 year wave was modelled using gridded wave data which details the fluid particle
velocity and accelerations at a number of points in a user defined grid.
The 100 year current profile is defined in Table 3 below.
Using ABAQUS AQUA, each of the five structures were simultaneously exposed to the 100
year wave, wind and current, and the equivalent load distribution determined at the point of
maximum base shear acting on the structure. This load distribution is hereafter referred to as
the Reference Load Set (RLS).
7
Table 3 100 Year current profile
Depth Below Free
Surface (m)
Current Magnitude
(ms-1)
0.0
1.66
8.0
1.66
19.6
1.48
25.5
1.46
35.5
1.41
44.49
1.13
44.50
0.0
8
3. STRESS REDISTRIBUTION STUDY
3.1 BACKGROUND
The Stress Redistribution Study was a comparative study that aimed to investigate the effects
of bracing configurations, and hence redundancy levels on the degree of stress redistribution
that occurs when a member fails. The study aimed to establish the stress distribution, in terms
of joint utilisation values, calculated in accordance with Reference 5, for all joints in an
undamaged structure, as a result of the structure being exposed to the Reference Load Set
(RLS). The structure was then re-analysed with a single member severed, and the
redistribution of the load determined by reassessing the joint utilisation values. In conducting
this study a total of 15 undamaged jacket FE analyses were performed along with 354 severed
member FE analyses.
The analysis considered a 100 year storm from the following three storm directions:
North
North East
East
To aid understanding of how each structure was able to accommodate a failed member two
levels of analysis were conducted. These are referred to as a global response analysis and a
local response analysis. The global response analysis aimed to capture the effect a failed
member had on the joint utilisation distribution of all joints in the structure, and to determine
the shift in the mean joint utilisation value as well as whether any joint exceeded a utilisation
value of unity. The local response analysis aimed to capture the effect at each joint group and
to establish, using the calculated change in utilisation value, how individual joints were
affected, thus indicating how the load paths in the structures changed. Reference 6 provides
an in depth description of these two levels of analyses.
3.2 RESULTS AND DISCUSSIONS
Table 4 summarises the mean joint utilisation values for the undamaged state obtained from
the global response analysis.
Table 4 Mean joint utilisation values for the undamaged structures
Bracing configuration
Storm direction
East
North east
North
X
0.1578
0.1791
0.1648
Diamond
0.1511
0.1761
0.1484
Inverted K
0.1518
0.1720
0.1394
K
0.1835
0.2141
0.1860
Single diagonal
0.1457
0.1577
0.1519
Reference 7 details the cumulative joint utilisation distribution curves and corresponding
density functions from the load redistribution analysis. Table 5 summarises the severed
9
member analyses that resulted in a significant shift in the mean joint utilisation value and
those analyses that resulted in joints exceeding the code based unity check.
Table 5 Summary of significant results from the stress redistribution study
Bracing
configuration
storm
Severed
member
Mean joint
utilisation
% shift
Maximum
utilisation
Joint
group
X
E
AL2L
0.1583
6.0
1.0057
L12A
N
2LBL
0.1643
4.3
1.1092
L12B
N
2LAU
0.1643
4.3
1.0779
L12B
E
AM1
0.2482
66.5
1.3803
L2A
E
AM2
0.2476
66.1
1.9704
L2A
N
2MA
0.2686
95.9
10.6249
L22
N
2MB
0.2709
97.6
8.8881
L22
N
2LA
0.1770
29.1
1.3729
L12B
N
2LB
0.1777
29.6
1.4101
L12A
NE
2MA
0.2262
34.7
1.5765
L22
NE
2MB
0.2271
35.3
1.2310
L22
E
AM1
0.2779
54.5
2.3276
L11A
E
AM2
0.2860
59
2.3787
L12A
E
AL1
0.2054
14.2
1.0471
ML1A
N
2UA
0.2429
33.3
1.1168
L31
N
2UB
0.2442
34.0
1.1282
L31
N
2MA
See Note 1
-
9.4972
L12
N
2MB
See Note 1
-
9.6407
L12
N
1MB
0.2139
17.4
1.3734
L11B
N
1MA
0.2125
16.6
1.3658
L11A
NE
AM1
0.2538
20.6
1.2103
L11A
NE
AM2
0.2568
22.1
1.1203
L12A
NE
2MA
0.2657
26.3
1.2042
L12A
NE
2MB
0.2645
25.7
1.7551
L12B
E
BM
0.2468
78.8
1.2992
L12B
E
AM
0.2500
81.1
1.0477
L12A
N
2U
0.2135
48.5
1.5368
L31C
N
2M
0.2838
97.4
1.5053
L12B
Inverted K
K
Single diagonal
Note 1: Owing to the impact on the calculated utilisation values the distribution for this particular
damage state became distorted, and as a result the curve fitting process described previously failed to
determine an accurate solution owing to the poor fit of the assumed distribution to the data set. As a
result it was not possible to determine the mean utilisation value for this particular damage state using
this approach.
10
Evidence from the stress redistribution analyses undertaken on the five bracing configurations
suggests that there were two distinct types of behaviour. The X-braced and the diamond
braced structures were able to accommodate member failures much more economically, in
terms of a smaller zone of influence than the inverted K-braced, K-braced, and single
diagonal braced structures. This behaviour was consistent with the perceived redundancy of
the five bracing configurations.
The lower redundancy structures incorporated a lower bay that was much stiffer than the
middle bay owing to the influence of the piles, and the end restraints on the conductors in the
lower half of the lower bay. The piles provided the lower legs with additional bending
restraint, and as such, in the event of a lower diagonal member failing, attracted the
redistributed load to the legs in the form of an axial load. However, upon failure of a middle
bay diagonal brace, the stiffness of the structure was more adversely affected, and as a result
the load from the failed member was accommodated throughout the structure. The structural
response was characterised by the structure bending about the upper half of the lower bay, at a
point coinciding with the top of the piles. In general, this response resulted in the joints at
Level 1 exhibiting higher utilisation values than other joints in the structure, as the induced
bending was reacted.
Figure 4 illustrates the impact on the distribution of joint utilisation values for the single
diagonal braced structure when a middle bay compression member was severed. From this
plot it can be seen that the general impact of this member having failed was a global increase
in the joint utilisation values throughout the structure resulting in utilisation values in excess
of the unity, thus exceeding the code based joint capacity of Reference 5. Table 6 and Figures
5 to 8 illustrate the shift in load distribution for the same case for all four frames (two parallel
to the load and two perpendicular). The figures take the form of coloured contour plots. The
following key has been used to represent the shift in joint utilisation values from the
undamaged case:
Red
= greater than 30% increase
Amber = an increase less than or equal to 30%
Black
= negligible effect
Green
= reduction
For the higher redundancy structures, the difference in stiffness between the middle and lower
bays was a lot less significant, thus the impact of a failed member was not as onerous in terms
of the induced global bending.
The difference in the global response between the X-braced and diamond braced response
was attributed to the resultant load paths when a member was severed. Failure of a diagonal
bracing member in the X-braced structure resulted in almost a total loss of the load bearing
capability of the other bracing member on the same diagonal, thus in effect two bracing
members were lost in a single bay. However, in the case of the diamond braced structure,
diagonals were split between two bays, and as such the effect on a single bay’s stiffness was
less.
Figure 9 illustrates the impact on the distribution of joint utilisation values for the X-braced
structure when a middle bay compression member was severed. From this plot it can be seen
that the global impact of this member having failed was negligible. Table 7 and Figure 10
illustrate the shift in load distribution for the same case, using the same colour code key as
previously described. The plot clearly illustrates the reduction in load on the severed
member’s diagonal, and the contiguous diagonals (i.e. the ‘zig-zag’). This is complemented
by an increase in load on the intact ‘zig-zag’.
11
0.16
260
1.05
0.47
L21A
0.29
0.38
0.08
62
0.35
L22A
0.16
380
0.23
0.45
0.11
62
0.31
0.06
0.04
314
0.22
0.05
0.08
60
0.19
ML2A
0.08
-40
0.58
0.06
41
0.59
0.18
0.13
0.05
0.54
30
0.47
0.34
400
0.08
0.17
0.09
0.46
0.28
29
0.45
Undamaged
0.53
0.01
0.56
-99
0.72
0.52
37
0.30
50
0.32
0.06
413
0.17
0.04
340
600
0.19
0.06
200
0.22
0.05
AM
AL
50
0.23
173
0.41
BL
46
0.03
150
BU
74
0.33
0.23
BM
40
2U
75
0.20
0.05
L2H1
64
0.33
2M
257
0.16
0.03
0.05
1U
L2HA
400
0.28
0.18
-45
0.14
0.03
1M
AU
57
0.15
0.17
367
AM
-14
0.01
0.37
-98
L2HB
300
0.27
0.11
143
MLH1
7
0.22
0.13
65
BL
36
0.67
MLH2
-25
0.69
175
L2H1
MLHB
Leg 2A
0.05
0.05
0.11
BM
MLHA
Leg 1B
0.10
0.64
L2H2
Leg 1A
ML1B
350
L2H2
Leg 2B
ML1A
0.25
0.34
L1HA
%
L1H2
L2HB
Leg 2A
L22B
0.16
L2HA
Leg 1B
0.27
100
L1HB
Leg 1A
L21B
0.23
0.95
%
L1H1
L1HA
Leg 2B
500
1L
Undamaged
0.56
0.13
0.05
Damaged
0.25
0.28
Undamaged
64
245
1M
L1HB
Leg 2A
L12B
0.09
%
Damaged
0.22
0.30
%
Damaged
0.36
0.11
Undamaged
0.30
Leg 1B
L12A
179
L1H1
86
%
Damaged
L11B
0.34
%
Undamaged
Leg 1A
0.64
Undamaged
Damaged
%
Damaged
L11A
Undamaged
Joint
Group
Damaged
Table 6 Joint utilisation values for single diagonal braced jacket in the undamaged
state and with member AM severed
0.52
MLH1
30
0.05
2L
100
0.19
0.05
0.09
1L
MLHA
300
0.57
0.54
350
AL
6
0.48
0.48
-2
ML2A
L11A
L12A
L21A
L22A
Leg 2A
0.07
0.07
0.30
0
0.12
0.23
0
0.13
0.11
4
0.34
0.07
0.11
0.15
29
0.05
0.03
-12
0.10
0.02
0.07
0.11
23
0.18
0.16
0.48
0.28
0.08
0.11
-14
0.05
0.08
0.10
0.06
10
0.18
0.15
0.75
0.67
0.12
0.11
-14
0.34
0.07
12
0.07
0.14
Undamaged
Damaged
Undamaged
Damaged
%
-6
0.40
-16
L1HA
22
0.41
0.12
AM1L
233
0.01
L1H1
11
0.23
0.25
15
0.30
0.09
-7
0.15
0.19
0.15
AL1U
-98
0.39
0.12
227
0.25
0.20
20
0.15
0.08
0.11
-11
0.11
29
AM1U
20
0.34
AU2L
28
0.44
2L2U
AU1L
L2HA
0
0.45
2M2L
L2HA
2MAU
-17
%
AL2L
1MAU
-23
%
1LAL
AL2U
71
Undamaged
0.13
1LAU
2UAL
-75
0.08
MLHA
1UAL
50
0
MLH1
AM2L
133
%
Damaged
Undamaged
0.08
1MAL
L2H2
-33
0.64
2LAL
L2H1
Leg 2A
0.05
0.14
10
AL1L
L1HA
Leg 1A
0.15
0.70
L1H1
Leg 2A
0.24
0.05
MLH2
Leg 1A
0.30
17
MLHA
Undamaged
0.06
%
Damaged
0.08
%
Damaged
0
Leg 1A
0.08
Undamaged
%
Damaged
ML1A
Undamaged
Joint
Group
Damaged
Table 7 Joint utilisation values for X-braced jacket in the undamaged state and with
member AM1L severed
0.19
83
AM2U
-29
0.02
0.30
-92
3.3 STRESS REDISTRIBUTION STUDY SUMMARY
x The X-braced and the diamond braced structures are able to accommodate member
failures much more economically than the inverted K-braced, K-braced, and single
diagonal braced structures. This behaviour is in-line with perceived redundancy of the
five bracing configurations.
x For the leaner structures, failure of a middle bay diagonal brace had the largest impact on
structural stiffness and joint utilisation values. In general, the joints at Level 1 exhibited
higher utilisation values than other joints in the structure, as the induced bending was
accommodated.
x For the higher redundancy structures, the impact of a failed member was generally not as
onerous as the case for the leaner structures. However severance of a lower bay member
had a significant impact locally on joint utilisation values.
x The difference in the global response between the X-braced and diamond braced
structures’ response was attributed to the resultant load paths when a member was
severed. Failure of a diagonal bracing member in the X-braced structure resulted in
almost a total loss of the corresponding diagonal’s ability to bear load, thus in effect two
bracing members were lost in a single bay. However, in the case of the diamond braced
structure, diagonals are divided between two bays, and as such the effect on a single bay’s
stiffness was not as severe.
13
BLANK PAGE 14
4. CRACKED MEMBER STUDY
4.1 BACKGROUND
In addition to the severed member runs detailed in Reference 6 a series of FE analyses were
performed on a part cracked member. Circumferential, through wall cracks were introduced
into a bracing member that was subjected to a tensile load to establish the impact on the load
distribution. This was limited to a single member on the single braced structure, subjected to
the East storm load condition, to limit the amount of data generated. The single braced
structure was chosen for the focus of this study owing to the limited number of load paths that
it possesses, and the impact of a failed member on the stress distribution. The member
selected for the insertion of a crack was member BM owing to its impact on the stress
distribution upon being severed and the fact that in the undamaged structure the member was
nominally in tension in the undamaged state.
4.2 MODIFICATIONS TO SINGLE DIAGONAL BRACED JACKET MODEL
The single braced jacket model was modified using shell elements to introduce a crack into
the middle bay diagonal brace in Frame B, i.e. member BM. This involved removing
approximately 4m of beam elements from the member about its mid span and replacing them
with two identical sub-models comprising of a cylinder, generated using a regular shell
element mesh. The sub-model was tied into the beam elements using ‘DCOUP3D’ type
elements from the ABAQUS (Reference 3) element library. These elements are specifically
formulated to enable beam to shell modelling.
The crack was introduced into the model by simply ‘stitching up’ the two shell sub-models.
This process basically involved tying together a number of the coincident nodes on the two
sub-models until the required crack length had been created, with the crack being defined by
the un-stitched coincident node pairs.
The cracked sizes introduced into the model ranged from 20% to 70% of the circumference.
Using the approach detailed here it was not possible to model crack sizes beyond 70% owing
to convergence problems in the FE analysis.
Figure 11 illustrates member BM with the shell element sub-models included.
4.3 RESULTS
The results from the cracked member study at joint groups L12B and L21B are illustrated in
Figures 12 and 13 in the form of bar charts signifying the joint utilisation at each joint within
the joint groups for a variety of crack sizes. Similar plots were generated for all the joint
groups at and below Level 2 in the structure, but these demonstrated little changes in
utilisation values except in the case where the member was fully severed. Figure 14 provides
an illustration of these plots for joint group L11A.
Figure 15 illustrates the displaced shape of the shell element sub-model for the 70% fully
circumferential crack and Figure 16 illustrates the Von-Mises stress contours local to the
crack for the same case.
15
4.4 DISCUSSION
In general, the impact of a crack being introduced into member BM at mid-span had limited
effect on the load distribution in comparison to the undamaged state, for crack sizes up to
70% of the circumference. However those joint groups that included the cracked member, i.e.
L12B and L21B were affected quite significantly.
At joint group L12B, the effect on the cracked member was a steady increase in the utilisation
value calculated as the crack grew to being 70% of the circumference. Such behaviour can be
attributed to the resultant bending of the member owing to its increased compliance due to the
local eccentricity of the neutral axis near the crack. The effect on member BL was limited,
with only a slight increase in load observed. However the effect on the horizontal brace at
Level 1 in Frame B, i.e. member L1HB was much more pronounced. As the crack grew more
load was redistributed to this member, resulting in an almost doubling of the undamaged
state’s utilisation value when the crack was 70% of the circumference.
The out of plane effects at joint group L12B were a slight increase in the load on member 2M,
and a reduction in load on members 2L and the horizontal brace at Level 1, i.e. member
L1H2. The limit on the out of plane effects was considered to be as a result of the stiffness of
the lower bay preventing rotation of the structure at Level 1.
At level 2, joint group L21B, the load on member BM again increased steadily as the crack
grew from 0% to 70% of the circumference, again attributed to the increased compliance of
the member. The effects on the horizontal member at Level 2 in Frame A was a steady
decrease in the load as the crack grew to 70% of the circumference, but a slight increase over
the undamaged state value for the severed condition. The effects on member BU were
negligible.
Out of plane, the effects were much more pronounced at Level 2 than at Level 1. A steady
increase in load was observed in member 1M as the crack grew, as was the case in the
horizontal member at Level 2, i.e. member L2H1. Such effects have been attributed to the
induced twisting of the jacket about the vertical axis.
Using the approach adopted here and the mesh refinement of the crack zone it was not
possible to obtain a converged solution for cracks in excess of 70% of the circumference, due
to numerical problems. It is considered that a revised approach to introducing cracks into the
structure, using a fracture mechanics mesh and the possible introduction of gap elements, to
model crack closure, would help the solution to converge and thus yield results. However, it
is considered that unzip times for larger cracks would be relatively short and therefore there
would be limited benefit in investigating the structural response for such cracks, in the context
of demonstrating increased global structural reliability.
4.5 CRACKED MEMBER STUDY SUMMARY
The study has demonstrated that for crack sizes up to 70% of the circumference of a bracing
member:
x The impact on the load distribution was limited. Significant effects were only observed in
regions of the structure that were local to the cracked member. The increased compliance
of the cracked member introduced twisting into the structure that resulted in out of plane
effects as well as local in-plane effects.
x The joint utilisation of the cracked member’s joints increased due to the increased
compliance of the member caused by the eccentricity of the member’s neutral axis local
to the cracked region.
16
The modelling approach adopted in this study to insert a crack into a bracing member was
inadequate for performing a fracture mechanics assessment on the cracked member. As a
result it was not possible to predict unzip times for the crack. However, it is considered that
unzip times for large cracks are relatively short and therefore there would be limited benefit in
investigating the structural response for larger cracks than those considered here.
17
BLANK PAGE 18
5. ULTIMATE STRENGTH ANALYSIS
5.1 BACKGROUND
Each of the five bracing configurations was subjected to a series of static non-linear, pushover
analyses, in both the damaged and undamaged states, for an East storm load case. The
purpose of the study was to establish the ultimate strength of the jackets in the undamaged
state (i.e. the reserve strength ratio, RSR) and to assess the impact on the ultimate strength
when the structure contained at least one severed member (i.e. to establish the damaged
strength ratio, DSR). This study aimed to establish a member criticality profile for each
bracing configuration to feed into the structural reliability assessment for each of the jacket
types.
Reference 9 provides further details and a detailed description of the study conducted.
5.2 RESULTS AND DISCUSSIONS
In the undamaged states the five bracing configurations can be ranked in descending order
according to the RSRs calculated for the East storm load case;
x X-braced (RSR = 2.51)
x Single diagonal braced (RSR = 2.23)
x K-braced (RSR = 2.07)
x Diamond braced (RSR = 2.27)
x Inverted K-braced (RSR = 2.43)
It is considered that this ranking can be attributed to the variation in the ‘step’ change in
stiffness between the lower and middle bays. The number of load paths available local to
Level 1, to react the resultant compressive load induced in the structure determines the
magnitude of this step. The more load paths available, the lower the axial compressive load
in a given member; therefore there is a rise in the calculated RSR. Furthermore, the presence
of more load paths also has the effect of reducing the bending of the structure and as such the
end moments acting on bracing members is limited. The effect of this is that the reduction in
the critical buckling load of a particular member due to bending, is limited.
From the single member severed study conducted, it is evident that there are two distinct
types of behaviour. As was the case in the stress redistribution study undertaken, the X­
braced and the diamond braced structures were able to accommodate member failures much
more economically than the lower redundancy structures, i.e. inverted K-braced, K-braced,
and single diagonal braced structures. This behaviour was consistent with the perceived
redundancy of the five bracing configurations, and is illustrated in Table 8 and Figure 17 by
the difference in the range of DSRs calculated for each of the bracing configurations.
Severance of a member in either the middle or lower bays of the lower redundancy structures
introduced twisting into the structures and resulted in an increase in load on the lower
members thus initiating buckling of such members at lower values of LPF, resulting in lower
DSR’s. Furthermore, in most cases the legs at the back of the structure, i.e. gridline 1
experienced plastic strains local to the top of the piles.
19
Table 8 Damaged jackets ultimate strength results
Bracing Configuration
Member
DSR
RRF
X
AL1L
2.32
0.924
AL1U
2.22
0.884
AM1L
2.49
0.992
AM1U
2.53
1.008
AL1L
1.96
0.879
AL1U
2.06
0.924
AM1L
1.93
0.865
AM1U
2.20
0.986
AL1
1.65
0.797
AL2
1.65
0.797
AM1
1.79
0.865
AM2
1.81
0.874
AU1
2.01
0.971
AL1
1.86
0.819
AL2
1.85
0.815
AM1
1.85
0.815
AM2
1.88
0.828
AU1
2.33
1.026
AL
1.94
0.798
AM
2.08
0.856
AU
2.45
1.008
BL
2.16
0.889
BM
2.27
0.934
BU
2.44
1.004
Diamond
Inverted K
K
Single Diagonal
Severance of an upper bay member, in the lower redundancy structures, generally resulted in
an increase in the jacket’s ultimate strength (i.e. collapse load). Such effects were attributed
to the induced torsion in the jackets and the impact that this had on the load distribution in the
lower bay. For such damaged states the load was distributed to the perpendicular frames as
they reacted rotation of the legs, and thus alleviated the load on the lower compression
members in the frames parallel to the storm direction.
The K-braced structure was found to be the least tolerant to a severed member. Regardless of
which member was severed in either the lower or middle bays there was a significant impact
on the calculated ultimate strength.
20
The multiple member severance study further highlighted the difference between the low and
high redundancy structures. Severance of two members on the inverted K-braced structure
had a significant impact on ultimate strength, resulting in a 40% reduction, whereas that
performed on the X-braced structure resulted in a 20% reduction. Table 9 provides details of
the DSR and RRF for these analyses.
Table 9 Multiple members failed ultimate strength results
Structure
DSR
RRF
Inverted K braced
1.22
0.589
X-braced
1.98
0.79
5.3 ULTIMATE STRENGTH STUDY SUMMARY
ƒ In the undamaged states the five bracing configurations can be ranked in descending order
according to the RSRs calculated for the East storm load case;
x
X
x
Single diagonal
x
K
x
Diamond
x
Inverted K
x It is considered that this ranking can be attributed to the variation in the ‘step’ change in
stiffness between the lower and middle bays. The magnitude of this step is determined by
the number of load paths available, local to Level 1, to react the resultant compressive
load induced in the structure. The more load paths available, the lower the axial
compressive load in a given member, therefore there is a rise in the calculated RSR.
Furthermore, the presence of more load paths also has the effect of reducing the bending
of the structure and as such the end moments acting on members is limited. The effect of
this is to limit the reduction due to bending of the critical buckling load of a particular
member.
x From the single member severed study conducted, it is evident that there are two distinct
types of behaviour. As was the case in the stress redistribution study undertaken, the X
braced and the diamond braced structures were able to accommodate member failures
much more economically than the lower redundancy structures, i.e. inverted K-braced, K­
braced, and single diagonal braced structures.
x Severance of a member in either the middle or lower bays of the lower redundancy
structures introduced twisting into the structures and resulted in an increase in load on the
lower members thus initiating buckling under reduced loads.
x
Severance of an upper bay member, in the lower redundancy structures, generally
resulted in an increase in RSR. Such effects were attributed to the induced torsion in the
jackets and the impact that this has on the load distribution in the lower bay.
x The K-braced structure was found to be the least tolerant to a severed member.
Regardless of which member was severed in either the lower or middle bays, the impact
was a significant reduction in the calculated ultimate strength.
x The dual member severed study further highlighted the difference between the lower and
higher redundancy structures. Severance of two members on the inverted K braced
21
structure had a significant impact on ultimate strength, resulting in a 40% reduction,
whereas that performed on the X braced structure resulted in a 20% reduction.
22
6. RELIABILITY STUDY
6.1 BACKGROUND
The ultimate aim of this project was to demonstrate the structural reliability of fixed jackets of
different bracing configurations designed to a given set of criteria, and in particular to
demonstrate the effect of stress redistribution due to damage on overall reliability.
In this work, five jackets were designed based on elastic limit state methods for the same
water depth, topside loads and environmental conditions, but with differing bracing
configurations.
Non-linear Ultimate Strength (Pushover) analyses were performed on each of these jackets in
their undamaged conditions. The analyses were also performed for a range of damaged
conditions for each of the jackets. (The term ‘damage’ here is used to refer to the complete
severance of a member – pushover analyses were not performed on partially cracked
members).
This study takes into consideration the findings from the stress redistribution study and the
ultimate strength study, in conjunction with published Environmental Load distributions to
produce through-life reliabilities for the different jackets and to demonstrate the ‘knock-on’
effect of redistributed stress on the reliability of the structures.
6.2 RELIABILITY ASSESSMENT
The method used to calculate structural reliability is described in detail in Reference 10.
Figure 18 is a flowchart that illustrates the steps taken to perform the reliability assessments
in this project.
As mentioned, the method is a two-legged approach based on the following equation:
Pf
i
storm
¦PP
i
i
where i represents the number of ‘states’ in which a structure can exist (since we are dealing
only with severed or unsevered members here, the mathematics is discrete). Pi is the
probability that the structure exists in the i’th state, and Pstormi is the probability of a storm
occurring with sufficient strength to cause the collapse of the structure in the i’th state.
The two legs of the approach are therefore based on
x Calculating the probability of the structure existing in the i’th state.
x Calculating the probability of a storm to cause the collapse of the structure in the i’th state.
As mentioned, this two-legged approach is illustrated in Figure 18 and is described in more
detail below.
23
6.2.1
Probability of Structure Existing in a Given State, Pi
If there are N members in a given structure and each of these members may exist in either an
intact or a severed condition then the structure may exist in any one of N! possible states.
In Reference 10 this method was developed for single member failure only – i.e. the
possibility of more than one member failing during an inspection interval was ignored. One
of the objectives of this study is to demonstrate the effect of considering multiple member
failure on structural reliability.
The method used to calculate the probabilities of member failure for single and multiple
member failure is described below.
Single Member Failure Probabilities
In Reference 10 a method was presented to predict the probability of member failure based on
probabilistic fracture mechanics methods. These methods use the calculated fatigue lives of
members and the time in service to estimate the accumulated fatigue damage (S3N) that a
member has endured at a given time. The results of probabilistic fracture mechanics
calculations performed using UMFRAP (Umist Fracture and Reliability Assessment Program
- see Reference 11) were plotted as probabilities of member failure versus the accumulated
fatigue damage for a given member. Different curves were generated for given member
dimensions, initial defect sizes and defect distributions.
Figure 19 is an example curve of cumulative probability of failure versus S3N for one
particular member geometry and defect case.
The probability of failure within a given time interval is calculated by assessing the
accumulated fatigue damage (S3N) at the beginning and the end of the inspection interval. The
probability of failure during the interval is then simply the difference between the cumulative
probabilities at the end and the beginning of the inspection interval. This may be expressed as
p interval
f
P S3N
end
PS
3
N
beginning
The method described above was developed using curves generated by Professor Burdekin of
UMIST (Reference 11) and shall be referred to as the Burdekin method from hereon.
The rate of accumulated fatigue damage is calculated using the design fatigue lives of
members (or individual welds if available). For example, for a Class W weld, the fatigue life
is deemed to have been expended when the accumulated fatigue damage, S3N = 1.4x1012. The
rate of accumulated fatigue damage is then simply calculated by scaling the appropriate factor
(eg S3N = 1.4x1012) by the proportion of the fatigue life that has been expended. Thus, a
member with a fatigue life of 100 years will have an accumulated damage of S3N = 1.4x1011
after a period of ten years.
As part of this study two reliability assessments have been performed. The first assessment
assumed a fatigue life of 100 years for each and every member whilst the second study
assumed a fatigue life of 50 years for each and every member. This was done because it was
considered more important to assess the effect of the different bracing configurations (i.e.
redundancy and stress redistribution) on the resultant, calculated reliabilities for the five
structures. If a distribution of fatigue lives had been used, the interpretation of the data would
have been more difficult. Of course, it is acknowledged that this assumption is unrealistic,
but it was considered to be worthwhile for making the demonstration of the effect of
redundancy on structural reliability.
Probabilities of failure for each member were calculated using the Burdekin method over a
period from the present day to the year 2025. The assumed installation date was 1985. The
method was applied assuming a 3 yearly, 100% effective FMD inspection regime. The
number of welds was calculated assuming approximately 4m long joint cans. The number of
24
defects was calculated assuming the defect distributions presented in Reference 11. The
initial defect size was assumed to be normally distributed with a mean depth of 6mm.
Multiple Member Failure Probabilities
As stated above, one of the key objectives of this work was to demonstrate the importance (or
not) of considering the effects of multiple member failure on jacket structural reliability.
When damage occurs to a jacket (in this case represented by the severance of a member) the
stresses are redistributed to other members in the jacket. This has been discussed earlier in
this report.
In general, when a member is severed the loads carried by adjacent members are increased.
This means that the rate of accumulated fatigue damage is accelerated. From the results
presented in Appendix B it is not unusual to see stresses in neighbouring members to increase
by 100%. This would mean that the rate of accumulated fatigue damage would be accelerated
by a factor of 8 (=23). Some members have even higher predicted redistributed loads with
associated consequences for the shortening of their fatigue lives.
Due to the many permutations associated with multiple member failure it was decided to
make the demonstration of multiple member failure on two bounding cases. These cases were
selected to encompass the overall range of jacket robustness and damage tolerance.
The first case chosen was for the inverted-K braced structure. This was chosen since it
demonstrated the lowest overall ultimate strength and a sensitivity to damage (the lowest
residual resistance factor for the inverted K-braced structure was 0.797). In this structure, the
two members that were severed for the multi-member study were the two tension members in
the middle bay.
The other case chosen for the multi-member study was the X-braced structure that
demonstrated a lower-bound RRF of 0.884. In this case, two members in the lower bay were
severed, one on each diagonal of the bay’s bracing.
Fatigue Acceleration
As mentioned above, when a member is damaged, adjacent members have to somehow
accommodate the load. In general this leads to an increase in stressing in the members and
joints. This leads to an acceleration in fatigue damage and an associated increase in the
probability of member failure during a given time interval.
From the detailed stress redistribution work (Appendix D) the stress enhancements were taken
for one of the members due to the failure of the other member used in the multi-member
study.
In the Inverted K braced structure, the failure of one of the middle bay tension members
produced an enhancement in stress in the middle bay tension member on the opposite frame
of 1.66.
For the X-braced structure the severance of one of the lower bay diagonals produced an
enhancement in stress in the other diagonal of 1.55.
The two stress enhancements above produced a fatigue damage acceleration of 4.1 for the
Inverted K braced structure and 3.7 for the X-braced structure.
These fatigue accelerations were taken into account when applying the Burdekin method to
calculate the probability of failure of the second member, subsequent to failure of the first
member. Again, for demonstrative purposes, it was assumed that the first member failure
occurs on the day after a FMD inspection returned a negative result, meaning that the
accelerated fatigue damage is present during the entire of the next inspection interval.
25
6.2.2
Probability of Storm to Cause Collapse in the i’th state, Pstormi
The probability of a structure collapsing, given that it exists in a certain state is simply
calculated by using the results of ultimate strength calculations cross-referenced with
environmental load distributions.
The environmental load distributions relate the environmental load that a storm produces to
the storm’s return period. Therefore, if we know the ultimate strength of a structure, we can
calculate the return period of the storm with a load equal to the structure’s strength. The
annual probability of failure is then simply the inverse of the return period.
In this work, the environmental load distribution that was used was
PE A exp§¨ E ·¸
Eo ¹
©
where P(E) is the annual probability of the occurrence of a storm exceeding a load, E, and
E=ERP/E100 where ERP is the load corresponding to a given return period, RP, and E100 is the
most probable 100 year load. In the above, A and Eo are constants. In this assessment, these
values were taken as 180 and 0.102 respectively, values typical of the Central North Sea
(Reference 4).
6.3 RESULTS
6.3.1
Single Member Failure
Reliabilities were calculated for all five structures assuming single member failure only in
addition to the following
x Installation date of 1985
x Initial mean defect depth = 6mm
x Aspect ratio = 0.2
x Number of defects per unit length of weld taken from defect distribution study of
Reference 3.
x FMD inspection interval = 3 years with first inspection in 2001.
As stated previously the reliabilities were calculated based upon a universal fatigue life of 100
years and 50 years. The calculated reliabilities are presented in Figures 20 and 21.
6.3.2
Double Member Failure
In addition to the single member failure cases, ultimate strength analyses were performed for
two multi-member failure cases.
Double member failure was treated in two ways. The first simply assumes that the probability
of failure of the second member is unaffected by the failure of the first. The second, more
realistic way of treating it was to assume that the failure of the first member redistributes
stress onto the second member, thereby accelerating fatigue damage and the associated
probability of failure. In conducting these studies a universal fatigue life of 100 years has
been applied.
The results of the reliability assessments for multi-member failure are presented in Figure 23.
26
6.4 DISCUSSION
6.4.1
Single Member Failure
The results of the reliability assessments assuming single member failure and 100 year fatigue
lives for all members confirm what would be expected given the results derived from the
ultimate strength analyses.
The most reliable bracing configuration is the X-braced, followed by the single diagonal, the
K-braced, the diamond braced and finally the inverted K-braced. This same order applies to
the ultimate strengths of the five (undamaged) jackets.
The other interesting thing to note about Figure 20 is that the curves for the X-braced and the
diamond-braced structures are significantly ‘flatter’ than the others. This is indicative of the
superior damage tolerance of these two structures compared with the others due to their
higher levels of redundancies. In terms of the ultimate strength analyses results, this is
apparent in the higher Residual Resistance Factors (RRF’s) of the X-braced and diamond
braced structures.
However, the curves for probability of failure versus time, assuming single member failure
and 50 year fatigue lives for all members (Figure 21), show an increase with time and then
after the year 2012 the predicted failure probabilities actually start to fall.
This is an artefact of the probabilistic fracture mechanics results (Figure 21), which, for a
given initial defect size predict the cumulative probability that the weld will fail. The
probability of weld failure at any point in time is proportional to the slope of the cumulative
probability curve and therefore, as the cumulative probability of failure approaches unity, the
probability of failure at that point in time starts to decrease.
Intuitively this seems wrong. However, what is actually being portrayed here is that for the
initial defect assumed, the probabilistic fracture and fatigue model predicts that the weld
should have (or be very close to having) failed. If after a given period of time the weld has
physically not failed, and our model predicts that it should have, then in all likelihood, this is
due to the fact that the assumption on initial defect size present in the weld was too onerous.
This could easily be built into an inspection scheme. For example, let us assume that an initial
defect size of 6mm exists in all welds and suppose that we start to predict failure probabilities
of these welds and the associated failure probabilities of the jackets.
After a period of time, the probability of the i’th weld having failed is Pi. The probability of
this weld NOT having failed is then (1-Pi). If, following an inspection, all N inspected
members are identified as being intact, then the probability of this actually occurring may be
written as
i N
Pno _ failures
– 1 P i
i 1
where the ‘pi’ symbol indicates the multiplication of all the terms (1-Pi).
Evidently, during the early life of the structure, the individual probabilities of member failure,
Pi, are very small and so the probability of no failures having occurred is close to unity. With
time, however, as the probabilities of member failure increase, the probability of there being
no failures decreases.
This information could be used to provide a Bayesian updating approach. Say, for example
that the results of an inspection show no failures and that our model predicts that this would
only be possible 1% of the time, based on our initial assumptions of defect size, then we can
state with 99% confidence that our initial assumption was too onerous. The assessment would
27
then be repeated for a less onerous initial defect assumption. This process could then be
repeated for subsequent inspections (see Figure 22).
At present, this functionality has not been built into the code that performs the reliability
assessments.
6.4.2
Multi-Member Failure
Figure 23 clearly shows the effect of stress redistribution on structural reliability. For both the
X-braced and the inverted K braced structures, the annual probability of failure is
significantly increased by considering the contribution due to redistributed stress and the
associated increase in the failure probabilities of adjacent members.
The relative increase in failure probability due to the stress redistribution is larger for the
inverted K than for the X braced structure. This is consistent with the general findings with
regard to the redundancies of the different jackets. That is to say that for the inverted K
structure, the stress redistribution is more pronounced and the effect of damage to the
structure reduces its ultimate strength drastically. For the X-braced structure, the stress
redistribution is less pronounced and the ultimate strength of the structure is less sensitive to
damage than for the inverted K braced structure.
It should be noted that the additional probability of failure shown in Figure 23 is only due to
one multi-member case. The case chosen for each bracing configuration was thought to be
one of the critical cases (ie to reduce the ultimate strength of the structure by one of the
largest possible amounts).
If all multi-member cases were studied, clearly the contribution to the predicted probabilities
of failure due to stress redistribution would be even greater. This would be particularly true
for lower redundancy (eg inverted K, single diagonal) structures where stresses are
redistributed throughout the structure. For higher redundancy structures (eg X-braced)
redistribution is more localised, and therefore it would be expected that the effect of stress
redistribution would be less significant than for lower redundancy structures.
Ideally, many more possible combinations of multi-member failure would have been
considered but the permutations of these cases grow rapidly. Whilst it was not possible to
address many cases of multi-member failure in this work, it is considered desirable to address
this issue in more detail in future.
6.5 RELIABILITY STUDY SUMMARY
x Reliability assessments have been performed for five jackets of different bracing
configurations, but designed for installation at the same location.
x Start-of-life reliabilities are dependent on the undamaged ultimate strengths of the jackets.
The elastic limit state design criterion used predicted that (in the undamaged condition) the
X-braced structure was the most reliable, followed by the Single Diagonal, then the K­
braced, the Diamond braced and finally, the Inverted K.
x The most reliable bracing configurations are those with higher levels of redundancy. These
jackets are shown to be more damage tolerant than jackets with low levels of redundancy
(ie they have higher Residual Resistance Factors).
x The effect of stress redistribution has been demonstrated for two multi-member failure
cases; one on the X-braced structure and one on the inverted K braced structure.
x Stress redistribution causes an acceleration in the rate of fatigue damage at neighbouring
members when damage occurs. This causes an increase in the probability of failure of the
neighbouring members and an associated increase in overall platform collapse due to
multi-member failure. This effect has been demonstrated for two multi-member failure
cases; one on the X-braced structure and one on the inverted K braced structure.
28
x Stress redistribution effects are more pronounced for low redundancy structures (eg
inverted K braced), where ultimate strengths are more sensitive to damage and stresses are
redistributed globally. This is in contrast to high redundancy structures (eg X-braced)
where stress redistribution tends to be more localised and the ultimate strength of the
structure is less sensitive to damage.
29
BLANK PAGE 30
7. CONCLUSIONS
A series of studies have been performed to investigate the impact of five different bracing
configurations on the structural response of a 3 bay, four-legged jacket standing in the
Southern North Sea in approximately 45m of water. The studies comprised of a stress
redistribution study, ultimate strength study and a reliability study for different damage states
within each of the five bracing configurations.
x The stress redistribution study provided a comprehensive assessment of the impact of
a severed member on the stress distribution in a jacket structure incorporating one of
the five bracing configurations, for three storm directions.
x In addition to the severed member redistribution study a limited study was performed
to establish the impact of a cracked member on the stress distribution of a structure
with a particular bracing configuration, for the East storm load case.
x The Ultimate strength study and the reliability study focussed on the East storm load
case for each of the five bracing configurations.
x The reliability assessment provided an insight into how the redistribution of load as a
result of one member being severed can accelerate the probability of a second
member failing and the resultant impact on jacket reliability.
Both the stress redistribution study and the ultimate strength study for the undamaged
structures, and those incorporating a single member severed, have highlighted two distinct
types of behaviour, i.e. that of the lower redundancy structures and that of the higher
redundancy structures. The higher redundancy structures were defined as the X and diamond
bracing configurations, whereas the lower redundancy structures were defined as the inverted
K, K and single diagonal bracing configurations.
Severance of a bracing member in one of the lower redundancy structures had a much wider
impact on the load distribution, with a resultant twisting of the structure about the vertical
axis. In terms of ultimate strength the impact was seen as a significant reduction in load
capacity, particularly for the case where a lower bay tension member was severed. Such
failures resulted in an increase in load on the lower bay compression members resulting in the
member buckling under a reduced applied load.
The higher redundancy structures demonstrated a higher resilience to member failure. From
the stress redistribution studies, the impact of a severed member was very localised, with the
zone of influence being restricted to Frame A for the cases considered. The ultimate strength
studies again demonstrated the damage tolerance of these structures, as relatively small
reductions in ultimate strength were observed, with severance of a lower tension member
having the biggest impact.
The dual member severed study was performed on the X-braced structure and on the inverted
K-braced structure, as these provided the extreme ultimate strength values. For the lower
redundancy structure, the impact of two members having been severed was a drastic reduction
in ultimate strength, whereas the effect observed in the case of the higher redundancy
structure was much less severe.
Two notable results from the ultimate strength studies were that of the K-braced structure and
the single diagonal braced structure. The K-braced structure proved to be the most sensitive
to a severed member. Although the size of the members was the same as the inverted K­
braced structure, its load paths were significantly different and as such, loss of any members
in the lower or middle bays resulted in significant twisting and bending of the jacket. The
impact of a severed member had a more pronounced impact on the deformations observed
local to Level 1.
31
Start-of-life reliabilities are dependent on the undamaged ultimate strengths of the jackets.
The elastic limit state design criterion used predicted that (in the undamaged condition) the X­
braced structure was the most reliable, followed by the Single Diagonal, then the K-braced,
the Diamond braced and finally, the Inverted K.
The most reliable bracing configurations are those with higher levels of redundancy. These
jackets are shown to be more damage tolerant than jackets with low levels of redundancy (i.e.
they have higher Residual Resistance Factors).
Stress redistribution causes an acceleration in the rate of fatigue damage at neighbouring
members when damage occurs. This causes an increase in the probability of failure of the
neighbouring members and an associated increase in overall platform collapse due to
multiple-member failure. This effect has been demonstrated for two multiple-member failure
cases; one on the X-braced structure and one on the inverted K braced structure.
It is considered that the work reported upon in this report and its associated appendices
provides the first steps towards developing a reliability based performance measure for
jackets. The report has provided evidence of the types of jackets that carry the largest risk of
structural failure.
32
8. RECOMMENDATIONS As a result of this study a number of recommendations are put forward to extend the work
completed to date aimed at investigating the effects of stress redistribution in damaged structures
and the impact that this has on the predicted reliability of jacket structures. These recommendations
are detailed below.
x Extend study to incorporate larger structures, i.e. deeper water 4 leg jackets and jackets with
more than 4 legs.
x Extend the analysis on dual member failures to incorporate all of the five bracing
configurations, taking into consideration critical members having failed and the stress
redistribution within the structure. The study would then be used to provide estimates for
fatigue acceleration factors, FAFs, for each member in a given bracing configuration to feed
into an estimation of the structural reliability prediction and thus provide guidance to operators
on how to determine the acceptability of damage within a structure.
x Devise methodology for Bayesian updating of a structure’s reliability prediction following a
structural inspection. The reliability prediction is based upon an assumed defect or defect
distribution that is present at the start of life. Through life modelling of a structure’s reliability
may yield a high probability of a member severing at some stage in the design life, which may
be invalidated by inspection results, thus necessitating the revision of initial assumptions and
the through life reliability profile.
It is anticipated that following completion of this proposed work, it will be possible to formulate
suitable guidance to enable an informed judgement to be made on the acceptability of damage in a
jacket structure, based upon the bracing configuration, and the impact that this will have on other
members in the structure. In addition, the future work will allow guidance to be formulated on
calculating a more accurate prediction of through life structural reliability using probabilistic
fracture mechanics and Bayesian updating.
33
BLANK PAGE 34
9. REFERENCES
1 Guidance on the Use of Flooded Member Detection for Assuring the Integrity of Offshore
Platform Substructures – EQE Report N° 179-03-R-07 Issue 1 – 6th June 2000
2 Stress Redistribution in Platform Substructures Due to Primary Member Damage and its
Effect on Structural Reliability – EQE Report N° 45-20-R-01 Draft – 19th January 2001 –
Appendix A – Model Description
3 ABAQUS 5.8 – Hibbitt, Karlsson & Sorensen, Inc.
4 API 2A-LRFD Recommended Practice for Planning, Designing and Constructing Fixed
Offshore Platforms – Load and Resistance Factor Design, First Edition 1993
5 Offshore Installations: Guidance on Design, Construction and Certification – Fourth
Edition-1990, HMSO – Appendix A21
6 Stress Redistribution in Platform Substructures Due to Primary Member Damage and its
Effect on Structural Reliability – EQE Report N° 45-20-R-01 Draft – 19th January 2001 –
Appendix B – Stress Redistribution Study
7 Stress Redistribution in Platform Substructures Due to Primary Member Damage and its
Effect on Structural Reliability – EQE Report N° 45-20-R-01 Draft – 19th January 2001 –
Appendix C – Joint Utilisation Value Distribution Plots
8 Stress Redistribution in Platform Substructures Due to Primary Member Damage and its
Effect on Structural Reliability – EQE Report N° 45-20-R-01 Draft – 19th January 2001 –
Appendix D – Joint Group Utilisation Value Plots
9 Stress Redistribution in Platform Substructures Due to Primary Member Damage and its
Effect on Structural Reliability – EQE Report N° 45-20-R-01 Draft – 19th January 2001 –
Appendix F – Ultimate Strength Study
10 Demonstration of the Effect of FMD on Structural Reliability (Appendix n to FMD JIP
Final Report) – EQE Report N° 179-03-R-06 Appendix N, Issue 1, 4 May 1999
11 Fabrication Defects Study (Appendix C to FMD JIP Final Report) - EQE Report N° 17903-R-06 Appendix C, Issue 1, 4 May 1999
12 Final Report on Reliability Aspects (Appendix K to FMD JIP Final Report) - EQE Report
N° 179-03-R-06 Appendix K, Issue 1, 28 April 2000
13 M Efthymiou, J W van de Graaf, P S Tromans and I M Hines, ‘Reliability based criteria
for fixed steel offshore platforms.’
35
BLANK PAGE 36
+21.5 m
+10 m
-8.5 m
-26 m
z
North
East
-43.5 m
Figure 1 Generic structure schematic
37
+21500
2000
6
5
+10000
2750 3250
7826
4
3
2
-8500
-26000
1
Section details
1. 1400 x 65
2. 1400 x 85
3. 1400 x 35
4. 1400 x 75
5. 1215 x 50
50
6. 1030 x 60
-43500
All dimensions are in mm
Figure 2 Generic jacket leg schematic
38
X-Braced
Diamond Braced
Inverted K-Braced
K-Braced
Single Diagonal Braced
Figure 3 Bracing configurations
39
Single Diagonal Braced East Storm S−AM Severed
Cumulative Distribution Function
1
Proportion of Joints
0.8
0.6
0.4
Undamaged − data
Undamaged − CDF
Damaged − data
Damaged − CDF
0.2
0
0
0.2
0.4
0.6
0.8
1
1.2
Probability Density Function
12
Probability Density Function
10
Undamaged PDF
Damaged PDF
8
Damaged mean = 0.2500
6
Undamaged mean = 0.1380
4
2
0
0
0.2
0.4
0.6
0.8
1
Joint Element Utilisation
Figure 4 Single diagonal braced structure - joint utilisation distribution plots
40
1.2
1A
2A
L2HA
L21A
1A
AM
L22A
2A
L1HA
L11A
1A
ML1A
AU
AL
MLHA
L12A
2A
ML2A
Figure 5 Single diagonal braced structure - Frame A stress redistribution contour
plot
41
1B
2B
L2HB
L21B
1B
BM
L22B
2B
L1HB
L11B
1B
ML1B
BU
BL
MLHB
L12B
2B
ML2B
Figure 6 Single diagonal braced structure - Frame B stress redistribution contour
plot
42
1U
1A
L2H1
L21A
1A
1M
L21B
1B
L1H1
L11A
1A
ML1A
1B
1L
MLH1
L11B
1B
ML1B
Figure 7 Single diagonal braced structure - Frame 1 stress redistribution contour
plot
43
2A
2B
L2H2
L22A
2A
2M
L22B
2B
L1H2
L12A
2A
ML2A
2U
2L
MLH2
L12B
2B
ML2B
Figure 8 Single diagonal braced structure - Frame 2 stress redistribution contour
plot
44
X−Braced East Storm C−AM1L Severed
Cumulative Distribution Function
1
Proportion of Joints
0.8
0.6
0.4
Undamaged − data
Undamaged − CDF
Damaged − data
Damaged − CDF
0.2
0
0
0.2
0.4
0.6
0.8
1
1.2
Probability Density Function
12
Probability Density Function
10
Undamaged PDF
Damaged PDF
8
Damaged mean = 0.1582
6
Undamaged mean = 0.1493
4
2
0
0
0.2
0.4
0.6
0.8
1
Joint Element Utilisation
Figure 9 X-braced structure - joint utilisation distribution plots
45
1.2
2A
1A
AU1L
AU2L
L2HA
L21A
AM1U
L22A
AM2U
2A
1A
LMA
AM2L
AM1L
L1HA
L11A
L12A
AL2U
AL1U
1A
2A
AL1L
ML1A
LLA
MLHA
AL2L
ML2A
Figure 10 X-braced structure - Frame A stress redistribution contour plot
46
Figure 11 Member BM
47
1.4
1.2
Utilisation
1.0
Leg 2B
L1HB
BM
BL
L1H2
2M
2L
0.8
0.6
0.4
0.2
0.0
0
20
40
60
80
100
Crack size
Figure 12 Joint utilisation plot – Joint group L12B
0.5
0.4
Leg 1B
L2HB
BU
BM
L2H1
1U
1M
Utilisation
0.3
0.2
0.1
0.0
0
20
40
60
80
Crack size
Figure 13 Joint utilisation plot – Joint group L21B
48
100
1.0
0.8
Leg 1A
L1H1
1M
1L
L1HA
AM
AL
Utilisation
0.6
0.4
0.2
0.0
0
10
20
30
40
50
60
70
80
90
Crack size
Figure 14 Joint utilisation plot – Joint group L11A
49
100
Figure 15 Displace shape plot for member BM – 70% crack case
50
1
2
3
ABAQUS VERSION: 5.8-1
1.00
STEP 3
TIME: 12:16:33
TOTAL ACCUMULATED TIME
INCREMENT 9
5.00
DATE: 12-DEC-2000
TIME COMPLETED IN THIS STEP
RESTART FILE = sin_e_cr30
DISPLACEMENT MAGNIFICATION FACTOR =
3.00
Figure 16 Von Mises stress plot for 70% crack case
51
MISES
3
+3.36E+09
+3.10E+09
+2.84E+09
+2.58E+09
+2.33E+09
+2.07E+09
+1.81E+09
+1.55E+09
+1.30E+09
+1.04E+09
+7.83E+08
+5.26E+08
+2.68E+08
VALUE
+1.11E+07
SECTION POINT 1
2
1
ABAQUS VERSION: 5.8-1
1.00
STEP 3
5.00
TIME: 12:16:33
TOTAL ACCUMULATED TIME
INCREMENT 9
DATE: 12-DEC-2000
TIME COMPLETED IN THIS STEP
RESTART FILE = sin_e_cr30
DISPLACEMENT MAGNIFICATION FACTOR =
3.00
2.7
2.5
2.3
Undamaged
Lower Compression
R
S 2.1
R
Lower Tension
Middle Compression
Middle Tension
Upper Compression
Upper Tension
1.9
1.7
1.5
X
Diamond
Inverted K
K
Single diagonal
Bracing Configuration
Figure 17 Plot of calculated RSR for the 5 bracing configurations for both
damaged and undamaged states
Demonstration of the change in probability of failure (collapse) of a structure when a member is severed (or inspection interval is increased).
i=N
j=M
Pf =
i
P jstorm
6
i
P sever
j=1
i=1
Probability of storm to cause collapse
Calculation of return
period to cause
member/joint failure
UR =
N
N100
Long Term Load
Distributions
Annual probability of a severed member over inspection period R
NNS
Experience Data
CNS
Theoretical Prediction
LPF
SNS
P
1.0
Modified Price
Coefficient
Return Peri od
100 yrs
1
Pf
Estimate P f from
ratio of applied
6 S 3n to design S 3N
10 -8
S3N
Pushover
Redundancy
analysis and code
check compliance
LPF
undamaged
FRACTURE MECHANICS FATIGUE & FRACTURE MODEL
damaged
damaged
1.0
FABRICATION DEFECT
INFORMATION
disp
STRESS
INTENSITY
FACTORS
ULTIMATE STRENGTH
SOLUTIONS
Figure 18 Flowchart illustrating the method of reliability calculation
52
PF
101
Probability of Fracture
Constant Amplitude Loading
Pure Tension
Brace Make-up Weld Defects - Thickness 60 mm
100
10
10-2
10-3
10-4
PF = 1.0
PFZ
-1
S^3N v Fracture 0.02
PFZ-1
10-5
10-6
10-7
10-8
10-9
10-10
10-11
10-12
3
S N at Z years = 1012
10-13
10-14
10-15
1010
S3N at PF 1.0 x Z / fatigue design life in years
1011
1012
3
S N at Z -1 years = 2x1011
3
S N at PF =1.0
3
S N at PF 1.0 x Z-1 / fatigue design life in years
1013
3
S N
Figure 19 Example plot of cumulative probability of failure versus accumulated
fatigue damage
53
1 .0 0E -0 4
1 .0 0E -0 5
1 .0 0E -0 6
X - b race d
D i am ond
Pf
K - braced
Inverted K
D iag ona l
1 .0 0E -0 7
1 .0 0E -0 8
1 .0 0E -0 9
1 980
19 85
19 90
199 5
2 000
2 005
20 10
201 5
2 02 0
2 025
y ear
Figure 20 Annual probability of failure for the five bracing configurations considering
single member failure only (100 year fatigue lives)
1.00E-04
1.00E-05
1.00E-06
Pf
X - braced
Diamond
K - braced
Inverted K
Diagonal
1.00E-07
1.00E-08
1.00E-09
1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
year
Figure 21 Annual probability of failure for the five bracing configurations considering
single member failure only (50 year fatigue lives)
54
Figure 22 Relationship between probability that member remains un-severed and
predicted structural reliability
55
1.00E-04
1.00E-05
1.00E-06
Pf
Inv
Inv
Inv
X X X -
1.00E-07
K - Sing le
K - Double ( R ed istribution ignored )
K - Doub le ( R edistr ibut ion inc luded)
S ingle
D ouble ( Red istr ibuti on ignored)
D ouble ( Red istr ibuti on included)
1.00E-08
1.00E-09
1980
1985
1990
1995
2000
2005
2010
2015
2020
2025
year
Figure 23 Annual probability of failure for the X-braced and Inverted K-braced
structures assuming (i) Single Member failure only, (ii) Double Member failure
ignoring the effects of redistribution and (iii) Double Member Failure including the
effects of redistribution
56
APPENDIX A
MODEL DESCRIPTION
57
BLANK PAGE 58
CONTENTS
Page
CONTENTS................................................................................................ 59
1. INTRODUCTION.................................................................................. 61
2. GENERIC DESIGN DESCRIPTION..................................................... 63
2.1
2.2
2.3
2.4
2.5
2.6
2.7
TOPSIDES ...................................................................................... 63 PILES ............................................................................................ 63 LEGS ............................................................................................. 64 CONDUCTORS AND GUIDES ............................................................. 64 LEVELS.......................................................................................... 64 TUBULAR JOINTS – GENERAL .......................................................... 66 JOINT GROUPS............................................................................... 66 3. BRACING CONFIGURATIONS ........................................................... 67
3.1
3.2
3.3
3.4
3.5
X-BRACED CONFIGURATION ............................................................ 67 DIAMOND BRACED .......................................................................... 68 INVERTED K-BRACED...................................................................... 70 K-BRACED ..................................................................................... 72 SINGLE DIAGONAL BRACED ............................................................. 73 4. ELEMENT FORMULATION................................................................. 75
5. MATERIAL MODEL............................................................................. 77
6. LOADING............................................................................................. 79
6.1
6.2
6.3
6.4
STORM CONDITIONS ....................................................................... 79 THE 100 YEAR MET-OCEAN EVENT ................................................. 79 REFERENCE LOAD SET ................................................................... 79 MODELLING OF FLUID-STRUCTURE INTERACTION .............................. 79 7. MODEL DEVELOPMENT .................................................................... 83
8. REFERENCES..................................................................................... 85
List of Tables
A1
Horizontal bracing members’ identifiers
A2
X-brace structure’s member sizes
A3
X-braced structure’s joint group details
A4
Diamond braced structure’s member sizes
A5
Diamond braced structure’s joint group details
A6
Inverted K-braced structure’s member sizes
A7
Inverted K-braced structure’s joint group details
59
A8
K-braced structure’s member sizes
A9
K-braced structure’s joint group details
A10
Single diagonal braced structure’s member sizes
A11
Single diagonal braced structure’s joint group details
A12
Plastic material properties for grade 355EM steel
A13
Baseline SNS location current data
List of Figures
A1
Generic structure
A2
Generic structure leg schematic
A3
Mud line frame
A4
Level 1 frame
A5
Level 2 frame
A6
Level 3 frame
A7
X-braced structure member identifiers – Frames A and B
A8
X-braced structure member identifiers – Frames 1 and 2
A9
X-braced structure joint group identifiers– Frames A and B
A10
X-braced structure joint group identifiers– Frames 1 and 2
A11
Diamond braced structure member identifiers – Frames A and B
A12
Diamond braced structure member identifiers – Frames 1 and 2
A13
Diamond braced structure joint group identifiers– Frames A and B
A14
Diamond braced structure joint group identifiers– Frames 1 and 2
A15
Inverted K-braced structure member identifiers – Frames A and B
A16
Inverted K-braced structure member identifiers – Frames 1 and 2
A17
Inverted K-braced structure joint group identifiers– Frames A and B
A18
Inverted K-braced structure joint group identifiers– Frames 1 and 2
A19
K-braced structure member identifiers – Frames A and B
A20
K-braced structure member identifiers – Frames 1 and 2
A21
K-braced structure joint group identifiers– Frames A and B
A22
K-braced structure joint group identifiers– Frames 1 and 2
A23
Single diagonal braced structure member identifiers – Frames A and B
A24
Single diagonal braced structure member identifiers – Frames 1 and 2
A25
Single diagonal braced structure joint group identifiers– Frames A and B
A26
Single diagonal braced structure joint group identifiers– Frames 1 and 2
A27
Member sizing design process
60
1. INTRODUCTION
In order to provide a systematic investigation into the influence of different bracing
configurations that are common place in the construction of offshore installations,
particularly in the North Sea, a generic structure was developed that consisted of the jackets
legs, horizontal plane framing, conductors, piles and topside weight. This generic structure
was based upon a current jacket that is located in the Southern sector of the North Sea. It is
an inverted K-braced, four-legged wellhead platform, and stands in approximately 45m of
water.
Figure 1 illustrates the generic structure along with the grid line references and the applied
storm directions.
A number of simplifications were made to the generic model as well as changes to the
dimensions of members/piles taken from the baseline jacket. These changes were as a
result of the model development phase and were due to the introduction of the different
bracing configurations to the generic model and the impact on the failure mode of the
structure in the ultimate strength studies.
61
BLANK PAGE
62
2. GENERIC DESIGN DESCRIPTION
2.1
TOPSIDES
The topsides’ weight was based upon that of the baseline jacket that weighs 1200 tonnes.
This was represented in the generic model as a single mass element located at a height of
5 metres above the stab-in points for the jacket, at the geometric centre of the jacket’s plan
view. The topsides were tied into the stab-in points using beam type ‘multi-point
constraints’ which effectively formed a rigid link between the topsides’ mass element and
the stab-in points.
2.2
PILES
The piles were originally modelled using design data from the baseline jacket, i.e. 8 insert
piles, 2 per leg, with the following cross-sectional dimensions:
Outer diameter: 1.829m
Wall thickness: 0.065m
The point of fixity for the piles was taken as being at a depth of 20m below the mud line
and extended from the mud line, up the legs to a height of 11.67m. To simplify the model,
and to reduce computational time in the finite element analyses a decision was taken to
simplify the modelling of the piles as much as possible. It was therefore decided to omit
the soil-structure interaction between the seabed and the piles. Since the study was aimed
at demonstrating the difference between bracing configurations on an arbitrary structure
such simplification was deemed valid and appropriate. However, it should be recognised
that the ultimate strength of a jacket is affected by the piles and therefore when analysing an
individual structure it is necessary to accurately model the soil-structure interaction at the
structure’s foundations. Furthermore, failure of the piles themselves was not captured as
part of this study, in particular ‘pile plunge’ and ‘pull out’ type failures.
At the point where the piles were sleeved and grouted and tied into the structure, an
effective cross section was calculated that would provide similar bending restraint to the
composite section.
The following dimensions were originally used; outer
diameter = 1.913.9m, wall thickness = 0.0896m.
Preliminary pushover analyses
demonstrated that the piles dominated the ultimate strength of the jacket, with failure of the
jacket occurring in the piles due to the formation of multiple plastic hinges. In an attempt
to de-sensitise the structural response from the behaviour of the piles, the cross-section
dimensions were increased by a factor of 1.2, thus increasing the bending capacity of the
piles and preventing premature yielding of the piles away from the point of built in
restraint. This gave rise to the following cross sectional dimensions:
Sleeved Pile:
Outer diameter = 2.2967m
Wall thickness = 0.1075m
Pile:
Outer diameter = 2.1948m
Wall thickness = 0.0780m
63
2.3
LEGS
The general layout of the structure’s elevations is illustrated in Figure A2, and provides
details of the cross-sectional dimensions of the legs. These dimensions were equal on all
four of the structure’s legs.
The leg geometry was based upon that of the baseline jacket. However, after attempting
pushover analyses on several bracing configurations it was determined that there was a
‘weak point’ in the legs. This corresponded to the point just above Level 1 where there was
a reduction in the wall thickness of the legs. At this point a plastic hinge was formed and
the analysis began to diverge. This resulted in no difference in the failure mechanisms
between different bracing configurations.
To alleviate this problem, the wall thickness of the legs between Levels 1 and 2 was
increased to the same value as that below Level 1, i.e. a 1400mm outer diameter and a wall
thickness of 65mm.
The batter applied to the structure was in line with the baseline structure and was as
follows:
North direction = 6.185°
East direction
2.4
= 1.606°
CONDUCTORS AND GUIDES
The baseline structure contained 18 conductors that were located along the east side of the
jacket. The wave loading on the conductors was transferred back into the structure via the
conductor framing (see Figures A4 to A6 for details of this framing). The conductors were
fully tied in at a depth of 10 metres below the mud line and as such contributed to the
overall stiffness of the structure’s foundation.
The conductors were tied into their associated framing using multi-point restraints that
allowed for axial sliding of the conductor within its guide, but prevented horizontal
movement of the conductor.
The modelling of the conductors was simplified using tubular beam elements with an outer
diameter of 0.685m and a wall thickness of 0.030m.
These simplifications used to model the conductors and the interaction with the jacket
framework was justified since the sole purpose of the conductors inclusion in the model
was to transmit load back into the primary structure of the jacket and add to the stiffness of
the foundation.
2.5
LEVELS
The generic structure comprised of four levels that are referred to as:
Mud line -
43.5m (below sea-level)
Level 1 -
26m (below sea-level)
Level 2 -
8.5m (below sea-level)
Level 3 -
10m (above sea-level)
64
The mud line frame contained no inter-frame bracing whereas the frames at Levels 1 to 3
contained the conductor framing and associated inter-frame bracing.
Figures A3 to A6 illustrate schematics of the four level frames along with details of the
members’ cross-sectional dimensions.
Table A1 details the member identifiers used in this document for the horizontal braces at
each of the above levels.
65
Table A1 Horizontal bracing members’ identifiers
2.6
Identifier
Location
MLHA
Mud Line Frame A
MLHB
Mud Line Frame B
MLH1
Mud Line Frame 1
MLH2
Mud Line Frame 2
L1HA
Level 1 Frame A
L1HB
Level 1 Frame B
L1H1
Level 1 Frame 1
L1H2
Level 1 Frame 2
L2HA
Level 2 Frame A
L2HB
Level 2 Frame B
L2H1
Level 2 Frame 1
L2H2
Level 2 Frame 2
L3HA
Level 3 Frame A
L3HB
Level 3 Frame B
L3H1
Level 3 Frame 1
L3H2
Level 3 Frame 2
TUBULAR JOINTS – GENERAL
Within the jacket structure all tubular joints were modelled as rigid connections; i.e. joint
flexibility ignored.
2.7
JOINT GROUPS
For the purpose of the analysis individual joints between chords and braces were grouped
together into joint groups. These joint groups were given a unique identifier within a
particular bracing configuration. Each joint group comprises a chord and up to 7 braces.
Within a joint group the chord was defined as the through member. All other members that
contribute to the joint group were referred to as the braces. In the case of the X-braced
structure there were a number of joint groups that solely comprised of members with
identical cross-sections. The way in which these joint groups were handled is subject to
further discussion under Section 3.1 that describes the crossed bracing configuration.
66
3. BRACING CONFIGURATIONS As stated earlier, five different bracing configurations were added to the generic model to
establish their impact on the load distribution and ultimate strength of the jackets in both
the damaged and undamaged states.
Each of the bracing configurations is described in more detail in the following sections.
3.1
X-BRACED CONFIGURATION
Figure A7 and Figure A8 illustrate the bracing configuration and naming conventions for
the members on the X-braced structure. The joint groups’ names and locations are
illustrated in Figure A9 and Figure A10. Table A2 details the bracing members’ cross­
sectional dimensions in terms of an outer diameter measurement and a wall thickness
measurement.
Table A2 X-braced structure’s member sizes
Bay
Slenderness
Member size
ratio
(mm)
Upper
54.78
700 x 55
Middle
51.03
750 x 55
Lower
45.02
850 x 40
Table A3 below provides details of the joint group identifiers for those joint groups in the
X-braced structure that were studied in detail as part of the stress redistribution study. For
each joint group, the table identifies which members form the chord and the braces. In
addition, the index in the table’s header is a cross-reference to the joint number in the plots
of Reference 0 containing the data output from the stress redistribution study. Index ‘1’
refers to the chord and indices 2 to 7 refer to the individual joints between the chord and the
brace identified in the table.
Joint cans were added to the bracing configuration at those joints that formed the X­
bracing, i.e. joint groups MLA/B/1/2, L1A/B/1/2, L2A/B/1/2, and L3A/B/1/2. These joint
cans were approximately 2 metres long and aimed to provide localised stiffening to the
joints by increasing the wall thickness of the bracing member. They possessed the
following cross section dimensions:
Between the mud line and Level 1:
800 x 60mm
Between Level 1 and Level 2:
750 x 60mm
Between Level 2 and Level 3:
700 x 60mm
In addition, for these particular joint groups the identification of chords and braces was
somewhat different to that employed for all other joint groups. Instead, utilisation values
were calculated based on one diagonal representing the chord and the other representing the
braces, and visa-versa. These utilisation values were then compared and the worst-case
values for the chord and braces selected.
67
Table A3 X-braced structure’s joint group details
Joint
group
Chord
Joint N°
1
2
3
4
5
6
7
ML1A
Leg 1A
MLHA
AL1L
MLH1
1LAL
ML2A
Leg 2A
MLH2
2LAL
MLHA
AL2L
L11A
Leg A1
L1H1
1MAL
1LAU
L1HA
AM1L
AL1U
L12A
Leg A2
L1HA
AM2L
AL2U
L1H1
2M2L
2L2U
L21A
Leg A1
L2H1
1UAL
1MAU
L2HA
AU1L
AM1U
L22A
Leg A2
L2H2
2UAL
2MAU
L2HA
AU2L
AM2U
ML1B
Leg 1B
MLHB
BL1L
MLH1
1LBL
ML2B
Leg 2B
MLH2
2LBL
MLHB
BL2L
L11B
Leg B1
L1H1
1MBL
1LBU
L1HB
1MBL
1LBU
L12B
Leg B2
L1HB
BM2L
BL2U
L1H2
2MBL
2LBU
L21B
Leg B1
L2H1
1UBL
1MBU
L2HB
BU1L
BM1U
L22B
Leg B2
L2HB
BU2L
BM2U
L2H2
2UBL
2MBU
3.2
DIAMOND BRACED
Figure A11 and Figure A12 illustrate the bracing configuration and naming conventions for
the members on the diamond braced structure. The joint groups’ names and locations are
illustrated in Figure A13 and Figure A14. Table A4 details the bracing members’ cross­
sectional dimensions in terms of an outer diameter measurement and a wall thickness
measurement.
Table A4 Diamond braced structure’s member sizes
Bay
Slenderness
Member size
ratio
(mm)
Upper
55.27
550 x 35
Middle
51.10
600 x 40
Lower
44.88
700 x 45
Table A5 below provides details of the joint group identifiers for those joint groups in the
diamond braced structure that were studied in detail as part of the stress redistribution
study. For each joint group, the table identifies which members form the chord and the
braces. In addition, the index in the table’s header is a cross-reference to the joint number
in the plots of Reference 0 containing the data output from the stress redistribution study.
68
Index ‘1’ refers to the chord and indices 2 to 8 refer to the individual joints between the
chord and the brace identified in the table.
Table A5 Diamond braced structure’s joint group details
Joint
group
Chord
Joint
1
2
3
4
5
6
7
8
ML1A
Leg 1A
MLH1
MLHA
-
-
-
-
-
ML2A
Leg 2A
MLH2
MLHA
-
-
-
-
-
ML11A
Leg 1A
1LAL
1LAU
AL1U
AL1L
-
-
-
ML12A
Leg 2A
2LAL
2LAU
AL2U
AL2L
-
-
-
L11A
Leg 1A
L1HA
L1H1
-
-
-
-
-
L12A
Leg 2A
L1H2
L1HA
-
-
-
-
-
L121A
Leg 1A
1MAL
1MAU
AM1L
AM1U
-
-
-
L122A
Leg 2A
2MAU
2MAL
AM2L
AM2U
-
-
-
L21A
Leg 1A
L2HA
L2H1
-
-
-
-
-
L22A
Leg 2A
L2HA
L2H2
-
-
-
-
-
ML1B
Leg 1B
MLH1
MLHB
-
-
-
-
-
ML2B
Leg 2B
MLH2
MLHB
-
-
-
-
-
ML11B
Leg 1B
BL1L
BL1U
1LBL
1LBU
-
-
-
ML12B
Leg 2B
BL2L
BL2U
2LBL
2LBU
-
-
-
L11B
Leg 1B
L1HB
L1H1
-
-
-
-
-
L12B
Leg 2B
L1H2
L1HB
-
-
-
-
-
L121B
Leg 1B
1MBL
1MBU
BM1L
BM1U
-
-
-
L122B
Leg 2B
2MBU
2MBL
BM2U
BM2L
-
-
-
L21B
Leg 1B
L2H1
L2HB
-
-
-
-
-
L22B
Leg 2B
L2H2
L2HB
-
-
-
-
-
MLA
MLHA
AL1L
AL2L
L1A
L1HA
AM1L
AM2L
AL2U
AL1U
-
-
-
L2A
L2HA
AU1L
AU2L
AM2U
AM1U
-
-
-
MLB
MLHB
BL2L
BL1L
L1B
L1HB
BM2L
BM1L
BL1U
BL2U
-
-
-
L2B
L2HB
BU2L
BU1L
BM2U
BM1U
-
-
-
ML1
MLH1
1LAL
1LBL
L11
L1H1
1MAL
1MBL
1LAU
1LBU
PLAN
PLAN
PLAN
L21
L2H1
1UAL
1UBL
1MAU
1MBU
PLAN
PLAN
PLAN
ML2
MLH2
2LAL
2LBL
L12
L1H2
PLAN
2MAL
2MBL
2LBU
2LAU
-
-
L22
L2H2
PLAN
2UAL
2UBL
2MBU
2MAU
69
3.3
INVERTED K-BRACED
Figure A15 and Figure A16 illustrate the bracing configuration and naming conventions for
the members on the inverted K-braced structure. The joint groups’ names and locations are
illustrated in Figure A17 and Figure A18. Table A6 details the bracing members’ cross­
sectional dimensions in terms of an outer diameter measurement and a wall thickness
measurement.
Table A6 Inverted K-braced structure’s member sizes
Bay
Slenderness
Member size
Ratio
(mm)
Upper
55.9
800 x 40
Middle
51.01
850 x 40
Lower
46.24
950 x 45
Table A7 below provides details of the joint group identifiers for those joint groups in the
inverted K-braced structure that were studied in detail as part of the stress redistribution
study. For each joint group, the table identifies which members form the chord and the
braces. In addition, the index in the table’s header is a cross-reference to the joint number
in the plots of Reference 0 containing the data output from the stress redistribution study.
Index ‘1’ refers to the chord and indices 2 to 6 refer to the individual joints between the
chord and the brace identified in the table.
70
Table A7 Inverted K-braced structure’s joint group details
Joint
group
Chord
Joint
1
2
3
4
5
ML1A
Leg 1A
1LA
MLH1
AL1
MLHA
ML2A
Leg 2A
2LA
MLH2
AL2
MLHA
L11A
Leg 1A
1MA
L1H1
AM1
L1HA
-
L12A
Leg 2A
2MA
L1H2
AM2
L1HA
-
L21A
Leg 1A
1UA
L2H1
AU1
L2HA
-
L22A
Leg 2A
2UA
L2H2
AU2
L2HA
-
ML1B
Leg 1B
1LB
MLH1
BL1
MLHB
ML2B
Leg 2B
2LB
MLH2
BL2
MLHB
L11B
Leg 1B
1MB
L1H1
BM1
L1HB
-
L12B
Leg 2B
BM2
L1HB
2MB
L1H2
-
L21B
Leg 1B
1UB
L2H1
BU1
L2HB
-
L22B
Leg 2B
2UB
L2H2
BU2
L2HB
-
L1A
L1HA
AL2
AL1
-
-
-
L2A
L2HA
AM1
AM2
-
-
-
L1B
L1HB
BL1
BL2
-
-
-
L2B
L2HB
BM1
BM2
-
-
-
L11
L1H1
1LB
1LA
PLAN
PLAN
PLAN
L21
L2H1
1MB
1MA
PLAN
PLAN
PLAN
L12
L1H2
2LA
2LB
PLAN
-
-
L22
L2H2
2MB
2MA
PLAN
-
-
71
6
3.4
K-BRACED
Figure A19 and Figure A20 illustrate the bracing configuration and naming conventions for
the members on the K-braced structure. The joint groups’ names and locations are
illustrated in Figure A21 and Figure A22. Table A8 details the bracing members’ cross­
sectional dimensions in terms of an outer diameter measurement and a wall thickness
measurement.
Table A8 K-braced structure’s member sizes
Bay
Slenderness
Member sizes
Ratio
(mm)
Upper
55.9
800 x 40
Middle
51.01
850 x 40
Lower
46.24
950 x 45
Table A9 below provides details of the joint group identifiers for those joint groups in the
K-braced structure that were studied in detail as part of the stress redistribution study. For
each joint group, the table identifies which members form the chord and the braces. In
addition, the index in the table’s header is a cross-reference to the joint number in the plots
of Reference 0 containing the data output from the stress redistribution study. Index ‘1’
refers to the chord and indices 2 to 6 refer to the individual joints between the chord and the
brace identified in the table.
72
Table A9 K-braced structure’s joint group details
Joint group
3.5
Chord
Joint
1
2
3
4
5
6
ML1A
Leg 1A
MLH1
MLHA
-
-
-
ML2A
Leg 2A
MLH2
MLHA
-
-
-
L11A
Leg 1A
L1HA
AL1
L1H1
1LA
-
L12A
Leg 2A
L1H2
2LA
L1HA
AL2
-
L21A
Leg 1A
L2H1
1MA
L2HA
AM1
-
L22A
Leg 2A
L2H2
2MA
L2HA
AM2
-
ML1B
Leg 1B
MLH1
MLHB
-
-
-
ML2B
Leg 2B
MLH2
MLHB
-
-
-
L11B
Leg 1B
L1HB
BL1
L1H1
1LB
-
L12B
Leg 2B
L1HB
BL2
L1H2
2LB
-
L21B
Leg 1B
L2H1
1MB
L2HB
BM1
-
L22B
Leg 2B
L2H2
2MB
L2HB
BM2
-
MLA
MLHA
AL1
AL2
-
-
-
L1A
L1HA
AM1
AM2
-
-
-
L2A
L2HA
AU2
AU1
-
-
-
MLB
MLHB
BL2
BL1
-
-
-
L1B
L1HB
BM2
BM1
-
-
-
L2B
L2HB
BU1
BU2
-
-
-
ML1
MLH1
1LA
1LB
-
-
-
L11
L1H1
PLAN
PLAN
PLAN
1MB
1MA
L21
L2H1
PLAN
PLAN
PLAN
1UB
1UA
ML2
MLH2
2LA
2LB
-
-
-
L12
L1H2
PLAN
2MA
2MB
-
-
L22
L2H2
PLAN
2UA
2UB
-
-
SINGLE DIAGONAL BRACED
Figure A23 and Figure A24 illustrate the bracing configuration and naming conventions for
the members on the single braced structure. The joint groups’ names and locations are
illustrated in Figure A25 and Figure A26. Table A10 details the bracing members’ cross­
sectional dimensions in terms of an outer diameter measurement and a wall thickness
measurement.
73
Table A10 Single diagonal braced structure’s member sizes
Bay
Slenderness
Member sizes
Ratio
(mm)
Upper
55.28
1100 x 70
Middle
50.06
1200 x 55
Lower
45.13
1350 x 45
Table A11 below provides details of the joint group identifiers for those joint groups in the
single diagonal braced structure that were studied in detail as part of the stress redistribution
study. For each joint group, the table identifies which members form the chord and the
braces. In addition, the index in the table’s header is a cross-reference to the joint number
in the plots of Reference 0 containing the data output from the stress redistribution study.
Index ‘1’ refers to the chord and indices 2 to 7 refer to the individual joints between the
chord and the brace identified in the table.
Table A11 Single diagonal braced structure’s joint group details
Joint
Group
Chord
Joint
1
2
3
4
5
6
7
ML1A
Leg 1A
MLHA
MLH1
-
-
-
-
ML2A
Leg 2A
MLH2
2L
MLHA
AL
-
-
L11A
Leg 1A
L1H1
1M
1L
L1HA
AM
AL
L12A
Leg 2A
L1HA
L1H2
-
-
-
-
L21A
Leg 1A
L2HA
L2H1
-
-
-
-
L22A
Leg 2A
L2H2
2U
2M
L2HA
AU
AM
ML1B
Leg 1B
MLHB
BL
MLH1
1L
-
-
ML2B
Leg 2B
MLH2
MLHB
-
-
-
-
L11B
Leg 1B
L1HB
L1H1
-
-
-
-
L12B
Leg 2B
L1HB
BM
BL
L1H2
2M
2L
L21B
Leg 1B
L2HB
BU
BM
L2H1
1U
1M
L22B
Leg 2B
L2H2
L2HB
-
-
-
-
74
4. ELEMENT FORMULATION Each structural member in the model was modelled using two-node linear beam elements,
which are referred to as B31 elements in the ABAQUS element library. These elements are
suitable for modelling both thick members, in which shear deformation is important, and
slender beams, in which shear deformation is not important. Since the structures’ members
were classified as thin walled sections, slender elements are more applicable, thus justifying
the use of such elements. Furthermore, the use of such elements in conjunction with the
applied mesh refinement in the model was deemed to provide a reasonable compromise
between analysis run times and accuracy of results owing to the large number of runs that
have been undertaken as part of this project.
75
BLANK PAGE 76
5. MATERIAL MODEL The material model used in the analysis is based upon a typical structural steel,
Grade 355EM, which is commonly used in the fabrication of offshore jacket
structures in the North Sea.
For the load redistribution study a linear elastic material has been used, as is the
case for the buckling analysis that feeds into the non-linear pushover analysis. The
values adopted for density, Elastic Modulus and Poisson’s Ratio are as follows:
Density:
7820kg/m3
Elastic Modulus:
206.8GPa
Poisson’s Ratio:
0.29
For the non-linear pushover analysis itself an elasto-plastic model was used, as
detailed in Table A12 below. It should be noted that ABAQUS requires that the
plasticity be defined in terms of true stress and strain as opposed to the more
conventional nominal stress and strain.
Table A12 Plastic material properties for grade 355EM steel
True Stress
True Strain
355.0
0.000
461.5
0.06780
537.7
0.12744
612.3
0.21708
681.8
0.33675
709.7
0.39662
797.1
0.63620
814.9
0.69612
847.4
0.81596
890.0
0.99576
77
BLANK PAGE 78
6. LOADING
6.1
STORM CONDITIONS
As part of the stress redistribution study three storm directions were considered, with their
point of origin in the following directions;
East
Northeast
North
These storm conditions comprised of a single pass of the 100 year met-ocean event wave
and the 100 year met ocean event current for the given baseline southern North Sea
location.
6.2
THE 100 YEAR MET-OCEAN EVENT
The loading applied in both the stress redistribution analysis and the ultimate strength
analyses was based on the 100 year storm wave, current and wind for the baseline location.
The wind loading applied was simplified as a concentrated load applied at the geometric
centre of the four stab-in points. It was representative of the wind loading that would be
introduced into the structure as a result of the wind resistance of the topsides. It had a
magnitude of 4.664kN.
The current-induced load and the wave-induced load result in both a buoyancy component
and a distributed drag load. These were determined by the use of the ABAQUS AQUA
analysis tool within the ABAQUS code (Reference 2).
6.3
REFERENCE LOAD SET
The Reference Load Set (RLS) was derived from the distributed 100 year storm loads that
were applied to the jacket structure in the form of distributed member loads that resulted in
the greatest base shear in the jacket structure. The RLS comprised of equivalent
concentrated loads distributed throughout the jacket structure. In order to determine the
RLS, the jacket structure was held fixed at every degree of freedom within the model and
subjected to just the wave passage loading and the wind loading on the topsides (gravity
loads and buoyancy loads excluded). ABAQUS AQUA was used in the analysis. The
analysis results file was then interrogated utilising in-house post processing subroutines to
derive the equivalent nodal forces that generate the same maximum base shear load as the
wave passage load case.
6.4
MODELLING OF FLUID-STRUCTURE INTERACTION
ABAQUS AQUA Analysis has been used to determine the loading induced into the
structure as a result of components being partly or fully submerged in a steady current or
during a wave passage.
AQUA requires the definition of the fluid properties, i.e. the fluid density, and the
elevations of the sea-bed and the free-surface. In this study the following values were used:
79
Density:
1025.0kg/m3
Sea bed:
-44.5m
Free-surface:
0.0m
The definition of the steady current vector was dependent on the storm direction, but is of a
constant magnitude for a given depth. Table A13 details the current magnitude and depth
input data applied in the model.
Table A13 Baseline SNS location current data
Depth below free surface Current magnitude
(m)
(ms-1)
0.0
1.66
8.0
1.66
19.6
1.48
25.5
1.46
35.5
1.41
44.49
1.13
44.50
0.0
The wave data used in the analysis was in the form of a binary data input file. It provided
the wave surface elevations, particle velocities and accelerations, and the dynamic pressure
at points in a user-defined grid.
The use of ABAQUS AQUA enables the algorithms within the finite element code to
determine the location of members in relation to the height of the waves free surface.
Based upon this, the algorithm is able to determine whether the member contributes to the
buoyancy of the structure and whether it’s subjected to drag loading.
In calculating the loading applied to the structure, a marine growth allowance was added to
the outer diameter dimension of all members in the structure, to define the effective outer
diameter that is required in the ABAQUS AQUA analysis. The value used was 100mm,
and was based upon what can reasonably be expected to occur for a jacket located in the
southern North Sea.
In calculating the drag loading acting on a member the ABAQUS AQUA analysis
determines both the transverse drag and tangential drag. The transverse drag is attributed to
the cross-sectional resistance to fluid motion and is given by the following equation for a
particular point in the wave passage time history:
80
FD
1
UC D DVn 2
2
where:
FD = force per unit length, transverse to member
U = density of fluid
CD = drag coefficient = 1.2
D = effective outer diameter
Vn = fluid particle velocity, normal to member
The tangential drag is attributed to the member’s skin friction, and is given by the following
equation for a particular point in the wave’s passage time history:
FT
1
UCT SDV h1
2
where:
FT = force per unit length, tangent to member
CT = Tangential drag coefficient = 0.002
VT = fluid particle velocity, tangential to member
h = constant = 2 (for quadratic dependence of force on velocity)
In both of the above equations the fluid particle velocity at a particular point in time is the
sum of the current and wave velocities in either the normal or tangential directions to the
given member.
81
BLANK PAGE 82
7. MODEL DEVELOPMENT As part of the model generation phase of the project an iterative process was
adopted to sizing the members for each bracing configuration. The process is
described below and illustrated in Figure A27.
Initially the bracing members were sized based upon a slenderness ratio that was
derived from the bracing members on the baseline jacket. One of the bracing
configurations was chosen and subjected to the 100 year storm event loading
scenario from the East direction. Upon completion of the finite element analysis,
the results file, generated by ABAQUS was interrogated using bespoke post
processing subroutines to assess the joint utilisation values at each joint group, in
accordance with Reference 0 and the member utilisation values for the primary
steel work in accordance with Reference 0. Failure of the code checks (i.e. a
calculated utilisation value in excess of unity) resulted in modifications to the failed
member cross sectional dimensions, whilst maintaining symmetry, and the process
repeated until the code check was satisfied. These modifications were then carried
over to the next bracing configuration to be considered, which was then subjected
to the 100 year storm event loading scenario and to the code checking routines.
Again, failure to comply with the code checks resulted in modifications to the
members and re-analysis of the current structure and those that had previously
passed the code check. This process continued until all baseline models had
identical frame members, legs, and bracing with consistent slenderness ratios, and
that all 3 storm direction loading scenarios didn’t result in failure of either the joint
or member code checks
83
BLANK PAGE 84
8. REFERENCES
1. Stress Redistribution in Platform Substructures Due to Primary Member
Damage and its Effect on Structural Reliability – EQE Report N° 45-20-R-01
Draft – 19th January 2001 – Appendix D – Stress Redistribution Study Joint
Group Utilisation Plots
2. ABAQUS 5.8 – Hibbitt, Karlsson & Sorensen, Inc.
3. Offshore Installations: Guidance on Design, Construction and Certification –
Fourth Edition-1990, HMSO – Appendix A21
4. API 2A-LRFD Recommended Practice for Planning, Designing and
Constructing Fixed Offshore Platforms – Load and Resistance Factor Design,
First Edition 1993
85
+21.5 m
+10 m
-8.5 m
-26 m
z
East
-43.5 m
North Storm
1
North
Northeast Storm
2
B
East Storm
A
Figure A1 Generic structure
86
+21500
2000
6
5
+10000
2750 3250
7826
4
3
2
-8500
-26000
1
Section details
1. 1400 x 65
2. 1400 x 85
3. 1400 x 35
4. 1400 x 75
5. 1215 x 50
50
6. 1030 x 60
-43500
All dimensions are in mm
Figure A2 Generic structure leg schematic
87
27400
13700
900x35
900x50
900x35
900x35
900x35
900x50
900x35
900x35
12250
24500
4500
900x50
Plan @ -43500
900x35
900x50
900x35
4500
Figure A3 Mud line frame
23518.7
10179.35
2920
900x25
900x50
900x25
3868.2
0x
20
700x30
1000x30
3120
1200x60
3500
950x50
800x35
700x30
23736.5
3750
4880
65
900x35
800x30
700x30
3120
700x30
900x35
20
4880
0x
800x30
65
700x30
3868.2
900x25
11759.35
900x25
900x50
9009.35
Figure A4 Level 1 frame
88
Plan @ -26000
22537.4
11268.7
8519.4
9178.7
3910
900x50
900x25
900x25
4880
800x30
2036.5
20
3000
0x
900x35
65
900x45
900x30
900x30
1000x30
3500
3750
800x30
4880
20
3000
900x35
0x
3120
406 0
900x30
65
20073
700x30
900x50
700x30
3120
406 0
1200x60
900x30
900x25
900x50
Figure A5 Level 2 frame
89
2036.5
900x45
900x25
Plan @ -8500
4000
13500
4000
10750
900x30
900x35
4980
4280
20
700x30
8100
800x35
0x
Plan @ +10000
0x
30
1400
70
800x35
20
30
Figure A6 Level 3 frame
90
0x
70
0x
900x35
21500
30
70
900x30
4980
800x25
0x
800x35
700x30
65
4280
16200
1400
800x25
70
30
0x
0x
30
70
65
AU1U
AU1L
BU1U
AU2U
BU1L
AU2L
BU2U
BU2L
AM1U
AM2U
BM1U
BM2U
AM1L
AM2L
BM1L
BM2L
AL1U
BL1U
AL2U
AL1L
BL2U
BL1L
AL2L
Frame A
BL2L
Frame B
Figure A7 X-braced structure member identifiers - Frames A and B
91
1UAU
1UAL
1UBU
2UAU
1UBL
2UAL
2UBU
2UBL
1MAU
1MBU
2MAU
2MBU
1MAL
1MBL
2MAL
2MBL
1LBU
1LAU
2LAL
1LBL
1LAL
2LBU
2LAU
Frame 1
2LBL
Frame 2
Figure A8 X-braced structure member identifiers - Frames 1 and 2 92
L31A
L32A
L31B
LUA
L21A
LUB
L21B
L22A
LMA
L12B
L11B
LLA
ML1A
L22B
LMB
L12A
L11A
L32B
LLB
ML2A
ML1B
Frame A
ML2B
Frame B
Figure A9 X-braced structure joint group identifiers - Frames A and B
93
L31A
L31B
L32A
LU1
L21A
LU2
L21B
LM2
L11B
L12A
LL1
ML1A
L22B
L22A
LM1
L11A
L32B
L12B
LL2
ML1B
ML2A
Frame 1
ML2B
Frame 2
Figure A10 X-braced structure joint Group identifiers - Frames 1 and 2 94
AU1U
AU1L
BU1U
AU2U
AU2L
AM1U
AM2U
AM1L
AM2L
AL1U
BU1L
BU2L
BM1U
BM2U
BM1L
BM2L
BL1U
AL2U
AL1L
BU2U
BL2U
BL1L
AL2L
Frame A
BL2L
Frame B
Figure A11 Diamond braced structure member identifiers - Frames A and B
95
1UAU
1UAL
2UAU
1UBU
1UBL
1MAU
1MBU
1MAL
1MBL
1LAU
2UAL
2UBL
2MAU
2MBU
2MAL
2MBL
2LAU
1LBU
1LAL
2UBU
2LBU
2LAL
1LBL
Frame 1
2LBL
Frame 2
Figure A12 Diamond braced structure member identifiers - Frames 1 and 2 96
L31A
L32A
L31B
L232A
L231A
L21A
L231B
L12A
ML11A
L122B
L12B
L11B
ML11B
ML12A
ML1A
L22B
L121B
L122A
L11A
L232B
L21B
L22A
L121A
L32B
ML2A
ML12B
ML1B
Frame A
ML2B
Frame B
Figure A13 Diamond braced structure joint group identifiers - Frames A and B
97
L31A
L31B
L32A
L232A
L231B
L231A
L21A
L21B
L121A
L122B
L12A
L12B
ML12A
ML11B
ML1A
L22B
L122A
L11B
ML11A
L232B
L22A
L121B
L11A
L32B
ML1B
ML12B
ML2A
Frame 1
ML2B
Frame 2
Figure A14 Diamond braced structure joint group identifiers - Frames 1 and 2 98
AU1
AM1
BU1
AU2
BM1
AM2
BM2
BL1
AL2
AL1
BU2
Frame A
BL2
Frame B
Figure A15 Inverted K-braced structure member identifiers - Fames A and B
99
1UA
2UA
1UB
2MA
1MB
1MA
1LA
2U2
2MB
2LA
1LB
Frame 1
2LB
Frame 2
Figure A16 Inverted K-braced structure member identifiers - Frames 1 and 2 100
L31A
L21A
L11A
L3A
L2A
L1A
ML1A
L31B
L32A
L22A
L21B
L11B
L12A
ML2A
L3B
L2B
L1B
ML1B
Frame A
L32B
L22B
L12B
ML2B
Frame B
Figure A17 Inverted K-braced structure joint group identifiers - Frames A and B
101
L31A
L21A
L11A
L31
L21
L11
ML1A
L32A
L31B
L21B
L22A
L12A
L11B
ML1B
L32
L2B
L22
L12
ML2A
Frame 1
L32B
L22B
L12B
ML2B
Frame 2
Figure A18 Inverted K-braced structure joint group identifiers - Frames 1 and 2 102
AU1
AM1
BU1
AU2
BM1
AM2
AL1
BU2
BM2
BL1
AL2
Frame A
BL2
Frame B
Figure A19 K-braced structure member identifiers - Frames A and B
103
1UA
2UA
1UB
1MA
2MB
2MA
1MB
1LA
2U2
2LA
1LB
Frame 1
2LB
Frame 2
Figure A20 K-braced structure member identifiers - Frames 1 and 2 104
L31A
L21A
L11A
ML1A
L31B
L32A
L2A
L1A
MLA
L21B
L22A
L11B
L12A
ML1B
ML2A
Frame A
L32B
L2B
L22B
L1B
MLB
Frame B
Figure A21 K-braced structure joint group identifiers - Frames A and B
105
L12B
ML2B
L31A
L21A
L11A
ML1A
L32A
L31B
L21
L11
ML1
L21B
L22A
L12A
L11B
ML1B
ML2A
Frame 1
L32B
L22
L2B
L12
L22B
L12B
ML2
Frame 2
Figure A22 K-braced structure joint group identifiers - Frames 1 and 2 106
ML2B
BU
AU
BM
AM
BL
AL
Frame A
Frame B
Figure A23 Single diagonal braced structure member identifiers - Frames A and B
107
1U
2U
1M
2M
1L
2L
Frame 1
Frame 2
Figure A24 Single diagonal braced structure member identifiers - Frames 1 and 2 108
L31A
L31B
L32A
L21B
L22A
L21A
L11A
L22B
L12B
L11B
L12A
ML1A
L32B
ML1B
ML2A
Frame A
ML2B
Frame B
Figure A25 Single diagonal braced structure joint group identifiers –
Frames A and B
109
L31A
L32A
L31B
L21B
L21A
L11A
L22B
L22A
L12A
L11B
ML1A
L32B
ML1B
L12B
ML2A
Frame 1
ML2B
Frame 2
Figure A26 Single diagonal braced structure joint group identifiers – Frames 1 and 2 110
Define bracing slenderness ratios
Run 100 year event analysis on
Type I jacket
Perform unity checks
<1
Run 100 year event analysis on
Type II jacket
Perform unity checks
<1
Run 100 year event analysis on
Type III jacket
Perform unity checks
<1
Run 100 year event analysis on
Type IV jacket
Perform unity checks
<1
Run 100 year event analysis on
Type IV jacket
Perform unity checks
<1
Generate Reference load set for
each jacket type
Figure A27 Member sizing design process
111
BLANK PAGE 112
APPENDIX B
STRESS REDISTRIBUTION STUDY
113
BLANK PAGE 114
CONTENTS
Page
CONTENTS ................................................................................................. 115
1.
INTRODUCTION ..................................................................................117
2.
ANALYSIS APPROACH......................................................................118
2.1
2.2
2.3
3.
RESULTS.............................................................................................121
3.1
3.2
4.
UNDAMAGED STRESS STATE ...................................................................118
SEVERED MEMBER ANALYSIS ..................................................................118
POST PROCESSING ......................................................................................119
GLOBAL RESPONSE ............................................................................121
LOCAL RESPONSE ...............................................................................123
DISCUSSION .......................................................................................125
4.1
4.2
4.3
4.4
4.5
X-BRACED CONFIGURATION ..............................................................125
DIAMOND BRACED CONFIGURATION ...............................................127
INVERTED K-BRACED CONFIGURATION...........................................129
K-BRACED CONFIGURATION ..............................................................130
SINGLE DIAGONAL BRACED CONFIGURATION................................133
5.
CONCLUSIONS ...................................................................................137
6.
REFERENCES .....................................................................................139
List of Tables
B1
Summary of members severed
B2
Mean joint utilisation values for undamaged structure
B3
Summary of significant results from stress redistribution study
List of Figures
B1
X-braced Frame A – Member AM1U severed
B2
X-braced Frame A – Member AM1L severed
B3
X-braced Frame A – Member AL1U severed
B4
X-braced Frame A - Member AL1L severed
B5
Diamond braced Frame A – Member AL1L severed
B6
Diamond braced Frame A – Member AL1U severed
B7
Diamond braced Frame A – Member AM1L severed
B8
Inverted K Frame A – Member AM1 severed
B9
Inverted K Frame B – Member AM1 severed
B10
Inverted K Frame 1 – Member AM1 severed
B11
Inverted K Frame 2 – Member AM1 severed
115
B12
Inverted K Frame A – Member AL1 severed
B13
Inverted K Frame B – Member AL1 severed
B14
Inverted K Frame 1 – Member AL1 severed
B15
Inverted K Frame 2 – Member AL1 severed
B16
K-braced Frame A – Member AL1 severed
B17
K-braced Frame B – Member AL1 severed
B18
K-braced Frame 1 – Member AL1 severed
B19
K-braced Frame 2 – Member AL1 severed
B20
K-braced Frame A – Member AL2 severed
B21
K-braced Frame B – Member AL2 severed
B22
K-braced Frame 1 – Member AL2 severed
B23
K-braced Frame 2 – Member AL2 severed
B24
K-braced Frame A – Member AM1 severed
B25
K-braced Frame B – Member AM1 severed
B26
K-braced Frame 1 – Member AM1 severed
B27
K-braced Frame 2 – Member AM1 severed
B28
K-braced Frame A – Member AM2 severed
B29
K-braced Frame B – Member AM2 severed
B30
K-braced Frame 1 – Member AM2 severed
B31
K-braced Frame 2 – Member AM2 severed
B32
Single diagonal braced Frame A – Member AL severed
B33
Single diagonal braced Frame B – Member AL severed
B34
Single diagonal braced Frame 1 – Member AL severed
B35
Single diagonal braced Frame 2 – Member AL severed
B36
Single diagonal braced Frame A – Member AM severed
B37
Single diagonal braced Frame B – Member AM severed
B38
Single diagonal braced Frame 1 – Member AM severed
B39
Single diagonal braced Frame 2 – Member AM severed
B40
Single diagonal braced Frame A – Member BL severed
B41
Single diagonal braced Frame B – Member BL severed
B42
Single diagonal braced Frame 1 – Member BL severed
B43
Single diagonal braced Frame 2 – Member BL severed
B44
Single diagonal braced Frame A – Member BM severed
B45
Single diagonal braced Frame B – Member BM severed
B46
Single diagonal braced Frame 1 – Member BM severed
B47
Single diagonal braced Frame 2 – Member BM severed
116
1. INTRODUCTION
The Stress Redistribution Study was a comparative study to investigate the effects of bracing
configurations, and hence redundancy levels on the degree of stress redistribution that
occurred when a member was fully severed. The study aimed to establish the load
distribution, in terms of joint utilisation values, for all joints in an undamaged structure, as a
result of the structure being exposed to the 100 year storm load. The structure was then re­
analysed with a single member severed, and the redistribution of the load analysed by
reassessing the joint utilisation values. In conducting this study a total of 15 undamaged
jacket FE analyses were conducted along with 354 severed member FE analyses.
The analysis considered the three storm directions as detailed in Reference 1.
117
2. ANALYSIS APPROACH
2.1
UNDAMAGED STRESS STATE
Each of the five models described in Reference 1 were subjected to each of the three storm
loads to determine the undamaged load distribution in terms of joint utilisation values
calculated in accordance with Reference 2 using in-house post processing sub routines. This
effectively derived a baseline load distribution within each structure for each load case to
compare the results from the severed member analysis with.
2.2
SEVERED MEMBER ANALYSIS
Severed members were introduced into the five jackets by removing the penultimate element
from the finite element mesh of the required member. The damaged structures were then
exposed to each of the three storm loads to establish the impact on the load distribution.
Table B1 details those member identifiers (See Reference 1) that were severed as part of this
study.
Table B1
Summary of members severed
Bracing Configuration
Storm
Severed Member Identifiers
X / Diamond
N/NE
AL1L, AL2L, AL1U, AL2U, AM1L, AM2L, AM1U, AM2U, AU1L, AU2L, AU1U, AU2U BL1L, BL2L, BL1U, BL2U, BM1L, BM2L, BM1U, BM2U, BU1L, BU2L, BU1U, BU2U 1LAL, 1LBL, 1LAU, 1LBU, 1MAL, 1MBL, 1MAU, 1MBU, 1UAL, 1UBL, 1UAU, 1UBU 2LAL, 2LBL, 2LAU, 2LBU, 2MAL, 2MBL, 2MAU, 2MBU, 2UAL, 2UBL, 2UAU, 2UBU Inverted K / K
E
AL1L, AL2L, AL1U, AL2U, AM1L, AM2L, AM1U, AM2U, AU1L, AU2L, AU1U, AU2U N/NE
AL1, AL2, AM1, AM2, AU1, AU2 BL1, BL2, BM1, BM2, BU1, BU2 1LA, 1LB, 1MA, 1MB, 1UA, 1UB 2LA, 2LB, 2MA, 2MB, 2UA, 2UB Single diagonal
E
AL1, AL2, AM1, AM2, AU1, AU2 N/NE
AL, AM, AU BL, BM, BU 1L, 1M, 1U 2L, 2M, 2U AL, AM, AU E
BL, BM, BU 118
2.3
POST PROCESSING
The output from the joint code checking analyses was subjected to two levels of data
processing to establish the global response and local response of the structure in terms of the
redistribution of load throughout the structure.
2.3.1
Global Response
The investigations to determine the global response provides an indication of the overall
ability of the jacket structure to absorb damage and redistribute the load. The global response
was measured in terms of a percentage shift in the mean joint utilisation value between the
damaged and undamaged states, and whether joint utilisation values exceeded unity when
subjected to the joint utilisation code check.
The output from the global analysis was represented in terms of a joint utilisation cumulative
distribution and the analytically derived density function of this distribution. In generating
the plots the joint utilisation values were subjected to a curve fitting sub-routine using linear
regression. An equation of the following type was assumed to represent the cumulative
distribution:
y 1 ae bx
The above equation was converted into linear form by taking natural logs to give an equation
of the form:
ln Y '
c bx
where;
Y'
c
1 y
ln a
The linearised equation and data were then subjected to a least squares approach to perform
the linear regression, using the ‘Gauss-Seidel’ approach to numerically solve the simultaneous
equations that were generated as part of the least squares method. The coefficients from the
simultaneous equations were then substituted into the original equation and plotted.
The plotted density functions represent the analytical solution to the differential of the
cumulative distribution function, i.e.
p ( x)
d
P( x)
dx
d
1 ae bx
dx
where;
p(x) = probability density function, pdf
119
P(x) = cumulative distribution function , cdf
and is used to derive an indication of the shift in the mean joint utilisation value in the
structure as a result of a member being severed. The mean value of the PDF is calculated
using the moment generating function of the density function and is given by the following
equation;
M
x t f
³ e px dx
tx
0
2.3.2
Local Response
The investigations to determine the local response provides a more in depth in-sight into how
individual joints were affected by the damaged member. The shifts in the calculated joint
utilisation values from the undamaged state have been mapped onto plots of the jacket’s four
elevations. The shift is represented by a simple colour code:
Red
= greater than 30% increase
Amber = an increase less than or equal to 30%
Black
= negligible effect
Green
= reduction
The shifts in joint utilisation values have been used to infer the redistribution of load as a
consequence of a member failing and the jacket being subjected to the 100 year storm load.
120
3. RESULTS The results from the stress redistribution study are detailed in References 3 and 4, and are
predominantly in a graphical format. The global effects were measured in terms of a
percentage shift in the mean joint utilisation from the undamaged to the damaged case and on
whether unity was exceeded at any of the joints. Where this was the case the joint has been
identified in terms of its joint group.
Local effects were analysed in more detail to establish how individual joints were impacted
by the load redistribution at selective joint groups, and plotted as contour plots in Figure B1 to
Figure B47.
3.1
GLOBAL RESPONSE
Reference 3 details the cumulative joint utilisation distribution curves and corresponding
density functions from the load redistribution analysis. Table B2 summarises the mean joint
utilisation values for the undamaged state.
Table B2
Mean joint utilisation values for undamaged structures
Bracing Configuration
Storm
East
North East
North
X
0.1578
0.1791
0.1648
Diamond
0.1511
0.1761
0.1484
Inverted K
0.1518
0.1720
0.1394
K
0.1835
0.2141
0.1860
Single diagonal
0.1457
0.1577
0.1519
Table B3 summarises the severed member analyses that resulted in a significant shift in the
mean joint utilisation value and those analyses that resulted in joints exceeding the code based
unity check.
121
Table B3
Summary of significant results from stress redistribution study
Bracing
Configuration
Storm
Severed
Member
Mean Joint
Utilisation
% Shift
Maximum
Utilisation
Joint
Group
X
E
AL2L
0.1583
6.0
1.0057
L12A
N
2LBL
0.1643
4.3
1.1092
L12B
N
2LAU
0.1643
4.3
1.0779
L12B
E
AM1
0.2482
66.5
1.3803
L2A
E
AM2
0.2476
66.1
1.9704
L2A
N
2MA
0.2686
95.9
10.6249
L22
N
2MB
0.2709
97.6
8.8881
L22
N
2LA
0.1770
29.1
1.3729
L12B
N
2LB
0.1777
29.6
1.4101
L12A
NE
2MA
0.2262
34.7
1.5765
L22
NE
2MB
0.2271
35.3
1.2310
L22
E
AM1
0.2779
54.5
2.3276
L11A
E
AM2
0.2860
59
2.3787
L12A
E
AL1
0.2054
14.2
1.0471
ML1A
N
2UA
0.2429
33.3
1.1168
L31
N
2UB
0.2442
34.0
1.1282
L31
N
2MA
See Note 1
-
9.4972
L12
N
2MB
See Note 1
-
9.6407
L12
N
1MB
0.2139
17.4
1.3734
L11B
N
1MA
0.2125
16.6
1.3658
L11A
NE
AM1
0.2538
20.6
1.2103
L11A
NE
AM2
0.2568
22.1
1.1203
L12A
NE
2MA
0.2657
26.3
1.2042
L12A
NE
2MB
0.2645
25.7
1.7551
L12B
E
BM
0.2468
78.8
1.2992
L12B
E
AM
0.2500
81.1
1.0477
L12A
N
2U
0.2135
48.5
1.5368
L31C
N
2M
0.2838
97.4
1.5053
L12B
Inverted K
K
Single diagonal
Note 1: Owing to the impact on the calculated utilisation values the distribution for this particular
damage state became distorted, and as a result the curve fitting process described previously failed to
determine an accurate solution owing to the poor fit of the assumed distribution to the data set. As a
result it was not possible to determine the mean utilisation value for this particular damage state using
this approach.
122
3.2
LOCAL RESPONSE
Reference 4 details the results of local effects due to the damage introduced into the jackets
and exposure to the 100 year storm event. Plots have been generated for a number of joint
groups, i.e. those located at and below Level 2 in the jackets. The study was limited to these
joint groups following an initial review of the results that highlighted above this level the
effect on joint utilisation was minimal in the majority of cases except where a member was
severed in the upper bay. For such damaged states the effect on the joint utilisation values
was concentrated about the upper bay.
As stated previously, the local response analysis focussed on the East storm direction only in
order to keep the data output and discussion to a manageable size.
123
BLANK PAGE 124
4. DISCUSSION
In general it can be seen that for the higher redundancy bracing configurations, i.e. those with
more bracing members, the global effect on the joint utilisation distribution is minimal. This
is clearly evident in Reference 3 for the diamond and X-braced configurations where the
cumulative distributions are almost identical to the damaged member cumulative
distributions, and illustrate a relatively small shift in the mean joint utilisation values between
the damaged and undamaged cases.
However, analysis of the cumulative distribution plots generated for the lower redundancy
structures, i.e. K-braced, inverted K-braced and single diagonal braced structures indicates a
different type of behaviour. These structures are affected much more by the severance of a
single member. In general, severance of a lower bay or middle bay bracing member has a
significant impact on the distribution of joint utilisation values and the potential for the code
based unity check to be exceeded. Such effects are subject to further discussion below, under
the appropriate bracing configuration sub-headings.
In addition to the global analysis performed as part of this study, data has also been generated
to investigate the local effects in more detail. Charts of joint utilisation values for individual
joint groups have been generated and are illustrated in Reference 3. These plots have been
further analysed and mapped onto the jacket structures to provide a visual ‘contour plot’ of
how joint groups throughout the structure are affected by a member being severed. These
‘contour plots’ are illustrated and discussed under the appropriate bracing configuration sub­
headings.
For the purpose of this discussion the concept of a ‘sensitivity zone’ shall be introduced. The
sensitivity zone comprises the zone in the damaged structure that is adversely affected, in
terms of a significant increase in the joint utilisation from the undamaged case, by the failure
of a member. ‘Significant’, in this context, infers an increase in excess of a 30% shift in the
joint utilisation, as calculated in accordance with Reference 2 using in-house data processing
routines.
4.1
X-BRACED CONFIGURATION
4.1.1
Global Analysis
From the plots of cumulative joint utilisation distributions, and their associated distribution
function, see Reference 3, it can be seen that severance of a member has little impact on the
structure. This is true regardless of the direction of the storm applied. This damage-tolerant
behaviour typifies the high degree of redundancy within the structure, such that in the event of
a load path being severed, there are a number of alternative load paths that are available at a
joint group to efficiently diffuse the load throughout the structure.
However, from Table B3 it can be seen that there are three failed member cases, from those
considered, that result in at least one joint in the structure experiencing a utilisation factor in
excess of one.
For the case of member AL2L having been severed, the load bearing capacity and the load
acting on the diagonal on which member AL2L lies, was significantly reduced. The impact of
this was a resultant increase in the load carried on the opposite diagonal on which member
AL2U lies, as the structure accommodated the severed member. It is this increase in load that
resulted in the utilisation value of the joint between member AL2U and leg 2A exceeding the
code based unity check.
For the case of member 2LBL or 2LAU having been severed (both members lie on the same
diagonal in the lower bay), a joint utilisation value of greater than one was observed at joint
125
group L12B, for the North storm RLS. The joint that is affected is that between Leg 2B and
the member 2LBU that lies on the opposite diagonal in the lower bay.
In general for the East storm condition, for the frames parallel to the storm direction, failure
of a lower bay diagonal member that was nominally (in the undamaged jacket) in tension,
resulted in the compressive diagonal members experiencing an increase in load. The impact
of this increase was a significant rise in joint utilisation values such that they either
approximated or exceed unity. For the North storm condition this effect was limited to Frame
2, and was attributed to the asymmetry of the structure about the storm direction’s axis owing
to the presence of the conductors. The conductors picked-up a significant amount of load
from the storm wave and as such transferred a significant proportion of this load into Frame 2.
The load was eccentric and induced a high degree of bending into Frame 2. However, for
both of these cases the effect on the overall distribution of joint utilisation values was
minimal, as can be seen from the shift in the calculated mean value in Table B3.
4.1.2
Local Analysis
From an initial review of the local analysis plots documented in Reference 4 an insight into
the redistribution of load, as a result of failure of a member in Frame A, can be gained. In
general, there was very little effect on joints in Frames B, 1 and 2 as a result of a member
being severed in Frame A. This was as a result of the limited impact on the stiffness of Frame
A as a result of a member from Frame A being severed, and thus insignificant torsional
effects being induced into the jacket structure. Based upon this initial review the contour
plots that have been generated from the local analysis have been limited to Frame A for the
following failed member analyses;
x AM1U (nominally in tension)
x AM1L (nominally in compression)
x AL1U (nominally in tension)
x AL1L (nominally in compression)
The study is limited to these cases because failure of members in the upper bay had negligible
impact on joint groups below Level 2 and also the magnitude of the utilisation values above
this level were significantly less than elsewhere in the structure. Also, owing to the structural
symmetry of Frame A about its centre line it was deemed unnecessary to provide a detailed
analysis for members AM2U, AM2L, AL2U and AL2L. An initial review of the joint
utilisation plots for the joint groups analysed in Reference 4 highlighted the similarity in both
the magnitude of joint utilisation values and the percentage shift induced as a result of a
similar loaded member being severed.
A common feature of the contour plots generated for the 4 member failure cases considered
was the limited impact that the failed member had on the utilisation values calculated for the
legs. This behaviour can be attributed to the stiffness of the X-braced configuration and its
ability to distribute the load throughout the structure, providing multiple load paths to the
piles where the load was reacted. As a result of a member failing, the load was redistributed
through the bracing and transferred to the piles via the mud line horizontal bracing. There
was a general relaxation of load in the contiguous diagonals (i.e. ‘zig-zag’) and an increase in
load in the opposite ‘zig-zag’. This effect is clearly visible in the contour plots.
Failure case specific features are discussed in more detail in the following sub-sections.
Member AM1U Failure
In the case of member AM1U having failed the sensitivity zone was localised about the
middle bay on Frame A and also encompassed the horizontal brace at the Mud line, as can be
seen in Figure B1.
126
Loss of member AM1U resulted in a relaxation of the load in member AM2L that lies on the
same diagonal. However, there was a corresponding increase in the utilisation values for
members AM1L and AM2U that form the intact diagonal in the middle bay. Furthermore
there was a near doubling of the utilisation value in the horizontal member at Level 1, joint
group L12A.
Member AM1L Failure
In the case of member AM1L having failed the sensitivity zone was slightly more localised
than was the case for member AM1U having failed, and was concentrated about the middle
bay on Frame A, as illustrated in Figure B2.
Loss of member AM1L resulted in a relaxation of the load in member AM2U that lies on the
diagonal. However, there was again a corresponding increase in the utilisation values for
members AM1U and AM2L that form the intact diagonal in the middle bay, and the
horizontal members at Levels 1 and 2.
Member AL1U Failure
In the case of member AL1U having failed the sensitivity zone was localised about the lower
bay on Frame A, as illustrated in Figure B3.
The impact on the intact diagonal brace was a 50% increase in the utilisation value at the joint
between leg 2A and member AL2U, resulting in a utilisation value of 0.99. The impact on the
horizontal member’s joint with Leg 2A at Level 1 was a factor of 2 increase in the utilisation
value. At the Mud line there was an increase in the joint utilisation value at the joints
between the Leg 1A and the horizontal member by a factor of 6. Furthermore there was an
increase in the joint utilisation between the intact diagonal and Leg 1A by a factor of 1.5
resulting in a utilisation value of 0.97.
Member AL1L Failure
In the case of member AL1L having failed the sensitivity zone was again highly localised
about the lower bay horizontal members and the intact diagonal brace, as illustrated in Figure
B4.
The impact on the intact diagonal brace and the horizontal members was a 50% increase in
the utilisation value at the joint between leg 1A and member AL1U, and a factor of 4 increase
in the utilisation value of the joint between leg 1A and the horizontal member at Level 1. At
the Mud line there was an increase in the joint utilisation value at the joints between the Legs
1A and 2A, and the horizontal member by a factor of 9. However, the actual utilisation value
was less than 0.55.
4.2
DIAMOND BRACED CONFIGURATION
4.2.1
Global Analysis
From the plots of cumulative joint utilisation distributions, and their associated distribution
functions in Reference 3, it can be seen that there was very little effect on the global
distribution of load in terms of utilisation values at joints, as a result of a single member being
severed. This behaviour typifies the damage tolerance of the diamond braced configuration.
For the diamond braced structure the impact of a lower bay member failing on the magnitude
of the maximum joint utilisation was not as dramatic as was the case for the X-braced
structure. However, loss of either of the upper bracing members in the lower bay resulted in a
shift in the maximum utilisation value from less than 0.8 in the undamaged case to
approximately 0.9 in the damaged case. This applied to such members in Frame A for the
east storm load and to members in Frame 2 for the North storm load case.
127
4.2.2
Local Analysis
From an initial review of the local analysis plots documented in Reference 4 an insight into
the redistribution of load, as a result of failure of a member in Frame A, can be gained. In
general, there was very little effect on joints in Frames B, 1 and 2 as a result of a member
being severed in Frame A. This can be attributed to the structure’s ability to diffuse the load
throughout the structure using the high number of alternative load paths available at any given
joint group. This resulted in limited impact on any one particular joint and relatively low
joint utilisation values throughout the structure.
The contour plots generated from the local analysis have been limited to the following failed
member analyses for the East storm RLS:
x AM1L (nominally in tension)
x AL1U (nominally in compression)
x AL1L (nominally in tension)
The study is limited to these cases because failure of members in the upper bay had negligible
impact on joint groups below Level 2 and also the magnitude of the utilisation values above
this level were significantly less than elsewhere in the structure. Also, owing to the structural
symmetry of Frame A about its centre line it was deemed unnecessary to provide a detailed
analysis for members AM2U, AM2L, AL2U and AL2L. An initial review of the joint
utilisation plots for the joint groups analysed in Reference 4 highlighted the similarity in both
the magnitude of joint utilisation values and the percentage shift induced as a result of a
similar loaded member being severed.
A common feature of the contour plots generated, for the 3 member failure cases considered,
was the load relaxation of diagonal braces that lie on the failed member contiguous diagonals
(i.e. ‘zig-zag’), and a corresponding increase of load on the intact ‘zig-zag’. This behaviour
was comparable to the behaviour of the X-braced structure.
Failure case specific features are discussed in more detail in the following sub-sections.
Member AL1L Failure
In the case where AL1L having failed from Figure B5 it can be seen that the sensitivity zone
was very localised. In fact only one joint group was significantly affected, MLA. The
apparent increase in load through the Mud line horizontal brace can be attributed to the
localised stiffening of the joint by a joint can, thus effectively attracting load to this joint
group component, and locally relieving the load in adjacent members.
Further study of the plots in Reference 4 sheds further light on this behaviour. There was a
degree of load redistribution through the lower level joints of Frames 1 and 2. This was
notably more than was the case for the X-braced configuration, but still nowhere near the
levels observed in the lower redundancy bracing configurations.
Member AL1U Failure
In the case of member AL1U having failed the sensitivity zone was relatively small, and
tended to be local to the lower half of the middle bay close to leg 1A, as illustrated in Figure
B6.
128
Member AM1L Failure
In the case of member AM1L having failed from Figure B7 can be seen that the sensitivity
zone was very localised. Increases in joint utilisation values were limited to the diagonal
braces (AM2L and AL1U) that pass through the joint group containing the failed member and
the horizontal brace (by a factor of approximately 2) at level 1. There was also a
corresponding increase in the utilisation of leg 1A, by an approximate factor of 2, local to the
failed member.
4.3
INVERTED K-BRACED CONFIGURATION
4.3.1
Global Analysis
From the plots contained in Reference 3 it can be seen that in general, loss of any diagonal
bracing member in a frame that was perpendicular to the storm direction resulted in an
appreciable shift in the distribution of joint utilisation values. For the North east storm load
condition the joint utilisation distribution was most sensitive to failure of the lower and
middle bays’ diagonal members in Frames A and 2. This can be attributed to the asymmetry
of the jacket about the storm’s axis due, to the presence of the conductors.
From Table B3 it can be seen that there were a number of failed member analyses that
resulted in utilisation values exceeding the code based unity check. For the east storm load
case failure of either of the middle bay members in Frame A, AM1 or AM2, resulted in a
utilisation greater than unity at joint group L2A for the joint between the undamaged member
and the horizontal member at Level 2.
Furthermore, there were a number of joints
throughout the structure that were significantly impacted by failure of either one of these
members, such that they exceeded unity or came close to unity. This further highlighted the
sensitivity of the load distribution to failure of either of these members.
For the North storm load case the structure was particularly sensitive to failure of a middle
bay diagonal brace in Frame 2. Under such scenarios the structure experienced very high
utilisation values at joint group L22. Such values were calculated for the remaining intact
brace within the middle bay, and were considered to be as a direct consequence of the
conductors. The conductors provided a substantial cross-sectional area to the storm wave and
as such were highly loaded. This load was transferred back into the primary structure through
the conductor support framing which tied into Frame 2, thus providing an eccentric load into
Frame 2 and hence into the intact diagonal brace in the middle bay.
Similar behaviour was observed for the Northeast storm load condition, with unity being
exceeded at joint group L22 for failure of a middle bay diagonal brace in Frame 2. However,
the resultant utilisation was significantly less, as the load was distributed more evenly through
Frames B and 2 owing to the angle of incidence of the storm.
4.3.2
Local Analysis
Unlike the X-braced and diamond braced structures, severance of a brace in Frame A had a
major impact on those frames that were perpendicular to the storm, i.e. Frames 1 & 2, and
also on the parallel frame, Frame B. The load was redistributed throughout the structure and
can be seen by the plots of joint utilisation for each of the joint groups as depicted in
Reference 4 for all joints up to and including those at Level 2.
Contour plots have been generated from the local analysis for the following failed member
cases:
x AL1
(nominally in compression)
x AL2
(nominally in tension)
x AM1
(nominally in compression)
129
x AM2
(nominally in tension)
However, owing to the similarities between the plots generated only those for the cases where
AL1 and AM1 were severed have been included.
From these plots one can determine the sensitivity zone for each failed member analysis.
Failure case specific features are discussed in detail in the following sub-sections.
Member AM1 Failure
In the case of member AM1 having failed, it can be seen, from the contour plots, Figure B8 to
B11, that the sensitivity zone was extensive. The sensitivity zone extended across all four
frames and covered the middle bay in Frames A and B, and the middle and lower bays in
frames 1 and 2 as the load was transmitted to the piles.
Loss of the load bearing capacity of AM1 resulted in a significant increase in the load through
the horizontal brace at Level 2 in Frame A, and member AM2. In fact, the utilisation of the
joint between member AM2 and the horizontal brace at Level 2 experienced a factor of
approximately 2.5 increase, and as a result exceeded unity, hence highlighting the potential
cascade failure of this joint. In addition there was a load increase at the joint between BM1
and L2HB, in Frame B. Here the compressive load on BM1 increased, and the utilisation of
the joint increased by approximately 50% to a utilisation of unity. This again highlighted the
potential for a cascade failure.
Member AM2 Failure
The general behaviour observed as a result of member AM2 having failed was comparable to
that for the case of member AM1 having failed. This is evident from the relevant plots in
Reference 3.
Member AL1 Failure
In the case of member AL1 having failed, it can be seen from Figure B12 to B15 that the
sensitivity zone was extensive. It extended across all four frames and covered the middle bay
in Frame A, the lower bay in Frame B, and the middle and lower bays in Frames 1 and 2 as
the load was transmitted to the piles.
In Frame A, failure of member AL1 resulted in a relaxation of the load in member AM2, with
the load being redistributed through the Mud line horizontal member and the Level 1
horizontal member.
In Frame B the effects were limited to the lower bay as the structure attempted to
accommodate the asymmetric stiffness as a result of the severed member in Frame A’s lower
bay. The resultant torsional effects due to the asymmetric stiffness was reacted in Frames 1
and 2 where both the middle and lower bay joints were affected by a significant increase in
joint utilisation.
Throughout the structure the effects were diffused beyond level 2 where there was limited
impact.
Member AL2 Failure
The general behaviour observed as a result of member AL2 having failed was comparable to
that for the case of member AL1 having failed. This is evident from the relevant plots in
Reference 3.
4.4
K-BRACED CONFIGURATION
4.4.1
Global Analysis
From the plots contained in Reference 3 it can be seen that for the East storm load case, loss
of a diagonal bracing member in the middle or lower bay of Frame A resulted in an
130
appreciable shift in the distribution of joint utilisation values. Failure of a middle bay member
however imparted a greater overall effect, whilst the failure of a lower bay brace affected a
minority of joints.
For the North storm load case, failure of any middle or upper bay diagonal brace on Frame 2
had an appreciable impact on the joint utilisation distribution. Very high utilisation values
were observed at joint group L12. As was the case for the inverted K-braced structure, such
increases can be attributed to the combination of the reduced stiffness of the middle bay due
to member failure and the significant eccentric loading imparted on Frame 2 by the
conductors. Failure of an upper bay diagonal brace also resulted in joint utilisation values
exceeding unity, but such joints were limited to the plan bracing at Level 3. Due to the
reduced stiffness of the upper bay, the load increased on the plan bracing as the structure
attempted to accommodate the resultant asymmetric stiffness.
Failure of a middle bay bracing member on Frame 1 also had an appreciable effect on the
distribution of joint utilisation values for the North Storm condition. However, the impact
was not as severe as that for failure of a corresponding member in Frame 2, but it still resulted
in unity being exceeded at either joint group L11B or L11A.
For the Northeast storm load case failure of a middle bay member in either Frames A or 2
produced an appreciable shift in the distribution of joint utilisation values. In such cases unity
was exceeded at either joint group L11A, L12A or L12B.
In general the distribution of joint utilisation values and hence the inferred redistribution of
the load within the K- braced jacket structure as the result a failed member, appeared to be
most sensitive to the failure of a middle bay brace. Unlike the higher redundancy structures
there was a considerable difference in stiffness between the middle and lower bays in the Kbraced structure due to the added bending restraint provided by the piles interaction with the
legs in the lower half of the lower bay. Thus, as a result of a failed member in the lower bay,
bending and the induced torsion was resisted by the legs and load gets transferred axially
through the legs to the piles. In the event of a middle bay member failing, there was a
significant reduction in the stiffness of the middle bay and induced torsional effects. The load
was redistributed throughout the structure as the structure accommodated the load from the
failed member. Since, locally, the legs do not provide the same level of restraint as they do in
the lower bay, the load was redistributed throughout the structure, the impact being a general
increase in joint utilisation values.
4.4.2
Local Analysis
As with the inverted K-braced structure the severance of a brace in Frame A had a major
impact on those frames that are perpendicular to the storm, i.e. Frames 1 & 2, and also on the
parallel frame, Frame B. The load was redistributed throughout the structure and can be seen
by the plots of joint utilisation for each of the joint groups as depicted in Reference 4 for all
joints up to and including those at Level 2 in the K-braced jacket structure. These plots have
been summarised in Figure B16 to B31 in terms of a shift in the calculated joint utilisation
value for the following failed member analyses;
x AL1
(nominally in tension)
x AL2
(nominally in compression)
x AM1
(nominally in tension)
x AM2
(nominally in compression)
From these figures one can determine what the sensitivity zone is for each failed member
analysis.
Failure case specific features are discussed in detail in the following sub-sections.
131
Member AL1 Failure
In the case of member AL1 having failed, it can be seen from Figure B16 to B19 that the
sensitivity zone was extensive. Load was redistributed throughout the structure as the
structure accommodated the change in stiffness of Frame A. The sensitivity zone extended
throughout the lower and middle bays of Frames 1 and 2 and into the horizontal member at
Level 1 of Frame B. The effect on Frame A was limited to the Mud line horizontal brace.
Throughout Frame A, there was a limited effect on the utilisation values of joints, particularly
in the diagonal bracing members’ joints. The intact lower bay member, AL2, endured little
change as a result of AL1 being severed. This behaviour can be attributed to the local
stiffening of the lower bay by the piles. The piles provide additional bending restraint to the
lower bay due to the nature in which they are tied into the structure and the increase in the
effective cross-sectional area that they contribute to the lower proportion of the leg. Instead
the load was redistributed to the upper proportion of the legs and the horizontal bracing at the
Mud line and Level 1. At the Mud line, the horizontal braces’ joint with Leg 1A experienced
a utilisation value that exceeded unity.
The frames that are perpendicular to the storm loading experienced a considerable increase in
load throughout the middle and lower bays as the structure accommodated the induced torsion
attributable to the asymmetrical stiffness between Frames A and B. The load was generally
diffused throughout the middle and lower bays’ diagonal and horizontal members.
The effect on Frame B was a general increase in joint utilisation values; however, this was
limited with the exception of the horizontal member at Level 1.
Member AL2 Failure
The general behaviour of the structure upon failure of member AL2 was similar to that
exhibited when member AL1 was severed (see Figure B20 to B23). The general load
redistribution was comparable.
Member AM1 Failure
In the case of member AM1 having failed, it can be seen from Figures B24 to B27 that the
sensitivity zone was extensive. Load was redistributed into frame B’s middle and upper bays
through the diagonal and horizontal braces in Frames 1 and 2. The sensitivity zone extended
across all four frames and covered the middle bay in Frames A and B, and all three bays in
frames 1 and 2 as the load was redistributed and transmitted to the piles.
In general the legs in the lower half of the lower bay were shielded from the load by the piles
and as such their interface with the Mud line framing endured limited impacted by member
failure.
Loss of the load bearing capacity of AM1 resulted in a significant increase in the load through
the horizontal brace at Level 1 in Frame A. In fact the utilisation of the horizontal brace’s
joints at Level 1 experienced a factor of approximately 4 increase at joint group L11A, a
factor of approximately 2 increase at joint group L1A and a factor of approximately 2.5
increase at joint group L12A. As a result of these increases the code based unity check was
exceeded, hence highlighting the potential cascade failure of these joints.
As a result of the imposed asymmetric stiffness between Frames A and B, load was
redistributed into the perpendicular frames, i.e. 1 and 2, as the structure accommodated the
induced torsion. The increased load in these frames was diffused throughout the three bays.
In general there was an increase by a factor of 2 in the joint utilisation values throughout the
joints in Frames 1 and 2.
The effect on Frame B was again an overall increase in joint utilisation values, with the
middle and upper bays more adversely affected. Although absolute values tended to be
higher in Frame B than in Frames 1 and 2, the percentage increase was a lot less severe.
132
Member AM2 Failure
The general behaviour of the structure upon failure of member AM2 was similar to that
exhibited when member AL1 was severed (see Figures B28 to B31). The general load
redistribution was comparable, and for this particular case, joint groups L12A and L1A
exceeded the code based unity check.
4.5
SINGLE DIAGONAL BRACED CONFIGURATION
4.5.1
Global Analysis
Unlike the other 4 jacket structures, the single diagonal braced jacket is asymmetric about the
east axis. Owing to this asymmetry between Frames A and B, the redistribution of the load
due to each of the six diagonal braces being severed was investigated.
From Reference 3 it can be seen that the global effect on the load distribution was minimal for
the case when either of the two lower members were severed. However, severance of either of
the two middle bay diagonal braces resulted in a significant shift in the distribution. It is
considered that the difference in the structural response between a member having failed in
the middle bay and one having failed in the upper bay is attributable to a step change in the
stiffness between the two bays. In the lower bay the piles provide the lower half of the legs
with additional bending restraint, thus adding to the bay’s stiffness. In the event of a lower
bay diagonal brace failing the load was redistributed to the legs and transferred axially to the
piles, thus relatively few joints were affected. However, the failure of a middle bay diagonal
brace, resulted in a significant reduction in the middle bay stiffness. The load was
redistributed throughout the structure as it accommodated the failed member. The resultant
response was observed as global bending and torsion of the structure about a point coincident
with the top of the piles. The impact of this was high utilisation values at Level 1 joints.
Severance of either of the two upper bay diagonal braces resulted in a slightly higher increase
in the mean joint utilisation. It is considered that this was as a result of loss of stiffness higher
up the structure leading to increased eccentricity of the topside load, and torsion effects that
were acting on the jacket due to a the resultant asymmetric stiffness
4.5.2
Local Analysis
In-line with the behaviour of the K-braced and inverted K-braced structures, severance of a
brace in Frame A had a major impact on those frames that are perpendicular to the storm, i.e.
Frames 1 & 2, and also on the parallel frame, Frame B. The load was redistributed
throughout the structure and can be seen by the plots of joint utilisation for each of the joint
groups as depicted in Reference 4 for all joints up to and including those at Level 2.
Those plots for each of the joint groups in Reference 4 have been summarised in terms of
contour plots (Figures B32 to B47) representing a shift in the calculated joint utilisation value
for each of the joints, up to Level 2, for the following failed member analyses;
x AL
(nominally in tension)
x AM(nominally in compression)
x BL
(nominally in compression)
x BM
(nominally in tension)
From these figures one can determine what the sensitivity zone is for each failed member
analysis.
Failure case specific features are discussed in more detail in the following sub-sections.
133
Member AL Failure
In the case of member AL having failed, it can be seen from Figures B32 to B35 that the
effect on the individual joint utilisation values was extensive. Significant increases were
observed throughout the structure. The sensitivity zone can be seen to extend across of four
frames and generally covers both the lower and middle bays. The impact on the members in
the upper bay was limited.
In Frame A’s lower bay there was a general relaxation in the joint utilisation values due to the
failed member. However, there was an increase at Level 1, particularly in the legs 1A and
2A, and the horizontal brace (albeit to a lesser extent). Throughout Frame A, there was a
general trend of the load increasing in the legs and very little effect on the braces. This
behaviour can be attributed to the increased compliance of Frame A provided by the resultant
reduction in stiffness of the lower bay.
Within Frame B there was a general increase in utilisation of the joints as the structure
accommodated the reduction in stiffness in the storm direction.
Frames 1 and 2 experienced a fairly extensive increase in joint utilisation values within the
lower and middle bays as a result of the induced torsion in the structure as a consequence of
the asymmetric stiffness between Frames A and B. The torsion was reacted by the diagonal
bracing members and the horizontal members at Level 1.
A review of the plots in Reference 4 highlights that the absolute joint utilisation values were
in general not as severe as the case for the failure of a middle bay brace.
Member AM Failure
In the case of member AM having failed, it can be seen from Figures B36 to B39 that the
effect on individual joint utilisation values was extensive. The sensitivity zone extended
across all four frames and covered both the lower and middle bays of the jacket and extended
into the upper bay. However, the absolute values of joint utilisation for joints at Level 2 and
above were much less than joints at Level 1.
In Frame A, failure of member AM resulted in a significant rise in the load on the horizontal
bracing members at Levels 1 and 2. In particular at Level 1 the increase in utilisation between
the horizontal bracing member and leg 2A increased by a factor of approximately 4, resulting
in the joint utilisation exceeding the code based unity check, thus highlighting a potential
cascade failure of this joint. Furthermore a similar increase was observed at this members
joint with Leg 1A, however in this case the code based unity check was not exceeded.
Within Frame A the failure of the member was accommodated by the legs 1A and 2A, which
both experienced a significant rise in utilisation, with leg 2A (the east most leg) enduring the
highest rise; by approximately a factor of 3 on the undamaged case.
As a result of the imposed asymmetric stiffness between Frames A and B there was a
significant increase in load in the members of Frame B as well as in Frames 1 and 2. The
joint utilisation values in Frame B generally increased throughout the three bays, with the
middle bay being the most adversely effected. However absolute values tended to be limited
to less than 0.6, and shifts, with the exception of legs 1B and 2B, limited to approximately
50%.
In Frames 1 and 2, as stated above there was also a significant shift in joint utilisation values
as these frames reacted the induced torsion as a result of the imposed asymmetry between the
stiffness of Frames A and B. The induced torsion of the jacket structure was reacted by the
horizontal and diagonal braces.
Member BL Failure
In the case of member BL having failed, it can again be seen from Figures B40 to B43 that the
effect on individual joint utilisation values was extensive. However, the general behaviour
was comparable to the case where member AL was severed.
134
Member BM Failure
In the case of member BM having failed, it can again be seen Figures B44 to B47 that the
effect on individual joint utilisation values was extensive. The general behaviour was
comparable to the analysis performed for case where member AM was severed, in terms of
the sensitivity zone.
However, a more detailed review of absolute joint utilisation values from the plots in
Reference 4 reveals a significant impact on utilisation values of joints in Frame B, in
particular the joint between the horizontal brace at level 1 and leg 2B. Here the joint
experienced an increase in utilisation by a factor of approximately 5, resulting in the joint
exceeding the code based unity check. This highlighted the potential for a cascade failure of
this joint.
135
BLANK PAGE 136
5. CONCLUSIONS
x The X-braced and the diamond braced structures are able to accommodate member
failures much more economically than the inverted K-braced, K-braced, and single
diagonal braced structures. This behaviour is in-line with perceived redundancy of the
five bracing configurations.
x For the leaner structures, failure of a middle bay diagonal brace had the largest impact on
structural stiffness and joint utilisation values. In general, the joints at Level 1 exhibited
higher utilisation values than other joints in the structure, as the induced bending was
accommodated.
x For the higher redundancy structures, the impact of a failed member was generally not as
onerous as the case for the leaner structures. However severance of a lower bay member
had a significant impact locally on joint utilisation values.
x The difference in the global response between the X-braced and diamond braced
structures’ response was attributed to the resultant load paths when a member was
severed. Failure of a diagonal bracing member in the X-braced structure resulted in
almost a total loss of the corresponding diagonal’s ability to bear load, thus in effect two
bracing members were lost in a single bay. However, in the case of the diamond braced
structure, diagonals were divided between two bays, and as such the effect on a single
bay’s stiffness was not as severe.
137
BLANK PAGE 138
6. REFERENCES
1 Stress Redistribution in Platform Substructures Due to Primary Member Damage and its
Effect on Structural Reliability – EQE Report N° 45-20-R-01 Draft – 19th January 2001 –
Appendix A – Model Description
2 Offshore Installations: Guidance on Design, Construction and Certification – Fourth
Edition-1990, HMSO – Appendix A21
3 Stress Redistribution in Platform Substructures Due to Primary Member Damage and its
Effect on Structural Reliability – EQE Report N° 45-20-R-01 Draft – 19th January 2001 –
Appendix C – Joint Utilisation Distribution Plots
4 Stress Redistribution in Platform Substructures Due to Primary Member Damage and its
Effect on Structural Reliability – EQE Report N° 45-20-R-01 Draft – 19th January 2001 –
Appendix D – Joint Group Utilisation Plots
139
BLANK PAGE (Figures not included)
140
APPENDIX C
JOINT UTILISATION VALUE DISTRIBUTION PLOTS
141
BLANK PAGE
142
CONTENTS
Page
CONTENTS ................................................................................................. 143
1.
INTRODUCTION ...................................................................................145
2.
REFERENCES ......................................................................................145
143
BLANK PAGE 144
1. INTRODUCTION
This appendix provides the results from the global analysis conducted as part of the Stress
Redistribution Study described in Reference 1. The data presented here takes the form of
cumulative joint utilisation value distribution plots and probability density functions for each
of the severed member cases considered. Reference 1 provides details of the analysis
conducted to generate these plots along with a summary of the severed member cases
considered.
2. REFERENCES
1
Stress Redistribution in Platform Substructures Due to Primary Member Damage and its
Effect on Structural Reliability – EQE Report N° 45-20-R-01 Draft – 19th January 2001 –
Appendix B – Stress Redistribution Study
145
BLANK PAGE (Figures not included)
146
APPENDIX D
JOINT GROUP UTILISATION VALUE PLOTS
147
BLANK PAGE 148
CONTENTS
Page
CONTENTS ................................................................................................ 149 1.
INTRODUCTION................................................................................150
2.
INTERPRETATION OF PLOTS.........................................................150 3.
REFERENCES...................................................................................150 149
1. INTRODUCTION
This appendix provides the results from the local analysis conducted as part of the Stress
Redistribution Study described in Reference 1. The data presented here takes the form of
joint utilisation values for a number of joint groups for each of the severed member cases
considered. Reference 1 provides details of the analysis conducted to generate these plots
along with a summary of the severed member cases considered.
2. INTERPRETATION OF PLOTS
Detail joint group utilisation plots are provided in this appendix for the east storm load case,
for those joint groups, which were located below Level 2 in the structures. The plots detail
the utilisation values, calculated in accordance with Reference 2 for the chord and each
member that intersects with the chord to form a joint. The x-axis index should be interpreted
as follows: Index ‘1’ refers to the joint group’s chord and indices 2 plus refer to the individual
joints between the chord and the braces. For those joint groups that were considered in detail
in the stress redistribution study, the brace member that forms the joint can be determined
from the tables in Reference 3.
3. REFERENCES
1 Stress Redistribution in Platform Substructures Due to Primary Member Damage and its
Effect on Structural Reliability – EQE Report N° 45-20-R-01 Draft – 19th January 2001 –
Appendix B – Stress Redistribution Study
2 Offshore Installations: Guidance on Design, Construction and Certification, Fourth
Edition – 1990, HMSO – Appendix A21 Steel – Joint Design for Welded Tubular Steel
Structures.
3 Stress Redistribution in Platform Substructures Due to Primary Member Damage and its
Effect on Structural Reliability – EQE Report N° 45-20-R-01 Draft – 19th January 2001 –
Appendix A – Model Description.
150
BLANK PAGE (Figures not included)
151
BLANK PAGE 152
APPENDIX E
ULTIMATE STRENGTH STUDY
153
BLANK PAGE 154
CONTENTS
Page
CONTENTS ................................................................................................ 155 1. INTRODUCTION ....................................................................................159
2. ANALYSIS APPROACH ........................................................................161
2.1
2.2
2.3
2.4
2.5
2.6
GENERAL.............................................................................................................161
RIKS ANALYSIS..................................................................................................161
SEVERED MEMBERS .......................................................................................162
TWO SEVERED MEMBERS.............................................................................162
FAILURE CRITERIA ...........................................................................................162
ASSUMPTIONS AND LIMITATIONS OF ANALYSIS APPROACH ............162
3. RESULTS...............................................................................................163
3.1 UNDAMAGED AND SINGLE MEMBER FAILED ULTIMATE STRENGTH ANALYSIS ...........................................................................................................163
3.2 MULTIPLE-MEMBER FAILED ULTIMATE STRENGTH STUDY................165
4. DISCUSSIONS.......................................................................................167
4.1 UNDAMAGED ULTIMATE STRENGTH STUDIES ...................................167 4.2 SINGLE MEMBER SEVERED ULTIMATE STRENGTH STUDY..............168 4.3 MULTIPLE MEMBER SEVERED PUSHOVERS ......................................178
5. CONCLUSIONS .....................................................................................179
6. REFERENCES .......................................................................................181
List of Tables
E1
Summary of severed members
E2
Undamaged jackets ultimate strength results
E3
X-braced structure ultimate strength results
E4
Diamond braced structure ultimate strength results
E5
Inverted K-braced structure ultimate strength results
E6
K-brace structure ultimate strength results
E7
Single diagonal braced structure ultimate strength results
E8
Multiple member failed ultimate strength results
E9
X-braced jacket single severed member study
E10
Diamond braced structure single severed member study
E11
Inverted K-braced structure single severed member study
E12
K-braced structure single severed member study
E13
Single diagonal braced structure single severed member study
155
List of Figures
E1
Plot of calculate RSR for the 5 bracing configurations for both damaged and
undamaged states
E2
Plot of calculate RRF for the 5 bracing configurations for both damaged and
undamaged states
E3
Undamaged jackets ultimate strength study
E4
X-braced structure – undamaged state – displaced shape plot
E5
Diamond braced structure – undamaged state – displaced shape plot
E6
Inverted K-braced structure – undamaged state – displaced shape plot
E7
K-braced structure – undamaged state – displaced shape plot
E8
Single diagonal braced structure – undamaged state – displaced shape plot
E9
X-braced structure – pushover curves
E10
Diamond braced structure – pushover curves
E11
Inverted K-braced structure – pushover curves
E12
K-braced structure – pushover curves
E13
Single diagonal braced structure – pushover curves
E14
X-braced structure – damaged state AL1L – displaced shape plot
E15
X-braced structure – damaged state AL1U – displaced shape plot
E16
X-braced structure – damaged state AM1L – displaced shape plot
E17
X-braced structure – damaged state AM1U – displaced shape plot
E18
Diamond braced structure – damaged state AL1L – displaced shape plot
E19
Diamond braced structure – damaged state AL1U – displaced shape plot
E20
Diamond braced structure – damaged state AM1L – displaced shape plot
E21
Diamond braced structure – damaged state AM1U – displaced shape plot
E22
Inverted K-braced structure – damaged state AL1 – displaced shape plot
E23
Inverted K-braced structure – damaged state AL2 – displaced shape plot
E24
Inverted K-braced structure – damaged state AM1 – displaced shape plot
E25
Inverted K-braced structure – damaged state AM2 – displaced shape plot
E26
Inverted K-braced structure – damaged state AU1 – displaced shape plot
E27
K-braced structure – damaged state AL1 – displaced shape plot
E28
K-braced structure – damaged state AL2 – displaced shape plot
E29
K-braced structure – damaged state AM1 – displaced shape plot
E30
K-braced structure – damaged state AM2 – displaced shape plot
E31
K-braced structure – damaged state AU2 – displaced shape plot
E32
K-braced structure – damaged state AU2 – plastic strain plot
E33
Single diagonal braced structure – damaged state AL– displaced shape plot
E34
Single diagonal braced structure – damaged state AL – plastic strain plot
E35
Single diagonal braced structure – damaged state AM – displaced shape plot
156
E36
Single diagonal braced structure – damaged state AU - displaced shape plot
E37
Single diagonal braced structure – damaged state BL - displaced shape plot
E38
Single diagonal braced structure – damaged state BL – plastic strain plot
E39
Single diagonal braced structure – damaged state BM - displaced shape plot
E40
Single diagonal braced structure – damaged state BM – plastic strain plot
E41
Single Diagonal Braced Structure – Damaged State BU - Displaced Shape Plot
E42
Inverted K-Braced Structure – Multiple-Member Severed Pushover Curves
E43
Inverted K-Braced Structure – Multiple-Member Severed Displaced Shape Plot
E44
X-Braced Structure – Multiple-Member Severed Pushover Curves
E45
X-Braced Structure – Multiple-Member Severed Displaced Shape Plot
157
BLANK PAGE 158
1. INTRODUCTION
Each of the five bracing configurations, described in Reference 1 was subjected to a series
of static non-linear, pushover analyses, in both the damaged and undamaged states, for an
East storm load case. The purpose of the study was to establish the ultimate strength of the
jackets in their undamaged states and to assess the impact on the strength when the
structures contained at least one severed member. This study aimed to establish a member
criticality profile for each bracing configuration to feed into the structural reliability
assessment for each of the jacket types.
Using the results from the single member analyses and the stress re-distribution
investigations a limited study was conducted to establish the impact on the structures’
ultimate strength as a result of two members having failed. The selection process for such
members is the subject of further discussion in this appendix.
159
BLANK PAGE 160
2. ANALYSIS APPROACH
2.1
GENERAL
The model was initially pre-stressed with gravity and buoyancy loads, and a *BUCKLE
analysis was performed on the structure based on the 100 year RLS. The *BUCKLE analysis
within ABAQUS (Reference 2) provides an estimate of the buckling mode shapes for the
structure.
The output from the buckling analysis was used to introduce imperfections into the model for
the ultimate strength analysis. The imperfections consisted of multiple superimposed
buckling modes about the pre-stressed state, and applied in the form of initial imperfections to
the model in the unstressed condition. The structural response was considered to be
sufficiently linear under gravity and buoyancy loads and therefore the principle of
superimposition remained valid.
The ultimate strength analysis was then performed utilising the ‘Riks method’ within
ABAQUS. This is the subject of further discussion below.
2.2
RIKS ANALYSIS
The Riks method allows for a static analysis to be performed on a model that exhibits
instabilities due to buckling or collapse. During buckling or collapse the structure may
exhibit a negative stiffness and therefore the structure needs to release strain energy to remain
in equilibrium, and thus enable the static analysis to converge. The Riks method enables the
static equilibrium state to be determined during the structures unstable response as a result of
buckling or collapse.
Unlike conventional static analysis where displacements are determined for a given load, the
Riks method uses the load as an additional variable and solves simultaneous equations to
determine load and displacements.
The Riks method requires the definition of ‘dead loads’, Pdead, and ‘reference loads’, Pref. In
the pushover analyses dead loads are defined as the structure’s pre-stressing loads, i.e. gravity
and buoyancy loads. The reference load is defined as the RLS. It is this load that is ramped
up from zero (initial pre-stressed state) to some pre-defined value as part of the Riks analysis.
The loading during the Riks analysis is always proportional and is related to the total load,
Ptotal, applied to the structure by the following relationship:
Ptotal = Pdead + O(Pref - Pdead)
‘O’ is the ‘load proportionality factor’, LPF, and it is this value which is solved for using the
simultaneous equations to calculate the load and displacement.
For the ultimate strength analysis conducted as part of this study automatic incrementation
was used to control the analysis. However, success of the analysis is dependent upon the user
defined limits on increment size, and as a result of this a degree of fine tuning was required in
order to achieve successful results.
Termination of the analysis is defined by the user and takes the form of a user defined,
maximum value of the load proportionality factor, or a maximum displacement at a specified
degree of freedom. The value of LPFmax utilised in this study was 3.0 and a maximum
displacement of the topsides of 3.0m was defined.
161
2.3
SEVERED MEMBERS
Table E1 details those members that were severed for each of the bracing configurations for
the East storm load scenario. The member identifiers are taken from Reference 1.
The same approach to severing a member as detailed in Reference 4 was adopted for these
analyses.
Table E1 Summary of severed members
2.4
Bracing configuration
Severed members
X
AL1L, AL1U, AM1L, AM1U
Diamond
AL1L, AL1U, AM1L, AM1U
Inverted K
AL1, AL2, AM1, AM2, AU1
K
AL1, AL2, AM1, AM2, AU1
Single diagonal
AL, AM, AU, BL, BM, BU
TWO SEVERED MEMBERS
Based upon the results obtained from the single severed member study a limited number of
analyses were performed on jackets that contained two severed members to assess the impact
on the RSR and RRF. The study focussed on the inverted K braced structure and the X
braced structure. The selection of these two bracing configurations and the members severed
was as a result of the findings from the ultimate strength study conducted on the undamaged
state and the single member severed state and is the subject of further discussion in Section
4.3.
2.5
FAILURE CRITERIA
Ultimate strength was defined at the point of first buckle for brittle type failures or a
displacement of 0.7m at the topsides reference node for ductile type failures. (The distinction
between ductile and brittle type failures is consistent with that detailed in Reference 3.) The
definition of the ductile failure criteria was based upon engineering judgement, since for a
jacket that is approximately 45m high it was deemed that a lateral displacement of 0.7m of the
topsides would compromise the integrity of the conductors and impact on platform operation.
2.6
ASSUMPTIONS AND LIMITATIONS OF ANALYSIS APPROACH
Throughout the pushover analysis it is assumed that the integrity of individual joints is
maintained. (Reminder: in the damaged state it is not the joint that is severed but the member
itself.) Such an assumption has not been validated as part of this analysis, however plots of
peak equivalent plastic strain have been generated for several of the cases considered which
demonstrate the degree of plasticity present in the structure at the point where the FE analysis
terminated. However, it is should be emphasised that there is considerable uncertainty in
quantifying the response of representative tubular joints under the extreme loading cases and
hence deformations that accompany this type of analysis.
162
3. RESULTS The results from the undamaged jackets’ ultimate strength study have been reported in the
form of a ‘Reserve Strength Ration’, RSR. The RSR is defined as the ratio of ultimate
strength to design load. The design load is equivalent to the 100 year storm event load, which
is equal to the RLS. Therefore the RSR is equal to the LPF that is output from the FE runs.
The results from the damaged jacket analyses have been reported in the form of an RSR and a
‘Residual Resistance Factor’, RRF. The RRF is defined as the ratio of the damaged jacket’s
ultimate strength to that of the undamaged jacket’s ultimate strength. The RRF provides an
indication of the robustness of the jacket to damage. An RRF of 1 indicates that the severed
member is fully redundant, whereas an RRF of 0 indicates that there is no redundancy in the
structure.
3.1
UNDAMAGED AND SINGLE MEMBER FAILED ULTIMATE STRENGTH
ANALYSIS
Table E2 details the Residual Strength Ratio, RSR, for all five bracing configurations in the
undamaged state.
Table E2 Undamaged jackets ultimate strength results
Bracing Configuration
RSR
X
2.51
Diamond
2.23
Inverted K
2.07
K
2.27
Single diagonal
2.43
Table E3 to Table E7 detail the results from the ultimate strength analysis in terms of the
Reserve Strength Ration, RSR, and the Residual Resistance Factor, RRF, for all five bracing
configurations in the damaged state.
Table E3 X-braced structure ultimate strength results
Severed Member
AL1L
AL1U
AM1L
AM1U
Member Type
LC
LT
MC
MT
RSR
2.32
2.22
2.49
2.53
RRF
0.924
0.884
0.992
1.008
163
Table E4 Diamond braced structure ultimate strength results
Severed Member
AL1L
AL1U
AM1L
AM1U
Member Type
LT
LC
MT
MC
RSR
1.96
2.06
1.93
2.20
RRF
0.879
0.924
0.865
0.986
Table E5 Inverted K-braced structure ultimate strength results
Severed Member
AL1
AL2
AM1
AM2
AU1
Member
Type
LC
LT
MC
MT
UC
RSR
1.65
1.65
1.79
1.81
2.01
RRF
0.797
0.797
0.865
0.874
0.971
Table E6 K-braced structure ultimate strength results
Severed Member
AL1
AL2
AM1
AM2
AU1
Member
Type
LT
LC
MT
MC
UT
RSR
1.86
1.85
1.85
1.88
2.33
RRF
0.819
0.815
0.815
0.828
1.026
Table E7 Single diagonal braced structure ultimate strength results
Severed Member
AL
AM
AU
BL
BM
BU
Member
Type
LT
MC
UT
LC
MT
UC
RSR
1.94
2.08
2.45
2.16
2.27
2.44
RRF
0.798
0.856
1.008
0.889
0.934
1.004
Figure E1 illustrates graphically the RSRs for each bracing configuration in both the
undamaged and damaged states. The plot identifies which member was severed in terms of
whether the member was nominally in tension or compression and in which bay of the
structure the member was located as detailed in Table E3 to Table E7.
164
3.2
MULTIPLE-MEMBER FAILED ULTIMATE STRENGTH STUDY
Table E8 summarises the results from the multiple-member failed study conducted on a
higher and lower redundancy structure.
Table E8 Multiple member failed ultimate strength results
Structure
RSR
RRF
Inverted K
1.22
0.589
X
1.98
0.79
165
BLANK PAGE 166
4. DISCUSSIONS
As with the stress redistribution study conducted previously, the purpose of the ultimate
strength study was to assess the relative impact on ultimate strength as a result of damage to
structures of five different bracing configurations. This discussion focuses on the relative
behaviour of the structures as opposed to the absolute strength.
4.1
UNDAMAGED ULTIMATE STRENGTH STUDIES
From the results obtained from the undamaged ultimate strength study conducted it can be
seen that there was not a distinct difference in the ultimate strength calculated between the
higher and lower redundancy configurations. Instead some of the lower redundancy
structures exhibited higher ultimate strengths in their undamaged states than the diamond
braced structure that has been classified as a high redundancy structure. The relative
behaviour between the five different bracing configurations is the subject of discussion here.
In the undamaged state, the bracing configurations can be ranked in descending order
according to their RSR;
x X-braced
x Single diagonal braced
x K-braced
x Diamond braced
x Inverted K-braced
An initial review of the displaced shape plots of the undamaged structures for each of the
different bracing configurations, Figure E4 to Figure E8, reveal that first buckle occurred in
the lower bay compression members in all cases. A closer look at the different bracing
configurations reveals a possible explanation for the observed behaviour.
The compressive load applied to members in the structure was as a result of the jacket
structural response about the points of ‘increased restraint’. As the pushover load was applied
to the jacket from the east direction, the general global response was characterised by shear
and bending of the structure about this point. This resulted in the majority of the load being
transmitted axially through the bracing members to the legs and hence the piles along grid
line 1 of the structure. The stiffness of the structure was clearly dependent upon the bracing
configuration applied.
The point of increased restraint was the region between the piles and Level 1 in the structure
that provided a step change in stiffness. The lower bay of each of the five jackets was the
stiffest of the three bays owing to the presence of the sleeved piles, the size of the bracing
members and the end restraints placed on the conductors at their tie-in point below the mud
line. At Level 1 there was a step change in stiffness, however, the ‘step’ varied between
bracing configurations. The magnitude of this step was determined by the relative stiffness of
the middle bay.
For those bracing configurations that were able to demonstrate higher ultimate strengths, the
structure’s middle bay was able to resist bending of the jacket, thus limiting the end moments
acting on the members in the lower bay and limiting the impact on the critical buckling load
of such members. Furthermore, they also possessed a number of bracing members able to
react the compression loading thus reducing the axial load on an individual member.
Therefore a higher applied load was required to initiate buckling, and hence the ultimate
strength of the structure increased. Figure E3 illustrates the change in stiffness between the 5
bracing configurations.
167
For the X-braced structure there were 2 load paths parallel to the storm direction at each of
the joint groups on grid line 2 that reacted the compressive load applied to the structure.
Figure E4 illustrates the high stiffness of the X-braced structure thus there was very little
bending response of the structure to the applied load (magnification factor on plot is 20). The
impact was critical buckling loads were maximised and individual member axial loads were
minimised owing to the presence of multiple load path, resulting in high ultimate strength.
However, for the inverted K-braced structure there was only one load path at each joint group
on grid line 2 that reacted the compressive load induced in the structure. This, combined with
the reduced stiffness of the structure as depicted in Figure E6 had the effect of minimising the
critical buckling load and maximising the individual member axial loads, resulting in a
relatively low ultimate strength.
The single diagonal braced structure possessed the second highest ultimate strength in the
undamaged state, with failure being defined as buckling of the lower bay compression
member, located in Frame B at joint group L12B. Figure E3 illustrates the reduced structural
stiffness of the single braced structure in comparison with the X braced structure. From
Figure E8 this reduction in stiffness was observed as an increased displacement of the
structure, both in and out of plane. The impact of this was increased loading on the lower bay
compression member due to both bending and shear resulting in buckling under a reduced
applied load to that of the X braced structure.
For the K-braced there were again two 2 load paths parallel to the storm direction at each of
the joint groups on grid line 2 that reacted the compressive load applied to the structure.
However, Figure E3 illustrates that the structure’s stiffness was significantly less than that of
the X braced structure, and that of the other bracing configurations. From Figure E7 this
reduction in stiffness resulted in a much greater structural response for the K-braced structure
in comparison to the X-braced structure. The increased levels of bending and shear observed
in Figure E7 resulted in higher bending moments and axial loads in the lower bay bracing for
a given applied load compared to the X braced structure. The impact of this was observed as
a reduction in the ultimate strength of the jacket in comparison to the X-braced structure.
However the structure out performed the diamond and inverted K-braced structures owing to
the presence of multiple load paths at Level 1, to react the compressive load.
The diamond braced structure provided the minimum number of load paths parallel to the
storm direction at each of the joint groups on grid line 2. However the bracing configuration
provided multiple restraints throughout the height of the structure, thus preventing bending of
the legs. As a result the structure is much stiffer and the step change in stiffness about Level
1 is reduced. The impact of this was that the global response as seen in Figure E5 was
predominantly shear of the structure. The shear manifested itself as an axial compressive load
in the lowest compression members of Frames A and B, resulting in the critical buckling
mode being reached at a lower LPF than in the case of the X, single diagonal and K braced
structures.
4.2
SINGLE MEMBER SEVERED ULTIMATE STRENGTH STUDY
Figure E1 illustrates, graphically, the impact on RSR as a result of severing a bracing
member. From this graph it can be seen that the spread in RSR values is much greater on the
lower redundancy structures than it is on the highly redundant structures.
Figure E2 illustrates, graphically the variation in RRF as a result of a bracing member having
been severed. It can be seen that the spread in calculated RRF is much greater for the lower
redundancy type structures than for the higher redundancy type structures.
In general, severance of a lower bay tensile member had the largest impact on ultimate
strength. The reason for this is considered to be the corresponding increase in load that
occurs on the compression member in the lower bay resulting in buckling of this member
under a reduced pushover load.
168
For the K-braced structure it is evident that loss of any bracing member below Level 2 in the
structure has a profound impact on RSR, thus highlighting the sensitivity of this bracing
configuration to a severed member.
169
Table E9 to Table E13 summarise the behaviour of each bracing configuration when a single
member was severed.
Figure E9 to Figure E13 illustrate the pushover curves for each of the jacket configurations.
170
Table E9 X-braced structure single severed member study
Member
Severed
AL1L
Bay /
Nominal
Load Case
RSR
Lower
2.32
RRF
Displaced Shape
Plot /
Peak equivalent
Plastic Strain Plot
(if applicable)
0.924
Figure E14
Compression
AL1U
Lower
Middle
2.22
0.884
Figure E15
Middle
First buckle – AL1L
Increase in load through intact
diagonal for given LPF, hence
decrease in RSR
2.49
0.992
Figure E16
Compression
AM1U
First buckle – BL1L
Increase in load on intact
diagonal in lower bay of Frame
A resulting in yielding.
Consistent with stress
redistribution study.
Tension
AM1L
Comments
First buckle – AL1L.
Increase in load on intact ‘zig­
zag’ – consistent with stress
redistribution study.
2.53
1.008
Figure E17
Tension
First buckle – AL1L and BL1L.
Behaviour comparable to
undamaged state.
Increase in RSR due to
relaxation of load down the
failed member zig-zag that
incorporates lower bay
compression members that
buckle first – hence buckle
occurs at higher LPF
171
Table E10 Diamond braced structure single severed member study
Member
Severed
AL1L
Bay /
Nominal
Load Case
RSR
Lower
1.96
RRF
Displaced Shape
Plot /
Comments
Peak equivalent
Plastic Strain Plot
(if applicable)
0.879
Figure E18
Tension
First buckle – member BL2L
SRS – load relaxation on intact
lower compression member in
Frame A, i.e AL2L, slight
increase in load on member
BL2L
For given LPF load on BL1L
greater than in undamaged state
– reduced RSR
AL1U
Lower
2.06
0.924
Figure E19
Compression
First buckle – member AL2L
SRS – load relaxation on failed
zig-zag, load increase on intact
zig-zag
AL2L on intact zig-zag.
For given LPF load on AL2L
greater than in undamaged state
– reduced RSR
AM1L
Middle
1.93
0.865
Figure E20
Tension
First buckle – member AL1U
SRS – load relaxation on failed
zig-zag, increase on intact zig­
zag
AL1U on intact zig-zag
For given LPF load on AL1U
greater than in undamaged state
– reduced RSR
AM1U
Middle
2.20
0.986
Figure E21
Compression
First buckle – member BL2L
SRS – slight reduction of load
on intact zig-zag, Frame A
For given LPF load on BL2L
greater than on AL2L
172
Table E11 Inverted K-braced structure single severed member study
Member
Severed
AL1
Bay /
Nominal
Load Case
RSR
Lower
1.65
RRF
Displaced Shape
Plot /
Peak equivalent
Plastic Strain Plot
(if applicable)
0.797
Figure E22
Compression
AL2
Lower
Middle
First buckle – member BL1
SRS – relaxation of load in
Frame A lower bay intact brace,
load increase on lower bay
braces on Frames 1,2 & B
For given LPF, greater loading
on BL1 than in undamaged state
hence reduced RSR
1.65
0.797
Figure E23
Tension
AM1
Comments
First buckle – member BL1
SRS – relaxation of load in
Frame A lower bay intact brace,
load increase on lower bay
braces on Frames 1,2 & B
For given LPF, greater loading
on BL1 than in undamaged state
hence reduced RSR
1.79
0.865
Figure E24
Compression
First buckle – member BL1
SRS – impact on Frame A lower
bay members negligible, load
redistributed to lower bay on
Frame B through Frames 1 and
2
For given LPF, greater loading
on BL1 than in undamaged state
hence reduced RSR
AM2
Middle
1.81
0.874
Figure E25
Tension
First buckle – member BM1
SRS – relaxation of load on
member AM1, increased load
on BM1
For given LPF, greater loading
on BM1 than in undamaged
state hence reduced RSR
AU1
Upper
2.01
0.971
Figure E26
Compression
First buckle – members AL1
and BL1
Reduction in RSR attributed to
increased eccentricity of
topsides resulting in increased
bending about lower bay hence
reduced critical buckling load
on lower bay compression
members.
173
Table E12 K-braced structure single severed member study
Member
Severed
AL1
Bay /
Nominal
Load Case
RSR
Lower
1.86
RRF
Displaced Shape
Plot /
Comments
Peak equivalent
Plastic Strain Plot
(if applicable)
0.819
Figure E27
Tension
First buckle – member BL2
SRS – Relaxation in member
AL2, increase in load in Frames
1,2 & B.
Hence for given LPF member
BL2 under higher load than in
undamaged state.
AL2
Lower
1.85
0.815
Figure E28
Compression
First buckle – member BL2
SRS – Relaxation in member
AL2, increase in load in Frames
1,2 & B.
Hence for given LPF member
BL2 under higher load than in
undamaged state.
AM1
Middle
1.85
0.815
Figure E29
Tension
First buckle – member BM2
Increased bending of structure
about Level 1, and twisting
about vertical axis
SRS – significant increase in
load on middle bay members of
Frame B
Hence for given LPF member
BM2 under higher load than in
undamaged state.
AM2
Middle
1.88
0.828
Figure E30
Compression
First buckle – member BM2
Increased bending of structure
about Level 1, and twisting
about vertical axis
SRS – significant increase in
load on middle bay members of
Frame B
Hence for given LPF member
BM2 under higher load than in
undamaged state.
174
Member
Severed
AU1
Bay /
Nominal
Load Case
RSR
Upper
2.01
RRF
Displaced Shape
Plot /
Comments
Peak equivalent
Plastic Strain Plot
(if applicable)
1.026
Figure E32
Tension
Ductile failure – high plasticity
in legs between top of piles and
Level 1
Structural response – bending
about top of piles, and twisting
about vertical axis.
Degree of twist decreased
towards piles – where restraint
on legs increased
Localised yielding of legs A1
and B1 between piles and
Level 1.
175
Table E13 Single diagonal braced structure single severed member study
Member
Severed
AL
Bay /
Nominal
Load Case
RS
R
Lower
1.94
RRF
Displaced
Shape Plot
Comments
Peeq Plot (if
applicable)
0.798
Tension
Figure E33
Figure E34
First buckle – member BL
High degree of twisting
about vertical axis
RSR – Increase load in
Frames 1, 2 & B
Hence for given LPF
member BL under higher
load than in undamaged
state.
High degrees of plasticity in
legs local to piles and Level
1 due to reacting twist.
AM
Middle
2.08
0.856
Figure E35
Compression
First buckle – horizontal
member at Level 1 in Frame
A, L1HA
Introduction of ‘soft storey’ –
structure bends about Level 1
SRS – L1HA subjected to
significant increase in load
for a given LPF
After first buckle load
redistributed – buckle of BL
AU
Upper
2.45
1.008
Figure E36
Tension
First buckle – member BL
Twisting of structure about
vertical axis.
Redistribution of load to
Frames 1 and 2
‘Shielding’ of members BL
and AL – increase in RSR
BL
Lower
Compression
2.16
0.889
Figure E37
Ductile failure
Figure E38
High degree of twisting
about vertical axis.
High degrees of plasticity in
legs local to piles and Level
1due to reaction of twist.
176
Member
Severed
BM
Bay /
Nominal
Load Case
RS
R
Middle
2.27
RRF
Displaced
Shape Plot
Comments
Peeq Plot (if
applicable)
0.934
Tension
Figure E39
Figure E40
Ductile failure
High degree of torsion about
vertical axis
SRS – significant increase in
load acting on legs local to
Level 1.
High degrees of plasticity in
legs local to piles and Level
1due to reaction of twist.
BU
Upper
2.44
1.004
Figure E41
Compression
First buckle – member BL
Twisting of structure about
vertical axis.
Redistribution of load to
Frames 1 and 2
‘Shielding’ of members BL
and AL – increase in RSR
177
4.3
MULTIPLE MEMBER SEVERED PUSHOVERS
Based upon the results from the single severed member ultimate strength study it was decided
to limit the dual member study to the X braced structure and the inverted K-braced structure,
since these two structures yielded the two bounding RSRs in the ultimate strength study. The
purpose of limiting the scope of the study was to facilitate the identification of differences in
the response between the higher and lower redundancy structures.
4.3.1
Lower Redundancy Structure
The results from the multiple severed member pushover analysis performed on the inverted
K-braced structure demonstrated a significant reduction in RSR to yield a value of 1.22,
resulting in an RRF of 0.589. This is a significant reduction in ultimate strength when
compared to the results for member AM2 having been severed, which yielded an RSR of 1.81
and an RRF of 0.874.
From Error! Reference source not found. it can be seen that the failure type is ductile when
the two middle bay tensile members were severed on Frames A and B. From Error!
Reference source not found. it can be seen that the structural response is characterised by
bending about the middle bay, due to the introduction of a soft storey. The bending resulted
in localised plasticity about points of increased restraint in the legs namely at Level 1 where
there is a significant step change in the structure’s stiffness.
4.3.2
Highly Redundant Structure
The results from the multiple severed member pushover analysis performed on the X braced
structure provided further evidence of the robustness of this structure. As stated previously,
the two members that were severed were those that had the greatest impact on the calculated
RSR from the single severed member study, i.e. AL1L and AL1U. The calculated RSR from
the dual severed member analysis was 1.98, at which point the lower bay compression
member in Frame B buckled, yielding an RRF of 0.79. This is significantly higher than that
calculated for the lower redundancy structure.
From Error! Reference source not found. it appears that the failure type for the damage
state was ductile. However, further assessment of the structure determined that during the
riks analysis the structure did lose some capacity attributed to the buckle of the lower bay
members in Frame B as illustrated in Error! Reference source not found.. Unlike in the
single severed member studies performed to determine the stress redistribution and ultimate
strength of the X braced jacket, where the structural response was almost planar, severance of
two members introduced twisting of the structure about the vertical axis. This was as a result
of the asymmetric stiffness between Frames A and B. As a consequence of this, Frame B’s
lower bay bracing members experienced a higher load than in the undamaged case resulting in
buckling of member BL1L under a reduced LPF.
178
5. CONCLUSIONS
In the undamaged states the five bracing configurations can be ranked in descending order
according to the RSRs calculated for the East storm load case;
x X
x Single diagonal
x K
x Diamond
x Inverted K
It is considered that this ranking can be attributed to the variation in the ‘step’ change in
stiffness between the lower and middle bays. The magnitude of this step is determined by the
number of load paths available, local to Level 1, to react the resultant compressive load
induced in the structure. The more load paths available, the lower the axial compressive load
in a given member, therefore there is a rise in the calculated RSR. Furthermore, the presence
of more load paths also has the effect of reducing the bending of the structure and as such the
end moments acting on members is limited. The effect of this is to limit the reduction in the
critical buckling load of a particular member.
From the single member severed study conducted, it is evident that there are two distinct
types of behaviour. As was the case in the stress redistribution study undertaken, the X
braced and the diamond braced structures were able to accommodate member failures much
more economically than the lower redundancy structures, i.e. inverted K-braced, K-braced,
and single diagonal braced structures. This behaviour was in-line with perceived redundancy
of the five bracing configurations, and is illustrated in Figure E1 by the difference in the range
of RSRs calculated for each of the bracing configurations.
Severance of a member in either the middle or lower bays of the lower redundancy structures
introduced twisting into the structures and resulted in an increase in load on the lower
members thus initiating buckling of such members at lower values of LPF, resulting in
reduced RSRs. Furthermore, in most cases the legs at the back of the structure, i.e. gridline 1
experienced plastic strains local to the top of the piles.
Severance of an upper bay member, in the lower redundancy structures, generally resulted in
an increase in RSR. Such effects were attributed to the induced torsion in the jackets and the
impact that this has on the load distribution in the lower bay. For such damaged states the
load is distributed to the perpendicular frames as they react rotation of the legs, and thus
alleviate the load on the lower compression members in the frames parallel to the storm
direction.
The K-braced structure was found to be the least tolerant to a severed member. Regardless of
which member was severed in either the lower or middle bays, the impact was a significant
reduction in the calculated ultimate strength.
The dual member severed study further highlighted the difference between the lower and
higher redundancy structures. Severance of two members on the inverted K braced structure
had a significant impact on ultimate strength, resulting in a 40% reduction, whereas that
performed on the X braced structure resulted in a 20% reduction.
179
BLANK PAGE 180
6. REFERENCES
1 Stress Redistribution in Platform Substructures Due to Primary Member Damage and its
Effect on Structural Reliability – EQE Report N° 45-20-R-01 Draft – 19th January 2001 –
Appendix A – Model Description
2 ABAQUS 5.8 – Hibbitt, Karlsson & Sorensen, Inc.
3 ULTIGUIDE – Best Practice Guidelines for Use of Non-linear Analysis Methods in
Documentation of Ultimate Limit States for Jacket Type Offshore Structures – April 1999
4 Stress Redistribution in Platform Substructures Due to Primary Member Damage and its
Effect on Structural Reliability – EQE Report N° 45-20-R-01 Draft – 19th January 2001 –
Appendix B – Stress Redistribution Study
181
BLANK PAGE (Figures not included)
182
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Stress redistribution in platform substructures due to primary member damage and its effect on structural reliability
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