Research Journal of Applied Sciences, Engineering and Technology 4(24): 5591-5601, 2012
ISSN: 2040-7467
© Maxwell Scientific Organization, 2012
Submitted: June 07, 2012
Accepted: June 09, 2012
Published: December 15, 2012
Fatigue Generation Mechanism in Touchdown Area of Steel Catenary Risers
in Non-Linear Hysteretic Seabed
1
1
Kosar Rezazadeh, 2Hodjat Shiri , 1Liang Zhang and 1Yong Bai
Ship Building College, Harbin Engineering University, Harbin, Heilongjiang 150001, China
2
Civil Engineering Department, Urmia University of Technology, Urmia, Iran
Abstract: The complex nature of seabed interaction with Steel Catenary Risers (SCR) in Touch Down
Zone (TDZ) and its vital impact on fatigue performance of SCRs makes serious difficulties against
proposing simplified and robust solutions for engineering design industry where the fatigue in touch down
zone is still considered as one the most challenging issues in riser design. In this study, authors have tried to
explore in deep the mechanism of fatigue generation in touchdown area with sophisticated numerical
simulations capturing the stress variation along the riser under complex load conditions in non-linear
hysteretic seabed. The results show interesting unknown stress variation trends which is believed to be
considerably useful in providing robust and simple solution for design industry.
Keywords: Fatigue, non-linear hysteretic seabed, Steel Catenary Riser (SCR), Touch Down Zone (TDZ)
embedment of the riser into the seabed and fatigue
damage generation, the area which is believed to be the
main root of the subject and needs to be further
understood.
Various non-linear models have been presented in
literature for pipeline-seabed interaction (Bridge and
Howels, 2007; Randolph and Quiggin 2009) but the
model proposed by Randolph and Quiggin (2009) is the
model simulating gradual seabed soil stiffness
degradation which in turn models the gradual riser
embedment into the seabed and trench formation due to
soil softening under cyclic loading. The study has been
conducted through numerical simulations in which the
complex non-linear hysteretic riser-seabed interaction
modeling the gradual soil stiffness degradation and soil
suction has been coupled with a full riser structural
model connected to a generic floating vessel. The
vessel is excited by a generic wave spectrum
throughout the displacement-controlled time domain
analysis and then the fluctuations of riser in touchdown
area and its impact on stress variation along the riser is
captured for detailed study. The seabed interactions and
the gradual variation of boundary conditions in floating
vessel has been coded in Fortran and linked to
ABAQUS. Post processing Excel macros have been
developed to calculate the cumulative fatigue damage
and variation of von Mises stress range.
INTRODUCTION
The complex riser-seabed interaction in touchdown
area is accepted today through ROV surveys where
trenches with several diameters depth have been
observed (Bridge and Howels, 2007). Various
researches presented in literature have tried to
investigate the effect of trench formation on fatigue
performance of SCRs, but the results show interesting
contradictions. Some authors report an increase in
fatigue damage due to trench creation (Giertsen et al.,
2004; Karunakaran et al., 2004) while others suggest
fatigue damage reduction (Clukey et al., 2007; Langner
2003; Nakhaee and Zhang 2008). Shiri and Randolph
(2010) have performed numerical simulations and
concluded that the source of contradiction is getting
back to the methodology undertaken for study. They
have proposed a study methodology letting the trench to
be gradually formed using a non-linear hysteretic
seabed interaction model. The final conclusion was
showing the increasing of peak fatigue damage for
deeper trenches. This totally different with findings of
Rezazadeh et al. (2012) where they showed that
implementing the effects of vessel slow drifts changes
the story to an unpredictable nature. Rezazadeh et al.
(2012) showed that depending on the load condition the
peak fatigue damage in touchdown area can be
increased or decreased for deeper trench depths proving
more complexity of the subject. In this study, authors
have tried to take a basic step and deeply explore the
nature of the relationship between the gradual
Global configuration of the model: The global
configuration of the numerical model which has been
constructed in ABAQUS is shown below in Fig. 1.The
Corresponding Author: Kosar Rezazadeh, Ship Building College, Harbin Engineering University, Harbin, Heilongjiang
150001, China
5591
Res. J. Appl. Sci. Eng. Technol., 4(24): 5591-5601, 2012
The riser is fixed at the anchor end in the seabed
and is attached to Spar vessel in a point which is lower
than center of gravity. The riser-seabed interaction has
been considered from an area beyond the Touchdown
Point (TDP) until the anchor point throughout the riser
lay down on the seabed. The numerical model has been
constructed in ABAQUS finite element software
considering simple beam elements for riser. The riserseabed interaction has been modeled via User Defined
Elements (UEL) with the behavior coded inside the
Fortran which has been suitably coupled with main
model.
In this example, the Spar has been perturbed by 10
regular sinusoidal cycles and the responses show a
number of features such as suction force mobilization,
gradual increasing penetration depth, and gradually
reducing mobilization of soil resistance at maximum
penetration. The seabed model parameters and the
characteristics of the SCR are presented in Table 1 and
2.
The manipulated wave scatter diagram applied in
analysis is based on typical conditions in the Gulf of
Mexico shown in Table 3.
Fig. 1: Global configuration of modeled SCR
Table 1: non-linear model parameters
Parameter
Mudline shear strength
Shear strength gradient
Power law parameter
Power law parameter
Normalized maximum stiffness
Suction ratio
Suction decay parameter
Repenetration parameter
Table 2: Riser pipe parameters
Parameter
Outer diameter, Do
Wall thickness, t
Bending stiffness
Submerged unit mass
Fatigue S-N curve
Symbol
su0
ρ
a
b
Kmax
fsuc
λsuc
λrep
Value
0.65 kPa
1.5 kPa/m
6
0.25
200
0.3
0.5
0.5
Value
0.324 m (123/4 “)
0.0205 m
4.67×107 Nm2
100 kg/m
DNV(2008), E Class:
SCF = 1.15,
= 3.0
a = 1.05×10-12 , m
floating vessel type, the overall model dimensions and
hydrocarbon field location (Gulf of Mexico) have been
selected as such to enable comparison with published
results in the literature if required.
The Mechanism of fatigue generation in TDZ: It is
believed that fatigue damage is mostly derived in
seabed trench mouth but still further explorations are
required. It is worth mentioning that in this paper, since
the main question is the fatigue derivation mechanism,
therefore the accurate estimation of the fatigue damage
itself is not a focus point. Hence for the cases that
fatigue damage has been calculated some
simplifications have been applied to facilitate the study.
As an instance, in non-linear plastic seabed since the
hierarchy of the sea states can affect themagnitude of
the ultimate cumulative damage, so the validity of
utilizing Miner’s rule for linear superposition of the
damages caused by various sea states is under question.
Shiri and Randolph (2010) showed that applying a
wave with higher significant height flatten the variation
of the von Mises stress range for the waves with less
height. This means if the biggest sea state hits to
Table 3: Manipulated wave scatter diagram for a 30 year service life in Gulf of Mexico
Sea State ID
Hs (m)
Tz (s)
N applied
Sea State ID
1
0.5
4.2
18011291
16
2
1.0
4.6
71370445
17
3
1.5
5.0
4844608
18
4
2.0
5.4
25187856
19
5
2.5
5.8
13529335
20
6
3.0
6.1
7473660
21
7
3.5
6.5
3080495
22
8
4.0
6.9
1631014
23
9
4.5
7.3
583770
24
10
5.0
7.7
363725
25
11
5.5
8.0
114700
26
12
6.0
8.4
33676
27
13
6.5
8.5
16907
28
14
7.0
8.7
10864
29
15
7.5
8.9
5421
30
5592 Hs (m)
8.0
8.5
9.0
9.5
10.0
10.5
11.0
11.5
12.0
12.5
13.0
13.5
14.0
14.5
15.0
Tz (s)
9.1
9.3
9.5
9.7
9.9
10.1
10.2
10.4
10.6
10.7
10.9
11.0
11.2
11.3
11.5
N applied
3389
3011
1822
1395
1070
1246
566
928
544
813
712
8.77
262
343
420
Res. J. Appl. Sci. Eng. Technol., 4(24): 5591-5601, 2012
8
0.000040
Fatigue
Shear far
6
0.000030
Peak fatigue location
Shear near
0.000020
Trench bottum point
2
0.000010
0
0.000000
-2
Fatigue damage
Shear Force kN
4
-0.000010
Scaled trench profile
TDP
-4
-0.000020
-370
-360
-350
-340
-330
-320
-310
-300
-290
-280
Horizontal coordinate (m)
Fig. 2: Peak fatigue position relative to trench and shear profile of near and far offsets
0.000040
7
wave 15
6
wave 10
5
Shear Force kN
0.000035
0.000030
0.000025
wave 5
4
0.000020
3
0.000015
2
0.000010
1
0.000005
0
0.000000
Fatigue damage
wave 20
-0.000005
-1
-370
-360
-350
Horizontal coordinate (m)
-340
-330
Fig. 3: Near and far offset shear profile compare with fatigure damage for various waves
the vessel first, for the rest of the sea states the von
Mises stress range will not be varied which in turn
means the application of Miner’s rule is allowed. In this
paper the described hypothesis has been undertaken
simplifying the calculation of the cumulative fatigue
damage and enabling authors to focus on subtle
mechanisms rather than the value of ultimate damage.
As apparently shown in Fig. 5 for a sample
analysis, the peak fatigue damage is interestingly
located at the point at which the shear force profiles of
near and far offsets are crossing each other. This is
exactly in agreement with basic mechanical rule, where
the bending moment is the gradient of shear force
which reaches its maximum value when the gradient
becomes zero. The bending moment itself is the main
component making the von Mises stress for riser
tubular section which in turn produce the fatigue
damage by its variation range.
Comparing the location of peak fatigue damage
with riser profile ( Fig. 2) shows that the fatigue is
5593 Res. J. Appl. Sci. Eng. Technol., 4(24): 5591-5601, 2012
120
0.000040
wave 20
0.000035
100
wave 15
0.000030
Bending Moment kN.m
80
60
Fatigue damage
0.000025
0.000020
wave 10
40
0.000015
0.000010
wave 5
20
0.000005
0
0.000000
-20
-0.000005
-370
-360
-350
-340
Horizontal coordinate (m)
-330
Fig. 4: Near and far offset bending moment profiles compared with fatigue damage for various waves
0.00004
4.5
wave 20
4
0.000035
0.00003
wave 15
3
0.000025
2.5
0.00002
2
wave 10
1.5
1
Fatigue damage
Contact envelope, kPa
3.5
0.000015
wave 5
0.00001
0.5
0.000005
0
0
-0.5
-0.00000
-1
-370
-360
-350
-340
Horizontal coordinate (m)
-330
Fig. 5: Contact envelope compared with fatigue damage for various waves
study was performed and a wide range of parameters
mostly derived in trench mouth where the TDP has
are examined. As expected, the wave characteristics,
longest travel courses.
seabed stiffness and the trench depth were found having
As will be shown in coming section, the shear
considerable impacts on fatigue performance which will
force crossing points of the near and far offsets are
be briefly reviewed in coming sections.
gradually moved toward the vessel end by increasing
the number of load cycles but then stabilized for higher
Influence of sea state characteristics: The sea states
number of cycles and it is due to stabilization of trench
No. 5, 10, 15 and 20 were selected and the initial
profile, a fact that will be used for some evaluations
analysis was repeated under selected loads. For easier
later in this study.
comparison of the results, only the near and far offset
This starting analysis encouraged authors to deeply
profiles at cycle 20 (end of the analyses) where plotted
explore the parameters affecting the shear force,
against the fatigue damage profiles ( Fig. 3, 4 and 5). As
bending moment, riser and contact profile etc., in the
seen, the wave characteristics is directly affecting the
proximity of trench mouth over the various
profile with a regular trend.
representative load cycles. Comprehensive parametric
5594 Res. J. Appl. Sci. Eng. Technol., 4(24): 5591-5601, 2012
7
0.000025
Far offset shear
Su0 = 1.0 kPa
5
0.000020
Su0 = 1.5 kPa
4
0.000015
3
0.000010
2
1
0.000005
Fatigue damage
6
Shear force kN
Fatigue
Near offset shear
Su0 = 0.65 kPa
0
0.000000
-1
-2
-0.000005
-370
-360
-350
-340
-330
Horizontal coordinate (m)
Fig. 5: Near and offset shear profiles compared with fatigue damage for different seabed stiffness
0.000025
120
Near offset bending Fatigue
0.000020
Su0 = 1.5 kPa
80
0.000015
Su0 = 1.0 kPa
60
Fatigue damage
Bending Moment, kN.m
100
Far offset bending
0.000010
40
Su0 = 0.65 kPa
20
0.000005
0.000000
0
-20
-0.000005
-370
-360
-350
-340
-330
Horizontal coordinate (m)
Fig. 7: Near and offset bending moment profile comared with fatigure damage for various seabed stiffness
The contact envelope shown in Fig. 5 is in quite
For all of the sea states the peak fatigue damage is
agreement with results above. An important point is that
about the location at which the shear profile of far and
the TDP location is gradually moved towards the vessel
near offsets are crossing. It is also interestingly seen
end by increasing the wave height. It means, the trench
that the variation of the peak shear force in near and far
mouth is still the most indicative area in which the
offsets are following opposite trends, but the average
fatigue damage is derived, this is in absolute correlation
shear in initial position is gradually changing parallel to
with Fig. 2 where the peak fatigue position is shown to
fatigue damage variation. This means though the near
be somewhere between the TDP and trench bottom
and far offset profiles are varying in relatively irregular
point.
scheme but the initial average can still be considered as
It is accepted that the fatigue damage is increased
a reference index for fatigue damage estimation which
for seabed with higher stiffness. This has been
will be further discussed in later sections. Illustration of
examined here to explore the effect of stiffness
the bending moment variation in far and near vessel
variation on fatigue derivation mechanism for seabed
offset over load cycles relative to fatigue damage in
with stiffness in range of 0.65 to 1.5 kPa for undrained
Fig. 4 shows logic correlation with shear force profiles
shear strength. As illustrated in Fig. 6, the peak values
as explained before in the current section.
5595 Res. J. Appl. Sci. Eng. Technol., 4(24): 5591-5601, 2012
of near and far offset shear forces are increased for
stiffer seabed soil and this is same for fatigue damage
itself. This in turn explains the main reason for such
ascending trend. The contact pressure is increased for
higher seabed stiffness which causes the increasing of
shear force as seen above. This makes inverse change in
bending moment particularly for near offset (Fig. 7) and
the results is wider clearance between far and near
bending moment profiles which means higher von
Mises variation over load cycles and higher fatigue
damage accordingly.
Influence of trench depth: ROV surveys proves trench
formation beneath the riser with couple of times of riser
diameter (Bridge and Howells, 2007). This has been
examined hear using extreme soil model parameters to
make a trench in initial stages of fatigue analysis. Two
trench depths have been examined here, 3D and 5D and
the results are shown in Fig. 8 to 10. It is interestingly
seen that insertion of deep trenches stabilize the
variation of shear force and bending moment profiles
keeping the peak fatigue position still at the point that
near and far shear offsets are crossing. For the cases
with presence of deep trenches most serious variations
occur in near offset profiles and this is getting back to
the high contact pressure of the riser with seabed in this
course. As a common trend in all of these analysis the
peak fatigue point is moved towards the vessel for
0.000035
10
Fatigue
8
Far offset shear
5D Trench
0.000030
Shear force kN
3D Trench
4
0.000020
2
0.000015
0
0.000010
-2
Fatigue damage
0.000025
6
0.000005
Near offset shear
0.000000
-4
-400
-380
-360
-340
-320
-300
Horizontal coordinate(m)
-280
Fig. 8: Near and for offset profiled compared with fatigue damage for various trench depths
0.000035
140
Fatigue
120
Far offset shear
0.000030
0.000025
5D Trench
80
0.000020
3D Trench
60
40
0.000015
20
0.000010
Fatigue damage
Bending Moment kN.m
100
0
0.000005
-20
Near offset shear
-40
-400
-380
-360
-340
-320
-300
Horizontal coordinate (m)
0.000000
-280
Fig. 9: Near and far offset bending moment profiles compared with fatigue damage for various trench depths
5596 Res. J. Appl. Sci. Eng. Technol., 4(24): 5591-5601, 2012
0.000035
8
Far offset shear
0.000030
5D Trench
0.000025
4
0.000020
2
0.000015
3D Trench
0
Fatigue damage
Contact pressure envelope kPa
Fatigue
6
0.000010
-2
0.000005
Near offset shear
-4
0.000000
-400
-380
-360
-340
-320
Horizontal coordinate(m)
-300
-280
Fig. 10: Contact envelope compared with fatigue damage for various trench depths
deeper trenches, stiffer seabed soil and more severe sea
states. It is worth reminding hear that this for the cases
having no slow drift and only the wave action is
implemented.
Figure 10shows contact pressure envelope in which
by increasing the trench depth, the TDP moves towards
the vessel end whilst the trench surface point in anchor
side dose not considerably changes. Since the nature of
fatigue is governed by changing in stress profiles, the
fatigue damage is derived in trench mouth where we
have the maximum variations.
Rough estimation of fatigue damage on non-linear
seabed without fatigue analysis: In a standard fatigue
calculation, for an operating life that incorporates many
millions of cycles of various stress ranges, the
accumulated fatigue damage can be calculated using a
linear cumulative damage, according to the well-known
Miner’s rule. The fatigue analysis itself is considered
as a time consuming process with extensive number of
analysis for various load conditions. In the early stages
of a project, designers usually wish to have a rough
estimation of riser fatigue life in TDZ as a red line of
riser projects based on seabed soil characteristics,
because, the seabed stiffness governs the bed response
to riser through contact pressure, which in turn makes
the shear force distribution. The shear force itself is the
gradient of bending moment, the key parameter to
calculate von Mises stress range which in turn produce
the fatigue damage and fatigue life accordingly. Since
the mechanism of fatigue derivation in TDZ was
relatively explored in the previous section, we are going
to propose an approximation methodology enabling a
rough estimation of peak fatigue damage of the riser in
TDP on a non-linear hysteretic seabed, which can be
quite valuable for designers in early stages of projects.
As described by Barltrop et al. (1991) a standard
form of S-N curves for marine structures to be used for
fatigue calculations is:
N = a .∆σ f
−m
(1)
where,
N = Is the number of cycles to failure
a = Is an empirical coefficient
∆σ f = Is the factored stress variation range in MPa
M = Is the inverse slope of the S-N curve
For tubular elements as pipelines under bending
moments, stress range variation is calculated in terms of
von Mises stress. For SCRs the maximum von Mises
stress can be written as follows:
σ
f − Max
=
H
M TDP . D
+
As
2I
(2)
where,
H
=
As =
D
=
I
=
MTDP =
Is tension force in riser
Is riser section area
Is riser diameter
Is section moment of inertia
Is bending moment in TDP
The fatigue damage is calculated using the von
Mises stress range ∆σ f within a load cycle, i.e., a
cycle of vessel perturbation. Ignoring the minor
changes in horizontal force in the Touchdown Zone
5597 Res. J. Appl. Sci. Eng. Technol., 4(24): 5591-5601, 2012
(TDZ) due to relocation of the touchdown point,
∆σ f
can be approximated by the following relation:
∆σ
f − Max
≈
∆M
TDP
.D
2I
(3)
This equation can be simplified in terms of bending
gradient, i.e., the product of average shear force and the
TDP relocation, as:
∆σ
f − Max
≈
V TDP
− ave
.∆ x TDP . D
2I
(4)
Fig. 6: Schematic view of vessel relocation and curve
variation
where,
∆xTDP =is the maximum TDP relocation under a
si = zi
vessel perturbation cycle
V = is the initial/static maximum shear force in the
sin θ i
1 − cos θ i
(5)
max
TDZ
ds i =
To avoid complex finite element analysis we would
need to propose closed form solutions for quick
calculation of the main parameters defined in equation
above. This can be done by combination of classical
catenary equations for estimation of TDP relocation and
an efficient boundary layer method for rough
calculation of average shear force in TDP.
TDP Relocation: Every change in vessel position due
to load cycles applied by sea states will cause cyclic
relocation of the touchdown point, which will in turn
affect the SCR profile and stress distribution at the
seabed. In a 2-Dimensional (2D) planar system, the
vessel can have vertical (heave) and horizontal (surge)
motion and the vessel rotation (pitch) can be converted
into equivalent vertical and horizontal displacements taking into account the position of the attachment point
of the riser, relative to the centre of gravity of the
vessel. Figure 11 shows a schematic configuration of
the SCR as the vessel moves from its initial position
(denoted by subscript i) to a new relocated position
(denoted by subscript r) under environmental loading.
The positive and negative sign of the heave and surge
offsets (a, b) are determined based on the designated
coordinate system. The catenary length of the SCR
hanging part, the horizontal distance of the TDP from
vessel and the distance of the vessel from the seabed are
taken to be always positive.
According to traditional catenary equations the
horizontal offset and the arc length in initial position
are the functions of depth and hang off angle, so the
TDP relocation can be expressed based on changes of
these 2 parameters:
si
zi
dz i −
dθ i
zi
1 − cos θ i
x TDPi = z i
dx TDPi =
arcsin h (tan θ i ) cos θ i
1 − cos θ i
x TDPi
z − x TDPi tan θ i
dz i + i
dθ i
zi
1 − cos θ i
(6)
(7)
(8)
The change in hang-off angle can be written as
below using catenary equations:
∆θ = θ r − θ i =
1 − cos θ i
2 z i − x TDPi tan θ i
⎛
x
− s i ⎞ (9)
⎜⎜ b − TDPi
a ⎟⎟
z
i
⎝
⎠
substituting the change in vessel vertical and horizontal
position, the TDP relocation can be written as below:
⎛s
⎞
xTDPi− si ⎞ ⎛
zi
⎟⎟a + ⎜⎜
⎟⎟b
∆xTDP = sr − si = ⎜⎜ i +
⎝ zi 2zi − xTDPitanθi ⎠ ⎝ 2zi − xTDPitanθi ⎠
(10)
TDZ peak shear force in initial configuration: Thus
far, a range of different boundary layer methodologies
have been to predict the analytical riser-seabed
interaction overcoming the discontinuity of shear force
and bending moment along the riser in the touchdown
area
(Palmer et al., 1974; Pesce et al., 1998; Croll,
2000; Lenci and Callegari, 2005). Such models are
aimed to precisely evaluate SCR curvature in the
touchdown zone, and also to ensure continuity of
displacement gradient and shear force. As an example
5598 Res. J. Appl. Sci. Eng. Technol., 4(24): 5591-5601, 2012
of these methods, the model presented by Pesce et al.
(1998) is selected and used in this work to find the
analytical stress distribution in touchdown area. They
applied a standard boundary layer technique to
construct local consistent analytical solutions for the
static/dynamic curvature problems, with the aim of
smooth matching of the corresponding ‘outer’ ideal
cable solution. A non-dimensional soil rigidity
parameter is defined as:
K = k λ 4 / EI = k λ 2 / H = kEI / H
2
(11)
where,
݇=
Is the soil rigidity per unit area
E=
Is the SCR Young’s Modulus
I=
Is the SCR second moment of inertia
‫=ܪ‬
Is the horizontal tension force at the TDP
ߣ is a flexural length parameter that provides the
boundary layer length scale, with a significant role in
local solution. Its value is also interpreted as the
distance between the actual and ideal cable TDP - given
by:
EI
H
λ =
(12)
Pesce et al. (1998) gives the following equations
for the shear force distribution in the TDZ:
V =
⎞⎫
⎞
⎛ K 0.25
⎞ ⎧ ⎛ K 0.25
⎛ K 0.25
ms gλ .K 0.25
exp ⎜⎜
(ξ − ξ f ) ⎟⎟ × ⎨cos ⎜⎜
(ξ − ξ f ) ⎟⎟ − sin ⎜⎜
(ξ − ξ f ) ⎟⎟ ⎬
2 + K 0.25
⎠⎭
⎠
⎝ 2
⎠ ⎩ ⎝ 2
⎝ 2
(13)
if ξ < ξ
f
or
m g λ . K 0 .25
V = s
exp( − (ξ − ξ f ))
2 + K 0 .25
if ξ ≥ ξ
(14)
f
f
=
1
2 + K
0 . 25
⎛ 1
− K
⎜
0 . 25
⎝ K
0 . 25
⎞
⎟
⎠
X
(15)
v max − in
m s g λ .K
2 + K
=
0 . 25
(16)
0 . 25
λ
2 + K
0 . 25
⎛ 1
⎜ 0 . 25 − K
⎝ K
0 . 25
⎞
⎟
⎠
(17)
Examination of proposed method: The vessel has
been exited by one cycle of sea state No. 20 on a nonlinear seabed with undrained shear strength of 0.65 kPa
at mudline and a gradient of 1.5 kPa per meter in depth.
Figure 12 shows the shear force distribution for far and
near offsets of the vessel comparing with vessel initial
configuration, the hang-off angle and water depth is as
per the configuration illustrated in Fig 1. The
magnitude of TDP relocation (XTDP) for Wave No.20
based on the Equation 10 extracted from traditional
catenary equations in last section is about 6.2 m. To
calculate the maximum shear force by boundary layer
method the linear seabed stiffness is required; for the
riser not deeply penetrated into the seabed this value
can be roughly taken as about ten times of undrained
shear strength in mudline which is 0.65 kPa in this
analysis, then the seabed stiffnes, k will be about 5.2
kPa. Using the boundary layer equation given before
the magnitude of parameter K will equals to 1.4, so the
maximum shear force for initial configuration can be
calculated as below (Eq.16):
− in
=
100 × 9 . 81 × 10 . 59 × (1 . 4 ) 0 . 25
= 4 . 52 kN
1000 × ( 2 + (1 . 4 ) 0 . 25 )
The calculated value is almost equal to the peak
shear force value obtained from finite element analysis
shown in Fig, 12.
Using the Eq. 5 the von Mises stress range can be
calculated as below:
∆σ
and ξ = ξ f is the non-dimensional form of actual TDP
=
− in
As shown before in this paper in parametric study
of the effect of load cycles and sea state characteristics
on shear force distribution, the peak shear force in TDZ
for initial vessel configuration is gradually varied for
cyclic loading on non-linear seabed. These effects shall
be implemented on analytical estimation of peak shear
force, but before that we need to examine the accuracy
of the proposed methodology for a given configuration.
V max
where, msg is the weight of the riser unit length, ξf is
the ideal position of the TDP, defined as:
ξ
V max
f − Max
≈
4 . 52 × 6 . 2 × 0 . 324
1000 × 2 × 0 . 000226
= 20 . 1 MPa
as shown in Fig. 13 the peak magnitude of von Mises
variation is about 18 MPa. This means the closed form
solution has an accuracy about 90% which is quit
interesting. In another word, the fatigue life can be
estimated by analytical solution without performing
5599 position (x/ λ ).
The peak value of shear force and its distance for
ideal TDP can be obtained by differentiation of Eq. (13)
and (14) which occurs, as expected, at ξ = ξ f :
Res. J. Appl. Sci. Eng. Technol., 4(24): 5591-5601, 2012
cycles. Comprehensive parametric study was performed
and a wide range of parameters are examined. As
expected, the wave characteristics, seabed stiffness and
the trench depth were found having considerable
impacts on fatigue performance.
Be side that an approximation methodology was
proposed to estimation of peak fatigue damage of the
riser in TDP on a non-linear hysteretic seabed, which
can be quite valuable for designers in early stages of
projects. The fatigue life can be estimated by analytical
solution without performing extensive fatigue analysis
with a tolerance of about 10% which can be very
appealing for design engineers.
6
Initial peak
Shear force, kN
5
4
Far offset
3
Near offset
2
1
Initial
0
-1
-400-390-380-370-360-350-340-330-320-310-300-290-280
Horizontal coordinate (m)
Voin Mises, MPa
Fig. 12: Initial, near and far offset shear profiles
30
20
10
0
-10
-20
-30
-40
-50
-60
REFERENCES
Peak von Mises Range
Von Mises Range
Max von Mises
Min von Mises
-400-390-380-370-360-350-340-330-320-310-300-290-280
Horizontal coordinate (m)
Fig. 7: Von Mises stress envelope and variation range
extensive fatigue analysis with a tolerance of about
10% which can be very appealing for design engineers.
Now it is time to implement the influence of
number of wave cycles as the parameter gradually
vitiating the shear force distribution along the riser in
TDZ. Combining the curve fits proposed before in
parametric study the Equation 16 can be written as
below:
V max − var = V max − in (
1
) 0 .08
n c ycle
(18)
This equation implements the invers influence of
number of wave cycles on peak shear force in initial
configuration.
CONCLUSION
The mechanism of fatigue generation in TDZ was
studied through use of the hysteretic non-linear seabed.
The nature of the relationship between the gradual
embedment of the riser into the seabed and fatigue
damage generation was investigated and the parameters
affecting the shear force, bending moment, riser and
contact profile was deeply explored in the proximity of
trench mouth over the various representative load
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