the finite element analysis on the submarine pipeline under the seismic loading
TRANSCRIPT
![Page 1: The Finite Element Analysis on the Submarine Pipeline under the Seismic Loading](https://reader031.vdocuments.site/reader031/viewer/2022022410/5750aa271a28abcf0cd5c278/html5/thumbnails/1.jpg)
The Finite Element Analysis on the Submarine Pipeline under the Seismic Loading
Yifei Yan1,a, Lufeng Cheng2,b
1College of Electromechanical Engineering, China University of Petroleum , Qingdao, Shandong, 266555, China
2China petroleum Engineering and Construction Corp, Drum Tower Street 28 in Dongcheng District, Beijing,100120,China
[email protected] , [email protected]
KEYWORDS :Submarine Pipeline; Seismic Loading; Finite Element Method; Numerical Simulation
ABSTRACT. Seismic loading is one of the most important factors of submarine pipeline damage,
so the research on submarine pipeline failure mechanism is still lifeline engineering frontier topics.
According to Biot consolidation theory, considering the interaction of submarine pipelines with the
soil medium under earthquake action, the model of the seabed-pipeline interaction is established.
The influences of wall thickness, radius and cover layer thickness on submarine pipeline strain
response are studied under El Centro seismic wave based on this model. The calculating results
show that effective stress and axial strain of the submarine pipeline increases with wall thickness,
radius and cover layer thickness increasing.
INTRODUTION
In recent years, with the development of offshore oil and gas, submarine pipeline has been widely
used all over the world, which becomes an important part petroleum development engineering of
oil-gas field engineering. However, the safety problem of submarine pipeline is aroused extensive
attention at home and abroad for its prohibitive costs, complex maintenance and environmental
pollution. Locating in the joint of two seismic belts, China is one of the countries in the world that
earthquake occurs frequently. The Bohai Bay region abound in natural gas resources, but this place
is the earthquake easy-happening area. So we must consider the impact of the earthquake in the
process of laying submarine pipelines. The seismic stress calculation is an important content of
submarine pipelines design. Currently, because of the experimental equipment restriction and the
practical problem complexity[1][2][3], the research of dynamic response analysis of submarine
pipelines under seismic load is very limited[4][5][6]. According to the Biot consolidation theory, the
model of the seabed-pipeline interaction is established. The influence and variation of submarine
pipeline strain response are studied with influence factors such as wall thickness, radius and cover
layer thickness under El Centro seismic wave based on this model. The examples show that
effective stress and axial strain of the submarine pipeline increase with wall thickness and cover
layer thickness increasing.
FINITE ELEMENT DYNAMIC EQUATION AND SOLUTION
Finite element dynamic equation. According to the Biot consolidation theory[7][8], when
considering the compressibility of fluid, mass conservation equation of saturated pore fluid is as
follows:
( ) 01
=∇−∇+∂
∂+
∂∂
pKTtt
p
K
n ii
ωω γε
(1)
Advanced Materials Research Vols. 490-495 (2012) pp 2977-2981Online available since 2012/Mar/15 at www.scientific.net© (2012) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/AMR.490-495.2977
All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP,www.ttp.net. (ID: 130.194.20.173, Monash University Library, Clayton, Australia-04/12/14,08:47:28)
![Page 2: The Finite Element Analysis on the Submarine Pipeline under the Seismic Loading](https://reader031.vdocuments.site/reader031/viewer/2022022410/5750aa271a28abcf0cd5c278/html5/thumbnails/2.jpg)
Where ∇ is the Laplacian; K is the matrix of permeability of soils; iiε is the volume strain of soil
skeleton; n is the porosity factor; ωK is the bulk modulus of fluid; p is the pore pressure; ωγ
is the weight per unit.
When the relative acceleration effect between the pore fluid and the soil skeleton is ignored, and
excluding the compressibility of soil particles, the dynamic equations of the saturated sea-bed is as
follows:
)3,2,1,('
, ==++ jiiibp iiijjjij ρρδσ (2)
Where '
, jijσ is the effective stress; ijδ is Kronecker symbol; ρ is the density of soil; ib is the
acceleration of volume force; iii is the acceleration of soil skeleton.
According to the elastic dynamics theory[9], the governing equation of the submarine pipeline is:
)3,2,1,(, ==+ jiiib pippipjpij ρρσ (3)
Where jpij ,σ is the submarine pipeline internal stress; pρ is the mass density of submarine
pipeline; pib is the volume force acceleration of submarine pipeline; iii is the acceleration of
pipeline.
Finite element equation of saturated seabed. According to the Galerkin method[10], after
applying finite element discrete to the equation (1), the coupled finite element equation can be
obtained:
=
+
+
+
+
+
+
+
++
+
+
++
+
+
++
pf
∆tt
u
∆tt
f
∆tt
∆tt
)(
pfpf
∆tt
upf
∆tt
uu
∆tt
f
∆tt
∆tt
)(
pfpf
∆ttT
upf
∆tt
∆tt
f
∆tt
∆tt∆tt
R
R
P
U
K -
K K
P
U
K K
C
P
U
M
2
1
0
0
00
0
�
�
��
��
(4)
Where:
∑∫ ∆+
∆+∆+∆+∆+∆+ =m
mtt
mttm
u
ttmttm
u
tt
uu
tt
v
T
vdBDBK)(
)()()()(
∑∫ ∆+
∆+∆+∆+∆+ =m
mtt
mttm
pf
ttmm
u
tt
upf
tt
v
T
vdHIBK)(
)()()()(
∑∫ ∆+
∆+∆+∆+∆+∆+ =m
mtt
mttm
pf
ttm
pf
ttmtt
f
pfpf
tt
v
T
vHHnK
K)(
)()()()()1( 1
∑∫ ∆+
∆+∆+∆+∆+∆+ =m
mtt
mttm
pf
ttmttm
pf
tt
f
pfpf
tt
v
T
vdBBBK)(
)()()()()2( 1
γ
( )∑∫ ∆+
∆+∆+∆+∆+∆+ =m
tSt
m
q
ttmttT
mtst
pf
tt
pf
tt
mq
mq SdqHR
)(
)()()()(
( )∑∫∑∫ ∆+
∆+∆+∆+∆+
∆+
∆+∆+∆+∆+ +=m
tSt
m
q
ttmttT
mtst
u
tt
mmtt
mttmttm
u
tt
u
tt
mq
mq
v
T
SdfHvdfHR)(
)()()()(
)(
)()()(
Where U is the nodal displacement vector of soil; fP is the pore pressure vector; M is the mass
matrix of soil; C is the damping matrix of soil; D is the elastic coefficient matrix of soil; f
and q are load vectors; uB and pfB are the geometry gradient matrix of soil nodal displacement
and hole hydraulic pressure respectively; uH is the nodal displacement of soil; pfH is the
interpolation function matrix of pore pressure; I is the identity matrix.
2978 Mechatronics and Intelligent Materials II
![Page 3: The Finite Element Analysis on the Submarine Pipeline under the Seismic Loading](https://reader031.vdocuments.site/reader031/viewer/2022022410/5750aa271a28abcf0cd5c278/html5/thumbnails/3.jpg)
Numerical solution. After using the equation (4) , the numerical solution can be obtained by using
step-by-step integral scheme of the Newmark-β:
++−=
⋅
++
+++
+
+
+
+
++++
f
t)(
pfpf
∆tttT
upf
∆tt
pf
∆tt
d
u
∆tt
f
∆tt
∆tt
)(
pfpf
∆ttT
upf
upf
∆tt∆tt∆tt
uu
∆tt
PKUKR∆t
R
P
U
K K
KC aMaK
1
1
10
(5)
( )p
tt
p
tt
uup
tt
p
ttd
up
tt CaMaKMR ∆+∆+∆+∆+∆+ ++= 10 (6)
Where:
0 2
1a
tα=
∆; 1a
t
βα
=∆
; 2
1a
tα=
∆; 3
11
2a
α= − ; 4 1a
βα
= − ; 5 12
a tβα
= ∆ −
.
ANALYSES OF CALCULATION RESULTS
In order to get the influence of wall thickness, pipe radius and cover layer thickness on the strain
response of submarine pipelines under seismic load, the proposed model in this paper is used to
gain the variation of submarine pipelines strain by taking the different values of these parameters.
The model parameter values are as follows: submarine pipeline diameter is 529 mm; wall thickness
is 7mm; pipe material is 16Mn; material yield limit sσ is 343MPa; ultimate strength bσ is
510MPa;pipeline pressure is 5MPa; sea-bed thickness is 40m;seismic intensity is 9 degrees; φK =0.4,
site soil type is III. Taking ak as 12 N/mm2; the vibration period of the soil T is 0.8s.and the other
parameter values are respectively pC =1.5×106mm/ s; or =1.4 g / cm
3; n= 60%. The calculated
results are shown in Fig.1 to 4.
The influence of radius-thickness ratio on submarine pipelines strain response. The
relationship between the radius-thickness ratio and effective stress and the one between the
radius-thickness ratio and axial strain are shown in Fig.1 and Fig.2 respectively.
35 40 45 50 55 60 65 70 75 8090
95
100
105
110
115
120
125
130
135
sM
ises
(MP
a)
radius-thickness ratio
t=7mm
Figure 1. Relationship curve between radius-thickness ratio and effective stress
Advanced Materials Research Vols. 490-495 2979
![Page 4: The Finite Element Analysis on the Submarine Pipeline under the Seismic Loading](https://reader031.vdocuments.site/reader031/viewer/2022022410/5750aa271a28abcf0cd5c278/html5/thumbnails/4.jpg)
35 40 45 50 55 60 65 70 75 80
-0.210
-0.205
-0.200
-0.195
-0.190
-0.185
radius-thickness ratio
ax
ial
stra
in(%)
t=7mm
Figure 2. Relationship curve between radius-thickness ratio and axial strain
The radius-thickness ratio may affect the interaction between submarine pipeline and soil, control
the integral deformation and critical load of the pipeline to some extent. With the increase of
radius-thickness ratio (decrease of thickness), the value of Misesσ also increases when other
conditions remained constant.
The influence of cover layer thickness on submarine pipelines strain response. The relationship
between cover layer thickness and effective stress and the one between the cover layer thickness
and axial strain are shown in Fig.3 and Fig.4 respectively.
0.5 1.0 1.5 2.0 2.5 3.080
100
120
140
160
180
200
220
240
sM
ises
(MP
a)
cover layer thickness(m)
t=7mm
Figure 3. Relationship curve between cover layer thickness and effective stress
0.5 1.0 1.5 2.0 2.5 3.0-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
axia
l st
rain(%
)
cover layer thickness(m)
t=7mm
Figure 4. Relationship curve between cover layer thickness and axial strain
2980 Mechatronics and Intelligent Materials II
![Page 5: The Finite Element Analysis on the Submarine Pipeline under the Seismic Loading](https://reader031.vdocuments.site/reader031/viewer/2022022410/5750aa271a28abcf0cd5c278/html5/thumbnails/5.jpg)
As illustrated in Fig.3 and Fig.4, the influence of cover layer thickness on strain response of
submarine pipelines can not be ignored. With the increase of cover layer thickness, σMises stress and
axial strain of submarine pipelines become larger obviously. The calculating results also show that
shallow-buried submarine pipeline can improve the ability of resisting fault, which mainly because
the resisting fault ability of submarine pipeline increases with the decrease of buried depth.
Shallow- buried submarine pipeline can decrease the pressure of soil and vertical friction, which
can lighten the damage of fault movement.
CONCLUSION
According to the model of the seabed-pipeline interaction, the influence and variation of submarine
pipeline strain response are studied with influence factors such as wall thickness, radius and cover
layer thickness under El Centro seismic wave based on this model. The examples show that
effective stress and axial strain of the submarine pipeline increases with wall thickness and cover
layer thickness increasing.
REFERENCES
[1] R.Romagnoli & R.Varvelli . “An integrated seismic response analysis of offshore pipeline-sea
floor systems.” Seven International Conference on Offshore Mechanics and Arctic Engineering,
March, 1988,139-145.
[2] N.Y. Kershenbaum, S.A. Mebarkia and H.S. Choi, Behavior of marine pipelines under seismic
faults. Ocean Engineering, May,2000, 473-483.
[3] K.Matsubara & M. Hoshiya. “Soil spring constants of buried pipelines for seismic design.”
Journal of Engineering Mechanics-ASCE, January,2002, 76-83.
[4] Xu, T., B.Lauridsen and Bai, Y. “Wave-induced fatigue of multi-span pipelines.” J. Marine
Structure, December,1999, 83-106.
[5] G.W.Housner. “Bending vibration of a pipeline containing fluid.” J. Journal of Applide
Mechanics, July,1952, 205-208.
[6] B.M. Sumer, J. Fredsøe and S.Christensen. “Sinking floatation of pipelines and other objects in
liquefied soil under waves.” J. Coastal Engineering, January,1999, 58-90.
[7] Gao, F.P., Gu, X.Y., Jeng, D.S., et al. “An experimental study for wave-induced instability of
pipelines: the breakout of pipelines.” J. Applied Ocean Research, May, 2002,83-90.
[8] Datta, T.K. and Mashaly, E.A. Seismic response of buried submarine pipelines. Journal of
Energy, Resources Technology, Transactions of the ASME, 1988,110: 4, 208-218.
[9] Datta, T.K. and Mashaly, E.A. Transverse response of offshore pipelines to random ground
motion.Earthquake Engineering & Structural Dynamics, 1990,19: 2, 217-228.
[10] Kershenbaum, N.Y., Mebarkia, S.A. et al. Behavior of marine pipelines under seismic faults.
Ocean Engineering, 2000,27: 5, 473-487.
[11] Zhou, J. and Li, X. Nonlinear seismic analysis of free spanning submarine pipelines under
spatially varying earthquake ground motions. Proceedings of 18th International Offshore and
Polar Engineering Conference, 2008.
Advanced Materials Research Vols. 490-495 2981
![Page 6: The Finite Element Analysis on the Submarine Pipeline under the Seismic Loading](https://reader031.vdocuments.site/reader031/viewer/2022022410/5750aa271a28abcf0cd5c278/html5/thumbnails/6.jpg)
Mechatronics and Intelligent Materials II 10.4028/www.scientific.net/AMR.490-495 The Finite Element Analysis on the Submarine Pipeline under the Seismic Loading 10.4028/www.scientific.net/AMR.490-495.2977