!
!
!
Faculty of Science and Technology !
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MASTER’S THESIS Study program/ Specialization: Offshore Technology Marine- and Subsea Technology
!Spring semester, 2013
Open access
Author: Ole-Erik Vestøl Endrerud
!…………………………………………
(Author’s signature) Faculty supervisor: Ljiljana Djapic Oosterkamp, PhD External supervisor: Per Nystrøm, IKM Ocean Design
Title of thesis: Parameter Study of the Effect of Boulders on Pipeline Free Span Sections
Credits (ECTS): 30 Key words: Free spanning pipeline Vortex induced vibrations Boulder supports Pipeline dynamics Fatigue lifetime
!Pages: 64
!+ enclosure: 8
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Stavanger, June 17th 2013 Date/year
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Front page for Master Thesis Faculty of Science and Technology
Decision made by the Dean October 30th 2009
x = 1TD= 100m
= 2 : 1 = 100m
= 1 : 1 = 100m
fn
L/D
↵
�
⌘
�
µ
⌫
!
!2
⇢cont
⇢corr
⇢c
⇢s
�T
�Y
✓x
x
✓y
y
✓z
z
⇠
�s
4T
Ae
C
CD
CL,max
CM
Cm
D
E
e m
es
fcn
FD
Ffriction
FI
fn
fv
k
kc
KL
KV,S
KV
kw
KC
L
le
m
ma
msubmerged
OCR
P
PE
Pi
Re
St
tcorr
tc
ts
Tw
U
Uc
Um
Uw
ux
x
uy
y
uz
z
Vr
z
e/D
0.30.3
KC < 40 � 50
KCKC
Re
Re =DU
⌘
D U ⌘
St
St =fv
D
U
fv
300Re3⇥ 105Re
0.2St
KC
KC =Um
Tw
D
Um
Tw
KC
KC =2⇡⇠
D
⇠
Vr
Vr
Vr
Vr
=U
fn
D
fn
fn
=C
L2
sEI
(m+ma
)
r1� P
PE
C L Em m
a
P
PE
Re Re
5 40Re Re40 200
300
0.2300Re 3⇥105Re
0.2St0.7
KC
x z (x� x0)2 + (z � z0)
2 =�⇠ · ekwz0
�2
KCKC > 7
Re 300 3 ⇥ 105
FIL
=1
2⇢C
D
DU |U |+ ⇢CM
AU̇ + ⇢AU̇
CD
Cm
Cm
= 1 KC
FIL
=1
2⇢C
D
DU |U |+ ⇢CM
AU̇
FD
=1
2⇢C
D
DU |U |
FI
= ⇢CM
AU̇
CM
CM
= 1 + Cm
90�
KC
FI
FD
=CM
⇡
4D2!U
m
12CD
DU2m
= ⇡2 D
Um
Tw
CM
CD
=⇡2
KC
CM
CD
CM
CD
FI,max
FD,max
=⇡2
KC
2
1u 20
KC
KCKC < 4
KC > 4KC > 7
KCKC
FL,max
=1
2⇢C
L,max
DU2m
CL,max
CL,max
KC = 10 V r = 6
(� [k]� [m]) ~W = ~0
k [k] [m]
� =1
!2
!2
~W =
8>>>>><
>>>>>:
W1
W2
W3
Wn
9>>>>>=
>>>>>;
~0 =
8>>>>><
>>>>>:
000
0
9>>>>>=
>>>>>;
! fn
(� [I]� [D]) ~W = ~0
[I]
[D] = [k]�1 [m]
~W
|� [k]� [m]| = 0
ux
uy
uz
✓x
✓y
✓z
le
Ae
[K] =EI
l3e
2
664
12 6le
�12 6le
6le
4l2e
�6le
2l2e
�12 �6le
12 �6l2e
6le
2l2e
�6l2e
4l2e
3
775
[M ] =⇢Al
e
420
2
664
156 22le
54 �13le
22le
4l2e
13le
�3l2e
54 13le
156 �22le
�13le
�3l2e
�22le
4l2e
3
775
u1 = W1 u2 = W2
W1 = 0W3 = 0
[K] =2EI
le
2 11 2
�
[M ] =⇢Al3
e
420
4 �3�3 4
�
����2EI
le
2 11 2
�� ⇢Al3
e
!2
420
4 �3�3 4
����� = 0
le
/2EI
����2� 4� 1 + 3�1 + 3� 2� 4�
���� = 0
� =⇢Al4
e
!2
840EI
����2� 4� 1 + 3�1 + 3� 2� 4�
���� = (2� 4�)2 � (1 + 3�)2 = 3� 22�+ 7�2
�1 =1
7) !1 =
s120EI
⇢Al4e
�2 = 3 ) !2 =
s2520EI
⇢Al4e
fn,i
!i
~W
Mode%1% Mode%2% Mode%3%
L/D = 93.8
Vr,IL
= 3 =) U = Vr
fn,1,ILD = 3 · 0.287Hz · 1.066m = 0.918m/s
VR,CF
= 8 =) U = Vr
fn,1,CF
D = 8 ·0.409Hz ·1.066m = 3.488m/s
KL
KV
KV
=0.88 ·G1� ⌫
KL
= 0.76 ·G · (1 + ⌫)
⌫ 0.45 0.35
G = 625 · OCRks
0.3 + 0.7e2s
p101 · �
s
OCR 1ks
es
�s
105 400MPa300MPa
D =X n
i
Ni
= 1
ni
i�i
Ni
�i
D 0.72.2 1
Lsh
> 6m
Lsh
< 6m L > 12m Lsh
< 1TD
1TD
L/D < 30
30 < L/D < 100
100 < L/D < 200
200 < L/D
� < 0.50.5 < � < 0.8
0.8 < �
� =Uc
Uc
+ Uw
Uc
Uw
� 0.8
TD 1.196 (47) m (inch)OD 1.084 (42) m (inch)ID 1.016 (40) m (inch)ts
0.034 (11/3) m (inch)tc
0.050 (2) m (inch)tcorr
0.006 (1/4) m (inch)�Y
448 MPa�T
531 MPaE 207 GPa⌫ 0.3↵ 1.17⇥ 10�5 C�1
⇢s
7850 kg/m3
⇢c
3040 kg/m3
⇢corr
900 kg/m3
⇢cont
1500 kg/m3
kc
0.25fcn
42 MPa
Soil type Clay � hardK
V
32 MPaK
L
23 MPaK
V,S
3.4 MPaSoil type Rock � boulder
KV
66 MPaK
L
45 MPaK
V,S
4 MPa
100m100m 0.5m 2100m 1m 2100m 2m 2100m 4m 2100m 6m 2100m 8m 2100m 0.5m100m 1m100m 2m 1100m 4m 1100m 6m 1100m 8m 1
100m xx = 0 x = 50 5m
ux
uy
uz
✓x
✓y
✓z
ux
uy
uz
ux
uy
uz
✓x
✓y
✓z
Tn
Tn
Tn
1951490000.983290
96m 1.192m
z =Pi
· ⇡ ·D2
4 · Ffriction
·4 · t
s
· E · ↵ ·4T
Pi
·D + (1� 2⌫)
�
z Pi
4T
Ffriction
= µ ·msubmerged
µ msubmerged
N/m
2000m 50m400m 2000m 3
1000m 2TD500m 2TD
TD x
x/L
fn
fn,IL,1 f
n,IL,2 fn,CF,1
0m 0.25 0.69 0.340.5m 0.60 (140 ) 1.51 (119 ) 0.62 (82 )1.5m 0.62 (3 ) 1.58 (5 ) 0.63 (2 )2m 0.60 (�3 ) 1.57 (�1 ) 0.62 (�2 )4m 0.62 (3 ) 1.67 (6 ) 0.64 (3 )6m 0.63 (2 ) 1.72 (3 ) 0.65 (2 )8m 0.63 (0 ) 1.71 (�1 ) 0.65 (0 )
0.5�1TD1.5
1TD
4
x = 1TD = 100m
= 2 : 1 = 100m
= 1 : 1 = 100m
x
1.5
L/D 60
x1TD
1TD
1TD
1TD
4m
L/D
L/D
84285642
1TD