!

!

!

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

!!!!!

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

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x

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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