EG55F2/G2 – 2010/11

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UNIVERSITY OF ABERDEEN SESSION 2010-11 Degree examination in EG55F2/G2 PIPELINE AND SOIL MECHANICS Tuesday 31 May 2011 Time 9 am – 12 noon

NOTES: (i) Candidates are permitted to use approved calculators.

(ii) Candidates are permitted to use the Course Formulae Handout, which will be made available to them.

(iii) Candidates should attempt ALL FIVE questions (iv) All questions carry 20 marks each

PLEASE NOTE THE FOLLOWING (i) You must not have in your possession any material other than that expressly

permitted in the rules appropriate to this examination. Where this is permitted, such material must not be amended, annotated or modified in any way.

(ii) You must not have in your possession any material that could be determined as

giving you an advantage in the examination. (iii) You must not attempt to communicate with any candidate during the examination,

either orally or by passing written material, or by showing material to another candidate, nor must you attempt to view another candidate’s work.

Failure to comply with the above will be regarded as cheating and may lead to disciplinary action as indicated in the Academic Quality Handbook: (www.abdn.ac.uk/registry/quality/appendix7x1.pdf) Sections 4.14 and 5.

EG55F2/G2 – 2010/11

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1. (a) Explain, briefly, the difference between Flow Theory and Deformation Theory in

the analysis of plastic deformation of engineering materials. Comment on the

suitability of these theories for the analysis of plastic deformation during installation

of subsea pipelines. [6 marks]

(b) A 16” (OD = 406.4 mm) line pipe has a wall thickness of 16 mm and it is made

from a material with Young’s modulus E = 205 GPa and Poisson’s ratio 0.5. The

uniaxial true stress (in MPa) versus plastic true strain response of the material

satisfies the relation 150300 . . A hydrostatic testing of the line pipe is

conducted by making use of blind flanges at the ends and subjecting the pipe to an

internal pressure of 15 MPa which causes plastic deformation. Determine the

circumferential and longitudinal components of the plastic strains induced in the

pipe during the hydrostatic testing. [14 marks]

2. (a) Describe, briefly, three of the limiting factors that dictate the selection of pipeline wall thickness assuming the pipeline material is known. [6 marks]

(b) A 6” nominal bore (OD = 168.3mm) X65 (SMYS = 450 MPa) carbon steel pipeline

is required to transport gas from the platform to a gas export system. The system

design pressure is 25 MPa, the water depth is 100 m and the pipeline will be at

seabed ambient conditions. The water density is 1025 kg/m3.

Determine the minimum pipeline wall thickness required for pressure containment

based on BS PD8010 thin-walled pipe requirements. [5 marks]

A 6” nominal bore X65 carbon steel spool is to be used to tie the pipeline on to a

riser base. Analysis of the pipeline indicates free-end expansion which develops a

bending moment of 50 kNm in the tie-in spool. Assuming negligible (true wall)

external axial force in the tie-in spool, calculate the von-Mises equivalent stress in

the spool using the calculated wall thickness required for pressure containment.

Comment on the design implications of the level of the equivalent stress.

[9 marks]

EG55F2/G2 – 2010/11

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3. (a) Describe, briefly, the process of reel-lay installation method. List two advantages

and disadvantages of the method. [6 marks]

(b) A 12” (OD = 304.8 mm) pipe with a wall thickness t = 12 mm, made from X70 API

grade steel, is to be installed using the reel-lay method.

(i) Neglecting any strain concentration, derive the expression for the maximum

strain in the pipe during the reeling as a function of the pipe’s outer diameter

D and the reel drum radius R. [5 marks]

(ii) Hence, determine the minimum radius of the drum that could be used for the

reeling based on DNV limiting bending strain requirement. Comment,

briefly, on the suitability of using DNV approach instead BD PD8010 to size

the drum. [9 marks]

4. (a) Explain, briefly, the difference between effective longitudinal force and true wall

force in a pipeline, and comment on the significance of each in pipeline design.

[6 marks]

(b) A 40 km long pipeline is to be constructed from X70 steel grade for use in 1500 m of

water. The pipe has an outer diameter of 406 mm and a wall thickness of 25 mm.

The installation and operating temperature are 5 oC and 100

oC, respectively, while

the internal pressure is 20 MPa. The pipe is fully filled with a fluid with density

f = 800 kg/m3. The other geometric and material parameters are:

Steel Grade X70 s = 7800 kg/m3; E = 205 GPa;

= 0.33; SMYS = 483 MPa;

= 1210-6

/oC

Axial pipe/seabed “friction” coefficient = 0.90

Seawater density w = 1028 kg/m3

Coating Thickness and density tc = 40 mm; c = 2400kg/m3

Determine

(i) the effective axial force, [4 marks]

(ii) the anchor location along the pipeline, and [5 marks]

(iii) the free-end expansion of the pipeline. [5 marks]

EG55F2/G2 – 2010/11

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5. (a) Describe, briefly, the types of subsea soil commonly defined as coarse grained and

fine grained. For the purpose of obtaining the geotechnical properties what

classification is used for each? Give a short description.

[6 marks]

(b) A pipeline is to be laid at the seabed floor (sand), at a depth of 100 m below the sea

level. The pipe has an outer diameter of 16’’ (OD = 406.4 mm), a wall thickness of

22 mm and made from a material with a density of s = 7800 kg/m3. The pipe is

fully filled with a gas with density f = 200 kg/m3.

(i) Calculate the total and effective stresses as well as the pore water pressures

at a location 0.5 m below the seabed. Take unit weight of saturated sand as

1700 kg/m3 and unit weight of water as 1024 kg/m

3. Assume that force of

the pipeline on the seabed acts over its full diameter.

[6 marks]

(ii) State the equilibrium equation that needs to be met to make a pipeline stable

in the soil. Use a sketch to show the forces identified. Describe, briefly, how

the equilibrium equation differs between steady and unsteady flow.

[4 marks]

(iii) For the case of a steady flow with a flow velocity of 1 m/s, calculate the

forces identified in (ii), indicating if the pipeline is stable. Assume the

friction coefficient between the pipeline and the soil is 0.6 while the drag

coefficient and lift coefficient are CD = 0.6 and CL = 0.8, respectively.

[4 marks]

EG55F2/G2 – 2010/11

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EG55F2/G2: PIPELINE AND SOIL MECHANICS

FORMULAE HANDOUT

1. Maximum stresses in a thick-walled pipe with end caps and subject to internal pressure Pi

and external pressure Po

22

22

22

22

; ;

io

ooiizoi

io

ioir

DD

DPDPPP

DD

DDP

2. von Mises equivalent stress, e, (in cylindrical polar coordinates)

21

222222

2

1/

zrzrrzzre

3. Equivalent plastic strain

21

2

13

2

32

2

213

2/

pppppppe

where superscript p denotes plastic, and 1, 2 and 3 are the principal strains

4. Hill’s anisotropic yield criterion

Lz

HLH

z

RH

z YSSSS

21

2

2222

2 11111

/

where L

HLHL

L

HH

L

RR

Y

YS

Y

YS

Y

YS ; ; ; YL is the yield stress in the longitudinal

direction; YH is the yield stress in the hoop direction; YR is the yield stress in the radial

direction; and YHL is the shear yield stress in the hoop-longitudinal plane.

5. Plastic stress versus strain relation (Deformation theory)

2121

33

3121

22

3221

11

e

pep

e

pep

e

pep

where superscript p denotes plastic, and 1, 2 and 3 are the principal strains

EG55F2/G2 – 2010/11

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6. Effective longitudinal force for a fully restrained pipe

iissoi

eff APTAEAt

DPF ....

2

where Ai in the internal cross-sectional area of the pipe and As is the cross-sectional area of

the pipe’s wall.

7. Upheaval buckling criterion

0LwF ,

where 2

eff

wFH

EIW

.

. is the imperfection download coefficient,

21/

EI

FL

effL is the is

the imperfection length coefficient

0

0.02

0.04

0.06

0.08

0.1

0 5 10 15 20 25 L

W

8. Uplift resistance for buried pipeline

o

rockorockrockuplift

D

HfDHWW 1..

where the uplift coefficient f = 0.7 for rock and 0.5 for sand.

9. Design factors (BS PD8010)

Hoop stress design factor, fh = 0.72

Equivalent stress design factor, fe = 0.96

EG55F2/G2 – 2010/11

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10. Resistance and material factors (DNV)

Safety Class

Low Medium High

Safety class resistance factor, sc 1.046 1.138 1.306

Strain resistance factor, 2.0 2.5 3.3

Material resistance factor, m 1.15 1.15 1.15

Material strength factor, u 0.96 0.96 0.96

11. Elastic buckling external pressure

3

21

2

oec

D

tEP

12. Plastic collapse pressure

t

D

P

Pf

P

P

P

P o

y

co

y

c

ec

c .

11

2

2

where fo is the ovality parameter, and Py is the yield external overpressure

5.0

22

11

ecy

cPP

P for perfectly circular pipe

oy

D

tYP

2

13. Burst pressure

...

tD

tYP

ob

2

3

2

14. Fully plastic bending moment

tYtDM op2

15. Collapse bending moment Mc and collapse bending strain bc

t

DMM o

pc 002401 . ;

2

15

obc

D

t

EG55F2/G2 – 2010/11

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16. Propagation buckle pressure

52

35

.

opr

D

tYP DNV

252

710

.

.

opr

D

tYP PD8010

17. Strain-based design criterion for external overpressure

1

80

c

dmsc

bc

d

P

P

.

DNV

1c

d

bc

d

P

P

PD8010

where d is the design compressive (bending and longitudinal) strain and Pd is the design

external overpressure.

18. Load-based design criterion for external overpressure

1

22

2

c

dscm

Y

dscm

c

dscm

P

P

S

S

M

M . DNV

where Pd, Md, and Sd are the design external overpressure, design bending moment, and

design effective longitudinal force respectively; SY is the yield longitudinal force.

19. Kellogs equation

32

164

G

M

G

FPP deff

where M is the bending moment, F is the tensile force, G is the mean gasket diameter, Pd is

the system design pressure, and Peff is the equivalent flange pressure.

EG55F2/G2 – 2010/11

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20. Maximum Strain in Reeled Pipeline

odrum

o

DR

D

2

21. Soil Unit Weight

Dry unit weight of soil :e

G wsd

1

. Bulk Unit weight of soil :

e

eG wsbulk

1

22. Plasticity (soil mechanics):

PLP wwI ; PL

PL

ww

wwI

;

)(%clay

IA P

where Ip is the plasticity index; IL is the liquid index; wL is the liquid limit; wP is the plastic

limit; w is the water content of the soil; and A is the activity.

23. Specific Volume of Soil

swGv 1 ;

1

1

w

sGv

where w – water content of the soil; Gs – specific gravity of the soil; w – unit weight of

water; - unit weight of the soil.

24. Morison’s equations

a. Steady flow

PDx AuCF 2

2

1 ; - drag force

PLy AuCF 2

2

1 ; - lift force

b. Unsteady flow

uVCAuuCF MPDx

2

1 ; - drag + inertia force

PLy AuCF 2

2

1 ; - lift force

where:

- density of water; Fx - horizontal force per unit length of pipeline;

Fy - vertical force per unit length of pipeline; CD, CM, CL – drag, inertia and lift

coefficients (hydrodynamic coefficients); u – velocity of water normal to the pipe axis; AP

– projected area

EG55F2/G2 – 2010/11

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25. Pipeline embedment

• Initial penetration due to submerged weight

ABqQ u '

where:

’ – submerged unit weight of the soil displaced; su - undrained shear strength;

A – cross section area of penetrated part of pipe; qu - the bearing pressure;

B – width of the pipe at the submerged level

BNqu '5.0 - for sand

ucu sNq - for clay

Nc = 5.14

• Additional penetration due to pipe motion in sand

For clay

For sand

where:

z – penetration; D – pipeline diameter; su - undrained shear strength;

Fz – vertical load per unit length of soil; a – amplitude of horizontal movement

E – work required to overcome passive soil resistance

26. Anode mass for cathodic protection

faa

cbeanode

ui

ifAM

8760

Where Ae is external surface area of the pipeline; fb is the coating breakdown factor; ic is

design current density, ia is the anode current density and ufa is the anode utilisation factor

17.054.0

max

1.1

D

a

D

s

Ds

F

D

z u

u

z

31.05.0

32

max '28.0

D

a

D

E

D

F

D

z z