ICSE-6 2012, Paris

Subsea Pipeline Stability Design

Development of a Novel 2D Pipe-Soil-Fluid Interaction Model

Terry J. Griffiths, Mengmeng XU, Wenwen SHEN, Marvin RAMSAWMY, Amar SHAH

J P Kenny

Perth, Australia

ICSE-6 2012, Paris

ICSE-6 2012, Paris

Background – status quo

With… present code and design models:

• ‘Coulomb’ friction pipe-soil model:

– Ignores passive resistance

– Ignores fluid effects on soil

• Verley passive resistance pipe-soil model:

– Ignores fluid effects

– e.g. scour

– e.g. piping

– e.g. liquefaction

Fx

x

Fx = m.Rz

Fx

x

Fx = m.Rz

ICSE-6 2012, Paris

Background – the problem

Stable pipelines on a mobile seabed?

• Sand unstable

• Pipe embeds

• Pipe stable

The problem?

“…it must follow that the seabed must become grossly unstable long before the

extreme design conditions. The traditional model is irrelevant: it makes no sense

to consider the stability of a stationary pipeline on a stationary seabed…”

A. Palmer (1996)

(Image courtesy Li & Cheng 2001)

ICSE-6 2012, Paris

We need a model which can bridge the gap between:

The (too simple) hysteresis friction models and

The (too expensive) continuum FEA / CFD models

JPK PSF Model

CO

MP

LE

XIT

Y

ACCURACY

?

Pipe-Soil-Fluid Interaction (PSF) Model

Fx

x

Fx =

m.Rz

ICSE-6 2012, Paris

Pipe-Soil-Fluid Interaction

• Pipe-Soil Interaction

– Vertical Reaction Force

– Soil Resistance

– Soil deformation due to pipe movement

• Pipe-Fluid Interaction

– Pipeline hydrodynamics

• Soil-Fluid Interaction

– Suspended sediment transport

What is the PSF Model?

Pipe Fluid

Soil

PF

PS FS PSF

Pipe Fluid

Soil

Rigid Pipeline on Sea Floor

ICSE-6 2012, Paris

Seabed

• Set of nodes at user defined, symmetric spacing, either side of the pipe

• Node parameters:

– Seabed elevation

– Suspended sediment concentration

Pipe

• Set of nodes (up/dn) with the same spacing as the seabed nodes

The PSF Model – Pipe/Soil P F

S

0

0.2

0.4

0.6

0.8

1

1.2

1.4

-3 -2 -1 0 1 2 3

Sbed

upPnod

dnPnod

ICSE-6 2012, Paris

• RULE 1: Conservation of soil

• RULE 2: Soil can’t exist inside pipe

The PSF Model – Pipe/Soil Step 2 Update soil profile to account for pipe motion

P F

S

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

-1.5 -1 -0.5 0 0.5 1 1.5

Ve

rtic

al P

osi

tio

n /

Pip

e D

iam

Lateral Position / Pipe Diam

Old Pipe Position

New Pipe Upper Nodes

New Pipe Lower Nodes

Old Seabed

Seabed Post Sweep

Swept area

ICSE-6 2012, Paris

• RULE 3: Soil cannot exceed its internal angle of repose

– “Slumps” down until the soil complies with this requirement

– Conservation of soil volume

The PSF Model – Pipe/Soil Step 3 Account for slope failure (Slumping)

P F

S

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

-1.5 -1 -0.5 0 0.5 1 1.5

Ve

rtic

al P

osi

tio

n /

Pip

e D

iam

Lateral Position / Pipe Diam

Old Pipe Position

New Pipe Position

Plough Seabed

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

Ve

rtic

al P

osi

tio

n /

Pip

e D

iam

Lateral Position / Pipe Diam

Old Pipe Position

New Pipe Position

Plough Seabed

Slumped Seabed

ICSE-6 2012, Paris

Algorithmic model

• Representation of seabed shear stress as local velocity

• Parametric based on CFD results

PSF Model: Sediment Transport P F

S

ICSE-6 2012, Paris

CFD by UWA CEED Students (Mengmeng Xu, Wenwen Shen)

• Parametric

• 2D initially

• Over 100 cases

– Geometries

– Wave and Currents

PSF Model: Sediment Transport P F

S

ICSE-6 2012, Paris

Study scaling factors

• Vary steady current Uc (up to 1.5m/s)

• Vary pipe diam. D (0.2m to 1.2m)

• Unscaled

results:

PSF Model: Sediment Transport P F

S

-1.5

-1

-0.5

0

0.5

1

1.5

2

-40 -30 -20 -10 0 10 20 30 40

Loca

l Ve

loci

ty (m

/s)

Lateral Position (m)

1

2

3

79

81

83

85

ICSE-6 2012, Paris

Study scaling factors

• Vary steady current Uc & Pipe Diam D (pipe on-bottom)

• Scale results by:

– Uc

– D

PSF Model: Sediment Transport P F

S

-1.5

-1

-0.5

0

0.5

1

1.5

-10 -5 0 5 10 15 20

Loca

l Ve

loci

ty /

Re

fere

nce

Ve

loci

ty

Lateral Position / Pipe Diam

1

2

3

79

81

83

85

ICSE-6 2012, Paris

Model Algorithm Equation:

• Vary Uw, T, D

• Scaled results:

PSF Model: Sediment Transport P F

S

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Soil

Pipe x

Case = 2

-1.5

-1

-0.5

0

0.5

1

1.5

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Compare at a given time

CaseCFD

CaseERR

TOTerr

CaseMOD

Pipe On-Bottom

ICSE-6 2012, Paris

• RED pipe =

– PSF Model but with Sediment Transport switched off

– Equivalent to & calibrated against Verley Model

• GREEN pipe =

– PSF model, with Sed. Trans. (looks more like reality?)

PSF Model: Random Wave Series P F

S

ICSE-6 2012, Paris

Thank you

Acknowledgements

Any Questions?

ICSE-6 2012, Paris

• The pipe acts as the moving reference frame for the soil nodes

• Soil nodes shift with the pipe in the horizontal axis

• Allows for a fine node mesh under the pipe and a coarse mesh for the

seabed extremities

The PSF Model – Pipe/Soil Step 1 Interpolate new profile from old profile

P F

S

ICSE-6 2012, Paris

Options:

• Iteratively find equilibrium pipe position at each timestep

• Fix horizontal, vertical or both axes for prescribed displacement

Pipe-Soil-Fluid Interaction Model Flowchart

No

Calculate new pipe based on:

• Hydrodynamic loads

• Soil reaction loads

• Accounting for embedment, trench

profile, and pipe velocity

Wave /

current

velocity

timeseries

Previous time

step / Initial

Condition

Estimate new pipe

acceleration,

velocity and

position based on

loads

Interpolate

new soil

profile from

old profile

Update new

soil profile to

account for

pipe motion

(sweep, suck, slump)

Update

new soil

profile to

account for

scour

Converged? Next time step

Yes

ICSE-6 2012, Paris

Soil Reaction Forces:

• Vertical force based on RP-F109

• Embedment vs penetration

• Contact angle

The PSF Model – Pipe/Soil P F

S

Em

be

dm

en

t (u

se

d in

PS

F)

Pe

ne

tra

tion

(u

se

d in

Ve

rle

y, F

10

9)

Contact angle (L&R)

ICSE-6 2012, Paris

Pipe-Soil Reaction Forces: Benchmark Against Published Model

• Pz vs Py graph

• Imposed lateral displacement

• Compare to Verley (Brennodden et al 1989)

The PSF Model – Pipe/Soil P F

S

-0.15

-0.13

-0.11

-0.09

-0.07

-0.05

-0.03

-0.01

0.01

-0.60 -0.40 -0.20 0.00 0.20 0.40 0.60

Pz vs Py (4 cycles)

NewPz

ICSE-6 2012, Paris

Flow Flow separation

High

pressure

Low

pressure

A typical scour process below a pipeline (Cheng et al.2009)

Water particles

PSF Model: Scour Mechanisms P F

S

• Onset of piping based on F109

• (drag force approximate to dp across soil)

(Diagram courtesy Shen 2011)

ICSE-6 2012, Paris

Study scaling factors

• Vary Zp & Zs

• Unscaled results:

(a.Zp^2+b.Zp+c).(d.Zs^2+e.Zs+f)

PSF Model: Sediment Transport P F

S

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

-10 -5 0 5 10 15 20

0h 2

28 29

30 35

37 38

39 48

50 51

75 87

89 91

93 95

-2

-1.5

-1

-0.5

0

0.5

1

1.5

-2 -1.5 -1 -0.5 0

Zso

il (m

)

Zpipe (m)

Zsoil (m)

ICSE-6 2012, Paris

Study scaling factors

• Vary Uw, T, D

• Unscaled results:

PSF Model: Sediment Transport P F

S

-2

-1

0

1

2

3

-10 -5 0 5 10

Unscaled axes 994586678097988284

ICSE-6 2012, Paris

Study scaling factors

• Vary Uw, T, D

• Scaled results:

PSF Model: Sediment Transport P F

S

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

-1 -0.5 0 0.5 1

x axis scaled by D*KC, y axis scaled by Uw.(g.T^2/L)^0.59945866780979882

ICSE-6 2012, Paris

Model Algorithm Equation:

• Vary Uw, T, D

• Scaled results:

PSF Model: Sediment Transport P F

S

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Soil

Pipe x

Case = 35

-1.5

-1

-0.5

0

0.5

1

1.5

2

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Compare at a given time

CaseCFD

CaseERR

TOTerr

CaseMOD

0.25D Trench

ICSE-6 2012, Paris

Model Algorithm Equation:

• Vary Uw, T, D

• Scaled results:

PSF Model: Sediment Transport P F

S

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Soil

Pipe x

Case = 48

-1.5

-1

-0.5

0

0.5

1

1.5

2

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Compare at a given time

CaseCFD

CaseERR

TOTerr

CaseMOD

0.5D Trench

ICSE-6 2012, Paris

• WAVE CASE

PSF Model: Sediment Transport P F

S

Series1

Series14

Series27

Series40

Series53

Series66

Series79

Series92

-2.6-2.4-2.2-2-1.8-1.6-1.4-1.2-1-0.8-0.6-0.4-0.200.20.40.60.811.21.41.61.822.22.42.6

1 14

27

40

53

66

79

92

10

5

11

8

13

1

14

4

15

7

17

0

18

3

19

6

20

9

22

2

23

5

24

8

26

1

27

4

28

7

30

0

31

3

32

6

33

9

35

2

36

5

37

8

39

1

40

4

41

7

43

0

44

3

45

6

46

9

48

2

49

5

CaseCFD (m/s)

Series1

Series13

Series25

Series37

Series49

Series61

Series73

Series85

Series97

-2.8-2.6-2.4-2.2-2-1.8-1.6-1.4-1.2-1-0.8-0.6-0.4-0.200.20.40.60.811.21.41.61.822.22.42.62.8

1 12

23

34

45

56

67

78

89

10

0

11

1

12

2

13

3

14

4

15

5

16

6

17

7

18

8

19

9

21

0

22

1

23

2

24

3

25

4

26

5

27

6

28

7

29

8

30

9

32

0

33

1

34

2

35

3

36

4

37

5

38

6

39

7

40

8

41

9

43

0

44

1

45

2

46

3

47

4

48

5

49

6

CaseMOD (m/s)

Upstream Downstream

Wave P

hase

ICSE-6 2012, Paris

Model Algorithm Equation:

• Parameter = F(Geom) * F(Flow)

• F(Geom) = (l*Zp^2 + m*Zp+ n) * (o*Zs^2 + p*Zs+ q) * (r*Lb^2 + s*Lb + t)

* (u*Zb^2 + v*Zb + w)

• F(Flow) = (a*Uc + b + (c*Uw +d) * (e + f*(g*T^2/L)^0.5) * (g*KC + h)

* (i*Alpha^2 + j*Alpha + k))

• Parameters are:

– WPASP Wave phase start

– CLM Phase length multiple

– LSP Position start

– LSW Position length

– Amp Amplitude

PSF Model: Sediment Transport P F

S

ICSE-6 2012, Paris

Pipe Hydrodynamic Forces:

• Near-bed velocity timeseries from JPK WaveForce

• Hydrodynamic force-time history from JPK WaveForce

(On-bottom stationary pipe)

• Force correction on-the-fly as per SIMULATOR

– Pipe horizontal velocity

– Shielding due to trench

– Shielding due to embedment

– Lift force reduction due to spanning

The PSF Model – Pipe/Fluid P F

S