Luo Chengcai 2012 Part 1 on Bottom Stability

ON-BOTTOM STABILITY OF SUBMARINE

PIPELINE ON MOBILE SEABED

Chengcai Luo

M.E. & B.E

School of Civil and Resource Engineering &

Centre for Offshore Foundation Systems

This thesis is presented for the degree of Doctor of Philosophy

of The University of Western Australia

2012

i

ABSTRACT

The current submarine pipeline on-bottom stability design method recommended by

DNV RP-F109 is flawed because it neglects the seabed mobility. This research aims to

improve the understanding of how seabed mobility, specifically local scour around a

pipe, influences pipeline stability under realistic storm conditions.

To investigate the on-bottom stability of a submarine pipeline that is controlled by the

flow-pipeline-seabed tripartite interaction, an innovative large experimental facility,

called the O-tube, was established at the University of Western Australia. The facility is

capable of simulating cyclonic storm-induced hydrodynamic conditions at seabed level

so that the responses of a model pipeline and a model seabed can be revealed at a

relatively large scale to minimize the potential scaling effects associated with

conducting physical model tests. The establishment of the O-tube facility forms a part

of this thesis. The functionality and calibration of the facility are described herein.

A wide range of pipeline dynamic stability tests were conducted in the O-tube facility,

with the pipe being actively controlled by an actuator system so that it can move freely

in response to hydrodynamic load and soil resistance. Physical model test results of a

model pipe installed on an erodible sediment bed demonstrated that local scour has a

significant effect on pipeline stability. Based on the pipeline initial embedment, local

scour affected pipeline stability in two different ways: (i) tunnel scour below a pipe with

a shallow initial embedment appeared to be beneficial to pipeline stability because

tunnel scour tended to cause the pipe sinking into the scour hole; whilst (ii) local scour

at either side of a pipe with a deep embedment (without tunnel scouring) appeared to

undermine the stability of the pipe because it reduced the pipe embedment depth.

In addition to pipeline self-weight, hydrodynamic forces and soil resistance, pipeline

on-bottom stability is also affected by two competing processes: the storm ramp-up

process (which is a destabilizing mechanism) and seabed scour and pipeline sinkage

process (which are stabilizing mechanisms). A pipeline will become more stable if it

sinks into the scour hole before the pipeline is exposed to the peak storm conditions.

The tests conducted in this study showed that a slow flow ramp-up rate allowed

sufficient time for the formation of a relatively deep scour hole underneath the pipeline

and sinkage of the pipeline before severe flow conditions destabilised the pipeline. A

fast flow ramp-up rate, on the other hand, did not allow sufficient time for scour

development and pipe sinkage before severe flow conditions destabilised the pipeline.

ii

Pipe-soil resistance on calcareous sand was investigated based on a range of O-tube

pullout tests in still water conditions. In these tests, the pipe-soil resistance from an

embedded condition in the O-tube soil is over-predicted by the Verley and Sotberg

(1994) model (which features in the current DNV design code), for both breakout and

residual resistance by a factor of over 2 on average. The large discrepancy is mainly

attributed to the different type of soil. Comparison of the breakout resistance from the

O-tube pullout tests and the UWAPIPE model of Zhang et al (2002) suggests that

UWAPIPE is more suitable for predicting pipe-soil breakout forces on calcareous sand.

The slope-adjusted friction approach provides a good basis for estimating the pullout

resistance from a scour hole, which is significantly lower than from an embedded

condition at the same elevation relative to the far field seabed.

The hydrodynamic load reduction due to pipe sinkage into a scour hole was examined.

The load reduction factors of the O-tube test results were between the load reductions

due to trenching and penetration recommended in DNV-RP-F109, due to the sheltering

effect of the scour hole in present tests being between that of trenching and penetration.

A pipe sinkage model was proposed, which incorporates 2D tunnel scour development,

scour propagation along the pipe and pipe sinkage due to soil failure of supporting

shoulders. The effect of pipe sinkage on 2D scour rate was also accounted for by

introducing a time adjusting factor. Predictions of the pipe sinkage development from

the model agreed reasonably well with test results. The hydrodynamic load reduction,

the pipe sinkage development model, and the new evidence of pipe-soil interaction on

calcareous soils, are contributions to an improved integrated pipeline stability analysis

approach.

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ACKNOWLEDGEMENT

I have been fortunate to have two supervisors with different backgrounds and to be able

to work in the O-tube team with a stimulating environment throughout my PhD study.

I would like to express my sincere gratitude to my co-ordinate supervisor Winthrop

Professor Liang Cheng, who is an expert on hydrodynamics and scour around

submarine pipelines and also the leader of the O-tube pipeline stability research team.

He has always been supportive in every aspects of my study, providing me with

direction, motivation, knowledge and resources to complete this research project

successfully.

Professor David White is my co-supervisor, who specializes in geotechnical engineering

of offshore pipelines. Every communication with him has been inspiring and rewarding.

I am greatly appreciated for his encouragement, patience and instruction throughout the

course of my PhD study.

Special thanks to Dr. Hongwei An. We did most of the experimental work together. His

initiative, responsibility and dedication to work have influenced me greatly and will

accompany me in the future. He has been like an older brother to me in life, always

considerate and caring. I feel so lucky to have him in the path of study.

I must also thank Tuarn Brown, the chief technician in the O-tube lab. In my eyes he is

not a technician but a contagious creator with innovation, positivity and optimism.

Almost every issue we encountered in the experiments was solved by him. These testing

day and nights I spent together with Tuarn and Hongwei are an invaluable treasure in

my life.

I also like to thank all of my fellow group members and friends who made my three

years study at UWA a colourful and enjoyable experience.

The financial support for my PhD study from the Scholarship for International Research

Fees (SIRF) provided by the University of Western Australia and the Australia-China

Natural Gas Partnership Fund Postgraduate Top-Up Scholarship are greatly appreciated.

The O-tube pipeline stability research project was funded by the Australia Research

Council (ARC) (Linkage Grant LP0899936), Woodside Energy Ltd, Chevron Australia

Pty Ltd, and the University of Western Australia. I like to express my gratitude to these

entities for enabling me to work on this exceptional research project.

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Last but not least, my biggest thanks to my parents and my own family. I am indebted to

my parents for their unconditional love and support that led me to where I am today. I

greatly appreciate my amazing wife, Haiyan, who sacrificed so much during my PhD

study. I am so proud of my one-year-old lovely son who has brought us so much fun,

making our life a lot easier than we expected.

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DECLARATION

I hereby declare that the contents of this thesis are original unless duly referenced. The

experiment works described in this thesis were carried out under the supervision of

Winthrop Professor Liang Cheng and Professor David White, in collaboration with Dr.

Hongwei An at the large O-tube facility at the University of Western Australia.

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LIST OF SYMBOLS

a Flow ramp up rate

ac Current ramp up rate

as Oscillatory ramp up rate

A Area of O-tube cross section

B Buoyance of the model pipe

c Friction damping coefficient

CD Drag force coefficient

CH Horizontal (in-line) force coefficient

CL Lift force coefficient

CM Inertial force coefficient

d Water depth

d50 Median grain size

D Outer diameter of model pipe

e Void ratio of the soil

e0 Pipe initial embedment

fw Wave friction factor

FAct,T Actuator force in tangential direction

FAct,R Actuator force in radial direction

FAct,H Actuator force in horizontal direction

FAct,V Actuator force in vertical direction

FHydro,H Hydrodynamic force in horizontal direction (pressure integration)

FHydro,V Hydrodynamic force in vertical direction (pressure integration)

FI Inertia force of the flow

FInert,H Pipe inertia force in horizontal direction

FInert,V Pipe inertia force in vertical direction

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FSoil,H Soil resistance in horizontal direction

FSoil,V Soil resistance in vertical direction

FSoil,T Soil resistance in tangential direction

FSoil,N Soil resistance in normal direction

Fx Calculated horizontal hydrodynamic force from Morison equation

Fy Calculated vertical hydrodynamic force from Morison equation

g Acceleration due to gravity

G Submerged weight of model pipe

H Pipe horizontal displacement

Hf Friction head loss

HI Inertia head loss

Hst Static head of the O-tube system

Hsys Total hydraulic head of the O-tube system

k Wave number

KC Keulegan-Carpenter number

l Length of model pipe, 0.888m

L Wave length

Lcrt Critical length of soil shoulder

m Current to oscillatory amplitude ratio (=Uc/ Um)

M Mass of the fluid in the O-tube system

N Pump rotation speed, RPM

No Maximum pump rotation speed for oscillatory flow, RPM

Ns Pump rotation speed for steady current, RPM

p Pressure of the water

qc Cone resistance

Q Flow rate in the O-tube (=UA)

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Qm Maximum flow rate in the O-tube (=UmA)

Re Reynolds number (=UD/)

Rr Radial load cells reading

Rt Tangential load cells reading

S Pipe sinkage depth

Sg Simulated specific gravity of the model pipe

St Scour depth at time t

Equilibrium scour depth

t Time

T Flow period

T1 Time when tunnel scour observed at ends of pipe

T2 Time when pipe starts rapid sinking

T3 Time when pipe sinkage becomes steady

u Horizontal water particle velocity

U Flow velocity in the O-tube

Uc Current velocity

Us Oscillatory velocity amplitude

Um Velocity amplitude of oscillatory flow (Chapter 2)

v Vertical water particle velocity

w Pipe submerged weight per unit length

Wp Submerged weight of model pipe

x Coordinate in horizontal direction

z Coordinate in vertical direction; pipe vertical displacement in pullout

tests

Density of water

Sediment particle density

Wave angular frequency, (=2/T)

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Water surface elevation

Velocity potential

Shields parameter

cr Critical Shields parameter

Rotation angle of actuator arms (Chapter 4)

Bed shear stress

s Submerged soil unit weight

Kinematic viscosity

x

TABLE OF CONTENTS

Abstract i

Acknowledgement iii

Declaration v

List of symbols vi

Chapter 1. Introduction 1

1.1 Research motivation 1

1.2 Current offshore pipeline stability design approach 1

1.2.1 Introduction to current pipeline stability design approach 1

1.2.2 Scientific implications 3

1.3 Research status regarding to pipeline stability 3

1.3.1 Hydrodynamic load acting on pipelines 3

1.3.2 Soil resistance 4

1.3.3 Seabed mobility 5

1.3.4 Pipeline on-bottom stability 6

1.4 New experimental facility used in this work 7

1.5 Thesis layout 8

Chapter 2. Calibration of UWAs large O-tube flume facility 10

2.1 Introduction to large O-tube flume facility 10

2.2 Calibration of large O-tube flume facility 11

2.2.1 Flow velocity at variable pump speeds 12

2.2.2 Pump speed-flow velocity relationship 14

2.2.3 Random velocity time series generation 17

2.2.4 Flow feature examination 18

2.3 Pressure variation in large O-tube flume 20

2.3.1 Pressure variation in O-tube flume 20

2.3.2 Pressure in field condition 22

2.3.3 Comparison of pressure variation in O-tube and in field 23

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2.4 Summary 24

Chapter 3. O-tube experiments description 35

3.1 Similarity analysis 35

3.1.1 Similarity requirement for pipeline stability 35

3.1.2 Similarity requirement for seabed sediment transport and liquefaction 36

3.2 Experimental setup 39

3.2.1 Instrumented model pipe 39

3.2.2 Pipe control system-actuator 42

3.2.3 Model seabed 44

3.2.4 Measurement instruments 46

3.2.5 O-tube control software and data logging system 48

3.3 General Testing procedures 50

Chapter 4. 2D experimental investigation into pipeline stability on erodible seabed 61

4.1 Introduction 61

4.2 Definition of quantities, terms and force calculation 62

4.2.1 Definition of Quantities 62

4.2.2 Definition of terms 62

4.2.3 Force Calculation 63

4.3 Testing programme 68

4.3.1 Flow conditions 68

4.3.2 Testing matrix 69

4.4 Test results - Stability of shallowly embedded pipeline 72

4.4.1 General findings 72

4.4.2 Case study (A4) 73

4.5 Test results - Stability of large initial embedded pipeline 78

4.5.1 General findings 78

4.5.2 Case study (B6) 80

4.5.3 Effect of initial embedment: sloped vs. flatbed profile 86

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4.6 Pore pressure variation in the model seabed 87

4.7 Conclusions 88

Chapter 5. Competition mechanism governing stability of shallow initial embedded

pipeline 113

5.1 Introduction 113

5.2 Effect of flow conditions on pipeline stability 114

5.2.1 Current ramp up rate 114

5.2.2 Steady current vs. oscillatory flow vs. combined flow 118

5.2.3 Current ratio: m = 0.5, 1 and 2 121

5.2.4 Effect of KC number 123

5.2.5 Regular vs. irregular flows 126

5.2.6 Storm seed number 128

5.2.7 Flow ramp up format 129

5.2.8 Summary 130

5.3 Effect of pipe SG on pipeline stability 131

5.3.1 SG of 1.5, 2 and 3 under currents with a ramp-up rate of 0.2m/s2 131

5.3.2 SG of 2 and 3 under current with a ramp-up rate of 0.02m/s2 132

5.3.3 SG of 1.2, 1.35 and 1.5 under storm S1 134

5.3.4 Summary 134

5.4 Effect of initial embedment on pipeline stability 135

5.4.1 e0/D = 0 vs. 12.7% and SG = 1.35 under storm S1 135

5.4.2 e0/D = 12% with and without wormhole 137

5.4.3 Summary 138

5.5 Conclusions 138

Chapter 6. Soil resistance on calcareous sand-O-tube pullout tests 170


6.2 Radial force updating during pull-out tests 171

6.3 Test conditions 173

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6.3.1 Soil properties 173

6.3.2 Pipe parameters 173

6.3.3 Series 1: Flat seabed tests 174

6.3.4 Series 2: Seabed scour hole tests 175

6.4 Results of flat seabed tests 176

6.4.1 Soil resistance and pipe trajectory 176

6.4.2 Interpretation as slope-adjusted Coulomb friction 177

6.4.3 Comparison with Verley & Sotberg (1994) pipe-soil resistance model 178

6.4.4 Comparison with UWAPIPE pipe-soil interaction model 182

6.4.5 Discussion of cyclic pullout tests 183

6.5 Results of seabed scour hole tests 185

6.5.1 Soil resistance and pipe trajectory 185

6.5.2 Interpretation as slope-adjusted Coulomb friction 186

6.6 Conclusions 187

Chapter 7. Hydrodynamic load reduction due to pipe sinkage and modelling of pipe

sinkage 202


7.2 Hydrodynamic load reduction due to pipe sinkage 202

7.2.1 Force coefficients calculation 203

7.2.2 Force coefficients variation with KC number 204

7.2.3 Load reduction due to pipe sinkage 206

7.3 Modelling of pipe sinkage induced by tunnel scour 208

7.3.1 2D Scour development model 208

7.3.2 Modelling pipe sinkage development 211

7.3.3 Model results 215

7.3.4 3D Scour and pipeline response in field 218

7.4 New pipeline stability design approach 220

7.5 Conclusions 221

xiv

Chapter 8. Conclusions 243

8.1 Conclusions 243

8.2 Suggestions for future work 246

Reference 247

Appendix A. Velocity time series at different pump speeds in O-tube calibration 251

Appendix B. Pipe self-weight calculation 255

1

CHAPTER 1. INTRODUCTION

1.1 RESEARCH MOTIVATION

With the ongoing development of oil and gas extraction activities in Australias North

West Shelf (NWS), the total length of submarine pipelines being installed and planned

for transporting oil and gas in Australias offshore area is increasing exponentially. For

instance, the total length of large diameter trunkline (36 inch) that was installed for the

Pluto project is approximately 165 kilometres. The total length of the trunkline for the

Greater Gorgon project is around 190 kilometres. The typical per kilometre cost of a

large diameter pipeline at NWS is approximately $4.5 million. On-bottom stabilisation

measures of the pipelines account for a significant proportion (approximately 30%) of

the total cost.

Although on-bottom stability of submarine pipeline design practice has been developed

since the 1950s, there are still some significant uncertainties in this subject. For

instance, the effect of seabed mobility on the pipeline stability, although observed in

practice, has still not been considered in the pipeline stability analysis. Furthermore,

pipeline on-bottom stability design in NWS is further complicated by the areas unique

features: (i) large diameter light gas trunklines crossing a shallow continental shelf, (ii)

severe tropical cyclonic loading conditions and (iii) erodible calcareous seabed. Given

the high costs of pipeline stabilization measures, understanding these uncertainties and

challenges within current practice will help to improve the safe operation of pipelines

and potentially lead to significant costs savings for the Australian oil and gas industry.

1.2 CURRENT OFFSHORE PIPELINE STABILITY DESIGN APPROACH

1.2.1 Introduction to current pipeline stability design approach

On-bottom stability of submarine pipelines is determined by the forces acting on the

pipeline under extreme hydrodynamic load conditions, shown in Figure 1.1. In

simplicity, if the horizontal hydrodynamic force exceeds the soil resistance, the pipe

loses lateral stability; if the lift force exceeds the pipe submerged weight, the pipe loses

vertical stability. Since the soil resistance is largely dependent on the pipe submerged

weight, the pipe self-weight is a determining factor for pipeline stability.

A commonly used offshore pipeline stability design method worldwide is the

recommend design practice by Det Norske Veritas (DNV) RP-F109, with the most

recent version released in 2011. Three different design approaches are outlined in this

2

recommended practice, dynamic lateral stability analysis, generalised lateral stability

design method and absolute lateral static stability method. The dynamic lateral stability

analysis calculates the pipeline accumulated dynamic response under a complete design

sea-state (irregular combined wave and current condition) in the time domain. The first

step of performing dynamic lateral stability analysis is to determine the flow velocity at

pipe level, based on the design current and wave conditions. The next step is to choose

appropriate force models to calculate the hydrodynamic loads. Load reduction due to a

permeable seabed, pipe penetration into the seabed and trenching may be applied to

update the hydrodynamic load. The available soil resistance comprises two parts,

Coulomb friction and passive resistance due to pipe penetration. The passive resistance

adopted in DNV RP-F109 is based on the pipe-soil interaction model proposed by

Verley et al. (1994), which was based on tests on siliceous sands. The generalized

lateral stability method provides the relationship between the required pipe weight

parameter and other relevant non-dimensional parameters that makes a virtually stable

pipe or allows 10 diameters of pipe lateral movement. The design curves of the

relationships are given based on dynamic analysis. The absolute lateral static stability

method checks the pipe static stability under the peak hydrodynamic load in a design

sea state. Several miscellaneous stated in this design guideline include free span of

pipeline induced by local scour, seabed mobility (sediment transport) and soil

liquefaction.

Another design approach for dynamic stability was proposed by the American Gas

Association (AGA). This approach allows the pipeline to have a maximum allowable

lateral displacement during the storm considered. The acceptance displacements are

modified to reflect the proximity of the pipeline to platforms or a shore crossing and the

consequence of pipeline failure. Passive soil resistance is taken into account in this

calculation procedure. However, the impacts of local scour and seabed liquefaction on

the pipeline stability are not included in these modules.

It can be seen that the current pipeline stability analysis does not account for seabed

mobility before and during the designed sea state. It was found that significant sediment

transport could take place long before the pipe starts to move horizontally (Palmer,

1996). Small scale model tests have also demonstrated that the seabed geometry and

pipe embedment conditions changed before and during the extreme design sea state

(Guo, 2008). DNV-RP-F109 design code itself states that by these formulae [with

regard to seabed stability], it may be shown that non-cohesive soil will in many cases

3

become unstable for water velocities significantly less than the velocity that causes an

unstable pipe.

1.2.2 Scientific implications

The design flaw of neglecting the effect of seabed mobility on pipeline stability may be

attributed to the fact that most of the current stability approaches treat the fluid-pipe and

pipe-soil interactions separately, whilst neglecting the fluid-seabed interaction. The real

situation is that pipeline stability involves flow-pipe-soil interactions, as shown in

Figure 1.2. In this triangular process, fluid-seabed interaction, taking the form of scour

or soil liquefaction, has a significant impact on the pipe response. Local scour may

increase or decrease pipe exposure to flow compared to the initial embedment condition

thereby changing the hydrodynamic load acting on the pipe and the available soil

resistance. Seabed liquefaction may also make the pipe float up or sink into the

liquefied seabed, resulting in different pipeline stability behaviour to that of a fixed

seabed. The aim of this thesis was to improve the understanding on the effect of seabed

mobility, specifically local scour, on pipe stability during storm conditions by capturing

the interaction between flow, seabed and pipeline through physical model tests.

1.3 RESEARCH STATUS REGARDING TO PIPELINE STABILITY

1.3.1 Hydrodynamic load acting on pipelines

Pipeline stability is largely determined by the hydrodynamic forces acting on the

pipeline and the available soil resistance to the movement of the pipeline. Extensive

research has been conducted on the hydrodynamic forces acting on pipelines. The

earlier research on this subject focused on the flow around a circular cylinder subject to

various flow conditions and the effect of a plane boundary near the cylinder. These

research works were summarized by Sumer and Fredsoe (1997). A comprehensive

study regarding the hydrodynamic forces subjected on a pipeline was carried out by

Danish Hydraulic Institute (DHI) (Sorenson et al., 1986). In this study, a wide range of

physical model tests, covering various flow conditions, model pipe setups and model

seabed roughness were conducted. The hydrodynamic force calculation methods based

on the Morison equation and Fourier model were examined and a set of Fourier

coefficients were proposed to predict more accurately the hydrodynamic loads. The

hydrodynamic forces on a partially buried pipe were also investigated. It should be

mentioned that an impermeable model seabed was employed in this study, so the force

due to seepage flow in the soil bed was not considered.

4

Wave forces on a buried pipeline in a permeable seabed have also been investigated

(Magda, 1999, Neelamani, 2011). Hydrodynamic forces on a sheltered pipeline due to

embedding has also drawn researcher attention (Jacobsen, 1988). Moreover, extensive

numerical studies on hydrodynamic forces acting on pipelines have been carried out. An

et al. (2011) investigated hydrodynamic forces of a partially buried pipeline by

numerical simulation, for the embedment up to e/D = 0.5. It was found that both the

horizontal (drag) force and the vertical (lift) force reduced linearly with the increase of

the pipe embedment in the range of 0 < e/D < 0.5. Although a large amount of research

has been done on hydrodynamic loads on pipelines, these studies were mainly for fixed

pipeline-seabed geometries. In reality, an erodible (sandy/silty) seabed can become

mobile during storm conditions, changing the pipeline-seabed contact conditions. The

hydrodynamic force variation with a mobile seabed under random storm conditions,

which is directly associated with pipeline stability, is still not fully understood.

1.3.2 Soil resistance

Soil resistance is also a determinant to the pipeline stability. The soil resistance model

adopted in DNV-RP-F109 is based on the model from siliceous sand. It was found that

pipe-soil interaction on carbonate soil, which prevails in offshore Australia, Africa,

Brazil and the Middle East, differs from that on siliceous sand (White and Cathie,

2010). Calcareous sand is distinguished from siliceous sand by its high compressibility

and high friction angle, and is composed of brittle angular particles. Because of these

physical features, calcareous sand in general exhibits less mobility and a different

stress-strain behaviour compared to siliceous sands.

A large programme of research into pipe-soil interaction on calcareous soil has been

carried out at the University of Western Australia. These pipe-soil interaction models

were developed within the framework of work-hardening plasticity, with the model

parameters determined from centrifuge test data. A representative of this type of model

in drained conditions was proposed by Zhang et al. (2002). The model can simulate the

response of a pipeline embedded in sandy soil under combined monotonic loading and it

can also predict the lateral breakout resistance, which is a critical parameter for

assessing the pipeline stability. Pipe-soil interaction that involves a pipeline with large

amplitude cyclic motions and soil berms created by pipeline motion was captured by a

kinematic hardening model (White and Cheuk, 2007). Randolph and White (2008)

developed a model for the limiting vertical-horizontal (V-H) load combinations in the

undrained condition. More recently, an advanced pipe-soil interaction model in

5

calcareous sand called UWAPIPE model was developed (Tian, et. al. 2010), which is an

implementation of the Zhang et al. (2002) model. This model works well for describing

the pipeline load-displacement behaviour subjected to combined vertical and horizontal

loading. However, these models were based on experiments with small diameter pipe

and there is little published knowledge on the pipe-soil interaction with the pipe sitting

in a scour hole.

1.3.3 Seabed mobility

Local scour around pipelines, as a major seabed mobility form, changes the seabed

profile and the pipe-seabed contact conditions. Local scour around submarine pipelines

under various flow conditions have been given particular attention in the last few

decades and was elaborated by Sumer and Fredse (2002). The initiation of local scour

beneath a shallow initial embedded pipeline is induced by the seepage failure due to the

pressure difference between the front and the rear of the pipe (Chiew et al., 1990; Luo et

al., 2008; Zang et al., 2009). The onset of scour and self-burial was investigated

experimentally using a small diameter model pipe (D

6

of an already self-buried pipe (large embedded pipe) subjected to severe storm

conditions, which is of practical concern for real-life situations. Furthermore, most of

the previous experiments were conducted using small diameter model pipes, which

brings more uncertainties regarding to the scaling effects and extrapolation to field

conditions. Experiments with a larger diameter model pipe could minimise scaling

effects to a certain degree and, therefore, produce more reliable results.

Seabed liquefaction also affects the pipeline stability, as a pipe can sink into or float up

from a liquefied seabed. Understanding of pipeline stability on a liquefied seabed was

greatly improved thanks to the research work done by Teh et al. (2003). Based on

physical model tests and theoretical analysis, an analytical model was proposed to

predict the embedment of a floating pipe on liquefied soil for different pipe specific

gravities (Teh et al., 2006). A new pipeline stability design approach, incorporating the

effect of soil liquefaction, was proposed by Damgaard et al. (2006).

It is seen that until now, a large knowledge gap between seabed mobility and pipeline

stability lies in the influence of local scour on the pipeline stability. This research will

focus on the subject of how local scour impacts the pipeline stability.

1.3.4 Pipeline on-bottom stability

It is seen from the above knowledge review that most previous research into pipeline

stability considered this issue within the discipline of hydrodynamics (flow-pipe

interaction) or geotechnical engineering (pipe-soil interaction). This might be partly

caused by lack of communications between the two disciplines and partly due to the

lack of an appropriate research facility that could capture the flow-pipe-soil triplet

interactions, particularly the interaction between seabed mobility and pipeline stability.

Some research aiming to address this issue from the flow-pipeline-soil coupling

perspective of view was completed by Gao et al. (2003, 2007, 2010, 2011). UWAPIPE

incorporates the hydrodynamic load calculation and pipe-soil interaction into the

pipeline stability analysis model. However, those works did not account for the vital

effect of seabed mobility on the pipeline stability analysis. This research project drew

together researchers with strong track records in the hydrodynamics, scour and

geotechnical aspects of pipeline engineering, allowing the challenge of pipeline stability

on a mobile seabed to be tackled in a multi-disciplinary fashion. The research aims to

deepen the understanding of how local scour impacts the pipeline stability under

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realistic storm conditions, contributing to the upgrading of the pipeline stability analysis

method.

1.4 NEW EXPERIMENTAL FACILITY USED IN THIS WORK

In order to investigate submarine pipeline stability that is controlled by the flow-

pipeline-seabed triangle interaction, an innovative experimental facility, called the

Large O-tube (LOT), was established at the University of Western Australia. The large

O-tube flume facility is capable of simulating hydrodynamic conditions induced by

cyclonic storms at seabed level so that the response of pipelines and a model seabed can

be investigated at a relatively large scale.

The O-tube flume distinguishes from the conventional wave flume and U-tube in terms

of its capability of simulating various flow conditions. For local scour induced by

extreme wave and current conditions, the dominant sediment transport mode is the sheet

flow regime. It is nearly impossible with a conventional open channel flume to generate

the wave-induced sheet flow with a high enough orbital velocity without the occurrence

of wave breaking. The O-tube can overcome this problem because it is a closed system

without a free wave surface. Flow is generated using an impeller, with free control to

the oscillatory periods within the capacity of the facility. It is capable of simulating the

velocity time history induced by a 100 year return period tropical cyclone on Australias

North West Shelf at the seabed level, for a water depth of 40m (the orbital oscillatory

velocity of 3 m/s with 15s period). This is difficult to achieve in conventional flume

facilities.

Most of the previous experimental studies on the hydrodynamic load acting on a pipe

were undertaken at a relatively small scale of approximately 1:20. In the O-tube facility,

a model scale of 1:5 for large diameter pipelines (up to 1 m in diameter) and 1:1 scale

for small diameter pipelines (up to 0.2m in diameter) can be achieved. In addition, an

active pipe control system was designed to provide feedback control to the pipe motion.

The advantage of this control system is that it not only restrains unrealistic motions of

the pipe, but also eliminates the interference from the control system to the pipe so that

the pipe can move freely in response to the hydrodynamic load and soil resistance.

Therefore, the testing facility used for this research is the most advanced facility for

dynamic response of subsea pipelines in the world.

8

1.5 THESIS LAYOUT

The background of the research into on-bottom stability of submarine pipelines on a

mobile seabed, research status to date and the brief introduction of the innovative

research facility for this research were set out in this chapter.

In Chapter 2, the large O-tube facility and the calibration of this facility is described.

The flow characteristics, including the pressure variation inside the O-tube, are

examined to understand the attributes of this new facility.

In Chapter 3, similarity analysis regarding the relevant physical phenomena involved in

the submarine pipeline stability is performed. In particular, the similarity requirement

for seabed sediment is elaborated. Then the O-tube pipeline stability experimental setup

is described and the general testing procedures are outlined.

In Chapter 4, the pipeline stability testing programme conducted in the large O-tube

facility is set out. Test results of the two groups, shallow initial embedded pipe and

large initial embedded pipe, are summarized. In each group, a typical case is discussed

in detail. The effect of local scour on pipeline stability was demonstrated in these tests.

A parametric comparison study regarding to the stability of shallowly initial embedded

pipeline is carried out in Chapter 5. The key factors that govern the pipeline stability,

i.e. flow condition, pipe specific gravity and initial embedment depth, are investigated

through a series of comparison studies. Pipeline stability competition mechanisms

between flow ramp up rate and pipe sinkage development are proposed based on the

parametric comparison studies.

Soil resistance in calcareous sand is investigated through a range of O-tube pullout tests

in Chapter 6. The soil resistance with pipe sinking in scour holes is also examined. The

breakout and residual forces measured in the tests are compared with predictions from

DNV-RP-F109 and the discrepancy was explained. The test results are also compared

with the UWAPIPE model.

In Chapter 7, hydrodynamic load reduction due to pipe sinkage is analysed. The load

reduction factors are compared with the load reduction due to penetration and trenching

in DNV-RP-F109. In addition, a preliminary pipe sinkage model due to tunnel scour is

developed, which captures the pipe sinkage development of O-tube tests. The

hydrodynamic load reduction and pipe sinkage model are to contribute to the integrated

pipeline stability assessment model that accounts for the effect of seabed mobility on

the pipeline stability.

9

The last chapter reviews the major points of this research and proposes future works

with the objective of developing an integrated model for submarine pipeline on-bottom

stability assessment.

Figure 1.1 Forces acting on a submarine pipeline

Figure 1.2 Fluid-pipe-soil interaction (White and Cathie 2010)

10

CHAPTER 2. CALIBRATION OF UWAS LARGE O-TUBE

FLUME FACILITY

2.1 INTRODUCTION TO LARGE O-TUBE FLUME FACILITY

Pipeline stability involves full tripartite pipe-flow-soil interaction. Unfortunately, most

research to date has focused on particular pieces of this comprehensive problem, rather

than treating this issue in an integrated manner. The best way to observe this tripartite

behaviour is through physical model tests. For this purpose, an innovative large testing

facility, called the O-tube facility, was built at the University of Western Australia

(UWA).

The O-tube is an entirely new innovation developed specifically for investigating the

pipeline stability on an erodible seabed under severe tropical storm conditions, allowing

the interaction between pipe, flow and seabed to be faithfully reproduced. It is capable

of simulating realistic hydrodynamic conditions near the seabed so that the response of

the seabed sediment and any infrastructure that is resting on it can be revealed at a

relatively large scale (e.g. 1:5 for a 40-inch diameter trunkline and 1:1 for an 8-inch

diameter pipeline). The generated oscillatory velocity amplitude can be up to 2.5 m/s at

a period of 13s and 1m/s at period of 5s. This allows severe field tropical storm

conditions with a return period of up to 10,000 years in Australian waters to be

modelled.

The O-tube facility, shown in Figure 2.1, is a continuous closed loop flume in which

water is circulated by an in-line pump system to generate steady currents, oscillatory

flows or combined steady currents and oscillatory flows. It is composed of tube

sections, a straight rectangular test section, and an inline turbine pump. The pump

impeller is driven by a motor which is controlled by a Variable Frequency Drive (VFD).

The test section is 1.4m in height, 1m in width and 17.6m in length. It can be filled with

sediments to model seabed conditions on which submarine structures are placed. The

major parameters of the large O-tube are listed in Table 2-1. The height of the test

section of 1.4m is the distance from the top to the bottom of the test section in the

absence of any sediment.

The O-tube flume is different from conventional wave flumes and U-tube flumes.

Firstly, for local scour induced by extreme wave and current conditions, the dominant

sediment transport mode is in the sheet flow regime. It is almost impossible with a

11

conventional open channel wave flume to generate the wave-induced sheet flow with

sufficiently high orbital velocity representative of the severe tropical storm conditions

without allowing wave breaking in the flume. The O-tube can well overcome this

problem because it is a closed system without a free wave surface and can simulate the

sheet flow regime. Secondly, the O-tube provides free control of the oscillatory periods

within the limits of the motor and turbine to generate oscillatory flows and combined

steady currents and oscillatory flows.

Table 2-1 Summary of O-tube specifications

Specification Quantity

Overall length 24.0 m

Overall breadth 7.8 m

Height of test section 1.4 m

Breadth of test section 1.0 m

Length of test section 17.6 m

Maximum steady velocity 3 m/s

Maximum oscillatory velocity at 5s period 1 m/s

Maximum oscillatory velocity at 13s period 2.5 m/s

Rated power of drive motor 580 kW

Maximum rotation speed 600 RPM

2.2 CALIBRATION OF LARGE O-TUBE FLUME FACILITY

The main objective of the calibration is to build up the relationship between the pump

rotation speed and the flow velocity in the test section so that any required steady,

periodic or random velocity time history can be generated in the O-tube test section.

The steady current is generated by specifying a constant motor rotational speed, whilst

the oscillatory flow of sinusoidal form is generated by specifying the period and

velocity amplitude of the motor rotation. The whole calibration for this system

comprises the following stages:

1) Measurement of flow velocities at variable pump speeds under steady current,

oscillatory flow and combined flow conditions;

12

2) Derivation of the relationship between flow velocity and pump speed (at all

oscillatory frequencies), as well as a basis for producing random velocity time

series in the O-tube.

3) Examination of flow uniformity across the test section, boundary layer and

turbulence intensity.

2.2.1 Flow velocity at variable pump speeds

Overview of calibration tests

The calibration velocity was measured with a Perspex false floor installed in the O-tube

test section. The false floor was 0.4m above the bottom of the test section so that the

floor was on the same level as the bottom of the tube sections. The flow velocity was

measured by an Acoustic Doppler Velocimeter (ADV), mounted 0.18m above the false

floor midway along the test section. A range of steady currents, oscillatory flows and

combined flows were generated under the corresponding pump rotational speeds. For

steady current, 35 differing flow velocities were measured. For oscillatory flow, five

different periods (T = 6s, 10s, 20s, 50s and 100s) with varying velocity amplitudes were

measured and for combined flow, varying current components were superimposed on

oscillatory flow with different periods. The calibration testing matrix is listed in Table

2-2, where in column 3, -408:24:408 means the pump speed was increased from -

408rpm to 408rpm in steps of 24rpm.

These flow conditions did not extend to the full capacity of the O-tube, but span the

conditions required for the particular projects performed during the initial period of

testing programme.

Steady current results

The variation of flow velocity with pump rotational speed for steady current conditions

is shown in Figure 2.2. It can be seen for steady current that the flow velocity increases

linearly with the pump rotational speed. This is in accordance with the Affinity law

which states that the flow discharge is proportional to the pump rotational speed under a

constant impeller diameter. It is noticeable that the slopes of the two lines

corresponding to the two pump rotational directions are different. This is attributed to

the asymmetric structure of the pump impeller which affects the efficiency of the pump.

Segments of the velocity time-series recorded by the ADV for each of the orthogonal

directions at several different pump rotation speeds are shown in Appendix A1.

13

Table 2-2 Calibration testing matrix

Case No. Flow condition Ns

(rpm)

No

(rpm)

T

(s)

1-35 Steady -408:24:408 0

36-50 Oscillatory 0 48:24:384 6

51-63 Oscillatory 0 48:24:336 10

64-75 Oscillatory 0 24:24:228 20

76-84 Oscillatory 0 24:24:216 50

85-97 Oscillatory 0 24:24:312 100

98-102 Combined 24 72:48:264 6

103-107 Combined 48 72:48:264 6

108-112 Combined 72 72:48:264 6

113-117 Combined 24 72:48:264 10

118-122 Combined 48 72:48:264 10

123-127 Combined 72 72:48:264 10

128-132 Combined 24 72:48:264 20

133-137 Combined 48 72:48:264 20

138-142 Combined 72 72:48:264 20

Oscillatory flow results

The amplitude of the oscillatory flow velocity versus the amplitude of the pump

rotational speed under varying flow periods is shown in Figure 2.3. It can be seen for

oscillatory flow conditions that the relationship between the flow velocity and pump

speed is no longer linear. Under the same pump rotational speed, the maximum flow

velocity drops with the decrease of the flow period. This is because under the oscillatory

flow condition, the head provided by the pump is mainly balanced by the acceleration of

the water in the O-tube. According to the Affinity law, the same pump rotational

amplitude results in the same hydraulic head. As the flow period decreases, the velocity

amplitude reduces accordingly to maintain the inertia force decided by the hydraulic

head loss.

Segments of the velocity time-series for oscillatory flow at different pump rotational

speeds for 10s flow period are shown in Appendix A2.

14

2.2.2 Pump speed-flow velocity relationship

Pump theory (Affinity law) and the fluid momentum equation were applied to the above

calibration results in order to derive an equation for calculating the corresponding pump

input speed for the desired flow conditions, and ultimately for generating an arbitrary

time-series of random flow conditions.

Derivation for oscillatory flow

For a constant pump impeller diameter, the Affinity law gives:

(2.1)

(2.2)

The pump characteristic curve for N = 485RPM is available from the pump

specification, which can be approximately expressed by a linear equation:

(2.3)

It should be mentioned that the coefficients of 5.0466 and 18.75 have units of s/m2 and

m, respectively, to ensure the equation is dimensionally correct. According to Eq. (2.1),

(2.2) and (2.3) the pump characteristic curves for any pump speed can be derived,

shown in the dotted line in Figure 2.4. The pump characteristic curve was expressed as

(2.4)

Each of the calibration results (N, U) satisfies Eq. (2.4). As such, the hydraulic head

loss (H) for each calibrated (N, Q) can be obtained according to Eq. (2.4). This set of

curves with differing flow periods are called the O-tube system curves, shown in Figure

2.4. It can be seen that the O-tube system head is a function of pump speed and flow

discharge.

For the pump-flow system with zero static head variation, the total hydraulic head

consists of friction head loss and inertial head loss,

(2.5)

The friction head loss and the inertial head loss can be expressed as

(2.6)

15

(2.7)

where the constant

. Thus, the total O-tube head loss for oscillatory flow is

(2.8)

The O-tube system curves show that the head loss for small periods (T = 6s, 10s, 20s)

oscillatory flow are significantly higher than that of the steady current. This indicates

the head loss under oscillatory flow conditions is dominated by the inertial head loss .

Therefore, it is reasonable to neglect the friction head loss for oscillatory flow

conditions. By rewriting the acceleration of the water

to the averaged form of

,

Eq. (2.8) is then simplified to

(2.9)

where k is a constant with the unit of s2/m

2. In order to obtain an equation that applies to

all the flow periods, the system curves for differing periods were normalised by the one

of T = 6s. It was found after normalization the three system curves of T = 6s, 10s, 20s

collapsed to a single line, as shown in Figure 2.5. The constant k in Eq. (2.9) was then

determined by the gradient of this line, which was calculated to be 46.42. Eq. (2.9)

indicates that the O-tube system head is also a function of flow discharge and period.

Until now, the O-tube system head was derived from the pump characteristic curves and

the flow momentum equation independently. Substituting Eq. (2.9) into (2.4), the

relationship between the maximum pump speed and the maximum discharge in the

O-tube and flow period T for oscillatory flow condition can be obtained:

(2.10)

This formula establishes the relationship between the pump rotation speed and the flow

discharge in the O-tube test section. It should be noted that this equation was derived for

oscillatory flow with periods less than 20s. For the higher periods flow condition, the

error induced by neglecting the friction head loss in Eq. (2.8) may be noticeable.

The cross-sectional area (A) of the O-tube test section during calibration was 1m2, which

yields the relationship between and :

16

(2.11)

Using the original calibrated data to check the accuracy of this equation, it was found

the relative error of the flow velocity calculated by Eq. (2.11) was less than 5% except

for a few cases with low pump rotational speeds.

Derivation for steady current

For steady current conditions, the head loss due to the inertia force is zero, so Eq. (2.8)

becomes

(2.12)

According to the O-tube system curve for steady current (Figure 2.4), friction damping

coefficients (c) for differing velocities were calculated and all listed in Table 2-3. It is

seen that the damping coefficients have an average value of 15.2, with a standard

deviation of 0.68. According to the calibration results and the Affinity law (Eq. (2.1)), a

linear relationship between pump rotational speed and flow velocity can be obtained:

(2.13)

The symbol + and denote the positive and negative flow directions. The positive

direction is defined such that the flow in the O-tube test section is moving from right to

left when observing in the O-tube control room (i.e. flow is clockwise when viewed

from above).

Table 2-3 Friction damping coefficients for steady current

U(m/s) H(m)

2.26 3.70 14.24

1.84 2.58 14.94

1.44 1.59 15.03

1.04 0.85 15.40

0.65 0.33 15.31

0.26 0.06 16.32

17

Combined flow condition examination

Combined flow conditions were generated by superimposing a steady current

component on an oscillatory flow. The purpose of conducting combined flow

calibration is to examine whether a combined flow can be generated by linear addition

of pump speeds derived for the corresponding current and oscillatory components.

Combined flow with velocity can be decomposed into steady component and

oscillatory component . The corresponding pump speeds are and respectively,

calculated by the current only and oscillatory only calibration results explained above.

The question is, whether the linear addition of pump speed of and can generate

the combined velocity . To answer this question, three steady motor speeds of = 24

RPM, 48 RPM and 72 RPM were superimposed onto the 6s period oscillatory flow with

five differing pump rotational amplitudes.

Figure 2.6 shows the comparison between the target velocities (only the maximum and

minimum values were shown) and the measured velocities. It is found that for = 24

RPM, the measured flow velocities are virtually equivalent to the target ones. However,

for the larger steady current component of = 48 RPM, the measured combined flow

velocity moved to the flow direction of the steady current. The deviation between the

measured and target velocities became more obvious for = 72 RPM. For flow

periods of T = 10s and T = 20s, similar trends were found.

The small deviation between the measured and target velocity stems from neglecting the

friction head loss in Eq. (2.8) when deriving the formula for the oscillatory flow

condition. The effect of omitting the friction head becomes larger with the increase of

the steady current component. Based on the combined flow calibration results, a steady

current dependent correction factor can be obtained. This correction factor was

incorporated when generating combined flow by using the formulae derived from

oscillatory flow only and steady current only.

Segments of the velocity time-series for combined flow of 10s period with differing

superimposed steady current components are shown in Appendix A3.

2.2.3 Random velocity time series generation

The ultimate goal of the calibration is to generate any required irregular velocity time

series within the capacity of the O-tube. The approach of obtaining a target random

velocity time-series comprises the following steps:

18

1) Separate the target velocity time history into two parts: the steady current

component and the oscillatory component. The steady current velocity can be

converted directly to the pump speed according to Eq. (2.13);

2) Decompose the irregular oscillatory velocity trains into single half periods and

approximate each of these half waves with a regular wave. The zero crossing

points of the velocity time-series are chosen to determine the period and the

maximum velocities in the half period duration are treated as the maximum

velocity of the corresponding regular waves.

3) For each regularized half wave, use Eq. (2.11) to calculate the pump rotational

speed.

4) Add the steady current pump speed onto the oscillatory pump speed, introduce

the current dependent correction factor from the combined flow calibration to

fine tune the total input pump speed.

The velocity time-series at 1m above the seabed during a 100 year return period scaled

(1:5.8) storm at the North West Shelf of Western Australia in 40 m water depth is

shown in Figure 2.7. It consists of a steady current with three stages (ramping up, steady

and ramping down) and a random oscillatory time-series with an average period of 6.1s.

It was reproduced in the O-tube using the above method. Figure 2.8 shows the measured

velocity time history in the O-tube and the target velocity time history, including an

enlarged duration. It is seen the measured velocity time-series agreed well with the

target one. Several other random velocity time histories were also reproduced in the O-

tube. This reproduction of the random flows demonstrates the capability of the O-tube

to simulate the severe ocean environment near the seabed, which enables physical

modelling studies to include the full fluid-structure-soil interaction.

2.2.4 Flow feature examination

Flow uniformity across test section

To check the flow uniformity across the test section, velocities at six locations (shown

in Figure 2.9) were measured by ADV. The cross section area is 1m 1m. The bottom

three locations A, B, C are 0.18m above the false floor, with B in the middle, A and C

being 0.12m away from the side walls. The top three locations are symmetrical to the

bottom ones. All the calibration results aforementioned were measured from location B.

For steady current, three different pump rotational speeds were run at each of these

locations. Figure 2.10 shows the velocity comparison for steady current at these

19

locations. It was found the discrepancy of the velocity among these locations increases

with flow velocity. The velocity near the inside wall (location A and D) is lower than

that close to the outside wall (location C and F), with a maximum difference of 18% at

velocity of about 1m/s. The velocity discrepancy is due to the centrifugal forces

generated at the bends pushing the flow towards the outside wall. Figure 2.11 shows

the maximum velocities of oscillatory flow with a period of 20s at these six locations.

The comparison shows a better uniformity for oscillatory flow, with an averaged

discrepancy of approximately 3%. This reflects the smaller influence of the bends to the

flow in middle test section where the particle orbits did not stretch from the

measurement locations out to these bends. Along the height of the cross-section, the

velocity difference between the top and bottom locations is within 2%, indicating a

relatively high uniformity in the vertical direction of the test section.

Bottom boundary layer

The velocity profile in the boundary layer was measured at the Perspex false floor prior

to the installation of the model seabed. The flow velocity was measured at a constant

pump speed of 72RPM, corresponding to the current velocity of 0.4 m/s. The velocity

profile within the boundary layer is plotted in Figure 2.12. It follows a logarithmic

variation and can be fitted approximately using the following non-dimensional

equation:

(2.14)

where z is the vertical coordinate from the bottom upward, is the friction velocity,

is von Karmans constant, which is 0.40, and is the roughness of the boundary. From

the measured boundary layer, it was found that and . It is

seen for z > 0.15m the flow velocity does not change significantly. Thus, the thickness

of the boundary layer on the Perspex floor is approximately 0.15m. The velocity

measurement points of A, B and C are 0.18m above the bottom, so that they are outside

of the boundary layer. The boundary lay at the side glass walls was found to be a similar

thickness to this one.

The velocity profile in the boundary layer of the model seabed was also measured after

the installation of the model seabed. The flow velocity within 200mm above the flat

seabed was measured by the Electromagnetic Flow Meter (EMS) at the constant pump

speed of 72 RPM, the same speed as that used with the Perspex false floor. 20 points in

20

one water column with the height increased by a step of 10mm starting at 10mm above

seabed were measured. At each measurement location, 20s of velocity time history was

recorded. The average velocity over the 20 seconds was treated as the velocity at the

corresponding location. The measured boundary layer is shown in Figure 2.13. The

velocity profile can be fitted with conventional form as:

(2.15)

The bed roughness can be related to grain size (which is ) as

(Soulsby, 1997). According to the measure velocity profile the friction

velocity and the coefficient c can be determined, which are and c=0.015,

respectively.

Turbulence intensity

The flow passing through the impeller of an axial flow pump is highly turbulent. The

laminators (honeycomb) at the ends of the test section are designed to break down large

turbulence structures. However, turbulence structures of a size smaller than the cell of

the honeycomb circulate in the O-tube. The turbulence intensity (I) was calculated from

the measured flow fluctuations. The turbulence intensity is defined as

(2.16)

where u' is the root-mean-square of the turbulent velocity fluctuation and is the mean

velocity. Figure 2.14 shows the turbulence intensity versus flow velocity for steady

current ranging from -1.6m/s to 1.6m/s. The turbulence intensity shows an average of

3%, indicating that the flow in the O-tube has a relative low turbulence level.

2.3 PRESSURE VARIATION IN LARGE O-TUBE FLUME

Pressure variation at the seabed affects not only the hydrodynamic forces on pipelines

but also the pore pressure variation in the seabed and the seabed response. In this

section, the pressure variations in the O-tube and in-field conditions are examined and

compared.

2.3.1 Pressure variation in O-tube flume

The water in the O-tube is driven by an axial-flow pump. Assuming at time t, the flow

direction in the O-tube is anti-clockwise in plan view, as shown in Figure 2.15. The

pressure and flow velocity at the outlet side of the pump are P1, U1 and at the inlet side

21

are P2, U2, respectively. The pressure variation along the O-tube under current and

oscillatory flow conditions are derived as follows.

By applying the flow momentum equation and neglecting the convection and viscosity

terms of the flow, the pressure gradient in the O-tube is balanced by the friction force

between tube surface and flow and the inertia force, which can be expressed as

(2.17)

in which x is the distance along the O-tube and is the friction head loss, which is

(2.18)

where D is the diameter of the tube, is the friction coefficient, depending on the

roughness of the inside surface of the O-tube and Reynoldss number.

Under steady current conditions,

. Substituting Eq. (2.18) into Eq. (2.17) gives

(2.19)

Integrating Eq. (2.19) along the length of the O-tube, it yields

(2.20)

where C is a constant. Under oscillatory flow conditions, the friction force can be

neglected because the dominant force is the inertia force. Therefore, Eq. (2.17) becomes

(2.21)

By integrating Eq. (2.21) with regard to x, it gives

(2.22)

where C is independent with x.

Since the flow velocity is a function of time, independent on position x in the O-tube,

the pressure therefore changes linearly with x. Note that the pressures at inlet and outlet

of the pump are identical but with opposite sign (based on the pump theory), i.e. P1+P2

= 0, this results in a zero pressure point at the geometrical middle point of the O-tube.

Defining this zero pressure point as x = 0, then C = 0 according to Eq. (2.22).

22

Assuming the velocity varies sinusoidally, i.e. , where A is the velocity

amplitude and is wave angular frequency, the pressure is defined as:

(2.23)

The pressure variation with x is

(2.24)

And the pressure time variation at any position x is

(2.25)

which also takes the sinusoidal form, with the same frequency as the velocity time

variation.

The pressure variation with distance in the O-tube and with time at a fixed position is

shown schematically in Figure 2.16. The model pipe was placed at the middle of the O-

tube which is close to the zero pressure point. So the pressure at the pipe position is

close to zero.

2.3.2 In-field pressure condition

The pressure variation in real world conditions under gravity waves was reviewed from

the book of Basic Coastal Engineering (Sorensen 2006). The definition sketch of the

progressive surface wave is shown in Figure 2.17. The water surface profile is

expressed as a function of the position and time, which is

(2.26)

The unsteady Bernoulli equation for irrotational flow can be written as:

(2.27)

The velocity potential is solved as:

(2.28)

The horizontal and vertical water particle velocity can be determined by the velocity

potential, which are:

23

(2.29)

(2.30)

Substituting the velocity potential into the linearized form of the Bernoulli equation, the

pressure can be obtained, which is:

(2.31)

The first part on the right hand side of Eq. (2.31) is the hydrostatic pressure caused by

the surface water elevation. The second part is the hydrodynamic pressure induced by

the water particle acceleration. The two parts are shown schematically in Figure 2.18.

The pressure variation with position x and time t on the seabed where can be

derived as follows:

(2.32)

(2.33)

2.3.3 Comparison of pressure variation in the O-tube and in-field

The pressure variation with position is related to the hydrodynamic forces on pipelines,

whilst the pressure variation with time is associated with the pore pressure variation and

the soil liquefaction potential. It is worthwhile to compare the pressure variation

between that in the O-tube and in-field.

In order to have a quantitative comparison of the pressure variation in the O-tube and

in-field, the wave condition of a 100 year return period storm on Australias North West

Shelf was utilized. The wave parameters are: = 12.94m; = 286.12m; = 55.8m; =

14.76s; = 0.02196; . Provided a model length scale of , based on

the Froude similarity criterion, the time-scale and velocity scale can be derived, which

are , , respectively. Therefore, the velocity frequency in the model

test is . The in-field velocity amplitude can be obtained from Eq. (2.29), which

is 1.77m/s. The velocity amplitude in model is therefore 0.735m/s. By substituting the

scaled wave parameters into Eq. (2.23) - (2.25) and the prototype wave parameters into

Eq. (2.31) - (2.33), and assuming the in-field pipe is located at the same position as in

24

the O-tube, where x = 0, the pressure variation with time and the pressure gradient with

distance both in field and in the O-tube can be calculated, as listed in Table 2-4.

The results show that the absolute pressure and pressure variation with time in the O-

tube are zero, whilst the in-field values are non-zero and dependent on the water depth

and wave parameters. The differing pressure variation with time may lead to differing

seabed liquefaction behaviour (if there is any) between the O-tube model tests and field

condition. However, the pressure gradient along the flow direction in the O-tube is in

the same magnitude as in-field. As the hydrodynamic forces on the pipeline are mainly

relevant to the pressure gradient, this means the effect of the pressure difference on the

hydrodynamic forces on pipelines in the O-tube and in-field is relatively small.

Table 2-4 Pressure comparison between field and O-tube

Field O-tube

0

0

2.4 SUMMARY

The O-tube is an entirely new innovation developed specifically for investigating the

pipeline stability on an erodible seabed under severe tropical storm conditions, allowing

the interaction between pipe, flow and seabed to be faithfully reproduced. In order to

generate any desired velocity time series, the O-tube flume was calibrated. The

calibration was to establish the relationship between the input pump rotational speed

and the generated flow velocity in the O-tube, and examine the flow features in the O-

tube. A wide range of flow conditions, including steady current, oscillatory flow and

combined flow conditions were run to obtain the flow velocities corresponding to the

input pump speeds.

By applying the Affinity law and the fluid momentum equation to the calibrated results,

formulas were derived to describe the relationship between the pump speed and the flow

velocity for both steady current and oscillatory flow. The combined flow feature was

also examined. The derived formulas can be utilized to generate any target random

velocity time history within the capacity of the O-tube. An approach to produce

25

irregular velocity time histories was proposed. Several random velocity series, including

a scaled (1:5.8) 100-year return period storm from the North West Shelf of Western

Australia in 40 m water depth, were successfully reproduced using the proposed random

storm generation approach.

Flow features of the O-tube flume were also examined as a part of the calibration work.

The flow uniformity across the test section was checked. The bottom boundary layers

on both the Perspex false floor and the model seabed were measured. The turbulence

intensity was also examined, which was around 3% under steady current conditions.

In addition, the pressure variation in the O-tube was discussed. It was found the

pressure changes linearly with distance, with the zero pressure point being at the middle

of the O-tube geometry. The pressure variation with time is sinusoidal for a sinusoidal

oscillatory flow. The pressure at seabed level under a gravity surface wave for in-field

conditions was also examined. Comparison of the pressure in the O-tube and in-field

indicates that at the position of the model pipe, the pressure and its variation with time

in the O-tube are close to zero whilst in field they are dependent on water depth and

wave parameters. However, the pressure gradient along the flow direction in the O-tube

is in the same magnitude as that in field, which means the effect of the pressure

difference on the hydrodynamic forces on pipelines in the O-tube and in-field is

relatively small.

26

motor

pump VFD

Figure 2.1 A view of UWAs large O-tube

0 100 200 300 400 5000

0.5

1

1.5

2

2.5

u (

m/s

)

N (rpm)

u = 0.0055N

-500 -400 -300 -200 -100 0-2.5

-2

-1.5

-1

-0.5

0

u (

m/s

)

N (rpm)

u = 0.0050N

(a) (b)

Figure 2.2 Relationship between flow velocity and pump rotational speed for steady

current: (a) positive direction; (b) negative direction

0 100 200 300 4000

0.5

1

1.5

2

2.5T = 6s

T = 10s

T = 20s

T = 50s

T = 100s

Nmax (rpm)

um

ax(

m/s

)

Figure 2.3 Relationship between maximum flow velocity and pump rotational speed for

oscillatory flow

27

Figure 2.4 O-tube system curves and pump characteristic curves

Figure 2.5 Normalized pump characteristic curves for oscillatory flow with periods of

6s, 10s and 20s

Q (m3/s)

H(m

)

0 0.5 1 1.5 2 2.5 3 3.5 40

5

10

15steady current

T=50s

T=20s

T=10s

T=6s

Pump characteristic curves

N=485 rpm

336 rpm

264 rpm

192 rpm120 rpm

408 rpm

Q (m3/s)

H(m

)

0 0.2 0.4 0.6 0.8 1 1.2 1.40

2

4

6

8

10

H=7.7374*(6/T)*Q

28

(a) Ns = 24 RPM (b) Ns = 48 RPM

(c) Ns = 72 RPM

Figure 2.6 Comparison between anticipated and measured velocity (maximum &

minimum) for combined flow with T = 6s

No (RPM)

Max

imum

&M

inim

um

vel

oci

ty(m

/s)

50 100 150 200 250 300

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Measured max & min velocity

Anticipated max & min velocity

Ns=24 RPM

No (RPM)

Max

imu

m&

Min

imu

mv

elo

city

(m/s

)

50 100 150 200 250 300

-0.2

0

0.2

0.4

0.6

0.8

1



Ns=48 RPM

No (RPM)

Max

imu

m&

Min

imu

mv

elo

city

(m/s

)

50 100 150 200 250 300

-0.2

0

0.2

0.4

0.6

0.8

1

1.2



Ns=72 RPM

29

Figure 2.7 Target storm velocity time history (a) oscillatory flow part; (b) steady current

part; (c) combined flow velocity

30

Figure 2.8 Comparison of generated and target velocity time history

Figure 2.9 Velocity measurement locations across the middle test section

top lid

false floor

outsidewall

insidewall

E FD

B CA

31

N (RPM)

Uc

(m/s

)

-200 -100 0 100 200-1.5

-1

-0.5

0

0.5

1

1.5

A

B

C

(a) steady current

u (

m/s

)

N (rpm) N (rpm)

u(m

/s)

-200 -100 0 100 200-1.5

-1

-0.5

0

0.5

1

1.5

D

E

F

u (

m/s

)

N (rpm)

Figure 2.10 Velocity comparison at six locations across test section (steady current)

Nmax (RPM)

Um

ax

(m/s

)

50 100 150 200 250 3000

0.2

0.4

0.6

0.8

1

1.2

1.4 AB

C

(b) oscillatory flow, T = 20s

N (rpm)

um

ax

(m/s

)

Nmax (RPM)

Um

ax

(m/s

)

50 100 150 200 250 3000

0.2

0.4

0.6

0.8

1

1.2

1.4 DE

F

(b) oscillatory flow, T = 20s

N (rpm)

um

ax

(m/s

)

Figure 2.11 Velocity comparison at six locations across test section (oscillatory flow, T

= 20s)

u(m/s)

z(m

)

0 0.1 0.2 0.3 0.4 0.50

0.05

0.1

0.15

0.2

u* = 0.01166u(z) = (u*/k)ln(z/z0)z0=v/9u* for smooth bounu(z) =0.02915ln(104933.92

Fitting equation:

u(z) =0.02915ln(104933.92z)

measured velocity

curve fitting

Figure 2.12 Velocity profile in the boundary layer at Perspex false floor

32

Figure 2.13 Velocity profile in the boundary layer at model seabed

Figure 2.14 Turbulence intensity of steady current

Velocity(m/s)

Tu

rbu

len

ce

Inte

nsity

(%)

-2 -1 0 1 20

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Frame 001 04 Mar 2010 Frame 001 04 Mar 2010

33

Figure 2.15 Schematic plan view of O-tube

Figure 2.16 Pressure variation in O-tube

34

Figure 2.17 Schematic of the progressive surface wave (Sorensen 2006)

Figure 2.18 Pressure distribution with water depth (Sorensen 2006)

35

CHAPTER 3. O-TUBE EXPERIMENTS DESCRIPTION

3.1 SIMILARITY ANALYSIS

3.1.1 Similarity requirement for pipeline stability

The physical process of pipeline stability involves hydrodynamic forces acting on the

pipeline and soil resistance. The stability criterion can be expressed by the ratio of the

hydrodynamic force, which is proportional to the square of the flow velocity, to the soil

resistance, represented by the effective pipe weight. Therefore, the Froude number,

reflecting the moving resistance of an object in the flow, is the governing parameter for

pipeline stability and needs to be satisfied in the physical model tests. The Froude

similitude requires:

(3.1)

where V is the flow velocity, g is the gravitational acceleration and L is the

characteristic geometry, which is the pipe diameter in the pipeline stability physical

tests.

In the flume tests, the gravitational acceleration, g, is kept the same as in the prototype,

i.e. . This gives and therefore , in which T is the time-

scale. Once the model pipe geometry scale is determined, the flow velocity and the

time can be scaled accordingly. The scale of pressure can also be derived based on flow

momentum equations, which is . Provided a fluid with the same density is

used in the model tests, the scale of the pressure becomes , indicating that the

scale of the pressure is the same as the length scale. The Froude similitude criterion is

also a scaling requirement for general hydrodynamic models (short-wave and long-wave

models), based on the governing equations of the momentum of incompressible fluid,

i.e. Navier-Stokes equations in the vertical direction (Hughes, 1993). The geometric

length here is the characteristic vertical length.

The scale requirement of the Reynolds number (

) and Keulegan Carpenter

number (

) should also be satisfied in the model tests. Similarity of the

Reynolds number requires

. Given the fluid with the same viscosity as

prototype is used in the model test, i.e. , the similarity requirement of Reynolds

36

number is . As the similarity of Froude number requires , it is

impossible to satisfy both the Froude similarity and Reynolds similarity. Since the

Froude number is the governing parameter in the hydrodynamic stability test, the

similarity of the Reynolds number can therefore not be satisfied.

According to the Froude similarity ( ), the scale of the KC number

is

, indicating that the similarity of the KC number is satisfied if the

Froude similitude is employed.

3.1.2 Similarity requirement for seabed sediment transport and liquefaction

One of the key physical phenomena involved in the pipeline stability process is the

seabed mobility, in the form of sediment transport and seabed liquefaction. The

similarity requirement for the seabed sediment transport and seabed liquefaction should

be considered in the pipeline stability model test.

Similarity of sediment transport

The bed load dominated sediment transport is governed by Shields parameter, which is

the non-dimensional seabed shear stress (Shields, 1936):

(3.2)

where is the particle density, is the water density, is the gravitational

acceleration, is the medium grain size of the sediment, is the bed shear stress.

Under oscillatory flow, the bed shear stress can be expressed as (Soulsby, 1997):

(3.3)

where is wave friction factor, and is the amplitude of the oscillatory flow just

above the seabed boundary layer.

Soulsby (1997) proposed an empirical formula for :

(3.4)

in which,

,

, is the Nikuradse equivalent sand grain roughness,

.

According to Eq. (3.2) - (3.4), the scale of the Shields parameter is

37

(3.5)

Eq. (3.5) indicates that in order to satisfy the similarity of Shields parameter, the size of

the sediment particle should be scaled by the same ratio as the pipe diameter. However,

the scaling down of the particle size may lead to non-cohesive sediment in prototype

becoming cohesive sediment in the model tests. The property change of the sediment

can cause a number of problems. The sediment transport process in the model test will

differ that in the prototype condition. In addition, the property change in the sediment

can lead to differing pipe-soil interaction, which is one of the key aspects in determining

the pipeline stability. Therefore, a prototype seabed sediment from the Australias North

West Shelf was employed in the O-tube pipeline stability model tests.

Since the prototype sediment was used in the model tests, i.e. , the scale of

Shields parameter becomes , indicating that the bed shear stress in the

model tests is lower than that in prototype. One possible scenario is that the shear stress

in the model test is below the threshold value of the sediment movement so that no

sediment movement would occur. To minimise the distortion of the sediment transport

behaviour, a larger length scale is preferred in the model tests.

Similarity of seabed liquefaction

Under progressive wave action, seabed liquefaction due to pore pressure build-up may

occur. The pore pressure build-up is governed by the simplified Biot equation (Sumer

and Freds e, 2002), which is

(3.6)

where is the excess pore pressure in the seabed, is the soil depth, is the

coefficient of consolidation, defined as

(3.7)

where is the coefficient of permeability and is the modulus of the soil. For sandy

soil, is proportional to the square of the grain size of 10% passing, i.e. .

denotes the source term, representing the cyclic shear stress generated from the

progressive wave action. f can be expressed as f

, in which is the number of

cycles to cause liquefaction, is the initial effective stress, which is

38

(3.8)

where is the submerged specific weight of the soil, is the soil depth from the seabed

surface downwards and is the coefficient of lateral earth pressure.

Scaling criteria can be derived from Eq. (3.6) with non-dimensional form, using the

following non-dimensional factors: degree of consolidation

, where is

pore pressure of the steady state; characteristic time for pore pressure dissipation

, where denotes the drainage path length; drainage path ratio

; Non-

dimensional source term

, where T is wave period and H is wave height.

The governing equation for pore pressure build-up is then expressed as

(3.9)

Similitude of the physical process governed by the above equation can be achieved if

the non-dimensional factors are the same in the model and in prototype. This requires:

1) The characteristic time for pore pressure dissipation to be identical in the model and

prototype, i.e.

. Assuming the same fluid is used in the model test as

in prototype condition, i.e. and the modulus of the soil is the same,

, the scaling requirement becomes

(3.10)

It should be noted that the geometric scale of pipe diameter and the sediment depth is

independent, which means the length scale of the sediment depth, , is not necessarily

identical to the length scale mentioned above. In the O-tube tests, the soil depth was

constrained by the height of the test section.

2) The source term is identical in the model and prototype, i.e.

. As

, this requirement will be satisfied given . However, this scale

requirement is satisfied only when the pressure on the model seabed is scaled

according to , which is not the case in the O-tube, as discussed in chapter2.

39

Summary

Similarity analysis of the sediment transport indicates that in order to achieve the same

sediment transport behaviour in the model tests, the size of the sediment particle should

be scaled by the same ratio as the pipe diameter. However, the scaling down of the

sediment particle size could transfer non-cohesive sediment into cohesive sediment and

therefore change the fundamental erosion property of the soil. The pipe-soil interaction

and seabed liquefaction behaviour will also be altered due to the change of the sediment

property. Therefore, prototype sized sediment was employed in the O-tube tests. As the

hydrodynamic parameters are scaled down in the model tests based on the Froude

criteria, the bed shear stress in the model tests is smaller than that in prototype, resulting

in less severe sediment transport in the model tests. To minimise the distortion of the

sediment transport behaviour, the tests were conducted at a relatively large scale in the

O-tube flume.

3.2 EXPERIMENTAL SETUP

The O-tube tests are distinguished from previous pipeline stability tests mainly in two

aspects. First, the large O-tube flume is capable of producing random storm histories at

a relatively large scale. Secondly, the active pipe control system can effectively isolate

the force between the model pipe and its control system so that the pipe is able to

respond freely to hydrodynamic loads and soil resistance, without the interference

arising from the control system. A typical experimental setup is shown in Figure 3.1.

The detailed test setup is set out as follows.

The instrumented model pipe and actuator control system, discussed in the following

sections, were designed, fabricated and installed by the O-tube team at UWA.

3.2.1 Instrumented model pipe

The instrumented model pipe is shown in Figure 3.2. It consists of a middle test section

and two dummy sections. The total length of the pipe is 990mm. The length of the test

section is 888mm and the length of the two dummy sections is 50mm. The gap between

the test section and dummy sections is sealed with an O

Documents

Luo Chengcai 2012 Part 1 on Bottom Stability