Content uploaded by David J White

Author content

All content in this area was uploaded by David J White on May 23, 2016

Content may be subject to copyright.

OTC-27034-MS

The Impact of Submarine Slides on Pipelines:

Outcomes from the COFS-MERIWA JIP

White D.J. (University of Western Australia, UWA), Randolph M.F. (UWA), Gaudin C. (UWA), Boylan N.P.

(Norwegian Geotechnical Institute, formerly with UWA), Wang D. (UWA), Boukpeti N. (UWA), Zhu H. (Fugro

Advanced Geomechanics, formerly with UWA) & Sahdi F. (Universiti Malaysia Sarawak, formerly with UWA)

Copyright 2016, Offshore Technology Conference

This paper was prepared for presentation at the Offshore Technology Conference held in Houston, Texas, USA, 2–5 May 2016.

This paper was selected for presentation by an OTC program committee following review of information contained in an abstract submitted by the author(s). Contents

of the paper have not been reviewed by the Offshore Technology Conference and are subject to correction by the author(s). The material does not necessarily reflect

any position of the Offshore Technology Conference, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the

written consent of the Offshore Technology Conference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words;

illustrations may not be copied. The abstract must contain conspicuous acknowledgment of OTC copyright.

Abstract

This paper presents key outcomes of a 3-year Joint Industry Project funded by 6 Operators on the impact

of submarine slides on pipelines. This JIP developed new techniques to simulate slide runout, and assess

the resulting loading and deformation of seabed pipelines. The work was distilled into guidance for

practical application, which has found adoption on projects.

The JIP spanned (i) characterization of soils at the solid-fluid transition, (ii) computational modelling of

slide runout – via depth-averaged and continuum finite element methods, (iii) physical and numerical

modelling of slide runout and pipeline impact, and (iv) analytical studies of pipeline response during

slide loading. These elements combine to provide an improved practical basis for quantifying the risk

associated with slide-pipeline interaction.

To characterize very soft seabed soils, a new geotechnically-based framework was devised based on

extensive measurements of different soils. This framework spans the solid-fluid boundary that is crossed

as slides evolve into a debris flow and turbidity current. It is shown that the geotechnical link between

water content and shear strength extends continuously – with no phase transformation – far into the fluid

domain, allowing a single rheology to be applied throughout.

Computational modelling of slide runout used a hierarchy of methods, from large deformation finite

element analysis (LDFE) (with rate effects and softening at soil element level), through depth-averaged

runout, to energy-based analytical solutions. In some regimes of behavior the simpler methods suffice,

allowing efficient use of Monte Carlo methods to tackle uncertainty. More complex runout modes can

be replicated by newly-developed LDFE techniques.

From a runout analysis results, pipeline impact loads can be assessed using new solutions for the bearing

capacity and drag forces on pipelines developed from numerical and physical modelling, which again

unify concepts from fluid dynamics and geotechnics. Finally, simple analytical methods for assessing

the structural response of a pipeline to a known slide loading are provided. These solutions allow rapid

assessment of the response of a pipeline to a specified slide loading.

These advances improve the methods available for quantitative assessment of slide runout and slide-

pipeline interaction, allowing better determination of the resulting geohazard risk.

2 OTC-27034-MS

Introduction

The Australian oil and gas industry is moving into deeper waters, further from shore. Around 2007,

when the present Joint Industry Project was conceived, planned gas developments off the continental

shelf of North West Australia faced significant geohazards that had not been encountered in this region

previously. These geohazards included interaction of submarine slides and pipelines, motivating

research to address the uncertainties in engineering assessments of slide-pipeline risk, particularly in the

context of the carbonate soils found offshore Australia, which have unusual geotechnical properties.

There has been extensive research into certain submarine slides systems that lie in oil and gas

development regions, such as the Storegga slide off the coast of Norway (Bugge et al. 1998) and the

margins of the Mississippi delta where mudslides are triggered by major hurricanes (Gilbert et al. 2007).

The submarine slide hazards of Australia’s North West Shelf have received less attention until recently

(Hengesh et al. 2011, 2013, Zhang et al. 2015).

In regions where slides may cross pipeline routes, designers must estimate the likelihood and severity of

future slides, and the consequence of impact by the slide material. Recent reviews of submarine slide

behaviour are presented by Locat & Lee (2002) and Masson et al. (2006). Parker et al. (2009) and Evans

(2010) review the best practices and challenges of engineering practice related to slide-infrastructure

impact behaviour, and highlight the difficulties associated with the quantification of slide strength and

the resulting impact forces.

The process of slide failure, run-out and fluidisation is accompanied by a change in strength (or

mobilised shear stress) of more than three orders of magnitude. Also, the strain rate within the

deforming soil is far higher than the rates in usual geotechnical problems. Figure 1 shows an idealised

cross-section through a seabed slope. A submarine slide is shown with indicative values of the mobilised

shear strength, velocity and density, based broadly on reported values and typical conditions for fine-

grained sediments (Schwab et al. 1996, Marr et al. 2002, Locat & Lee 2002, Masson et al. 2006).

Evaluation of the risk associated with slide – pipeline impact requires assessment of:

the likelihood of a submarine slide occurring;

whether the slide (or distribution of probable slides) will impact the pipeline;

the consequential (distribution of) loading and deformation/strain in the pipeline.

The JIP addressed the latter two steps, focusing on the geotechnical aspects of geohazard assessment.

Figure 1. Schematic of submarine slide behavior showing typical material parameter ranges

OTC-27034-MS 3

Project aims

The overall aim of the project was to address particular technical challenges of assessing the effect of

submarine slides on pipelines. These included evaluating how to:

1. Select a geotechnical model to capture the behavior of a submarine slide, from initiation

through the run-out process, as the material properties change from solid towards fluid.

2. Apply that geotechnical model in a simulation of slide runout, using various computational

techniques (continuum FE, depth-averaged and analytical energy-balance), to yield estimates

of slide geometry and properties on impact with a pipeline.

3. Assess the impact forces on a pipeline caused by a slide with given geometry and material

properties.

4. Assess the resulting strain and deformation in a pipeline caused by these impact forces, also

considering the soil restraint on the pipeline outside of the slide impact.

These four challenges represent key steps in assessments of the impact of a given slide on a pipeline.

The project tackled these aims through physical model tests, using the geotechnical centrifuge facilities

at UWA, and large deformation finite element analysis. In addition, a characterisation study was

performed to investigate the mechanical behaviour of soil across the solid-fluid boundary, and a new

depth-averaged approach was used to allow comparisons with industry standard procedures, and for this

modelling approach to be refined and extended.

The objectives and the associated activities are summarised in Figure 2. The following sections describe

the key activities and outcomes:

1. Soft soil characterization – models across the solid-fluid boundary

2. Modelling of slide runout, including (a) physical modelling, (b) large deformation finite

element analysis, (c) depth-averaged numerical analysis and (d) energy balance methods;

3. Modelling of slide-pipeline interaction, including (a) physical modelling and (b) finite

element analysis, leading to (c) practical calculation methods for design;

4. Modelling of pipeline structural response – simple design expressions.

Potential slide

Volume, weight

Effect on pipeline / infrastructure

Slide loading: magnitude, duration:

contributions from soil strength and inertia

Seabed erosion profile

Predicted slide

runout

Height, velocity,

internal strength

Site investigation

Seabed strength

characteristics

Project focuses on measuring

and quantifying these links, within a

geotechnical framework

Initial volume, strength

slide velocity, height, reduced strength

V

v

H

su1

su2

Centrifuge and numerical modelling,

distilled into simple methods for design

su1

su2

v

F

Slide properties

pipe force, movement, seabed erosion

Slide behaviour

Slide-pipeline

interaction

Figure 2. Project scheme showing targeted areas of uncertainty

4 OTC-27034-MS

Soft soil characterization – models across the solid-fluid boundary

Background

The rheology of soils across a range of water content spanning the conditions relevant to intact soil and

to a weak fluidised submarine slide was studied. A key aim was to devise a basis for characterising the

strength behaviour of both a fluid-like material (relevant to the final run-out stages of a slide) and a solid

material (representative of the intact material) using the same type of material model.

In current engineering practice geotechnical parameters such as shear strength, sensitivity and water

content are used to characterise the constitutive properties of the intact seabed from which submarine

slides form. These parameters form the basis of any assessment of the stability of a slope, and therefore

the tendency for a slide to be triggered. However, in current practice, these parameters are usually set

aside after failure, and the sliding material is then characterised by ‘fluid’ properties – such as yield

stress and viscosity, within a Bingham-type viscoplastic material model. These properties are usually

assessed based on a back-analysis of historic slide features, and are not connected to the geotechnical

parameters derived for the site.

The accuracy of hindcasting and forecasting methods would be improved if a connection could be

created between the geotechnical properties of the intact soil and the material properties that govern the

run-out behaviour as the slide transforms from the intact condition, through a debris flow, into a

turbidity current. To create this connection it is necessary to bridge the domains that are traditionally

termed ‘solid’ and ‘fluid’.

Material models for thick fluids and soft solids

Models for the strength of two-phase materials that are considered to be either thick fluids or soft solids

take into account two principal effects – the rate at which the material is being strained, and the relative

proportions of the solid and fluid fractions.

It is widely recognised that soils sheared at different strain rates show different shear strengths (Dayal &

Allen 1975, Biscontin & Pestana 2001). The equivalent relationships for a fluid have evolved from

Newton’s law of viscosity and in thick fluids, the shear stress, , must reach a minimum (yield) value,

y, before flow commences. This behaviour can be described by the general relation

n

y (1)

where μ represents the viscous property of the fluid. With n equal to 1, Equation (1) represents the two-

parameter Bingham model, which assumes a linear variation of the shear stress with shear strain rate,

once the yield stress is exceeded. In its general three-parameter form, Equation (1) is referred to as the

Herschel-Bulkley model. The Herschel-Bulkley model, with y = 0 is exactly equivalent to the soil

mechanics power law model (e.g. Biscontin & Pestana 2001). The modelling of strain rate effects

therefore has obvious similarities within the solid and fluid domains.

The treatment of moisture content, w, or the relative proportions of the solid and fluid fractions, is not so

directly comparable, although similarities exist. For example, critical state soil mechanics theory leads to

exponential relationships between moisture content and shear strength (e.g. Wroth & Wood 1978) that

are well established for remoulded clays via index tests and the liquidity index parameter (LI). Within

the fluid mechanics literature, the equivalent behaviour is often described by empirical relationships that

OTC-27034-MS 5

link the yield stress and viscosity to the volumetric concentration of solids, Csv (O’Brien & Julien 1988,

Major & Pierson 1992). Csv is the quantity commonly used within the fluid dynamics literature instead

of moisture content. These relationships are often in the form of exponential functions such as

sv1sv2 C

1

C

2y e,e (2)

with the parameters 1, 2, 1, 2 being determined by laboratory test measurements. Although the

functional form is different from the soil mechanics approaches, the general trends are similar. In order

to apply these relationships to submarine slides, in which material transitions from a solid to a fluid, the

key issue is whether these relationships are continuous across the solid-fluid boundary, or whether a

distinct phase transformation exists, marking a step change in strength properties as the moisture content

of a given solid-fluid mixture changes.

The JIP undertook a range of laboratory tests to characterise the strength behaviour of different soft soils

across the solid-fluid boundary. These tests included T-bar and ball penetrometer, vane shear,

viscometer and fall cone tests. The three soils were Burswood clay (a natural clay from nearby Perth),

kaolin clay, and a natural carbonate silt from offshore Australia. These soils were tested at 6-8 levels of

moisture content, with the tests being performed at up to 8 different rates (spanning approximately 2

orders of magnitude of strain rate). Theoretical solutions were used to link the rate at which the tests

were performed to a representative strain rate for the deforming soil. This allowed the effects of strain

rate to be identified across a wider range of strain rates, due to the different ranges achievable in each

type of test.

The principal observation from this study, which is described in more detail by Boukpeti et al. (2012a,

2015), was that there is a continuous relationship between moisture content – via whichever measure is

chosen – and shear strength across the solid-fluid boundary (Figure 3). The tests spanned a range of

liquidity index from 0.7 to 6 and a range of shear strength from 0.01 kPa to 10 kPa. For all three

soils, the variation in strength, su, with moisture content (or the related parameters, LI and Csv) was well

captured by any of the following three forms of equation:

1

b

u1

saw

(3)

2

b

u2

saLI

(4)

3sv

b

C

u3

sae (5)

where different values of the parameters a1-a3 and b1-b3 were found for each soil.

A notable difference between the soils is that at high moisture contents the carbonate silt is significantly

weaker than the other soils tested. This may be due to the lack of electrochemical effects present. Soil

particles with a clay mineralogy have attractive forces arising from the ionic layer present on the surface

of clay particles. In contrast, carbonate particles do not feature this effect. This implies that for a given

level of water entrainment – during a submarine slide, for example, but also during disturbance during

pipeline laying – a carbonate soil will be more susceptible to a loss of shear strength due to water

entrainment.

In all soils tested, the transition in the governing behaviour is gradual and continuous, and there is no

evidence of a distinct phase transformation at a boundary between regions that might be termed solid or

fluid behaviour.

6 OTC-27034-MS

The shear strength measurements obtained for different strain rates confirmed that the strength of the

material was higher at higher rates of shearing (Figure 4). This non-linearity of the strength – strain rate

relationship favours the use of the Herschel-Bulkley model (Eq. (1)), with normalized strain rate

parameters, over the simpler Bingham approach; or alternatively, a logarithmic relationship as shown in

Figure 4. These rate-dependency parameters did not vary across the range of moisture contents tested.

As a result of this study, a model has emerged that combines the influences of strain rate, remoulding

and changes in moisture content across gross changes in the operative soil strength, su-op, – spanning the

solid-fluid boundary. The model takes the general form

95

1ξ3ξ-

remrem

ref

1op-u eδ1δ

γ

γ

1s

n

b

wa

(6)

where rem is the inverse of the soil sensitivity and , 95 are the cumulative shear strain and that required

to achieve 95 % softening. The final bracket links the accumulated plastic strain with the degradation

from the intact to the fully remoulded strength, following the approach used widely in numerical

analysis of large deformation problems (Wang et al. 2015). Parameters for a specific soil can be derived

from laboratory or in situ tests using penetrometers and viscometers, as well as conventional index tests.

0123

Water content, w

0.001

0.01

0.1

1

10

Shea

r

st

r

ength, s

u

(kPa)

kaolin

Burswood

carbonate soil

0123456

Li

q

u

i

d

i

t

y

i

n

d

ex, LI

0.001

0.01

0.1

1

10

100

Shea

r

st

r

ength, s

u

(

k

Pa)

kaolin

Burswood

Critical State Line

carbonate soil

s

u

= 170 exp(

4.6

.

LI)

Figure 3. Effect of water content on soil strength across the solid-fluid boundary – comparison of three soils

Figure 4. A unified relationship between strain rate and soil strength – comparing data obtained with kaolin tested across 5

orders of magnitude of strain rate and 3 orders of magnitude of strength

OTC-27034-MS 7

Equation (6), with a single set of the material parameters, can characterise the soil response across three

orders of magnitude in strength, and five orders of magnitude variation in strain rate. These relations are

amenable to inclusion in numerical modelling of large deformation processes. In these analyses, a

simple Tresca or von Mises failure criterion is commonly adopted for the material strength, updating the

strength according to the current strain rate or accumulated strain (e.g. Zhou & Randolph 2007). This

study highlighted how changes in moisture content could also be incorporated in the same numerical

modelling strategy, so the transition from solid to fluid can be captured without the need to consider

multiple material phases. The benefit of this unified framework is that it allows the full process of slide

triggering, run-out and resedimentation to be simulated without needing to distinguish between different

material phases, and without needing to discard the geotechnical framework that underpins conventional

engineering techniques for site characterisation and the design of seabed infrastructure.

Modelling of slide runout

Physical modelling of slide runout

An ambitious aim of this project was to simulate submarine slides in the geotechnical drum centrifuge at

UWA, to provide slide runout observations for well-characterised material in controlled conditions, to

compare with numerical analysis. Centrifuge modelling has not been widely used to model submarine

slides, despite being a common technique for simulation of other aspects of offshore geotechnics.

The majority of previous experimental studies of submarine slides begin with a fully fluidised slide

mass, with a strength of < 100 Pa (Mohrig et al., 1999; Mohrig and Marr, 2003; Mohrig et al., 1998 and

Ilstad et al. (2004a; 2004b; 2004c)). There had previously been no experiments that simulated the

transition from the intact (but post-failure) state to the fluidised condition, preventing a connection being

made between the in situ geotechnical properties and the fluidised behaviour in the subsequent run-out.

The experimental arrangement allowed slides to be triggered from an intact block within the drum

centrifuge channel, with the block then running out over an erodible seabed (Figure 5). A block of clay

was consolidated in a release box from a slurry. After consolidation, the box was rotated to an inclined

position, so that the block lost potential energy when the slide was initiated. The slide was triggered by a

door in the box being rapidly pulled upwards whilst concurrently a heavy mass was released to push

against the rear of the slide.

Figure 5. Arrangements for slide run-out modelling in drum centrifuge (Boylan et al. 2010)

8 OTC-27034-MS

The observed run-out distances, from the centre of the intact block to the toe of the run-out debris,

ranged from 30.7 m to 119 m (in prototype dimensions). The tests were rather complex, involving high

speed events with measurements of pressure, forces and displacements over a very short period

(typically lower than 200 ms), as well as concurrent high speed image capture. A novel high-speed

wireless data acquisition system was developed for this project (Gaudin et al. 2009). To differentiate the

seabed from the run-out material and to evaluate potential seabed erosion, a dyeing technique was

developed to colour the seabed (Sahdi et al. 2010).

Example profiles of post-test slide debris geometry and moisture content are shown in Figure 6. The

slides are thinner at the toe and show increasing moisture content with increasing runout distance –

indicative of water entrainment. The post-slide consolidation of the debris exceeded the wetting of the

material during the slide event (Figure 6b). The relict slide debris is denser, i.e. at lower moisture

content, than prior to failure because the undrained failure during run-out is accompanied by the

generation of positive excess pore pressure (because the slide material is initially on the wet side of the

critical state). Subsequent reconsolidation of the debris material leads to a reduction in moisture content

as the excess pore pressure dissipates. The final state is therefore denser than the initial state, and also

denser than the normally consolidated state at the same stress level (indicated by point A on Figure 7),

even if water is entrained during the run-out. This observation, and the theoretical background in Figure

7, should be considered when interpreting the present-day strength measurements of relict slides. A

similar effect has been hypothesised by Palmer (1997) as a tool for identifying relict iceberg scours

beneath the seabed.

Visual examination of the run-out material revealed morphological differences between the run-out

slides. At very low initial strength (< 1 kPa), the depositied material appeared homogenous and there

was little evidence of distinct features on the surface. At higher initial strength (> 1 kPa), a zone of

distinct compression ridges was evident at the terminal lobe, perpendicular to the run-out direction

(Figure 8a). The compression zones were similar in geometry to those identified in the field, such as the

examples shown in the southern flank of the Storegga slide, offshore Norway (Gafeira et al. 2007). At

very high initial strength (> 10 kPa), retrogressive wedge failures were observed (Figure 8b), similar to

retrogressive wedges identified in the upper part of the Storegga submarine slide (Bryn et al. 2004).

Figure 6. Example post-slide surface profiles and moisture content distribution

OTC-27034-MS 9

The mobility and scale of the centrifuge slides is characterised by the run-out ratio, H/L, and the slide

volume, V. To illustrate the relevance of the model slides to field conditions, these characteristics can be

compared with relict slides observed in the field (Elverhøi et al. 2005, Figure 9). These centrifuge results

fall within the range of field observations of submarine slides, albeit at the lower end of the volume

scale due to the limited volume of sliding material. Given that the overall behaviour appears broadly

representative of field conditions, the local measurements of changing strength and water content

provide valuable evidence to support the development of models for simulating these phenomena that

will ultimately be applicable to field scale events.

Figure 7 Simplified stress-specific volume path during slide run-out and debris reconsolidation

Figure 8 Morphological features in centrifuge models (a) compression ridges at toe (b) retrogressive wedge failures at scarp

10 OTC-27034-MS

Figure 9. Relationship between runout geometry and slide size: centrifuge results vs. field data (H is the maximum vertical

height of the debris flow source above the deposit, and L is the horizontal distance from source to deposit)

Numerical modelling of slide runout – large deformation finite element analysis

The two main objectives of the numerical modelling of slide runout in this project were to

Investigate the feasibility of using modern large deformation finite element (LDFE) analysis to

model slide run-out, allowing conventional geotechnical soil models to be used for the flowing

material and the seabed.

Develop a depth-integrated numerical approach (similar to BING and its variants, Niederoda et

al. 2003) with extended flexibility in terms of rheological models for the slide material and the

geometry of the seabed and the initial slide block.

The second objective is discussed in the following section.

The large deformation finite element (LDFE) approach developed during this project was a variation of

the so-called ‘remeshing and interpolation technique with small strain’ (RITSS) originally developed by

Hu and Randolph (1998). The overall scheme of the RITSS is to divide the overall displacements of the

continuum element into a series of incremental steps. The displacements of the element in each step

have to be small enough to avoid gross distortion of the soil element, in order that each small strain step

is accurate. A Lagrangian calculation is thus performed in each increment, followed by remeshing the

deformed geometry and Eulerian ‘convection’ of the stresses and material properties from the old mesh

to the new mesh.

The approach was implemented with the commercial finite element package, ABAQUS. A master

program, coded in Fortran, calls ABAQUS and the subroutine that performs interpolation of the field

variables. Several Python (the script language built into ABAQUS) files were written to extract the field

variables from the result files and to control the mesh regeneration.

For analysis of submarine slides, the technique was extended from static to dynamic analysis, using the

techniques described by Wang et al. (2013). In addition, a technique termed ‘element addition’ was

OTC-27034-MS 11

developed to improve the computational efficiency of both static and dynamic LDFE analyses that

involve moving boundaries. The RITSS approach is based on frequent mesh generation to avoid element

distortion. In dynamic RITSS, the field variables mapped from the old to the new mesh involve not only

the stresses and material properties, but also the nodal velocities and acceleration. Using the element

addition technique, new soil elements are attached to the domain boundaries periodically when the soil

near the boundaries becomes affected by large displacements of the sliding material.

The robustness of the techniques was validated and assessed through example problems including

vibration of an elastic plate, large-amplitude lateral displacement of a seabed pipeline, and movement of

a non-deforming landslide down a slope (Wang et al. 2013). Rate-dependent and softening undrained

shear strength was implemented in the LDFE analyses.

A parametric study was then undertaken considering slide mass running out over a firm (non-deforming)

seabed (Figure 10). The varied parameters included (i) initial strength (su), (ii) sensitivity (St), (iii)

brittleness (95), (iv) slide size (H, L) and (v) seabed slope (β). In addition, LDFE analyses that

represented each of the centrifuge model slides were performed using the relevant geometry and soil

properties.

Figure 10. Initial geometry explored in parametric study of slide run-out behaviour

The resulting mechanisms of runout fell into three distinctive patterns comprising (i) elongation (a single

stable slide mass), (ii) breakaway (where the head of the slide mass separated from the following

material) and (iii) block sliding (where the slide mass underwent little internal deformation but

accelerated down the slope in an unstable – accelerating – manner). The overall length of run-out varied

from as little as 20 m to over 2 km (at the point where the analysis had to be terminated – due to the

slide not decelerating even after several days of computation).

Example results highlighting these different mechanisms are shown in Figure 11 and Figure 12. Velocity

contours for an elongation case are shown for different stages of run-out in Figure 11. The LDFE shows

successive overtopping of the toe material by faster moving material behind the toe (see material at -

60 m at t = 10 s, and at -252 m at t = 50 s). Contrasting results for a breakaway case are shown in Figure

12 where separation of the faster moving front end of the slide occurs at times of 25.2 s (at -55 m) and

29.2 s (at -240 m).

Space constraints prevents a full description of all observations, but additional information is provided

in White et al. (2011). The parametric study showed that run-out length is a function of several

combined factors. It increases with decreasing interface strength, increasing slope inclination and

increasing height of the slide mass. These are generally intuitive. More surprising is the influence of the

internal shear strength. A higher internal shear strength of the soil mass (e.g. due to low sensitivity) can

limit the internal shearing (and thus elongation) resulting in a higher ratio of driving force to basal

resistance and a consequently longer run-out.

Elongation tends to occur when the basal resistance along the seabed is relatively large compared with

the driving force. For example, ductile elongation is more likely to occur as the interface shear strength

12 OTC-27034-MS

increases or the slope inclination is reduced. Decreasing the mobilised soil strength in the mass has a

similar effect to increasing the interface shear strength, since that leads to greater elongation and thus

increased sliding resistance.

The LDFE study demonstrated the capability of modern continuum-based solid-body finite element

techniques to mimic submarine slide run-out behaviour. This has been proven using a technology that is

already widely used for geotechnical boundary value problems involving gross deformations and

changes in geometry. This opens up the possibility of modelling submarine slide run-out using soil

constitutive models and input parameters that are consistent with geotechnical site characterisation

studies, albeit through considerable computational effort.

Figure 11. Velocity distributions (in m/s) for LDFE runout case with elongation and progressive failure developing in the

middle slide zone

Run-ou

t

(

m

)

Slide thickness (m)

-300 -250 -200 -150 -100 -50 050

0

2

4

6

Vel

9.0

8.0

7.0

6.0

5.0

4.0

3.0

2.0

1.0

Case 2, t = 10 s

Run-out

(

m

)

Slide thickness (m)

-65 -60 -55 -50 -45

0

2

4

6

Scaled size

Run-ou

t

(

m

)

Slide thickness (m)

-300 -250 -200 -150 -100 -50 050

0

2

4

6

Vel

6.0

5.0

4.0

3.0

2.0

1.0

Case 2, t = 60 s

Run-out (m)

Slide thickness (m)

-310 -305 -300 -295 -290

0

2

4

6

Scaled size

R

u

n

-ou

t

(

m

)

Slide thickness (m)

-300 -250 -200 -150 -100 -50 050

0

2

4

6

Vel

7.0

6.0

5.0

4.0

3.0

2.0

1.0

Case 2, t = 50 s

Run-ou

t

(

m

)

Slide thickness (m)

-258 -256 -254 -252 -250 -248

0

1

2

3

Scaled size

OTC-27034-MS 13

A remaining key limitation of the LDFE approach is that the influence of water entrainment and

changing moisture content, as identified in the centrifuge model tests, is not yet explicitly accounted for.

It can be incorporated implicitly by adopting a higher sensitivity parameter than is measured in

undrained (constant moisture content) conditions but this form of correction is somewhat artificial. The

effects of water entrainment will presumably be more significant near the top and base of the slide –

where water can enter the main body of material – and will be more significant in material that is more

susceptible to cracking and water ingress.

Run-ou

t

(

m

)

Slide thickness (m)

-250 -200 -150 -100 -50 050

0

2

4

6

Vel

6.0

5.5

4.9

4.4

3.8

3.3

2.7

2.2

1.6

1.1

0.5

Case 3, t = 10 s

Run-ou

t

(

m

)

Slide thickness (m)

-250 -200 -150 -100 -50 050

0

2

4

6

Vel

6.0

5.4

4.8

4.2

3.6

3.0

2.4

1.8

1.2

0.6

0.0

Case 3, t = 25.2 s

Run-ou

t

(

m

)

Slide thickness (m)

-250 -200 -150 -100 -50 050

0

2

4

6

Vel

5.0

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Case 3, t = 29.2 s

Figure 12. Velocity distributions (in m/s) for LDFE runout case with repeated breakaway of outrunner blocks

14 OTC-27034-MS

Depth-averaged numerical modelling of slide runout

Numerical modelling of debris flow run-out is commonly modelled using finite difference flow models

based on depth-integrated equations of mass and momentum conservation, solved within a Lagrangian

framework. Examples of this approach include the program BING, developed by Imran et al. (2001).

Except for changes in the shear strength due to viscous strain rate effects, the shear strength remains

constant during the runout process. Although the BING software is freely available, it is not possible to

alter the rheological model or the other elements of the program.

For this project, coding was developed in MATLAB® entitled UWA-SM3 (Submarine Mass Movement

Modeller), which is described in Boylan and White (2016). This code allowed for the implementation of

additional features that are not included in BING, and permitted this project to explore in more detail the

underlying behaviour of the debris flow (e.g. different constitutive models, fluid drag on the slide front

and strain softening behaviour), with full control of the input and output.

The key building blocks of the depth-averaged numerical techniques for simulating slide run-out, such

as the BING program, are the vertical profiles of velocity and mobilised shear strength at any ‘slice’

within the slide. New solutions for these building blocks have been generated for additional forms of

rheological model not previously explored (Boukpeti et al. 2012b). These solutions provide a simple

method to explore the loading on a pipeline that is oriented across the path of the slide, for a given slide

height and speed, and given rheological properties. The solutions show the relative contributions of the

soil strength and the inertial drag, as well as the influence of the vertical position of the pipeline within

the slide (Figure 13).

04080120

Shear strain rate, (s

-1

)

0.0

0.4

0.8

1.2

1.6

2.0

Shear stress,

(kPa)

Bingham B1, B2, B3

Herschel-Bulkley

power

log

kaolin measurements

B2 B1

B3

b

= 1.28

12 13 14 15 16 17

q

(

k

Pa)

0.0

0.5

1.0

1.5

2.0

y (m)

B2

HB

power

log

y = 0.125

(a) (b)

Figure 13. Analytical modelling of steady slide flow: (a) rheological models fitted to test data, (b) consequent loading on a

pipeline as a function of distance above the rigid (non-eroding) seabed level (Boukpeti et al. 2012b)

In UWA-SM3, the debris is modelled using either a Bingham rheology, where the mobilised shear

strength varies linearly with the shear strain rate, or the Herschel-Bulkley model where the relationship

is non-linear. Softening of the slide material can also be included using parameters that are obtained

directly from the results of cyclic full flow penetrometer tests, while hydrodynamic drag forces on the

runout material can also be applied.

Figure 14 shows an example of the run-out of a slide down a 5º slope, modelled using the UWA-SM3

software, illustrating the influence of softening effects. Cases are shown for material with a shear

strength that remains intact (or constant), su-Intact, during the run-out, and for a softening case (su-With

OTC-27034-MS 15

Softening) so that the shear strength degrades towards the remoulded value. In this case, inclusion of

softening increased the run-out distance by a factor of 2.4 (Figure 14a).

Figure 14b shows the evolving slide shape for the softening case. The initial slide block collapses very

early and the run-out stretches almost uniformly. As well as providing information on the run-out

distance and the geometry of the debris, the analysis also provides the velocity of the slide mass. Figure

14c shows the time-velocity relationship for the front of the slide and at two fixed points relative to the

toe of initial slide block – 40 m and 150 m ahead of the initial toe position. These results highlight how

the time-velocity profile seen by an obstacle differs depending on the location within the slide run-out

path. For assessment of the impact loading from slides on infrastructure, the time-velocity profile at the

position of the asset should be considered rather than solely the toe velocity.

50 100 150 200 250 300

Position along run-out (m)

2

4

6

8

10

Height (m)

(b)

2

4

6

Velocity (m/s)

Front

40m from toe

150m from toe

10 20 30 40 50 60 70 80

Time (sec)

(c)

Evolution

of runout

Initial slide block

Final

geometry

50 100 150 200 250 300

Position along run-out (m)

2

4

6

8

10

Height (m)

Initial slide block

Run-out - s

u-Intact

Run-out - s

u-With Softening

(a)

Figure 14. Example analyses of submarine slide run-out, using UWA-SM3 depth-averaged software (a) Comparison of

runouts (b) Snapshots of softening case during runout (c) Time – Velocity profiles (White et al. 2013)

16 OTC-27034-MS

A second example is shown in Figure 15 using a cross-section profile obtained from a seismic survey of

a location from the North-West Shelf, offshore Australia. The water depth at the left hand extremity is

approximately 700 m, and the scarp has a maximum slope of 5, at the location of the initial slide.

The initial slide geometry was defined by examining the continuity of layers within the profile to

identify the level at which failures appear to be taking place. Different run-out cases were considered,

with (i) non-softening intact rate-dependent soil during run-out, (ii) soil softening, and (iii) inclusion of

soil softening and hydrodynamic drag effects. The results showed that inclusion of softening resulted in

greater run-out than for cases where the soil remained intact, while inclusion of both softening and drag

effects resulted in a shorter run-out than with softening alone. Whilst both of these results are intuitive,

the benefit of the analysis is that the relative influence of these effects can be quantified, and further runs

can be performed to explore the sensitivity of the response to the assumptions made when devising the

input parameters. These results illustrate how the additional features included in UWA-SM3 can

influence the run-out distance and their relative effects.

Figure 15. Example of debris flow run-out on cross-section of North West shelf, Australia using UWA-SM3

In practice, the process of predicting the run-out of a potential debris flow carries with it various levels

of uncertainty (i.e. volumes of debris mobilized, range of rheological properties, evolution of debris

properties during run-out). This uncertainty and the subtle interplay between these parameters

complicates the process of assessing whether a potential debris flow meets a particular characteristic (i.e.

passes a particular location, or applies an unacceptable impact to infrastructure).

To overcome this challenge, UWA-SM3 has the feature to conduct Monte Carlo type run-out

assessments where probability distributions describing the uncertainity attached to each parameter are

used as input. Many thousand run-out assessments are carried out, each using a random selection of

input parameters to evaluate all the different possibilities. By quantifying the uncertainty attached to

each input parameter in terms of probability distribution, the outputs of these simulations can be used to

assess the probability of specific aspects of these events. Figure 16(a) shows an example of a Monte

Carlo assessment, showing the variation in the slide toe velocity versus slide toe position for a large

number of simulations. These simulations used a natural seabed topography, which led to the irregular

OTC-27034-MS 17

initial acceleration of the slides. An example of the type of output produced by this analysis is on Figure

16(b), which shows the probability density function (PDF) related to the final slide toe position.

Alternative outputs include the slide thickness and velocity when passing a particular location where a

pipeline will be crossed. This information can in turn be converted into a distribution of expected

pipeline stress, using the methods described later in this paper.

Figure 16. Example of Monte-Carlo analysis using UWA-SM3 (a) Velocity at slide toe as a function of postion, (b)

Probability distribution of final position of slide toe

UWA-SM3 has also been used to examine the response of a flexible pipeline to the impact of a debris

flow normal to the pipeline. Using analytical expressions described later in this paper, the deflection of

the pipeline is tracked dynamically using an equation of motion that accounts for the portion of the slide

loading that is resisted by the membrane tension and internal bending moments in the pipeline. Figure

17 shows an example of the deflection calculated using the UWA-SM3 routine and the conventional

static approach, in which the instantaneous maximum slide load is used to assess the potential pipeline

deflection. Using the dynamic analysis, the deflection of the pipeline is 40% of that calculated using the

conventional approach.

The difference between the two results is due to the temporary nature of the maximum slide loading.

The pipeline does not instantaneously assume the equilibrium geometry that this load corresponds to,

but instead accelerates progressively, at a rate attenuated by the inertia of the moving pipe, ultimately

reaching a smaller displacement within the time-scale of the slide loading. This example analysis

highlights the conservatism of the conventional design approach, which is to perform a static analysis

based on the transient maximum load.

Using the UWA-SM3 software, a parametric study was undertaken to examine the effect on run-out

length of slope angle, initial slide volume, strength properties and the rate-dependency of the debris

strength. Back-analysis of the run-outs has shown that a simple energy balance approach compares

reasonably with predictions of the UWA-SM3 results. In the energy balance approach, the run-out

distance of the slide toe is estimated by assuming that the slide fails by uniform elongation, with the rear

of the slide fixed at the initial position (which is consistent with many of the LDFE analyses). Plastic

work is done through basal sliding and internal shearing, whilst potential energy is lost as the material

18 OTC-27034-MS

falls. This simple energy balance is a reasonable idealisation of slides that fall into the ‘elongation’ class.

It is not appropriate for slides that fail by block sliding (in which the rear is not anchored) or through

‘breakaway’ of successive outrunner blocks.

Geometric scaling relationships from the literature, linking slide size and run-out lengths based on field

observations gathered in the area of the Storegga slide off Norway, also show good agreement with the

trends shown by the UWA-SM3 results and the energy-based back-analysis. These tools – the depth-

averaged software and the simpler energy-based approach – therefore provide a basis for extending these

relationships from purely geometric considerations, to incorporate the influence of soil properties.

An extended version of the depth-averaged approach was developed following the JIP (named UWA-

SM4, White et al. 2013), which solved the governing equations using a smoothed particle

hydrodynamics approach and included lateral spreading of material over a three dimensional domain.

Example results for a slide spreading over a realistic seabed topography are shown in Figure 18.

0 0.5 1 1.5 2

Time (mins)

0.5

1

1.5

2

2.5

3

No

r

malised pipe displacement, y

pipe

/B (-)

Pipeline

Deflection from

static calculation,

y

max

/B

Figure 17. Comparison of pipeline deflection calculated using UWA-SM3 and conventional static calculation

Figure 18. Example of submarine slide runout calculated using UWA-SM4 (White et al. 2013)

OTC-27034-MS 19

Modelling of slide-pipeline interaction

Introduction

The prior sections have explored methods for assessing whether a slide will reach a given loacatoin, and

what the thickness, velocity and properties of the slide material will be in that event. To convert these

parameters into distributed loads on a pipeline requires solutions to link the strength, density and

velocity of the slide material to the net pressure (or force per unit length) on an impacted pipeline.

Activities on this topic included the following components:

1. Physical modelling of slide-pipeline interaction (for flow over a fully engulfed pipeline)

2. Numerical modelling of slide-pipeline interaction (to explore the influence of rate effects)

3. Collation of published data to develop an approach for non-perpendicular attack

They led to an approach for the drag on engulfed pipelines, taking proper account of the influences of

both the strength and self-eight of the flowing material, and also strain rate effects on strength.

Physical modelling of slide-pipeline interaction

A new experimental apparatus was developed to allow a buried model pipeline to be translated at

various velocities through a soil sample contained within the drum centrifuge channel, simulating a pipe

engulfed within a submarine slide flowing perpendicular to the pipe axis. By using a soil sample that

was initially unconsolidated, the tests were performed at different consolidation levels leading to varying

sample properties (density ρ and undrained strength su).

A total of 37 model pipe translation tests spanning a wide range of velocities and soil strengths. The

tests were designed so that the relative influence of ‘fluid’ drag and ‘solid’ bearing resistance varied.

This was achieved by covering 4 orders of magnitude of pipe velocity (from 0.0036 – 4.2 m/s) and two

orders of magnitude of soil strength (from 0.08 to 1.7 kPa), measured via extensive cyclic T-bar tests at

different degrees of consolidation (Sahdi et al. 2014a; Sahdi et al. 2014b). In all tests the pipe was

translated horizontally, at an embedment with the crown of the pipe located two diameters below the soil

surface.

The measured net lateral pressure on the pipe, qH, was affected by both the velocity and the soil strength,

but with no unique trend evident for either parameter (Figure 19). This indicates the need to separate the

resistance into two components to capture both the inertia-dominated and strength-dominated domains.

0.1

1

10

100

0.001 0.01 0.1 1 10

Horizontal pressure on model pipe, q

H

(kPa)

Horizontal velocity, v (m/s)

1-PS1 to 1-PS4 3-PS1 to 3-PS3

4-PS1 to 4-PS3 5-PS1

6-PS1 8-PS1 to 8-PS5

10-PS1 to 10-PS6 11-PS1 to 11-PS4

12-PS1

0.1

1

10

100

0.1 1 10

Horizontal pressure on model pipe, q

H

(kPa)

s

u-op

(kPa)

1-PS1 to 1-PS4 3-PS1 to 3-PS3 4-PS1 to 4-PS3

5-PS1 6-PS1 8-PS1 to 8-PS5

10-PS1 to 10-PS6 11-PS1 to 11-PS4 12-PS1

N

H

= 7.35

Figure 19. Drag forces during lateral pipe-slide interaction, for a range of strengths that cross the solid-fluid boundary

20 OTC-27034-MS

A better interpretation of the results links qH to both the operative soil shear strength su-op (adjusted for

strain rate effects) and also the soil density ρ and relative pipe-soil velocity v (which can be combined

into the non-Newtonian Reynolds number, v2/su-op).

Using this approach, all results follow a unique trend line (Figure 20) that supports a general expression

for active slide pipeline loading:

opuHDH sNvC

2

2

1

q

(7)

The full data set is predicted well using a unique combination of a bearing capacity factor NH of 7.35

(which is approapriate for this level of pipe embedment, Martin & White 2012) and a drag factor CDrag

of 1.06. Additional data is also shown on Figure 20 from flume tests and centrifuge tests reported by

Zakeri et al. (2008) and Zakeri et al. (2011), and fits the same trends with appropriately modified

parameters (see Sahdi et al. 2014c for further discussion).

The establishment of Equation (7) as a general approach for assessing active slide-pipeline loading

rationalizes the previous inconsistency between fluid-based (with only the CD term) and geotechnically-

based (with only the NH term) approaches. The components of loading from inertial drag and from the

material strength may be superposed additively, with the material strength being adjusted to account for

the imposed strain rate. This approach is robust in the limits of weightless or inviscid flow, and fits the

wide database of experimental results across the solid-fluid boundary.

1

10

100

1000

0.00001 0.0001 0.001 0.01 0.1 1 10 100 1000

Horizontal bearing capacity factor, NH

Renon-Newtonian = ρv2/su-op

Zakeri et al. (2008; 2011) fit - Eq.7 1-PS1 to 1-PS4

3-PS1 to 3-PS3 4-PS1 to 4-PS3

5-PS1 6-PS1

8-PS1 to 8-PS5 10-PS1 to 10-PS6

11-PS1 to 11-PS4 12-PS1

Zakeri et al. (2011) Zakeri et al. (2008)

Eq.7 (current data fit) Martin & White (2012) - lower bound

Martin & White (2012) - upper bound

0

20

40

60

80

100

120

10 30 50 70 90 110 130 150 170 190

Horizontal bearing capacity factor, N

H

Re

non-Newtonian

= ρv

2

/s

u-op

3-PS1 & 3-PS2

5-PS1

6-PS1

10-PS1 & 10-PS2

11-PS1

12-PS1

Eq.7 (current data fit)

Figure 20. Drag forces during lateral pipe-slide interaction, across the solid-fluid boundary (Sahdi et al. 2014)

Numerical modelling of slide-pipeline interaction

Two studies used finite element analysis to explore in more detail the interaction between a slide and

pipeline during perpendicular attack.

In the first study, large deformation finite element (LDFE) analysis was used to simulate static

deformation of a landslide moving past a partially-embedded pipeline, to quantify the loads and

OTC-27034-MS 21

displacements imposed on pipe. These analyses used an elastic perfectly plastic soil model and plane

strain conditions. The pipeline was restrained by a set of springs so that the active load built up to a

stable value, representing the limiting load at which the debris flowed over the pipeline. A parametric

study was undertaken by varying the pipeline embedment and the relative strengths of the debris and

seabed, which is reported by Zhu & Randolph (2010).

The analyses showed that the various combinations of soil strength and embedment depth lead to

different debris-pipeline movement patterns and consequently lead to rather different magnitudes of the

loads imposed on pipelines. An example of different pipeline and seabed responses is shown in Figure

21. For debris that is much stronger than the seabed, erosion can lead to the pipeline becoming entirely

engulfed by the debris (Figure 21c), whereas for a relatively stronger seabed (or weaker debris) after

some erosion the debris flows over the top of the pipeline (Figure 21d). The pipeline is subjected to the

largest load (an equivalent pressure of 11.5 times the debris strength) from the landslide when it rests on

the weakest seabed. The pressure is proportional to the debris material strength but varies inversely with

the seabed strength for partially embedded pipelines. For all strength combinations, there is a critical

embedment depth beyond which the force on the pipeline reduces to a very small magnitude due to the

protective effect of the initial embedment. The parametric study showed that the seabed mudline

strength and initial pipeline embedment are the two main parameters that affect the debris-pipeline

movement patterns and consequently the magnitude of loads imposed on pipelines.

(a) Initial state

(c) Pipeline engulfed by debris

(b) Debris eroding the seabed

(d) Debris flowing over top of pipeline

Figure 21. Different debris flow patterns for an initial pipeline embedment zi/D = 1.1

In the second study, the influence of strain rate effects on active slide-pipeline loading was examined.

The purpose of this work was to establish the link between the rate-dependency of the soil strength and

the resulting rate-dependency of the active slide-pipeline loading (Zhu & Randolph 2011). These

22 OTC-27034-MS

analyses adopted a fully engulfed (i.e. buried) pipe and the normalised form of the Herschel-Bulkley

model, expressed as:

uy

ref

us1s

(8)

where represents a viscosity parameter and the parameter β is often referred to as the shear-thinning

index. The relative magnitudes of ‘static’ and ‘viscous’ resistance for a given rate of soil flow is

expressed by the Oldroyd number (Od) given by:

D/v

1

Od ref

(9)

where v/D represents a nominal strain rate in the soil around the pipe, and the other parameters are rate-

dependency properties of the soil.

The LDFE analyses investigated the undrained limiting loads on a cylinder moving steadily through

imponderable (i.e. weightless) soft rate-dependent material. The flow mechanism and the effects of the

shear-thinning index and Oldroyd number on the shear zones were explored. The average rate of strain

experienced by the soil flowing past the cylinder was estimated for a given flow velocity and an

expression in the form of a conventional bearing capacity equation, but with shear strength linked

directly to the normalised flow velocity, was established to predict the magnitude of the viscous force

exerted by the debris flow.

Figure 22 shows the effect of velocity, and thus strain rate, on the failure mechanism. At very low

velocity (Od = 104) the mobilized viscous component of soil strength is negligible, and so the classical

plasticity solution of a concentrated velocity discontinuity (Martin & Randolph 2006) is recovered. At

very high velocity (Od = 0.1), where the viscous enhancement is significant, the shear strains become

much more diffuse.

In spite of the changing shear strain patterns, it was found that the force exerted on the pipe could be

expressed in terms of a constant bearing factor, NH, and a nominal shear strength based on a strain rate

of D/fv

, where f is an adjustment factor lying between 0.8 and unity. Thus, for the Herschel-

Bulkley rheological model, the net pressure on the cylinder can be expressed as

op,uH

ref

uyHH sN

d/vf

1sNq

(10)

Figure 23 shows that the nominal bearing factor, NH, (taking f = 1) becomes increasingly independent of

the velocity (expressed in terms of the Oldroyd number) as the value of the strain rate power

coefficient reduces. For values of relevant to real soils (for which < 0.3, generally), it is therefore

sufficient to evaluate the impact force by adopting a constant, velocity independent, bearing factor based

on plasticity solutions but using an operative shear strength based on a strain rate of v/D. This finding

underpins the general expression, for weighty soil, given by Equation (7).

OTC-27034-MS 23

Figure 22. Effect of velocity on shear strain pattern around a smooth pipe (

= 0.26)

4

6

8

10

12

14

16

0.1 1 10 100 1000 10000

Oldroyd number, Od

N

nom

Ful ly bonded

Fully smooth

= 1

= 0.26

= 0.5 = 0.75

Figure 23. Variation in nominal resistance factor with velocity for different values of

Non-perpendicular slide-pipeline interaction: Inclined attack

To extend the solution for perpendicular slide-pipeline loading given by Equation (7) to other angles of

attack, data from computational fluid dynamic (CFD) numerical analyses of slide-pipeline interaction

forces, published by Zakeri (2009b), were reviewed. This allowed a re-interpretation of the data within

the new framework proposed in the project, in which the geotechnical resistance and inertial fluid drag

components of pipeline loading are treated separately (Randolph & White 2012). Dr Zakeri assisted by

providing additional information beyond his original publication.

NH

24 OTC-27034-MS

Zakeri (2009b) used the CFD software ANSYS CFX to analyse the pipeline response, extracting net

forces normal and parallel to a pipe segment placed at different angles to the flow direction. His data

have been replotted in Figure 24, considering separately the resulting drag factors for flow normal to the

pipe (angle of 90º) and parallel to the pipe (angle of 0º).

The results for normal flow at low values of non-Newtonian Reynolds number, i.e. low v2/su-op, are

consistent with the conventional geotechnical treatment of flow around a cylindrical object, with a

bearing resistance factor, Np, (the ratio of net pressure to material strength – at strain rate of v/D –

equivalent to the gradient of the lines shown) of 12 being identified. At higher rates of flow, a

consistent drag factor of 0.4 was found, with a geotechnical resistance component that remained

consistent with the resistance factor of 12 and a rate-enhanced soil strength (Figure 24). The

geotechnical resistance component is dominant in most cases.

For axial flow the deduced frictional drag can be expressed as Fa = fasu,opD, where su,op is the rate-

enhanced shear strength for a strain rate of v/D. The theoretical value of fa for the power law rheological

model adopted is about 1.4 (Einav & Randolph 2006), which is approximately 10 % below the gradient

from Zakeri’s numerical results. This discrepancy may be attributed to the high spatial gradients of

velocity very close to the pipe, which are only approximated within the numerical analysis.

To allow the interaction forces to be determined for any angle of attack, the variation of bearing and

friction factors with the angle of the flow relative to the pipeline axis were interpreted in terms of a

failure envelope, as shown in Figure 25. The dashed curve is a fit to the numerical data, expressed as

1

N

N

f

f1

90,p

p

3

0,a

a

(11)

where, consistent with the data, fa,0 was taken as 1.54 and Np,90 was taken as 12.8.

Although the envelope provides a reasonable fit to the data points for 45º and 60º, the data point

for 30º lies well within the envelope, and indeed implies some concavity in the envelope. The

reason for this is unclear, and requires further detailed numerical simulation for flow angles

lying between 0 and 45 º to resolve.

y = 12.82 9x

R² = 0.9984

y = 11.721x

R² = 0.9892

y = 10.602x

R² = 0.9957

y = 7.4724x

R² = 0.9766

0

2

4

6

8

10

12

14

16

18

00.511.52

Lateral drag coefficient, C

d-90

Factored inverse of Reynolds number: 2/R

e

90 degrees 60 degrees

45 degrees 30 degrees

Normal component

y = 1.5359x, R

2

= 0.9996

y = 0.9616x, R

2

= 0.996

y = 0.8797x

R

2

= 0.9967

y = 0.7045x, R

2

= 0.992

0

0.5

1

1.5

2

2.5

00.511.5

Axial drag coefficient, C

d-0

Factored inverse of Reynolds number: 2/R

e

0 degrees 30 degrees

45 degrees 60 degrees

Theory Theory

Axial component

(a) Flow components normal to pipe (b) Flow components parallel to pipe

Figure 24. CFD Results: Replotted drag coefficient data for general flow conditions

OTC-27034-MS 25

Figure 25. Failure envelope derived from CFD results for varying flow angle relative to pipe axis

A design envelope is then proposed that is constrained to the theoretical limiting bearing factors of

fa,0 = 1.4 and Np,90 = 11.9 (see the solid curve in Figure 25). In addition to the failure envelope, a

relationship is required to determine the position on this envelope that corresponds to a particular angle

of flow, and hence provide the resulting bearing factors Np (and fa). The resultant force on the pipe,

which is the vector sum of Fn and Fa, is not parallel to the flow direction.

Instead, the bearing factor, Np, may be expressed as

7.07.0

90,pp sin9.11sinNN (12)

with the corresponding value of fa then being found from Equation (11). Equation (12) is a purely

empirical relationship, which appears to give reasonable predictions of the numerical data. The proposed

failure envelope, together with spot values of the factors for the same angles as examined by Zakeri

(2009b), are shown in Figure 25. The calculated factors all lie within 10 % of those deduced from the

numerical data.

This methodology provides, for the first time, a robust approach for deriving the drag forces from debris

loading of a pipeline under an arbitrary angle of attack. For the realistic range of rheological parameters

considered, the total drag load is dominated by the component derived from the rate-enhanced material

strength (as opposed to the inertia). This supports the use of a geotechnically-based interpretation, using

bearing and ‘skin friction’ factors akin to the loading on piles. As identified in the LDFE study

illustrated in Figure 22 and Figure 23, it is appropriate to use a rate-enhanced material strength

corresponding to a strain rate of approximately v/D.

Modelling of pipeline structural response

The previous sections described new techniques developed within this project to assess the local loading

on an element of pipeline that is impacted by a slide. In order to assess the severity of this geohazard, the

next task is to assess the structural response of the pipeline, and the resulting bending and tensile stresses

as it is deformed. A new simplified technique for performing this assessment was developed within the

project, as summarised here. Additional information is provided in Randolph et al. (2010).

26 OTC-27034-MS

The structural response of a pipeline impacted by a slide was investigated analytically, with additional

validation using the finite element software, ABAQUS. The slide was modelled as ‘active’ loading over

a finite length of the pipeline, balanced by passive resistance and friction provided by the seabed on each

side of the slide, extending the work of Sweeney et al. (2004). The bending and membrane tension

induced in the pipeline were evaluated by means of analytical non-dimensional solutions. A schematic

of the problem is shown in Figure 26.

As a pipeline impacted by a submarine slide deforms, it will be restrained by lateral and axial resistance

in adjacent passive zones. Ultimately the pipeline may come to a stable deformed shape where continued

active loading from the slide is equilibrated by membrane tension in the pipeline in addition to the

passive resistance. Parametric solutions of the problem in terms of general values of the pipeline

properties and pipe-soil load transfer parameters were developed during this project (Randolph et al.

2010). The aim was to provide generic design charts giving the resulting pipeline response – the stresses

resulting from bending moments and tensile forces, and lateral displacement – as a function of the input

parameters, but with all quantities expressed in terms of appropriate non-dimensional groups. In spite of

some idealisations of the problem, the charts provide an initial design basis and a framework for more

detailed numerical analysis as necessary. They are simple and rapid to apply, and therefore amenable to

Monte Carlo simulations within a quantitative geohazard assessment – where full FE structural

modelling would not be practical.

The pipeline is assigned an elastic axial stiffness, EA, bending stiffness, EI, and diameter, D (although,

for a given wall thickness ratio, D/t, the last quantity may be derived from the ratio of I/A). Focusing on

slide loading normal to the pipeline, the main output quantities of interest are: the induced tension, T,

and bending moment, M; the maximum lateral motion, ymax; and the length of pipeline, s, that feeds into

the deformed shape local to the slide.

Flow direction

q

y

q

x

p

f

p

f

Active region

loaded by slide

Passive region

resisting movement

Passive region

resisting movement

Flow direction

q

y

q

x

p

f

p

f

Active region

loaded by slide

Passive region

resisting movement

Passive region

resisting movement

(a) Schematic of general slide loading on pipeline

y

x

q

p

B

x

a

x

m

y

x

q

p

B

x

a

x

m

(b) Nomenclature for analysis of normal loading acting on pipeline

Figure 26. Idealisation of pipeline loading by slide and resulting deformation

OTC-27034-MS 27

The outputs may be non-dimensionalised and expressed in terms of non-dimensionalised inputs:

EI

EA

B,

p

f

,

q

p

,

EA

Bq

,

EA

qB

g

B

s

;

EI

EA

B,

p

f

,

q

p

,

EA

Bq

,

EA

qB

g

B

y

EI

EA

B,

p

f

,

q

p

,

EA

Bq

,

EA

qB

g

EI

MB

;

EI

EA

B,

p

f

,

q

p

,

EA

Bq

,

EA

qB

g

EA

T

f

4

f

3

max

f

2

f

1

(13)

Analytical solutions, validated from numerical analysis, were developed to evaluate these quantities,

which were then expressed as functions of the input quantities using multiple regression analysis. A

typical set of results is shown graphically in Figure 27, where the vertical axes shows the magnitude of

tensile and bending strain, /E, induced in the pipe by slides of different magnitude, qB/EA, and

different widths, B/D.

Regression analysis allowed the tensile and bending strains to be expressed as functions of the non-

dimensionalised input quantities according to:

2

k0.22

0.075 0.75

t

10.2

2

BqBpf

0.28

EDEAqp

BqB

where k 0.075 2.0 DEA

(14)

2.006.0

27.098.0

b

p

f

q

p

EA

qB

D

B

E

(15)

Corresponding expressions for other output quantities are provided in Randolph et al. (2010).

These solutions provide an effective design tool for quantitative assessments of submarine slide hazards.

Based on an active loading over a defined length and specified values of passive lateral and axial soil

resistance outside the slide zone, the analysis allows the maximum deflection and the maximum stresses

within the pipeline to be estimated directly – for example, using a simple spreadsheet. In an extension to

previously published solutions, the bending resistance of the pipeline has been considered in addition to

the tensile response.

The inclusion of bending effects showed that for narrow slides and stiff pipelines, the bending stresses

dominate the structural load, whereas for wider slides and more flexible pipelines the maximum stress is

predominantly from tensile loading due to stretching of the pipeline. The effect of the passive soil

restraint on the maximum pipeline stress also depends on the width of the slide. For narrow slides, high

soil restraint leads to reduced pipeline stresses whereas for a wide slide the maximum pipeline stress is

reduced by lower soil restraint. Randolph et al. (2010) provide methods to extend the analysis to account

for a finite length of anchorage and a non-zero initial tension in the pipeline.

28 OTC-27034-MS

0.00001

0.0001

0.001

0.01

10 100 1000 10000

Normalized debris flow width, B/D

Computed strain,

/E

Bending

Tension

Combined

qB/EA =

0.001

0.0005

0.0002

0.0001

0.00005

0.00002

p/q = f/p = 0.5

Figure 27. Effect of slide loading and width on maximum pipeline strains

Conclusions and outcomes

The assessment of geohazards, such as submarine slides and their potential impact on pipelines, is a

highly multi-disciplinary activity, requiring contributions from a variety of geo-specialists including

geologists and geophysicists, as well as geotechnical engineers. Naturally, the assessment of slide-

pipeline interaction also involves pipeline engineering.

This Joint Industry Project was focused on geotechnical aspects of this problem, and has made research

contributions that have already been adopted in design practice for projects located in Australia and

elsewhere globally.

The project has established a framework for the material response of seabed sediments that is applicable

from their intact condition through to a fully mobilised fluid state of debris flow. By characterising the

seabed material in this framework, the material response during relict slides can be constrained,

enhancing the back-analysis of existing slides. Once these refined back-analyses are complete, new

techniques of slide simulation can be applied, including enhanced depth-averaged methods, and also

full-blown continuum LDFE. This project has demonstrated that continuum LDFE can recreate a range

of realistic flow mechanisms.

Once the potential slide hazard has been quantified in terms of the expected size, speed and strength of

the flows, a much more sophisticated assessment of the resulting slide-pipeline interaction can be

performed using techniques developed in this project. New simple analytical solutions have been

derived to assess the pipeline loading for given slide characteristics and the relevant pipeline properties

and orientation. These solutions can also be applied to other infrastructure in the path of a slide. In

addition to the local loading, solutions are also available for the consequent structural response –

capturing the influence of both tensile and bending stresses on the pipeline response.

These outcomes have been applied to projects in various ways. They have led to better-constrained

characterisation of relict slides, and more detailed assessment of the impact of potential future slides. By

OTC-27034-MS 29

eliminating some of the assumptions within current practice, and using more refined calculation models,

improved design efficiency has been achieved. The simple analytical solutions for slide loading and

pipeline response have unlocked the possibility of Monte Carlo-based quantitative assessments of

potential pipeline damage – allowing true risk-based decision making. As a result, designers have a basis

to demonstrate an acceptable probability of survival of a slide hazard, rather than needing to route a

pipeline entirely around the hazard.

Bibliography

Additional information on the activities performed during this Joint Industry Project can be sourced

from the cited references or the JIP Final report, published by MERIWA:

White D.J., Randolph M.F., Gaudin C., Boylan N., Wang D., Boukpeti N. & Sahdi F. 2011. MERIWA-administered Joint

Industry Project: The impact of submarine slides on pipelines: Final report to MERIWA and the project participants.

UWA GEO report 10538 1025 pp., MERIWA report 290.

Acknowledgements

This JIP was administered by the Minerals and Energy Research Institute of Western Australia

(MERIWA), which also contributed to the project funding. Six oil and gas Operators were project

sponsors: BP, BHP Petroleum, Chevron, Petrobras, Shell and Woodside. Additional support was

received from the CSIRO Flagship Collaboration on Subsea Pipelines, hosted at UWA, and the ARC

Federation and Future Fellowship Schemes (supporting Mark Randolph and David White, respectively).

The opinions expressed in this paper and in the JIP reports and publications are those of the authors and

may not reflect the views of the sponsors or MERIWA.

The authors acknowledge the advice and support received from the project steering committee, which

included Pam Smith (MERIWA), Paul Dimmock (BP), Trevor Evans (BP), Philippe Jeanjean (BP), Joe

Straub (BHP), Steve Paulson (Chevron), Jen-Hwa Chen (Chevron), Rob Little (Chevron), Leopoldo

Paganelli (Petrobras), Jason Newlin (Shell), TG Tan (Shell), Andrew Pearce (Woodside) and Marc

Senders (Woodside).

This paper forms part of the activities of the Centre for Offshore Foundation Systems (COFS), currently

supported as a node of the Australian Research Council Centre of Excellence for Geotechnical Science

and Engineering (grant CE110001009) and through the Fugro Chair in Geotechnics (held by the second

author), the Lloyd’s Register Foundation Chair and Centre of Excellence in Offshore Foundations and

the Shell EMI Chair in Offshore Engineering (held by the first author).

References

Biscontin, G. and Pestana, J.M. (2001). Influence of peripheral velocity on vane shear strength of an artificial clay.

Geotechnical Testing Journal 24, No. 4, 423-429.

Boukpeti N., White, D.J., Randolph, M.F., & Low, H.E. (2012a). The strength of fine-grained soils at the solid-fluid

transition Géotechnique, 62(3):213-226

Boukpeti N., White D.J., Randolph M.F. (2012b). Analytical modelling of the steady flow of a submarine slide and

consequent loading on a pipeline Géotechnique, 62(2):137-146

Boukpeti, N., White D.J. & Randolph M.F. & Boylan N.P. (2015). Strength of a carbonate silt at the solid-fluid transition and

submarine landslide run-out. Proc. Int. Symp. on Frontiers in Offshore Geotechnics (ISFOG). 1043-1048

Boylan, N.P. & White, D.J. (2016). Depth-averaged numerical modelling of submarine slide run-out in softening soil. In

review.

30 OTC-27034-MS

Bryn, P., Kvalstad, T.J., Guttormsen, T.R., Kærnes, P.A., Lund, J.K., Nadim, F. and Olsen, J. (2004). Storegga slide risk

assessment, Proc. 2004 Offshore Technology Conference, OTC-04, Houston, pp. OTC-16560.

Bugge, T., Belderson, R.H. and Kenyon, N.H. (1998). The Storrega slide. Phil. Trans. Royal Soc. of London 325, 357-388.

Dayal, U. and Allen, J.H. (1975). The effect of penetration rate on the strength of remolded clay and sand samples. Canadian

Geotechnical Journal 336, 336-348.

Einav, I. and Randolph, M. (2005). Combining upper bound and strain path methods for evaluating penetration resistance.

International Journal for Numerical Methods in Engineering 63, 1991-2016.

Elverhøi, A., Issler, D., De Blasio, F.V., Ilstad, T., Harbitz, C. and Gauer, P. (2005). Emerging insights into the dynamics of

submarine debris flows. Natural Hazards and Earth System Sciences, 5, 633–648.

Equid, D. (2008). Challenges of the Jansz deepwater tie-back. Proc. Deep Offshore Technology Conference (Asia-Pacific),

Perth, Australia.

Evans T.G. 2010. A systematic approach to offshore engineering for multiple-project developments in geohazardous areas.

Proc. Int. Symp. on Frontiers in Offshore Geotechnics (ISFOG). 3-32

Gafeira, J., Bulat, J., Evans, D. (2007). The southern flank of the Storegga slide: Imaging and geomorphological analysis

using 3D seismic, in: Lykousis, V., Sakellariou, D., Locat, J. (Eds.), Proc. of 3rd Int. Symp. on Submarine Mass

Movements and Their Consequences, pp. 57-65.

Gaudin, C., White, D.J., Boylan, N.P., Breen, J., Brown, T., De Catania, S., Hortin, P. (2009). A wireless high speed data

acquisition system for geotechnical centrifuge testing. Measurement Science and Technology. 20 paper 095709, 11pp

Gilbert R.B., Nodine, M.C., Wright, S.G., Cheon, J.Y., Wrzyszczynski, M., Coyne, M. and Ward, E.G. (2007). Impact of

hurricane-induced mudslides on pipelines. Proc. Offshore Technology Conference, Houston, Paper OTC 18983.

Hengesh, J., Whitney, B., Rovere, A. (2011) A Tectonic Influence on Seafloor Stability along Australia’s North West Shelf.

International Offshore and Polar Engineering Conference (ISOPE), USA, II, pp. 596-604.

Hengesh, J., Dirstein, J.K., Stanley, A.J. (2013) Landslide geomorphology along the Exmouth plateau continental margin,

North West Shelf, Australia. Australian Geomechanics J., 48(4):71-92.

Ilstad, T., De Blasio, F.V., Elverhøi, A., Harbitz, C.B., Engvik, L.E., Longva, O. and Marr, J.G. (2004a). On the frontal

dynamics and morphology of submarine debris flows. Marine Geology, 213, 481-497.

Ilstad, T., Elverhøi, A., Issler, D., and Marr, J.G. (2004b). Subaqueous debris flow behaviour and its dependence on the

sand/clay ratio: a laboratory study using particle tracking. Marine Geology, 213, 415-438.

Ilstad, T., Marr, J.G., Elverhøi, A., and Harbitz, C.B. (2004c). Laboratory studies of subaqueous debris flows by

measurements of pore-fluid pressure and total stress. Marine Geology, 213, 403-414.

Imran, J., Harff, P. and Parker, G. (2001). A numerical model of submarine debris flow with graphical user interface.

Computers and Geosciences, 27:717-729.

Jeong, S.W., Leroueil, S. and Locat, J. (2009). Applicability of power law for describing the rheology of soils of different

origins and characteristics. Canadian Geotechnical J., 46,

Locat, J. and Lee, H.J. (2002). Submarine landslides: advances and challenges. Canadian Geotechnical Journal, 39 (1), 193-

212.

Major, J.J. and Pierson, T.C. (1992). Debris flow rheology: experimental analysis of fine-grained slurries. Water Resources

Research 28, No. 3, 841-857.

Marr, J.G., Elverhoi, A., Harbitz, C., Imran, J. and Harr, P. (2002). Numerical simulation of mud-rich subaqueous debris

flows on the glacially active margins of the Svalbard – Barents Sea. Marine Geology 188, 351-364.

Martin, C.M. and Randolph, M.F. (2006). Upper bound analysis of lateral pile capacity in cohesive soil. Géotechnique, 56(2),

141-145.

Martin C.M. & White D.J. (2012). Limit analysis of the undrained capacity of offshore pipelines. Géotechnique, 62(9):847-

863

Masson, D.G., Harbitz, C.B., Wynn, R.B., Pedersen, G., and Løvholt F. (2006) Submarine landslides: processes, triggers and

hazard prediction. Phil. Trans. R. Soc. A August 15, 2006 364:2009-2039

Mohrig, D., Elverhøi, A. and Parker, G., (1999). Experiments on the relative mobility of muddy subaqueous and subaerial

debris flows, and their capacity to remobilize antecedent deposits. Marine Geology, 154, 117-129.

Mohrig, D. and Marr, J.G., (2003). Constraining the efficiency of turbidity current generation from submarine debris flows

and slides using laboratory experiments. Marine and Petroleum Geology, 20, 883-889.

Mohrig, D., Whipple, K.X., Hondzo, M., Ellis, C. and Parker, G. (1998). Hydroplaning of subaqueous debris flows. GSA

Bulletin, 110(3): 387-394.

Niedoroda, A., Reed, C., Hatchett, L., Young, A. and Kasch, V. (2003). Analysis of past and future debris flows and turbidity

currents generated by slope failures along the Sigsbee escarpment. Proc. Offshore Technology Conference, Houston,

Paper OTC 15162.

O’Brien, J.S. and Julien P.Y. (1988). Laboratory analysis of mudflow properties. Journal of Hydraulic Engineering 114, No.

8, 877-887.

Palmer A. (1997). Geotechnical evidence of ice scour as a guide to pipeline burial depth. Canadian Geotechnical Journal.

34(6):1002-1003

Parker, E., Traverso, C.M., Giudice, T.D., Evans, T. and Moore, R. (2009). Geohazard risk assessment – vulnerability of

subsea structures to geohazards – some risk implications. Prof. Offshore Technology Conference, Houston. Paper

OTC20090

OTC-27034-MS 31

Randolph M.F., Seo D. and White D.J. (2010). Parametric solutions for slide impact on pipelines ASCE Journal of

Geotechnical and Geoenvironmental Engineering. 136(7):940-949

Randolph M.F. & White D.J. (2012). Interaction forces between pipelines and submarine slides - a geotechnical viewpoint.

Ocean Engineering. 48:32-37

Sahdi F., Boylan N., Gaudin C., &, White D.J. (2010). The influence of coloured dyes on the undrained shear strength of

kaolin. Int. Conf. on Physical Modelling in Geotechnics. Zurich, Switzerland, 165-170

Sahdi, F., Gaudin, C., and White, D.J. (2014a). Strength properties of ultra-soft kaolin. Canadian Geotechnical Journal, 51(4):

420-431.

Sahdi, F., Gaudin, C., White, D.J., and Boylan, N. (2014b). Interpreting T-bar tests in ultra-soft clay. International Journal of

Physical Modelling in Geotechnics, 14(1): 13-19.

Sahdi F., Gaudin C., White D.J. Boylan, N.P. & Randolph M.F. (2014c). Centrifuge modelling of active slide-pipeline

loading in soft clay Géotechnique, 64(1):16-27

Schwab, W.C., Lee, H.J., Twichell, D.C., Locat, J., Nelson, H.C., McArthur, M. and Kenyon, N.H. (1996). Sediment mass-

flow processes on a depositional lobe, outer Mississippi Fan. Journal of Sedimentary Research 66, 916–927.

Sweeney, M., Gasca, A., Garcia Lopez, M., and Palmer, A. (2004). Pipelines and landslides in rugged terrain: a database,

historic risks and pipeline vulnerability. Proc. Int. Conf. On Terrain and Geohazard Challenges Facing Onshore Oil and

Gas Pipelines, Thomas Telford, London, 641-659.

Wang, D., Bienen, B., Nazem, M., Tian, Y., Zheng, J., Pucker, T. and Randolph, M.F. (2015). Large deformation finite

element analyses in geotechnical engineering. Computers and Geotechnics, 65, 104-114.

Wang, D., Randolph, M.F. & White, D.J. (2013). A dynamic large deformation finite element method based on mesh

regeneration. Computers and Geotechnics, 54, 192-201.

White D.J., Boylan N. & Levy, N. (2013). Geotechnics Offshore Australia: Beyond text book soil mechanics. Australian

Geomechanics: Special Issue on Offshore Geotechnics 48(4):25-47

Wroth, C.P. and Wood, D.M. (1978). The correlation of index properties with some basic engineering properties of soils.

Canadian Geotechnical Journal 15, 137-145.

Zakeri, A. (2009). Submarine debris flow impact on suspended (free-span) pipelines: normal and longitudinal drag forces.

Ocean Engineering, 36(6-7), 489-499.

Zakeri, A., Høeg, K. and Nadim, F. (2008). Submarine debris flow impact on pipelines — Part I: Experimental investigation.

Coastal Engineering, 55 (12), 1209-1218.

Zakeri, A., Chi, K. & Hawlader, B. (2011) Centrifuge modeling of glide block and out-runner block Impact on submarine

pipelines. Proceedings of the offshore technology conference. Houston, Texas.

Zhang J., Erbrich C.T., Finnie I., Neubecker S., White D.J., Deeks A.D., Doh G., Cumming G., Brown N. & Little R. 2015.

Geotechnical design and construction aspects of a pipeline-escarpment crossing. Proc. Int. Symp. on Frontiers in Offshore

Geotechnics (ISFOG). 495-500

Zhou, H. and Randolph, M. F. (2007) Computational techniques and shear band development for cylindrical and spherical

penetrometers in strain-softening clay. ASCE Int. J. Geomech., 7(4), 287-295.

Zhu, H. and Randolph, M.F. (2010). Large deformation finite element analysis of submarine landslide interaction with

embedded pipelines. Int. J. of Geomech., ASCE, 10(4), 145-152.

Zhu, H. and Randolph, M.F. (2011). Numerical analysis of a cylinder moving through rate-dependent soils. Ocean

Engineering 38(7):943-953