EFFECT OF EMBEDMENT, PRELOAD AND CONSOLIDATION ON

THE SERVICEABILITY AND BEARING CAPACITY OF SHALLOW

EMBEDDED PIPELINES IN URBAN SPRAWL

Final Report

CiSTUP Indian Institute of Science

Bangalore 560 012

S.K. Valavala and T. G. Murthy

Dept. of Civil Engineering

Indian Institute of Science, Bangalore – 560012.

   

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Introduction

Pipelines are a critical component in both onshore and offshore infrastructure projects,

especially as the most important means of transportation of water, sewage, oil, hydrocarbons

and many cases as a housing for electronic and communication channels. Pipelines that are

either resting on the ground surface, or those which are embedded to shallow depths, are very

frequently encountered in urban environs. Design considerations for these pipelines have

very often been simplified to consideration of the pipe as a line load on the soil, largely

ignoring servicebility of the pipeline.

Servicebility challenges often encountered in pipelines can be broadly classified under

buckling and walking (progressive axial displacement arising from cycles of expansion and

contraction of the pipeline due to the temperature and pressure changes within the pipeline

and its containing fluid, Carr et al 2006) . These issues can be marginally controlled by using

mechanical devices such as expansion joints and anchors, however such an alternative is

quite expensive for both installation and maintenance (Perinet and Frazer 2006). So, an

economic alternative would be to allow controlled buckling within the limits of strength and

serviceability at the design stage of the pipeline (Bruton et al 2007). This report presents the

highlights of a computational study which has been made on the behaviour of shallow

embedded pipelines at small emdedments.

Background

Considering pipes of various diameters with varying ratios of embedment, Aubeny et al 2005

investigated the incerase in strength of the clay with change in soil strength profile. In this

numerical study the authors infer a steady increase in the collapse load with increasing

embedment of the pipeline. They draw upper and lower bound estimates of the collapse load

for this problem with varying depths of embedment. In a more detailed study of the undrained

resistance of partially embedded pipelines, Merifield et al 2008 present results of a detailed

FE analysis with both horizontal and vertical loads applied to the pipeline. Yield envelopes

with combinations of vertical (V) and horizontal (H) loading is (V-H) obtained from their

research. Randolph and White (2008) propose upper bound yield envelopes for pipelines at

shallow embedment in clay subjected to vertical and horizontal loads.

In a recent study on the consolidation around partially embedded pipelines Krost et al 2011

study the effects of pore pressure dissipation and consolidation around pipelines. The curved

   

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shape of the pipeline increased the rate of consolidation compared with a regular strip

footing. The effect of embedment on the rate of consolidation was investigated in this paper.

They also show that an overall increase in the axial resistance of the pipeline occurs due to

consolidation, due to a ‘wedging effect’.

Through controlled usage of the pipeline (i.e. by filling it to a fraction of its full capacity)

and allowing for the consolidation of the clay (drainage at the surface) significant

improvement of the bearing capacity can be achieved. This, also corresponds to the long

term settlement of the pipeline, and the strength gain associated with it. Such a quantification

exercise for seabed pipelines has already been made by Krost et al, 2011. This contact buit up

between the pipeline and the clayey soil, can be compared to pile setup. (Krost et al 2011)

The soil response to the laying of a pipeline at the short term can be regarded as undrained.

With elapse of time, this excess pore pressure built up due to the undrained behaviour

dissipates and the soil gains strength. The strength of the soil increases with depth and hence

the bearing capacity of the soil increases with increasing embedment of the pipeline. The

current study aims to quantify the concomitant effects of embedment, preload and

consolidation on the bearing capacity of partially embedded pipelines. This study extends the

study made by Krost et al 2011 for a pipeline that is partially embeded and examines the

effect of long term strength gain due to consolidation around the pipeline.

Finite Element Analysis

(a) Geometry

The finite element analyses was carried out with the commercially available finite-element

software ABAQUS Version 6.11 (Dassault Systemes). Pipes of unit diameter embeded to

different depths into a fine grained soil was modelled here. The pipe is considered to be rigid

and no deflection of the pipe itself is allowed. The problem is analyzed under plane strain

conditions, wherein length of the pipeline is considered to be much larger than its diameter.

Pipeline embedment ratios depth of embedment to the diameter (d/D) = 0.1, 0.2, 0.3, 0.4 and

0.5 were considered in this analyses.

The boundaries are placed sufficiently far away from the pipeline such that the boundaries

have no effect on calculation of the ultimate bearing capacity and development of an ideal

collapse mechanism is not hindered. The boundaries of the soil, are placed at about 20D on

   

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either side of the pipeline, and about 10D underneath the pipeline, a Figure showing the

schematic of the boundary condition is presented in Fig.1. (Additionally, the failure

mechanism obtained from this analysis clearly shows no interaction with the boundary as

inferable from Figure 13a).

Fig. 1 Typical mesh for d/D = 0.1 showing the distribution of element density

The pipeline is assumed to be a rigid body in this analysis, with rigid body elements used to

model the pipeline. The rigid body elements are governed by a single reference point for

defining all the displacement, loading and other boundary conditions that need to be applied

to the clay (ABAQUS - 6.11 User’s Manual). The soil (clay) is represented by linear strain

quadrilateral pore pressure elements (library elements from ABAQUS CPE8RP), these

elements have eight displacement nodes and four pore pressure nodes positioned at the

corners of each element. A high density of elements is placed around the pipeline, which

have an average size of about t=0.03D close the pipe-soil contact, in order to determine the

shear stresses and strains with high precision; larger elements(with dimension t=1.45D) were

placed in the soil mass away from the pipeline. A constant number of elements was not used

in all the meshes, an optimum mesh size was obtained through a mesh sensitivity study.

(b) Interface and Drainage Conditions

   

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The interface between the pipeline and the soil is modelled to be rough so that slippage of the

pipeline does not occur during loading; however no special interface elements were used in

the simulations. The pipeline is assumed to be in contact with the soil at all times without any

separation. A schematic of the FE model showing size and boundary conditions is presented

in Fig. 2

The sides, base of the model and the pipe surface are all rendered impermeable and a

drainage boundary is provided at the top surface to allow pore-pressure dissipation. The base

of the model is fixed and the sides are restrained for displacement in the horizontal direction.

Fig. 2 Boundary Conditions used in the model

(c) Soil Conditions

The soil in the analysis is modeled with a Modified Cam Clay (MCC) constitutive model

with shear strength linearly varying with depth. The saturated unit weight of the soil is

Drainage boundary

 

                     

   

   

   

   

   

B’

B (or D)

8B

16B

                               

   

   

   

 

   

   

 

   

   

   

   

6  

considered to be 17.18kN/m3 and the soil is modeled with a surcharge on the top surface

representing 1 m overburden. The shear strength profile of the soil is assumed to vary linearly

with depth, as described Eq. 1 and presented in the schematic in Fig. 3

            (1)  

where, su0 is the undrained shear strength of the soil at the pipeline invert

k is the gradient of the shear strength variation with depth.

 

Fig. 3 A schematic of the geometry of the problem, indicating the presence of soil overburden, and shear strength profile with depth.

Modified Cam Clay Model Application in ABAQUS

The modified cam clay model (MCC) – which is quite routinely used to model fine grained

soils, is used in these simulations. A comprehensive description of the MCC model is not

provided in this report, however a brief description of the MCC model and its implementation

into Abaqus is provided below

The modified Cam-Clay theory is an extension of the original Cam Clay formulation which

effectively combines the idea of plastic flow or failure, which can be attained either through

isotropic compression or shear stresses along with the attainment of a unique void ratio. The

modified cam clay formulation is a slightly enhanced version of this idea. The MCC

0u us s kz= +

   

7  

fornulation here can be decomposed into an elastic and plastic part, the plastic part of the

model is defined with a yield surface, a flow rule and a hardening rule – which includes

dilatancy (or volume change). The evolution of these quantities is controlled by the strain

rate in the model. The numerical integration of the model is performed using backward Euler

integration of the flow rule and the hardening rule.

The elastic part of the model is based on a simple premise of poroelasticity, and is based on

the experimental observation that in porous materials during elastic straining, the change in

the void ratio – e – and the change in the logarithm of the mean stress – p – are linearly

related,

(2)

where, κ is the material parameter. In other words, the elastic part of the model follows the

swelling line (or the unload-reload) line during an oedometer experiment on a soft clay.

The MCC yield surface is defined by,

(3)

Where, t is the deviatoric stress, M the slope of the critical state line, β and a are constants.

a(θ,fα) defines the hardening in the materia.

An associated flow rule is used in the MCC model and the size of the yield surface is defined

by a. The hardening or softening in the soil is controlled by the evolution of the parameter a

The strain in the material, is computed from eq. 4 below

(4)

The modified shape of the critical state line (from the regular Drucker Prager shape of a

circle) is shown below in Fig. 3

( )( )lnelde d pκ= −

( )2 2

2

1, , 1 1 0p tf p q ra Maβ

⎛ ⎞ ⎛ ⎞= − + − =⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

( )( )lnde d pλ= −

   

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Fig. 3 Modified shape of yield surface used for modelling MCC in ABAQUS

(Ref: ABAQUS Version 6.11 User’s Manual)

Modified Cam Clay Parameters

The parameters used for the model clay in the analyses are presented in Table.1. These are

extracted from (Stewart 1992)

   

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Table 1 Input parameters for the Modified Cam Clay Model extracted from Stewart (1992)

Parameter input for analysis Magnitute

1. Parameters describing clay plasticity a. Log of Bulk Modulus (χ) 0.205 b. Stress ratio at Critical State (M) 0.898 c. Initial Yield Surface Size 0 d. Wet Yield Surface Size 1 e. Flow Stress Ratio 1 f. Intercept 2.14

2. Parameters describing index and engineering properties of clay a. Mass density 1.718 b. Permeability 1.123 E-005 c. Void ratio 1.5

3. Parameters describing elastic response (as a porous elastic material) a. Log of Bulk Modulus (κ) 0.044 b. Poisson’s ratio 0.25 c. Tensile limit 0

(d) Loading

Each analysis regime in this research is carried out in 4 stages. The first stage consisted of

creating the geostatic (equillibriation) stresses in the soil. This geostatic stresses in the soil

ensures increase in stresses with depth. Subsequently, the excess pore water pressures was

set up in the soil by applying the amount of preload to the footing (defined as a proportion of

the undrained bearing capacity without preload) over a short period of time allowing no

drainage. In the subsequent stage of the analysis, different periods of consolidation were

permitted (total primary consolidation, T100) and finally, a displacement was applied in the

vertical direction on the center of the pipeline such that the soil would reach a state of

continued plastic flow mechanism (or critical state). The reaction force provided by the soil

is determined at the center of the footing.

1. Geostatic Step - The first step consisted of creating the geostatic stresses in the soil by

providing self-weight and surcharge to the soil by considering the unit weight of the

soil and the gravity load as a body force on the soil. Under equilibrium of stress

conditions in the soil, a linearly varying shear strength profile of the clay is obtained.

   

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For the case of “no preload capacity” or calculation of the ultimate undrained bearing

capacity of the pipe embeded into clay.

2. Preload - A proportion of this ultimate undrained bearing capacity of the soil – called

‘preload’ - is applied at the reference point at the centre of the pipeline, for a short

period of time without allowing any drainage; this sets up the pore pressures in the

soil.

3. Consolidation – In the subsequent step, once the pore pressures are set up due to the

application of a preload, the soil is allowed to consolidate, i.e. dissipation of the

excess pore pressure by permitting drainage of the pore water through the drainage

boundary provided at the free surface of the soil (excluding the pipe which is

considered impermeable). The pore pressures generated is allowed to dissipate

completely in order to achieve a 100% primary consolidation.

4. Loading - Finally, a vertical displacement is applied to the reference point of the

pipeline such that the soil would reach a state of continued plastic flow (or critical

state). The diplacement is applied sufficiently quickly such that no pore pressure

dissipation maybe permitted during this step, thus obtaining the undrained shear

strength of the soil. The reaction force provided by the soil is determined at the

reference point of the pipeline.

Assessment of Stresses and Bearing Capacity Factor

The ultimate bearing capacity (q) of the soil is calculated from the reaction force (RF) that the

soil provides to the movement of the rigid pipeline. In order to obtain the bearing pressure,

the distribution of the reaction force over the length of contact of the pipeline with the clay is

considered. The bearing capacity factor, Nc, is calculated from eq. 5 considering appropriate

correction factors for depth, shape, inclination and strength non-homogeneity.

          (5)  

Su0 is the shear strength of the soil in line with the pipeline invert, the shear strength of the

clay from the MCC model is calculated as per the procedure outliend by Potts and

Zdravkovic (2000). The depth factor (dc) shape (sc) and inclination (ic) factors are obtained

from Salgado (2008); and strength non-homogeneity factor (F) from Gourvenec et al (2003).

The factors considered are provided below (eq.6-eq.10)

0c c c u cq F d i s s N= ⋅ ⋅ ⋅ ⋅ ⋅

   

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Depth factor, dc (6)

Where, D’ is the depth of the pipeline invert and;

B is the effective width of the footing (in contact with the soil)

Inclination factor, ic (7)

Qh is the stress in the horizontal direction and;

Qv, the stress in the vertical direction

Shape factor, sc       (8)  

Factor for strength non-homogeneity, F (9)

 

where, κ is the degree of non-homogeneity,                              (10)

Calculation of the undrained shear strength of the clay from MCC is given below, su0

(11)

where, σv is the stress in the vertical direction,

K0NC- co-efficicent at rest for the normally consolidated clay

given by,

(12)

Critical state friction angle, ϕcs; (13)

M is the critical state stress ratio i.e. the slope of the critical state line in stress space (in the q-

p’ space)

'

1 0.27cDdB

= +

1 1.3 hc

v

QiQ

= −

1 0.2cBsL

= +

( )( )

2 31 2 31

0F

a a aF

κκ κ κ= + + +

0u

kBs

κ =

( )2

02

1 2 1 2cos3 2 1

NCu

v

s K BgB

κλ

θ θσ

+ + ⎛ ⎞= ⎜ ⎟+⎝ ⎠

0 1 sinNCcsK φ= −

3sin6csMM

φ ⎛ ⎞= ⎜ ⎟+⎝ ⎠

   

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(14)

g(θ) is a mathematical function that defines the shape of the plastic potential surface,

θ being the Lode angle (θ = -300 for Tri-axial compression

θ = 0 for plane strain condition)

 

(15)

Benchmarking

The accuracy and precision of the mesh, along with the boundary conditions imposed was

assessed using a standard case of a shallow strip footing founded on a soft clay. The analyses

was carried out for the case of a normally consolidated clay. The bearing capacity factor Nc

assessed from this FE simulation was compared to analytical / semi-analytical solutions

available from method of characteristics and numerical limit analysis (i.e. for a rough footing

– soil interface and with no surcharge the bearing capacity factor is (2+π) (Salgado 2008).

Mesh Sensitivity Study

Convergence of the FE analyses is sensitive to the characteristics of the mesh used,

additionlly, the time required for analyses also is dependent on the characteristics of the FE

mesh. A mesh sensitivity study was carried out in order to accurately assess the optimum

number of elements for the analysis which would satisfy criteria of both accuracy and time of

analyses.

Meshes with different density of elements was used and the analyses was performed, the

bearing capacity factor was computed, along with the time taken for each of these analyses.

The bearing capacity factors obtained from the analyses are presented in Table 2. Increase in

the mesh density (i.e. number of elements) resulted in a better prediction for the Nc value i.e.

( ) sin1cos sin sin3

cs

cs

g φθθ θ φ

=+

( )( )

0

0

3 1

30 1 2

NC

NC

KB

g K

−=

⎡ ⎤− +⎣ ⎦

   

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higher accuracy, based on which the number of elements in the mesh were optimised for the

different embedment ratios.

No. of elements Nc

520 6.1

650 6.01

825 5.95

1020 5.73

1560 5.74

1944 5.68

2728 5.72

Nc, analytical = 5.14

Results

A FE study has been made here to understand the effect of embedment and preloading on a

pipeline bearing on a soft normally consolidated clayey soil. The ultimate undrained vertical

capacity of the clay, while the pipeline was placed on the surface of the clay was first

estimated and is designated as Vult. Effects of embedment depth and preload applications

are outlined here.

1. Effect of Embedment

Embedment of the pipeline into the surface of the clay is examined in this simulation, The

embedment ratios of d/D = 0.1 to d/D = 0.5 are simulated here. The vertical load carrying

capacity increases with increase in the embedment depth of the pipeline; and there is a 95%

increase in the bearing capacity from with a 5 time increase in embedment. Figure 5 shows

the load versus normalised displacement (normalised with respect to diameter of the pipe) for

pipelines at different embedment depths. The load carrying capacity of the soil is calculated

from the resistance force (RF) on the pipeline ;

   

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Figure 5 Load vs normalised displacement curves for pipelines with different embedment

depths; inset shows the increasing trend of the normalised load, Vmax/su0D, with

increasing embedment depth.

The load normalised with the undrained shear strength of the soil at the level of the pipeline

invert, su0 and the width of the footing, which is the diameter of the pipeline, D - Vmax/su0D -

increases with embedment of the pipeline as shown in the plot inset in figure 5.

The bearing capacity factor, Nc is calculated from the reaction force on the pipeline at the

reference point (RP),. From figure 6, it is observed that the value of Nc decreases with

increase in embedment depth.

   

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Figure 6 Bearing Capacity Factor, Nc for pipeline at different embedment ratios

2. Effect of Preloading

Fractions of the ultimate load bearing capacity, ranging from 10% to 70%, were applied as

preload on the soil at the reference point of the pipe and the soil was allowed to consolidate.

The consolidation was allowed till all the pore pressure was dissipated from the soil

ensemble. The consolidation hardens the soil but also brings forth settlement in the soil, and

the improvement in the strength due to this consolidation is estimated by applying an

additional vertical displacement to the pipeline until failure. Figure 7 presents the load versus

displacement during the loading stage after complete primary consolidation under different

preloads on the pipeline with embedment ratio, d/D = 0.3. Almost a 50% increase in the

bearing capacity of the soil is seen with application of a 70% preload.

   

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Figure 7 Increase in the vertical capacity of a normally consolidated soil, with the

application of various magnitudes of preload for a pipeline embedment ratio d/D = 0.3

Figure 8 shows the increase in the normalised bearing capacity load of the soil with increasing preload

for various depths of embedment. The increase in depth of embedment does not change the trend or

the slope of the curves. About 20% gain in the bearing capacity was increased immaterial of the

depth of embedment.

Figure 8 Increase in the normalised bearing force, Vmax/suD with preloading

   

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3. Consolidation

Fractions of the ultimate load was applied to the pipeline as a preload, and the soil was

allowed to consolidate for a time elapse sufficient enough so that all the excess pore water

pressure built up due to the application of preload. The extent of consolidation is presented as

a displacement vs. time elapse in days. At the end of consolidation, the displacement of the

pipeline equilibrates to a constant value and correspondingly, the pore pressure values at the

nodes of the soil elements are almost equal to zero (a tolerance of around 10-3 kPa is deemed

acceptable). The time required for complete primary consolidation is around 105 days, and

the displacement – time cures are presented for the case of an embedment depth ratio of 0.1

for various values of preloads is presented in Figure 9(a).

Figure 9(a) Time histories of consolidation settlement under different preloads on a pipeline

at an embedment ratio, d/D = 0.1

From the time histories of normalised settlement due to consolidation; i.e. the ratio of

settlement at any time, t, to the settlement after primary consolidation (wf) of the footing as

shown in figure 9(b), it can be observed that the plots collapse into one trajectory, with minor

differences in the rate of consolidation.

   

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Figure 9(b) Time histories of normalised consolidation settlement for consolidation

under different preloads on pipeline at embedment ratio, d/D = 0.1

A similar normalized time history of settlement, with increasing d/D is shown in Figure 10. The plot

indicates that the consolidation is faster for pipelines at lower embedment depths.

Figure 10  Time histories of normalised consolidation settlement

   

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Figure 11 shows time histories of excess pore pressure dissipation at the pipe invert for each

of the pipe embedment ratios during consolidation under a 70% preload. The excess pore

pressures are normalised by the initial excess pore pressure immediately after application of

the load, ui; and time shown is in logarithmic scale.

Krost et al (2011) report similar behaviour and explain it by the Mandel–Cryer effect “a

stress transfer phenomenon in which the dissipation process creates a local rise in total stress,

leading to an increase rather than a decrease in excess pore pressure (Mandel, 1950; Cryer,

1963)” which is evident for all embedment depths; but as the consolidation process stabilizes

it is observed that the rate of dissipation of excess pore water pressure is faster for lower

embedment depths and becomes slower with an increase in the embedment depth.

Figure 11 Time histories of normalised excess pore water pressure dissipation

4. Comparison of Bearing Capacity with existing studies:

The values of the bearing capacity normalised with the diameter of the pipeline and the

undrained shear strength of soil obtained from the current study are compared with those

obtained from previous studies. The current study estimates a higher bearing capacity over

the estimates from previous studies.

   

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Figure 12 Comparison of the increase in normalised bearing capacity, Vmax/suD from the

current study with existing data

5. Displacement Fields:

Typical displacement fields obtained at failure for an embedment ratio (d/D=0.3) is

shown in Fig. 13a, the figure shows a quiver plot showing the direction of traverse of

the soil, with application of an axial load to the pipeline. The displacement field is

similar in general feature to a strip footing resting on a normally consolidated clayey

soil. A region of velocity right at the invert region shows an almost vertical direction

with a magnitude equal to the pipe displacement, akin to a dead wedge seen in a strip

footing.

   

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Figure 13 (a) The displacement field at failure obtained from ABAQUS, for embedment

ratio, d/D=0.3

Fig. 13b shows the displacment field obtained from the FE analysis and a upper

bound displacement field (from Merifield et al 2008) used to calculate the upper

bound limit load, qualitatively confirming the accuracy of the analyses.

Figure 13 (b) Comparison of displacement fields at failure obtained from analyses to the

failure envelope from upper-bound solution, for d/D = 0.3

   

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Conclusion

Finite element analyses has been used to investigate the improvement of the vertical

bearing capacity of a pipeline founded on a soft clayey soil, with application of a long

term vertical loads. These vertical loads can be envisioned as partial service of the

pipeline (fractional filling of the pipeline) over long times to allow consolidation of

the clay.

Due to this consolidation, an increase in the bearing capacity is seen over long time

periods which increases with the magnitude of preload

The effect of the depth of embedment of the pipeline is also investigated in this

research, with higher depths of embedment showing a substantial increase in the

bearing capacity

With these findings from the FE analysis, it maybe concluded that a sufficient

emebedment would not only anchor the pipeline, but would also increase the bearing

capacity of the clay – pipeline system. Additionally, in designing the pipeline for

long service periods, the long term loading, which causes settlement of the underlying

clay needs to be considered. It is conservative to ignore consolidation strengthening

in design, however, this may lead to a non optimal design solution.

   

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NOMENCLATURE

D – Width of the footing/ Diameter of the pipeline

D’ – Depth of the pipeline invert

B – Effective width of the footing

d – Embedment depth of the pipeline

Nc – Bearing Capacity Factor

PP/u – Excess pore pressure dissipated from the soil from the boundary layer at the free

surface at any time instant, t

PPi/ui – Excess pore pressure developed in the soil at the instant immediately after loading

su – Undrained shear strength of the soil

su0 – Undrained shear strength of the soil at invert of the pipe

Vmax – Maximum vertical force per unit length of pipe

w – Displacement of the pipeline reference point at a time t

wf – Final displacement of the pipeline reference point at failure

   

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REFERENCES:

1.) Aubeny, C. P., Shi, H. & Murff, J. D. (2005). Collapse load for cylinder embedded in trench

in cohesive soil. Int. J. Geomech. 5, No. 4, 320 – 325.

2.) Bruton, D., Carr, M. & White, D. J. (2007). The influence of pipe-soil interaction on lateral

buckling and walking of pipelines: the SAFEBUCK JIP. Proc. 6th Int. Conf. Offshore Site

Investigation Geotech., London, 133-150.

3.) Carr, M., Sinclair, F. & Bruton, D. (2006). Pipeline walking – understanding the field layout

challenges, and analytical solutions developed for the SAFEBUCK JIP. Proceedings of the

offshore technology conference, Houston, Texas, USA, Paper OTC17945.

4.) Dassault Systemes. (2011). ABAQUS Users’ Manual, Version 6.11. Providence Rhode Island.

USA.

5.) Gourvenec, S. & Randolph, M. (2003). Effect of strength non-homogeneity on the shape of

failure envelopes for combined loading of strip and circular foundations on clay.

Geotechnique 53, No. 6, 575 – 586.

6.) Hill, A. J. & Jacob, H. (2008). In-situ measurement of pipe-soil interaction in deep water.

Proceedings of the offshore technology conference, Houston, Texas, USA, Paper OTC19528.

7.) Krost, K., Gourvenec, S.M. & White, D. J. (2011). Consolidation around partially embedded

seabed pipelines. Geotechnique 61, No. 2, 167-173.

8.) Merifield, R., White, D. J. & Randolph, M. F. (2008). The ultimate undrained resistance of

partially embedded pipelines. Geotechnique 58, No. 6, 461 – 470.

9.) Murff, J. D., Wagner, D. A. & Randolph, M. F. (1989). Pipe penetration in cohesive soil.

Geotechnique 39, No. 2, 213 – 229.

10.) Perinet, D. & Frazer, I. (2006). Mitigation methods for deep water pipeline instability

induced by temperature and pressure. Proceedings of the offshore technology conference,

Houston, Texas, USA, Paper OTC17815.

11.) Potts,D.M., Zdravkovic, L. (1999). Finite element analysis in geotechnical engineering:

Theory. London: Thomas Telford.