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 Proceedings of OMAE ’01
20th International Conference on Offshore Mechanics and Arctic Engineering
June 3-8, 2001, Rio de Janeiro, Brazil

OMAE01/PIPE-4118

NUMERICAL AND CENTRIFUGE MODELLING OF THE UPHEAVAL RESISTANCE

OF BURIED PIPELINES

M.F.Bransby T.A.Newson
Department of Civil Engineering, Department of Civil Engineering,
University of Dundee, Dundee DD1 4HN, University of Dundee, Dundee DD1 4HN,
Scotland. Scotland.
Email: m.f.bransby@dundee.ac.uk Email: t.a.newson@dundee.ac.uk

P.Brunning M.C.R.Davies
Stolt Offshore Bucksburn House, Department of Civil Engineering,
Howes Road, Aberdeen AB16 7QU University of Dundee, Dundee DD1 4HN,
Scotland. Scotland.
Email: paul.brunning@stoltoffshore.com Email: m.c.r.davies@dundee.ac.uk

ABSTRACT are prone to floatation during installation, "snap" upheaval

A combined study has been undertaken using numerical buckling on pipeline start-up, or progressive upheaval creep
analysis and scaled physical model testing to investigate soil failure (cyclic ratchetting) during long term operation. All of
resistance to upwards pipeline movement. Peak resistance these types of failure can cause the pipe to resurface at the
forces and the displacements required to mobilise these forces seabed and this presents considerable operational problems and
were investigated for varying geometries, soil properties and unplanned costs for the operators on the one hand and to the
boundary conditions using finite element analysis. These results fishing industry on the other.
were compared with a series of centrifuge and laboratory model There have been a number of reported cases of upheaval
tests. Soil deformation mechanisms calculated in the finite buckling in the North Sea, some of which have been
element analysis and those observed in the centrifuge model documented. Nielson et al. (1990), investigated one of the first
tests were compared. The role of the deformation mechanism on cases where the July 1986 annual survey of the 17km long Rolf
the load-displacement behaviour of the pipe and the failure load A to Gorm E pipeline revealed that the 8" pipe had arched out
was also examined. Results suggested that the peak uplift loads of the seabed to a height of 1.1m above seabed level and free-
and mobilisation displacements were dependent on the soil spanned a distance of 10m. In September, just two months after
movements during gap formation and not the mechanisms this discovery, a comprehensive out of straightness survey was
observed after failure in the model tests. In addition, the carried out to measure the in situ profile along the pipeline
distance required to mobilise the peak uplift load scaled with length. This second survey not only identified another free span
embedment depth, giving δ/H ≈ 0.5 % at peak uplift load. that had not existed during the previous annual survey but also
Keywords: pipe uplift, drained, capacity, displacement detected excessive vertical displacements of unexposed pipeline
sections at numerous other locations. On the basis of the
1 INTRODUCTION damage assessment, the remedial works that were implemented
involved the replacement of the two free span sections and
Offshore oil and gas pipelines are commonly buried to
remedial rock dumping of a further 29 locations where the
provide environmental stability, thermal insulation and
safety margin against upheaval buckling was found to be
mechanical protection from fishing activities. More high
inadequate. The costs associated with this work are not
temperature and pressure reserves are now being transported
reported, however they would have been significant.
through small diameter insulated pipes, particularly on the
Whilst it is true that some buckle type imperfections are
North Sea Continental Shelf. These pipes are frequently
induced during installation, many can be attributed to the
relatively light compared to the surrounding backfill soil and
natural seabed profile and the geotechnical properties of the soil

1 Copyright © 2001 by ASME

environment above and around the pipe. As a result of academic Fu − 1
fd =
interest in the subject together with industry sponsored research
studies, it is now widely accepted that uplift resistance is a ( )
H
D
(1)

complex problem and relates directly to the geotechnical where H is the instantaneous embedment depth measured to
properties of the soil. the crown of the pipe, D is the pipeline diameter and Fu is the
non-dimensional uplift force given by
Wu
1.1 Review of Research Fu = (2)
As the costs of upheaval buckling have been carried by the γ ′DHL
offshore industry, the geotechnical aspects associated with the where Wu is the net uplift force, γ' is the effective unit
phenomenon have received considerable attention over the last weight of the soil and L is the pipe length. Schaminee et al.,
decade (eg. Bolton and Baumgard, 2000; Dickin, 1994; Maltby (1990) and later workers have expressed pipe capacities in
and Calladine, 1995; Moradi and Craig, 1998; Ng and terms of uplift factor, fd and this has become an accepted design
Springman, 1994). The focus of this attention has been aimed at parameter.
the mechanism of soil failure and the measurement of uplift Stolt Offshore sponsored the University of Dundee to
load for various soil types. Because of practical difficulties and undertake a research project to improve understanding of the
the high cost of conducting full-scale field tests, the majority of failure mechanisms associated with pipeline uplift and the
this work has been carried out at small scale, using geotechnical monotonic uplift resistance. Model tests and finite element
centrifuge modelling to simulate the full scale site conditions analysis were to be carried out for drained loading conditions as
(e.g. Bolton and Baumgard, 2000; Dickin, 1994; Moradi and a first stage in a project incorporating a wider range of soil
Craig, 1998). Finch et al. (2000) reports some full scale types, and because it is often the drained soil conditions which
laboratory testing. Limited numerical analysis of the uplift provide least uplift resistance (Finch et al., 2000).
behaviour of buried objects has been carried out using finite The soil mass overlying any offshore pipeline will have
element analysis (Rowe and Davis, 1982) and numerical bound been subject to trenching processes and will have undergone
solutions (Merifield et al, 1999). some degree of disturbance. As little information is available
Design methods are based on pipe element analysis and so the concerning the geotechnical properties of back-filled trench
behaviour of an infinitely long pipe is of interest. Hence, the material, Stolt Offshore and Dundee University felt that it was
pipe geometry investigated is shown in Figure 1a using important to establish first the soil mechanics of uplift
the definitions shown. An embedded pipe moves vertically behaviour in engineered soils before moving on to apply these
towards the seabed surface and requires a force Wt. This models to actual field samples and conditions.
comprises the effective weight of the pipe, W' (known for a
given effective unit weight) and the net uplift force Wu (i.e. Wt
= W' + Wu). The net uplift force depends on the resistance of 2 FINITE ELEMENT MODELLING
the soil above and therefore changes with different soils and soil Finite element analysis was carried out to investigate the
states. An accurate method is needed to predict Wu using uplift behaviour of circular pipelines and rectangular anchors.
ground investigation data. This was done to identify the most important parameters for
Line of symmetry later experimental study and to understand the mechanics of the
soil around the pipeline. Uplift capacities and soil failure
Soil mechanisms were calculated for different soil conditions and
H Zone of FE pipe/anchor geometries and preliminary findings are presented
H below for a simplified pipe geometry.
modelled
D D soil
Pipe 2.1 Soil conditions and pipeline
D Rigid geometries
Pipe
Wt Finite element analysis was conducted using the package
SAGE-CRISP. Finite element modelling was carried out using a
non-associated Mohr-Coulomb elastic-perfectly plastic soil
(a) Field Geometry (b) FE model geometry model. This had a fixed angle of friction, φ’, a non-associated
dilation angle, ψ’, a Young's modulus, E, and Poisson's ratio, ν'
Figure 1. Pipe geometry and definitions and a bulk modulus, γ’.
The net uplift force, Wu can be non-dimensionalised and Results from a preliminary study using a square cross-
re-expressed as an uplift factor, fd as suggested by Schaminee et section pipeline are reported in this paper. Dickin (1994)
al., (1990). This is calculated using reported that centrifuge model test results from an anchor were

2 Copyright © 2001 by ASME

similar to a circular pipeline, which agrees with some design this was not done, the mobilisation distance to peak load would
methods. Hence, it is expected that the results for a square be underestimated. For many of the tests, a grid of black
pipeline are likely to be representative of the general mechanics markers at approximately 50 mm centres were placed in the soil
of the system. The geometry is shown in Figure 1b. There is a touching the perspex front face while the soil was being
line of symmetry in the centre of the pipe, so only half of the prepared.
pipe-soil system needed to be modelled and the line of The pipe was then pulled out of the soil using a rigid
symmetry was replaced by a rolling, rigid boundary. The soil hanger arrangement to ensure that the pipe moved
was modelled using 525 linear strain triangles. Rigid boundaries monolithically and vertically. Load was measured using a load
were located remote from the anchor so as not to interfere with cell and displacement using a potentiometer or LVDT. For tests
failure mechanisms or affect effective stresses in the deforming with the soil marker grids, a series of digital photographs or
zone. The pipe was rigid and was displaced vertically upward analogue video was taken of the front face of the box as the
using displacement control over 50 to 100 equal-sized pipe moved towards the surface displacing the soil and the
increments to failure to reduce numerical errors. The anchor markers.
was surrounded by slip elements, and thus detachment could
occur between the anchor and the soil, and roughness 3.3 Programme of tests
conditions could be varied. The total resistive force, Wu was
calculated by summating the stresses at the integration points in
The tests reported in this paper were conducted on dry and
the soil immediately adjacent to the sides of the anchor (top,
saturated silica sand and dry gravel. The sand was uniformly
side and bottom).
graded with d50 = 0.18 mm, Gs = 2.65 and the particles were
subrounded. Shearbox tests were carried out which measured
3 EXPERIMENTAL METHOD the angle of friction, φ'
crit ≈ 30 .
o

Model tests were conducted in loose sand in the centrifuge

3.1 Geometry and the laboratory. Dense sand tests were carried out only in the
laboratory. Other variables investigated were the diameter of the
Scaled physical model testing was carried out both in the pipe and its embedment ratio (H/D). The series of tests is
laboratory (at 1g) and in a 5g acceleration field in the Dundee summarised in Table 1 below.
Geotechnical centrifuge. Both series of tests consisted of the
extraction of a circular pipe from a box of soil with continuous
measurement of force and pipe displacement. The front face of Table 1: The series of physical model tests
the soil boxes were perspex and the pipe was positioned Test number Soil type Density (kg/m3) Pipe H/D
perpendicular to the perspex front face, allowing the soil (and diameter,
pipe) to be observed as pull-out progressed. D (mm)
Pipes of 32 mm or 48 mm outside diameter and length of Laboratory test Dry sand Loose (1447 32 3.3
5 kg/m3)
495 mm were tested in the laboratory, whilst pipes of diameter Laboratory test Dry sand Loose (1447 48 3.0
48 mm and length 498 mm were tested at 5g and 5.2g in the 6 kg/m3)
geotechnical centrifuge. Scaling laws (as reported by Schofield, Laboratory test Dry sand Dense (1550 48 3.1
1980) ensured that the 48 mm pipe at 5g would behave exactly 9 kg/m3)
as a prototype 5 times larger (i.e. D = 5 x 48 mm = 240 mm). Laboratory test Dry gravel Dense (1550 48 3.04
13 kg/m3)
Centrifuge test Dry sand Loose 240* 3.1
1
Centrifuge test Dry sand Loose 240* 2.1
3.2 Testing methodology 2
Centrifuge test Dry sand Loose (1457 250+ 3.5
The preparation procedures were the same for both types of 3 kg/m3)
Centrifuge test Saturated Loose (1800 250+ 3.6
test. Sand was pluviated to a depth of 30-50 mm in the base of
4 sand kg/m3)
the box and the pipe was positioned on the surface of the soil. Centrifuge test Saturated Loose (1800 250+ 2.75
The pipe was located with its ends almost in contact with the 7 sand kg/m3)
front and back perspex faces of the box and grease was pushed * Pipe diameter at prototype scale (5 g centrifuge test, D = 48
into the gap to prevent soil entering the gap between the pipe mm at model scale)
+
and the front face. More sand was then added until the final Pipe diameter at prototype scale (5.2 g centrifuge test, D = 48
height gave the required pipe embedment depth. Whilst the mm at model scale)
sand was being placed above the pipe, it was important that the
pipe was free to settle vertically so that a net vertical load was
not applied to the pipe before the pull-out test commenced. If

3 Copyright © 2001 by ASME

 9000
8000 120
7000 100 B C
Total
L o a d , N /m .

6000 80
5000 A
centrifuge test 1 (D =

Pressure, kPa.
60
4000
240 mm) 40
3000
2000 finite element analysis 20 O Front
1000 (D = 250 mm: square) 0 face
0 -20 0 0.005 0.01 0.015 0.02

0 2 4 6 -40 Back face

Displacement, mm. -60
Displacement, m.
Figure 2. Comparison between finite element calculation and
centrifuge model test for loose sand (H/D ≈ 3). Figure 5a. Load-displacement response using finite element
analysis: H/D = 3,D = 1m

Calculated soil
H= 0.75 displacements
m

D=0.25 Pipe Pipe

m Wt

Figure 3. Calculated soil displacements at failure during finite Figure 4b. Incremental soil displacements at '
O'
element analysis of equivalent square pipe.

4 NUMERICAL RESULTS
4.1 Case specific analysis
Results from preliminary finite element analysis are
compared to centrifuge test 1 (loose, dry sand, H/D = 3.3) in
Figure 2. The finite element analysis investigated an equivalent
square pipe with D = 0.25 m and H = 0.75 m in elastic-perfectly
plastic soil with γ = 14 kN/m3, φ’ = 32o, ψ = 0o, Poisson’s ratio,
ν’ = 0.3, and Young’s modulus, E = 4000z. There is good
agreement between the results, although the initial stiffness of Figure 4c. Incremental soil displacements at '
B'
the centrifuge model test is not well predicted. The finite
element analysis models the gapping mechanism, but not the The soil deformation mechanisms occurring at different
large strain behaviour and so can only capture the initial pipe- displacements are examined in more detail in Figure 4 for an
soil interaction behaviour when peak uplift load is mobilised. embedment ratio, H/D = 2.5 with the soil properties given
The calculated soil displacements (Figure 3) suggest a above. The load-displacement response is shown in Figure 4a
mechanism similar to the vertical slip model (also shown in with the contributions of the top and base shown (plotted as
Figure 3; Majer, 1955; Schotman et al., 1990) with gap changes in normal stress). The normal stress on the back face
formation behind the pipe, but with a slightly wider zone of soil reduces to zero when the gap is fully open. Hence, the change in
movement above the pipe. pressure in the back face reaching a fixed pressure after δ ≈

4 Copyright © 2001 by ASME

 140 1.2

120
Uplift pressure, W u /D

Uplift load/capacity
100
0.8
80
0.6
60 H/D = 2, D = 1 m
H/D = 2, D = 1 m
0.4 H/D = 3, D = 1 m
40 H/D = 3, D = 1 m
H/D = 2.5, D = 1 m 0.2 H/D = 2.5, D = 1 m
20
H/D = 3, D = 0.25 m H/D = 3, D = 0.25 m
0 0
0 0.005 0.01 0.015 0.02 0.025 0 0.2 0.4 0.6 0.8 1 1.2
Displace ment, m. (δ) Displacement/embedment depth, % (δ/H).
Figure 5. Load-vertical displacement response for increasing Figure 8. Normalised load-displacement response for increasing
embedment ratio. (φ’ = 32o; γ = 14 kN/m3; ψ = 0o; Ko = 1; E = embedment ratio. (φ’ = 32o; γ'
= 14 kN/m3; ψ = 0o; Ko = 1; E =
4000 z) 4000z)
0.006 m shows that the gap has formed behind the pipe. normalising the displacement for the geometry and soil
Calculated incremental soil displacements are shown at key conditions given should be embedment depth, H.
stages in the pipe movement in Figures 4b, c and 3. The initial At failure, a mechanism similar to the vertical slip plane
elastic response with no gap (Figure 5b; near ' O'on Figure 5a) failure occurs (Majer, 1955; Shaminee et al., 1990) with
gives way to some plastic yielding and a different soil detachment at the lower side of the anchor for all three
deformation mechanism with a displacement of 0.004 m. When embedment ratios (e.g. Figure 3). Despite this similarity of
the displacement, δ = 0.008 m (' B'on Figure 4a), the gap has mechanism between the three embedment ratios, there are
formed and the soil displacements are shown on Figure 4c. With changes in fd with depth.
further displacement (point C), plastic failure is observed (e.g
Figure 3). 4.2.2 Diameter, D
Results from analyses with pipe diameters of 1 m and 0.25
4.2 Parametric study m are shown together on Figures 5 and 6. Failure load is
Parametric studies were carried out on a square ‘pipe’ mobilised quicker when the diameter is smaller (Figure 5), but
geometry. The base case for comparison was with H/D = 3, the displacement ratio (δ/H) is almost identical when the results
using elastic-perfectly plastic Mohr-Coulomb material with the are normalised by the peak uplift load and the embedment depth
same properties as previously: φ’ = 32o; ψ = 0o; γ = 14 kN/m3, (Figure 6). For analyses with H/D = 3, using a pipe diameter of
Ko = 1 and E = 4000z. The effect of varying different D = 1 m, peak uplift factor, fd = 0.635, whereas when D = 0.25
parameters is investigated below. m, fd = 0.651.

4.2.1 Embedment depth, H/D 5 EXPERIMENTAL RESULTS

Three different embedment ratios were investigated H/D =
3, H/D = 2.5 and H/D = 2. Load-displacement responses for the 5.1 Uplift forces
three different geometries are shown in Figure 5 and the Typical resistive force against pipe displacement plots are
increased capacity with embedment is shown clearly. The shown for centrifuge test 1 in loose sand in Figure 7. The results
mobilisation distance for peak load is also increased with are shown using units for the equivalent full-scale prototype
embedment. (pipe of prototype diameter, D = 240 mm; initial embedment
Uplift load in terms of uplift factor, fd is plotted against ratio, H/D = 3.1; Soil density, γ = 14.2 kN/m3). Clearly, peak
embedment ratio in Figure 8 for each analysis together with the uplift load is mobilised very quickly, and the uplift resistance
model test results. There is a significant change in fd as the then reduces as the pipe approaches the soil surface and the soil
embedment ratio changes from 2 to 3, with fd increasing with cover reduces.
decreasing H/D. The uplift force at any instant during pipe pull-out can be
The load-displacement results are re-plotted normalised by non-dimensionalised to find the uplift factor, fd as suggested by
peak load and embedment depth respectively in Figure 6. There Schaminee et al., (1990) and explained above. This is calculated
is excellent agreement between the results for the three different using the instantaneous embedment depth (assumed to be Hi –
embedment ratios with all showing similar normalised
δ). For any single uplift test, fd can be plotted against H/D as
stiffnesses and that δ/Η ≈ 0.5 % at failure. There is less good the pipe is pulled out and H/D reduces (e.g. Figure 8).
agreement when the results are shown normalised by pipe
diameter. This suggests that the characteristic length for

5 Copyright © 2001 by ASME

 16 1.2
14 test 9: dense sand
1
test 13: dense gravel
Vertical load, kN/m

12
Lab test 6: loose sand 0.8

Load, W/Wu.
10 test 6 (loose sand) D = 48mm
0.6 centrifuge test 1 (D = 240 mm)
8 Centrifuge test 2 (D = 240mm)
0.4
6 cmt 3 (dry sand 3.5)
0.2 cmt 4 (sand 3.6)
4
cmt 7 (sand 2.75)
2 0
0 0.01 0.02 0.03 0.04 0.05 0.06
0 -0.2
0 200 400 600 800 1000 Displacement/diameter.
Upwards displacement, mm
Figure 9. Normalised load-displacement data: loose sand.
Figure 7. Load-displacement response of pipelines: prototype
scale.
quickly by half to a residual pull-out force. This residual force
then reduces as the pipe moves towards the surface. This
5.1.1 Loose sand corresponds to a peak uplift factor (fd ≥ 1) on initial movement
Figure 8 shows the results of the tests on loose sand as a which then reduces to values similar to the loose sample after a
plot of fd against H/D. A single data set starts on the right of the small pipe displacement. For the sand, the distance required to
reach the residual value of fd is 5 mm. Interestingly, in separate
graph (at H/D ≈ 3) and then reflects changes in fd as the pipe is
tests using gravel, the residual mobilisation distance was 15mm.
pulled out and H/D reduces. There is no peak of fd at the start of
movement before there is general failure of the soil and so the
results for a single continuous test may be representative of the 5.2 Load-displacement response
peak resistance for a range of H/D. Typical centrifuge results
give an uplift factor, fd ≈ 0.55 for 1.5 < H/D < 3. The uplift 5.2.1 Loose sand
factor increases for lower embedment ratios. For embedment
The initial load-displacement data for the tests on loose
ratios higher than 3 it appears that fd may reduce somewhat with
sand are shown in Figure 9. Uplift load (Wu) is normalised by
increasing embedment ratio. This effect needs to be studied in
the peak uplift load (Wu,max) and the displacement was
more detail.
normalised by pipe embedment depth, H. There is good
agreement between results for different pipe sizes and it appears
5.1.2 Dense sand that 90% of the maximum uplift load is mobilised when δ/D ≈
Load-displacement plots are shown for laboratory tests in 0.005. Because the embedment ratio, H/D was not varied
dense sand and dense gravel in Figure 7. Both tests were widely during the test series, normalisation by diameter, D gives
conducted with a pipe of diameter, D = 48 mm and an initial similar results but with a normalised displacement, δ/H ≈ 0.015
embedment ratio, H/D ≈ 3. There is a difference compared to (1.5 %).
the loose sand tests, with a peak uplift resistance, which drops
5.3 Observed soil displacement
2 Test 5 (D = 32 mm)
1.8
Test 4 (D = 48 mm) mechanisms
Test 6 (D = 48 mm)
1.6 Vertical slip model
1.4
Centrifuge test 1 (D = 240 mm)
5.3.1 Loose sand
Uplift factor, fd

cmt 3 (D = 250 mm)

1.2 cmt 4 (D = 250 mm) Figure 10a shows a digital photograph of the soil model
Finite element analysis
1 cmt 7 (D = 250 mm) after a pipe displacement of δ/D ≈ 1.3 through loose sand in the
0.8 laboratory (test 1). The initial embedment ratio, H/D = 3 and
0.6 the embedment ratio when the photograph was taken was H/D ≈
0.4 1.7. There appears to be negligible surface soil movement (even
0.2 after δ/D = 1.3) and only the two markers above the pipe appear
0 to have moved from their initial grid position and these have
0 1 2 3 4 only moved about 1/10th of the distance of the pipe movement.
Cover ratio, H/D In all tests, a gap formed behind the pipe with sides of angle ≈
Figure 8. Uplift factors for loose sand samples (laboratory and 30o and this remained at a constant size after initial formation.
centrifuge model tests and FE analysis)

6 Copyright © 2001 by ASME

To sustain the constant gap size with the upward moving pipe
there was flow of soil around the pipe as sketched in Figure 10.

5.3.2 Dense sand sample

Dense sand movements showed gapping behind the pipe of
Soil displacements
similar size to the loose samples but that there was a larger
region of deforming soil above the pipe together with more
Gap
surface movement. The soil moved upwards in a region about
2D wide near the surface. Two types of soil displacement Initial pipe
position
mechanism were observed after peak load: (i) soil flow around
the pipe to maintain the gap at constant size, and (ii) uplift of a
zone of soil above the pipe.

6 DISCUSSION
Pipeline design and installation work is frequently awarded Figure 10. Laboratory test 1 in loose sand.
as an integral part of an EPIC (Engineering Procurement,
Installation and Commissioning) contract where the contractor It is suggested that a number of different deformation
assumes the risks associated with soil conditions and upheaval modes occur during the extraction of a pipeline. Initial vertical
buckling; at least for the specified warranty period. Therefore, movements of the pipe provoke a pseudo-elastic response in the
until such time as Operators share some of these risks, it is soil, with movement all around the pipe and heave occurring
becoming increasingly important that the contractor understands generally in the soil mass (rather like Figure 4b). This causes an
the mechanisms of upheaval buckling to be able to define an increase in normal stress at the front of the pipe and a reduction
adequate depth of burial and soil cover to provide sufficient behind it and a consequently stiff load-displacement response.
restraint. Where the depth of burial is at the limit of, or beyond, With increasing vertical pipe displacement, soil stresses
the capability of the selected trenching and burial tool, an continue to increase on the top of the pipe and decrease behind
allowance has to be made in the bid for the cost of rock until the normal stress at the back of the pipe reduces to zero.
dumping sections of pipeline identified to be at risk. This can The reduction of stress to zero causes detachment between the
be an expensive process and accurate prediction of the soil- pipe and the soil mass and a softening of the load-displacement
pipeline interaction behaviour and the uplift capacity of the soil response. As this is occurring, the soil ahead of the pipe begins
can reduce unnecessary quantities of rock being dumped. to yield and soil deformation will become localised towards the
The numerical and scaled model testing has shown region above the pipeline (e.g. Figure 4c). As the pipe moves
consistent uplift factors for both loose and dense granular further upwards, the soil behind the pipe remains essentially
materials. For loose sands, fd was found to be approximately rigid and a gap forms and enlarges behind the pipe (Figure 3). It
0.55. For dense sand and gravel, peak uplift factors were found is as this mechanism is occurring that the peak uplift load is
to be greater than one on initial loading, eventually reducing to mobilised. Further pipe displacement causes the gap size to
a residual value after a displacement, which appears to be increase until the side slopes reach the angle of repose (φ' )
proportional to particle diameter. These factors are comparable (Figure 10). Model tests suggest that this requires a
with those found previously in similar studies (e.g. Trautman et displacement, δ/D ≈ 0.3. Further vertical pipe movement
al., 1985; Dickin, 1994). The vertical slip surface model of the requires soil to flow around the pipe ensuring the gap remains
form suggested by Majer (1955) (shown in Figure 3) was used the same size (Figure 10). Thus, the gap size is maintained until
to give an alternative calculation of fd. Using a shear stress pipe breakout occurs. As the pipe approaches the surface, the
along the slip planes, τ = Ko σ' v tan φ'
, where Ko= 1-sin(φ' ) gave uplift resistance decreases, reflecting the reducing amount of
the line shown dotted in Figure 8 and a conservative soil available to resist pipe movement.
approximation to the uplift force. Due to the complexity of the soil deformation mechanism
The load-displacement results from the scaled model described, the analysis of the entire pipe pullout problem is
testing shows the displacement required to mobilise full soil extremely difficult. Current models and design approaches can
resistance (δ) should be normalised by either pipe diameter (D) only predict certain facets of the behaviour. The vertical slip
or cover depth (H) with full load mobilisation occurring at model (Majer, 1955; Schaminee et al., 1990; Bolton and
approximately δ/D = 1 % or δ/H = 0.5 %. This is consistent Baumgard, 2000) appears to predict the peak pullout resistance
with the findings of previous studies (e.g Trautman et al., 1985; reasonably well and this may be a simplification of the soil
Dickin, 1994). The finite element analysis suggested that deformation mechanism occurring when peak load is mobilised.
displacements should be mobilised by embedment depth, H Finite element analysis gives a good approximation to the
rather than diameter. system behaviour prior to the full-size gap formation. Hence,
detachment and gap formation/opening may be modelled and

7 Copyright © 2001 by ASME

the finite element method may provide a reasonable prediction The results of the finite element analysis were in good
of the distance required to mobilise peak load. In either case, agreement with results from the scaled model tests. With some
the choice of soil parameters is extremely important since the refinement, a combination of finite element analysis and
predictions will be sensitive to in situ stress conditions and soil centrifuge testing has potential for use in design.
stiffness.
More extensive comparison of the 1g and centrifuge model REFERENCES
tests (Bransby et al., 2001) has suggested that measurement of Bolton, M.D. & Baumgard, A.J. (2000) Minidrum Centrifuge
peak uplift loads requires correctly scaled models. This is Uplift Resistance Testing, Final Report of Halfdan Pipeline
because some difference was observed between normalised Project.
uplift factors for small pipes and large ones (Bransby et al., Bransby, M.F., Newson, T.A., Brunning, P., Davies, M.C.R.,
2001). Furthermore, the load-displacement data could be (2001). Physical modelling of upheaval buckling of buried
normalised by diameter for both sets of data. This suggests that offshore pipelines, Submitted for ISOPE 2001, Stavanger,
continuum deformation takes place during pick up of peak load June.
rather than localised slip plane formation. Thus, the centrifuge Dickin, E.A. (1994) Uplift Resistance of Buried Pipelines in
model tests are likely to scale correctly. Centrifuge modelling is Sand. Soils and Foundations, Vol.34, No.2, p 41-48.
a useful technique as the subtle variations of soil properties with Finch. M, Fisher. R, Palmer A, and Baumgard. A, (2000). An
depth that are difficult to incorporate in closed form or Integrated Approach to Pipeline Burial in the 21st Century,
numerical analyses can be included. Deep Offshore Technology 2000.
Despite the simplicity of the finite element modelling, the Majer, J. (1955) Zur berechnung von zugfundamenten.
important soil deformation mechanisms were identified and the Osterreichister Bauzeitschift, 10, 5, p. 85-90.
load-displacement response of the pipeline approximated up to Maltby, T.C. & Calladine, C.R. (1995) An Investigation into
mobilisation of peak load. This suggests that with some Upheaval Buckling of Buried Pipelines-I. Experimental
refinement, a combination of finite element analysis and Apparatus and Some Obseravations. Int. J. Mech. Sci.,
centrifuge testing has potential for use in design. Vol.37, No.9, p 943-963.
Matyas, E.L. and Davis, J.B. (1983) Prediction of vertical earth
7 CONCLUSIONS loads on rigid pipes. J. Geo. Eng. Div., ASCE, 109, GT2, p.
A series of finite element analyses and scaled model tests have 190-201.
been described that have been used to examine the effects of Merifield, R., Sloan, S. and Yu, H. (1999) Stability of plate
soil properties and pipe geometries on the uplift capacity and anchors in undrained clay. Internal report No 174.02.1999,
mobilisation displacement to failure of a pipeline subject to University of Newcastle, Australia.
vertical uplift. The following conclusions have been drawn from Moradi, M., and Craig, W.H. (1998) Observation of Upheaval
this study: Buckling of Buried Pipelines. Centrifuge 98, Kimura,
• Consistent uplift factors were found for the pipelines: for Kusakabe & Takemura (eds), p 693-698.
loose sand fd ≈ 0.55 and for dense sand and gravel, peak Ng, C.W.W. & Springman, S.M. (1994) Uplift Resistance of
uplift factors, fd > 1 were found on initial loading, which Buried Pipelines in Granular Materials. Centrifuge 94,
reduced to a residual value after a displacement which Leung, Lee& Tan (eds), p 753-758.
appears to be proportional to particle diameter. Nielsen, N-J.R., and Lyngberg, B. (1990) Upheaval Buckling
• For loose sand, there was good agreement with predictions Failures of Insulated Buried Pipelines: A case story. OTC
using the vertical slip surface model (Majer, 1955) using 6488, 22nd Annual Offshore Technology Conference,
Ko = 1 - sin(φ') and the experimental data. Houston, Texas, May 7-10, p581-592.
• The load-displacement behaviour of the all of the pipes in Rowe, R.K. & Davis, E.H. (1982). The behaviour of anchor
the model tests show the normalised displacement required plates in clay. Geotechnique, 32, 1, p. 9-23.
to mobilise full soil resistance was approximately δ/D = 1 Schaminee, P.E.L., Zorn, N.F. and Schotman, G.J.M. (1990)
% or δ/H = 0.5 % Soil Response for Pipeline Upheaval Buckling Analyses:
• Soil deformation mechanisms after failure vary with initial Full-Scale Laboratory Tests and Modelling. OTC 6486, 22nd
soil density, but all contain soil flow around the pipe and Annual Offshore Technology Conference, Houston, Texas,
gapping behind the pipe. This occurs after peak resistance May 7-10, 563-572.
is mobilised, so that this may not be important for Schofield, A.N. (1990). Cambridge University Geotechnical
prediction of ultimate uplift capacity, Wu. Centrifuge Operations. Rankine lecture, Geotechnique 30,
• Comparison of 1-g model test data with centrifuge model No. 3, pp. 227-268.
test data suggests the results scale correctly, thus elevated-g Trautmann, C.H, O’ Rourke, T.D. and Kulhaway, F.H. (1985)
levels are required to correctly reproduce the pipe uplift Uplift Force-Displacement Response of Buried Pipe.
behaviour in scaled models. Journal of Geotechnical Engineering, Vol.111, No.9, p.
1061-1076.

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