Physical Modelling of the Upheaval Resistance of Buried Offshore ...

Physical Modelling of the Upheaval Resistance of Buried Offshore
Pipelines
M.F.Bransby, T.A.Newson, M.C.R.Davies
Department of Civil Engineering. University of Dundee, Dundee, Scotland.
P.Brunning
Stolt Offshore, Aberdeen, Scotland.
ABSTRACT: This paper describes a programme of scaled physical model tests investigating the uplift
behaviour of buried offshore pipelines. Model tests were conducted using sand and gravel in the laboratory
and in a large geotechnical centrifuge. During the tests, the resistance forces for vertical pipe pullout and the
mobilisation distance for peak resistance were investigated for varying model geometries and soil properties.
Of particular interest were the soil deformation mechanisms observed for different soil states. Dense and loose
sand samples were seen to undergo different deformation mechanisms after peak uplift load was mobilised
due to volumetric response and this was reflected in the uplift forces. The effect of scaling was also
investigated: results were compared for models conducted at 1g and in the centrifuge.
1 INTRODUCTION
Offshore oil and gas pipelines are commonly buried
to provide environmental stability, thermal
insulation and mechanical protection from fishing
activities. More high temperature and pressure
reserves are now being transported through small
diameter insulated pipes, particularly on the North
Sea Continental Shelf. These pipes are frequently
relatively light compared to the surrounding backfill
soil and are prone to "snap" upheaval buckling on
start-up due to axial forces caused by pipe heating.
To prevent upheaval buckling, the pipeline must
be buried sufficiently deeply in the seabed to prevent
upwards pipeline movement or expensive ’rockfill’
berms must be laid on the surface of the seabed to
provide additional restraint (Figure 1).
Operators, offshore contractors and designers have
therefore commissioned research studies that have
been undertaken to find out how much restraint to
upwards pipe movement is provided by the seabed
(eg. Dickin, 1994; Moradi and Craig, 1998; Ng and
Pipe
H
Wt
Soil surface
D
Pipe
Wt
(a) no berm (b) with berm
Figure 1. Embedded pipe geometry and definitions
H
D
Springman, 1994).
The geotechnical focus of previous research has
been the uplift capacity for various soil types. The
majority of this work has been carried out at small
scale using geotechnical centrifuges to simulate the
full-scale site conditions (e.g. Dickin, 1994; Moradi
and Craig, 1998). Finch et al. (2000) also reported
on full scale laboratory testing.
Design methods are based on pipe element
analysis and so the behaviour of an infinitely long
pipe is of interest. Hence, the pipe geometry
investigated is shown in Figure 1. For an embedded
pipe to move vertically towards the seabed surface, it
requires a force Wt. This comprises the effective
weight of the pipe, W’ and the net uplift force Wu
(i.e. Wt = W’ + Wu). The net uplift force, Wu is the
resistance of the soil to pipeline movement and its
maximum resistance, Wumax therefore changes with
different soils, soil states, and embedment depths.
The net uplift force, Wu can be calculated using an
equation suggested by Schaminee et al. (1990):
Wu
⎛ H ⎞
= 1+
f d ⎜ ⎟
γ ′ HDL ⎝ D ⎠
where H is the instantaneous embedment depth, D is
the pipeline diameter, γ’ is the effective unit weight
of the soil and L is the pipe length under
consideration and fd is the uplift factor. Schaminee et
al. (1990) and later workers have expressed pipe
capacities in terms of the uplift factor, fd and this has
become an accepted industry design parameter.
(1)

Stolt Offshore sponsored the University of
Dundee to undertake a research project to improve
understanding of the failure mechanisms associated
with pipeline uplift and the monotonic uplift
resistance. This paper reports some of the model
tests carried out for drained loading conditions.
2 EXPERIMENTAL METHOD
2.1 Test geometry
Model testing was carried out both in the laboratory
(at 1g) and in a 5g acceleration field in the Dundee
Geotechnical centrifuge. Both series of tests
consisted of the extraction of a 500 mm length of
pipe from a box of soil with continuous
measurement of force and pipe displacement.
Because both geometries modelled plane strain
conditions and both pipes were rigid; results are
presented later per unit length of pipe. The front face
of the soil boxes were perspex and the pipe was
positioned perpendicular to the perspex front face,
allowing the soil (and pipe) to be observed as pullout
progressed.
Pipes of 32 mm and 48 mm outside diameter and
length of 495 mm were tested in the laboratory,
whilst pipes of diameter 48 mm and length 498 mm
were tested at 5g (and 5.2g) in the geotechnical
centrifuge. Scaling laws (as reported by Schofield,
1980) ensured that the 48 mm pipe at 5g would
behave as a prototype 5 times larger (i.e.
D=5x48mm= 240 mm).
2.2 Laboratory and centrifuge testing
methodology
The preparation procedures were the same for both
types of tests. Sand was placed to a depth of 30-50
mm in the base of the box and the pipe was
positioned on the surface of the soil. The pipe was
located with its ends almost in contact with the front
and back perspex faces of the box (Figure 2a) and
grease was pushed into the gap to prevent soil
entering the gap between the pipe and the front face.
Additional sand was then added until the required
pipe embedment depth was achieved. Whilst the
sand sample 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 this were not
done, the mobilisation distance to peak load would
be underestimated. During a number of the tests, a
grid of black markers at approximately 50 mm
centres were placed in the soil touching the perspex
front face while the soil was being prepared. This
allowed later photographic measurement of soil
movements through the perspex front face (Figure
2a).
Figure 2. Testing apparatus - (a) the laboratory test
apparatus (b) centrifuge model package
The pipe was then pulled out of the soil using a
rigid hanger arrangement to ensure that the pipe
moved with uniform displacement and vertically
(Figure 2a, b). Load was measured using a load cell
and displacement using a potentiometer or LVDT.
This was done using an Instron device in the
laboratory or a specially designed actuator in the
centrifuge. For tests with the soil marker grids, a
series of digital photographs or analogue video was
taken of the front face of the box as the pipe moved
towards the soil surface.
Soil preparation varied depending on the required
density and whether the soil was dry or saturated.
High sand and gravel dry densities (close to ρmax)
were achieved by layered compaction. Loose, dry
sand was prepared by quick sand pouring. Loose,
saturated sand samples were prepared by pluviating
sand through air into 200 mm of water. A sand or
gravel berm was constructed once the strongbox was
placed on the centrifuge arm by pouring through a
funnel onto the soil surface. This would have created
an intermediate density berm.
2.3 Programme of tests
The tests reported in this paper were conducted on
either silica sand or gravel. The sand was uniformly
graded with d50 = 0.3 mm, Gs = 2.65 and the
particles were subrounded. The angle of repose of
the loose soil was measured to be 32 o and this is
believed to be close to the critical state angle of
friction, φcrit. The gravel was subangular with d50 = 5
mm and had an angle of repose of 35 o .
Model tests were conducted in loose sand in the
centrifuge and the laboratory. Other variables
investigated were the diameter of the pipe, its
embedment ratio (H/D), whether the soil was dry or
saturated and the presence of a berm. The series of
tests is summarised in Table 1.

Table 1. The series of physical model tests.
Test
number
Test type Density
(Effective soil
unit weight, γ’ ,
kN/m 3 )
Pipe
diameter
D (mm)
Initial
embed.
ratio,
H/D
L5 Dry sand Loose (14.5) 32 3.3
L6 Dry sand Loose (14.5) 48 3.0
L8 Dry sand Dense (15.5) 48 3.3
L9 Dry sand Dense (15.5) 48 3.1
L11 Dry sand Dense (15.5) 32 3.0
L12 Dry gravel Loose (14.7) 48 3.04
L13 Dry gravel Dense (15.5) 48 3.04
C1 Dry sand Loose (14.5) 240* 3.1
C2 Dry sand Loose (14.5) 240* 2.1
C3 Dry sand Loose (14.5) 250 +
3.5
C4 Saturated Sand Loose (9) 250 +
3.5
C5 Saturated Sand Dense (10) 250 +
2.3
C7 Saturated sand Loose (9) 250 +
2.7
C8 Saturated sand +
gravel berm
Loose (9) 250 +
2.8 + 1
C9 Saturated sand +
sand berm
Loose (9) 250 +
2.8 + 1
* Pipe diameter at prototype scale (5 g centrifuge test, D = 48 mm at
model scale)
+
Pipe diameter at prototype scale (5.2 g centrifuge test, D = 48 mm at
model scale)
3 EXPERIMENTAL RESULTS
3.1 Typical data
Typical resistance force against pipe displacement
data are shown for a centrifuge test (C1) and a
laboratory test (L6) in dry, loose sand in Figure 3.
The centrifuge test is shown using units for the
equivalent full-scale prototype (pipe of prototype
diameter, D = 240 mm; initial embedment ratio, H/D
= 3.1; Soil density, γ = 14.2 kN/m 3 ). The results of
the laboratory test of a pipe of diameter 48 mm and
embedment ratio, H/D = 3.0 are scaled as if the 1g
test was a 1/5 th scale model.
Peak uplift load is mobilised very quickly for each
test and uplift resistance then reduces as the pipe
approaches the soil surface and the cover reduces.
The scaled-up laboratory tests results do not agree
well with the centrifuge test results suggesting that
pipe diameter affects uplift capacity even for loose
sand.
Load, kN/m.
9
8
7
6
5
4
3
2
1
Centrifuge test: D = 240 mm
Centrifuge test: D = 240 mm
1g test: D = 48 mm
1g test: D = 48 mm
0
0 100 200 300 400 500 600 700 800
Displacement, mm
Figure 3. Load-displacement data: centrifuge model test C1
(H/D = 3.1) and scaled 1g test L6 (H/D = 3)
Uplift factor, fd
Uplift factor, fd
1.4
1.2
1
0.8
0.6
0.4
0.2
0
1 1.5 2 2.5 3 3.5 4
Embedment ratio, H/D
Figure 4. Uplift factors for loose sand samples (laboratory
and centrifuge model tests)
3.2 Uplift forces
3.2.1 Loose sand
Figure 4 shows the results of the tests on loose sand
as a plot of fd against H/D. A single data set starts
on the right of the graph (at H/D ≈ 3) and then
reflects changes in fd as the pipe is pulled out and
H/D reduces. There is good agreement between the
1g tests on 48 mm and 32 mm diameter pipes where
fd ≈ 0.5 for 2 < H/D < 3. There is no peak of fd at the
start of movement, and so the results for a single
continuous test may be representative of the peak
resistance for a range of H/D. The results from
centrifuge test C1 (loose sand with H/D = 3.1; D =
240 mm; γ = 14.2 kN/m 3 ) gives an uplift factor, fd =
0.67 at initial failure and a residual uplift factor, fd ≈
0.6 for 1.5 < H/D < 3.
The uplift force for loose sand may be predicted
using the vertical slip surface model (Majer, 1955)
and using τ = Ko γ ] WDQ φ crit on the slip surface,
where Ko = 1 – sin(φ crit) is the at rest lateral earth
pressure coefficient. The results using this
relationship are shown in Figure 4 using φ crit = 32 o .
The vertical slip surface model appears to give a
slightly conservative prediction of uplift capacity for
loose sand when the initial horizontal stress
conditions are used.
Vertical load, N/m
600
500
400
300
200
100
Dense gravel
Dense gravel sand
Cover ratio, H/D
‘
L5 (D = 32 mm)
L4 (D = 48 mm)
L6 (D = 48 mm)
Vertical slip model
C1 (D = 240 mm)
C3 (D = 250 mm)
C4 (D = 250 mm)
C7 (D = 250 mm)
0
0 20 40 60 80 100 120 140
Upwards displacement, mm
L9: dense sand
L13: dense gravel
L6: loose sand
Figure 5. Load-displacement response of 48 mm pipes in
dense sand and gravel.

Uplift factor, fd
Uplift factor, fd
Uplift factor, fd
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
C5 (dense sand)
L5 (D = 32 mm) L6 (D = 48 mm)
C3 (D = 250 mm) C5 (D = 250 mm)
L8 (D = 48 mm) L13 (D = 48 mm)
L12 (D = 48 mm)
L13 (dense gravel)
L8 (dense
sand)
0
1 1.5 2 2.5 3
Embedment Cover ratio, ratio, H/D H/D
3.5 4
Figure 6. Uplift factors for 1g tests in dense sand and gravel.
3.2.2 Dense sand and gravel
Load-displacement plots are shown for the
laboratory tests in dense and loose sand and dense
gravel in Figure 5. Tests were conducted with a pipe
of diameter, D = 48 mm and an initial embedment
ratio, H/D ≈ 3. There is a clear difference compared
to the loose sand tests, with a peak uplift resistance,
which drops quickly by half to a residual pull-out
force. This residual force then reduces as the pipe
moves towards the surface. The pattern is reflected
in the uplift factors (Figure 6). A peak uplift factor
(fd ≥ 1) on initial movement then reduces to values
similar to the loose sample after a small pipe
displacement. For the sand, the distance required to
reach the residual value of fd is 5 mm, for gravel, it
is 15 mm (see Figure 5). Further experiments are
needed to examine this behaviour for a wider range
of H/D and soil types.
3.2.3 Sand and gravel berms
Uplift factors are shown against reducing
embedment ratio for the tests with and without
gravel or sand berms on loose, saturated sand in
Figure 7. There is a clear increase in uplift resistance
with either a gravel or sand berm, but this is more
marked with the gravel berm. Indeed, the increase in
uplift resistance due to the gravel berm compared to
pure loose sand increases with the displacement of
the pipe. This may be due to the rising soil surface
due to the dilation of the angular gravel berm during
pipe displacement, which ensures that the pipe burial
is greater than calculated assuming H = Hi - δ.
Uplift factor, fd
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
Vertical slip model
C4 (sand)
C7 (sand)
C8 (gravel berm)
C9 (sand berm)
0
1 1.5 2 2.5 3 3.5 4 4.5
3.3 Mobilisation of peak uplift load: initial loaddisplacement
response
3.3.1 Loose sand
The initial load-displacement data for the tests on
dry loose sand are shown in Figure 8. Uplift load
(Wu) is normalised by the peak uplift load (Wumax)
for each model test to allow comparison of
mobilisation distances. For the laboratory tests
(when D = 32 mm or 48 mm), 90 % of peak uplift
load was mobilised when pipe displacement, δ ≈ 0.5
mm and the peak capacity was reached by about 1
mm. However, the prototype displacement for 90%
mobilisation in the centrifuge model tests was 3 or 4
mm.
If the displacement is further normalised by
embedment depth, H, the graph shown in Figure 9 is
produced. There is good agreement between results
for different pipe sizes in loose sand and it appears
that 90% of the maximum uplift load is mobilised
when δ/H ≈ 0.4 %. This agrees well with δ/H = 0.5
% recommended by Matyas and Davies (1983) in
their laboratory tests and δ/H = 1 % recommended
by Trautman et al. (1985).
3.3.2 Dense sand and gravel
Normalised initial load-displacement behaviour from
the laboratory tests in dense sand and gravel is also
shown on Figure 9. Peak uplift load is mobilised
within significantly smaller displacements than for
loose sand. Further centrifuge tests are required to
ascertain how this scales with pipe size or
embedment depth.
Embedment Cover ratio, ratio, H/D H/D
Figure 7. Uplift factors for loose, sat. sand with/without berms. Figure 9. Normalised load-displacement data.
Load, Wu/Wumax.
Load, Wu/Wumax.
0.6
L5 (D = 32mm)
0.4
Centrifuge tests
L6 (D = 48 mm)
0.2
0
C1 (D=48 mm)
C2 (D=240 mm)
-0.2
0 1 2 3 4 5
1
0.8
0.6
0.4
0.2
-0.4
0
1.2
1
0.8
1g tests
Displacement, mm
Figure 8. Load-displacement behaviour of pipes in loose sand
L8 (dense sand)
L13 (dense gravel)
L6 (loose sand)
C1 (loose sand)
C3 (loose sand)
C4 (loose sand)
C7 (loose sand)
C8 (gravel berm)
C9 (sand berm)
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014
Displacement/Embedment depth.

3.3.3 Rockfill berms
Normalised load-displacement graphs for the loose
sand with and without berms is also shown in Figure
9. There is some suggestion of a slightly softer
normalised response for the gravel and sand berms
compared to tests without berms. This is likely to be
because the stiffness of the soil around the pipe for
the same cover (whether consisting of only sand, or
sand plus rockfill) will not be affected by the berm
material, but the uplift capacity will be increased.
3.4 Soil displacement mechanisms
3.4.1 Loose sand
Figure 10 shows a digital photograph of the front
face of the soil model after a pipe displacement of
δ/D ≈ 1.3 through loose sand in the laboratory. The
initial embedment ratio, H/D = 3 and the embedment
ratio when the photograph was taken was H/D ≈ 1.7.
There appears to be negligible surface soil
movement and only the two markers above the pipe
appear to have moved (about 1/10 th of the pipe
displacement) from their initial grid position.
In all tests, a gap formed between the soil and pipe
with sides of angle ≈ 30 o and this remained at a
constant size after initial formation. To sustain the
constant gap size with the upward moving pipe there
was flow of soil around the pipe as sketched in
Figure 10. During centrifuge test 2 (C2) there
appeared to be some upwards movement of the soil
surface as well as gapping beneath the pipe, but
again there is negligible movement of soil markers
to the sides of the pipe.
3.4.2 Dense sand sample
Observed dense sand movements showed gapping
behind the pipe of a similar size to the loose samples
but there was a larger region of soil deforming above
the pipe together with more surface movement
(Fig.11). The top layer of marker pellets in Figure 11
(which were initially in a horizontal line) show that
the soil moves upwards in a region about 2D wide
near the surface. In addition, soil flowed around the
pipe to maintain the gap at a constant size.
Figure 10. Laboratory test in loose sand.
Soil
Gap
Initial
pipe
position
Gap
Figure 11. Laboratory test in dense sand.
3.4.3 Berms
Soil displacements as the pipe approaches the soil
surface (Figure 12) reveal that there is more
distortion of the top soil surface and the gravel/sand
interface with a gravel berm than for the equivalent
sand only tests (Figure 10). This suggests that the
berm may be dilating during initial pipe
displacement and this may contribute towards the
higher uplift resistance. Details of this mechanism
need to be confirmed by further study.
4 DISCUSSION
Marker
displacements
Gap
Initial
pipe
position
Uplift load and mobilisation distance to peak are
dependent on the soil properties, the pipe geometry
and the soil deformation mechanism. The digital
photography of the markers in the soil during pipe
uplift tests has allowed determination of soil
deformation mechanisms after failure. However,
because full load is mobilised within a model
displacement of less than 1 mm, the mechanism of
initial load pick-up is harder to measure visually due
to the small soil displacements.
Post-peak deformation mechanisms suggest that
soil flow around the pipe is a large component of the
soil deformation because of a constant volume gap
behind the pipe. This is very different from the
mechanism proposed by Majer (1955). For dense
sand, the increasing soil volume due to dilation
causes soil displacements somewhat similar to the
vertical slip plane model (Majer, 1955) which extend
towards the soil surface.
The peak uplift load, however, is mobilised while
the gap is being formed (when there are only small
displacements). This appears to be a process which
requires a mobilisation distance which scales with
embedment depth (H) (see Figure 9) as confirmed by
Bransby et al. (2001). This suggests that for the soil
conditions and embedment ratios tested, the peak
uplift force is not generated by the formation of a
discrete slip plane because the mobilisation distance
of a slip plane would depend on soil particle size

Gravel
berm
Loose
sand
Pipe
(a) (b)
Figure 12. Soil deformation: loose sand with gravel berm
(C8) at different stages of the test.
rather than the pipe diameter/embedment. The
mobilised displacement ratios to peak load, δ/H ≈
0.5 % and these agree well with previous workers
(eg. Matyas and Davis, 1983; Trautmann et al.,
1985).
As shown earlier, the uplift force for loose sand
may be predicted conservatively using the vertical
slip surface model (Majer; 1955) and using φ RQ WKH
slip surface, and Ko = 1 – sin(φ WKH DW UHVW ODWHUDO
earth pressure coefficient (Figure 4) despite the
different post-failure mechanism observed. The
load-displacement response for the dense sand and
gravel shows a peak uplift resistance before the
uplift resistance reduces to a residual value similar to
the values for a loose sand. The dense soil sample is
dilating, but then post-peak strain softening reduces
the mobilised angle of friction to φ’ as for the loose
sand tests.
5 SUMMARY AND CONCLUSIONS
Tests have been carried out to study the uplift
behaviour of pipelines in the laboratory and the
geotechnical centrifuge. The pipes were of prototype
diameter 32 mm, 48 mm, 240 mm and 250 mm and
soil conditions consisted of dry, loose or dense sand
or gravel with or without a berm.
Uplift factors are presented for the tests. Loose
sand gave fd ≈ 0.5. Dense sand and gravel gave a
peak uplift factor, fd > 1 on initial loading, but this
reduced to a residual value, fd ≈ 0.6 after a
displacement that may be proportional to the
diameter of the soil particles. For design, it is
therefore important to either know the density of the
seabed or otherwise use a conservative uplift factor.
The load-displacement behaviour of the pipes
shows the displacement required to mobilise full soil
resistance, δ/H ≈ 0.4 % for all loose sand tests. Peak
load is mobilised more quickly in dense soil (δ/H ≈
0.1 %).
Soil deformation mechanisms were examined by
taking digital photographs/video of the front face of
the test box. Photographs are presented which
indicate soil displacement mechanisms after failure
for the different soil types. These vary with initial
soil density, but all included gap formation behind
the pipe while the peak uplift force is being
mobilised and soil flow around the pipe after failure.
Results from centrifuge model tests with gravel
berms showed a significant increase in uplift
capacity (fd ≈ 0.8) but a less significant increase was
found for sand berms. It is believed that dilation of
the berm during initial pipe displacement together
with the weight of the berm increases the uplift
capacity.
ACKNOWLEDGEMENTS
The work described in this paper was supported by
funds from Stolt Offshore and this support is
gratefully acknowledged. The authors would like to
thank Mr. Colin Fyfe and Dr. Shiping Yao for their
hard work during the testing programme and to the
technical staff of the Department of Civil
Engineering, University of Dundee for all of their
help.
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