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4.3.2 Soil properties
Normally consolidated clay samples were prepared by mixing commercially available
kaolin clay powder with water to form a slurry at 120 % (i.e. twice the liquid limit, see
Table 4.3) and subsequently de-aired under a vacuum close to 100 kPa. The clay slurry
was carefully transferred into a rectangular strongbox, with internal dimensions 650 mm
long, 390 mm wide and 325 mm deep, before self-weight consolidation in the centrifuge
at 200 g for approximately four days to create a normally consolidated clay sample. A
10 mm sand layer at the base of the clay permitted drainage towards the base of the
sample and a 5 to 10 mm layer of water was maintained at the sample surface to ensure
saturation. Additional clay slurry was added to the sample during consolidation to
achieve the required sample height of 230 mm. Pore pressure transducers placed at
various depths within the sample allowed for the measurement of excess pore water
pressures and these, together with T-bar penetration tests, served to indicate the degree
of consolidation of the sample.
Table 4.3. Kaolin clay properties (after Stewart 1992)
Liquid limit, LL (%) 61
Plastic limit, PL (%) 27
Specific gravity, G 2.6
s
Angle of internal friction, ' (°) 23
Effective soil unit weight, γ' (kN/m3) 6.5
Voids ratio at p' = 1 kPa on critical state line, e 2.14
cs
Slope of normal consolidation line, ς 0.205
Slope of swelling line, κ 0.044
Coefficient of vertical consolidation, c (m2/yr) 4.5
v
(at OCR = 1 and σ' = 150 kPa)
v
Soil characterisation tests were performed using a T-bar penetrometer (Stewart and
Randolph 1991) from which a continuous profile of the undrained shear strength, s ,
u
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was derived using the commonly adopted T-bar factor, N = 10.5. The T-bar tests
T-bar
were conducted at a velocity of 1 mm/s, which corresponds to a dimensionless velocity,
V = vd /c in the range 32 to 113 (where v is the velocity, d is the T-bar diameter
T-bar v T-bar
and c is the vertical coefficient of consolidation, varying from 1.4 to 5 m2/yr for σ' in
v v
the range 10 to 300 kPa), thus ensuring undrained conditions (House et al. 2001).
T-bar penetration tests were conducted during the latter stages of consolidation and
before, during and after the anchor tests to observe any changes in strength with time.
Typical shear strength profiles from Samples 1 and 2 conducted before and after testing
are provided on Figure 4.2. Centrifuge strength data tend to deviate from the expected
linear profile for normally consolidated clays in the lower third of the sample. This
effect is due to the slight increase in radial acceleration level and effective unit weight
with increasing sample depth. The variation in radial acceleration and effective unit
weight has therefore been accounted for in the theoretical strength profile on Figure 4.2,
which was obtained using an undrained shear strength ratio, s /σ' = 0.22. Although the
u v
theoretical and measured profiles deviate beyond 140 mm, the theoretical profile
provides a good approximation of the strength over the range of interest for the DEPLA
plate (up to 103 mm).
Undrained shear strength, s (kPa)
u
0 20 40 60 80 100
0
Sample 1, T-bar 1
20
Sample 1, T-bar 2
) 40 Sample 1, T-bar 3
m
Sample 2, T-bar 1
m
60
( Sample 2, T-bar 2
z
,h 80
Sample 2, T-bar 3
tp
e
d
100
n
o 120
ita
r
te 140
n
e
P 160
180
s/' = 0.22
u v
200
Figure 4.2. Undrained shear strength profiles
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4.3.3 Experimental arrangement and testing procedures
The model DEPLAs were installed in-flight by allowing them to ‘free-fall’ through the
elevated acceleration field from a drop height of 300 mm. This approach has been
adopted for the installation of dynamically installed ‘torpedo piles’ in centrifuge tests
(Richardson et al. 2009, O’Loughlin et al. 2013b) and has resulted in anchor impact
velocities of the order of 30 m/s at 200 g, similar to that expected in the field. The
rotation of the centrifuge requires the anchors to be installed through a guide to prevent
lateral movement of the anchor during free-fall due to Coriolis acceleration. The anchor
installation guide (Figure 4.3) was fabricated from polyvinyl chloride (PVC) and
featured a 1.0 mm wide slot to accommodate one of the four DEPLA flukes and a 8.3
mm diameter channel machined into the front face of the guide to accommodate the
DEPLA sleeve (7.8 mm diameter). Two PVC rails with an internal circular profile of
8.3 mm diameter were attached to the guide with brackets to prevent the model DEPLA
falling away from the guide. The rails permitted an open slot over the length of the
guide, allowing unobstructed access for the follower and plate anchor lines. Anchor
release was achieved in-flight by a resistor which, when supplied with current, heated
and subsequently burned through an anchor release cord attached to a DEPLA fluke.
This eliminated the need for a shear pin, since the release cord connected to the DEPLA
fluke ensured that the follower and flukes stayed together prior to release. The anchor
velocity was measured using multiple photoemitter-receiver pairs (PERPs) positioned at
10 mm intervals along the guide. The DEPLA fluke travelling through the guide slot
during free-fall would temporarily interrupt each PERP signal and the time between the
trailing edges of consecutive PERP signals together with the fixed PERP spacing of 10
mm allowed the instantaneous velocity of the DEPLA to be determined at various
points above the clay surface.
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Model
Rails
DEPLA
Rails
PERPs
Bracket Bracket
Bracket Figure 4.3. Anchor installation guide
The testing arrangement is shown on Figure 4.4a. Before each DEPLA installation the
model DEPLA was positioned within the installation guide such that the follower tip
was 300 mm above the clay surface (apart from one test with a 200 mm drop height).
The follower line was connected to the actuator and the plate anchor line was
temporarily connected to a fixed point at the base of the actuator with sufficient slack
such that it would not impede the flight of the DEPLA during installation. Each DEPLA
test was conducted at 200 g and comprised the following stages (summarised
schematically in Figure 4.4):
1. Anchor installation:
The model DEPLA was released by burning through the temporary release cord (as
described previously) and the DEPLA travelled vertically through the installation
guide before impacting the clay surface. After anchor release the fluke passing the
highest PERP in the installation guide triggered the high speed data acquisition and
PERP data were logged at 100 kHz.
2. Follower recovery:
The actuator was driven horizontally 43 mm (offset between the vertical axes of the
actuator and the installation guide) such that the vertical axis of the actuator was
directly above the anchor drop site. The follower was extracted by driving the
actuator vertically away from the sample surface at a rate of 0.3 mm/s; this rate was
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selected so that the dimensionless velocity, V = vD/c (where v is the extraction
f v
velocity, D is the follower diameter and c is the vertical coefficient of
f v
consolidation quantified previously) exceeded 10, so that the response is primarily
undrained (House et al. 2001). Follower extraction was continued until video
footage confirmed that the follower was free from the clay surface.
3. Exchange anchor line:
Immediately after follower extraction the centrifuge was stopped for approximately
five minutes to disconnect the follower line from the load cell and to connect the
plate anchor line. The centrifuge was then restarted and a reconsolidation period of
just over 13 minutes (equivalent to one prototype year at 200 g) was permitted
before commencing the anchor pullout test. The DEPLA plate embedment depth
remains constant during this process.
4. Plate anchor keying and pullout:
The plate anchor keying and pullout were performed continuously at an actuator rate
of 0.1 mm/s such that V > 10 (for the lowest plate anchor diameter, D = 16 mm) to
ensure undrained conditions. Each anchor pullout was vertical, causing the plate
anchor to key from the initial vertical orientation to a final horizontal orientation,
before loading to failure. Pullout of the plate anchor was continued until the plate
was fully extracted from the clay.
The presence of a radial acceleration field limited anchor installation sites to the
longitudinal centreline of the beam centrifuge strongbox. To minimise interaction
effects, installation sites were located at least 20 DEPLA follower diameters (i.e. 120
mm) from rigid boundaries and adjacent installation sites were separated by at least 12
DEPLA follower diameters (i.e. 72 mm). In addition to the dynamic installation tests,
two further, installations were conducted in which the DEPLA was jacked at a constant
penetration rate of 1 mm/s at 1 g using a custom-built 6 mm diameter shaft connected to
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4.4.1 Impact velocity
Anchor velocities determined from the measured PERP data are shown on Figure 4.5
together with theoretical velocity profiles generated using Equation 2.17 albeit with the
frictional and bearing resistance terms omitted whilst accounting for the radially varying
acceleration field in the centrifuge. The theoretical velocity profiles have been adjusted
to fit the PERP data; this adjustment is necessary to account for friction along the
anchor-guide interface, which varies in accordance with the contact area between the
plate anchor and the guide. The reduction of the theoretical velocity for the three tests
shown in Figure 4.5 is in the range 8 to 16%, which is typical for the entire dataset. This
is consistent with a kinetic friction coefficient, μk = 0.17 to 0.36, between the anchor
and the guide, which is reasonable for a plastic-metal interface. As shown in Figure 4.5,
the impact velocity is taken from the adjusted velocity profile at the clay surface. The
impact velocities achieved in the centrifuge tests (for the 300 mm drop height) are in the
narrow range v = 27.5 to 30.0 m/s, which is typical for a drop height of 300 mm
i
(Richardson 2008) and is at the upper end of the range from field experience of v in the
i
range 24.5 to 27.0 m/s (Lieng et al. 2010) and 16 to 27 m/s (Brandão et al. 2006).
350
300
)
m
250
m
(
e
l
p
m200
a
s v/v = 93%
e theor
v
o150 v/v = 92%
b theor
a
t
h
g
i e100 v/v = 89%
H theor
v/v = 84%
50 theor
0
0 5 10 15 20 25 30 35
Velocity, v (m/s)
Figure 4.5. Velocity profiles during centrifuge free-fall
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4.4.2 Embedment depth
The DEPLA tip embedment, z was determined using the approach adopted by
e
Richardson (2008) (see Figure 4.6), where by z is calculated from:
e
z z z z L Equation 4.1
e chain LC slack f
where z is the initial vertical position of the actuator load cell above the sample
LC
surface, z is the length of the follower chain, L is the follower length and z is the
chain f slack
amount of slack removed from the follower chain prior to the onset of a significant
tensile load during follower extraction. The vertical installation guide located above the
centerline of the soil sample prevents the anchor tilting during the free-fall stage.
Although there is potential for the anchor to deviate slightly from a vertical trajectory
for the remaining one anchor length (on average) embedment, previous centrifuge
studies reported by O’Loughlin et al. (2009) report a maximum inclination of 3 for
dynamically installed anchors in normally consolidated kaolin clay. In the case of the
DEPLA, a 3° inclination would have little bearing on the capacity mobilisation of the
plate, other than a negligible error in determining the embedment depth using Equation
4.1.
z
Z iez,e
Figure 4.6. Determining anchor tip embedment during centrifuge tests
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DEPLA tip embedments were in the range 144 to 186 mm, or 1.6 to 2.8 times the length
of the DEPLA follower, where the lower and upper bounds correspond to the longest
and shortest DEPLA followers respectively (51.5 mm and 101.5 mm). The majority of
the test data relate to the 76 mm follower (L/D = 12.7), for which z is in the range 144
f f e
to 162 mm, or 1.9 to 2.1 times the follower length. This is in good agreement with
reported field experience of 1.9 to 2.4 times the anchor length for a 79 tonne
dynamically installed anchor with L/D = 10.8 and 4 wide flukes (Lieng et al. 2010).
f f
4.4.3 Follower extraction
Figure 4.7 presents typical load versus displacement data for the extraction of the
DEPLA follower. The extraction response was characterised by a sharp increase in load
after the follower line slack had been taken up, towards an initial maximum (Peak 1)
followed by a sudden drop in load and a subsequent gradual increase towards a
secondary maximum (Peak 2) of lower magnitude than Peak 1. In some instances the
load increased rapidly towards a further maximum (Peak 3), similar to Peak 1, before
reducing suddenly again. The Peak 1 and Peak 2 response has been observed during
extraction of geometrically similar dynamically installed anchors (Richardson et al.
2009) and is considered to be due to the different rates of mobilisation for frictional and
bearing resistance as observed for suction caissons (Jeanjean et al. 2006). It appears that
high, but brittle, frictional resistance along the follower shaft (either against soil or the
DEPLA sleeve) is mobilised first (Peak 1), before a more gradual mobilisation of
bearing resistance at the follower padeye (Peak 2). The reason for Peak 3 and its
sporadic occurrence is not wholly understood, although it may be due to secondary
frictional resistance that occurs as the follower emerges from the upper end of the
DEPLA sleeve. The average displacement to Peak 1 was one follower diameter, with a
range of 0.7 to 1.3 times the follower diameter arising from uncertainties regarding the
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onset of follower movement. Interestingly the displacement between Peak 1 and Peak 3
is also approximately one follower diameter.
The magnitude of the Peak 1 capacity ranged from 2.2 to 3.2 times the dry weight of the
follower, with capacity increasing with follower length and hence frictional surface
area. These capacity ratios are lower than those reported for geometrically similar
dynamically installed anchors (e.g. 3 to 5, O’Loughlin et al. 2004b), mainly because the
DEPLA sleeve reduces the frictional surface area of the follower by between 30 and
50% depending on the model anchor configuration. Furthermore, minimal
reconsolidation was permitted before extraction of the follower (limited by the
minimum time required to adjust the actuator position and take up slack in the follower
line). Thus the measured follower extraction resistance represents short term capacity
that is likely to be 20 to 30% of the long term capacity (Richardson et al. 2009).
80
)
N
( 70
fv
F
,e
c 60 Peak 3
n
a
t
s
i 50
s e Peak 1
r
n
o 40
i
t
c
a Peak 2
r
t x 30
e
r
e
w 20
o
l
l
o
F 10
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
z /D
e,follower f
Figure 4.7. Follower load-displacement response
4.4.4 Plate anchor keying and capacity
Example plate anchor keying and capacity curves are provided on Figure 4.8 for a
square and circular plate anchor installed both dynamically and statically. The keying
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and anchor pullout response is characterised by three distinct stages. After recovering
the slack in the plate anchor line, the load, F , starts to increase as the anchor starts to
vp
key (Stage 1). During Stage 2 F begins to plateau and then reduce slightly. This
vp
reduction was not observed by Gaudin et al. (2006) and Song et al. (2006) in their
respective centrifuge studies on square plates. The reason for this slight reduction is not
understood, but may be attributed to local softening of the soil as the plate rotates. As
keying progresses the effective eccentricity of the padeye reduces, which requires
higher padeye tension to maintain sufficient moment on the plate to continue rotation.
This increase in tension is shown by Stage 3, which continues until the projected plate
area reaches its maximum value, at which point a peak capacity is observed before
reducing again as the plate displaces towards the soil surface through soil of reducing
strength. It is noteworthy that the dynamic installation process does not appear to have a
discernible effect on either the plate anchor keying response or the magnitude of the
peak load.
300
250
) 200
N
(
p
v
F
,d 150
3
a
o
L A1: circular plate,
dynamically installed
100
2 A1: circular plate,
statically installed
A6: square plate,
50 dynamically installed
A6: square plate,
1
statically installed
0
0 10 20 30 40 50
Padeye displacement, d (mm)
v
Figure 4.8. Load-displacement response during anchor keying and pullout
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The anchor keying process gives rise to two effects. Firstly, the soil in the immediate
vicinity of the plate will be partially remoulded, and secondly, the anchor embedment
depth will reduce as the plate rotates and translates vertically (Randolph et al. 2005).
The loss of embedment due to the latter effect is more significant as any loss in
embedment will correspond to a non-recoverable loss in potential anchor capacity (for
offshore clay deposits that are typically characterised by an increasing strength profile
with depth). The loss in plate anchor embedment during keying is demonstrated by
Figure 4.9, which plots dimensionless load-displacement response for all tests. Loads
are normalised by the area of the plate, A , and the undrained shear strength at the
p
estimated anchor embedment at peak capacity, s , which was selected using the T-bar
u,p
test data most relevant to each DEPLA test. The vertical displacement of the anchor
padeye is normalised by the diameter, D, or breadth, B, of the plate anchor for circular
and square plates respectively. The occasional sharp drops in the response curves are
considered to be due to minor mechanical effects such as adjustments of the anchor line
at the padeye.
20
18
16 (F -W)/(As )
p ,u vp s p u,p
s
p
A 14
/
p
v
F
,d
12
a
o
l
d
10
e
s
i l 8 circular plate,
a
m dynamically installed
r o 6 circular plate,
N statically installed
square plate,
4
dynamically installed
square plate,
2 statically installed
0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
Normalised padeye displacement, d /B or d /D
v v
Figure 4.9. Dimensionless load-displacement response during keying and pullout
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In the main, the load-displacement responses in Figure 4.9 are typical of those observed
experimentally for plate anchors (e.g. Song et al. 2006, Gaudin et al. 2006), with an
initial stiff response as the anchor begins to rotate, followed by a softer response as the
rotation angle increases, and a final stiff response as the anchor capacity is fully
mobilised. The range of (F -W )/A s values, adjusting the peak force by the
vp s p u,p
submerged weight of the anchor, W , are also indicated in Figure 4.9, and are compared
S
with theoretical bearing capacity factors later in the chapter. The vertical displacement
of the anchor padeye, d , is in the range 0.96 to 1.12 times the diameter for circular
v
plates and 1.16 to 1.26 times the breadth for square plates. However d represents the
v
displacement of the anchor padeye rather than the loss in plate anchor embedment
which may be calculated as:
z d esin Equation 4.2
e,plate v pull
where e is the padeye eccentricity and θ is the load inclination (to the horizontal) at
pull
the anchor padeye. Hence for a vertical pullout ∆z is in the range 0.50 to 0.68 times
e,plate
the diameter for circular plates and 0.53 to 0.63 times the breadth for square plates. This
is shown on Figure 4.10 together with other centrifuge data for square, rectangular (L/B
= 2) and strip anchors. The horizontal axis on Figure 4.10 combines the two main
parameters that influence the keying response, padeye eccentricity and plate thickness
(and hence anchor weight). Also shown on Figure 4.10 are numerical data reported by
Wang et al. (2011), who showed that embedment loss increases with increasing shear
strength for a given eccentricity and anchor thickness to a limiting value at a normalised
shear strength, s /γ' B ≈ 0.75. Wang et al. (2011) approximate this maximum loss in
u a
embedment for square anchors as:
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Δz 0.144
e,max Equation 4.3
B e t 0.21.15
BB
Equation 4.3 is also shown on Figure 4.10 and represents the theoretical maximum loss
in embedment for a given anchor eccentricity and thickness. Experimental data for the
DEPLA square plates are in reasonable agreement with Equation 4.3, ranging between
94 and 113% of Δz calculated using Equation 4.3. Applying Equation 4.3 to the
e,max
circular DEPLA plate, but with D instead of B, reduces the agreement to 61 to 79%.
The poorer agreement for the circular plate data is not unexpected as Wang et al. (2011)
note that the maximum embedment loss differs for different plate shapes. Figure 4.10
indicates that the loss in DEPLA plate embedment during keying could be reduced if
either the eccentricity or anchor thickness was increased (relative to the plate diameter
or breadth), or if the soil was weaker (relative to the initial moment applied to the
anchor at the onset of keying). The most influential of these factors is the eccentricity
(O’Loughlin et al. 2006, Song et al. 2009, Wang et al. 2011) and the embedment loss
for the DEPLA should be lower if the padeye eccentricity was increased (albeit that this
would require a different plate geometry). Whilst an increase in plate thickness may be
attractive in that it should reduce embedment loss during keying and hence the loss in
potential anchor capacity, this may be offset by the cost implications of increasing the
thickness of the plate.
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more soil in the failure mechanism and results in higher bearing capacity factors. The
DEPLA cruciform fluke arrangement ensures that the failure surface extends to at least
half the plate diameter (D/2) from the plate, which should result in a higher bearing
capacity factor for the DEPLA compared with a flat plate. From a design perspective,
anchor capacity would be based on the (higher) strength at the initial plate location. The
average experimental capacity factor determined in this way is N = 11.8, 21% lower
c
than the average N = 15 based on the strength at the anchor embedment at peak
c
capacity.
The final plate embedment of the anchor (at peak anchor capacity) is in the range 1.8 to
5.8 times the plate diameter or breadth, with lower values corresponding with larger
plates and vice versa. The lower bound of this range is still sufficiently high to mobilise
a deep failure mechanism (Song and Hu 2005, Song et al. 2008b, Wang et al. 2010).
This is supported by the observation that the experimental N values do not reduce over
c
this range of normalised embedment, indicating that the DEPLA mobilises a deep
failure mechanism at relatively shallow plate embedment ratios.
18
16
c 14
N
,
r
o 12
t
c
a
f
y 10
t
i
c
a
p 8
a
c
g
n 6 Ciruclar plates
i
r a Square plates
e
B 4 Martin and Randolph (2001)
Son and Hu (2005)
2 Song et al. (2008b)
Wang and O'Loughlin (2014)
0
0 1 2 3 4 5 6 7 8
z /B or z /D
e,plate e,plate
Figure 4.11. Comparison of experimental and numerical bearing capacity factors
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4.5 Conclusions
This chapter has presented centrifuge data from a series of beam centrifuge tests
undertaken to assess the penetration and capacity response of dynamically embedded
plate anchors in normally consolidated clay. The main findings from this study are
summarised in the following.
At mudline impact velocities of approximately 30 m/s, DEPLA tip embedment
depths are in the range 1.6 to 2.8 times the length of the DEPLA follower, which is
in good agreement with reported field experience of 1.9 to 2.4 times the anchor
length for a 79 tonne dynamically installed anchor with L/d = 10.8 and 4 wide
flukes (Lieng et al. 2010).
Extraction of the DEPLA follower is characterised by an initial sharp increase in
pullout resistance corresponding with frictional resistance along the follower shaft,
followed by reduction in soil (and mechanical) friction and then a more gradual
increase in pullout resistance corresponding with bearing resistance at the follower
padeye. In some instances a second frictional capacity peak was observed at
approximately one follower diameter after the first frictional capacity peak. This is
considered likely to arise from frictional resistance as the follower emerges from the
top of the DEPLA sleeve. Follower pullout resistances quantified using the initial
capacity peak were in the range 2.2 to 3.2 times the dry weight of the follower.
The anchor keying and pullout response is typical of that for plate anchors, with an
initial stiff response as the anchor begins to rotate, followed by a softer response as
the rotation angle increases, and a final stiff response as the effective eccentricity of
the padeye reduces and anchor capacity is fully mobilised. The dynamic installation
process does not appear to have a discernible effect on either the plate anchor keying
response or the magnitude of the peak load.
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CHAPTER 5 IN SITU MEASUREMENT OF THE
DYNAMIC PENETRATION OF FREE-
FALL PROJECTILES IN SOFT SOILS
USING A LOW COST INERTIAL
MEASUREMENT UNIT
5.1 Abstract
Six degree-of-freedom motion data from projectiles free-falling through water and
embedding in soft soil are measured using a low-cost inertial measurement unit,
consisting of a tri-axis accelerometer and a three-component gyroscope. A
comprehensive framework for interpreting the measured data is described and the merit
of this framework is demonstrated by considering sample test data for free-falling
projectiles that gain velocity as they fall through water and self-embed in the underlying
soft clay. The chapter shows the importance of considering such motion data from an
appropriate reference frame by showing good agreement in embedment depth data
derived from the motion data with independent direct measurements. Motion data
derived from the inertial measurement unit are used to calibrate a predictive model for
calculating the final embedment depth of a dynamically installed anchor.
5.2 Introduction
An inertial measurement unit (IMU) is an electromechanical device that measures an
object’s six degree of freedom (6DoF) motion in three-dimensional space using a
combination of gyroscope and accelerometer sensors. The development of micro-
electro mechanical systems (MEMS) gyroscope and accelerometer technology has
significantly reduced the cost, size, weight and power consumption of IMUs, and
enhanced their robustness.
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MEMS accelerometers and gyroscopes are typically fabricated on single-crystal silicon
wafers using micromachining to etch defined patterns on a silicon substrate. These
patterns take the form of small proof masses that are free from the substrate and
surrounded by fixed plates. The proof mass is connected to a fixed frame by flexible
beams, effectively forming spring elements. Low-cost consumer grade MEMS
gyroscopes typically use vibrating mechanical elements to sense angular rotation rate.
During operation the proof mass is resonated with constant amplitude in the ‘drive
direction’ by an external sinusoidal electrostatic or electromagnetic force. Angular
rotation then induces a matched-frequency sinusoidal Coriolis force orthogonal to the
drive-mode oscillation and the axis of rotation. The Coriolis force deflects the proof
mass and plates connected to the proof mass move between the fixed plates in the sense-
mode. The operational principle for MEMS accelerometers is much simpler;
accelerations acting on the proof mass cause it to displace, and plates connected to the
proof mass move between fixed plates. For both sensors, the movement of the plates
cause a differential capacitance that is measured by integrated electronics and is output
as a voltage that is proportional to either the applied angular rotation rate (in the case of
MEMS gyroscopes) or acceleration (in the case of MEMS accelerometers). The
operational principles of the MEMS accelerometers and gyroscopes as described above
are shown schematically in Figure 5.1.
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for geotechnical applications has not been reported. However, MEMS accelerometers
have been used for in situ geotechnical applications to measure: inclinations in
boreholes (Bennett et al. 2009), soil displacement associated with rapid uplift of
footings (Levy and Richards 2012) and the motion of free-falling cone penetrometers
(e.g. Stegmann et al. 2006, Stephan et al. 2012, Steiner et al. 2014). In geotechnical
centrifuge modelling MEMS accelerometers have been used to measure: the
acceleration response of a free-falling projectiles in clay (O’Loughlin et al. 2014a,
Chow et al. 2014), earthquake accelerations (Cilingir and Madabhushi 2011, Stringer et
al. 2010) and rotation of structures during slow lateral cycling and dynamic shaking
(Allmond et al. 2014). Although, accelerometers are often used to measure the rotation
of objects at constant acceleration, they cannot distinguish rotation from linear
acceleration if the object’s orientation and acceleration is changing. However,
gyroscopes are unaffected by linear acceleration, and the rotation of accelerating objects
can be derived from their measurements. Hence the combination of accelerometer and
gyroscope measurements enables an object’s linear acceleration to be determined
relative to a reference frame that is not necessarily coincident with the reference frame
of the object. This becomes important for the applications considered in this chapter,
where dynamically installed anchors and a free-falling sphere (collectively referred to as
‘projectiles’ from this point forward) free fall through water and bury in the underlying
soil. As described later, the motion response of the projectile must be considered from
the appropriate reference frame. From the viewpoint of the hydrodynamic and
geotechnical resistances acting on the projectile during motion, it becomes important to
consider the projectile’s trajectory, whereas from a geotechnical design viewpoint the
final depth and orientation of the projectile relative to a fixed inertial frame of reference
(with an axis in the direction of Earth’s gravity) is important as this will dictate the local
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soil strength in the vicinity of the embedded projectile and (for the case of the anchors)
how this strength will be mobilised during loading.
This chapter describes a custom-design, low-cost MEMS based IMU and presents a
comprehensive framework for interpreting the IMU measurements (which are made in
the body frame of reference) so that they are coincident with a fixed inertial frame of
reference. The framework is implemented to establish rotation, acceleration and velocity
profiles for the projectiles during free-fall in water and embedment in soil. The final
projectile embedment depths established from the IMU data are compared with direct
measurements, and the merit of collecting motion data during dynamic penetration is
demonstrated by using such data to verify the appropriateness of an embedment
prediction model for dynamically installed anchors.
5.3 Free-falling projectiles
5.3.1 Deep penetrating anchor
The deep penetrating anchor (DPA) is a proprietary term for a dynamically-installed
anchor design. The DPA is designed so that, after release from a designated height
above the seafloor, it will penetrate to a target depth in the seabed using the kinetic
energy gained through free-fall. The DPA data considered here are from tests using a
1:20 reduced scale model anchor based on an idealised design proposed by Lieng et al.
(1999). The model DPA (see
Figure 5.2), was fabricated from mild steel and had an overall length of 750 mm, a shaft
diameter of 60 mm and a mass of 20.7 kg. The anchor had an ellipsoidal tip and
featured four clipped delta type flukes (separated by 90º in plan) with a forward swept
trailing edge. The anchor shaft was solid with the exception of a watertight cylindrical
void towards the top to house the IMU.
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Figure 5.2. Deep penetrating anchor
5.3.2 Dynamically embedded plate Anchor
The dynamically embedded plate anchor (DEPLA, O’Loughlin et al. 2013a) is an
anchoring system that combines the capacity advantages of vertically loaded anchors
with the installation advantages of dynamically installed anchors. The DEPLA
comprises a removable central shaft or ‘follower’ and a set of four flukes (see Figure
5.3). A stop cap at the upper end of the follower prevents it from falling through the
DEPLA sleeve and a shear pin connects the flukes to the follower. The DEPLA is
installed in a similar manner as the DPA, but after coming to rest in the seabed the
follower retriever line is tensioned, which causes the shear pin to part (if not already
broken during impact) allowing the follower to be retrieved for the next installation
whilst leaving the anchor flukes vertically embedded in the seabed. These embedded
anchor flukes constitute the load bearing element as a plate anchor.
In the tests considered here the DEPLA was modelled at a reduced scale of 1:4.5 and
fabricated from mild steel. The follower (and hence DEPLA) length was 2 m, the
follower diameter was 160 mm, the fluke (plate) diameter was 800 mm and the overall
mass was 388.6 kg. As with the DPA, the DEPLA follower was solid with the exception
of a cylindrical void at the top to house the IMU. The model DEPLA is shown in Figure
5.3.
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Figure 5.3. Dynamically embedded plate anchor
5.3.3 Instrumented free-falling sphere
The instrumented free-falling sphere (IFFS) has been proposed as an in situ
characterisation tool for soft soils (Morton and O’Loughlin 2012, O’Loughlin et al.
2014a). The IFFS is a steel sphere that dynamically embeds in soft soil in a manner
similar to dynamically installed anchors. IMU data measured during embedment in soil
can be used to estimate undrained shear strength. As such, the IFFS is conceptually
similar to a free fall cone penetrometer, but the simple spherical geometry of the IFFS is
beneficial as the projected area does not change with rotation and the bearing factor for
the ball is more tightly constrained than for the cone. The IFFS data considered here are
from tests using a 250 mm diameter mild steel sphere with a mass of 50.8 kg. The IFFS
was fabricated as two hemispheres (that could be bolted together) with an internal
vertically orientated cylindrical void to accommodate the IMU (see Figure 5.4)
Figure 5.4. Instrumented free-falling sphere
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5.3.4 Inertial measurement unit
The IMU was used to measure projectile accelerations and rotation rates during free-fall
in the water column and embedment in the soil. The IMU (see Figure 5.5) includes a 16
bit three component MEMS rate gyroscope (ITG 3200) and a 13 bit three-axis MEMS
accelerometer (ADXL 345). The gyroscope had a resolution of 0.07 °/s with a
measurement range of +/- 2000 °/s. The accelerometer had a resolution of 0.04 m/s2
with a measurement range of +/- 16 g. Data were logged by an mbed micro controller
with an ARM processor to a 2 GB SD card at 400 Hz. Internal batteries were capable of
powering the logger for up to 4 hours. The IMU was contained in a watertight
aluminium tube 185 mm long and 42 mm in diameter and was located in a void (with
the same dimensions) within the projectile. The IMU had a mass of approximately 0.5
kg (including the batteries).
The accelerometer and gyroscope are aligned with the body frame of the projectile and
the IMU as shown in Figure 5.6 (for the DEPLA). The body frame is a reference frame
with three orthogonal axes x , y and z that are common to both the IMU and the
b b b
projectile and where the z -axis is parallel to the direction of earth’s gravity when the
b
projectile is hanging vertically. The accelerometer measures accelerations A , A and
bx by
A in the body frame along these three axes. These accelerometer measurements
bz
include a component of gravitational acceleration (depending on the orientation of the
accelerometer) and linear acceleration. The gyroscope measures angular velocities ω ,
bx
ω and ω in the body frame about the same orthogonal axes. Accelerometers are often
by bz
used to measure the rotation of quasi-static objects but cannot distinguish rotation from
linear acceleration if an object is in motion. However gyroscopes are unaffected by
linear acceleration and the rotation of objects in motion can be derived from their
measurements.
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5.4 Interpretation of IMU measurements
As the body frame is not fixed in space, it is necessary to define an inertial frame,
defined here and used in this chapter, as a local fixed reference frame, with the z-axis
aligned in the direction of the Earth’s gravitational vector, and with undefined
orthogonal x- and y-axes, that are fixed at their orientation at the start of each test. If the
projectile pitches and/or rolls whilst in motion, the body frame will move out of
alignment with the inertial frame of reference and the rotation rates ω , ω and ω and
bx by bz
accelerations A , A and A measured by the IMU will not be coincident with the
bx by bz
inertial frame (see Figure 5.7). As a consequence gravitational acceleration, g, and
linear acceleration, a, (required for velocity and translation calculations as described
later), components cannot be distinguished from the accelerometer measurements.
Hence the IMU measurements were ‘transformed’ from the body frame to the inertial
frame. This was accomplished using transformation matrices as described in the
following sections.
x
b
y
x
y
b
μ
z
b
z
Figure 5.7. Body and inertial frames of reference
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5.4.1 Rotations
The body frame rotation rates ω , ω , and ω were transformed from the body frame
bx by bz
to the inertial frame to correspond with rotation rates about the inertial frame ω , ω and
x y
ω using an angular velocity transformation matrix (AVTM),Ti(Fossen 2011):
z b
x bx
Ti Equation 5.1
y b by
z bz
1 sin tan cos tan
b b b b
Ti 0 cos sin Equation 5.2
b b b
0 sin /cos cos /cos
b b b b
where ϕ and θ are the current rotation angles about the body frame axes x and y
b b b b
respectively established from numerical integration of ω and ω :
bx by
t
(t) (t)dt Equation 5.3
b b0 bx
0
t
(t) (t)dt Equation 5.4
b b0 by
0
Similarly, the rotation angle ψ about the body frame axis z was established by
b b
numerical integration of ω :
bx
t
(t) (t)dt Equation 5.5
b b0 bz
0
Numerical integration of the angular velocities ω , ω and ω derived from the AVTM
x y z
allowed the roll, ϕ, pitch, θ and yaw, ψ, rotations about the inertial frame axes z, y and z
respectively (Euler angles) to be established:
t
(t) (t)dt Equation 5.6
0 x
0
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t
(t) (t)dt Equation 5.7
0 y
0
t
(t) (t)dt Equation 5.8
0 z
0
5.4.2 Accelerations
The accelerometer measurements A , A and A were converted to accelerations
bx by bz
coincident with the inertial frame A , A and A using a direction cosine matrix (DCM),
x y z
Ri
(Nebot and Durrant-Whyte 1999, Jonkman 2007, King et al. 2008, Fossen 2011):
b
A A
x bx
A Ri A Equation 5.9
y b by
A A
z bz
Ri R ()R ()R () Equation 5.10
b z y x
The DCM relates the accelerations measured in the body frame to the inertial frame by
considering three successive rotations of yaw -ψ, pitch -θ, and roll, -ϕ, about the inertial
frame axes z, y and x respectively. These rotations are represented by the yaw R (-ψ),
z
pitch R (-θ) and roll R (-ϕ), matrices that are used to rotate the measured acceleration
y x
vectors A , A and A in Euclidean vector space:
bx by bz
cos sin 0
R sin cos 0 Equation 5.11
z
0 0 1
cos 0 sin
R 0 1 0 Equation 5.12
y
sin 0 cos
1 0 0
R 0 cos sin Equation 5.13
x
0 sin cos
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Multiplication of the R (-ψ), R (-θ) and R (-ϕ) rotation matrices gives the DCM:
z y x
cos cos cos sin cos sin sin sin sin cos cos sin
i
R cos sin cos cos sin sin sin cos sin cos sin sin
b
sin cos sin cos cos
Equation 5.14
The linear accelerations coincident with the inertial frame a , a and a were derived
x y z
from the transformed accelerometer measurements A , A and A (A is a negative
x y z z
output, i.e. when the projectile is at rest, a = A + g = 0) using the following expression:
z z
(Stovall 1997, Noureldin et al. 2012):
a Ax 0
x
a Ay0 Equation 5.15
y
a Az g
z
The resultant linear acceleration, a (acceleration in the direction of motion), was
calculated as:
a A2 A2 A2 g Equation 5.16
x y z
5.4.3 Velocities and distances
The linear accelerations corresponding to the inertial frame a , a and a were
x y z
numerically integrated to establish the projectile velocities coincident with the inertial
frame v , v and v during free-fall in the water column and embedment in the soil:
x y z
t
v (t)v a (t)dt Equation 5.17
x x0 x
0
t
v (t)v 0a (t)dt Equation 5.18
y y y
0
t
v (t)v a (t)dt Equation 5.19
z z0 z
0
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The resultant projectile velocity, v, was calculated using the following expression:
v v2 v2 v2 Equation 5.20
x y z
The resultant projectile velocity, v, was numerically integrated to establish the distance
travelled by the projectile along its trajectory, s:
t
s(t)s v(t)dt Equation 5.21
0
0
The distance travelled by the projectile along the inertial z axis s (required to calculate
z
the vertical embedment depth of the projectile relative to the soil surface, z ), was
e
established by numerically integrating the vertical velocity, v :
z
t
s (t)s v (t)dt Equation 5.22
z z0 z
0
5.4.4 Tilt angles
Following dynamic penetration the projectile is at rest in the soil and has no linear
acceleration. Under these conditions the accelerometer measurements can be used to
derive the final pitch, ϕ , roll, θ , (coincident with the inertial frame) and resultant
acc acc
tilt, μ, (tilt relative to Earth’s gravitational vector, see Figure 5.7) angles using the
following expressions:
A
sin1 by (King et al. 2008) Equation 5.23
acc g
A
sin1 bx(King et al. 2008) Equation 5.24
acc g
A
cos1 bz(Stephan et al. 2012) Equation 5.25
g
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5.5 Test sites and soil properties
The IMU performance has been examined using projectile data from two sites. The
DEPLA data considered here relate to tests conducted in the Firth of Clyde which is
located off the West coast of Scotland between the mainland and the Isle of Cumbrae.
The DPA and IFFS data are from tests conducted in Lower Lough Erne, which is an
inland lake located in County Fermanagh, Northern Ireland. At Lough Erne the water
depths at the test locations varied between 3 and 20 m whereas at the Firth of Clyde test
locations the water depth was typically 50 m. Both test locations are shown in Figure
5.8.
The seabed at the DEPLA test locations in the Firth of Clyde is very soft with moisture
contents in the range 50 to 100% (close to the liquid limit). Consistency limits plot
above or on the A-line on the Casagrande plasticity chart, indicating aclay of
intermediate to high plasticity. The unit weight increases from about γ = 14 kN/m3 at
the mudline to about γ = 18 kN/m3 at about 3.5 m (limit of the sampling depth). Figure
5.9a shows profiles of undrained shear strength, s , with depth derived from piezocone
u
and piezoball tests, and calibrated using lab shear vane data and fall cone tests, to give
piezocone bearing factors N = 17.8 (5 cm2 cone) and N = 16.9 (10 cm2 cone), and
kt kt
piezoball bearing factors N = 11.5 (50 cm2 ball) and N = 12.2 (100 cm2 ball). The
ball ball
s profile is best idealised as s (kPa) = 2 + 2.8z over the upper z = 5 m of the
u u
penetration profile, which is the depth of interest for the DEPLA tests. The sensitivity
ratio of the remoulded to intact soil restance is in the range 0.19 to 0.33 as assessed
from piezoball cyclic remoulding tests. This range is similar, but not identical to the
range of soil sensitivity, as the bearing factor for remoulded soil is greater than for intact
soil (Yafrate et al. 2009, Zhou and Randolph 2009).
The Lough Erne lakebed is very soft clay with moisture contents in the range 270 to
520%, typically about 1.5 times the liquid limit. The measured unit weight of the Lough
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Erne clay is only marginally higher than water at γ = 10.8 kN/m3. This is considered to
be due to the very high proportion of diatoms that are evident from scanning electron
microscopic images of the soil (e.g. see Colreavy et al. 2012) and which have an
enormous capacity to hold water in the intraskeletal pore space (Tanaka and Locat
1999). Colreavy et al. (2012) report data from piezoball penetration tests (using a 100
cm2 ball) at the Lough Erne site to depths of up to 8 m. Figure 5.9b shows s profiles
u
with depth, obtained from the net penetration resistance using N = 8.6, calibrated
ball
using in situ shear vane data. The undrained shear strength profile is best idealised over
the depth of interest (0 to 2.2 m) as s (kPa) = 1.5z. Piezoball cyclic remoulding tests
u
show that the ratio of remoulded to intact soil resistance is in the narrow range 0.4 to
0.5, indicating a low sensitivity soil.
Firth of Clyde
Lough Erne
Figure 5.8. Test site locations
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Figure 5.13. Image capture from ROV camera showing the follower retrieval line
at the seabed
5.7 Results and discussion
The IMU data were interpreted within the framework described above, which can be
readily implemented in a spreadsheet application such as Microsoft Excel or
alternatively using numerical analysis software such as MATLAB.
5.7.1 Rotations
Rate gyroscopes are subject to an error known as bias drift where the zero rate output
drifts over time (Sharma 2007). However, the duration of a projectile drop never
exceeded 6.5 s, which is too short for any measurable bias drift to accumulate. This was
confirmed by comparing the zero rate outputs before the drop when the anchor was
hanging in the water with the zero rate outputs after the drop when the anchor was at
rest in the soil. No change was observed for any test.
Figure 5.14 shows typical rotation profiles during free-fall in water and embedment in
the lakebed for each of the three projectiles, released from drop heights of 17.69 m
(DEPLA), 5.95 m (IFFS), and 3 m (DPA). In Figure 5.14 ϕ and θ are rotations
acc acc
relative to the inertial frame deduced from the horizontally orientated y- and x-axes
accelerometers using Equation 5.23 and Equation 5.24, ϕ , θ and ψ are rotations about
b b b
the body frame axes x , y and z established using Equation 5.3, Equation 5.4 and
b b b
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Equation 5.5, and ϕ, θ and ψ are the pitch, roll and yaw rotations about the inertial frame
axes x, y and z derived using Equation 5.6, Equation 5.7 and Equation 5.8.
In Figure 5.14a, prior to release (time, t = 0 to 1.1 s) the DEPLA was swaying in the
water, suspended from the installation line, during which time rotations derived from
the accelerometer measurements (ϕ and θ ) and from the gyroscope measurements
acc acc
(ϕ and θ ) were in broad agreement. During free-fall (t = 1.1 s to 3.59 s) rotations can
b b
only be interpreted from the gyroscope measurements as the accelerometer
measurements include both acceleration and rotation components. The gyroscope
measurements indicate that rotations reached ϕ = 17.3 and θ = -8.3° when the anchor
b b
came to rest in the lakebed at t = 4.2 s. There is a discrepancy of Δϕ = 1.7 and Δθ =
3.1° between the accelerometer and gyroscope measurements whilst the anchor is at
rest. However, when the anchor was at rest in the soil the ‘transformed’ rotations
derived from the gyroscope measurements (ϕ and θ) were in good agreement with
rotations derived from the accelerometer measurements, as both were coincident with
the inertial frame of reference.
Figure 5.14b shows that the IFFS rotated about all three axes during free-fall in water
and penetration in soil. Indeed, the non-zero ψ and ψ response started whilst the IFFS
b
was hanging in water, indicating that the IFFS started to spin before it was released.
After the IFFS came to rest in the soil there is a discrepancy of Δϕ = 4.1 and Δθ = 2.8
between the final accelerometer and gyroscope measurements. As with the DEPLA test,
the transformed rotations derived from the gyroscope measurements were in good
agreement with rotations derived from the accelerometer measurements. This highlights
the importance of using the AVTM to transform the angular velocities measured by the
gyroscope from the body frame to the inertial frame to establish rotations that relate to
the inertial frame.
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5.7.2 Accelerations
Figure 5.15 shows acceleration profiles for the same tests as shown in Figure 5.14. In
Figure 5.15 A , A and A are the accelerometer measurements and A , A and A are
bx by bz x y z
the transformed accelerometer measurements that are coincident with the inertial frame
(i.e. A is the acceleration measurement in the direction of gravity). In Figure 5.15a the
iz
DEPLA was initially hanging in the water experiencing only gravitational acceleration
with A = 0 (a = 0), A = 0 (a = 0) and A = -9.81 m/s2 (i.e. a = 0, refer to Equation
x x y y z z
5.15). Following release at t = 1.1 s the anchor began to free-fall in water with an abrupt
change in A to -0.81 m/s2 (a = 9 m/s2). From t = 1.1 to 3.59 s the anchor was in free-
z z
fall through water and A (and hence a ) steadily reduced as the fluid drag resistance
z z
increased with increasing anchor velocity. Impact with the mudline occurred at t = 3.59
s and is characterised by a rapid deceleration to a maximum value of approximately A
z
= -41.6 m/s2 (a = -3.2g = -31.8 m/s2). The anchor came to rest at t = 4.2 s before
z
rebounding slightly. This rebound has been reported in other studies involving free-fall
objects (e.g. Dayal and Allen 1973, Chow and Airey 2010, Morton and O’Loughlin
2012, O’Loughlin et al. 2014a), and is attributed to elastic rebound of the soil. The
importance of transforming the measured accelerations to the inertial frame using the
DCM is evident from the soil penetration phase where the magnitude of the peak
inertial frame deceleration, A , is 3.7% lower than the peak body frame deceleration,
z
A . Furthermore, when the anchor was at rest the inertial frame accelerations A and
bz x
A , sensibly returned to zero and A = -9.81 m/s2 (a = 0) in the absence of linear
y z iz
acceleration, whereas the body frame accelerations, A and A are non-zero, and A ≠
bx by bz
-9.81 m/s2 due to anchor rotations causing misalignment between the body and inertial
frames.
The acceleration response of the IFFS (Figure 5.15b) is broadly similar to that of the
DEPLA, with the expected change in acceleration upon release and the subsequent
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5.7.3 Velocity profiles
Figure 5.16 shows velocity profiles for free-fall in water and embedment into soil for
the three tests considered previously and shown in Figure 5.14 and Figure 5.15. The
velocity, v , and distance, s (i.e. depth), relative to the inertial frame were established
z z
using Equation 5.19 and Equation 5.22. The velocity, v , and distance, s , were also
bz bz
derived from Equation 5.19 and Equation 5.22, albeit with, a = A + g, instead of a
bz bz z
and A . v and s represent the values that would otherwise be used if the IMU
z bz bz
measurements were not corrected using the AVTM and DCM. The importance of
implementing the transformation matrices is demonstrated in Figure 5.16a where the
final embedment depth and impact velocity of the DEPLA are over estimated by 12%
and 7% respectively. This would correspond to an over prediction of the local undrained
shear strength (and hence capacity) at the mid-height of the DEPLA plate (following
installation but prior to keying) of 17% based on the final tip embedment of z = 3.31 m
e
and the idealised strength profile, s (kPa) = 2 +2.8z . Figure 5.16b indicates that the
u z
embedment depth and impact velocity of the IFFS are over predicted by 27% and 10%
respectively. The over prediction for the IFFS is higher than for the DEPLA as the IFFS
rotations are higher (i.e. greater misalignment between the body- and inertial frames).
Figure 5.16a and Figure 5.16b also show that the velocity, v , established from the
bz
integration of the body frame ‘linear’ acceleration, a , does not return to zero despite
bz
motion having ceased. This is because the body frame acceleration measurement, A ,
bz
(from which a is derived) is not coincident with the inertial frame and does not return
bz
to zero following installation (i.e. A > -9.81 m/s2). The DPA body frame and inertial
bz
frame velocity profiles (Figure Figure 5.16c) are in excellent agreement as the rotations
are relatively low and the misalignment between the body frame and inertial frame is
negligible. Also shown on Figure 5.16 are direct measurements of the final embedment
depths based on mudline observations of markings on the retrieval line using a ROV in
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Firth of Clyde and an underwater drop camera in Lough Erne. Final embedment depths
derived from the IMU data are within 3.3% of the direct measurements, with differences
of Δz = 0.09 m (DEPLA), 0.06 m (IFFS) and 0.035 m (DPA). However, the direct
e
measurements are simply to confirm the lack of any gross error in the analysis, and have
a much lower accuracy than is possible from the IMU data. A more rigorous verification
of the IMU derived measurements was undertaken for a number of tests as described in
the following section.
5.7.4 Verification of the IMU derived measurements
Independent verification of the IMU-derived measurements of the projectile
displacement (Equation 5.22) was obtained by comparison with those obtained from a
draw wire sensor (also known as a string potentiometer) with a 10 m measurement
range. The draw wire sensor was connected between a fixed point on the deployment
platform and the free falling projectile (i.e. in parallel with the deployment and retrieval
line), and the data acquired using an independent 24-bit data acquisition system. Five
tests were undertaken using the IFFS projectile released from 0 to 4.8 m above the
lakebed.
Comparisons of displacements derived from the IMU measurements and the draw wire
sensor data are provided in Figure 5.17. The IMU-derived displacements are shown
both using the body reference frame and the inertial reference frame. This shows that
the inertial frame-derived displacements correctly remain constant when the projectile
comes to rest in the soil. In contrast, the body frame-derived displacements continue to
increase as the resultant linear acceleration, a, has not returned to zero due to the
rotation of the body (see also Figure 5.16). Importantly, excellent agreement is apparent
between the inertial frame displacements and those measured by the draw wire sensor
(within 1% of the measurement range), providing verification of the analysis approach
outlined here.
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Figure 5.17. Comparison of IMU derived displacement measurements with those
obtained using a draw wire sensor
5.7.5 Example application of projectile IMU data
For the projectiles considered in the previous section, understanding the soil-structure
interaction at such high strain rates is crucial for predictive tools that calculate the final
embedment depth of the anchors (DEPLA and DPA, e.g. O’Loughlin et al. 2013b) or
estimate the undrained shear strength based on the interpreted inertial frame
accelerations (IFFS, e.g. O’Loughlin et al. 2014a, IFFS, Morton et al. 2015). This is
because those strain rates are up to seven orders of magnitude higher than used for
strength determination in a standard laboratory element test. It follows that motion data
such as those presented in Figure 5.14 and Figure 5.15 play an important role in the
validation and calibration of such predictive models. An example comparison is
provided in Figure 5.18. for the DEPLA, where the predictions are based on an
analytical model described in brief here, but in more detail by O’Loughlin et al.
(2013b). The model formulates conventional end bearing and frictional resistance acting
on the anchor during penetration in a manner similar to suction caisson or pile
installation, but scales these resistances to account for the well-known dependence of
undrained shear strength on strain rate (Casagrande and Wilson 1951, Graham et al.
1983, Sheahan et al. 1996), whilst also accounting for fluid drag resistance and the
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buoyant weight of the displaced soil. Consideration of these resistance components
leads to the following governing equation:
d2s
m W F R (F F )F Equation 5.26
dt2 s b f frict bear d
where m is the anchor mass, s is the distance travelled by the projectile, t is time, W is
s
the submerged weight of the anchor in water, F is frictional resistance, F is bearing
frict bear
resistance, F is the buoyant weight of the displaced soil and F is fluid drag resistance,
b d
formulated as:
1
F C A v2 Equation 5.27
2 d s f
where ρ is the submerged density of the soil, C is the fluid drag coefficient, A is
s d f
anchor frontal area and v is the instantaneous resultant anchor velocity. The inclusion of
fluid drag, F , is essential in situations where (non-Newtonian) very soft fluidised soil is
d
encountered at the surface of the seabed, and has been shown to be important for
assessing loading from a submarine slide runout on a pipeline (Boukpeti et al. 2012,
Randolph and White 2012, Sahdi et al. 2014). O’Loughlin et al. (2013b) and Blake and
O’Loughlin (2015) further showed that inertial drag is the dominant resistance acting on
a dynamically installed anchor in normally consolidated clay during initial embedment
and typically to about 30% of the penetration.
Frictional and bearing resistances are formulated as:
F s A Equation 5.28
frict u s
F N s A Equation 5.29
bear c u f
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where α is an interface friction ratio (of limiting shear stress to undrained shear
strength), A is anchor shaft area, N is the bearing capacity factor for the projectile tip
s c
or fluke, and s is the undrained shear strength averaged over the contact area, A or A .
u f s
The reference undrained shear strength adopted in Equation 5.28 and Equation 5.29 is
the idealised profile shown in Figure 5.9a, which is enhanced using a power law strain
rate function (Biscontin and Pestena 2001, Peuchan and Mayne 2007, Randolph et al.
2007, O’Loughlin et al. 2013b) expressed as:
v d
R n Equation 5.30
f v d
ref ref
where β is the strain rate parameter, v/d is an approximation of the operational shear
strain rate, and the subscript ‘ref’ denotes the reference shear strain rate (v/D = 0.18 s-
ball
1) associated with the measurement of the undrained shear strength. The factor n in
Equation 5.30 accounts for the greater rate effects reported for shaft resistance
compared to tip resistance (Dayal et al. 1975, Chow et al. 2014, Steiner et al. 2014) and
is taken as n = 1 for tip resistance (Zhu and Randolph 2011) and as a function of β
(adopted from Equation 8b in Einav and Randolph 2006) for estimating rate effects in
shaft resistance according to:
n
n2 l n 2 Equation 5.31
β l
where n is for axial loading.
l
The predictions Figure 5.18 on were obtained using bearing capacity factors of N = 7.5
c
for the leading and trailing edges of the flukes (analogous to a deeply embedded strip
footing) and N = 12 for the follower tip, but not for the padeye as the hole formed by
c
the passage of the anchor was assumed to remain open. This is appropriate since ROV
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video capture of the drop sites (see Figure 5.13) showed an open crater and the
dimensionless strength ratio at the trailing end of the embedded DEPLA follower, s /γ'd
u
= 6.9 (where d is the diameter of the DEPLA sleeve and γ' is the effective unit weight of
the soil), which is sufficient to maintain an open cavity above the follower (Morton et
al. 2014). Values for the drag coefficient, C , were determined from the free-fall in
d
water phase of the tests, which gave an average C = 0.7 (Blake and O’Loughlin 2015).
d
The strain rate parameter was taken as β = 0.08, which is typical of that measured in
variable rate penetrometer testing (Low et al. 2008, Lehane et al. 2009) and
approximates to an 18% change per log cycle change in strain rate, typical of that
measured in laboratory testing (e.g. Vade and Campenella 1977, Graham et al. 1983,
Lefebvre and Leboeuf 1987). The interface friction ratio, α, was varied to obtain the
best match between the measured and predicted velocity profiles. The comparison
between these on Figure 5.18 indicates that the inclusion of a fluid-mechanics drag
resistance term is appropriate for projectiles penetrating soft clay at high velocities.
There is excellent agreement between the measured and predicted velocity profiles
using α = 0.27, which is within the range deduced from the cyclic piezoball remoulding
tests (0.19 to 0.33). In contrast, the best agreement that could be obtained without the
inclusion of inertial drag resistance required α = 0.38, which is inconsistent with results
from the cyclic piezoball remoulding tests and gave a much poorer match.
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Resultant velocity, v (m/s)
0 1 2 3 4 5 6 7 8 9 10 11 12
0.0
0.5
1.0
)
m 1.5
(
s
,e
2.0
c
n
a
t
s i 2.5
D
3.0
IMU data
3.5 C = 0.7, = 0.27
d
C = 0, = 0.38
d
4.0
Figure 5.18. DEPLA velocity profile derived from the IMU data measured at the
Firth of Clyde test site and corresponding theoretical profile
5.8 Conclusions
This chapter describes a fully self-contained low cost MEMS-based IMU consisting of a
tri-axis accelerometer and a three-component gyroscope, and considered sample data
captured by the IMU during field tests on dynamically installed projectiles. Such data
are important for understanding the soil-structure interactions that occur at the elevated
shear strain rates associated with dynamic penetration events. To the authors’
knowledge these data are the first reported use of a 6DoF IMU for a geotechnical
application.
A comprehensive framework for interpreting the IMU measurements so that they are
coincident with a fixed inertial frame of reference was described and implemented to
establish projectile rotations, accelerations and velocities during free-fall in water and
embedment in soil. It is often the final embedment depth of a dynamically embedded
projectile that is of interest. The chapter showed that embedments calculated from the
body frame acceleration measurements, rather than from accelerations transformed to an
inertial frame of reference, led to derived embedment depths that were in error by up to
27%. In contrast, embedment depths derived from IMU data interpreted from within an
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CHAPTER 6 INSTALLATION OF DYNAMICALLY
EMBEDDED PLATE ANCHORS AS
ASSESSED THROUGH FIELD TESTS
6.1 Abstract
A dynamically embedded plate anchor (DEPLA) is a rocket shaped anchor that
comprises a removable central shaft and a set of four flukes. The DEPLA penetrates to a
target depth in the seabed by the kinetic energy obtained through free-fall in water.
After embedment the central shaft is retrieved leaving the anchor flukes vertically
embedded in the seabed. The flukes constitute the load bearing element as a plate
anchor.
This chapter focuses on the dynamic installation of the DEPLA. Net resistance and
velocity profiles are derived from acceleration data measured by an inertial
measurement unit during DEPLA field tests, which are compared with corresponding
theoretical profiles based on strain-rate enhanced shear resistance and fluid mechanics
drag resistance. Comparison of the measured net resistance force profiles with the
model predictions shows fair agreement at 1:12 scale and good agreement at 1:7.2 and
1:4.5 scales. For all scales the embedment model predicts the final anchor embedment
depth to a high degree of accuracy.
6.2 Introduction
A new hybrid anchoring system referred to as the Dynamically Embedded PLate
Anchor (DEPLA), combines the capacity advantages of vertically loaded anchors
(Murff et al. 2005, Gaudin et al. 2006, Wong et al. 2012) with the installation
advantages of dynamically installed anchors (Medeiros et al. 2001, Zimmerman et al.
2009, Lieng et al. 2010). The DEPLA comprises a removable central shaft or ‘follower’
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that may be fully or partially solid and a set of four flukes (see Figure 1.17). A stop cap
at the upper end of the follower prevents the follower from falling through the DEPLA
sleeve and a shear pin connects the flukes to the follower. After release from a
designated height above the seabed (typically <100 metres), The DEPLA penetrates to a
target depth in the seabed by the kinetic energy obtained through free-fall and the self-
weight of the anchor. After embedment the follower line is tensioned, which causes the
shear pin to part (if not already broken during impact) allowing the follower to be
retrieved for the next installation, whilst leaving the anchor flukes vertically embedded
in the seabed. These embedded anchor flukes constitute the load bearing element as a
plate anchor. A mooring line attached to the embedded flukes is then tensioned, causing
the flukes to rotate or ‘key’ to an orientation that is perpendicular to the direction of
loading, ensuring that maximum anchor capacity is achieved through bearing resistance.
The installation and keying process are summarised in Figure 1.18 and Figure 1.19
respectively.
The holding capacity of a plate anchor such as the DEPLA is relatively straightforward
to determine for a given shear strength profile and a known embedment depth (Cassidy
et al. 2012). However predicting the final plate anchor embedment is challenging as it
firstly requires an assessment of the final DEPLA penetration depth after free-fall in
water, and secondly requires an assessment of the extent of embedment loss of the plate
anchor keying. The loss in embedment during keying has been investigated
experimentally for suction embedded plate anchors (e.g. O’Loughlin et al. 2006, Gaudin
et al. 2006, Gaudin et al. 2009, Wang et al. 2011, Cassidy et al. 2012, Yang et al. 2012),
the results of which are relevant to the DEPLA. Predicting the final embedment of the
DEPLA after free-fall is complicated by the very high penetration velocities, as this
significantly enhances the available shear resistance and for very soft normally
consolidated clay, introduces fluid drag resistance and inertia effects. As the velocity of
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dynamically installed anchors when they impact the seabed is typically between 10 and
30 m/s (Lieng et al. 2010), for a typical anchor with a shaft diameter of about 1 m, the
strain rates in the soil during installation are three orders of magnitude higher than that
in vane test (0.029 s-1, Einav and Randolph 2006) and seven orders of magnitude higher
than the standard laboratory testing rate of 1%/hour (2.8 × 10-6 s-1). O’Loughlin et al.
(2013b) showed that, for anchor geometries similar to the DEPLA in normally
consolidated clay, fluid drag resistance dominates for embedment depths up to 0.84
times the anchor length. The importance of combining fluid mechanics drag resistance
with soil mechanics strain rate enhanced shear resistance has also been demonstrated for
other applications involving high displacement velocities (e.g. Zhu and Randolph 2011,
Randolph and White 2012, Randolph 2013, Sahdi et al. 2014). Failure to account for
strain rate enhanced shear resistance and fluid mechanics drag resistance during
dynamic embedment of anchors in clay has been shown to give prediction errors of the
order of 40% (O’Loughlin et al. 2004a).
A series of field tests were designed to provide a basis for understanding the behaviour
of the DEPLA during (i) free-fall and dynamic embedment in soil, and (ii) quantifying
the loss in embedment during keying and the subsequent plate anchor capacity. This
chapter considers the installation aspects of the field tests, whereas keying and anchor
capacity aspects of the field tests are considered in Chapter 7.
6.3 Experimental program
6.3.1 Instrumented model anchors
The DEPLA was modelled at reduced scales of 1:12, 1:7.2 and 1:4.5, and fabricated
from mild steel. The reduced scale infers a full scale anchor (or follower) length of 9 m,
which for a typical offshore seabed strength profile of 1.5 kPa/m would result in a plate
anchor capacity of the order of about 500 tonnes, suitable for temporary drilling
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Table 6.1. DEPLA anchors
1:12 scale 1:7.2 scale 1:4.5 scale
Follower length, L (mm) 750 1250 2000
f
Tip length, L (mm) 50 83.3 133.3
tip
Follower diameter, D (mm) 60 100 160
f
Sleeve diameter, D (mm) 71 115 184
s
Sleeve height, H (mm) 290 487 779
s
Plate diameter, D (mm) 300 500 800
Fluke thickness, t (mm) 4.5 6.25 10
Padeye eccentricity, e (mm) 125 212.5 348
Eccentricity ratio, e/D (-) 0.42 0.43 0.44
Follower mass (kg) 14.8 73.7 297
Plate (flukes) mass (kg) 5.5 22.3 91.6
Total mass (kg) 20.3 96 388.6
6.3.2 Inertial Measurement Unit
An inertial measurement unit (IMU) housed within a void at the top of the DEPLA
follower was used to measure anchor acceleration and rotation rates during free-fall in
the water column and embedment in the soil. The IMU (see Figure 5.5) included two
micro-electro mechanical systems (MEMS) sensors; a 13 bit three-axis accelerometer
(ADXL 345) and a 16 bit three component rate gyroscope sensor (ITG 3200). The
accelerometer had a resolution of 0.04 m/s 2 with a measurement range of +/-16 g. The
rate gyroscope sensor had a resolution of 0.07 °/s with a measurement range of +/-
2000°/s. Data was logged by an mbed micro controller with an ARM processor to a 2
GB SD card at 400 Hz. Internal batteries were capable of powering the logger for up to
4 hours. The IMU was contained in a watertight aluminium tube 185 mm long and 42
mm in diameter and located in a void (with the same dimensions) at the top of the
follower. The accelerometer and rate gyroscope are aligned with the body-frame of the
DEPLA and the IMU as shown in Figure 5.6. The body frame is a reference frame with
three orthogonal axes x , y and z that are common to both the IMU and the DEPLA
b b b
and where the z -axis is parallel to the direction of earth’s gravity when the DEPLA is
b
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hanging vertically. The rate gyroscope measures angular velocities ω , ω and ω in
bx by bz
the body-frame about three orthogonal axes x , y and z . The accelerometer measures
b b b
accelerations A , A and A in the body-frame along the same orthogonal axes. These
bx by bz
accelerometer measurements include a component of gravitational acceleration
(depending on the orientation of the accelerometer) and linear acceleration.
Accelerometers are often used to measure the rotation of quasi-static objects but cannot
distinguish rotation from linear acceleration if an object is in motion. However
gyroscopes are unaffected by linear acceleration and the rotation of objects in motion
can be derived from their measurements. If the DEPLA pitches and/or rolls whilst in
motion the measured angular velocities and accelerations will correspond to a reference
frame that is not fixed in space. As a consequence the gravitational and linear
acceleration components cannot be distinguished from the accelerometer measurements.
Hence it is important to define an inertial frame of reference, and to transform the body
frame acceleration measurements A , A and A to accelerations that are coincident
bx by bz
with this inertial frame A , A and A using rotation matrices as described in detail by
x y z
Blake et al. (2016). The inertial frame used here is a local fixed reference frame, with
the z-axis aligned in the direction of the Earth’s gravitational vector, and with undefined
orthogonal x- and y-axes, that are fixed at their orientation at the start of each test. The
linear accelerations a , a and a coincident with the inertial frame, which are required to
x y z
calculate velocity and displacement components (including the vertical embedment
depth of the anchor relative to the soil surface, z , and the distance travelled by the
e
anchor along its direction of motion), can then be calculated using the following
expression:
a A 0
x x
a A 0 Equation 6.1
y y
a A g
z z
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where g is gravitational acceleration and A is an negative output (i.e. when the anchor
z
is at rest a = A + g = 0).
z z
6.3.3 Test site and soil properties
The tests reported here were conducted in Lower Lough Erne, a glacial lake in Co.
Fermanagh, Northern Ireland in water depths between 3 and 12 m. The lakebed is very
soft clay with moisture contents in the range 270 to 520%, typically about 1.5 times the
liquid limit. The measured unit weight of the Lough Erne clay is only marginally higher
than water at γ = 10.8 kN/m3. This is considered to be due to the very high proportion of
diatoms that are evident from scanning electron microscopic images of the soil (e.g. see
Colreavy et al. 2012) and which have an enormous capacity to hold water in the
intraskeletal pore space (Tanaka and Locat 1999). However the water that rests within
this pore space is not considered to play a role in soil behaviour, and as such the
measured unit weight and other index properties that are expressed in terms of the
measured moisture content are not considered to be useful indicators of soil behaviour.
Colreavy et al. (2012) report results from piezoball and in situ shear vane tests
conducted at the test site to depths of up to 11 m. Figure 6.2 shows profiles of undrained
shear strength, s , with depth where s is derived from the net penetration resistance
u u
using N = 8.6 (calibrated using in situ shear vane data). As will be shown later, the
ball
1:12 scale anchor achieved maximum tip embedment depths of 1.76 m. Over this depth
s is best idealised as s = 1.5z (kPa), where z is depth, and this profile was adopted in
u u
the analysis of the test data using this anchor. The 1:7.2 and the 1:4.5 scale anchors
achieved maximum tip embedment depths of 3.66 m and 6.94 m respectively. Over this
range of embedment s may be idealised as s = 0.45 + 0.9z (kPa) and this profile was
u u
adopted in the analysis of the test data using the 1:7.2 and the 1:4.5 scale anchors. The
sensitivity of the soil is in the narrow range S = 2 to 2.5 as assessed from in situ vane
t
tests and piezoball cyclic remoulding tests.
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6.4 Results and discussion
6.4.1 Accelerations
Figure 6.7 shows a typical acceleration during free-fall in water and embedment in the
lakebed for an installation using a 1:12 scale DEPLA released from a drop height of
6.86 m. In Figure 6.7 A is the accelerometer measurement and A is the transformed
bz z
accelerometer measurement that is coincident with the inertial frame (i.e. A is the
z
acceleration measurement in the direction of gravity). The DEPLA was initially hanging
in the water experiencing only gravitational acceleration with A = -9.81 m/s2 (i.e. a =
z z
0, refer to Equation 6.1). Following release at t = 1 s the anchor began to free-fall in
water with an abrupt change in A to -0.92 m/s2 (a = 8.9 m/s2). From t = 1 to 2.55 s the
z
anchor was in free-fall through water and A (and hence a ) steadily reduced as the fluid
z z
drag resistance increased with increasing anchor velocity. Impact with the lakebed
occurred at t = 2.55 s and is characterised by a rapid deceleration to a maximum value
of approximately A = -27.4 m/s2 (a = -1.8g = -17.6 m/s2). The anchor came to rest at t
z z
= 3.16 s before rebounding slightly. This rebound has been reported in other studies
involving free-fall objects (e.g. Dayal and Allen 1973, Chow and Airey 2010, Morton
and O’Loughlin 2012, O’Loughlin et al. 2014a), and is attributed to elastic rebound of
the soil. The importance of transforming the measured accelerations to the inertial frame
using the DCM described by Blake et al. (2016) is evident from the soil penetration
phase where the magnitude of the peak inertial frame deceleration A , is 2.8% lower
z
than the peak body frame deceleration A . Furthermore, when the anchor was at rest
bz
the inertial frame acceleration A = -9.81 m/s2 (a = 0) in the absence of linear
z z
acceleration, whereas the body frame acceleration A ≠ -9.81 m/s2 due to anchor
bz
rotations causing misalignment between the body and inertial frames.
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t
s(t)s v(t)dt Equation 6.6
0
0
The distance travelled by the projectile along the inertial z-axis,s (required to calculate
z
the embedment depth of the anchor relative to the soil surface, z ) was established by
e
numerically integrating the vertical velocity, v :
z
t
s (t)s v (t)dt Equation 6.7
z z0 z
0
The motion of the anchor during free-fall in water can be quantified by considering
Newton’s second law of motion and the forces acting on the anchor during free-fall
(Fernandes et al. 2006, Shelton et al. 2011, Hasanloo et al. 2012, Hossain et al. 2014):
d2s
(mm') W F F Equation 6.8
dt2 s d,a d,l
where m is the anchor mass, m' is the added mass, z is the distance travelled by the
anchor along its trajectory, t is time, W is the component of the submerged anchor
s
weight of the anchor acting in the direction of motion, F is the fluid drag resistance
d,a
acting on the anchor and F is the fluid drag resistance acting on the mooring and
d,l
follower recovery lines. The added mass, m', in Equation 6.8 is the mass of the fluid that
is accelerated with the anchor. However for slender bodies such as the DEPLA, m' is
negligible and can be taken as zero (Beard 1981, Shelton et al. 2011).
As an object moves through a viscous fluid it is subjected to fluid drag resistance which
is attributed to; (i) friction drag (commonly referred to viscous drag) generated by
viscous stresses that develop in the boundary layer between the object and fluid, and (ii)
pressure drag (independent of viscous effects) caused by an adverse pressure gradient
(related to the stagnation pressure, P = P + 1/2ρv2) between the front and rear
stagnation static
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of the object which creates a force opposite to the direction of motion (Hoerner 1965).
The fluid drag resistance terms are formulated as (Fernandes et al. 2006):
1
F C A v2 Equation 6.9
d,a 2 d,a w f
1
F C Av2 Equation 6.10
d,l 2 d,l w s
where C is the drag coefficient of the anchor, C is the drag coefficient of the
d,a d,l
mooring and follower recovery lines, ρ is the density of the water, A is the frontal area
w f
(of the follower, sleeve and flukes), A is the surface area of the mooring and follower
s
recovery lines in contact with water and v is the anchor (and hence line) velocity. In
cases where pressure drag (e.g. dynamically installed anchors such as the DEPLA), it is
common practice to use the frontal area, A, to calculate the fluid drag resistance (e.g.
f
Fernandes et al. 2006). Conversely, as the drag acting on the mooring line is purely
frictional, the surface area, A , is adopted for the calculation of drag on the mooring
s
lines.
Figure 6.8 shows the dependence of anchor drag coefficient, C , on Reynolds number,
d,a
Re, for each anchor scale based on back analyses of the accelerations and velocities
derived from the IMU measurements using the following formulations:
W ma1 2C A v2
C s d,l w s Equation 6.11
d,a 1 2 A v2
w f
vd
Re w eff Equation 6.12
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where d is the effective anchor diameter (d = (4A/π)0.5), μ is the dynamic viscosity
eff eff f
of water taken as 1.307x10-3 Pa s at 10°C (Kestin et al. 1978) and a is the resultant
acceleration (acceleration in the direction of motion):
a a 2 a 2 a 2 Equation 6.13
x y z
The maximum Reynolds numbers achieved during free-fall in the water column are Re
= 0.33x106 (v = 4.9 m/s, 1:12 scale), Re = 0.68x106 (v = 6.3 m/s, 1:7.2 scale) and Re =
1.73x106 (v = 10.2 m/s, 1:4.5 scale). Figure 6.8 indicates that fluid drag resistance
acting on the anchor 1:4.5 scale anchor during free-fall in water may be approximated
using a constant mean drag coefficient of C = 0.7 for Re > 1.0x106 (v > 5.9 m/s). The
d,a
mean constant drag coefficient is representative of the fluid drag resistance at high
Reynolds numbers where the pressure drag component is dominant and the viscous drag
component is negligible. The 1:12 and 1:7.2 scale anchors did not reach Reynolds
numbers high enough to allow the constant mean drag coefficient to be back-analysed.
However, since the 1:12, 1:7.2 and 1:4.5 scale anchors are geometrically identical, C
d,a
= 0.7 may be inferred for all scales. This drag coefficient is at the upper range of values
typically reported for dynamically installed anchors and free-fall penetrometers; e.g. C
d
= 0.7 (True 1976), C = 0.63 (Øye 2000). The geometry of the mooring and follower
d,a
recovery lines is analogous to an ‘infinite cylinder’ and as such the fluid drag resistance
can be attributed exclusively to viscous effects (i.e. no pressure drag component). Due
to viscous effects C will vary at relatively low Re and become constant at higher Re.
d,l
However, it is not possible to isolate the viscous drag resistance through back analysis
of the IMU data. Instead, a constant C value is adopted which should reflect the fluid
d,l
drag resistance of the lines at high Re (and hence velocities). In the case of the anchor
penetrating into the lakebed following free-fall (considered later) the constant C value
d,l
should best represent the viscous drag of the lines during initial penetration where it is
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most prevalent. Back analysis of the IMU data suggest a C of 0.015 was necessary to
d,l
predict the increase in fluid drag resistance due to the paying out of the mooring and
follower recovery lines during installation.
5
1:12 scale
1:7.2 scale
1:4.5 scale
a ,d 4 Re = 0.33x106
C
(v = 4.9 m/s, 1:12 scale)
,
t
n
e
i
c
i 3
f f Re = 0.68x106
e
o (v = 6.3 m/s, 1:7.2 scale)
c
g
a
r 2
d Re = 1.73x106
r
o (v = 10.2 m/s, 1.4.5 scale)
h
c
n
A 1
C = 0.7
d,a
0
0.0 5.0x105 1.0x106 1.5x106 2.0x106
Reynolds number, Re
Figure 6.8. Dependence of DEPLA drag coefficient on Reynolds number
Figure 6.9 shows typical velocity profiles for the 1:12, 1:7.2 and 1:4.5 anchor scales
during free-fall in water together with theoretical profiles based on a finite difference
approximation of Equation 6.8 using C = 0.015 and C = 0.7. This provides a good fit
d,l d,a
to the 1:4.5 scale anchor velocity profiles. There is relatively poor agreement between
the theoretical and measured velocity profiles for the 1:12 and 1:7.2 anchor scales as the
constant mean coefficient does not account for the viscous component of fluid drag
resistance which dominates at low Reynolds numbers and hence velocities. However, as
described later, the dynamic penetration of the DEPLA in soil can be predicted by
considering a fluid drag resistance term with a constant mean drag coefficient (in the
form of Equation 6.9), and a soil mechanics term that accounts for the strain rate
enhanced shear resistance attributed to viscous effects.
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(Lieng et al. 2010). The results indicate that anchor embedment increases with
increasing impact velocity, which is sensible as the anchor possesses more kinetic
energy when it impacts the lake bed.
True (1976) proposed a method for predicting the dynamic penetration of projectiles
penetrating soil after free-fall in water. The method considers Newton’s second law of
motion and the net resistance on the projectile during penetration, where the resistance
to motion is due to fluid mechanics drag resistance (analogous to Equation 6.9) and soil
mechanics shear resistance.
Numerous studies on free-falling penetrometers (e.g. Beard 1981, Levacher 1985,
Aubeny and Shi 2006) and dynamically installed anchoring systems (e.g. O’Loughlin et
al. 2004a, Audibert et al. 2006, O’Loughlin et al. 2009, Shelton et al. 2011, Gaudin et
al. 2013, O’Loughlin et al. 2013b) have adopted True’s method for predicting the
embedment of projectiles penetrating the seabed, with slight variations on the inclusion
and formulation of the forces acting on the projectile during penetration. The governing
equation may be expressed as:
d2s
m W F R (F F )F F Equation 6.14
dt2 s b f frict bear d,a d.l
where z is the distance travelled by the anchor tip along its trajectory in the soil, F is
e b
the buoyant weight of the displaced soil, F is frictional resistance and F is bearing
frict bear
resistance. The shear strain-rate function, R, is included to account for the well know
f
dependence of soil strength (and hence frictional and bearing resistance) on strain rate;
this is discussed in more detail later in the chapter. F and F account for drag
d,a d,l
resistance on the anchor as it moves through the soil, and the lines as they move through
the soil and the water. R and F both relate to the high penetration velocity of the
f d
anchor, but as described later in the chapter, R accounts for viscous effects arising from
f
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the very high strain rate in the soil, whereas F accounts for pressure drag which is
d
independent of viscosity. The added mass term, which is negligible for long slender
bodies and was ignored in Equation 6.8, is also ignored in Equation 6.14.
Frictional and bearing resistances are expressed as:
F s A Equation 6.15
frict u
F N s A Equation 6.16
bear c u
where α is a friction ratio (of limiting shear stress to undrained shear strength), N is the
c
bearing capacity factor for the anchor tip, sleeve or fluke and s is the undrained shear
u
strength averaged over the contact area, A. Reverse end bearing at the top of the
DEPLA flukes and follower (accounted for in Equation 6.16) was treated in a similar
manner to that proposed by O’Loughlin et al. (2013b), where it would only be included
if the cavities formed by the passage of the anchor follower and flukes immediately
close during penetration. The cavity formed by the flukes was assumed to close owing
to their relatively low thickness and apparent plane strain conditions, whereas the
cylindrical cavity created by the passage of the follower would remain open during the
time taken for dynamic penetration, and collapse shortly after. This assumption requires
that the buoyant weight of the displaced soil, F , be calculated using a displaced volume
b
equal to the sum of the DEPLA volume and a cylindrical shaft (with diameter D )
s
extending from the top of the DEPLA follower to the soil surface.
The high penetration velocity of the anchor requires that the dependence of soil strength
on shear strain-rate is accounted for in Equation 6.14. This can be achieved by scaling a
reference value of soil strength using either semi-logarithmic or power functions
(Biscontin and Pestena 2001, Peuchan and Mayne 2007, Randolph et al. 2007 and
O’Loughlin et al. 2013b):
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v d
R 1log 1log Equation 6.17
f v d
ref ref
v d
R Equation 6.18
f v d
ref ref
where λ and β are strain-rate parameters in the semi-logarithmic and power functions
respectively,γ is the shear strain rate andγ is the reference shear strain rate associated
ref
with the reference value of undrained shear strength. As described by Einav and
Randolph (2006) and O’Loughlin et al. (2013b), γ will vary through the soil body, but
at any location the operational strain rate may be approximated by the normalised
velocity, v/d. The approximated reference value of operational strain rate, (v/d) , is
ref
that associated with the measurement of the undrained shear strength. As shown on
Figure 6.2, the s measurements were made using a 113 mm piezoball penetrated at 20
u
mm/s (Colreavy et al. 2012), such that (v/d) = 0.18 s-1, two orders of magnitude lower
ref
that the maximum v/d values in the DEPLA tests.
It is worth noting that the effect of strain-rate on mobilised shear stress can also be
described from within a fluid mechanics framework by treating the soil as a non-
Newtonian fluid and using a viscoplastic model such as the Herschel-Bulkley model
(Zhu and Randolph 2011):
K Equation 6.19
y
where τ is the mobilised shear stress, τ is the yield stress, K represents the viscosity of
y
the soil (often referred to as the consistency parameter) and δ is the shear thinning
index.
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It may be argued that such an approach is appropriate in view of the very soft fluidised
soil encountered at the surface of the seabed. Indeed the loading from a submarine slide
runout on a pipeline is typically assessed using such an approach (Randolph and White
2012). However, as shown by Zhu and Randolph (2011) and Boukpeti et al. (2012), the
Herschel-Bulkley model resorts to the soil mechanics power law formulation (Equation
6.18) when τ = 0, Ks γβ and δ = β. Hence using either Equation 6.18 or
y u,ref ref
Equation 6.19 describes the viscous response of the soil attributed to strain rate effects.
However, both equations neglect the pressure drag component of fluid drag resistance
which is independent of viscous effects and related to the stagnation pressure (Zhu and
Randolph 2011, Randolph and White 2012, Sahdi et al. 2014). In the case of submarine
slide runout loading on a pipeline, pressure drag has been observed to dominate at non-
Newtonian Reynolds numbers, Re > 3 (Sahdi et al. 2014) and Re >
non-Newtonian non-Newtonian
10 (Zhu and Randolph 2011, Randolph and White 2012), where the non-Newtonian
Reynolds number is defined as:
v2
Re Equation 6.20
nonNewtonian s
u,op
where s is the operative undrained shear strength.
u,op
Hence Re > 3 to 10 corresponds to combinations of low strength and high
non-Newtonian
velocities, and as such the pressure drag component of fluid drag resistance needs to be
accounted for separately from the viscous component during dynamic penetration of
dynamically installed anchors such as the DEPLA. Therefore, an appropriate
embedment model for the DEPLA, accounting for effects arising from the high
penetration velocity, is to use Equation 6.18 to account for viscous effects and to use a
constant drag coefficient in Equation 6.9 (i.e. making it independent of viscous effects)
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to account for pressure drag on the anchor and to use a constant drag coefficient in
Equation 6.10 to account for viscous effects on the lines.
This ‘superposition’ approach is adopted in a finite difference approximation of
Equation 6.14 to predict the dynamic penetration of the DEPLA in soil. Predictions
were made for each anchor scale assuming idealised strength profiles, s (kPa) = 1.5z
u
for the 1:12 scale tests, and s (kPa) = 0.45 + 0.9z for the 1:7.2 and 1:4.5 scales (see
u
Figure 6.2), where z = s cos(μ), i.e. the vertical depth, which will be different from the
distance travelled by the anchor, s, if the anchor tilts by an angle, μ during installation.
Bearing resistance (Equation 6.16) was calculated using N = 12 and N = 7.5 for the tip
c c
and flukes respectively (O’Loughlin et al. 2004b, O’Loughlin et al. 2009, Richardson et
al. 2009, Jeanjean et al. 2012, O’Loughlin et al. 2013b). The interface friction ratio, α,
was initially taken as the ratio of intact to remoulded penetration resistance from cyclic
piezoball tests, which gave q /q = 0.4 to 0.5. As will be shown later, slight
in rem
adjustments beyond the lower and upper bound of this range were required to achieve
good agreement across all three anchor scales. The strain rate parameter, β, in the power
law (Equation 6.18) is typically in the range 0.05 to 0.17 (Jeong et al. 2009) and
increases with the order of magnitude difference between the operational strain rate and
the reference strain rate (Biscontin and Pestana, 2001, Peuchen and Mayne 2007,
O’Loughlin et al. 2013b). The maximum v/d values associated with the DEPLA tests
considered here is v/d = 67 s-1, which is two orders of magnitude higher than (v/d) =
ref
0.18 s-1. This is similar to the range in v/d associated with variable rate penetrometer
tests, which tends to give β values close to the lower end of the range quoted above, e.g.
β = 0.06 to 0.08 (Lehane et al. 2009). β = 0.06 was adopted here, consistent with β =
0.055, which was shown by Biscontin and Pestana (2001) to satisfactorily describe the
increase in s over three orders of magnitude increase in peripheral shear vane velocity.
u
Drag resistance was modelled using C = 0.7 and C = 0.015 in Equation 6.9 and
d,a d,l
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Equation 6.10 for the anchor and lines respectively (as deduced from data measured
during free-fall in water, see Figure 6.8). The density of soil rather than water was used
for the anchor, whereas both the density of soil and the density of water were used for
the lines depending on the current calculated anchor embedment depth which
determines if the line drag mobilised in water or soil. C = 0.7 (derived from the
d,a
acceleration data measured during anchor free-fall in water) was used to model anchor
embedment in the soil without adjusted for the viscosity of soil as it is representative of
the fluid drag resistance at high Reynolds numbers where the pressure drag component
is dominant and the viscous drag component is negligible.
Measured and predicted DEPLA velocity profiles are provided on Figure 6.10 for each
anchor scale for impact velocities of 5.6 m/s (1:12 scale), 7.5 m/s (1:7.2 scale) and 9.7
m/s (1:4.5 scale). These velocity profiles consider the anchor displacement in the
direction of motion, rather than anchor penetration depth, as the velocities are calculated
from the resultant acceleration (i.e. in the direction of anchor motion, Equation 6.13).
The predictions were obtained using the parameters introduced in the preceding
discussion, but by varying α to achieve agreement with the measured embedment depth.
This permitted a basis for examining the potential of the model to describe the
mechanisms taking during dynamic embedment. The best agreement was obtained for
each anchor scale using α = 0.46 (1:12 scale), 0.45 (1:7.2 scale) and 0.32 (1:4.5 scale).
These values are generally consistent with the range of intact to remoulded penetration
resistance ratios from cyclic piezoball tests, which gave α = 0.4 to 0.5.
The performance of the embedment model is better assessed from accelerations rather
than velocities as velocity is the integral of accelerations and by definition loses some of
the detail. To this end, Figure 6.10 also shows profiles of the calculated resistance
forces in Equation 6.14 together with the predicted and measured net resistance, F .
net
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The predicted net resistance is the sum of the terms on the right hand side of Equation
6.14, whereas the measured net resistance is taken as the mass of the anchor multiplied
by the resultant acceleration, a.
For the 1:12 anchor scale the fluid drag resistance attributed to the mooring line and
follower recovery lines, F , is the dominant resistance up to s = 1.2L, whereas for the
d,l f
1:7.2 and 1:4.5 anchor scale the fluid drag resistance acting on the anchor, F , is the
d,a
dominant resistance up to s = 0.8L (1:7.2 scale) and 1.2L (1:4.5 scale). This relative
f f
reduction in F with increasing anchor scale is due to the constant line diameter used
d,l
for each anchor scale, which leads to reducing ratios of line surface area in contact with
the water, A (contributing to F ) to anchor frontal area, A (contributing to F ) as the
s d,l p d,a
anchor scale increases.
The fluid drag resistance is dominant during shallow embedment as the anchor velocity
is high and the undrained shear strength of the soil is low (i.e. for high Re ).
non-Newtonain
This has also been demonstrated for debris flow on submarine pipelines (Zhu and
Randolph 2011, Randolph and White, 2012 Sahdi et al. 2014). As the anchor penetrates
deeper into the soil the anchor velocity reduces, decreasing the fluid drag resistance of
the anchor, F , and the mooring and follower recovery lines, F . At the same time the
d,a d,l
strain rate enhanced shearing resistance increases due to the increasing undrained shear
strength and anchor contact area mobilised in the soil. This contact area is low to s =
0.6L at which point the flukes start to penetrate the soil. From s = 0.6L the circular
f f
fluke geometry causes a non-linear increase in shear resistance until z = L when the
e f
DEPLA is fully submerged in soil and the strain rate enhanced bearing and frictional
resistances are approximately equal. From to s = 1.2L (1:12 and 1:4.5 scale) and 0.8L
f f
(1:7.2 scale) the strain rate enhanced frictional resistance is the dominant resistance. The
power strain rate law using β = 0.06 increases both the frictional and bearing resistance
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by almost 50% (R = 1.46, 1:12 scale; R = 1.44, 1:7.2 scale; R = 1.42, 1:4.5 scale) over
f f f
the majority of the embedment. Soil buoyancy, F , increases with depth as the hole
b
formed by the advancing anchor is considered to remain open to the soil surface over
the period of time required for the anchor to come to rest in the soil (typically 0.6 to 1.4
s). Soil buoyancy never exceeds 8% of the strain enhanced bearing resistance since the
effective unit weight of the soil for the Lough Erne clay is very low.
For the 1:7.2 and 1:4.5 anchor scales the net resistance force is initially positive as the
anchor had not reached terminal velocity during free-fall in water and becomes negative
at s = 0.6L (1:7.2 scale) and s = 0.8L (1:4.5 scale) when sufficient resistance develops
f f
to decelerate the anchors. Over the entire penetration depth good agreement between the
measurements and predictions is obtained for the 1:7.2 scale test and to a slightly lesser
extent the 1:4.5 scale test. Despite the less than perfect agreement between the measured
and predicted net resistance for the 1:12 scale test, the over prediction mainly balances
the under prediction such that the energy dissipated by the anchor during penetration is
approximately the same for both the predictions and the measurements. This has the
effect of predicting the final embedment depth adequately, as shown clearly by Figure
6.11, which shows the measured DEPLA tip embedments against impact velocity
together with the corresponding predictions obtained using Equation 6.14. The best
agreement with the measurements was obtained using the parameters adopted for the
predictions on Figure 6.11, with upper and lower bounds to the predictions obtained
using; α = 0.39 and α = 0.53 (1:12 scale), α = 0.42 and α = 0.48 (1:7.2 scale), α = 0.3
and α = 0.34 (1:4.5 scale). As discussed previously in relation to Figure 6.10, this range
in α is similar to that which would be inferred from cyclic full-flow penetrometer tests,
which gave q /q = 0.4 to 0.5 for this soil. It should be noted that from a design
in rem
perspective, it is this value (or range) that would be used to calculate the embedment
depth. Adopting the median α = 0.45 would result in predictions that deviate by no more
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Impact velocity, v (m/s)
i
0 1 2 3 4 5 6 7 8 9 10 11 12
) m0
(
s
= 0.53
, l1 = 0.46
i
o
s
n
i 2 = 0.48
p = 0.45
i
t
= 0.39
r
o
h3
c
n
a
y4
b
d = 0.34 = 0.42
e
l l e5 = 0.32
v
a
r
t
e6
1:12 scale
c 1:7.2 scale
n
a t 1:4.5 scale
s i d7 Model - best fit = 0.3
l a Model - lower/upper bound
t
o8
T
Figure 6.11. Dependence of tip embedment on impact velocity
6.5 Conclusions
The installation response of DEPLAs was assessed though an extensive field testing
campaign undertaken at a lake underlain by very soft clay, using 1:12, 1:7.2 and 1:4.5
reduced scale anchors. This chapter makes a particular contribution to the body of
literature on dynamic penetration problems by presenting and analysing acceleration
data measured by an inertial measurement unit during DEPLA installation. Such data
are rarely available, but are important for assessing the mechanisms associated with
dynamic penetration in soil and for the calibration and validation of embedment models
for dynamically installed anchors. Back analysis of the acceleration data measured
during anchor installation allowed the relationship between the anchor drag coefficient
and Reynolds number (in water), and profiles of net anchor resistance and velocity
during free-fall in water and soil penetration to be established. These profiles, together
with back analysed drag coefficients, were used to assess the merit of a simple anchor
embedment model formulated in terms of strain rate enhanced shear resistance and
strain rate independent fluid mechanics drag resistance. Qualitatively, the model
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CHAPTER 7 CAPACITY OF DYNAMICALLY
EMBEDDED PLATE ANCHORS AS
ASSESSED THROUGH FIELD TESTS
7.1 Abstract
A dynamically embedded plate anchor (DEPLA) is a rocket shaped anchor that
penetrates to a target depth in the seabed by the kinetic energy obtained through free-fall
and by the anchor’s self-weight. After embedment the central shaft is retrieved leaving
the anchor flukes vertically embedded in the seabed. The flukes constitute the load
bearing element as a plate anchor. This chapter presents and considers field data on the
embedment depth loss due to the plate anchor keying process and the subsequent
bearing capacity factor of the plate anchor element. The loss in plate anchor
embedment was significantly higher than that reported from corresponding centrifuge
tests and is reflected in the larger padeye displacements required to mobilise peak
capacity in the field tests. Measured plate capacities and plate rotations during keying
indicate that the end of keying coincides with the peak anchor capacity. Experimental
bearing capacity factors are in the range N = 14.3 to 14.6 which are consistent with
c
those reported from corresponding centrifuge tests but appreciably higher than existing
solutions for vanishingly thin circular plates. The higher N for the DEPLA is
c
considered to be due to a combination of the cruciform fluke arrangement and the fluke
(or plate) thickness.
7.2 Introduction
Deep water floating oil and gas facilities such as SPAR platforms, tension leg platforms
and semi-submersibles are typically moored using taut-leg or vertical mooring systems.
These systems require anchors that can sustain significant components of vertical load
while maintaining installation costs at a reasonable level (Ehlers et al. 2004). Drag-in
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anchors and direct embedment anchors resist vertical loading through a plate oriented
such that its projected area is normal (or near-normal) to the direction of loading. A
drag-in plate anchor is designed to embed when pulled along the seabed by a wire rope
or chain. When the target installation load is reached, the anchor is triggered into its
mooring position by rotating or ‘keying’ the plate such that it becomes approximately
normal to the direction of the applied load. In the case of a direct embedment plate
anchor, a follower (such as a suction caisson) is used to install the plate to the design
embedment depth, before being recovered for reuse in future installations. The plate
remains vertical in the seabed until sufficient load develops in the mooring line to cause
the plate anchor to key to an orientation that is approximately perpendicular to the
direction of loading at the padeye, allowing the full bearing resistance of the plate to be
mobilised.
Dynamically installed anchors are rocket or torpedo shaped and are designed so that,
after release from a designated height above the seafloor, they will penetrate to a target
depth in the seabed by the kinetic energy gained during free-fall. The ease and speed of
installation makes dynamically installed anchors an attractive option in deep water.
However, their axial capacity to weight ratios are low (typically less than five times the
anchor dry weight, O’Loughlin et al. 2004a, Richardson et al. 2009), and very large
anchors are required for permanent installations. The dynamically embedded plate
anchor (DEPLA) is a hybrid anchor that combines the geotechnical efficiency of plate
anchors with the low installation costs of dynamically installed anchors. The DEPLA
comprises a removable central shaft or ‘follower’ and a set of four flukes (see Figure
1.17) arranged on a cylindrical sleeve and connected to the follower with a shear pin.
The DEPLA is installed in a similar manner to other dynamically installed anchors.
After the DEPLA has come to rest in the seabed, the follower retriever line is tensioned,
which causes the shear pin to part (if not already broken during impact) allowing the
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follower to be retrieved for the next installation, whilst leaving the anchor flukes
vertically embedded in the seabed. These embedded anchor flukes constitute the load
bearing element as a plate anchor. When sufficient load develops in the mooring line the
plate rotates to an orientation that is approximately perpendicular to the direction of
loading at the padeye, allowing full bearing resistance of the plate to be mobilised. The
DEPLA installation and keying processes are summarised in Figure 1.18 and
respectively Figure 1.19.
The holding capacity of a plate anchor such as the DEPLA is controlled by the
embedment depth achieved after dynamic installation, the loss in this embedment
during keying, and the geometry dependent anchor capacity factor. Approaches for
calculating the embedment of dynamically installed anchors generally considers the
forces acting on the anchor during penetration, whilst accounting for the enhancement
of the available soil strength due to the high penetration velocities and hence strain rates
(e.g. O’Loughlin et al. 2004a, Richardson et al. 2006, Audibert et al. 2006, O’Loughlin
et al. 2013b). The merit of this approach has been demonstrated by Blake and
O’Loughlin (2015) by predicting the final embedment depth for a series of model
DEPLA field tests to within 10% of the measurements. A series of field tests were
designed to provide a basis for understanding the behaviour of the DEPLA during (i)
free-fall and dynamic embedment in soil, and (ii) quantifying the loss in embedment
during keying and the subsequent plate anchor capacity. The dynamic embedment
aspects of the study are reported by Blake and O’Loughlin (2015). This chapter
considers the keying and capacity mobilisation aspects of the field tests.
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7.3 Experimental program
7.3.1 Model anchors and instrumentation
The model DEPLAs were manufactured from mild steel and modelled at reduced scales
of 1:12, 1:7.2 and 1:4.5. This reduced scale infers a full scale anchor with a follower
length of 9 m, a combined mass (follower and flukes) of 37 tonnes, which for a typical
offshore seabed strength profile of 1.5 kPa/m would result in a plate anchor capacity of
the order of about 500 tonnes, suitable for mooring mobile offshore drilling units. The
follower was solid, except for a 185 mm long, 42 mm diameter void at the top of the
follower, which housed an inertial measurement unit that measured accelerations and
rotations during free-fall and embedment (Blake at al. 2016).
A schematic of the model DEPLA and the notation used for the main dimensions are
shown in Figure 6.1, with the main dimensions and mass of each model DEPLA
summarised in Table 6.1. 12 mm diameter Dyneema SK75 rope was used to install the
DEPLA (and to retrieve the follower) and as the mooring line connected to one of the
DEPLA flukes. This rope was selected because it was more flexible and much lighter
than wire rope, whilst maintaining high tensile strength and stiffness (<3.5% extension
at 50% of the maximum breaking load).
Follower recovery loads and plate capacities were measured above the waterline using a
tension load cell connected in series with the winch cable and the Dyneema rope. The
displacement of the follower retrieval line and mooring line was measured using a draw
wire sensor with a range of 10 m, connected in parallel with the winch line. As
described later, in a number of tests the DEPLA was jacked in the lakebed. In these tests
the orientation of the plate during keying and pullout was determined from a tri-axis
micro-electro mechanical systems (MEMS) accelerometer with a range of +/- 3g on
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each axis (ADXL 335) that was potted with Urethane compound into an 8 mm thick
polyethylene housing and bolted to one of the DEPLA flukes.
7.3.2 Test site and soil properties
Tests were carried in Lower Lough Erne, a glacial lake located in Co. Fermanagh,
Northern Ireland, in water depths varying from 3 to 12 m. The lakebed soil is a very soft
clay with high moisture contents in the range 270 to 520% (1.2 to 1.7 times the liquid
limit) and high Atterberg limits with plastic limits of 130 to 180% and liquid limits of
250 to 315% (Colreavy et al. 2012). The unit weight of the soil is constant with depth
and is marginally higher than that of water at 10.8 kN/m3. The very high moisture
content and very low unit weight is considered to be due to the very high proportion of
diatoms that are evident from scanning electron microscopic images of the soil (e.g. see
Colreavy et al. 2012). Diatoms have an enormous capacity to hold water in the
intraskeletal pore space (Tanaka and Locat 1999). However this intraskeletal pore water
is not considered to play a role in soil behaviour, and as such the measured unit weight
and other index properties that are expressed in terms of the measured moisture content
are not considered to be useful indicators of soil behaviour.
Colreavy et al. (2012) reported results from piezoball and in situ shear vane tests
conducted at the anchor test sites to depths of up to 11 m. The undrained shear strength
profiles are shown on Figure 6.2 and were derived from the net penetration resistance
data using N = 8.6 (calibrated using in situ shear vane data). The analysis of the
ball
DEPLA test data used the strength over the range of interest for each anchor scale. As
will be discussed later, the 1:12 scale DEPLA achieved maximum tip embedment
depths of z = 2.2 m. Over this depth s is best idealised as s (kPa) = 1.5z and this
e u u
profile was adopted in the analysis of the test data using this anchor. The 1:7.2 and the
1:4.5 scale DEPLAs achieved maximum tip embedment depths of z = 4.1 m and 7.5 m,
e
respectively. Over this range of embedment s is best idealised as s (kPa) = 0.45 + 0.9z
u u
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and this profile was adopted in the analysis of the test data using the 1:7.2 and the 1:4.5
scale anchors. The sensitivity of the soil is in the narrow range S = 2 to 2.5 as assessed
t
from in situ vane tests and piezoball cyclic remoulding tests.
7.3.3 Testing setup and procedure
Tests were carried out from a fixed jetty (1:12 scale DEPLA only) and from the deck of
a 15 m self-propelled barge with a 13 t winch and 2 t crane (Figure 5.11). The testing
procedure (summarised schematically for the barge tests in Figure 7.1) was as follows:
1. The DEPLA was released from a designated drop height above the mudline
allowing it to free-fall and penetrate into the lakebed. The anchor tip embedment, z ,
e
was measured by sending an underwater camera to the mudline to inspect markings
on the follower retrieval line.
2. Following dynamic installation the load cell was connected in series with the winch
cable and follower retrieval line, and the draw wire sensor was connected in parallel
with the winch cable. The winch was used to extract the follower at approximately
10 mm/s for the jetty tests and approximately 30 mm/s for the barge tests. These
were the maximum winch velocities achievable with the winches used in the
respective tests. Movement of the follower relative to the stationary flukes causes
the shear pin to break, allowing the follower to be retrieved on the barge deck (or
the jetty).
3. The plate anchor mooring line was connected to the winch cable and extracted from
the lake bed at approximately 10 mm/s for the jetty tests and approximately 30
mm/s for the barge tests. This was continued until the DEPLA plate was retrieved
from the lake.
As the aim of the field tests was to measure vertical monotonic capacity, the winch
position was maintained directly above the anchor drop site for the DEPLA keying and
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7.4 Results and discussion
7.4.1 Follower extraction
DEPLA tip embedment, z , was in the ranges: 1.495 to 2.19 m (2 to 2.9L, 1:12 scale),
e f
2.56 to 4.1 m (2.1 to 3.3L, 1:7.2 scale) and 6.197 to 7.493 m (3.1 to 3.7L, 1:4.5 scale).
f f
These data, together with other relevant data presented later, are summarised in Table
7.1 for each anchor scale. A typical load-displacement response of the 1:12 scale
follower extraction is shown in Figure 7.2. The extraction is characterised by a stiff
response to an initial peak at a displacement, Δz = 0.094 to 0.154 m, followed by a
e
sharp reduction as the follower mobilises progressively weaker soil as it becomes
shallower. An increase in resistance is consistently observed when the follower tip
begins to enter the base of the sleeve (Δz = 0.05 m), reducing just after the tip emerges
e
from the top of the sleeve (Δz = 0.8 m). This increase in resistance is likely to be due to
e
the development of suction at the follower tip as it enters the anchor sleeve (see Figure
7.2). Considering the aspect ratio of the sleeve, the soil is expected to plug, leaving a
gap underneath the follower tip where suction is generated. The maximum follower
extraction resistance, F , was in the range 419 to 590 N and typically 2.9 to 4.1 times
vf
the dry mass of the follower. This range reflects the range in embedment depths
achieved by varying the drop height and hence the range in undrained shear strength
mobilised during follower extraction. The follower extraction resistance is slightly
higher than measured in DEPLA centrifuge tests (2.2 to 3 times the follower dry mass;
O’Loughlin et al. 2014b). This reflects the higher tip embedments achieved in the field
tests, noting that the strength profiles and nondimensional reconsolidation times, T =
c t/D2, are broadly similar between the centrifuge and field tests. As only a few minutes
h f
elapsed between anchor installation and follower recovery, the follower resistance is
likely to be 20 to 30% of the potential follower extraction resistance following full
reconsolidation (Richardson et al. 2009).
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7.4.2 Plate keying and capacity
Initial plate embedment, z , was in the range: 0.890 to 1.585 m (3 to 5.3D, 1:12
e,plate,0
scale), 1.554 to 3.094 m (3.1 to 6.2D, 1:7.2 scale) and 4.587 to 5.883 m (5.7 to 7.4D,
1:4.5 scale). The load-displacement responses of the 1:12, 1:7.2 and 1:4.5 scale plate
anchors during keying and pull-out are provided on Figure 7.3, together with the
centrifuge data reported in O’Loughlin et al. (2014b) for a geometrically similar
DEPLA tested in normally consolidated kaolin clay. The capacity of the plate is
expressed in terms of the dimensionless plate anchor capacity factor, N , defined as:
c
F
N v,net Equation 7.1
c A s
p u,p
where F is the peak load minus the submerged weight of the plate anchor in soil, W ,
v,net s
A is the area of the plate calculated as A = πD2/4 (plate orientation idealised as
p p
perpendicular to the direction of load following keying) and s is the undrained shear
up
strength at the anchor embedment corresponding with peak capacity. As mentioned in
Section 7.3.3 the piezoball penetrated at a strain rate (v/D = 0.18 s-1) which is
ball
expected to give undrained conditions. This strain rate is comparable (within one order
of magnitude) to the range associated with extraction of the plate for the three anchor
scales (v/D = 0.01 to 0.09 s-1). Hence, experimental capacity factors may be determined
without correction for strain rate effects, particularly as the penetrometer strength will
include effects of strain softening not included in mobilisation of the peak anchor
capacity.
As the anchor load is adjusted by the submerged weight of the plate in soil, N , is
c
initially slightly negative (at zero displacement), but reaches a maximum anchor
capacity factor that is directly comparable with theoretical capacity factors, as discussed
later. The occasional sharp drops in the response curves are due to momentary pauses in
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the loading which were periodically required for resetting the draw wire sensor and load
cell on the mooring line.
18
16
c 14
N
,
r o 12
t
c
a
f 10
y
t
i
c 8
a
p
a
c 6
g
n
i 4
r 1:12 scale
a
e 1:12 scale (jacked)
B 2
1:7.2 scale
1:4.5 scale
0
DEPLA centrifuge
-2
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Mooring line displacement, d /D
v
Figure 7.3. Typical load-displacement responses of during keying and pullout
Also included on Figure 7.3 are the corresponding responses for a DEPLA (1:12 scale)
that was jacked vertically into the lakebed. The DEPLA was jacked-in to a tip
embedment of 1.855 m (z = 1.25 m, 4.2D) typical of that achieved for a dynamic
e,plate,0
installation with an impact velocity of ~7 m/s. Results for both dynamic and jacked
installations are similar, indicating that dynamic installation does not affect either the
peak capacity or the keying response. The response is qualitatively consistent with
centrifuge test data in normally consolidated kaolin clay, including the DEPLA
centrifuge data on Figure 7.3, and data from tests on square plate anchors installed in
the vertical orientation (e.g. Gaudin et al. 2006, Blake et al. 2010). However, the loss in
embedment during keying is much higher as discussed below.
The vertical displacement of the mooring line up to the peak load, d , was determined
v
from the draw wire sensor measurements and was in the range 0.544 to 0.668 m (1:12
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Also shown on Figure 7.4 is the expression:
z 0.144
e,max Equation 7.3
B
e t
0.21.15
BB
where B is the plate breadth for square and strip anchors. Equation 7.3 was proposed
by Wang et al. (2011) as the limiting loss in embedment for square plate anchors and is
seen to provide a reasonable limit to the previously reported experimental data, but not
the DEPLA field data. It is evident from Figure 7.4 that despite the geometrical
consistency between the field and centrifuge DEPLA tests, the loss in embedment in the
field tests (∆z = 1D to 1.8D) is much higher than that in the centrifuge tests (∆z
e,plate e,plate
= 0.5D to 0.7D). This disparity was explored further by considering the following
dimensionless groups which are considered to affect the keying response (Wang et al.
2011):
z e t s kD ' t E
e,plate f , , u0 , , a , Equation 7.4
D D D 'D s s s
u0 u0 u0
where s is the local undrained shear strength at the initial embedment depth of the
u0
anchor (i.e. as distinct from s in Equation 7.1, which is the local undrained shear
up
strength at the embedment depth corresponding with peak capacity), γ' is the
a
submerged unit weight of the anchor in soil and E is Young’s modulus of the soil.
Equation 7.4 uses the DEPLA plate diameter, D, rather than the plate breadth, B, as
utilised in the original form of this equation in Wang et al. (2011) in their consideration
of rectangular and strip anchors.
Table 7.2 summarises the range of values for each group in Equation 7.4 for the DEPLA
centrifuge tests and the DEPLA field tests, with the exception of E/s , which was not
u0
measured in either the centrifuge tests or in the field tests, and which has a limited effect
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on the loss of embedment as demonstrated by Wang et al. (2011). There is broad
agreement for groups: e/D, t/D, kD/s , γ' t/s , but in the field tests s /γ'D = 4.5 to 7.5,
u0 a u0 u0
much higher than s /γ'D = 0.61 to 1.44 in the centrifuge tests. This is consistent with
u0
numerical analyses reported by Wang et al. (2011), which demonstrated that higher
strength at the anchor embedment depth resulted in higher loss of embedment, as the
moment applied to the anchor by the mooring line at the point of zero net vertical load
becomes less significant in relation to the moment capacity.
Table 7.2 Comparison between the field and centrifuge tests of the non-
dimensional groups that govern keying behaviour
Group Field Centrifuge
e/D 0.42–0.44 0.38–0.36
t/D 0.01–0.02 0.02–0.05
0.61–1.44
s /γ'D 4.5–7.5
u0
0.16–0.38
kD/s 0.16–0.25
u0
γ 't/s 0.14–0.20 0.37–0.45
a u0
Figure 7.4 indicates that the loss in DEPLA plate embedment during keying could be
reduced if either the eccentricity or anchor thickness was increased (relative to the plate
diameter or breadth). The most influential of these factors is the eccentricity
(O’Loughlin et al. 2006, Song et al. 2009, Wang et al. 2011) and the embedment loss
for the DEPLA should be lower if the padeye eccentricity was increased (albeit that this
would require a different plate geometry).
The keying and capacity response of additional jacked installation tests are reported in
Figure 7.5, where the plate was loaded at pullout angles in the range θ = 18.6° to
pull
91.5° (to the horizontal). The plate rotation, θ (with respect to the horizontal), was
p
determined from the MEMS accelerometer attached to one of the DEPLA flukes. The
vertically loaded anchor test on Figure 7.5 (91.5° load inclination) is the same jacked
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These stages become progressively less distinct as the load inclination reduces. For
instance the capacity curve for θ = 18.6° is characterised by an initial soft response,
pull
with a large padeye displacement required to initiate capacity mobilisation (N = 1.1 at
c
d = 0.5 m and θ = 1.5°), followed by a stiffer response towards a peak capacity factor,
v p
N = 10.5. The slow build up in rotation and capacity with line displacement indicates
c
that the initial soft response is mainly due to movement of the line through the soil
rather than movement of the plate. Hence the magnitude of N for the inclined loading
c
cases is overestimated as the measured capacity includes the resistance of the inclined
line in the soil. It is worth noting that Figure 7.5 shows that for each load inclination the
end of keying coincides with the peak anchor capacity at a plate rotation that is tolerably
equal to the load inclination. Figure 7.5 also indicates that N decreases with reducing
c
load inclination (for z /D < 4), as also shown numerically by Song et al. (2008) and
e,plate
Yu et al. (2011) for strip anchors, and recently by Wang et al. (2014) for DEPLAs.
The peak plate anchor resistance, F , was in the range: 0.52 to 1.46 kN (6 to 31W,1:12
vp
scale), 3.64 to 7.78 kN (19 to 42W,1:7.2 scale) and 23.76 to 32.37 kN (31 to 42W,1:4.5
scale), where W is the dry weight of the plate. As shown by Figure 7.6, F increases
vp
linearly with depth, reflecting the linear increase in s with depth on Figure 5.9b. Also
u
shown on Figure 7.6 are the predicted anchor capacities using Equation 7.1, where N
c
was varied to give the best overall agreement between the measurements and
predictions for each anchor scale. This resulted in N = 14.6 for the 1:12 scale anchor,
c
N = 14.5 for the 1:7.2 scale anchor, and N = 14.3 for the 1:4.5 scale anchor. This range
c c
is in good agreement with capacity factors back analysed from DEPLA centrifuge test
data, which are in the range N = 14.2 to 15.8 with an average N = 15.0 (O’Loughlin et
c c
al. 2014b), and capacity factors determined numerically which gave N = 14.9 (Wang et
c
al. 2014).
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The exact solution for a deeply embedded vanishingly thin circular plate is N = 12.42
c
for a smooth interface and N = 13.11 for a rough interface (Martin and Randolph
c
2001). However, finite element results reported by Wang et al. (2010) show that N
c
increases from 13.75 for a vanishingly thin rough circular plate (4.7% higher than the
exact solution) to N = 14.35 for a rough circular plate with t/B = 0.05. As noted by
c
Zhang et al. (2012), soil is forced to take a deeper and longer route to flow around
thicker plates, which mobilises more soil in the failure mechanism and results in higher
bearing capacity factors. This, together with the cruciform fluke arrangement on the
DEPLA sleeve, will result in a larger failure surface (and hence a higher capacity factor)
compared with a flat vanishingly thin circular plate.
Plate capacity, F (kN)
vp
0 5 10 15 20 25 30 35
0
D 1:12 scale
/ 1:7.2 scale
e
ta
lp1 1:4.5 scale
,e
z Equation 7.1
,
t
n
e 2
m
d
e
b
m
3
e N = 14.3
c
e
t
a
l
p
4
d
e
s
i
l
a
m 5
N = 14.5
r c
o
N
N = 14.6
c
6
Figure 7.6. Measured and predicted capacity for each anchor scale
7.5 Conclusions
A series of field tests were carried out to assess the installation process and holding
capacity of dynamically embedded plate anchors (DEPLAs) at a lake underlain by very
soft clay. This chapter considered the embedment depth loss due to the plate anchor
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keying process and the subsequent bearing capacity factor of the plate anchor element.
Results from tests on three different reduced scale DEPLAs (1:12, 1:7.2 and 1:4.5 scale)
were presented, along with supplementary data from centrifuge tests investigating the
influence of reconsolidation following anchor installation on the keying induced loss in
DEPLA. The main findings are summarised in the following:
The load-displacement response of the DEPLA during keying and pullout is
qualitatively consistent with that observed in DEPLA centrifuge tests and other plate
anchors installed in the vertical orientation. Results for both dynamic installed and
‘jacked-in’ DEPLAs are similar, indicating that dynamic installation does not affect
either the peak capacity or the keying response.
The loss in plate anchor embedment was in the range 1D to 1.8D, which is
considerably higher than the range 0.5D to 0.7D reported from centrifuge tests in
kaolin clay on DEPLAs with the same geometry. The higher embedment loss for the
field tests is reflected in the much softer load-displacement response compared with
the centrifuge tests, and may also be due to the difference in normalised strength,
which was s /γ'D = 4.5 to 7.5 in the field tests, compared with s /γ'D = 0.61 to 1.44
u u
in the centrifuge tests.
Rotation data measured during keying and pullout of ‘jacked-in’ DEPLAs show that
the end of keying coincides with mobilisation of peak anchor capacity, and that the
bearing capacity factor decreases moderately with reducing load inclination (for
normalised plate embedment ratios less than 4).
Average experimental bearing capacity factors were in the range N = 14.3 to 14.6,
c
which are in good agreement with N = 15 as back analysed from corresponding
c
centrifuge data, but are larger than capacity factors for circular plates due to a
combination of the cruciform fluke arrangement and the fluke thickness.
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CHAPTER 8 TOWARDS A SIMPLE DESIGN
APPROACH FOR DYNAMICALLY
EMBEDDED PLATE ANCHORS
8.1 Abstract
A DEPLA is a rocket shaped anchor that comprises a removable central shaft and a set
of four flukes. The DEPLA penetrates to a target depth in the seabed by the kinetic
energy obtained through free-fall in water. After embedment the central shaft is
retrieved leaving the anchor flukes vertically embedded in the seabed. The flukes
constitute the load bearing element as a plate anchor.
This chapter considers the results from field trials on a 1:4.5 reduced scale DEPLA at a
site off the west coast of Scotland. The data gathered in these trials are considered in
parallel with DEPLA field and centrifuge data from earlier in the experimental
campaign to assess the merit of anchor embedment and capacity models. The anchor
embedment model is cast in terms of inertial drag resistance and strain rate enhanced
shear resistance. The latter is described using a power law with separate dependence for
bearing and frictional resistance. Back analysis of acceleration data captured during
dynamic embedment indicated that the power law is capable of describing the strain rate
dependence of undrained shear strength at the very high strain rates associated with the
dynamic embedment process. Back analysed peak bearing capacity factors from the
centrifuge and field data were compared with corresponding numerically derived
values. This comparison indicated the potential for soil tension to be lost at the
underside of the anchor plate at shallow embedment, resulting in a lower capacity
factor. A simple design chart, presented in terms of the total energy of the anchor at
impact with the mudline for a range of strength gradients and soil sensitivities, is shown
to be a useful approach for predicting anchor capacity.
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8.2 Introduction
The advent of floating liquid natural gas facilities will bring an associated increase in
mooring line loads, requiring either an upscale in current anchor technology such as the
suction caisson or more technically efficient and cost-effective anchor concepts.
Dynamically installed anchors such as the torpedo pile are attractive in this regard due
to the minimal installation times, although their relatively low capacity to weight ratio
means that they must be significantly upscaled to provide the required capacity. This
has obvious cost and operational implications. Vertically loaded plate anchors are
geotechnically efficient, offering a high capacity to weight ratio, but can be difficult to
install, particularly if they are drag embedded.
A relatively new anchor concept, referred to as the dynamically embedded plate anchor
(DEPLA), combines the installation advantages of dynamically installed anchors with
the capacity advantages of vertically loaded plate anchors. The DEPLA comprises a
removable central shaft or ‘follower’ and a set of four flukes arranged on a cylindrical
sleeve and connected to the follower with a shear pin (Figure 1.17). The DEPLA is
installed in a similar manner to other dynamically installed anchors, by releasing the
anchor from a height above the seafloor, chosen such that the anchor will impact the
seabed at a velocity approaching its terminal velocity and subsequently self-bury in the
ocean floor sediments. After the DEPLA has come to rest in the seabed, the follower
retriever line is tensioned. This causes the shear pin to part (if not already broken during
impact) allowing the follower to be retrieved for the next installation, whilst leaving the
anchor flukes vertically embedded in the seabed. These embedded anchor flukes
constitute the load bearing element as a plate anchor. When sufficient load develops in
the mooring line the plate rotates to an orientation that is approximately perpendicular
to the direction of loading at the padeye, allowing full bearing resistance of the plate to
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be mobilised. The DEPLA and its installation and keying processes are summarised in
Figure 1.18 and Figure 1.19 respectively.
Predicting the holding capacity of a plate anchor such as the DEPLA is relatively
straightforward for a given shear strength profile and a known embedment depth. Plate
anchor capacity prediction is based on bearing capacity factors which are well
established e.g. Martin and Randolph (2001), Song et al. (2008b), Wang et al. (2010),
Wang and O’Loughlin (2014). However predicting this final plate anchor embedment is
challenging as it firstly requires an assessment of the final DEPLA penetration depth
after free-fall in water, and secondly requires an assessment of the extent of embedment
loss of the plate anchor keying. The loss in embedment during keying has been
investigated experimentally for suction embedded plate anchors (e.g. O’Loughlin et al.
2006, Gaudin et al. 2006, Gaudin et al. 2009, Wang et al. 2011, Cassidy et al. 2012,
Yang et al. 2012), the results of which are relevant to the DEPLA. Predicting the final
embedment of the DEPLA after free-fall is complicated as the high penetration
velocities associated with dynamic installation process requires interpretative
frameworks that are capable of scaling the soil strength from nominally undrained
values to the strain rate enhanced values associated with the very high strain rates in the
soil, and that account for hydrodynamic effects, notably the pressure drag resistance that
dominates at shallow embedment in soft soils.
The DEPLA is attractive for facilities with higher mooring loads, as relative to current
technology such as suction caissons, the anchor will be much smaller and less expensive
to install. However, the anchor concept is recent and hasn’t yet been trialled at full
scale. Towards this eventual aim of qualifying the anchor at full scale, has been an
experimental phase of proof-of-concept centrifuge tests (O’Loughlin et al. 2014b) and
reduced scale field trials (Blake et al. 2014, Blake and O’Loughlin 2015). This chapter
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considers data from the final phase of reduced scale field trials, which focused on
DEPLA installation and capacity mobilisation at a soft seabed site off the west coast of
Scotland. Measurements in the trials include accelerations during free-fall in water and
embedment in soil, and pullout resistance as the DEPLA was loaded to failure and
subsequently retrieved to the deck of the installation vessel. These data, together with
previously reported centrifuge data (O’Loughlin et al. 2014b) and field data from the
onshore site (Blake et al. 2014, Blake and O’Loughlin 2015) are considered to
investigate the merit of frameworks for predicting anchor embedment depth after
dynamic installation and subsequent anchor capacity.
8.3 Field Trials
The field tests were conducted at the Firth of Clyde which is located off the West coast
of Scotland between the mainland and the Isle of Cumbrae. At the Firth of Clyde the
water depth was typically 50 m. The test location is shown in Figure 8.1.
Figure 8.2 summarises index properties for the seabed sediments at Firth of Clyde. The
soil is very soft with moisture contents in the range 50 to 100% (close to the liquid
limit). Consistency limits plot above or on the A-line on the Casagrande plasticity chart,
indicating a clay of intermediate to high plasticity. The unit weight increases from about
γ = 14 kN/m3 at the mudline to about γ = 18 kN/m3 at about 3.5 m (limit of the sampling
depth). Figure 8.3 shows profiles of undrained shear strength, s , with depth derived
u
from piezocone and piezoball tests, and calibrated using lab shear vane data and fall
cone tests, to give piezocone bearing factors N = 17.8 (5 cm2 cone) and N = 16.9 (10
kt kt
cm2 cone), and piezoball bearing factors N = 11.5 (50 cm2 ball) and N = 12.2 (100
ball ball
cm2 ball), similar to that suggested by Low et al. (2010). The s profile is best idealised
u
as s = 2 + 2.8z (kPa) over the upper 5 m of the penetration profile, which is the depth
u
of interest for the DEPLA tests. The piezoball tests including cyclic remoulding
episodes, where the piezoball was moved vertically by ± 0.5 m (4.4 to 6.25 piezoball
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8.4 Instrumented reduced scale DEPLA
The DEPLA was modelled at a reduced scale of 1:4.5, based on a full scale anchor with
a follower length of 9 m (appropriate for typical mobile drilling operations). It was
manufactured from mild steel with a total mass, m = 388.6 kg, of which the follower
mass, m = 297 kg and the plate mass, m = 91.6 kg. A schematic of the model DEPLA
f p
and the notation used for the main dimensions are shown in Figure 6.1, with the main
dimensions of the anchor summarised in Table 6.1. The onshore trials reported by Blake
at al. (2014) and Blake and O’Loughlin (2015) tested this same 1:4.5 scale anchor and
two smaller anchors at scales of 1:7.2 and 1:12. As these data are also considered
throughout the chapter their dimensions are masses are also listed on Table 6.1. 12 mm
diameter Dyneema SK75 rope was used to install the DEPLA (and to retrieve the
follower) and as the mooring line connected to one of the DEPLA flukes.
The DEPLA follower was solid, except for a 185 mm long, 42 mm diameter void at the
top of the follower, which housed a custom-design, low-cost, six degree of freedom
Inertial Measurement Unit (IMU). The IMU includes a 16 bit three component MEMS
rate gyroscope (ITG 3200) and a 13 bit three-axis MEMS accelerometer (ADXL 345).
The gyroscope had a resolution of 0.07 °/s with a measurement range of +/- 2000 °/s.
The accelerometer had a resolution of 0.04 m/s2 with a measurement range of +/-16 g.
Data were logged by an mbed micro controller with an ARM processor to a 2 GB SD
card at 400 Hz. Internal batteries were capable of powering the logger for up to 4 hours.
The IMU was contained in a watertight aluminium tube 185 mm long and 42 mm in
diameter.
The IMU measurements were relative to the body-axis of the DEPLA which was free to
pitch and/or roll during free-fall in the water column and embedment in the soil. Hence,
it was necessary to convert these measurements to a fixed inertial frame of reference
using transformation matrices as described in detail by Blake et al. (2016).
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8.5 Test procedure
The field trials were conducted from the RV Aora, a 22 m research and survey vessel in
Firth of Clyde (see Figure 5.10) equipped with several winches and an 8 tonne crane.
The testing procedure involved the following stages:
1. The IMU was powered up and secured in the follower.
2. The DEPLA was assembled on the deck of the RV Aora by lowering the follower
through the flukes and connecting the follower and flukes with a shear pin (see
Figure 8.5)
3. The anchor was then lowered in the water to the required drop height and then
released by opening a quick release shackle connecting the follower retrieval line to
the crane, allowing the anchor to free-fall and penetrate the seabed.
4. The anchor tip embedment depth, z , was measured by sending a remotely operated
e
vehicle to the seabed to inspect markings on the follower retrieval line (see Figure
8.6).
5. Following dynamic installation the load cell was connected in series with the winch
cable and follower retrieval line, and the winch was used to extract the follower at
approximately 30 mm/s. Movement of the follower relative to the stationary flukes
causes the shear pin to break, allowing the follower to be retrieved to the vessel
deck.
6. The plate anchor mooring line was then connected to the winch cable and a draw
wire sensor was connected in parallel with the winch cable to allow for monitoring
of the line displacement. The plate was loaded using the winch, which caused the
winch line to move at 30 mm/s (as for the follower retrieval) and effected the keying
and capacity mobilisation of the DEPLA plate. This was continued until the DEPLA
plate was retrieved from the seabed and recovered on the vessel deck.
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Table 8.1. Summary of field test results at the Firth of Clyde
Test Anchor Anchor Anchor tip Anchor Peak Initial plate Final plate Plate Anchor
no. release impact embedment, travel anchor embedment embedment embedment capacity
height, velocity, z (m) distance, capacity, depth, depth, ratio, factor,
e
(m) v (m/s) s (m) F (kN) z (m) z (m) z /D N
i z vp e,plate,0 e,p,final e,p,final c
1 42.508 12.9 4.010 4.19 31.2 2.4 1.589 2 9.4
2 40.552 12.4 3.685 3.8 32 2.075 1.264 1.6 11.2
3 48.426 11.5 3.292 3.46 29.5 1.682 0.871 1.1 12.9
4† 47.223 11.4 3.504 3.76 - - - - -
5# 46.464 12.3 3.874 4.22 - - - - -
6 49.3# - 3.7* - 21.9 2.090 1.279 1.6 7.6
7 47.25 11.8 3.326 3.62 25.6 1.716 0.905 1.1 10.9
8 48.797 12.1 3.386 4.15 29.9 1.776 0.965 1.2 12.3
9 47.824 11.7 3.611 3.86 23.8 2.001 1.19 1.5 8.6
10** 48.472 10.8 3.3* - 20.2 1.69 0.879 1.1 9.7
11 50# - 3.7* - 29.5 2.090 1.279 1.6 10.3
12 2.259 5.6 2.754 2.77 6.9 1.144 0.333 0.4 4.2
13 17.678 10.6 3.305 3.53 21.9 1.695 0.884 1.1 9.4
# Determined from RV Aora’s echo sounder measurements.
* Determined from ROV video capture.
† ROV tangled in mooring follower, follower and plate recovered together.
# Load cell data acquisition system failed.
** IMU failed after impact with the lakebed.
8.6.1 Impact velocity and embedment
Anchor impact velocities achieved in the field tests were in the range 5.6 to 12.9 m/s,
corresponding to anchor release heights of 2.3 to 42.5 m. Corresponding anchor tip
embedments were in the range 2.75 to 4.01 m (up to 2 times the anchor length). These
results are shown on Figure 8.7 and compared with results from the onshore trials
(Blake and O’Loughlin 2015) conducted in a lake underlain by clay with a strength
gradient of about 1 kPa/m (i.e. almost 3 times lower than that at Firth of Clyde). Figure
8.7 shows a clear dependence of embedment depth on impact velocity, with similar
dependence for both datasets. Although the stronger soil at the Firth of Clyde site
reduces the embedment depth by about 50%, as will be shown later in the chapter the
anchor capacity is not significantly affected. As shown by O’Loughlin et al. (2013b),
comparisons of embedment trends between anchors of different geometries and mass,
installed in seabeds with different strength profiles can be simplified by considering the
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total energy of the anchor, defined as the sum of the kinetic and potential energy
(relative to the final embedment depth) of the anchor as it impacts the soil:
1
E mv2 m'gz Equation 8.1
total 2 i e
where m' is the effective mass of the anchor (submerged in soil). The data considered
here are plotted in non-dimensional form on Figure 8.8, with tip embedments expressed
as z /d , (where the effective anchor diameter, d accounts for the additional projected
e eff eff
area due to the anchor flukes) and total energy is expressed as E /kd 4 (removing the
total eff
influence of soil strength gradient, k and anchor diameter) together with previously
reported DEPLA field and centrifuge data (O’Loughlin et al. 2014b, Blake and
O’Loughlin 2015) and other available centrifuge and field data for dynamically installed
anchors. The data form a relatively tight band that can be conservatively fitted by the
following expression suggested by O’Loughlin et al. (2013b):
13
z E
e total Equation 8.2
d kd4
eff eff
Where d is calculated from:
eff
4A
d f Equation 8.3
eff
As shown by O’Loughlin et al. (2014b), Equation 8.2 has merit in obtaining a first order
approximation of the anchor scale required for a given mooring design, However, the
normalisation in Figure 8.8 has further benefits as demonstrated later in the chapter.
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8.6.2 Plate anchor capacity
After removing the DEPLA follower, the plate anchor mooring line was tensioned such
that the DEPLA plate was vertically loaded. This loading causes the DEPLA to rotate or
‘key’ in the soil, undergoing a loss of embedment in the process. This is shown clearly
by Figure 8.9, which plots the mooring line displacement, d , as a function of the anchor
v
load, F . Also shown on Figure 8.9 is an example response reported by Blake et al.
vp
(2014) from the onshore site with k = 1 kPa/m. It is worth noting the similar capacity
for both sites despite the much shallower embedment from the Firth of Clyde tests
associated with the much higher strength gradient. This is because the capacity of
dynamically installed anchors such as the DEPLA is governed by the soil strength at the
final embedment depth. Embemdent will be higher in weaker soils and lower in stronger
soils but with approximately the same strength at the final plate embedment depth in
either case.
Although in principle the loss in embedment may be established from the mooring line
displacement (that was measured on the vessel deck), the elongation of the high-
modulus polyethylene (HMPE) rope makes attempts to derive the plate displacement
from the mooring line displacement erroneous and certainly unreliable. This is more
pronounced on Figure 8.9 for the results from Firth of Clyde than for the lake tests
reported by Blake et al. (2014) as the water depth, and hence elongation of the rope, is
much higher at Firth of Clyde. However, the loss in embedment during keying has been
extensively investigated for plate anchors (e.g. Song et al. 2006, O’Loughlin et al. 2006,
Gaudin et al. 2006) and as shown by O’Loughlin et al. (2014b) the loss of embedment
for a DEPLA is similar to that of a geometrically comparable plate and can be
calculated from:
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z 0.144
e,max Equation 8.4
D
e t
0.21.15
DD
Hence for the 1:4.5 scale DEPLA considered here, the loss in embedment is calculated
to be Δz ~1D (or 0.8 m).
e,max
The DEPLA capacity may be expressed as an anchor capacity factor:
F
N v,net Equation 8.5
c A s
p u,p
where F is the peak load minus the submerged weight of the plate anchor in soil, A
v,net p
is the area of the plate and s is the undrained shear strength at the estimated anchor
u,p
embedment at peak capacity, accounting for the loss of embedment calculated using
Equation 8.4. For determination of N using Equation 8.5 to be meaningful it is
c
important that the strain rates associated with mobilisation of anchor capacity are
comparable with those associated with measurement of s . As described earlier, s was
u u
determined using 5 cm2 and 10 cm2 piezocones and 50 cm2 and 100 cm2 piezoballs,
penetrated at the standard 20 mm/s. The average strain rate in the soil surrounding the
penetrometers may therefore be approximated by v/D = 0.25 to 0.18 s-1 and v/D =
ball cone
0.79 to 0.56 s-1. This overall range is comparable (within one order of magnitude) to
v/D = 0.04 s-1 associated with loading of the DEPLA plate. Hence, in this instance
experimental capacity factors may be determined without correction for strain rate
effects, particularly as the penetrometer strength will include effects of strain softening
not included in mobilisation of the peak anchor capacity.
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35
30
)
N
k 25
(
p
v
F
20
,
y
t
i
c
a 15
p
a
c
e 10
t
a
l Test 7
P
5 Test 8
Blake et al. (2014)
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Mooring line displacement, d /D
v
Figure 8.9. Typical load-displacement responses during keying and pullout
N values for the Firth of Clyde trials are compared with other DEPLA centrifuge and
c
field data on Figure 8.10. Evidently the plate anchor embedment at peak capacity for the
current data are much shallower than for the other field and centrifuge data, due to the
much higher strength gradient at Firth of Clyde. Wang and O’Loughlin (2014) report
DEPLA capacity factors derived from large deformation finite element analyses for the
case where soil tension is permitted at the base of the DEPLA plate (the so-called ‘no
breakaway’ or ‘attached’ case) and for the case where soil tension is not permitted at the
base of the plate (the so-called ‘immediate breakaway’ or ‘vented’ case). The results
from these analyses are shown on Figure 8.10 for a fully rough interface and t/D =
0.027 (rather than t/D = 0.0125 as used in the field tests). Experimentally derived
DEPLA capacity factors at deep embedment (i.e. at z/D ≥ 2.5) have a mean N = 14.6,
c
and as shown by Figure 8.10, are in good agreement with the (deep) no-breakaway
capacity factor, N = 14.9. This limiting capacity factor is 13.7% higher than N =
c c
13.11, which is the exact solution for a deeply embedded infinitely thin rough circular
plate (Martin and Randolph 2001), but only 3.5% higher than the numerically derived
N = 14.4 for a deeply embedded rough circular plate with the same t/D = 0.027 (Wang
c
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and O’Loughlin 2014). This suggests that the failure mechanism for a circular plate and
a circular DEPLA are broadly similar for the same plate thickness. For shallow
embedment, the experimentally derived DEPLA capacity factors are in the range N =
c
4.2 to 12.9. These values are much lower than N at deep embedment, which indicates
c
that breakaway may have occurred.
18
b 16
Nc No breakaway
d 14 (N)
n c
a
0 c 12
N
,
c 10
N
,
r
o 8
t
c
a
f 6
y
t i Breakaway (N ), 'z /s = 1.5
c a 4 cb e,p,fimal u
p Breakaway, (Equation 5)
a
C 2 weightless soil (N )
c0
0
0 1 2 3 4 5 6
z /D
e,p,final
Current study
Field data, Blake et al. (2014)
Centrifuge data, O'Loughlin et al. (2014b)
Numerical solutions (Wang and O'Loughlin 2014)
Figure 8.10. Experimental and numerical anchor capacity factors
Several studies including Das and Singh (1994), Merifield et al. (2001, 2003), Wang et
al. (2010) and Wang and O’Loughlin (2014) have shown that the immediate breakaway
capacity factor may be expressed as:
'z
N N e,plate N Equation 8.6
cb c0 s c
u
where N is the immediate breakaway capacity factor in weightless soil (also shown on
c0
Figure 8.10) and the dimensionless term, γ'z/s , captures the effect of overburden
u
pressure. Figure 8.10 shows that at deep embedment the experimentally derived
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capacity factors are in quite good agreement with the numerical no-breakaway values,
whereas at shallower embedment (i.e. relating to the current dataset), the experimental
capacity factors lie within the bounds of the (soil weight adjusted) immediate
breakaway case (Equation 8.6) and the no-breakaway case. This observation appears
completely reasonable as at shallow embedment the failure mechanism extends to the
soil surface, such that the gap formed during breakaway may be filled with the free
water above the mudline. In contrast, at deep embedment where the mechanism is
localised, the formation of a gap beneath the DEPLA plate appears implausible as (for
this rate of loading) water would not be able to fill the void.
8.6.3 Embedment depth prediction model
For typical offshore seabed deposits that are generally characterised by increasing
strength with depth, reliability in the calculated anchor capacity firstly requires accurate
prediction of the final anchor embedment depth after dynamic installation. In practice
this can be confirmed by retrieving instrumentation of the type used in these tests from a
‘pod’ located on the exterior of the anchor (Lieng et al. 2010), but from a design
perspective the final embedment depth needs to be precalculated so that the anchor can
be scaled for the design mooring line load. As shown by Figure 8.8, a first order
estimate of the embedment depth for a given anchor geometry, mass and seabed
strength profile may be obtained using Equation 8.2. However, this approach does not
capture subtleties of the dynamic embedment process, including the influence of the
variation in soil strength with strain (i.e. sensitivity) or strain rate, or geometrical
aspects of the anchor that may influence the hydrodynamic response. A more rigorous
approach would be to consider the forces acting on the anchor during dynamic
embedment in soil and to calculate anchor velocities and displacements from the net
acceleration associated with the resultant force. Several studies (e.g. True 1976,
Levacher 1985, Beard 1981, Aubeny and Shi 2006, Audibert et al. 2006, O’Loughlin et
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al. 2004b, 2009, 2013b) have adopted such an approach, with variations on the inclusion
and formulation of the various forces acting on the anchor (or projectile) during
penetration. Figure 8.11 shows the forces acting on the DEPLA during embedment in
soil. Consideration of these forces leads to a governing equation of:
d2s
m W F R (F F )F F Equation 8.7
dt2 s b f frict bear d,a d.l
where m is the anchor mass, z is depth , t is time, W is the submerged anchor weight (in
s
water), F is the buoyant weight of the displaced soil, R is a shear strain rate function,
b f
F is the bearing resistance, F is the frictional resistance and F is the inertial drag
bear frict d
resistance. The added mass, m', in Equation 8.7 is the ‘added’ mass of the soil that is
accelerated with the anchor. However for slender bodies such as the DEPLA, m' is
negligible and can be taken as zero (Beard 1981, Shelton et al. 2011). Frictional and
bearing resistances are formulated as
F s A Equation 8.8
frict u
F N s A Equation 8.9
bear c u
where α is a friction ratio (of limiting shear stress to undrained shear strength), N is the
c
bearing capacity factor for the projectile tip or fluke, and s is the undrained shear
u
strength averaged over the contact area, A.
The inclusion of F in Equation 8.7 may appear controversial as this term is typically
d
associated with a fluid mechanics framework for Newtonian materials. However, it is
also justified for the (non-Newtonian) very soft fluidised soil typically encountered at
the surface of the seabed, and has been shown to be important for assessing loading
from a submarine slide runout on a pipeline (Boukpeti et al. 2012, Randolph and White
2012, Sahdi et al. 2014). O’Loughlin et al. (2013b) and Blake and O’Loughlin (2015)
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further showed that fluid drag is the dominant resistance acting on a dynamically
installed anchor in normally consolidated clay during initial embedment and typically to
about 30% of the penetration. Inertial drag resistance includes pressure drag created by
the pressure gradient between the rear and the front of the projectile and friction drag
generated by viscous stresses that develop in the boundary layer between the anchor and
the soil. For a free-falling anchor at the high non-Newtonian Reynolds numbers
associated with dynamic installation, the pressure drag component is due to the frontal
area of the anchor, whereas the friction drag component is mainly due to the contact
area of the trailing mooring and follower recovery lines. The fluid drag resistance terms
are formulated as (Fernandes et al. 2006):
v2
F F F C A C A Equation 8.10
d d,a d,l 2 d,a s f d,l w s
where C is the drag coefficient of the anchor, C is the drag coefficient of the line, ρ
d,a d,l s
is the density of the soil, A is the frontal area of the anchor, A is the surface area of the
f s
line in contact with water and v is the anchor (and hence line) velocity. It is worth
noting that Equation 8.10 uses the density of water rather than soil for the drag on the
lines as for most applications most of the contact with the line will be in water,
particularly if the hole caused by the passage of the anchor remains open. ROV video
capture of the drop sites (see Figure 8.6) showed an open crater. Sabetamal (2014) used
the Arbitrary Lagrangian Eulerian method in finite element analyses to show that the
hole formed by the passage of the anchor would close immediately at a strength ratio,
s /γ'D = 3.6, but would stay open at a strength ratio, s /γ'D = 10.6. This is consistent
u u
with the field data, which have an average strength ratio at the top of the follower,
s /γ'D = 7.3, and also with experimental work reported by Morton et al. (2014) that
u
shows that at this strength ratio, hole closure would be expected at a tip embedment of
3.85 m, which is the limit of the embedments achieved in the field tests (see Table 8.1).
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Drag coefficients for the anchor and the lines can be established from acceleration data
measured during free-fall in water using a reduced form of Equation 8.7 that does not
include the geotechnical resistance terms:
d2z v2
m W F W C A C A Equation 8.11
dt2 s d s 2 d,a s f d,l w s
where d2z/dt2 is the measured acceleration. Equation 8.11 includes two unknowns, C
d,a
and C . C is best selected by optimising the fit between the theoretical and
d,l d,a
experimental velocity profiles at depths less than the terminal velocity where pressure
drag dominates the resistance, whereas C may be obtained by considering the fit at
d,l
depths greater than the terminal velocity when additional drag resistance is due solely to
the increase in drag resistance on the lines. Example comparisons are provided in Figure
8.12, where the theoretical velocity profile was established from a finite difference
approximation of Equation 8.11 and the experimental velocity profile was established
from double numerical integration of the measured acceleration data (see Blake et al.
2016 for further details). In this instance C = 0.7 and C = 0.004 and 0.005 provide
d,a d,l
the best fit to each dataset. The latter are lower than C = 0.015 reported by Blake and
d,l
O’Loughlin 2015) for the onshore site, and is considered to be due to the different
anchor deployment and line arrangement at each site.
The frictional resistance term in Equation 8.8 comprises friction on the follower, sleeve
and flukes, whereas the bearing resistance term in Equation 8.9 comprises bearing on
the follower tip and at the base and upper end of the flukes (but not at the upper end of
the follower due to the assumption that the cavity created by the passage of the
advancing anchor remains open).
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Velocity, v (m/s)
0 2 4 6 8 10 12 14
0
Lf
/ 5
'z
,e
c
n
a 10
t
s
i
d
l
l
a f 15
- e C = 0.005
e d,l
r
f
d e 20 C = 0.004
s d,l
i
l
a
m
r 25
o
N Measured
Equation 8.11
30
Figure 8.12. Determining drag coefficients C and C by optimising the fit
d,al d,l
between measured and theoretical velocity profiles in water
Soil strength depends on the rate at which it is sheared. This has been quantified in
laboratory element tests reported by Vade and Campenella (1977), Graham et al.
(1983), Lefebvre and Leboeuf (1987) and others, where a 10 to 20% increase in
undrained shear strength was typically observed for every log cycle increase in shear
strain rate. Similar dependence has been observed in shear vane tests (e.g. Biscontin and
Pestana 2001, Peuchen and Mayne 2007) and in variable rate penetrometer tests (Chung
et al. 2006, Low et al. 2008, Lehane et al. 2009). This dependence of shear strength on
shear strain rate is generally formulated using either semi-logarithmic or power
functions (e.g. Biscontin and Pestana 2001), with the power function being more suited
to the higher orders of magnitude variation in shear strain rate associated with dynamic
installation problems. The power law function is expressed as:
R Equation 8.12
f
ref
where β is a strain rate parameter,γ is the strain rate and γ is the reference strain rate
ref
associated with the reference value of undrained shear strength. A similar formulation,
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originating from fluid mechanics, is the so-called Herschel-Bulkley law. This law
describes the same form of strain rate dependence as the power law, but avoids the need
to limit R at strain rates lower than the reference strain rate by also including a limiting
f
yield stress, making it more suited to implementation in numerical models. During
dynamic penetration, the shear strain rate will vary through the soil body, but for
shearing around an axially loaded cylindrical object such as the DEPLA, it is reasonable
to assume that at any given location the operational strain rate will be proportional to
the normalised velocity, v/d, such that Equation 8.12 may be replaced by:
v d v d
R n or n Equation 8.13
f v d
ref ref
If the reference strength is determined from laboratory element tests, γ in Equation
ref
8.13 is the strain rate employed in the element test, whereas if the reference strength is
determined from a penetrometer test (such as the cone, T-bar or ball),γ may be
ref
approximated by (v/d) , where v is the penetration velocity and d is the diameter of the
ref
penetrometer. An important point to note is that in situ strengths determined from
penetrometer tests are typically similar in magnitude to those determined in the
laboratory (Low et al. 2010), despite a typical 5 orders of magnitude difference in the
strain rates associated with the laboratory test (e.g. 1%/hr, 3 × 10-6 s-1) compared with
approximately 0.18 s-1 associated with for example a piezoball test (Randolph et al.
2007). This is due to the compensating effects of strain softening associated with the
penetrometer strength and lower strain rate dependency at strain rates closer to the
laboratory strain rate (Hossain and Randolph, 2009). Hence, caution is required if
Equation 8.13 is adopted using a laboratory reference strain rate and strength, as the
(intact) laboratory strength needs to be adjusted to reflect the strain softening associated
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with a penetrometer or anchor installation and the strain rate dependency needs to be
more moderate over the first few decades increase in strain rate.
The parameter n in Equation 8.13 is introduced to account for the greater rate effects
reported for shaft resistance compared to tip resistance (Dayal et al. 1975, Steiner et al.
2014, Chow et al. 2014). It is quite probable that the higher rate effect for shaft
resistance is due to the higher strain rate at the cylindrical shaft involving curved shear
bands, which can be estimated to be about 20 to 40 times v/d (for β = 0.10 and 0.05
respectively) using a rigorous energy approach maintaining equilibrium (Einav and
Randolph 2006). Therefore, n is taken as 1 for bearing resistance (Zhu and Randolph
2011) and as a function of β (adopted from Einav and Randolph 2006) for estimating
rate effects in frictional resistance according to:
n
n2 1 n 2 Equation 8.14
1
where n is taken as 1 for axial loading.
l
The acceleration data measured during penetration allows for an assessment of the
suitability of the power law at the high strain rate associated with dynamic embedment.
R values for bearing and friction may be back-analysed from the acceleration data by
f
rearranging Equation 8.7, noting that R = nβR to give:
f,frict f,bear
d2z
W m F F
s dt2 b d
R Equation 8.15
f,bear nF F
frict bear
R values for bearing and friction were obtained from the acceration data using C =
f d,a
0.7 as determined from the free-fall in water phase of the test (see Figure 8.12), but
taking C = 0 for penetration is soil, as the lines were assumed to become slack on
d,l
impact with the relatively strong seabed at Firth of Clyde. Bearing resistance was
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calculated using Equation 8.9 using N = 12 for the follower tip (O’Loughlin et al.,
c
2013b) (but not for the padeye as the hole formed by the passage of the anchor was
assumed to remain open during anchor penetration) and N = 7.5 for the leading and
c
trailing edges of the flukes (analogous to a deeply embedded strip footing). The strain
rate parameter was fixed at β = 0.08, which is typical of that measured in variable rate
penetrometer testing (Low et al. 2008, Lehane et al. 2009) and approximates to an 18%
change per log cycle change in strain rate, typical of that measured in laboratory testing
as discussed earlier. The back-analysed values of R for friction and bearing (denoted as
f
‘measured’ in Figure 8.13) are compared for two example tests in Figure 8.13 with R
f
formulated using the power law (Equation 8.13). The best agreement between the
backfigured R and that predicted by the power law was obtained using α = 0.22 (Test
f
12) and 0.29 (Test 2). This is within the range established from cyclic piezoball
remoulding tests, which gave q /q = 0.2 to 0.32. Encouragingly, the power law is
in rem
seen to satisfactorily quantify the correct amount and variation in strain rate dependence
over the range of strain rates associated with dynamic penetration. However, Figure
8.13 also plots the same R data against depth, revealing that there are other mechanisms
f
during initial penetration that are not captured by Equation 8.7. Nonetheless, Figure
8.14 shows that the embedment model is seen to predict the experimental velocity
profiles with bounds on α of 0.22 and 0.29, similar to the bounds of q /q from the
in rem
cyclic piezoball remoulding tests. More importantly the final embedment depths are
predicted accurately, which in turn increases the reliability of anchor capacity
calculations. This is made clear by Figure 8.15, which shows embedment test data for
all the Firth of Clyde tests together with the corresponding embedment model
predictions using an average α = 0.26, presented in the ‘total energy’ format of Figure
8.14. Also shown on Figure 8.15, are predictions formulated using Equation 8.2, which
are in good agreement with the experimental data and the embedment model
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E /kd 4
total eff 3
0 1 2 3 4 5 6 7 8 9 10× 10
0
Measurements
Embedment model = 0.26)
Equation 8.2
5
10
dffe
z/e
15
20
25
Figure 8.15. Measured and predicted DEPLA follower tip embedments
8.7 Design approach
Figure 8.16 summarises embedment predictions made using Equation 8.7 for s = 0 (at
u
the mudline), undrained strength gradients, k = 1, 2 and 3 kPa/m and interface friction
ratios, α = 0.1, 0.2, 0.3, 0.4 and 0.5 (α may be determined from the inverse of the soil
sensitivity as assessed from piezoball cyclic remoulded tests i.e. α = 1/S). In this
t
example β = 0.08, which is typical of that derived from variable rate penetrometer
testing in normally consolidated clay (Low et al. 2008, Lehane et al. 2009), although
additional charts may be generated for different strain rate parameters and indeed
different strength gradients. Although total energy is normalised by the strength
gradient, the predicted embedments still demonstrate some dependence on k, which is to
be expected as the normalisation does not account for inertial drag which will vary
relative to the shear resistance as the strength gradient changes. Figure 8.16 can be used
to scale a DEPLA for a given design load as described in the following steps and
summarised schematically in Figure 8.17:
1. Select a DEPLA plate diameter, D, thickness, t, and padeye eccentricity, e.
2. Calculate the embedment depth loss of the plate, Δz using Equation 8.4.
e,plate
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3. Select a capacity factor from Figure 8.10: N = 14.9 assuming deep embedment
c
(z ≥ 2.5D).
e,p,final
4. Calculate the required follower tip embedment, z , required for the chosen D value,
e
using a modified version of Equation 8.5:
F
z vp z L H Equation 8.16
e N kA e,plate f s
c p
5. Select the other anchor dimensions (L, D, L , t, t , H etc.).
f f tip s s
6. Calculate z using the expression:
e,p,final
z z L 0.5H z Equation 8.17
e,p,final e f s e,plate
7. If z ≥ 2.5D, proceed to step 7, if z < 2.5D repeat steps 1 to 6 choosing an
e,p,final e,p,final
alternative D.
8. Calculate the anchor mass, m, and effective mass, m'.
9. Calculate the anchors impact velocity, v, based on 80% of terminal velocity, v (this
i t
is a simplified and conservative approach to account for the drag of the follower
recovery line and mooring lines):
2mg
v 0.8v 0.8 Equation 8.18
i t A C
w f d,a
10. Calculate the total energy, E, using Equation 8.1.
t
11. Calculate the effective diameter of the anchor, d : using Equation 8.3.
eff
12. Repeat steps 1 to 11 until the normalised tip embedment, z /d , sit on the prediction
e eff
line for the required k and α in Figure 8.16.
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E /kd 4
total eff 3
0 2 4 6 8 10 12 14× 10
5
k = 1 kP/a
k = 2 kP/a
k = 3 kP/a
10
Site B:
D = 3.8 m, L = 9.5 m
f
m = 33 t, m = 26 t
15 f p
d
z/ff
ee
S
D
mi t =e
=
4A 4.:
21 tm
,
,
m
L
f
== 31 30 . t3 m
20 f p
25
= 0.1, 0.2, 0.3, 0.4, 0.5
30
Figure 8.16. DEPLA design chart for a range of seabed strength gradients and
interface friction ratios
Two example sites are now considered, making use of the design procedure outlined
above, but limiting the anchor impact velocity to 80% of its terminal velocity to keep
the anchor drop height within practical limits. The first site, referred to as site A has a
mudline strength of 0 and a strength gradient of 1 kPa/m and the second site, referred to
as site B also has a mudline strength of 0, but with a strength gradient of 2 kPa/m. Both
sites have a sensitivity, S = 5, such that α = 0.2. The factored design mooring line load
t
is 5 MN. Site A requires an anchor with a follower length L = 10.3 m, a plate diameter
f
D = 4.1 m and a total anchor mass, m = 75 tonnes, of which the plate = 33 tonnes. Site
t
B requires a smaller anchor, with a follower length L = 9.5 m, a plate diameter D = 3.8
f
m and a total anchor mass, m = 59 tonnes, of which the plate = 26 tonnes.
t
The above example includes a number of simplifying assumptions to demonstrate the
merit of the design approach, but would be refined for an actual design. These include
the loss of embedment during keying, which has been conservatively calculated
assuming vertical loading, whereas the loss of embedment will be lower for inclined
loading (Gaudin et al. 2009, Song et al. 2009, Yu et al. 2009, Wang et al. 2011) and the
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adopted capacity factor which may need to be reduced for inclined loading at shallow
embedment (Song et al. 2005, Wang and O’Loughlin 2014).
Step 1: Select DEPLA plate diameter, D, thickness, t, and padeyeeccentricity, e
Step 2: Calculate the embedment depth loss of the plate, Δz using Equation 8.4
e,plate
Step 3: Select a capacity factor from Figure 8.10: N = 14.9
c
assuming deep embedment (z ≥ 2.5D)
e,p,final
Select
Step 4: Calculate the required follower tip embedment, z, required for the chosen D value,
e alternative
using a modified using Equation 8.16
D
Step 5: Select the other anchor dimensions (L, D, L , t, t, H etc.).
f f tip s s
Step 6: Calculate z using the expression Equation 8.17
e,p,final
Select
alternative
D
Step 7:z ≥ 2.5D? No
e,p,final
Yes
Step 7: Calculate the anchor mass, m, and effective mass, m'
Step 8: Calculate the anchors impact velocity, v, based on 80% of terminal velocity, vusing Equation 8.18
i t
Step 9: Calculate the total energy, E, using Equation 8.1
t
Step 10: Calculate the effective diameter of the anchor Equation 8.18
Step 11: Is z/d , sitting on the prediction line for
No e eff
the required k and α in Figure 8.16?
Yes
Preliminary sizing of DEPLA complete
Figure 8.17. Flow chart for DEPLA design approach
8.8 Conclusions
As part of the development path towards qualification of the DEPLA, a series of
centrifuge and reduced scale field trials, supplemented by analytical and numerical
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studies has been undertaken. This chapter considers the results from the final
experimental campaign, in which field trials on a 1:4.5 reduced scale DEPLA were
conducted in approximately 50 m water depth at a site off the west coast of Scotland.
The data gathered in these trials have been considered in parallel with DEPLA field and
centrifuge data from earlier in the experimental campaign to assess the merit of anchor
embedment and capacity models. The anchor embedment model is cast in terms of
inertial drag resistance and strain rate enhanced shear resistance, the latter described
using a power law with separate dependence for bearing and frictional resistance. Back
analysis of measured acceleration data during dynamic embedment indicated that the
power law is capable of describing the strain rate dependence of undrained shear
strength at the very high strain rates associated with the dynamic embedment process,
although complexities associated with initial embedment (up to one anchor length) are
not captured by the model. However, these shortcomings do not appear to unduly lessen
the capability of the embedment model to predict the measured velocity profiles and
importantly the final anchor embedment depth, which is a prerequisite for reliable
calculation of anchor capacity.
Comparison of the field data from Lough Erne and the Firth of Clyde showed that
similar capacity was achieved at both sites, despite the much shallower embedment
from the Firth of Clyde tests associated with the much higher strength gradient. This is
because the capacity of dynamically installed anchors such as the DEPLA is governed
by the soil strength at the final embedment depth. Embedment will be higher in weaker
soils and lower in stronger soils but with approximately the same strength at the final
plate embedment depth in either case.
Back analysis of anchor capacity from each of the experimental campaigns was
considered in terms of a dimensionless capacity factor and compared with
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CHAPTER 9 CONCLUSIONS
9.1 Summary
The dynamically embedded plate anchor (DEPLA) has been proposed as a cost effective
and technically efficient anchor for deepwater mooring applications. The DEPLA is
rocket or torpedo shaped anchor that comprises a removable central shaft and a set of
four flukes. The DEPLA penetrates to a target depth in the seabed by the kinetic energy
obtained through free-fall in water. After embedment the central shaft is retrieved
leaving the anchor flukes vertically embedded in the seabed. The flukes constitute the
load bearing element as a plate anchor. The DEPLA combines the installation
advantages of dynamically installed anchors (no external energy source or mechanical
operation required during installation) and the capacity advantages of vertical loaded
anchors (sustain significant horizontal and vertical load components).
Despite these advantages there are no current geotechnical performance data for the
DEPLA, as development of the anchor is in its infancy. This thesis has focused on
assessing the geotechnical performance of DEPLAs through an experimental study
involving a centrifuge testing program and an extensive field testing campaign. The
centrifuge tests were carried out on 1:200 reduced scale model DEPLAs in kaolin clay
and are reported in Chapter 4. The centrifuge tests provided early stage proof of concept
for the DEPLA and motivation for subsequent field testing. The tests examined: anchor
impact velocity, initial anchor embedment depth following dynamic installation,
follower recovery load, embedment depth loss due to the keying process and the
subsequent plate anchor capacity.
The field tests were conducted on 1:12, 1:7.2 and 1:4.5 reduced scale DEPLAs
(geometrically similar to those adopted for the centrifuge tests) at two sites: (i) Lough
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Erne, which is an inland lake located in County Fermanagh, Northern Ireland and (ii)
Firth of Clyde (1:4.5 scale anchor only) which is located off the West coast of Scotland.
The reduced scale anchors were instrumented with a custom-design, low cost, six
degree of freedom (6DoF) inertial measurement unit (IMU) for measurement of anchor
motion during installation. This represented the first reported use of a 6DoF IMU for a
geotechnical application. The field tests served to validate the centrifuge findings and
demonstrate DEPLA deployment in an aquatic environment. The field tests provided a
basis for understanding the behaviour of DEPLA during free-fall in water and dynamic
embedment in soil (investigated in Chapters 5, 6 and 8), and quantify the loss in
embedment during keying (examined in Chapter 7) and the subsequent plate anchor
capacity (determined in Chapters 7 and 8). Analytical design tools for the prediction of
DEPLA embedment and capacity were verified, refined and calibrated using the
centrifuge and field data.
9.2 Main findings
9.2.1 Inertial measurement unit
This thesis makes a particular contribution to the body of literature on dynamic
penetration problems by presenting and analysing motion data measured by an IMU
during DEPLA installation. Such data are rarely available, but are important for
assessing the mechanisms associated with dynamic penetration in soil, and represents an
essential step towards anchor qualification.
A comprehensive framework for interpreting the IMU measurements so that they are
coincident with a fixed inertial frame of reference was developed and implemented to
establish anchor rotations, accelerations and velocities during free-fall in water and
embedment in soil. Assessment of this framework showed that embedments calculated
from the body frame acceleration measurements, rather than from accelerations
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