Access to this full-text is provided by Emerald.
Content available from Geotechnique
This content is subject to copyright. Terms and conditions apply.
Monopile rotation under complex cyclic lateral loading in sand
IONA A. RICHARDS, BYRON W. BYRNE†and GUY T. HOULSBY‡
Monopiles supporting offshore wind turbines experience combined moment and horizontal loading
which is both cyclic and complex –continuously varying in amplitude, direction and frequency.
The accumulation of rotation with cyclic loading (ratcheting) is a key concern for monopile designers
and has been explored in previous experimental studies, where constant-amplitude cyclic tests have
shown rotation to accumulate as a power-law with cycle number. This paper presents results from
laboratory tests in dry sand, which explore the rotation response to constant and variable amplitude,
unidirectional and multidirectional cyclic loading. The tests are designed to inform model development
and provide insight into key issues relevant to monopile design. Unidirectional tests show behaviour
consistent with previous studies and provide a basis for interpreting more complex tests;
multidirectional tests provide new insight into the monopile response to multidirectional cyclic
loading; and multi-amplitude storm tests highlight salient features of the response to realistic loading.
Tests are conducted in both very loose and dense sand, where the behaviour is found to be qualitatively
similar.
KEYWORDS: laboratory tests; piles & piling; repeated loading; sands; soil/structure interaction
INTRODUCTION
The vast majority of offshore wind turbines (OWTs) are
supported on monopile foundations; in Europe monopiles
represent 87% of all installed OWT foundations (Wind
Europe, 2018). The monopile’s prevalence is largely due to
their simple design, robust installation procedures and
established supply chain. These large-diameter open-ended
steel piles have increased in size over time to support larger
OWTs, and in deeper water, as the industry has matured.
Modern monopiles have diameters up to 8 m (Sørensen
et al., 2017) with length (L) to diameter (D) ratios (L=D)of
3–6 (Schroeder et al., 2015; Sørensen et al., 2017); next-
generation monopiles might be 10 m in diameter. The OWT
structure is exposed to significant lateral loads caused by
a combination of wind, waves and current. The resultant
combined moment and horizontal loads experienced by the
monopile are cyclic and complex, varying continuously in
amplitude, direction and frequency.
The recent PISA project focused on understanding, and
developing better methods to predict, the monopile’s
response to monotonic lateral loading, which is necessary
for ultimate limit state (ULS) design and provides initial
stiffness values for initial natural frequency calculations
(Byrne et al., 2017). This work demonstrated the inherent
conservatism embedded in design guidelines originally
developed for slender piles used in the offshore oil and gas
industry (e.g. API, 2011; DNV GL, 2016), and should enable
the design of more efficient monopiles. However, as con-
servatism in ULS design is reduced, and as the magnitude of
cyclic lateral loads increase with increasing monopile
diameter, increasing water depth and increasing turbine
size, design for cyclic lateral loading becomes more
important. Turbine manufacturers typically specify strict
tolerances on OWT structure rotation over their lifetime, and
accumulation of foundation rotation due to cyclic loading
(ratcheting) is a key concern.
Many previous experimental studies have explored the
monopile response to cyclic lateral loading in sands,
providing valuable insight. Most studies have focused on
the monopile rotation response under constant-amplitude,
unidirectional cyclic loading, with studies performed at both
1g(e.g. Leblanc et al., 2010a; Nicolai & Ibsen, 2014; Arshad
& Kelly, 2017) and in the centrifuge (e.g. Klinkvort &
Hededal, 2013; Truong et al., 2019). The monopile response
to fan-type multidirectional loading has also been explored
at 1g(Dührkop & Grabe, 2008; Rudolph & Grabe, 2013) and
in the centrifuge (Rudolph et al., 2014a), where multi-
directional loading was found to be more damaging than
unidirectional loading.
Monopile rotation has typically been found to evolve as
a power-law with cycle number, and empirical relationships
have been widely used to capture this behaviour (Leblanc
et al., 2010a; Klinkvort & Hededal, 2013). Achmus et al.
(2009) incorporated a semi-empirical power-law expression
into an elasto-plastic soil model to allow numerical calcu-
lation of monopile displacement, and this method has been
shown to predict the results of Leblanc et al. (2010a) with
reasonable accuracy. Meanwhile, Bayton et al. (2018) used
centrifuge testing to develop contour diagrams, following the
Norwegian Geotechnical Institute (NGI) cyclic degradation
approach (Andersen, 2015), which allow prediction of a
monopile’s response to multi-amplitude cyclic loading.
Linear superposition methods have also been adopted for
multi-amplitude loading (Leblanc et al., 2010b).
Although empirical methods and the cyclic degradation
approach provide insight into the monopile’s response to
cyclic lateral loading and may be useful for initial design,
they are not well adapted for prediction of the monopile
response to the complex cyclic loading that would be
Department of Engineering Science, Oxford University, Oxford,
UK (Orcid:0000-0003-4241-6031).
†Department of Engineering Science, Oxford University, Oxford,
UK (Orcid:0000-0002-9704-0767).
‡Department of Engineering Science, Oxford University, Oxford,
UK (Orcid:0000-0001-5807-8781).
Manuscript received 12 November 2018; revised manuscript
accepted 22 August 2019. Published online ahead of print
26 September 2019.
Discussion on this paper closes on 1 February 2021, for further
details see p. ii.
Published with permission by the ICE under the CC-BY 4.0 license.
(http://creativecommons.org/licenses/by/4.0/)
Richards, I. A. et al. (2020). Géotechnique 70, No. 10, 916–930 [https://doi.org/10.1680/jgeot.18.P.302]
916
experienced in the field. For example, it is not clear how these
methods can account for the impact of multi-amplitude load
order, which appears to be significant, particularly when load
amplitude and average load varies between load packets
(Truong et al., 2019), and adaptation for multidirectional
loading is likely to be challenging.
Models based on multi-surface plasticity are able to
capture hysteretic behaviour, can respond to any arbitrary
load history and can be adapted for multidimensional
loading. Page et al. (2018) developed a multi-surface
macro element for application to monopiles in clays, while
Houlsby et al. (2017) developed a flexible multi-surface
model supplemented with a ratcheting component (hyper-
plastic accelerated ratcheting model (HARM)). HARM has
been shown to predict the response of a monopile to constant
and multi-amplitude cyclic loading at both model scale
(Abadie et al., 2019a) and large scale (Beuckelaers, 2017).
However, validation of the performance of HARM under
complex loading, and development of the calibration
procedure for full-scale design, is necessary.
This paper explores the response of a monopile to
unidirectional, multidirectional and multi-amplitude storm-
type cyclic loading through 1gmodel tests. These tests
provide insight into the monopile’s response to complex
cyclic loading, and have been designed to facilitate develop-
ment of models in the HARM framework. The uni-
directional tests add to the growing database of similar
tests performed at 1gand in a centrifuge, demonstrating
consistent behaviour, providing a basis for understanding
the response to more complex loading, and later informing
model calibration. The multidirectional cyclic response is
then explored through perpendicular and radially spread
(fan-type) loading tests. These constant-amplitude tests are
not intended to be completely realistic, but instead provide
insight into the monopile’s fundamental multidirectional
behaviour and can inform multidirectional model develop-
ment. Finally, multi-amplitude, unidirectional and multi-
directional storm-type loading is applied to the model
monopile. These tests begin to show how behaviour observed
in contrived laboratory tests may translate to behaviour
under realistic cyclic loading; these tests may also be useful
for model validation.
Several important phenomena occur during cyclic loading.
Alongside ratcheting of the monopile, evolution of cyclic
stiffness and hysteretic damping with cycles has been
observed (Leblanc et al., 2010a; Klinkvort & Hededal,
2013; Abadie et al., 2019b), which is of concern for foun-
dation designers. The response of a monopile to a single
large load following cycling is also an important concern.
However, this paper focuses primarily on the important
phenomenon of evolution of monopile rotation, or ‘ratchet-
ing’, under many cycles.
LABORATORY-SCALE TESTS
Laboratory set-up
Figure 1 shows the laboratory apparatus used to investigate
the response of a model monopile to cyclic lateral loading.
A rigid, hollow aluminium pile was used, at approximately
1:100 scale, with diameter D= 80 mm, wall thickness
t= 5 mm and an embedded length L= 320 mm (L=D¼4).
The pile is classified as smooth (average surface roughness,
Ra¼06μm) in contrast to typically rough full-scale mono-
piles; however, surface roughness has been shown to have
only a small impact on the monopile’s lateral response
(Klinkvort, 2012). Following sand sample preparation, the
pile was driven to the target embedment manually using a
gravity hammer with drop height 300 mm and mass 1·4 kg
and 2·8 kg for very loose and dense samples, respectively.
Continually varying, multidirectional lateral load can be
applied under load control with two electric actuators at
a fixed eccentricity of h= 800 mm (h=L¼25), while six
displacement transducers allow resolution of the monopile’s
position in six degrees of freedom. Further details on the
apparatus design and associated software can be found in the
paper by Richards et al. (2018).
Sand sample
The sand sample was prepared in a cylindrical tank with
internal diameter 800 mm (10D) and height 800 mm, chosen
to be practical while introducing minimal boundary effects,
in line with, for example, the numerical investigation of
Achmus et al. (2007). Yellow Leighton Buzzard 14/25 sand,
with properties summarised in Table 1, was used for the tests
presented here. Tests were conducted at two sand densities,
and all tests were in dry sand to model fully drained
conditions. Very loose samples were prepared by manual
pouring from a very low drop height to achieve a unit weight
of γ′¼1446 kN=m3+06%, corresponding to a relative den-
sity RD¼1%. Dense samples were prepared by air pluvia-
tion with a purpose-built sand-raining apparatus, achieving
a unit weight of γ′¼1620 kN=m3+04%, corresponding
to a relative density RD¼60%. Conical depressions with
diameter around 2Dwere observed following pile installation
at both densities, indicative of some local densification.
The stated relative densities must therefore be considered
pre-installation values.
The interaction between stress level, relative density and
friction angle is important for laboratory-scale tests. Given
the lower stress level at model scale, the sand relative density
should be reduced to better approximate dilation and
friction angles at full scale, where the stress level is higher
(Bolton, 1986, 1987; Altaee & Fellenius, 1994). The
relationship presented by Bolton (1986) is commonly used
to calculate corresponding model- and full-scale relative
densities (Leblanc et al., 2010a; Zhu et al., 2017). However,
there are limited data supporting the proposed relationship of
Bolton (1986) at very low stress levels, and the relationship
was subsequently modified (Bolton, 1987) to limit dilatant
behaviour at very low stress levels.
Pile
Two actuators
Two load cells
Six displacement
transducers
Fig. 1. Laboratory apparatus
MONOPILE ROTATION UNDER COMPLEX CYCLIC LATERAL LOADING IN SAND 917
The dilatant behaviour of sands at very low stress levels is
still relatively poorly understood. Therefore, the relations
from Bolton (1986, 1987) are used to provide upper and
lowerestimates, respectively, of the full-scale relative densities
equivalent to the laboratory tests. Using equations (16) and
(14) from Bolton (1986), and using the updated equation
for relative dilatancy index presented by Bolton (1987),
expressions for friction angle ϕ′
pat model-scale and full-scale
representative stress levels are equated and solved for
full-scale relative density. The vertical effective stress at
70% pile embedment (σ′
v¼07γ′L) is chosen as the repre-
sentative stress.
Table 2 shows how the very loose sample at model scale
unambiguously represents a very loose sample at full scale;
however, Bolton’s two methods give a wide range for the
equivalent dense sample at full scale (65 RD115%). The
equivalent full-scale density could only be resolved
with further research into sand behaviour at very low stress
levels, specifically examining the variation of dilatancy with
stress level, as reported by, for example, Lauder & Brown
(2014). Here, the exact equivalent full-scale density for the
denser sample is left open, and referred to as ‘dense’
throughout.
Scaling and normalisation
Leblanc et al. (2010a) derived a dimensionless framework
for laterally loaded monopiles, incorporating an established
relationship between shear modulus and stress level. Table 3
presents the key dimensionless parameters which can be used
to translate between model scale and full scale. However, to
facilitate comparison of results in very loose and dense sands
it is more useful to normalise the data by moment and
rotation reference values (MR;θR). Typically monopiles
in sand do not reach well-defined failure, and instead
show continued hardening to large rotations. It is therefore
necessary to (arbitrarily) define a reference rotation or
displacement value, from which a reference load value can
be determined. A variety of different reference rotation and
displacement values have been used by previous researchers
in this area; for example, Leblanc et al. (2010a) use a
dimensionless rotation of 4°, Abadie (2015) uses pile ground
level displacement of 0·1Dat model scale, Arshad & O’Kelly
(2017) use a rotation of 1·5° at model scale, while Bayton
et al. (2018) define a reference rotation of 0·25° on unloading
to correspond to the serviceability limit state suggested by
DNV GL (2016). In this work a reference rotation θR¼2°at
model scale is defined, broadly consistent with Abadie (2015)
and Arshad & O’Kelly (2017). According to the dimension-
less framework of Table 3, this corresponds to a larger
reference rotation at full scale; however, the results could be
recast with different reference values if required.
Monotonic response
The monotonic response of the monopile is an essential
reference point for the cyclic behaviour and must be
established first. Fig. 2(a) shows the average monotonic
response from three pile tests at each density, while Figs 2(b)
and 2(c) show the normalised average monotonic response,
with upper- and lower-bound responses shown dashed. For
the very loose sample, the tests were conducted in three
different directions to check the invariance of the apparatus
to load direction. Taking θR¼2°gives projected values of
MR¼26 Nm for the very loose sample and of MR¼95 Nm
for the dense sample. Rate effects were investigated for
loading rates between 008 and 08Nm=s for the very loose
sample, and found to be negligible.
Cyclic definitions
Figure 3 shows a schematic representation of the cyclic
loading response. Rotation per cycle is defined at the average
cyclic load magnitude (MAV ¼1=2ðMMIN þMMAXÞ),
as the mean of the rotation value on reload and unload,
indicated by points ‘a’and ‘b’respectively. For constant-
amplitude loading, MAV is constant, whereas for multi-
amplitude loading MAV varies with each reload or unload
half-cycle (e.g. MR;AV;n;MU;AV;n). For both cases the total
mean rotation at cycle nbecomes
θMn¼1
2θanþθbn
ðÞ ð1Þ
Cycle 0 is defined for constant-amplitude loading as the
first load–unload cycle, corresponding to the undisturbed
response. With cycle 0 defined, the accumulated mean
rotation at cycle nis
ΔθMn¼θMnθM0ð2Þ
Table 2. Relative densities at model scale and full scale
Model-scale R
D
: % Lower estimate full-scale R
D
:%
(Bolton, 1987)
Upper estimate full-scale R
D
:%
(Bolton, 1986)
Classification at full scale
1·0 1·1 1·1 Very loose
60 65 115 Dense to very dense
Table 1. Yellow Leighton Buzzard 14/25 sand properties
Particle sizes: mm D10;D30 ;D50;D60 0·56, 0·69, 0·81, 0·87
Maximum unit weight: kN/m
3
γ′
MAX 17·64
Minimum unit weight: kN/m
3
γ′
MIN 14·43
Critical friction angle (Schnaid, 1990): degrees ϕ′
cr 34·3
Table 3. Key dimensionless parameters (Leblanc et al., 2010a)
Horizontal force
˜
H¼H
L2Dγ′
Moment
˜
M¼M
L3Dγ′
Rotation
˜
θ¼θffiffiffiffiffiffiffi
pa
Lγ′
r
Eccentricity ˜
e¼h
L
RICHARDS, BYRNE AND HOULSBY918
Accumulated rotation is useful for interpreting
constant-amplitude tests, where it provides information
about the evolution of rotation caused solely by cyclic
loading.
This rotation definition has been selected so that the effect
of ratcheting is not conflated with stiffening, softening or
change in hysteresis loop shape. This definition is also
aligned with the typical definition of strain per cycle used
in element testing (the value of strain at average stress on
reloading) (e.g. Andersen, 2015).
As described by Leblanc et al. (2010a), the cyclic loading is
characterised by ζcand ζb
ζc¼MMIN
MMAX
ð3Þ
ζb¼MMAX
MR
ð4Þ
ζccharacterises the load symmetry (ζc¼0 for one-way
loading, ζc¼1 for symmetric two-way loading and ζc¼1
100
80
60
40
20
00 0·5 1·0
θ: degrees
1·5 2·0
(a)
M: N m
RD = 1%
RD = 60%
θ/θR
0 0·2 0·4 0·6 0·8 1·0
θ/θR
(b) (c)
0 0·2 0·4 0·6 0·8 1·0
M/MR
1·0
0·8
0·6
0·4
0·2
0
M/MR
1·0
0·8
0·6
0·4
0·2
0
RD = 60% RD = 1%
Fig. 2. Monotonic response: (a) average monotonic response; (b) normalised monotonic response in very loose sand; (c) normalised monotonic
response in dense sand
MM
a0
b0
an
an
bn
bn
MAV
MMIN
MMAX MMAX,n
MU,AV,n
MR,AV,n
MU,MIN,n
MR,MIN,n
θθ
Reload
Unload
Cycle 0
Cycle 1 Cycle nCycle n
(a) (b)
Fig. 3. Cyclic response definition: (a) constant-amplitude; (b) multi-amplitude
MONOPILE ROTATION UNDER COMPLEX CYCLIC LATERAL LOADING IN SAND 919
for constant loading), while ζband ζctogether describe
the load amplitude, relative to the reference moment MR.
The average load amplitude MAV and cyclic load amplitude
MCYC ¼1=2ðMMAX MMINÞare also important in con-
trolling the cyclic response.
UNIDIRECTIONAL CONSTANT-AMPLITUDE
CYCLIC RESPONSE
Table 4 summarises the unidirectional constant-amplitude
tests presented in this paper. Sinusoidal cyclic loading was
applied for all constant-amplitude cyclic tests. Both one-way
(ζc¼0) and partial two-way (1,ζc,0) tests were
performed. The partial two-way tests were focused near ζc¼
06, as a number of studies at 1ghave reported a maximum
increase in ratcheting for this load condition (Leblanc et al.,
2010a; Zhu et al., 2013; Nicolai & Ibsen, 2014; Albiker et al.,
2017). The ζbvalues were chosen to be as small as possible,
while still allowing accurate application of load and
resolution of the pile’s full cyclic rotation response with the
apparatus presented. Unidirectional, one-way tests were
conducted to 10 000 cycles. Other tests were conducted to
1000 cycles as the ratcheting behaviour evolves logarithmi-
cally and there are diminishing returns associated with
performing longer-term tests.
Figure 4 presents the monopile’s ratcheting response
for the tests presented in Table 4. The impact of ζcon the
ratcheting response is clear, impacting both the magnitude of
rotation and the shape of the evolution of rotation with cycle
number in both the very loose and dense samples. For
example, for the very loose sample with loading at ζb¼04,
the accumulated pile rotation at the 1000th cycle is 2·5 times
larger when ζc¼06, compared to ζc¼0.
Two different empirical approaches are followed to
consider the impact of ζcon the ratcheting response, both
of which assume a power-law fit for evolution of the chosen
strain variable εwith cycle number N
ε¼ANαð5Þ
The empirical framework of Leblanc et al. (2010a)
assumes a constant exponent α, while Truong et al. (2019)
let αvary with relative density RDand load type ζc.
Table 4. Unidirectional constant-amplitude test series
Test name Sand density ζbζcCycles, N
L.C1 Very loose 0·20 0 10 000
L.C2 Very loose 0·30 0 10 000
L.C3 Very loose 0·40 0 10 000
L.P1 Very loose 0·20 0·60 1000
L.P2 Very loose 0·40 0·60 1000
D.C1 Dense 0·05 0 10 000
D.C2 Dense 0·10 0 10 000
D.C3 Dense 0·20 0 10 000
D.C4 Dense 0·30 0 10 000
D.P1 Dense 0·20 0·45 1000
D.P2 Dense 0·20 0·60 1000
D.P3 Dense 0·20 0·75 1000
D.P4 Dense 0·10 0·60 1000
100
10–1
10–2
10–3
10–4
100101102
Cycle no.
103104100101102
Cycle no.
103104
ΔθM/θR
100
10–1
10–2
10–3
10–4
ΔθM/θR
100
10–1
10–2
10–3
10–4
100101102
Cycle no.
103104100101102
Cycle no.
(a) (b)
(c) (d)
103104
ΔθM/θR
100
10–1
10–2
10–3
10–4
ΔθM/θR
RD = 1%, One-way RD = 60%, One-way
RD = 1%, Partial two-way RD = 60%, Partial two-way
Power-law fits equation (5)
ζb = 0·4
ζb = 0·4, ζc = –0·60
ζb = 0·2, ζc = –0·60
ζb = 0·1, ζc = –0·45
ζb = 0·2, ζc = –0·60
ζb = 0·2, ζc = –0·75
ζb = 0·1, ζc = –0·60
ζb = 0·3
ζb = 0·2
ζb = 0·3
ζb = 0·2
ζb = 0·1
ζb = 0·05
Fig. 4. Ratcheting response under unidirectional constant amplitude cyclic loading: (a) very loose sample, one-way cycling; (b) dense sample,
one-way cycling; (c) very loose sample, partial two-way cycling; (d) dense sample, partial two-way cycling
RICHARDS, BYRNE AND HOULSBY920
Following Leblanc et al. (2010a), the dashed lines in
Fig. 4 show the result of fitting equation (5) to all uni-
directional constant-amplitude tests with equal weighting,
assuming a common exponent αc. A good fit is obtained
to the one-way data and to the partial two-way data for
N.100, and there is no clear impact of load amplitude
on goodness of fit. With the strain variable chosen here,
ΔθM, the common exponent αc¼026. However, if the
accumulated rotation at cycle peak (Δθp) is used as the
strain variable, consistent with previous work, then α¼
030, aligned with Leblanc et al. (2010a) and Abadie
(2015).
In the approach of Leblanc et al. (2010a), the coefficient A
is expressed as the product of two independent para-
meters, A¼TcTb, where Tc¼fðζcÞand Tb¼fðζb;RDÞ.
The impact of ζcon ratcheting behaviour is therefore
entirely characterised by Tc
. Fig. 5 compares the Tcvalues
obtained in this work to other studies, with tests conducted
to a range of cycle numbers, 1000 ,N,100 000. Despite
some scatter, there is a clear trend for increased Tc,
and therefore increased ratcheting, for partial two-way
loading at ζc06. The highest Tcvalues occur for very
loose sand samples. It should be noted that the choice
of strain variable impacts the Tcvalues obtained, and the
choice of accumulated or total strain is particularly signifi-
cant (Albiker et al., 2017). However, all studies presented
in Fig. 5 use an accumulated rotation value (Δθ) as the
strain variable.
An alternative approach for assessing the impact of ζcon
ratcheting behaviour is to let αvary with ζc, following the
approach of Truong et al. (2019). To assess the variability of
exponent αfor the tests in this study, equation (5) is fitted to
each individual unidirectional constant-amplitude test to
obtain α. Fig. 6 shows how αhas some dependency on ζc:
increasing with decreasing ζcfor 075 ,ζc,0. A small
dependency on RDmay also be seen, with higher αvalues for
the looser sample. These trends are broadly in agreement
with Truong et al. (2019).
Both interpretations of the test results (Figs 5 and 6)
demonstrate the importance of load asymmetry in con-
trolling the ratcheting behaviour, and this must be accounted
for in design methods. Qualitatively, the impact of ζcon
ratcheting may be understood as a competition between
(a) an increasing cyclic amplitude with increasingly negative
ζc, which increases pile movement and therefore soil particle
movement, and (b) a decreasing mean load with increasingly
negative ζc. Increased particle movement is likely to increase
ratcheting, which has been observed to occur through a
convective mechanism (Cuéllar, 2011; Nicolai, 2017), while
reducing the mean load will reduce ratcheting behaviour as
the mechanism becomes more symmetric.
MULTIDIRECTIONAL CONSTANT-AMPLITUDE
CYCLIC RESPONSE
In practice, monopiles are subjected to complex multi-
directional loading as the wind and wave directions
continually vary; Fig. 7 shows the spatial variation of wind
and waves for an example site offshore the Netherlands
(Bierbooms, 2003). Fan-type tests allow systematic investi-
gation of the impact of spread angle (variation in
loading direction) and closely follow tests performed by
Dührkop & Grabe (2008), Rudolph & Grabe (2013) and
Rudolph et al. (2014a), while novel perpendicular loading
5
4
3
2
1
0
–1·0 –0·5 0·5 1·00
ζc
Tc
RD = 60%, ζb = 0·2
RD = 60%, ζb = 0·1
RD = 1%, ζb = 0·4
RD = 1%, ζb = 0·2
Leblanc et al. (2010a): RD = 38%, 0·20<ζb <0·53
Leblanc et al. (2010a): RD = 4%, 0·20<ζb <0·53
Zhu et al. (2013): RD = 20%, ζb = 0·5
Albiker et al. (2017) (sys 1): RD = 44%, ζb = 0·3
Nicolai & Ibsen (2014): RD = 90%, 0·25<ζb <0·45
Fig. 5. Variation of Tcwith ζc, following the empirical approach of
Leblanc et al. (2010a)
–1·0 –0·5 0·50
ζc
RD = 1%
RD = 60%
2·0
1·5
1·0
0·5
0
α/αc
Fig. 6. Variation of αwith ζc, following the empirical approach of
Truong et al. (2019)
90
60
30
120
150
180
210
240
270
300
330
00·25
0·20
0·15
0·10
0·05
Fig. 7. Frequency of occurrence of wave direction (grey area) and wind
direction (hashed area) for a site offshore the Netherlands. Modified
from Bierbooms (2003)
MONOPILE ROTATION UNDER COMPLEX CYCLIC LATERAL LOADING IN SAND 921
tests provide fundamental insight into the multidirectional
response.
Perpendicular loading
Table 5 and Fig. 8 summarise the perpendicular cyclic
loading tests performed. These novel tests provide funda-
mental insight and may also represent misaligned wind and
wave loading, which is common at some sites (Van Vledder,
2013). To isolate the effect of load direction, perpendicular
tests are performed at the same cyclic amplitude (MCYC) and
average load (MAV) as the corresponding unidirectional test.
The T-shape tests have average load perpendicular to the
cyclic loading direction, while the L-shape tests have equal
average load applied both perpendicular and aligned to the
cyclic loading direction. Load is first increased to MAV in
the direction of constant load, and then held constant while
cyclic loading is applied. The notation I and II refer to
arbitrary perpendicular directions normal to the pile’s
vertical axis.
Figure 9 presents the monopile’s continuous total rotation
response for the perpendicular loading tests, alongside the
corresponding unidirectional tests. In all cases, ratcheting
is mostly aligned with the direction of the average load,
regardless of the cyclic loading direction; for the L-shaped
test, this is at approximately 45° to the I-direction as equal
average load is applied in the I- and II-directions.
Figure 10 presents the monopile’s ratcheting response in
the I-direction for the T-shaped tests and in both the I- and
II-direction for the L-shaped tests. The ratcheting responses
for the corresponding unidirectional tests are also plotted.
The ratcheting magnitude and evolution for the perpendicu-
lar tests is broadly similar to that under corresponding
unidirectional loading, suggesting that ratcheting is approxi-
mately independent of the cycling loading direction for a
given cyclic amplitude and average load. For the L-shape
tests, the ratcheting magnitude perpendicular to the cycling
direction (I) is smaller than that aligned with the cycling
direction (II) in both the very loose and dense samples,
suggesting some non-linear dependency of ratcheting on load
magnitude.
These results show how ratcheting is aligned to the direction
of average load, and suggest that –to a first approximation –
the magnitude of ratcheting may be considered independent
of the cyclic loading direction. These observations have
important implications for modelling the multidirectional
cyclic response; ratcheting in the direction of the applied load
is a key feature of, for instance, the HARM modelling
approach (Houlsby et al., 2017), and may be included as a
feature of explicit ratcheting models.
Table 5. Perpendicular loading test series
Test name Corresponding
unidirectional test
Sand density Load case ζbζcCycles, N
L.X1 L.C3 Very loose T-shape 02inMI,02inMII 1inMI,1inMII 1000
L.X2 L.C3 Very loose L-shape 02inMI,04inMII 1inMI,0inMII 1000
D.X1 D.C3 Dense T-shape 01inMI,01inMII 1inMI,1inMII 1000
D.X2 D.C3 Dense L-shape 01inMI,02inMII 1inMI,0inMII 1000
MII MII MII
MI
MCYC MAV
MI
MI
Unidirectional T-shape L-shape
Fig. 8. Schematic representation of perpendicular loading cases
θI/θR
θII/θR
0·15
0·10
0·05
0
–0·05
–0·05 0 0·05 0·10 0·15 0·20
θI/θR
(a) (b)
–0·05 0 0·05 0·10 0·15 0·20
θII/θR
0·15
0·10
0·05
0
–0·05
Unidirectional
Unidirectional
L-shape L-shape
T-shape T-shape
RD = 1% RD = 60%
Fig. 9. Total rotation response for perpendicular loading tests: (a) very loose sample; (b) dense sample
RICHARDS, BYRNE AND HOULSBY922
Fan-type loading
Table 6 summarises the fan-type loading tests performed,
and Fig. 11 demonstrates the loading applied to the
monopile for the example case of D.F1. In MI–MII space
the loading traces the sector of a circle with radius ζbMR
and half internal angle Φ, which is referred to as the spread
angle. The loading direction varies sinusoidally at a
frequency 1/100 of the cyclic loading frequency, fc,so
1000 cycles corresponds to ten complete sweeps of the
sector. Equations (6)–(8) define the MIand MII direction
loads, while Fig. 11 also shows the example MIand MII
loading for half a sweep.
AtðÞ¼MRζb
21þsinð2πfctÞ½ ð6Þ
MI¼AtðÞcos Φsin 2πfct
100
ð7Þ
MII ¼AtðÞsin Φsin 2πfct
100
ð8Þ
Figure 12 shows the evolution of the magnitude of
ratcheting for the tests summarised in Table 6, alongside
the corresponding unidirectional response (Φ¼0°). For the
fan tests, the rate of change of ratcheting varies as the loading
angle changes, seen as ‘ripples’in the ratcheting evolution.
The magnitude of these ripples increases with increasing
multidirectionality. Similar behaviour is observed in the very
loose and dense samples.
The impact of spread angle on overall ratcheting rate can
be assessed by finding the change in exponent αwith Φ.
Equation (5) is fitted to each of the ten fan-type tests, fixing
the intercept Ato the value of Afor the corresponding
unidirectional test. Ais not expected to vary with Φ,as
loading is close to unidirectional during the first few cycles.
The fits are shown for the fan-type tests in Fig. 12, whilst the
variation of αwith spread angle Φis shown in Fig. 13. There
is a clear dependency of exponent αon spread angle Φ, with
peak exponent amplification (worst case) occurring at Φ¼
90°for both very loose and dense sand. The dependency is
less pronounced in the dense sand than in the very loose
sand, although the trend is similar.
The impact of spread angle can also be assessed with the
ratio of displacement at cycle Nunder multidirectional
loading to that under equivalent unidirectional loading. This
multidirectional factor is summarised for the worst-case
spread angles for this study and similar studies in Table 7.
100101102
Cycle no.
103104
(a)
100101102
Cycle no.
103104
(b)
10–1
10–2
ΔθM/θR
10–1
10–2
ΔθM/θR
RD = 1% RD = 60%
Unidirectional
T-shape
L-shape (I)
L-shape (II)
Unidirectional
T-shape
L-shape (I)
L-shape (II)
Fig. 10. Ratcheting response under perpendicular cyclic loading: (a) very loose sample; (b) dense sample
Table 6. Fan-type loading test series
Test name Corresponding
unidirectional test
Sand density Spread angle, ΦζbζcCycles, N
L.F1 L.C3 Very loose 15° 0·40 0 1000
L.F2 L.C3 Very loose 30° 0·40 0 1000
L.F3 L.C3 Very loose 45° 0·40 0 1000
L.F4 L.C3 Very loose 60° 0·40 0 1000
L.F5 L.C3 Very loose 90° 0·40 0 1000
L.F6 L.C3 Very loose 120° 0·40 0 1000
L.F7 L.C3 Very loose 150° 0·40 0 1000
D.F1 D.C3 Dense 30° 0·20 0 1000
D.F2 D.C3 Dense 90° 0·20 0 1000
MII
MI
MII, MI
Time
Φ
ζbMR
Fig. 11. Schematic representation of fan-type loading
MONOPILE ROTATION UNDER COMPLEX CYCLIC LATERAL LOADING IN SAND 923
Although an increase in pile displacement under spread
cyclic loading is observed in all studies, there is significant
variation in multidirectional factor and worst-case spread
angle.
The applied loading pattern will be critical for the
observed ratcheting behaviour, and the worst-case spread
angle and multidirectional factor are likely to vary with
specific load regime, as reported by Rudolph et al. (2014a).
Direct application of a multidirectional factor is therefore
not recommended, but these results highlight the need
to account for multidirectionality to ensure conservative
design.
Similarly to partial two-way loading, the impact of
increasing spread angle on the ratcheting behaviour may be
understood qualitatively as a competition between increasing
pile and therefore soil movement and a decreasing mean load
in the dominant loading direction.
1·5
1·0
0·5
00 50 100
Φ: degrees
150
α/αc
RD = 1%, ζb = 0·4
RD = 60%, ζb = 0·2
Fig. 13. Variation of αwith spread angle Φfor fan-type tests
10–1
10–2
Δ|θ|M/θR
100101102
Cycle no.
103104
(a)
10–1
10–2
Δ|θ|M/θR
100101102
Cycle no.
103104
(c)
10–1
10–2
Δ|θ|M/θR
100101102
Cycle no.
103104
(b)
RD = 1%, ζb = 0·4 RD = 1%, ζb = 0·4
RD = 60%, ζb = 0·2
Power-law fits equation (5)
Φ = 0°
Φ = 15°
Φ = 30°
Φ = 0°
Φ = 120°
Φ = 150°
Φ = 0°
Φ = 30°
Φ = 90°
Φ = 45°
Φ = 60°
Φ = 90°
Fig. 12. Ratcheting response under multidirectional fan-type loading: (a) very loose sample, low Φ; (b) very loose sample, high Φ; (c) dense sample
Table 7. Factors on unidirectional displacement from multidirectional fan-type studies
Study Displacement metric Laboratory conditions Cycles, NWorst-case
spread
angle, Φ
Multidirectional
factor
Dührkop & Grabe (2008) Pile head displacement 1g, medium-dense sand 50 000 45° 13
1g, dense sand 50 000 45° 2–3
Rudolph et al. (2014b) Displacement at lowest LVDT 1g, medium-dense sand 10 000 90° 1·2
1g, dense sand 10 000 120° 1·4
200g, medium-dense sand 3000 30° 1·7
200g, dense sand 3000 90° 1·5
Present study Accumulated pile rotation 1g, very loose sand 1000 90° 2·3
1g, dense sand 1000 90° 1·8
RICHARDS, BYRNE AND HOULSBY924
RELOADING RESPONSE
Reloading tests to 0·8M
R
were performed to explore
the post-cyclic capacity of the monopile, which is of great
importance for ULS design. Understanding the monopile’s
post-cyclic response also informs interpretation of multi-
amplitude loading. Fig. 14 shows the post-cyclic response
of tests in Tables 4 and 6 (except test L.C1 where reload-
ing was not performed). The cyclic response is omitted
from the plots for clarity, and the undisturbed mono-
tonic response (backbone curve) is plotted dashed for
comparison.
All reloading responses exhibit a higher stiffness in
the cyclic loading region, relative to the backbone curve,
shown clearly when the reloading responses are re-zeroed
(Figs 14(c) and 14(d)). In many cases, the total reloading
curve (Figs 14(a) and 14(b)) crosses the backbone curve,
indicating a true increase in capacity. In other cases –
particularly where significant ratcheting has occurred –the
reloading test has not been displaced enough to reach the
backbone curve. However, these tests clearly approach
the backbone curve and would either meet or cross the
backbone curve given sufficient rotation. Although the
total reloading curves indicate a greater increase in capacity
for the dense sand, on average less ratcheting occurs
for the dense tests presented. With the reloading responses
re-zeroed the behaviour is qualitatively similar at both
densities.
Truong et al. (2019) and Nicolai et al. (2017) also report an
increase in post-cyclic monotonic capacity, and Nicolai et al.
(2017) are further able to quantify the increase in capacity in
terms of cycle number, ζcand ζb, given that their reloading
tests reach clear yield. The increase in post-cyclic capacity in
sand is also likely to be caused by the same mechanisms that
lead to an increase in secant stiffness with cyclic loading,
as observed in other studies (Leblanc et al., 2010a; Abadie,
2015; Truong et al., 2019).
Established approaches for designing piles for cyclic lateral
loading in sand apply reduction factors to derived p–ycurves
to reduce the pile’s lateral capacity (e.g. Murchison &
O’Neill, 1984). However, the current experimental evidence
does not support a decrease in post-cyclic capacity in dry
(fully drained) sands, and indeed an increase in capacity
is often observed, which may be exploited to optimise
monopile design.
REALISTIC STORM LOADING
The constant-amplitude tests presented in previous
sections allow systematic investigation of the monopile’s
response. In practice, however, foundations experience
environmental loading which continually varies in ampli-
tude, frequency and direction. The tests presented in this
section –with loading derived from wave tank experiments –
highlight salient features of the foundation’s response to
realistic loading and are useful for model validation and
verification. These tests therefore complement the constant-
amplitude tests.
Tests have only been conducted in very loose sand in
this section, but given the consistent behaviour between
densities reported in the previous sections of this paper,
qualitatively similar behaviour may be expected in dense
sand.
M/MR
1·0
0·8
0·6
0·4
0·2
0
M/MR
1·0
0·8
0·6
0·4
0·2
0
0 0·1 0·2 0·3
θ/θR
0·4 0·5 0·6 0 0·1 0·2 0·3
θ/θR
0·4 0·5 0·6
M/MR
1·0
0·8
0·6
0·4
0·2
0
M/MR
1·0
0·8
0·6
0·4
0·2
0
0 0·1 0·2 0·3
θ/θR
0·4 0·5 0·6 0 0·1 0·2 0·3
θ/θR
(a) (b)
(c) (d)
0·4 0·5 0·6
RD = 1% RD = 60%
RD = 1% RD = 60%
Fig. 14. Reloading response: (a) very loose sample, total rotation on reloading; (b) dense sample, total rotation on reloading; (c) very loose sample,
rotation zeroed from onset of reloading; (d) dense sample, rotation zeroed from onset of reloading (monotonic response shown dashed)
MONOPILE ROTATION UNDER COMPLEX CYCLIC LATERAL LOADING IN SAND 925
Wave tank experiments
A number of model-scale wave loading tests were
performed at the Danish Hydraulic Institute (DHI) to
explore wave–structure interaction as part of the DeRisk
project, a large multi-centre research project aimed at
reducing the risk associated with predicting ULS wave
loads on OWT structures (Bredmose et al., 2016). The
DeRisk tests were performed at 1:50 scale in a shallow water
basin. The monopile was modelled as a stiff cylinder of
diameter 140 mm, instrumented with (among other instru-
ments) four load cells to allow resolution of the total
horizontal and moment load applied to the cylinder.
A range of wave conditions were generated, representative
of large waves in severe storms in the North Sea. Both
unidirectional and directionally spread sea states were
investigated (Bredmose et al., 2016).
Generation of model-scale loads
The tests presented in this paper have been derived
from two DeRisk wave tests: a unidirectional test (UD95)
and a multidirectional test (MD95). These wave tests
were conducted in the equivalent of 33 m water depth
with peak spectral period 15 s and significant wave height
9·5 m at prototype scale. The multidirectional sea state has
a spreading angle of 22°. Measured loads (HI;HII;MI;MII )
on the cylinder were provided at prototype scale, and a
number of basic processing steps were performed before
applying the loads to the model monopile: (a) addition
of constant wind loading; (b) application of a transfer
function to model the structure’s dynamic response;
(c) projection of loads to constant eccentricity; (d) scaling
to model scale.
To represent real loading on an OWT, the measured
wave loads are combined with wind loading, approximated
as a constant force. Given the large significant wave height in
the DeRisk tests, the turbine is assumed to be in a parked
condition in an extreme storm. A wind load of 1·4 MN
acting at a height 85·5 m above the mudline (120 MN m) is
estimated, assuming appropriate OWT dimensions and a
50 year design wind speed of 50 m/s. Wind loading is aligned
with the dominant wave loading direction.
A transfer function is applied to the loads to capture the
dynamic response of the OWT structure. This process is
necessary as the DeRisk tests were performed on a very stiff
cylinder, with no dynamic amplification of loads. The OWT
structure is approximated as a single-degree-of-freedom
system with a natural frequency f0and damping ratio ξ.
For such a system the ratio of transmitted force Fto
excitation force Pcan be found as
F
P¼1
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1f=f0
ðÞ
2
hi
2þ2ξf=f0
ðÞ½
2
rð9Þ
This simple transfer function is thought to capture
the OWT’s key dynamic behaviour, and has been used
by, for example, Arany et al. (2017). The prototype structure’s
first natural frequency is estimated as f0¼026 Hz, between
the 1Pand 3Pexcitation frequencies for a Vestas
V164-8·0 MW turbine (ESRU, 2015). Estimating the
damping coefficient is more difficult, as there is much
variation in values reported in the literature, and damping
varies with turbine operation conditions (Devriendt &
Weijtjens, 2015). For parked conditions, where aerodynamic
damping is negligible, the total damping is estimated as ξ¼
065%, in line with Kementzetzidis et al. (2019) for dense
sand.
This transfer function (equation (9)) is approximated
by an arbitrary magnitude digital filter and applied to
the load signals in the frequency domain using Matlab
function ‘filter’. Fig. 15(a) shows the significant impact of
the transfer function on the moment (MI) transmitted to
the foundation for 100 s of signal at prototype scale, for the
example case of test MD95 with additional constant wind
loading.
Next, the loads are projected to a constant load eccen-
tricity (M=H), as shown in Fig. 15(b) for the example
case of tests MD95 with wind loading. This is necessary
as the measured wave loads have a variable load eccentricity,
but the laboratory apparatus can only apply loads at a
single eccentricity. Loads are projected onto a ‘load line’
in M–Hspace, with gradient equivalent to the fixed
loading eccentricity of the laboratory apparatus, in a
direction parallel to a monopile yield surface. An approxi-
mate expression for a monopile yield surface is obtained
by assuming a distributed lateral load per unit length of
DKγ′z, taking K¼3Kp(Broms, 1964) with ϕ′¼40°and
linearising the yield surface in the region of interest (where
M=His positive)
M=ðL3Dγ′Þþ075H=ðL2Dγ′Þ¼029Kpð10Þ
600
400
200
–200
–400
0
M: MN m
1·5
1·0
0·5
0
–0·5
MI/(L3Dγ')
tt + 50
Time: s
t + 100
HI/(L2Dγ')
0·40·20–0·2
No TF applied
Loads before
projection
Projected loads
Monopile yield surface
TF applied
(a) (b)
Fig. 15. Processing DeRisk load data for the example case of test MD95 with wind loading: (a) impact of transfer function (TF) on MI;
(b) demonstration of projection of I-direction wave loads to constant eccentricity
RICHARDS, BYRNE AND HOULSBY926
For multidirectional loading, the I- and II-direction
components are projected independently.
Finally, the processed prototype-scale loads are translated
to model scale using the dimensionless framework presented
in Table 3. The prototype monopile is assumed to have
diameter D¼8 m and length L¼32 m, which may be
appropriate for very loose sand. The prototype soil unit
weight is estimated as γ′¼10 kN=m3, given that it would be
saturated.
Table 8 summarises the storm loading tests presented in
this paper. All tests include approximately 5000 load cycles
(with the transfer function applied) and are derived
from either DeRisk test UD95 or MD95. The maximum
normalised load MMAX =MR(equivalent to ζb) varies from
0·40 to 0·53 across the test series. Wind loading is added to
alternate cases, increasing the average normalised moment to
produce overall partial two-way loading (MAV =MR.0),
consistent with the findings of Jalbi et al. (2019) for extreme
storm loading in deep waters.
Tests L.DR5 and L.DR6 are unidirectional (UD) versions
of the multidirectional (MD) tests L.DR3 and L.DR4,
respectively; only the dominant I-direction component of
loading is applied in these tests, as demonstrated in Fig. 16
for L.DR6 and L.DR4.
Figure 17 presents the distribution of MCYC=MRand
MAV=MR(and equivalently ζband ζc) considering
each half-cycle, for the example case of test L.DR4
(corresponding to wave test MD95 with wind loading) in
the I-direction. The majority of the loading occurs at ζb,
025, with the largest amplitude cycles partially two-way
(1,ζc,0).
Monopile response
The response of the monopile to the storm loading
is presented in Fig. 18. For the multidirectional tests,
only the behaviour in the direction of dominant loading
(I-direction) is presented. The moment–rotation plots
show the foundation’s hysteretic response, while the foun-
dation’s total rotation with cycle number is used to present
the ratcheting behaviour. Some stiffening can be observed
in the moment–rotation plots, but is not discussed
further here.
In general, the increase in pile rotation is dominated
by the large load events –as seen in both the moment–
rotation plots and the ratcheting evolution plots. The
moment–rotation plots also show how the response generally
follows the backbone curve (shown grey dashed) when loads
exceed those previously applied, broadly aligned
with observations from constant-amplitude reloading tests.
The maximum rotation during a short storm may, therefore,
be approximated by the monotonic response.
Tests L.DR1 and L.DR2, and tests L.DR3 and L.DR4 are
each derived from the same DeRisk load signals, but L.DR2
and L.DR4 have an additional wind loading bias. The
impact of the load bias is clear, with greater ratcheting
recorded for L.DR2 and L.DR4 than L.DR1 and L.DR3,
respectively.
Comparing tests L.DR3 and L.DR5, and L.DR4 and
L.DR6 provides insight into the impact of multidirectional
loading. Fig. 17 shows a slight increase in total rotation
at a given cycle number for the multidirectional cases
(D.LR3 and L.DR4), with the increase in total rotation
increasing with cycle number. These results are broadly
consistent with the behaviour under constant-amplitude
fan-type loading at small fan angles (Φ,30°).
Overall, these tests provide insight into the monopile’s
response to realistic multi-amplitude, multidirectional
0·4
0·2
–0·2
–0·4
–0·4 –0·2 0
MI/MR
0·2 0·4 0·6
0
MII/MR
L.DR4 (MD)
L.DR6 (UD)
Fig. 16. Comparison of multidirectional and unidirectional loads, for
the example cases of L.DR4 and L.DR6
0·6
0·5
0·4
0·3
0·2
0·1
0
0 0·2
MAV/MR
0·4 0·6
MCYC/MR
3
2
1
0
–1
Occurrences
[10i]
ζc = 0
ζb = 0·50
ζc = 1
ζb = 0·25
ζc = –1
Fig. 17. Distribution of MIloads for example case of test L.DR4
Table 8. Storm loading test series
Test
name
Sand
density
Source DeRisk
test
Directionality Wind
load
I-direction II-direction
MMAX=MRMAV =MRMMAX=MRMAV =MR
L.DR1 Very loose UD95 Unidirectional N 0·40 0·00 0·00 0·00
L.DR2 Very loose UD95 Unidirectional Y 0·46 0·07 0·00 0·00
L.DR3 Very loose MD95 Multidirectional N 0·47 0·00 0·13 0·00
L.DR4 Very loose MD95 Multidirectional Y 0·53 0·07 0·13 0·00
L.DR5 Very loose MD95 Unidirectional N 0·47 0·00 0·00 0·00
L.DR6 Very loose MD95 Unidirectional Y 0·53 0·07 0·00 0·00
MONOPILE ROTATION UNDER COMPLEX CYCLIC LATERAL LOADING IN SAND 927
loading, and importantly show behaviour that is consistent
with the previous constant-amplitude tests.
CONCLUSIONS
This paper has presented results from cyclic lateral loading
tests on a laboratory-scale monopile foundation in dry sand
at 1g. The results are consistent with previous experimental
studies, and provide new insights in terms of the response
of the monopile to perpendicular cyclic loading and
realistic multi-amplitude and multidirectional cyclic
loading. The following key observations are made.
(a) The rotation response in very loose and dense, dry sand
is qualitatively similar, increasing confidence in the
application of theoretical models developed for very
loose sands (e.g. Abadie et al., 2017) to denser material
typically encountered offshore.
0·6
0·4
0·2
M/MR
0
–0·2
–0·4
–0·02 0 0·02 0·04
θ/θR
0·06 0·08 0·10
0·08
0·06
0·04
θM/θR
0
0·02
0 1000 2000 3000
Cycle no.
4000 5000
L.DR1 L.DR1
0·6
0·4
0·2
M/MR
0
–0·2
–0·4
–0·02 0 0·02 0·04
θ/θR
0·06 0·08 0·10
0·08
0·06
0·04
θM/θR
0
0·02
0 1000 2000 3000
Cycle no.
4000 5000
L.DR2 L.DR2
0·6
0·4
0·2
MI/MR
0
–0·2
–0·4
–0·02 0 0·02 0·04
θI/θR
0·06 0·08 0·10
0·08
0·06
0·04
θMI/θR
0
0·02
0 1000 2000 3000
Cycle no.
4000 5000
L.DR3
L.DR5
L.DR3
L.DR5
0·6
0·4
0·2
MI/MR
0
–0·2
–0·4
–0·02 0 0·02 0·04
θI/θR
0·06 0·08 0·10
0·08
0·06
0·04
θMI/θR
0
0·02
0 1000 2000 3000
Cycle no.
4000 5000
L.DR4
L.DR6
L.DR4
L.DR6
Fig. 18. Response to storm loading in dominant (I) loading direction (monotonic response shown dashed)
RICHARDS, BYRNE AND HOULSBY928
(b) Partial two-way loading can cause greater ratcheting
than one-way loading to the same peak load, and
multidirectional fan-type loading can cause greater
ratcheting than unidirectional loading to the same
peak load.
(c) Ratcheting occurs in the direction of load bias, and is
largely unaffected by the cyclic loading direction; this
observation has important implications for theoretical
modelling.
(d) Monopile capacity is either maintained or increased
following cyclic loading in dry (fully drained) sand, at
odds with the idea that cyclic loading is always a
damaging process.
(e) The response to realistic multi-amplitude,
multidirectional storm-type loading is consistent with
observations from constant-amplitude tests.
(f) The maximum rotation during a short storm in dry
(drained) sand may be approximated by the monotonic
response.
Because great care is necessary in scaling laboratory-scale
responses to full scale, and the process is subject to
uncertainties, these results should not be directly applied
for full-scale design. Nevertheless, these patterns of
behaviour are broadly consistent with those observed under
unidirectional cyclic loading at large field scale (Beuckelaers,
2017), and are therefore expected to translate to full scale.
These results can inform development of models, such as
HARM; specifically, the constant-amplitude results can be
used for model calibration, while the realistic loading tests aid
validation. Of course, before application for full-scale design,
such a model would need to be developed to account for
scaling effects and validated at full scale.
ACKNOWLEDGEMENTS
This work was supported by grant EP/L016303/1 for
Cranfield University, the University of Oxford and
Strathclyde University, Centre for Doctoral Training in
Renewable Energy Marine Structures (REMS, http://www.
rems-cdt.ac.uk/) from the UK Engineering and Physical
Sciences Research Council (EPSRC). The storm loading data
used in this paper came from the DeRisk project, funded by
Innovation Fund Denmark.
The research materials supporting this publication can be
accessed by contacting byron.byrne@eng.ox.ac.uk.
NOTATION
Afitting parameter
Dpile diameter
D10;D30 ;D50;D60 soil particle sizes
˜
edimensionless loading eccentricity
Ftransmitted force
f0natural frequency
fccyclic loading frequency
Hhorizontal load
˜
Hdimensionless horizontal load
hpile loading eccentricity
Kpcoefficient of passive earth pressure
Lpile embedded length
Mmoment load
˜
Mdimensionless moment load
MAV average moment load
MCYC cyclic moment load
MDdesign moment load
MMAX maximum moment load
MMIN minimum moment load
MRreference moment load
Ncycle number
Pexcitation force
paatmospheric pressure
Raaverage surface roughness
RDrelative density
tpile wall thickness
γ′effective unit weight
γ′
MAX maximum unit weight
γ′
MIN minimum unit weight
Δθaccumulated pile rotation ( per cycle)
ΔθMaccumulated mean pile rotation (per cycle)
εstrain
ζbload amplitude characterisation parameter
ζcload symmetry characterisation parameter
θpile rotation
˜
θdimensionless pile rotation
θDdesign rotation
θMtotal mean pile rotation (per cycle)
θRreference pile rotation
θRL pile reloading rotation
ξdamping ratio
σ′
vvertical effective stress
Φspread angle
ϕ′friction angle
ϕ′
cr critical friction angle
ϕ′
ppeak friction angle
REFERENCES
Abadie, C. N. (2015). Cyclic lateral loading of monopile foundations
in cohesionless soils. DPhil thesis, University of Oxford,
Oxford, UK.
Abadie, C. N., Byrne, B. W. & Houlsby, G. T. (2017). Modelling of
monopile response to cyclic lateral loading in sand. In
Proceedings of the 8th international conference on offshore site
investigation and geotechnics, pp. 1046–1053. London, UK:
Society for Underwater Technology.
Abadie, C. N., Byrne, B. W. & Houlsby, G. T. (2019a). Rigid pile
response to cyclic lateral loading: laboratory tests. Géotechnique
69, No. 10, 863–876, https://doi.org/10.1680/jgeot.16.P.325.
Abadie, C. N., Houlsby, G. T. & Byrne, B. W. (2019b). A method for
calibration of the hyperplastic accelerated ratcheting model
(HARM). Comput. Geotech. 112, 370–385.
Achmus, M., Abdel-Rahman, K. & Kuo, Y. (2007). Numerical
modelling of large diameter steel piles under monotonic and
cyclic horizontal loading. In Proceedings of 10th international
symposium on numerical models in geomechanics (eds
G. N. Pande and S. Pietruszczak), pp. 453–460. London, UK:
CRC Press.
Achmus, M., Kuo, Y. S. & Abdel-Rahman, K. (2009). Behavior of
monopile foundations under cyclic lateral load. Comput.
Geotech. 36, No. 5, 725–735.
Albiker, J., Achmus, M., Frick, D. & Flindt, F. (2017). 1gmodel tests
on the displacement accumulation of large-diameter piles under
cyclic lateral loading. Geotech. Testing J. 40, No. 2, 173–184.
Altaee, A. & Fellenius, B. H. (1994). Physical modeling in sand.
Can. Geotech. J. 31, No. 3, 420–431.
Andersen, K. H. (2015). Cyclic soil parameters for offshore
foundation design. In Fontiers in offshore geotechnics III
(ed. V. Meyer), pp. 3–82. Leiden, the Netherlands: CRC Press/
Balkema.
API (American Petroleum Institute) (2011). Geotechnical and
foundation design considerations ANSI/API RP 2GEO.
Washington, DC, USA: API.
Arany, L., Bhattacharya, S., Macdonald, J. & Hogan, S. J. (2017).
Design of monopiles for offshore wind turbines in 10 steps. Soil
Dynamics Earthquake Engng 92, 126–152.
Arshad, M. & O’Kelly, B. C. (2017). Model studies on monopile
behavior under long-term repeated lateral loading.
Int. J. Geomech. 17, No. 1, 1–12.
Bayton, S. M., Black, J. A. & Klinkvort, R. T. (2018). Centrifuge
modelling of long term cyclic lateral loading on monopiles.
In Physical modelling in geotechnics –ICPMG 2018 (eds
A. McNamara, S. Divall, R. Goodey, N. Taylor, S. Stallebrass
and J. Panchal), pp. 689–694. London, UK: CRC Press.
Beuckelaers, W. J. A. P. (2017). Numerical modelling of laterally
loaded piles for offshore wind turbines. DPhil thesis, Universityof
Oxford, Oxford, UK.
MONOPILE ROTATION UNDER COMPLEX CYCLIC LATERAL LOADING IN SAND 929
Bierbooms, W. (2003). Wind and wave conditions, DOWEC (Dutch
Offshore Wind Energy Converter Project). Delft University of
Technology, Delft, the Netherlands.
Bolton, M. D. (1986). The strength and dilatancy of sands.
Géotechnique 36, No. 1, 65–78, https://doi.org/10.1680/geot.
1986.36.1.65.
Bolton, M. D. (1987). Discussion: the strength and dilatancy of
sands. Géotechnique 37, No. 2, 219–226, https://doi.org/10.1680/
geot.1987.37.2.219.
Bredmose, H., Dixen, M., Ghadirian, A., Larsen, T. J., Schløer, S. &
Hanson, T. D. (2016). Derisk –accurate prediction of ULS wave
loads. Outlook and first results. Energy Procedia 94, 379–387.
Broms, B. B. (1964). Lateral resistance of piles in cohesionless soils.
ASCE J. Soil Mech. Found. Div. 90, No. May, 123–156.
Byrne, B. W., McAdam, R. A., Burd, H. J., Houlsby, G. T.,
Martin, C. M. & Plummer, M. A. L. (2017). PISA: new design
method for offshore wind turbine monopiles. In Proceedings
of the 8th international conference on offshore site investigation
and geotechnics, vol. 1, pp. 142–161. London, UK: Society for
Underwater Technology.
Cuéllar, V. P. (2011). Pile foundations for offshore wind turbines:
numerical and experimental investigations on the behaviour under
short-term and long-term cyclic loading. PhD thesis, Technischen
Universitat, Berlin, Germany.
Devriendt, C. & Weijtjens, W. (2015). The overall damping of
an offshore wind turbine during different operating conditions.
EWEA (European Wind Energy Association) offshore 2015,
Copenhagen, Denmark.
DNV GL (2016). DNVGL-ST-0126: Support structures for wind
turbines (April ed.). Oslo, Norway: DNV GL.
Dührkop, J. & Grabe, J. (2008). Monopilegründungen von
Offshore-windenergieanlagen –zum Einfluss einer
veränderlichen zyklischen Lastangriffsrichtung. Bautechnik 85,
No. 5, 317–321 (in German).
ESRU (The Energy Systems Research Unit) (2015). XL monopiles.
Glasgow, UK: University of Strathclyde, see http://www.esru.
strath.ac.uk/EandE/Web_sites/14-15/XL_Monopiles/structural.
html (accessed 30/10/2018).
Houlsby, G. T., Abadie, C. N., Beuckelaers, W. J. A. P. &
Byrne, B. W. (2017). A model for nonlinear hysteretic and
ratcheting behaviour. Int. J. Solids Structs 120,67–80.
Jalbi, S., Arany, L., Salem, A., Cui, L. & Bhattacharya, S. (2019).
A method to predict the cyclic loading profiles (one-way
or two-way) for monopile supported offshore wind turbines.
Mar. Structs 63,65–83.
Kementzetzidis, E., Corciulo, S., Versteijlen, W. G. & Pisanò, F.
(2019). Geotechnical aspects of offshore wind turbine dynamics
from 3D non-linear soil–structure simulations. Soil Dynamics
Earthquake Engng 120, 181–199.
Klinkvort, R. (2012). Centrifuge modelling of drained lateral pile–soil
response. PhD thesis, Technical University of Denmark, Lyngby,
Denmark.
Klinkvort, R. & Hededal, O. (2013). Lateral response of monopile
supporting an offshore wind turbine. Proc. Instn Civ. Engrs –
Geotech. Engng 166, No. 2, 147–158, https://doi.org/10.1680/
geng.12.00033.
Lauder, K. & Brown, M. J. (2014). Scaling effects in the 1g
modelling of offshore pipeline ploughs. In Physical modelling
in geotechnics –ICPMG 2014 (eds C. Gaudin and D. White),
pp. 377–383. London, UK: CRC Press.
Leblanc, C., Byrne, B. W. & Houlsby, G. T. (2010a). Response of stiff
piles to random two-way lateral loading. Géotechnique 60,
No. 9, 715–721, https://doi.org/10.1680/geot.09.T.011.
Leblanc, C., Houlsby, G. T. & Byrne, B. W. (2010b). Response
of stiff piles in sand to long-term cyclic lateral loading.
Géotechnique 60, No. 2, 79–90, https://doi.org/10.1680/
geot.7.00196.
Murchison, J. M. & O’Neill, M. W. (1984). Evaluation of p–y
relations in cohesionless soils. In Proceedings of the ASCE
symposium on analysis and design of pile foundations (ed.
J. R. Meyer), pp. 174–191. New York, NY, USA: American
Society of Civil Engineers.
Nicolai, G. (2017). Cyclic behaviour of laterally loaded monopiles in
sand supporting offshore wind turbines. PhD thesis, Aalborg
University, Aalborg, Denmark.
Nicolai, G. & Ibsen, L. B. (2014). Small-scale testing of cyclic
laterally loaded monopiles in dense saturated sand. J. Ocean
Wind Energy 1, No. 4, 240–245.
Nicolai, G., Ibsen, L. B., O’Loughlin, C. D. & White, D. J. (2017).
Quantifying the increase in lateral capacity of monopiles in sand
due to cyclic loading. Géotechnique Lett. 7, No. 3, 1–8,
https://doi.org/10.1680/jgele.16.00187.
Page, A. M., Grimstad, G., Eiksund, G. R. & Jostad, H. P. (2018). A
macro-element pile foundation model for integrated analyses of
monopile-based offshore wind turbines. Ocean Engng 167,
23–35.
Richards, I. A., Byrne, B. W. & Houlsby, G. T. (2018). Physical
modelling of monopile foundations under variable cyclic lateral
loading. In Physical modelling in geotechnics –ICPMG 2018
(eds A. McNamara, S. Divall, R. Goodey, N. Taylor,
S. Stallebrass and J. Panchal), pp. 737–742. London, UK:
CRC Press.
Rudolph, C. & Grabe, J. (2013). Untersuchungen zu zyklisch
horizontal belasteten Pfählen bei veränderlicher Lastrichtung.
Geotechnik 36, No. 2, 90–95 (in German).
Rudolph, C., Bienen, B. & Grabe, J. (2014a). Effect of variation of
the loading direction on the displacement accumulation of
large-diameter piles under cyclic lateral loading in sand. Can.
Geotech. J. 51, No. 10, 1196–1206.
Rudolph, C., Grabe, J. & Bienen, B. (2014b). Drift of piles subjected
to lateral loading from a varying direction: system vs. soil
element behaviour. Proceedings of ASME 2014 33rd inter-
national conference on ocean, offshore and arctic engineering,
San Francisco, CA, USA.
Schnaid, F. (1990). A study of the cone-pressuremeter test in sand.
DPhil thesis, University of Oxford, Oxford, UK.
Schroeder, F. C., Merritt, A. S., Sørensen, K. W., Muir Wood, A.,
Thilsted, C. L. & Potts, D. M. (2015). Predicting monopile
behaviour for the Gode wind offshore wind farm. In Frontiers in
offshore geotechnics III (ed. V. Meyer), pp. 735–740. Leiden, the
Netherlands: CRC Press/Balkema.
Sørensen, S. P. H., Augustensen, A. H., Leth, C. T.,
Ostergaard, M. U. & Møller, M. (2017). Consequences of p–y
curve selection for monopile design for offshore wind turbines.
In Proceedings of the 8th international conference on offshore
site investigation and geotechnics, vol. 2, pp. 1062–1069. London,
UK: Society for Underwater Technology.
Truong, P., Lehane, B. M., Zania, V. & Klinkvort, R. T. (2019).
Empirical approach based on centrifuge testing for cyclic
deformations of laterally loaded piles in sand. Géotechnique
69, No. 2, 133–145, https://doi.org/10.1680/jgeot.17.P.203.
Van Vledder, G. P. (2013). On wind-wave misalignment, directional
spreading and wave loads. Proceedings of the 32rd international
conference on ocean, offshore and Arctic engineering
OMAE2013, Nantes, France.
Wind Europe (2018). Offshore wind in Europe: key trends and
statistics 2017. Brussels, Belgium: Wind Europe, see https://
windeurope.org/wp-content/uploads/files/about-wind/statistics/
WindEurope-Annual-Offshore-Statistics-2017.pdf (accessed
30/10/2018).
Zhu, B., Byrne, B. W. & Houlsby, G. T. (2013). Long-term lateral
cyclic response of suction Caisson foundations in sand.
J. Geotech. Geoenviron. Engng 139, No. 1, 73–83.
Zhu, F. Y., O’Loughlin, C. D., Bienen, B., Cassidy, M. J. &
Morgan, N. (2017). The response of suction caissons to
long-term lateral cyclic loading in single-layer and layered
seabeds. Géotechnique 67, No. 11, 1–13, https://doi.org/
10.1680/jgeot.17.P.129.
RICHARDS, BYRNE AND HOULSBY930
Available via license: CC BY 4.0
Content may be subject to copyright.
