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Simplified model for the stiffness of suction caisson foundations under 6 dof loading

Authors:
1. Introduction
Despite the current dominance of monopile
foundations for offshore wind turbines, there is
increasing interest in deploying suction caisson (or
suction bucket) foundations (e.g. for jacket
structures) for offshore wind farms located in deeper
waters due to economic advantages. Once installed,
the caisson foundations will experience vertical (V),
horizontal (Hx, Hy), overturning moment (Mx, My)
and torsional (T) loading during normal operations.
Although the ultimate capacity of the foundation is
important, the general operation of a wind turbine
means assessment of the dynamic and fatigue
performance of the foundation and structure is
particularly important. For such assessments, the soil
response can be approximated as linear elastic, as
the applied loads are within the lower ends of the
expected range during the lifetime. Care is needed,
however, in the selection of appropriate soil stiffness
parameters for use in these assessments.
For a linear elastic soil, it is known from previous
research (Doherty et al., 2005) that the resultant
forces (Hx, Hy, V, Mx, My, T) acting on a caisson
foundation are related to the displacements (Ux, Uy,
Uz, Θx, Θy, Θz) through global stiffness coefficients,
as shown in Eq. 1. KV, KH, KM, KT and KC are the
vertical, lateral, rotational, torsional and lateral-
rotational coupling stiffness respectively.
z
y
x
z
y
x
T
MC
MC
V
CH
CH
y
x
y
x
U
U
U
K
KK
KK
K
KK
KK
T
M
M
V
H
H
00000
0000
0000
00000
0000
0000
(1)
The main design challenge is that a large number of
analyses are required for fatigue assessments. Unlike
the small number of caisson foundations used for
bespoke offshore structures in oil and gas projects, a
typical new offshore wind farm may have hundreds
of such foundations (Byrne et al., 2015).
Optimisation of the caisson foundations for this new
application therefore requires design methods that
are both fast and reliable.
Unfortunately, existing design methods for assessing
stiffness of suction caisson foundations under low
operational loads are limited either by their
efficiency or the level of detail of soil profiles that
can be modelled. For example, some methods are
not efficient enough to handle the large number of
analyses required for fatigue design while others are
applicable only for relatively simple ground profiles.
There is clearly a need for new design methods that
are robust, fast and general enough to handle the
SIMPLIFIED MODEL FOR THE STIFFNESS OF SUCTION
CAISSON FOUNDATIONS UNDER 6 DOF LOADING
SK Suryasentana, BW Byrne and HJ Burd
University of Oxford, Oxford, UK
A Shonberg
Dong Energy Wind Power, London, UK
Abstract
Suction caisson foundations are increasingly used as foundations for offshore wind turbines. This paper pre-
sents a new, computationally efficient, model to determine the stiffness of caisson foundations embedded in
linearly elastic soil, when subjected to six degree-of-freedom loading; vertical (V), horizontal (Hx, Hy), over-
turning moment (Mx, My) and torsion (T). This approach is particularly useful for fatigue limit analyses,
where the constitutive behaviour of the soil can be modelled as linearly elastic. The paper describes the
framework on which the new model is based and the 3D finite element modelling required for calibration.
Analyses conducted using the proposed approach compare well with results obtained using 3D finite element
analysis. The possibility of low-cost analysis, coupled with a simple calibration process, makes the proposed
design method an attractive candidate for intensive applications such as foundation design optimisation.
widely varying heterogeneities in most real-world
ground profiles. This paper sets out a new design
method that addresses this need, and which can be
applied to large scale projects that require
optimisation, such as offshore wind farms.
2. Existing Design Methods
2.1 Macro Element model
The macro element model (e.g. Doherty et al., 2005)
represents the caisson foundation as a single
element, where the behaviour is described purely in
terms of the resultant forces acting on it and the
corresponding displacements. In other words, this
model directly provides the stiffness coefficients in
Eq. 1. This model has several key advantages such
as computational efficiency and easy integration
with most structural analysis programs.
However, there are some notable limitations. First,
the calibration process for this model is cumbersome
as a different set of stiffness coefficients is required
for every unique combination of soil and caisson
stiffness. Second, this model is accurate only for
soils where the stiffness increases continuously with
depth. As most ground conditions encountered in
practice involve layered soils, using simplified soil
profiles may introduce significant errors. This is
especially true when there is a stiff layer overlying
softer layers (Suryasentana et al., 2017).
2.2 3D Finite Element (3D FE) method
The 3D FE method is a rigorous design method and
is often the standard against which other design
methods are benchmarked. It can provide accurate
stiffness predictions for complex ground profiles,
soil constitutive behaviour and structural geometries.
However, it is limited by the high computational
cost and modelling complexities, relative to other
design methods. It is generally unsuitable for the
design and optimisation of foundations in large scale
projects such as for an offshore wind farm.
2.3 Winkler model
Winkler based models have been used successfully
for the design of deep foundations such as
monopiles (API, 2010; DNV, 2014). More recently,
this approach has been applied to shallow
foundations (e.g. Houlsby et al., 2005; Gerolymos &
Gazetas, 2006). In this modelling approach, the soil
continuum is represented by a series of independent
springs, each of which captures the local soil
reaction. This approach has several key advantages.
Similar to the macro element model, it is
computationally efficient and easily coupled with
structural analysis programs. However, a major
advantage over the macro element model is the
localised nature of the soil reactions, which allows
models that are based on the Winkler approach to be
used for any type of non-homogeneous elastic soil,
including layered soil.
Nevertheless, the Winkler approach is not without
limitations. The assumption that the springs are
independent ignores the continuum nature of soil.
This assumption may introduce significant errors in
stiffness predictions for highly heterogeneous
ground profiles. Furthermore, an issue with the
Winkler model, specific to caisson foundations, is
that it is incomplete. The available Winkler models
for caisson foundations are limited to lateral loading
only (Davidson et al., 1982; Gerolymos & Gazetas,
2006). The current Winkler approaches, unlike other
design methods, cannot be readily used to assess the
stiffness of caisson foundations under 6 degree-of-
freedom (dof) loading.
3. Proposed Design Method
This paper proposes a new Winkler-based model,
termed ‘1D caisson model’, to predict the stiffness
of caisson foundations in linear elastic soil. Unlike
existing Winkler models for caisson foundations,
this model is complete and can provide stiffness
predictions for 6 dof loading. Moreover, the
formulations of the Winkler spring forces, hereafter
referred to as 1D soil reactions, are calibrated
against rigorous 3D FE solutions. The model offers
the speed of the Winkler modelling approach and the
accuracy of the 3D FE method.
3.1 Theory
In this model, the global coordinate system is
defined at the centre of the suction caisson lid base
(i.e. the interface between the lid and the soil
medium). Furthermore, this origin is adopted as the
point of applied loading (LRP), as shown in Fig. 1.
Figure 1: Schematic representation of a caisson foundation
and the point of applied loading (D is the caisson diameter, L
is the skirt length and z is the depth below ground surface)
The caisson is assumed to be fully rigid and no slip
or gap is allowed between the foundation and soil.
For each cross section along the caisson skirt, the 3D
soil stresses acting on it can be resolved into 1D soil
reactions, which are essentially the resultant soil
forces acting on each cross section.
Figure 2: Sign conventions for the global applied loads and dof
of the foundation, with respect to the 1D soil reactions and
local dof of each cross section
There are six 1D soil reactions (hx, hy, v, mx, my, t)
and six local dof (ux, uy, uz, θx, θy, θz) associated
with each cross section. Figure 2 shows the sign
convention for the global and local dof with the
relation between the two defined by Eq. 2.
z
y
x
z
y
x
z
y
x
z
y
x
U
U
U
z
z
u
u
u
100000
010000
001000
000100
00010
00001
(2)
Since the caisson skirt can be divided into an infinite
number of infinitesimally thin cross sections, the 1D
soil reactions acting on it, henceforth known as the
skirt 1D soil reactions, would be distributed in
nature. Furthermore, there is an additional non-
distributed 1D soil reaction acting at the base of the
foundation, termed the base 1D soil reaction. This is
the resultant force acting across the base cross
section, which includes both the skirt tip annulus and
the soil plug base.
Fig. 3 shows a schematic diagram of the transfer of
the applied vertical load (V) into the respective 1D
soil reactions. As shown in Fig. 3a, V is balanced by
the soil reactions as follows:
(3)
where vtip, vskirt, vskirt, plug, vlid are the soil reactions on
the skirt tip annulus, skirt exterior, skirt interior and
the lid base respectively. The skirt 1D soil reaction
is vskirt while the base 1D skirt reaction (vbase) is:
plugbasetipbase vvv ,
(4)
where vbase, plug is the soil reaction on the base of the
soil plug. From Fig. 3b, it is shown that:
lid
Lplugskirtplugbase vdzvv
0
,,
(5)
(a) Force equilibrium between caisson foundation, applied
load and local soil reactions
(b) Force equilibrium between internal soil plug and local
soil reactions
Figure 3: Transfer of vertical load into the 1D soil reactions
Substituting Eqs. 4 and 5 into Eq. 3 gives:
base
Lskirt vdzvV
0
(6)
Thus, the skirt and base 1D soil reactions complete
the set of soil reactions acting on the caisson.
3.2 Calibration of 1D soil reactions
To calibrate the 1D soil reactions, the caisson-soil
interaction problem is analysed using the 3D FE
method. Then, the 3D soil stresses from the adjacent
soil elements are resolved into 1D soil reactions.
It is assumed that the 1D soil reactions at each depth,
z, depend only on the soil properties at that depth.
This assumption implies that the model only needs
to be calibrated against the 3D FE results for a
homogeneous elastic soil, with the calibrated
reactions being applicable to non-homogeneous
elastic soil too. This model also assumes that the 1D
soil reactions are independent of the caisson stiffness
properties. Therefore, the model only needs to be
calibrated against a rigid caisson, with the calibrated
reactions also applying to caissons with flexible
skirts. An examination of these assumptions is not
provided here but will be addressed in future work.
To determine the 1D soil reactions, the nodal force
results from the 3D FE analyses are used.
Specifically, the 1D soil reactions are computed
from the contact nodal forces of the soil elements
adjacent to the foundation (including the soil plug).
For the skirt 1D soil reactions, contact nodal forces
refer to nodal forces from nodes shared by the skirt
exterior and surrounding soil elements. For each
‘ring’ of soil elements in contact with the skirt
exterior, the skirt 1D vertical and lateral reactions
are computed as the sum of the contact nodal forces
in the respective axes, divided by the soil element
thickness. The computed value corresponds to the
local soil reaction at the depth of the ‘ring’ of soil
elements. For the skirt 1D moment and torsional
reactions, the computation involves the sum of the
moment induced by each contact nodal force about
the centre of the cross section, divided by the soil
element thickness.
For the base 1D soil reactions, contact nodal forces
refer to nodal forces from nodes shared by the
interface between the bases of the internal soil plug
and skirt tip annulus and the soil elements directly
below them. The base 1D vertical and lateral soil
reactions are the sum of the contact nodal forces in
the respective axes while the base 1D moment and
torsional soil reactions are the sum of the moment
induced by each contact nodal force about the centre
of the cross section.
Finally, mathematical formulations are derived to
approximate these 1D soil reactions; these
formulations form the predictive basis of the 1D
caisson model.
3.3 Global stiffness equations
One advantage of the Winkler assumption is the
availability of analytical solutions to derive the
global stiffness of a rigid caisson directly from the
1D soil reactions, which are shown in Table 1.
Table 1: Analytical solutions to compute the global stiffness of
the foundation directly from the 1D soil reactions. L refers to
the caisson skirt length. KH, KM and KC can be similarly
defined in terms of hx and my, but with some minor
modifications
Equation
KV
z
base
L
z
skirt
u
v
dz
u
v
0
KH
y
base
y
L
y
skirt
yu
h
dz
u
h
0
KM
 
   
 
LL
u
hh
dzzz
u
hh
L
u
mm
dzz
u
mm
y
base
y
x
base
y
L
y
skirt
y
x
skirt
y
y
skirt
x
x
base
x
y
skirt
x
L
x
skirt
x
0
0
KT
z
base
L
z
skirt t
dz
t
0
KC
)()(
0
L
u
h
u
m
dzz
u
h
u
m
y
base
y
y
base
x
y
skirt
y
L
y
skirt
x
or
 
L
u
hh
dzz
u
hh
y
base
y
x
base
y
L
y
skirt
y
x
skirt
y
0
3.4 Relation to the approach of Byrne et al. (2015)
Whilst the 1D caisson model is similar to the PISA
design approach for short monopile foundations
(Byrne et al., 2015), there are also important
differences. First, it provides the 1D soil reactions
corresponding to the vertical and torsional dof. Thus,
it can handle fully three-dimensional loading.
Second, unlike the PISA approach, this model has
coupling between the lateral and rotational dof. A
local cross section rotation induces a local lateral
soil reaction and a local lateral displacement would
induce a local moment soil reaction. This coupling
has thus far been ignored by existing Winkler
models, such as the p-y method for pile foundations
(API, 2010; DNV, 2014).
4. Numerical Example
This section illustrates the process of calibrating the
1D soil reactions using the solutions of 3D FE
analyses. In this numerical example, a 3D FE model
of a caisson foundation embedded in incompressible
linear elastic soil was implemented in the finite
element program ABAQUS (version 6.13). The
global coordinate system adopted in the FE model is
the same as defined in Fig. 1.
The foundation has a unit diameter (D), a unit skirt
length (L = D) and a skirt thickness of 0.0025D.
Mesh convergence analyses were carried out to
determine the required mesh fineness. Moreover, a
mesh domain of 80D for both diameter and depth
was found to be sufficient to avoid boundary effects.
A typical mesh of the FE model is shown in Fig. 4.
Figure 4: Mesh of the complete 3D FE model, with an enlarged
partial view of caisson foundation
Displacements were fixed in all directions at the
bottom of the mesh domain and in the radial
directions on the periphery. Contact breaking
between the foundation and soil was not allowed and
this was implemented using tie constraints at the
foundation-soil interface.
The soil was weightless and homogeneous isotropic
linear elastic. A Young’s modulus of 100MPa and a
Poisson’s ratio of 0.49 was assigned to the soil
elements, for which eight-noded linear brick
elements C3D8RH (Dassault Systèmes, 2010) were
used. The foundation was assumed to be entirely
rigid and the rigid behaviour was simulated using
rigid body constraints. The reference point was set to
be the point of applied loading as defined in Fig. 1.
To fully calibrate the 1D soil reactions, four sets of
3D FE results are required. These four sets of results
are obtained from the 3D FE analyses of the caisson
foundation under four different prescribed
displacements. These prescribed displacements were
implemented by applying different boundary
conditions to the reference point of the caisson
foundation, as detailed in Table 2.
Table 2: Boundary conditions for the four types of prescribed
displacements applied in the 3D FE analyses
Ux/D
Uy/D
Uz/D
Θx
Θy
Θz
Vertical
0
0
0.1
0
0
0
Lateral
0
0.1
0
0
0
0
Rotational
0
0
0
0.1
0
0
Torsional
0
0
0
0
0
0.1
To verify that the 3D FE model has been set up
correctly, the normalized global stiffness
coefficients resulting from the prescribed
displacements are compared against known results
from previous work (in this case Doherty et al.,
2005), as shown in Table 3.
Table 3: Comparison of normalised stiffness coefficients from
the 3D FE results and values reported in previous work
Stiffness
Doherty et al. (2005)
3D FE
Difference
KV/GD
6.64
6.68
0.60 %
KH/GD
7.54
7.68
1.86 %
KM/GD3
7.40
7.11
-3.92 %
KT/GD3
4.04
4.07
0.74 %
KC/GD2
-4.69
-4.66
-0.64 %
The normalised stiffness coefficients computed by
the 3D FE model matched the values reported by
Doherty et al. (2005) well, with the maximum
deviation being only 3.92%. This provides
confidence that the FE model had been set up
correctly.
5. Results
Fig. 5 shows the 1D soil reactions profile that
resulted from the 3D FE analyses of the four sets of
prescribed displacements given in Table 2. Note that
the values depicted in Fig. 5 are with respect to the
global dof, and not the local dof.
(a)
(b)
(c)
(d)
(e)
(f)
Figure 5: Skirt and base 1D soil reactions from 3D FE results
As shown in the figure, most skirt 1D soil reactions
appear to be constant along the skirt length, apart
from the reactions nearest to the ground surface and
skirt tip. The only exception is the hy coupling
reaction, which changes with depth (see Fig. 5f).
This is expected as it is evident from Eq. 2 that a
pure global rotation Θx would result in local lateral
displacements that increase with depth.
Furthermore, Fig. 5d shows that a rigid lateral
displacement induces local moment reactions along
the skirt and at the base. Most existing Winkler
formulations for monopiles (API, 2010) or suction
caissons (Gerolymos & Gazetas, 2006) ignore these
coupling terms and doing so might introduce errors
in reproduction of the 3DFE results.
Next, simplifying approximations were made when
deriving the mathematical formulations for these 1D
soil reactions. Specifically, all the skirt 1D soil
reactions were assumed to be constant along the
skirt, apart from the hy coupling reaction, which
varies linearly with depth. This extra complexity is
necessary for accurate KM computations. The
constant or linearly varying profiles were found
using ordinary least square regression against the
true skirt 1D soil reactions and the best fit,
simplified skirt 1D soil reaction profiles are shown
in Fig. 5.
Table 4 shows the formulations that were derived
based on the simplified 1D soil reactions. A two-step
process was used to derive the formulations of these
reactions. First, these reactions were formulated with
respect to the global dof. Thereafter, these
formulations were transformed into the local dof
space using Eq. 2. The finalised formulations of the
1D soil reactions are as follows.
Table 4: Approximate formulations of the 1D soil reactions
following calibration against the 3D FE results. Formulations
for hx and my are similar to that of hy and mx
Formulations
Vertical
vskirt = 4.28 G uz
vbase = 2.4 GD uz
Torsional
tskirt = 3.66 GD2 θz
tbase = 0.41 GD3 θz
Rotational
mxskirt = GD2 (-0.12 uy/D + (1.17 - 0.12 z/D) θx)
mxbase = GD3 (-0.12 uy/D + 0.42 θx)
Lateral
hyskirt = GD (6.51 uy/D + (-19.83 * z/D + 10.28) θx)
hybase = GD2 (1.17 uy/D - 0.6 θx)
6. Discussion
To verify that the calibration was robust and that the
simplification in the formulations did not introduce
significant errors, the normalised global stiffness
coefficients computed using the formulated 1D soil
reactions were compared against the actual 3D FE
results. For this exercise, the global stiffness
coefficients were computed using the analytical
solutions in Table 1 and the 1D soil reaction
formulations in Table 4. Table 5 shows the
normalised global stiffness coefficients predicted by
the 1D caisson model and the original 3D FE results.
As can be observed, the formulated 1D soil
reactions, albeit simplified, can reproduce the 3D FE
results well.
Table 5: Comparison of normalised stiffness coefficients
computed by the formulated 1D soil reactions and the 3D FE
model. The first and second KC predictions by the 1D soil
reactions were computed using the mx and hy based equations
in Table 1 respectively
Stiffness
3D FE
1D Soil Reactions
Difference
KV/GD
6.68
6.68
0 %
KH/GD
7.68
7.68
0 %
KM/GD3
7.11
7.12
0.06 %
KT/GD3
4.07
4.07
0 %
KC/GD2 (1)
-4.66
-4.66
0 %
KC/GD2 (2)
-4.66
-4.66
0 %
An important result to note is the computational time
required for each set of predictions. While the 3D
FE analyses took an hour in total to compute the
stiffness coefficients shown in Table 3, the proposed
1D model takes only milliseconds. This shows the
potential of an efficient design process, which can be
broken down into an offline and online stage.
In the offline stage, the time intensive 3D FE
analyses are carried out to calibrate the proposed
model (which only needs to be done once). In the
online stage, the calibrated 1D caisson model is used
with minimal computational effort. This allows a
rapid turnover of design evaluations, which is a
crucial part of many time critical design activities
such as foundation design optimisation. This is a
very significant improvement over the current state
of practice.
Nevertheless, the proposed model does have some
limitations. The paper has shown that the modelling
approach is satisfactory and has been implemented
correctly; given the excellent agreement between the
model predictions and the 3D FE results as shown in
Table 5. However, these results do not provide any
evidence that the proposed model, in its current
form, has any predictive capabilities beyond the
single case of a caisson foundation of L/D = 1 in
incompressible elastic soil. Nevertheless, it is not
difficult to run a more extensive offline stage with
more 3D FE analyses to derive generalised 1D soil
reaction formulations for different caisson
dimensions and elastic soil properties. Although this
work has been completed it is not reported here as
the focus of this paper is on the underlying
modelling approach. The work on generalised 1D
soil reactions will be reported at a later stage.
7. Conclusion
Fatigue design of caisson foundations usually
requires a large number of analyses. Thus, a suitable
design method for fatigue design must be efficient,
in addition to being accurate. However, existing
design methods are limited by efficiency or the level
of detail of soil profiles that can be modelled.
This paper addresses this issue by proposing a
computationally efficient design method that can
provide accurate predictions of the stiffness of
caisson foundations in elastic soil. Compared to the
3D FE model, the proposed model can provide
stiffness predictions at similar levels of accuracy but
at a small fraction of the computational cost. Unlike
existing macro element models, the proposed model
is applicable for any non-homogeneous soil,
including layered soil.
It is evident that the proposed model offers
significant advantages over existing methods,
especially ease of calibration and computational
efficiency. Most of the limitations of the model are
related to the incomplete formulations of the 1D soil
reactions, which can be rectified with further
calibration against more 3D FE results, following
the methodology illustrated in this paper.
8. Acknowledgments
The first Author acknowledges the generous support
by DONG Energy Wind Power through a DPhil
Scholarship at the University of Oxford.
9. References
API. 2010. RP 2A-WSD - Recommended Practice
for Planning, Designing and Constructing Fixed
Offshore Platforms. Washington: American
Petroleum Institute.
Byrne, B.W., McAdam, R., Burd, H.J., Houlsby, G.,
Martin, C., Zdravkovic, L., Taborda, D., Potts,
D., Jardine, R. and Sideri, M., 2015. New design
methods for large diameter piles under lateral
loading for offshore wind applications. 3rd
International Symposium on Frontiers in
Offshore Geotechnics, Oslo, Norway, June 10-
12.
Davidson, H.L. 1982. Laterally loaded drilled pier
research, Vol 1: Design methodology, Vol. 2:
Research documentation. Final Report by GAI
Consultants Inc., to Electric Power Research
Institute (EPRI).
Dassault Systèmes. 2010. Abaqus analysis users’
manual. Simula Corp., Providence, RI.
DNV. 2014. OS-J101 - Design of Offshore Wind
Turbine Structures. Oslo: Det Norske Veritas.
Doherty, J.P., Houlsby, G.T. and Deeks, A.J. 2005.
Stiffness of flexible caisson foundations
embedded in nonhomogeneous elastic soil.
Journal of Geotechnical and Geoenvironmental
Engineering 131(12): 1498-1508.
Gerolymos, N. and Gazetas, G., 2006. Winkler
model for lateral response of rigid caisson
foundations in linear soil. Soil Dynamics and
Earthquake Engineering, 26(5), 347-361.
Houlsby, G. T., Cassidy, M. J. and Einav, I. (2005).
A generalised Winkler model for the behaviour
of shallow foundations. Geotechnique 55, No. 6,
449460
Suryasentana, S.K., Byrne, B.W., Burd, H.J. and
Shonberg, A. 2017. Weighting functions for the
stiffness of circular surface footings on multi-
layered non-homogeneous elastic half-spaces
under general loading. Proceedings of the 19th
International Conference on Soil Mechanics and
Geotechnical Engineering, Seoul, South Korea
... Winkler models are widely used to design deep foundations such as piles. However, in recent work (Gerolymos and Gazetas, 2006;Varun et al., 2009;Suryasentana et al., 2017), Winkler models have also been developed for shallow foundations such as caisson foundations. While these design methods may not be as accurate as more rigorous approaches such as the three-dimensional finite element (3DFE) method, Winkler models have the advantages of being relatively fast and easy to use. ...
... Recently, Suryasentana et al. (2017) developed a 1D Winkler model, calibrated against 3DFE analyses, to accurately predict suction caisson behaviour in linear elastic soil for six degrees of freedom (dof) loading. However, this model can only be applied to loading conditions where the soil response can be approximated as linear elastic. ...
... This paper extends the 1D Winkler model developed in Suryasentana et al. (2017) to allow predictions of non-linear caisson behaviour in undrained clay under combined planar vertical V, horizontal H and moment M loading. The extension involves coupling linear elastic soil reactions with local plastic yield surfaces, which are calibrated against rigorous 3DFE failure state analyses. ...
... Winkler models are widely used to design deep foundations such as piles. However, in recent work (Gerolymos and Gazetas, 2006;Varun et al., 2009;Suryasentana et al., 2017), Winkler models have also been developed for shallow foundations such as caisson foundations. While these design methods may not be as accurate as more rigorous approaches such as the three-dimensional finite element (3DFE) method, Winkler models have the advantages of being relatively fast and easy to use. ...
... Recently, Suryasentana et al. (2017) developed a 1D Winkler model, calibrated against 3DFE analyses, to accurately predict suction caisson behaviour in linear elastic soil for six degrees of freedom (dof) loading. However, this model can only be applied to loading conditions where the soil response can be approximated as linear elastic. ...
... This paper extends the 1D Winkler model developed in Suryasentana et al. (2017) to allow predictions of non-linear caisson behaviour in undrained clay under combined planar vertical V, horizontal H and moment M loading. The extension involves coupling linear elastic soil reactions with local plastic yield surfaces, which are calibrated against rigorous 3DFE failure state analyses. ...
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Most existing Winkler models use non-linear elastic soil reactions to capture the non-linear be-haviour of foundations. These models cannot easily capture phenomena such as permanent displacement, hys-teresis and the influence of combined loading on the failure states. To resolve these shortcomings, an elasto-plastic Winkler model for suction caisson foundations under combined loading is presented. The proposed model combines Winkler-type linear elastic soil reactions with local plastic yield surfaces to model the non-linear soil response using standard plasticity theory, albeit in a simplified one-dimensional (1D) framework. The results demonstrate that the model reproduces the appropriate foundation behaviour, comparing closely to three-dimensional finite element (3DFE) analyses but with the advantage of rapid computation time.
... A similar process to calibrate the design model for a representative offshore clay till site (not discussed in the current paper) is described in Byrne et al. 2017. ...
... Similar to the assumptions commonly adopted for spudcan analyses (Houlsby, 2014) and as described by Dekker (2014) with specific reference to suction bucket foundations, a structural analysis of the jacket structure often requires the geotechnical engineer to provide a 6X6 stiffness matrix for use as the boundary condition in the jacket model. Numerous authors have proposed methods for estimating the 6DOF suction bucket response to loading (Doherty et al., 2005;Suryasentana et al., 2017) using a limited number of site specific inputs such as soil stiffness and suction bucket dimensions. Due to the 'push-pull' nature of the loading on the SBJ, the vertical stiffness will typically dominate the response in terms of soil structure interaction. ...
... Both the Doherty et al. (2005) and Suryasentana et al. (2017) methods are calibrated from extensive numerical modelling. A key assumption of both methods is that the lid is a rigid element, although variations in skirt stiffness are taken into account by the former. ...
... Analytical solutions for computing the elastic stiffness of shallow foundations exist in the literature (e.g. Bordón et al., 2016;Doherty and Deeks, 2003;Gazetas, 1983;Suryasentana et al., 2017;Vabbersgaard et al., 2009). A viable alternative to the linear elastic models is the so called macro-element approach. ...
... The research considers different foundation geometries and ground conditions, and provides closed form solutions for estimation of the stiffness coefficients. Gazetas, (1983) summarized most of the existing formulations available at that time, Bell, (1991), Doherty and Deeks (2003) and Suryasentana et al., (2017) examine the effect of combined loading in more detail and Doherty et al. (2005) addresses the effect of skirt flexibility. The research consistently suggests that the decoupling coefficient increases with embedment depth (or skirt length), thus it cannot be ignored for typical caisson geometries. ...
Thesis
The thesis focuses on the modelling of the response of shallow skirted foundations supporting offshore wind turbines (OWT). OWT-structures need to be optimized in design to reduce the cost of energy from offshore wind production. The optimization is demanding since OWTs are dynamically sensitive structures exposed to loads with a complex load frequency content. To capture the coupling between non-linear actions and reactions from wind, wave, turbine controller, structural dynamics and foundation response, it has become industry standard to carry out so so-called integrated dynamic analyses in the time domain. However, the foundation response of a skirted foundation is typically modelled in a simplified manner in design. This is unfortunate as research, including studies performed in this PhD, show that foundation behaviour significantly influences the dynamics of OWTs. Accurate geotechnical analyses, which typically model the soil by continuum elements and complex non-linear constitutive models, are unsuitable for integrated time-domain analyses, as they significantly increases the computation time. Foundation modelling by macro-elements is a promising method that balances the requirements of accuracy and computational efficiency. A macro-element represents the whole foundation and the soil by a non-linear formulation at one point. This point can for example be connected to the structure at seabed. Existing research and development of macro-elements has been largely based on results from small scale 1g-tests, centrifuge tests and a few field tests. This gives the models a firm scientific basis. However, the research has been less focused on the challenges of practical usage of the foundation models, and nor the adaption to other conditions than those considered in the model tests. This prevents usage of macro-elements in design, leaving practitioners with only the simplified analysis options. A macro-element is proposed in this PhD-thesis aiming to address some of these challenges. The macro-element formulation is based on results from finite element analyses of skirted foundations. These results are presented as a separate study of foundation behaviour subjected to general loading. The NGI-procedure accounting for cyclic loads is used to define the soil behaviour, and the study investigates the capacity and stiffness response of the foundation. The study considered combined vertical, horizontal and moment loads and combined static and cyclic loading. The results are used to define a procedure for estimating the response of a skirted foundation subjected to general loading, accounting for cyclic soil degradation at foundation level. The study also reveals how the load-displacement response for pure vertical displacement, horizontal displacement and rotation, denoted uniaxial response, can be used to estimate general load paths. Thus, the uniaxial response is considered to define the fundamental behavioural characteristics of the behaviour for a specific foundation. This idea is brought on into the development of a macro-element, by requiring the uniaxial response curves as model input. The macro-element is formulated within the multi-surface plasticity framework. The framework is well suited for modelling of cyclic response, as it has a memory of the recent history through the back stress vector, which contain the coordinates of the origin of the yield surfaces. The Piecewise linear hardening makes the macro-element flexible in the sense that different load-displacement curves can be reproduced. The hardening is anisotropic based on interpolation between the uniaxial responses using the flow direction vector. Requiring the uniaxial responses as input makes the macro-element behaviour site-specific and able to capture the variations in response due to non-homogeneous profiles. This makes the macro-element more suitable for practical use than other macro-elements presently available in the public domain. The macro-element response is compared with finite element analyses and a field test, and the agreement is found to be very good. Assessment of accumulated displacement is addressed outside the integrated analyses. For this reason, the macro-element was formulated with a pure kinematic hardening rule such that no accumulation of displacements occur during a cyclic history. Special attention is given to the problem of numerical ratchetting, which is reported to be a problem in several cyclic models. Testing showed that the macro-element is rigorously formulated with respect to ratchetting. The macro-element is also formulated to include internal flexibility of the foundation. This addresses recent full scale measurements of a jacket founded on caisson foundations (Suction Bucket Jacket) where the caisson flexibility contributed significantly to the total stiffness. The flexibility is included in the formulation as an elastic correction, implemented as a series coupled three-dimensional spring. The macro-element is found to include the effect of caisson flexibility with sufficient accuracy when compared to FEA results. The PhD-thesis address the challenges of foundation modelling from the perspective of practitioners. The proposed procedures and the macro-element can be used in practical design, and should contribute to improved accuracy in the prediction of foundation behaviour in integrated analyses.
... The size of the soil contour is specified such that any stress increase on the boundary is absorbed without rebounding and disturbing the model results. Suryasentana et al. [29] presented a mesh domain of 80D (D is the diameter of the suction caisson) for both diameter and depth to analyse vertically loaded foundations, while Latini et al. [30] used 100D and 30D for the diameter and depth respectively. Moreover, Sloan [31] adopted 5D for the mesh dimensions when analysing vertically loaded rigid circular footing. ...
Article
Full-text available
Suction Bucket Jackets (SBJs) need to be fundamentally designed to avoid rocking modes of vibration about the principal axes of the set of foundations and engineered towards sway-bending modes of tower vibration. Whether or not such type of jackets exhibit rocking modes depends on the vertical stiffness of the caissons supporting them. This paper therefore derives closed form solutions for vertical stiffness in three types of ground profiles: linear, homogenous, and parabolic. The expressions are applicable to suction caissons having an aspect ratio (depth: diameter) between 0.2 and 2 (i.e., 0.2 < L/D < 2). The work is based on finite element analysis followed by non-linear regression. The derived expressions are then validated and verified using studies available in literature. Finally, an example problem is taken to demonstrate the application of the methodology whereby fundamental natural frequency of SBJ can be obtained. These formulae can be used for preliminary design and can also be used to verify rigorous finite element analysis during detailed design.
... The finite element method is routinely used for the design of offshore wind turbine foundations, with complex time-consuming three-dimensional (3D) FEA typically performed to calibrate simplified macro element or one-dimensional (1D) finite models for rapid foundation design calculations across large wind farms (e.g. Erbrich et al., 2010;Byrne et al., 2017;Suryasentana et al., 2017;Skau et al., 2018). ...
Thesis
Full-text available
The finite element method is routinely used for the design of offshore wind turbine foundations, with complex time-consuming three-dimensional (3D) finite element analysis (FEA) typically performed to calibrate site-specific simplified macro element or one-dimensional (1D) finite models for rapid foundation sizing design calculations. The soil constitutive model used in a FEA calculation significantly influences the predicted foundation response. Therefore, given the uptake by industry of FEA for offshore wind turbine foundation design, it is important that practical advanced constitutive models are available which can be demonstrated to work robustly and accurately as design tools. There have been significant advances in constitutive modelling of soils over the last few decades, with many advanced models presented in the literature. However, the uptake of such advanced models in industry, for foundation design FEA, is still relatively low with more basic robust models typically preferred. The principal reasons for this are considered to be: difficulties in calibrating model parameters to standard laboratory test data; robust implementation of advanced constitutive models in FEA software is time consuming and complex; excessive analysis run times and convergence issues makes the use of some advanced models on design projects unfeasible; and there are few examples that demonstrate the robustness and predictive capabilities of many advanced models for complex 3D soil-structure interaction problems. It is therefore important that practical constitutive models are also developed which can be demonstrated to work robustly and accurately as useful tools for design FEA. This project therefore considers the development and use of practical constitutive models for design, and includes a review of some existing models, with a focus on the predictive capability and parameter calibration process for foundation design FEA. A practical robust sand model formulation and implementation is presented for use in design analysis with extensive calibration of the model to laboratory tests data, at a number of different sites, followed by FEA of monopile and suction bucket foundations. In addition, the formulation and implementation of a multi-surface soil plasticity model, termed the PIMS model, which is suitable for short-term storm type loading conditions, is presented. Calibration of the PIMS model to North Sea overconsolidated clay laboratory test data is performed, followed by FEA of monopiles foundations under monotonic and cyclic loading. The suitability of a bounding surface plasticity model for sand to predict the uplift response of a suction bucket foundation under different loading rates is also investigated, with comparison of FEA predictions to previously-published centrifuge test results. Finally, numerical analysis of monopile foundations performed as part of geotechnical design progression for a large offshore wind farm development, in the North Sea is presented using a number of different constitutive models. In all cases extensive calibration to laboratory element tests (primarily from North Sea soil units) is presented, followed by the comparison of FEA predictions to foundation load tests, where possible, to demonstrate that the models are suitable for design FEA of offshore wind turbine foundations.
... In the current work, a novel elastoplastic Winkler model, termed 'OxCaisson-LEPP' is used to model the suction caisson foundation behavior. OxCaisson-LEPP combines linear elastic soil reactions (Suryasentana et al. 2017) with local plastic yield surfaces, which have been calibrated using threedimensional (3D) finite element analyses. Compared to non-linear elastic Winkler models such as the p-y and t-z methods (API, 2010;DNV, 2014), this elastoplastic Winkler model offers significant advantages such as realistic modelling of phenomena such as hysteresis and the interaction of different local load and moment components at failure. ...
Conference Paper
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This paper describes an automated approach for determining the optimal dimensions (length and diameter) of a suction caisson foundation subject to lateral loads, to minimise the foundation weight, whilst satisfying installation requirements, serviceability and ultimate limit states. The design problem was cast as a constrained optimisation problem. Solutions were initially developed using a graphical approach; the solution process was then repeated with an automated approach using an optimisation solver. Both approaches were feasible because a computationally efficient elastoplastic Winkler model was used to model the suction caisson foundation behavior under applied loading. The automated approach was found to be fast and reasonably accurate (when compared to more computationally expensive design procedures using three-dimensional finite element analyses). The benefits of this approach, made possible by the efficiency of the models employed, include better design outcomes and reduced design time.
... Analytical solutions for computing the coefficients of linear elastic springs for shallow foundations exist in the literature (e.g. Bordón, Aznárez, and Maeso 2016;Doherty and Deeks 2003;Gazetas 1983;Suryasentana et al. 2017;Vabbersgaard et al. 2009). ...
Conference Paper
The concept of macro-element modelling – which was first introduced almost 30 years ago – has proven to be a convenient and accurate technique for modelling offshore foundations, but historically these models have mainly been used for academic purposes. Recent developments in foundation modelling now allow for application of such models in engineering practise and design. One such example is the family of new macro-element models that have been developed in the research project REDWIN to represent the foundation behaviour in dynamic analyses of Offshore Wind Turbines (OWTs). These models exhibit characteristic foundation behaviour such as nonlinearity, coupling of the load from different load components and hysteretic load dependent damping. This paper presents two of the REDWIN models, one applicable for monopile foundations and one for skirted suction caisson foundations. Use of the models are demonstrated through two practical problems that reflect typical design analyses of OWTs: the first example shows a fatigue damage assessment for a monopile, and the second considers an extreme load event for a suction bucket jacket. The structural response is computed using the REDWIN foundation models and compared with the response based on distributed API p-y springs for the monopile and clamped legs at seabed for the jacket. Special emphasis is devoted to how the model input is obtained to guide readers on practical use of the models.
Conference Paper
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Offshore wind turbines are typically founded on single large diameter piles, termed monopiles. Pile diameters of between 5m and 6m are routinely used, with diameters of up to 10m, or more, being considered for future designs. There are concerns that current design approaches, such as the p-y method, which were developed for piles with a relatively large length to diameter ratio, may not be appropriate for large diameter monopiles. A joint industry project, PISA (PIle Soil Analysis), has been established to develop new design methods for large diameter monopiles under lateral loading. The project involves three strands of work; (i) numerical modelling; (ii) development of a new design method; (iii) field testing. This paper describes the framework on which the new design method is based. Analyses conducted using the new design method are compared with methods used in current practice.
Article
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A theoretical model is described for the behaviour of rigid foundations subjected to combined vertical, horizontal and moment loading. The model is based on a generalisation of the Winkler concept of subgrade reaction. Non-linearity of the stress-displacement response is introduced using the concepts of hyperplasticity, and the integration of the stresses over the foundation area is treated within this theoretical framework. The resulting model exhibits (with some limitations) behaviour that quite closely resembles that obtained from experiments and from more sophisticated numerical analyses. The performance of the model is illustrated by calculations for selected load and displacement histories. The primary purpose is to derive models, based on clearly articulated principles, that are capable of describing cyclic behaviour of foundations, and yet retain sufficient simplicity that they can be coupled with analyses of structures. Such models have important applications in the offshore industry for prediction of foundation response under environmental loads.
Article
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Solutions are presented for stiffness coefficients to represent the elastic behavior of a caisson foundation embedded in soil. The solutions use a novel numerical technique, the scaled boundary finite element method, combined with shell elements to represent the foundation itself The stiffness coefficients take into account the possibility of nonhomogeneity in the soil (stiffness varying with depth), the geometry of the foundation, and the contribution to the stiffness of the skirt of the caisson foundation. Tabulated values allow a simple curve fit to the stiffness values to be employed for particular cases. The accuracy of the method is tested against previous solutions for particular cases. Example calculations are given to illustrate the method.
Article
A generalized spring multi-Winkler model is developed for the static and dynamic response of rigid caisson foundations of circular, square, or rectangular plan, embedded in a homogeneous elastic. The model, referred to as a four-spring Winkler model, uses four types of springs to model the interaction between soil and caisson: lateral translational springs distributed along the length of the caisson relating horizontal displacement at a particular depth to lateral soil resistance (resultant of normal and shear tractions on the caisson periphery); similarly distributed rotational springs relating rotation of the caisson to the moment increment developed by the vertical shear tractions on the caisson periphery; and concentrated translational and rotational springs relating, respectively, resultant horizontal shear force with displacement, and overturning moment with rotation, at the base of the caisson. For the dynamic problem each spring is accompanied by an associated dashpot in parallel. Utilising elastodynamic theoretical available in the literature results for rigid embedded foundations, closed-form expressions are derived for the various springs and dashpots of caissons with rectangular and circular plan shape. The response of a caisson to lateral static and dynamic loading at its top, and to kinematically-induced loading arising from vertical seismic shear wave propagation, is then studied parametrically. Comparisons with results from 3D finite element analysis and other available theoretical methods demonstrate the reliability of the model, the need for which arises from its easy extension to multi-layered and nonlinear inelastic soil. Such an extension is presented in the companion papers by the authors [Gerolymos N, Gazetas G. Development of Winkler model for lateral static and dynamic response of caisson foundations with soil and interface nonlinearities. Soil Dyn Earthq Eng. Submitted companion paper; Gerolymos N, Gazetas G. Static and dynamic response of massive caisson foundations with soil and interface nonlinearities—validation and results. Soil Dyn Earthq Eng. Submitted companion paper.].
Article
This paper presents the results of an applied research study directed at improving the state-of-practice, and resulting foundation economy, in the design of laterally loaded drilled pier foundations subjected to high ground-line moments or high ground-line shears. A theoretical four-spring, subgrade modulus model was developed in this study and was subsequently modified using the results of 14 full-scale load tests. The resultant semi-empirical nonlinear model formed the basis for the development of a design/analysis computer program (PADLL) for drilled pier foundations embedded in multi-layered subsurface profiles. The predicted behavior of two test piers, using both state-of-practice techniques and PADLL, are compared with measured behavior. Potential cost savings associated with piers designed using the semi-empirical model are discussed.
Weighting functions for the stiffness of circular surface footings on multilayered non-homogeneous elastic half-spaces under general loading
  • S K Suryasentana
  • B W Byrne
  • H J Burd
  • A Shonberg
Suryasentana, S.K., Byrne, B.W., Burd, H.J. and Shonberg, A. 2017. Weighting functions for the stiffness of circular surface footings on multilayered non-homogeneous elastic half-spaces under general loading. Proceedings of the 19th International Conference on Soil Mechanics and Geotechnical Engineering, Seoul, South Korea
OS-J101 -Design of Offshore Wind Turbine Structures. Oslo: Det Norske Veritas
  • Dnv
DNV. 2014. OS-J101 -Design of Offshore Wind Turbine Structures. Oslo: Det Norske Veritas.