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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:

lid

Lplugskirt

Lskirttip vdzvdzvvV 0

,

0

(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,

449–460

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