Mooring Systems for OWT

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NTNU
Norwegian University of Science and Technology
Department of Marine Technology

M.Sc.THESIS

Title:

Delivered:

Design analysis and optimisation of
mooring system for floating wind turbines

14.06.2011
Availability:
Open

Student:

Number of pages:

Tore Hordvik

71

Abstract:
Lately, focus is put on renewable energy resources as the environmental concerns regarding exploitation of
hydrocarbons are increasing. The enormous energy potential found in offshore wind fields is proposed utilized
by installing floating wind turbines in interconnected wind farms. As for all other floating structures operating
within a limited area, stationkeeping is needed in order to keep the motions of the floating structure within
permissible limits. In this study, methods for selecting and optimising the mooring system for floating wind
turbines in shallow water are investigated. The design of the mooring system is checked against the governing
rules and standards.
Initially, the forces and moments associated with such structures are identified as the various terms in the
equations of motions.
Furthermore, the different mooring system concepts investigated in the study are described. They include
distributed mass-, clump weight-, and buoyancy element mooring system. They are all based on the Hywind
design with three distributed main mooring lines, each split into two delta-lines. Software programs suitable for
analysing the system behaviour are recognized as SIMO, Riflex and TDHMILL3D. The analysis methods
include quasi-static catenary analysis, eigenvalue analysis and decay analysis, in addition to integrated time
domain analysis.
The mooring system concepts are studied, and the clump weight mooring system is shown to be the preferred
one with respect to limiting peak tensions in the mooring lines. The selected design concept is subjected to an
optimisation procedure, where the main focus is to select mooring line segments with adequate breaking
strength to sustain the maximum line tension with sufficient margins and to avoid vertical forces on the anchors.
From parameter studies, the size of the clump weight is shown to be the most influential design parameter.
Other parameters investigated include the position of the clump weight, pretension, overall length of the
mooring system, chain and wire weight/dimension, vertical fairlead position and the delta-line length.
Finally, the intact optimised mooring system is checked against the Ultimate limit state, while Accidental limit
state control is performed for the mooring system in damaged condition. Both the cases of loss of line and loss
of clump weight are investigated. The Troll field is selected as design location. For the Ultimate limit state, the
criteria given in the standards are fulfilled for all directions. For the Accidental limit state, the mooring system
design fails to meet the criteria given in the standards. Lack of redundancy is shown as this may cause loss of
additional anchorlines.

Keyword:

Advisor:

Floating wind turbine
Mooring system
Optimisation
Address:
NTNU
Department of Marine Technology
N-7491 Trondheim

Professor Carl Martin Larsen

Location
Marinteknisk Senter
O. Nielsens vei 10

Tel.
Fax

+47 73 595501
+47 73 595697

NTNU Trondheim
Norwegian University of Science and Technology
Faculty of Engineering Science and Technology
Department of MarineTechnology

M.Sc. thesis 2011
for

Stud.tech. Tore Hordvik

Design analysis and optimisation of mooring system for
floating wind turbines
Renewable energy is considered to be the only sustainable way for future energy supply. Norway
is blessed with topography and sufficient rainfall that makes it possible to produce sufficient
electricity from hydropower. However, future growth in domestic energy demand and export will
require unwanted encroachments on rivers and lakes. Alternative energy production is therefore
encouraged. Wind energy is an obvious alternative, but wind turbines are not always wanted on
land. Offshore windmills have therefore been proposed. For several reasons one would prefer to
have such installations at some distance from the coast, but the water depth on the Norwegian
continental shelf is too large for the use of bottom fixes turbines. It is therefore proposed to have
floating wind turbines and the design of cheap but reliable mooring systems for such structures
will hence crucial for the economy of this concept.
The purpose of this project is to describe a rational method for design verification analysis and
mooring line optimisation for floating wind turbines on shallow water.
The work is a continuation of the pre-project that reported basic features of floating wind turbines
and relevant analysis methods. Subjects that have been reported in the pre-project should not be
repeated in the MSc thesis.
The work may be carried out in steps as follows:
1. Select realistic design parameters for a floating wind turbine that might be applied for large
scale power production on 85-100 meters water depth in Norwegian waters.
2. Discuss alternative mooring system designs, and select the topography for a system that should
be subjected to further studies.
3. Define all needed parameters for the selected system, either from optimisation or based on
experience and sound engineering judgement.
4. Describe methods for a complete design verification including the use of actual computer
programs and analysis procedures.
5. Carry out and report selected parts of a design verification. The selection of actual analyses
should be discussed with the supervisor.
The will be carried out in cooperation with Statoil Bergen, where student will stay most of the
time during the MSc thesis period.

NTNU
Norwegian University of Science and Technology

Faculty of Marine Technology
Department of Marine Structures

The work may show to be more extensive than anticipated. Some topics may therefore be left out
after discussion with the supervisor without any negative influence on the grading.
The candidate should in her/his report give a personal contribution to the solution of the problem
formulated in this text. All assumptions and conclusions must be supported by mathematical
models and/or references to physical effects in a logical manner.
The candidate should apply all available sources to find relevant literature and information on the
actual problem.
The report should be well organised and give a clear presentation of the work and all conclusions.
It is important that the text is well written and that tables and figures are used to support the verbal
presentation. The report should be complete, but still as short as possible.
The final report must contain this text, an acknowledgement, summary, main body, conclusions
and suggestions for further work, symbol list, references and appendices. All figures, tables and
equations must be identified by numbers. References should be given by author name and year in
the text, and presented alphabetically by name in the reference list. The report must be submitted
in two copies unless otherwise has been agreed with the supervisor.
The supervisor may require that the candidate should give a written plan that describes the
progress of the work after having received this text. The plan may contain a table of content for
the report and also assumed use of computer resources.
From the report it should be possible to identify the work carried out by the candidate and what
has been found in the available literature. It is important to give references to the original source
for theories and experimental results.
The report must be signed by the candidate, include this text, appear as a paperback, and - if
needed - have a separate enclosure (binder, DVD/ CD) with additional material.

Supervisor at NTNU:
Contact person at Statoil:

Carl M. Larsen
Tor Hanson

Trondheim, January 2011

Carl M. Larsen
Submitted:
Deadline:

January 2011
June 2011

Preface
This report is the result of the course TMR4900 Marine Structures - Master thesis at the
Department of Marine Technology at the Norwegian University of Science and Technology
(NTNU) in Trondheim. The work is carried out at the Statoil research centre at Sandsli,
Bergen. The study elaborates on optimising the mooring system design for offshore floating
wind turbines in shallow water. A water depth of 100 m is assumed. The design is based on
the Hywind design with modified draft, accounting for the reduced water depth.
In an attempt to maintain the motion characteristics of the Hywind pilot, the draft is only
reduced by 20 m to 80 m. Whether the vertical distance between the tower bottom and the sea
bed of only 20 m is sufficient from a design perspective is not investigated. The same is the
case for whether a deep-draft SPAR concept is the most cost-effective concept for such water
depths. Focus is mainly put on how the mooring system can be selected, optimised, and
designed according to the governing rules and standards for the selected design concept.
Several people have contributed to the realization of this report. First and foremost I would
like to thank NTNU and my supervisor Professor Carl Martin Larsen, and the Statoil research
centre represented by my supervisor Tor David Hanson for the cooperation and contributions
during the thesis work. I would also like to thank Finn Gunnar Nielsen and Rune Yttervik at
the Statoil research centre for their contributions. Vryhof anchors in the Netherlands are also
acknowledged for their helpfulness. Gratitude is finally addressed to my office mates Jon Erik
Lygren and Ingebjørg Hage for making my stay at the Statoil research centre memorable.

Tore Hordvik
Bergen, June 14th, 2011

I

II

Abstract
Lately, focus is put on renewable energy resources as the environmental concerns regarding
exploitation of hydrocarbons are increasing. The enormous energy potential found in offshore
wind fields is proposed utilized by installing floating wind turbines in interconnected wind farms.
As for all other floating structures operating within a limited area, stationkeeping is needed in
order to keep the motions of the floating structure within permissible limits. In this study, methods
for selecting and optimising the mooring system for floating wind turbines in shallow water are
investigated. The design of the mooring system is checked against the governing rules and
standards.
Initially, the forces and moments associated with such structures are identified as the various
terms in the equations of motions.
Furthermore, the different mooring system concepts investigated in the study are described. They
include distributed mass-, clump weight-, and buoyancy element mooring system. They are all
based on the Hywind design with three distributed main mooring lines, each split into two deltalines. Software programs suitable for analysing the system behaviour are recognized as SIMO,
Riflex and TDHMILL3D. The analysis methods include quasi-static catenary analysis, eigenvalue
analysis and decay analysis, in addition to integrated time domain analysis.
The mooring system concepts are studied, and the clump weight mooring system is shown to be
the preferred one with respect to limiting peak tensions in the mooring lines. The selected design
concept is subjected to an optimisation procedure, where the main focus is to select mooring line
segments with adequate breaking strength to sustain the maximum line tension with sufficient
margins and to avoid vertical forces on the anchors. From parameter studies, the size of the clump
weight is shown to be the most influential design parameter. Other parameters investigated
include the position of the clump weight, pretension, overall length of the mooring system, chain
and wire weight/dimension, vertical fairlead position and the delta-line length.
Finally, the intact optimised mooring system is checked against the Ultimate limit state, while
Accidental limit state control is performed for the mooring system in damaged condition. Both the
cases of loss of line and loss of clump weight are investigated. The Troll field is selected as design
location. For the Ultimate limit state, the criteria given in the standards are fulfilled for all
directions. For the Accidental limit state, the mooring system design fails to meet the criteria
given in the standards. Lack of redundancy is shown as this may cause loss of additional
anchorlines.

III

II

List of abbreviations

ALS
COB
COG
DLL
DNV
DOF
FFT
FLS
JONSWAP
LF
MPM
OS-E301
SLS
ULS
VIV
WF

Accidental Limit State
Centre of Buoyancy
Centre of Gravity
Dynamic Linked Library
Det Norske Veritas
Degree of Freedom
Fast Fourier Transform
Fatigue Limit State
Joint North Sea Wave Project
Low-Frequency
Most Probable Maximum
DNV-OS-E301 “Position Mooring”
Serviceability Limit State
Ultimate Limit State
Vortex-induced vibrations
Wave-Frequency

III

Table of Contents
1. Introduction .......................................................................................................................... 1
1.1 General ............................................................................................................................. 1
1.2 Spar concept ..................................................................................................................... 1
1.3 Hywind pilot ..................................................................................................................... 2
2. System motions and forces .................................................................................................. 3
2.1 General ............................................................................................................................. 3
2.2 The equations of motions ................................................................................................. 3
2.3 Mass matrix ...................................................................................................................... 4
2.4 Damping ........................................................................................................................... 4
2.5 Restoring matrix ............................................................................................................... 4
2.5.1 Hydrostatic ................................................................................................................ 5
2.5.2 Catenary .................................................................................................................... 5
2.6 Excitation forces and moments ........................................................................................ 7
2.6.1 Wave forces ............................................................................................................... 7
2.6.2 Current forces ............................................................................................................ 8
2.6.3 Wind forces ............................................................................................................... 8
2.7 A discussion on natural periods ....................................................................................... 9
2.7.1 General ...................................................................................................................... 9
2.7.2 Mathieu instability................................................................................................... 10
3. Catenary mooring systems ................................................................................................ 11
3.1 General ........................................................................................................................... 11
3.2 Distributed mass mooring system .................................................................................. 11
3.3 Clump weight mooring system ...................................................................................... 12
3.4 Buoyancy element mooring system ............................................................................... 12
4. Analysis software ................................................................................................................ 13
4.1 SIMO .............................................................................................................................. 13
4.2 TDHMILL3D ................................................................................................................. 13
4.3 Riflex .............................................................................................................................. 13
4.4 Integrated analysis .......................................................................................................... 14
5. Analysis models .................................................................................................................. 15
5.1 General ........................................................................................................................... 15
5.2 Finite element model ...................................................................................................... 15
5.3 Tower structure .............................................................................................................. 16
5.4 Mooring system .............................................................................................................. 17
5.4.1 Distributed mass mooring system ........................................................................... 18
5.4.2 Clump weight mooring system ............................................................................... 18
5.4.3 Buoyancy element mooring system ........................................................................ 20
6. Analysis methods ................................................................................................................ 23
6.1 Catenary analysis............................................................................................................ 23
6.2 Eigenvalue analysis ........................................................................................................ 24
6.3 Motion decay test ........................................................................................................... 24
6.3.1 General .................................................................................................................... 24
6.3.2 Natural periods ........................................................................................................ 25
6.3.3 Damping .................................................................................................................. 25
6.4 Time domain analysis procedure.................................................................................... 27
6.5 Data handling ................................................................................................................. 28

IV

7. Concept selection ................................................................................................................ 29
7.1 General ........................................................................................................................... 29
7.2 Quasi-static analysis ....................................................................................................... 29
7.3 Motion decay analysis .................................................................................................... 31
7.3.1 Natural periods ........................................................................................................ 31
7.3.2 Damping .................................................................................................................. 32
7.4 Time domain analysis..................................................................................................... 33
7.5 Conclusion and selection of concept for further studies ................................................ 35
8. Mooring system optimisation ............................................................................................ 37
8.1 General ........................................................................................................................... 37
8.2 Clump weight size .......................................................................................................... 38
8.3 Clump weight position ................................................................................................... 40
8.4 Pretension ....................................................................................................................... 41
8.4 Total line length ............................................................................................................. 42
8.5 Chain and wire dimension .............................................................................................. 43
8.6 Vertical fairlead position ................................................................................................ 44
8.7 Delta-line length ............................................................................................................. 46
8.8 Design mooring system .................................................................................................. 48
9. Design check........................................................................................................................ 51
9.1 General ........................................................................................................................... 51
9.2 Limit states ..................................................................................................................... 52
9.2.1 Ultimate limit state (ULS) ....................................................................................... 52
9.2.2 Accidental limit state (ALS) ................................................................................... 52
9.2.3 Fatigue limit state (FLS) ......................................................................................... 52
9.2.4 Serviceability limit state (SLS) ............................................................................... 53
9.3 Environmental conditions .............................................................................................. 53
9.3.1 Waves ...................................................................................................................... 53
9.3.2 Wind ........................................................................................................................ 53
9.3.3 Current ..................................................................................................................... 54
9.3.4 Directions ................................................................................................................ 54
9.3.5 Drag force coefficients ............................................................................................ 55
9.4 Mooring system analysis ................................................................................................ 55
9.4.1 Time domain analysis.............................................................................................. 55
9.4.2 Characteristic line tension ....................................................................................... 56
9.4.3 Characteristic capacity ............................................................................................ 56
9.4.4 Design equation and partial safety factors .............................................................. 56
9.4.5 Horizontal offset and permissible line length ......................................................... 57
9.5 Results – ULS................................................................................................................. 58
9.6 Results – ALS................................................................................................................. 61
9.6.1 Loss of one line ....................................................................................................... 61
9.6.2 Loss of one clump weight ....................................................................................... 63
10. Conclusion ......................................................................................................................... 65
11. Recommendations for further work ............................................................................... 67
References ............................................................................................................................... 69
Appendices .............................................................................................................................. 71
List of appendices................................................................................................................. 71

V

List of Figures
Figure 1-1: Hywind prototype .................................................................................................... 2
Figure 2-1: Definition of coordinate system .............................................................................. 3
Figure 2-2: JONSWAP wave spectrum ..................................................................................... 7
Figure 2-3: Kaimal wind spectrum............................................................................................. 9
Figure 3-1: Mooring system concepts ...................................................................................... 12
Figure 5-1: Test model, finite element model .......................................................................... 15
Figure 5-2: Test model, tower structure ................................................................................... 16
Figure 5-3: Layout, distributed mass mooring system ............................................................. 18
Figure 5-4: Layout, clump weight mooring system ................................................................. 19
Figure 5-5: Layout, buoyancy element mooring system .......................................................... 20
Figure 6-1: Motion decay signal .............................................................................................. 26
Figure 6-2: Overview of analysis methods .............................................................................. 28
Figure 7-1: Mooring line configuration ................................................................................... 29
Figure 7-2: Mooring line characteristics for three mooring system concepts .......................... 30
Figure 7-3: Surge damping ....................................................................................................... 32
Figure 8-1: Line configuration for various clump weight sizes ............................................... 38
Figure 8-2: Mooring line characteristics for various clump weight sizes ................................ 39
Figure 8-3: Mooring line characteristics for various clump weight positions ......................... 40
Figure 8-4: Mooring line characteristics for various line lengths ............................................ 42
Figure 8-5: Vertical fairlead position ....................................................................................... 45
Figure 8-6: Mooring system layout .......................................................................................... 46
Figure 8-7: Static equilibrium configuration ............................................................................ 48
Figure 9-1: Overview of standards ........................................................................................... 51
Figure 9-2: Definition of directions ......................................................................................... 54
Figure 9-3: Distribution of maximum line tension ULS .......................................................... 59
Figure 9-4: Finite element model, ALS – Loss of line............................................................. 61

VI

List of Tables
Table 1-1: Hywind prototype main data........................................................................................... 2
Table 5-1: Segment lengths ............................................................................................................ 17
Table 5-2: Segment properties, distributed mass mooring system ................................................. 18
Table 5-3: Segment properties, clump weight mooring system ..................................................... 19
Table 5-4: Clump weight properties ............................................................................................... 19
Table 5-5: Segment properties, buoyancy element mooring system .............................................. 20
Table 5-6: Buoyancy element properties........................................................................................ 21
Table 7-1: Natural periods .............................................................................................................. 31
Table 7-2: Relative damping, heave and pitch ............................................................................... 33
Table 7-3: Environmental conditions ............................................................................................. 33
Table 7-4: Response statistics, operational condition .................................................................... 34
Table 7-5: Response statistics, storm condition ............................................................................. 34
Table 8-1: Clump weight size ........................................................................................................ 38
Table 8-2: Dynamic response as function of pretension ................................................................ 41
Table 8-3: Check of vertical forces on anchor ............................................................................... 43
Table 8-4: Chain and wire properties ............................................................................................. 43
Table 8-5: Response from time domain analysis ........................................................................... 49
Table 8-6: System natural periods .................................................................................................. 49
Table 8-7: Single line natural periods ............................................................................................ 50
Table 8-8: Mooring line resonance test .......................................................................................... 50
Table 9-1: Troll field sea state ........................................................................................................ 53
Table 9-2: Troll field wind speed ................................................................................................... 53
Table 9-3: Modified Troll field current profile .............................................................................. 54
Table 9-4: Drag force coefficients.................................................................................................. 55
Table 9-5: Partial safety factors...................................................................................................... 56
Table 9-6: Results ULS analysis .................................................................................................... 58
Table 9-7: MPM and expected value for maximum line tension ULS........................................... 59
Table 9-8: Design equation results ULS ........................................................................................ 60
Table 9-9: Results ALS analysis – Loss of line ............................................................................. 62
Table 9-10: Results ALS analysis – Loss of clump weight............................................................ 63

VII

0

1. Introduction
1.1 General
As the demand for energy is increasing and the oil and gas deposits are limited, focus is put on
renewable energy sources. Wind energy, being one of this renewable energy sources, has been
utilized for agricultural purposes for centuries, and became important also for power production in
the second half of the 20th century. As one wants to take advantage of the enormous wind power
potential offshore, several participants in the international energy business have installed and
commercialized interconnected bottom-fixed wind turbine structures in areas of shallow water.
The water depth is however strongly limiting the extent of such applications, as the support
structures of offshore wind turbines become highly dynamic, having to cope with combined wind
and hydrodynamic loading in addition to the complex dynamic behaviour of the wind turbine
itself (Hordvik, 2010). Wind turbines installed on floating substructures are therefore proposed in
order to utilize the potential for harvesting wind energy in areas that are not feasible for bottomfixed structures. Developing and the possibility of commercializing floating offshore wind
turbines are presently being investigated by several developers, technology providers and research
institutes worldwide. The Spar concept is one of the designs that have been proposed as
substructure for floating offshore wind turbines.

1.2 Spar concept
The Spar concept is not by any means a new concept. It has been used in marine applications for
decades as marker buoys and for gathering oceanographic data. Later it was scaled up and
introduced as production platform in the offshore energy market. The world’s first production spar
was the Neptune Spar installed in 1996 by Oryx Energy Company and CNG (Chakrabarti 2005).
In 2009, Statoil introduced a floating wind turbine based on the Spar concept, which is reviewed
in the following section.
Simplified we can say that the Spar consists of a large cylinder floating vertically in the water. A
Spar platform is weight stabilized, which implies a design where the centre of gravity (COG) is
located below the centre of buoyancy (COB). The low COG is obtained by heavy ballasting in the
bottom part of the cylinder. The concept is characterized by its deep draft which gives the Spar
concept favourable motion characteristics compared to other floating concepts; because the wave
action at the surface is damped by the counter balance effect of the structural weight (Hordvik,
2010).
Some of the key features of the Spar concept include:
- Feasible for water depths up to 3000 m.
- Possibility for a large range of payloads
- Is always stable because the COB is located above the COG
As for any other floating structure operating within a limited area, stationkeeping becomes
important. Spars are traditionally moored by the means of spread catenary moorings. The
restoring forces are then provided by the weight of the mooring lines. When the water depth is
reduced to only 100 m, as investigated in this study, catenary mooring becomes challenging
because the suspended length of the mooring lines, and hence the submerged weight, is limited.
Focus is put on these issues later in the report.

1

1.3 Hywind pilot
As this study is investigating the mooring system of a floating wind turbine structure similar to the
Hywind pilot, a short introduction to the concept is given in the following.
According to Statoil’s homepage, the world’s first operational deep-water floating large-capacity
wind turbine is the Hywind pilot, which is a prototype of the Hywind concept. The pilot is located
about ten kilometers off the coast of Karmøy on the west coast of Norway; it is still in operation,
generating electricity to the Norwegian grid. The main purpose of the pilot project is to investigate
how wind and waves are affecting the structure.
The design is owned by Statoil while Technip built the floater and Siemens manufactured the
turbine. The concept is based on a Spar buoy type design. A 2.3 MW turbine is mounted on the
tower 65 m above the water line. The draft is 100 m and the buoy is moored at a water depth of
approximately 210 m. The tower and substructure is made in steel with water and rock ballasting.
The installation is expected to generate about 9 GWh of electricity annually.
The Hywind mooring system consists of a three-point catenary spread with an angular spacing of
120°. The mooring lines are composed of a combination of chain and steel wire segments. A
clump weight of 60 tons is attached to each mooring line. Each of the main mooring lines is split
into two separate lines (forming a bridle) that are attached to the fairlead. This arrangement
provides increased yaw stiffness.
The main characteristics of the Hywind pilot are collected in table 1-1.

Hywind Prototype Main Data
WTG (Wind Turbine
2.3 MW
Generator)
Turbine weight
138 tons
Nacelle height
65 m
Rotor diameter
82.4 m
Draft hull
100 m
Water depth
210 m
Displacement
5300 m3
Diameter (Water Line)
6m
Diameter (Submerged Body) 8.3 m
Rated wind speed
12 m/s
Mooring
3 lines
Pitch control
Dynamic
Table 1-1: Hywind prototype main data

Figure 1-1: Hywind prototype
(Source: http://www.statoil.com)

2

2. System motions and forces
2.1 General
In this chapter, motions and forces associated with floating structures are briefly discussed. When
appropriate, reference is made to the literature for further details.
It is assumed that we are dealing with a catenary moored vertical cylinder, similar to the Hywind pilot.
The coordinate system for a segmented vertical column is defined in figure 2-1.

Figure 2-1: Definition of coordinate system

2.2 The equations of motions
For steady-state sinusoidal motions, Faltinsen (1990) showed that the equations of motions can be
expressed as:
6

∑ [( M

− iω t
η k ] Fj e =
( j 1,..., 6)
+ Ajk )η + B jkηk + C jk=

(2.1)

e

jk

k =1

On the left side of the equation, the three terms represent the inertia, damping and restoring forces and
moments respectively. On the right side, Fj are the complex amplitudes of the exciting forces and
moment-components with the force and moment-components given by the real part of Fj e − iω t .
e

For a structure with lateral symmetry (symmetry about the x-z-plane) the six coupled equations
reduces to a set of two equations. We see that for the floating structure considered in figure 2-1, the
motions in six degrees of freedom are described by two sets of three coupled equations; one set for
surge, heave and pitch and one set for sway, roll and yaw. Hence, the lateral motions are uncoupled
from the vertical and longitudinal motions.

3

In the following, the various terms of the equations of motions (2.1) are briefly discussed.

2.3 Mass matrix
The forces on a structure proportional to the acceleration are denoted inertia forces. These are
composed of mass- and hydrodynamic forces and moments.
Keeping in mind that we are considering a structure with lateral symmetry, Nielsen (2007) showed that
the mass matrix for vertical and longitudinal motions can be written as:

 M + A11

=
M
0

 Mz + A
 G 51



0

2

I 55 + MzG + A55 
MzG + A15

0
M + A33
0

(2.2)

Here M denotes the total mass of the system, Aij are the hydrodynamic masses, zG is the vertical
position of the centre of gravity and I 55 is the vertical moment of inertia about the centre of gravity.
For a structure with no forward speed and no current present it can be shown that Akj = Ajk, hence A51
= A15.

2.4 Damping
Damping is the structures ability to dissipate energy and becomes very important in order to limit
resonant motions of the structure.
For a floating wind turbine structure, Nielsen (2007) recognized the main contributions to the total
damping as:
- Wave radiation damping
- Viscous damping on the submerged hull
- Viscous damping on the tower due to the relative wind velocity
- Damping due to the velocity dependent forces on the wind turbine
For a detailed description on how the various damping effects are found, reference is made to Nielsen
(2007). Later in the report, it is outlined how the linear and quadratic damping levels can be estimated
from motion decay tests.

2.5 Restoring matrix
The restoring forces will work to pull the structure back to its equilibrium position and consist of the
stiffness forces proportional to the motion of the structure. For a freely floating structure the restoring
forces will appear from hydrostatic and mass considerations, while for a moored structure, restoring
forces from the mooring system have to be added. The total restoring matrix will therefore be:
=
C CH + CM

4

(2.3)

2.5.1 Hydrostatic
By considering the vertical and longitudinal motions, the hydrostatic contribution to the restoring
matrix for a vertical column will be:
0
0
2

C H = 0 ρ gπ RWL

0
0




0


ρ g ( IWL + Vz B ) − mgzG 
0

where RWL is the radius in the water line, V is the displaced volume of the column and IWL =

(2.4)

4
π RWL

4

is the

surface moment of inertia of the water line area.

2.5.2 Catenary
In general, the restoring matrix for a catenary mooring system will depend on the offset. Nielsen
(2007) demonstrated how the restoring matrix for a mooring system could be calculated from the
restoring matrices for the individual lines at a given offset level.
It is assumed that the line initially only will have restoring effects from motion in the catenary plane,
i.e. an x-z-plane with the local x-axis parallel to the extension of the catenary. The only non-zero
contributions to the line restoring matrix will therefore be C11( l ) , C13( l ) , C31( l ) , C33( l ) .
The catenary plane is rotated an angle θ relative to the floater coordinate system, where θ denotes the
azimuth angle of the fairlead coordinates relative to the floater coordinate system.
By introducing the transformation matrix:

 cos(θ ) sin(θ ) 0 


γ= − sin(θ ) cos(θ ) 0


 0

0
1



(2.5)

the restoring effect in a coordinate system parallel to the platform coordinates can be found as:
(2.6)
By using the line upper connection point (fairlead) coordinates [XT,YT,ZT], the line’s contribution to
the restoring matrix for the mooring system will become:

 C( 0 )α C( 0 ) 
CM =  T ( 0)

T
(0)
α C α
α C

5

(2.7)

where α is given as:

 0

α= − Z T

 Y
 T



XT


0 

−YT

ZT
0
−XT

(2.8)

Hence for a spread mooring system consisting of N l lines, the main contributions to the 3dof (surge,
heave and pitch) restoring matrix will be:
Nl

C M ,11 =

∑C

(l )

11

cos θ n
2

n =1

Nl

CM ,33 = ∑ C33( l )
n =1

(2.9)

Nl

CM ,15 = ∑ C ZT cos θ n
(l )
11

2

n =1

Nl

C M ,55
=

∑ [C

(l )

11

Z T + C33 rM ] cos θ n
2

(l )

2

2

n =1

The superscript (l ) refers to the line restoring coefficient C jk ; θ n is the azimuth angle of line number n;
ZT is the vertical coordinate of the fairlead; and rM is radius of mooring line attachments. For the three

point equally spread mooring system utilized on the Hywind (see figure 1-1), equation (2.9) simplifies
to:
CM ,11 =

3
2

C11( l )

CM ,33 = 3C33( l )
CM ,15 =
=
CM ,55

3
2
3
2

C11( l ) ZT

(2.10)

[C11( l ) ZT2 + C33( l ) rM2 ]

One should note that only contributions to the restoring matrix from the catenary plane are included in
the above derivation. These will form the main contributions, but restoring effects from out of plane
motions will also be present. These effects will form the yaw stiffness of the mooring system, which is
briefly discussed in Chapter 8. For further details on how the yaw restoring coefficients are derived,
reference is made to Nielsen (2007).

6

2.6 Excitation forces and moments
The excitation forces and moments are added to the right side of the equations of motions (2.1). The
external forces on the structure are typically environmental loads and may be composed of wave
forces, current forces and wind forces.

2.6.1 Wave forces
By using linear theory, the wave elevation can be described as a sum of individual sinusoidal wave
components. From Faltinsen (1990) we have that for N waves, the total wave elevation for a longcrested wave propagating along the positive x-axis can be expressed as:
=
ζ

N

∑ A sin(ω t − k x + ε
j

j

j

j

)

(2.11)

j =1

where subscript j denotes wave number j , A is the wave amplitude, ω , k and ε are the circular
frequency, wave number and random phase angle respectively.
Furthermore, the relationship between the wave amplitude and wave spectrum is given as:
1 2
=
Aj S (ω j ) ∆ω
2

(2.12)

where S (ω j ) is the spectral density for wave component j , and ∆ω is a constant difference between
successive frequencies. By considering a wide range of frequencies, the wave spectrum will indicate
which frequencies that are contributing to the total energy in the sea state.
A JONSWAP wave spectrum is typically used for describing North Sea sea states.

Figure 2-2: JONSWAP wave spectrum
HS = 12m, TP = 16s

7

Furthermore, a description on how linear and second-order wave forces are obtained is included in the
following. A short summary is reproduced here, while reference is made to Faltinsen (1990) for further
details.
By solving the linear problem, i.e. satisfying the free-surface and body boundary condition on the
mean position of the free-surface and submerged hull, first-order wave forces on the structure are
obtained. These forces will induce first-order motions known as wave-frequency (WF) motions.
However, in order to capture motions in severe sea states and for moored structures, the problem has
to be solved to the second order. This implies accounting for the zero-normal flow condition through
the body at the instantaneous position of the body. The solution of the second-order problem will
result in mean forces and forces oscillating with the sum and difference frequency in addition to the
linear solution. The steady component is known as mean wave-drift forces, while the oscillating
component may act together with environmental forces to induce low-frequency (LF) motions.
For a catenary moored structure, mean and slowly-varying wave forces (difference frequency forces)
are of importance. For a lightly damped moored structure, slow-drift resonant motions occur in surge,
sway and yaw.

2.6.2 Current forces
The current velocity is assumed to be constant with time, and is described by the speed and direction.
For a cylinder with current perpendicular to the cylinder axis, vortices will be shed on alternating
sides, giving rise to drag and lift force on the cylinder. When the vortex-shedding frequency is close to
the natural frequency of the cylinder, large vibrations may occur in both cross-flow and in-line
direction. These vibrations are recognized as vortex-induced vibrations (VIV). When the two
frequencies coincide, the vortex-shedding frequency locks on to the natural frequency of the cylinder
and large resonant motions may occur. The phenomenon is known as lock-in, which in addition to
increased motion amplitudes will cause increased in-line drag forces due to a larger effective drag
area.

2.6.3 Wind forces
The wind speed is typically composed of a rapidly fluctuating gust wind superimposed onto the
slowly-varying mean wind speed. Haver (2010) expressed the total wind speed at time instant t as:
V=
(t ) Vm (t ) + Vt (t )

(2.13)

where Vm (t ) is the mean wind speed and Vt (t ) is the turbulent (gust) wind speed at time instant t . The
mean wind force will give rise to a steady-state wind force; while for a moored structure, the gust wind
may excite resonant slow-drift motions of the structure.
A Kaimal wind spectrum is recommended used for representing the spectral density of the wind
process (DNV-OS-J101), and is shown in figure 2-3.

8

Figure 2-3: Kaimal wind spectrum
Um = 12m/s, TI = 0.1, λ=42

2.7 A discussion on natural periods
2.7.1 General
As the mass and stiffness matrices are found for vertical and longitudinal motions, the natural periods
can be obtained for the same motion modes.
Faltinsen (1990) expresses the natural period for degree of freedom i as:
1

 M + Aii  2
Tni = 2π  ii

 Cii 

(2.14)

Remembering that we defined M as the total mass, including the hydrodynamic mass; by using a strip
theory approach to obtain the added mass, the natural period in surge is written as:
1

1

1

 M + A11  2
 2 ρ wV  2
 M 2
=
Tn1 2=
2π  =
π  11 
 2π 

 C11 
 CM ,11 
 CM ,11 

(2.15)

where ρ w is the water density and V is the displaced volume. Since there is no hydrostatic stiffness
contribution in surge, only the mooring line stiffness will contribute to the stiffness matrix.
9

In heave, we get:
1

1

1

 M + A33  2
 M 2
 M + A33  2
π  33 
2π 
=
Tn 3 2=
 ≈ 2π 
2 
 C33 
 ρ gπ Rwl 
 CH ,33 + CM ,33 

(2.16)

Since the mooring line contribution to the heave stiffness is minimal compared to the hydrostatic
contribution, it can be neglected. The vertical added mass will be very small compared to the mass and
may also be neglected. We see that the natural period in heave is strongly dependent on the waterplane
area.
By considering a reference point close to the vertical COG and assuming ρ wV = mg , the natural period
in pitch becomes:
1

1

1

1

 I + A55  2
 I 55 + A55  2
 M 2
 I 55 + A55  2
2π  55  =
2π  55
2
π
Tn 5 =



 ≈ 2π 

 C55 
 ρVg ( z B − zG ) 
 CH ,55 + CM ,55 
 CH ,55 

(2.17)

where z B and zG is the vertical position of the centre of buoyancy and gravity respectively. The mooring
system effect on the pitch restoring coefficient is neglected.
Typically, for moored structures, the natural period in surge is in order of minutes. For heave and pitch
it is usually required that the natural periods are larger than T = 20 s , above most wave periods in open
sea (4-20s).

2.7.2 Mathieu instability
According to Nielsen (2007), the Mathieu instability is related to a time dependent restoring term in
the equation of motion and is a well-known dynamic phenomenon for spar platforms.
For the coupled heave-, pitch motions, instabilities can occur when the pitch natural period is close to
the heave natural period or twice the heave natural period.
Haslum (2000) showed another effect that may cause Mathieu effects. For a certain wave period,
denoted Twave ,cr , the combined action of wave induced heave and resonant heave may excite pitch
resonance. The critical wave period is given as:
Twave , cr =

1
1

+

Tn 5

10

1
Tn 3

(2.18)

3. Catenary mooring systems
3.1 General
As seen in the previous chapter, the mooring system contributes to providing restoring forces and
moments on a floating structure, pulling the structure back against its equilibrium position. A wide
selection of mooring systems are applied in the offshore industry; ranging from tension leg moorings,
with small horizontal offsets and large vertical forces on the anchors, to catenary moorings, with larger
horizontal offsets and no vertical forces on the anchors. In the present study, only catenary mooring
systems are considered.
A catenary mooring system may be composed of one or several individual lines connected to the
floating structure at the fairlead and the sea bottom at the anchors. The suspended part of each line will
form a catenary, where the shape is dependent on the weight of the line in addition to the horizontal
and vertical distance between the fairlead and anchor. The line arrives at the sea bottom horizontally,
so that the anchor is only subjected to horizontal forces. The initial horizontal holding capacity, often
referred to as the pretension, is dependent on the horizontal distance between the fairlead and the
anchor. The restoring forces are provided by the weight of the line. Hence the major contribution to
the stiffness matrix from the mooring system comes from the geometric stiffness of the line, i.e.
stiffness due to the change of geometry of the catenary.
As the top end point of the mooring line is moved, the initial configuration of the mooring line is
modified; and assuming that part of the line is resting on the sea bottom, the new position is
determined by the geometric stiffness of the line. The restoring force from the mooring system will be
non-linear as the catenary configuration of the mooring lines and the existence of the sag introduce
geometric non-linearity (Loukogeorgaki et al. 2005). In chapter 6, it is shown how the restoring forces
from each mooring line can be calculated.
Typically, the mooring lines are segmented in order to optimise the force/displacement characteristics
known as the mooring line characteristics. In addition to anchors and connectors, the lines may be
composed of chains, wire ropes and synthetic fiber ropes. For details regarding the different mooring
components, reference is made to Hordvik (2010).
In this report, three different concepts based on catenary moorings are considered. They are presented
in the following.

3.2 Distributed mass mooring system
For the distributed mass mooring system, the restoring stiffness is obtained by applying mooring line
segments with large submerged weight. Typically, large diameter chains are used as they have
significantly larger self-weight than wire and synthetic fiber ropes. The bottom chain can either have
the same weight as the rest of the line, or larger weight for increased geometric stiffness. This mooring
system concept is widely used for stationkeeping of offshore applications.

11

3.3 Clump weight mooring system
For the clump weight mooring system, the restoring force is mainly provided by attaching a large mass
clump weight to the mooring lines. The clump weight will increase the vertical component and the
total tension in the line. The stiffness of the system increases accordingly providing more restoring
forces.
Luo (1992) argues that the clump weights should be installed near the line’s touchdown point, causing
increased stiffness and a steeper tension excursion curve as the weight is lifted off from the sea
bottom. The stage when the clump weight is lifted off the bottom is referred to as the effective stage,
and may be tuned to optimise the mooring characteristics. Nielsen (2011) however claims that in
conventional mooring designs involving clump weights, the weights are installed so that they will not
touch the sea bottom during normal operation. This reduces the risk of the clump weights digging into
the soil, causing large, uncontrollable forces and overshoot in the anchor lines as they are lifted off.
The restoring force is then merely provided by the line configuration.

3.4 Buoyancy element mooring system
The buoyancy element mooring system has a buoyancy element attached to the mooring lines, creating
an upward force. This results in a virtual displacement of the top end point, so that the main
contribution to the restoring forces is provided by the suspended part of the mooring lines below the
buoyancy element. Such a layout is especially attractive for deep water applications, to limit the
mooring line dynamics. As for the other concepts, combination of chain and wire segments may be
used.
All three concepts are illustrated in figure 3-1.

Figure 3-1: Mooring system concepts
From left to right: Clump weight-, distributed mass- and buoyancy element mooring system
12

4. Analysis software
In order to investigate the performance of the different mooring system concepts, various computer
programs dedicated to analysis of marine structures are applied. In the following, these computer
programs are presented.

4.1 SIMO
According to the user manual, SIMO (Simulation of Marine Operations) is a time domain simulation
program for study of motions and stationkeeping of multibody systems. The program is typically
applied for time domain simulation of surface vessels and for simulation of complex marine
operations. The results are presented as time series, statistics and spectral analysis of all forces and
motions of the bodies in the analysed system. SIMO is interactive and modular, i.e. the results from
one module becomes the input for the next module.
In the present study, SIMO is used for environmental modelling (waves and current) and for its ability
to include wind forces from an external force subroutine (TDHMILL3D) linked into the program.
Waves can be modelled by regular waves and by various model spectra for irregular waves. The
current speed and direction is assumed to be constant with time. However it can vary with depth by
specifying a current profile.

4.2 TDHMILL3D
TDHMILL3D is, according to the User Documentation, a simplified computer tool developed by
MARINTEK for analysis of floating wind power facilities. The code is a numerical model of thrust
from a wind turbine rotor onto the nacelle, and consists of coefficients for thrust (force in axial
direction of the rotor axis) tabulated as a function of relative velocity between the rotor and the wind.
Gyro-moments from the rotor when it is rotating about an axis in the rotor plane are also included.
The wind speed at hub height can be specified by the user directly as a time series, or by specifying a
dynamic wind spectrum and let the program generate an irregular wind speed time series. The Kaimal
wind spectrum (see figure 2-3) is used for generating irregular wind speed time series.
The thrust force from the rotor onto the rotor axis at time t is calculated from the wind speed time
series and loaded by SIMO at runtime through a DLL (Dynamic Linked Library).
By using a built-in notch filter tuned to the pitch natural period of the system, the user can choose to
include the control system in a very simplistic way. A notch filter is designed such as to remove the
contribution from a certain frequency band of a given signal.

4.3 Riflex
Originally, according to the user manual, Riflex is a finite element program developed as a tool for
analysing flexible marine riser systems. However the program can also be used for analysing other
types of slender marine structures (e.g. mooring lines and umbilicals). The program features an
extremely efficient and robust non-linear time domain formulation applicable for irregular wave
analysis; and high flexibility in modelling, enabling analysis for a wide range of structures. The
hydrodynamic loading is described by the generalized Morison’s equation.

13

4.4 Integrated analysis
By coupling the computer programs described above together, one can take advantage of the features
characterizing each program and combine them. SIMO, for instance, models all structures as rigid
bodies, i.e. internal forces are not captured. The complete structure (including the mooring system) is
therefore modelled in Riflex, allowing for flexible modelling. SIMO does however as mentioned, offer
the option of including an external force through a DLL, in addition to excellent modelling of waves
and current. SIMO in combination with TDHMILL3D is therefore used for environmental modelling
(wind, waves and current).
The combined SIMO-Riflex simulation is widely used to simulate floating offshore structures. In order
to couple the programs together, the different modules of the programs must be run in a specific order:
1.
2.
3.
4.
5.

Riflex inpmod
SIMO stamod
Riflex stamod
SIMO dynmod
Riflex dynmod

Of course additional modules for postprocessing (e.g. s2xmod and outmod) may be added
subsequently. For details regarding the different modules of the program, reference is made to the
respective user manuals.

14

5. Analysis models
5.1 General
The models used in this study are based on an early phase Hywind design with a steel tower and a
concrete substructure.
The original model was used by Furunes (2010). As the study is focusing on the mooring system
design and not the structural design of the support structure, this tower model is conveniently used as a
starting point. All structural properties remain unchanged, while major adjustments have been made
with respect to the heading of the mooring lines. Furthermore, the water depth is modified, and the
mooring system is adjusted to reproduce the three concepts described in Chapter 3. The model applied
for shallow water ( 100m ) analysis is henceforth referred to as the test model. In the following the test
model will be reviewed.

5.2 Finite element model
Figure 5-1 shows the finite element model and coordinate system for the test model. SN i refers to
supernode i , while the bracket numbers refers to the Riflex line numbers. The main mooring lines and
delta-lines are named Anch.line 1-3 and DL 1-6 respectively.

Figure 5-1: Test model, finite element model

We see that the system topology is defined in terms of branching points and terminal points called
supernodes. Lines are defined between the supernodes, and subsequently split into segments consisting
of equally sized elements. The element mesh is automatically computed based on the topology, line
and component description. SN 1, which is the tower bottom, is fixed; while the anchornodes (SN 10 –
12) are given prescribed displacements. All other supernodes are free, i.e. nodal position and rotations
are unknown prior to the analysis. SN 3, which is located at the top of the tower, is connected to a

15

mass free SIMO body through a floater force model, accounting for the thrust force from the wind.
The substructure has a draft of 80m, and the water depth is set to 100m.

5.3 Tower structure
All the elements in the tower structure are modelled as 3D beam elements with an axi-symmetric cross
section and constant axial-, bending-, and torsional stiffness. The beam element formulation uses a corotated ghost reference description, with three translational and three rotational degrees of freedom at
each node. For further details regarding the beam theory, reference is made to the Riflex theory
manual.
The tower structure layout, including section levels, diameter and weight is shown in figure 5-2.

Figure 5-2: Test model, tower structure
Source: Furunes (2010)

16

5.4 Mooring system
The mooring system is represented by 3D bar elements, specified with axial stiffness only. The bar
element is described in a total Lagrangian formulation, and adjusted to a formulation based on
integrated cross-section forces and small strain theory.
The three-point lateral symmetric mooring system is laid out with an angular spacing of 120o. Each
mooring line is attached to the tower structure at the fairlead. Two lines are connected to each fairlead
point so that the upper part of each mooring line forms a bridle. These upper line segments are denoted
delta-lines. In the original model, the water depth is 220m and the length of each delta-line is 50m. For
the test model, the water depth is reduced to 100m. The length of each delta-line is accordingly
reduced to 40m in order to have adequately vertical distance between the sea bottom and the delta-line
connection points. A single line is extending from the delta-lines to the anchor. The anchornodes are
given a prescribed displacement in order to obtain the desired pretension. The length of the delta-lines
is further assessed in Chapter 8.
The modelling of the different mooring system concepts is reviewed in the following. The layout
described here is merely used for comparing the concepts, i.e. segment lengths and weights are not
optimised. The total line length is for simplicity equal for all three mooring system concepts and is set
to 513 m.
The delta-lines consist of only one segment, while the main mooring lines are composed of 7 segments
each. Table 5-1 shows segment lengths and total weight for the three different mooring system
concepts considered.

Distributed mass mooring system

Clump weight mooring system

Buoyancy element mooring system

Segement type

Segment length [m]

Segement type

Segment length [m]

Segement type

Segment length [m]

Chain (delta-line)

40,00

Chain (delta-line)

40,00

Chain (delta-line)

40,00

Chain

70,00

Chain

5,00

Chain

5,00

Chain

70,00

Wire

25,02

Wire

76,02

Chain

70,00

Chain

5,00

Chain

5,00

Chain

70,00

Clump weight

1,00

Buoyancy element

1,00

Chain

40,00

Chain

5,00

Chain

5,00

Chain

53,04

Wire

332,02

Wire

281,02

Chain

100,00

Chain

100,00

Chain

100,00

Total length [m]
Total submerged

513,04

513,04

513,04

676,03

527,03

120,12

weight [kN]

Table 5-1: Segment lengths

17

5.4.1 Distributed mass mooring system
For the distributed mass mooring system, all segments are composed of chain. The layout is shown in
figure 5-3, while the main parameters describing the chain modelling is given in table 5-2.

Figure 5-3: Layout, distributed mass mooring system

Segment type
Chain

Mass/unit
length [t/m]
0,1545

External C-S area
[m2]
0,0197

Axial stiffness
[kN]
7,09 E+5

Hydrodynamic diameter
[m]
0,1583

Table 5-2: Segment properties, distributed mass mooring system

5.4.2 Clump weight mooring system
In addition to the clump weight, the clump weight mooring system is composed of a combination of
chain and steel wire segments in order to introduce more elasticity and ease the handling. Chains are
used for the delta-lines and for connecting different segments together. The mooring system layout and
main segment properties are shown in figure 5-4 and table 5-3 respectively.
The clump weight is modelled as an axi-symmetrical line segment, i.e. a cylinder. The clump weight
properties are shown in table 5-4.

18

Figure 5-4: Layout, clump weight mooring system

Segment type
Chain
Wire
Clump Weight

Mass/unit
length [t/m]
0,1545
0,0379
24,66

External C-S area
[m2]
0,0197
0,0057
3,14

Table 5-3: Segment properties, clump weight mooring system

Material
Density [kg/m3]
Young’s modulus [N/m2]
Diameter [m]
Thickness [m]
Length [m]
Volume [m3]
Mass [kg/m]
Area moment of inertia [m4]
Gyration radius [m]
Buoyancy force [kN]
Gravity force [kN]
Net force (positive upwards) [kN]
Weight in water [kN/m]

STEEL
7850
2,0 E+11
2,0
2,0
1,0
3,14
24662
0,8836
0,53
31,59
241,9
-210,34
210,34

Table 5-4: Clump weight properties

19

Axial stiffness
[kN]
7,09 E+5
3,43 E+5
6,28 E+9

Hydrodynamic diameter
[m]
0,1583
0,0850
2,0

5.4.3 Buoyancy element mooring system
The buoyancy element mooring system is composed of a combination of chain and wire segments in
addition to the buoyancy element. The mooring system layout and main segment properties are shown
in figure 5-5 and table 5-5 respectively.
As for the clump weight, the buoyancy element is modelled as a line segment with axi-symmetrical
cross-section. The buoyancy element modelling is based on the properties given in table 5-6.

Figure 5-5: Layout, buoyancy element mooring system

Segment type
Chain
Wire
Buoyancy element

Mass/unit
length [t/m]
0,1545
0,0379
19,41

External C-S area
[m2]
0,0197
0,0057
38,48

Table 5-5: Segment properties, buoyancy element mooring system

20

Axial stiffness
[kN]
7,09 E+5
3,43 E+5
1,10 E+9

Hydrodynamic diameter
[m]
0,1583
0,0850
7,0

Material
Density [kg/m3]
Young’s modulus [N/m2]
Diameter [m]
Thickness [m]
Length [m]
Volume buoy [m3]
Volume steel [m3]
Mass [kg/m]
Equivalent density buoy [kg/m3]
Area moment of inertia [m4]
Gyration radius [m]
Buoyancy force [kN]
Gravity force [kN]
Net force (positive upwards) [kN]
Weight in water [kN/m]

STEEL
7850
2,0 E+11
7,0
0,025
1,0
38,48
2,47
19406
504
117,5
1,75
387
190
196,6
-196,6

Table 5-6: Buoyancy element properties

21

22

6. Analysis methods
In the following, the theoretical basis underlying the analysis methods used in the study are described.

6.1 Catenary analysis
In Chapter 2, it was shown how the catenary contribution to the total stiffness matrix was obtained
from the single line stiffness matrix. In this section it is shown how the single line stiffness matrix is
obtained.
Nielsen (2007) demonstrated a stepwise procedure for how the restoring coefficients in surge and
heave may be calculated:



Assuming that the horizontal position of the upper mooring line end is known, a small
perturbation of the horizontal force is made.
The corresponding variation in end point coordinates and vertical force are found and denoted
∆x1 , ∆z1 and ∆H 1 , ∆V1 respectively.



A similar perturbation is made for the depth, and the end point coordinates and vertical force
are respectively denoted ∆x2 , ∆z 2 and ∆H 2 , ∆V2 .



The stiffness components are then found as:
C11 =
(l )

C13 =
(l )

C31 =
(l )

C33 =
(l )

∂H
∂x
∂H
∂z

(6.1)

∂V
∂x
∂V
∂z

The restoring force can be written on matrix and compact form as:

 ∆x
 ∆x

 0

 0

1

∆z1

0

0

2

∆z 2

0

0

0

∆x1

∆z1

0

∆x2

∆z 2

 ∂H 
 ∂x 
  ∂H   ∆H
    ∆H
  ∂z  = 
  ∂V   ∆V
  ∂x  
    ∆V
 ∂V 
 
 ∂z 

1

2

1

2








(6.2)

(6.3)

23

And the restoring force coefficients on compact form are found as:
(6.4)
Each mooring line will be subjected to direct action of waves and current, but the principal loads are
the forces transmitted by the moored structure. By assuming a horizontal sea bed, and neglecting
bending stiffness, dynamic effects in the line and current forces, the x- and z-coordinates can therefore
be found quasi-statically for a range of horizontal force levels by applying the catenary equations. In
cases with high tension in the line, stretching becomes important. The effect of axial elasticity can be
included to form the elastic catenary equations as shown by Triantafyllou (1990). Elasticity effects are
accounted for in the present study. The equations are derived in Appendix A.
A Matlab routine (Nielsen, 2004) for computing mooring line geometry and restoring characteristics
for multi-segment mooring lines has been modified and adapted to quasi-static analysis of the mooring
system concepts presented in this study. The mooring lines are modelled as continuous lines, not
accounting for the stiffness effect of the delta-lines. The weight of the upper segment is therefore
adjusted according to the weight of the delta-lines. Quasi-static analysis is very convenient in the
initial design phase due to the minimal computational effort required.

6.2 Eigenvalue analysis
Finding the natural frequencies of an inclined catenary is not straight forward as the static quantities
are varying in space. By modelling a single mooring line in Riflex, the lines’ eigenfrequencies and
eigenvectors can be found by using the built-in eigenvalue analysis option. Lancros’ method for
solution of eigenvalue problems is utilized.

6.3 Motion decay test
6.3.1 General
A motion decay test, often called a free oscillation test, is carried out by giving the system an initial
displacement and then leaving the system free to oscillate. After the system is released, and by
assuming linear damping, the motion in the degree of freedom regarded can be described by:
Mx + Bx + kx =
0

(6.5)

where M is the structural and added mass of the system, B is the linear damping coefficient and k is the
stiffness coefficient. x , x and x are the translation/rotation, velocity and acceleration of the system
respectively.
By using the dynamic nodal forces option in Riflex, a motion decay test can be simulated by applying
a ramp force/moment to the COG of the structure in the desired degree of freedom. When the ramp
force is switched off, the system is released and free to oscillate. Natural periods and damping levels
can be found from the decay test, and the respective procedures are reviewed in the following.

24

6.3.2 Natural periods
The natural periods may be obtained from the decay time series by measuring the time difference
between two consecutive peaks. Another method, which is utilized here, is to apply a Fast Fourier
Transform (FFT) on the time series. The natural period is then taken as the period corresponding to the
frequency level containing the most energy in the power spectrum.

6.3.3 Damping
By assuming quadratic damping, the damping term of equation (6.5) becomes:
FD (=
x ) B1 x + B2 x | x |

(6.6)

We see that the damping force is split into two contributions, where the first term represents the linear
damping force proportional to the velocity, while the second term represents the quadratic damping
force proportional to the velocity squared.
The linear damping term includes hydrodynamic damping from wave generation in addition to
structural damping, while the quadratic damping term includes the eddy-making damping or drag
damping.
By dividing both sides of (6.5) with M and insert (6.6), we get:

x + b1 x + b2 x | x | +b3 x =
0

(6.7)

where b1 , b2 and b3 are the linear and quadratic damping coefficients and the stiffness coefficient divided
by M respectively.
Nielsen (2007) showed that equation (6.7) can be linearized by introducing an equivalent damping
coefficient be :

x + be x + b3 x =
0

(6.8)

For a motion decay signal with n cycles, the equivalent linearized damping can be expressed as:
be =+
b1 K L b2 =+
b1
*

16 xn
3 Tn

b2

(6.9)

where xn and Tn are the motion amplitude and period for cycle n respectively, and K L* is the linearization
coefficient. The linearization coefficient is found by using the value that will minimize the error
(Larsen 2010).

25

The equivalent linear damping may be estimated within each half cycle of the decay signal by using
the logarithmic decrement. By considering two consecutive peaks in the motion decay signal, as
shown in figure 6-1, we can define the logarithmic decrement as:
δ = ln

xn

(6.10)

x n +1

Figure 6-1: Motion decay signal

Furthermore we introduce the relative damping, which can be expressed as a function of the
logarithmic decrement:
ζ (δ ) =

δ
4π + δ
2

(6.11)
2

The critical damping is given as:
b=
crit

Bcrit

ω0
= 2=
M
T0

26

(6.12)

By expressing the relative damping as a fraction of the critical damping, we get:
=
ζ

be
T
=
be 0

bcrit

(6.13)

The equivalent linearized damping is now found from the decay signal as:
=
be ζ=
bcrit



δ

T0

4π + δ
2

(6.14)
2

The measurements in equation (6.14) can be fitted to equation (6.9); and by linear regression the linear
and quadratic contribution to the damping can be estimated as a function of motion amplitude.

6.4 Time domain analysis procedure
The equations of motions can be solved in the time domain by dividing the desired time period into a
number of time steps and perform equilibrium iterations at each time step. The solution is obtained by
using the start conditions from the previous time step and assuming a motion pattern. The solution will
then in turn become the start conditions for the next time step.
According to the theory manual, non-linear time domain analysis in Riflex, which is utilized in this
study, is performed by using a true Newton-Raphson type of equilibrium iteration. This implies
recalculating the tangential mass, damping and stiffness matrices at each iteration cycle. The procedure
offers a quadratic convergency rate. A modified Euclidean displacement norm is used as convergence
criterion, i.e. the sum of displacements must be below a certain value.
The numerical integration is based on the Newmark β-family. By assuming an acceleration pattern, i.e.
choosing the parameters β and γ ; and denoting the time step increment ∆τ , the velocity and
displacement at time step t + ∆τ is found as:
rt + ∆τ = 
rt + (1 − γ ) 
rt + ∆τ ∆τ + γ 
rt +∆τ ∆τ
rt + ∆τ = rt + rt ∆τ +

( )
1

2

− β 
rt ( ∆τ ) + β 
rt + ∆τ ( ∆τ )
2

(6.15)

2

A β -value of ¼ gives constant average acceleration, while a γ -value of ½ gives no numerical
damping. For all the analyses presented in this study, these values are used.
The overall structural damping matrix is described by a Rayleigh damping formulation:
=
C α 1M + α 2 K

(6.16)

The global mass proportional damping contribution ( α ) is omitted to avoid unphysical structural
1

damping due to rigid body motions. The global stiffness proportional damping contribution ( α ) shall
2

give a realistic energy dissipation at the peak period of the loading. Since α is omitted, α simply
becomes 2λ / ω and is set to 0,01. λ is the relative structural damping.
1

2

At each time step, the external loads are updated due to improved estimates of structural velocities.
The other contributions to the load vector are kept constant.
27

The hydrodynamic contributions to the external forces are found by using a long wave length
approximation for the wave-induced excitation forces and a generalized Morison’s equation
formulation for the viscous forces. They are calculated to the actual instantaneous structural position.

6.5 Data handling
A Matlab routine is developed to run the coupled software programs described in Chapter 5 and
implement the theory described in this chapter. The structural properties and main dimensions of the
three models with different mooring system concepts are incorporated in Excel. The same is the case
for the environmental input and time domain simulation parameters. Matlab reads data from Excel and
applies it to the selected types of analysis to be performed. Postprocessing data and calculating
statistics from time domain simulations are also incorporated.
Because this study includes a large number of analyses with different system configurations, the
Matlab routine and Excel sheets are proven invaluable. In Excel, system properties and simulation
parameters are easily altered and presented in a clear manner, while Matlab is an excellent tool for
handling large amount of data and for postprocessing purposes.
An overview of the analysis methods is shown in figure 6-2.

Figure 6-2: Overview of analysis methods

28

7. Concept selection
7.1 General
In this chapter, the three different mooring system concepts introduced in Chapter 5 are compared and
one of the concepts is selected for further studies based on the results.
The concepts are analysed quasi-statically to obtain line configuration and mooring line characteristics.
Furthermore, motion decay tests are performed in surge, heave and pitch to find natural periods and
damping levels. Finally, dynamic response and statistics are obtained for operational and severe
environmental conditions by the means of non-linear time domain analysis.

7.2 Quasi-static analysis
By varying the horizontal force levels, line configurations for the three mooring system concepts are
obtained as shown in figure 7-1.

Figure 7-1: Mooring line configuration
Top: Distributed mass mooring system, Middle: Clump weight mooring system, Bottom: Buoyancy element
mooring system

29

We see that as the horizontal force is increased, the catenary geometry changes due to fairlead
displacements and consequently chain lifted off from the sea bottom. For the buoyancy element
mooring system, no line is left resting at the sea bottom as the horizontal force reaches the largest
value of 1500 kN. For the other two concepts however, a great portion of the line is still left on the sea
bottom at the same horizontal force level.
The mooring line characteristics are shown in figure 7-2. Both the horizontal top tension and the total
top tension is plotted for the three mooring system concepts.

Figure 7-2: Mooring line characteristics for three mooring system concepts

Because of the buoys attached to the lines of the buoyancy element mooring system, it is seen that
initially for a large fairlead displacement range, the top tension is kept almost constant as the line
between the fairlead and the buoy is “tightened up” (see figure 7-1). A further increase in displacement
beyond this range will give non-linear restoring forces from the geometric stiffness as line is lifted off
from the sea bottom. However, already at a top tension of approximately 1200 kN, the whole line
length is suspended, i.e. all the line is lifted from the sea bottom. Additional increase in top tension
beyond this point is therefore due to the combined effects of non-linear restoring forces from the
change in geometry as the buoy is pulled down, and linear restoring forces from elasticity in the line.
As a result of the buoys effect on the line configuration, the total top tension will be almost identical to
the horizontal top tension for the whole tension range considered.
The distributed mass mooring system, solely consisting of chain segments, will respond by an increase
in top tension as soon as the fairlead displacements increase. Because of the large submerged weight
of the line, parts of the line remain resting on the sea bottom through the whole top tension range
considered. This provides geometric stiffness contributions to the restoring forces. However, the large
axial stiffness of the chain segments leads to increasingly mooring line response due to stretching as
the tension increases.

30

For the clump weight mooring system, the tension-displacement curve will initially be steep due to the
increased stiffness when the clump weight is partially lifted off the sea bottom. Furthermore, when
fairlead displacements increase, the wire segments in the lines will reduce the stiffness of the system,
resulting in a smaller top tension gradient than the case with the distributed mass mooring system.
Because of the clump weight’s effect on the line configuration (see figure 7-1) the total top tension
will have a significant vertical component. The effect is primarily seen for low top tension levels.

7.3 Motion decay analysis
Motion decay tests have been carried out on the test model. Results for vertical and longitudinal
motion modes for the three different mooring system concepts are found.
The structure is initially given 500 s to obtain equilibrium before the ramp force is applied for 600 s.
For translational motion modes (surge and heave) the ramp force is 5 kN/s, while for the rotational
motion mode (pitch) the ramp force is 1500 kNm/s. For all three concepts, the anchors where given a
prescribed displacement corresponding to a pretension of 500 kN.
The main results are presented in the following.

7.3.1 Natural periods
The natural periods obtained from the motion decay tests are presented in table 7-1.
Mooring system concept
Distributed mass

Clump weight

Buoyancy element

Degree of freedom
Surge
Heave
Pitch
Surge
Heave
Pitch
Surge
Heave
Pitch

Natural period [s]
54,1
28,8
25,6
82,5
27,5
25,4
52,4
26,4
26,4

Table 7-1: Natural periods

It is seen that the natural periods in all the degrees of freedom considered are above the WF range, i.e.
resonant WF motions are avoided. The surge natural period is significantly larger for the clump weight
mooring system than for the others. This is because all three mooring systems have an equal
pretension of 500 kN, and with respect to the mooring line characteristics (see figure 7-2) we see that
the clump weight mooring system is significantly “softer” than the other concepts at low tension
levels. For the buoyancy element mooring system it is seen that the heave and pitch natural periods are
identical and possible Mathieu effects must be considered. It is however important to note that the
natural periods of the system are not tuned for these initial concept studies.

31

7.3.2 Damping
The relative damping (ζ) from the logarithmic decrement is presented as a function of surge
displacement in figure 7-3 (left), while the ratio between linear and quadratic damping as a function of
surge displacement is shown in figure 7-3 (right).

Figure 7-3: Surge damping
Left: Relative damping (ζ) as function of surge displacement. Right: Damping ratio (linear/quadratic) as
function of surge displacement
Top: Distributed mass-. Middle: Clump weight-. Bottom: Buoyancy element mooring system.

Generally, the relative damping decreases with decreasing motion amplitudes which is obvious from
studying figure 7-3 (left). From the plots on the right side, it is seen that the effect from quadratic
viscous damping is prominent for large motion amplitudes, while we are left with the linear damping
as the motion amplitudes approaches zero. The mooring system itself has little effect on the overall
system damping, and the differences are mainly due to different displacement levels.
For the other motion modes considered (heave and pitch), the viscous damping is not as prominent as
for surge. For heave, the linear damping contribution is in order of 10-100 times larger than the
32

viscous damping, and is therefore close to constant; while a larger viscous damping contribution is
seen in pitch. The relative damping levels presented in table 7-2 are mean values over the decay signal
considered. As expected, the type of mooring system has negligible effect on the heave and pitch
damping.

Mooring concept Distributed mass
Degree of freedom
Relative damping ζ
Heave
0,0295
Pitch
0,0201

Clump weight

Buoyancy element

Relative damping ζ
0,0283
0,0196

Relative damping ζ
0,0266
0,0203

Table 7-2: Relative damping, heave and pitch

7.4 Time domain analysis
In order to compare the different concept’s response to environmental loads and capture dynamic
effects in the mooring lines, time domain analysis is performed. Two environmental load conditions
are considered. The first condition, denoted operational condition, is taken as an environmental
condition where the wind turbine is operating at maximum effect, i.e. with wind speeds close to the
rated wind speed. The second condition, denoted storm condition, is taken as a non-operating
condition with combination of wind and waves with 100-year return periods and current with 10-year
return period. Typical values for the Northern North Sea as given in DNV-OS-E301 are used.
The environmental conditions are shown in table 7-3.

Wave
Wind

Current

Opertional Condition

Storm Condition

Hs [m]

1,0

15,0

Tp [s]

6,6

16,0

Umean [m/s]
Turb. Intensity
V0 [m/s]

11,0
0,1
0,5

40,5
0,1
1,6

V20 [m/s]

0,4

1,1

V40 [m/s]

0,3

1,1

V60 [m/s]

0,2

0,7

V80 [m/s]

0,1

0,7

V100 [m/s]

0,0

0,6

Table 7-3: Environmental conditions

All the environmental loads are applied to the structure with a heading of 0° relative to the x-axis, in
the direction of the anchorline parallel to the x-axis (Anch.line 1). The anchor nodes are given a
prescribed displacement corresponding to a pretension of 500 kN for all three concepts. An 1-hour
simulation is carried out for each environmental condition and the main results are presented for the
operational- and storm condition in table 7-4 and 7-5 respectively.

33

Mooring system concept
Distributed mass
Response
Mean Std.
Min
Max
Surge - Waterline [m]

4,8

0,7

2,0

6,8

Mean
7,3

Clump weight
Std.
Min
0,7

4,0

Max
9,4

Buoyancy element
Mean Std.
Min
Max
4,8

0,7

2,1

6,7

Sway - Waterline [m]

0,0

0,0

-0,1

0,1

0,0

0,0

-0,1

0,1

0,0

0,1

-0,1

0,1

Heave - Waterline [m]

4,1

0,1

3,6

4,5

3,6

0,2

3,1

4,1

6,8

0,2

6,2

7,3

3,8

0,8

0,9

6,1

4,2

0,8

1,4

6,6

-73,0

0,2

-73,8

-72,4

3,9

0,8

1,0

6,2

Tower bottom heave [m]

Pitch - Waterline [m]

-75,7

0,1

-76,2

-75,3

-76,3

0,1

-76,7

-75,8

Axial force - DL1 [kN]

462,4

16,3

400,7

510,0

433,7

11,7

382,1

471,1

408,7

15,6

351,9

458,0

Axial force - DL2 [kN]

462,5

15,7

407,7

501,6

433,8

11,3

390,5

467,6

408,7

15,9

352,2

457,1

352,0

14,2

305,4

396,7

257,9

3,9

245,9

270,2

244,9

3,3

235,4

262,7

Axial force - DL3 [kN]

364,4

11,9

318,8

401,4

Axial force - DL4 [kN]

253,6

12,9

214,3

306,9

239,4

14,4

199,7

294,4

Axial force - DL5 [kN]

253,7

13,2

214,3

309,8

239,3

14,7

201,1

298,8

244,9

3,7

234,6

260,6

Axial force - DL6 [kN]

364,3

12,1

316,9

403,5

352,0

14,5

303,9

399,8

257,9

3,3

248,0

274,5

Axial force - Anch. Line 1 [kN]

829,4

31,8

713,6

913,6

816,6

22,7

728,1

879,8

801,9

30,5

692,8

895,1

Axial force - Anch. Line 2 [kN]

516,9

5,4

499,2

540,9

527,8

4,4

516,1

547,3

493,4

5,6

478,7

517,4

Axial force - Anch. Line 3 [kN]

516,8

5,5

498,8

541,3

527,7

4,4

516,1

547,4

493,4

5,7

479,0

517,9

Table 7-4: Response statistics, operational condition

Mooring system concept
Distributed mass
Response
Mean Std.
Min
Max
Surge - Waterline [m]

3,8

4,8

-12,8

18,4

Mean
7,3

Clump weight
Std.
Min
4,8

-8,8

Max
21,6

Buoyancy element
Mean Std.
Min
Max
3,1

5,0

-13,3

21,4

Sway - Waterline [m]

0,0

0,0

-0,1

0,0

0,0

0,0

0,0

0,0

0,0

0,0

0,0

0,1

Heave - Waterline [m]

3,5

1,4

-1,4

8,3

3,0

1,5

-2,7

8,4

5,0

3,7

-11,8

17,0

Pitch - Waterline [m]
Tower bottom heave [m]

2,0

3,0

-8,5

12,2

1,9

3,1

-9,8

12,3

2,1

3,2

-7,9

14,7

-76,3

1,3

-81,3

-71,7

-76,8

1,5

-82,4

-71,5

-74,8

3,7

-91,7

-62,9

Axial force - DL1 [kN]

570,1

353,7

-105,1

2459,8

535,5

156,4

83,7

1454,0

591,5

453,2

-75,1

3101,2

Axial force - DL2 [kN]

584,0

385,8

-100,9

2487,6

542,4

194,2

63,6

1557,7

603,0

462,7

-56,7

3145,3

Axial force - DL3 [kN]

332,0

64,2

83,3

726,3

316,8

77,4

101,2

501,7

343,4

163,1

125,5

1321,4

Axial force - DL4 [kN]

252,7

89,4

62,6

856,7

254,4

83,8

85,5

523,5

203,1

70,2

51,1

782,4

Axial force - DL5 [kN]

259,7

98,7

31,6

907,3

258,1

86,4

86,6

553,7

208,3

66,2

61,7

743,9

Axial force - DL6 [kN]

325,0

42,4

85,9

573,5

312,7

75,8

97,0

474,8

337,6

144,7

139,9

1159,6

Axial force - Anch. Line 1 [kN]

1061,7

746,6

-332,2

4875,5

1030,4

354,1

114,4

2942,2

1176,4

912,5

-150,4

6211,9

Axial force - Anch. Line 2 [kN]

481,9

118,6

33,2

1272,7

506,5

23,8

430,0

649,4

537,0

173,5

273,2

1537,1

Axial force - Anch. Line 3 [kN]

481,6

118,7

41,4

1270,6

506,1

23,4

425,6

636,3

536,3

173,9

275,8

1583,5

Table 7-5: Response statistics, storm condition

See figure 5-1 for definition of the anchorline directions. Waterline is referring to the waterline at zeroload initial configuration ∗.
Generally, it is seen that the mean mooring line tensions are approximately equal for the three
concepts for both environmental conditions. For the operational condition, the mean mooring line
tension is slightly larger for the clump weight concept than for the other two concepts; while for the
storm condition, the buoyancy element concept experiences the largest mean mooring line tension.
The maximum values and variation in line tension (expressed in terms of the standard deviation) are
however significantly larger for the concepts utilizing distributed mass and buoyancy element than for
the clump weight concept ∗∗.
The effects described above can be explained by the mooring line characteristics (see figure 7-2). At
the applied pretension level, the total tension is significantly larger for the clump weight mooring


Mean heave response should be zero at the actual waterline.
The negative minimum values for axial force are not physical, i.e. chain segments are not in compression.

∗∗

34

concept than for the other two concepts, i.e. the vertical tension component is larger. At the same time,
the tension-excursion curve gradient is smaller. When the environmental load is applied, the clump
weight concept will therefore experience a large surge offset due to the load while the line tension
remains approximately the same as for the other concepts. Due to the large gradients of the tensionexcursion curves, the distributed mass- and buoyancy element concepts will have large tension
variations even for relatively small variations in horizontal offset. Actually, for the buoyancy element
concept in storm condition, maximum line tension in the most heavily loaded line reaches a value
above 6000 kN, while the same value is just below 5000 kN and 3000 kN for the distributed mass- and
clump weight concept respectively. The same effect is observed for the most heavily loaded deltalines.
It is observed that even though the initial gap between the tower bottom and sea bottom was only 20
m, neither of the concepts are risking bottom contact during the storm condition.
The complete response time series from the concept comparison are found in Appendix B.

7.5 Conclusion and selection of concept for further studies
By studying the three concepts, pros and cons for each concept are revealed.
The buoyancy element concept is desirable for deep water mooring systems because the weight and
stiffness is reduced, and dynamic effects in the mooring line are limited to the part of the line
extending from the buoy to the sea bottom. For the application investigated in this study however, the
buoyancy element concept is failing when it comes to limiting the maximum line tension. Because the
suspended length of the line is very limited for the water depth considered, the soft nature of the
mooring system will result in large peak tensions. Also, the buoy may cause challenges during
installation and handling. Furthermore, by using the present layout we risk having vertical forces on
the anchor. This can be resolved by increasing the line length or bottom segment weight, further
complicating the handling and compromising on the mooring system cost.
The distributed mass concept may be the most desirable when it comes to installation and handling
purposes. In addition, the large submerged weight allows for short line lengths and ensures no vertical
forces on the anchor. However, the large tension-excursion curve gradient gives large tension
variations during severe weather conditions.
When it comes to limiting maximum line tension, the clump weight concept is superior to the other
two concepts. The relatively small tension-excursion curve gradient over a large displacement range
ensures good control with the line tension even in severe weather conditions. As for the distributed
mass concept, the large submerged weight allows for shorter line lengths and limits the risk of vertical
forces on the anchor. The drawback is that the horizontal offset will be large, resulting in a large
footprint and possibly inflicting damage on the power cable. The offset can however be controlled by
tuning the pretension, compromising on the maximum line tension level.
Based on the discussion in this chapter, the clump weight mooring system is selected for further
studies. The two other concepts will not be further discussed.

35

36

8. Mooring system optimisation
8.1 General
A number of key parameters defining the mooring system have been selected and subjected to a
parameter study. Their effects on the system performance are investigated in order to optimise the
mooring system. The main concerns that need to be considered when selecting the design parameters
may be summarized as:






Avoiding vertical forces on the anchors
Select segments with adequate breaking strength to resist the maximum line tension with
sufficient margins
Avoiding clump weight touchdown
Keeping the mooring lines as short as possible
Utilize the geometric stiffness range by tuning the pretension

For a mooring system with clump weights, the most influential design parameters are the size (mass)
of the clump weights and their position along the mooring line. Emphasis is therefore put on these two
design parameters.
Other parameters that are investigated include:
• Pretension
• Overall length of the mooring system
• Chain and wire weight/dimension
• Vertical fairlead position
• Delta-line length
The parameter study is carried out by the means of quasi-static and dynamic analysis. The clump
weight size and position are investigated by utilizing a quasi-static approach. Furthermore, by applying
the optimised values for the clump weight size and position; the pretension, overall length of the
mooring system and chain- and wire weight/dimension are determined by the means of time domain
analysis. The storm condition defined in Chapter 7 is applied with environmental loading acting with
an heading of 0° relative to the x-axis. The vertical fairlead position and delta-line lengths are selected
based on theoretical considerations.

37

8.2 Clump weight size
In order to investigate the effect of the clump weight size, all other parameters are kept constant while
the clump weight size is varied according to table 8-1.
Diameter Volume
[m]
1
2
3
4
5

3

[m ]
0,79
3,14
7,07
12,57
19,63

Mass
[tons]
6,17
24,66
55,49
98,65
154,13

Gyration radius Buoyancy force
[m]
0,35
0,53
0,76
1,01
1,25

[kN]
7,90
31,59
71,08
126,36
197,43

Gravity force

Weight in water

[kN]
60,48
241,93
544,34
967,72
1512,06

[kN/m]
52,58
210,34
473,26
841,36
1314,62

Table 8-1: Clump weight size

The resulting line configuration, here presented for a pretension level of 700 kN, is shown in figure 81.

Figure 8-1: Line configuration for various clump weight sizes

As the line configuration is determined by the submerged weight of the line, it is seen that the size of
the clump weight is of major importance for the configuration. For the largest clump weights, the short
suspended part of the mooring line is close to vertical while the major part of the line is resting on the
sea bottom. Even in equilibrium position, the largest clump weights are close to the sea bottom and
will therefore experience touchdown on the leeward side when the floater is displaced due to
environmental loading. This will not be the case for the smaller clump weights as the reduced weight
ensures adequate vertical distance to the sea bottom. Problems with possible vertical forces on the
anchors may occur however, as the catenary sag is relatively small.

38

The mooring line characteristics for the selection of clump weights are shown in figure 8-2.

Figure 8-2: Mooring line characteristics for various clump weight sizes

It is seen that for all the applications, the tension-extension curves initially have small gradients at low
and moderate horizontal top tension levels. The restoring forces are obtained from the catenary
(geometric) stiffness contribution as the line curvature changes when bottom chain is lifted off due to
increasing fairlead displacements. For higher tension levels, the lines will respond increasingly by
stretching, i.e. the elastic stiffness contribution is governing the restoring forces. The tension-extension
curve will eventually approach a straight line and the mooring lines will fail structurally when the
breaking strength is exceeded. The dynamic tension may become very large in the elastic region as a
small change in displacement causes large changes in tension. The transition to the elastic region
occurs at much lower tension levels for the small clump weights than for the larger ones. For the large
clump weights, the weights will be resting on the sea bottom for low horizontal top tension levels. A
large pretension is thus required to prevent leeward weights from touchdown, which in turn can give
rise to large impact forces.
Ultimately, the choice of clump weight size becomes a trade-off between increased pretension and
reduced dynamic tension for the large weights; and reduced pretension and increased dynamic tension
for the smaller weights. The latter will be preferable in most operational conditions, but will fail to
limit the peak tension in severe weather conditions.
A clump weight with diameter 3,5 m and mass 75,5 t is selected. By choosing this relatively large
clump weight size, we ensure that the non-linear restoring forces from the catenary stiffness are acting
over a large top tension range; hence limiting the maximum tension. Though even larger clump
weights would give slightly more favourable line characteristics in the high tension range, a large
pretension would be required to prevent clump weight touchdown on the leeward side, resulting in
larger mean tension in the lines. In addition, very large clump weights would increase the cost and
complicate the installation.

39

8.3 Clump weight position
By varying the distance between the clump weight and the fairlead, and keeping all other parameters
constant, the effect of the clump weight position can be investigated. The distance between the fairlead
and the clump weight is increased in steps of 5 m. Mooring line characteristics for 6 different clump
weight positions are shown in figure 8-3.

Figure 8-3: Mooring line characteristics for various clump weight positions

We see that after the clump weights are lifted from the sea bottom, the horizontal top tension levels are
almost identical for all applications. This is due to the fact that only the clump weight position is
varied, i.e. the submerged weight of the mooring lines which governs the top tension is constant.
The vertical distance between the fairlead and the sea bottom is only 54 m, and in addition, delta-lines
are used. Attaching clump weights to the delta-lines is not desirable as this will add further complexity
to the system, especially with respect to installation. It may also influence the delta-lines’ effect on the
yaw restoring coefficient. Depending on the size of the clump weight and the pretension in the lines,
we are therefore left with a narrow range of positions for where the clump weight may be attached to
the main mooring line. As the position is not affecting the tension in the lines much, a clump weight
position close to the delta-lines is preferred. This will reduce the possibility of clump weight
touchdown on leeward side during severe weather conditions.
A distance of 56 m along the cable from the fairlead to the clump weight is selected. This is
sufficiently close to the delta-lines so that problems with clump weight touchdown on the leeward
lines are avoided. It will also allow us to use a short wire segment between the delta-lines and the
clump weight, introducing some additional elasticity to the upper part of the mooring lines.

40

8.4 Pretension
The pretension of a mooring system is important for limiting the horizontal offset. For the considered
mooring system, the pretension is tuned by analysing the line tension and horizontal offset for various
pretension levels. The surge response and axial forces in the most heavily loaded line (Anch.line 1)
and one of the leeward lines (Anch.line 2) are presented in table 8-2.
Response
Pretension

Mean

300 kN
500 kN
600 kN
700 kN
900 kN
1100 kN

17,60
13,13
11,04
9,34
6,83
5,24

Surge - Waterline [m]
Std
Min
Max

4,91
5,23
5,26
5,27
5,32
5,38

2,64
-2,34
-4,64
-6,65
-9,83
-11,99

37,85
32,10
29,74
27,75
24,91
23,23

Axial force - Anch.line 1 [kN]
Mean
Std
Min
Max

1027,23
1225,02
1312,71
1400,95
1588,42
1776,36

65,62
114,23
149,60
186,08
276,89
383,90

883,87
934,65
870,49
821,16
749,02
641,61

1643,65
2211,16
2608,74
2965,65
3713,12
4479,17

Axial force - Anch.line 2 [kN]
Mean
Std
Min
Max

455,56 267,35
763,40 73,77
834,77 23,89
902,31 24,09
1052,32 38,15
1209,98 59,92

-261,39
-117,22
405,22
791,24
893,62
993,40

1106,34
1021,04
933,73
1034,93
1280,41
1585,92

Table 8-2: Dynamic response as function of pretension

We see from the results that low pretension is favourable with respect to limiting the mean and
maximum tension in the lines. However, the lines on the leeward side may become slack which can
give rise to snap loads and impact forces from clump weight touchdown. For large pretension values,
the mean- and maximum tension in the lines are increased, and the standard variation of axial force in
the most heavily loaded line increases due to stretching.
For conventional offshore production units, the risers are limiting the permissible horizontal offsets.
This does not apply to the considered application, but it is important to limit offsets of concern to the
power cable and adjacent structures.
A pretension level of 700 kN is selected. This will give a reasonable compromise between line tension
and floater excursions. It is important to note that the pretension is not given explicitly as input to
Riflex. The input is given as prescribed displacements of the anchors, which in turn will govern the
pretension. The relationship between the two is found quasi-statically. Since the quasi-static analysis is
not accounting properly for the effect of the delta-lines, the pretensions given in table 8-2 will slightly
overestimate the actual horizontal top tension as it appears from the time domain analysis.

41

8.4 Total line length
By increasing the horizontal distance between the anchor and the fairlead, the total length of the
mooring system is increased. All other parameters are kept constant while the lower wire segment
length is varied. The effect on the mooring line characteristics is presented in figure 8-4.

Figure 8-4: Mooring line characteristics for various line lengths

As expected, the length of the line has no effect on the line characteristics for low tension levels. Part
of the line is resting on the sea bottom for all considered applications, providing the same restoring
forces. As the top tension increases however, we see that the transition to elastic stiffness dominance
appear earlier for the shorter lines. This is simply because they have less bottom line length; which
thus will be exhausted at smaller excursion levels than for the longer lines.
Ideally, one would want as short lines as possible. This is favourable because it will reduce the cost of
the mooring system. If we also assume that the floating wind turbine is one of multiple turbines in a
wind farm, reducing the mooring line length will increase the income as more wind turbines can be
installed in the same area.
However, the most important from a design perspective is that we limit the peak tension and ensure no
vertical forces on the anchor. The mooring line length must therefore be determined by analysing in
the time domain. The three shortest line lengths from figure 8-4 are analysed, and it is checked for
vertical forces on the anchor of Anchorline 1 during the time of maximum surge offset of the floater.

42

The results are presented in table 8-3.

Mooring line length [m] Vertical force on anchor
385,4
513
768,6

YES
NEGLIGIBLE
NO

Table 8-3: Check of vertical forces on anchor

For the shortest line length, maximum vertical forces in the order of 102 kN are observed on the
anchor. For the line of length 513 m, the line 10 m from the anchor was lifted only a few centimetres
above the sea bottom during the instant of maximum line tension; hence the vertical force on the
anchor will be very small compared to the weight of the anchor. For the longest line length, no line
lift-up close to the anchor was observed. Based on the results, mooring lines with a total length of 513
m are selected.

8.5 Chain and wire dimension
Changing the weight of the suspended chain and wire segments to manipulate the mooring line
characteristics is unnecessary as the weight of the suspended catenary effectively can be controlled by
the clump weight size. Our only concern when choosing chain and wire dimensions will therefore be
to provide sufficient breaking strength to resist the maximum tension with adequate safety margins.
The effect of the bottom chain weight has been investigated quasi-statically. The results showed that
for the mooring system considered, the mooring line characteristics are not very sensitive to this
parameter. However, due to the fact that analysis showed a very small vertical force on the anchor for
the selected line length, bottom chain slightly heavier than the chain used in the suspended line is
selected. The length of the bottom chain is 150 m. As tensions in the delta-lines are approximately half
the tensions in the upper part of the main mooring line, the delta-line chains are somewhat reduced in
dimension compared to the chain segments in the main mooring line.
The chain and wire diameter is selected to fulfil the design criteria, based on the maximum tension
values in table 8-2. Data is taken from Vryhof anchors (2010) and presented in table 8-4. For details on
how the design mooring system components are modelled in Riflex, see Appendix C.

Component type
Class/Type
Diameter [mm]
Proof load [kN]
Break load [kN]
Weight [kg/m]
Axial stiffness [MN]

Chain - Connectors Chain - Delta lines
R4-RQ4 studless
R4-RQ4 studless
87
73
5355
3884
7682
5572
151
107
-

Chain - Bottom
R4-RQ4 studless
105
7497
10754
221
-

Wire
Six strand wire rope
96
6965
40,5
483,8

Table 8-4: Chain and wire properties

Studless chain is applied as recommended for permanent moorings. This type of chain is attractive
with respect to the fatigue life and weight per unit strength ratio. For the wire segments, six strand wire
rope is applied. This gives high elasticity and flexibility, and relatively low axial stiffness. The
drawback is that it is only recommended for up to 10 years design life.

43

8.6 Vertical fairlead position
Ideally, the vertical fairlead position should be located at a point where there is no coupling between
surge and pitch, i.e. at the vertical position of the centre of rotation. By doing so, the wind and wave
induced dynamic loading in the mooring lines will be minimized. According to Nielsen (2009), this
position will for a deep-draft floating wind turbine structure oscillating at its pitch natural period be
located somewhere between the COB and COG, closer to the COG. However, since the vertical
distribution of wave forces is frequency dependent, so is the vertical position of the centre of rotation.
This frequency dependency can be shown mathematically. By utilizing the description of the motion
of any point on the floating body, as shown by Faltinsen (1990), we get:
s = (η1 + zη 5 − yη 6 )i + (η 2 − zη 4 + xη 6 ) j

(8.1)

+ (η 3 + yη 4 − xη 5 )k

where η1− 6 are the translational and angular rigid body motions. Furthermore, by choosing a point z '
close to the COG of the body, Nielsen (2009) demonstrated that the horizontal motion of this point is
described by:
η1 ( z ')= η1 + z 'η 5

(8.2)

The vertical position of the centre of rotation will then be the point where the horizontal motion of z ' is
zero, hence:
z 'rot = −

η1

(8.3)

η5

By assuming zero damping, and surge and pitch excitation forces in phase, the motions in surge and
pitch may be approximated as:
η1 
η5 

F1
−ω ( m + A11 ) + C11
2

(8.4)

F5
−ω ( I 55 + A55 ) + C55
2

If z 'F is the resultant position of the horizontal wave forces, the pitch moment may be approximated as
F5  F1 z 'F . Furthermore C11  0 and ( I 55 + A55 )  ( m + A11 ) r 2 =
Mr 2 , where r is the radius of inertia in
pitch.

The vertical position of the centre of rotation is then obtained as:
F1 −ω Mr + C55
2

z 'rot  −

F1 z F

2

−ω M
2

C
1  2
r − 2 55
=


zF 
ω M




(8.5)

When excited by waves of high frequency, the vertical centre of rotation will be located close to the
bottom of the cylinder; while it moves towards plus infinity as the excitation frequency goes to zero.

44

It is obvious that we cannot choose a single point that will have no coupling between surge and pitch
for the whole WF range. A fairlead connection point far up on the cylinder will be favourable in
survival conditions, while moving the point down towards the bottom of the cylinder is favourable for
most operational conditions. It is also important to consider that lowering the fairlead position will
increase the overturning moment on the support structure from the wind thrust, and hence increase the
static pitch angle.
With respect to the design of the mooring system, the most important consideration is however to
choose a fairlead position that will give sufficiently suspended line length to achieve the desired
mooring line characteristics. With the COG located 28 m from the bottom of the cylinder, i.e. only 48
m from the sea bottom, it is obvious that the fairlead has to be located above the COG. Especially
since the length of the delta-lines further limits the length of suspended main mooring line to play
with. The vertical fairlead position has not been subjected to a parameter study like other key
parameters of the mooring line. It is chosen based on the issues discussed here and is subsequently
verified by the means of time domain analysis. The mooring lines are attached to the fairlead 46,4 m
below the mean water line as indicated in figure 8-5.

Figure 8-5: Vertical fairlead position

45

8.7 Delta-line length
The delta-lines will contribute to increased yaw stiffness because they are attached to the fairlead with
an angle to the centre line of the structure. Nielsen (2009) demonstrated that the yaw restoring
coefficient can be written as:




n

C66
=

∑ TR cos ϕ  1 +
i =1

R
LH





(8.6)

where T is the top tension, R is the distance from the centre of the structure to the ”effective” mooring
line connection point, ϕ is the top angle between the mooring line and the horizontal plane, and LH is
the horizontal distance from the “effective” mooring line connection point to the anchor. n is the
number of mooring lines. When delta-lines are applied, the “effective” mooring line connection point
is the point where the two delta-lines meet the main mooring line (see figure 8-6).
Furthermore, the delta-lines will act as a rigid connection as long as they are in tension, which is
governed by the yaw angle. Nielsen (2009) showed that the delta-lines are in tension as long as the
yaw angle is less than given by:
η6 <

LH
LH + R

tan β

(8.7)

Here η6 is the yaw angle in radians and β is the angle between the delta-lines and the centre line of the
structure, as indicated in figure 8-6.

Figure 8-6: Mooring system layout

46

By assuming that the total mooring line length is constant, it is seen that by using long delta-lines, the
maximum yaw angle before the delta-lines go slack is reduced, and the yaw restoring coefficient is
increased. Shorter delta-lines will allow for larger yaw angles before the delta-lines go slack, but the
restoring coefficient is reduced and the yaw natural period will increase. From equation (8.6) we see
that the yaw restoring coefficient, and consequently the natural period can however be effectively
controlled by the pretension.
The main consideration when selecting the delta-line length will be the water depth. As discussed
earlier, the clump weight should preferable not be attached to the delta-lines. Hence, the delta-lines
must be relatively short in order to achieve adequate length of main mooring line to play with. A
length of 40 m is selected for the delta-lines, which means that the yaw angle must be below 6° in
order to maintain tension in the delta-lines.
With all the other parameters defined as given in the previous sections, we get the top tension
T  807 kN (total top tension from stamod), the angle ϕ  43° , R = 42,15 m and LH = 457, 3 m . By
using the data from figure 5-2 we get I 6 = 6, 28 E 07 kgm 2 . Hence the yaw restoring coefficient will be
81, 5 MNm / rad and a natural period in yaw of approximately 5, 5 s is obtained. The low natural period
will contribute to minimize rotations induced by asymmetric forces on the rotor.

47

8.8 Design mooring system
In this section, some key features of the design mooring system are presented.
The static equilibrium configuration is shown in figure 8-7.

Figure 8-7: Static equilibrium configuration
Top: x-z-plane, Bottom: x-y-plane

48

The results obtained from 1-hour time domain analysis in operational- and storm conditions (from
Chapter 7) are presented in table 8-5. Note that the standard deviation of surge motion is significantly
smaller at the fairleads than in the waterline and at the rotor.
Operational condition
Response

Storm condition

Mean

Std

Min

Max

Mean

Std

Min

Max

Surge - Waterline [m]

7,37

0,69

3,88

9,46

9,34

5,27

-6,65

27,75

Sway - Waterline [m]

0,00

0,00

0,00

0,00

0,00

0,00

0,00

0,01

Heave - Waterline [m]

-0,60

0,10

-0,93

-0,31

-1,01

1,09

-5,63

2,43

Pitch - Waterline [deg]

3,29

0,67

0,95

5,67

1,77

3,78

-9,61

14,86

Surge - Rotor [m]

11,12

1,39

5,45

15,40

11,34

9,51

-17,57

44,11

Sway - Rotor [m]

0,00

0,00

0,00

0,00

0,00

0,00

0,00

0,00

Heave - Rotor [m]

63,28

0,13

62,77

63,66

62,82

1,19

57,63

66,27

Surge - Fairlead [m]

4,73

0,39

2,79

5,64

7,91

2,37

0,90

16,16

Sway - Fairlead [m]

0,00

0,00

0,00

0,00

0,00

0,00

0,00

0,01

Heave - Fairlead [m]

-46,92

0,08

-47,18

-46,68

-47,29

1,06

-51,88

-43,79

Z-pos - Clump weight 1 [m]

-83,49

0,44

-85,66

-82,39

-79,81

3,88

-90,91

-62,92

Z-pos - Clump weight 2 [m]

-90,42

0,18

-90,92

-89,57

-91,89

1,36

-97,87

-88,18

Z-pos - Clump weight 3 [m]

-90,42

0,18

-90,92

-89,57

-91,89

1,36

-97,87

-88,18

Axial force - Anch.line 1 [kN]

1177,97

18,75

1090,65

1231,36

1400,95

186,08

821,16

2965,65

Axial force - Anch.line 2 [kN]

939,82

4,82

926,62

966,23

902,31

24,09

791,24

1034,88

Axial force - Anch.line 3 [kN]

939,82

4,82

926,62

966,23

902,31

24,09

791,24

1034,93

Axial force - DL1 [kN]

616,73

9,18

574,19

643,02

721,21

94,17

405,83

1501,65

Axial force - DL2 [kN]

616,73

9,18

574,19

643,02

721,20

94,16

405,63

1501,65

Axial force - DL3 [kN]

625,13

30,16

525,94

728,00

578,18

195,33

28,56

927,62

Axial force - DL4 [kN]

377,52

30,14

281,73

476,77

389,33

203,57

-11,39

1002,68

Axial force - DL5 [kN]

377,52

30,14

281,73

476,77

389,32

203,57

-11,41

1002,72

Axial force - DL6 [kN]

625,13

30,16

525,94

728,00

578,18

195,33

28,56

927,81

Heave - Tower bottom [m]

-80,47

0,08

-80,71

-80,24

-80,80

1,06

-85,46

-77,18

Total surface elevation [m]

0,00

0,25

-0,94

0,85

0,00

3,74

-12,47

11,89

Wind speed [m/s]

10,97

1,19

6,24

14,46

40,45

3,11

27,63

50,98

Vertical force on anchor
NO
Table 8-5: Response from time domain analysis

NO

The natural periods of the whole system and for one single line are presented in table 8-6 and 8-7
respectively.
Degree of
freedom
Surge
Heave
Pitch

Natural period
[s]
84,6
27,7
23,9

Table 8-6: System natural periods

49

It is seen that all the natural periods are above the WF range. Furthermore, Mathieu effects due to
coincident heave and pitch natural periods are avoided; while the critical wave period Twave , cr = 13 s may
excite pitch resonance.

Pretension
[kN]

Mode

Eigenvalue

700

1
2
3
4
5

0,62
6,76
20,88
28,21
28,65

Circular frequency Natural period
[rad/s]
[s]
0,79
7,96
2,60
2,42
4,57
1,38
5,31
1,18
5,35
1,17

Table 8-7: Single line natural periods

From table 8-7 it is seen that only the 1st natural period is in the wave period range, while the other
modes have lower natural periods. It is therefore checked for resonance in the mooring lines by
exposing the system for waves with peak periods close to the 1st natural period. The results are shown
in table 8-8. No significant increase of the axial force and motions in the mooring lines are observed,
i.e. no mooring line resonance. This is probably due to the large drag damping in the mooring lines; in
addition to the fact that for the considered wave periods, almost all wave kinematics are eliminated at
the depth of the mooring lines.
Significant wave height Peak period
Axial force
Hs [m]
Tp [m]
Mean
Std
4
7,66
1451,33 35,26
4
7,96
1450,62 34,55
4
8,26
1450,04 33,90
Table 8-8: Mooring line resonance test

Response
anchorline 1
X-pos - anchorline top
Min
Max
Mean
Std
Min
Max
1305,12 1580,54 -30,56
0,05
-30,83 -30,33
1307,06 1576,41 -30,56
0,05
-30,83 -30,37
1300,81 1575,57 -30,56
0,05
-30,83 -30,38

50

9. Design check
9.1 General
Since floating offshore wind turbines is a relatively new concept that has yet to be fully
commercialized, there is currently no unique standard governing the design of such structures. Until a
standard that fully covers these structures is established, DNV proposed to use the standard DNV-OSJ101 “Design of Offshore Wind Turbine Structures” together with DNV Guideline for Offshore
Floating Wind Turbine Structures. The former provides principles, technical requirements and
guidance for design, construction and in-service inspection of offshore wind turbine structures. The
latter discusses issues related to design principles, site conditions, loads, stability and stationkeeping of
floating wind turbine structures.
The guideline states that: “Until loads and response of catenary moored floating wind turbine
structures are more thoroughly understood, the permanent mooring line tension as well as the dynamic
mooring line tension shall be taken according to DNV-OS-E301 “Position Mooring”, which applies to
the design of the mooring line as well as to the design of the anchor that transfers the loads to the
supporting seabed soils.” DNV-OS-E301 “Position Mooring” is henceforth referred to as OS-E301. It
provides environmental conditions and methods for mooring system analysis, in addition to
requirements regarding mooring equipment.
When it comes to mooring line components, requirements concerning materials, manufacture, testing,
dimensions and tolerances are given for mooring chain and steel wire ropes in DNV-OS-E302
“Offshore Mooring Chain” and DNV-OS-E304 “Offshore Mooring Steel Wire Ropes” respectively.
Figure 9-1 illustrates the relationships discussed here, and how the standards are referring to each
other.

Figure 9-1: Overview of standards

51

9.2 Limit states
The Framework Regulations enforced by the Norwegian Petroleum Safety Authority, refers to
NORSOK Standards when it comes to design of offshore structures. The NORSOK standards will in
turn refer to the rules of classification societies, as represented with DNV in the previous section.
According to Haver (2007), the structural design of offshore structures is based on the limit states
design method; where a limit state is referred to as a state where the structure or a part of the structure
no longer fulfils the requirements ensuring that the structure performs according to the design
specification.
The four limit states are recognized as:
• Ultimate limit state
• Accidental limit state
• Fatigue limit state
• Serviceability limit state

9.2.1 Ultimate limit state (ULS)
The ultimate limit state (ULS) corresponds to the resistance to maximum applied loads. The control
shall demonstrate that all foreseen loads can be resisted with an adequate margin.
Typically, according to ISO 19900, the ULS for offshore structures include:
• Loss of static equilibrium of the structure (e.g. overturning or capsizing)
• Failure caused by exceeding the ultimate strength
• Transformation of the structure into a mechanism
• Loss of structural stability
• Sinking
• Loss of stationkeeping
With respect to the ULS, control against loss of stationkeeping, as given in OS-E301, is emphasized in
this study. It is stated that the ULS is introduced to ensure that the individual mooring lines have
adequate strength to withstand the load effects imposed by extreme environmental conditions.

9.2.2 Accidental limit state (ALS)
The accidental limit state (ALS) corresponds to accidental situations or abnormal events. The control
ensures that a given accidental scenario does not lead to a complete loss of the integrity of the
structure. Also some very rare accidental loads are to be checked under the ALS.
As for the ULS, the ALS requirements for the stationkeeping system, as given in OS-E301, are
emphasized in this study. The limit state is introduced to ensure that the mooring system has adequate
capacity to withstand the failure of one mooring line. For cases where the mooring lines are equipped
with clump weights, the loss of a clump weight due to failure of the connection to the mooring line is
included as a single failure event.

9.2.3 Fatigue limit state (FLS)
The fatigue limit state (FLS) refers to the cumulative damage due to repeated loads. The control
ensures that the structure is designed with proper margins against fatigue failure. The FLS control is
not considered in this study.

52

9.2.4 Serviceability limit state (SLS)
The serviceability limit state (SLS) addresses the effect on comfort and non-structural components
from the motions and structural responses. The control is carried out to ensure that the structure fulfils
the functional requirements adequately. The SLS control is not considered in this study.

9.3 Environmental conditions
For details on environmental conditions, DNV standards generally refer to DNV-RP-C205
“Environmental Conditions and Environmental Loads”. However, for simplicity, the environmental
conditions applied here are taken directly from OS-E301. Northern North Sea – Troll field is selected
as design location. This location has a water depth of slightly above 300 m, while the water depth in
this study is set to 100 m. The current profile is therefore adjusted, while the wave and wind conditions
are taken as given in OS-E301. In the following, details about the waves, wind and current are given,
in addition to the drag force coefficients.

9.3.1 Waves
Sea states with return periods of 100 years shall normally be used. Combinations of significant wave
height and peak period along the 100-year contour, defined by the inverse FORM technique, shall be
applied. In cases with limited environmental data, typical sea states for specific areas can be applied
for preliminary design. This is utilized in the present study. The peak period is then determined from
the range of peak periods given by the means of a sensitivity analysis.
The 100-year sea state for the Troll field is given in table 9-1.

Northern North Sea - Troll field

Hs [m]
15,0

Tp [s]
15,5 - 17,5

Table 9-1: Troll field sea state

Based on the maximum axial force response in the anchor lines for the peak period range considered, a
design peak period of 16,5 s was selected. A JONSWAP wave spectrum is used for modelling the sea
state. The waves are given with an average propagation direction including a cosine spreading
function.

9.3.2 Wind
According to OS-E301, a mean wind speed 10 m above sea level, with a return period of 100 years
based on the marginal distribution of wind speeds at the specific location, should normally be used.
The wind load is treated as a steady component in combination with a time varying gust component.
The time varying wind is here described by a Kaimal wind spectrum.
In the standard, a 1-hour mean wind speed 10 m above the sea level, with a return period of 100 years
is given. This is taken as the 3-hour mean wind speed at hub height in the analysis. The turbulence
intensity is set to 0,1.
The 100-year mean wind speed for the Troll field is given in table 9-2.

U [m/s]
Northern North Sea - Troll field
40,5
Table 9-2: Troll field wind speed

53

9.3.3 Current
OS-E301 states that a surface current speed with a 10-year return period should normally be used,
based on the marginal distribution of current speeds at the location. Based on measurements from the
Troll field, Mathiesen et al. (2008) proposed a current profile. Since the water depth at the Troll field
far exceeds the water depth used in this study, only the part of the profile down to a water depth of 100
m is used.
The 10-year current profile applied is given in table 9-3.

Northern North Sea - Troll field

U [m/s] Level [m]
1,59
0
1,14
-20
1,06
-40
0,72
-60
0,72
-80
0,72
-100

Table 9-3: Modified Troll field current profile

9.3.4 Directions
All the environmental loads are assumed to be acting in the same direction. All directions from 0° to
360°, with a spacing of 30°, are investigated. 0° is along the positive x-axis, while the other directions
are defined clockwise accordingly as shown in figure 9-2.

Figure 9-2: Definition of directions

54

9.3.5 Drag force coefficients
The drag force coefficients for the mooring line components are taken according to OS-E301 and
presented in table 9-4.

Drag coefficients, Cd
Component type Transverse Longitudinal
Studless chain
2,4
1,15
Stranded rope
1,8
Table 9-4: Drag force coefficients

Marine growth and special sea bed soil conditions are not considered in this study.

9.4 Mooring system analysis
According to OS-E301, mooring system analysis can be performed by applying a frequency domain or
a time domain method. The latter is utilized in this study, due to the possibility of including drag
forces and non-linear mooring systems.

9.4.1 Time domain analysis
In general, the required simulation length is governed by the number of maxima per unit time of the
combined WF/LF process. The duration of an environmental state is usually taken as 3 hours, which is
the simulation length used here.
From one 3-hour time series, a global maximum, which forms the basis for the extreme value
statistics, is referred to as the maximum response between two successive mean-up-crossings. The
global maxima are assumed to be independent stochastic variables.
The required extreme value for the line tension is taken as the Most Probable Maximum (MPM) value
of the extreme value distribution. This distribution is found by simulating, say 20, realizations of
duration 3 hours. The largest global maxima from each realization form the extreme sample, which
then is fitted to an extreme value distribution. For a large extreme sample, the distribution will
approach a Gumbel distribution; and the MPM value will correspond to the 37% percentile, i.e. 63%
probability of exceedance. An alternative approach could be to use the expected value from the
extreme sample. This would be conservative as it corresponds to the 57% percentile value of the
Gumbel distribution.

55

9.4.2 Characteristic line tension
In the standard, two components of the characteristic line tension are considered:



TC-mean – The characteristic mean line tension, due to pretension and mean environmental
loads.
TC-dyn – The characteristic dynamic line tension, induced by LF and WF motions.

When analysing in the time domain, the former is taken as the mean of the time series. The latter is
taken as the difference between the MPM value of the extreme value distribution and the characteristic
mean line tension. The characteristic line tensions are thus found as:
TC-mean = mean tension of the time series
TC-dyn = TMPM - TC-mean

9.4.3 Characteristic capacity
For cases where statistics for the breaking strength of mooring line components are not available, the
characteristic strength may be taken according to
SC = 0, 95S mbs

(9.1)

where S mbs is the minimum breaking strength for new components as given in table 8-4.

9.4.4 Design equation and partial safety factors
In OS-E301, the mooring system is categorized according to the consequences of mooring system
failure. The two categories are:
Class 1 Class 2 -

Mooring system failure is unlikely to lead to unacceptable consequences such as loss of
life, collision with adjacent platform, capsize or sinking.
Mooring system failure may well lead to unacceptable consequences of these types.

Furthermore, the design equation is introduced as:
SC − TC − meanγ mean − TC − dynγ dyn ≥ 0

(9.2)

where the characteristic quantities are defined in the previous sections, and the partial safety factors
are given in table 9-5.
ULS
ALS
Partial safety factor Partial safety factor Partial safety factor Partial safety factor
on mean tension
on dynamic tension
on mean tension
on dynamic tension
Consequence class
1
2

γmean

γdyn

γmean

γdyn

1,10
1,40

1,50
2,10

1,00
1,00

1,10
1,25

Table 9-5: Partial safety factors

56

It is seen that the safety factors for ALS are relatively small. Conservatism is however ensured by the
very small probability of coincident line failure and characteristic loads with return period of 100
years.

9.4.5 Horizontal offset and permissible line length
The standard states that the horizontal offset of a given reference point shall be within the operational
service limitation both for intact mooring system and in the case of a single line failure. For riser
applications, the riser manufacture specification will govern the maximum permissible horizontal
offset. Floating wind turbine applications are not specifically addressed in the standards; it is however
obvious that the horizontal offset will be limited by the power cable configuration and the distance to
adjacent structures.
When it comes to permissible line lengths, the following applies to design where anchors that cannot
take uplift forces are used:
- The mooring lines shall have enough length to avoid uplift at anchors for all relevant design
conditions in the ULS.
- Vertical forces on the anchors can be accepted in the ALS, if it is documented that these forces
will not significantly reduce the characteristic resistance of the anchors.
Furthermore, it is stated that the maximum permissible line length is limited to the suspended length at
a line tension equal to the breaking strength of the line plus 500 m.

57

9.5 Results – ULS
For the ULS, analyses of duration 3 hours are carried out with the mooring system in intact condition.
The environmental conditions described in Chapter 9.3 are applied. Analyses are performed with
environmental loads from 0° to 360° with an angular increment of 30° according to figure 9-2, i.e. a
total of 12 analyses. The main results are presented in table 9-6, while complete results are found on
the attached DVD.
Axial forces [kN]
Direction

Chain segment

Wire segment

Max

Anch.

Horizontal plane

Lift-off

line

excursion

Mean

Max

Mean

Max

[m]

nu.

[m]

0

1399,35

3547,12

1397,56

3546,26

0,01

1

30,74

30

1370,86

2682,69

1368,93

2681,46

0,02

1

31,97

60

1296,66

1934,28

1294,43

1932,64

0,00

1

38,91

90

1299,14

2391,42

1297,10

2390,09

0,00

2

30,14

120

1340,95

2912,33

1339,08

2911,36

0,01

2

29,25

150

1300,81

2169,52

1298,79

2167,71

0,00

2

28,26

180

1188,83

1657,21

1186,44

1655,57

0,00

2

38,49

210

1294,93

2165,74

1292,90

2163,87

0,00

3

28,68

240

1336,88

3234,03

1335,00

3233,07

0,02

3

29,17

270

1296,52

2531,76

1294,48

2530,43

0,00

3

30,65

300

1294,50

1682,10

1292,27

1680,23

0,00

1

35,39

330

1367,88

2964,16

1365,95

2963,26

0,01

1

32,56

Table 9-6: Results ULS analysis

We see that as expected, the maximum tension will be largest in the cases where the environmental
loads are acting directly towards one of the anchorlines, i.e. for directions 0°, 120° and 240°. This is
because almost all the forces are taken up by only one anchorline in these cases. For all directions,
very small differences are observed between the most heavily loaded chain segment and the most
heavily loaded wire segment.
The anchorline number refers to the most heavily loaded anchorline in each case. See figure 5-1 for
definition of anchorline numbering.
The horizontal plane excursion refers to the maximum horizontal offset during each of the 3 hours
simulations. The maximum offsets vary between 28 m and 39 m. We see that the largest offsets occur
in cases where the environmental loads are acting in between adjacent lines. The maximum tension in
these cases are however limited because the forces are distributed almost evenly between two lines
instead of only one. Since the power cable configuration nor the possibility of adjacent wind turbines
is investigated in this study, the ULS requirements regarding permissible horizontal offset are assumed
fulfilled.
Maximum lift-off refers to the maximum lift-off of a point located 10 m from the anchor of the most
heavily loaded anchorline during each 3 hour simulation. This value will thus strongly indicate
whether we are experiencing vertical forces on the anchors or not. Lift-off is only observed for cases
58

where the environmental loads are acting close to or directly towards an anchorline. However, when
accounting for the weight of the anchor, a lift-off of 2 cm of a point 10 m from the anchor will give
negligible vertical forces on the anchor.
Ideally, 20 simulations of duration 3 hours should be performed for each direction in order to establish
an extreme value distribution for the line tension. This would however demand an unrealistic amount
of computational effort. The extreme value distribution is therefore conservatively fitted to 20 3-hour
simulations for the case with largest maximum line tension, i.e. environmental loads with a direction
of 0°. By using different seed number for each simulation and fitting the extreme line tension sample
to a Gumbel distribution, the extreme value distribution is obtained as shown in figure 9-3. The
Gumbel parameters are obtained according to Leira (2010). Complete results from all the 20
simulations are found on the attached DVD.

Figure 9-3: Distribution of maximum line tension ULS

The distribution of global maxima from a single 3-hour simulation is fitted to a Weibull distribution
and plotted in dotted lines. Both distributions shown are for the most heavily loaded chain segment.
The MPM- and expected value for the maximum line tension is indicated in dotted red lines, and
correspond to the 37% percentile and 57% percentile value of the Gumbel distribution respectively.
The results are presented in table 9-7 for both the most heavily loaded chain- and wire segment.

MPM value [kN]
Expected value [kN]

Chain
Wire
3534,90 3534,04
3362,37 3361,43

Table 9-7: MPM and expected value for maximum line tension ULS

59

By applying the MPM value when calculating the characteristic dynamic line tension, the design
equation (eq. 9-2) is presented for all considered directions in table 9-8.

Direction
0

30

60

90

120

150

180

210

240

270

300

330

Consequence

Design equation

class

Chain

Wire

1

2814,09

2133,62

2

1216,47

536,03

1

2802,69

2122,17

2

1196,53

515,99

1

2773,01

2092,37

2

1144,59

463,84

1

2774,01

2093,44

2

1146,33

465,71

1

2790,73

2110,23

2

1175,60

495,10

1

2774,68

2094,11

2

1147,50

466,89

1

2729,88

2049,18

2

1069,11

388,25

1

2772,32

2091,76

2

1143,38

462,77

1

2789,10

2108,60

2

1172,75

492,24

1

2772,96

2092,39

2

1144,49

463,88

1

2772,15

2091,51

2

1143,08

462,33

1

2801,50

2120,98

2

1194,45

513,90

Table 9-8: Design equation results ULS

We see that for both consequence classes 1 and 2, all values are positive, and the design equation is
hence fulfilled for all directions. It is safe to assume that unless the structure is placed in a wind farm
very close to adjacent structures, a floating wind turbine will be classified as a class 1 type of structure.
Regardless, the criteria given in the ULS control will be fulfilled.

60

9.6 Results – ALS
For the ALS, analyses of duration 3 hours are carried out with the mooring system in damaged
condition. Two damaged conditions are examined. The first is investigating the case of loss of one
anchorline, while the second case investigates the loss of a clump weight. The environmental
conditions described in Chapter 9.3 are applied. Analyses are performed with environmental loads
from 0° to 360° with an angular increment of 30° according to figure 9-2, i.e. a total of 12 analyses for
each of the two ALS cases. The main results are presented here, while complete results are found on
the attached DVD.

9.6.1 Loss of one line
For the purpose of analysing the effect of loss of an anchorline, a new Riflex analysis model is made
with anchorline 1 missing. The new finite element model is presented in figure 9-4.

Figure 9-4: Finite element model, ALS – Loss of line

61

The results from the 12 analyses are presented in table 9-9.
Axial forces [kN]
Direction

Chain segment
Mean

Max

Max

Wire segment
Mean

Max

Lift-off
[m]

Anch.
Li
line
nu.

Max horizontal-

Yaw angle

plane excursions

[deg]

[m]

Mean

Max

0

968,27 1154,54 965,40 1152,07

0,00

3

500,04

52,38

66,28

30

932,16 1203,16 929,32 1201,46

0,00

2

484,86

54,06

64,54

60

905,14 1288,62 902,28 1285,98

0,00

2

407,71

47,00

51,76

90

450,82 4620,97 446,96 4749,10

0,00

3

228,02

28,75

30,56

120

519,88 2911,31 516,00 2291,19

0,00

3

47,55

4,73

7,47

150

961,97 1282,92 959,23 1280,18

0,00

2

29,75

0,83

3,52

180

900,75 1040,48 897,73 1035,78

0,00

3

25,90

0,00

0,00

210

963,59 1282,55 960,86 1280,14

0,00

3

29,54

-0,86

-5,07

240

910,97 1253,22 908,15 1250,29

0,00

3

47,61

-4,73

-8,04

270

450,97 5631,22 447,12 5653,40

0,00

2

226,54

-28,70

-30,54

300

905,01 1288,85 902,15 1286,22

0,00

3

407,80

-47,03

-51,76

330
928,57 1149,49 925,72 1147,20
Table 9-9: Results ALS analysis – Loss of line

0,00

3

483,09

-54,20

-62,86

We see that as one anchorline is removed, the horizontal plane excursions are significantly increased.
This is especially prominent for the directions where the environmental loads are acting towards the
removed anchorline, i.e. for directions 0°-90° and 270°-330°. The same directions are also associated
with very large mean and maximum yaw angles. Because there is no anchorline present to resist the
motions, the floater will drift off and rotate around its z-axis (yaw) until the two originally leeward
anchorlines are tightened and equilibrium is regained. In practice, this new equilibrium position would
cause very large tension levels in the delta-lines as the two delta-lines on the leeward side of the new
equilibrium position will be pinched around the floater circumference. This does not appear from the
analyses however, as the delta-lines go directly through the body of the floater in a non-physical
manner. It is therefore fair to assume, though it is not supported by the analyses, that when
environmental loads with a return period of 100 years are applied on the structure from the discussed
directions, we run an impending risk of losing additional anchorlines. Hence, the mooring system
lacks redundancy for these directions. It is also obvious that with horizontal offsets up to 500 m, there
is a large risk of running into adjacent structures if we assume that the floating wind turbine is located
in a wind farm.
For the other directions considered, 120°-240°, sufficient restoring forces are provided by the
remaining two anchorlines. Mean and maximum tension in the most heavily loaded anchorline will be
relatively low and horizontal plane excursions are somewhat in the same range as experienced in the
ULS case.
Vertical forces on the anchors are not observed for any of the directions considered.
Using the worst case as basis for calculating extreme value statistics will be futile as the missing
anchorline makes the response for each case strongly dependent on the direction of the environmental
loads. The maximum value from each simulation is therefore taken as the MPM value when
performing the design check; the design equation is calculated for consequence class 1 and 2 for each
direction. The results are found in Appendix D. The design equation is satisfied for all directions
except for environmental loads from 90° and 270°. However, the results can as mentioned not be taken
as the truth as larger tension levels are expected in real life. When the large horizontal offset values are
62

added, the conclusion is that when considering the case of loss of one anchorline, the mooring system
fails to meet the criteria given in the ALS.

9.6.2 Loss of one clump weight
For these analyses, the clump weight on anchorline 1 is removed from the Riflex model and replaced
by a regular chain segment. The results from the 12 analyses are presented in table 9-10.
Axial forces [kN]
Direction

Chain segment
Mean

Max

Max

Wire segment
Mean

Lift-off
[m]

Max

Anch.
i
line

plane excursions

nu.

[m]

Max horizontal-

0

1130,30 6916,15 1130,09 6916,42

2,05

1

32,43

30

1085,61 6492,04 1085,23 6492,23

1,80

1

34,10

60

962,56

4317,10

1,14

1

37,10

90

1159,58 2187,49 1157,30 2186,14

0,00

2

38,90

120

1152,37 2113,67 1150,16 2111,95

0,00

2

26,32

150

1075,56 1549,36 1073,11 1546,78

0,00

2

20,36

180

972,76

1159,67

0,00

2

18,04

210

1076,54 2231,08 1074,09 2229,61

0,00

3

27,27

240

1151,45 1893,37 1149,25 1891,36

0,00

3

25,80

270

1156,56 1801,67 1154,27 1799,67

0,00

3

34,60

300

960,12

4242,69

1,00

3

38,60

330

1080,96 6093,79 1080,59 6093,98

1,84

3

34,16

4317,20

1162,27

4242,72

961,89

969,91

959,46

Table 9-10: Results ALS analysis – Loss of clump weight

The results show that we can expect large peak tensions in the mooring lines for the directions where
the environmental loads are acting towards the removed clump weight. The effect is prominent for the
directions 0°-60° and for 300°-330°. This is due to the fact that when the clump weight is removed
from an anchorline, the restoring forces from the geometric stiffness contribution of the considered
line are dramatically reduced. Hence, the line will respond by stretching and the elastic stiffness
contribution will govern the restoring forces. It is also seen that the horizontal plane excursions are
larger for these directions, and that vertical forces on the anchors are expected. The sum of these
effects may result in loss of the anchorline, and we are back to the first ALS case discussed in the
previous section.
For the other directions considered, the results are similar to the ULS case.
As for the first ALS case, the maximum line tension from each of the 12 simulations is taken as the
MPM value when checking the design equation. The results, which are found in Appendix E, show
that the design equation is not fulfilled for directions 0°, 30°, 300° and 330°.
The mooring system is seen not to fulfil the design criteria for neither of the two investigated ALS
cases. Introducing additional anchorlines to increase the redundancy of the mooring system may
therefore be considered.

63

10. Conclusion
The purpose of this study has been to select and optimise the mooring system design for floating
offshore wind turbine structures in shallow water. Furthermore, methods for designing the mooring
system according to the governing standards were demonstrated.
The design of the floating support structure was based on the Hywind concept, utilizing a deep-draft
Spar floater. The draft of the substructure was reduced to 80 m to accommodate to the water depth of
only 100 m. Only catenary mooring systems were considered since other types of stationkeeping
systems would compromise the design concept. Three types of catenary mooring systems were
defined, distributed mass-, clump weight- and buoyancy element mooring system. They were analysed
by the means of quasi-static and dynamic analysis in order to determine the system behaviour. The
mooring line characteristics obtained from quasi-static analysis showed that the clump weight mooring
system had favourable characteristics compared to the other two mooring system concepts considered.
The relatively low submerged weight of the buoyancy element mooring system will reduce the
geometric stiffness. When the horizontal offset is increased, the line length would therefore have to be
very large in order to ensure non-linear restoring forces and preventing vertical forces on the anchors.
The distributed mass mooring system had a larger submerged weight and consequently more
geometric stiffness. The large axial stiffness of the chain gave however a large elastic stiffness, and a
transition to the elastic stiffness range was quickly observed as the horizontal offset increased. The
clump weight mooring system had large geometric stiffness due to the large catenary sag from the
clump weight, while the elastic stiffness was reduced due to the wire segments in the mooring lines.
This combination of stiffness contributions was proven effective, as the transition to the elastic
stiffness range was observed to occur at larger tension levels than for the other two concepts. Peak
tensions in the mooring lines were then limited. This was also supported by time domain analysis,
which demonstrated that the maximum tension observed in the mooring lines during a 1-hour
simulation in severe environmental conditions were 40% and 53% larger for the distributed mass- and
buoyancy element mooring system respectively than for the clump weight mooring system.
Sensitivity studies were carried out with respect to a number of mooring system parameters. As the
main problem was to get sufficient geometric stiffness from the limited suspended line length, the size
of the clump weight was seen to be the most influential parameter on the system behaviour. Various
sizes, ranging from 6 – 154 tons were investigated. The heaviest ones had major impact on the
catenary sag, resulting in favourable mooring line characteristics. However, using clump weights with
mass above 100 tons would require very large pretension in order to prevent clump weight touchdown
on leeward lines when the floater is offset. In addition, issues related to installation and handling arise
for the largest clump weights. Clump weights of size 75 tons were therefore selected. As the
suspended line length was limited, and attaching the clump weights to the delta-lines not desirable, a
clump weight position on the main mooring line very close to the delta-lines was selected. The
pretension needed to be large enough to avoid slack leeward lines and small enough to limit the mean
and maximum tension in the weather ward lines. A pretension corresponding to a horizontal top
tension of 700 kN was used. The total line length and chain and wire segments were selected to meet
the criteria given in the standards with respect to vertical forces on the anchors and permissible line
tension. The vertical fairlead position and the length of the delta-lines were merely assessed by
theoretical considerations. The former is ideally located close to the vertical centre of rotation, which
was shown to be frequency dependent. The vertical fairlead position was set to a point between the
centre of gravity and the centre of buoyancy of the floating structure, mainly to provide enough
suspended line length. The delta-line length, which influences the yaw restoring coefficient and
consequently the yaw natural period was set to 40 m. As the vertical distance between the sea bottom
and the fairlead is only 53,6 m, this gave some suspended main mooring line length left to play with.
The yaw natural period was estimated to 5,5 s, while the natural periods for the other motion modes
were kept above the wave period range.
65

There is no unique standard governing the design of floating wind turbines, but a guideline assessing
the key issues regarding the floating body of such structures is established by DNV. The guideline
refers to DNV-OS-E301 “Position Mooring” for design of mooring system. The Troll field was
selected as design location, and analyses were carried out against the ULS and ALS. Environmental
loading from a total of 12 directions were considered for each limit state, ranging from 0°-360°
relative to the floating structure. The results showed that the line tensions were within the acceptable
limits for all directions in the ULS. For the ALS, both the cases of loss of line and loss of clump
weight were considered. For the first case, large tensions exceeding the criteria given by the standard
were observed when the environmental loads were acting in the direction of the missing line. Very
large horizontal offsets in the range of the length of the mooring system were also observed. For the
case with the loss of clump weight, tensions exceeding the permissible limits and vertical forces on the
anchor were observed for directions were the environmental loads were acting towards the line with
the missing clump weight. The ALS analyses proved the lack of redundancy in the mooring system in
the cases of line breakage and loss of clump weight. Using more than three mooring lines must be
considered in order to limit the mooring line tension and horizontal offsets in the ALS cases.

66

11. Recommendations for further work
The detail design of the clump weights is not studied here, but must be investigated if such
components are to be used in a mooring system. E.g. by designing a round or coned clump weight
without a large suction surface, the clump weight may partly rest on the sea bottom which will
improve the mooring line characteristics. This is especially relevant for shallow water applications, as
utilizing larger clump weights would increase the geometric stiffness contribution to the restoring
forces. Other aspects concerning the detail design of the clump weights include selecting material and
investigate how they should be installed and attached to the mooring line.
In this study, the design check focused on the ultimate limit state and the accidental limit state. In
order to complete the design check, also the fatigue limit state should be assessed. This involves
calculating the fatigue damage arising in the long term environment the mooring system is subjected
to, represented by a number of discrete environmental conditions. Furthermore, VIV analyses must be
carried out both for the ULS and for the ALS to include the VIV effects on the mean and lowfrequency components of line tension. Related to the ALS control, one would need to adjust the design
(e.g. by adding additional anchorlines) so that the redundancy of the system increases. This can be
challenging as the diameter of the substructure is small, and one would want to include delta-lines to
maintain the low yaw natural periods.
As floating wind turbines are intended to be installed in wind farms consisting of a large number of
structures, issues related to the mooring system arise. When using catenary moorings, the mooring
system may in fact be the limiting factor on how close the wind turbines can be installed; especially if
one assumes a design where mooring lines for different structures are not crossing. To save cost on the
anchors, one may also investigate the possibility of using one common anchor point for two or several
mooring lines of different structures.

67

References
Chakrabarti, Subrata (2005)

Handbook of Offshore Engineering Volume 1. Illinois,
USA: Elsevier Science.

Faltinsen, O.M. (1990):

Sea Loads on Ships and Offshore Structures.
Cambridge, UK: Cambridge University Press.

Furunes, E.W. ( 2010)

“Floating Wind Turbines at Medium Water Depths”.
M.Sc. thesis, Dept. of Structural Engineering, NTNU,
Trondheim.

Haslum, H.A. (2000)

“Simplified methods applied to non-linear motion of
spar platform”. Dr.ing thesis, Dept. Of marine
hydrodynamics, NTNU, Trondheim.

Haver, Sverre K. (2007):

“Prediction of Characteristics Response for Design
Purposes”. Lecture notes in TMR4195 Design of
Offshore Structures. Trondheim; Norway: Norwegian
University of Science and Technology.

Haver, Sverre K. (2010):

Lecture notes in TMR4195 Design of Offshore
Structures. Trondheim; Norway: Norwegian University
of Science and Technology.

Hordvik, T. (2010)

“Alternative Design of Anchor Systems for Floating
Windmills”. Pre-project, Dept. of marine
hydrodynamics, NTNU, Trondheim.

Langen, I., Sigbjørnsson,R. (1979)

Dynamisk Analyse av Konstruksjoner. Trondheim;
Norway: SINTEF, Avdeling for Konstruksjonsteknikk.

Larsen, C.M. (2010)

Lectures notes for special topic: Dynamic analysis of
marine structures. Trondheim; Norway: Norwegian
University of Science and Technology.

Leira (2010)

Lecture notes in TMR4235 Stochastic theory of sea
loads. Trondheim; Norway: Norwegian University of
Science and Technology.

Loukogeorgaki, E., Angelides, D. C.

“Stiffness of Mooring Lines and Performance of
Floating Breakwater in Three Dimensions”. Division of
Hydraulics and Environmental Engineering, Department
of Civil Engineering, Aristotle University. Thessaloniki,
Greece: Elsevier Science Limited

Luo, Y. (1992)

“Optimum Design of Clump Weights for Offshore
Mooring Systems”. Published in the proceedings of the
Proceedings of the Second International Offshore and
Polar Engineering Conference, USA. Noble Denton.
London, U.K.

69

Mathiesen, M., Nygaard, E. (2008):

“Hywind Metocean Design Basis”. Statoil internal
document.

Nielsen, F.G. (2004)

Matlab catenary calculations routine
(mooring_characteristics.m). Statoil internal file.

Nielsen, F.G. (2007):

“Design Brief for Offshore Floating Wind-Mills”.
Statoil internal document.

Nielsen, F.G. (2009):

“Tuning the Geometric and Mass Properties of
Hywind”. Statoil internal document.

Nielsen, F.G. (2011)

Personal communication.

Triantafyllou, M.S. (1990)

“Cable Mechanics with Marine Applications”. Dept. of
Ocean Engineering, Massachusetts Institute of
Technology, Cambridge, USA.

Yttervik, R. (2009)

TDHMILL3D User Documentation. Statoil internal
document.

DNV Guideline for Offshore Floating Wind Turbine Structures
DNV-OS-J101

Design of Offshore Wind Turbine Structures.

DNV-OS-E301

Position mooring.

DNV-OS-E302

Offshore Mooring Chain

DNV-OS-E304

Offshore Mooring Steel Wire Ropes

DNV-RP-C205

Environmental Conditions and Environmental Loads

ISO 19900

Petroleum and Natural Gas Industries – General
Requirements for Offshore Structures

Riflex Theory Manual
Riflex User Manual
SIMO Theory Manual
SIMO User Manual
Vryhof anchors (2010)

Anchor manual. Capelle a/d Yssel, the Netherlands.

www.statoil.com

70

Appendices

List of appendices
Appendix A: Catenary equations, including the effect of elasticity .........................................A1
Appendix B: Time series, comparison of mooring system concepts ........................................ B1
B.1 Operational condition .......................................................................................................... B1
B.2 Storm condition ................................................................................................................... B4
Appendix C: Riflex modelling of design mooring system components ...................................C1
Appendix D: Design equation results ALS – Loss of line .........................................................D1
Appendix E: Design equation results ALS – Loss of clump weight ......................................... E1
Appendix F: Content on the attached DVD ............................................................................... F1
F.1 T. Hordvik Master Thesis 2011 – 2 sided print (pdf -file):.................................................. F1
F.2 Presentation_Statoil_09062011 (power-point presentation):............................................... F1
F.3 Other matlab routines (folder): ............................................................................................ F1
F.4 Analyses (folder):................................................................................................................. F1

71

72

Appendix A: Catenary equations, including the effect of
elasticity
Deriving the catenary equations is taken from Faltinsen (1990).
Bending stiffness and dynamic effects in the line are neglected and we assume a horizontal
seabed.
In figure A1 an element of the line is shown. The mean hydrodynamic forces per unit length in the
normal and tangential direction are denoted D and F respectively. W is the submerged weight of
the line per unit length, A is the cross-sectional, E is the elastic modulus and T is the line tension.
Due to the submerged weight, the correction forces − ρ gAz and − ρ gAZ − ρ gAdz are introduced at
the end of the element.

Figure A1: Forces acting on an element of an anchor line (Source: Faltinsen (1990))

From equilibrium we find

[ w sin φ − F (1 + T / ( AE )) ] ds
φ [ w cos φ + D (1 + T / ( AE )) ]
Tdφ − ρ gAzd=
=
dT − ρ gAdz

(3)
(4)

By neglecting the effect of current forces F and D, and neglect the effect of elasticity the analysis
is simplified. The cable line is assumed to have constant weight per unit length.
Introducing
T =' T − ρ gzA

And write
A1

(5)

dT ' = w sin φ ds
T ' dφ = w cos φ ds

(6)
(7)

Eq. (4) and (5) can be divided to obtain

dT '

=

T'

sin φ
cos φ

T ' = T0 '



(8)

cos φ0

(9)

cos φ

By integration we get
s − s0
=

1

φ

T0 ' cos φ0


∫ =
w cos θ cos θ

T0 ' cos φ0

φ0

w

[tan φ − tan φ0 ]

(10)

dx = cos φ and we can write
1 T0 ' cos φ0
x − x0 =

w φ cos θ
φ


0

=

T0 ' cos φ0
w

  1
 log 
  cos φ

 1

+ tan φ  − log 

 cos φ

+ tan φ0
0





(11)

dz = sin φ and we can write
1 T0 cos φ0 sin θ
z − z0 =

2

cos θ
φ


0

=

T0 ' cos φ0
w

 1
 cos φ



1
cos φ0




(12)

If φ0 is the point of contact between the cable line and the sea bed so φ0 = 0 , we see that
T0 ' = T 'cos φ

(13)

The horizontal component of the tension at the sea bed can be written as
TH = T cos φw

By comparison we see that
A2

(14)

T0 ' = TH

The angle φ can be eliminated from Eq.(8) and (10), and (9) can be written as
xw
TH

 1 + sin φ 

 cos φ 

= log 

And

 wx 
=
T 

1  1 + sin φ

 wx 
=
T 

1  1 + sin φ

sinh 

H

cosh 

H


2

cos φ


2



=

1 + sin φ 

+

=

1 + sin φ 

cos φ

cos φ

cos φ

tan φ
1
cos φ

And we may write

w 
x
w
T 
T 
w  
cosh 
  T x  − 1
w 

s=

TH

sinh 

(15)

H

=
z+h

H

(16)

H

By combining Eq. (3), (10) and (11) the line tension can be found as
TH
=TH + w( z + h )
T − ρ gzA =
cos φ

i.e.
T = TH + wh + ( w + ρ gA) z

(17)

Tz = ws

(18)

In the waterplane we have

By using the above derived formulas, the following quantities can be found with reference to
figure A2.

A3

Figure A2: Vessel moored with one anchor line (Source: Faltinsen (1990))

()
()
x

l s = a sin




=
h a cosh

(19)

a

x




−1

a

(20)

where
a=

TH

(21)

w

By a combination of Eq. (17) and (18) we obtain
l=
h + 2 ha
s
2

2

(22)

The maximum tension in the cable can be written as
Tmax= TH + wh

(23)

And the minimum length of the cable becomes

(

=
l min h 2

Tmax

−1

wh

)

1
2

(24)

The horizontal distance X is found as
X =l − ls + x

A4

(25)

Triantafyllou (1990) showed how the effects of stretch could be accounted for in the catenary
equations. By assuming that the cross-sectional area after stretching A , has been replaced by the
unstretched area A0 , the x-coordinate is obtained by integration and reads:
dx
Te 
H

= cos φ (1 + e ) ≅ cos φ  1 +
= cos φ +
ds
EA0
 EA0 
H

=
x

w0

sinh


−1

(

)

V − w0 (l − s )
H

− sinh

−1

(

V − w0 l
H

)

+


(26)
Hs
EA0

The z-coordinate is obtained in a similar fashion and reads:
dz

= sin φ (1 + e ) ≅ sin φ

ds

z =

H
w
0



 1 +
 

(

1 +



e

EA
0

V − w0 (l − s )
H

+

1
EA0

=



T

)

sin φ +

V − w0 (l − s )
EA0

1
2





2


− 1+



(

V − w0 l

Vs − w ls + 1 w s 


2
2

0

A5

0

H

)


 
 
 

1

2

2

(27)

Appendix B: Time series, comparison of mooring system
concepts
B.1 Operational condition

Figure B1: Comparison of axial forces – main mooring lines

Figure B2: Comparison of axial forces – delta-lines

B1

Figure B3: Comparison of tower bottom heave motions

Figure B4: Comparison of fairlead translations

B2

Figure B5: Comparison of waterline translations

Figure B6: Comparison of weight element heave motions

B3

B.2 Storm condition

Figure B7: Comparison of axial forces – main mooring lines

Figure B8: Comparison of axial forces – delta-lines

B4

Figure B9: Comparison of tower bottom heave motions

Figure B10: Comparison of fairlead translations

B5

Figure B11: Comparison of waterline translations

Figure B12: Comparison of weight element heave motions

B6

Appendix C: Riflex modelling of design mooring system
components
The design mooring system components are modelled in Riflex according to table C1.

Component type
Parameter Dimension Chain (Connectors) Chain (Delta-lines)
AMS
[t/m]
0,151
0,107
0,01189
0,00837
[m2]
AE
0
0
AI
[m2]
RGYR
[m]
0
0
0,01189
0,00837
[m2]
AST
0,0001827
0,0001079
WST
[m3]
EA
[kN]
7,09E+05
7,09E+05
D
[m]
0,174
0,146
Table C0-1: Riflex modelling of mooring system segments

C1

Chain (Bottom)
0,221
0,0173
0
0
0,0173
0,0003208
7,09E+05
0,21

Wire
0,0405
0,00724
0
0
0,00724
0,0000869
4,84E+05
0,096

Clump weight
75,526
9,6211
0
0,88510
78,54
98,175
1,92E+09
3,5

Appendix D: Design equation results ALS – Loss of line
The results from calculating the design equation for the 12 directions considered in the ALS –
Loss of line are shown in table D1.

Direction
0
30
60
90
120
150
180
210
240
270
300
330

Consequence
class
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2

Design equation
Chain
Wire
6124,74
6096,80
6067,64
6027,00
5970,94
5913,41
2259,91
1634,39
4147,45
3788,73
5982,89
5934,75
6243,45
6222,49
5983,45
5935,61
6010,46
5959,12
1148,65
371,62
6392,89
6392,89
6369,33
6369,33

5259,34
5231,34
5115,94
5075,12
4908,69
4851,14
-2864,70
-3510,03
2372,85
2106,57
4983,53
4935,38
5429,11
5408,41
4985,40
4937,50
4990,10
4938,78
-4763,56
-5544,51
4908,06
4850,45
5225,92
5192,70

Table D0-1: Design equation results ALS – Loss of line

D1

Appendix E: Design equation results ALS – Loss of clump
weight
The results from calculating the design equation for the 12 directions considered in the ALS –
Loss of line are shown in table E1.

Direction
0
30
60
90
120
150
180
210
240
270
300
330

Consequence
class
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2

Design equation
Chain
Wire
-196,83
-1064,71
265,22
-545,74
2645,23
2142,04
5007,62
4853,43
5088,10
4943,91
5701,16
5630,10
6116,68
6088,25
4951,37
4778,19
5330,34
5219,05
5431,72
5334,95
6337,78
6337,78
6216,94
6216,94

-6664,63
-7532,58
-5823,17
-6634,22
-1391,09
-1894,37
3298,90
3144,57
3446,83
3302,56
4548,94
4477,89
5248,35
5219,89
3116,08
2942,75
3909,07
3797,76
4107,14
4010,33
-1237,50
-1729,98
-4991,96
-5743,97

Table D1: Design equation results ALS – Loss of clump weight

E1

Appendix F: Content on the attached DVD
F.1 T. Hordvik Master Thesis 2011 – 2 sided print (pdf -file):
Master thesis.

F.2 Presentation_Statoil_09062011 (power-point presentation):
Power point presentation for Statoil research centre 09.06.2011. Summarizes the highlights of the
study.

F.3 Other matlab routines (folder):
Contains matlab scripts and functions that are not directly related to running the analyses.
Scripts:
- damping.m
o Finding linear and quadratic damping from decay test. Calls on subroutine
SPEGEN_T.m.
- design_config.m
o Plot static equilibrium configuration of mooring system from Riflex stamod
results.
- Gumbel_fit.m
o Fit extreme sample to Gumbel distribution and plot. Calls on subroutine weibull.m
- JONSWAP.m
o Plots JONSWAP-spectrum from given Hs and Tp
Functions:
- SPEGEN_T.m
o FFT-routine for generating power spectrum from given time history xt. By Finn
Gunnar Nielsen.
- weibull.m
o Fits sample to a Weibull distribution.

F.4 Analyses (folder):
Contains the input files and results (tables and plots) from all the analyses. Contains 4 subfolders.

1. RUN - Comparison (subfolder):
Contains the input files and results (tables and plots) from the comparison analyses.
-

model.xls
o All structural properties, environmental input and simulation
parameters defined in excel.

Scripts :
- Run_script.m
o The main script which controls the analyses. Calls on numerous
subroutine

F1

Functions:
- make_directories.m
o Make directories for saving the results from the analyses.
- user_input.m
o Controls the user interface of the program.
Subfolders:
- Anchor routines (folder)
o Contains all the subroutines necessary for running the catenary and
mooring system calculations.
- Decay test (folder)
o Contains all the input files and subroutines necessary for running the
decay analysis.
- Dynamic analysis routines (folder)
o Contains all the input files and subroutines necessary for running the
dynamic analysis.
- Eigenvalue analysis routines (folder)
o Contains all the input files and subroutines necessary for running the
eigenvalue analysis.
- Results (folder)
o Contains plots and statistics for various analyses of the different
mooring system concepts, and also the results for the sensitivity
analyses. The Riflex result files are not included due to the size of
these files.

2. RUN – Optimized system (subfolder):
Contains the input files and results (tables and plots) from the comparison analyses.
-

model.xls
o All structural properties, environmental input and simulation
parameters defined in excel.

Scripts:
- Run_script.m
o The main script which controls the analyses. Calls on numerous
subroutines.
Functions:
- make_directories.m
o Make directories for saving the results from the analyses.
- user_input.m
o Controls the user interface of the program.
Subfolders:
- Anchor routines (folder)

F2

-

-

-

-

o Contains all the subroutines necessary for running the catenary and
mooring system calculations.
Decay test (folder)
o Contains all the input files and subroutines necessary for running the
decay analysis.
Dynamic analysis routines (folder)
o Contains all the input files and subroutines necessary for running the
dynamic analysis.
Eigenvalue analysis routines (folder)
o Contains all the input files and subroutines necessary for running the
eigenvalue analysis.
Results (folder)
o Contains plots and statistics for various analyses of the optimized
mooring system. The Riflex result files are not included due to the size
of these files.

3. Parameter study (subfolder):
Contains the input files and results for all the parameters that are studied by the means of
quasi-static analysis.
4. Design check (subfolder):
Contains the input files and results for the design check.
Subfolders:
- ALS (folder)
o Input files and results from two ALS cases
- ULS (folder)
o Input files and results from one ULS case

F3

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