GRAND RENEWABLE ENERGY 2018 Proceedings
June 17(Sun) - 22(Fri), 2018
Pacifico Yokohama, Yokohama, Japan

O-We-12-2

AN EMPIRICAL DESIGN FORMULA OF A SHARED PILE ANCHORFOR A FLOATING OFFSHORE WIND TURBINE
1211Kenji. Shimada , Tetsuji. Shiroeda , Hiroyuki. Hotta , Pham van Phuc and Takumi. Kida

312

Institute of Technology, Shimizu Corporation,135-8530 Japan
Engineering Headquarters, Shimizu Corporation, 104-8370 Japan
3Moricho Corporation, 160-0004 Japan

In order to widely promote the large-scale floating offshore wind farm among the private sector, it is the decidingfactor how much economical installation method can be developed with regard to the installation cost which accounts for alarge proportion in investment costs. In this paper a preliminary design of a shared pile anchor was made based on theresult of dynamic mooring simulation and it was found that a simple empirical design formula of an optimum pile
specification can be established against N-value, which is useful for preliminary estimation of the installation cost.
Keywords: floating wind turbine, shared pile anchor, empirical design formula, mooring analysis, N-valueINTRODUCTION
In order to widely promote the large-scale floating
offshore wind farm among the private sector, it is thedeciding factor how much economical installation method
can be developed with regard to the installation costwhich accounts for a large proportion in investment costs.
The sharing of anchor points by fixed anchors suchas pile or suction caisson anchor (Fig. 1, Fig. 2b) clearly
reduces cost compared to non-shared anchor (Fig. 2a)
However, in terms of installation, since the water depth isdeep, there are difficulties of handling multiple mooring
chains, and its mechanical behaviors are not wellunderstood.
In this paper, at first simulation considering theinteraction between the mooring chain and the seabed iscarried out, from which the anchoring force acting on theshared anchor is obtained. Then a preliminary design of apile is made based on the result, and an empirical design
formula relating to the optimum pile dimensions useful for
estimation of the installation cost was developed. Finally,a comparison was made for the installation cost of thedrag embedment anchor and the shared pile anchor.

Fig. 1. Schematic view of shared anchor (space amongturbines are narrowed for facilitating visualization).

(a)Non-shared anchor (drag embedment anchor)(b)Shared anchor (pile anchor or suction bucket anchor)
Fig. 2. Anchor for an offshore wind turbine.
ANALYSIS METHOD OF ANCHORING FORCE
The mooring cable acts as a position keeping
function and as a restoring force of the floating body. In
general, in the floating motion analysis, the main focus isplaced on capturing the fluctuation behavior of the floatingbody, and the mooring is often modeled by a simplifiedlinear spring. However, in this research as it is necessary
to calculate the mooring force as accurately as possible, aseries of time dependent mooring force simulation [1]based on geometric nonlinear finite element method
considering geometric nonlinearity of mooring chains andfrictional contact between mooring chain and sea
subsurface was performed.
Wind turbine and floater that were analyzed are 2
MW semisubmersible "Mirai" [2] which locates 20 km off
the coast of Fukushima prefecture (water depth 120 m). In
the analytical models, the wind turbine and the floating
body were simplified as a rigid body, but the mooring wasmodeled by using 40 elastic truss elements / direction × 3
directions=120 elements in which its volume is equivalent
to the actual mooring cable. For external force, the windload and the ocean current load were given as steadyload and the regular wave load was given by Morrison

GRAND RENEWABLE ENERGY 2018 Proceedings
June 17(Sun) - 22(Fri), 2018
Pacifico Yokohama, Yokohama, Japanequation, in which drag and inertial force coefficients are
0.7 and 1.9, respectively, using linear regular wave ofextreme wave height, with extreme load of 50 years ofrecurrence.
The mooring consists of an R3 type chain with studs(Table 1). The contact between the mooring chain and theseabed surface is modeled by a virtual subgrade reaction
spring in the vertical direction and by applying explicitly an
external force based on the Coulomb friction using thevertical reaction force at the moment on the mooring cableelement in the horizontal direction. The friction coefficient
was set to 1.0 according to Ref. [3].

ANALYSIS OF ANCORING FORCE
Anchoring force characteristics of a single floaterAt first, anchoring force characteristics areinvestigated for a single floater. Fig. 4 shows the
expanded shape of the mooring line at the equilibrium
position with the loading angle of α = 0° (no wave) with 4
different cable length of L = 450, 460, 470 and 480 m. At L
= 450 m it is in tension over almost all of the line. On theother hand, it can be found by the nonlinear contact
analysis that as the length of the line becomes longer thetension loosens and the mooring part which contacts withseabed increases.

z(m)120Wind andcurrent

L=450m
L=460m
L=470m
L=480m0a-120-500-400-300-200b,c-100

0100200300x(m)Fig. 4. Finite element analysis of mooring lines at theequilibrium state under steady wind and current loads.

Table 2 Metocean conditions.
Wind speed at hub height
Significant wave height
Significant wave period
Surface current
Water depth

50m/s
11.7m (Extreme wave
height : 21m)
13s
1.5m/s120m

Honeycomb arrangement of wind turbine and anchor
was assumed (Fig. 3) which is based on a hexagonal
module consisting of three or four wind turbines keeping
wind turbine spacing of 10D (D: rotor diameter = 80 m)
commonly used for an offshore wind turbine to minimize
the effect of wake loss. In this situation, four types ofanchors are defined, that are, three-direction mooring R,
two-direction mooring G and B, and one direction mooring
Y. Although six chains are used for mooring in "MIRAI", forsharing of an anchor, in the following, three-direction
mooring which unites two chains is used. Irregular wave
should be used, however, in order to obtain extreme value
wave loads with stable values, enormous computation
time is required, so in this study linear regular wave withthe maximum wave height of 21 m (significant wave
height H1/3 = 1.86 times 11.7 m) and period of 13s wasused. For the sake of simplicity, wind, wave, and current(Table 2) are assumed to be aligned, and the loading
angle is set as shown in Table 3 by considering rotational
symmetry.

5000

0

4000

Tension (mooring-a)

3000

Mooring shape (mooring-a)
Mooring shape (mooring-b,c)Tension(mooring-b,c)-20-40

2000
1000

-60
-80
-10000100200300z(m)Specification of mooring chain.
Diameter
132 mmWeight (in water) 331.76 kg/m
Weight (in air)381.59 kg/m
Stiffness (EA)
156,006 t

Fig.5 shows tension distribution along the L = 470m
mooring lines at the instant of the maximum anchoring
force in which wind, wave and current combined loads areapplied. Because the mooring lines have initial tension,
the tension does not vanish even laying on the seabed.

-120
500

400

|x|(m)

Fig.5. Tension distributions along mooring lines andmooring shapes at the instant of the maximum anchoringforce (L=470m).
41.2 10Windwavecurrent

41 10Tension |T|(kN)

Table 1

Layout of wind turbines and anchors.

T(kN)

Fig. 3.

8 10
6 104 103333

2 10

0450

460

470480L(m)Fig.6. Maximum anchoring force “a” of single floater
against length of mooring chain.
Fig. 6 shows the relationship between the mooring
length and the maximum tension “a” acting on the anchor
when the loading angle α = 0°. When the mooring lengthis shorter than 470 m, the tension acting on the anchor
rapidly increases. If it is too short, the mooring cable
becomes taut and a pull out force is generated in theanchor. Therefore, from the viewpoint of anchor design, itis preferable that the mooring cable is as long as possible.

Loading angle α
0°
30°
90°
180°
240°
270°

R
2643
―
2042
3078
―
―

G
3310
3049
976
―
2198
―

B
3004
3113
1730
2845
―
2314

Y
1177
―
988
2845
2605
2623

Weight (t)

120
100
80
Optimum pile60
40

Length (m)

20

N=200
1.5

2.0kh = kh 0δ

(1)

M max p =22H
H
3
3DK pγ ′(2)where, δ : dimensionless pile head displacement = δ δ 0 ,δ : pile head displacement (cm), δ 0 : reference
displacement and taken as δ 0 = 1cm , kh 0 and kh : horizontal
subgrade reaction force coefficient at δ 0 according to JRA
specification [6] and that takes into account subgrade
reduction. Although AIJ guideline [8] takes δ > 0.1 as arange of application of Eq. (1), here it is taken as δ > 1 forconservative estimation. The maximum bending momentof an anchor pile was taken as whichever smaller of themaximum bending moment by Chang’s method with Eq.
(1) and that by Broms’s method [9] which is expressed as
Eq. (2). Here, H : pile head horizontal applied load, D :pile diameter, and γ ′ : unit volume weight in water
3(=8kN/m ). K p is the passive earth pressure coefficient,and Coulomb earth pressure was used.

3.0

3.5

4.0Fig. 7. Variation of weight, thickness and length of theanchor pile against pile diameter (N=20).
10

CalculatedEq.(3)

CalculatedEq.(3)

86100

5Soil : Linear elastic

432Soil : Linear elastic

w/Eq.(1) and (2)w/Eq.(1) and (2)1011Fig. 8 also shows the result which takes the reductionof subgrade due to strain into account. Here, according toprevious studies [5][6][7][8], reduction of subgrade
reaction due to strain was incorporated by Eq. (1) whichempirically reduces the subgrade reaction force
coefficient according to -1/2 power law,

2.5

Pile diameter (m)EMPIRICAL DESIGN FORMULA OF OPTIMUMSHARED PILE ANCHOR

101100N-value

10100

N-value(a) Pile diameter(b) Pile length
10000

100

CalculatedEq.(3)

80

Pile thickness (mm)Assuming ideal uniform sandy soil of constantN-value, pile length = 3 β ( β :characteristic pile length),pile head displacement / pile diameter ≦ 1% and pilethickness / pile diameter ≧ 1.5% by considering thesafety margin against buckling when a pile is driven, arelationship between pile diameter and geometricaldesign values of a pile was obtained for various N-valuesby Chang’s method [4]. Fig. 7 shows a variation of pilethickness, length and weight against pile diameter forN=20 for example. Pile weight becomes the minimum
when the pile diameter is 2m. As a result of similarcalculations for different N-values from 1 to 50, similarly
optimum pile size was found in each N-value as Fig.8.

Thickness (mm)Pile length (m)Table 3. Maximum tension (kN) acting on anchors fordifferent loading angles.

14060

Soil : Linear elastic

100050Pile weight (t)Table 3 summarizes the results of the maximum
mooring tension acting on each shared anchor pile fordifferent loading angles in case of a chain length of
L=470m. The maximum anchoring force was found onanchor “G” when its loading angle was α = 0°. In thefollowing, a preliminary design is carried out against thisloading case.

Pile diameter (m)Anchoring force acting on the shared pile anchor

Pile thickness(mm), lenght(m)and weight(t)GRAND RENEWABLE ENERGY 2018 Proceedings
June 17(Sun) - 22(Fri), 2018
Pacifico Yokohama, Yokohama, Japan

4030w/Eq.(1) and (2)20

Soil : Linear elastic
100w/Eq.(1) and (2)10CalculatedEq.(3)
1101

10100

N-value1(c) Pile thickness

10100

N-value(d) Pile weightFig.8. N-value and dimensions of an optimum anchor pile.
Based on these results, a simple design formula foranchor piles that can be applied in a preliminary design inhomogeneous sandy soil sites was developed. The resultis expressed by the following formula,y = aN b(3)where, y represents the optimum anchor geometricaldimensions, i.e. pile diameter (m), pile length (m), plate
thickness (mm) and pile weight (t), and N is the N-value
by the standard penetration test of the ground under sea
bed. Parameter a and b are shown in Table 4.
Table 4.

Parameters of Eq. (3) for optimum pile.
Soil

Linear elastic

Ultimateabab

Diameter (m)

6.3

-0.38

2.5-0.10

Length (m)117-0.63

86

-0.50

Thickness (mm)94-0.38

37-0.078

Weight (t)

1689

-1.39

190

-0.68

GRAND RENEWABLE ENERGY 2018 Proceedings
June 17(Sun) - 22(Fri), 2018
Pacifico Yokohama, Yokohama, JapanESTIMATION OF ANCHOR INSTALLATION COST
In this section, installation cost is compared between
conventional drag embedment anchor (Fig.9a) andshared pile anchor (SPA) (Fig.9b). The critical point of
selection of SPA installation method is the selection of piledriving method and connection operation of mooring line
to anchor, which is operated submerged or in air. For thepile driving, hydraulic hammer (Fig. 9b) and underwater
hydraulic hammer can be considered, but the former
which is less influenced by the tidal current was adopted.
In addition, in mooring line connection, what was adopted
was not underwater installation which requires expensive
remote control device to handle heavy weight mooring
cable, but “in air” installation procedure which fixes themooring cable to a ring onboard and launches into thewater.

installation operation and material that are mooringlines and anchors (steel pipe pile or dragembedment anchor).
Table 5 Shared pile anchor dimensions for installation
cost evaluation.
Diameter(m)1.9Length(m)20Thickness(mm)30Weight(t)25Table 6 shows the results of estimation of theinstallation cost. The critical factor that contributed to thereduction of the installation cost of SPA is the reduction of
the chartering cost of the work vessel due to the decreasein the number of anchors.
Table 6

Cost evaluation of anchor installation.

Cost ratio

Drag embedment
anchor
1.0

Shared pile anchor
0.6

CONCLUSION(a) Drag embedment anchor

Using the 2 MW floating offshore wind turbine"Fukushima Mirai", optimal specification of piled sharedanchor was investigated under the 50-year recurrence
storm condition. Also, in consideration of the developmentof the floating wind farm in the future, a simple design
formula that can be applied in preliminary study for
uniform sandy soil was developed. As a result of theconstruction cost examination, it was found that there is apossibility of a reduction of about 40% compared to thecost of the 7 MW floating offshore wind turbine"Fukushima Shimpuu".
ACKNOWLEDGEMENT

For the cost comparison, the following assumptions
were made.

This research is a part of Fukushima Floating
Offshore Wind Farm Demonstration (FORWARD)
Research Project of 2011-2013 Fiscal Year, which wassupported by Ministry of Economy, Trade and Industry.
The authors also appreciate Mitsui E&S for providing
design data of "Fukushima Mirai".

(i)

References

Fig.9.

(ii)

(iii)
(iv)

(v)
(vi)
(vii)

(b) Shared pile anchor
Anchor installing procedures.

As for the oceanic condition at the time of installation
operation, the Pacific Ocean offshore which isrecognized as being severe worldwide as the wave
height is high and the tidal current is fast is assumed.
As the installation cost of the drag embedment
anchor, installation result of the 7 MW offshore windturbine "Fukushima Shimpuu" which was designed
to improve the efficiency of the mooring line
installation operation using a winch is referred to.
A wind farm which consists of 10 floating offshore
wind turbines is assumed.
The parameters of the anchor pile are as shown in
Table 5, assuming N = 20 as a standard value of thesandy soil in Eq. (3) (considering the soilnonlinearity).
Steel pipe piles and mooring chains are loaded onto
a work vessel at a base port and are transported tothe installation site.
Construction occupancy rate is assumed 50% forboth anchors.
The installation cost is assumed to consist of the[1] P.V. Phuc, T. Ishihara, K. Shimada, and T. Shiroeda,“Dynamic tension analysis of a slack mooring for a floating
offshore wind turbine”, Proceedings of RE2014, 2014.
[2] Fukushima consortium hope page.
http://www.fukushima-forward.jp/[3] DNV-OS-E301, Position mooring, 2013.
[4] Y. L. Chang, Discussion on “Lateral Pile Loading Tests” by L.
B. Feagin, A.S.C.E Transaction, 102, pp272-278, 1937.
[5] T. Imai, A study on horizontal K-value (3), K-value adopted ina design, Soil mechanics and foundation engineering, 17(11) (InJapanese).
[6] Japan Road Association, Specifications for highway bridge
Part IV Substructures, 2012.
[7] Japan Road Association, Pile foundation design handbook,2015 (In Japanese).
[8] Architecture Institute of Japan, Recommendations for designof building foundations, 2001 (In Japanese).
[9] B.B. Broms, Lateral resistance of piles in cohesionless soils,
Journal of the Soil Mechanics and Foundations Division, Proc. ofthe ASCE, SM3, pp123-156, 1964.