Comparison sghof Structural Properties Between Monopile And

Hindawi Publishing CorporationAdvances in Mechanical EngineeringVolume 2013, Article ID 175684, 9 pageshttp://dx.doi.org/10.1155/2013/175684

Research ArticleComparison of Structural Properties between Monopile andTripod Offshore Wind-Turbine Support Structures

Da Chen,1,2 Kai Huang,1,2 Valentin Bretel,1,2 and Lijun Hou1,2

1 Key Laboratory of Coastal Disaster and Defence, Ministry of Education, Hohai University, Nanjing 210098, China2 College of Harbor, Coastal, and Offshore Engineering, Hohai University, Nanjing 210098, China

Correspondence should be addressed to Lijun Hou; ljhou [email protected]

Received 28 June 2013; Revised 22 September 2013; Accepted 23 September 2013

Academic Editor: Luigi Cappelli

Copyright © 2013 Da Chen et al.This is an open access article distributed under the Creative Commons Attribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Offshore wind power provides a new kind of green energy. This paper presents a comparison study on the structural propertiesof monopile and tripod wind-turbine support structures, which are used extensively in offshore wind farms. Both structures havethe same upper tower, but different lower structures, one with a monopile and the other with a tripod. Static, fatigue, and modalanalyses indicate that both the tripod and monopile structures are feasible in the field, but that the tripod structure is superior tothe monopile structure. Static analysis reveals that the location of maximum stress in the monopile structure is different from thatin the tripod structure, and that the tripod structure shows higher stiffness and greater stress-control capacity than the monopilestructure. Fatigue analysis indicates that the tripod structure has a longer lifetime than the monopile structure. Modal analysisindicates that the two structures exhibit large differences in their natural frequencies. Unlike the monopile structure, the third andfirst modes both have a substantial influence on the dynamic response of the tripod structure.

1. Introduction

In recent years, clean energy strategies have been givengreat importance in environment protection and durabledevelopment. In the case of electricity, offshore wind farmspromise to become an important source of energy in the nearfuture to decrease reliance on traditional coal-fired power.In the past three decades, nations around the world withwind energy have led the way in the development of offshorewind farms.Thirty to forty percent of all new installed powergeneration capacity in Europe and the United States is nowassociated with wind energy. It is expected that wind energyfarms with a total of 80 GW will be installed in Europe andthe United States by 2020 [1].

It is worth noting that the support structures of a wind-turbine system act as the main structural members of awind electricity farm and are closely related to the structure’ssafety, stability, and durability. In general, the upper tower iscomposed of a conical steel pipe, whereas various types ofsubstructures can be designed according to field conditions.

The substructure is used to anchor the support structure tothe seabed and typically belongs to one of six types: gravity,monopile, tripod, jacket, suction, and floating foundation[2, 3]. Based on current design philosophy, gravity-basedstructures are preferred for shallow waters (up to 5m),whereas the monopile foundation is used for wind farms inwater depths up to 20m. For deeper water, tripod or jacketsupport structures are often considered. Floating supportstructures remain a challenge due to their high cost, but thischallenge will need to bemet for countries with fewer regionsof shallow water [4]. However, Scharff and Siems [5] haveexplored the application of monopile foundations in waterdepths of up to 20–40m and have provided two detaileddiscussions of design examples.

The support structures (tower and foundation) are sub-jected to a variety of combined static and dynamic loads suchas gravity, wind, waves, tides, and earthquakes. The designand analysis of these support structures are key parts of thedesign of the whole wind-turbine system. A fatigue propertyanalysis of a monopile structure by Mo et al. [6] indicated

2 Advances in Mechanical Engineering

that turbine-system vibration was a main source of load,resulting in structural fatigue damage. Torcinaro et al. [7]presented a structural optimization design for a tripod sup-port structure through stress and stability analysis. Agbayani[8] reviewed damage to monopile structures subjected tohigh-cycle fatigue and proposed a series of repair measures.Bazeos et al. [9] investigated the static, seismic, and stabilitycapabilities of the monopile support structure of a windturbine and found that refined finite-element models werenecessary at specific critical locations for a more accuratestructural analysis.

However, few studies have yet been performed on thedifferences in structural properties among the differenttypes of wind-turbine support structures. Moreover, a newplanned wind-power installation in Donghai, China, is inthe discussion stage, waiting for a decision on the type offoundation. In China, grouped pile foundations are usedin most wind-turbine support structures. However, com-pared with monopile and tripod foundations, the groupedpile foundation involves more complex construction andhigher cost. Given these points, to provide a reference forfoundation-type selection, this paper presents a study ona support structure where the lower support structure isdesigned as a monopile or tripod structure, but the upperone remains the traditional tower structure. Results of static,fatigue, and modal analysis using the SOLIDWORKS2012general FEM software were compared betweenmonopile andtripod structures.

2. Description of Support Structures

In the present study, two types of offshore wind-turbinesupport structures were investigated. In these structures, theupper towers were the same, but the lower structures weredifferent, one being a monopile and the other a tripod.Moreover, the support structure was made of high-strengthsteel S620M with a yield strength of 620MPa.

2.1. Upper Tower Structure. Figure 1 shows a sketch of theupper tower.This upper tower consisted of four pieces of steelshell with diameters linearly varying along their height. Theupper tower was 60m in height, and each piece of shell hadthe same length, 15m.The bottom diameter of the tower wasdesigned as 5400mm, which is identical to that of the uppertower in a similar wind-turbine system built in Donghai. Thecross-sectional thickness of the tubular shell was designedbased on design standard NORSOK N-004, where the ratioof diameter𝐷 to the thickness 𝑡 of the tubular shell is requiredto be 𝐷/𝑡 < 120 [10]. Note that the thickness of steel tubularwas determined according to the bottom diameter D𝑏 ofeach piece and the D/t ratio of 110. These four pieces oftubular shell were labeled as A to D in sequence according todecreasing diameter. Details of all the pieces of tubular shellare summarized in Table 1.

Two steel transition pieces, as shown in Figure 1, wereused as the end configuration of each steel shell and werewelded onto the steel shell. The transition pieces of adjacent

Table 1: Details of tubular shell pieces of the upper tower.

Piece 𝐷𝑡(mm) 𝐷

𝑏(mm) t (mm)

A 4800 5400 49B 4200 4800 44C 3600 4200 38D 3000 3600 33Note:𝐷𝑡 and𝐷𝑏 were the top and bottom diameters of different pieces; t wasthe thickness of steel shell concerning the bottom diameter𝐷𝑏.

𝜙3000

𝜙3600

𝜙4200

𝜙5400

𝜙480060000

15000

15000

15000

15000 A

B

C

DRivet

Rivet

160

160

Steelshell

Steelshell

Weld

200

200

100

40

700

Transition piece

800

Figure 1: Configuration of the upper tower.

steel shells were connected together by rivets to make up theupper tower.

2.2. Lower Support Structures. Figure 2 shows details of themonopile and tripod substructures. Both types of substruc-tures were 40m long. The monopile structure had a constantdiameter of 3600mm, or in other words, the diameterdecreased from 5400mm in the upper tower to 3600mm inthe lower monopile. The thickness of the steel-pipe pile was45mm. The tripod structure consisted of a central column,three diagonal bracings, and three supporting pile sleeves.For the central column, the diameter of the top was 5.4mand then decreased to 4.08m. Each pile sleeve was 13m high,was located at 12.5m from the central column, and had adiameter of 2.4m. The thickness of the pipes in the tripodsubstructure was constant at 40mm. A diagonal transitionmember was used to connect the upper tower and the lowersupport structure together. All the joints between the steelshells were welded together.

Note that for the lower monopile support structure, itsdiameter is supposed to increase with water depth becauseof the increased bending moment and compressive force.However, it is also true that the wave loading on a pile,as one of the main loads considered in structural design,becomes larger with increasing pile diameter. Moreover, thepile-sinking construction of themonopile foundation ismoredifficult with the increasing diameter from the viewpoint of

Advances in Mechanical Engineering 3

𝜙3600

𝜙5400

40000

Elevation

45

Plane

(a)

120∘

𝜙2400

𝜙2400

𝜙2400

𝜙4080

𝜙5400

40000

12500

Elevation

Plane

(b)

Figure 2: Detail of lower support structures: (a) monopole and (b) tripod.

the local stability. Given these two points, the authors used amonopile foundation as the lower support structure that wasmade of high-strength steel with a yield strength of 620MPa,and thus a diameter (3600mm), smaller than the 5400mmbottom diameter of the upper tower, was utilized.

2.3. Applied Load. Offshore wind-turbine structures are notonly exposed to highly corrosive environmental conditions,but are also subjected to various quasi-static, periodic,stochastic, and transient loads. For convenience in structuraldesign, it is necessary to perform a reasonable load simplifica-tion. In this research, the main loads experienced, includinghorizontal wind load, wave load, and vertical gravity, weresimplified as described below.

2.3.1. Wind Load. Wind conditions are important not onlyin defining the loads imposed on turbine structural com-ponents, but also in designing the support structures of thewind-turbine system.Themeasured on-site wind parametersstrongly influence the design of wind-turbine support struc-tures.Thewind load can be obtained through a formula basedon lift theory:

𝜉 =1

2𝜌airV2

wind𝑆𝐶𝑧, (1)

where 𝜉 is the force of the wind on the blades (kN), 𝜌air is thedensity of air (1.225 kg/m3), Vwind is the wind speed (m/s), 𝑆is the surface area of the blades (m2), and 𝐶𝑧 is the portancecoefficient, assumed to be 0.8 for a classic blade.

According to observed data and information, the surfacearea of the blades was 50m × 1.5m × 3 blades = 225m2,and the maximum speed before installation of the wind farmwas 34m/s. Therefore, the wind load calculated by (1) was127 kN. Furthermore, assuming a safety coefficient 𝑘 of 1.35(as recommended in DNV-OS-J101 [11]), the horizontal forceapplied on the structure by the wind would be 172 kN. Inaddition, according to the structural offshore wind-turbine

optimization method, the wind exerted a pressure of 5 kN/mon one side of the upper tower.

2.3.2. Wave Load. In the ocean environment, wave force isalso a major load imposed on the structure. The maximumhorizontal wave force was calculated based on Airy’s lineartheory. In this theory, the horizontal and vertical water-particle velocity at coordinates (𝑥, 𝑦) and time (𝑡) can beexpressed as [12]

𝑢 =𝜔𝐻

2

cosh 𝑘𝑦

sinh 𝑘𝑑cos (𝑘𝑥 − 𝜔𝑡) ,

V =𝜔𝐻

2

sinh 𝑘𝑦

sinh 𝑘𝑑sin (𝑘𝑥 − 𝜔𝑡) ,

(2)

where 𝑢 and V are the horizontal and vertical velocity of water,𝐻 denotes wave height, and 𝑘 and𝜔 represent thewave lengthand wave angular frequency. Based on Airy’s linear theory,the correlation between 𝑘 and 𝜔 is given by the dispersionequation

𝜔2= 𝑔𝑘 tanh 𝑘𝑑. (3)

Furthermore, the water-particle accelerations 𝑎𝑥 and 𝑎𝑦

can be obtained based on 𝑎𝑥 ≈ 𝑑𝑢/𝑑𝑡 and 𝑎𝑦 ≈ 𝑑V/𝑑𝑡 usingthe corresponding velocity (2):

𝑎𝑥 =𝜔2𝐻

2

cosh 𝑘𝑦

sinh 𝑘𝑑sin (𝑘𝑥 − 𝜔𝑡) ,

𝑎𝑦 =𝜔2𝐻

2

sinh 𝑘𝑦

sinh 𝑘𝑑cos (𝑘𝑥 − 𝜔𝑡) ,

(4)

where 𝑦 is the distance from the vertical position of the wavesurface to the seabed and can be calculated as

𝑦 = 𝜂 + 𝑑, (5)

where 𝑑 is the water depth, the distance from the seabed tothe still-water level, and 𝜂 is the distance from the vertical


position of the wave surface to the still-water level and can beobtained by [13]

𝜂 =𝐻

2cos (𝑘𝑥 − 𝜔𝑡) . (6)

For slender offshore structures such as monopiles,tripods, or offshore template structures, the Morison equa-tion can be used to convert the velocity and acceleration termsinto wave forces [14].TheMorison equation can be written as

𝐹 =1

2𝜌𝐶𝐷𝐷 |𝑢| 𝑢 + 𝜌𝐶𝐼

𝜋𝐷2

4𝑎𝑥,

(7)

where 𝜌 denotes water density, 𝐶𝐷 and 𝐶𝐼 denote the dragand inertia coefficients, and𝐷 is the diameter of the structuralmember.Thefirst termon the right-hand side of this equationis referred to as the drag term and is proportional to thesquare of the water velocity. The second term is referred toas the inertial term and is proportional to water acceleration.For the case under study, the parameters were taken as H =10.66m, 𝐶𝐷 = 1.0, and 𝐶𝐼 = 2.0. The predicted wave forcewas 357.46 kN. Assuming a safety factor of 1.04 (according tothe DNV-OS-J101 standards), the horizontal wave force forthe current case was 371.76 kN.

2.3.3. Blade and Rotor Loads. According to a real offshorewind farm such as M5000, the mass of the top structure(blades and rotor) is approximately 49.5 tons (or 493 kN).Thisload can be equivalently applied on the top of the tower in thevertical direction for calculating the wind-turbine supportstructure. Detailed data on the M5000 wind farm can beobtained on the AREAVA website [15].

2.3.4. Gravity Load of the Structure. The acceleration ofgravity was assumed to be 9.81m/s2. The total load conditionof themonopile structure is shown in Figure 3 and is identicalto that of the tripod structure.

3. Numerical Analysis and Discussion

3.1. Static Analysis

3.1.1. Stress Comparison. Figure 4 shows the calculated stressnephograms for the monopile and tripod support structures.Comparing the stress nephograms in Figures 4(a) and 4(b),it is apparent that the tripod structure shows the maximumstress at the transition junction from the lower supportstructure to the upper tower, whereas the monopile structurehas its maximum stress value at the end of the lower pile. Inaddition, as shown in Figure 4, the maximum stress of themonopile structure is approximately 2.35 times greater thanthat of the tripod structure, but it is still far less than theyield strength of 620MPa, and therefore these two structuresremained in the elastic stage. For the monopile structure, themaximum tensile and compressive stresses were, respectively,486.6MPa and 499MPa, while the corresponding values forthe tripod structure were 279.2MPa and 211.8MPa. Giventhese points, the tripod structure was more effective than themonopile structure from a stress-control point of view.

493kN

172kN

G

371.76kN

5kN

/m

Figure 3: Load distribution on the monopile support structure.

Figure 5 shows the tensile and compressive stresses dis-tribution along the longitudinal height of the two supportstructures. It is clear that the stress distributions in the uppertower are similar for the tripod and monopile foundations,whereas a large difference is apparent along the lower supportstructures. The stress was only 27MPa at the foot of thetripod structure, where themaximum stress was observed forthe monopile structure. Moreover, as the diameter increasedfrom 4.08m to 5.4m, the stress rapidly dropped fromthe maximum value to 70MPa for the tripod foundationstructure. In addition, the maximum stress for the tripodfoundation was observed in the transition section, a valueclose to the stress of 274MPa at the same location in themonopile foundation. Judging from these points, the tripodstructural system can be said to be superior to the monopilestructural system from the structural stress distributionviewpoint.

As shown in Figure 5, note that the maximum stress inthe tripod support structure and the tower structure waslower than the yield strength of 355MPa for S355 steel.Therefore, the high-strength steel S620Mcanbe replacedwiththe normal steel S355 to make full use of tensile strength ofsteel.

3.1.2. Deformation Comparison. Figure 6 shows the deforma-tion nephogram for the monopile and tripod support struc-tures. It is apparent that the deformation increased with theheight above the seabed and that the maximum displacementoccurred at the top of the structure in the lateral direction.The monopile structure showed a maximum deformationof 486mm, whereas the tripod structure had a maximumdisplacement of 368mm. In addition, the displacement of thetripod structure was less than that of the monopile structureat the same longitudinal location. In other words, the tripodstructure had greater flexural stiffness than the monopilestructure.


486.6

404.5

322.3

240.2

158.1

75.9

−6.2

−88.3

−170.5

−252.6

−334.7

−416.9

−499.0SY

(N/m

m2

(MPa

))

𝜎t,max = 486.6MPa 𝜎c,max = 499MPa

(a) Monopile

279.2

238.3

197.4

156.5

115.5

74.6

33.7

−7.2

−48.1

−89.1

−130.0

−170.9

−211.8

SY (N

/mm

2(M

Pa))

𝜎c,max = 211.6MPa𝜎t,max = 79.22 MPa

(b) Tripod

Figure 4: Stress nephogram in the longitudinal direction.

0 20 40 60 80 100 120

Height above the seabed (m)

Stre

ss (M

Pa)

MonopileMonopile

TripodTripod

−600

−400

−200

0

200

400

600

Figure 5: Comparison of stress distribution along the longitudinalheight of the support structures.

With respect to the maximal lateral deformation ℎ andthe height of the structure H, the deflection factor 𝑎 can becalculated based on DNV-OS-201J [11]:

𝑎 =𝐻

ℎ, 𝑎 > 200. (8)

In the cases studied, when 𝐻 = 100m, the computedvalues of 𝑎 for these two structures were 206 and 271.7,respectively, which both satisfied the requirements of DNV-OS-201J [11].

In summary, the tripod structure is clearly more stableand resistant to applied loads than the monopile structure.

3.2. Fatigue Analysis. Figure 7 shows the number of cyclicloads carried up to fatigue failure for the monopile and

tripod structures. The most fatigue-affected locations stillcorresponded with the locations of the maximum tensilestress in the static analysis. However, the number of loadingcycles carried by the tripod structure was far larger than thatof the monopile structure. With respect to the most damagedstructural position, the maximum number of load cycles wasonly 210,000 for the monopile structure, whereas the tripodstructure was able to endure at least 410,000. In other words,the tripod support structure had a lifetime 48.5% greater thanthat of the monopile support structure. Judging from thesepoints, the tripod structure is more resistant to fatigue thanthe monopile structure.

Both support structures satisfied the minimum cyclenumber of 1.0𝑒 + 05 recommended in DNV-OS-J101 [11].However, it is also necessary to determine the lifetime of thesetwo structures.The parameters were defined according to thestudy by Agbayani [8]. First, for these two structures, thenumber of loading cycles was estimated to be 40 per day. Itshould be highlighted that the stress on a structure subjectedto different loading cycles varies between the minimum andmaximum stresses, and some cycles must result in a stresslower than themaximumvalue. Indeed, all loads are not equalin intensity and always occur in a random time distribution.However, the forces and pressures applied in the present studyhave been set to theirmaximumvalues.Therefore, to performa realistic calculation, the number of loading cycles has beenassumed to be 40 per day.

Second, the working time ratio (proportion of workinghours in each 24 hours) had to be determined for eachstructure. According to investigations of the structures understudy, themaximumworking time ratio was set to 0.85 for thetripod structure and 0.8 for the monopile structure [16]. Notethat these ratios are defined in a conservative way because ofsafety considerations and that the actual ratios are probablyless than these values.


Δmax = 486mm

UX

(mm

)

4.864e + 002

4.459e + 002

4.053e + 002

3.648e + 002

3.242e + 002

2.837e + 002

2.026e + 002

1.621e + 002

1.215e + 002

8.096e + 001

4.041e + 001

−1.407e − 001

2.431e + 002

(a) Monopile

Δmax = 368mm

UX

(mm

)

3.687e + 002

3.378e + 002

3.069e + 002

2.759e + 002

2.450e + 002

2.141e + 002

1.831e + 002

1.522e + 002

1.213e + 002

9.034e + 001

5.941e + 001

2.848e + 001

−2.455e + 000

(b) Tripod

Figure 6: Displacement nephogram in the lateral direction.

Knowing all these factors, the lifetime can be calculatedfor each structure. For the monopile structure, the numberof load cycles is 11,680 per year considering the assumedworking ratio. The lifetime durability can then be obtainedas

𝑇 =𝑁min𝑁py

, (9)

where 𝑇 is the lifetime (in years), 𝑁min is the minimumnumber of loading cycles, and 𝑁py is the loading cycles peryear. For the case studied, the lifetime durability obtainedby (9) was approximately 18 years. For the tripod supportstructure, the number of load cycles per year was 12,400assuming a working ratio of 0.85. The lifetime durabilitycalculated based on (9) was then approximately 33 years.From these results, it can be concluded that the tripodsupport structure can survive longer than the monopilestructure, which is advantageous over the long term.

3.3. Modal Analysis. When a structure is subjected todynamic loads, its natural structural frequencies should beadjusted to be far from the dynamic load frequency to avoidthe resonance. If the natural structural frequency is close tothe load frequency, even small driving forces can producelarge-amplitude oscillations.

Modal analysis is the basis of dynamic analysis. A wind-turbine support structure is subjected to many periodicactions such as winds and waves. In general, these loads haveprogressive and changeable frequencies within a known andspecific domain. Therefore, the risks of resonance can beestimated and eliminated through calculating and adjustingthe natural frequencies of the structures.

Table 2 lists the natural frequency and period of the firstthree vibrationmodes for themonopile and tripod structures.The tripod structure was found to have higher natural

Table 2: Results of modal analysis.

Series Nf # Frequency(Hz) Period (s)

Maximumdisplacement

(mm)

Monopile1 0.389 2.570 3.2672 2.508 0.398 3.9123 6.401 0.156 4.674

Tripod1 0.797 1.254 3.9272 4.188 0.238 4.6633 7.108 0.140 2.517

Note: Nf # denotes the number of each natural frequency.

frequencies and shorter periods than the monopile structure.To estimate whether resonance will occur, the dynamic loadfrequency must be established. In this research, only themain load (wind load) was taken into account to simplifythe analysis. In fact, the vibration of structures subjected towind load arises from rotary turbulences due to the impact ofwind on the structure. The frequency of these rotations canbe determined using the Strouhal number, a dimensionlessnumber describing oscillating flow mechanisms.

Based on the theory for calculation of the Strouhalnumber, the turbulence frequencies can be obtained as

𝑓V =𝑆𝑡V𝑤𝐿𝑐

, (10)

where𝑓V is the frequency of the vortex, V𝑤 is thewind velocity,and 𝐿𝑐 is the characteristic length of the structure. In thecase under study, the Strouhal number (𝑆𝑡) was in the rangefrom 0.1 to 0.2. The minimum wind velocity for the structurewas 11m/s and the maximum 34m/s. The characteristiclength was taken as the length of the upper tower structure


1.000e + 006

9.342e + 005

8.683e + 005

8.025e + 005

7.367e + 005

6.708e + 005

6.050e + 005

5.392e + 005

4.733e + 005

4.075e + 005

3.417e + 005

2.758e + 005

2.100e + 005Nmax = 210000

Num

ber o

f cyc

lic lo

ads

(a) Monopile

1.000e + 006

9.508e + 005

9.017e + 005

8.525e + 005

8.033e + 005

7.542e + 005

7.050e + 005

6.558e + 005

6.067e + 005

5.575e + 005

5.083e + 005

4.592e + 005

4.100e + 005

Nmax = 410000Nmax = 512000

Num

ber o

f cyc

lic lo

ads

(b) Tripod

Figure 7: Number of load cycles carried by the structures.

(60 meters), and then the calculated vortex frequency (𝑓V)

was in the range from 0.0183Hz to 0.1130Hz. As listed inTable 2, the lowest natural frequencies of the two structureswere 0.390Hz and 0.797Hz. Therefore, resonance of thesestructures due to rotary turbulence can be eliminated.

Figures 8 and 9 show the first three mode shapes forthe monopile and tripod structures. These mode shapeswere similar for both structures, whereas the variance lawof displacement coordinates showed a large difference. Themaximum displacement coordinates are listed in Table 2.It is apparent that the maximum displacement graduallyincreased with increasing frequency for the monopile struc-ture, whereas the tripod structure showed an increase firstand then a drop with frequency.

Based on the mode shape, the mass participation factor𝑀𝑗 can be calculated as

𝑀𝑗 =

[∑𝑛

𝑘=1𝜙𝑘𝑗𝑚𝑘]

2

∑𝑛

𝑘=1𝜙2

𝑘𝑗𝑚𝑘

, (11)

where 𝑚𝑘 is the mass of the 𝑘th mass particle and 𝜙𝑘𝑗

is the displacement coordinate of this point for the 𝑗thmode. Figure 10 shows the mass participation factor ofdifferent modes for these two types of structures. For themonopile structure, the first mode shape, with a frequencyof 0.390Hz, has a maximum mass participation factor of46%, approximately 3.5 times that of the second mode.


Figure 8: First three modes of the monopile structure.

Figure 9: First three modes of the tripod structure.

This implies that the first mode plays a controlling role inthe dynamic response of monopile structures. However, forthe tripod structure, the third mode, with a frequency of7.108Hz, showed the maximum mass participation factor of30.2%, slightly larger than the value of 24.5% for the firstmode, but far greater than 9.6% for the secondmode. It can beconcluded that both the third and first modes play key rolesin the dynamic response of tripod structures, which is clearlydifferent from the response of monopile structures.

Moreover, the frequency separation can be furtherdefined by the difference between any two adjacent fre-quencies. For the monopile structure, the first two modespresented the smallest frequency separation, 2.111 Hz, andthe sum of the corresponding mass participation factors was59%. In the tripod case, the smallest frequency separationwas2.920Hz, between the second and third modes, and the total

50

40

30

20

10

00 1 2 3 4 5 6 7 8

Frequency (Hz)

Mj

MonopileTripod

Figure 10: Comparison of the mass participation factor of differentmodes.

mass participation factor of these twomodeswas 39.8%. It canbe concluded that the tripod is the safer structure because ofits wider frequency separation and smallermass participationfactor.

The static, fatigue, and modal analyses of monopile andtripod support structures described above have demonstratedthat both the monopile and tripod support structures areapplicable under the field conditions considered. Note thatthe designed pile diameter and the use of high-strength steelare feasible for the support structures described in this paper.In contrast, a previous investigation by Scharff and Siems[5] indicated that for a wind-turbine system similar to thosestudied here, the pile diameter was increased to 7500mmfrom 5500mm of the upper tower for a water depth of 20–40m.Comparing Scharff ’s studywith the current one, severaldifferences are evident. First, the type of steel used in Scharff ’sstudy was S355, with a yield strength of 355MPa, whereashigh-strength steel with a yield strength of 620MPa was usedin this study. High yield strength of steel is supposed to resultin a smaller diameter based on the design of the ultimatelimit state. Moreover, because the pile diameter was smallerthan that in Scharff ’s study, the wave load applied to the pilewas less in the current study, which is helpful to know whendecreasing pile diameter.

4. Conclusions

This paper has presented an investigation into the structuralproperties of monopile and tripod wind-turbine supportstructures. Based on a comparison of the results of static,fatigue, and modal analyses results for these two structures,the following conclusions can be drawn.

(1) The maximum stress in the monopile structure wasat the base, whereas the transition location from thelower central column to upper tower showed themaximum stress for the tripod structure. Moreover,


for the case under study, the maximum stress anddisplacement for themonopile structurewere approx-imately 2.35 and 1.32 times greater than those of thetripod structure. The tripod showed greater stiffnessand better stress-control capacity than the monopilestructure.

(2) Under the same cyclic loading, the tripod structurehas a longer lifetime than themonopile structure.Thisis beneficial for saving engineering cost in the longrun.

(3) The modal analysis indicated that the first three nat-ural frequencies of the tripod structure were higherthan the corresponding frequencies of the monopilestructure. The first mode played a controlling rolein the dynamic response of the monopile structure,whereas both the third and first modes had a stronginfluence on the tripod structure. The results forfrequency separation and mass participation factorindicated that the tripod structure was more reliablethan the monopile structure.

(4) The analytical results indicated that both monopileand tripod structures can be used as wind-turbinesupport structures in the environment considered.However, comparison of structural responses usingstatic, fatigue, and modal analyses revealed that thetripod structure is superior to themonopile structure.Moreover, it is effective to use high-strength steel inthe monopile structure for optimizing the monopilediameter to be smaller than that of the upper towerbottom.

Acknowledgments

This research was supported by National Natural ScienceFoundation of China (51137002) and Natural Science Foun-dation of Jiangsu Province (BK2011026).

References

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