Suction Bucket Pile–Soil–Structure Interactions of Offshore Wind

Journal of Marine Science and Engineering

Article Suction Bucket Pile–Soil–Structure Interactions of Oﬀshore Wind Turbine Jacket Foundations Using Coupled Dynamic Analysis

Pasin Plodpradit 1, Osoon Kwon 2, Van Nguyen Dinh 3,* , Jimmy Murphy 3 and Ki-Du Kim 1

1 Department of Civil and Environmental Engineering, Konkuk University, Seoul 05029, Korea; [email protected] (P.P.); [email protected] (K.-D.K.) 2 Director of Coastal and Ocean Engineering Division, Korea Institute of Ocean Science & Technology, Busan 49111, Korea; [email protected] 3 MaREI Centre, ERI Beaufort Building and School of Engineering, University College Cork, P43C573 Cork, Ireland; [email protected] * Correspondence: [email protected] or [email protected]

Received: 30 April 2020; Accepted: 6 June 2020; Published: 8 June 2020

Abstract: This paper presents a procedure for the coupled dynamic analysis of offshore wind turbine–jacket foundation-suction bucket piles and compares the American Petroleum Institute (API) standard method and Jeanjean’s methods used to model the piles. Nonlinear springs were used to represent soil lateral, axial, and tip resistances through the P–Y, T–Z, and Q–Z curves obtained by either API’s or Jeanjean’s methods. Rotational springs with a stiffness equated to the tangent or secant modulus characterized soil resistance to acentric loads. The procedure was implemented in X-SEA program. Analyses of a laterally loaded single pile in a soft clay soil performed in both the X-SEA and Structural Analysis Computer System (SACS) programs showed good agreements. The behaviors of a five MW offshore wind turbine system in South Korea were examined by considering waves, current, wind effects, and marine growth. In a free vibration analysis done with soil stiffness through the API method, the piles were found to bend in their first mode and to twist in the second and third modes, whereas the first three modes using Jeanjean’s method were all found to twist. The natural frequencies resulting from Jeanjean’s method were higher than those from the API method. In a forced vibration analysis, the system responses were significantly influenced by soil spring stiffness type. The procedure was found to be computationally expensive due to spring nonlinearities introduced.

Keywords: oﬀshore wind turbine; jacket foundation; coupled analysis; soil–pile–structure interaction; suction bucket; ﬁnite element model (FEM)

1. Introduction Renewable energy is becoming increasingly necessary in many countries where wind is one of most available renewable sources. There are higher potential, steadier, and less-constraining sources of wind energy in offshore locations compared to the onshore ones. In order to ensure the feasibility, viability, safety, and serviceability of an offshore wind farm, an engineer needs to select proper foundations for wind turbines and to develop accurate and computationally feasible models at the design stage. The selection should be based on water depth, seabed conditions, installation equipment, and supply chains. There are three common types of offshore wind foundations, as shown in Figure1. The monopile is one of simple and most widely applied foundation types [1], and it is suitable to water depth of 20–40 m [2,3]. Tripod foundations, which have an excellent stability and overall stiffness when compared with the monopiles, are utilized in deeper waters [4]. However, the tripod concept is

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and overall stiffness when compared with the monopiles, are utilized in deeper waters [4]. However, lessthe tripod preferable concept in terms is less of preferable scour, ship in collision, terms of complexityscour, ship ofcollision, joints, deflection complexity at of the joints, tower deflection top, and overallat the tower weight top when, and comparedoverall weight to the when jacket compar concepted [ 5to]. the jacket concept [5]. AA jacketjacket foundation consists consists of of three three or or four four legs. legs. The The four four-legged-legged jacket jacket,, which which is supported is supported by bymain main piles piles,, is particularly is particularly suitable suitable for the for offshore the offshore wind wind industry industry [6]. The [6]. benefits The benefits of using of usingjacket jacketfoundations foundations are its are lower its lower impact impact of environmental of environmental loads, loads, higher higher level level of of stiffness, stiffness, lower soilsoil dependency,dependency, andand suitabilitysuitability forfor installationsinstallations at sites with poor soil, deep water,water, or high waves. ComparedCompared toto monopilesmonopiles andand tripods,tripods, jacket foundations are more suitable to changing water depths. However,However, aa steelsteel jacketjacket foundationfoundation isis moremore complexcomplex thanthan otherother foundationsfoundations andand isis thereforetherefore moremore costlycostly [[7].7]. AtAt thethe designdesign stage,stage, understandingunderstanding the behaviorbehavior of ooffshoreffshore jacketjacket foundationsfoundations andand theirtheir pilepile supportssupports under dynamic loading loading and and practical practical environment environment and and soil soil conditions conditions would would assist assist in inlowering lowering their their costs costs while while ensuring ensuring safety. safety. Nevertheless, Nevertheless, very very few few studies studies have investigatedinvestigated thethe dynamicdynamic behaviorbehavior of of o ffoffshoreshore wind wind turbine–jacket turbine–jacket foundation foundation coupled coupled systems systems [8,9] particularly[8,9] particularly those supportedthose supported by suction by suction bucket bucket piles. piles.

(a) Monopile (B) Tripod (C) Jacket

Figure 1. Three common types of offshore wind turbine foundations. Figure 1. Three common types of offshore wind turbine foundations. A suction bucket is open at the bottom and completely sealed at the top, like an upturned bucket. It is penetratedA suction bucket into the is open seabed at the to abottom certain and depth completely under its sealed own at weight, the top, with like thean upturned outlet valves bucket. on theIt is top penetrated open to allowinto the water seabed inside to a the certain caisson depth escape. under Suction its own is weight processed, with by the pumping outlet valves out encased on the watertop open with to all allow the closed water outlet inside valves, the caisson driving escape. the suction Suction caisson is processed to penetrate by the pumping designed out embedded encased depthwater [with10,11 ].all Anthe advantage closed outlet is that valves, the buckets driving do the not suction require caisson heavy equipmentto penetrate for the installation designed becauseembedded the drivendepth pile[10,11]. foundations’ An advantage installations is that can the be buckets completed do fasternot require than those heavy of driven equipment piles [ 12for]. Latiniinstallation and Zania because [13] the investigated driven pile the foundations dynamic responses’ installation of suctions can be caissons, completed and thefaster skirt than length those was of founddriven to piles be a[12]. significant Latini and parameter Zania [13] in determining investigated theirthe dynamic behavior. responses The results of suction from the caissons, model tests and andthe skirt field installationslength was found of suction to be caissons a significant have provenparameter that in the determining installation their under beh suctionavior. is The extremely results efromffective the inmodel fine-or tests medium-sized and field installations sands, primarily of suction due caissons to the reduction have prove inn resistance that the installation that results under from seepage.suction is In extremely addition, the effective dynamic in stifineffness-or coemediumfficients-sized of suction sands, caissons primarily were due found to the to increase reduction when in theresistance skirt length that results was increased. from seepage Consequently,. In addition, a coupled the dynamic dynamic stiffness analysis coefficients of offshore of suction wind turbinescaissons thatwere considers found to soil–structure increase when interactions the skirt islength necessary was forincreased. a rational Consequently, structural design a coupled [14]. dynamic analysisIn recent of offshore studies wind of off turbinesshore wind that turbine consider jackets soil foundations,–structure interactions the turbine responsesis necessary were for simulated a rational bystructural coupled design dynamic [14]. analysis using Fatigue, Aerodynamic, Structures and Turbulence (FAST), which was developedIn recent studies by the Nationalof offshore Renewable wind turbine Energy jacket Laboratory foundations, (NREL). the FAST turbine joins responses aerodynamic, were hydrodynamic,simulated by coupled and structural dynamic modules analysis and using is able Fatigue, to solve Aerodynamic, land or offshore Structures fixed-bottom and Turbulence or floating structures(FAST), which quickly was [15 developed]. In order by to obtainthe Nat accurateional Renewable results for Energy a sub-structure, Laboratory the (NREL). loads simulated FAST join bys waves,aerodynamic, currents, hydrodynamic and wind are, applied and structural into decoupled modules and and coupled is able models to solv [16e ]land that passor offshore displacement fixed- andbottom velocity or floating information structure to thes quickly aerodynamic [15]. In module order andto obtain return accurate the loads results at each for time a sub step.-structure, Those loads the

J. Mar. Sci. Eng. 2020, 8, 416 3 of 24 pass through the layer of soft, poorly consolidated marine clays and then into stiffer clay or sand strata [17,18]. The interactions among environmental load conditions, the structure of the pile, and the soil around the pile constitute complex vibrations in the system. Wei et al. [8] investigated soil–structure interaction effects on the responses of an offshore wind turbine with a jacket-type foundation. Two jacket models using different configurations of braces were used to compare the loads and responses that resulting from coupled dynamic analyses [19]. In the literature, there have been several methods for analyzing pile–soil–structure interactions (PSSIs). One of the most popular methods is the transfer of soil strata properties to spring stiffness. Matlock [20] presented a method for determining the lateral load displacement curve (P–Y) in soft clay from static and cyclic loads. The American Petroleum Institute (API) [21] recommends methods for determining the pile capacity for lateral and axial end bearing loads in either clay or sandy soils in which all the information on lateral and axial loads at specific locations with offshore data are from laboratory soil sample data tests. Thus they are called the P–Y, axial load displacement (T–Z), and tip load (Q–Z) data. However, because these methods were formulated using results obtained from experiments on piles with small diameters, they have a limited ability to predict the behavior of larger-scale piles such as suction buckets [22,23]. In this paper, the theoretical background of the coupled dynamic analysis of turbine and support structures implemented and validated in the previous studies [6,24,25] are improved by including PSSIs and suction bucket pile models. Soil lateral, axial, and tip resistances are included by considering the P–Y, T–Z, and Q–Z curves of soil behavior. Coupled dynamic analyses of a turbine–tower–foundation system including PSSIs were performed by using the concept of exchanging of motion and force components between the X-SEA and FAST programs at the interface nodes. Furthermore, parametric studies of suction bucket piles supporting an offshore wind turbine jacket foundation at a specific site in Korea were conducted in which nonlinear translational springs represent soil lateral, axial, and tip resistances, and rotational springs characterize soil resistance to acentric loads in suction bucket piles.

2. Coupled Analysis of Turbine and Support Structure X-SEA ﬁnite element analysis software was developed for the design and analysis of onshore and oﬀshore wind turbine platforms. The current version of X-SEA was developed at Konkuk University, Seoul, Korea [24]. The program has an extensive range of uncoupled and coupled analyses between the turbine and sub-structure using the FAST v8 program [15]. In each coupled analysis, the eighteen n . o n .. o components of motions represented by the displacement Ut , velocity Ut , and acceleration Ut { } vectors are input into the X-SEA program. Simultaneously, X-SEA returns the reaction force vector (Ft(t)) at the interface position every analysis time t, as depicted in Figure2. This “coupling” concept implemented and validated in the study [25] is expressed by:

n .. o n . o [Mt] Ut + [Ct] Ut + [Kt] Ut = Ft(t) (1) { } where Mt,Ct, and Kt are the mass, damping, and stiﬀness matrices, respectively, of the coupled system at the time t. J. Mar. Sci. Eng. 2020, 8, 416 4 of 24 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 4 of 26

{Ftt ()} Interface position

  {UUUttt},,{ } { }

Figure 2.2. The concept of coupled analysisanalysis through thethe interface.interface. 3. Nonlinear Soil Springs 3. Nonlinear Soil Springs The API has developed a method for determining the pile capacity for lateral and axial bearing The API has developed a method for determining the pile capacity for lateral and axial bearing loads in either clay or sandy soils. All the information on pile load tests was derived in the laboratory loads in either clay or sandy soils. All the information on pile load tests was derived in the laboratory from soil sample data. These datasets describe the lateral load deflection (P–Y), axial load displacement from soil sample data. These datasets describe the lateral load deflection (P–Y), axial load (T–Z), and tip load (Q–Z) at specific offshore sites [21]. The pile length is required to achieve tension displacement (T–Z), and tip load (Q–Z) at specific offshore sites [21]. The pile length is required to (pullout) and compression capacities necessary to support the offshore wind turbine foundation. achieve tension (pullout) and compression capacities necessary to support the offshore wind turbine The soil around the pile must resist lateral and axial bearing loads, which correspond to skin friction foundation. The soil around the pile must resist lateral and axial bearing loads, which correspond to and end bearing capacity, respectively. These should not exceed a certain limit under similar conditions skin friction and end bearing capacity, respectively. These should not exceed a certain limit under with the same pile diameter and equipment used in the design. similar conditions with the same pile diameter and equipment used in the design. 3.1. Pile Lateral Loads 3.1. Pile Lateral Loads Pile foundations should be designed to sustain lateral loads, whether static or dynamic. A proper analysisPile offoundations lateral loads should in cohesive be designed or cohesionless to sustain lateral soils loads, should whether use P–Y static data, or which dynamic. are typicallyA proper providedanalysis of by lateral geotechnical loads in engineers. cohesive P–Yor cohesionless data describe soils the nonlinearshould use relationship P–Y data, which between are lateral typically soil resistanceprovided by and geotechnical the depth ofengineers. the piles P [20–Y]. data For describe each layer the of nonlinear the soil along relationship a pile depth, between the lateral P–Y data soil showresistance a nonlinear and the relationship depth of the between piles [20]. the lateralFor each pile layer displacement of the soil and along lateral a pile soil depth, resistance the P per–Y data unit length.show a Fornonlinear static lateral relationship loads, the between ultimate the unit lateral lateral pile bearing displacement capacity and of soft lateral clay soil has beenresistance found per to unit length. For static lateral loads, the ultimate unit lateral bearing capacity of soft clay has been vary between 8cs and 12cs, where cs is the undrained shear strength. In the absence of more definitive criteria,found to the vary following between relationship 8cs and 12c iss, where recommended cs is the undrained by the API shear for soft strength. clay: In the absence of more definitive criteria, the following relationship is recommended by the API for soft clay: 1 P y 3 Py= 0.5( ) 1 (2) Pu = 0.5(yc )3 (2) Pyuc where P is the actual lateral resistance, Pu is the ultimate resistance, y is the actual lateral deflection, and y is the soil coefficient in terms of the pile diameter. In a more recent study, Jeanjean [26] showed wherec P is the actual lateral resistance, Pu is the ultimate resistance, y is the actual lateral that in conventional methods for assessing the lateral performance of conductors using the P–Y curves deflection, and y is the soil coefficient in terms of the pile diameter. In a more recent study, resulting from thec API method, the soil springs might be too conservatively soft. That leads to the predictionJeanjean [26] of larger showed cyclic that lateral in displacementsconventional methods and bending for stressesassessing for the a given lateral load performance range than theof P–Yconductors curves obtainedusing the from P–Y centrifuge curves result testsing and from finite the element API method, analysis. the The soil latter springs is expressed might asbe [ 26too]: conservatively soft. That leads to the prediction of larger cyclic lateral displacements and bending stresses for a given load range than the P–Y curves obtained from centrifuge tests and finite element analysis. The latter is expressed as [26]:

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PyG 0.5 = tanhmax ( ) (3) J. Mar. Sci. Eng. 2020, 8, 416 Puu100. SD 5 of 24

where G is the shear modulus of the soil, S is the undrained shear strength, y is the lateral max "u # P G y 0.5 displacement, and D is the pile diameter.= tanhThe actualmax lateral( ) load and ultimate lateral load relations (3) can be obtained in terms of cumulativePu shear strain100. (ξSu) asD [26]: where Gmax is the shear modulus of the soil, Su is(−ξ thedD /) undrained shear strength, y is the lateral Puu=12 − 4 e DS (4) displacement, and D is the pile diameter. The actual lateral load and ultimate lateral load relations can bew obtainedhere in terms of cumulative shear strain (ξ) as [26]:

( ξd/D) Su0 Pu = 12 4e − DSu < 6 (4)  − Su0 0.25+ 0.05 for dDsu ξ = dD (5) where  su  for SSu0  0.25 +0.550.05 Su0 f or u0 <>66  dsuD dsuD ξ =  dDSsu (5)  0.55 f or u0 > 6 dsuD The above equations were applied to soft clay. The ultimate resistance ( P ) for sand has been The above equations were applied to soft clay. The ultimate resistance (uPu) for sand has been foundfound to to vary vary with with the the depth depth ( H( H) of) of the the soil soil layer, layer, as as described described by by [ 26[26]]:: (()mH+ mDγ H (m121H + m2D)γH PuPu==  (6) (6)  mDm11Dγγ HH

EquationEquation (5) (5) gives gives the the minimum minimum valuevalue of the ultimate resistance, resistance, where where mmm121,, m2, and mm33are are the soilthe coe soilﬃ cientscoefficients determined determined from from the frictionthe friction angle angle and andγ is γ the is soil the density. soil density.

3.2. Pile Axial Loads and Tip Loads 3.2. Pile Axial Loads and Tip Loads TheThe axial axial resistance resistance of theof the soil soil provides provides axial axial adhesion adhesion along along the side the of side the pile.of the Several pile. Several empirical relationsempirical and relations theories and are availabletheories are for available producing for curves producing for axial curves load for transfers axial load and transfers pile displacements, and pile ordisplacements, T–Z curves. Lymon or T–Z and curves. Michael Lymon [27 and] developed Michael [27] a load developed deflection a load relationship deflection fromrelationship a pile load from test ina representative pile load test in soil representative profiles based soil on profiles laboratory based soil on tests.laboratory The recommended soil tests. The recommended curves are displayed curves in Figureare displayed3 for cohesive in Figure soil. 3 Similarly,for cohesive the soil. relationship Similarly, the between relationship mobilized between end mobilized bearing resistance end bearing and axialresistance top deflection and axial is top described deflection using is described a Q–Z curve using [28 a ],Q as–Z showncurve [28] in Figure, as shown4. in Figure 4.

J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 6 of 26 Figure 3. Typical axial pile load transfer–displacement (T–Z) curve for cohesive soil. Figure 3. Typical axial pile load transfer–displacement (T–Z) curve for cohesive soil.

FigureFigure 4. Typical 4. Typical tip loadtip load transfer–displacement transfer–displacement (Q–Z) (Q–Z) curve. curve.

3.3. Spring Stiffness Structural engineering normally employs a constant spring stiffness for soil, which results in a linear force–displacement relation. However, as the nature of soil behavior is similar to plastic, this relation is not linear. Therefore, the interactions between the pile and the soil were modeled as a system of nonlinear springs, as illustrated in Figure 5. The information of P–Y, T–Z, and Q–Z was used in the present study to predict the stiffness of these nonlinear elastic springs applied along the pile length. However, in the model of the soil surrounding the pile with several translational springs, the whole system is subject to moments and acentric forces (see Figure 6). Consequently, its accuracy is not sufficient when using the API model [21] or Jeanjean’s method [26]. In this study, additional rotational springs were therefore proposed to be included in the model, where their rotational stiffness was determined by equating to tangent or secant modulus [29].

Figure 5. Soil idealization model with soil translational nonlinear springs.

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Figure 4. Typical tip load transfer–displacement (Q–Z) curve. 3.3. Spring Stiffness 3.3. Spring Stiffness Structural engineering normally employs a constant spring stiffness for soil, which results in a Structural engineering normally employs a constant spring stiffness for soil, which results in a linear force–displacement relation. However, as the nature of soil behavior is similar to plastic, this linear force–displacement relation. However, as the nature of soil behavior is similar to plastic, this relation is not linear. Therefore, the interactions between the pile and the soil were modeled as a relation is not linear. Therefore, the interactions between the pile and the soil were modeled as a systemsystem of nonlinear of nonlinear springs, springs as, as illustrated illustrated inin FigureFigure 55.. The information information of ofP– P–Y,Y, T–Z, T–Z, and and Q–Z Q–Z was was usedused in the in presentthe present study study to predictto predict the the sti stiffnessffness ofof thesethese nonlinear nonlinear elastic elastic springs springs applied applied along along the the pile length.pile length. However, However, in thein the model model of of the the soil soil surroundingsurrounding the the pile pile with with several several translational translational springs, springs, the wholethe whole system system is subject is subject to to moments moments and and acentricacentric forces (see (see Figure Figure 6).6 ).Consequently, Consequently, its accuracy its accuracy is notis su notffi cientsufficient when when using using the the API API model model [ 21[21]] oror Jeanjean’sJeanjean’s method method [26]. [26 In]. Inthis this study, study, additional additional rotationalrotational springs springs were we thereforere therefore proposed proposed to be to included be included in the in model, the model, where where their their rotational rotational stiff ness was determinedstiffness was bydetermined equating by to equating tangent to or tangent secant or modulus secant modulus [29]. [29].

J. Mar. Sci. Eng. 20Figure20, Figure8, x FOR 5. Soil 5. PEER Soil idealization REVIEWidealization model model withwith soil translational translational nonlinear nonlinear springs. springs. 7 of 26

FigureFigure 6. 6.New New soil model model for for a suction a suction bucket bucket pile with pile both with translational both translational and rotational and nonlinear rotational nonlinearsprings. springs.

4. Pile–Soil4. Pile–S Structureoil Structure Interaction Interaction DamianiDamiani and and Wendt Wendt simulated simulated the the dynamic dynamic analysis analysis of anof an off shoreoffshore wind wind turbine turbine on on a fixed-bottoma fixed- bottom foundation while accounting for the super-element of the foundation and the piles [30]. This foundation while accounting for the super-element of the foundation and the piles [30]. This paper paper considered two methods for predicting the responses of suction bucket pile systems that can considered two methods for predicting the responses of suction bucket pile systems that can be used be used in offshore wind turbine foundations. The pile–soil interaction (PSI) method is a simulated in offbehaviorshore wind between turbine the foundations.pile and soil. PSI The analysis pile–soil is highly interaction essential (PSI) for methodpredicting is the a simulated responses behaviorof a betweenpile itself. the pile However, and soil. this PSI method analysis does is not highly consider essential the interactions for predicting between the the responses pile and the of asuper pile- itself. structure at the time of analysis. The pile–soil–structure interaction (PSSI) method was designed for solving the interactions between the soil, the pile, and the structure [5]. This can be introduced into a global equation of motion,

[M]{ U} ++[ C]{ U  } [ K]{ U} ={ Ft()} (7)

where {Ft()} is the time-dependent force vector, [M ] is the mass matrix describing the distribution of mass along the structure, [C] is the damping matrix that assumes 2% of critical

damping [16], [K ] is the stiffness matrix, and {u} and {u} are the first and second order derivatives of the displacement, respectively. The global matrices can then be formed from the corresponding matrices of the tower (denoted by subscript ‘t’), the sub-structure (denoted by subscript ‘s’), and the pile (denoted by subscript ‘p’). Furthermore, PSSIs can be assembled into the global matrices for determining the deflection along the pile length, as presented in [6] and [25]. Thus, Equation (8) can be written as:

M  UC  UK  U t tt t t t  ++ = Ms  U s C ss  U K s  U s{ Ft()} (8)     MUpp  CUpp  KUpp 

In reality, the movement of soil is difficult to predict, and figuring out a closed-form solution to such a problem is extremely complicated. In this study, a numerical solution for soil movement was therefore obtained by controlling the iterations and preventing the overshoot value for soil stiffness by using the utilized value N : i

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However, this method does not consider the interactions between the pile and the super-structure at the time of analysis. The pile–soil–structure interaction (PSSI) method was designed for solving the interactions between the soil, the pile, and the structure [5]. This can be introduced into a global equation of motion, n .. o n . o [M] U + [C] U + [K] U = F(t) (7) { } where F(t) is the time-dependent force vector, [M] is the mass matrix describing the distribution of mass along the structure, [C] is the damping matrix that assumes 2% of critical damping [16], [K] is n . o n..o the stiffness matrix, and u and u are the first and second order derivatives of the displacement, respectively. The global matrices can then be formed from the corresponding matrices of the tower (denoted by subscript ‘t’), the sub-structure (denoted by subscript ‘s’), and the pile (denoted by subscript ‘p’). Furthermore, PSSIs can be assembled into the global matrices for determining the deflection along the pile length, as presented in [6] and [25]. Thus, Equation (8) can be written as:

  ..    .      Mt  Ut   Ct  Ut   Kt  Ut    ..    .      M   +  C   +  K  U  = F(t) (8)  s  Us   s  Us   s  s    ..    .     Mp  Up  Cp  Up  Kp Up

In reality, the movement of soil is difficult to predict, and figuring out a closed-form solution to such a problem is extremely complicated. In this study, a numerical solution for soil movement was therefore obtained by controlling the iterations and preventing the overshoot value for soil stiffness by using the utilized value Ni : Ki+1 Ni = (9) Ki+1 until Ni converges closely to 1.0, at which, Ki+1 is the new stiffness at an iteration point and Ki is the stiffness matrix at the previous iteration.

5. Wave Excitations and Hydrodynamics

5.1. Hydrodynamic Forces, Added Mass and Damping The hydrodynamics of fixed offshore structures can be carried out by using hydrodynamic modules in the X-SEA program. The hydrodynamic forces, added mass, and damping and incident wave excitations are computed by using the Morison equation [25]. For a single element, the motion equation in terms of mass (m), damping (c), and stiffness (k) that is limited by the assumption of small dimension/wavelength ratio is:

.. . 1 ∂v (m + me)w + (c +ec)w + kw = CdρA v v + Cmρ∆ (10) 2 | | ∂t where ρ is a water density; Cd and Cm are drag and inertia coeﬃcients, respectively; and v is the velocity of the water particle acting on the structural node and normal to the structure [25]. The term A is the cross-sectional area of the element, and ∆ denotes the volume of the displaced ﬂuid. The terms .. . w, w, and w are the displacement, velocity, and acceleration, respectively, of the structure in its local coordinate, which are normal to or in its longitudinal axis. When the motion of the structure is considered, the inertia force is reduced by a factor proportional to the structural acceleration, and the drag force is reduced by the relative velocity and given in the form [25]:

me = ρ(Cm 1)∆ − (11) ec = CdρAv in which v is the time-dependent cylinder velocity [25]. The terms in Equation (1) obtained in structure local coordinates are then transformed to the global coordinates. When the diameter (D) of the cross J. Mar. Sci. Eng. 2020, 8, 416 8 of 24 section in the structure is considerably larger than the wavelength (L), i.e., D/L 0.2, the Morison ≥ theory is considered to be inapplicable and a diﬀraction theory implemented in X-SEA [31] can be considered.

5.2. Random Waves The Pierson–Moskowitz (P–M) wave spectrum is an empirical relationship that defines the distribution of energy over frequencies within the ocean, and it has been found to fit ocean surface elevation measurements. It assumes that if the wind blows steadily for a long time over a large area, then the waves will eventually reach a point of equilibrium with the wind [32]. The international electrotechnical commission (IEC) announced that this spectrum model is best for using at specific site areas [33]. The parameters required for determining a wave spectrum are the significant wave height (Hs) and the peak period (Tp). The P–M spectrum can be written as:

4 2 5 ( 1.25c− ) S(ωn) = 0.04974Hs Tpc− e − (12)

ωnTp where c = 2π . Based on the nonlinearity of wave characteristics, the statistical distribution of wave surface elevation (η) can be described by using the random phase angle (εn), wave angular velocity (ωn), and wave number (kn)[34] as:

η = ΣAn sin(ωnt knx + εn) (13) n − in which An is a wave amplitude corresponding to each set of wave height, frequency, and phase angle. The wave amplitude can be expressed by using the P–M spectrum in Equation (11) in terms of the angular velocity interval (∆ω) as: p An = 2Sn∆ω (14) For each state of wave surface elevation, the associated horizontal velocity and acceleration of the water particles are determined from the basic wave theory [35]. Assuming an one-dimension sea where all waves are running in the same direction, the horizontal water velocity (u) and acceleration (a) in the direction of wave propagation are given at an elevation (z) by the equations:

= cosh(knz) ( + ) u ΣAnωn sinh(k d) cos knx ωnt εn n n − (15) 2 cosh(knz) a = Σ Anωn sin(knx ωnt + εn) n − sinh(knd) −

6. Numerical Study

6.1. Verification of Soil–Pile Interactions A single pile that had been driven 42.7 m into a single soft clay layer was considered. A numerical model of this case using 11 nodes and 10 elements per layer is shown with the soil properties in Figure7. The simulation of the pile foundation involved a lateral load of 445 kN. The nonlinear behavior for the pile–soil interactions was based on the geotechnical P–Y data from the API [21] and Jeanjean methods [26]. This can be considered as loads corresponding to the lateral deflection along the pile. A commercial package called “Structural Analysis Computer System” (SACS) [36] was used to perform the analysis. The loads corresponding to the P–Y deflection curve were simulated during the iterative process of the X-SEA program. This was used to obtain soil stiffness and to input additional stiffness into the structure. The resulting loads corresponding to the deflection are plotted in Figure8, which indicates that the maximum lateral resistance using Jeanjean’s data was 1.33 times more than that found when using the API data. Moreover, Figure9 shows that the lateral deflections resulting from the X-SEA and SACS programs by using the API method were in good agreement. The deflections resulting from both programs when using the Jeanjean method also agreed well with each other, as seen in Figure9. J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 9 of 26

η= ωε −+ ΣAnsin( nn t kx n) (13) n

in which An is a wave amplitude corresponding to each set of wave height, frequency, and phase angle. The wave amplitude can be expressed by using the P–M spectrum in Equation (11) in terms of the angular velocity interval ( ∆ω ) as:

ASnn=2 ∆ω (14)

For each state of wave surface elevation, the associated horizontal velocity and acceleration of the water particles are determined from the basic wave theory [35]. Assuming an one-dimension sea where all waves are running in the same direction, the horizontal water velocity ( u ) and acceleration ( a ) in the direction of wave propagation are given at an elevation ( z ) by the equations: cosh(kz ) = ω n −+ωε uΣ Ann cos(kxn n t n) n sinh(kdn ) (15) cosh(kz ) =−ω2 n −+ωε aΣ Ann sin(kxn n t n) n sinh(kdn )

6. Numerical Study

6.1. Verification of Soil–Pile Interactions A single pile that had been driven 42.7 m into a single soft clay layer was considered. A numerical model of this case using 11 nodes and 10 elements per layer is shown with the soil J. Mar. Sci. Eng. 2020, 8, 416 9 of 24 properties in Figure 7. The simulation of the pile foundation involved a lateral load of 445 kN. The nonlinear behavior for the pile–soil interactions was based on the geotechnical P–Y data from the API These[21] agreements and Jeanjean validated methods the[26]. implementation This can be considered of the as API loads and corresponding Jeanjean methods to the lateral and deflection the nonlinear along the pile. A commercial package called “Structural Analysis Computer System” (SACS) [36] was springs in X-SEA, which were used for further analyses in this paper. used to perform the analysis.

Lateral Force : 445 kN ------Clay ------Unit Weight : 1490 kg/m3 Undrained Shear Strength : 48 kPa Empirical Parameter J : 0.25 Reference Strain for Clay : 0.02 Pile Length : 42.7 m 42.7 m

J.J. Mar.Mar. Sci.Sci. Eng.Eng. 20202020,, 88,, xx FORFOR PEERPEER REVIEWREVIEW 1010 ofof 2626

andand SACSSACS programsprograms byby usingusing thethe APIAPI methodmethod wewerere inin goodgood agreement.agreement. TheThe deflectionsdeflections resultresultinging fromfrom bothboth programsprograms whenwhen usingusing thethe JeanjeanJeanjean methodmethodOD : 0.9144 alsoalso m , agreetagree : 0.0254dd mwellwell withwith eacheach otherother,, asas seenseen inin FigureFigure 9.9. TheseThese agreementsagreements validatevalidatedd thethe implementationimplementation ofof thethe APIAPI andand JeanjeanJeanjean methodsmethods andand thethe nonlinearnonlinear springsspringsFigure ininFigure XX--SEA,SEA, 7. Model7. whichModelwhich of weweof a reare single single usedused for pileforpile furtherfurther with single singleanalysesanalyses st stratumratum inin thisthis soil paper.paper. soil layer. layer.

The loads corresponding to the P–Y deflection curve were simulated during the iterative process of the X-SEA program. This was used to obtain soil stiffness and to input additional stiffness into the structure. The resulting loads corresponding to the deflection are plotted in Figure 8, which indicates that the maximum lateral resistance using Jeanjean’s data was 1.33 times more than that found when using the API data. Moreover, Figure 9 shows that the lateral deflections resulting from the X-SEA

FigureFigureFigure 8. Loads 8.8. LoadsLoads corresponding correspondingcorresponding to to thethe the deflectiondeflection deﬂection (P(P––YY (P–Y curve).curve). curve).

FigureFigureFigure 9. Lateral 9.9. LateralLateral deﬂection deflectiondeflection alongalong thethe the pilepile pile length.length. length.

J. Mar. Sci. Eng. 2020, 8, 416 10 of 24

6.2. Coupled Dynamic Analysis of Turbine and Support Structure with Pile–Soil–Structure Interaction (PSSI) In this example, a 5 MW offshore wind turbine [37] jacket foundation system [38] was simulated. J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 11 of 26 The significant wave height (Hs) was 3.3 m, and the wave period (Tp) was 8.0 s. A constant current velocity of6.2. 1.2 Coupled m/s and Dynamic mean Analysis wind of speed Turbine ofand 13.156 Support m Structure/s at the with Buan Pile–S countryoil–Structure site Interaction in South Korea were considered.(PSSI) The turbulent wind simulator (TurbSim) program [39] was used to generate a stochastic of wind velocityIn this model example, based a 5 MW on offshore the IEC wind standard turbine [37 [33] jacket], as foundation illustrated system in Figure [38] was 10 simulated.. The simulation was carriedThe out significant using thewave wind height velocity (Hs) was in3.3 timem, and domain the wave that period is required(Tp) was 8.0 in s. FASTA constant v8, current as illustrated in Figure 10.velocity A marine of 1.2 growth m/s and 0.1 mean m wind thick speed with of a 13.156 weight m/s density at the Buan of 1100country kg site/m 3inwas South used Korea in we thisre example considered. The turbulent wind simulator (TurbSim) program [39] was used to generate a stochastic to representof thewind actual velocity size model and base weightd on the of IEC the standard jacket structure [33], as illustrated along waterin Figure depth. 10. The The simulation foundation was connectedwas with carried four circularout using tubethe wind suction velocity piles, in time each domain 8 m inthat diameter is required and in FAST 0.05 mv8,thick, as illustrated and embedded in in a single layerFigure soil 10. at A a marine depth growth of 18 m.0.1 m A thick frame with element a weight modeldensity of was 1100 validated kg/m3 was [use40]d andin this used example to investigate the behaviorto represent of the suction the actual bucket size and pile weight through of the jacket the pile structure length along without water depth. considering The foundation the super-element, was connected with four circular tube suction piles, each 8 m in diameter and 0.05 m thick, and embedded as illustratedin a insingle Figure layer 11 soil. Theat a depth piles-supported of 18 m. A frame foundation element model was was modeled, validated and [40] the and e usedffects to of the soil behavior usinginvestigate the API the behavior and Jeanjean of the suction methods bucket were pile compared; through the this pile formedlength without an approach considering for the determining the pile capacitysuper-element for lateral, as illustrated loads in in soft Figure clay. 11. The The horizontal piles-supported stiff nessfoundation and end wasbearing modeled in, and either the soil were used in accordanceeffects of the with soil API behavior recommendations. using the API and A Jeanjean coupled methods dynamic were analysis compared module; this form wased connectedan to approach for determining the pile capacity for lateral loads in soft clay. The horizontal stiffness and the PSSI program,end bearing which in either considered soil were used the in interactions accordance with among API recommendations. the pile, soil, and A foundationcoupled dynamic to determine the behavioranalysis of the module whole was system connected as to a functionthe PSSI program, of time. which The considered analysis the period interactions was selectedamong the as the first 200 s, whichpile, included soil, and foundation both transient to determine and steady the behavior responses. of the whole The system geometric as a function and material of time. The properties of the jacket foundationanalysis period are was given selected in as Table the first1. Seismic200 s, which excitations included both [ 41 transient] were and not steady accounted responses. for, but they The geometric and material properties of the jacket foundation are given in Table 1. Seismic should beexcitations considered [41] in were future not accounted analysis for, and but design. they should be considered in future analysis and design.

FigureFigure 10. 10.A A wind wind velocity simulation. simulation.

Table 1. Material and geometric properties of the jacket structure.

Geometric Properties Parameter Value Unit Jacket leg diameter 1.053 m Jacket leg thickness 0.019 m Diagonal member diameter 0.508 m Diagonal member thickness 0.013 m Transition piece diameter 5.500 m Transition piece thickness 0.700 m Material Properties Parameter Value Unit Steel weight density 7850 kg/m3 Elastic of modulus 2.1 1011 N/m2 × Shear modulus 8.08 1010 N/m2 × J. Mar. Sci. Eng. 2020, 8, 416 11 of 24

Figure 11. Model of jacket foundation supported by suction bucket piles and soil properties for pile–soil–structure interaction analysis.

The asymmetrical loads caused the structure to resonate due to the environmental loads and the fact that the natural frequencies of the system were close to those of the turbine blades. In order to avoid resonance, a free vibration analysis of the suction pile foundation with fixed boundary conditions was first carried out using the X-SEA program. The natural frequencies—those related to the type of boundary condition—were compared, and the three mode shapes were modeled, as shown in Figure 12. A scale factor of 10–15 was used to amplify the mode shapes of the jacket foundation. The first mode shape was a bending mode of the whole structure with a 1.537 Hz natural frequency, as illustrated in Figure 12a, where the suction pile with fixed boundary condition is oscillating globally in the x-direction. The second mode shape was the same as the first mode but oscillating in y-direction, as illustrated in Figure 12b. The third mode shape was a torsional mode about the z-axis with the natural frequency of 1.451 Hz, where twisting was occurring from the free end to the fixed boundary, as illustrated in Figure 12c. In the second free vibration analysis, the soil spring stiffness determined from P–Y, T–Z, and Q–Z curves were applied along the pile length and modelled by using both the API and Jeanjean methods. The first mode shape of the suction piles with the API method was the movement in x-direction with a natural frequency of 1.087 Hz, as illustrated in Figure 13a. In the second and third modes, the natural frequencies were 1.213 and 1.357 Hz, respectively. The twisting occurred at the suction bucket piles and caused the different shape size of the pile. Meanwhile, the first to the third mode shapes using the Jeanjean method were all twisting, as shown in Figure 14a–c. By comparing the natural frequencies resulting from soil stiffness models by using the API and Jeanjean methods, it could be seen that natural frequencies resulting from Jeanjean’s method were, respectively, 1.118, 1.115, and 1.005 higher than those from the API method for the first to the third modes. It was obvious that the pile with fixed boundary conditions was stiffer than the spring model, and it had less inertia. Hence, the natural frequencies corresponding to the fixed boundary condition were higher than those of the spring models determined from the P–Y, T–Z, and Q–Z curves. J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 13 of 26

J. Mar. Sci. Eng. 2020, 8, 416 12 of 24 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 13 of 26 (a) Mode 1 (b) Mode 2 (c) Mode 3 f = 1.537 Hz f =1.537 Hz f =1.451 Hz

Figure 12. Mode shapes of the jacket-suction bucket piles with fixed boundary conditions. (a) 1st mode shape; (b) 2nd mode shape; (c) 3rd mode shape.

In the second free vibration analysis, the soil spring stiffness determined from P–Y, T–Z, and Q– Z curves were applied along the pile length and modelled by using both the API and Jeanjean methods. The first mode shape of the suction piles with the API method was the movement in x- direction with a natural frequency of 1.087 Hz, as illustrated in Figure 13a. In the second and third modes, the natural frequencies were 1.213 and 1.357 Hz, respectively. The twisting occurred at the suction bucket piles and caused the different shape size of the pile. Meanwhile, the first to the third mode shapes using the Jeanjean method were all twisting, as shown in Figure 14a–c. By comparing the natural frequencies resulting from soil stiffness models by using the API and Jeanjean methods, it could be seen that natural frequencies resulting from Jeanjean’s method were, respectively, 1.118, (a) Mode 1 (b) Mode 2 (c) Mode 3 1.115, and 1.005 higher than those from the API method for the first to the third modes. It was obvious = 1.537 Hz =1.537 Hz =1.451 Hz that the pile withf fixed boundary conditions wasf stiffer than the spring model,f and it had less inertia. Hence,FigureFigure the 12. natural12.Mode Mode shapes frequencies shapes of of the the jacket-suctioncorresponding jacket-suction bucketbucket to the pilesfixed with with boundary fixed ﬁxed boundary boundary condition conditions. conditions. were higher (a) (1ast ) thanmode 1st mode those ofshape; theshape; spring (b) ( 2ndb )models 2nd mode mode determined shape; shape; ( c(c)) 3rd3 rdfrom mode mode the shape shape. P–Y,. T–Z, and Q–Z curves.

In the second free vibration analysis, the soil spring stiffness determined from P–Y, T–Z, and Q– Z curves were applied along the pile length and modelled by using both the API and Jeanjean methods. The first mode shape of the suction piles with the API method was the movement in x- direction with a natural frequency of 1.087 Hz, as illustrated in Figure 13a. In the second and third modes, the natural frequencies were 1.213 and 1.357 Hz, respectively. The twisting occurred at the suction bucket piles and caused the different shape size of the pile. Meanwhile, the first to the third mode shapes using the Jeanjean method were all twisting, as shown in Figure 14a–c. By comparing the natural frequencies resulting from soil stiffness models by using the API and Jeanjean methods, it could be seen that natural frequencies resulting from Jeanjean’s method were, respectively, 1.118, 1.115, and 1.005 higher than those from the API method for the first to the third modes. It was obvious that the pile with fixed boundary conditions was stiffer than the spring model, and it had less inertia. Hence, the natural frequencies corresponding to the fixed boundary condition were higher than those of the spring models determined from the P–Y, T–Z, and Q–Z curves. (a) Mode 1 (b) Mode 2 (c) Mode 3 f = 1.087 Hz. f =1.213 Hz f =1.357 Hz

FigureFigure 13. Mode 13. Mode shapes shapes of of the the jacket-suction jacket-suction bucket piles piles with with soil soil behavior behavior using using the American the American J.Petroleum Mar. Sci. PetroleumEng. Institute 2020, 8 ,Institute x (API)FOR PEER method.(API) REVIEW method. (a ) 1st (a mode) 1st mode shape; shape; (b) ( 2ndb) 2nd mode mode shape;shape; (c) 3 3rdrd mode mode shape shape 14 of 26

(a) Mode 1 (b) Mode 2 (c) Mode 3 f = 1.087 Hz. f =1.213 Hz f =1.357 Hz

Figure 13. Mode shapes of the jacket-suction bucket piles with soil behavior using the American Petroleum Institute (API) method. (a) 1st mode shape; (b) 2nd mode shape; (c) 3rd mode shape (a) Mode 1 (b) Mode 2 (c) Mode 3 f = 1.216 Hz f = 1.353 Hz f = 1.364 Hz

FigureFigure 14. 14.Mode Mode shapes shapes of of the the jacket-suction jacket-suction bucket piles piles with with soil soil behavior behavior using using Jeanjean’s Jeanjean’s method method (a) 1st(a) mode1st mode shape; shape; (b ()b 2nd) 2nd mode shape; (c (c) )3 3rdrd mode mode shape shape..

In the forced vibration analysis, random waves were simulated by using Equations (12)–(15); a wave surface elevation profile is shown in Figure 15. The angular velocity interval ( ∆ω ) was assumed to be at 0.01 rad/sec, and the time interval was 0.1 sec, which was sufficiently small compared to the wave period and structural vibration periods. In order to validate the random wave simulations, the fast Fourier transform (FFT) was used to transform time series to frequency domain [42], and 10 realizations of wave surface elevation profiles were used. The averaged power spectrum density of the wave elevation simulations was in good agreement with the theoretical spectrum, as shown in Figure 16.

Figure 15. A wave surface elevation simulation.

J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 14 of 26

(a) Mode 1 (b) Mode 2 (c) Mode 3 f = 1.216 Hz f = 1.353 Hz f = 1.364 Hz

Figure 14. Mode shapes of the jacket-suction bucket piles with soil behavior using Jeanjean’s method st nd rd J. Mar.( Sci.a) 1 Eng. mode2020 shape;, 8, 416 (b) 2 mode shape; (c) 3 mode shape. 13 of 24

In the forced vibration analysis, random waves were simulated by using Equations (12)–(15); a waveIn surface the forced elevation vibration profile analysis, is shown random in Figure waves 15. were The simulated angular by velocity using intervalEquations (  (12)–(15); ) was aassumed wave surface to be elevation at 0.01 profile rad/sec is, shownand the in time Figure interval 15. The was angular 0.1 velocity sec, which interval was (∆sufficientlyω) was assumed small tocompared be at 0.01 to rad the/s, wave and theperiod time and interval structural was 0.1 vibration s, which periods. was su ffiInciently order to small validate compared the random to the wavewave periodsimulations, and structural the fast Fourier vibration transform periods. (FFT) In order was toused validate to transform the random time series wave simulations,to frequency thedomain fast Fourier[42], and transform 10 realizations (FFT) was of wave used surf to transformace elevation time seriesprofiles to were frequency used. domain The averaged [42], and power 10 realizations spectrum ofdensity wave of surface the wave elevation elevation profiles simulations were used. was Thein good averaged agreement power with spectrum the theoretical density spectrum of the wave, as elevationshown in simulationsFigure 16. was in good agreement with the theoretical spectrum, as shown in Figure 16.

J. Mar. Sci. Eng. 2020, 8, x FOR PEERFigure REVIEW 15. A wave surface elevation simulation. 15 of 26 Figure 15. A wave surface elevation simulation.

Figure 16. Power spectral density of surface elevation. Figure 16. Power spectral density of surface elevation. In the iterative process of the forced vibration analysis, the lateral and horizontal displacements wereIn received the iterative at the process interface of and the transferredforced vibration through analysis, the spring the lateral supports. and Thesehorizontal motion displacements components werewere received used to generate at the interface the P–Y, and T–Z, transferred and Q–Z curvesthrough and the applied spring tosupports. calculate These the sti motionffness of components the springs. wereAt the used same to time,generate six reactionthe P–Y, components T–Z, and Q– wereZ curves fed backand toapplied the tower to calculate and turbine. the stiffness The iteration of the springs.continued At until the allsame of the time, components six reaction converged. components In order were to fed avoid back diverging to the towerwith asymmetrical and turbine. loads, The iterationthe rotational continued stiffness until was all applied, of thewhereas components frame converged. elements were In orderused to to model avoid the dive jacketrging and with the asymmetricaljacket foundation loads resisted, the rotational for a moment. stiffness This was did applied not influence, whereas the frame P–Y, elements T–Z, and were Q–Z used curves to usedmodel in thethe jacket API and and Jeanjean the jacket methods. foundation resisted for a moment. This did not influence the P–Y, T–Z, and Q–Z curves used in the API and Jeanjean methods. The resulting time histories of the translation velocity (V), rotational velocity (Vr), acceleration (A), rotationalThe result accelerationing time (A historiesr), and rotational of the translation displacement velocity (Ur) ( atV the), rotational interface in velocity the x-, y-, (V andr ), acceleration z-directions

( A ), rotational acceleration ( Ar ), and rotational displacement (U r ) at the interface in the x-, y-, and z-directions in equation of motion, as described in Equation (8), are shown in Figures 17–21. The averaged displacements, velocities, and accelerations in Table 2 show that the API method made the foundation model more flexible than Jeanjean’s method.

Table 2. Ratio of averaged motion components resulting from the API and Jeanjean methods.

Factors Motion Components x-Direction y-Direction z-Direction

Rotational displacement (U r ) 1.067 1.061 1.343 Velocity (V ) 1.062 1.064 1.339

Rotational velocity (Vr ) 1.073 1.067 1.336 Acceleration ( A ) 1.069 1.072 1.327

Rotational acceleration ( Ar ) 1.065 1.069 1.333

J. Mar. Sci. Eng. 2020, 8, 416 14 of 24 in equation of motion, as described in Equation (8), are shown in Figures 17–21. The averaged displacements, velocities, and accelerations in Table2 show that the API method made the foundation model more ﬂexible than Jeanjean’s method. J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 16 of 26

(a) x-direction.

(b) y-direction.

FigureFigure 17. 17.Velocity Velocity components components at the the interface. interface.

J. Mar. Sci. Eng. 2020, 8, 416 15 of 24 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 17 of 26

(a) x-direction.

(b) y-direction.

FigureFigure 18. 18.Rotational Rotational velocity velocity componentscomponents at at the the interface. interface.

J. Mar. Sci. Eng. 2020, 8, 416 16 of 24 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 18 of 26

(a) x-direction.

(b) y-direction.

FigureFigure 19. 19.Acceleration Acceleration components at at the the interface. interface.

J. Mar. Sci. Eng. 2020, 8, 416 17 of 24 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 19 of 26

(a) x-direction.

(b) y-direction.

Figure 20. Rotational acceleration components at the interface. Figure 20. Rotational acceleration components at the interface.

J. Mar. Sci. Eng. 2020, 8, 416 18 of 24 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 20 of 26

(a) x-direction.

(b) y-direction.

FigureFigure 21. 21.Rotational Rotational displacementdisplacement components components at atthe the interface. interface.

Comparing the displacement of the jacket foundation in Figure 22 shows that the API method led to more flexible responses than Jeanjean’s method by an average factor of 1.062 in the x-direction. As the lateral stiffness of a single point affected the horizontal stiffness of other points along the pile J. Mar. Sci. Eng. 2020, 8, 416 19 of 24 depth, it caused different responses in the y- directions and z-directions by factors of 1.069 and 1.303, respectively, as illustrated in Figures 23 and 24. The results in Figure 24 show high vertical responses at starting up times. In order to compare the difference between two soil modelling methods, the average percentage results are presented in Figure 25. The responses of the jacket foundation were seen to be significantly influenced by the environmental loads, turbine responses, structural stiffness, and the type of nonlinear three-dimensional soil spring stiffness.

TableJ.J. Mar.Mar. Sci.Sci. 2. Eng.RatioEng. 20202020 of,, 88 averaged,, xx FORFOR PEERPEER motion REVIEWREVIEW components resulting from the API and Jeanjean methods.2121 ofof 2626

CComparingomparing thethe displacementdisplacement ofof thethe jacketjacket foundationfoundation inin FigureFigureFactors 2222 showsshows thatthat thethe APIAPI methodmethod ledled toto moremoreMotion flexibleflexible Components responsesresponses thanthan JeanjeanJeanjean’s’s methodmethod byby anan averageaverage factorfactor ofof 1.0621.062 inin thethe xx--direction.direction. AsAs thethe laterallateral stiffnessstiffness ofof aa singlesingle pointpoint affectaffectx-Directioneded thethe horizontalhorizontal y-Direction stiffnessstiffness ofof otherother pointspoints z-Direction alongalong thethe pilepile depth, it caused different responses in the y- directions and z-directions by factors of 1.069 and 1.303, depth,Rotational it caused displacement different responses(Ur) in the y- directions1.067 and z-directions 1.061 by factors of 1.069 1.343 and 1.303, respectively,respectively, Velocity asas illustratedillustrated(V) inin FigFiguresures 2323 andand 24.24.1.062 TheThe resultsresults inin FigureFigure 1.064 2424 showshow highhigh verticalvertical 1.339 reresponsessponses at starting up times. In order to compare the difference between two soil modelling methods, the at starRotationalting up times. velocity In order(V rto) compare the1.073 difference between 1.067 two soil modelling 1.336 methods, the averageaverage percentagepercentageAcceleration resultsresults(A )areare presentedpresented inin FigureFigure1.069 25.25. TheThe responsesresponses 1.072 ofof thethe jacketjacket foundationfoundation 1.327 werewere seen to be significantly influenced by the environmental loads, turbine responses, structural stiffness, seenRotational to be significantly acceleration influenced(Ar) by the environme1.065ntal loads, turbine 1.069 responses, structural 1.333 stiffness, andand thethe typetype ofof nonlinearnonlinear threethree--dimensionaldimensional soilsoil springspring stiffness.stiffness.

Figure 22.FigureFigureComparison 22.22. ComparisonComparison of the ofof displacements thethe displacementsdisplacements in inin the thethe xx x-direction--directiondirection ofof the ofthe the jacketjacket jacket foundationfoundation foundation resultingresulting resulting fromfrom from two methodstwotwo methodsmethods of nonlinear ofof nonlinearnonlinear soil stisoilsoilﬀ stnessstiffnessiffness models. models.models.

Figure 23.FigureFigureComparison 23.23. ComparisonComparison of the ofof displacements thethe displacementsdisplacements in inin the thethe yy y-direction--directiondirection ofof the ofthe the jacketjacket jacket foundationfoundation foundation resultingresulting resulting fromfrom from two methods of nonlinear soil stiffness models. two methodstwo methods of nonlinear of nonlinear soil stisoilﬀ nessstiffness models. models.

J. Mar. Sci. Eng. 2020, 8, 416 20 of 24 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 22 of 26 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 22 of 26

Figure 24. Comparison of the displacements in the z-direction of the jacket foundation resulting from Figure 24.FigureComparison 24. Comparison of the of displacementsthe displacements in in the the z-directionz-direction of of the the jacket jacket foundation foundation resulting resulting from from two methods of nonlinear soil stiffness models. two methodstwo methods of nonlinear of nonlinear soil stisoilﬀ stiffnessness models. models.

Figure 25. Averaged percentage difference between soil conventional methods. FigureFigure 25. Averaged 25. Averaged percentage percentage di differenceﬀerence between soil soil conventional conventional methods methods..

During the period in which the loads were acting on the foundation, the structure should be DuringDuring the period the period in which in which the the loads loads were were actingacting on on the the foundation, foundation, the structure the structure should should be be against and sustaining the loads. They were transferred through to the pile, corresponding to the end against andagainst sustaining and sustaining the the loads. loads. They They were transferred transferred through through to theto pile, the corresponding pile, corresponding to the end to the bearing and soil skin friction. These produced a distribution of deflection along the pile length. The bearing and soil skin friction. These produced a distribution of deflection along the pile length. The end bearingresponses and of the soil pile skin heads friction. in the Thesefour piles produced resulting afrom distribution the API method of deﬂection were more along flexible the than pile length. responses of the pile heads in the four piles resulting from the API method were more flexible than The responsesthose result ofing the from pile Jeanjean’s heads in method the four by piles factors resulting of 5.300, from7.330, the7.0290, API and method 12.158 weretimes, moreas shown ﬂexible than those resulting from Jeanjean’s method by factors of 5.300, 7.330, 7.0290, and 12.158 times, as shown those resultingin Figure 26. from Eventually, Jeanjean’s the methodtotal computational by factors time of 5.300, on a 7.330,dual CPU 7.0290, (Intel and i7-7820HQ 12.158 times,2.9 GHz as-8 shown in in Figure 26. Eventually, the total computational time on a dual CPU (Intel i7-7820HQ 2.9 GHz-8 cores) was 72.03 h for coupled analysis with PSSIs and 5.06 h without considering PSSIs. Figure 26cores). Eventually, was 72.03 h the for total coupled computational analysis with PSSIs time and on a5.06 dual h without CPU (Intel considering i7-7820HQ PSSIs. 2.9 GHz-8 cores) was 72.03 h for coupled analysis with PSSIs and 5.06 h without considering PSSIs.

J. Mar. Sci. Eng. 2020, 8, 416 21 of 24 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 23 of 26

(a) Pile 1 (b) Pile 2

FigureFigure 26. 26. PilePile deflection deﬂection along along the the pile pile length. length.

7.7. Conclusion Conclusions AA theoretical theoretical background background of of the the coupled coupled dynamic dynamic analysis analysis of of offshore offshore wind wind turbine turbine and and support support structuresstructures implemented implemented and and validated validated in the in authors’ the authors’ previous previous publications publications was improved was improved by including by includingPSSIs and PSSIs suction and bucket suction pile bucket models. pile Approaches models. Approaches to computing to computing soil lateral, soil axial, lateral, and tipaxial resistances, and tip resistanceswere provided were by provided considering by considering the P–Y, T–Z, the andP–Y, Q–Z T–Z curves, and Q of–Z soilcurves behavior of soil obtainedbehavior byobtained either theby eitherAPI or the Jeanjean API or methods. Jeanjean Themethods. loads correspondingThe loads corresponding to these curves to these could curves be simulated could be by simulated an iterative by anprocess iterative of the process X-SEA of program. the X-SEA Such program soil resistances. Such soil were resistances represented were by represented nonlinear springs by nonlinear in the springslateral and in the vertical lateral directions and vertical along directions the piles. along In order the piles. to more In accuratelyorder to more simulate accurately the suction simulate bucket the suctionpiles subject bucket to piles acentric subject forces to andacentric moments, forces rotationaland moments, springs rotational were added springs to were the models, added whereto the models,their rotational where their stiffness rotational was determined stiffness was by determined equating to by the equating tangent orto secantthe tangent modulus or secant obtained modulus from obtainedJeanjean’s from method. Jeanjean’s method. TheThe implementation implementation of of the the improved improved PSSI PSSI models models using using soil soil springs springs a andnd the the API and Jeanjean methodsmethods in in the the X X-SEA-SEA program program was was verified verified in in an example of of a laterally loaded single single pile pile driven 42.742.7 m m into into a asoft soft clay clay soil. soil. The The soil soil spring spring stiffness stiffness values values were were based based on the on P the–Y data P–Y obtained data obtained from bothfrom methods. both methods. The PSSI The PSSI modellin modellingg and and analysis analysis were were performed performed in in both both the the X X-SEA-SEA and and SACS programs. The The maximum maximum lateral lateral resistance resistance result resultinging from from Jeanjean Jeanjean’s’s method method was was 1.33 1.33 times times larger larger thanthan from thethe API.API. TheThe lateral lateral deflections deflections resulting resulting from from X-SEA X-SEA and and SACS SACS are inare good in good agreement agreement with witheach eac otherh other when when using using either either the API the orAPI Jeanjean or Jeanjean methods. methods. InIn order order to to study the the behavior of of suction bucket bucket piles piles and and offshore offshore wind turbine turbine–jacket–pile–jacket–pile systems,systems, a a five five MW MW offshore offshore wind turbine turbine in in the the Buan Buan country country site site in in Korea Korea was was examined examined in in X X-SEA-SEA coupledcoupled with with FAST. FAST. Random Random wind wind and and waves waves with with a asignificant significant height height of of 3.3 3.3 m m,, a period a period of of8.0 8.0 s, a s, current velocity of 1.2 m/s, a mean wind speed of 13.156 m/s, and a marine growth of 0.1 m thick with a weight density of 1100 kg/m3 were considered. The four suction bucket files penetrated into a single

J. Mar. Sci. Eng. 2020, 8, 416 22 of 24 a current velocity of 1.2 m/s, a mean wind speed of 13.156 m/s, and a marine growth of 0.1 m thick with a weight density of 1100 kg/m3 were considered. The four suction bucket ﬁles penetrated into a single clay lay of 18 m thick. Free vibration and coupled dynamic analyses of the system were performed, and the following conclusions were drawn:

1) In the free vibration analysis with fixed boundary conditions (rigid soil), the first and second modes were globally bending and of the same natural frequencies, where the piles oscillated in two horizontal axes. The third mode was torsional about the vertical axis. 2) In the free vibration analysis with the soil spring stiffness determined from P–Y, T–Z, and Q–Z curves using the API method, the suction piles were of lateral movement in the first mode with a distinctly lower natural frequency, and they were twisting in their second and third modes, whereas the first to the third modes of the suction piles using Jeanjean’s method were all twisting. The natural frequencies of the first to the third modes resulting from Jeanjean’s method were higher than those from the API method. 3) In the forced vibration analysis, the API method made the foundation model more flexible than that of Jeanjean’s method, particularly the pile head. The jacket foundation responses were seen to be significantly influenced by the environmental loads, turbine responses, structural stiffness, and the type of nonlinear soil spring stiffness. The coupled analysis with PSSIs was quite computationally expensive.

Scour eﬀects, soil damping models, and seismic excitations are recommended to be considered in future research for the further understanding of the system behaviors.

Author Contributions: Formal analysis, P.P.; investigation, P.P. and V.N.D.; validation, P.P.; conceptualization, P.P., O.K., V.N.D., and K.-D.K.; methodology, V.N.D., J.M., and K.-D.K.; writing—original draft preparation, P.P. and V.N.D.; writing—review and editing, V.N.D., J.M., and K.-D.K.; funding acquisition, K.-D.K. All authors have read and agreed to the published version of the manuscript. Funding: This work is supported by Korea Electric Power Corporation (Development of analysis program of offshore wind turbine structure and design example using FAST turbine aerodynamic load), Korea. This work was supported by KEPCO(2017), Korea. The third author (V. N. Dinh) and the fourth author (J. Murphy) have been supported by the Science Foundation Ireland (SFI) MaREI Centre, the Sustainable Energy Authority of Ireland under the SEAI RS&D Funding Programme 2019 (Grant number 19/RDD/545), and the VeriX-SEA project. The authors are grateful for the support. Conflicts of Interest: The authors declare no conflict of interest.

References

1. Zhang, J.; Sun, K.; Wang, Z.; Zhang, L. Static and Dynamic Analysis of Monopile Foundation for Offshore Wind Farm. In Proceedings of the International Offshore and Polar Engineering Conference, Beijing, China, 20–25 June 2010. 2. Scharff, R.; Siems, M. Monopile foundations for offshore wind turbines—Solutions for greater water depths. Steel Constr. 2013, 6, 47–53. [CrossRef] 3. De, C.; Kai, H.; Lijun, H. Comparison of Structural Properties between Monopile and Tripod Offshore Wind-Turbine Support Structure. Adv. Mech. Eng. 2013, 2013, 1756849. 4. Georgia, M.; Anastasios, P.; Dimosthenis, B.; Charis, J.G.; Christos, P.G. Design of Monopile and Tripod Foundation of Fixed Offshore Wind Turbine via Advanced Numerical Analysis. In Proceedings of the 8th GRACM International Congress on Computation Mechanics, Volos, Greek, 12–15 July 2015. 5. Schaumann, P.; Böker, C. Can jackets and tripods compete with monopiles? In Proceedings of the Copenhagen Offshore Wind, Copenhagen, Denmark, 26–28 October 2005. 6. Plodpradit, P.; Dinh, V.N.; Kim, K.-D. Coupled Analysis of Offshore Wind Turbine Jacket Structures with Pile-Soil-Structure Interaction Using FAST v8 and X-SEA. Appl. Sci. 2019, 9, 1633. [CrossRef] 7. Wei, S.; Chinwha, C. Comparison of Dynamic Response of Monopile, Tripod and Jacket Foundation System for a 5-MW Wind Turbine. In Proceedings of the 21st International Offshore and Polar Engineering Conference, Maui, HI, USA, 19–24 June 2011. J. Mar. Sci. Eng. 2020, 8, 416 23 of 24

8. Wei, S.; Park, H.C.; Han, J.H.; Na, S.K.; Kim, C.W. A Study on the Effect of Different Modeling Parameters on the Dynamic Response of a Jacket-Type Offshore Wind Turbine in the Korean Southwest Sea. Renew. Energy 2013, 58, 50–59. 9. Ingrif, B.L.; Amir, M.K. Effect of Foundation Type and Modelling on Dynamic Response and Fatigue of offshore wind turbine. Wind Energy 2012, 22, 12. 10. Wu, Y.; Li, D.; Zhang, Y.; Chen, F. Determination of Maximum Penetration Depth of Suction Caissons in Sand. KSCE J. Civ. Eng. 2017, 22, 2776–2783. [CrossRef] 11. Wang, X.; Yang, X.; Zeng, X. Lateral response of improved suction bucket foundation for offshore wind turbine in centrifuge modelling. Ocean Eng. 2017, 141, 295–307. [CrossRef] 12. Tasan, H.E.; Yilmaz, S.A. Effects of installation on the cyclic axial behaviour of suction buckets in sandy soils. Appl. Ocean Res. 2019, 91, 101905. [CrossRef] 13. Latini, C.; Zania, V. Dynamic lateral response of suction caissons. Soil Dyn. Earthq. Eng. 2017, 100, 59–71. [CrossRef] 14. Mohammadm, A.; Saif, H. Optimized frequency-based foundation design for wind turbine towers utilizing soil-structure interaction. J. Frankl. Inst. 2010, 348, 1470–1487. 15. Jonkman, J. FAST v8. National Renewable Energy Laboratory (NREL): Golden, CO, USA, 2018. Available online: https://nwtc.nrel.gov/FAST8 (accessed on 19 September 2017). 16. Chen Ong, M.; Bachynski, E.E.; David Økland, O. Dynamic Responses of Jacket-Type Offshore Wind Turbines Using Decoupled and Coupled Models. ASME J. Offshore Mech. Arct. Eng. 2017, 139, 041901. [CrossRef] 17. Bin, Z.; De-qiong, K.; Ren-peng, C.; Ling-gang, K.; Yun-min, C. Installation and lateral loading tests of suction caissons in silt. Can. Geotech. J. 2011, 48, 1070–1084. 18. Wang, P.; Zhao, M.; Du, X.; Liu, J.; Xu, C. Wind, wave and earthquake responses of offshore wind turbine on monopile foundation in clay. Soil Dyn. Earthq. Eng. 2018, 113, 47–57. [CrossRef] 19. Shi, W.; Park, H.; Chung, C.; Baek, J.; Kim, Y.; Kim, C.-W. Load analysis and comparison of different jacket foundations. Renew. Energy 2013, 54, 201–210. [CrossRef] 20. Matlock, H. Correlations for Design of Laterally Loaded Piles in Soft Clay. In Proceedings of the 2nd Offshore Technology Conference, Houston, TX, USA, 22–24 April 1970; pp. 577–594. 21. American Petroleum Institute. Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms-Load-Working Stress Design API Recommended Practice 2A-WSD; American Petroleum Institute: Washington, DC, USA, 2007. 22. Asitha, I.M.J.S. Design of Large Diameter Monopiles for Offshore Wind Turbine in Clay. Ph.D. Thesis, University of Texas at Austin, August, TX, USA, 2016. 23. Ortolani, C. Laterally Loaded Monopiles for Offshore Wind Turbines: Analysis and Improvement of the P-Y Curve; University de Liege: Milano, Italy, 2015. 24. Kim, K.D.; Vachirapanyaku, S.; Plodpradit, P.; Dinh, V.N.; Park, J.-H. Development of offshore structural analysis software X-SEA and FAST. In Proceedings of the ASME 2019 38th International Conference on Ocean, Offshore & Arctic Engineering, Glasgow, UK, 9–14 June 2019; p. OMAE 2019-96778. [CrossRef] 25. Plodpradit, P.; Dinh, V.N.; Kim, K.-D. Tripod-Supported Offshore Wind Turbines: Modal and Coupled Analysis and a Parametric Study Using X-SEA and FAST. J. Mar. Sci. Eng. 2019, 7, 181. [CrossRef] 26. Jeanjean, P. Re-Assessment of p-y Curve for Soft Clays form Centrifuge Testing and Finite Element Modeling. In Offshore Technology Conference; OTC: Houston, TX, USA, 2015. 27. Lymon, C.R.; Michael, W.O. Criteria for the Design of Axially Drilled Shafts; The Texas Hight Department, The University of Texas at Austim: Austin, TX, USA, 1971. 28. Reese, L.C.; O’Neill, M.W. An Evaluation of p-y Relationships in Sands; A report to the American Petroleum Institute; University of Houston: Houston, TX, USA, 1983. 29. Lam, I.; Martin, G.R. Seismic Design of Highway Bridge Foundations. In Lifeline Earthquake Engineering: Performance, Design and Construction; ASCE: Reston, VA, USA, 1986. 30. Damiani, R.; Wendt, F. Development and Verification of Soil-Pile Interaction Extension for SubDyn. In Proceedings of the AWEA Offshore WINDPOWER 2017, New York, NY, USA, 24–25 October 2017. 31. Kim, B.J.; Plodpradit, P.; Kim, K.D.; Kim, H.G. Three-dimensional analysis of prestressed concrete offshore wind turbine structure under environmental and 5-MW turbine loads. J. Mar. Sci. Appl. 2018, 17, 625–637. [CrossRef] J. Mar. Sci. Eng. 2020, 8, 416 24 of 24

32. Pierson, W.J.; Moskowitz, L. A proposed spectral form for fully developed wind seas. J. Geophys. Res. 1964, 69, 5181–5203. [CrossRef] 33. International Electrotechnical Commission. IEC 61400–3 Wind Turbines–Part 3: Design Requirements for Offshore Wind Turbines, 1st ed.; International Electrotechnical Commission (IEC): Geneva, Switzerland, 2009. 34. Dinh, V.N.; Basu, B. Passive Control of Floating Offshore Wind Turbine Nacelle and Spar Vibrations by Multiple Tuned Mass Dampers. Struct. Control Health Monit. 2015, 22, 152–176. [CrossRef] 35. Thomas, H.D. Offshore Structure Engineering; Prentice-Hall. Inc.: Englewood Cliffs, NJ, USA, 1983. 36. SACS. PSI/Pile User’s Manual; Engineering Dynamic, Inc.: Englewood, CO, USA, 2005. 37. Jonkman, J.; Butterfield, S.; Musial, W.; Scott, G. Definition of a 5-MW Reference Wind Turbine for Offshore System Development; Technical Report, NREL/TP-5000-38060; National Renewable Energy Lab.: Golden, CO, USA, 2009. 38. Park, G.S. 5.5 MW Offshore Jacket Modeling of Korean Western Sea; Research Report; Seil Engineering: Seoul, Korea, 2018. 39. Jonkman, B.J. TurbSim User’s Guide Version 1.50; National Renewable Energy Laboratory Technical report, NREL/TP-500-46198; National Renewable Energy Lab.: Golden, CO, USA, 2009. 40. Kim, K.D. X-SEA Validation; Konkuk University: Seoul, Korea, 2018. 41. Basu, B.; Staino, A.; Dinh, V.N. Vibration of wind turbines under seismic excitations. In Proceedings of the Fifth Asian-Pacific Symposium on Structural Reliability and its Applications, Singapore, 23–25 May 2012. [CrossRef] 42. MATLAB. Fourier Analysis and Filtering; The MathWorks, Inc.: Natick, MA, USA, 2020; Release.

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