response of stiff piles in sand to long term cyclic lateral loading

LeBlanc, C., Houlsby, G. T. & Byrne, B. W. (2010). Geotechnique 60, No. 2, 79–90 [doi: 10.1680/geot.7.00196]

79

Response of stiff piles in sand to long-term cyclic lateral loading

C. LEBLANC�, G . T. HOULSBY† and B. W. BYRNE†

The driven monopile is currently the preferred founda-tion type for most offshore wind farms. While the staticcapacity of the monopile is important, a safe designmust also address issues of accumulated rotation andchanges in stiffness after long-term cyclic loading.Design guidance on this issue is limited. To address this,a series of laboratory tests were conducted where a stiffpile in drained sand was subjected to between 8000 and60 000 cycles of combined moment and horizontal load-ing. A typical design for an offshore wind turbinemonopile was used as a basis for the study, to ensurethat pile dimensions and loading ranges were realistic.A complete non-dimensional framework for stiff piles insand is presented, and applied to interpret the testresults. The accumulated rotation was found to bedependent on relative density, and was strongly affectedby the characteristics of the applied cyclic load. Parti-cular loading characteristics were found to cause asignificant increase in the accumulated rotation. Thepile stiffness increased with number of cycles, whichcontrasts with the current methodology where staticload–displacement curves are degraded to account forcyclic loading. Methods are presented to predict thechange in stiffness and the accumulated rotation of astiff pile due to long-term cyclic loading. The use of themethods developed is demonstrated for a typical full-scale monopile.

KEYWORDS: laboratory tests; piles; repeated loading; sands;settlement; stiffness

Le monopieu battu est actuellement le type de fondationprefere pour la plupart des parcs eoliens en mer. Bienque la capacite statique du monopieu soit importante,une conception sans danger doit egalement tenir comptedes problemes de la rotation accumulee et de variationsdans la rigidite, a la suite d’efforts cycliques de longueduree. Les conseils et indications conceptuels relatifs acette question etant limites, on a procede a une seried’essais en laboratoire, dans le cadre desquels on asoumis un pieu rigide, enfonce dans du sable draine, aun nombre de cycles de moment de charge et de chargeshorizontales allant de 8000 a 60 000. On a utilise, commeelement de base de cette etude, un modele typique demonopieu pour eolienne en mer, afin d’assurer que lesdimensions du pieu et les plages de charge etaientrealistes. Pour interpreter les resultats de cet essai, onpresente et on applique un cadre non dimensionnelcomplet pour pieux rigides dans le sable. La rotationcumulee, qui s’est averee tributaire du poids specifique,etait affectee dans une grande mesure par les caracteris-tiques de la charge cyclique appliquee. On s’est apercuque certaines caracteristiques particulieres de la chargeengendraient une augmentaiton significative de la rota-tion cumulee. La rigidite du pieu augmentait avec lenombre de cycles, contrairement a la methodologie ac-tuelle, dans laquelle les courbes charge statique/deplace-ment sont degradees pour tenir compte des chargescycliques. La communication presente des methodes per-mettant de predire les variations de la rigidite et larotation cumulee d’un pieu rigide due a des chargescycliques a long terme. L’application des methodes devel-oppees est demontree pour un monopieu typique gran-deur nature.

INTRODUCTIONWind power currently offers a very competitive source ofrenewable energy, and therefore the market for onshore andoffshore wind farms is projected to expand rapidly withinthe next decade. There are strong political and industrialforces, especially in northern Europe, supporting thedevelopment of offshore wind power to reduce reliance onfossil fuels and control greenhouse gas emissions.

There are several foundation concepts for offshore windfarms. The cost-effectiveness of a particular concept dependsto a large extent on the site conditions. Most currentfoundations are ‘monopiles’, which are stiff piles with largediameters, driven 20–30 m into the seabed. Recently in-stalled monopiles have diameters in the range of 4–6 m anda length/diameter ratio of approximately 5. Fig. 1 illustrates

the proportions of a typical offshore wind turbine on amonopile foundation.

The design of monopiles relies on standards and empiricaldata originating from the offshore oil and gas sector. How-ever, the loading of an offshore wind turbine is very differ-ent, in both magnitude and character, from that of oil andgas installations. It is characteristic for offshore wind tur-bines that the substructure will be subjected to strong cyclicloading, originating from the wind and wave loads. Thisoccurs not only during extreme conditions but also duringnormal service conditions. This can lead to accumulatedrotation of the wind turbine tower, adversely affecting itsultimate strength or fatigue life. The long-term movementsof the foundation may significantly impact on all parts ofthe wind turbine, including the support structure, machinecomponents and blades. Therefore it is of great importanceto investigate the effects of cyclic loading.

The primary design drivers for offshore wind turbinefoundations are deformation and stiffness rather than ulti-mate capacity. Modern offshore wind turbines are designedas ‘soft-stiff’ structures, meaning that the first natural fre-quency is in the range between the excitation frequencybands, 1P and 3P, in order to avoid resonances. 1P and 3Pdenote the frequency bands of the rotor rotation and theblade passing, typically in the range of 0.3 Hz and 1 Hz

Manuscript received 6 November 2007; revised manuscript accepted8 April 2009. Published online ahead of print 15 December 2009.Discussion on this paper closes on 1 July 2010, for further detailssee p. ii.� Department of Civil Engineering, Aalborg University, andDepartment of Offshore Technology, DONG Energy, Copenhagen,Denmark.† Department of Engineering Science, University of Oxford, UK.

respectively. Long-term cyclic loading of the foundation islikely to change the stiffness of the surrounding soil andtherefore the interaction of the foundation and the soil,owing to the accumulation of irreversible deformations. Anysignificant change in stiffness may result in interferencebetween the first natural frequency and the excitation fre-quencies, 1P or 3P, which would be highly problematic. Thusit is important to assess the concepts of stiffness and/orstrength changes during long-term cyclic loading.

The performance of monopiles subjected to long-termcyclic loading must therefore be addressed to achieve a safedesign of an offshore wind turbine. Although many usefulmethods have been proposed to predict the response of pilesto lateral cyclic loading, methods predicting the accumulatedrotation and resulting stiffness due to long-term cyclic load-ing are limited. This paper explores the load–displacementbehaviour of stiff monopiles in sand subjected to long-termcyclic loading. The objective is to provide information forthe development of a conceptual model capable of predictingthe response of monopiles to this loading.

Laboratory tests were conducted to simulate a drivenmonopile in drained conditions subjected to 8000–60 000load cycles of combined moment and horizontal loading. Incomparison, a typical offshore wind turbine is designed for afatigue load with 107 cycles. The laboratory tests werecarried out on the laboratory floor, with due consideration ofissues of scaling of the results. The main advantage ofperforming the experiments at 1g was the capability to applyup to 60 000 load cycles in a realistic time frame whilemaintaining high-quality displacement measurements. It waspossible to isolate the testing rig from the effect of external

vibrations, so that the displacements of the pile measuredwere related solely to the applied loading conditions.

CURRENT METHODOLOGYPiles are widely used for various structures, such as

bridges, high-rise structures and offshore oil and gas installa-tions. The interactions between soil and laterally loaded pilesare typically accounted for by the use of p–y curves,originally introduced by Reese & Matlock (1956) andMcClelland & Focht (1958). The p–y curves adopt theWinkler approach by uncoupling the response of variouslayers in the soil, and can therefore easily include effects ofnon-linearity, soil layering and other soil properties. A p–ycurve defines the relationship p(y) between the soil resis-tance p arising from the non-uniform stress field surroundingthe pile mobilised in response to the lateral pile displace-ment y, at any point along the pile. The implementation ofp–y curves requires a numerical procedure to solve thefourth-order differential equation for beam bending withappropriate boundary conditions

Ep Ip

d4 y

dz4� p yð Þ ¼ 0, z 2 0; L½ � (1)

in which Ep and Ip denote the elastic modulus and secondmoment of area of a pile respectively.

The p–y curves evolved primarily from research in the oiland gas industry, as the demand for large pile-supportedoffshore structures increased during the 1970s and 1980s.Research has included testing of full-sized piles in sandunder both static and cyclic loading conditions. An overviewof the important tests and results is given by Reese & Impe(2001). The p–y curves for piles in sand described by Reeseet al. (1974) and O’Neill & Murchison (1983) led torecommendations in the standards (DNV, 1977; API, 1993)for oil and gas installations. In 2004 these recommendationswere adopted in the standard Design of offshore wind turbinestructures (DNV, 2004), which represents the current state ofthe art for design of monopiles in the offshore wind indus-try.

The method adopted in the standards uses a procedure toconstruct non-linear p–y curves for monopiles in sand sub-jected to cyclic loading as a function of the static ultimatelateral resistance pu,

p ¼ Apu tanhBz

Apu y

� �(2)

where A ¼ 0.9 for cyclic loading, and B is an adjustmentparameter to account for the relative density of the sand.This method was originally developed by O’Neill &Murchison (1983), and has some theoretical basis. However,it relies to a high degree on empiricism, using data obtainedprimarily from two full-scale load tests reported by Cox etal. (1974). These tests were conducted using two slenderpiles, with diameter 0.61 m and length 21 m. The piles weresubjected to static and cyclic lateral load. To assess thevalidity of the method, systematic studies were conducted byMurchison & O’Neill (1984), which proved the method tobe superior to other methods. However, the validity of themethod relies on very few tests on relatively flexible drivensteel piles subjected to cyclic loading.

Shortcomings of current methodologyThe current design methodology, based on p–y curves,

has gained broad recognition, owing to the low failure rateof piles over several decades. However, when applied tooffshore wind turbine foundations, the design methodology

H

e

L

z

y

D

Fig. 1. Typical offshore wind turbine installed on monopilefoundation

80 LEBLANC, HOULSBY AND BYRNE

is being used outside its verified range, and several designissues are not properly taken into account.

First, current standards rely on methods built upon empiri-cal data obtained from long, slender and flexible piles. Whenscaling to large-diameter piles, a distinction must be madebetween a pile that behaves in an almost rigid fashion andone that is relatively flexible, since this affects the soil–pilebehaviour (Briaud et al., 1984). A rigid pile rotates withoutflexing significantly, and develops a ‘toe kick’ under momentand lateral loading. Criteria for rigid or flexible behaviourhave been proposed by various researchers (e.g. Dobry etal., 1982; Budhu & Davies, 1987; Carter & Kulhawy, 1988).The range of transition from flexible to rigid pile behaviourmay, according to Poulos & Hull (1989), be evaluated by

4:8 ,Es L4

Ep Ip

, 388:6 (3)

in which Es denotes the elastic modulus of the soil.A typical monopile has a diameter of 4 m, wall thickness of0.05–0.07 m and penetration depth of 18 m. According toequation (3), the transition from rigid to flexible pile be-haviour occurs in the range from Es � 14 MPa toEs � 1121 MPa. Thus for most sands encountered the mono-pile behaviour tends toward the rigid case.

Second, the recommended p–y curves for cyclic loadingare designed primarily for evaluation of the ultimate lateralcapacity. Important design issues, such as accumulated rota-tion and stiffness changes due to long-term cyclic loading,are poorly accounted for. Long-term cyclic loading is likelyto densify, or in some circumstances possibly loosen, thesurrounding soil, resulting in changes to the stiffness of thefoundation. Additionally, an accumulated rotation duringthe lifetime of an offshore wind turbine is expected, sincethe cyclic loading often occurs from one direction. Thecurrent design methodology is not capable of predictingeither effects of soil densification or long-term movementsof the monopile.

Finally, the current methodology accounts for cyclic load-ing in an incomplete manner. Repetitive lateral load tests ontwo offshore piers in Tampa Bay, reported by Long &Vanneste (1994), showed much greater displacements thanpredicted using the p–y curves proposed by Reese et al.(1974). The reason for this discrepancy, according to Long& Vanneste (1994), is that the cyclic p–y curves do notaccount for such factors as installation method, load charac-teristics or number of load cycles.

METHODS FOR PREDICTING THE RESPONSE TOLONG-TERM CYCLIC LOADING

The inadequacy of the current methodology for predictingthe cyclic loading response of piles means that new models,incorporating factors affecting the cyclic behaviour, must bedeveloped. Results from 34 full-scale cyclic lateral load testsof piles in sand were collected by Long & Vanneste (1994)to identify the factors affecting the cyclic behaviour. Theseincluded soil density, pile type, installation method and, mostimportantly, the characteristics of the cyclic load. Long &Vanneste (1994) adopted a method, originally introduced byLittle & Briaud (1988), to account for cyclic loading. Themethod is based on the deterioration of static p–y curves,which is taken into account by reducing the static soilreaction modulus according to

RN

R0

¼ N�Æ (4)

in which R0 and RN denote the soil reaction modulus on thefirst and Nth load cycle respectively, and Æ is an empirically

determined degradation parameter that depends on the in-stallation method, soil density and load characteristics.

By investigating a subset of the full-scale tests, Lin &Liao (1999) proposed that the accumulated displacement ofpiles can be predicted by

uN � u0

u0

¼ � ln Nð Þ (5)

in which u0 and uN denote the pile-head deflection in thefirst and Nth load cycle respectively, and � is an empiricaldegradation parameter, similar to Æ, depending on the in-stallation method, soil density and load characteristics.

The methods proposed by Long & Vanneste (1994) andLin & Liao (1999) provide simple means for predicting theeffects of cyclic loading. However, the determination of theempirical degradation parameters relies on a small numberof tests carried out on long, flexible piles subjected to fewerthan 50 cycles of loading. Further investigations are neededto verify the form of the models, and to extend them for usein predicting the long-term behaviour of stiff, driven piles.Other investigations include small-scale tests on stiff pilessubjected to 10 000 cycles, as reported by Peng et al.(2006). However, only a few tests are reported, and the datainterpretation is limited. A more theoretical approach isgiven by Lesny & Hinz (2007), who attempt to predictaccumulated displacements using data from cyclic triaxialtests and a finite element model incorporating Miner’s law.The method is theoretical, and still requires validationagainst experimental data.

DIMENSIONLESS EQUATIONS FOR SCALING OFLABORATORY TESTS

The basis of this paper is a set of laboratory floorexperiments on stiff monopiles in sand. Results from labora-tory tests of foundations in sand must be carefully scaled topredict the behaviour of a full-scale structure. As is wellrecognised for structures on sand, the loading response isgoverned by the frictional behaviour of the sand, which inturn is governed by the isotropic stress level. In the labora-tory the isotropic stress level controlling the test behaviouris low, resulting in higher friction angles but lower shearstiffnesses, in comparison with a full-scale test. These issuesof scaling can be addressed by choosing appropriate scalingmethods, as presented in the following.

To ensure that the peak friction angle in a laboratory testcorresponds to the value in a full-scale test, the soil sampleis prepared at a lower relative density. This is straightfor-ward, but the issues of stiffness are more complex. Anattempt to account for the influence of isotropic stress levelis made by expressing the shear modulus G as

G

pa

¼ c1

� 9vpa

� �n

(6)

in which pa is the atmospheric pressure, c1 is a dimension-less constant, � 9v is an appropriate effective vertical stress,and n is the pressure exponent (Kelly et al., 2006). Evalua-tion of the shear modulus using equation (6) requires thedetermination of a representative vertical effective stress, � 9v.The vertical effective stress around a pile varies with depth.Thus an appropriate choice is to use the vertical stress at adepth c2L below the sea-bed, given by

� 9v ¼ c2 Lª9 (7)

in which ª9 is the effective unit weight and c2 is adimensionless constant. The pressure exponent in equation(6) is reported to vary from 0.435 at very small strains to0.765 at very large strains (Wroth et al., 1979). The shear

RESPONSE OF STIFF PILES IN SAND TO LONG-TERM CYCLIC LATERAL LOADING 81

strain range of greatest interest is likely to fall in the range103 to 104 (Simpson, 2002). In this range n is reported to bearound 0.75 for sands (Park & Tatsuoka, 1994; Porovic &Jardine, 1994). However, a value of 0.5 may capture most ofthe important features of increased shear stiffness withpressure (Wroth & Houlsby, 1985). This is confirmed byKelly et al. (2006), who successfully adopted a value of 0.5to compare the results of laboratory and full-scale tests ofsuction caisson foundations.

For the case of a monopile subjected to a horizontal loadH and moment M at the sea-bed, the resulting lateraldisplacement u and rotation Ł can be obtained from anelastic stiffness relation, expressed as

M

L

H

264

375 ¼ DG

k1 k2

k2 k3

� �LŁu

� �(8)

in which k1, k2 and k3 are dimensionless constants. Toobtain the moment–rotation relationship, u can be elimi-nated to give

M ¼ GL2 D k1 k3 � k22

� �k3 � k2 HL=Mð Þ

" #Ł (9)

The issue of scaling is addressed by incorporating equations(6) and (7) in equation (9) to obtain a moment–rotationrelationship given entirely in terms of non-dimensional para-meters,

M

DL3ª9|fflffl{zfflffl}~MM

¼c1

ffiffiffiffiffiffiffiffic2ð Þ

pk1 k3 � k2

2

� �k3 � k2 HL=Mð Þ|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

~kk

ffiffiffiffiffiffiffiffipa

Lª9

rŁ|fflfflfflffl{zfflfflfflffl}

~ŁŁ

(10)

in which ~kk is the non-dimensional stiffness, and ~MM and ~ŁŁare the non-dimensional values of moment and rotationrespectively. The non-dimensional moment/force ratio arisingin ~kk will be denoted ~ee ¼ M=HL, called the non-dimensionalload eccentricity. This suggests that a satisfactory compari-

son between tests can be obtained by plotting ~MM against~ŁŁ while ~ee and other parameters influencing ~kk are keptconstant.

Several other parameters may influence the ~MM – ~ŁŁ rela-tionship. These can be understood by investigating the staticmoment resistance of a monopile. Consider the idealisedhorizontal stress distribution, in the ultimate lateral limitstate, along a stiff pile in sand, as illustrated in Fig. 2. Theresulting distributed horizontal load along the pile is deter-mined by KD� 9v ¼ KDª9z, in which K is a factor depend-ing on the friction angle (e.g. Broms, 1964) and d is thedepth of the pivot point. The pile toe is assumed to shearat the critical state friction angle �cr. Thus the shearresistance at the bottom of the pile is governed by thevertical effective force arising from the overburden sand,(�/4)D2Lª9, plus a contribution arising from the structure,c3V, in which V is equal to the gravity force acting on thestructure, and c3 is a dimensionless constant between 0 and1. On the basis of these assumptions, the equations ofhorizontal equilibrium and moment equilibrium at the pilehead are given by

H þ c3V þ �

4D2 Lª9

� �sin�cr ¼ d2 � 1

2L2

� �KDª9

(11)

M � c3V þ �

4D2 Lª9

� �L sin�cr ¼ 1 L3 � 2d3ð ÞKDª9

3

(12)

respectively. These equations can be combined to eliminated and give the interaction equation

1

2þ 3

2Æ� 3

2

M

L3 KDª9

� �2

¼ 1

2þ Æ þ H

L2 KDª9

� �3

(13)

Æ ¼c3V þ �

4D2 Lª9

� �sin�cr

L2 KDª9(14)

where Æ is introduced for simplicity. This relation can berearranged to obtain an expression given entirely in non-dimensional parameters,

3

K

M

DL3ª9|fflffl{zfflffl}~MM

¼ Æ þ 1 � 2

�1

2þ Æ þ 1

K

H

L2 Dª9|fflfflffl{zfflfflffl}~HH

�32

(15)

Æ ¼�

c3

V

DL2ª9|fflffl{zfflffl}~VV

þ�

4

D

L|{z}1=�

�sin�cr

K(16)

introducing the pile aspect ratio � and the non-dimensionalvertical and horizontal loads ~VV and ~HH respectively. The non-dimensional horizontal load ~HH can be replaced by ~HH ¼ ~MM=~ee.Thus it follows from equations (15) and (16) that the staticmoment capacity, in terms of ~MM , is uniquely determined bythe non-dimensional parameters ~VV , ~ee and �. This suggeststhat the non-dimensional moment–rotation relationship inequation (10) could be written as

~MM ¼ ~kk ~VV , ~ee, ��

~ŁŁ (17)

Thus a satisfactory comparison of both stiffness andstrength, between laboratory and full-scale tests, is likely tobe obtained by plotting ~MM against ~ŁŁ, while keeping ~VV , ~ee and� constant. This scaling law derived for monotonic loading

L d�

d

KD zγ�

H

V

M

KD zγ�

��c V3 �

π4

D L2 γ� sinφcr��

Fig. 2. Horizontal stress distribution in ultimate limit state forlaterally loaded stiff pile in sand


is also assumed to cover the cyclic response of stiff piles insand. The non-dimensional parameters are listed in Table 1.

EXPERIMENTAL EQUIPMENTA simple and efficient mechanical load rig is used to

apply loads to the pile. The rig was originally developed byRovere (2004) for testing of caisson foundations. The rigconsists of a 550 mm 3 600 mm 3 600 mm container forsand, a steel frame with pulleys, three weight hangers, and alever with a driving motor, as illustrated in Fig. 3. The leveris attached to the steel frame through a pivot, and carries amotor, which rotates a mass m1 to cause cyclic loading. Themotor is a geared single-phase AC motor rotating at afrequency of 0.106 Hz. The pulley ropes are 3 mm low-stretch spectral ropes.

The load rig is a simple static system. Initially, whenm1 ¼ m2 ¼ 0, the weight of the mass m3 is chosen tobalance any force acting on the lever. Thus, assuming thatŁ � �/2, as is the case for minor lever deflections, anysinusoidal load in the form f (t ) ¼ f0 + fasin(øt ) can beapplied to the pile by appropriately choosing m1 ¼[(l2/la)fa]/g and m2 ¼ [(lc/la)fa � f0]/g. Since m2 . 0, itfollows that la or lc must fulfil the condition la/lc , fa/f0. Theload rig is very stable, and can accurately provide a sinus-oidal loading for more than 1 000 000 cycles.

The experiments were conducted using unsaturated yellowLeighton Buzzard silica sand. The characteristics of the sandare summarised in Table 2, and further information is givenby Schnaid (1990).

The container for the sand was carefully filled by pouringsand from a low drop height to achieve a very loose state. Adenser state was also obtained using a hammer drill tovibrate the bottom plate of the sand container.

The tests were conducted using a stiff copper pile. Theouter dimensions of the pile are scaled to approximately1:50, in relation to a typical monopile. The pile propertiesare listed in Table 3. The pile was driven into the sand bygentle driving with a plastic hammer from a fixed dropheight. The number of strokes needed to reach the finalpenetration depth varied from 460 � 20 to 740 � 30 forloose and medium dense sand respectively. The monopilewas fixed horizontally during installation using side supports.Horizontal deflections were measured by two dial gauges.The load rig is illustrated in Fig. 4.

TEST PROGRAMMEThe test programme was designed to investigate the re-

sponse of the pile and its dependence on the relative densityof the sand and the characteristics of the applied cyclic load.

The average relative densities were Rd ¼ 4% andRd ¼ 38%, corresponding to a loose and a medium-densestate respectively. A relationship between effective stress,relative density and peak friction angle for Yellow BuzzardSand is given by Schnaid (1990), and is used to comparepeak friction angles between the laboratory tests and a full-scale monopile. For the calculation it is assumed that arepresentative effective stress can be taken at 0.8L beneaththe sea-bed. Fig. 5 illustrates that the peak friction anglesused in the laboratory were estimated as 358 and 438, whichequate to field conditions of Rd ¼ 8% and Rd ¼ 75%, corre-sponding to a loose and a dense state respectively.

The characteristics of the applied cyclic load must beuniquely defined. In the following, load levels are referred toin terms of the applied moment M. The correspondinghorizontal force follows from H ¼ M/e. Two independentparameters are defined to characterise the applied sinusoidalloading,

Table 1. Non-dimensional parameters

Moment loading ~MM ¼ M

L3 Dª9

Vertical force ~VV ¼ V

L2 Dª9

Horizontal force ~HH ¼ H

L2 Dª9

Rotation: degrees ~ŁŁ ¼ Łffiffiffiffiffiffiffiffipa

Lª9

r

Load eccentricity ~ee ¼ M

HL

Aspect ratio � ¼ L

D

π2

θ �

Motor

80 mm

360 mm

la

l2

430 mm

m2

m3

lc

m1

Fig. 3. Mechanical load rig used to investigate response of stiffpiles to long-term cyclic loading

Table 2. Characteristics of yellow Leighton Buzzard Sand(Schnaid, 1990)

Property Value

Particle sizes, D10, D30, D50, D60: mm 0.63/0.70/0.80/0.85Specific gravity, Gs 2.65Minimum dry unit weight, ªmin: kN/m3 14.65Maximum dry unit weight, ªmax: kN/m3 17.58Critical angle of friction, �cr: degrees 34.3

Table 3. Properties of the copper monopile

Property Value

Pile diameter, D: mm 80.0Wall thickness: mm 2.0Penetration depth, L: mm 360.0Load eccentricity, e: mm 430.0Pile weight, V: N 35.0


�b ¼ Mmax

MR

�c ¼ Mmin

Mmax

(18)

in which MR refers to the static moment capacity of the pile,and Mmin and Mmax are the minimum and maximum in aload cycle. The ratio �b is a measure of the size of the

cyclic loading, normalised with respect to the static momentcapacity. It follows that 0 , �b , 1. The ratio �c 2 [�1; 1]quantifies the characteristics of the cyclic load, and takes thevalue 1 for a static test, 0 for one-way loading, and �1 fortwo-way loading. A visual interpretation of the load ratios isgiven in Fig. 6.

Initially, static load tests were performed to determine thestatic moment capacity in terms of ~MMR, as shown in Fig. 7.From the moment–rotation curves it is not possible toidentify a distinct point of failure. Thus failure is defined by~ŁŁ ¼ 48 ¼ 0.0698 rad. The moment–rotation curves in Fig. 7are for convenience fitted by ~ŁŁ � 0:038 rad 3 ( ~MM= ~MMR)2:33

and ~ŁŁ � 0:042 rad 3 ( ~MM= ~MMR)1:92 for Rd ¼ 4% and Rd ¼38% respectively, valid in the range 0:25 ~MMR , ~MM ,0:50 ~MMR.

It is important to select appropriate values of �b so thatthe experiments reflect realistic loading conditions. Typicaldesign loads for an offshore wind turbine are shown in Table4. The limit state ULS refers to the ultimate load-carryingcapacity and ULS/1.35 to the worst expected transient load.SLS and FLS are the serviceability and fatigue limit statesoccurring 102 and 107 times during the lifetime of the windturbine respectively. Further information is given by DNV(2004).

The design loads are compared with the laboratory load-

a b

c

d

Fig. 4. Experimental set-up: (a) mechanical load rig; (b) side supports used during installation; (c) installed pile with two dial gaugesmeasuring horizontal deflections; (d) driving motor

0 50 100 150

34

36

38

40

42

44

46

48

Rd 0%�

Rd 25%�

Rd 50%�

Rd 75%�

Rd 100%�

LaboratoryFull-scale

38%

4%

75%

8%

p�: kPa

φ: d

egre

es

Fig. 5. Friction angles of yellow Leighton Buzzard Sand asfunction of effective isotropic stress p9 and relative density Rd


ing, in terms of non-dimensional parameters ~MM and ~HH, byscaling the design loads such that ULS coincides with thestatic moment capacity of the laboratory pile. Fig. 8 showsthis static capacity, determined from equation (15), com-pared with the capacities determined from five static loadtests in loose sand, conducted at different values of ~ee. Alsoshown on the figure are ranges of �b for ~ee ¼ 1:19. Thecomparison suggests that 30% , �b , 50% is the range ofprimary interest for piles with designs governed by the ULS.

The value of �c is expected to vary between �0.5 and 1,since the response of a wind turbine is governed by largeaerodynamical damping, resulting in one-way cycling ratherthan two-way cycling. For completeness, �c was investigatedin the full range from �1 to 1. The chosen test programmeis summarised in Table 5.

DISCUSSIONThe results of the laboratory tests are investigated by

plotting the angular rotation of the pile Ł in response tothe applied moment M for both static and cyclic tests. Themethod for data extraction is outlined in Fig. 9. Thegathered data provides information on both stiffness andaccumulated rotation as functions of N, the number of load

cycles. The evolution of the accumulated rotation is evalu-ated in terms of the dimensionless ratio

˜Ł Nð ÞŁs

¼ ŁN � Ł0

Łs

(19)

which expresses the magnitude of the rotation ˜Ł(N) causedby cyclic loading in terms of the rotation Łs that wouldoccur in a static test when the load is equivalent to themaximum cyclic load (as defined by �b 3 MR). The non-dimensional stiffness ~kk is obtained substituting measuredvalues of k ¼ M/Ł (see Fig. 9) into equation (10), which isrearranged to give

~kk ¼ k

L5=2 Dffiffiffiffiffiffiffiffiffipaª9

p (20)

Accumulated displacementsThe method proposed by Lin & Liao (1999) suggests that

accumulated rotation is proportional to ln(N). This approachwas investigated by plotting ˜Ł/Łs as a function of ln(N). Agood fit was obtained for N , 100, but extrapolation beyondN . 500 underestimated the accumulated rotation. A betterfit was found if the accumulated rotation was modelled asincreasing exponentially with N rather than logarithmically,as is in agreement with the method proposed by Little &Briaud (1988) and Long & Vanneste (1994). The exponentialbehaviour appears as straight lines in double logarithmicaxes, as shown in Fig. 10.

The results for one-way loading, plotted in Figs 10(a) and10(b), show a very good fit with an exponential expression.The results include approximately 104 load cycles, whereasthe fatigue limit state is governed by 107 load cycles. Thecloseness of fit up to 104 cycles indicates that, in theabsence of further experimental data, it might be reasonableto extrapolate to N ¼ 107. Further data are, of course,required to confirm this hypothesis.

The results obtained by varying �c, plotted in Figs 10(c)

�c 0·0� �c �

M

MR

0

0·25

0·5

0·75

1·0

0·5

0·0

�0·5

�1·0

�b � �b 0·5�

Fig. 6. Characteristics of cyclic loading defined in terms of �band �c

~1·24MR �

~0·6MR �

θ~

0 0·02 0·04 0·06 0·08 0·10

0·2

0·4

0·6

0·8

1·0

1·2

1·4

Rd 38%�

Rd 4%�

M~

Fig. 7. Moment capacity determined from static load tests for~ee 1:19

Table 4. Typical design loads for a 2 MW turbine

N M: MN m H: MN V: MN

ULS 1 95 4.6 5.0ULS/1.35 1 70 3.4 5.0SLS 102 45 2.0 5.0FLS 107 28 1.4 5.0

H~

M~

0 0·2 0·4 0·6 0·8 1·0 1·20

0·2

0·4

0·6

0·8

1·0

ULS

ULS/1·35

SLS

FLS

20%

30%

40%

50%

60%

K 10�

Bearing capacity: test results

Bearing capacity: theory

Scaled design loads

Cyclic loading ranges: �b

Fig. 8. Cyclic loading ranges, in terms of �b, in relation todesign loads of a typical offshore wind turbine


and 10(d), exhibit a more volatile behaviour, particularly for�c , 0. However, the trend in the data also follows theexponential behaviour shown in the one-way load tests.Based on these observations, it is proposed that displace-ments due to cyclic loading can be predicted by

˜Ł Nð ÞŁs

¼ Tb �b, Rdð ÞTc �cð Þ � N 0:31 (21)

in which Tb and Tc are dimensionless functions, dependingon the load characteristics and relative density. The functionTc is defined such that Tc(�c ¼ 0) ¼ 1. The expression inequation (21) was fitted to the data in Fig. 10 (the dottedlines) to empirically determine values of Tb and Tc. Thesevalues are plotted in Fig. 11 as functions of �b and �c

respectively. The behaviour of the functions Tb(�b, Rd) andTc(�c) is clearly apparent, and curves were easily fitted.Generally, the loose sand results in low values of Tb ascompared with the denser sand. The value of Tc is found tobe independent of relative density.

The Tc curve in Fig. 11 shows a remarkable result.Clearly, when �c ¼ 1, then Tc must be zero, since noaccumulated displacement will occur under static load. Also,when �c ¼ �1, then it is expected that Tc will be zero, sincethe force applied is equal in both directions. The maximumone-way load is obtained when �c ¼ 0, and intuitively itseems reasonable to expect that this loading will cause thelargest accumulated rotation. This assumption is commonly

accepted, and the majority of lateral load tests reported inthe literature are conducted at �c ¼ 0, with some at �c ¼ �1.However, the results presented here clearly illustrate thatloading with �c � �0.6 causes an accumulated rotation thatis more than four times larger than for one-way loading,that is, �c ¼ 0. The authors are not aware of similar observa-tions in cyclic loading tests, but clearly this result hasprofound implications for assessing the results of cycling.

Variation of pile stiffnessInterpretation of the stiffness results involves a greater

scatter of the data. This is partly because the measurementof secant stiffness in a cycle involves differences of smalldisplacements. Plotting ~kk N as a function of ln(N) indicatesthat the stiffness evolves approximately logarithmically withcycle number, as shown in Fig. 12. This suggests that theevolution of stiffness can be approximated by

~kk N ¼ ~kk0 þ Ak ln Nð Þ (22)

where Ak is a dimensionless constant. It is observed fromFig. 12 that all slopes are almost equal. This suggests thatAk is independent of both relative density and load charac-teristics within the observed range. The expression in equa-tion (22) was fitted to the data in Fig. 12 (the dotted lines)using the value Ak ¼ 8.02, and values of ~kk0 were determinedfrom the point of intersection with the ~kk-axis where N ¼ 1.The empirically determined values of ~kk0 can be expressedby

~kk0 ¼ Kb �bð ÞKc �cð Þ (23)

in which Kb and Kc are dimensionless functions, dependingon the load characteristics and relative density. The functionKc is defined such that Kc(�c ¼ 0) ¼ 1. The empiricallydetermined values of Kb and Kc, as functions of �b and �c

respectively, are illustrated in Fig. 13. The behaviour of thefunctions Kb(�b) and Kc(�c) was easily determined andcurves fitted. It is not possible to make a clear distinctionbetween the results for Rd ¼ 4% and Rd ¼ 38%. This indi-cates that values of stiffness are somewhat independent ofthe relative density, at least for the low to medium densitiestested. However, this is unlikely to hold for Rd ! 100%,

Table 5. Test programme

No. Type ~ee Rd: % �: degrees �b �c N

1 Static 0.10 4 35 – – –2 Static 0.42 4 35 – – –3 Static 0.78 4 35 – – –4 Static 1.19 4 35 – – –5 Static 3.33 4 35 – – –6 Cyclic 1.19 4 35 0.20 0 8 2007 Cyclic 1.19 4 35 0.27 0 18 2008 Cyclic 1.19 4 35 0.34 0 8 4009 Cyclic 1.19 4 35 0.40 0 17 70010 Cyclic 1.19 4 35 0.53 0 8 60011 Cyclic 1.19 4 35 0.40 �0.98 8 51012 Cyclic 1.19 4 35 0.40 �0.67 7 40013 Cyclic 1.19 4 35 0.40 �0.33 8 80014 Cyclic 1.19 4 35 0.40 0.33 65 37015 Static 1.19 38 43 – – –16 Cyclic 1.19 38 43 0.27 0 8 09017 Cyclic 1.19 38 43 0.40 0 7 42318 Cyclic 1.19 38 43 0.52 0 17 53219 Cyclic 1.19 38 43 0.40 �0.50 9 00320 Cyclic 1.19 38 43 0.40 �0.80 9 81421 Cyclic 1.19 38 43 0.40 0.50 9 862

M

k0 kN

∆θ( )N

M

Mmin θNθ0

Mmax

θs

θ(b)

θ(a)

Fig. 9. Method for determination of stiffness and accumulatedrotation: (a) cyclic test; (b) static test


since no increase in stiffness is expected for sand in itsdensest state.

The most important outcome of the results is that stiffnessalways tends to increase. This observation opposes thecurrent methodology of degrading static p–y curves toaccount for cyclic loading.

ExampleAn example is given to demonstrate the use of the

proposed methods. Consider a stiff monopile, with L ¼ 18 mand D ¼ 4 m, driven into sand with a friction angle of 358.The task is to determine the increase in stiffness andaccumulated rotation due to 107 load cycles characterised by�b ¼ 0.3 and �c ¼ �0.2.

Initially, values of Łs and ~kk0 must be determined. Thesecan be calculated by various methods, for example usingp–y curves, finite element models or, alternatively, using thenon-dimensional framework which has been presented here.The non-dimensional approach requires that the full-scalestructure and laboratory pile have comparable values of ~��, ~VVand ~ee, as is the case in this example. The non-dimensionalstatic rotation for �b ¼ 0.3 gives a non-dimensional momentof ~MM ¼ 0:3 3 ~MMR ¼ 0.3 3 0.6 ¼ 0.18, at which point thenon-dimensional rotation is ~ŁŁ ¼ 0.0023. The correspondingstatic rotation of the full-scale monopile follows from thedefinition of ~ŁŁ, which gives Łs ¼ 0.0033. The initial non-dimensional stiffness is determined from equation (23), byevaluating Kb and Kc from Fig. 13, to obtain ~kk0 ¼ 240 30.9 � 216. The non-dimensional stiffness can optionally betransformed to the absolute value of the full-scale stiffnessusing the relationship in equation (20).

Given Łs and ~kk0, it is possible to estimate the accumulatedrotation and stiffness change due to long-term cyclic load-ing. Values of Tb and Tc are determined from Fig. 11, withthe representative relative density chosen as Rd ¼ 4%, sincethe angle of friction is 358. The resulting increase instiffness follows from equation (22), as

~kk N ¼ ~kk0 þ 8:02ln 107ð Þ � 345

)~kk N � ~kk0

~kk0

¼ 60%(24)

This result indicates that the stiffness can be expected toincrease by approximately 60% during the lifetime of thewind turbine. The accumulated rotation follows from equa-tion (21), as

˜Ł

Łs

¼ 0:047 3 1:5 3 107ð Þ0:31 � 10:4

) ˜Ł ¼ 0:0344 rad (� 28)

(25)

The accumulated rotation is estimated to be 28, which is avalue that would breach the tolerance criterion. It should benoted that the accumulated rotation is calculated on the basisof 107 load cycles, acting in the same direction. Lessrotation must be expected, since the actual loading would bemultidirectional. Of course, if �b is in the range between�0.7 and �0.4, then much higher rotation is predicted.

If the monopile is more conservatively designed, say byusing a static design capacity equal to 1.5 times ULS, then�b will be approximately 0.2. In this case, the predicted

100 101 102 103 104 10510�2

10�1

100

101

�c � 0·00

Rd � 38%

N(b)

�b 0·52�

�b 0·40�

�b 0·27�

∆θ

θs

100 101 102 103 104 10510�2

10�1

100

101�b � 0·40

Rd � 38%

N(d)

�c 0·00�

�c 0·50� �

�c 0·81� �

∆θ

θs

100 101 102 103 104 10510�2

10�1

100

101�b � 0·40

Rd � 4%

N(c)

�c 0·33�

�c 0·00�

�c 0·34� �

�c 0·67� �

�c 0·98� �

∆θ

θs

�c 0·50�

100 101 102 103 104 10510�2

10�1

100

101

�c � 0·00

Rd � 4%

N(a)

�b 0·53�

�b 0·40�

�b 0·34�

�b 0·27�

�b 0·20�

∆θ

θs

Fig. 10. Measured displacements as a function of N, Rd, �b and �c. Dotted lines obtained using equation (21)


accumulated rotation and increase in stiffness are 0.278 and42% respectively.

CONCLUSIONA series of tests was conducted on small-scale driven

piles subjected to long-term cyclic loading. A typical designof a monopile was adopted and used to quantify realisticpile dimensions and loading ranges. Furthermore, a completenon-dimensional framework for stiff piles in sand is pre-sented and applied to interpret the test results.

The accumulated rotation of a stiff pile is largely affectedby the characteristics of the applied cyclic load. Thusparameters characterising the load, other than maximum loadlevels, are required for accurate predictions. For example,results for one-way loading were found to differ by a factorof four as compared with two-way loading. A very signifi-cant result was that the most onerous loading condition wasfound to be between one-way and two-way loading. Amethod to predict the accumulated rotation during the life-time of an offshore wind turbine foundation is presented.When applied, the method predicts that typical tolerances foraccumulated rotation are breached if the foundation isdesigned so that the design capacity is equal to the ULSload. This suggests that considerations of accumulated rota-tion are the primary design driver. The proposed methoddoes not account for multidirectional loading, which is likely

to be less severe in terms of accumulated rotation, ascompared with unidirectional loading.

The tests showed that cyclic loading always increased thepile stiffness, and the increase was found to be independentof relative density. This contrasts with the current method-ology of degrading static p–y curves to account for cyclicloading. A method, based on the experimental work carriedout, is presented to predict changes in stiffness due to long-term cyclic loading.

The results in this paper lay out a basic framework toincorporate effects of cyclic loading in a simple manner.Further work should be carried out to investigate pilesinstalled in very dense sand, the effect of altering piledimensions, and how a representative cyclic load is chosen.The effect of the loading frequency on the drained responseof laterally loaded piles in sand is limited. However, owingto the scale of field monopiles it is possible that theresponse in saturated sand may not be completely drained,and further work on the effects of loading frequency willneed to be undertaken. Finally, comparisons with full-scalemeasurements should be carried out to ensure that theproposed methods are reliable and valid.

NOTATIONc1, c2, c3 dimensionless constants

D pile diameterD10, D60 particle sizes

d pile pivot pointEp elastic modulus of pileEs elastic modulus of soile load eccentricity

f, f0, fa load rig forcesG shear modulus

Gs specific gravityg gravitational accelerationH horizontal load at sea-bedIp moment of inertia of pileK Broms factor

Kb, Kc dimensionless functionsk pile stiffness

k1, k2, k3 dimensionless parametersk0 pile stiffness in first cycle

kN pile stiffness in Nth cycleL penetration depth of pile

l2, la, lc load rig dimensionsM, Mmin, Mmax moment at sea-bed

MR static moment resistance of pilem1, m2, m3 load rig masses

N number of load cyclespa atmospheric pressurep9 effective isotropic stressRd relative density

Tb, Tc dimensionless functionst time

V gravity force acting on the structurey horizontal deflectionz depth below sea-bedÆ dimensionless parameter

ªmin, ªmax dry unit weightª9 effective unit weight

�b, �c load characteristic parameters� pile aspect ratioŁ pile rotationŁ0 pile rotation in first cycleŁN pile rotation in Nth cycleŁs static pile rotation� 9v effective vertical stress� angle of friction

�cr critical state angle of frictionø rotational frequency

Note: , above parameters indicates corresponding dimen-sionless values: see Table 1.

�c

(b)

0 0·2 0·4 0·6 0·80

0·05

0·10

0·15

0·20

0·25

Rd 4%�

Rd 38%�

Tb

Tc

�1·0 �0·5 0 0·5 1·00

1

2

3

4

5

Rd 4%�

Rd 38%�

�b

(a)

Fig. 11. Functions relating (a) Tb and (b) Tc to relative densityRd, and characteristics of cyclic load in terms of �b and �c


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�

�R

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150

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�c

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450 0·50�c �

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N(c)

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�1·0 �0·5 0 0·5 1·00·4

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Rd 4%�

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(b)

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