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Page 1: Centrifuge modelling of monopiles subjected to lateral loadingscientiairanica.sharif.edu/article_20222_8afc3dc690c5227863a72e6… · 2 centrifuge at University of Tehran. The centrifuge

Scientia Iranica A (2019) 26(6), 3109{3124

Sharif University of TechnologyScientia Iranica

Transactions A: Civil Engineeringhttp://scientiairanica.sharif.edu

Centrifuge modelling of monopiles subjected to lateralloading

S. Darvishi Alamouti, M. Moradi�, and M.R. Bahaari

School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iran.

Received 5 February 2017; received in revised form 11 October 2017; accepted 5 March 2018

KEYWORDSMonopile;Lateral loading;Short pile;Centrifuge modelling;p-y curve;Secant sti�ness.

Abstract. Monopiles are the most common foundation type used for �xed-bottomsubstructures in o�shore wind installations. In an o�shore environment, the predominantload is cyclic, which a�ects the sti�ness and deformation properties of foundation systems,especially monopiles. To investigate the e�ect of cyclic loading on a short (rigid) steelmonopile, a set of displacement-controlled �g laboratory tests were designed. This paperpresents the procedure and results of eight centrifuge tests investigating monopile behaviourwhen subjected to lateral monotonic and cyclic loading. The general trend of monotonicresponse was in good agreement with the results of similar experimental studies; however,much softer behaviour was observed than that of the equivalent Winkler model on APIp-y curves. The cyclic tests focused on the sti�ness and deformation properties of a soil-pile system under fatigue loading. Increases, decreases, or no changes in secant sti�nesswere observed depending on the regime of the applied cyclic displacements, which werein contradiction to the current design methodology in which only cyclic degradation wasassumed. In uence of load cycling on cyclic bending moments along the pile shaft wasdiscussed and found to be of minor signi�cance.© 2019 Sharif University of Technology. All rights reserved.

1. Introduction

Piled foundations are frequently used in marine struc-tures to resist the lateral cyclic loading produced bywind, waves, or ship berthing. A monopile is a singlepile with a small aspect ratio (length over diameter),which rotates in rigid form instead of bends whensubjected to lateral loads [1,2]. The current O�shoreWind Turbine (OWT) design practice uses the Winklerapproach for analysis of monopile foundations. In thismethod, the pile is modelled as a beam on a set of

*. Corresponding author. Tel.: +98 21 88909468;Fax: +98 21 88911070E-mail addresses: saeed [email protected] (S. DarvishiAlamouti); [email protected] (M. Moradi);[email protected] (M.R. Bahaari)

doi: 10.24200/sci.2018.20222

nonlinear uncoupled springs as p-y curves representingsoil-pile interaction [3-6].

The main shortcoming of the current method-ology is that the p-y curves are based on empiricaltesting on the long slender piles, which are adoptedand implemented in o�shore oil and gas standards [1].However, some di�erences exist between wind turbinefoundations and those of o�shore platforms. Thehigh ratio of horizontal to vertical loading and smallaspect ratio of the piles in OWTs are the major dif-ferences. Moreover, knowledge and prediction of long-term performance of foundations in terms of sti�nessand deformation are very important in OWT monopilestructures. Short-term data on the existing structuresin the early years of operation have shown that thefundamental frequency of the structures (f0) has beenunder-predicted at the design stage [7].

Cyclic lateral loading a�ects pile behaviour in twoways; accumulation of rotation and changes in secant

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3110 S. Darvishi Alamouti et al./Scientia Iranica, Transactions A: Civil Engineering 26 (2019) 3109{3124

sti�ness [1,8]. Recent studies have shown that thee�ect of cyclic loading on a pile strongly depends onthe load characteristics and number of cycles, e.g. [1,9-12]. Several studies have investigated accumulateddisplacement and changes in sti�ness of monopilesunder cyclic loading. Long and Vanneste (1994) [9]and Lin and Liao (1999) [10] reviewed earlier studiesand proposed a new method based on �eld tests toreduce soil resistance using power law as a function ofthe number of cycles. Several authors have proposedapproaches to determining the e�ect of cyclic loadingbased on di�erent theories. Triaxial tests with theo-retical and numerical models were employed by Lesnyand Hinz (2007) [13] and Achmus et al. (2009) [14].Rosquo�et et al. (2007) [11] investigated the changein tangent sti�ness and accumulation of displacementunder lateral cyclic loading on a scaled monopile inan �g model. They observed that accumulation ofdisplacement followed a logarithmic trend.

Leblanc et al. (2010) [1] introduced new param-eters to identify the load characteristics of magnitudeand direction. Their accumulation model obeyed powerlaw as proposed by Long and Vanneste (1994) [9] andLin and Liao (1999) [10]. Klinkvort et al. (2010) [15]performed six lateral cyclic centrifuge tests on laterally-loaded piles in dense and dry sand. They observed thatcyclic loading increased the secant sti�ness and theyestimated accumulated cyclic displacement. Rudolphet al. (2014) [16] considered the e�ect of load direc-tionality on the cyclic behaviour of monopiles and con-cluded that a change in loading direction signi�cantlyincreased accumulation of displacement over the unidi-rectional loading. Although much signi�cant work hasbeen done in recent years, the lack of comprehensivedata to create general rules about the cyclic behaviourof monopoles is a major problem. For instance, Leblancet al. (2010) [1] reported only increases in monopilesecant sti�ness in sandy soil, whereas Klinkvort andHededal (2013) [12] also observed decreases underspeci�c loading patterns.

General design rules have not yet been estab-lished or adopted in design codes considering soil-pile interaction issues, speci�cally for short monopiles.To this aim, it is required to build a comprehen-sive database which includes di�erent soil and pileinformation. This database should encompass manydi�erent conditions including di�erent soil types andproperties (e.g. di�erent relative densities for sand),di�erent pile geometries (diameter, length, eccentric-ity, aspect ratio), and di�erent loading patterns incyclic behaviour. Further laboratory investigations areneeded to extend the application of the experimentaldata generated and add to the existing database onmonotonic and cyclic behaviours of monopiles. Inaddition, because of di�erent observations reported forlaterally loaded rigid monopiles, it is still needed to

improve the knowledge of this subject. This paperpresents a series of displacement-controlled centrifugetests to investigate the lateral behaviour of a shortmonopile in sand with approximate relative densityof 60%, which is considered as an average value formedium-dense sand. The data collected gives goodinformation about the monotonic and cyclic responsesof monopiles and provides further insights into themonopile load-displacement and sti�ness behaviour.

2. Methodology

2.1. Centrifuge modelling, scaling law, anddimensional analysis

In soil, especially in sand, stress-strain-strength be-haviour depends on the e�ective stress. It is expectedthat in a geotechnical centrifuge, the in situ level ofstress can reproduce approximately the same stress-strain behaviour as is found in the �eld [17]. Therefore,equivalence between model and prototype stress levelsand stress-strain-strength behaviours establishes simil-itude laws. Table 1 shows correlation between modeland prototype parameters at generated centrifugalacceleration of �g.

In all physical modelling, it is important to per-form dimensional analysis on all independent governingparameters of the modelled phenomenon. Dimensionalanalysis leads to a set of non-dimensional ratios ofgoverning parameters in order to transform modelresults into prototype scale. For this purpose, non-dimensional ratios should be identical between modeland prototype to avoid scale e�ects. On the subjectof the present study, a dimensional analysis has beenperformed by Klinkvort et al. (2013) [18]. Following isthe results of their analysis:

H 0D3 = f

�yD;LD;eD;EP IPESD4 ; �

0; Rad50

;Dd50

�; (1)

where H is applied load, D is pile diameter, y is pilelateral displacement, e is load eccentricity, Ra is pileaverage roughness, and d50 is soil average grain size.

Table 1. Scaling law in centrifuge modelling.

Parameters Scaling law

Density 1Length 1=�a

Displacement 1=�Strain 1Stress 1Force 1/ �2

Bending sti�ness 1=�4

Acceleration �a� is scaling factor.

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Table 2. Test program (in model scale).

Test ID Type No. of cycles yamax (mm) ymin (mm) Rate of app. disp.

TM1 Monotonic { 35 0 0.1 mm/sTC1 Cyclic 130 12 {5.8 0.1 HzTC2 Cyclic 100 4 {2 0.1 HzTC3 Cyclic 110 4 0 0.1 HzTC4 Cyclic 120 4 {4 0.1 HzTC5 Cyclic 100 4.5 1.5 0.1 HzTC6 Cyclic 100 3 {2 0.1 HzTC7 Cyclic 100 5 {3 0.1 Hz

ay : applied displacement.

Other parameters are well known. Thanks to centrifugetechnology, all these ratios are identical across thescale, except the last one. This ratio should be keptlarge enough to avoid scale problems.

The centrifuge tests designed in the present worksought to determine the cyclic behaviour of a sti�monopile under lateral loading. The program forthe tests consisted of one monotonic and seven cyclicloading experiments at 40 g (Table 2). Note that alltests were carried out under displacement-controlledloading. All tests were performed by Actidyn C67-2 centrifuge at University of Tehran. The centrifugebeam (radius 3.5 m) was equipped with a pendulumswinging platform that would accommodate a modelup to 1 m � 0.8 m � 0.8 m and could accelerate a one-tone package to 130 g. The centrifuge was controlled bya state-of-the-art computer management system. Theplatform radius was 3.0 m and the nominal radius was2.7 m. Further information about the centrifuge facilitycan be found in [19].

2.2. Properties and preparation of the sandsample

A rectangular strongbox 80 cm � 60 cm � 50 cm insize was used to prepare the soil sample. Firoozkuh-161 standard sand with an approximate relative densityof 60% was used. This sand is used as the standardin geotechnical testing in Iran and several researchpapers can be found dealing with the behaviour ofthis sand in di�erent states. The sand is producedby crushing of parent rocks from Firoozkuh minein the north-east of Tehran. It mainly consists in�ne- and medium-sized golden subangular particles.Further information regarding the sand properties andmechanical behaviour can be found in Farahmand et al.(2016) [20]. Table 3 compares properties of the sandwith other standard types found in the literature.

For preparation of soil samples, soil weight-volume relationships were used. Strongbox walls weredivided into 2.5 cm layers for soil compaction. There-fore, having volume of each layer of the sand, moisture

Table 3. Sand properties compared to other standardsoils.

Sand type d50 (mm) Cau emin emax Gs

Firoozkuh 161 0.30 1.87 0.574 0.874 2.658Fontainebleau 0.17 1.60 0.548 0.859 2.646Toyoura 0.18 1.54 0.597 0.977 2.650

aCu: Coe�cient of uniformity.

content (5% was used to facilitate compacting), relativedensity, and thereby speci�c weight, it was easy tocalculate weight of the required soil for compactionin each layer. The sand was poured almost evenlydistributed in the box. After pouring, it was compactedusing a manual compactor until the compacted soil�tted the speci�ed layer of the box. In this method, therelative density was not expected to be exact; however,approximate relative density of 60% was achieved withacceptable accuracy.

The scaling of the ratio of grain size to pilediameter is di�cult to achieve [17], because a modeluses the same soil as that used in the prototype,meaning that the grain size to pile diameter ratio in themodel is n times larger than the actual size. M�uhlhausand Vardoulakis [21] showed that progressive failure insmall model tests with the material same as that in theprototype was questionable. The ratio of particle size(d50) to structure size (B) should be su�ciently smallto overcome this drawback. Ovesen (1979) [22] showedthat for a vertical loaded plate, scale e�ect could beneglected if B=Dn50 > 30. If Dn50 = 0:3 mm andB = 50 mm, the ratio would be greater than 166 andthe scale e�ect would have a negligible e�ect on theresults of the present experiments.

2.3. Modelled pileThe model pile was a circular stainless steel pile withan outer diameter of 5 cm and thickness of 1.25 mm. At40 g of acceleration, the pile at prototype scale shouldbe 2 m in diameter and 5 cm in thickness in dry sand.Summary of structural properties of the modelled pileis shown in Table 4 in model scale.

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Table 4. Model pile properties.

Property Value in model scale Unit

Pile diameter 50 mm

Wall thickness 1.25 mm

Embedded length 250 mm

Load eccentricity 350 mm

Total length 750 mm

Young's modulus 207 GPa

EI 11:78� 109 N.mm2

Weight 11.2 N

Half-bridge strain gauges were attached to thepile at the six stations at distances of 6.5, 12, 17.2,21.7, 27.3, and 32.5 cm from the pile bottom. The pilebending moments were calculated at di�erent depthsfor moment calibration against voltage. Figure 1presents a schematic sketch of the test setup. In alltests, embedded length and load eccentricity were keptconstant at 25 cm (5D) and 35 cm (7D), respectively.

2.4. InstrumentationIn all tests, cyclic displacements applied by the loadingshaft were measured using a Linearly Variable Di�eren-tial Transformer (LVDT). Another LVDT was placed15 cm beneath the loading point. This extra LVDTwould help to measure pile de ections at the soil sur-face. The magnitude of the lateral load caused by theapplied displacement was measured using a load cell.The load cell non-linearity and non-repeatability were

� 0:03%R.O. and � 0:02%R.O., respectively (R.O.denotes rated output). Testing and pile movementswere �lmed by a set of cameras for monitoring thetest procedure. Agilent E1422 data acquisition systeminstalled in the centrifuge was used to collect and storeoutput data. Sampling rate was 0.01 s for monotonicand 0.05 s for cyclic tests. Low-pass Butterworth�ltering type was used for data processing.

All the measurement devices were calibrated sev-eral times during the work to ensure their linearresponse. Load cell was calibrated using di�erentknown weights applied and measuring output voltages.Similar method was used for LVDTs with knowndisplacement. For calibration of strain gauges of thepile, the pile was placed on two simple supports anddi�erent weights were applied to the middle of thebeam. Then, the calculated moments at the half-bridgestations were calibrated against voltages.

2.5. Loading and tests procedureBefore cyclic testing, a monotonic loading test was per-formed to make an approximation of the monopile load-bearing capacity. Recent studies [1,12] have reportedthe e�ect of load characteristics and the number of loadcycles on monopile cyclic behaviour. They de�ne twonon-dimensional parameters as follows:

�b =Maximum Load

Ultimate Capacity;

�c =Minimum LoadMaximum Load

: (2)

The load used in this de�nition applies to either

Figure 1. (a) Schematic sketch of test setup. (b) Strain gauge locations.

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horizontal force, bending moment, or any parameterrepresenting lateral demand on the pile.

Note that in an actual o�shore environment, theload level is not constant and varies from cycle to cycle.In the cyclic tests, except TC1, the load levels werechosen to re ect the fatigue limit state. The primarycyclic loads causing high cycle fatigue in OWTs areabout one-third the ultimate capacity of the pile [1].

A new stepper motor was programmed to gen-erate controlled displacement. The rotation of thestepper shaft was transferred to a ball screw by meansof a toothed belt. The ball screw transformed ro-tation to translation and the translational movementwas conveyed to a loading shaft, which displaced the

monopile. Figure 2 shows the main components andassembly of the loading device. The stepper motor wasable to create displacement in ramp, stair, triangular,and sinusoidal patterns. A combination of ramp andsinusoidal patterns was used. Only the ramp patternwas used to change the cyclic ratio at the beginningof loading. It is noted that the accuracy of thestepper motor was 2000 pulse/round and a calibrationcoe�cient of 0.365 was used to convert round to mm ofdisplacement. Complete setup of the present work canbe seen in Figure 3.

For each test, the soil sample was newly preparedas discussed previously in Section 2.2. Then, loadingframe was installed on the strongbox and the position

Figure 2. Loading device: (a) Stepper motor, (b) ball screw, (c) wagon, and (d) device assembly.

Figure 3. Complete test setup and instrumentation.

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of the loading shaft was adjusted. Afterwards, thepile was driven gradually into the soil by a hammervertically until the desired penetration was achieved.After pile installation, loading shaft was attached tothe pile with a hinged round clamp. The preparedheavy model was moved to the machine basket witha small crane. Before spinning the basket, all cablescoming from strain gauges, LVDTs, and loadcell wereconnected to data logger channels. Also, steppermotor was triggered by attaching its wires to a powersupply and command drive. Then, the centrifuge wasaccelerated up to 40 g and �nally, displacements wereapplied to the pile.

2.6. Dry versus saturated sandAll tests were carried out under dry conditions. Themoisture content of 5% was used to facilitate compact-ing; this value was not expected to a�ect the test resultsbased on previous experiences in the physical modelingand centrifuge laboratory testing on wet and dry sand.As the study mainly deals with o�shore wind turbineswith their monopile foundations installed in saturatedsoils, scaling factor for equivalent saturated conditionis also introduced. The procedure proposed by Lie etal. (2010) [8] was used to scale the test results undersaturated conditions. In this procedure, it was assumedthat no pore pressure was generated during loading ande�ective stress under saturated conditions would beequivalent to that under dry conditions after adjustingthe geometrical scaling factor. In other words, theincrease in gravitational acceleration was not equalto the geometrical scaling factor. This approachwas validated by Klinkvort and Hededal (2014) [23],who conducted a series of identical tests on dry andsaturated sand and compared the results. By de�ninggeometrical scaling factor, Ns, and the increase ingravitational acceleration, �, the prototype parametersunder saturated conditions would correlate with themodel parameters under dry conditions using the newgeometrical scaling factor as follows:

Ns = 0dry

0sat� �: (3)

It should be noted that, accordingly, the tests are onlyvalid for completely drained conditions.

2.7. Limited number of cyclesDuring the lifetime of an o�shore structure, about 107

load cycles are expected from environmental loading.These cycles can vary one by one in magnitude,direction, cycling, and frequency; however, an actualo�shore environment cannot be simulated in the lab.Testing for cycle numbers is time-consuming and ex-pensive, especially in centrifuge modelling. It is usualto carry out tests with a limited number of cycles andthen, extrapolate the results for the target numbers.

Note that the trend of results based on a limitednumber of cycles can change after covering a largernumber of cycles [16] and this requires examinationin future studies. In the present study, limitationsrequired that the number of cycles be limited to 130.

2.8. Limitations of test setup and experimentsIn physical modelling investigations, exact prototypecondition is almost impossible to replicate and someapproximations have to be accepted [17]. Limitedspace of the centrifuge basket is a restriction on themodel size. This imposes limitation on the strongboxdimensions and consequently, further limitations on themonopile geometry including diameter, embedment,and load eccentricity. In real o�shore wind turbines,the applied load eccentricity is considerably high;therefore, we decided to take 1D clearance below piletip [24,25] to have maximum load eccentricity. Exceptpile self-weight, there was no additional counter weightor vertical load on the pile. Therefore, consideringpurely lateral behaviour and small vertical stressesbeneath the pile, it was expected that the pile responsewould not be in uenced by the bottom boundary [25].The pile was installed at 1 g by driving with ahammer weighing 1.455 kg. Installation at 1 g wouldnot reproduce prototype stress condition around pile;nevertheless, this di�erence would not a�ect the pilelateral response, signi�cantly [26]. Box boundariesmight a�ect pile response. Liu et al. (2011) [27]showed that the soil zone at most 6 � 9 times thepile diameter would be deformed in loading direction.Considering box length (80 cm) and the pile diameter(5 cm), at least the distance of 6D (30 cm) betweenouter face of the pile and inner face of the box waskept in all tests to minimize boundary e�ects. Anotherdrawback of centrifuge modelling is non-uniform �eldof acceleration in the whole model. This is becausethe inertial acceleration (r!2) is proportional to radiusof rotation (r), which varies throughout the model.The error coming from this limitation will be negligible(less than 3%) if the ratio of model depth (hm) toe�ective rotational arm (Re) is less than 0.2 [17]. Inthe present study, Re is 2.7 m and hm is 0.3 m, givinghm=Re = 0:11; therefore, error of vibrational g-level isnegligible.

3. Results and discussion

The results of the test are presented in prototype scale.To facilitate comparison between the results regardlessof dry or saturated condition of the sand, normalizedparameters are used as listed in Table 5. Here, the pilediameter, D, and sand e�ective density, 0, are chosenfor normalization.

3.1. Monotonic testMonotonic testing was performed at a constant loading

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Table 5. Non-dimensional parameters.

Horizontal force ( ~H) H 0D3

Bending moment ( ~M) M 0D4

Displacement yD

Aspect ratio LD

Load eccentricity eD

Figure 4. Monotonic test results in comparison withAPI/springs Winkler model, Alderlieste et al. (2011) [25],and Klinkvort and Hededal (2014) [23].

rate of 0.1 mm/s to ensure drained conditions (pseudo-static). The results of monotonic testing on normalizedpile de ection at the soil surface are shown in Figure 4.Results are compared with two similar experimentalstudies as well as an equivalent Winkler model; theirspeci�cations are shown in Table 6. In Winkler model,soil was modelled using p-y curves recommended byAPI code [28]. These curves relate soil reaction p topile local horizontal displacement y in di�erent depthsvia the following equation:

p = APu tanh�KzyAPu

�; (4)

where K is initial modulus of subgrade reaction andA is an empirical constant given for monotonic loadingas:

A =�

3� 0:8zD

� � 0:9: (5)

Pu is ultimate soil reaction calculated at a given depthas:

Pu = min

((C1z + C2D) 0zC3D 0z

(6)

For the Winkler analysis, C1, C2, and C3 are chosen3.3, 3.7, and 63, respectively. Initial modulus Kis considered 26.2 MN/m3 according to API sugges-tion for the sand below water table (note that theWinkler methods correspond to equivalent saturatedconditions). There are three main di�erences betweenWinkler/API and the test results, including degreeof nonlinearity, sti�ness of the soil-pile system, anddetermination of bearing capacity; Winkler/API showssti�er, more linear response, with a sudden failurecorresponding to the ultimate capacity, than the testresults do. It can be concluded that the sti�nesses ofAPI p-y curves are overestimated for the studied shortmonopile in sand and the shape (or equation) of thesecurves does not re ect the true nonlinear response ofsuch monopiles.

The results are also compared with those of simi-lar experimental studies conducted by Alderlieste et al.(2011) [25] and Klinkvort and Hededal (2014) [23]. Itshould be noted that these studies have been carriedout under various test setup and, therefore, direct anddetailed comparison is not possible; because there aremany parameters a�ecting the results including pilediameter, aspect ratio, pile-soil sti�ness, load eccen-tricity, and soil condition (density and compaction).For example, previous studies have concluded that thebehaviour of cohesionless soil depends signi�cantly onthe density of the material used [29]. However, somegeneral remarks can be given as follows. The com-parison indicates similar general nonlinear responsesbetween three experimental results, but various sti�-ness and ultimate capacities. Very sti� response andremarkably higher lateral capacity of Klinkvort andHededal (2014) [23] highlights the e�ect of 1D morepenetration depth and 30% increase in relative densityon monopile behaviour. The present test conditionhas the most similarity to that of Alderlieste et al.(2011) (almost identical L=Ds and relative densities);however, ultimate pile capacity was somewhat largerin the results of Alderlieste et al. (2011) [25] becauseof the smaller load eccentricity, despite identical L=D(11/2.2=5) with the current study.

Table 6. Speci�cations of the present study compared to two similar works.a

Test D L e Dr (%) Sand type

Present study 2 (3.2b) 5D 7D � 60 Froozkuh-161

Alderlieste et al. 2011 [25] 2.2 5D 2.18D 58-62 d50 = 0.24 mm

Klinkvort and Hededal 2014 [23] 3 6D 10.5D 90 FontainebleauaD: diameter; L: embedded length; e: load eccentricity; Dr: relative density;b Equivalent saturated condition.

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Figure 5. Pile bending-moment diagram for di�erentnormalized horizontal loads; experimental results versusAPI/springs Winkler model.

The preliminary calibrations for the half-bridgecoupled strain gauge arrangement were used to producea diagram for distribution of bending moments alongthe pile length. This distribution was also comparedwith the results of the numerical Winkler model usingAPI recommendations for p-y formulation (Figure 5).The results are presented for some typical normalizedhorizontal load levels. The general shape of the curvesshows the adequacy of the strain gauge stations. Withincreasing soil depth, bending moments increased untilreaching their maximum values and then, decreasedgradually. The location of the maximum value becamedeeper as the load level increased. This implies thatby increasing the applied load, upper layers of thesoil reached their ultimate resistance. Although themeasured moments were in good agreement with thenumerical Winkler results, the depths of maximumvalues in Winkler model were somewhat lower thanthose in the test measurements.

Experimental p-y curves can be derived fromthe measured moments. The �fth-order polynomialfunction introduced by Wilson (1998) [30] was used to�t discrete moments (Eq. (7)). Double di�erentiatingand double integrating of the �tted equations givethe soil reaction, p, and displacement of the pile y,respectively, at any desired depth, z. Note that theprototype values in the equivalent saturated sand (i.e.D = 3:2 m) were used here.

M(z) = a+ bz + cz2:5 + dz3 + ez4 + fz5: (7)

The derived data are illustrated in Figure 6 together

Figure 6. Derived, �tted, and API p-y curves for themonotonic test (D = 3:2 m, and Dr �60%).

with the corresponding API p-y curves for four typicaldepths. The derived p-y points were also �tted toa hyperbolic function �rstly proposed by Kondner(1963) [31] and then, identi�ed by Georgiadis et al.(1992) [32] (see Eq. (8)).

p =y

1ki + y

pu

; (8)

where ki is the initial sti�ness and pu is ultimate soilreaction. As it was not possible to identify pu fromthe test, an estimation of 1.2 times that proposed byAPI was assumed for pu, which gave the best resultsfor �tting curves. Looking at the graph, the hyperbolicfunction seems to well �t the test data. API p-y curvesobviously failed to predict real soil springs in terms ofboth formulation and initial sti�ness values, as theyhighly over-predicted the soil sti�ness. To quantifythis, the calculated values of ki are plotted and com-pared with those of API for the present sand in satu-rated condition (Figure 7). It can be seen that ki variesalmost linearly with depth in agreement with the APIsuggestion; however, the API estimation for modulusof subgrade reaction is about 8 times larger than thatof the present study. Looking at the load-displacementresponses (Figure 4) and the corresponding p-y curves(Figure 7), one may conclude that the general load-displacement response of the pile almost follows thegeneral shape (or formulation) of the p-y curves.

Normalised pile de ections along depth underthe various horizontal loads are provided in Figure 8.As shown, the pile behaves in a rigid manner. Asdistinguishing limits for rigidity of a pile, the followingcriteria are often used for sandy soils, which often have

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Figure 7. Initial sti�ness variation in the monotonic test(D = 3:2 m, and Dr �60%).

Figure 8. Normalized pile de ections along depth fordi�erent normalized load levels.

linearly varying modulus of subgrade reaction withdepth [33,34]:

LT� 2; Rigid piles;

LT� 4; Slender piles; (9)

where L is the pile embedded length and T is the rel-ative sti�ness factor introduced by Reese and Matlock

(1956) [3]:

T = (EP IPnh

)15 : (10)

nh is coe�cient of subgrade reaction modulus. The pilewill be considered rigid if nh is:

nh � 32EP IPL5 : (11)

For the present case in equivalent saturated condition(L = 16 m, D = 3:2 m, t = 8 cm, and E = 207 GPa),the pile behaves in a rigid pattern if nh � 6. Thevalue of nh for the present study is estimated to be 3.33(Figure 7), which denotes that the pile can be classi�edwithin rigid category.

3.2. Cyclic testsNon-dimensional results of the four representative testswere used to investigate the load response and load-displacement behaviours of the monopile.

Figure 9 shows the monopile load response versusmodel time for representative tests TC1, TC2, TC3,and TC6. An increase in time (or number of loadcycles) caused a change in the minimum and maximumloads. In all tests, the rate of change was rapid duringthe �rst few cycles (maximum of 20 cycles for TC1).After about 100 cycles in all tests, the variation inload magnitude became very slow. Di�erent rates ofchanging in applied loads were observed for di�erentloading patterns. This was due to restructuring ofthe soil body and sand owing around the pile un-der applied cyclic displacements. Under load controlcondition, this restructuring and sand owing causedaccumulation of irreversible displacement of pile inloading direction [35].

3.2.1. Load-displacement response and soildeformation

Figure 10 shows the load-displacement responses ofthe pile in non-dimensional form. Displacement wasmeasured at the load point. All tests showed nonlinearhysteretic behaviour for the soil-pile system. Fortests TC1, TC2, and TC6 with ymin=ymax < 0, asoftening portion could be observed in the response.This softening portion was remarkable in TC1 wherethe maximum displacement amplitude was applied.Generally, components of soil-pile interaction a�ect soilload-displacement response. These components aremainly resistance of the soil against pile moving, gapdevelopment (sometimes �lling by sand owing), anddrag force (moving the pile in the gap) [36,37]. Itseems that the softening is the result of mechanicaldegradation under cyclic loading [38], which consists ingap development and local plastic deformations in thesoil body. In all cases, nonlinearity in terms of elasto-plastic response was observed, which should be taken

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3118 S. Darvishi Alamouti et al./Scientia Iranica, Transactions A: Civil Engineering 26 (2019) 3109{3124

Figure 9. Time history of the resultant applied loading for cyclic tests.

Figure 10. Hysteretic load-displacement curves for cyclic tests.

into consideration in the design stage. From the pointof view of dynamics, this nonlinearity would result inchanges in the system sti�ness and consequently, thenatural frequency depending on applied load levels.

Despite overall nonlinearity and elasto-plastic re-sponse, loading and unloading curves were close tolinear for small applied cyclic amplitudes. This nearlylinear loading and unloading region suggests that the

sti�ness of the soil-pile system remains linear if the loadlevel remains small. This is in agreement with Zaaijer(2006) [39], who showed that linear sti�ness matrixmodels of OWT foundations could be used for dynamicmodelling to provide enough accuracy when comparedwith fully nonlinear soil spring models correspondingto loading conditions that re ected fatigue limit state.

Figure 11 shows soil deformation around the pile

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Figure 11. Soil deformation around pile head after cyclic testing: (a) TC1, (b) TC2, (c) TC3, and (d) TC6.

head. Conical depressions were observed around thepile after all tests because of the dryness of the sandand its low relative density. Similar to softening inhysteretic curves, size of the depression is remarkablefor TC1, where displacement amplitude is large com-pared to other tests. Note that when the circular holeis formed, the embedded portion of the monopile willdecrease and a�ect the load-displacement response ofthe pile. It should be noted that other phenomena,including change in soil properties (e.g. relative den-sity), local plasticization, gapping, and back�lling thegap, will a�ect the results. However, as the resultsof the following sections will demonstrate, degree ofin uence of each phenomenon strongly depends onloading pattern.

3.2.2. Cyclic secant sti�nessIn uence of load cycling and pattern was investigatedon sti�ness behaviour of the monopile-soil system.Figure 12 shows how the secant sti�ness was measuredin the present displacement-controlled cyclic load tests.The secant sti�ness of the system was calculated at theload point, i.e. at 7D above the sand surface. Non-dimensional secant sti�ness in the Nth cycle is de�nedas:

~KN =~Hmax;N � ~Hmin;N

~ymax � ~ymin: (12)

The calculated non-dimensional secant sti�ness wasnormalized using non-dimensional secant sti�ness ofthe �rst cycle, i.e. ~K1. The measured data werealso �tted to a logarithmic evolution expressed as the

Figure 12. De�nition of cyclic secant sti�ness.

equation below:

~KN~K1

= 1 + a ln(N); (13)

where the coe�cient a is the changing rate. Table 7summarizes the calculated parameters of logarithmic �tfor the cyclic tests. The secant sti�ness versus numberof cycles for all tests is shown in Figure 13. Fittedcurves are depicted with continuous black line andrepresentative measured data are plotted by points. Itis shown that most tests well follow the logarithmictrend. However, a degree of scattering is seen in

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3120 S. Darvishi Alamouti et al./Scientia Iranica, Transactions A: Civil Engineering 26 (2019) 3109{3124

Figure 13. Measurements and logarithmic �t for normalized cyclic secant sti�ness.

Table 7. Calculated parameters for logarithmic �t.

Test ymin=ymax K1 a b(ymax) b(ymin)

TC1 {0.48 43 0.055 0.0084 0.0324TC2 {0.50 92 {0.0046 {0.0049 0.0041TC3 0 105 {0.0154 0.0009 0.0056TC4 {1 67 0.0215 0.0047 0.0029TC5 0.33 98 0.0004 {0.0009 0.0409TC6 {0.67 89 0.0188 {0.0069 {0.0078TC7 {0.60 77 0.0077 0.0077 0.0133

TC3 and TC5, where ymin=ymax > 0. Increasing,decreasing, and invariable trends in secant sti�ness canbe observed in the results. This makes prediction ofthe long-term behaviour of the monopile-soil systemmore challenging. Recent studies [1,12] have solvedthis problem by quantifying the cyclic load content inboth direction and magnitude. Although these datamay not be enough to achieve a general conclusion, itcan be stated that in one-way applied displacementsor initial one-way loading condition (i.e. ymin=ymax >0), increase in secant sti�ness is unlikely. In two-way applied displacements or initial two-way loadingcondition (i.e. ymin=ymax < 0), both increasing anddecreasing trends are observed in the results.

The greatest increase occurred in test TC1 towhich the largest ymax=yult was applied. In most tests,changes in cyclic secant sti�ness after cycle 50 were

very slow and the greatest change was observed in the�rst 10 cycles.

At this point, it is worth noting that the currentdesign codes such as API [28] and DNV.GL [40]consider the e�ect of cyclic load only by decreasingthe soil ultimate reaction. It is obvious that theresults of the present study are in contradiction to theassumption of these methods, i.e. always reducing thepile secant sti�ness under cyclic load.

3.2.3. Cyclic bending momentsMaximum bending moments of the pile shaftOne key parameter in the structural design ofmonopiles is maximum bending moment, which iscritical to sections such as weld connections that areimportant to fatigue design. It is important to knowhow the maximum bending moment will be a�ectedby the cyclic process on the pile. To investigate this,dimensionless moment arm is de�ned as follows:

~dN =~MN~HN

; (14)

It is obvious that ~dN is always> eD = 7. This de�nition

allows eliminating the e�ect of variation of appliedload on the maximum bending moments and therefore,considering only the e�ect of cycling process on theresults. The relative maximum ~dN for the pile shaftunder maximum and minimum applied displacements(maximum ~dN is measured separately for ymax and

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Figure 14. Measurements and logarithmic �t for normalized maximum moment arm of the pile when maximum andminimum displacements are applied.

ymin) against the number of cycles is presented for fourtypical tests. The results are �tted to a logarithmicevolution de�ned as:

~dN~d1

= 1 + b ln(N): (15)

The values of b from curve �tting are presented inTable 7. As the graphs in Figure 14 show, logarithmicvariation is present in most cases, but this is not ageneral �nding. E�ect of cyclic load on variation ofmaximum bending moment is observed to be less than5% in most tests, except TC7 at ymin. Evolution ofmaximum bending moment was investigated by cyclicload-controlled testing by Rosquo�et et al. (2007) [11].They concluded that the change in maximum bendingmoment was less than 8%, which is in agreement withthe results of the present study. Therefore, it can beconcluded that the e�ect of cyclic load on maximumbending moment will not be of great concern in designpractice.

Bending moments distribution along the pile lengthNormalized moments measured at each of the straingauges are shown in Figure 15. M is the measuredbending moment when the maximum applied loadoccurs during a load cycle and M0 is the correspondingapplied bending moment at the pile head. As it isshown, the general shape of the bending pro�le along

the pile length remains relatively unchanged despitechanging in the applied cyclic characteristics. However,the location of the maximum bending moment isexchanged between z

D = 0:66 and zD = 1:56 in all tests

except TC3.

4. Conclusion

A series of centrifuge tests were conducted to in-vestigate the behaviour of sti� monopiles on sand.One test was performed under monotonic conditionand seven tests were cyclic. Displacement-controlledcyclic loading was applied to the monopile. In alltests, relative density of the sand was approximately60% and the embedded pile length of 5D and loadeccentricity of 7D were kept constant during testing.Cyclic tests focus on loading levels of the fatigue limitstate. The monotonic test results were comparedwith those of the numerical Winkler beam on APIrecommendation springs and two similar laboratorytests. Some conclusion remarks can be summarizedas:

� Experimental results gave consistent results, inagreement with the existing literature; however,the Winkler/API springs model predicted a sti�erresponse than the present centrifugal test did. Also,

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3122 S. Darvishi Alamouti et al./Scientia Iranica, Transactions A: Civil Engineering 26 (2019) 3109{3124

Figure 15. Bending moment distribution along pile when maximum displacement is applied. M0 is correspondingmoment at the pile head.

nonlinear response was more pronounced in labora-tory tests than in API/Winkler;

� The p-y curves derived from bending moment mea-surements of the monotonic test well �tted a hy-perbolic function, while the tangent hyperbolic APIp-y curves showed a larger value of initial modulusof subgrade reaction (about 8 times larger than thatin this study);

� In some cyclic tests, di�erent rates of change weremonitored for applied loads for maximum and mini-mum applied displacements due to plastic deforma-tions in the soil. The hysteretic behaviour in load-displacement curves signi�ed energy dissipation inthe soil-pile system;

� De�nition of secant sti�ness was used to study thesti�ness of the soil-pile system. The results showedthat the cyclic sti�ness of the system stronglydepended on the applied cyclic displacement char-acteristics and degradation; almost no variation andan increase in sti�ness occurred;

� Most tests followed a logarithmic trend. The resultsof tests with one-way applied cyclic displacements(ymin=ymax > 0) showed almost no increase insecant sti�ness. In cases with two-way applied cyclicdisplacements, both decrease and increase in thesti�ness were observed. Maximum increase in the

secant sti�ness occurred for the case of ymin=ymax <0 with maximum ymax=yult;

� It was found that the load cycling e�ect on thepile maximum bending moment was not remarkable.The maximum bending moment of the pile shaftchanged to less than 5% in all cases except one.Also, the moment distribution along the pile wasless a�ected by the cycling process.

Acknowledgements

This work was carried out at the Physical Modellingand Centrifuge Laboratory of the Department of SoilMechanics and Foundation Engineering, School of CivilEngineering, University of Tehran. The authors wouldlike to thank all the experts and personnel at thelaboratory, especially Mr. Salimi and Mr. Jabbarzade,for their helpful assistance.

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Biographies

Saeed Darvishi Alamouti is now a PhD candidatein Marine Structures Engineering at School of CivilEngineering, College of Engineering, University ofTehran, Iran. He received his BSc in Civil Engineeringfrom University of Tehran in 2010. He was grantedMSc straight entrance for talented BSc students andreceived his MSc in Marine Structures Engineeringform University of Tehran in 2012. He is accomplishinghis PhD thesis on the subject of o�shore monopile windturbines behavior and has published and submittedjournal and conference papers on this subject. Hisresearch interest and professional career include analy-sis and design of coastal and o�shore structures, portengineering, dynamic analysis, p-y methods for soil-pileinteraction, and o�shore wind turbines.

Majid Moradi is an Associate Professor in theSchool of Civil Engineering, College of Engineering,University of Tehran, Iran. He received his BSc inCivil Engineering in 1989 and MSc in GeotechnicalEngineering in 1992 both form University of Tehran,and PhD in Geotechnical Engineering from Universityof Manchester, UK, in 1999. He has broad experi-ence in physical modelling in geotechnics, especiallyemploying geotechnical centrifuge facility. Moreover,he has supervised numerous MSc and PhD studentswith the research subject of the physical and numericalmodelling. He is author and co-author of severalresearch papers in the �eld of geotechnical engineering,especially physical modelling with centrifuge facility.

Mohammad Reza Bahaari is a Professor in theSchool of Civil Engineering, College of Engineering,University of Tehran, Iran. He received his BScin Civil Engineering in 1986 and MSc in StructuralEngineering in 1989 both form Sharif University ofTechnology, Tehran, Iran, and PhD in Solid Mechanics(Structures) from University of Waterloo, Waterloo,Ontario, Canada in 1994. His research area mainlyincludes o�shore structures and sea lines analysis andperformance, steel structures, beam to column connec-tions, and multi-planar tubular connections. He alsohas broad experience in o�shore industry, especiallySouth Pars Gas Field development projects. He isauthor and co-author of several research papers in the�eld of structural and o�shore engineering.