Aalborg Universitet

Response of a stiff monopile for a long-term cyclic loading

Lada, Aleksandra; Gres, Szymon; Nicolai, Giulio; Ibsen, Lars Bo

Publication date:2014

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Citation for published version (APA):Lada, A., Gres, S., Nicolai, G., & Ibsen, L. B. (2014). Response of a stiff monopile for a long-term cyclic loading.Department of Civil Engineering, Aalborg University. DCE Technical Memorandum No. 45

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ISSN 1901-7278

DCE Technical Memorandum No. 45

Response of a stiff monopile for a long-term cyclic loading

Aleksandra LadaSzymon GresGiulio NicolaiLars Bo Ibsen

DCE Technical Memorandum No. 45

Response of a stiff monopile for a long-term cyclic loading

by

Aleksandra Lada Szymon Gres Giulio Nicolai Lars Bo Ibsen

June 2014

© Aalborg University

Aalborg University Department of Civil Engineering

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Published 2014 by Aalborg University Department of Civil Engineering Sohngaardsholmsvej 57, DK-9000 Aalborg, Denmark Printed in Aalborg at Aalborg University ISSN 1901-7278 DCE Technical Memorandum No. 45

Response of a stiff monopile for a long-term cyclic loading

Aleksandra Lada Szymon Gres Giulio Nicolai Lars Bo Ibsen

Aalborg University

Department of Civil Engineering

Abstract

In the Geotechnical Laboratory at Aalborg University a number of small scale tests havebeen performed to analyze the behavior of a rigid monopile subjected to a long-term cycliclateral loading. Only a dense state of sand is considered. A cyclic loads cause the permanentdisplacement of soil and rotation of a pile, effecting in the accumulated rotation and the changein soil-pile stiffness. These aspects, as poorly accounted in current standards, require thoroughanalysis. The design methods and a current state of art in cyclic loading field is discussed. Oneof the aims of the article is to validate the method established by LeBlanc (2010) in order toconfirm its reliability. In addition, the results of performed tests are presented to obtain thefurther conclusion on the cyclic behavior of monopiles.

1 Introduction

In the past few years a strong impact has beenput on the contribution of the renewable en-ergy sources in the total energy consumption.According to the statistics, the wind poweris the leading renewable energy resource inNorthern Europe. In Denmark, the data showsthat wind energy contributes 27% to totalelectricity consumption and by 2025 it shouldrise to 50% [EWEA, 2013]. Among the windenergy structures the offshore wind turbines,OWT, withstand the most harsh and variousenvironmental conditions, therefore a stronginfluence should be put on their design andthe cost optimalization.

The foundation concept for OWT structures isvery dependent on the site parameters. Thereare several types of foundations used: grav-ity based foundation, monopile foundation,

jacket, tripod foundation and bucket founda-tion. For the average water depth, 10-30 m, themost common type of a foundation is a steelmonopile. It consists of a large diameter steeltube driven directly into the seabed and con-nected with a tower through a transition piece.Currently used monopiles have diameters inrange 4-7 m and slenderness ratio around 5.Average length of a monopile foundation is15-40 m.The monopile foundation concept for offshorewind turbines originates from the offshore oiland gas sector. However, the physical behav-ior and the loading type differ. An offshorewind turbine structure is exposed to a stronglong-term cyclic lateral loading through it’slifetime due to environmental loads. The num-ber of loading cycles that a structure mustwithstand varies depending on the situation.Storms cause approximately 1000 - 5000 cy-cles, where the FLS is assessed for 107 cycles.

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As a consequence, it leads to rotation of amonopile and rearrangement of soil particles,causing changes in the natural frequency of asoil-structure system. As a result, it stronglyinfluences the design criteria of all parts of awind turbine. Hence the main design factorfor OWT is serviceability limit state and along-term cyclic lateral loading contributes topermanent deformations in soil and changesin the soil stiffness, therefore it is essential topredict the effects of horizontal loading onmonopile foundation.The 1g tests have being performed in theGeotechnical Laboratory at Aalborg University.A high-quality experimental equipment allowsto perform static and both one-way and two-way cyclic tests for the pile under differentlong-term horizontal loading, with accuratedisplacements measurements.

In the article the results of tests performedby LeBlanc et al. [2010] are compared withthe new test results in order to confirm thereliability of used methods. Another aim of thearticle is to draw further conclusion regardingthe behavior of cyclic loaded monopiles.The current research was started by M.G.Onofrei et al. [2012] and their results, amongothers, are used in further analysis.

2 Current design standards

Current design standards for monopile foun-dations embedded in sand are based on theempirically derived p-y curves approach,[API,2005] and [DNV, 2011]. The approach wasoriginally presented by Reese et al.[1974] andsubsequently improved and re-formulated byMurchison and O’Neil [1984] by the full scaletests carried out on the Mustang Islands. Phys-ically, p-y curves implemented to Winkler ap-proach are described as series of uncoupledsprings, showing a non-linear relation betweenthe lateral displacement of the pile and the soil

resistance. A non-linear soil behavior corre-sponds to the subgrade reaction modulus func-tion. The numerical solution to this problem isprovided by solving the 4th order differentialequation for a beam deflection.Recent design regulations define hyperbolicformulation for constructing the non-linear p-y curves for monopiles in sand, dependent onthe ultimate soil resistance and the soil stiff-ness.

p(y) = A · pu · tanh(

k · zA · pu · y

)(1)

whereA The loading coefficientk The initial modulus of subgrade reactionpu The ultimate soil resistancez The soil depth

For a cyclic lateral loading coefficient A isequal 0.9. This indicates that the ultimate soilresistance is reduced. The method was empir-ically derived from few full scale test of veryslender, flexible piles (L/D = 34.4). Currentlyused monopiles for OWT have the slendernessration around 5. According to Poulos & Hull[1989] a pile behaves as a rigid when the equa-tion (2) is fulfilled, whereas the flexible pilebehavior is expected for piles that satisfied theequation (3), [Sørensen et al., 2012].

L < 1.48 ·(

Ep Ip

Es

)0.25(2)

L > 4.44 ·(

Ep Ip

Es

)0.25(3)

For offshore steel monopiles in dense sandthese expressions are presented in Figure 2.1.A thickness of a monopile wall is expressed asa function of a pile diameter, t = D/80. Thelimit values of Young’s modulus for the densesand, Es, are considered.

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Figure 2.1: Criterion for a pile behavior

Even though, the currently used piles arenot precisely fitted to rigid behavior, unques-tionable they cannot be analyzed as flexible.Presently, the monopiles used offshore are con-sidered as rigid. The difference in those twobehavior of laterally loaded pile is presentedin Figure 2.2. Due to different deformationpattern the soil-pile interaction changes, whichcould possibly influence the p-y curve formu-lation.

Figure 2.2: Difference between the rigid and theflexible pile behavior [Sørensen et al., 2012]

In addition, OWT during its lifetime is sub-jected to a large number of cycles leading toaccumulated rotation and hardening (or soft-ening) of the soil. Moreover, the pile rotationand changes in soil stiffness are dependent onthe direction and the magnitude of loading,which is presented hereafter. However, the

p-y curve formulation neglects the influenceof these loading parameters. Therefore currentdesign standards are not reliable in describingthe long term cyclic effects on a rigid monopilefoundation. Methodology for cyclic loadedpiles still requires further investigation.

3 State of art

Recently a number of research have been con-ducted in order to estimate the influence of acyclic lateral loading on a monopile founda-tion. The number of proposed methods is vast,from full scale tests to the advanced numeri-cal models and different kind of small-scaleexperiments. Some of the studies related toanalyzed problem are presented.

Little & Briaud [1998] conducted researchfocuses on effects of a cyclic loading on pileslateral displacement. Obtained results arebased on 6 full scale tests on slender pileswith different material properties such as re-inforced concrete, pre-stressed concrete andsteel. These piles were subjected to 10 − 20number of cycles. The data was analyzed byusing the cyclic p-y curve approach presentedby Little & Briaud [1987], which describes apower law dependency between the numberof cycles and the pile displacement.

yN = y1 · Nα (4)

whereyN The lateral displacement after N cyclesy1 The lateral displacement after 1st cycleα The cyclic degradation parameter

Results from research lead to the followingconclusions:- the traditional p-y curve approach overesti-mates a pile displacement during cyclic load-ing,- a pile displacement obtained by the cyclic p-ycurve approach are undervalued in compari-

7

son to the measured data,- a pile-soil stiffness has a major influence onsoil displacements,- a soil densification occurs after the first seriesof cycles (around 10 cycles) resulting in a stifferresponse during the second series.

Long & Vanneste [1994] analyzed results of34 full scale tests conducted in the TampaBay, Florida, in order to investigate effectsand parameters influencing a pile responseto a repetitive lateral loading. Piles were sub-jected to varying number of cycles (50-100cycles). The invented method includes theeffects of loading characteristics, a pile installa-tion method and a soil density. The equation(5), based on Little&Briaud solution, involvesdeterioration of a static p-y curve resistance toaccount all mentioned effects.

pN = p1 · N(α−1)t (5)

wherepN The soil resistance after N cyclesp1 The soil resistance after 1st cycleα The degradation factort The degradation parameter

A pile deflection obtained by using deterio-rated static p-y curve method is more accu-rately fitted to full scale tests than deflectioncalculated by using the standard p-y curveapproach.

Lin & Liao [1999] conducted a study in eval-uating a strain accumulation for repetitivelaterally loaded piles in sand. The datawas obtained from 20 full scale tests per-formed for piles with varying slenderness(L/D = 4.1 − 84.14), number of cycles be-tween 4 − 100 cycles and different installationmethods. The results confirmed that the cyclicstrain ratio is determined by the load charac-teristics, the pile installation method, the soilproperties and a relation between soil/pilestiffness. By definition of strain, cyclic strainratio can be used to calculate pile head dis-

placement ratio as following:

εNε1

= 1 + t · ln(N) (6)

whereεN The soil strain after N cyclesε1 The soil strain after 1st cyclet The degradation parameter

The formula was additionally validated by 6full scale tests. The predicted and measureddisplacements were in a good fit for the mostof cycles, however during the last stage of load-ing there were some differences. It is assumedthat it was caused by an increase of the soildensity with the number of cycles.

LeBlanc et al. [2010] introduced an innovativeapproach based on 1g small-scale laboratorytests, where the predicted accumulated rota-tion and the change in stiffness of a pile-soilsystem were analyzed in relation to the loadcharacteristics and the soil density. The testedpile was subjected to 8 000 - 60 000 number ofcycles in realistic time frame. Different loadingcombinations were analyzed. Obtained resultswere scaled to the full scale through scalinglaw, allowing an accurate comparison to otherresults from full-scale tests.The difference in the isotropic stress level be-tween a small scale and a full scale test wasincluded. A corresponding friction angle wasachieved by lowering the relative soil density.The influence of the effective vertical stresswas considered in shear modulus calculations.This experiment was conducted on a mechani-cal rig, where the cyclic loading characteristicswere controlled by a system of pulleys andwires between the pile and weight hangers.Tests were performed with a use of the rigidcooper pile, (L/D = 4.5), embedded in drysand. The research was performed for ID = 4%and ID = 38%, corresponding to the loose andmedium-dense state in full scale respectively.The deflections were measured by two dialgauges.

8

Figure 3.1: The mechanical rig used for tests

The analyzed data revealed an exponential cor-relation between the accumulated rotation andthe number of cycles. Subsequently, the accu-mulated rotation was dependent on the magni-tude and the loading direction. The obtainedresults showed that the maximum value foraccumulated rotation is between one way andtwo way loading, which contradicts the generalbeliefs that the largest accumulated rotation isfor one way cyclic loading. For the soil stiff-ness the logarithmic increase with the numberof cycles was revealed. This change was ob-served as independent on the soil density, butonly related to the load characteristics. Thisincrease undermines the existing regulationsused in standards, [DNV, 2011], indicating thedegradation of p-y curves due to a cyclic load-ing.

4 Test Set-up

Based on the equipment used by LeBlanc etal. [2010], a similar rig has been constructed inthe AAU laboratory. The research equipmentis illustrated in Figure 3.1.

A cylindrical container is filled with sandof properties presented in Table 4.1. Theseparameters were obtained by previous testsperformed in the laboratory. The inner diame-ter of the container is 2000 mm and the depthis equal to 1200 mm. At the bottom a drainage

system is installed in order to provide satura-tion of sand. The system includes pipes andthe gravel layer of 300 mm, covered by thegeotextile.

Table 4.1: Properties of the sand used at AalborgUniversity Laboratory

Property ValueSpecific grain density, ds [g/cm3] 2.64Maximum void ratio, emax [-] 0.858Minimum void ratio, emin [-] 0.549

In order to simulate the offshore conditions,the sand must be fully saturated and dense.Before each test a hydraulic gradient is appliedand a loose state of sand is obtained by reduc-ing the effective stress. Next sand is vibratedmechanically in order to achieve a small voidratio. The density of soil is established throughperforming cone penetration tests, [Ibsen et al.,2009]. The variation of the relative densities,ID, from different tests is presented in Table4.3. From the results it can be concluded thatthe soil conditions are similar between eachperformed test. The target results of ID laybetween 80 to 90 %, what indicates a densestate of sand.

Table 4.2: The variation of the relative soil density

Number of tests µID σID

15 88.34 % 4.12 %

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An open-ended, aluminum pile is used fortests. The pile characteristics are presented inTable 4.3. The reason of chosen eccentricity isdue to the expected eccentricity level of waveloads acting on a pile in the most commoncases [Onofrei et al., 2012]. The pile behavior isassumed to be rigid. The small variation of theload eccentricity, ± 5 mm, that can be causedby different level of soil, are included in thecalculations of the moment on the seabed.

Table 4.3: Characteristics of the pile

Property Length [mm]Embedded length,L 500Diameter,D 100Slenderness ratio, L

D 5Thickness, t 5Load eccentricity, a 600 ± 5

The monopile is installed in sand by using anelectrical motor working with the velocity of0.02 mm/s. This ensures a small disturbanceof the soil.

The different part of the rig are presentedin Figure 4.1 and described hereafter.

Figure 4.1: A test set-up with the dimensions andthe localizations of transducers [Onofrei et al., 2012]

At the top of the pile a rigid tower withforce transducers is mounted, F1 and F2.A steel frame situated above the containerconsists of a system of pulleys and wires,that are used to transfer the loads fromweights, m1, m2 and m3, to the rigid tower.A beam with three displacement transducers,D1, D2 and D3, is fixed to the steel framein order to measure the displaced positionof the pile. This information are used toextrapolate a rotation to the ground level.Two types of loading are performed, indicat-ing the two different loading systems.The static loading is a displacement controlledtest performed with the use of a motor at-tached to the steel frame. The motor createsa pulling horizontal force acting on the tower,which is recorder by F1. The main aim of thistest is to obtain the ultimate resistance momentof soil, MR. The speed of pulling is equal to0.02 mm/s, so in case of creating the excesspore pressure, it can easily dissipate.A cyclic loading is initiated by m1 and m2,which create forces recorded by F1 and F2. Themass m3 is a counter-weight of the rig. Themass m2 is directly connected to F2 througha wire and a pulley, what result in the forceequal to m2g. On the other side the mass m1 isput on a rotating hanger, controlled by a motorwith the loading frequency of 0.1 Hz. Thiscorrespond to a common wave loads frequency[Onofrei et al., 2012].

The rotating hanger works on a lever con-nected to the frame through a pinned joint.When the motor starts to rotate m1, the forceincreases until it reaches the maximum value,when the mass is in the most further position,equation (7). While the cycle is continued,the force decreases till minimum, when themass returns to the starting position - the mostclosest to the force transducers, equation (8).

Fmax = 3 · m1g − m2g (7)

Fmin = m1g − m2g (8)

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An accurate determination of the loading mag-nitude is difficult due to the loss in force.Partly, it can be caused by the friction in themechanical system. In addition, some lossesappear due to the lever tilting. As long as thewire connecting F1 and the lever is of a fixedlength, every time when the pile rotates, theposition of the lever will change in some smallextent.

5 Tests methodology

A presented research methodology is based onthe concept described by LeBlanc et al. [2010].A comparison with the full-scale is not a partof the research, therefore no scaling law isused.

All tests are identified by the load charac-teristic parameters ζb, equation (9) and ζc,equation (10). The cyclic loading parametersdescribe the magnitude and direction of load-ing respectively. The visual interpretation isillustrated in Figure 5.1.

ζb =Mmax

MR(9)

ζc =MminMmax

(10)

whereMmax The maximum moment[Nm]Mmin The minimum moment [Nm]MR The static moment capacity [Nm]

Figure 5.1: Characterization of cyclic loading[LeBlanc et al., 2010]

The value of the static moment capacity is ob-tained from a static loading test. The valueof MR is determined in reference to moment-rotation curves. The moment of failure is iden-tified for the maximum value, before the mag-nitude starts to decrease. The results of statictests are illustrated in Figure 5.2.

Figure 5.2: The static test results

The applied magnitude of loading is deter-mined in reference to FLS, where ζb for thetypical design load for OWT fluctuates aroundvalue of 0.3. The assumed range of ζc is−1 < ζc < 1, where ζc = 1 describes theone-way loading and ζc = −1 describes thetwo-way loading. The research pays attentionon the negative values of ζc, regarding to theconclusion made by LeBlanc et al. [2010], thatthe worse cyclic conditions are obtained fortests with loading between one-way and two-way.

The data obtained in tests provide informationabout the change in stiffness during the cyclicloading, k, and the accumulated rotation afterlong-term cyclic loading, ∆θ(N). The assump-tions concerning these two parameters aredescribed in following sections. The methodfor determining both values is presented inFigure 5.3.During the cyclic test 50 000 load cycles areapplied. The FLS is assessed for 107 numberof cycles, however such a big number of cycles

11

is time consuming. The adopted number of cy-cles is assumed to be sufficient for describingthe behavior of monopiles for FLS.

Figure 5.3: A method for determining stiffness andaccumulated rotation [LeBlanc et al., 2010]

In order to fully refer to the research per-formed by LeBlanc et al. [2010] the sand shouldbehave as drained during the loading. Asfar as for static tests this is provided by thesmall velocity of pulling, the conditions dur-ing cyclic tests must be analyzed. Therefore,the results of first cycle in each test, the maxi-mum moment and the corresponding rotation,are plotted and compared with the static re-sults. Figure 5.4 indicates that during the cyclictests, the drained condition is preserved. Theonly result that does not fit to the static curveis from the test characterized with ζb = 0.41,where the sand behaviour can be interpretedas a partially drained.

Figure 5.4: The reference static test with the resultsfor first cycle in each cyclic test

6 The accumulated rotation

A method for describing accumulated rotationis express by equation (11), using the powerlaw of the same form as it was done in LeBlancet al. [2010].

∆θ(N)

θ0=

θN − θ0

θ0= Tb · Tc · Nn (11)

whereθ0 The rotation after 1st cycleθN The rotation after N cycleTb and Tc Dimensionless functionsn The power fitting parameter

It was already proved by others researchers,that the power dependency between the ac-cumulated rotation and the number of cyclesgives a good fit with the real tests values.The magnitude of the rotation caused by cyclicloading should be normalized by the corre-sponding rotation from the static tests, θs,Figure 5.3. However, some differences betweenstatic moment capacity was revealed after per-forming few static tests in the AAU laboratory,as there are always some small discrepanciesin the test set-up between performed tests.Furthermore, while the two-way cyclic testsare being performed, there is a risk of a smallnegative rotation to occur before the 1st cycle,what might have effects on the initial rotation.Therefore, the initial rotation is used whennormalizing ∆θ(N).

LeBlanc et al. [2010] revealed that a powerfitting parameter for all loading conditions canbe set to n = 0.31. However, this fit is notvalid for dense sand, as illustrated in Figure6.1 for one-way and two-way loading tests(ζc = −0.55).The fitting parameter is therefore adjustedfor each singular test. So far, no dependencybetween power fitting parameters and loadcharacteristics have been found, however themean value for all tests is n = 0.14, which is a

12

half of the value given by LeBlanc.

Figure 6.1: Normalized rotation for one-way load-ing test (upper plot) and two-way loading test (lowerplot)

Tb and Tc functions depend on the load char-acteristics and soil density. Tb can be obtainedby performing tests with ζc = 0 and varyingζb. Figure 6.2 presents the relation of Tb forperformed tests in correlation to the resultsobtained by LeBlanc et al. [2010]. The changein soil relative density seems to increase thevalues of Tb, what could indicate the increaseof the accumulated rotation. However, as adifferent power fitting parameter is applied,the value of accumulated rotation cannot besolely based on Tb value.

It is assumed that Tc(ζc = 0) = 1. As for thestatic test no accumulated rotation is expected,therefore Tc(ζc = 1) = 0. The same is pre-dicted for two-way cyclic loading, as the loadis equal in both direction, Tc(ζc = −1) = 0.The rest of the values are empirically deter-mined by fitting to the laboratory results. Onlythe negative values of ζc are analyzed. Figure6.3 illustrates the tests results, along with thetrend found by LeBlanc et al. [2010].

Figure 6.2: A dimensionless functions Tb

Figure 6.3: A dimensionless function Tc

Despite that the values of Tc are smaller incomparison with LeBlanc et al. [2010], it doesnot indicate that the accumulated rotation issmaller for denser sand, as it depend on both,

13

Tb and Tc. Both these values could be alsoaffected by a power fitting parameter. How-ever, the shapes of functions are similar, withextreme values for tests between one-way andtwo-way loading.

More results of accumulated rotation withdependency on ζc are presented in Figure 6.4with logarithmic axes and in Figure 6.5 withnormal axes. Selected tests are described byζb ≈ 0.3.

Figure 6.4: The increase of accumulated rotation forvarying ζc - logarythmic axes

Figure 6.5: The fitting function for accumulatedrotation for varying ζc - normal axes

The value of ∆θ / θ0 is overestimated by the

power function for the first loading cycles, buta good fit is provided for a large number ofcycles, what is crucial for FLS design. Theaccumulated rotation gets the biggest value forζc = −0.44, whereas the smallest increase isobserved for ζc = −0.83. Similar observationwas obtain by LeBlanc et al. [2010], where themaximum accumulated rotation was obtainedfor loading condition between one-way andtwo-way. When the fitting functions are plot-ted in normal axes a significant accumulatedrotation can be observed for couple first cyclesand more constant behavior is found withincreasing N.

Generally, the values of ∆θ / θ0 are biggerfor dense sand in comparison to loose andmedium-dense sand.

7 The change in stiffness

The stiffness in relation to the number of cycles,kN , is described by the equation 12, likewise inthe research of LeBlanc et al. [2010].

kN = k0 + Ak · ln(N) (12)

k0 = Kb(ζb)Kc(ζc) (13)

whereAk A dimensionless parameterk0 The initial stiffnessKb and Kc Dimensionless functions

Even though a larger scatter of data is notice-able for stiffness results, they can be fitted toabove mentioned function. The dimension-less parameter Ak was found to be constantfor results obtained by LeBlanc et al. [2010],Ak = 8.02, not depending on ID.

Figure 7.1 presents the results for dense sand,where the data are fitted for fixed value ofAk in comparison to the best possible fit. Theresults reveal that for dense sand the param-eter Ak is of larger value. The parameter isobtained for each test.

14

Figure 7.1: The change in stiffness for one-way load-ing test (upper plot) and two-way loading test (lowerplot)

A large discrepancy of Ak is observed, butclearly there is an increase in Ak for increasingζb, what can be found in Figure 7.2. No such adependency was found for different values ofζc.

Figure 7.2: The increase of Ak as a function of ζb

According to LeBlanc et al. [2010] the dimen-sionless function Kb and Kc are only dependenton the load characteristics. In order to distin-guish between two functions it is assumedthat Kc(ζc = 0) = 1, so the values of Kb arefound for one-way cyclic loading and the restof tests results are extrapolated. Functions arepresented in Figure 7.3 and 7.4 along with theresults obtained by LeBlanc et al. [2010].

Figure 7.3: The dimensionless functions Kb

Figure 7.4: The dimensionless functions Kc

The results for dense sand indicate the increasein the initial stiffness comparing to loose andmedium sand. The values of Kc, despite avisible scatter of data, seem to fit the curve ob-

15

tained by LeBlanc et al. [2010], whereas thereis a significant increase in the values of Kb.The same trend is preserved, as an increaseof ζb decreases the value of Kb. It can be con-cluded that values of Kc are independent onID, however this does not hold for values of Kb.

More results of the change in stiffness forchanging ζc are presented in Figure 7.5. Se-lected tests are described with ζb ≈ 0.3.The biggest increase of stiffness is observed forone-way cyclic loading, whereas the smallestincrease occurred for the two-way loading test.The same behaviour was obtain by LeBlancet al. [2010]. Furthermore, the most of soilstiffness is mobilized during first loading cy-cles. This behavior indicates a high, nonlinearincrease is soil stiffness, that occurs due tocyclic sequence of loading and unloading,which might influence the relative soil densityaround the pile by increasing it. With increas-ing N, the value becomes more constant.

Figure 7.5: The change of stiffness for varying ζc

Generally, the increase of stiffness is found tobe much bigger for dense sand in comparisonto loose and medium-dense sand.

8 The post-cyclic soil resis-tance

The results reveals that the ultimate resistancealmost always increases as a result of largenumber of cycles, Figure 8.1. The increasemight be caused by the previously mentionedrise in the soil stiffness in the cyclic loading.The significant increase of the static stiffness isalso noticed from the figure.

Figure 8.1: The change in soil ultimate resistancefor one-way loading test

The results of post-cyclic resistance for all testsare plotted in Figure 8.2. All of the points ex-ceed the ultimate bearing capacity given by thestatic tests. The average increase of the bearingcapacity is assessed for around 10%.

Figure 8.2: The results of the post-cyclic resistancefor different tests

16

9 Conclusions

The presented paper provides the results ofsmall scale tests conducted on the rigid pilefoundation in dense, saturated sand. Themonopile is subjected to a long-term cyclic lat-eral loading. The article relates to the resultsobtained by LeBlanc et al. [2010] for laterallyloaded pile in loose and medium dense sands.

In the research the accumulated rotation andthe change in cyclic stiffness are analyzed.Both illustrate that the loading characteristicshave a significant effects on the pile behaviorunder a cyclic loading conditions. This find-ing is an important aspect for a future piledesign, as the current standards do not in-clude the load characteristics while designinga monopile subjected to the cyclic loading.The function for the accumulated rotationestablished by LeBlanc et al. [2010] was mod-ified for dense sand. The power dependencyfor a growing number of cycles reveals themaximum accumulated rotation for tests be-tween one-way and two-way loading, as it wasobtained for medium and loose sand. How-ever, the magnitude of accumulated rotationincreases for dense sand.The logarithmic function for the change in soilstiffness obtained by LeBlanc et al. [2010] wasalso modified for piles embedded in densesand. The increase of stiffness is found to besignificantly bigger for dense sand comparingto medium and loose sand.The results reveal that first cycles are impor-tant for a whole cyclic process, as the most ofrotation is mobilized in these first cycles. Thisis undoubtedly influenced by the nonlinearincrease of stiffness in its initial cyclic part.As the soil-pile system becomes more stiff,the accumulated rotation is more constant forlarger number of cycles.

Furthermore, a series of post-cyclic tests re-vealed the increase of post-cyclic bearing ca-

pacity for both one-way and two-way cyclicloading. Following results contradicts currentdesign standards, which involves degradationof stiffness for p-y curves by factor of 0.9 forincluding the effects of cyclic loading.

For more thorough summary of cyclic load-ing behavior of offshore monopiles in densesand further research, focused on larger di-versification of load characteristics, ought tobe conducted. Finally, in order to create thegeneral design method, obtained data mustbe compared with full scale results to verifyproposed solutions.

References

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Ibsen, L. B., Hanson, M., Hjort, T., & Thaarup,M. 2009. MC- Parameter Calibration forBaskarp Sand No. Department of Civil En-gineering, University of Aalborg.

LeBlanc, C., Houlsby, G.T., & Byrne, B.W. 2010.Response of stiff piles in sand to long-termcyclic lateral loading. Geotechnique 60, No.2,79–90.

Lin, S., & Liao, J. 1999. Permanent Strains ofPiles in Sand due to Cyclic Lateral Loads.Journal of Geotechnical and GeoenvironmenralEngneering, 798–802.

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Long, J.H., & Vanneste, G. 1994. Effects ofCyclilc Lateral Loads on Piles in Sand. Jour-nal of Geotechnical Engineering, Vol.120, No.1,225–244.

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2012. Small-Scale Modelling of Monopilesin Sand Subjected to Long-Term Cyclic Load.Department of Civil Engineering, Aalborg Uni-versity.

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Recent publications in the DCE Technical Memorandum Series

DCE Technical Memorandum no. 45, Response of a stiff monopile for a long-term cyclic

loading, Aleksandra Lada, Szymon Gres, Giulio Nicolai and Lars Bo Ibsen, June 2014.

DCE Technical Memorandum no. 46, The stiffness change and the increase in the ultimate

capacity for a stiff pile resulting from a cyclic loading, Aleksandra Lada, Lars Bo Ibsen and

Giulio Nicolai, June 2014.

DCE Technical Memorandum no. 47, The behaviour of the stiff monopile foundation

subjected to the lateral loads, Aleksandra Lada, Lars Bo Ibsen and Giulio Nicolai, June 2014.

ISSN 1901-7278

DCE Technical Memorandum No. 45