1 INTRODUCTION

Offshore wind turbines are being installed in ever greater numbers around the UK and Europe. The most common foundation design is the large diame-ter monopile; a single pile upon which the turbine is located. These piles are substantially larger than piles used for oil and gas applications, with diame-ters up to 10 m being considered for future designs. Consequently there are concerns about whether cur-rent design approaches imported from oil and gas design, particularly for lateral loading, are robust. In addition there is limited guidance for assessing the effects of cyclic loading on pile response, both dur-ing storm loading and also over the lifetime of the structure.

To respond to these concerns a number of recent research programs have focused on cyclic loading of piles, principally through laboratory model testing. The aim of these testing programs has been to ex-plore pile response under constant amplitude cyclic loading, and in particular the evolution of the foun-dation response (e.g. rotation, stiffness) with the number of cycles (e.g. Leblanc et al., 2010a; Peralta, 2010; Klinkvort, 2012; Cuéllar, 2011). It is recog-nised that the loading on the foundation, caused by the wind and wave environment, is likely to com-prise a range of amplitudes rather than a single, or constant, amplitude. Therefore further experimental work is needed to determine the equivalence be-

tween multi-amplitude and constant amplitude cyclic loading.

This paper presents experimental results, from model scaled pile tests in sand that explores multi-amplitude loading. The experimental equipment is described along with the framework for interpreting both constant amplitude and multi-amplitude test re-sults. The results from a number of constant ampli-tude cyclic loading tests along with two multi-amplitude tests are presented. They are interpreted using currently available methods, and provide a ba-sis against which future work can be developed.

2 LATERAL LOADING MODEL PILE TESTS

2.1 Background and motivation

Recent research on pile response to cyclic lateral loading (e.g. Leblanc et al. 2010a; Peralta, 2010; Klinkvort, 2012; Cuéllar, 2011; Abadie & Byrne, 2014) demonstrates that constant amplitude cyclic loading can cause significant increases in pile de-flection and rotation over time. This effect is typical-ly described as accumulated displacement with cycle number, and experimental data from such experi-ments have been fitted using both power and loga-rithmic laws by a range of Authors.

For example Leblanc et al. (2010a) show that the evolution of the accumulated rotation for con-stant amplitude cyclic loading can be described by

Model pile response to multi-amplitude cyclic lateral loading in cohesionless soils

C.N. Abadie & B.W. Byrne Department of Engineering Science, University of Oxford

S. Levy-Paing Département THEMIS, EDF R&D

ABSTRACT: Monopile foundations for offshore wind turbines are subjected to many cycles of loading dur-ing their lifetime. This loading consists of a range of amplitudes, applied in various sequences, of many dif-ferent cycle numbers. Calculation of the accumulated rotation experienced by the monopile as a result of this cyclic loading, and whether this exceeds allowable limits, is an important part of the design process. This pa-per provides an overview of recent research exploring laterally loaded pile response relevant to the design of offshore wind turbine monopiles. Experimental equipment for carrying out cyclic lateral loading tests is in-troduced, along with considerations of scaling for model testing. Results from a series of small scale model tests covering realistic multi-amplitude testing are then presented, providing new insight into the behaviour of rigid piles subjected to cyclic loading. The results are interpreted using a linear superposition method, as typi-cally used for structural fatigue calculations, and this shows a good fit to the experimental results.

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cycle number for both tests. An interesting outcome of test MA2 is that the increase in rotation due to cy-clic load amplitude C0 reduces to approximately ze-ro following the fourth peak load event (b=0.46, corresponding to a load magnitude of the SLS). Sim-ilar tests with larger cycle number would be helpful to assess the above statement for larger cycle num-bers (107), though it would require a higher cyclic frequency for tests to run in a reasonable time frame.

The two tests indicate that the pile displacement response, following a change in load, depends on whether there is an increase in load or decrease. Fig-ure 6 demonstrates this by plotting the differences in pile head rotation against differences in load, when a change in load amplitude occurs. Decreases in load magnitude are displayed on the left, and increases on the right. It also shows that the order in which loads occur matters, by highlighting a sharper increase in pile rotation during the first storm events (top right ellipse) compared with the subsequent events (bot-tom right ellipse). The graph shows that there is sig-nificant non-linearity involved, corresponding to substantial plastic deformations occurring.

4 METHOD FOR PREDICTION OF PILE ACCUMULATED ROTATION

4.1 Linear superposition model description

The investigation of the relationship between spec-trum loading and fatigue lifetime is important to ac-curately predict the evolution of pile deflection through random cyclic loading. First, the random loading history is decomposed into an equivalent set of uniform load reversals. This is a common proce-dure in fatigue life assessment and can be performed with extended rain-flow counting (Rychlik 1987). The decomposition of the load series enables a dam-

age rule to be applied for predicting the fatigue life-time. A common method is the linear cumulative damage rule, initially proposed by Palmgren (1924), and then popularised by Miner (1945). This concept was applied to laterally loaded piles by Lin & Liao (1999), following the work of Stewart (1986). They demonstrated a good fit to their experimental results; however, their experiments only involved 50 cycles maximum. Extending this, Peralta (2010) performed tests of up to 45,000 cycles, finding that the method underestimated the final pile deflection. In contrast Leblanc et al. (2010b) found that such a method provided a good prediction to their test results.

The superposition method adopted here is de-scribed in detail by Leblanc et al. (2010b). If there are two load sequences subscripted a and b, in the order Na then Nb, then firstly the accumulated rota-tion a caused by Na cycles of lateral load a is de-

Figure 6. Analysis of the change in rotation during the loading sequence changing phases

Decreasing - Test MA1 first jumpDecreasing - Test MA1 second jumpDecreasing - Test MA2Fitting curveIncreasing - Test MA1 first jumpIncreasing - Test MA1 second jumpIncreasing - Test MA2Fitting Curve

StiffenRetardation

�

= (

-)

[rad

.]N

(N-1

)

�� � �b bN b(N-1)= -

Steady-stateHardening

-0.5 0 0.5-1

0

1

2

3

4

5

6 x 10-3

InitialHardening

y(x)= .x�

(a) (b)

Figure 5. (a) Test MA1: maximum rotation evolution with number of cycles superimposed with predictions from the linear superposition model as proposed by Leblanc et al. (2010b) and modifications from Equation 8. (b) Test MA2: rotation evolution with number of cycles

0 2000 4000 10000 120000

0.005

0.01

0.015

Number of cycles

Pil

e ro

tati

on

[ra

d.]

Experimental resultsPrediction with linear conservative modelPrediction with modified model

0 2000 120000

0.1

0.3

0.5

0.7

N

M/M

R

0 2000 4000 10000 120000

1

2

3

4

5

6

7

8

No. of cycles

Rota

tion (

[rad

.]x 1

0)

-3

RotationMaximum rotation

0 2000 100000

0.2

0.4

0.6

N

M/M

R

termined using Equation (1): 31.0)()( aascba NTT (4)

This can be made equivalent to eqabN cycles of load

type b using the calculation: 31.0

)(

bscb

aeqab TT

N

(5)

If Nb cycles of load b are then applied to the pile, the overall accumulated rotation is given by:

31.0)()( eqabbbscbtot NNTT (6)

The total pile rotation is then calculated as:

batotb ,0,0 ,max (7)

4.2 Modification based on experimental results

Tests C1 to C3 make it possible to deduce the corre-sponding values of Tb, Tc and s for each load type applied in the multi-amplitude tests. The above line-ar superposition method is applied to test MA1 with the results shown in Figure 5(a). The model broadly captures the results, slightly over-predicting the final pile rotation but with an acceptable error of 3.7%. We propose modifying the calculation, taking ac-count of observations from Figure 6 for decreases in load, by changing the term max0,a, 0,b} in Equa-tion (7) to:

0,max

0,max

,0,0

,0,0

bbba

bbath f

if

(8)

In this Equation, is the slope of the fitting law for descending load sequences. The results of such a calculation are given in Figure 5(a), showing a better prediction of the final rotation (error of 0.16%). Ad-ditional work is needed to develop a better under-standing of the term th. New methods must capture the non-linearity of pile response more accurately, recognising that the cyclic accumulated pile load-displacement response is unlikely to be calculated precisely using linear superposition methods.

5 CONCLUSION

This paper presents a series of laboratory floor mod-el tests exploring pile response under multi ampli-tude cyclic loading, representing storm loading on the pile. An important observation from this work is that the pile rotation appears to reach a limiting val-ue following a series of maximum storm type loads. The paper shows that the pile response to multi am-plitude cyclic loading involves significant non-linearity, particularly when large plastic defor-

mations occur. A linear superposition method, such as described by Leblanc et al. (2010b), is shown to provide a reasonable but conservative approximation to the final pile rotation. This is modified to predict the pile response more accurately.

To further develop these methods research must focus on understanding the non-linearity highlighted in section 3.2, for both loading and unloading. Tar-geted laboratory floor testing and field testing, along with theoretical development, will be needed. The resulting model would improve design guidance for cyclic loading of offshore wind turbine monopiles.

6 ACKNOWLEDGEMENTS

The first author thanks the generous support from EDF R&D and EDF Energies Nouvelles.

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