Nadine Christelle

Byron Abadie

Guy Byrne

Harvey Houlsby

Ross Burd

William J A P Mcadam

Beuckelaers

Mcadam

Christelle N Abadie

Byron W Byrne
email: byron.byrne@eng.ox.ac.uk

Guy T Houlsby
email: guy.houlsby@eng.ox.ac.uk

Harvey J Burd
email: harvey.burd@eng.ox.ac.uk

Ross A Mcadam
email: ross.mcadam@eng.ox.ac.uk

William J A P Beuckelaers
email: william.beuckelaers@jandenul.com

Jan De Nul

Modelling of offshore wind monopile lifetime performance

Keywords: monopile foundation, cyclic loading, constitutive modelling, lifetime prediction

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Offshore wind turbines are commonly founded on short rigid monopiles, of typical length to diameter ratio, L/D, of 3 to 6 (Fig. 1). The foundation is subjected to large lateral loads, comprising a combined moment and a horizontal load, arising from the action of the wind, waves and currents on the support and super-structure, as well as the operation of the turbine. Due to the repetitive nature of these loads, the design load scenarios include cyclic load Fig. 1. Current modelling method for laterally loaded monopile packets of variable amplitudes and magnitudes, with very large cycle numbers. Robust design of the foundation requires ensuring that the capacity is sufficient as well as limiting the deformation over 25 years of service life, typically 10 8 cycles, to acceptable levels. However, both the monotonic and cyclic responses are highly non-linear, and assessing the pile deformation over a large number of cycles accurately can be computationally prohibitive.

As a result, methods often used for pile design (e.g. the p-y method, DNV, 2014), typically employ simplified approaches adopting the Winkler modelling assumptions [START_REF] Winkler | Die Lehre von der Elasticität und Festigkeit[END_REF]. The pile is modelled as a 1D beam with the pile-soil interaction response represented by nonlinear independent springs down the pile length. These springs relate the local soil resistance p to the pile displacement y at each depth (Fig. 1). Soil layers can be considered, but the model typically does not capture any interaction between the strata. Cyclic loading is typically addressed by applying degradation factors to the monotonic p-y curves, to represent degradation of the soil-pile springs with cyclic loading and to capture accumulation of permanent deformation for a representative number of cycles. Figure 2 illustrates how pile cyclic response may be modelled using such degradation factors for the Mustang Island pile [START_REF] Reese | Analysis of laterrally loaded piles in sand[END_REF]. As the global pile response is derived from the combined effect of these degraded curves, the global ground-level pile response would also display similar behaviour. This approach is computationally fast, and has been adopted in the offshore wind industry as a satisfactory compromise between conservative design and computation time. Industry practice sometimes adopts cyclic p-y springs to capture the degraded secant stiffness only, applied to both quasi-static and dynamic loads for structural design purposes. Pile accumulated rotation is assessed by applying the maximum FLS load to the static monotonic curve, and unloading with the initial stiffness using an isotropic hardening model (Fig. 2(b)).

With the increasing growth of the offshore wind industry, combined with strong governmental and industrial incentive for design optimization and cost reduction, there is a strong motivation to develop pile design methods further, particularly for cyclic loading. Monitoring of full-scale turbines (e.g. [START_REF] Kallehave | Modification of the API formulation of initial stiffness of sand[END_REF] demonstrates that the natural frequency of wind turbines is higher than that predicted using the normal p-y methods. In addition, the degradation factors currently employed to capture the design for cyclic loads are independent of the number of cycles applied (e.g. Fig. 2), and of the amplitude of those cycles. In response to these concerns, recent research has led to improved design approaches guidelines for ULS conditions (e.g. the PISA method - Byrne et al., 2019a;[START_REF] Jeanjean | A Framework for Monotonic p-y Curves in Clays[END_REF]the SOLCYP project -Puech, 2017) that should enable better optimisation of future monopile foundations. However, optimization of pile geometry for ULS design might lead to excessive deformations caused by long-term small-magnitude cyclic loads. Hence the development of more accurate and rigorous approaches for SLS and FLS design is needed.

Recently a new method for fast computation of long-term cyclic loading response of monopiles is emerging through the HARM framework [START_REF] Abadie | Cyclic lateral loading of monopile foundations in cohesionless soils[END_REF]Abadie et al., 2017b[START_REF] Abadie | A method for calibration of the Hyperplastic Accelerated Ratcheting Model (HARM)[END_REF]Houlsby et al., 2017). This paper outlines a numerical modelling approach, combining the PISA design model and the HARM framework, to enable prediction of the pile ULS, SLS and FLS performance. An example application to a full-scale monopile, installed in a layered soil profile and subjected to a 25 year lifetime load signal, followed by a storm is used to illustrate the method.

MODELLING FRAMEWORK

The method employed in this paper consists of using the 1D PISA design model to derive the monotonic response accurately, followed by application of the HARM macro-element (0D) model to compute the cyclic response. The monotonic response is used as the input backbone curve. This analysis scheme is illustrated in Fig. 3. This approach has computational time advantages over a fully-integrated 1D model (discussed further in Beuckelaers ( 2017)).

1D PISA Design Model for Monotonic Loading

The 1D PISA modelling approach is described in Byrne et al. (2019aByrne et al. ( , 2019b) ) and Burd et al. (2020b), with further details about the modelling in layered soils provided in Burd et al. (2020a).

In the method the monopile is represented by a line mesh of two-noded Timoshenko beam finite elements. The soil lateral response acting at the nodes is captured through four components: distributed lateral load p, distributed moment m, base horizontal force H B and base moment MB, as shown in Fig. 3, top left. These encapsulate the combined action of the lateral soil resistance and shear along the pile shaft and base.

Calibrated parametric "soil reaction curves" are derived to capture the soil reaction with local pile displacement v and rotation . A conic function is used for each of the soil reaction curves, and normalised (Byrne et al., 2019b). During the first phase of the PISA project, a method for calibration of the conic function for homogeneous soils was derived and validated for sitespecific homogeneous soil profiles. The calibration process is derived from 3D finite element analyses, with the procedure outlined in Byrne et al. (2019b) for stiff glacial clay till and Burd et al. (2020b) for marine sand with varying relative densities ( = 45% to = 90%).

Modifications for layered soils

Extension for layered soil profiles is achieved through the hypothesis that the soil reaction curves calibrated using homogeneous soil profiles can be employed directly to conduct 1D analyses of monopiles embedded in a layered soil (Byrne et al., 2019a). In other words, the interaction between layers is ignored in the 1D model. Within each layer, the normalised soil reaction curves are computed using the appropriate sand or clay framework derived from the homogeneous soil calibration, and the local values of small strain shear modulus , undrained shear strength and initial vertical effective stress ′ (e.g. Fig. 4). Nodes are generated at the soil layer boundary to facilitate the layer change. Validation of this hypothesis is demonstrated by Burd et al. (2020a), showing that the 1D PISA design model provides sufficiently accurate predictions for most practical design cases.

The PISA method gives the monotonic pile response at ground level, to enable assessment of pile capacity and initial stiffness. This response also forms the backbone curve in the HARM approach. One of the more realistic soil profiles and pile geometry -case F1 in Byrne et al.

(2019a) -is used for the example calculation presented in this paper. Details of the soil profile for F1 are shown in Fig. 4, together with the pile response, as well as the , and ′ profiles. The pile geometry is given in Table 1. Comparison with the computed 3D FE response shows that, in this case, the 1D model demonstrates excellent accuracy.

0D HARM Macro-Element for Cyclic Loading

The HARM approach is a development of constitutive modelling, derived through the hyperplasticity framework [START_REF] Houlsby | Principles of Hyperplasticity[END_REF], specifically intended to capture ratcheting. The full details of the model are presented in Houlsby et al. (2017), with a calibration method and applications to rigid pile design to lateral cyclic loading shown in [START_REF] Abadie | A method for calibration of the Hyperplastic Accelerated Ratcheting Model (HARM)[END_REF]. HARM combines a ratcheting element with a kinematic hardening plasticity model (Fig. 3, top right), which provides both the accumulation of deformation with cycling, and the Masing behaviour commonly observed in pile tests (see for example Fig. 3). The amount of ratcheting strain accumulated during any un-load re-load loop is controlled through the family of parameters , while the shape of the loop is defined by the backbone curve, itself described by the set of parameters , and (see further detail in [START_REF] Abadie | A method for calibration of the Hyperplastic Accelerated Ratcheting Model (HARM)[END_REF].

One of the strengths of this model is that any amount of ratcheting strain accumulated within a group of cycles of the same magnitude and amplitude can be accelerated by simply multiplying the ratcheting rate by the number of cycles to be skipped, enabling very fast computation for a large cycle number. The model naturally tracks each load increment, regardless of the load history. This means that, in the case of multi-amplitude load packets, the model captures the response to complex load scenarios, without the need to introduce additional assumptions such as Miner's rule (e.g. [START_REF] Leblanc | Response of stiff piles to random two-way lateral loading[END_REF][START_REF] Miner | Cumulative damage in fatigue[END_REF]. On changing load magnitude and/or amplitude, the acceleration factor must be disabled. The HARM framework can be applied as the constitutive relationship for the stress/strain response at any level (macro-response of the pile or local soil response). Hence, HARM could be integrated within any of the monopile modelling approaches adopted to characterize cyclic behaviour at element level for 3D FE modelling, local response for 1D modelling or macroresponse (0D model). However, the simplest and fastest approach is the 0D model, where the foundation reaction is captured using a macro moment-rotation spring (Fig. 3) only. Even as simplified to moment-rotation the current 0D model implementation provides a highly efficient link to structural analysis, and provides a very fast tool for investigation and modelling of wind turbine performance. For accuracy, it is recognised that future development could include the " -" component and the induced cross-coupling terms between " " and " ", but it is unlikely that these developments would incur any great computational cost.

Calibration

The model relies on accurate prediction of the backbone curve, here produced using the 1D PISA design model. This backbone curve is used as an input for calibration of parameters , and , and corrected to account for ratcheting, as described by [START_REF] Abadie | A method for calibration of the Hyperplastic Accelerated Ratcheting Model (HARM)[END_REF]. This provides the monotonic response shown in Fig. 3, which matches that obtained from the 1D PISA design model in Fig. 4(b).

Calibration of the ratcheting behaviour is achieved through the choice of the ratcheting rate , according to:

0 s r m m n n o U o k R R k σ β β σ -      =           Equation 1
Where is the accumulated ratcheting strain, which acts as a memory of the cyclic history. is an arbitrarily small value used for normalisation purposes, is the ultimate stress level, is the initial ratcheting rate and and are empirical exponents that control the evolution of the ratcheting rate with load history and stress/load level respectively. Accordingly, the ratcheting rate decreases with the accumulation of load cycles and increases with load magnitude.

The calibration method follows that outlined in [START_REF] Abadie | A method for calibration of the Hyperplastic Accelerated Ratcheting Model (HARM)[END_REF] for laboratory piles in sand, with the same methodology and set of ratcheting parameters applied successfully for the modelling of large-scale field tests in clay by Abadie et al. (2017a). A consistent set of ratcheting parameters are hence adopted in this paper, as provided in Table 2. Given that the cyclic behaviour for clay and sand is very similar, it is likely that the framework applies similarly for layered soil profiles comprising of the same materials.

The modelling framework as presented here is used (i) to illustrate the design method, (ii) to Exponent defining the increase of ratcheting rate with load intensity 8.9

Initial ratcheting rate 1.7 identify the potential of the method, and (iii) to display the type of behaviour expected from lifetime response. Of course more detailed analysis might require a 1D layered model, adapted to the HARM formulation; however, that is beyond the scope of this paper. It would also come at a higher computational cost.

MODELLING OF LIFETIME PERFORMANCE IN LAYERED SOIL

Loading History

The above framework was applied to the pile specified in Table 1, for the layered soil profile of Fig. 4, to explore performance under the loading given in Fig. 5. The monotonic response computed with the 1D PISA design model predicts an ultimate capacity of = 3045kNm, obtained for a maximum ground level displacement of , = 0.875 m = 10% , and rotation of = 2.43 degrees. The loading represents a lifetime load signal, immediately followed by an extreme storm, and has been computed for a full scale offshore wind turbine. The loads have been scaled to be appropriate for foundation F1. Table 3 provides the characteristics of both the short storm and lifetime signals, with the ultimate moment capacity, and the maximum and minimum moment values.

The signal (Fig. 5(a)) includes ≈ 3 × 10 cycles, consisting of 65,534 individual load packets (referred to as "No. of load events" in Table 3), occurring in a random order. This was modelled using an acceleration programme that computed the first cycle of each load packet incrementally, with the remainder of each load series accelerated by a factor equal to the number of cycles of the series minus 2, with the last cycle of each load packet being computed incrementally. The first cycle must be computed incrementally to preserve the Masing behaviour and not distort the backbone curve; the remainder of the series can be accelerated without loss of accuracy. Computing the last cycle incrementally allows the cyclic response at the end of each load packet to be obtained independently. However, this is unnecessary if the intermediate response is not needed, with a small saving in computational time. In total, the acceleration procedures mean that 131,068 cycles were modelled for the lifetime load, with 500 load increments per computed cycle. The computation took approximately 30 minutes on a standard laptop (Table 3). Further reduction in computational time can be achieved by reducing the number of increments.

The lifetime signal is immediately followed by an extreme storm event (Fig. 5(b)), consisting of 150 cycles of random amplitude, all modelled incrementally. The maximum load of this signal is equal to = 1.35 = 0.74 × ⁄ .

Pile response

The resulting pile response is provided in Fig. 6, showing the evolution of the rotation with both moment loading and cycle number. Figure 6(b) highlights the evolution of the ratcheting strain, i.e. the proportion of permanent deformation caused by cyclic loading within the ratcheting element in HARM. The remainder of the deformation is caused by kinematic hardening plastic strain. Figure 6(b) also displays the final residual rotation, i.e. the rotation after complete unloading to zero. Typically for design, the residual rotation has to be limited to 0.5 degrees overall, with a maximum of 0.25 degrees caused by cyclic loading (e.g. [START_REF] Achmus | Behavior of monopile foundations under cyclic lateral load[END_REF][START_REF] Dnv | Offshore Standard DNV-OS-J101, Design of offshore wind turbine structures[END_REF]Section 10.3.2.6, p. 173).

Figure 6(b) shows that the effect of ratcheting on the response is significant during long-term cyclic loading at moderated load magnitude, as shown by the final residual ratcheting deformation highlighted by the dashed grey line. During the final short storm event, the effect of ratcheting on the overall response is limited, and the response is dominated by the deformations induced by the largest load event. When comparing with the behaviour obtained from conventional cyclic p-y approach (e.g. Fig.

2), the key differences are: (i)

The integrated PISA-HARM approach captures unloading, and hence, residual deformation following a specific load series, (ii)

The model accounts for cycle number, (iii)

The model captures the response to load packets of varying magnitude and can capture the change in behaviour between long-term cyclic loading of medium intensity, followed by a storm, (iv)

The model tracks the evolution of the pile response over time/cycle number, and could enable to assess lifetime extension for already installed monopiles if the past load history were known.

CONCLUSIONS

This paper outlines a method for computation of the response of large diameter monopiles to long-term cyclic loading, representative of the service life for an offshore wind turbine. The model combines the 1D PISA design model and the HARM framework, enabling the computation of pile response to very large cycle number, of varying load magnitudes and amplitudes.

The method is demonstrated through modelling of a pile in a layered soil profile subjected to a realistic load signal representing lifetime loading, followed by a large storm. The results illustrate the accumulation of permanent deformation throughout the 3 × 10 cycles, predicting both pile deformation caused by cyclic loading and residual deformation after unloading. The model shows progressive accumulation of permanent deformation over the lifetime of the turbine, with the response to the final storm dominated by the monotonic response to the largest load.

This modelling framework is a useful tool that enables further understanding of pile response to cyclic loading, and could, for example, be used to investigate the effect of load history on pile response. The HARM model adopted for the example accounts only for kinematic hardening and ratcheting, but other phenomena, such as rate dependency and gapping, could also be incorporated in the future.

Fig. 2 .

 2 Fig. 2. Schematic representation of (a) the use of degradation factor for p-y curves to (b) compute the FLS pile response for Mustang Island pile (Reese et al., 1974)

Fig. 3 .

 3 Fig. 3. Design Method (illustrated based on Case F1 response, see Fig. 4)

  Fig. 4. Layered case F1 (Byrne et al., 2019a)

  Predicted pile response: (a) moment-rotation curve; (b) Evolution of the rotation with cycle number

Table 1 . Monopile dimensions used for modelling

 1

	Pile	D (m)	h (m)	h/D	L (m)	L/D	t (mm)	D/t
	D2t	8.75	87.5	10	35	4	150	59

Table 2 . Parameters for calibration of the HARM 0D model

 2

	Definition

Table 3 . Load regime characteristics

 3

	Lifetime	Short Storm

ACKNOWLEDGMENTS

The authors acknowledge the financial and in-kind support of Ørsted. Byrne is supported by the Royal Academy of Engineering under the Research Chairs and Senior Research Fellowships scheme.


J Seong

C N Abadie

S K Haigh

S P G Madabhushi

SEISMIC RESPONSE OF OFFSHORE WIND MONOPILES IN COHESIONLESS SOILS

Keywords: monopile foundation, seismic loading, centrifuge testing

Development of offshore wind farms in seismic zones requires consideration of monopile foundation design subjected to dynamic earthquake-induced loads. This paper presents the results of a dynamic centrifuge test, investigating the monopile response to seismic loads in dry cohesionless soils. The test involved two identical instrumented monopiles, driven into a layered soil sample, with a loose layer overlying a very dense layer. A servo-hydraulic earthquake actuator was used to generate sine sweep and sinusoidal bedrock motions, during which pile and soil accelerations, dynamic bending moments and pile rotation were assessed. A monotonic push was performed on one of the piles prior to the earthquakes to assess initial capacity, while the second pile was pushed after completion of the dynamic load sequence to establish the post-seismic capacity. The results show strong acceleration amplification for earthquake loading frequencies close to the first mode of frequency of the pile-soil system. The monotonic tests demonstrate that, for the layered sand configuration considered here, the monotonic behaviour of the pile is strongly affected by the dynamic loading history.

INTRODUCTION

Offshore wind has developed rapidly over the past decade, mostly in Europe, and has an enormous potential for providing renewable energy across the globe. Methods used for the design of foundations have improved massively over the last 5 to 10 years, enabling significant and robust optimisation of the geometry (e.g. the PISA project - [START_REF] Byrne | PISA Design Methods for Offshore Wind Turbine Monopiles[END_REF][START_REF] Jeanjean | A Framework for Monotonic P-Y Curves in Clays[END_REF]the SOLCYP project -Puech, 2017). However, they focused on quasi-static loading cases, mostly relevant to the North Sea and the Irish Sea. For further development, such as deployment in East Asia and North American waters, a wider range of loading scenarios need to be addressed, and in particular earthquake-induced dynamic loads.

Offshore wind turbines are gigantic structures (e.g. Figure 1), that are commonly supported by monopile foundations. The environmental loads acting on an offshore wind foundation comprise of wind, wave and current-induced hydrodynamic loads, as well as in specific zones, earthquake, snow and ice loads (Figure 1). Despite the number of projects currently planned and undertaken in seismic zones, the understanding of pile response to earthquake loads is still in its infancy, but is a real concern for designers across the globe (e.g. the ACE project -DNV-GL, 2019). Current guidelines provide limited recommendations on structural design with regards to both earthquakes and earthquake-induced tsunamis (e.g. DNV, 2014, section 4.5.8). For foundation design, the understanding of pile response is limited and current design guidelines recommend to employ the same method as for cyclic design (e.g. see [START_REF] Abadie | Example modelling of monopile lifetime performance for offshore wind applications[END_REF] for description of the method) and degrade the p-y curves using factors that must be evaluated for site-specific conditions (DNV, 2014, section 10.1.4.4). There is no further detail on the range of values for these degradation factors, nor insight on whether the method is applicable or not.

The use of degradation factors to derive the cyclic response was originally proposed by [START_REF] Reese | Analysis of laterrally loaded piles in sand[END_REF], based on field tests performed by [START_REF] Cox | Field Testing of Laterally Loaded Piles in Sand[END_REF] for pile geometries and load scenarios adapted to oil and gas pile design. It is broadly acknowledged that these methods are inappropriate for offshore wind piles and significant progress in research worldwide has been published over the last decade to provide improved guidelines for the design of monopiles to cyclic lateral loading (e.g. [START_REF] Abadie | Cyclic Lateral Loading of Monopile Foundations in Cohesionless Soils[END_REF][START_REF] Abadie | Example modelling of monopile lifetime performance for offshore wind applications[END_REF][START_REF] Achmus | Behavior of monopile foundations under cyclic lateral load[END_REF][START_REF] Andersen | Cyclic soil parameters for offshore foundation design[END_REF][START_REF] Kirkwood | Cyclic lateral loading of monopile foundations in sand[END_REF][START_REF] Klinkvort | Centrifuge modelling of drained lateral pile-soil response[END_REF][START_REF] Lau | Cyclic behaviour of monopile foundations for offshore wind turbines in clay[END_REF]LeBlanc et al., 2010aLeBlanc et al., , 2010b;;[START_REF] Peralta | Investigations on the Behavior of Large Diameter Piles under Long-Term Lateral Cyclic Loading in Cohesionless Soil[END_REF][START_REF] Puech | Recommandations pour le dimensionnement des pieux sous chargements cycliques projet national SOLCYP[END_REF][START_REF] Zhang | Monotonic and Cyclic p-y Curves for Clay Based on Soil Performance Observed in Laboratory Element Tests[END_REF]. However, these studies all focus on quasistatic wind and wave-induced cyclic loads and do not address the case of dynamic earthquake-induced loads.

To date, limited research has been performed and published to address this knowledge gap (e.g. [START_REF] Kim | Seismic fragility analysis of 5 MW offshore wind turbine[END_REF]. This paper aims to address this issue by providing the first-of-a-kind experimental centrifuge test on large-diameter monopiles subjected to earthquake ground motions, followed by an extreme wind-wave monotonic load on the sub-structure.

EXPERIMENTAL METHODS

This paper examines the result of a dynamic test, undertaken using the 10 m diameter Turner beam centrifuge at the Schofield Centre at the University of Cambridge. The benefits of centrifuge modelling in geotechnics are widely recognised [START_REF] Madabhushi | Centrifuge Modelling for Civil Engineers[END_REF], and principally enables to perform reduced-scale model tests while preserving the stress-strain behaviour of the soils by scaling up the gravity by a factor . Hence, stress and strain similarity is achieved for a soil sample prepared at the same relative density as in the field, and scaling factors originally listed by [START_REF] Schofield | Cambridge Geotechnical Centrifuge Operations[END_REF] can be used to relate model to prototype behaviours. The test set-up discussed in this paper is shown in Figure 2(a).

Layered soil sample

The tests were conducted using an Equivalent Shear Beam model container (Figure 2(b)), consisting of alternating layers of durnal and rubber rings [START_REF] Brennan | Comparing laminar and equivalent shear beam (ESB) containers for dynamic centrifuge modelling[END_REF]. A layered soil profile of Hostun HN31 sand (Table 1) was poured using an automatic sand pourer [START_REF] Chian | Use of automatic sand pourers for loose sand models[END_REF] and dry pluviation through air. Two layers were poured: a dense layer at = 88%, overlaid by a loose layer at = 36%. The bottom 50% of the embedded length of the piles was in the dense layer, while the remaining top 50% was in the loose layer, with the rest of the pile above the soil representing the free superstructure of the wind turbine mast, with a lumped mass on the top (Figure 2(a)).

An air hammer was installed at the bottom of the sample, together with accelerometers at selected depth within the soil (Figure 2(a)). This enabled to log the shear wave velocity and determine the small strain shear modulus before and after earthquakes. This is shown in Figure 3, together with profiles obtained following [START_REF] Hardin | Shear Modulus and Damping in Soils: Design Equations and Curves[END_REF] and [START_REF] Oztoprak | Stiffness of sands through a laboratory test database[END_REF].

Piles geometry

The model piles used for testing were the same as those used by [START_REF] Kirkwood | Cyclic lateral loading of monopile foundations in sand[END_REF] and [START_REF] Lau | Cyclic behaviour of monopile foundations for offshore wind turbines in clay[END_REF], for which the dimensions are reminded in Table 2. The test was performed at a centrifugal acceleration of 60g, leading to the prototype pile dimensions listed in Table 2. Due to space restriction, it was not possible to achieve the prototype dimensions of Figure 1; however, the prototype piles are geometrically equivalent to a typical offshore wind monopile, and is representative of a 35 m long monopile scaled down to 1/3. They therefore provide good insight into dynamic monopile behaviour.

Both piles were gently driven in the soil sample using a hammer at 1-g, and hence be considered to be 'wished-in-place'. They were located ~6 diameters apart and ~4.5 diameters from the box walls, enabling sufficient clearance to avoid interaction between the two piles.

Pile-0 (Figure 2) was used as a reference pile and was loaded monotonically prior to triggering any model earthquakes, while Pile-PE was used to assess the effect of seismic loads on monotonic lateral pile capacity. Pile-PE was also instrumented with strain gauges to directly measure the bending moments of the pile. The geometry and location of the strain gauges is shown in Figure 2(a).

In order to simulate the inertia of the blades, turbine, gearbox etc and their effect on the pile response during earthquake ground motion, a lumped mass was located at the top of each pile (Figure 2(c)), representing the combined mass of the upper-structure, nacelle, rotor and blades. The mass was equal to 1.8 kg, corresponding to a vertical load of = 4 .

Ground motion

A series of horizontal input motion was applied at the bedrock level using a servo-hydraulic earthquake actuator. The series of ground motions applied is detailed in Table 3. In this paper, the results from the following input motions are considered:

-Test EQ1: A sine sweep of increasing frequencies from 0~1 Hz, which enabled to establish the natural frequency of the pile-soil system. -Test EQ5: A series of 10 cycles at the natural frequency 0.5 Hz (30 Hz model scale) -Test EQ6:A series of 10 cycles at twice the natural frequency 1 Hz (60 Hz model scale) -Test EQ8: A final sine sweep at increasing frequencies post -strong earthquakes.

Horizontal load

Finally, a horizontal push was applied to the pile using a displacement-controlled actuator. The pile-top displacement was checked using LVDTs, which reached their final stroke along the monotonic test at 0.38 m for Pile-PE and 0.17 m for Pile-0. Extrapolation of the data was then achieved for both piles, assuming a linear push from the actuator.

Data acquisition

The instrumentation used to monitor both pile deformation and ground motion during earthquakes consisted of miniature piezoelectric accelerometers, located as shown in Figure 2(a). Pile displacement and horizontal load during monotonic loading were recorded using a linear variable differential transducer (LVDT) and a load-cell, located at the top of the pile and at the point of load application respectively (Figure 2(c)). The accelerometers located at the top of the pile also enabled to derive the pile rotation.

SEISMIC RESPONSE

The results of the pile-head response to the input ground motions EQ1, 5, 6 and 8 are shown in Figure 4. The response to the initial sine sweep (Test EQ1, Figure 4(a)) shows that the natural frequency of the structure is 0.5 Hz at prototype scale (30 Hz model scale). The final sine sweep (Figure 4(b)) shows that the natural frequency of the structure post-earthquake is comparable to the original pre-earthquake first mode of vibration, suggesting that the dynamic stiffness of the pile-soil system is relatively unchanged.

The large earthquake of 10 cycles at 0.5 Hz prototype scale (30 Hz model scale) shows a large resonance effect of the structure in first mode, even for a small magnitude of the earthquake (Figure 4(c), Table 3), with an amplification factor of 5.2. When a higher frequency earthquake at 1 Hz prototype scale (60 Hz model scale) is applied (Figure 4(d)), the pile top response is much smaller compared to 0.5 Hz earthquakes with a reduced amplification factor of 0.8. Figure 4(d) also reveals a strong amplification at 0.5 Hz, although the amplification has very little energy present at this frequency. This is due to the resonance effects as before. While the amplification at resonant frequency of the pile-soil system is expected, the magnitude of this amplification is striking. In contrast the second mode of vibration (2 fn) is attenuated suggesting that the dynamic effects for second mode and higher are negligible and that the monopile is more vulnerable to earthquakes with strong, low frequency components.

POST-EARTHQUAKE MONOTONIC RESPONSE

Comparison between the pile monotonic response before (solid grey line) and postearthquake (dashed black line) is shown in Figure 5(a,b). The horizontal load vs. pile displacement at point of load application for large displacements ( = 25% ) is shown in Figure 5(a), and for small displacements ( = 1% ) in Figure 5(b). The results clearly show that the pile behaviour, both in terms of stiffness and strength is affected by the earthquake history. The post-earthquake large displacement response in Figure 5(a) can be divided into three almost-elastic regions, with the initial stiffness clearly softer than the pre-earthquake pile ) and the two subsequent phases displaying increasingly large strain-hardening. This change in behaviour is hypothesized to have been caused by (i) densification of the top loose layer during the series of earthquakes, while (ii) degradation of the soil-pile interface caused by soil grains re-arrangements as the pile vibrates under each earthquake loading (Figure 5(d)). It is likely that the bottom layer relative density is not greatly affected by the earthquakes, although small changes in small strain shear modulus are observed (see Figure 3). Since the behaviour of short piles is dominated by the wedge mechanism at the top of the pile, rather than the soil flow-around at depth, when the pile is then pushed laterally, the behaviour is largely affected by the top layer grains re-arrangement: on initial loading, the behaviour is dominated by the degraded soil-pile interface, and is hence softer. Once the lateral displacements are large enough and this zone has been sufficiently loaded, the denser layer provides a stiffer lateral reaction. It is likely that there is a transition zone between the degraded zone and far-field dense zone, explaining the second portion of the dashed curve in Figure 5(b).

Finally, Figure 5(c) provides the bending moment profile of the post-earthquake pile during the final lateral load. At the soil surface, the pile bending moment could also be derived from the load-cell data multiplied by the load eccentricity, and shows good agreement with the measurements from the strain gauges close to the soil surface.

CONCLUSIONS

Pile response to earthquake loads is currently modelled by degrading the monotonic and/or cyclic response post-installation. In this paper, the pile response during and post-earthquake was evidenced via a dynamic centrifuge experiment. Two identical piles were installed in a dense layer of sand, overlaid by a loose layer of the same sand. The first pile was laterally loaded prior to triggering any ground motions, to establish the initial pile capacity, while the second pile, instrumented with strain gauges, was used to record the earthquake response and estimate the subsequent monotonic pile response.

It was concluded that the pile response to ground motions close to the first mode of resonance displays large amplification that require further investigation for development of design guidelines. Furthermore, the pile response to post-earthquake lateral loading is greatly affected by the re-arrangement of the loose layer grains over the earthquake history. The monotonic behaviour differs from the pre-seismic monotonic behaviour and is unlikely to be captured via degradation of the monotonic p-y curves.

Figure 1 .

 1 Figure 1. Typical loading and dimensions of offshore wind turbines

  Evolution of measured (a) shear wave velocity and (b) small strain shear modulus with depth and comparison with theoretical profiles from Hardin and Drnevich (1972) and Oztoprak and Bolton (2013)

Figure 4 .

 4 Figure 4. Pile top response to EQ1,5,6 and 8 ground motions

  Pile response to monotonic loading before and after earthquakes: Load-displacement curves at (a) large ( = % ) and (b) small displacements ( = % ); (c) bending moment; (d) schematic representation of soil layout response post-earthquake under lateral load

Table 1 . Properties of Hostun HN31 sand

 1

	Property	Symbol	Unit			Value
	Minimum void ratio			-			0.555
	Maximum dry unit weight			-			1.01
	Specific gravity			-			2.65
	Critical angle of friction			degrees			33
	Mean particle size			mm			0.424
	Uniformity coefficient			-			1.67
	Table 2. Pile properties
		Embedded length	Diameter	Load eccentricity	Wall thickness	/	/	/	/
	Model	200mm	38.1mm	300 mm	1.59 mm 7.87 1.5 5.25 24
	Prototype	12 m	2.29 m	18 m	2.86 cm	7.87 1.5 5.25 48

Table 3 . Characteristics of ground motions (*sat : MEMS saturated, cannot obtain peak)

 3

	EQ No.		EQ1	EQ2 EQ3 EQ4 EQ5 EQ6 EQ7 EQ8
	Peak	Input	0.05	0.13 0.13 0.1	0.05 0.15 0.12 0.05
	acceleration (g)	pile Top	0.2	0.09 *sat	*sat	0.26 0.12 0.06 0.31
	No of cycles		Sweep Kobe 15	15	15	15	15	Sweep
	Frequency (Hz)		0-1		0.5	0.5	0.5	1	1.5	0-1
	Duration (prototype, s.)	80	10	30	30	30	15	10	80
	Amplification factor	4	-	-	-	5.2	0.8	-	6.2
	(top pile/input)

© 2020 Deep Foundations Institute

ACKNOWLEDGEMENTS

The authors are thankful to the assistance of the technicians from the Schofield Centre, who helped carrying out the test, as well as the help of Jad Boksmati, Alessandro Fusco and Thejesh Kumar Garala who advised on test set-up and calibration.