Seismic excitation of offshore wind turbines and transition piece response

Expansion of the offshore wind industry in seismically active areas has raised concerns regarding the structural integrity of offshore wind turbines under earthquake loading. This paper details a 3D finite element study to investigate the behaviour of the structure, and in particular the transition piece (TP), under seismic loads. The work focuses on equivalent grouted connection and TP‐less designs, selected as promising design solutions for seismic zones. The numerical model is validated against a medium‐scale 4‐point bending laboratory test, and scaled up to a representative 8 MW turbine. The results show that cracking of the grout occurs due to earthquake excitation at the top of the TP; a location that is typically undamaged during monotonic loading. This can lead to excessive settlement of the transition piece and loss of axial capacity caused by deterioration of the grout‐steel bond and water ingress. The residual hub displacement after earthquake excitation is around 0.1 m. The global monotonic response post‐earthquake excitation is not significantly altered, with apparent stiffness and ultimate strength maintained. An equivalent TP‐less design is shown to have a 5% lower natural frequency than an equivalent grouted connection design, suggesting a reduced global stiffness, with reduced structural damping due to the absence of grout. However, TP‐less design eliminates the risk of grout deterioration and settlement and may therefore be a safer design option for offshore wind turbines installed in seismic zones in the future.

F I G U R E 1 Schematic overview of a representative OWT model with a grouted connection (GC) and TP-less design.
80% of currently installed offshore wind turbines are installed on monopile (MP) foundations, 2 with a transition piece (TP) connecting the foundation to the superstructure ( Figure 1). The most common type of MP-TP connection is a grouted connection (GC), consisting of a cementitious ultra-high-strength grout cast between concentric steel tubes. Load transfer occurs via shear friction mobilised by normal stress induced through interlocking of imperfections and compression of the grout. Grouted connections were first used for oil and gas installations, with transfer of the technology to offshore wind applications in 2002. 3 However, in 2009, DNV highlighted concerns regarding insufficient axial capacity of grouted connections following observations of significant settlement of newly installed transition pieces. 4 This was attributed to the direct application of design practice from the oil and gas industry to monopiles of much larger diameters, and hence higher flexural rigidity, with significantly higher overturning loads. Following experimental testing, Dallyn et al. 4 concluded that the significantly larger bending moments observed in the grouted connection in offshore wind structures (compared with oil and gas installations) resulted in ovalisation of the tubular connection and the formation of gaps between the grout and the surrounding steel in the connection. This led to a reduced axial capacity of the connection and excessive relative displacements under loads significantly lower than the ultimate limit state. The effect can also be worsened by the possibility of water ingress between the grout and steel following the formation of cracks in the grout, further reducing the integrity of the bond and axial capacity. This led to adjustments in the DNV-OS-J101 guidelines 3 (now known as DNVGL-ST-0126 5 ) and improved design practice, including the use of conical interface surfaces 3 and the addition of bolts. 6 The most commonly adopted modification consists of the addition of circumferential welds to act as shear keys in the grout (Figure 1) as this significantly reduces settlement while retaining manufacturing simplicity. 3,7 The design guidelines consider fatigue damage in grouted connections due to cyclic loading under operational loads, 5 but reduced confidence in grouted connections in the offshore wind industry remains and the effect of large stress cycles on the connection due to seismic loads is not well documented.
Alternative designs for the connection have been explored and adopted, and Table 1 provides a comparison of these alternatives. Bolted flange connections commonly use M72 bolts and have been deployed since 2009. 8 However, this type of connection is vulnerable to loosening of nuts 9 under dynamic loads, and therefore may be a higher risk solution in seismic areas. Slip joint connections have been developed much more recently, 10,11 and deployed for the first time in 2020. 12 They consist of a simple friction connection between conical surfaces of the monopile and transition piece, with integrity of the connection introduced through vibration-assisted gravity fitting of the transition piece. However, settlement of the connection during installation has been observed for frequencies below 20 Hz, 10 and therefore harmonic excitation of the TA B L E 1 Comparison of current MP-TP connection design practices. connection under high-frequency seismic loading could potentially cause disengagement of the friction connection and excessive displacements. The most recent design development is to construct the monopile and tower as a single piece (TP-less, Figure 1). Initial assessment of this type of design by Empire Engineering and Wood Thilsted 13 estimates a reduction in operational expenditure (OPEX) of 6%-10%, and opportunity for significant life extension. This design method is only now becoming feasible due to the introduction of larger installation vessels which can transport considerably longer monopiles. There is significant risk associated with the increased cost of manufacture of the support structure as one piece, and the necessity of driving the pile directly on the tower interface flange. As a result, widespread deployment of TP-less designs is likely to take time. Nevertheless, the simplicity of the design is likely to offer good performance under seismic loads.
It is likely that designers will pursue designs with grouted connections in seismically active zones in the immediate future, particularly due to the accumulated experience of using this type of connection in the industry, and design improvement. TP-less designs may offer a good alternative once the technology and supply chain are mature.
Research of the structural behaviour of offshore wind turbines under dynamic loads is increasing. De Risi et al. 14 Vacareanu et al. 15 and Kaynia 16,17 showed high sensitivity of OWT structures to historical seismic events, accounting for the combination of seismic and environmental (wind/wave) loading. Sensitivity to the operational conditions (e.g. idle or maximum power generation) was also observed by Mo et al., 18 highlighting the importance of considering operational loads in seismic analyses. However, these studies did not model the transition piece explicitly. This paper focuses on establishing a 3D finite element model to assess the seismic response of the transition piece and support structure of a representative 8 MW turbine with both a grouted connection and TP-less design ( Figure 1). Validation of the numerical model is achieved via comparison with a medium-scale experimental test on a grouted connection under quasi-static four-point bending, performed by Wilke. 19 The specific interest of this study is to verify the gapping failure mode in the grouted connection identified by Dallyn et al. 20 under seismic excitation and assess cracking, and to investigate the effect of the connection on the dynamic response of the structure. This paper provides a comparison of the performance of a grouted connection compared with a TP-less design under seismic excitation, and assesses the post-seismic monotonic response of both structures, including latent hub displacements, stiffness and strength.

NUMERICAL MODELLING
The results presented in this paper were obtained through 3D finite element analysis using the general-purpose multiphysics finite element package LS-DYNA. 21 LS-DYNA has been specifically designed for dynamic analyses with high degrees of non-linearity, and therefore offers excellent explicit time integration capability. It has formulations for advanced contact modelling, and includes robust constitutive models developed to capture cracking in cementitious materials. Monotonic analyses were performed using the implicit solver, enabling higher computational efficiency over the explicit solver for static loading conditions. Dynamic analyses were performed using implicit-explicit switching, with an initial implicit analysis to preload the structure, followed by dynamic excitation using the explicit solver, and finally followed by an implicit analysis to obtain the post-earthquake monotonic response. This numerical modelling scheme was chosen following work by Asnaashari et al. 22 and Vieira et al. 23 who demonstrated the effectiveness of 3D FE analysis to model grouted connections under static loads. Natural frequencies and modeshapes were determined using the Block Shift and Invert Lanczos method. 21

Geometry and discretisation
Dynamic analyses were performed using 2 full-scale models: one with a grouted connection, and one with a TP-less design. Geometries were chosen to capture a representative design for the support structure of an 8 MW turbine based in South-East Asia (e.g. Formosa 1), based on the Vestas V164 8 MW wind turbine generator. 24 A monopile diameter of 8.75 m was selected, both because it is representative of an 8 MW turbine support structure, and also because this corresponds to one of the standard design cases of the PISA project 25 (Geometry D2 25,26 ), allowing for the use of a representative PISA soil response (Section 2.3). A water depth of 30 m was chosen, representative of installations in East Asia. The dimensions of the upper structure were then selected to be coherent with the foundation, and based on typical dimensions to support the Vestas V164 8 MW turbine generator. The key dimensions of the models are provided in Figure 1.

Grouted connection model
The dimensions of the grouted connection are in accordance with DNVGL-ST-0126 guidelines 5 ( Figure 1), with shear keys occupying the centre third of the grouted length. Exact dimensions were adjusted to be coherent with the medium-scale laboratory model detailed by Wilke,19 whose test data was also used for model validation (Section 3). The height of the TP flange above the mean sea level was 22.9 m, with mean sea level positioned at the centre of the grouted connection. The support structure was discretised using eight-node hexahedral solid elements with a constant stress formulation, with the exception of the central elements of each shear key, which used six-node tetrahedral solid elements. Solid elements were selected over shell elements to better capture through-thickness stresses and to allow for more robust frictional contact to be defined between the steel and grout. A minimum of three elements through the material thickness was ensured throughout the model. The mesh of the GC model was refined around the connection itself, as shown in Figures 2A and 2B. Table 2 provides further details on the dimensions of the connection used in the GC model.

TP-less model
The TP-less support structure geometry consists of a linear taper from the monopile diameter at the mudline ( = 8.75 m), to the diameter of the base of the turbine tower ( = 7.7 m), with the same wall thickness as the monopile ( = 91 mm). No localised mesh refinement was required for the TP-less model ( Figure 2C).

Superstructure
The LEANWIND 8MW reference turbine geometry 27 was used to model the turbine tower, with the exception of the individual tower can thicknesses. Early monotonic analyses of the structure exhibited unrealistic local buckling of the tower base under relatively small loads. Therefore, the diameters and heights of each can were taken from the reference geometry (Table 3), but the thicknesses were adjusted to obtain sufficient bending stiffness and reasonable bending stress distribution, while maintaining representative natural frequencies of the structure. A similar average thickness over the length of the tower was maintained compared with the reference turbine. The entire turbine assembly (including blades) was lumped at hub height as a 495 tonne point mass, in-line with the axis of the tower. Many turbine models have an offset of the rotor-nacelle assembly centre of gravity from the tower axis, but this distance is small compared with the vertical distance between the TP and the hub (i.e., the tower height), which dominates the bending moment in the tower and foundation. As such, this offset and its effect on the three-direction mass inertia of the RNA was not considered. The turbine tower was discretised using fully integrated quadrilateral shell elements with a significantly coarser mesh density than for the support structure, as the global structural response of the tower was of interest, rather than local stresses. The tower was connected to the top of the transition piece using rigid connections between adjacent nodes, as this connection is suitably far from the grouted connection, and is usually a bolted flange allowing limited relative displacements in the plane of the section. Table 3 details the tower can dimensions, with arrows indicating a step-change in wall thickness at a particular elevation.

Grout
The physical properties of the grout were defined according to Wilke 19 and Ducorit S5 product specifications (the grout manufacturer), 29 and are representative of the grout used for grouted connections offshore. The Winfrith material model was used to model the grout. This is a plasticity model that simulates Mohr-Coulomb like behaviour, with the inclusion of the third stress invariant that enables both triaxial compression and triaxial extension to be accounted for. 30 The model is based on the four parameter model proposed by Ottosen,31 and allows for up to three orthogonal crack planes per element. Figure 3 shows a schematic view of a block of elements failing in the shear cracking mode under compressive load captured by the material model. A fracture energy approach was used 32 to avoid using a strain formulation, which has been reported to cause numerical instabilities in concrete-related analyses. 33 The fracture energy, was determined from the CEB model code for concrete structures 34 : where 0 is the base fracture energy as a function of aggregate size, and 0 = 10 MPa. The material properties for the grout used in the FE analysis are summarised in Table 4.

Soil-structure interaction
The response of the foundation to lateral loads was captured using lateral and rotational macro-element springs located at the mudline ( Figure 1). This was chosen as an alternative to the more traditional 1-D p-y curve method due to the ability to capture load reversal behaviour under cyclic loading. The load-displacement behaviour of the soil under repeated load cycles, as well as the resulting hysteretic damping, has a significant effect on the dynamic response of the structure, and needs to be accounted for in seismic design. While not providing information about the detailed load distribution along the pile, a macro-element model allows for a very efficient representation of the soil structure interaction for structural analysis. This efficiency was required in this case to permit more detailed and complex analysis of the transition piece. A discussion of the advantages of this modelling technique, compared with 1-D representations, is provided by Abadie et al., 35,36 showing the computational efficiency of a well-calibrated macro-element model similar to the one used in this paper. This approach also allows for simple application of the seismic loads, with the ground motions applied to the free end of each spring (Section 2.5.2). The lateral and rotational macro-element springs were assumed to be uncoupled, which is unlikely to be the case in reality and is a limitation of this work. Further research is needed to develop a rigourous formulation of this coupling, and there is currently very limited guidance in published literature.
The unload-reload response needed to capture the response to cyclic loading was obtained through a kinematic hardening model. The hysteretic loop follows the Masing rule, 37 with the response to perfectly symmetric loading such that (i) the unloading and reloading curves are defined based on the initial loading curve (the backbone curve) scaled by a factor of 2 and (ii) after any load reversal, the tangent shear modulus is the same as the initial shear modulus of the backbone curve. This captures a reverse loading response that is representative of the macro response of the pile, but relies greatly on an appropriate choice of backbone curve, discussed in the following sections. The model does not account for ratcheting, gapping and excess pore water pressure 35,38 and was implemented through a parallel-series Iwan model. 39,40 Further work is needed in the future to account for these effects, with excess pore water pressure and local liquefaction along the pile shaft being of particular interest. However, there is not currently any robust spring model able to capture this adequately for monopile design.

Lateral response
The backbone curve for the torsional − and lateral − springs were chosen based on the PISA work, 25,26 with and being the moment and lateral load at ground level, respectively, and and the pile rotation and displacement at ground level, respectively. The PISA project was a joint industry project run through the Carbon Trust from 2013 to 2017. 26 The project enabled the development of improved numerical methods for the design of monopiles subjected to monotonic loading. The findings are now widely adopted by the offshore industry, and it is regarded as a robust method for the prediction of the response of large diameter monopiles at ground level. PISA 2 (2017-2018) 25 expanded the PISA design method to layered soil profiles. In this paper, the case of a relatively realistic stiff layered soil profile (E3) was chosen, consisting of alternating layers of Cowden till and Dunkirk sand of varying relative densities ( Figure 4A). The macro-response published by Burd et al. 25 Figure 4B also shows the − response of the final macro-element Iwan model used in the model presented here. This is compared with the monotonic response published by Burd et al. 25 for validation. Particular focus is drawn to the small displacement region of the curve, as accurate estimation of the small-strain stiffness plays an important role in the determination of the structural natural frequencies.

Axial response
The axial response was not considered in the PISA work, and instead was derived from first principles and the API design method. 41 The backbone curve response was idealised as elastic-perfectly plastic. The ultimate axial capacity was derived using the API method for driven piles in sand and clay, 41 with the shaft resistance integrated over each soil layer. A capacity of 185 MN was obtained for the selected soil profile ( Figure 4A). The axial pile stiffness was derived based on the assumption of a rigid pile 42 : where is the vertical load and is the pile vertical settlement at ground level (1). is the pile radius (4.35 m). is the shear stiffness at the pile base, is the mean shear stiffness along the pile shaft, and is the Poisson's ratio. This elasto-plastic model was also implemented through an Iwan formulation to enable modelling of load reversal following the Masing rule. 37

Boundary conditions
Seismic excitation was applied in all three directions at ground level, and therefore no axis of symmetry could be used and the entire structure was modelled. The nodes of the monopile at the mudline were connected by a nodal rigid body (NRB), allowing global displacement and rotation of the node set, but no relative displacements within the set. The SSI macro-element springs described in Section 2.3 were connected to the central node of the mudline NRB. In addition to this SSI condition, a clamped support condition was also analysed for comparison by constraining this mudline NRB in all 6 degrees of freedom. Going forward, the two support conditions are referred to as 'stiff soil' and 'clamped'. Contact was defined between the grout and steel surfaces using a penalty-based formulation and a coefficient of friction of = 0.4.
A non-reflecting boundary was defined at the mudline using an impedance matching formulation in order to avoid contamination of the results of the dynamic analyses by the re-entry of reflected stress waves at the fixed end of the soil springs.

Quasi-static loads
Load arising from self-weight was simulated using translational base acceleration in the vertical direction equal to 9.81 m s −2 , resulting in the appropriate inertial body force loads being imposed on the nodes of the structure due to gravity.
The importance of considering operational loads when considering the seismic response has been highlighted by Esfeh 43 and Kaynia. 16 For this reason, operational wind and wave loads were applied to the structure during all dynamic analyses. To allow for independent assessment of the dynamic response to seismic excitation alone, the operational loads were considered to be quasi-static, and the dynamic excitation due to wind and wave loads was not considered. The quasistatic loads were based on an operating state of maximum power generation at a wind speed at hub height ℎ = 13 m s −1 and a representative sea state of significant wave height = 4 m and period = 8 s. Equivalent static loads for these environmental conditions were calculated using the method summarised in Appendix A. The wind load on the rotornacelle assembly was concentrated as a point load at hub height and was equal to 1.36 MN. The wind load on the rest of the structure varied nonlinearly from 0.06 kN m −1 at mean sea level to 0.2 kN m −1 at hub height. Wave load varied nonlinearly from 143 kN m −1 at mean sea level to 48 kN m −1 at the mudline. The directions of wind and wave loading were assumed to be coincident, to capture a severe loading condition.

Seismic loads
Ground motions were applied to the model as imposed velocities at the free end of each soil spring, with baseline correction to eliminate drift. Applying ground motions as velocities is a common practice to avoid instability and error associated with double integration of acceleration time histories when imposing displacement instead. The most severe direction of ground motion for the historical earthquake records considered was aligned with the directions of both wind and wave loading, to capture the most severe case. Ground motions were applied in all three directions using available accelerometer time histories. 44 Given the complexity of the grouted connection model and the associated high computational cost, the selection of a limited number of relevant earthquake motions was essential. As such, two earthquake records were selected for this study, enabling direct comparison with published work on offshore turbines under seismic loads 17,18,45 : (i) Kobe, Japan, Nishi-Akashi, January 17, 1995, and (ii) Chi-Chi Taiwan-03, CHY082, September 20, 1999. These were also selected because of their significantly contrasting characteristics, enabling further insight into the dynamic behaviour of the structure under varying seismic loads: • The Kobe motion has a high peak ground acceleration (PGA), of 0.5 g, whereas the CHY082 Chi-Chi motion has a much lower PGA of 0.05 g • Ground displacements are higher during the Chi-Chi motion compared to the Kobe motion • The two records have very different frequency characteristics -the Kobe motion is largely composed of higher frequency accelerations, with the major peak at approximately 2 Hz, whereas the CHY082 Chi-Chi motion has a more even distribution of accelerations, with significant low frequency oscillation between 0.1 and 1 Hz The ground motions observed during the Chi-Chi earthquake were heavily dependent on local geological conditions, with high PGA and frequencies observed south of the epicentre, and low PGA and very low frequency (and subsequent high ground displacements) in the north. 46 The CHY082 station observed the latter characteristics, and was chosen in this paper as a comparison to the Kobe motion. Figures 5A and 5B show the unscaled ground acceleration and displacement time histories for the two earthquake records, in the most severe accelerometer direction.
Finally, in addition to the historical input motions, an artificial sinusoidal input of magnitude 0.3 at the first natural frequency 0 of the structure was also analysed, with an acceleration of: The sinusoidal excitation was applied in one direction only, aligned with the direction of operational loading, allowing for more rigourous investigation of the structural response at resonance. Seismic analyses were followed by a monotonic lateral load, applied at the hub height and up to the capacity of the structure, allowing for investigation of the post-seismic performance of the structure.

Damping
The overall damping of an offshore wind turbine consists of aerodynamic, hydrodynamic, structural, and soil damping. Aerodynamic damping was estimated to be 3.5% from Liu et al., 47  damping consists of radiation and viscous damping, and values suggested by Germanischer Lloyd 48 of 0.22% and 0.15% were used. Structural damping was estimated based on material damping of steel of 0.3%. 48 Soil damping was not added, both because it is already accounted for by the energy contained within the hysteresis loop of the constitutive model described in Section 2.3, and also because it is difficult to estimate accurately. 48 The influence of additional damping through the use of tuned mass dampers in the tower was not considered, but could form part of future research.
Damping was applied using frequency-independent damping stresses applied to the elements of the structure, a technique developed by Richard Sturt and Yuli Huang (Arup) for use in automotive and seismic vibration problems, and implemented in LS-DYNA. 21 The damping model allows for uniform damping to be applied to a wide frequency range, does not damp rigid body modes which would not be dissipative in reality, and captures diminished damping once stresses exceed the elastic range. 49 Structural damping was applied to all elements of the model, and aerodynamic and hydrodynamic damping was applied only to those elements above or below the water line, respectively.

Analysis programme
The numerical analysis programme involved (i) validation of the model, (ii) eigenvalue analysis, (iii) seismic analysis, and (iv) monotonic analysis, both before and after seismic excitation. Validation was achieved via comparison with experimental test data for a medium-scale model, described in Section 3. The seismic analyses consumed the vast majority of the computational time, and dictated the choice of combinations of geometry, support condition and input motion to analyse. All combinations of support condition and geometry were investigated for the Kobe ground motion, as it is the most representative record for earthquakes in East Asia. The stiff soil support condition for both geometries was then used for analysis with the Chi-Chi ground motion. Both the grouted connection and TP-less models with stiff soil support conditions were subjected to sinusoidal oscillation at the first natural frequency.
Eigenvalue analyses and pre-and post-seismic monotonic analyses were performed for all combinations of geometry and support conditions.

Medium-scale physical test model
Very little published data on physical tests is available to validate numerical models of transition pieces, largely due to the size of the tests required. No data was found regarding dynamic response, but Wilke 19 performed a quasi-static 4-point bending test on a medium-scale grouted connection which was used for validation of the material models at the same scale. Wilke's 4-point bending test reproduces a representative bending moment in the grouted connection to reproduce the governing failure mode identified by Dallyn et al. 4 While axial load was not considered in Wilke's test, the test provides very useful data for validation of the numerical model as it is capturing the behaviour under the governing load in isolation.
A schematic of this test is shown in Figure 6A. Figure 6B shows the equivalent 3D FE model developed for validation, making use of the symmetry plane to reduce computational cost. The simply-supported boundary conditions were replicated through the use of point constraints. The grout material used in the test model (Ducorit S5) was representative of grout used in full-scale offshore installations, particularly with regards to geometric specifications (e.g., aggregate size), and as such is representative of the behaviour of the grout at full-scale. The frictional capacity of a full-scale connection would be expected to be lower than that of the small scale test specimen because of (i) the scale independency of fabrication parameters, typically resulting in a relatively rougher surface for smaller diameters; and (ii) the reduction in activated hoop/compression stress and associated reduced bond strength with increasing diameter. However, Wilke 19 quantified this reduction for a range of connection designs, showing that this reduction is very small for grouted connections with shear keys, where the response is dominated by the compressive strength of the grout and is effectively independent of scale effects. As a result, this test model captures the behaviour of a full-scale grouted connection well.
The steel material properties used in the FE model were defined according to the tensile tests performed by Wilke. 19 Load was applied to a set of nodes on each loading flange over an area equivalent to that of the physical test. The load eccentricity present in the physical test was replicated through calculation of the equivalent forces applied to each loading flange.
The  DNVGL-ST-0126. 5 Tziavos et al. 51 also developed a detailed 3D FE model of this test specimen to study the effect of additional shear keys on the settlement of the transition piece, and these numerical results were used for further validation.
The response of the FE model during the 4-point bending test is assessed by plotting the displacement of reference point 1 ( Figure 6B) in the direction of loading. The results shown in Figure 7A demonstrate very good agreement between the FE models and the experimental data, with the initial stiffness, peak displacement and latent plastic deformation within 2% of the experimental results. The gap opening at reference point 2 ( Figure 6B) also shows good agreement, with the maximum gap opening within 6% of the experimental results ( Figure 7B). The stress distribution and magnitudes observed in the FE model also displayed good agreement with both the numerical and experimental results from Wilke and Tziavos, respectively. These results provide confidence in the material models selected for the numerical analysis, along with their constitutive properties.

Comparison with analytical model
The analytical model from Lotsberg et al. 50 was used as a secondary approach to validate the FE model. The total moment at transition piece level, is related to the nominal radial contact pressure, at the top and bottom of the connection: where , , and are the radius and thickness of the monopile and transition piece, respectively. is the Young's modulus of the steel, is the grout length and is the friction coefficient of the grout-steel interface.
is an effective vertical stiffness per circumferential length representing the resistance of the shear keys, derived based on structural mechanics as: where and are the effective number and spacing of the shear keys, is the grout thickness, and is the Poisson's ratio of steel. The contact pressure is then related to the vertical displacement of the transition piece relative to the monopile : Figure 8A shows the displacement predicted by the analytical model at the final applied load of 1 MN for the model test described in Section 3.1. This is also compared with the results from Tziavos. 7 There is very good agreement between the FE model and the analytical model, particularly at the final applied load of 1 MN, providing further confidence in the numerical modelling of the frictional interface between the grout and the steel.
As the validated model is of a smaller scale than the full-scale models described in Section 2 and used for subsequent dynamic analysis, the test geometry was scaled up by a factor of 10. This enabled the modelling of an 8 m diameter grouted connection, with the applied load increased to 100 MN to achieve a similar level of plasticity. This provided a geometry similar to the geometry of the grouted connection model (Section 2.1), to bridge the gap between the medium-scale and full-scale models. Scaling of the grout material model is not necessary, as the grout used in the experimental test was representative of grout used for full-scale installations in terms of strength and aggregate size. Scaling of the frictional characteristics between the grout and steel is also not necessary, as explained in Section 3.1 and shown by Wilke. 19 Figure 8B shows the displacements predicted by the analytical and FE models at this larger scale. There is very good agreement at the final applied load of 100 MN, providing further confidence in the model described in Section 2, and confidence in the extension of the model to full-scale.

Mechanism of deformation
Grouted connections have been shown to be susceptible to the formation of gaps between the grout and steel due to ovalisation of the circular cross-section under large bending moments. 20  through the course of the dynamic analysis, with displacements magnified 500x for clarity. Under operational load alone the connection ovalises subtly, and gaps form at the top and bottom of the connection. The deformed shape agrees well with that observed by Wilke, 19 with a characteristic s-shaped deformation, more pronounced in the less stiff pile section. As the earthquake progresses and the structure oscillates in its first bending mode, the ovalisation of the circular crosssection significantly worsens, the gaps increase in size and the grout begins to debond from the steel in these areas. After the ground motion has finished, the ovalised shape returns to that observed before excitation, but the grout-steel bond is compromised due to the repeated cycles of severe ovalisation.This is analysed further in Section 4.2. Finally, Figure 9E shows the deformed shape under a monotonic load equivalent to four times the operational load. This is applied after seismic excitation has finished, capturing an extreme monotonic load to ultimate capacity. Unsurprisingly, this extreme case exhibits more ovalisation of the connection than the other cases, and a similar deformed shape would be obtained without prior earthquake excitation. Nevertheless, the ovalised shape observed under maximum bending during the earthquake ( Figure 9C) is similar to that observed in Figure 9E, highlighting the severity of the deformation caused by seismic excitation.

Grout deterioration
Along with gap formation, damage of the grout material itself can lead to water ingress as the grout fails and powder forms, which can result in loss of bond extent, corrosion and excessive settlement. 20 Therefore, confidence in grout integrity during and after seismic excitation is essential. The load transfer mechanism through the grout occurs through the development of compressive struts between adjacent shear keys, clearly evidenced by the numerical analyses. Figure 10 shows contours of the compressive stress in the grout at the centre line cross section on the primarily compressive side of the connection (opposite operational load application -point 2 in Figure 1) 15 s after the start of the Kobe ground motion. During dynamic oscillation of the structure these compressive struts undergo corresponding oscillation in magnitude, and on the opposite side of the connection similar oscillating tensile zones occur in the grout. However, during the earthquake and subsequent free vibration, the cyclic loading of the grout between adjacent shear keys causes significant cracking. Figures 11A and 11B show damage in the grout before and after the earthquake. In these Figures, blue indicates an uncracked, healthy element, green indicates initialisation of a crack, with strains on the softening curve (tensile stresses remain), light orange indicates a developed but closed crack (compressive stresses remain), and magenta indicates a fully cracked element (the crack is open and no tensile/compressive stress can be generated).
Under operational load ( Figure 11A), the initialisation of cracks remains limited, and is confined to the upper shear keys on the compressive side of the connection. On the tensile side, the development of cracks is uniform across all shear keys, but limited in extent to approximately 10% of the circumference for each shear key. This failure mode of the grout is in good agreement with experimental observations from Wilke 19 and numerical computations from Tziavos et al. 51 Following the earthquake (Figure 11B), the circumferential cracks on the tensile side developed and propagated to approximately 50% of the circumference at each shear key location. Cracks on the compressive side at the top of the connection also developed more severely. These zones of extensive damage are due to initiation and propagation of cracks in in-plane shear (Mode II, Figure 3), caused by the large compressive stress concentration at the top of the transition piece during dynamic oscillation of the structure. Figure 12 shows a time history of percentage of cracked elements in this compressive region in the top 1.5 m of the connection during seismic excitation, alongside the lateral TP displacement (Figure 13A Point 2) and input acceleration time histories. It is clear that the initiation and propagation of cracks (shown by the accumulation of cracked elements) correspond with the large oscillations of the structure in the first mode, with significant propagation after each compressive cycle. By the end of the motion, approximately 8% of the elements in the top 1.5 m of the connection have cracked, and these elements are almost exclusively on the compressive side. Under monotonic loading alone, even at four times the operational load, no cracking in the top 1.5 m of the connection was observed. This cracking is likely to reduce the groutsteel bond strength as grout powder formation occurs, and significantly increase the risk of water ingress and corrosion. Further cyclic loading could cause progressive failure further down the connection as the extent of bond is reduced, and further impact capacity. It is of particular concern that while the structure is expected and designed to be able to withstand an earthquake event like the one analysed, significant damage may be caused to the grout that could significantly impact its lifespan, and this is not something that is currently considered in design, with cracking in the upper compressive zone unique to seismic excitation. Design of connections for future use in seismic zones should require remediation of the high stress concentrations at the top and bottom of the connection, as well as consideration of cracking between adjacent shear keys to avoid risk of extensive grout damage and unexpected settlement and reduction in capacity.

Modal analysis and natural frequencies
Natural frequencies and modeshapes for each model were determined using the implicit solver and the Block Shift and Invert Lanczos method in LS-DYNA. Due to the symmetry of the structure, identical modes exist in both the fore-aft and side to side directions, and for the purpose of this modal analysis one of these directions was constrained. Only bending modes were considered, so the rotational degree of freedom about the axis of the monopile was also constrained. Figure 13A  shows exaggerated views of the first, second and third modeshapes, with reference points labelled for analysis in the following sections. The support type of transition piece (grouted connection or TP-less) were not found to significantly alter the mode shapes. Figure 13B shows the normalised peak spectral acceleration for the 8 MW LEANWIND reference turbine, with the computed natural frequencies and earthquake ground motions. This is shown on a logarithmic scale to facilitate comparison with the earthquake spectra. The first natural frequency in all cases was found to lie between the 1P (turbine rotation) and 3P (blade passing) frequency ranges (the 'soft-stiff' domain), which is in line with design practice. Figure 13B shows the effect of the transition piece on the natural frequencies of the structure. While the equivalent TP-less structure has less steel at connection level, and therefore a reduced global stiffness, the inclusion of the (softer) grout also softens the response. Figure 13B shows that the first natural frequency for the TP-less model supported by stiff soil is approximately 5% lower than that of the grouted connection model, with the same conclusion for the clamped support condition. The second natural frequency is very similar for both models ( Figure 13A).

5.2
Hub displacement during seismic excitation Figure 14 shows a comparison between the relative hub displacement due to the Kobe ground motion for the grouted connection and TP-less models. The reduced stiffness of the TP-less model is clearly evidenced by the lower frequency of oscillation. For the stiff soil case, displacements in the first 10 s of excitation are almost identical between the two models, but the second peak is approximately 5% larger for the TP-less geometry. This amplification is magnified further for the case with a clamped support condition, with peak hub displacements 20% larger with the TP-less geometry. Figure 14 shows approximately 0.4% greater structural damping in the case of the grouted connection model with a clamped support condition, with the grout contributing to the overall structural damping.
Latent deformation at hub height after earthquake excitation can also be seen for both geometries, due to soil failure and associated deformation at the mudline. While the hub displacements observed during this severe dynamic excitation are temporary and may be acceptable for the turbine due to being accounted for with generator shutdown and other fault avoidance controller strategies, any permanent deformation due to soil failure is of particular importance due to the often very tight out-of-vertical alignment tolerances that the turbine generator can withstand during normal operation.

F I G U R E 1 4
Effect of connection type on hub displacements in the direction of operational load during the Kobe ground motion.

5.3
Response to low-frequency seismic excitation Figure 15A shows hub displacement during the Chi-Chi ground motion. The peak displacement observed for the TP-less geometry is approximately 20% larger than for the grouted connection. However, the peak displacements for both geometries are 40%-60% larger than for the Kobe ground motion, despite the peak ground acceleration of the Chi-Chi earthquake being an order of magnitude lower. Accelerations at hub height are also high, with amplification factors exceeding 2. This highlights the severe impact of the low frequency components of the Chi-Chi motion. The dynamic response in all cases is dominated by the first mode, and even small ground accelerations near the first natural frequency can cause severe excitation of this mode. The GC and TP-less models were subjected to six cycles of sinusoidal acceleration of magnitude 0.3 and frequency equal to their respective first natural frequencies, to further investigate pure excitation of the first mode. Figure 15B shows a comparison of the relative hub displacements and accelerations caused by this ground motion. Increased damping and reduced peak displacements for the grouted connection model are also evidenced here, with the magnitudes of displacement greatly increased because of the severe motion applied. While this regular sinusoidal motion at the first natural frequency is unlikely to occur in reality, it highlights the severe hub displacements that can occur if there are frequency components close to the natural frequency. High accelerations at hub height are again clear, with amplification factors exceeding 2.
In both cases latent deformation at hub height is again observed, with associated risk for turbine operation as previously discussed.
It should be noted that the above conclusions do not account for the addition of dampers in the tower of the turbine, which would likely be added. However, these results show that the TP-less designs may be more vulnerable to seismic excitation and may require further additional damping.

5.4
Post-seismic monotonic response The structure was allowed to undergo free vibration with zero ground motion after each seismic event until it returned to equilibrium. An implicit switch was then executed to perform a static analysis on the structure. The static loads were removed, and the structure was linearly reloaded to approximately 4 times the operational load. An independent and identical static analysis was performed for each model without prior seismic excitation, to allow for comparison between the pre-and post-seismic response. Figure 16A compares the load-displacement response at hub height before and after the Kobe ground motion under varying support conditions, alongside a zoomed view of the initial section to allow for direct comparison of stiffness. These results show that despite accumulated deformation caused by the earthquake, neither the load-deflection response nor the global stiffness are significantly affected by the seismic event. The post-earthquake monotonic responses rejoin the pre-seismic backbone curve after approximately 2 m of hub displacement.
It is important to note that there are limitations to this conclusion, however. The constitutive model used for the soil response, which is a kinematic hardening model (Section 2.3), does not account for the effects of ratcheting, gapping, excess pore water pressure and potential liquefaction on the permanent deformation and stiffness of the soil during seismic excitation. These effects could in reality cause more disturbance to the monotonic response observed in Figure 16A. Further research into the effect of excess pore water pressure and liquefaction will be needed to extend this research in the future. 43,45 The analytical model introduced by Lotsberg et al. 50 to compute the vertical displacement of the transition piece relative to the monopile under bending (Equations 4 to 6) was compared with the displacements obtained using the numerical model. The application of the model to the experimental tests performed by Wilke 19 neglected axial load, and therefore Equation 6 was modified to account for self-weight: F I G U R E 1 6 (A) Pre and post-seismic monotonic response; (B) Vertical displacement of the transition piece relative to the monopile, compared with analytical prediction from Lotsberg et al. 50 where is the self-weight of the structure above the monopile, including the full self-weight of the transition piece. The analytical model describes a linear relationship between the relative vertical displacement and the total moment applied at transition piece level, with an initial offset due to the self-weight. This analytical relationship is shown in Figure 16B for the grouted connection geometry described in Section 2.1, compared with the relative displacement obtained numerically both before and after the Kobe and Chi-Chi earthquakes, and at a total moment corresponding to roughly twice the operational load considered in this study. Because the self-weight and monotonic loads are applied linearly for the numerical models, comparison with the analytical model is only possible once the full self-weight has been applied, and therefore only the final displacement is shown for the numerical models.
Very good agreement can be seen between the analytical model and the numerical model with clamped support conditions. Accounting for SSI with the stiff soil response increases the relative displacement by approximately 16%, to a maximum displacement of 2 mm. A further increase in relative displacement is observed following the Kobe earthquake -almost 30% greater than the analytical prediction.
The analytical model is therefore suited if both the soil-structure interaction and deterioration of the grout during a cyclic loading event are disregarded. The design of the shear keys relies on the above analytical model, and as a result the underestimation of settlements (and corresponding shear forces on individual shear keys) shown in Figure 16B suggests that the design calculations presented in DNVGL-ST-0126 5 may be under-conservative in the case of seismic loads.

CONCLUSIONS
This paper investigates the response of a grouted connection and equivalent TP-less design for a generic monopilesupported 8 MW turbine design to seismic excitation. The results highlight the effects of dynamic loads on the structural integrity and capacity of grouted connections and form a basis for further research to inform the design process. For this purpose, this paper details a numerical finite element model for modal and transient dynamic analysis of the structure, with detailed study of the grouted connection response to seismic excitation. A finite element model replicating the medium-scale test performed by Wilke 19 was developed for validation, and excellent agreement is obtained between the numerical model and the experimental data. Further comparison with a similar numerical study performed by Tziavos et al. 51 and the analytical model used in the DNV design guidelines 3,50 provides confidence in the numerical method adopted in this paper. The model was then scaled up to simulate an 8 m diameter grouted connection, representative of a full-scale 8 MW offshore wind turbine, and compared with the analytical model; the only available model available for comparison at such large scale. Excellent agreement between the numerical and analytical models provides confidence in the scaling method.
Based on this validation, 3D finite element models of a representative 8 MW offshore wind turbine with a grouted connection and TP-less design have been developed. Soil-structure interaction is implemented through a macro-element model at the mudline with kinematic hardening and soil response defined according to the PISA project. 25 An operational loading condition is captured for all analyses using a quasi-static representation of the wind and wave load, disregarding dynamic effects to allow for assessment of the dynamic response to seismic excitation in isolation. Future research extending the findings of this paper to consider the combined dynamic effects of wind and wave alongside seismic excitation would be valuable.
Detailed analysis of the grouted connection under seismic excitation shows that a short, severe seismic event can cause significant cracking of the grout in locations typically not observed under monotonic loading. This is of particular concern due to historical issues of settlement and reduced capacity of grouted connections, caused by grout deterioration and subsequent water ingress. The failure mode observed, with extensive cracking in the top region of the connection, is unique to seismic excitation and not currently considered in design. This does not invalidate the use of grouted connections for seismic zones, but further understanding and consideration of this behaviour under dynamic cyclic loading is required in design. In particular, damage due to seismic loading should be considered in combination with prior accumulated fatigue damage during normal operation, which will further add to the risk of capacity reduction.
A reduction of 5% of the natural frequency is found from an equivalent TP-less design. The presence of the grout also increases global damping by approximately 0.4% compared with the equivalent TP-less structure. Consideration of the reduced damping of a TP-less design and appropriate compensation if necessary should be made in practice. Excitation by the Chi-Chi ground motion highlights that earthquakes with prominent low frequency characteristics can be catastrophic, even at low accelerations.
Comparison with the analytical model from DNV 3,50 to predict the vertical displacement of the transition piece relative to the monopile demonstrates that the design guidelines under-predict the settlement due to lack of consideration of the soil response. The results also show that the model, developed without accounting for the effects of seismic excitation, may be non-conservative in the event of an earthquake during the lifetime of the turbine, potentially resulting in an increase in relative displacement of over 30% compared with that predicted by the analytical model. Further investigation of this behaviour and revision of the analytical model for use in seismic zones could be beneficial to ensure robust design of the shear key arrangement in grouted connections and provide greater confidence in the axial capacity and longevity of the connection. This will be particularly important in the next few years, while TP-less designs are still in development.

A C K N O W L E D G M E N T S
The authors are thankful for the contributions of the specialist structures and mechanical group at Arup in providing support, access to computing facilities, as well as the LS-DYNA and Oasys Suite licenses for the development of this work. The authors also acknowledge the contribution of the PISA project team in providing data for the lateral soil response. Fruitful advice and discussion with Alasdair Parkes (Arup), Dr Nikolaos Tziavos (University of Cambridge), Geert Weymeis (Jan de Nul) and Professor Ali Mehmanparast (University of Strathclyde) was also very valuable for the development of this project, together with the help of Carlos Español-Espinel and Professor Robin Langley (University of Cambridge) during the writing phase of this paper.

D ATA AVA I L A B I L I T Y S TAT E M E N T
The data that support the findings of this study are available from the corresponding author upon reasonable request. where ℎ ℎ is the vertical distance between the hub centre and the water line, and ℎ is the wind velocity at this height. The equivalent horizontal force, ( ) can then be calculated: where ( ) is the projected area of the tower section considered, and is the drag coefficient. Finally an additional concentrated wind load is applied at hub height. The force is evaluated through the formulation by Frohboese and Schmuck 53 for wind speeds less than or equal to the rated wind speed, : where is the area swept by the turbine blades and is calculated as: = 3.5 ⋅ (2 ⋅ + 3.5) 1 3 (A4) Equivalent static wave loads were calculated through integration of Morison's equation: where ( ) is the equivalent horizontal force at water depth , is the monopile diameter, is its cross-sectional area, is the drag coefficient, and is the intertia coefficient. The water particle horizontal velocity, and acceleration are undisturbed values that would apply at the member centreline, calculated according to linear Airy wave theory: where is the velocity potential, is the significant wave height, is the gravitational constant, = 2 ∕ , is the wave angular frequency, is the mean water depth, is the horizontal coordinate parallel to the direction of wave motion, and is time. Peak drag loading occurs as the wave passes the monopile, but the peak inertial load occurs at ∕4 before this time, and contributes the vast majority of load. As such, the forces applied to the structure were calculated at time = ∕4. The drag and inertia coefficients were determined according to the relationships between the Keulegan-Carpenter number, , steady-flow drag coefficient, , wake amplification factor, suggested in DNVGL-ST-0437. 54 The monopile was assumed to be a rough cylinder.