Dynamic and monotonic response of Monopile Foundations for Offshore wind turbines using centrifuge testing

The seismic response of monopile foundations is a growing area of research as the offshore wind industry expands worldwide, including in earthquake prone regions of the world. This paper presents dynamic centrifuge tests aimed at investigating the dynamic response of monopiles in both dry and saturated sandy soils. The latter case includes soil liquefaction under strong input motions, with measured excess pore pressures indicating liquefaction. The natural frequency of the monopile-soil system is experimentally determined by measuring the response to a sine sweep motion. Strong earthquakes are then applied at this frequency and its harmonics. This paper discusses the response of the monopile in terms of the peak accelerations observed in the dry and saturated tests, as well as using response spectra and amplification ratios. The dynamic bending moments along the pile are also measured to infer the bending moment profile with depth. Finally, two identical monopiles are pushed-over in each of the centrifuge tests to establish the pre and post-earthquake monotonic response, including the lateral stiffness and capacity, which are compared for the dry model tests and the saturated case.


D R
is the relative density e min is the minimum void ratio e max is the maximum void ratio G s is the specific gravity ϕ crit is the critical angle of friction d 50 is the mean particle size C u is the uniformity coefficient G o is the Initial shear modulus ρ is the soil density V s is the shear wave velocity f n is the natural frequency η is the nominal damping BM is the bending moment F h is the horizontal force applied by the top mass h is the height of the horizontal force application point from mudline m is the weight of the top mass a is the acceleration of the top mass h e is the height of the top mass from mudline V h is the deflection of the monopile at actuator level V g is the deflection of the monopile at mudline H is the horizontal load

Introduction
Monopile foundations are the most commonly employed foundation types for offshore wind turbines (OWTs). With the growth in the offshore wind industry worldwide, new development sites are increasingly being located in seismically active regions of the world, along the so-called ring of fire. In addition to the normal operational loads, earthquake loading will impart additional loads on the monopile and superstructure due to inertial and kinematic effects. There is an urgent need to understand the seismic behaviour of monopiles. Designers of offshore wind projects are interested in both the dynamic response of monopile foundations and their pre and post-seismic lateral response to ensure smooth operations following an earthquake event.
Much of the previous research on monopiles has been motivated by optimising the engineering of the foundation and potential cost reductions Page et al. 2019), and targeted mostly to North-European waters. In the past decades, a number of large research projects have enabled significant progress on the understanding of: • the initial monotonic response in both homogeneous and layered soils (e.g. the PISA/ PISA2 projects (Abadie et al. 2020b), Byrne et al. 2019;Burd et al. 2020). • the influence of pile installation and improved driving methods for large-diameter monopiles (e.g. Achmus et al. 2020; the BLUE Piling project, IQIP 2020). • the influence of long-term quasi-static cyclic loading on pile response and permanent deformation (e.g. Leblanc et al., 2010;Houlsby et al. 2017;Richards et al. 2019;Staubach and Wichtmann 2020;Klinkvort et al. 2020; and currently under development, the PICASO project, Byrne et al. 2020;) • better integrated structural and geotechnical design tools (e.g. the REDWIN project, Skau et al. 2018;the WAS-XL project, Paget et al., 2020).
Several researchers have attempted to numerically analyse offshore foundations under seismic loading. Prowell et al (2010) analysed an OWT under seismic loading with a fixed base with Hongwang (2012) extending this to include soil-structure interaction effects including both horizontal and vertical shaking. The seismic behaviour of the monopile foundations has also recently been investigated recently using 3D finite element analyses (Esfeh and Kaynia, 2020;Kaynia, 2020). A review and benchmarking of existing design methods for piles in seismic environments is also currently being undertaken as part of the ACE joint-industry project (Klose, 2020) as an exploration for knowledge transfer to offshore wind monopile design.
There is a need to obtain high quality experimental data to validate such analyses. Early research used small scale tests at 1 g (Lombardi et al. 2013;Futai et al. 2021Futai et al. , 2021 have shown that it is necessary to investigate the monopile-soil interaction using centrifuge testing as 1 g tests will under-predict the dynamic response of the monopile. Early dynamic centrifuge tests were carried out by Yu et al. (2015) and Wang et al. (2020) looking at uniform deposits of sand with OWTs supported on bucket foundations. Seong et al. (2017) and Seong and Kim (2019) investigated the dynamic response of different offshore foundations using dynamic centrifuge modelling. However, this research was on dry uniform soil beds. This paper outlines the results of dynamic centrifuge tests aimed at investigating the seismic response of monopiles embedded in layered soil profiles in dry and saturated conditions. The dry tests provide a benchmark for dynamic response while the saturated case is more representative of offshore conditions. A series of specially designed centrifuge tests are presented to investigate the pre and post seismic lateral capacity of the monopiles as well as their dynamic response. A typical soil profile considered in this research is shown in Fig. 1 with a loose, liquefiable, sand layer that is underlain by a dense sand layer. The monopile typically penetrates some distance into the dense sand layer extending to the bedrock. The seismic accelerations due to the earthquake loading are applied at the bedrock level and propagate upwards to the seabed in the form of S h waves. Loose sand layers are liable to liquefaction due to cyclic shear strains when the lateral accelerations are typically above 0.1 g . In the field, the liquefaction susceptibility is established by conducting CPT tests at the site and utilising the charts proposed by Robertson and Wride (1998), or similar methodologies such as that proposed by Boulanger and Idriss (2016).
The focus of this research is on experimentally establishing the dynamic response of relatively rigid monopiles as well as the pre and post-seismic lateral capacity in layered sandy soils, as shown in Fig. 1, where the upper layer is liable to liquefaction. A series of dynamic centrifuge tests were conducted at a centrifugal acceleration of 60 g to investigate this. All models were subjected to a series of lateral shaking inflight, using the servo-hydraulic earthquake actuator . Centrifuge tests JS01 and JS03 were on dry soil whereas JS02 was on saturated soil. It must be pointed out that the operational lateral loads due to wind and waves shown in Fig. 1 were not modelled in this research. It is appreciated that the operational loads on the wind turbine may be present at the time of earthquake loading, but this aspect will be investigated in future research.

Model monopile foundations and test configuration
The principles of dynamic centrifuge modelling are well established and the scaling laws that relate to the model behaviour of the prototype were derived by Schofield (1980), and more recently presented by Madabhushi (2014). In this research a soil profile with a 6 m thick loose, Hostun HN31 sand layer of relative density D R ≈ 44% overlying a 10.8 m thick dense Hostun sand layer of D R ≈ 90% was considered as shown in Fig. 2. The properties of the Hostun HN31 sand are shown in Table 1. Two identical monopiles of 2.3 m diameter were driven to a depth of 12 m and were fitted with a brass head mass of 1.88 kg, which would apply a prototype vertical load of 4 MN to the monopile. This configuration has an L/D ratio of 5.3, within the range considered for current monopile foundations. The model monopiles had an outer diameter of 38 mm wall thickness of 3.125 mm. The flexural stiffness of the model monopile was 2.27 kNm 2 with an equivalent prototype steel monopile having a flexural stiffness of 87.9 GNm 2 .
Lateral movement of each monopile was monitored using two LVDTs. Each monopile could be pushed-over laterally inflight using an actuator, each of which, at the time of application of the lateral shaking, was retracted and not in contact with the monopile. The lateral load applied by the actuator was monitored using load cells as indicated in Fig. 2. This experimental set up enabled measurement of the monotonic response of the monopile pre (P1) and post (P2) earthquake. A view of the package on the centrifuge is shown in Fig. 3. In the case of saturated test (JS02), the fluid level was maintained about 25 mm above the soil surface. Using an air hammer device and piezoelectric accelerometers, the shear wave velocity V s was measured before and after the earthquake loading, following Ghosh and Madabhushi (2002). The small strain shear modulus G o was hence calculated from the shear wave velocities using Eq. 1 as shown in Fig. 4 for centrifuge tests JS01 and JS02. In this figure the empirical relations proposed by Hardin and Drnevich (1972) and more recently by Oztoprak and Bolton (2013) are also plotted for the loose and dense layers. Soil density used for the calculation is presented in Table 2. Figure 4 shows that the shear wave velocities are smaller in JS02 than in JS01 due to the lower effective stresses in the saturated model. There is also a greater increase in V s in the loose sand layer in JS02 after earthquake loading due to the densification of this layer. The increase in V s in the dry test JS01 is smaller by comparison.

Centrifuge testing sequence
One of the key aims of this research is to investigate the variation of soil and hence foundation stiffness before and after seismic loading. In order to achieve this, monopile P1 ( Fig. 2)  was subjected to an increasing push-over lateral load from the actuator at the beginning of the test. Both the load and lateral displacements were recorded during this phase. Following this, monopile P1 was left in its deformed state for the rest of the centrifuge test. The next aim of the research was to establish the dynamic response of the monopile, for which a sequence of earthquakes were applied using the servo-hydraulic earthquake actuator. Examples of the input motions applied are presented in Fig. 5 and the details of the input motions for all the centrifuge tests are given in Table 3. The first earthquake Eq. 1 was a sine sweep motion from 0 to 1.5 Hz with a very small peak amplitude of 0.05 g. This motion was used to identify the natural frequency f n of the soil-monopile system in each centrifuge test. Subsequent earthquakes Eq. 3, Eq. 4 and Eq. 5 were all sinusoidal input motions with frequencies of f n , 2f n and 3f n respectively. Equation 2 was a scaled Kobe motion that was used to determine the response of the monopile under realistic earthquake motions. During all these earthquake sequences the dynamic response of monopile P2 (Fig. 2) was monitored using 4 different MEMS accelerometers. The dynamic lateral displacements were also recorded by the two LVDTs on this monopile. In test JS02 the pore pressures in the free field soil and next to the monopile were also recorded.
It must be pointed out that many offshore wind turbine structures have a natural frequency of about 0.25 ~ 0.3 Hz. The natural frequency of monopile-soil system considered in this research had a natural frequency of about 0.45 Hz owing to the distance to the head mass being only 20.6 m above the seabed. For the dry tests (JS01 and JS03) the natural frequency f n is 0.5 Hz and for saturated test (JS02) it was 0.45 Hz. Future research will include a more realistic tower structure with greater lengths above the seabed to simulate the natural frequency more closely.
Once all the earthquake loading sequences were completed, monopile P2 ( Fig. 2) was subjected to an increasing lateral push-over load from the second actuator, with both the load and lateral displacement recorded. This data was used to establish the post-earthquake stiffness and lateral capacity of the monopile, and directly compared to the pre-earthquake values obtained for monopile P1.

Soil response
The soil response itself needs to be measured in order to assess the response of the monopiles. This was carried out in all of the centrifuge tests by using miniature Piezo-electric accelerometers that were also used to measure V s as discussed previously and the excess pore pressures and settlement of the soil surface were also measured.

Soil accelerations
The accelerations imparted by the input motion were measured at different depths in the free-field away from the monopiles. An example of the soil accelerations that were measured at different depths in dry and saturated tests, JS01 and JS02 respectively is presented in Fig. 6.
In Fig. 6 it can be seen that the accelerations undergo amplification in the dry test as they propagate upwards. This is well known and has been observed by many researchers, e.g. Teymur and Madabhushi (2003), Jabary and Madabhushi (2015). The accelerations in the saturated soil undergo attenuation particularly in the top, loose sand layer. This is clearly seen in the acceleration measured in test JS02 at a depth of 2.3 m. This is clearly due to the loss of shear stiffness owing to the excess pore pressure generation and again was observed by many researchers before, e.g. Adamidis and Madabhushi (2017). 1 f n sine wave, 10 cycles 0.14 0.17 0.14 Equation 4 2 f n sine wave, 10 cycles 0.16 0.18 0.25 Equation 5 3 f n sine wave, 10 cycles 0.09 0.09 0.16  Figure 7 shows the settlement recorded at the soil surface for test JS02 during Eq. 3 motion.

Settlement of soil surface
The soil surface has settled by nearly 0.6 m during this strong input motion. It is clear that most of the settlement occurs during the co-seismic period and the post-seismic reconsolidation settlements are relatively small. This is in line with the similar observations in terms of

Dynamic response of the monopile
One of the main objectives of this research was to establish the dynamic response of a monopile under seismic loading. Monopile P2 was instrumented with MEMS accelerometers, LVDTs and miniature strain gauges that measure bending moments as indicated in Fig. 2.

Acceleration response of the monopile
As explained earlier the natural frequency f n of the monopile-soil system was identified using the monopile response to the sine sweep motion applied during input motion Eq. 1. During Eq. 3 a sinusoidal motion of about 0.15 g peak amplitude was applied as input motion at this frequency. Figure 8 shows the input motions at the base, compared with the lateral accelerations recorded at the top of the pile head mass in centrifuge tests JS01 and JS02. As expected there is significant amplification of the input accelerations due to resonant vibrations of the monopile. It is however interesting to see that peak acceleration was about 0.6 g for the dry test JS01 and nearly 1.5 g for the saturated test JS02 respectively. This massive increase in the lateral accelerations in the saturated case may be linked to the excess pore pressure generation adjacent to the monopile that will be presented in Sect. 7.1. The data also clearly display an asymmetrical response of the monopile. This suggests that the monopile-soil system may acquire a bias during the shaking, with the very first halfcycle load responsible for moving the monopile in one direction. Again this bias is much larger for the saturated test JS02. Furthermore, the model monopile systems tested in this research are very symmetric compared to real prototype monopiles, which have more of an eccentricity due to the RNA (Rotor-Nacelle assembly) at the top of the tower. This may further increase this bias.

Response spectra
The lateral acceleration measured at the top mass level were used to obtain the response spectra as shown in Fig. 9 for input motion Eq. 3 (see Table 3) for the tests JS01 and JS02. Figure 9 also displays the earthquake spectra of the input motion at the base for comparison. These spectra were all plotted with a nominal damping of η = 5%. The response spectra clearly reveal the first, second and third harmonic peaks in each test. It is also interesting to see that the peak response in the saturated test JS02 occurs at a lower frequency than in the dry test JS01. This lowering of natural frequencies in saturated test is due to lower effective stresses within the saturated model, exacerbated by the softening of the soil due to excess pore pressure generation.

Amplification ratio
It is also possible to plot the amplification ratio at different frequencies using the sine sweep motion applied in Eq. 1 (see Table 3) by normalising the measured response by the base input in the frequency domain. These are shown for the two dry tests JS01, JS03 and the saturated test JS02 in Fig. 10 for the frequency range of interest. The figure shows that the maximum amplification is smaller in the saturated test compared to the dry tests. Figure 10 displays the amplification ratio obtained in Eq. 3, Eq. 4 and Eq. 5, at f n , 2 f n and 3 f n frequencies. The response of the monopile is much smaller in Eq. 4 and Eq. 5 compared to Eq. 3 as would be expected. The amplification ratios are also smaller in these larger magnitude earthquakes than in the case of sine sweep motion imparted by Eq. 1. This is because the larger cyclic strains induced by these strong earthquakes cause a reduction in the secant shear modulus of the soil and hence a reduction in the lateral foundation stiffness. This begets a smaller amplification ratio compared to a smaller magnitude earthquake, where amplification ratios can be large. Fig. 9 Response spectra for the monopiles in dry and saturated centrifuge models JS01 and JS02 respectively for Eq. 3

Lateral displacement
The lateral displacement of the monopile at the mudline (V g ) can be estimated from the measurements of the displacements obtained using the top two LVDTs and assuming that the monopile itself is rigid. This was only possible for dry test JS03 and saturated test JS02, due to an LVDT malfunction in test JS01. The lateral displacements for Eq. 3 motion are shown in Fig. 11. In this figure it can be seen that during this strong input motion, a peak lateral

Dynamic bending moments in the monopile
An important consideration in the structural design of a monopile is the bending moment. Earthquake motions can induce large dynamic bending moments in the monopiles. It would be interesting to compare these to the peak operational bending moment of about 54 MNm applied by the wind and wave loads shown in Fig. 1. The dynamic bending moments recorded at a depth of 4 m below the mudline are shown in Fig. 12 for the three centrifuge tests. The results show a peak dynamic bending moment of about 30 MNm for Eq. 3 motion.
The dynamic bending moments seem to be larger in the first few cycles in test JS02 and reduce in subsequent cycles as the excess pore pressures are generated in the upper, loose sand layer.
Variations of peak bending moment with depth are plotted in Fig. 13 for different earthquake motions (see Table 3) for centrifuge test JS01. The largest bending moments occur for Eq. 3 at f n frequency and they reduce considerably for 2 f n and 3 f n frequencies of Eq. 4 and Eq. 5. Many of the strain gauges malfunctioned in centrifuge tests JS02 and JS03 and hence only the available data at a depth of 4 m is shown for these tests. It is interesting to note that while there is an increase in peak dynamic bending moment from the base to the top of the monopile in Eq. 4 and Eq. 5, in Eq. 3 the peak dynamic bending moment does not vary in the upper loose layer and starts to decrease only in the dense layer. This indicates that the horizontal earth pressures exerted by the loose layer are relatively small and are not causing a decrease in the bending moment. It is hypothesised that for a larger diameter monopile this may not be the case. The peak dynamic bending moment is marginally larger in the saturated test JS02 than in JS03 at the depth were data is available.
Using the peak acceleration of the top mass of 0.6 g for JS01 seen in Fig. 8, the peak dynamic bending moment at the mudline can be calculated using; This gives a peak dynamic bending moment of 35.3 MNm that compares well with the recorded value of 30 MNm measured at the mudline level. This peak bending moment is comparable to the 54 MNm from the wind and wave loading. From a design perspective these two bending moments may be additive as earthquake loading needs to be considered alongside the operational wind and wave loads. One of the concerns with a shallow, loose sand layer is its susceptibility to liquefaction when subjected to earthquake loading. Excess pore pressures were recorded in the free field and on either side of the monopile during centrifuge test JS02. These are presented in Figs. 14 and 15 for short term and long term cases respectively.

Short term excess pore pressures
The excess pore pressures measured at adjacent locations on either side of the monopile are presented in Fig. 14, with the excess pore pressure recorded in the free-field at comparable depth also included. It must be noted that the location of the 'free-field' PPTs is in between the two monopiles as shown in Fig. 2 and is liable to have some interaction effects. In all cases the excess pore pressures reach the full liquefaction level for that depth indicated by the horizontal dotted line. However, the excess pore pressures next to the monopile show very large suction pressures induced by the oscillation of the monopile due to dilation when large strains are applied to the soil at moments of peak acceleration (twice per cycle). These suction pressures will cause a temporary but sudden increase in the effective stresses in the soil, which will increase the soil stiffness. This phenomenon leads to large accelerations spikes at the top mass level seen in Fig. 8. The free-field excess pore pressures do not experience these large suction spikes in excess pore pressures as the shear strains at these locations are small, therefore the free-field remains more or less liquefied.

Long term excess pore pressures
The long-term excess pore pressures are shown in Fig. 15 for Eq. 3 motion in test JS02 at different depths. It can be seen that the excess pore pressures reach full liquefaction level Fig. 13 Variation of maximum dynamic bending moment with depth at all the depths within the loose sand layer and close to the interface with the dense sand layer. The data shows that it takes nearly 110 s after the earthquake loading for the excess pore pressures to fully dissipate. Figure 14 also shows that the upper layers of the loose sand deposit retain higher excess pore pressures longer than the deeper levels. This is due to the pore fluid migration from the deeper layers towards the soil surface, which keeps the shallow layers liquefied for longer.

Monotonic response of monopile during push-over phase
One of the aims of this research was to investigate how the lateral resistance of monopiles changes before and after seismic loading. This is important from a design point of view as both the lateral capacity of the monopile at about 0.1% D deflection and the initial stiffness mobilised during push over, are considered. In this research two identical monopiles were present in each test with the push-over tests conducted before and after seismic loading was applied, as explained earlier.
For the dry soil test JS01, the bending moments in the monopile were monitored during the push-over phase, with the monopile tested after all the seismic loading sequences were applied. The evolution of the bending moment with depth is presented in Fig. 16 at different levels of deflections. The deflections at the actuator level V h were normalised with the diameter D of the monopile in this figure. In this test it was not possible to derive the horizontal deflection at the mudline level as one of the two LVDT's on the monopile malfunctioned. In centrifuge tests JS02 and JS03 the horizontal deflections V g were reported at the mudline level as all the LVDT's functioned well. Figure 16 shows that the bending moments steadily increase as the lateral deflection increases, as would be expected. A point of inflexion in the bending moment profile develops within the dense sand layer at larger deflections as the lateral earth pressures generated in the dense sand will be much larger than in the loose sand layer. Figure 17 shows the evolution of the horizontal load H g with the horizontal deflection V h at the actuator level in centrifuge test JS01 for monopiles tested pre and post seismic loading. The inset on this figure shows the initial sections of the curves for very small lateral deflections of 0 ~ 3 mm range. The results show that, although the post-earthquake lateral capacity is higher at 0.3 m of lateral deflection, the initial stiffness of the monopile-soil system is smaller compared to the pre-earthquake case. Seong et al. (2020) suggested that this may be due to the loose sand layer adjacent to the monopile not densifying as much as the free-field sand due to interface friction between the monopile surface and the sand akin to negative skin friction that develops around piles in consolidating soft clays. This creates a small zone of loose sand layer around the monopile that reduces its initial lateral stiffness as seen in Fig. 17, compared to the pre-earthquake case. At larger lateral deflections, the monopile moves away from this zone and can mobilise much larger lateral stiffness, indicated in Fig. 17 by the increasing slope of the dashed line. As the design of wind-turbine foundations is typically governed by stiffness rather than strength due to the very small allowable deformations, the reduction in stiffness will be dominant in design rather than the increase in strength at large deformations. Figure 17 also shows that the post-earthquake case reaches a horizontal load of about 1.8 MN at a lateral deflection of 0.3 m (13% D). Using Eq. 2, the peak bending moment for this load can be calculated as 32.4 MNm, knowing the height of the actuator above the mudline, at which the horizontal load is applied. This matches well with the bending moment recorded by the strain gauges at this depth as seen in Fig. 16. It is of course more interesting to investigate the push-over loads for the saturated case of JS02 where the loose sand layer has suffered liquefaction during seismic loading. Figure 18 shows the push-over loads H g, plotted against the mudline lateral deflections V g for centrifuge tests JS02 and JS03. In Fig. 18 again insets show the initial lateral deflections in 0 ~ 3 mm range. For the saturated JS02 test, the initial stiffness is higher for the post-earthquake case compared to the pre-earthquake case. This may be due to liquefaction of the soil adjacent to the monopile, undergoing reconsolidation in the post-seismic period in the same manner as the free-field soil, i.e. the negative skin friction effects are very small. As a result the densified soil in the post-seismic period can offer higher lateral resistance compared to the pre-earthquake case. In comparison, for the dry sand test JS03, the initial stiffness is higher for the pre-earthquake case compared to the post-earthquake case. This result for test JS03 is similar to the JS01 test described earlier, which gives confidence in the repeatable observation of this phenomenon. It is acknowledged that the peak lateral loads applied by the actuator were different in JS01 and JS03, due to actuator limitation and to the relative density of the loose and dense sand layers being slightly higher in test JS03.

Conclusion
The seismic response of a monopile foundation can have significant impact on its design when such foundations are located in earthquake-prone regions around the world. This paper presented the first study on the seismic response of monopiles, embedded in a layered soil profile that includes liquefiable layers. A relatively rigid monopile with an L/D ratio  Fig. 17 Push-over load versus horizontal deflection at actuator level (V h ) in test JS01 of 5.3 was considered. The soil profile consisted of 6 m thick loose sand layer overlying a 10.8 m thick dense layer above the bedrock. In-flight characterisation of these soil layers was carried out using V s profiling and compared to theoretical predictions. Three centrifuge tests were carried out, two on dry soil models and one on saturated soil model. First, the natural frequency f n of the monopile-soil system was determined in-flight using a sine sweep motion. This was followed by a scaled Kobe motion and strong, sinusoidal earthquakes at f n , 2 f n and 3 f n frequencies.
The response of the monopile was investigated using measured accelerations as well as by constructing the response spectra and amplification ratio plots. As expected, the response of the monopile system is the strongest during the f n earthquake and the response drops off significantly for 2 f n and 3 f n earthquakes. This was confirmed using amplification ratio plots. In addition, the saturated case produces a larger response but a lower natural frequency compared to the dry cases. Large acceleration spikes are observed during the saturated test. The excess pore pressures measured adjacent to the monopile show large suction spikes developing, leading to the soil stiffening temporarily and causing acceleration spikes. This phenomenon can be important while assessing the monopile behaviour in soil layers susceptible to liquefaction.
The dynamic bending moments were also measured for first dry test and only partially for other tests. The bending moment reveal similar shape profiles compared to previous numerical studies on laterally loaded piles in layered soils. The loose sand layer does not produce much lateral earth pressure to reduce the bending moments in the monopile, with the point of inflection in the bending moment profile located some depth into the dense sand layer. This aspect needs to be further investigated with much larger pile diameters in the future as it can have significant design consequences.
Another novel feature of this research is that the monotonic response of the monopile pre and post-earthquake was explored through lateral push-over tests, with two different monopiles tested in this phase. For the dry soil tests, the initial lateral stiffness is higher in the pre-earthquake than post-earthquake case, although the post-earthquake lateral capacity increases at larger lateral deflections. This is reversed in the saturated test with preearthquake lateral stiffness being smaller than the post-earthquake case. It is hypothesised that in the dry case the soil adjacent to the monopile settles less due to skin friction than in the far-field that densifies, akin to negative skin friction in piles located in consolidating clay layers. This seems to manifest itself as a smaller lateral stiffness in the post-earthquake case. In the saturated models, the soil around the monopile and in the far-field liquefies and therefore reconsolidates without much negative skin friction. This densified soil seems to offer a higher lateral stiffness than the pre-earthquake case.
This research has revealed some interesting aspects of seismic behaviour of monopiles both in terms of dynamic response as well as the lateral stiffness in the pre and post-earthquake scenarios. Further research is needed in this area particularly by considering larger diameter monopiles that are currently used to support OWTs. article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.