New method for incorporating foundation damping in time-domain analysis of integrated offshore wind turbine structures

Foundation damping has significant potential for reducing the loads of monopile-supported offshore wind turbines. However, the contribution of foundation damping is not well understood, primarily because of the absence of suitable methods for incorporating it into the time-domain analysis of wind turbine structures. This paper presents a novel approach for this purpose. In this approach, a dashpot is attached parallel to each of the p-y springs along a monopile, which models the stiffness and damping of soil-pile interactions. Employing this approach, the influence of foundation damping on the structural dynamic response is investigated using the time-domain analysis of a monopile-supported IEA 15 MW reference wind turbine. The results demonstrate that foundation damping has a limited impact on the overall dynamic response and fatigue loads of wind turbines during power production. However, the foundation fatigue loads after an emergency shutdown can be reduced by 29-46% owing to the inclusion of foundation damping. In addition, foundation damping is found to significantly influence the bending moment, horizontal displacement, and angular rotation of the monopile at the mudline under parked conditions, with load reductions of up to 20%.


Introduction
As of 2022, the global cumulative installed capacity of offshore wind power stood at 57.6 GW.The offshore wind energy industry was established to maintain a robust growth momentum.However, the high cost associated with the design and construction is a major obstacle to the development of offshore wind energy.The foundation structures of offshore wind turbines (OWTs) play a prominent role, representing approximately 30% of the capital costs of offshore wind farms [1] .Monopiles are the predominant substructures supporting OWTs owing to their rapid manufacturing and extensive fabrication experience.They currently account for approximately 80% of installed OWTs and are regarded as some of the most promising concepts for the future [2].
The overall damping of OWTs is crucial during design because it significantly reduces the dynamic response amplitude, especially at near-resonance frequencies.The pile interaction damping (foundation damping) is considered the second most important contributor to overall OWT damping during power production, following aerodynamic damping.In parked conditions, foundation damping plays a principal role as aerodynamic damping becomes almost negligible.Hence, accounting for foundation damping has substantial potential for the optimization of monopile designs.
However, the exact contribution of foundation damping is not well understood, primarily because of the absence of an accurate calculation method and suitable methods for incorporating it into the 1337 (2024) 012070 IOP Publishing doi:10.1088/1755-1315/1337/1/012070 2 time-domain analysis of wind turbine structures.Although numerous studies have been conducted on the damping properties of various soils at the soil element level [3][4][5][6][7][8][9] , studies on damping at the foundation level are relatively limited.For monopile applications, [10] presented a case study investigating foundation damping for OWTs using Plaxis 3D.However, this study utilized the HSS constitutive model for the soil, which is constrained to small strain ranges (<10-3) and lacks the accuracy to model the hysteresis response of soil-pile interactions under medium to high strains.[11] proposed a macro-element model that lumped the response of the foundation and surrounding soil at the seabed through a force-displacement relationship evaluated using 3D finite element analyses.The model employed Masing's rule to depict the hysteresis behavior of the foundations.Its primary advantage was its simplicity.However, the model may significantly overestimate foundation damping and is only applicable to low load levels.Similarly, [12] presented a theoretical model to describe the non-linear and hysteretic behavior of a one-dimensional mechanical system within a hyper plasticity framework.They also employ Masing's rule.[13,14] relied on the principle that soil-pile interaction damping refers to the overall energy dissipation of soil under cyclic shearing effects within the influence zone of the pile and calculated this total energy dissipation using an in-house finite element (FE) software and subsequently transformed it into a mudline damping matrix to characterize the foundation damping.There is no consensus on the calculation method for foundation damping.
Using a finite-element approach similar to that in [13,14] , [15] conducted extensive FE analyses and found that, at the p-y spring level, there is a convenient mapping relationship between the cyclic horizontal displacement-damping ratio curve of the soil-pile interaction and the cyclic shear straindamping ratio curve at the soil element level.The mapping model allows for a quick assessment of the soil-pile interaction damping at the p-y spring level based on the site-specific soil data, obviating the necessity for intricate 3D finite element analysis and its associated post-processing.This model can accurately capture the characteristics of the nonlinear response of foundation damping.This method provides an innovative paradigm for the evaluation of soil-pile interaction damping.
[ [16][17][18][19][20][21][22][23] investigated the overall structural response of OWTs using a finite element method.[24][25][26][27][28] investigated the effects of soil-pile interactions on the dynamic response of an NREL 5 MW OWT using FAST software.However, these studies did not incorporate the effects of soil-pile interaction damping.In contrast, [29] accounted for the effects of foundation damping, which was modelled in the form of dissipative springs distributed along the embedded length of a pile.[30] employed a numerical model of an OWT to study the influence of foundation damping on the fatigue life of a structure using the FAST software.However, in their time-domain analyses, foundation damping was considered a proportion of the overall system damping.[31] studied the effect of foundation damping on the fatigue damage of an OWT with a monopile foundation.However, in their study, foundation damping was a function of the load amplitude based on Masing's rule, which overestimated damping at higher load levels.[32] investigated the effects of soil damping, which was modelled as Rayleigh damping, on the fatigue life of an OWT.In conclusion, methods that incorporate soil-pile interaction damping into the integrated time-domain analysis of OWTs are still under development and further research is required.
Given that [8] provides a robust method for the calculation of soil-pile interaction damping at the py spring level, the purpose of this study is to utilize the mapping model proposed in [8] and develop a method for incorporating foundation damping into the time-domain analysis of integrated offshore wind turbine structures.Specifically, a new approach was proposed and examined in this study.In this approach, a dashpot is attached parallel to each p-y spring along the monopile.By employing this approach, the influence of foundation damping on the structural dynamic response was investigated in time-domain analyses of a monopile-supported IEA 15 MW reference wind turbine using the OpenFAST software.

Essence of pile-soil interaction hysteretic damping
Foundation damping includes both radiation and hysteretic damping.In the context of OWTs, radiation damping can be disregarded when the frequencies of wind and wave loading typically remain below 1 Hz [33].Therefore, only the contribution of hysteretic damping was considered in this study.The essence of hysteretic damping is the energy dissipation resulting from the nonlinear hysteresis response of soil under cyclic loading, as illustrated in figure 1.The shaded area represents the maximum stored strain energy (Ws) within a cycle, and the area enclosed by the hysteresis loop represents the energy dissipated (WD) during the cycle.The damping ratio d describes the extent of energy loss in the soil during cyclic loading and is generally defined by equation ( 1).= 4 . ( Figure 1.Hysteresis response of soil under cyclic loading. Existing studies have substantially advanced the knowledge of the hysteretic damping of soil at the soil element level ( [3,[5][6][7] ), yielding a well-established understanding.Soil damping can be determined through soil element tests (such as resonant column tests, cyclic triaxial tests, and cyclic direct simple shear tests, etc.).Typically, a larger cyclic strain amplitude results in a higher damping ratio.The relationship between the soil damping ratio and cyclic strain is characterized by an S-shaped curve on the logarithmic scale of strain.

Approach: Framework for the calculation of distributed damping coefficients
For pile foundations subjected to horizontal cyclic loading, foundation damping is essentially the total energy loss of the soil elements within the influence range of the pile foundation.Based on the definition in equation ( 1), [15] conducted extensive finite element analyses and found that, at the p-y spring level, there was a mapping relationship between the cyclic horizontal displacement-damping ratio curve of the soil-pile interaction and the cyclic shear strain-damping ratio curve at the soil element level, as shown in figure 2. The normalized lateral displacement (y/D) is 3.6 times the corresponding shear strain at the same damping ratio, that is, ξ=3.6.
As illustrated in figure 3, the distributed damping coefficient at each p-y spring level is calculated using the following steps [8]:  Determine the deformation mode of the pile and calculate the (cyclic) lateral displacement magnitude yi along the pile under a typical (cyclic) pile head load using a beam-column analysis, as illustrated in figure 3.  The foundation damping ratio di is obtained by interpolating the damping ratio-lateral displacement curve yi at each p-y spring.
 (Calculate the damping coefficient ci based on the foundation damping ratio (d) and secant stiffness (k) of the p-y spring using the equation below: where w is the angular velocity (rad/s) of cyclic loading.

New SoilDyn module in OpenFAST
The integrated time-domain analyses were performed using OpenFAST.However, in the current public release, the role of the pile interaction is considered only through a lumped stiffness matrix at the mudline.To incorporate the approach described above, a SoilDyn module was developed and integrated into the OpenFAST software.The overall computational scheme of OpenFAST including the SoilDyn module is illustrated in figure 4.
As shown in figure 5, the newly implemented SoilDyn module functioned analogously to the HydroDyn module.Specifically, the SoilDyn module initially received motion data from the SubDyn module.Subsequently, it computes and relays the forces and moments resulting from the soil-structure interaction output to the SubDyn module at each time step.In the SoilDyn module, the pile-soil interaction stiffness was modelled by configuring the p-y curves along the pile.

Application
An approach to incorporate soil damping into integrated time-domain analyses of OWTs is described in detail.The SoilDyn module was developed using the OpenFAST software.In the following section, we employ the proposed method to conduct time-domain analyses of a wind turbine under various conditions and investigate the impact of foundation damping on the loads in OWTs.

IEA 15 MW reference turbine and foundation
An IEA 15 MW Reference Turbine (IEA 15 MW) was used for the analysis in this study.The design parameters are listed in table 1.The IEA 15 MW was used because it aligns with the current development needs of large megawatt-scale OWTs.The monopile foundation was redesigned to satisfy the geotechnical conditions of a typical site in the offshore Southern Sea.The total length of the monopile was 90 m, with a penetration depth into the seabed of 45 m and a water depth of 30 m.The monopile had a diameter of 10 m and a simplified uniform wall thickness of 0.1 m.Based on this monopile design and geotechnical conditions detailed in Section 3.2, the wind turbine system's firstorder fore-aft (f-a) natural frequency was 0.1766 Hz, and the first-order side-side (s-s) natural frequency was 0.1749 Hz, which all lie in between the 1P and 3P blade passing frequency ranges, and stays sufficiently away from the typical wave frequencies of the studied area (0.08 Hz-0.13 Hz).

Soil conditions
A typical offshore wind site in Southern China was considered for the analysis.Table 2 summarizes the soil layering and parameters.The p-y springs for the clay layers were constructed according to the method proposed in [35] by which the p-y curves were scaled from the stress-strain curves, as illustrated in figure 7.For simplicity, a single normalized stress-strain curve is assumed for all clay layers, as illustrated in figure 8. Notably, the cyclic undrained shear strength and stress-strain curves should be used to generate the p-y curves.Instead, the static undrained shear strength presented in table 2 was used, ignoring the potential cyclic loading effect on the strength.For the sand layers, the API sand p-y model was used to generate the soil reaction curves.Similarly, for simplicity, a single damping ratio versus cyclic shear strain curve was assumed for all the clays (figure 9), and a separate damping curve was assumed for all the sand layers (figure 10).The purpose of the current analyses was to demonstrate the method proposed herein for incorporating soil damping into integrated wind turbine analyses.Therefore, these simplifications were considered acceptable.In a more realistic calculation for an actual project, the cyclic soil strength and layer-specific cyclic stress-strain and damping curves should be evaluated and used as inputs for the SoilDyn module.

Design load cases
To evaluate the impact of foundation damping on the dynamic response and fatigue loads of windturbine structures under various operational states, we selected five load conditions from the IEC 61400-3 standard [36] for which time-domain analyses were performed with and without foundation damping.The load cases are listed in table 3.

Power production
The operational state of power production for OWTs requires consideration of wind speeds ranging from cut-in to cut-out (3-25 m/s).Therefore, the rated wind speed (10.59 m/s) and near-cut-out wind speed (24 m/s) were used in the time-domain analyses of the OWT under DLC 1.1, DLC 1.2, and DLC 1.6.The wave conditions for DLC1.1 and DLC1.2 are identical.Based on the significant wave heightperiod joint distribution for the site, a significant wave height of 1.75 m and a peak period of 7.5 s were selected as the wave inputs for DLC1.1 and DLC1.2.For DLC1.6, a wave height of 10.43 m and a period of 12 s were selected as the wave inputs.The wave files were generated using the JONSWAP spectrum.
In accordance with the IEC 61400-3 standard [36] , six 10-minute time domain simulations for DLC1.1, DLC1.2, and DLC1.6 were conducted under conditions with and without foundation damping.To assess the stable operational response of the wind turbine, time-domain simulations were consistently set to 720 s, with an initial 120-second start-up phase for the OWT.

Emergency shutdown
An emergency shutdown occurs when the safety supervisor system turns off the OWT to prevent damage.The process of simulating an emergency shutdown in OpenFAST is as follows.
 (1) The generator is turned off at t = 200 s during the time history simulation. (2) Pitch control is overridden at time t = 200 s, and the blade pitch is set to 90º (feathered blades for the IEA 15 MW) at the rated limit of 8º/s.The emergency shutdown case (DLC 5.1) uses the same wind and wave file inputs as in DLC 1.1.Twelve 10-minute time-domain simulations were conducted under conditions with and without foundation damping.

Parked Conditions
Extreme wind and sea conditions were considered for the parked conditions.Based on typhoon data from the site, a wind speed of 53 m/s, wave height of 10.43 m, and period of 12 s were used for DLC 6.1.
For DLC 6.1, the blade pitch angle was maintained at 90º (feathered blade position) and the generator was turned off.In accordance with the IEC 61400-3 standard [36] , six 1-hour time domain simulations were conducted at of 0º and 8°with and without foundation damping.

Results and discussion
Table 4 presents a comparison of the OWT responses at the mudline of the monopile and at the top of the tower between the damped and undamped conditions.Table 5 presents the percentage reduction in the response owing to the effect of foundation damping.For DLC 1.1, which belongs to the ultimate limit state (ULS), at the rated wind speed and near the cut-out wind speed, the foundation damping shows the most significant load reduction effect on the ultimate horizontal mudline force (figure 11), amounting to 3% and 15%, respectively.The load reduction effect on the mudline moment was smaller (only 1%), and it had almost no impact on the displacement response at the top of the tower.For DLC 1.2, which belongs to the fatigue limit state (FLS), the one standard deviation (1σ) of the time domain simulation results was used to represent the fatigue loads, which are summarized in table 4. From the results, it is evident that under the rated and near-cut-out wind speed conditions, foundation damping reduces the fatigue load of the horizontal mudline force Fx by 7% and 13.5%, respectively, and the load reduction effect on the mudline moment My is 3% and 5%, respectively.Unlike DLC 1.1, for ULS DLC 1.6, foundation damping had almost no effect on the horizontal mudline force Fx; however, it reduced the mudline moment My by 3%.Compared to the normal sea conditions of DLC 1.1, the influence of foundation damping on the dynamic response of the wind turbine was relatively weakened owing to the increased wave load.Overall, the impact of foundation damping on the dynamic response of the wind turbine structure was relatively low.
Under the conditions of both rated and near-cut-out wind speeds, the effect of foundation damping on the response of the OWT after an emergency shutdown was significant.In the presence of foundation damping, the response of the turbine structure decreased faster and stabilized sooner after shutdown (figure 12).Foundation damping significantly reduced the ultimate horizontal mudline force Fx, with a reduction of up to 20.5%, but had almost no effect on the ultimate mudline moment My.DLC 4.1 is a fatigue limit state (FLS) controlling case, with wind and wave conditions similar to those of DLC 5.1.Therefore, the reduction effect of foundation damping on the fatigue load after emergency shutdown in DLC 5.1 was used to represent DLC 4.1.One standard deviation of the loads after an emergency was used to represent the fatigue loads, as summarized in table 4. It was observed that foundation damping significantly reduced the OWT fatigue load.Under rated and near-cut-out wind speed conditions, foundation damping reduced the fatigue horizontal mudline force Fx by 35% and 25%, respectively, and the mudline moment My by 37% and 29%, respectively.
For ULS DLC 6.1, both the dynamic response of the wind turbine structure and ultimate loads were significantly reduced owing to foundation damping (figure 13).The ultimate values of the horizontal mudline displacement Ux and rotational mudline angle θy were reduced by 22% and 21%, respectively, whereas the ultimate horizontal displacement at the top of the tower was reduced by 22%.The ultimate horizontal mudline force Fx was reduced by 6.8%, and the mudline moment My was reduced by 21%.

Conclusions
In this study, a new method for incorporating foundation damping into the time-domain analysis of integrated offshore wind turbine structures was proposed and implemented using a SoilDyn module developed in OpenFAST.
Extensive comparative time-domain analyses of OWTs were conducted, including scenarios with and without foundation damping, to reveal the effect of foundation damping on the overall dynamic response and fatigue loads of OWTs.The results indicated that foundation damping has a minor effect on the dynamic response and fatigue loads for power production and only significantly reduces the ultimate horizontal mudline force (ranging from 3% to 15%).However, the impact of foundation damping on fatigue loads following an emergency shutdown was significant, with reduction effects reaching 29-46%.Moreover, foundation damping significantly affected the moment, horizontal IOP Publishing doi:10.1088/1755-1315/1337/1/01207014 displacement, and rotational angle at the monopile mudline under parked conditions, with reduction effects reaching 20%.These findings demonstrated the potential for monopile design optimization by considering soil damping.

Figure 2 .
Figure 2. Scaling of soil-pile interaction damping from damping response measured at soil element level [15].

Figure 3 .
Figure 3. Deformation mode of pile under typical pile head load.

Figure 5 .
Figure 5. Schematic representation of spring and dashpot in SoilDyn.

Figure 8 .
Figure 8. Normalized stress-strain curve assumed for all clay layers.

Figure 11 .
Figure 11.Time history example of horizontal mudline force and mudline moment for DLC 1.1.

Figure 12 .
Figure 12.Time history example of horizontal mudline force and mudline moment for DLC 5.1.

Figure 13 .
Figure 13.Time history example of horizontal mudline force and mudline moment for DLC 6.1.

Table 2 .
Soil layering and parameter for typical site.

Table 3 .
IEC offshore wind turbine design load cases.

Table 4 .
Comparison of OWT responses between damped and undamped analyses in OpenFAST.

Table 5 .
Percent reduction of OWT response due to the foundation damping.