Ice-Induced Vibration Analysis of Fixed-Bottom Wind Turbine Towers

Abstract

This research tackles the challenge of ice-induced vibrations in fixed-bottom offshore wind turbines, particularly the risk of frequency lock-in (FLI), a critical loading condition arising from slow ice movement against structures. We introduce an innovative FLI analysis process grounded in the ductile damage–collapse (DDC) mechanism, which offers a more accurate and significantly lower probability of FLI occurrence than conventional methods. Through dynamic evaluations employing a time-domain ice load model and FLI displacement analyses, we demonstrate that FLI can lead to higher structural vibrations than those caused by continuous brittle ice crushing. A case study of a 5 MW monopile wind turbine tower utilising Abaqus confirms the necessity for incorporating FLI considerations into structural design to ensure safety and performance in ice-prone environments. Comparing the DDC mechanism with the ISO method, our study reveals that the DDC approach predicts higher displacement and acceleration values during FLI, nearly an order of magnitude greater than those induced by ice loads with a 50-year return period. The research underscores the importance of robust ice-load integration in design strategies for offshore wind turbines, especially in regions susceptible to ice. It highlights the DDC mechanism as a novel strategy for enhancing structural resilience against ice-induced hazards.

1. Introduction

The rapid growth of offshore wind energy, as demonstrated by the widespread construction of wind farms in regions such as northern Europe, the United States, Japan, South Korea, and the coastal areas in north China, highlights the importance of addressing ice-induced vibrations. Unlike rigid structures such as oil platforms and lighthouses, offshore wind turbines are characterised by their tall, flexible designs. These designs include key components such as rotors, blades, drivetrains, control cabins, and support towers—all susceptible to failure under severe vibrations.

The severity of ice-induced vibrations varies markedly depending on the structural characteristics and the prevailing ice conditions. Various monitoring efforts have identified three forms of ice structure vibrations. According to ISO 19906 [1], intermittent ice crushing can occur if a compliant structure is exposed to actions from slow-moving ice. Under low ice velocity conditions, the coupling of crushing failure of sea ice and structural vibrations can lead to ice loads that are frequency-locked to structural vibrations, resulting in severe structural vibrations. This phenomenon is known as frequency lock-in (FLI) vibration. FLI represents the most dangerous loading condition for offshore structures under ice action [2,3].

Continuous brittle crushing can occur at ice velocities much higher than at which frequency lock-in is observed. During these episodes, the ice forces and structural responses exhibit random characteristics. These phenomena are especially critical for structural design, as they can lead to maximum loads and peak oscillation amplitudes.

Huang [4] conducted an extensive study investigating how structural stiffness and mass changes influence the range of indentation speeds at which frequency lock-in (FLI) occurs. Their findings indicate that an increase in a structure’s mass or natural frequency shifts the FLI regime boundaries towards lower ice velocities. Wang Bin et al. [5] developed a ductile damage–collapse failure mechanism for FLI, grounded in the characteristics of ice–structure interactions as measured during on-site lock-in vibrations. They introduced an analysis method that utilises the relationship between ice failure length and structural amplitude. Hendrikse et al. [6] conducted a comparative analysis of the prevalent analysis methods used in the industry. Their study revealed that the range of ice velocities at which FLI occurs can vary by a factor of tens, which is a considerable discrepancy.

Without a comprehensive understanding of the effects of frequency lock-in (FLI) not only involves substantial additional investment but also complicates transportation, installation, operation, and maintenance processes [7,8]. Although international standards like IEC 61400 [9], and ISO 19906 [10] are predominantly utilised in designing current offshore wind turbines, these standards do not provide a unified analysis method for addressing ice-induced vibrations [11,12]. Researchers have conducted extensive studies on ice loads and wind turbines. Zhu Benrui et al. [13] discovered that the wind turbine tower and foundation top vibration characteristics vary between low and high ice velocities. Zhang Dayong et al. [14] applied a method outlined in ISO 19906 and found that ice-induced vibrations are substantially more significant than the response to extreme gust wind conditions.

This study employed a time-domain ice load model and FLI displacement analysis to conduct dynamic evaluations of two distinct vibration scenarios for better readability and to emphasise the methodological approach. The FLI analysis method based on the ductile damage–collapse mechanism and practices provided by ISO 19906 was employed to analyse FLI on an offshore wind turbine tower. The responses from continuous brittle crushing ice loads and FLI, with ice load return periods of 1 year, 5 years, and 50 years, were compared. Moreover, the probability of an FLI occurrence on fixed wind turbines was computed, demonstrating a significant reduction compared to jacket platforms and lighthouses. The magnitude of the structural response of a 5 MW sample monopile wind turbine tower was investigated using Abaqus 2020. This study establishes an analysis method and provides valuable conclusions for future reference.

2. A Brief Introduction to the Ductile Damage–Collapse (DDC) Mechanism

By analysing the ice and structure interaction process in the field measurement, Wang Bin et al. [5] introduced a sea-ice failure model tailored explicitly for the frequency lock-in (FLI) process, which is characterised by the following features:

Simultaneously crushing and lock-in: The ice loads exhibit synchronisation across multiple channels, indicating that the sea ice undergoes simultaneous fracturing along the entire interface in contact with the structure.

Periodic coupling: Ice loads are consistently synchronised during the loading and unloading phases. Sea-ice failure is a ductile process. The process shows in Figure 1.

The ice failure length (L_ib) is a crucial factor in the ductile damage–collapse process. In structures such as lighthouses and jacket platforms, when the ice velocity approaches the failure length ratio to the structure’s natural period, it triggers the ductile damage–collapse process, leading to frequency lock-in (FLI).

$$V_i=\frac{L_{ib}}{T}$$

(1)

After taking into account the local failure length of the sea ice occurring during the damage phase, the structural vibration amplitude A can be obtained as

$$A=\frac{[1-(m+k)]L_{ib}}{\sin (2k\pi )}$$

(2)

Here, m is the ratio of the failure length generated during the collapse phase to the overall failure length. k is the ratio between the loading and unloading times. According to Karna’s experimental observations, the m value can be 0.7. Field measurements of sea ice indicate that k can be taken in the range of 0.5 to 1. When m = 0.7, the failure length is about 1.3~2.2 times the structure’s vibration amplitude.

3. FLI Occurrence Conditions

For the FLI of offshore wind turbines, sea-ice parameters can be limited by two aspects: ice speed and ice thickness.

3.1. Ice Speed Limitation

The relationship between the failure length during FLI and the ice velocity during the structural vibration period is shown in Equation (1). This can be the limitation for ice speed once the L_ib is confirmed.

The ice velocities at which FLI occurs for different structures in the Bohai Sea are shown in

Table 1. FLI parameters of different structures in the Bohai Sea.

Structure	Natural Frequency (Hz)	Failure Length (cm)	Ice Velocity of FLI (cm/s)
JZ20-2MSW platform	2	1~2	2~4
5 MW wind turbine	0.27	1~2	0.27~0.54

below.

Monitoring ice velocities in the Bohai Sea revealed that when considered separately, the probability distributions of ice velocity and ice direction follow a Rayleigh distribution. Its parameters are shown in

Table 2. The probability of FLI occurrence on offshore platforms in different areas of the Bohai Sea when only considering ice speed.

Monitoring Periods	Sea Area	σ	Probability
1997–2000	JZ20-2	28	0.01%

.

3.2. Ice Thickness Limitation

According to the DDC theory, FLI requires the structure to couple displacement and failure length at the ice’s point of action. Once the ice’s thickness can be restricted, the failure length, structural stiffness, and dynamic magnification factor at the ice force application point are determined.

Three distinct relationships illustrate different interaction dynamics between sea ice and structures for failure length, dynamic magnification factor, and static displacement of the action point. If the failure length exceeds the product of the structural dynamic amplification factor and the static displacement of the structure, intermittent crushing will occur. This interaction includes phases of load accumulation and unloading. Elastic energy builds up until brittle ice failure occurs, spreading rapidly and causing the structure to rebound as energy is released. The structure’s displacement and the ice at the waterline show a sawtooth pattern with steady growth followed by swift unloading.

If the failure length exceeds the product of the structural dynamic amplification factor and the structure’s static displacement, intermittent crushing will occur. The interaction comprises stages of load buildup and unloading. Elastic energy gradually accumulates until a brittle failure of the ice occurs, which then spreads rapidly, causing the structure to rebound as the power is released. The displacement of the structure and the ice at the waterline displays a sawtooth pattern, featuring linear growth followed by a swift unloading phase as shown in Figure 2.

If the failure length is equal to the product of the structural dynamic amplification factor and the structure’s static displacement, phase-locked loading will occur.

In Figure 3, the interaction within a single cycle can be divided into two phases: loading and unloading. During the loading phase, intact ice exerts pressure on the structure, initiating microcracks within the ice sheet. These cracks progressively saturate the ice, eventually causing it to collapse. In the unloading phase, the collapsed ice results in spalls that are extruded from the contact surface between the ice and the structure. Once the extrusion ceases, the intact ice resumes pressure on the structure, initiating a new cycle.

A typical frequency lock-in will occur as the Figure 4, if the failure length is smaller than the product of the structural dynamic amplification factor and the structure’s static displacement. In this case, the ice failure frequency aligns with one of the structure’s lowest natural frequencies. The period between ice-crushing failures and amplification depends on ice properties, velocity, and structural dynamics. The structure’s motion is nearly sinusoidal, influenced by the interplay of ice and structural attributes.

The above description shows that FLI only occurs when the failure length is less than or equal to the dynamic amplification factor multiplied by the maximum static displacement.

Owing to the relationship between the maximum static ice force and ice thickness, the ice thickness can be constrained by the static displacement of the structure at the point of sea-ice action. The monitoring results of Bohai ice exhibit a lognormal distribution. Ice thickness meets μ = 1.9407 σ = 0.5732 lognormal distribution [16].

$$f(t)=\frac{1}{0.5732t\sqrt{2\pi }}\exp \left[-\frac{1}{2}{\left(\frac{\ln t-1.9047}{0.5732}\right)}^2\right]$$

(3)

According to the DDC theory, the occurrence of FLI requires the structure to couple displacement and failure length at the point of ice action. The structural stiffness at the point of sea-ice action is about 2.4104 × 10¹⁰ N/m. It can be calculated that the ice thickness corresponding to a failure length of 1 cm is 0.05 m. The probability of ice thickness less than this value is 0.31. The probability of FLI when considering ice thickness when the failure length is 1 cm is shown in Figure 5.

By combining the two limiting conditions of ice thickness and ice velocity, the joint probability distribution reveals that using the DDC method, the likelihood of FLI occurrence in

Table 3. The probability of FLI when considering ice thickness and ice speed when the failure length is 1 cm.

Monitoring Periods	Sea Area	Probability
1997–2000	JZ20-2	0.007%

is approximately 100 times lower than the probability calculated with existing methods calculated by Wang Guojun et al. [17].

4. Random Vibration Caused by Continuous Brittle Crushing

Continuous brittle crushing at high ice velocities induces random vibrations within wind turbine structures. Wind turbine structures, typically with diameters exceeding 6–7 m, are comparable in scale to lighthouses. This analysis utilised measured load data, specifically ice loads from the Norströmsgrund Lighthouse in the Baltic Sea. This lighthouse, featuring a diameter of roughly 7.5 m at the waterline and a total height of 42.3 m, is considered an excellent reference structure for comparison.

The selection of ice load data in this paper was based on the following principles: The number of channels with data is sufficiently large. Ice loads from three events with ice thicknesses at 0.14 m, 0.23 m, and 0.32 m were selected to denote 1 year, 5 years, and 50 years of ice thicknesses in the Bohai Sea and shown in Figure 6. The effect of increasing ice thickness on ice force and pressure should be considered [18,19].

5. Different IIV Analysis Methods

5.1. FLI Analysis Method Based on DDC Mechanism

Based on the relationship between the structure’s vibration amplitude at waterline elevation and the ice failure length derived in this paper, the wind turbine’s FLI vibration can be analysed using the straightforward procedures below.

We determined the displacement amplitude A of the structure at waterline elevation. We inputted sinusoidal displacement excitation with magnitude A into the wind turbine model at waterline elevation and estimated the system’s response. The process is shown in Figure 7.

A time series of the structure’s displacements at the ice action elevation can be derived using the method above. The necessary analytical parameters are provided in

Table 4. Analysis parameters of FLI analysis based on the DDC mechanism.

Tidal (m)	1st Natural Frequency of Structure (Hz)	Ice Failure Length (cm)
2.535	0.261	2

below.

Taking the above parameters into Equation (2), the displacement amplitude A in the FLI process can be obtained to generate a displacement time series as excitation to the structures. FLI occurs between 250 and 430 s in the simulation; no load is added in addition to this period.

5.2. The Analysis Method of FLI Provided in ISO19906

For FLI analysis within ISO19906 frameworks, a simplified forcing function at the resonant frequency can effectively estimate structural responses during lock-in conditions, as illustrated in Figure 8. This function, devoid of random variations, operates at a frequency f = 1/T, aligning with one of the structure’s identified unstable natural modes. In our study, the first two modes of the tower are considered unstable [20].

Furthermore, ISO19906 outlines an FLI analysis methodology based on stable peak values F_max and a consistent double amplitude ΔF = F_max − F_min throughout the ice action series. The amplitude range ΔF, influenced by the structure’s natural modes and the ice’s velocity, was quantified as a fraction q of the peak action F_max. We adopted a fraction value of 0.3 for q. The peak value F_max was estimated from the global ice action F_G impacting the structure, calculated according to ISO19906 in the above. After determining the value, the following forms of loads were generated. Afterwards, we added the load to the application point.

5.3. Continuous Brittle Crushing Simulation and Paraments

To compare the FLI response with the random vibrations caused by continuous brittle crushing of the ice, the reactions under the action of the ice load at ice thicknesses of 0.14 m, 0.23 m, and 0.32 m were calculated by using the same model. The ice load data were extracted from the load measurement system on the lighthouse with about 7 m diameter. The ice thickness was considered with a return period of 5, 10, and 50 years for the Bohai Sea. The ice load information used is listed in

Table 5. Parameters for continuous brittle crushing ice load.

Return Period (y)	Ice Thickness (m)
1	0.14
5	0.23
50	0.32

. The ice load was directly added at a height of 2.535 m above the water surface of the wind turbine tower.

6. Tower Model Parameters in Abaqus

In this study, we examined the effects of ice-induced vibrations using the tower of a 5 MW monopile offshore wind turbine, as reported by NREL [21]. The critical parameters of the wind turbine are detailed in

Table 6. The main parameters of a 5 MW monopile offshore wind turbine.

Paraments	Value
Rating	5 MW
Hub Height	90 m
Rated Speed	11.4 m/s
Rotor Mass	110,000 kg
Nacelle Mass	240,000 kg
Tower Mass	347,500 kg

. For this analysis, the water depth was assumed to be 20 m, and the total height of the monopile foundation was set at 30 m.

The wind turbine tower’s numerical model was constructed in Abaqus, utilising beam elements for the structure. The rotor and nacelle mass were treated as a concentrated mass and applied to the top of the tower. A fixed support was implemented at the base of the structure. The approximate element size was 0.1 m. Figure 9 illustrates the Abaqus model of the monopile offshore wind turbine tower.

Specifically, the first mode involves the tower’s front and back vibrations, while the second mode corresponds to its left and right vibrations. Ice-induced vibrations are linked to the interplay between ice fracture and tower motion; therefore, the investigation concentrated on the first two modes. The modal analysis was performed in Abaqus, and the first two natural frequencies for each mode are listed in

Table 7. The first two natural frequencies of 5 MW monopile offshore wind turbine tower.

Mode	Frequency (Hz)
1	0.261
2	0.261

.

7. Results and Discussion

Figure 10, Figure 11 and Figure 12 are the results of different return periods and other FLI mechanisms. This paper focused on the reaction of the tower’s base and top.

Figure 13, Figure 14 and Figure 15 compare the maximum values in each time series sequence diagram.

This study conducted a comprehensive analysis of the impact of ice-induced vibrations on fixed-bottom cylindrical wind turbine structures, focusing mainly on the critical nature of frequency lock-in (FLI) vibrations. The dynamic evaluations, utilising a time-domain ice load model and FLI displacement analysis, revealed that FLI poses a significantly higher structural integrity risk than random vibrations caused by continuous brittle ice crushing.

The analysis framework for frequency lock-in (FLI) was developed based on the ductile damage–collapse (DDC) mechanism. This mechanism computes the probability of FLI occurrence, revealing that the conditions required for FLI are significantly less frequent than those estimated by conventional calculation methods, approximately 100 times lower.

Two distinct analytical approaches for assessing FLI were outlined: the ductile damage–collapse failure mechanism and the ISO-recommended method. The study compared the responses to continuous brittle crushing ice loads and FLI, with ice load return periods set at 1 year, 5 years, and 50 years. The results show that the probability of FLI occurrence is significantly reduced when considering the ductile damage–collapse mechanism, suggesting a more nuanced understanding of the ice–structure interaction dynamics.

The ISO method provides a valuable benchmark for evaluating FLI. Nonetheless, the ductile damage–collapse mechanism offers a more comprehensive analysis, particularly in scenarios where the ice’s failure process is ductile.

The response of a fixed offshore wind turbine tower during FLI is significantly greater than during random vibrations. The DDC mechanism led to the highest levels of displacement and acceleration at the top of the structure. Notably, the peak acceleration was nearly ten times greater, and the maximum displacement was approximately six times higher than those induced by ice loads with a 50-year return period. Regarding the shear force at the mudline, the ISO method yielded the highest value, underscoring the varying impacts of the two analytical approaches.

These findings underscore the importance of integrating comprehensive ice load considerations into offshore wind turbines’ design and operational strategies, particularly in ice regions. Introducing the ductile damage–collapse (DDC) failure mechanism offers a more accurate prediction model for FLI, presenting a novel approach to enhancing the resilience of these structures against ice-related hazards.

However, the measured ice force calculation is not necessarily the maximum random vibration. Because the ice force value will be much smaller than the maximum static ice force calculated, it can only be considered a typical value.

Limited research exists on the failure length L_ib as a critical parameter of FLI. There is little data; the actual test results are insufficient, and the experimental phenomena are inconsistent.

For the probability calculation in this article, we assumed that the failure length is an intrinsic property of the ice sheet and not influenced by the structure. However, is L_ib consistent when FLI occurs on platforms and wind turbines with the same sea ice? This is the focus of our subsequent research.

8. Conclusions

This research analysed ice-induced vibrations on fixed-bottom wind turbine structures, particularly on frequency lock-in (FLI) vibrations. The dynamic assessments, which employed a time-domain ice load model and FLI displacement analysis, disclosed that FLI presents a notably elevated risk to structural integrity compared to the stochastic vibrations resulting from continuous brittle ice failure. The principal conclusions drawn from this study are as follows:

• The ductile damage–collapse (DDC) mechanism suggests that the likelihood of FLI occurrence is substantially lower than that estimated by conventional calculation methods.
• During FLI, maximum displacements and accelerations at the top of the structure were approximately greater than those caused by ice loads with a 50-year return period.
• In terms of the shear force at the mudline, the ISO method yielded the highest value, indicating its effectiveness in assessing this critical parameter.

These findings underscore the necessity of incorporating robust ice load considerations into offshore wind turbine design and operational strategies, particularly in ice regions. Future research will investigate failure length (L_ib) consistency across different structures, as current data show no significant relationship between L_ib and ice thickness.