Multi-body dynamic analysis of offshore wind turbine considering soil-structure interaction for fatigue design of monopile
Introduction
Offshore wind farms have gained popularity in the recent past due to its various advantages, e.g. steady wind flow over an extended period and vast space in the marine environment. Many of these turbines in shallow water (depth around 3050 m) are supported by monopiles, whose dimensions depend on the size and power rating of the turbines, besides other environmental factors. The design of these structures is challenging and requires a high-fidelity model of the complete multi-body rotating system, where soil-structure interaction (SSI) plays a vital role.
Various methods are proposed in the literature to model the soil-structure interaction. For example, a closed-form expression for finding the fundamental frequency of a wind turbine tower under SSI was developed and experimentally validated by Adhikari and Bhattacharya [1]. Finite element analysis of monopile supported offshore wind turbine is a popular approach, where soil properties are modelled by linear or non-linear springs [2]. The dynamic interaction results in an increased response of the combined system. Zuo et al. [3] modelled NREL 5 MW benchmark wind turbine in the finite element framework using ABAQUS and observed a significant reduction of the tower natural frequencies due to SSI. They also noticed that blade and tower responses increased with rotor speed. Thus, monopile design without considering blade rotation led to gross underestimation that could subsequently affect the structure. Bisoi and Haldar [4] studied soft-soft and soft-stiff monopile design and checked the overall safety against serviceability and fatigue limit states. They observed that the length of monopile below its critical depth had a negligible impact on its design.
Rong et al. [5] derived an analytical formula for the natural frequency of monopile supported wind turbine using Euler-Bernoulli beam model with p-y curves for foundation stiffness. In this context, different aspects of offshore foundation design may be found in Bhattacharya [6]. This book explains the importance of soil-structure interaction and multiple methods to evaluate the foundation stiffness. It also provides a comprehensive review of different methods used for long-term behaviour estimation. Banerjee et al. [7] modelled the effect of foundation flexibility using an equivalent spring-dashpot model for monopile below the mudline. They carried out dynamic analysis using four different soil conditions and observed that the total displacement at the tower-top increased with reduced shear wave velocity, especially for lower soil stiffness. Kementzetzidis et al. [8] studied different geotechnical aspects of monopile foundation using 3D non-linear finite element analysis with a significant emphasis on the robustness of soft-stiff design, particularly in the extreme weather. In this context, impact load test on pile [9,10] is a standard tool to estimate its stiffness and in-situ frequency response function for finite element modelling.
Over the last decade, offshore wind turbines witnessed significant growth in its size to meet the power demand. Due to this reason, the load-carrying capacity of monopile has to increase to accommodate more giant turbines. This requirement has led to developing the new methodologies to improve the bearing capacity using stiffener to avoid the abnormal size of monopile [11]. In general, fatigue design focuses on the short-term effects, while long-term effects are equally crucial for serviceability. Katsikogiannis et al. [12] studied the stress due to axial force and bi-directional bending moments for damage estimation. They compared the sensitivity of three soil modelling techniques (viz. macro-element model, linear elastic stiffness model with soil damping and p-y curves) under wind-wave misalignment. Their study concluded that significant fatigue damage might occur for misalignment greater than 30°.
In general, soil type around the monopile affects its design life. Schafhirt et al. [13] investigated this influence on long-term performance due to cyclic loading. They modelled soil-structure interaction by non-linear p-y curves to estimate the fatigue life using the mudline bending moment, which was affected by the softening of the surrounding soil. Besides spring stiffness, aero-elastic and hydrodynamic damping play a significant role in fatigue life and cost-effective design [14,15]. In this context, current industry standards are often inadequate [16] for the upcoming large turbines due to their simplified approach for stiffness and damping characterisation and wind-wave modelling in the light of misalignment and soil-structure interaction. These shortcomings often lead to underestimation of fatigue damage accumulation and subsequent design life of the foundation. Marino et al. [17] compared the linear and non-linear wave models for fatigue load estimation. They concluded that the linear wave model underestimated fatigue load in the non-operating (or parked) condition, where hydrodynamic loads predominate. Simultaneously, the non-linear wave model was less critical in normal operating conditions, where aerodynamic loads dictated the design. Risi et al. [18] investigated the performance of offshore wind turbine under extreme events, e.g. earthquake along with wind and wave loads. In their study, a finite element model of an offshore wind turbine was developed for seismic fragility analysis to investigate its vulnerability, particularly under crustal earthquakes in soft soils. Loken and Kaynia [19] estimated the fatigue life of monopile and caisson foundation of offshore wind turbine using the mudline bending moment, which concluded that fixed bottom boundary condition over-estimated the design length.
Monopiles in the marine environment are often subjected to stress reversal caused by the environmental loads. Thus, fatigue crack propagation in these structures is the subject of various studies [20,21], where residual stress has a significant role in the performance of welds and connections. In this context, structural loads in the marine environment are highly uncertain. Hence, stochastic analysis of monopile has remained a significant area of research, where the overall reliability index is often quantified by approximate models [22] or Monte Carlo simulation [23]. Haldar et al. [24] studied the stochastic response of monopile supported offshore wind turbine in clay using non-linear p-y curves. They observed that the increase of embedded length reduced the mean of maximum tilt at the mudline, while marginally influencing its fatigue life. Teixeira et al. [25] used kriging for stress-cycle analysis of offshore wind turbine at a reduced computational cost without compromising its accuracy. Velarde et al. [26] conducted a sensitivity analysis of fatigue loads due to uncertainty in environmental, structural and geotechnical parameters. They observed that the uncertainties in turbulence intensity and wave load had a significant influence on fatigue loads. A comprehensive review of stochastic fatigue damage analysis for offshore wind turbine may be found in Jimenez-Martinez [27].
Section snippets
Problem formulation
The above literature review clearly shows the importance of fatigue design and long-term behaviour analysis of monopile supported offshore wind turbines. These studies use models which can be broadly classified into two major subgroups - (i) static or quasi-static analysis with soil springs, where the turbines and blades are lumped at the tower-top and (ii) dynamic analysis using software, e.g. FAST [28], Bladed [29], 3DFloat [30], HAWC2 [31]. Since monopile fatigue analysis depends on the
Multi-body dynamics of an offshore wind turbine on monopile
This section presents the modelling of a three-bladed horizontal axis offshore wind turbine, as shown in Fig. 1 supported over monopile foundation.
Forces acting on offshore wind turbine
Offshore wind turbines are exposed to aerodynamic and hydrodynamic loads in addition to the gravitational field, as shown in Fig. 1. IEC 61400–3 [43] recommends different wind flow conditions, including operating and non-operating regions for fatigue analysis with six simulated time-histories of 10 min each or a single 1-h response time-history. The details of these loads are briefly described with only the relevant formulations in the following subsections.
Fatigue analysis of monopile
Fatigue damage due to cyclic loading often starts at the surface (i.e. extreme fibre) and eventually grows to the failure. It may occur even when the stresses are below the yield strength of the material. Thus, fatigue damage assessment is essential while designing the structures that are subjected to load reversal. In this study, the fatigue life of monopile is estimated using stress at the extreme fibre. Fig. 4 shows the axial force and bending moment acting on a monopile, where the total
Long-term performance
Long-term offshore wind turbines behaviour is designed by satisfying the serviceability limit state (SLS) as per DNV guideline [39]. In general, the accumulation of rotation (or tilt) and the deflection (or strain) at the seabed must be within the allowable limits (i.e. serviceability). The long-term strain accumulation is investigated from the lifetime stress-based damage-equivalent load. In this context, different methods are often prescribed in the literature for finding the accumulated
Numerical results and discussion
In this study, a benchmark NREL 5 MW OC3 Phase II [62] wind turbine on a monopile foundation is considered for numerical analysis. It has three blades of length 61.5 m, connected to a hub of diameter 3 m. The nacelle of this turbine is placed at the height of 87.6 m from the mean sea level. The blades are made of 8 different airfoils, whose lift and drag coefficients, mass distribution, bending stiffness, aero-twist are given in the NREL report [62]. It operates within the wind speeds of 3 m/s
Conclusions
The work presented in this paper develops a multi-body dynamic soil-structure interaction model of an offshore wind turbine for fatigue design and long-term performance evaluation. The paper demonstrates stress-based fatigue analysis considering various monopile parameters, water depth and operational conditions. The significant contributions of this study are as follows.
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The combined system is modelled in Kane's approach using equivalent monopile properties obtained from a detailed substructure
Credit Author Statement
M. Mohamed Sajeer: Conceptualization, Methodology, Software Development and Writing - Original draft preparation
Arka Mitra: Multi-body dynamic analysis including SSI, Software Development and Writing - Original draft preparation
Arunasis Chakraborty: Conceptualization, Investigation, Supervision, Writing- Reviewing and Editing
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
References (67)
- et al.
Dynamic analysis of offshore wind turbine in clay considering soil–monopile–tower interaction
Soil Dynam Earthq Eng
(2014) - et al.
Dynamic analyses of operating offshore wind turbines including soil-structure interaction
Eng Struct
(2018) - et al.
Design of monopile supported offshore wind turbine in clay considering dynamic soil–structure-interaction
Soil Dynam Earthq Eng
(2015) - et al.
Dynamic analysis of an offshore wind turbine under random wind and wave excitation with soil-structure interaction and blade tower coupling
Soil Dynam Earthq Eng
(2019) - et al.
Geotechnical aspects of offshore wind turbine dynamics from 3D non-linear soil-structure simulations
Soil Dynam Earthq Eng
(2019) - et al.
A comparison of initial stiffness formulations for small-strain soil–pile dynamic Winkler modelling
Soil Dynam Earthq Eng
(2016) - et al.
Experimental application of FRF-based model updating approach to estimate soil mass and stiffness mobilised under pile impact tests
Soil Dynam Earthq Eng
(2019) - et al.
The loading behavior of innovative monopile foundations for offshore wind turbine based on centrifuge experiments
Renew Energy
(2020) - et al.
Influence of soil parameters on the fatigue lifetime of offshore wind turbines with monopile support structure
Energy Procedia
(2016) - et al.
Fatigue life sensitivity of monopile-supported offshore wind turbines to damping
Renew Energy
(2018)
Foundation damping and the dynamics of offshore wind turbine monopiles
Renew Energy
Offshore wind turbine fatigue loads: the influence of alternative wave modeling for different turbulent and mean winds
Renew Energy
Seismic performance assessment of monopile-supported offshore wind turbines using unscaled natural earthquake records
Soil Dynam Earthq Eng
Experimental and numerical investigation of residual stress effects on fatigue crack growth behaviour of S355 steel weldments
Int J Fatig
Waveform and frequency effects on corrosion-fatigue crack growth behaviour in modern marine steels
Int J Fatig
Probabilistic analysis of monopile-supported offshore wind turbine in clay
Soil Dynam Earthq Eng
Stress-cycle fatigue design with kriging applied to offshore wind turbines
Int J Fatig
Global sensitivity analysis of offshore wind turbine foundation fatigue loads
Renew Energy
Fatigue of offshore structures: a review of statistical fatigue damage assessment for stochastic loadings
Int J Fatig
Spinning finite element analysis of longitudinally stiffened horizontal axis wind turbine blade for fatigue life enhancement
Mech Syst Signal Process
Simple rainflow counting algorithms
Int J Fatig
Behavior of monopile foundations under cyclic lateral load
Comput Geotech
Vibrations of wind-turbines considering soil-structure interaction
Wind Struct
Analytical solution for natural frequency of monopile
Wind Struct
Design of foundations for offshore wind turbines
Fatigue sensitivity to foundation modelling in different operational states for the DTU 10MW monopile-based offshore wind turbine
J Phys Conf
Effect of foundation modelling on the fatigue lifetime of a monopile-based offshore wind turbine
Wind Energy Science
Effect of foundation type and modelling on dynamic response and fatigue of offshore wind turbines
Wind Energy
Reliability analysis of laterally loaded piles for an offshore wind turbine support structure using response surface methodology, Wind and Structures
Int J
Natural frequency of bottom-fixed offshore wind turbines considering pile-soil-interaction with material uncertainties and scouring depth
Wind Struct
Fast user's guide, Tech. rep
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