Natural frequency of offshore wind turbines on rigid and flexible monopiles in cohesionless soils with linear stiffness distribution

A simplified method is introduced to obtain the fundamental frequency of offshore wind turbines supported by monopile foundations. Soil-pile interaction is modeled based on Winkler approach and concept of beam on elastic foundation. The soil is considered to have linearly varying modulus of subgrade reaction along depth which is a typical assumption for cohesionless soils. Rayleigh method which is based on conservation of total energy of the system is utilized. Firstly the natural frequency of the system with rigid pile is derived and then an innovative procedure is introduced to take pile flexural stiffness into consideration. Comparison between results of the present method with those of a numerical FE model for a typical 2 MW wind turbine structure shows excellent agreement for rigid pile and flexible pile with small value of slenderness ratio. The agreement is also good for flexible pile with higher slenderness ratios. A parametric study is carried out to investigate the effect of important parameters of foundation including pile slenderness ratio, pile aspect ratio and pile mass on the system natural frequency.     

Effect of scouring in sand on monopile-supported offshore wind turbines

This paper analyzes the influence of scour on the overall response of monopile-supported offshore wind turbines (OWTs) in 20-m water depth. Scouring effects on OWTs have been often studied within the geotechnical domain, considering static loads at the mudline. The present work attempts to address the scour-induced problems in OWTs by making use of an integrated aerodynamic–hydrodynamic load approach in sandy soils. The OWT analysis is simulated for operational and shut-down (parked) condition. Under parked situations, the OWT blades are feathered, and power production is suspended, owing to structural safety concerns. The 50 Monte Carlo responses of stochastic sea-state condition (wind speed with turbulence, significant wave height, and peak spectral period) are generated. Irregular, long-crested waves are generated using the Joint North Sea Wave Project (JONSWAP) spectrum. Then from each simulation, the ensemble response is obtained. Sandy soils of varying densities are considered. Results indicate that OWTs founded on loose sands suffer significant stiffness (and hence natural frequency) reductions, shifting the structure into the resonance regime. Lateral responses also show an escalation with reduction in density of sandy soil.     

Dynamic analysis of offshore wind turbine in clay considering soil–monopile–tower interaction

A comprehensive study is performed on the dynamic behavior of offshore wind turbine (OWT) structure supported on monopile foundation in clay. The system is modeled using a beam on nonlinear Winkler foundation model. Soil resistance is modeled using American Petroleum Institute based cyclic p–y and t–z curves. Dynamic analysis is carried out in time domain using finite element method considering wind and wave loads. Several parameters, such as soil–monopile–tower interaction, rotor and wave frequencies, wind and wave loading parameters, and length, diameter and thickness of monopile affecting the dynamic characteristics of OWT system and the responses are investigated. The study shows soil–monopile–tower interaction increases response of tower and monopile. Soil nonlinearity increases the system response at higher wind speed. Rotor frequency is found to have dominant role than blade passing frequency and wave frequency. Magnitude of wave load is important for design rather than resonance from wave frequency.     

Closed form solution of Eigen frequency of monopile supported offshore wind turbines in deeper waters incorporating stiffness of substructure and SSI

Offshore wind turbines (OWTs) are dynamically loaded structures and therefore the estimation of the natural frequency is an important design calculation to avoid resonance and resonance related effects (such as fatigue). Monopiles are currently the most used foundation type and are also being considered in deeper waters (>30 m) where a stiff transition piece will join the monopile and the tapered tall tower. While rather computationally expensive, high fidelity finite element analysis can be carried to find the Eigen solutions of the whole system considering soil–structure interaction; a quick hand calculation method is often convenient during the design optimisation stage or conceptual design stage. This paper proposes a simplified methodology to obtain the first natural frequency of the whole system using only limited data on the WTG (Wind Turbine Generator), tower dimensions, monopile dimensions and the ground. The most uncertain component is the ground and is characterised by two parameters: type of ground profile (i.e. soil stiffness variation with depth) and the soil stiffness at one monopile depth below mudline. In this framework, the fixed base natural frequency of the wind turbine is first calculated and is then multiplied by two non-dimensional factors to account for the foundation flexibility (i.e. the effect of soil–structure interaction). The theoretical background behind the model is the Euler–Bernoulli and Timoshenko beam theories where the foundation is idealised by three coupled springs (lateral, rocking and cross-coupling). 10 wind turbines founded in different ground conditions from 10 different wind farms in Europe (e.g. Walney, Gunfleet sand, Burbo Bank, Belwind, Barrow, Kentish flat, Blyth, Lely, Thanet Sand, Irene Vorrink) have been analysed and the results compared with the measured natural frequencies. The results show good accuracy (errors below 3.5%). A step by step sample calculation is also shown for practical use of the proposed methodology.     

Dynamic response of a monopile wind turbine in waves: Experimental uncertainty analysis for validation of numerical tools

The responses of a monopile offshore wind turbine subjected to irregular wave loads are investigated numerically and experimentally, considering a range of sea states. An extensive experimental campaign was carried out on a fully flexible model, representative of a 5 MW offshore wind turbine, at 1:40 scale. An assessment of the experimental results for the response amplitude operator for regular waves and the 90th percentile seabed bending moment in long-crested irregular waves is carried out using two models (analytical and numerical) for uncertainty propagation, suggesting that bias errors in the model properties and in the wave elevation contribute the most to the total uncertainty. The experimental results are also compared to a numerical model using beam elements and Morison-type wave loads with second order wave kinematics. The numerical model does not capture all of the responses within the level of uncertainty of the experiments, and possible reasons for the discrepancies are discussed.     

The nature of scour development and scour protection at offshore windfarm foundations

Analysis and interpretation of monitoring data for the seabed bathymetry local to offshore windfarm foundations has shown how the scour develops in time and highlighted variations between sites with different seabed sediment characteristics, i.e. sands and clays. Results from European offshore windfarms have generated a unique dataset for comparison with previously published data. Where surficial sediment is underlain by a marine clay the scour (to date) has been limited, whilst those with unconstrained depths of sandy sediments show scour as deep as 1.38 times the monopile diameter. Scour protection has been installed at some sites for structural stability of the foundation or for cable protection. The flow interaction with the protection causes edge scour or secondary scour in the seabed around the protection. In some cases this scour is deeper than the unprotected case. The analysis has resulted in an improved evidence base for scour in the marine environment.     

考虑水-桩-土相互作用的单桩式海上风机结构系统自振频率解析解

海上风机结构系统频率是海上风机结构和基础设计考虑的关键因素之一,桩-土相互作用对海上风机结构系统频率影响显著。基于欧拉-伯努利梁理论和传递矩阵方法,考虑水-桩-土相互作用及塔筒变截面特性,建立单桩式海上风机结构系统横向振动自振频率特征方程;将桩-水相互作用等效为附加质量、桩-土相互作用等效为线性弹簧,变截面塔筒等效为多段均匀梁,利用MATLAB中fsolve函数求解固有频率。通过与有限元分析结果进行对比,验证本文方法精度与有效性,并将本文方法应用于实际工程中,研究桩基础埋深、上部质量、转动惯量和桩-水相互作用对单桩式海上风机结构系统自振频率的影响。