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A barrier to the development of the offshore wind resource along the U.S. Atlantic coast is a lack of quantitative measures of the risk to offshore wind turbines (OWTs) from hurricanes. The research presented in this paper quantifies the risk of failure of OWTs to hurricane-induced wind and waves by developing and implementing a risk assessment framework that is adapted from a well-established framework in performance-based earthquake engineering. Both frameworks involve the convolution of hazard intensity measures (IMs) with engineering demand parameters (EDPs) and damage measures (DMs) to estimate probabilities of damage or failure. The adapted framework in this study is implemented and applied to a hypothetical scenario wherein portions of nine existing Wind Farm Areas (WFAs), spanning the U.S. Atlantic coast, are populated with ∼7000 5 MW OWTs supported by monopiles. The IMs of wind and wave are calculated with a catalog representing 100,000 years of simulated hurricane activity for the Atlantic basin, the EDPs are calculated with 24 1-h time history simulations, and a fragility function for DM is estimated by combining variability observed in over one hundred flexural tests of hollow circular tubes found in the literature. The results of the study are that, for hurricane-induced wind and wave, the mean lifetime (i.e., 20-year) probability of structural failure of the tower or monopile of OWTs installed within the nine WFAs along the U.S. Atlantic coast ranges between 7.3 × 10−10 and 3.4 × 10−4 for a functional yaw control system and between 1.5 × 10−7 and 1.6 × 10−3 for a non-functional yaw control system.

The evaluation of natural catastrophe risk to structures often includes consideration of uncertainty in predictions of some measure of the intensity of the hazard caused by the catastrophe. For example, in the well-established method of probabilistic seismic hazard analysis, uncertainty in the intensity measure for the ground motion is considered through so-called ground motion prediction equations, which predict ground motion intensity and uncertainty as a function of earthquake characteristics. An analogous method for evaluating hurricane risk to offshore structures, referred to herein as probabilistic offshore hurricane hazard analysis, has not been studied extensively, and analogous equations do not exist to predict offshore hurricane wind and wave intensity and uncertainty as a function of hurricane characteristics. Such equations, termed here as wind and wave prediction equations (WWPEs), are developed in this paper by comparing wind and wave estimates from parametric models with corresponding measurements during historical hurricanes from 22 offshore buoys maintained as part of the National Data Buoy Center and located near the US Atlantic and Gulf of Mexico coasts. The considered buoys include observations from 27 historical hurricanes spanning from 1999 to 2012. The 27 hurricanes are characterized by their eye position, translation speed, central pressure, radius to maximum winds, maximum wind speed, Holland B parameter and direction. Most of these parameters are provided for historical hurricanes by the National Hurricane Center’s H*Wind program. The exception is the Holland B parameter, which is calculated using a best-fit procedure based on H*Wind’s surface wind reanalyses. The formulation of the WWPEs is based on two parametric models: the Holland model to estimate hurricane winds and Young’s model to estimate hurricane-induced waves. Model predictions are made for the 27 considered historical hurricanes, and bias and uncertainty of these predictions are characterized by comparing predictions with measurements from buoys. The significance of including uncertainty in the WWPEs is evaluated by applying the WWPEs to a 100,000-year stochastic catalog of synthetic hurricanes at three locations near the US Atlantic coast. The limitations of this approach and remaining work are also discussed.

In comparison with monopile support structures commonly used for offshore wind turbines (OWTs) in shallow water, fixed bottom support structures for deeper water such as jackets tend to lack axisymmetry and have different capacities when loaded in different directions. Design of such a structure may therefore benefit from consideration of the directional characteristics of loading. This paper focuses on a rational and efficient approach to assess the structural safety of jacket type OWTs under directionally dependent extreme environmental loads. The Incremental Wind–Wave Analysis (IWWA) framework is reviewed and used to assess capacity of jacket-type OWTs under directional environmental wind–wave conditions. The approach uses static pushover analysis of OWT jackets subject to combined wind and wave load patterns corresponding to increasing mean return periods (MRPs). The wind and wave conditions are calculated independently and assumed to occur simultaneously. The loading direction and jacket orientation are both included in the analysis. To illustrate the approach, metocean conditions at different sites along the U.S. Atlantic coast are obtained from the historical database of the National Oceanic and Atmospheric Administration (NOAA) Data Buoy Center. Two models are introduced for estimating the occurrence probability of wave direction, one of which directly uses the frequency of wave directions and the other uses a Gaussian kernel to represent the range of wave directions represented by given directional spectra. For each combination of wind–wave direction and structural orientation, an IWWA analysis gives the capacity in terms of the MRP conditions leading to formation of a fully developed plastic mechanism in the jacket. Those capacities, convolved with MRP models for loading intensity, yield direction-dependent structural reliabilities, and when those reliabilities are convolved with the probability density function for load direction, a total failure probability is obtained that accounts for wave directionality. Example analyses are conducted for an OWT supported by a four-leg jacket adapted from a design published as part of the European Union UpWind Project. Effects of extreme load directionality, structural orientation, structural geometry and site specification on the ultimate capacity of the jacket are carefully discussed.

A monopile supporting an offshore wind turbine (OWT) is currently designed for both strength and stiffness. Regarding strength, the monopile is designed to have sufficient capacity to withstand demands under both 50-year operational conditions, when the rotor is spinning and blades are oriented to optimize power generation, and 50-year extreme conditions, when the rotor is parked and the blades feathered to minimize aerodynamic loads. Regarding stiffness, the monopile is designed to have sufficient stiffness such that the first structural frequency of the OWT falls between the 1P and 3P frequencies (rotation frequency and blade passing frequency for a three-bladed turbine). For six case studies, including three sites along the U.S. Atlantic coast and two mudline conditions (fixed and compliant), this paper delineates the conditions under which stiffness and strength govern the design of the monopile. This distinction has important implications for the overall risk profile of an OWT, as monopiles controlled by stiffness will have more reserve capacity than monopiles controlled by strength. The six case studies are intended to consider a range of water depths, metocean environments and mudline conditions that is representative of conditions suitable for installing OWTs supported by monopiles along the U.S. Atlantic coast. The monopile designs are controlled by stiffness for two of the six cases studies and, for these two cases, a modest (6–8%) reduction in monopile area (and mass) could be achieved if dynamic design requirements were achieved through means other than increasing monopile stiffness. Monopile designs for the remaining four cases are controlled by operational moment demands.

Most offshore wind turbines (OWTs) are designed according to the international standard IEC 61400-3 which requires consideration of several design load cases under 50-year extreme storm conditions during which the wind turbine is not operational (i.e. the rotor is parked and blades are feathered). Each of these load cases depends on combinations of at least three jointly distributed metocean parameters, the mean wind speed, the significant wave height, and the peak spectral period. In practice, these variables are commonly estimated for the 50-year extreme storm using a simple but coarse method, wherein 50-year values of wind speed and wave height are calculated independently and combined with a range of peak spectral period conditioned on the 50-year wave height. The IEC Standard does not provide detailed guidance on how to calculate the appropriate range of peak spectral period. Given the varying correlation of these parameters from site-to-site, this approach is clearly an approximation which is assumed to overestimate structural loads since wind and wave are combined without regard to their correlation. In this paper, we introduce an alternative multivariate method for assessing extreme storm conditions. The method is based on the Nataf model and the Inverse First Order Reliability Method (IFORM) and uses measurements or hindcasts of wind speed, wave height and peak spectral period to estimate an environmental surface which defines combinations of these parameters with a particular recurrence period. The method is illustrated using three sites along the U.S. Atlantic coast near Maine, Delaware and Georgia. Mudline moments are calculated using this new multivariate method for a hypothetical 5 MW OWT supported by a monopile and compared with mudline moments calculated using simpler univariate approaches. The results of the comparison highlight the importance of selecting an appropriate range of the peak spectral period when using the simpler univariate approaches.

SUMMARY In this paper, considering horizontal components of seismic excitation, an algorithm for the nonlinear multi-component analysis of building structures by the Endurance Time (ET) method is proposed, and results of the ET method for various steel moment frames with one to seven stories are verified by comparing with the results from Nonlinear Time History Analysis with use of two different sets of ground motions. In addition, several parameters such as eccentricities and irregularities in structure, rotational and lateral stiffness, effect of hysteresis type and ductility have been considered for sensitivity analysis on results, obtained by ET method. Results show that on the basis of recommendations of structural codes for bidirectional time history analysis, which requires applying horizontal components of earthquakes simultaneously, the ET method can be used to predict the seismic response of structures with reasonable approximation and reduced computational effort. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, application of the Endurance Time (ET) method in seismic analysis of concrete gravity dams has been investigated. The ET method is based on time history analysis of structures, subjected to specially designed intensifying acceleration functions. It is expected that by developing its application in analysis of concrete dams, useful information on the seismic behavior of such dams at various excitation intensities can be obtained. Results from linear analysis of Folsom and Koyna dams under real earthquakes and ET acceleration functions have been compared. It is shown that the ET method can predict the response of concrete gravity dams to individual earthquakes with reasonable accuracy in linear analysis. In order to evaluate concrete gravity dams by linear analysis, the target time has been assumed to correspond to the OBE level of earthquake. Endurance criteria can be set as the time when the desired damage index(es), e.g. maximum principal stress, reaches its allowable value. The design can be considered satisfactory if endurance time is more than target time and vice versa. Also, potential application of the ET method in non-linear analysis of concrete gravity dams has been investigated. It is shown that crack profiles during earthquakes could be traced by the ET method.

SUMMARY The endurance time (ET) method is a time history-based dynamic pushover analysis procedure that utilizes special intensifying acceleration functions for estimating the seismic performance of structures at different excitation levels. One of the potential applications of the ET method is in the three-dimensional analysis of buildings considering multidirectional excitation. In this paper, a procedure for multi-component analysis by the ET method has been developed. Several steel moment frames with heights from 9.6 to 48 m were designed according to the Iranian National Building Code. By applying the proposed algorithm for three-dimensional analysis of structures by the ET method, these frames were analyzed, and results have been compared with static, response spectrum and response history methods considering typical code recommendations. Results show that for all studied models, even when irregularity and height of structure increase, the ET method estimates the seismic response of steel frames with reasonable accuracy compared with other investigated approaches. Copyright © 2010 John Wiley & Sons, Ltd.

The Endurance Time (ET) method is a time-history based dynamic pushover procedure for seismic analysis and design of structures. In this procedure, structures are subjected to a specially designed intensifying accelerogram and their Endurance Time is measured based on the time interval during which they can resist the imposed dynamic actions. In this paper, application of the ET method in linear seismic analysis of structures has been investigated. The procedure for generating code compliant uniformly intensifying ET accelerograms has been explained. A set of three such accelerograms have been applied to various moment and braced steel frames and the results of analysis are compared to conventional equivalent static and response spectrum seismic analysis procedures. Code compliant ET analysis and base shear scaling in this method is discussed. Story drifts and internal forces are shown to be consistent with response spectrum analysis and static analysis results within acceptable tolerances. In the case of irregular structures, when static analysis results tend to diverge from response spectrum analysis results, the ET method’s results are closer to the response spectrum’s results. In general, it has been concluded that ET method can be considered as an alternative time-history based analysis in the linear range.

The development of renewable energy sources is a critical global need. The Atlantic coast and Gulf of Mexico of the U.S., with large wind resources and proximity to major population centers, are natural places for such development; however, these regions are also at considerable risk from severe hurricanes or tropical cyclones. Current international guidelines for the design of offshore wind turbines (OWTs) do not explicitly consider loading under hurricane conditions, however subsequent editions are anticipated to include language specific to hurricanes. Variability in extreme loads is greater in areas where hurricanes are likely and the design loads and risk profile of offshore structures installed in such areas are expected to be strongly influenced by hurricanes. For many offshore structures, environmental conditions at design recurrence periods and beyond are often estimated through extrapolation of long-term (i.e. multiple decades) wind and wave measurements from buoys, however, for offshore structures located at areas exposed to hurricanes, it is accepted practice to use physics-based models to augment the historical record of Atlantic hurricane activity and generate a stochastic catalog of synthetic hurricanes that provides tens of thousands of realizations for one year of potential hurricane activity. Once a stochastic catalog has been established, appropriate hazard intensity measures (e.g. the one-minute sustained wind speed, the significant wave height, and the peak spectral wave period) can be estimated for each storm at any site using well-known wind and wave parametric models. In this study, we consider several sites along the Atlantic coast and quantify the impact of estimating hazard for design recurrence periods and beyond for three different methods. The first is based on an extrapolation of wind and wave measurements from buoys, and the second and third are based on a stochastic catalog of synthetic hurricanes with wind and wave intensities estimated based on deterministic and probabilistic relationships.Copyright © 2015 by ASME

Aerodynamic damping has an important effect on the seismic response of horizontal axis wind turbines (HAWTs). Some researchers have estimated that aerodynamic damping in operational HAWTs is ∼5% of critical in the fore-aft direction (i.e., perpendicular to the rotor and parallel to the prevailing wind). In most recent studies, dynamic analyses of HAWT towers under seismic loads have neglected aerodynamic damping, and this assumption has significant implications in the predicted seismic response. This paper presents a closed-form solution for the aerodynamic damping of HAWTs responding dynamically in the fore-aft and side-to-side directions. The formulation is intended as a convenient method for structural earthquake engineers to include the effect of aerodynamic damping in the seismic analysis of HAWTs. The formulation is based on blade element momentum theory and is simplified by assuming a rigid rotor subjected to a steady and uniform wind oriented perpendicular to the rotor plane. This paper ex...

Most offshore wind turbines (OWTs) are designed according to the international standard International Electrotechnical Commission (IEC) 61400-3 which requires consideration of several design load cases under extreme sea state conditions during which the wind turbine is in survival mode (i.e. the rotor is parked and blades are feathered). Each of these load cases depends on combinations of two random variables, the mean wind speed and the significant wave height, both with a mean return period of 50 years. The response of an offshore wind turbine under wave loading is known to be sensitive to both the significant wave height and a frequency measure of the sea state such as the peak spectral period. The IEC standard states that design calculations for the extreme sea state should be based on values of peak spectral period which result in the highest loads acting on the structure, but does not provide additional guidance. The Standard does provide a deterministic range for the period of the extreme wave conditioned on the significant wave height, and this can be converted to a range of peak spectral period using published empirical relationships. This paper considers an offshore location off the coast of Georgia, where the National Oceanic and Atmospheric Administration (NOAA) buoy 41008 is located, and shows that a deterministic range of peak spectral period converted from the range provided in the IEC Standard may not accurately represent measured data. Moreover, the paper shows that the response of a hypothetical offshore wind turbine, installed at this location and supported by a monopile foundation, is sensitive to variation in the peak spectral period, emphasizing the importance of modeling the turbine for an appropriate and possibly site-specific range of peak spectral periods. A probabilistic approach is proposed to find an appropriate and site-specific range of the peak spectral period for the design of offshore wind turbines under the extreme sea state.

The Endurance Time (ET) method is a time history-based dynamic analysis procedure which uses special intensifying acceleration functions for evaluation of the seismic response of structures. One of the potential applications of the ET method is in the three-dimensional analysis of buildings under multi-directional excitations. In this paper, considering horizontal components of excitation, an algorithm for the multi-component analysis of building structures by the ET method is proposed, and results of the ET method for various steel moment frames with 1 to 7 stories are compared with results from time history analysis with real earthquakes. Results show that based on recommendations of structural codes for bi-directional time history analysis, which requires applying horizontal components of earthquakes simultaneously, the ET method can be used to predict the seismic response of structures with appropriate approximation.