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The loss and abandonment of fishing gear has resulted in one of the most visible signs of growing pollution in the marine environment. The entanglement of whales in fishing gear has been the subject of increasing documentation. The interpretation of the documented incidents to address the risk of whale entanglement is presented. An initial risk-based model is derived that reflects published information on multi-year fishing gear accumulation rates and entanglement data. A fault tree framework is adopted to organize the data, allowing for the continual improvement of the risk-based model predictions through the incorporation of new data and inclusion of additional sub-events. Analytic distribution functions are introduced to augment incomplete data and explore hypothetical scenarios. Data reported for the US Atlantic and Pacific coastlines are used in illustrative examples, that address both regional and multi-regional applications, and the sensitivity of the risk-based predictions to the reported field data.

The analysis of members that can be modeled as extensible elastic slender rods is investigated. A meshfree formulation using a Local Radial Point Interpolation Method (LRPIM) is developed that utilizes radial basis functions in curvilinear coordinates. This approach bypasses the need to utilize more conventional element meshes and significantly reduces the number of equations needed for the numerical solution. The slender rod formulation presented allows for tension variation, axial stretch, incremental loading and distributed load variation along the rod. It is well suited for nonlinear problems that involve large deflections and rigid rotations. The position and tangent vectors are expressed using Hermite-type approximations, and radial basis functions, while the interpolation of tension variation and distributed loads are described using polynomials. The solution procedure of weighted residuals Galerkin weak formulation combined with an incremental iterative numerical scheme is introduced to address the incremental loading and large deflection issues for static and quasi-static problems. The implementation of the analytical formulation and the numerical procedure are illustrated using three nonlinear problems. The first two examples provide insight into the validity, accuracy, and efficiency of the methodology. The third example presents the case of a moving boundary condition problem which models a cable entangled by fishing boat-trawling equipment.

There are many offshore applications that incorporate vertical cylindrical-shaped structural elements such as marine risers, TLP tendons and near shore pier designs. A better understanding of complex wake flows on the drag dominated force predictions is very much of interest for offshore design problems. This study investigates the Huse-Muren analytical wake model, whose mathematical formulation was founded on the earlier definitive studies of Prandtl and Schlichting. Developing a deeper understanding of their key findings that were based upon central assumptions and key approximations is central to this research. Analysis of their model leads to the development of dimensionless expressions for the drag coefficient correction ratio. Both the DNV-RP recommended drag force coefficients and some of Sarpkaya's U-tube measurements are used to investigate whether their analytical model could be used to bound the experimental data. The Keulegan-Carpenter number, A 0 / D ratios, Sarpkaya's Beta parameter and Reynold's number are used to interpret the range of model applicability. For the current cross flow case, variables identified in Huse and Muren's formulation lead to a dimensionless expression involving the period of in-line oscillation and the velocity of the cross-current resulting in a parameter similar to the Keulegan-Carpenter number. The ratio of this parameter to the Keulegan-Carpenter number allows one to address the drag coefficient correction ratio where a cylinder is simultaneously subjected to in-line oscillatory flow and a steady cross current coming from the transverse direction. A numerical simulation is performed to investigate the behavior of the correction ratio in this flow condition, and the results are presented and discussed.

Long slender cylindrical structures are widely used in offshore structural designs. Their interactions with random waves are very complicated and it is extremely difficult to model their motions in a direct analytical approach. Accurate characterization of the observed extreme values in their response behavior is of vital importance for the safety of the designed structure. In this study a general statistical methodology based on generalized extreme value (GEV) family of distributions is formulated for the characterization of both laboratory and field data associated with the wave-cylinder interactions in random waves. An iterative process is developed to determine the most appropriate block size and the corresponding statistical model for the block maxima constructed from the time series of the target variable. The model's capability to fit the data is assessed using the Anderson-Darling (AD) test criterion, visually with quantile plots and histograms. Special attention is paid to the quality of fit in the upper tail of the distribution, which corresponds to the data points of the extreme statistical events. Case studies are performed that investigate the performance of the statistical methodology in characterizing the measured data from two industrial scale model basin test programs. The first case study addresses data on the in-line interactions of closely spaced deep-water cylinder arrays for two- and three-cylinder configurations and the second considers the VIV response amplitudes of a slender horizontal cylinder. In both test programs the random seaways were generated using JONSWAP wave amplitude spectrum. The effectiveness of this statistical methodology in characterizing the response behavior observed in the model basin experimental data is discussed in detail using both tabular and graphical interpretations.

Several floating wind turbine designs whose hull designs reflect those used in offshore petroleum industry have emerged as leading candidates for the future development of offshore wind farms. This article presents the research findings from a model basin test program that investigated the dynamic response of a 1:50 scale model OC3 spar floating wind turbine concept designed for a water depth of 200 m. In this study the rotor was allowed to rotate freely with the wind speed and this approach eliminated some of the undesirable effects of controlling wind turbine rotational speed that were observed in earlier studies. The quality of the wind field developed by an array of fans was investigated as to its uniformity and turbulence intensity. Additional calibration tests were performed to characterize various components that included establishing the baseline wind turbine tower frequencies, stiffness of the delta type mooring system and free decay response behaviour. The assembled system was then studied under a sequence of wind and irregular wave scenarios to reveal the nature of the coupled response behaviour. The wind loads were found to have an obvious influence on the surge, heave and pitch behaviour of the spar wind turbine system. It was observed from the experimental measurements that bending moment at the top of the support tower is dominated by the 1P oscillation component and somewhat influenced by the incoming wave. Further it was determined that the axial rotor thrust and tower-top shear force have similar dynamic characteristics both dominated by tower’s first mode of vibration under wind-only condition while dominated by the incident wave field when experiencing wind-wave loading. The tensions measured in the mooring lines resulting from either wave or wind-wave excitations were influenced by the surge/pitch and heave couplings and the wind loads were found to have a clear influence on the dynamic responses of the mooring system.

A variety of innovative airborne concepts are being developed to capture the wind energy available at higher altitudes, facilitate wireless communication and provide heavy lift capability. These airborne systems will be in close proximity to cloud cover and exposed to increased risk of lightning strikes. A two-dimensional physics based formulation that was recently developed to investigate the potential field behavior about circular sections was used to develop uniform and tapered cylindrical elements. These elements were then combined to approximate the total charge and lightning behavior about an airborne wind turbine and a heavy lift airship. Surface electrical charge and lightning collection area are developed as a function of elevation, body shape, cloud cover and leader properties. The surface charge density is utilized to compute the degree of field intensification on the body periphery in order to determine the level of susceptibility of the airborne system to lightning strikes. It was observed that as airborne bodies move closer to the thundercloud the ambient potential field becomes more highly perturbed and leads to greater risk of lightning strikes. The lightning collection area was shown to increase with elevation of the airborne body and decrease with increase in the leader propagation angle.

The severity of lightning strikes on offshore wind turbines built along coastal and nearshore regions can pose safety concerns that are often overlooked. In this research study the behavior of electrical discharges for wind turbines that might be located in the nearshore regions along the East Coast of China and Sea of Japan were characterized using a physics-based model that accounted for a total of eleven different geometrical and lightning parameters. Utilizing the electrical potential field predicted using this model it was then possible to estimate the frequency of lightning strikes and the distribution of electrical loads utilizing established semi-empirical relationships and available data. The total number of annual lightning strikes on an offshore wind turbine was found to vary with hub elevation, extent of cloud cover, season and geographical location. The annual lightning strike rate on a wind turbine along the nearshore region on the Sea of Japan during the winter season was shown to be moderately larger compared to the lightning strike frequency on a turbine structure on the East Coast of China. Short duration electrical discharges, represented using marginal probability functions, were found to vary with season and geographical location, exhibiting trends consistent with the distribution of the electrical peak current. It was demonstrated that electrical discharges of moderately long duration typically occur in the winter months on the East Coast of China and the summer season along the Sea of Japan. In contrast, severe electrical discharges are typical of summer thunderstorms on the East Coast of China and winter frontal storm systems along the West Coast of Japan. The electrical charge and specific energy dissipated during lightning discharges on an offshore wind turbine was found to vary stochastically, with severe electrical discharges corresponding to large electrical currents of long duration.

As a result of the recent severe storm events in the Gulf of Mexico and along the East Coast there is increasing concern over the volume of man-made debris that has been observed entering the coastal marine ecosystems. Understanding the movement and accumulation patterns of debris within a flow is important for gaining knowledge on how the presence of debris affects the performance of marine facilities. Runoff from storm water discharge introduces a considerable amount of debris into waterways that either float on the surface or travel within the water column. This discharge impacts coastal areas and contributes to the accumulation of trash in the oceans. This research study reports on some of the published field data on flow density of natural and anthropogenic debris that has been reported in the open literature. This includes data reported on the amounts, types, and distributions of marine debris. Several predictive models that have been created to simulate the transport and accumulation of marine debris are discussed. These models were developed to address local knowledge of ocean and river currents and wind patterns. Studies on the influence of debris accumulation at riverine and coastal structures such as bridge piers and hydroelectric dams are also noted. The accumulation of debris at these structures is particularly important due to the risk of blockage, scour, or structural failure. In one of these studies a probabilistic model that investigates the interaction of marine life with hydrokinetic devices is discussed that is based on a limited amount of field data. Of particular concern was the presence of a rotating device and the additional risk of the quantification of various aspects including injury to aquatic life and damage to the structure. This study identifies the need to better understand the distribution and behavior of hard and soft debris and its distribution within a flow in order to more accurately predict its interaction and accumulation patterns about a wide range of constructed facilities.

The modeling of lightning strike behavior and estimation of the subsequent electric discharge is of great practical importance. In this study, a complete two-dimensional physics-based analytic formulation is presented for elevated grounded systems that can be envisioned to be contained within two non-concentric circular domains. The inner circle encompasses the body or system of interest, and the periphery of the outer circle addresses the cloud coverage. The potential field between the circular domains is modeled as the sum of two separate contributions. The first is formulated in terms of an eigen-function expansion involving simple radial functions and Legendre polynomials, while the second contribution is developed using two different approaches. The first approach utilizes an eigen-function expansion incorporating spherical Bessel functions and Legendre polynomials, while the second approach uses a Green’s function expansion also involving orthogonal polynomial functions. Each of the contributions to the total potential field leads to linear systems of equations that are solved for the unknown series expansion coefficients. The accuracy of the potential field solution is investigated with regard to convergence, stability, and error compared with an exact solution. The potential field solution is then used as the basis to evaluate leader formation, as a function of elevation, extent of cloud coverage, and propagation angle of the downward leader. Regions of high risk to lightning strikes on the grounded structure are developed in terms of joint probability functions. The electric discharge is estimated using electric current and is shown to be in the range of presently available information.

There have been many interesting technical ideas and parallels in thinking that have resulted from the technical discussions that I have had with Professor Jerome J. Connor since 1986. This brief article provides a context and reflects upon his mentorship, which helped shape the thinking of a then young professor from another University, and on the impact that Professor Connor has had on his students and others beyond the halls of MIT’s Building 1. The optimization topic presented here provides an example of that influence. Extracting the desired response information from an instrumented slender structure, while minimizing the number of sensors, is a challenging problem requiring well-defined objectives that can be used in an optimization process. In this study, a methodology that builds upon a Genetic Algorithm optimization procedure is used to investigate sensor placement needed to recover specific vibration modes. Data recorded from an experiment investigating the flow-induced vibration of a smooth horizontally towed cylinder is used to explore the optimization process and subtleties associated with its application subject to single or multiple objectives and gaps in sensor data due to several possible constraints. The use of the Paterno Front Method and the difficulty in accurately capturing higher modes are addressed.

Many significant engineering challenges have emerged as the petroleum industry has moved their field development and production activities into increasingly deeper water depths. The design of deepwater marine risers presents the combined challenges to minimize top tensioning requirements, mitigate any flow-induced vibrations, and if possible to increase the expected fatigue life of these slender structural members. As part of the design process to achieve these goals external buoyancy modules and strakes have been employed. To gain insight into the complex multi-mode response behavior a recent experimental study was performed and the analysis of selected data sets is presented. In the experiments a horizontal cylinder with a length to diameter ratio of 263 was fitted with a variety of strake and buoyancy element configurations. The models were towed at uniform speeds ranging from 0.4 to 2.0 m/s and fiber optic strain gages were used to measure both in-line and cross-flow strain response. The resulting time series information was processed utilizing the method of time domain decomposition formulated for strain data input and the introduction of modal assurance criterion to resolve the modal strain information that included frequency, mode shape, and critical damping ratio information. The pre-tensioned cylinder without appendages was used as a base case and the results were basically consistent with expectations. In the case of 0.8 m/s low-tension test, multiple closely spaced non-overlapping peaks were observed in both in-line and cross-flow directions and were identified as being of the same mode with mode shapes distorted away from purely sinusoidal behavior. The test data for the 100% coverage by helical stakes demonstrated the effectiveness of that suppression device over the range of current velocities investigated. The most interesting case was that of a staggered combination of helical strakes and buoyancy element whose total for each type of coverage was equal. This effective asymmetric VIV suppression approach is presented and discussed in detail.

Cables and various subsea product fl ow-lines are often subjected to fl ow-induced vibrations as a consequence of wave or wave and current fl ow excitation. An experimental study that explores the comparative suppression effectiveness of airfoil and ribbon fairings is presented. In the experimental investigation, an instrumented tensioned 29 m horizontal composite cylinder with a length to diameter ratio of 760 is subjected to a range of uniform current and combined current and regular wave conditions. In the analysis of the cross-fl ow response amplitude ratios, modal parameters, such as mode shape, damping ratio were extracted. The analytical procedures were performed using a modifi ed time domain decomposition technique. The analysis illustrated the amplifi ed response behavior for bare cylinders, and illustrated that full coverage by airfoil and ribbon fairings could effectively suppress fl ow-induced vibrations in current only conditions, but both fairings were ineffective when regular wave conditions were superimposed on the uniform current conditions, even though the airfoil provided larger damping than ribbon fairings. Under combined wave and current conditions, the response behavior of either suppression device was found to be insensitive to coverage densities.

An experimental study was conducted to investigate the ability of ribbon fairings to suppress fl ow-induced vibrations on a long fl exible horizontal cylinder. The test matrix included towing the cylinder at various speeds, towing the cylinder in regular waves, and investigating the infl uence of partial coverage on the response behavior. The test cylinder was 29 m long with a length to diameter (L/D) ratio of ~760. Interior to the tensioned cylinder model were six sets of unequally spaced biaxial accelerometers in a lightly pressurized environment keeping the interior dry. A string potentiometer was externally attached at the center of the model to provide a reference for later displacement estimates based on integration of the acceleration data. The time domain decomposition method (TDD) was used to recover mode shapes, damping characteristics, and modal contribution factors. For the uniform current cases, the fi ndings illustrate that ribbon fairings are effective and provide increased damping when compared with bare cylinders. Partial coverage demonstrates that localized suppression becomes increasingly less effective as the percentage coverage is reduced. The introduction of regular waves to the towed cylinder cases illustrates the ineffectiveness of ribbon fairing to suppress the orbital motions induced by the waves, which is preferable to the amplifi cation typically observed for airfoil fairings.

The use of multi-parameter distribution functions that incorporate empirically derived parameters to more accurately capture the nature of data being studied is investigated. Improving the accuracy of these models is especially important for predicting the extreme values of the non-linear random variables. This study was motivated by problems commonly encountered in the design of offshore systems where the accurate modeling of the distribution tail is of significant importance. A four-parameter Weibull probability distribution model whose structural form is developed using a quadratic transformation of linear random variables is presented. The parameters of the distribution model are derived using the method of linear moments. For comparison, the model parameters are also derived using the more conventional method of moments. To illustrate the behavior of these models, laboratory data measuring the time series of wave run-up on a vertical column of a TLP structure and wave crests interacting in close proximity with an offshore platform are utilized. Comparisons of the extremal predictions using the four-parameter Weibull model and the three-parameter Rayleigh model verify the ability of the new formulation to better capture the tail of the sample distributions.

The realistic assessment of an ocean wave energy resource that can be converted to an electrical power at various offshore sites depends upon many factors, and these include estimating the resource recognizing the random nature of the site-specific wave field, and optimizing the power conversion from particular wave energy conversion devices. In order to better account for the uncertainty in wave power resource estimates, conditional probability distribution functions of wave power in a given sea-state are derived. Theoretical expressions for the deep and shallow water limits are derived and the role of spectral width is studied. The theoretical model estimates were compared with the statistics obtained from the wave-by-wave analysis of JONSWAP based ocean wave time-series. It was shown that the narrow-band approximation is appropriate when the variability due to wave period is negligible. The application of the short-term models in evaluating the long-term wave power resource at a site was illustrated using wave data measured off the California coast. The final example illustrates the procedure for incorporating the local wave data and the sea-state model together with a wave energy device to obtain an estimate of the potential wave energy that could be converted into a usable energy resource.

Wave run-up on multi-column compliant and rigid platforms both on the weather-side and beneath the platform deck is a complex wave–structure interaction problem. Predictions based upon higher order hydrodynamic design codes have been improved our understanding of this phenomena but have not appreciably reduced the reliance on model tests and statistical analyses. In this study a three parameter distribution model is developed based upon the inclusion of linear, second-order, and mean contributions to the wave run-up utilizing the method of L-moments. Explicit expressions are derived relating the L-moments and the input from experimental data. The sample L-moments are developed from a linear combination of ordered sequence of the data and consequently the high order L-moments, i.e. L-skewness and L-kurtosis, are less biased than the corresponding ordinary moments. The L-moment definitions of the variance, skewness and kurtosis are numerically compared with values obtained using the more standard definitions for these parameters. Rigid hull measurements are compared with the compliant hull configuration for a mini-TLP model. The sea-states investigated include the relatively benign sea conditions off of West Africa and the more extreme sea environments of Gulf of Mexico.

The design of fixed or floating offshore structures requires accurate information of the met-ocean data at the intended offshore site. In the design process it is recognized that this environmental data is modified in the near-field by the interaction with the particular geometrical configuration of the offshore structure. This transformation of the incident wave field around and beneath an offshore structure presents a challenge for ocean engineers when specifying the wave gap elevation to avoid impact loads on the underside of the deck and inundation of the topsides. Thus, the accurate estimation of the wave crest distributions from measurements at various locations near and under the offshore structure during model test studies is essential. A semi-empirical approach is presented herein that builds upon the findings of previous studies and introduces the Method of L-moments. A three parameter model for a wave crest probability distribution function is presented and explicit relationships between the parameters of the distribution and its’ first three L-Moments are established. Furthermore, three narrow-band models from earlier research studies are reviewed and compared with the new model. Wave measurements from a mini-TLP model test program are used as the basis for comparison of the four distributions. The root-mean-square error is used as a metric to quantify the overall fit of the data and its accuracy in the high end tail of the data. The L-Moment model is shown to be more robust in representing the data in both the far-field and beneath the deck of the mini-TLP where the wave field demonstrates increased non-linear behavior.

The earthquake induced upper story pounding response of two buildings in close proximity is investigated. The formulation models each building as two degree of freedom oscillators and allows for impact at mid-level and top-level elevations. Variable friction base isolation modeling Teflon bearings are introduced into the formulation and it is assumed that the earthquake induced motion is one dimensional in that it excites each building from the same direction for each building. Three illustrative examples are presented that provide a basis for comparison of fixed base and base isolated buildings models. In the numerical simulations, four earthquake records from different sites were used to excite the buildings and were scaled to the same spectral acceleration at the period of the fixed-base building natural period in order to provide a common seismic hazard level. The number of upper story building collisions is presented as a function of the gap spacing between the buildings, and results illustrate the effect of altered structural kinematics due to impact. The number of upper story impacts for the fixed base and the base isolated structure configurations and the effect of friction varying base isolation on the number of building impacts is shown through example to be a function of earthquake ground motion specifics.

The dynamically coupled interaction between the hull of a floating platform and its risers and tendons plays an important role in the global motions of the platform and the tension loads in the tendons and risers. This is an especially critical design issue in the frequency ranges outside the wave frequencies of significant energy content. This study examines the importance of this coupled dynamic interaction and the effectiveness of different approaches for their prediction. A numerical code, named COUPLE, has been developed for computing the motions and tensions pertaining to a moored floating structure positioned and restrained by its mooring/tendon and riser systems. In this study the experimentally measured motions of a mini-TLP are compared with those computed using COUPLE and alternative predictions based upon quasi-static analysis. The comparisons confirm that COUPLE is able to predict the dynamic interaction between the hull and its tendon and riser systems while the related quasi-static analysis fails. The comparisons also show that wave loads on the mini-TLP can be accurately predicted using the Morison equation provided that the wavelength of incident waves is much longer than the diameters of the columns and pontoons and that the wave kinematics used are sufficiently accurate. Although these findings are based upon the case of a mini-TLP, they are expected to be relevant to a wide range of floating or compliant deepwater structures.

In many engineering problems one deals with quantities that must be considered to be of a stochastic or random nature. This is true for the natural environment such as wind, waves, and earthquakes, which are the driving mechanism behind the loadings on a wide variety of land-based and offshore structures. From a design perspective it is important to determine the expected highest value of a stochastic process, and structural fatigue life. The relevant procedures are reasonably well established for processes that have narrow band spectra, but it is much less clear how to deal with non-narrow band cases. In this paper it is shown that the extremes of a Gaussian, non-narrow band process are asymptotically equal to the extremes calculated according to the narrow band formula. Also demonstrated is that fatigue estimates may, with good accuracy, be based on the narrow band formula unless the bandwidth becomes extremely large. These statements are illustrated by examples of a process with (1) a low pass box spectrum, and (2) a Pierson–Moskowitz wave amplitude spectrum. It is also shown that the bandwidth parameter may in some cases be counter-intuitive, as the Pierson–Moskowitz spectrum has a larger bandwidth parameter than the box spectrum, even when both cover the same frequency range.

This research study investigates the practicality of using a Slepian model to model the earthquake excitation and structural response behavior of structures during the strong ground motion portion and entire duration of earthquake acceleration records. Of particular interest was the extreme response behavior of basic linear and nonlinear hysteretic oscillators. Predictions for the linear oscillators were found to be good, while predictions for the highly nonlinear oscillators were poorer until corrected for the change in equilibrium position experienced during the motion response behavior. Based upon the experience gained from these examples, a three-story frame whose beam-to-column connections were modeled as trilinear hysteretic systems were investigated. The accuracy of the Slepian response prediction for the seismic response was confirmed and the expected value form was coupled with a drift-based limit state function to estimate a conditional form of the first order structural reliability. Since the coefficient of variation of the seismic demand is not explicitly known, the reliability estimates were bounded based upon observations of typical seismic demand variation in engineered structural systems.

The development of a definitive predictive model that accurately accounts for the nonlinear hydrodynamics and structural response behavior observed in arrays of closely spaced risers on deep water structures will require a more detailed understanding of this fluid–structure interaction. Through the analysis and interpretation of data from model basin tests on single and paired tandem cylinder configurations this study is directed at uncovering the nature of some aspects of this nonlinear response behavior using an orthogonal third-order Volterra technique that can delineate between linear, quadratic and cubic nonlinear frequency dependent behavior. As part of the analysis procedure the data was organized in input–output pairs that would provide logical groupings of the measured quantities. The data pairs presented in this study include wave excitation and inline cylinder displacement, wave excitation and transverse cylinder displacement, wave excitation and inline reaction force, and, upstream cylinder and downstream cylinder response. This information is presented in terms of spectral and coherence plots. The single cylinder data is presented as a means to contrast the behavior of the tandem cylinders. Both configurations were analyzed at two different pretensions adding another dimension to this investigation. It is shown that although a primary variable such as displacement may be more easily measured, pretension and force measurements provide an important key to our understanding of this difficult problem.

Modeling engineering problems of interest often requires some type of discretization model of the physical system and quite naturally leads to a mathematical description involving partial differential equations whose coefficients are dependent on both time and spatial location. In this study a reverse system identification approach is presented that utilizes generalized coordinate and force functions to recover the value of the key system parameters for each mode of vibration. To illustrate the analysis procedures, a single marine riser with general damping-restoring types of non-linearities subject to random wave excitation is considered. Analytical expressions as functions of the modes for bending stiffness and tension are derived and used for comparison with the results obtained using system identification. Numerical simulations including band-limited white noise and random wave excitation are used to explore the adequacy of the methodology and the benefits of using modal analysis in the system identification procedure. Finally, the use of and comparison with experimental data is presented and the frequency variation of parameters obtained resulting from system identification procedures discussed. Collectively, the examples demonstrate that this system identification methodology accurately identifies system parameters over portions of the frequency range of interest.

The design of deepwater compliant offshore structures requires engineers to address many difficult challenges including defining and modeling the local offshore environment, specifying the associated combined global loading on innovative platform designs, and numerical simulation and model test verification of the platform response characteristics. The focus of this research investigation is the recovery of key parameters from time series measured during an industry type model basin test program using the reverse multiple input/single output technique. In particular, this study confronts critical problems of practical interest and extends the methodology to address the inclusion of nonlinear coupled systems in which the parameters of interest can be frequency-dependent. The analysis is developed around the nonlinear coupled equations of motions for a deepwater mini-TLP design and includes the consideration of nonlinear stiffness, quadratic damping, surge/pitch and sway/roll coupling and the frequency dependency of both the hydrodynamic added-mass and damping coefficients. A series of complementary model test measurements for the complete compliant model and the rigidly restrained hull by itself were used as the basis for the data in the system identification procedures. In addition, behavior of the hydrodynamic added-mass and damping coefficients as a function of frequency was simulated for the mini-TLP using an industry standard radiation–diffraction software package. These results were used in evaluating the accuracy of some of the key problem parameters. The results presented demonstrate the methodology as modified in this study is quite robust and yields predications that are more accurate for the parameters associated with the largest motions of the platform. Practical issues regarding the application of this approach, utilization of both force and moment measurements, and observed strengths and weakness in dealing with data regardless of its source are discussed.

This study presents an Inverse-First Order Reliability Method (FORM) approach to generating site-specific composite seismic response spectra. The proposed technique searches the surfaces of Inverse-FORM generated contours for the earthquake statistically most likely to produce the target spectral acceleration at the desired structural period, as modelled by the appropriate attenuation relation. Identification of this spectral acceleration level over a range of periods produces a composite design response spectrum consisting of spectral acceleration levels most likely to occur and all lying on the surface of the n-year contour, hence possessing the desired n-year return period. This composite seismic response spectrum can be used in design and analysis of structural systems having variable levels of complexity. The result is an n-year composite, seismic design response spectrum, found using Inverse-FORM generated contours that are generated in a discrete four-dimensional space. The random variables associated with this four-dimensional space are earthquake magnitude, site-to-source distance, attenuation relation uncertainty, and fault of origin. This study outlines the technique and presents a hypothetical example for a region threatened by three behaviourally different earthquake source mechanisms. An illustrative example is presented for target spectral accelerations of 0.1g and 0.4g, having two different return periods. The number of different earthquakes contributing to each spectrum varied between three and nine, depending on the specifics.

Subsea pipelines transporting hydrocarbons from very deepwater wells or at arctic sites for long distances present some challenging technical problems. The ambient temperature at the seafloor in deepwater may be about 5°C (∼ 41°F or 278 K) and can be even lower in the arctic regions, while the wellhead hydrocarbon temperatures can be in excess of 149°C (∼ 300°F or 422 K). Insulation of these buried pipelines to mitigate this large temperature gradient can be only part of the solution as temperature losses over long distance may require heating systems to avoid deposition of impurities and clogging of the pipeline. The near field thermal gradient in surrounding soil is investigated using complementary 2-D numerical simulations of finite element and boundary element numerical models. A finite element hydraulic-thermal code designed for porous media was used to investigate the time evolution of the natural convection effects due to pipeline heating of the seawater in soil. For a seabed of clay under these conditions, it was determined that the boundary element model could be directed at steady state heat transfer about the pipeline in layered soil conditions addressing trenching and backfill consistent with the burial of the pipeline by a remotely operated vehicle. Parameters that may affect the thermal field around the subsea buried pipeline such as burial depth, thermal power loss and thermal properties of backfilling soils were investigated. It was shown that the thermal conductivity of the backfill has a critical influence on temperature distribution at the pipe wall, and that the pipe burial depth significantly affects temperature distribution on the seabed right above the pipe in deepwater.Copyright © 2014 by ASME

A finite-difference scheme and a modified marker-and-cell (MAC) method are used for numerical wave tank (NWT) simulations to investigate the characteristics of nonlinear multidirectional waves. The Navier-Stokes (NS) equations are solved for two fluid layers and the boundary values updated at each time step by a finite-difference time-marching scheme in the frame of rectangular coordinate system. The fully nonlinear kinematic free-surface condition is satisfied by the density-function technique developed for two fluid layers. The directional incident waves are generated from the inflow boundary by prescribing a snakelike motion along the wavemaker direction. The outgoing waves are numerically dissipated inside an artificial damping zone located at the end of the tank. Using the NS-MAC NWT with both solid and transparent side-wall conditions, the effects of side-wall reflections are studied. Bull’s-eye waves are also numerically generated by the phase control of neighboring wavemaker segments or the reverse process of cylindrical wavemakers. The simulation results are compared with the computations by an independently developed potential-based NWT and the experiments conducted in the Offshore Technology Research Center’s 3-D wave basin.

In many engineering problems the uncertainty in the design and analysis process is dominated by uncertainty concerning the environmentally induced loading on the system. One such type of system is a structure located in high seismic zones, where there is a high level of uncertainty associated with the ground acceleration. In this study the demand caused by the environmental loads is statistically characterized in terms of magnitude, site-to-source distance and attenuation error at a specified structural period. Through the use of a reliability-based procedure known as the Inverse-First Order Reliability Method all of the combinations of the random loading variables that produce a response spectrum with the specified return period may be identified. These infinite number of combinations produce an Environmental Contour that may be derived for the two, three, or four-dimensional case. Because these contours represent an infinite number of combinations of environmental loading random variables, and in turn, a family of response spectra with the same return period, one need only search the Environmental Contour for the response spectrum producing the peak spectral acceleration at the structural period of interest. This study presents a general multi-variate framework focusing on the derivation of these two, three, and four-dimensional Environmental Contours. Initially, the magnitude and site-to-source distance are assumed to be statistically independent. Two and three-dimensional Environmental Contours are derived for this case and critical response spectra for three different, commonly used return periods are examined. Then a hypothetical example in which the site-to-source distance is assumed LogNormal and dependent on magnitude, is used as a basis for discussion for a generic California site. A qualitative discussion between the assumption of independence and dependence between magnitude and site-to-source distance is addressed. Finally, the peak spectral accelerations for the dependent two, three, and four-dimensional cases are compared to one another and the possible consequences associated with increasing the complexity of the environmental contour model analyzed and discussed.

This study presents a methodology to rank the possible earthquake events through the estimation of a reliability importance parameter, which is a function of each event's magnitude M and site-to-source distance R. This allows one to rank the importance of each design earthquake not in terms of the acceleration of a single-degree-of-freedom oscillator, but rather in terms of the displacement-based reliability of a multiple-degree-of-freedom representation of the structure. A simulation procedure is introduced that couples a technique similar to seismic hazard analysis with performance-based reliability estimates that consider interstory drift criteria. The simulation procedure allows for the inclusion of response spectra uncertainty and structural resistance uncertainties in the mass, stiffness, and damping at each story level. The reliability importance factor leads to the definition of a cumulative earthquake hazard function. This function may be used as a basis in selecting the number of design earthqua...

The extreme behavior of surface waves as they encounter and pass compliant deepwater platforms is an important class of problems for offshore engineers attempting to specify the platform deck elevation. In this study analytical expressions for the probability density and cumulative distribution functions that utilize empirical coefficients in an attempt to accurately model surface wave runup and airgap problems are presented. The analysis focuses upon interpreting the tails of the measured data histograms using two parameter Weibull distribution models. The appropriate empirical constants, assumed to be solely dependent upon the significant wave height, were evaluated and compared for all the test data. Based upon a small select set of data, for a mini-TLP and two Spar platforms, the airgap problem was found to be adequately modeled using a Rayleigh distribution. Further, for the seven seastates analyzed, the Weibull shape parameter was nearly constant and the data confirmed that the exclusive fit of the scale parameter assuming dependence only on the significant wave height was a reasonable approach for modeling the wave runup. Finally, by combining these models with a Poisson return model for each storm the associated reliability estimates for various deck heights were estimated.

The response of a long flexible cylinder excited by random waves in a large model basin was investigated. The linear and non-linear physical mechanisms associated with the wave–cylinder interaction were analysed using system identification and modelling techniques. A third-order frequency domain Volterra model and its orthogonalized counterpart were used to analyse the relationships between wave elevations at various locations in the vicinity of the cylinder and cylinder acceleration data at various cylinder longitudinal locations. It was found that linear mechanisms dominate, particularly at the frequency band where the majority of the wave energy is located. At higher frequencies, the cubic component of the Volterra model is the main contributor to the total model coherence, i.e. the fraction of the measured output power that can be approximated by the model output, whereas the quadratic component's contribution to the total model coherence was in general quite small. This process of identification and quantification of the non-linear mechanisms of the unknown physical system can lead to the design of improved parametric models for the cylinder response, which should by design simulate non-linearities such as the ones identified by the Volterra model. The estimated linear and non-linear Volterra transfer functions were also used to predict the cylinder acceleration under excitation inputs not used in the estimation of the model transfer functions. The good match between predicted and measured output auto-power spectra suggests that the estimated transfer functions are indeed true models of the underlying physical mechanisms of the interaction. However, the latter can only be achieved if a minimum number of data segments, as determined by an error analysis involving modelling and prediction errors, is used in the estimation of the Volterra transfer functions.

The definition and subsequent use of dimensional and dimensionless parameters to characterize various nonlinear aspects of ocean surface waves has again become a matter of great interest to the offshore community. The desire to ascertain whether laboratory simulations are adequately representing the surface waves found in the oceans and the concern over the mechanisms behind platform response phenomena, like ringing, has driven this resurgence of interest. This paper presents a depth independent characterization of single design waves, from which improved estimates of localized wave crest front and back slopes follow that are consistent with discrete time series analysis. Characterization of the nature of the entire wave data recorded requires a combination of spectral parameters and probabilistic models in addition to those used in the design wave characterization. A new expression for the direct evaluation of the kurtosis from knowledge of the spectral bandwidth, the relationship between some of the common spectral parameters, and some modified spectral parameters are presented and discussed. Three illustrative examples are presented. The first example provides a detailed examination of wave data measured from a series of random amplitude and random phase tests in a large model basin. The second presents estimates of the various parameters for the Pierson-Moskowitz and Wallops wave spectrum models. The third example investigates the use of the spectral peakedness ratio for comparing data with selected wave spectrum models. The examples illustrate how the formulae can provide a comprehensive local and global parametric characterization of surface wave elevation data.

The direct measurement of displacement time histories, obtained by tracking illuminated targets located on the exterior surface of submerged objects, has significant advantages for large-scale model tests. Many problems of interest require the simultaneous measurement of three-dimensional motions at several elevations on the same body or on several bodies in close proximity. Thus, optical tracking of targets in air or water or some combination of the two required the development of a general analytical formulation capable of converting local data measured from multiple camera locations to a global coordinate system for further analysis. The formulation presented is quite general and allows one to study the displacement behavior of single or multiple targets located on the same object or on different moving objects. As part of the analysis, calibration issues, possible sources of error and the optimal choice of camera location are discussed in detail. Data obtained from a large-scale model test of deepwater platform TLP tendons subjected to random design seas is used to illustrate the methodology. In the example, four different cameras were used to record the tendon displacements. To illustrate the methodology, five different camera combinations were used to compute the target location. The results indicate that the formulation is quite robust and that, although only a two-camera system is required to resolve the three-dimensional global coordinates of a single target, the use of a third camera can enhance the accuracy of the results. Guidelines for using cameras to track target motion were developed and are presented.

A regressive form of Slepian modelling was used to develop predictive models for the key variables associated with three quite different experimental data sets. The first data set provided a time series record of the surface elevation for a moderate random seaway. The second data set provided measurements of the wave elevation at the front of a finite draft deep water platform. This data set was significantly more nonlinear since the local wave field was amplified by the presence of the platform. The final data set dealt with the rate of wave run-up and this involved the derivative of the second data set. The results consistently illustrated the need to have an adequate number of events to use as the basis for the regression model. The study presents guidelines for selecting the initial crossing level which is crucial to the Slepian model development. Once the regression model has been established the model allows one to make predictions for other values of level crossing. It was found that the accuracy of those predictions depends on the accuracy of the initial regression process and that reasonable estimates can be obtained.

This paper describes a method developed to estimate the three-dimensional displacement field of long, flexible cylinders subjected to wave loading. The method makes use of the relationship between curvature and displacement of a uniform beam. The technique was implemented in a large-scale experimental study to investigate the response of a pair of flexible cylinders in close proximity, with an emphasis on the collision behavior between them. The model cylinders were designed to be representative of risers or tendons of a tension-leg platform in approximately 1000 m of water. The cylinder models, approximately 17-m long and 0.03-m diameter, were instrumented to measure the cylinder curvature at discrete locations along their length. At each time step the displacement field was computed from the curvature measurements using a ‘shoot-to-fit’ numerical-integration scheme. This procedure yielded a complete description of displacement along the cylinder as a function of time. The number and location of the curvature measurements were optimized by simulating the wave-flexible cylinder interaction with a finite-element model that was also used to demonstrate the accuracy of the method. The effectiveness of the technique is demonstrated by results from the experimental program, and it appear to be feasible to adapt this approach for field experiments.

A large-scale experimental study to investigate the dynamic response of a single flexible cylinder in waves is presented. The cylinder was designed to exhibit the dynamic characteristics of a TLP riser or tendon in approximately 1000 m of water. Instrumentation provided detailed information on the inline and transverse curvature along the length of the cylinder. Wave loading mechanisms and the resulting response were investigated and compared with previous studies of rigid cylinders in oscillating flow. It was found that the complicated multifrequency response at large Keulegan-Carpenter numbers could be explained by introducing the depth dependence of the Keulegan-Carpenter number. The predicted inline response was shown to be reasonable for the wave frequency component of the measured inline response. Similarities between the measured transverse response and the high-frequency inline response were also shown. Probability density functions of the measured curvature were non-Gaussian, leading to significantly higher probabilities of curvature than would be predicted based on assuming a Gaussian process.

Ocean engineers are routinely faced with design problems for coastal and deepwater structures that must survive a wide range of environmental conditions. One of the most challenging problems in the field of ocean engineering is the accurate characterization and modeling of the interaction of ocean waves with these offshore structures. The random characteristic of ocean environment requires engineers to consider the effects of random variability of the pertinent variables in their predictive models and design processes. Thus, for ocean engineering purposes, one needs to have accurate estimates of the probability distribution of the key random variables that will be used in sensitivity studies, reliability analysis, and risk assessment in the design process. In this study, a family of semi-empirical probability distribution is developed based on the quadratic transformation of linear random variable assuming that the linear random variable follows a Rayleigh distribution law. The estimates of model parameters are obtained from two moment based parameter estimation methods, i.e. method of moments and method of linear moments. The studied semi-empirical distribution can be applied to estimate the probability distribution of a wide range of non-linear random variables in the fields of ocean wave mechanics and wave-structure interaction. As examples, the application of the semi-empirical model in estimation of probability distribution of: a) ocean wave power, b) ocean wave crests interacting with an offshore structure is illustrated. For this purpose, numerically generated timeseries and experimentally measured data sets are utilized.

A probabilistic model for the collision between a pair of cylinders in tandem subjected to random waves is presented and compared to experimental data. The model is developed by adapting first-passage time formulations from probabilistic mechanics, and is extended to account for a non-Gaussian collision process by applying a Hermite transformation technique. Large-scale experiments were conducted to study the fluid-structure interaction between water waves and a pair of flexible cylinders, designed to represent TLP tendons and risers in approximately 1000m of water. Comparisons between the probabilistic model and the experimental data showed the first-passage formulation for the probability of cylinder collision to be appropriate. The Hermite models provided an accurate-to-conservative bound on the experimental data while the Gaussian model was unconservative. The comparisons also demonstrated the importance of accounting for the non-Gaussian nature of the response for predicting the extreme statistics.

A small-scale experimental study was performed to investigate wave runup on rigid full-length and truncated circular cylinders under regular and random sea conditions. Wave elevations were measured around one-half of the cylinder circumference together with the total in-line wave force. The regular wave data were compared with predictions obtained using linear diffraction theory, and the results were consistent with the findings of earlier researchers. A regression analysis was performed on the regular wave data to obtain a relationship between the wave runup and the velocity head. The resulting empirical equation can be used to make preliminary estimates of wave runup on truncated circular cylinders. An approximate formula for predicting the time-dependent wave force on a truncated cylinder is presented. Transfer functions relating the enhanced wave-surface-elevation spectrum and the wave-force spectrum to the incident-wave spectrum are derived. The validity of the wave-force approximation and the adequacy of the linear transfer functions are examined in light of the new experimental data. As in the case of regular waves, the random-wave spectrum model does not adequately predict the root-mean-square (RMS) surface elevation at the front of the cylinder, but does provide a reasonably good estimate of the wave force on full-length and truncated cylinders. Extreme value estimates based on standard statistical procedures are compared with the experimental data and generally found to be conservative.

The response of a nonlinear marine riser model to both parametric and external excitation is examined using Markov methods. Moment-closure techniques are used to predict the response of the riser in a random seaway. An approximate nonlinear polynomial representation of the hydrodynamic damping term is developed in order to implement Gaussian and non-Gaussian moment-closure schemes. These methods are applied to solve the case of pure parametric excitation and the results are compared with those obtained using stochastic averaging. It is shown that as the parametric excitation level is varied, the response predictions from different techniques exhibit the same linear trends. However, the non-Gaussian closure scheme provides improved response estimates that are closer to stochastic averaging results. Moment-closure techniques are then extended to consider a riser under combined parametric and external excitation. For a fixed level of parametric excitation, the response statistics are found to vary nonlinearly with external excitation levels. The Gaussian closure scheme is found to overpredict structural response for the case of pure parametric excitation and to underpredict structural response for the case of pure external excitation.

The design and application of shaping filters for random response analysis of offshore structures is presented. The approach is based upon Markov methods and its suitability for use in offshore engineering is demonstrated through a series of numerical examples. Shaping filters are designed for generating the wave elevation, wave kinematics and wave forces from white noise. The filter equations are combined with state-space equation models of two different types of offshore structures. Moment equations are generated using Ito's rule and solved for the structural response in terms of statistical moments. This filter methodology is applied to both linear and non-linear structural models of offshore platforms. The strengths and limitations of the filter approach are examined through direct comparison with time domain simulations.

The design of deep water offshore platforms requires the analysis of wave-structure interaction phenomena which have not been as critical for shallower water platform designs. In the case of tension leg platforms (TLPs) interaction phenomena such as wave run-up on the vertical legs and the amplification of the waves beneath the deck are major design considerations. The research investigation reported here focuses on a series of small scale wave tank tests on four column TLP models examining these phenomena. The role of vertical leg spacing and comparative tests of the TLP models with and without pontoons was investigated. As the vertical legs were moved closer an increase in wave run-up and a shifting of the incident wave period corresponding to the maximum wave upwelling were noted. Comparisons with wave measurements for single cylinders from previous experimental studies and the TLP configurations used in this study are presented. A design formula for estimating wave run-up on TLPs is suggested based upon these experiments. The wave run-up on a leg directly in the wake of another leg is presented. A comparison of the wave upwelling measurements with previously published numerical results are discussed. A wave uplift force model which allows for the inclusion of the experimentally obtained wave upwelling measurements is presented and discussed with regard to the design specification of platform deck elevation.

Compliant offshore platforms are designed to allow controlled movement of the platform as an alternative to near-rigid resistance to wind, wave and current loading by fixed platform designs. The equations of motion, valid for both single and multi-articulated towers, are derived using a Lagrange equation approach. The resulting equations are then used to study the sensitivity of a tri-articulated tower to select design parameters. A tension-restrained articulated platform (TRAP) proposed by the offshore industry for use in 914 m (3000 ft) of water is used for comparison in the sensitivity studies. Dimensionless parameters are developed and used to identify the roles of several key variables in altering the natral periods of tower vibration in order to avoid regions of significant environmental excitation.

The design of fixed or floating offshore structures requires accurate information of wave crest maxima to avoid topside inundation and minimize the wave impact on the underside of the deck structure. The extreme value theory is utilized to obtain the distribution of wave crest maxima in vicinity of offshore structures. The theory requires the accurate estimates of wave crests distribution especially in the very upper tail of the distribution. In order to include the wave-structure interaction into the model a three-parameter semi-empirical model developed in the earlier studies is utilized. The semi-empirical distribution is developed based on a second order Rayleigh-Stokes model and takes advantage of method of L-moments for parameter estimation. The wave crest distributions obtained from the semi-empirical model are compared with linear and nonlinear models utilizing model test data from a mini-TLP experiment. The analysis indicates that the semi-empirical model is robust in approximating the probability distribution of data and consequently results in more reliable estimates of wave crest maxima. In addition, the spatial variation of wave crest maxima in the vicinity and underneath of the offshore structure and consequently the statistics of wave crest maxima in the area around the offshore structure are studied.

A historical perspective on the performance of vertical and inclined flare structures is provided to illustrate the breadth of the problem and provide a basis to appreciate the engineering solutions to the issue of flow-induced vibrations.