Evaluation of the Floater N219 Structure with CEVL Material in Response to Random Wave Excitation

Preliminary results of spectral and Preliminary results of spectral and probabilistic analysis of wave and wave-induced loads probabilistic analysis of wave and wave-induced loads on the main tower and wave staff of the Christchurch Bay experiments are presented. The results obtained to date show reasonable agreement with linear random-wave solutions and the influence of the non-linear drag element of the loading is apparent. The data needs to be expanded with particular reference to fluid kinematics in the presence of waves and currents, and their effect on wave loading. Introduction Part II of this paper discusses the results obtained to date from an analysis of the Christchurch Bay data in spectral and probabilistic terms. Again, it is noted that the results presented here are interim in that further analysis and cross-checking of the data is continuing. 2. THEORETICAL BACKGROUND 2.1 The Wave Conditions A method of predicting wave induced forces on offshore structures which has found increasing application to design problems in recent years is based on the concept of considering the wave motion as a stationary random process. Incident wave conditions are expressed in terms of the surface-elevation spectrum, Sn(w), such as the Pierson-Moskowitz or Jonswap formulations. These Pierson-Moskowitz or Jonswap formulations. These can be related to the usual parametric descriptions of wave conditions in terms of the significant wave height, H1/3, and the zero-crossing period, Tz, and it is sometimes appropriate to use a 'spreading-function' giving a two-dimensional spectrum Sn(w, 0) representing a three-dimensional sea-state. In parallel with the spectral formulation are the probabilistic properties of the surface-elevation which, under certain assumptions, can be considered as a Gaussian process with probability density function, (p.d.f): (1) It has been shown by several authors, notably Longuet-Higgins, that for certain conditions the p.d.f of wave-height is approximated by the Rayleigh density function which in cumulative form is given by: (2) Thus the wave condition can be described by the spectrum, the Gaussian p.d.f of surface-elevation and the Rayleigh p.d.f of wave height. 2.2 The Loading Model Morison's equation for the in-line horizontal force per unit length on a vertical cylinder represents the total force as the sum of a non-linear drag component and a linear inertial component. (3) where being the density of sea-water; Cd and Cm are the drag and inertia coefficients, u is the horizontal water particle velocity and u is the acceleration. particle velocity and u is the acceleration. There are obviously deficiencies in this representation, for example, transverse forces are not included and the coefficients Cd and Cm are considered to be constants. However, the wide-spread use of the Morison equation in design and, as yet, the absence of a reliable alternative justify its use as the 'core' of spectral and probabilistic extentions. P. 187

Fixed offshore structures are operated in shallow water depths up to 500 feet and are often subjected to huge wave loading. The huge waves destabilize the structures, which then can cause widespread damage to the local ecology, coastal towns, and the environment. Mitigating the impact of wave loading requires the accurate prediction of wave induced forces, which is used for the structural assessment. Determination of wave induced forces requires solution of two problems. The prediction of wave kinematics by using an appropriate wave theory and then the prediction of the pressure and viscous forces due to the wave impact loading. This paper focuses on the hydrodynamic wave loading of fixed offshore structures in shallow water. Accurate modeling of huge waves in shallow water is more challenging compared to deep water due to higher relative wave height (wave height to water depth ratio). In this paper, we propose a Computational Fluid Dynamics (CFD) solution using Volume of Fluid (VOF) method and fifth order solitary wave theory for modeling huge waves in shallow water with very high accuracy. This model is validated with experiment for the physical mechanisms in the wave loading of the structures such as wave propagation, run up and interactions. Finally, this model is used for the wave- in-deck analysis of a fixed offshore oil rig in shallow water. In this study, we use a 20m (65.6 feet) wave in 41m (134.5 feet) water depth (Relative wave height of 0.49), which is not possible to model using Airy and Stokes wave theories. The wave-in-deck analysis is carried out for three different wave heights and the effect of wave height on the wave run-up and loads is analyzed. Introduction Hydrodynamic wave loading on fixed offshore structures has been an issue of concern to the offshore oil and gas industry. A huge wave hitting the offshore platform leads to high wave-in-deck loads that can eventually result in significant platform damage and collapse. Fatalities and damages costing hundreds of millions of dollars can occur. From 2004–2008, five major hurricanes (Ivan, Katrina, Rita, Gustav, Ike) destroyed 180 structures and 1,070 wells in Gulf of Mexico [Kaiser, M.J, 2011]. About 50 Russian crew members were killed after a jack up oil rig capsized and sank in a 6m (19.68feet) wave hitting [News: Reuters, December 2011]. Some of the possible causes of the accidents are:Some areas of the Gulf of Mexico floor have experienced several feet of subsidence, which leads to lower deck height and are more vulnerable to wave loading [Laurendine, T., 2007].The wave crest height according to RP 2A of the American Petroleum Institute (API) is higher than the lower deck elevations of many existing platforms [Bea, R.G., et all,1999]With the occurrence of a tropical storm or hurricane, the wave height exceeds the design height.Old structures are designed to a lower environmental criterion and have lower strength characteristics. So a structural assessment is necessary to determine whether the structure can withstand the peak loads during the huge wave impact. The wave-in-deck loading is very complex and difficult to model with traditional analytical tools. It is also very difficult to assess the loading very accurately in physical model tests carried out in a small scale wave basin, which introduces inaccuracies in the measurements [Grønbech, M. J.et all. 2011]. With the recent advancements in CFD and increased computing power, CFD can be a valuable tool for the assesment of the structures subjected to wave loading.

Recently, some integrated structural identification/damage detection and reliability evaluation of structures with uncertainties have been proposed. However, these techniques are applicable for off-line synthesis of structural identification and reliability evaluation. In this paper, based on the recursive formulation of the extended Kalman filter, an on-line integration of structural identification/damage detection and reliability evaluation of stochastic building structures is investigated. Structural limit state is expanded by the Taylor series in terms of uncertain variables to obtain the probability density function (PDF). Both structural component reliability with only one limit state function and system reliability with multi-limit state functions are studied. Then, it is extended to adopt the recent extended Kalman filter with unknown input (EKF-UI) proposed by the authors for on-line integration of structural identification/damage detection and structural reliability evaluation of stochastic building structures subject to unknown excitations. Numerical examples are used to demonstrate the proposed method. The evaluated results of structural component reliability and structural system reliability are compared with those by the Monte Carlo simulation to validate the performances of the proposed method.

The API RP 2A 20ttt Edition allows for directionally in wave loading, with the wave height in the minimum direction as low as 70% of the wave height in the maximum direction. The resulting statically applied loads may differ by as much as 50% from the maximum to the minimum wave directions. This paper describes the finding that dynamic directional wave loading design according to API IV 2A can result in much larger than expected loads along the "reverse" direction to thatof the major wave heading, Rigorous random wave analyses on jackets in 600 to 900 ft water depths using RP 2A and accounting for dynamic structural behavior, revealed significant "rebound" (opposite to major wave heading) inertial Loading. These rebound loads were target than the applied loads from the minimum wave specified by RP 2A directional criteria. Results quantify and explain the components of the rebound load. This paper develops a practical recipe, using RP 2A, that accounts for dynamic structural response. The design procedure is verified with rigorous random wave analysis results Introduction Prior to 1994, most fixed offshore structures designed for installation in the Gulf of Mexico were analyzed using wave loads based on a single, unidirectional wave height. In other words, the maximum wave (typically close to 72 ft in height in deep water) was assumed to approach the structure from all directions. The same assumption was made for the current profile. Depending on the geometry of the structure, this generally resulted in static base shears and overturning moments of similar magnitudes in all directions. For the design of dynamically active (high natural period) structures, the static wave and current loads are typically combined with inertia loads to account for dynamic loading. A common design approach is to calculate a Dynamic Amplification Factor (DAF), based on the ratio of dynamic load to static bad, determined from a random wave dynamic analysis. (As with static wave and current loading, random wave dynamic analyses have typically used an unidirectional procedure, in which the maximum sea state is assumed to approach the platform from all directions). The static wave and current load. multiplied by (DAF-1.0) gives the required magnitude of the inertial loading. Using DAFs calculated for base shear and overturning moments, an inertia load set may be calculated from the combination of two modes (Kint and Morrison, 1990). With the adoption of API Recommended Practice 2A, 20th Edition. the wave load criteria for the Gulf of Mexico was changed to a multi-directional formulation. The multi-directorial criteria, judged by the API Task Group on Wave Force Commentary to be a more accurate representation of reality, allows the use of reduced wave heights in several directions. The direction wave heights for a structure in 900 ft water depth (WD), based on RP 2A 20th Ed., are illustrated in Figure 1. In this case, the maximum wave height is 70.3 ft. for a wave traveling in the 290° compass direction.

The N219 floatplane improves PT Dirgantara Indonesia’s N219 aircraft, suited for maritime operations. During operation, the wave stress on the floater structure must be factored into the aircraft design. This study presents a method for evaluating the design of the N219 aircraft’s floater structure using criteria for withstanding static and dynamic loads from irregular waves during maritime operations. Dynamic loads are estimated using ANSYS AQWA, which uses a 3D diffraction theory and assumes a fluid with no viscosity. The operational condition simulations include wave height variations of 0.5m, 1m, and 1.5m, as well as five changes in the aircraft’s direction relative to the wave direction. The floater model is simulated at a constant speed in the time domain to get vertical bending moment outputs along the aircraft structure. The structural stress is computed by dividing the bending moment by the structural modulus at the region where the maximum bending moment occurs. The design feasibility is evaluated using a structural reliability model that considers wave load unpredictability and structural material strength, with three material types tested: aluminium, HDPE, and CFRP. The simulation findings show that the aluminium and CFRP structural designs are highly reliable in withstanding wave loads, with safety factors of 1.38 and 21.47, respectively. However, this is not the case for HDPE material construction, which has a safety index of -1.57 when wave height surpasses 1.5m, This necessitates an increase in the construction’s transverse modulus to reduce the magnitude of stress induced by wave loads, providing practical guidance for optimizing the structural design of floatplanes operating in maritime environments.

Foundation design for offshore structures on soil requires a knowledge of the design storm wave time history and the corresponding strength of the soil subjected to cyclic stresses that simulate this design wave loading. Suggestions are given for a useful method of expressing the design storm loading, and of interpreting the strength data from cyclic tests on undisturbed samples of soil. INTRODUCTION Conventional geotechnical engineering practice requires that the soil strength be obtained by an appropriate laboratory test that simulates on a soil specimen the significant load and drainage time history which this element will feel in the field. This paper presents some of the procedures and thoughts pertaining to cyclic testing of soils for ocean wave loading problems developed by the writers over the past few years of involvement in foundation stability analyses, for both ocean wave and earthquake cyclic loading. Emphasis is placed on methodology rather than data. However, the form of the data curves that are used herein for illustration are based on actual data believed to be realistic, although in some cases not extensive. NATURE OF WAVE LOADING A 4-minute portion of an actual storm wave record16 is shown in Fig. 1. The impression conveyed by the record is that the wave heights are random, although the period is reasonably constant at about 12 seconds per cycle. Hydraulic model and analytical methods can be used to estimate forces on the structure caused by wave action such as this. Knowing the boundary forces, the wave-induced stresses in the foundation soil below the structure can also be calculated. These pulsating stresses will also be cyclic at approximately the same period as the waves, and for the purposes of the following discussion, can be considered roughly proportional to the wave heights. Thus ideally, to follow a true stress path method of analysis, a laboratory test on a typical soil specimen should follow a cyclic stress-time history similar to the irregular wave form of the design storm. Although technically feasible, this is presently not practical for at least the following two reasons:The most severe time history wave pattern is not known in; advance.Analytical methods are not presently able to use the results of such a sophisticated test efficiently. Instead, the most advanced techniques today (1975) use an intended " equivalent" uniform cyclic loading, sometimes coupled with static loading, to simulate the design irregular cyclic effect. The next obvious difficult question concerns how to define a uniform cyclic load to be equivalent to the random wave loading of an extended ocean storm. One possible approach might be to follow the lead of the oceanographic engineers who have coined the terms " significant wave" height and period. The significant wave is a probabilistic ideal and not. a real wave. It was first developed to be the average height estimated by observers of the largest 20 to 40 percent of the waves in a group.

Under the influence of long-term external and internal dynamic conditions such as waves, tides, and earthquakes, coastal rock masses may slide along unfavorable structural planes, leading to landslide disasters. These events pose threats to offshore engineering facilities, coastal tourism, and economic production safety. To elucidate the impact of wave loading on the stability of coastal rocky slopes, this paper first establishes a generalized geological model and a computational mechanics model of coastal rocky slopes. Using computational fluid dynamics programs, the study analyzes the magnitude and distribution characteristics of wave pressure on coastal slopes with different inclinations under varying wave heights. The results indicate that the maximum wave pressure and resultant wave forces acting on the slope surface decrease with increasing slope angle and decreasing wave height. The relationship between the maximum wave pressure or resultant wave force with the wave height and slope angle conforms to an exponential mathematical model. By decomposing the wave force along the potential sliding surface, the variation in shear stress caused by wave pressure can be calculated. Considering the effects of wave, tide, and seismic loads, the study further analyzes the long-term weakening patterns of shear strength due to the variation in shear stress on the sliding surface induced by wave action. Based on the limit equilibrium theory and the constitutive model of strain-softening in rock and soil material, this paper proposes a method to calculate the current and long-term factor of safety (FOS) of coastal rocky slopes under wave loading.

Experimental and numerical study of a barge-type FOWT platform under wind and wave load

An efficient third-moment saddlepoint approximation for probabilistic uncertainty analysis and reliability evaluation of structures

This study establishes a multi‐hazard probabilistic assessment framework for assessing the integrity of monopile offshore wind turbines (OWT) under the stochastic coupled effect of wind, wave and earthquake loading. The procedure deals with the entire operational range of inflow wind speed (i.e., 3–25 m/s), for which the probability of failure under multi‐hazard excitations is found to be non‐negligible. Numerical analysis is performed by implementing nonlinear finite‐element models of the OWT developed in OpenSees. The dynamic response of the OWT system under wind‐ and wave‐load combinations is individually validated against those obtained from the aero‐hydro‐servo‐elastic simulator OpenFAST. Following the Latin‐hypercube approach, a cloud‐based assessment procedure is then performed with an ensemble of 300 earthquake ground motions, from which the multi‐hazard performance of the OWT regarding the serviceability limit state (SLS) and the ultimate limit state (ULS) can be evaluated. The epistemic uncertainty associated with various loads, structural properties, and soil conditions is also accounted for. Based on this probabilistic assessment framework, the sensitivity of the resulting OWT fragility surfaces to different statistical regression methods and wind—ground motion intensity measure pairs (IM‐pairs) is further scrutinised. Regression methods are comparatively evaluated. The efficiency, practicality, proficiency and sufficiency of various IM‐pairs are examined for the purpose of assessing operating OWT multi‐hazard fragility functions. The optimum IM‐pair is then employed in a trained Gaussian Process Regression (GPR) scheme for cloud data regression to assess the multi‐hazard fragility of the system. The derived multi‐hazard fragility function shows that the contribution of seismic forces in structural demand for a design‐level earthquake is comparable to those caused by operational‐level wind and wave loads.

Dynamic analyses of offshore triceratops in ultra-deep waters under wind, wave, and current

A floater is a buoyant apparatus employed to enable a floatplane to remain afloat and operate on the water surface. During its operational period, the floater experiences stress and deformation as a result of hydrodynamic loads. This study primarily focuses on providing a comprehensive examination of the structural strength of the proposed floater design. The determination of the structural integrity is achieved by the use of the finite element approach which is a popular method for numerically solving, and where in the wave-induced loads experienced by the floater structure are utilized as input parameters. The stress intensity in the floater structure is resulted in relation to the wave load parameters, specifically wave height and wave heading angle. The use of a structural reliability approach involves the consideration of the inherent randomness associated with both the load imposed on a structure and its strength. The Monte Carlo method is utilized to generate randomness of in order to determine the Probability Density Function (PDF) of both the structure’s stresses and its strength. The computational findings elucidate that the floater structure exhibits reliability level of 97 % to 71% in a range of wave height between 0.5 to 3 meters and including reliability level of 100 % to 92% in a similar wave height factor, based on construction materials of aluminium and steel, respectively. This reliability level was indicating toughness of floater structure in each wave condition, smaller reliability level means there is high chance of structural failure.

Offshore structures are subjected to wave, wind, and earthquake loads. The failure of offshore structures can cause sea pollution as well as loss of property and life. Therefore, the safety of such structures is an important issue. The reduction of the dynamic response of an offshore structure subjected to wind-generated random ocean waves is another critical problem with regard to the serviceability, fatigue life, and safety of the structure. In this article, the responses of offshore structures under random ocean waves are controlled using a modified probabilistic neural network (MPNN). As a more advanced method, it uses the global probability density function (PDF) produced by summing the heterogeneous local PDFs automatically determined from the individual standard deviation of each variable. The state vectors in a state-space model of a structure and the resulting control forces made by a linear quadratic regulator algorithm were used to generate the training patterns for the MPNN and a conventional multilayer perceptron (MLP). The results were compared with those produced by back-propagation based on the MLP. The proposed MPNN method shows good results not only in controlling the responses but also in terms of the computation time.

A procedure for estimating simultaneous wave and iceberg loading is developed based on Monte Carlo techniques. Iceberg impact loading is determined using an established energy balance method. Associated wave loads are introduced to the method using a wave height distribution, weighted by the monthly occurrence of icebergs, and prudent simplifying assumptions as to iceberg/structure/ wave interactions. Estimates of the return period loads are made for a large diameter gravity base structure, and for the example selected, the combined loads increase modestly compared to the iceberg impact only loads INTRODUCTION Offshore design practice often assumes the simultaneous occurrence of extreme environmental events. For conventional structures in familiar offshore areas, the assumption has no great impact on design. However, for other applications, joint occurrence of extremes leads to unrealistic and overly conservative load estimates. Such an application is a fixed large diameter gravity base structure (GBS) in an iceberg environment. Methods of computing zero-wave iceberg impact loads are addressed by various authors (ex. [1]). In such methods, the wave load simultaneous with the impact load is ignored (Le. the zero-wave load case). Neglecting any simultaneous wave load is an unconservative assumption, and is usually avoided. However, the simultaneous occurrence of the extreme wave event and the extreme iceberg impact event is a very rare event. To produce reasonable first estimates of, a Monte Carlo model is adapted to estimate rationally the total combined wave and iceberg load. The Monte Carlo model and the description are a first order approximation to the iceberg impact and wave load phenomenon. Full and detailed modeling of an impact event is complex and the present state-of-the-art capabilities and input accuracy do not presently justify increased modeling accuracy. Sufficient and reasonable conservatism is included in the simple method described below to ensure that results represent an upper bound estimate. As an example, a GBS with typical North Atlantic arctic environmental and iceberg values are input into the Monte Carlo model. ICEBERG IMPACT MODEL Iceberg impacts are complex events dependent on many variables. Typically the iceberg impact models are based on a zero-wave assumption (i.e., wave loads are ignored) and use an energy balance method in the computation. An example of one iceberg impact model is given in [1] which is used in this work. The energy based iceberg impact model equates the far field kinetic energy of the iceberg to the energy expended in crushing ice. The modeling equation is (MATHEMATICAL EQUATION AVAILABLE IN FULL PAPER) where Cm is the added mass, m is the iceberg mass, u is the far field iceberg speed, 0 is the strength of the iceberg ice and V is the volume of the crushed ice. Equation (1) is used to predict the volume of crushed ice, and from the volume, the projected contact area (A) can be computed. The force (F) on the structure is calculated as

Probabilistic modelling of quasi-static response of offshore structures subject to nonlinear wave loading: Two approximate approaches