Extreme Environmental Loads Research Articles

Coupled Analysis of a Spar Structure: Monte Carlo and Statistical Linearization Solutions

The response of a combined dynamic system consisting of a Spar, a mooring line system, and top tension risers is presented. The top tension of a riser is provided by a buoyancy-can that is laterally supported by a preloaded compliant guide. The overall system is nonlinear due to the mooring line restoring force, the friction between the buoyancy-cans and the compliant guides, and the friction between the risers and the guides at the Spar keel. The friction between the Spar and the riser system is captured by a Coulomb model, whereas the stiffness of the mooring line system is accounted for by using a nonlinear regression analysis of pertinent load versus displacement data. The combined model is numerically integrated using input time histories of force and moment that are compatible with a random representation (Jonswap spectrum) of a typical extreme environmental loading in the Gulf of Mexico. The input time histories of the force and the moment for the combined model are obtained at the center of gravity of the Spar by using a standard motion analysis program (MLTSIM). The numerical results of the time domain analysis of the combined model, in conjunction with ergodicity, are used for an associated Monte Carlo study. The Monte Carlo study provides useful information regarding the probability densities and the power spectra of various response components of the combined system. These results serve as a benchmark for additional analytical studies that call attention to the potential usefulness of the technique of statistical linearization for efficient dynamic analyses of preliminary design decisions regarding the combined Spar–Risers–Mooring lines system.

Buckling and ultimate strength criteria of stiffened shells under combined loading for reliability analysis

The work presented in this paper forms part of a broader task in establishing a guide to serve as technical documentation for buckling and ultimate strength assessment of various types of marine structural components using the best state-of-the-art knowledge for extreme environmental loading. This paper concentrates on buckling and ultimate strength assessment of ring stiffened shells and ring and stringer stiffened shells involving various modes of buckling and under various loading like axial compression, radial pressure and combined loading. Comparisons are made with screened test data, which have realistic imperfections and various radius to thickness ratio values in the range generally used in offshore structures. The statistical data of model uncertainty factors in terms of bias and coefficient of variation (COV) are calculated and may be used in a further reliability study. Comparisons are also made with the codified rules, API BUL 2U and DNV buckling strength of shells.

Developments in structural system reliability assessments of fixed steel offshore platforms

In recent years there have been significant developments in the area of system reliability assessments which are becoming increasingly important given the framework of the ‘goal setting’ regime and other changes that are taking place within the offshore industry. The objective of this paper is to review and critically examine recent developments in system reliability methods for fixed steel offshore platforms specifically and identify areas that need to be examined further to maximise the benefits from the use of these techniques. The paper examines the range of proposed methods for system reliability assessment of fixed steel offshore structures under extreme environmental loading. The associated characteristics of the various methods are examined and the paper concentrates in particular on the treatment of the resistance. The various system effects including both deterministic and probabilistic effects and their relative contribution to the overall system reliability are addressed. Key issues such as the modelling uncertainties and sensitivities, validation and benchmarking of the proposed methods are also examined. The study also highlights a number of technical and philosophical issues which need to be addressed to increase the benefits from system reliability applications in design and re-assessment of fixed platforms.

Open Ocean Aquaculture Engineering: Numerical Modeling

Finite element analysis (FEA) is used to predict the dynamic performance of an offshore fish cage and submerged mooring grid system. The system has been deployed at an exposed demonstration site in 55 meters of water south of the Isles of Shoals, New Hampshire. Computer simulations were performed to investigate the dynamics of the cage motion and to calculate mooring line tensions. The results were used to establish the baseline design specifications and to evaluate the overall performance of the system.Both surface and submerged positions of the net pen are considered. It is shown that the extreme environmental loading conditions at the demonstration site produce 60% less mooring tension in the case of a submerged cage. According to the analysis, the case when one of four mooring legs becomes disabled will not produce the failure of the mooring system.The problem of adequate modeling of net is addressed. A simple technique is proposed to approximate the effect of netting on the overall dynamic response offish cage/mooring systems.

Multivariate extrapolation in the offshore environment

We consider the estimation of the extremes of the metocean climate, in particular those of the univariate and joint distributions of wave height, wave period and wind speed. This is of importance in the design of oil rigs and other marine structures which must be able to withstand extreme environmental loadings. Such loadings are often functions of two or more metocean variables and the problem is to estimate the extremes of their joint distribution, typically beyond the range of the observed data. The statistical methodology involves both univariate and multivariate extreme value theory. Multivariate theory which avoids (often very inappropriate) prior assumptions about the nature of the statistical association between the variables is a fairly recent development. We review and adapt this theory, presenting simpler descriptions and proofs of the key results. We study in detail an application to data collected over a nine-year period at the Alwyn North platform in the northern North Sea. We consider the many problems arising in the analysis of such data, including those of seasonality and short-term dependence, and we show that multivariate extreme value theory may indeed be used to estimate probabilities and return periods associated with extreme events. We consider also the confidence intervals associated with such estimates and the implications for future data collection and analysis. Finally we review further both the statistical and engineering issues raised by our analysis.

Nonlinear Control Strategies for Limiting Dynamic Response Extremes

Under extreme environmental loadings such as winds, waves, and earthquakes, civil engineering structures are known to undergo large vibration responses, often resulting in severe damage. Recent developments in active structural control have focused on limiting the amplitude of oscillation of a structure to be within safe, allowable bounds. In this paper, a nonlinear control approach that is capable of limiting extreme dynamic responses of a structure at a reduced expense in control effort is studied. To derive the nonlinear control law, a performance index that is quartic in the states and quadratic in the control is defined. Utilizing a tensor expansion solution procedure for the resulting nonlinear optimal control problem, general polynomial representations of the nonlinear control law are obtained in illustrative problems. Numerical examples of a seismically excited, controlled structure are presented to demonstrate the ability of selected nonlinear control strategies to expend a smaller control effort than an equivalent linear control strategy while limiting the extreme displacement responses.

Failure probability of a jack-up under environmental loading in the central North Sea

The annual probability of failure has been calculated for a jack-up subjected to extreme storm loading in the central North Sea. Statistics of extreme loads were generated using models that account for the combined behaviour of winds, waves and current in severe storms. The fluid loading is calculated using well validated theories for the kinematics of extreme random waves and currents and hydrodynamic models of jack-up legs. Non-linear push-over analysis is used to evaluate the ultimate strength and the overturning resistance of the jack-up unit. In the non-linear analysis, windward spudcan sliding is included by means of a force constraint method. The likelihood of structural failure or overturning is the probability that the environmental load will exceed the overturning or structural resistance of the rig. Physical uncertainty in the extreme environmental load dominates the problem and is fully analysed. The effects of physical uncertainty in resistance of the structure are discussed. The results indicate a failure rate of order 10 -5 per year.

Role of Control-Structure Interaction in Protective System Design

Most of the current research in the field of structural control for mitigation of responses due to extreme environmental loads does not directly account for the effects of control-structure interaction and actuator/sensor dynamics in analysis and design. The importance of including control-structure interaction when modeling a control system is discussed herein, and a general framework within which one can study its effect on protective systems is presented. A specific model for hydraulic actuators typical of those used in many protective systems is developed, and a natural velocity feedback link is shown to exist which tightly couples the dynamics of the hydraulic actuator to the dynamics of the structure to which it is attached. Experimental verification of this model is given. Numerical examples are provided that use seismically excited structures configured with active bracing, active tendon, and active mass driver systems. These examples show that accounting for control-structure interaction and actu...

Reliability analysis of a pile design

Abstract This paper presents a stochastic pile design for a wellhead platform designed for Danish waters. The relevant failure modes for both ultimate and serviceability limit states are defined. Failure modes for the pile as well as failure in the soil are thereby considered. Reliability criteria are suggested based on requirements formulated by the Nordic Committee for Building Structures. An uncertainty modeling for the environmental conditions, the response and the soil stiffness and strength is suggested. The choice of distribution types by and large follows that suggested by the Nordic Committee for Building Structures. The effects of spatial variation of soil properties are assessed both in terms of varying positions of layer boundaries and in terms of spatially varying soil properties. The model uncertainty in the soil strength for axial compressive and tensile loading is quantified. The most important uncertainties are due to uncertainties in the extreme environmental parameters and load model parameters, and for the soil failure modes also due to the model uncertainty. The uncertainties in soil stiffness, strength and spatial variation play a very small role in all failure modes.

Substantiated Risk Assessment of Jacket Structure

We demonstrate a rational approach to structural reliability based on state‐of‐the‐art models. The risk of failure was calculated for a jacket structure in the Gulf of Mexico subjected to environmental loading. This was done both for one particular extreme hurricane that the structure survived and also for long‐term loading. Statistics of extreme loads were generated from a hindcast study. The fluid loading was calculated using well‐validated theories for the kinematics of extreme random waves and currents. Nonlinear pushover analysis was used to evaluate the ultimate strength of the structure. The likelihood of structural failure was predicted by calculating the probability that the environmental load would exceed the resistance of the structure. Physical uncertainty in the extreme environmental load and the resistance of the structure were included. These results and those from a previous analysis of a damaged structure match well with observations, corroborating the approach and its wider application.

On the Strength of Composite Steel-Concrete Structure of Sandwich System (6th Report: Ultimate Toughness under Shear and Bending Model)

Offshore structure should have a high degree of structural safety even under extreme environmental load conditions. The authors have suggested an importance of use of composite steel concrete structure of sandwich system for the strength members of huge offshore structures.In the previous papers, the authors carried out both experimental and theoretical investigations on the toughness of the sandwich composite structures. Experiments were carried for the two dimentional models of composite structures under pure bending and combined shear and bending as well. A nonlinear analysis was made to predict the toughness of sandwich beam under pure bending.In the present paper, the authors have carried out model tests under shear and have developed a nonlinear analysis method to predict the toughness of sandwich beam under shear and combined shear and bending. In the nonlinear analysis the material nonlinearities of both concrete and steel plate have been taken into consideration. The results of nonlinear ultimate deformation analysis have been found to be very close to the test results.

Evaluation of Uncertainties in Loadings on Offshore Structures due to Extreme Environmental Conditions

Abstract This paper summarizes results from a Canadian Standards Association (CSA) sponsored study of the uncertainties associated with extreme (1000 to 10,000-yr return periods) environmental loadings acting on offshore structures (Bea, 1991). The evaluations of the loadings addressed loading effects that resulted from dynamic and nonlinear interactions of the structures. Loading uncertainties were organized and characterized in two categories: 1) inherent randomness (aleatory uncertainty), and 2) analytical variability (epistemic uncertainty). The study addressed the global ultimate limit state performance of three structures designed according to the provisions of the draft CSA guidelines (1989a, 1989b) for offshore structures: 1) a concrete Gravity Base Structure (GBS) located off the East coast of Canada (Hibernia), 2) a steel pile template located on the Scotian Shelf off Sable Island, and 3) a caisson retained island located in the Mackenzie Delta area of the Beaufort Sea (Amuligak). The results of this study indicate that, based on presently available information and data, it is often not possible to develop unambiguous characterizations of uncertainties. The different technical communities that background environmental conditions and forces (storms, earthquakes, ice) recognize and integrate these uncertainties into loading characterizations in different ways. In many cases, major sources of uncertainty are not included in probabilistic characterizations. Because of the needs for design code information sensitivity and consistency in demonstrating compliance with target reliability goals, there is a need for well-organized and definitive evaluations of uncertainties in extreme environmental loadings and load effects (Bitner-Gregersen et al., 1993).

Design of Fixed Offshore Platforms to Dynamic Ship Impact Loads

A ship impact is a dynamic phenomenon and the dynamic global load effects can be significant, especially for small platforms where dynamic loads from the ship impact can be larger than the extreme environmental loads and the ship impact can govern the design of the platform. This paper describes a detailed procedure for dynamic analysis of fixed offshore platforms exposed to ship impacts. The procedure includes: • a consistent description of the motion of the vessel and dynamic interaction with the platform during the impact; • a realistic description of the global dynamic behavior of the platform during the impact; • detailed calculation of the transient hydrodynamic pressure forces acting on the vessel during the impact; and • a realistic description of the local deformation zone at the point of impact. The equations of motion for the vessel and the platform are solved simultaneously in the time domain, and the overall dynamic loads acting on the platform during the impact are determined by means of the modal superposition principle. The procedure has been applied for the design and subsequent risk analysis of three small tripod tower-type platforms to impacts from drifting supply vessels. The effect of the number of mode shapes used for representation of the dynamic behavior of the platforms, and the influence of the transient hydrodynamic pressure forces have been investigated. Critical velocity tables for different impact situations have been developed. For nearly all the situations investigated, the critical collapse criterion was overturning of the platform due to pull-out of piles in tension.

Systems reliability of offshore structures including fatigue and extreme wave loading

Traditionally, the focus of systems reliability analysis has been on estimating the reliability under either fatigue loading or extreme environmental loading. However, for many offshore structures, a combination of these two sources of risk may be more critical, e.g. initial failures may occur in fatigue and subsequent collapse under an extreme wave. In this paper, a probabilistic formulation for such a sequence of combined failures is presented. A formulation for a sequence of failures under an extreme wave, with realistic failure criteria for offshore structures, is also presented. With these formulations, it is possible to account for both fatigue and extreme wave failures. An application of such a unified approach to a steel jacket platform is presented. It is found that, for an individual member, the most probable cause of failure is fatigue, but for overall structural failure, overload and a combination of fatigue and overload are more important.

A reliability assessment of tubular joint specifications

The limit states design of structural components involves the use of resistance factors which account for the variabilities and uncertainties which exist in both load effect and element resistance. In this paper, the rational development of such resistance factors is examined for axially loaded K, T, and Y joints between steel circular hollow section members subject to predominantly static loading. The development of these factors is primarily oriented to the design of such joints in offshore structures under extreme environmental loading conditions, but onshore applications to buildings are also considered. A level II method of reliability analysis has been used for the derivation of the resistance factors. The joint strength criteria from seven prominent code and noncode design documents have been considered, and recommendations for resistance factors to be used in the design of offshore and onshore tubular joints are made. Key words: steel, offshore structures, tubes, joints, reliability analysis, structural safety.

2 nd Report : Nonlinear Analysis using the Finite Element Method

Offshor structures should have a high degree of structural safety even under extreme environmental loadings. The authors have developed a composite steel-concrete structure of sandwich system for the strength members of huge offshore structures, where concrete is placed between steel plates.In the previous paper, the authors carried out both experimental and theoretical investigations into the strength of the composite structure, It was clarified that the composite structure has various excellent properties : The ultimate load-bearing capacity of the composite structure is very high and it can absorb a great deal of energy until failure under any type of loading conditions.The composite structure exhibits nonlinear behavior before its ultimate strength, caused by the following phenomena; 1) cracking of concrete under tension, 2) plastification of concrete under compression, 3) plastification of steel plate and 4) gap between steel plate and concrete.In the present paper, the authors developed a method of the nonlinear analysis using the finite element method. In the analysis, the material nonlinearities of both concrete and steel are fully taken into account as well as the nonlinearity caused by the gap between steel and concrete. The nonlinear analysis accurately represented the behavior of the composite structure under tests.