Characteristic Levels of Strongly Nonlinear Extreme Wave Load Effects

2016 ◽  
Author(s):  
Thomas B. Johannessen ◽  
Øistein Hagen
Keyword(s):  
Wave Breaking ◽  
Nonlinear Problems ◽  
Offshore Structures ◽  
Short Term ◽  
Nonlinear Load ◽  
Load Effect ◽  
Strongly Nonlinear ◽  
Load Effects ◽  
Term Analysis

Offshore structures are typically required to withstand extreme and abnormal load effects with annual probabilities of occurrence of 10−2 and 10−4 respectively. For linear or weakly nonlinear problems, the load effects with the prescribed annual probabilities of occurrence are typically estimated as a relatively rare occurrence in the short term distribution of 100 year and 10 000 year seastates. For strongly nonlinear load effects, it is not given that an extreme seastate can be used reliably to estimate the characteristic load effect. The governing load may occur as an extremely rare event in a much lower seastate. In attempting to model the load effect in an extreme seastate, the short term probability level is not known nor is it known whether the physics of the wave loading is captured correctly in an extreme seastate. Examples of such strongly nonlinear load effects are slamming loads on large volume offshore structures or wave in deck loads on jacket structures subject to seabed subsidence. Similarly, for structures which are unmanned in extreme weather, the governing load effects for the manned structure will occur as extremely rare events in a relatively frequent seastate. The present paper is concerned with the long term distribution of strongly nonlinear load effects. Using a simple point estimate of the wave elevation correct to second order and a crest kinematics model which takes into account the possibility of wave breaking, the long term distribution of drag load on a column above the still water level is studied and compared with a similar loading model based on second order kinematics which does not include the effect of wave breaking. The findings illustrate the challenges listed above. Model tests are useful in quantifying strongly nonlinear load effects which cannot be calculated accurately. But only a relatively small number of seastates can be run in a model test campaign and it is not feasible to estimate short term responses far beyond the three hour 90% fractile level. Similarly, Computational Fluid Dynamics (CFD) is increasingly useful in investigating complex wave induced load effects. But only a relatively small number of wave events can be run using CFD, a long term analysis of load effects cannot in general be carried out. It appears that there is a class of nonlinear problems which require a long term analysis of the load effect in order for the annual probability of occurrence to be estimated accurately. For problems which cannot be estimated by simple analytical means, the governing wave events can be identified by long term analysis of a simple model which capture the essential physics of the problem and then analysed in detail by use of CFD or model tests.

Long Term Analysis of Steep and Breaking Wave Properties by Event Matching

2018 ◽  
Author(s):  
Thomas B. Johannessen ◽  
Øystein Lande
Keyword(s):  
Wave Breaking ◽  
Offshore Structures ◽  
Return Periods ◽  
Short Term ◽  
Nonlinear Load ◽  
Load Effect ◽  
Strongly Nonlinear ◽  
Load Effects ◽  
Term Analysis

Offshore structures are typically required to withstand extreme and abnormal load effects with annual probabilities of occurrence of 10−2 and 10−4 respectively. For linear or weakly nonlinear problems, the load effects with the prescribed annual probabilities of occurrence are typically estimated as a relatively rare occurrence in the short term distribution of 100 year and 10 000 year seastates. For strongly nonlinear load effects, it is not given that an extreme seastate can be used reliably to estimate the characteristic load effect. The governing load may occur as an extremely rare event in a much lower seastate. In attempting to model the load effect in an extreme seastate, the relevant short term probability level is not known nor is it known whether the physics of the wave loading is captured correctly in an extreme seastate. Examples of such strongly nonlinear load effects are slamming loads on large volume offshore structures or wave in deck loads on jacket structures subject to seabed subsidence. The present paper is concerned with the long term distribution of strongly nonlinear load effects and a methodology is proposed which incorporates CFD analysis in a long term Monte Carlo analysis of crest elevations and wave kinematics. Based on a long term time domain simulation of a linear surface elevation, a selection of events is run in CFD in order to obtain a database of linear and corresponding fully nonlinear wave fields with the possibility of wave breaking included. In the subsequent long term analysis, a large linear event is then replaced by the closest matching event in the database. A technique is developed to Froude scale the database results and shift the origin in time and plane so that the database of typically only 100 events give a close match to all the events in the simulation. The method is applied to the simple case of drag loading on a cylinder which is truncated above the still water level such that only the largest waves impact with the structure. It is observed that whereas the Event Matching method agree well with a second order model for return periods lower than 100 years, the loading on the cylinder is significantly larger for longer return periods. The deviation is caused by the increasing dominance of wave braking in the largest crest and illustrates the importance of incorporating wave breaking in the analysis of wave in deck loading problems.

Environmental Contour Lines: A Method for Estimating Long Term Extremes by a Short Term Analysis

2008 ◽  
Author(s):  
S. Haver ◽  
S. R. Winterstein
Keyword(s):  
Major Part ◽  
Offshore Structures ◽  
Environmental Load ◽  
Short Term ◽  
Sea State ◽  
Contour Lines ◽  
Linear Problems ◽  
Term Analysis ◽  
Do So

Design of offshore structures involves the calculation of reliable estimates for loads and responses corresponding to annual exceedance probabilities of 10-2 and 10-4. In order to do so, all sources of inherent randomness must be accounted for, i.e. the short term variability of say the 3-hour extreme value in a given sea state should be combined with the long term variability of the sea state characteristics. This calls for some sort of a long term analysis. For linear or nearly linear problems this can easily be done, while such an analysis becomes more complicated and time consuming for strongly non-linear response problems. The difficulties are greater if a major part of the environmental load is of an on-off nature. This paper illustrates an approximate approach, the environmental contour line method, for obtaining proper estimates of long term extremes utilizing a short term analysis. Examples are also included.

LOCA analysis of BWR-4/Mark-I nuclear power plant with TRACE

Kerntechnik ◽  
2021 ◽  
Vol 86 (2) ◽  
pp. 128-142
Author(s):  
J.-J. Huang ◽  
S.-W. Chen ◽  
J.-R. Wang ◽  
C. Shih ◽  
H.-T. Lin
Keyword(s):  
Nuclear Power ◽  
Coupled Model ◽  
Short Term ◽  
Containment System ◽  
Loss Of Coolant Accident ◽  
Main Steam Line ◽  
Main Steam ◽  
Temperature Responses ◽  
Term Analysis

Abstract This study established an RCS-Containment coupled model that integrates the reactor coolant system (RCS) and the containment system by using the TRACE code. The coupled model was used in both short-term and long-term loss of coolant accident (LOCA) analyses. Besides, the RELAP5/CONTAN model that only contains the containment system was also developed for comparison. For short-term analysis, three kinds of LOCA scenarios were investigated: the recirculation line break (RCLB), the main steam line break (MSLB), and the feedwater line break (FWLB). For long-term analysis, the dry-well and suppression pool temperature responses of the RCLB were studied. The analysis results of RELAP5/CONTAN and TRACE models are benchmarked with those of FSAR and RELAP5/GOTHIC models, and it appears that the results of the above four models are consistent in general trends.

Strength Performance of Steel Catenary Riser Using Short Term and Long Term Analysis Methodologies

2016 ◽  
Author(s):  
Feng Wang ◽  
Roger Burke ◽  
Anil Sablok ◽  
Kristoffer H. Aronsen ◽  
Oddgeir Dalane
Keyword(s):  
Bending Moment ◽  
Current Profile ◽  
Short Term ◽  
Sea State ◽  
Strength Performance ◽  
Steel Catenary Riser ◽  
Analysis Methodology ◽  
Riser Design ◽  
Term Analysis

Strength performance of a steel catenary riser tied back to a Spar is presented based on long term and short term analysis methodologies. The focus of the study is on response in the riser touch down zone, which is found to be the critical region based on short term analysis results. Short term riser response in design storms is computed based on multiple realizations of computed vessel motions with various return periods. Long term riser response is based on vessel motions for a set of 45,000 sea states, each lasting three hours. The metocean criteria for each sea state is computed based on fifty six years of hindcast wind and wave data. A randomly selected current profile is used in the long term riser analysis for each sea state. Weibull fitting is used to compute the extreme riser response from the response of the 45,000 sea states. Long term analysis results in the touch down zone, including maximum bending moment, minimum effective tension, and maximum utilization using DNV-OS-F201, are compared against those from the short term analysis. The comparison indicates that the short term analysis methodology normally followed in riser design is conservative compared to the more accurate, but computationally more expensive, long term analysis methods. The study also investigates the important role that current plays in the strength performance of the riser in the touch down zone.

A LRFD Code Format for Accounting Long-Term Variation of Multiple Load Effects

2002 ◽  
Author(s):  
Paulo Mauricio Videiro ◽  
Luis Volnei Sudati Sagrilo ◽  
Edison Castro Prates de Lima
Keyword(s):  
Extreme Value ◽  
Structural Components ◽  
Short Term ◽  
Resistance Factors ◽  
Term Variation ◽  
Load And Resistance Factors ◽  
Load Effects ◽  
Code Format ◽  
Multiple Load

This paper proposes a Load and Resistance Factors Design (LRFD) code format for structural components of offshore structures under multiple load effects. This code format accounts for the long-term variation of seastate and the actual correlation between dynamic load effects due to environmental actions. Ultimate limit states are formulated in terms of an Interaction Ratio (IR) random variable, such that the long-term extreme value of IR greater than unity means component failure. The long-term distribution of IR is obtained by combining the distribution of each short-term seastate. The short-term response of the generally nonlinear IR is determined by time domain simulation, taking into account partial load and resistance factors. The IR short-term distribution may be fitted, for instance, by using Rayleigh or Weibull distribution. The main advantages of the proposed code format are: • This code format accounts implicitly and correctly for the actual correlation among all dynamic environmental load processes. • Structural designers have used interaction ratios for a long time. Hence, it is straightforward to evolve from a deterministic stage of looking for IR < 1, as in old Working Stress Design codes, to a code format where the aim is to design structural components with long term IR extreme value < 1. The feasibility of the proposed code format is demonstrated by calibrating partial factors for beam-column cylindrical members based on components of a Floating Production System Semi-submersible hull.

Estimating Loads From Breaking Waves Using Operational Modal Analysis

2020 ◽  
Author(s):  
Michael Vigsø ◽  
Christos Georgakis
Keyword(s):  
Modal Analysis ◽  
Wave Breaking ◽  
Dynamic Properties ◽  
Structural Response ◽  
Wave Theory ◽  
Breaking Waves ◽  
Offshore Structures ◽  
Operational Modal Analysis ◽  
Wave Flume ◽  
Load Effects

Abstract Load effects from breaking waves on offshore structures may be a driving point for the design. It is hence important to assess the likelihood of occurrence along the magnitude of the loads in the event of an impact. Traditionally, loads are predicted using wave theory combined with a load model such as the Morison. This paper features an alternative approach in determining the loads from wave breaking. It is demonstrated how the structural response can be used for (indirectly) estimating the magnitude of the loads caused by wave breaking. The theory is applied to an experimental setup in a wave flume, where a flexible model is subjected to loads from breaking waves. The dynamic properties are mapped using operational modal analysis and it is consequently shown that the loads can be identified using the vibration measurements.

Long-term and short-term analysis of the natural rubber market

1989 ◽  
Vol 125 (4) ◽  
pp. 718-747 ◽  
Author(s):  
Kees Burger ◽  
Hidde P. Smit
Keyword(s):  
Natural Rubber ◽  
Short Term ◽  
Rubber Market ◽  
Term Analysis

Methods of Computing the Probability of Failure Under Extreme Values of Bending Moment

1972 ◽  
Vol 16 (02) ◽  
pp. 113-123
Author(s):  
Alaa Mansour
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Extreme Values ◽  
Bending Moment ◽  
Random Variable ◽  
Probability Of Failure ◽  
Short Term ◽  
Term Analysis

Methods for predicting the probability of failure under extreme values of bending moment (primary loading only) are developed. In order to obtain an accurate estimate of the extreme values of the bending moment, order statistics are used. The wave bending moment amplitude treated as a random variable is considered to follow, in general, Weibull distribution so that the results could be used for short-term as well as long-term analysis. The probability density function of the extreme values of the wave bending moment is obtained and an estimate is made of the most probable value (that is, the mode) and other relevant statistics. The probability of exceeding a given value of wave bending moment in "n" records and during the operational lifetime of the ship is derived. Using this information, the probability of failure is obtained on the basis of an assumed normal probability density function of the resistive strength and deterministic still-water bending moment. Charts showing the relation of the parameters in a nondimensional form are presented. Examples of the use of the charts for long-term and short-term analysis for predicting extreme values of wave bending moment and the corresponding probability of failure are given.

Extreme Storm Wave Histories for Cyclic Check of Offshore Structures

2010 ◽  
Author(s):  
O̸istein Hagen ◽  
Gunnar Solland ◽  
Jan Mathisen
Keyword(s):  
Structural Reliability ◽  
Failure Modes ◽  
Structural Integrity ◽  
Offshore Structures ◽  
Load History ◽  
Load Effect ◽  
Design Point ◽  
Design Storm ◽  
Existing Structures ◽  
Load Effects

Offshore platform resistance to cyclic storm actions is addressed. In order to achieve the best economy of the structure especially when assessing existing structures, the ultimate capacity of the structure is utilized. This means that parts of the structure may be loaded into the non-linear range and consequently the load-carrying resistance of the structure against future load cycles may be reduced. In such cases it is required to carry out a check of the cyclic capacity of the structure. Such checks are required in the ISO 19902 code for Fixed Steel Offshore Structures. The paper presents a proposal for how a load history for cyclic checks can be established. The method is in line with what is included in the NORSOK N-006 standard on “Assessment of structural integrity for existing load-bearing structures”. The load-history for the waves in the design storm may be expressed as ratio of the dimensioning wave. The ratio will be different for check of failure modes where the entire storm will be relevant such as crack growth, compared to failure modes like buckling where only the remaining waves after the dimensioning wave need to be accounted for. Using simple order statistics and simulation, the statistics for the ith (Hi), i = 1, 2, 3, 4 etc. highest wave in the storm is studied in some detail, assuming that the maximum wave (H1) is equal to an extreme wave obtained by a code requirement. Environmental contours for the pair (H1,H2) are established by Inverse FORM for design conditions. Further, the long term statistics for load effects that are expressed as a function of H1, .., H4, i.e. L = f(H1, .., H4), are determined. The R-year value LR for the load effect L is determined by structural reliability techniques, and the most probable combination (design point) (H1*, .., H4*) for L = LR is determined. The design point values Hi*, as well as the design point value for the significant wave height, are determined for different load effects, and their characteristics for different types of load effects are discussed. The paper gives advice also on how to establish the magnitude for the remaining waves in the storm.

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