0
Journal of Offshore Mechanics and Arctic Engineering | Volume 138 | Issue 5 | research-article
Research Papers: Ocean Engineering

Estimating Long-Term Extreme Slamming From Breaking Waves

[+] Author and Article Information
Gunnar Lian

Statoil ASA,
Forusbeen 50,
Stavanger 4035, Norway;Department of Mechanical and Structural
Engineering and Materials Science,
University of Stavanger,
Kjell Arholms gate 41,
Stavanger 4036, Norway
e-mail: glia@statoil.com

Sverre K. Haver

Department of Mechanical and Structural
Engineering and Materials Science,
University of Stavanger,
Kjell Arholms gate 41,
Stavanger 4036, Norway
e-mail: sverre.k.haver@uis.no

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received August 24, 2015; final manuscript received June 4, 2016; published online July 22, 2016. Editor: Solomon Yim.

J. Offshore Mech. Arct. Eng 138(5), 051101 (Jul 22, 2016) (11 pages) Paper No: OMAE-15-1092; doi: 10.1115/1.4033935 History: Received August 24, 2015; Revised June 04, 2016
Article
References
Figures
Tables
Citing Articles

Characteristic loads for design of offshore structures are defined in terms of their annual exceedance probability, q. In the Norwegian Petroleum Regulations, q = 10−2 is required for the ultimate limit state (ULS), while q = 10−4 is required for the accidental limit state (ALS). In principle, a full long-term analysis (LTA) is required in order to obtain consistent estimates. This is straightforward for linear response problems, while it is a challenge for nonlinear problems, in particular if they additionally are of an on–off nature. The latter will typically be the case for loads due to breaking wave impacts. In this paper, the challenges related to estimation of characteristic slamming loads are discussed. Measured slamming loads from a model test are presented, and the observed large variability is discussed. The stochastic nature of slamming loads is studied using a simplified linear relation between the sea states and the Gumbel distribution parameter surfaces. The characteristic slamming loads with q-annual probability of exceedance are estimated from an LTA using the short-term distribution of the slamming loads and the long-term distribution of the sea states. The effect of integrating over a smaller area of the scatter diagram of the sea states is studied. The uncertainties in response from slamming loads are compared to a more common response process, and the relation between variability and the number of realizations in each sea state is looked into.
Copyright © 2016 by ASME
Topics: Seas , Waves , Stress , Uncertainty
Your Session has timed out. Please sign back in to continue.

References

1
PSA, 2015, “ The Facilities Regulations,” P. S. A. Norway , ed., Petroleum Safety Authority Norway.
2
Norsok, 2007, “ N-003 Actions and Actions Effects,” Standards Norway.
3
Baarholm, G. S. , and Haver, K. S. , 2009, “ Application of Environmental Contour Lines—A Summary of a Number of Case Studies,” International Conference on Floating Structures for Deepwater Operations University of Strathclyde Glasgow, Scotland, UK.
4
Suyuthi, A. , and Haver, S. K. , 2009, “ Extreme Loads Due to Wave Breaking Against Platform Column,” International Offshore and Polar Engineering Conference, Osaka, Japan, July 21–26, pp. 472–479.
5
Roos, J. , Swan, C. , and Haver, S. , 2010, “ Wave Impacts on the Column of a Gravity Based Structure,” ASME Paper No. OMAE2010-20648.
6
Clauss, G. N. F. , Haver, S. K. , and Strach, M. , 2010, “ Breaking Wave Impacts on Platform Columns-Stochastic Analysis and DNV Recommended Practice,” ASME Paper No. OMAE2010-20293.
7
Oberlies, R. , Khalifa, J. , Huang, J. , Hetland, S. , Younan, A. , Overstake, M. , and Slocum, S. , 2014, “ Determination of Wave Impact Loads for the Hebron Gravity Based Structure (GBS),” ASME Paper No. OMAE2014-23503.
8
Haver, S. , 2007, “ A Discussion of Long Term Response Versus Mean Maximum Response of the Selected Design Sea State,” ASME Paper No. OMAE2007-29552.
9
Baarholm, G. S. , Haver, S. , and Økland, O. D. , 2010, “ Combining Contours of Significant Wave Height and Peak Period With Platform Response Distributions for Predicting Design Response,” Mar. Struct., 23(2), pp. 147–163. [CrossRef]
10
Winterstein, S. R. , Ude, T. C. , Cornell, C. A. , Bjerager, P. , and Haver, S. , 1993, “ Environmental Parameters for Extreme Response: Inverse FORM With Omission Factors,” International Conference on Structural Safety and Reliability (ICOSSAR), Innsbruck, Austria, Aug. 9–13.
11
Haver, S. , and Kleiven, G. , 2004, “ Environmental Contour Lines for Design Purposes—Why and When?,” ASME Paper No. OMAE2004-51157.
12
Bury, K. V. , 1975, “ Statistical Models in Applied Science,” A Wiley Publication in Applied Statistics, Wiley, New York, pp. 371–375.
13
DNV, 2014, “ C205—Environmental Conditions and Environmental Loads,” Det Norske Veritas AS, Hovik, Norway, Recommended Practice DNV-RP-C205.
14
Forristall, G. Z. , 2000, “ Wave Crest Distributions: Observations and Second-Order Theory,” J. Phys. Oceanogr., 30(8), pp. 1931–1943. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Contour lines of sea states with constant annual probability of exceedance

+Contour lines of sea states with constant annual probability of exceedance
View Large  |  Save Figure  |  Download Slide (.ppt)
Contour lines of sea states with constant annual probability of exceedance
Grahic Jump Location
Fig. 2

Contour lines with tested sea states and rate of slam contour for the panel

+Contour lines with tested sea states and rate of slam contour for the panel
View Large  |  Save Figure  |  Download Slide (.ppt)
Contour lines with tested sea states and rate of slam contour for the panel
Grahic Jump Location
Fig. 3

Estimate of the Gumbel location (α) and scale (β) parameters from model test results shown versus Hs

+Estimate of the Gumbel location (α) and scale (β) parameters from model test results shown versus Hs
View Large  |  Save Figure  |  Download Slide (.ppt)
Estimate of the Gumbel location (α) and scale (β) parameters from model test results shown versus Hs
Grahic Jump Location
Fig. 4

Estimate of the Gumbel location (α) and scale (β) parameters from model test results shown versus Tp

+Estimate of the Gumbel location (α) and scale (β) parameters from model test results shown versus Tp
View Large  |  Save Figure  |  Download Slide (.ppt)
Estimate of the Gumbel location (α) and scale (β) parameters from model test results shown versus Tp
Grahic Jump Location
Fig. 5

Gumbel location (α) and scale (β) parameters versus steepness based on significant wave height

+Gumbel location (α) and scale (β) parameters versus steepness based on significant wave height
View Large  |  Save Figure  |  Download Slide (.ppt)
Gumbel location (α) and scale (β) parameters versus steepness based on significant wave height
Grahic Jump Location
Fig. 6

COV versus steepness and Tp

+COV versus steepness and Tp
View Large  |  Save Figure  |  Download Slide (.ppt)
COV versus steepness and Tp
Grahic Jump Location
Fig. 7

Contour of Gumbel location parameter

+Contour of Gumbel location parameter
View Large  |  Save Figure  |  Download Slide (.ppt)
Contour of Gumbel location parameter
Grahic Jump Location
Fig. 8

Contour of Gumbel scale parameter

+Contour of Gumbel scale parameter
View Large  |  Save Figure  |  Download Slide (.ppt)
Contour of Gumbel scale parameter
Grahic Jump Location
Fig. 10

Gumbel location (α) and scale (β) parameters versus Hs. Dashed line is true, and solid line is fitted to observations from the randomly drawn parameters, varying seeds per sea state.

+Gumbel location (α) and scale (β) parameters versus Hs. Dashed line is true, and solid line is fitted to observations from the randomly drawn parameters, varying seeds per sea state.
View Large  |  Save Figure  |  Download Slide (.ppt)
Gumbel location (α) and scale (β) parameters versus Hs. Dashed line is true, and solid line is fitted to observations from the randomly drawn parameters, varying seeds per sea state.
Grahic Jump Location
Fig. 9

Bootstrap from the true Gumbel distribution at the peak of 10−4 contour

+Bootstrap from the true Gumbel distribution at the peak of 10−4 contour
View Large  |  Save Figure  |  Download Slide (.ppt)
Bootstrap from the true Gumbel distribution at the peak of 10−4 contour
Grahic Jump Location
Fig. 11

Gumbel scale (β) parameter versus Hs. Dashed line is true, and solid line is fitted to observations from the randomly drawn parameters, varying seeds per sea state, second and third trials.

+Gumbel scale (β) parameter versus Hs. Dashed line is true, and solid line is fitted to observations from the randomly drawn parameters, varying seeds per sea state, second and third trials.
View Large  |  Save Figure  |  Download Slide (.ppt)
Gumbel scale (β) parameter versus Hs. Dashed line is true, and solid line is fitted to observations from the randomly drawn parameters, varying seeds per sea state, second and third trials.
Grahic Jump Location
Fig. 12

Gumbel scale (β) parameter versus Hs. Dashed line is true, and solid line is fitted to observations from the randomly drawn parameters, varying seeds per sea state, fourth and fifth trials.

+Gumbel scale (β) parameter versus Hs. Dashed line is true, and solid line is fitted to observations from the randomly drawn parameters, varying seeds per sea state, fourth and fifth trials.
View Large  |  Save Figure  |  Download Slide (.ppt)
Gumbel scale (β) parameter versus Hs. Dashed line is true, and solid line is fitted to observations from the randomly drawn parameters, varying seeds per sea state, fourth and fifth trials.
Grahic Jump Location
Fig. 13

Gumbel location (α) and scale (β) parameters versus Hs. Dashed line is true, and solid line is fitted to observations from the randomly drawn parameters, ten seeds per sea state.

+Gumbel location (α) and scale (β) parameters versus Hs. Dashed line is true, and solid line is fitted to observations from the randomly drawn parameters, ten seeds per sea state.
View Large  |  Save Figure  |  Download Slide (.ppt)
Gumbel location (α) and scale (β) parameters versus Hs. Dashed line is true, and solid line is fitted to observations from the randomly drawn parameters, ten seeds per sea state.
Grahic Jump Location
Fig. 14

Gumbel location (α) and scale (β) parameters versus Hs. Dashed line is true, and solid line is fitted to observations from the randomly drawn parameters, 100 seeds per sea state.

+Gumbel location (α) and scale (β) parameters versus Hs. Dashed line is true, and solid line is fitted to observations from the randomly drawn parameters, 100 seeds per sea state.
View Large  |  Save Figure  |  Download Slide (.ppt)
Gumbel location (α) and scale (β) parameters versus Hs. Dashed line is true, and solid line is fitted to observations from the randomly drawn parameters, 100 seeds per sea state.
Grahic Jump Location
Fig. 15

Contributions to 10−4 response for simulation with 20 seeds

+Contributions to 10−4 response for simulation with 20 seeds
View Large  |  Save Figure  |  Download Slide (.ppt)
Contributions to 10−4 response for simulation with 20 seeds
Grahic Jump Location
Fig. 16

Contribution to 10−4 pressure in the true sea state for 20 seeds using a reduced area of integration

+Contribution to 10−4 pressure in the true sea state for 20 seeds using a reduced area of integration
View Large  |  Save Figure  |  Download Slide (.ppt)
Contribution to 10−4 pressure in the true sea state for 20 seeds using a reduced area of integration
Grahic Jump Location
Fig. 17

Statistics of MPM estimated from 1000 repetitions. Effect of increasing number of seeds in each sea state for estimating the 10−4 load effect. No of seeds: 5, 10, 20, 40, 100, and 1000.

+Statistics of MPM estimated from 1000 repetitions. Effect of increasing number of seeds in each sea state for estimating the 10−4 load effect. No of seeds: 5, 10, 20, 40, 100, and 1000.
View Large  |  Save Figure  |  Download Slide (.ppt)
Statistics of MPM estimated from 1000 repetitions. Effect of increasing number of seeds in each sea state for estimating the 10−4 load effect. No of seeds: 5, 10, 20, 40, 100, and 1000.
Grahic Jump Location
Fig. 18

Contribution to 10−4 crest using true response

+Contribution to 10−4 crest using true response
View Large  |  Save Figure  |  Download Slide (.ppt)
Contribution to 10−4 crest using true response
Grahic Jump Location
Fig. 19

Bootstrap for different number of seeds from the true Gumbel distribution at the peak of 10−4 contour

+Bootstrap for different number of seeds from the true Gumbel distribution at the peak of 10−4 contour
View Large  |  Save Figure  |  Download Slide (.ppt)
Bootstrap for different number of seeds from the true Gumbel distribution at the peak of 10−4 contour
Grahic Jump Location
Fig. 20

Normalized confidence 90% interval. Bootstrapping from true Gumbel distribution at the top of 10−4 contour line for slamming and crest height.

+Normalized confidence 90% interval. Bootstrapping from true Gumbel distribution at the top of 10−4 contour line for slamming and crest height.
View Large  |  Save Figure  |  Download Slide (.ppt)
Normalized confidence 90% interval. Bootstrapping from true Gumbel distribution at the top of 10−4 contour line for slamming and crest height.

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Geophysical Data Processing and Identifying for Gas Hydrate in the Slope of South China Sea
International Conference on Electronics, Information and Communication Engineering (EICE 2012)
On the Evaluation of Thermal and Mechanical Factors in Low-Speed Sliding
Tribology of Mechanical Systems> Chapter 11
Appendix: Non-Biomedical Application
Modified Detrended Fluctuation Analysis (mDFA)
Land and Sea Transportation
Machines That Made History> Chapter 5
Introduction
Nanomaterials in Glucose Sensing> Chapter 1
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
This site uses cookies. By continuing to use our website, you are agreeing to our privacy policy. | Accept
Sign In