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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

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
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References

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Norsok, 2007, “ N-003 Actions and Actions Effects,” Standards Norway.
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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.
Roos, J. , Swan, C. , and Haver, S. , 2010, “ Wave Impacts on the Column of a Gravity Based Structure,” ASME Paper No. OMAE2010-20648.
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.
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.
Haver, S. , 2007, “ A Discussion of Long Term Response Versus Mean Maximum Response of the Selected Design Sea State,” ASME Paper No. OMAE2007-29552.
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]
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Bury, K. V. , 1975, “ Statistical Models in Applied Science,” A Wiley Publication in Applied Statistics, Wiley, New York, pp. 371–375.
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Figures

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Fig. 1

Contour lines of sea states with constant annual probability of exceedance

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Fig. 2

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

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Fig. 3

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

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Fig. 4

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

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Fig. 5

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

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Fig. 6

COV versus steepness and Tp

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Fig. 7

Contour of Gumbel location parameter

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Fig. 8

Contour of Gumbel scale parameter

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Fig. 9

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

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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.

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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.

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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.

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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.

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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.

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Fig. 15

Contributions to 10−4 response for simulation with 20 seeds

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Fig. 16

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

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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.

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Fig. 18

Contribution to 10−4 crest using true response

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Fig. 19

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

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Fig. 20

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

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