422 Arctic Offshore Structures

Calibration of action factors for ISO 19906 Arctic offshore structures

Report No. 422December 2010

I n t e r n a t i o n a l A s s o c i a t i o n o f O i l & G a s P r o d u c e r s

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Report № 422

December 2010

Acknowledgements

This report was compiled by the OGP Offshore Structures Standards Committee with the assistance of experts from the ISO committees mentioned in this report.

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International Association of Oil & Gas Producers

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Table of Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Calibration methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Ice-structure interaction load distribution data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Reliability targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Calibration results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Application to ISO 19906 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Annex A – Development of ice design loads & criteria for various Arctic regions . . . . . . . . . . . . . . . . 9

Annex B – Calibration analysis of action factors for ISO 19906 Arctic offshore structures . . . . . . . . . 75

Annex C – Tails of probability distributions for structures with sloping and conical vs vertical sides . . .155

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This report presents the results of work to calibrate the partial action factors for environmental actions for ISO 19906:2010 Petroleum and natural gas industries – Arctic offshore structures, with emphasis on ice actions. It also presents the calibration procedure for future reference. The work was commissioned by the OGP Offshore Structures Committee at the instigation and under the technical direction of Working Group 8 Arctic offshore structures of ISO Technical Committee 67 Subcommittee 7 Offshore structures.

WG8 was established by SC7 in 2002 and was given the responsibility to develop an International Standard on arctic offshore structures. The work has been well supported by industry, therefore OGP agreed to accept funding from its members for the calibration work specified by WG8. OGP placed contracts for two activities as follows:

1) Development of Ice Design Loads & Criteria for Various Arctic Regions by C-CORE and Ian Jordaan and Associates, see Annex A;

2) Calibration Analysis of Action Factors for ISO 19906 Arctic Offshore Structures by Aleatec Advisory Services, see Annex B

With assistance from OGP and advised by its technical panels, WG8 applied the results of these two activities to the final provisions of ISO 19906:2010. In so doing, anomalies were identified in the load distribution curves for Barents Sea first-year ridges, and for actions on slope-sided structures generally.

In response, C-CORE provided updated load distribution curves for Barents Sea first-year ridges, see Annex A Addendum A. The impact of the updated curves on the results of the calibration analy-sis is discussed in Annex B Appendix C.

For slope-sided structures, a brief report entitled “Tails of Probability Distributions for Structures with Sloping and Conical vs Vertical Sides” was provided by C-CORE and Ian Jordaan and Associ-ates. This is included as Annex C to this report, and provided the basis for these specific results to be reassessed by WG8.

With support from OGP, WG8 reviewed all the results of the calibration analysis and decided on the factors to be specified in ISO 19906.

ISO 19906 allows a user to perform a calibration of environmental action factors for use in place of the action factors presented in ISO 19906. ISO 19906:2010 refers to this OGP report for informa-tion on the methodology of a calibration. ISO 19906:2010 also refers to this OGP report for infor-mation on the action factors calibrated for L3 structures. Consequently this OGP report is listed as a bibliographic reference, A.7-2, in ISO 19906:2010.

Introduction

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The calibration procedure and methodology used for ISO 19906:2010 is described in Annex B section 5. The calibration accounts for weighted combinations of all action effects over all design equations and load combinations, for different resistance models, for different levels of action effect model uncertainties, for different levels of statistical uncertainty, and for different mean action event occurrence rates. The methodology involves a weighted optimization process with the objec-tive function minimizing the deviation from L1, L2 and L3 targets, with checks that upper bound failure probability constraints are not violated.

Calibration methodology

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Ice-structure interaction scenarios for different arctic and sub-arctic regions were developed by WG8 in consultation with the contractors.

All zones and structure types to be considered are summarised in Annex B section 7 and Table 5 – Zones and structural systems. This table also shows where different regions were considered to have statistical distributions of actions sufficiently similar for one region to be analysed as representative of the others, despite the actual values of actions possibly being different.

The structure types identified for each region were those considered more likely to be used, in order to develop meaningful statistical weightings. This does not preclude any structure type actually being used in any region. The combinations of regions and structure types for which load distri-butions were developed are shown in Annex A section 1 and Table 1.1 – Geographic regions and ice-structure interaction scenarios. The relative weighting given to the structure types in each zone of regions is shown in Annex B section 7 and Table 6 – Relative weights of structural systems used in a specific region/ice environment.

Ice-structure interaction load distribution data

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The reliability targets to which the calibration analysis was performed are set out in ISO 19906:2010 Table A.7-1. The reliability targets include consideration of both life-safety and environmental pro-tection through the exposure levels L1, L2 and L3 as explained in ISO 19906:2010 subclause 7.1.4 and subclause A.7.2.4.

Reliability targets

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The results and verification for environmental action factors are described in Annex B section 8 for L1 structures and section 10 for L2 and L3 structures. Section 9 describes the derivation of the default (to be used in the absence of a full probabilistic analysis) companion environmental action factors.

The calibration analysis for environmental actions for L1 structures was performed for two sets of gravity action factors and action combinations; firstly a set based on ISO 19902 Fixed steel offshore structures and secondly a set based on the draft ISO/DIS 19906 issued in 2008.

Following review of results for slope-sided (conically-sided) structures, a briefing note was devel-oped, see Annex C. Consequently, the high values for these partial factors as reported in Annex B Table 12 were concluded to be spurious.

The overall summary of results is presented in Annex B section 11 and Table 18 – Calibrated design check equations for exposure levels L1, L2 and L3.

Calibration results

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Following consultation with its parent committee, SC7, WG8 decided to provide action factors and combinations for permanent and variable actions based on those of ISO 19902.

WG8 also noted that the calibrated values of the environmental action factors were relatively insen-sitive to the different values of the action factors for permanent and variable actions. Therefore ISO 19906 allows the use of the different factors for permanent and variable actions as presented in ISO 19903 Fixed concrete offshore structures and ISO 19904-1 Floating offshore structures respectively, in order to provide for consistency between structures in ice and in non-ice environments. Many such structures will be in an ice environment for part of the year only, therefore it is consistent to consider ice actions as giving rise to additional action combinations rather than changing the factors for permanent and variable actions in the "conventional" action combinations which continue to be applicable.

For L1 structures, the calibrated environmental action factor for extreme-level actions other than ice was calculated as 1.35. After resolving the anomalies of slope-sided structures, the calibrated extreme-level ice action factors ranged from 1.15 to 1.35 while region-wide averages ranged from 1.20 to 1.35, see Annex B Table 12. The "all regions, all structures" average for ice actions was cal-culated as 1.30. WG8 concluded that an environmental action factor of 1.35 would encompass the most unfavourable calculated ice action factor, while being consistent with the factor for other envi-ronmental actions and therefore simplifying the specification of action combinations to be used in the design process.

For L2 structures, the calibrated environmental action factor for extreme-level actions for all envi-ronmental actions was calculated consistently as 1.10, see Annex B Table 16. This value was accepted and adopted by WG8.

For L3 structures, WG8 decided not to present action factors in ISO 19906 but to refer the user to this OGP report. The intent is for the user to make a considered decision on whether an L3 designa-tion is appropriate, on the basis that it is "non standard".

For abnormal-level action factors, the annual probability to achieve the reliability target for L1 structures was calculated at 10-3.8. WG8 considered that such precision was not necessary, and that an annual probability of 10-4 could be slightly conservative but was also consistent with the value of other abnormal and accidental events used in the design process. For L2 structures, WG8 accepted and adopted the region-wide annual probability calibrated at 10-3.

WG8 accepted and adopted the companion environmental action factors as presented in Annex B, for use in ISO 19906:2010 Table 7-3. These values are relatively insensitive to exposure level (L1, L2 or L3), and therefore apply for all.

Application to ISO 19906

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• International Organization for Standardization (ISO), “Petroleum and natural gas industries – Arctic offshore structures”, International Standard ISO 19906, ISO, 2010.

• Bercha, F.G., Gudmestad, O.T., Foschi, R.O., Nevel, D., Nikitina, N., and Sliggers, F. “Reli-ability of Arctic Offshore Installations.” Proceedings, Icetech06, Banff, Canada, July, 2006.

• CSA S471-04 “General requirements, design criteria, the environment and loads” for the Code for the design, construction, and installation of offshore structures, Canadian Standards Asso-ciation, February 2004.

• Jordaan, I.J. and Maes, M.A., 1991. Rationale for load specifications and load factors in the new CSA Code for Fixed Offshore Structures, Canadian Journal of Civil Engineering, Vol. 18, No. 3, pp. 404-464.

References

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Annex A

Development of ice design loads & criteria for various Arctic regions

Development of ice design loads & criteria for various Arctic regions

Final Report prepared for OGP JIP25 committee.

C-CORE Report R-09-27-654 v1, September 2010.

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Development of Ice Design Loads & Criteria for Various Arctic Regions

FINAL REPORT R-09-027-654

Prepared for: OGP JIP25 Committee

September, 2010

Captain Robert A. Bartlett BuildingMorrissey Road

St. John’s, NL Canada A1B 3X5

T: (709) 737-8354 F: (709) 737-4706

Info@c-cor

www.c-cor e.ca


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Development of Ice Design Loads & Criteria for Various Arctic Regions FINAL REPORT Version 1

Captain Robert A. Bartlett Building Morrissey Road St. John's, NL Canada A1B 3X5 T: (709) 737-8354 F: (709) 737-4706 [email protected] www.c-cor e.ca

Prepared for: OGP JIP25 Committee

Prepared by: C-CORE and Ian Jor daan and Associates

C-CORE Report: R-09-27-654 September, 2010

Notes:

Updated results for G rand Banks and Labrador iceberg loa ds and B arents Sea fi rst-year ri dge loads give n necessar y modifica tion of inputs subsequent to fir st draft issue of this re port are provided in Addendum A of this report.

A brie f re port enti tled “ Tails of Probability Distributions for Structures with Sloping and Conical vs Vertical Sides” was pr ovided subsequent to the first dra ft issue of thi s report. The report included a discussion of the model used for e stimating loads due to mu lti-year ridges on c onical structures, and limitations in the model that could resu lt in probability tail s that are too “ fat” and hence result in overly pessimistic action factors.


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The correct citation for this report is:

C-CORE. Development of Ice Design Loads & Criteria for Various Arctic Regions, C-CORE Report R-09-27-654 v1, September, 2010.

Project TeamMark Fuglem (Project Manager) Freeman Ralph Ian Jordaan Paul Stuckey Grant Parr Daryl Burry Jim Bruce


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Development of Ice Design Loads & Criteria for Various Arctic Regions OGP JIP25 Committee Report number: R/P-09-027-654 V.1.0 September 23, 2010

REVISION HISTORY VERSION SVN # NAME COMPANY DATE OF

CHANGES COMMENTS

1.0 Mark Fuglem, Freeman Ralph, Ian Jordaan and Paul Stuckey

C-CORE Sep. 23, 2010

DISTRIBUTION LIST

COMPANY NAME NUMBER OF COPIES OGP JIP25 committee and ISO Committee TP10 Graham Thomas 1 - electronic


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EXECUTIVE SUMMARY

An important part of the development the new ISO Code for design of offshore structures is the validation and development of calibration (action) factors for design ice loads in arctic and subarctic regions. Good calibration requires that the slope of the tails of annual maximum load distributions be well defined. For example, if the design load is the 100-year load multiplied by an action factor, then to ensure reasonably consistent reliability levels, the probability of exceeding loads at different percentages larger than the 100-year load must be reasonably well established. Given that ice conditions vary significantly between different regions (as a result varied presence and characteristics of first-year sea ice, multi-year sea ice and icebergs) and that ice loads vary significantly depending on the ice type, environment, and platform characteristics, it was necessary to evaluate and provide annual maximum load distributions for a significant number of regions and platform types.

C-CORE and Ian Jordaan and Associates were invited to work with ISO in developing ice structure interaction scenarios and corresponding load distributions for a number of platform types and arctic and subarctic regions because of their experience in evaluating probabilistic design ice loads over a broad range of scenarios. This report gives an overview of the scenarios run and the methods used. Monte-Carlo simulation techniques were used in conjunction with site specific ice and environmental data and appropriate ice structure interaction models to simulate appropriate numbers of interactions per year and maximum ice loads for each interaction. For each scenario (region, ice types and platform type), the annual maximum load distribution, parent load distribution (maximum load per interaction event), and statistics on the number of load interactions and parent distribution are provided.

Based on the initial results provided in February, 2009, it was found that several scenarios required action factors higher than 1.35. On subsequent examination of the scenarios involved, it was confirmed that for multi-year ridges interacting with conical structures, current models do result in load distributions with relatively fat tails, requiring higher load factors. It is believed that the fatter tail for conical structures occurs in part because the effect of scaling on flexural strength is not taken into account, and that a higher load factor is not necessarily warranted. Additionally, after necessary modifications to model inputs for the analysis of first-year ridge loads on different structures in the Barents Sea region, the load probability tails were found to be more in line with load scenarios requiring lower action factors.


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A brief report entitled “Tails of Probability Distributions for Structures with Sloping and Conical vs Vertical Sides” was provided (June 25, 2009) that included: a) updated load curves for first-year ridge loads on Barents Sea structures incorporating

necessary modifications to inputs; andb) a discussion of the model used for estimating loads due to multi-year ridges on conical

structures, and limitations in the model that could result in probability tails that are too “fat” and hence result in overly pessimistic action factors.

An addendum (Addendum A) has been attached to this report with updated results for first-year ridge loads on Barents Sea structures and an updated discussion of the limitations in available models for estimating loads due to multi-year ridges on conical structures and a recommended strategy for improvement will be provided in the near future. A second addendum (Addendum B) has been added addressing TP10 comments on the ISO/DIS 19906 Calibration Draft Report that relate to inputs provided by C-CORE in the initial report provided in February.


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TABLE OF CONTENTS

1 INTRODUCTION ...........................................................................................................................................................1

2 APPROACH ....................................................................................................................................................................2

3 BEAUFORT AND CHUKCHI SEAS: MULTI-YEAR FLOES.................................................................................. 3

4 GRAND BANKS AND LABRADOR SEA: ICEBERGS...........................................................................................14

5 SAKHALIN ISLAND: FIRST-YEAR RIDGES.........................................................................................................19

6 BARENTS SEA: ICEBERGS AND FIRST-YEAR RIDGES ...................................................................................23

7 CASPIAN SEA: FIRST-YEAR LEVEL ICE .............................................................................................................29

8 REFERENCES ..............................................................................................................................................................33

ADDENDUM A – REVISED PLOTS FOR GRAND BANKS AND LABRADOR ICEBERG LOADS AND BARENTS SEA FIRST-YEAR RIDGE LOADS .............................................................. A.1 ADDENDUM B – RESPONSE TO COMMENTS ON ISO/DIS 19906 CALIBRATION DRAFT REPORT ....... B.1


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LIST OF TABLES

Table 1.1 Geographic regions and ice-structure interaction scenarios ............................................. 1 Table 3.1 Beaufort and Chukchi Sea ice conditions ......................................................................... 7 Table 4.1 Grand Banks ice conditions ............................................................................................ 15 Table 4.2 Labrador Sea ice conditions............................................................................................ 17 Table 5.1 Sakhalin Island ice conditions ........................................................................................ 20 Table 6.1 Barents Sea iceberg conditions ....................................................................................... 24 Table 6.2 Barents Sea first-year ridge conditions ........................................................................... 26 Table 7.1 Caspian Sea ice conditions.............................................................................................. 30

LIST OF FIGURES

Figure 3.1 Variation in multi-year concentration and water depth over Beaufort Sea lease area.. 5 Figure 3.2 Variation in multi-year concentration and water depth over Chukchi Sea lease area .. 5 Figure 3.3 Multi-year ridge profile options.................................................................................... 6 Figure 3.4 Multi-year ridge approach angle................................................................................... 6 Figure 3.5 Beaufort & Chukchi Seas: 100 m diameter GBS and 0.5/10ths MY concentration ...... 8 Figure 3.6 Beaufort & Chukchi Seas: 50 m wide FPSO and 0.5/10ths MY concentration............. 8 Figure 3.7 Beaufort & Chukchi Seas: 20 m diameter column and 0.5/10ths MY concentration .... 9 Figure 3.8 Beaufort & Chukchi Seas: 100 m slope-faced GBS and 0.5/10ths MY concentration.. 9 Figure 3.9 Beaufort & Chukchi Seas: 100m diameter GBS and 1.5/10ths MY concentration ..... 10 Figure 3.10 Beaufort & Chukchi Seas: 50 m wide FPSO and 1.5/10ths MY concentration........... 10 Figure 3.11 Beaufort & Chukchi Seas: 20 m diameter column and 1.5/10ths MY concentration

11 Figure 3.12 Beaufort & Chukchi Seas: 100 m slope-faced GBS and 1.5/10ths MY concentration 11Figure 3.13 Beaufort & Chukchi Seas: 100m diameter GBS and 3/10ths MY concentration ........ 12 Figure 3.14 Beaufort & Chukchi Seas: 50 m wide FPSO and 3/10ths MY concentration.............. 12 Figure 3.15 Beaufort & Chukchi Seas: 20 m diameter column and 3/10ths MY concentration . 13 Figure 3.16 Beaufort & Chukchi Seas: 100 m slope-faced GBS and 3/10ths MY concentration13Figure 4.1 Grand Banks: iceberg interactions with 100 m diameter GBS ................................... 16Figure 4.2 Grand Banks: iceberg interactions with 50 m wide FPSO ......................................... 16 Figure 4.3 Labrador Sea: iceberg interactions with 100 m diameter GBS................................... 18Figure 4.4 Labrador Sea: iceberg interactions with 50 m wide FPSO......................................... 18 Figure 5.1 Sakhalin Island: first-year ridge interactions with 100 m diameter GBS ................... 21Figure 5.2 Sakhalin Island: first-year ridge interactions with 50 m wide FPSO.......................... 21 Figure 5.3 Sakhalin Island: first-year ridge interactions with 20 m diameter column................. 22


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TABLE OF CONTENTS

1 INTRODUCTION ...........................................................................................................................................................1

2 APPROACH ....................................................................................................................................................................2

3 BEAUFORT AND CHUKCHI SEAS: MULTI-YEAR FLOES.................................................................................. 3

4 GRAND BANKS AND LABRADOR SEA: ICEBERGS...........................................................................................14

5 SAKHALIN ISLAND: FIRST-YEAR RIDGES.........................................................................................................19

6 BARENTS SEA: ICEBERGS AND FIRST-YEAR RIDGES ...................................................................................23

7 CASPIAN SEA: FIRST-YEAR LEVEL ICE .............................................................................................................29

8 REFERENCES ..............................................................................................................................................................33

ADDENDUM A – REVISED PLOTS FOR GRAND BANKS AND LABRADOR ICEBERG LOADS AND BARENTS SEA FIRST-YEAR RIDGE LOADS .............................................................. A.1 ADDENDUM B – RESPONSE TO COMMENTS ON ISO/DIS 19906 CALIBRATION DRAFT REPORT ....... B.1


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LIST OF TABLES

Table 1.1 Geographic regions and ice-structure interaction scenarios ............................................. 1 Table 3.1 Beaufort and Chukchi Sea ice conditions ......................................................................... 7 Table 4.1 Grand Banks ice conditions ............................................................................................ 15 Table 4.2 Labrador Sea ice conditions............................................................................................ 17 Table 5.1 Sakhalin Island ice conditions ........................................................................................ 20 Table 6.1 Barents Sea iceberg conditions ....................................................................................... 24 Table 6.2 Barents Sea first-year ridge conditions ........................................................................... 26 Table 7.1 Caspian Sea ice conditions.............................................................................................. 30

LIST OF FIGURES

Figure 3.1 Variation in multi-year concentration and water depth over Beaufort Sea lease area.. 5 Figure 3.2 Variation in multi-year concentration and water depth over Chukchi Sea lease area .. 5 Figure 3.3 Multi-year ridge profile options.................................................................................... 6 Figure 3.4 Multi-year ridge approach angle................................................................................... 6 Figure 3.5 Beaufort & Chukchi Seas: 100 m diameter GBS and 0.5/10ths MY concentration ...... 8 Figure 3.6 Beaufort & Chukchi Seas: 50 m wide FPSO and 0.5/10ths MY concentration............. 8 Figure 3.7 Beaufort & Chukchi Seas: 20 m diameter column and 0.5/10ths MY concentration .... 9 Figure 3.8 Beaufort & Chukchi Seas: 100 m slope-faced GBS and 0.5/10ths MY concentration.. 9 Figure 3.9 Beaufort & Chukchi Seas: 100m diameter GBS and 1.5/10ths MY concentration ..... 10 Figure 3.10 Beaufort & Chukchi Seas: 50 m wide FPSO and 1.5/10ths MY concentration........... 10 Figure 3.11 Beaufort & Chukchi Seas: 20 m diameter column and 1.5/10ths MY concentration

11 Figure 3.12 Beaufort & Chukchi Seas: 100 m slope-faced GBS and 1.5/10ths MY concentration 11Figure 3.13 Beaufort & Chukchi Seas: 100m diameter GBS and 3/10ths MY concentration ........ 12 Figure 3.14 Beaufort & Chukchi Seas: 50 m wide FPSO and 3/10ths MY concentration.............. 12 Figure 3.15 Beaufort & Chukchi Seas: 20 m diameter column and 3/10ths MY concentration . 13 Figure 3.16 Beaufort & Chukchi Seas: 100 m slope-faced GBS and 3/10ths MY concentration13Figure 4.1 Grand Banks: iceberg interactions with 100 m diameter GBS ................................... 16Figure 4.2 Grand Banks: iceberg interactions with 50 m wide FPSO ......................................... 16 Figure 4.3 Labrador Sea: iceberg interactions with 100 m diameter GBS................................... 18Figure 4.4 Labrador Sea: iceberg interactions with 50 m wide FPSO......................................... 18 Figure 5.1 Sakhalin Island: first-year ridge interactions with 100 m diameter GBS ................... 21Figure 5.2 Sakhalin Island: first-year ridge interactions with 50 m wide FPSO.......................... 21 Figure 5.3 Sakhalin Island: first-year ridge interactions with 20 m diameter column................. 22


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Figure 5.4 Sakhalin Island: first-year ridge interactions with 100 m diameter slope-faced GBS 22Figure 6.1 Barents Sea: iceberg interactions with 100 m diameter vertically-sided floater ........ 25Figure 6.2 Barents Sea: iceberg interactions with 50 m wide FPSO ........................................... 25 Figure 6.3 Barents Sea: first-year ridge interactions with 100 m diameter vertically-sided floater

27 Figure 6.4 Barents Sea: first-year ridge interactions with 50 m wide FPSO ............................... 27 Figure 6.5 Barents Sea: first-year ridge interactions with 100 m diameter slope-faced floater... 28 Figure 7.1 Caspian Sea: first-year level ice interactions with 100 m wide vertically-faced GBS31Figure 7.2 Caspian Sea: first-year level ice interactions with 20 m diameter column................. 31 Figure 7.3 Caspian Sea: first-year level ice interactions with 100 m wide slope-faced GBS...... 32


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1 INTRODUCTION

C-CORE and Ian Jordaan and Associates were invited to work with ISO in developing ice structure interaction scenarios and corresponding load distributions for offshore platforms in different arctic and subarctic regions. The purpose of the work was to provide a basis for validating and calibrating action factors to be included in the new ISO Code for design of offshore structures. The geographic regions and ice-structure interaction scenarios considered are listed in Table 1.1.

Table 1.1 Geographic regions and ice-structure interaction scenarios

Icebergs First-year

Level IceFirst-year Ridges

Multi-year Ridges

Beaufort & Chukchi Seas

• 100 m vertically sided GBS

• 50 m wide FPSO • 20 m column • 100 m conical GBS ‡ results are provided for 0.5, 1.5 and 3.0 tenth’s MY concentration

Grand Banks • 100 m GBS • 50 m wide FPSO

Labrador Sea • 100 m GBS • 50 m wide FPSO

SakhalinIsland

• 100 m GBS • 50 m wide FPSO • 20 m column • 100 m conical

GBS

Barents Sea • 100 m vertically sided floater

• 50 m wide FPSO

• 100 m vertically sided floater

• 50 m wide FPSO • 100 m conical

floater

Caspian Sea

• 100 m GBS • 20 m column • 100 m GBS with

upward slope face


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1 INTRODUCTION

C-CORE and Ian Jordaan and Associates were invited to work with ISO in developing ice structure interaction scenarios and corresponding load distributions for offshore platforms in different arctic and subarctic regions. The purpose of the work was to provide a basis for validating and calibrating action factors to be included in the new ISO Code for design of offshore structures. The geographic regions and ice-structure interaction scenarios considered are listed in Table 1.1.

Table 1.1 Geographic regions and ice-structure interaction scenarios

Icebergs First-year

Level IceFirst-year Ridges

Multi-year Ridges

Beaufort & Chukchi Seas

• 100 m vertically sided GBS

• 50 m wide FPSO • 20 m column • 100 m conical GBS ‡ results are provided for 0.5, 1.5 and 3.0 tenth’s MY concentration

Grand Banks • 100 m GBS • 50 m wide FPSO

Labrador Sea • 100 m GBS • 50 m wide FPSO

SakhalinIsland

• 100 m GBS • 50 m wide FPSO • 20 m column • 100 m conical

GBS

Barents Sea • 100 m vertically sided floater

• 50 m wide FPSO

• 100 m vertically sided floater

• 50 m wide FPSO • 100 m conical

floater

Caspian Sea

• 100 m GBS • 20 m column • 100 m GBS with

upward slope face


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2 APPROACH

For each region and applicable ice structure interaction scenario noted in Table 1.1, a maximum annual impact load probability distribution was required. Given the purpose of the overall study (to determine appropriate loads factors rather than specific design loads), it is important that the slope of the tails of the load distributions are appropriate. The specific load values and the shape of the distributions over the lower ranges of values are not as critical. Annual maximum loads to an annual probability of exceedence as low as 10-4 were required. In addition, ‘parent’ load distributions representing the probability specified loads given a single impact (as opposed to the annual maximum) along with associated mean and standard deviation values were required.

In determining the load distributions, the population of ice features (numbers, sizes and shapes of features), the effect of the structure shape and size, the movements of ice features and environmental forces, and the dynamics of the ice-structure interactions including the failure mechanisms of the ice need to be considered. Seasonal operations and ice management (detection, towing and moving floating systems off site to avoid ice interactions) were not considered.

For each geographic region and structure type, Monte-Carlo simulation techniques were applied to determine the annual maximum load distribution. First the exposure, in terms of number of features or duration of interaction is calculated based on site specific information regarding the length of the ice season, the number of features and movement of ice. Given the number of features, or amount of ice encountered in a given year, then ice-structure interaction models are used to simulate random loads for each feature or appropriate length of ice encountered. First, the maximum load per interaction is determined, and then the maximum load during all of the interactions in the year is determined and stored. Once interactions over a sufficient number of years have been simulated, the annual maximum load curve is output.

Only loads associated with the dominant types of ice features in each region (as shown in Table 1.1)were considered. The ice failure models used were developed with the more severe types of events in mind (for example, for multi-year ridges interactions, ice crushing across the contact face is considered and the possibility of a floe splitting or failing in flexure is ignored). The resulting load distributions are believed to be sufficiently accurate in the tail of the distribution.


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3 BEAUFORT AND CHUKCHI SEAS: MULTI-YEAR FLOES

In the Beaufort and Chukchi Seas, the dominant loads are associated with multi-year floes with embedded ridges. Ice generally moves across the region from east to west and the variation in multi-year ice concentration across the two seas is considerably larger from south to north than the variation from east to west. Figure 3.1 and Figure 3.2 illustrate the strong north-south variation in multi-year concentration over the exploration leases in the two seas. Design loads were calculated for three different ice concentration levels (0.5, 1.5 and 3 tenths), otherwise assuming the same ice characteristics. While there is some reduction in concentration and change in ice characteristics from east to west, this is less critical.

In modeling interactions between multi-year ice and vertically faced structures, the embedded multi-year ridges are idealized as triangular in profile (Figure 3.3a) and impacting with ridge length oriented normal to the direction of motion (Figure 3.4). Failure by crushing is assumed to occur across the complete width of contact. The depth of contact at each penetration is defined by the local thickness of the keel.

The failure strength of the multi-year ice was simulated using a pressure-averaging algorithm that accounts for reductions in peak failure pressure with contact width observed for interactions predominantly involving crushing of ice (Jordaan et al., 2005). The driving force acting on the back of the multi-year floes as a result of ridging of surrounding ice was modeled using the method recommended in ISO 19906; namely the unit driving force FL in MPa/m is given as FL = R h1.25 D-0.54 where h is the level ice thickness of the surrounding ice, D is the diameter of the multi-year floe and R equals 10 MPa / m. The thickness h of the surrounding ice was set equal to the mean monthly average first-year thickness.

For the 100 m conical GBS, the model developed by Wang for infinitely long ridges and referenced in the API RP 2N (API 1995, Wang, 1984, Nevel, 1991) was used to estimate the peak failure force that will occur given sufficient impact momentum and driving force. The force is assumed to increase linearly from one half to all of this maximum value over the width of the ridge. If there is insufficient momentum and driving force, the maximum value will not be achieved. When using the Wang model, the ridges are idealized as being truncated in profile (Figure 3.3b).

Data on multi-year ice features is limited, especially for the Chukchi Sea. For the Chukchi Sea, the same parameters were assumed as for the Beaufort Sea; this is a reasonable approximation as the prevailing currents tend to bring ice into the Chukchi Sea from the Beaufort Sea. From Figure 3.1and Figure 3.2, it is seen that the water depth varies from 30 to 1000 m over the lease area in the Beaufort Sea, but only from 30 to 50 m over the lease area in the Chukchi Sea. A sensitivity


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2 APPROACH

For each region and applicable ice structure interaction scenario noted in Table 1.1, a maximum annual impact load probability distribution was required. Given the purpose of the overall study (to determine appropriate loads factors rather than specific design loads), it is important that the slope of the tails of the load distributions are appropriate. The specific load values and the shape of the distributions over the lower ranges of values are not as critical. Annual maximum loads to an annual probability of exceedence as low as 10-4 were required. In addition, ‘parent’ load distributions representing the probability specified loads given a single impact (as opposed to the annual maximum) along with associated mean and standard deviation values were required.

In determining the load distributions, the population of ice features (numbers, sizes and shapes of features), the effect of the structure shape and size, the movements of ice features and environmental forces, and the dynamics of the ice-structure interactions including the failure mechanisms of the ice need to be considered. Seasonal operations and ice management (detection, towing and moving floating systems off site to avoid ice interactions) were not considered.

For each geographic region and structure type, Monte-Carlo simulation techniques were applied to determine the annual maximum load distribution. First the exposure, in terms of number of features or duration of interaction is calculated based on site specific information regarding the length of the ice season, the number of features and movement of ice. Given the number of features, or amount of ice encountered in a given year, then ice-structure interaction models are used to simulate random loads for each feature or appropriate length of ice encountered. First, the maximum load per interaction is determined, and then the maximum load during all of the interactions in the year is determined and stored. Once interactions over a sufficient number of years have been simulated, the annual maximum load curve is output.

Only loads associated with the dominant types of ice features in each region (as shown in Table 1.1)were considered. The ice failure models used were developed with the more severe types of events in mind (for example, for multi-year ridges interactions, ice crushing across the contact face is considered and the possibility of a floe splitting or failing in flexure is ignored). The resulting load distributions are believed to be sufficiently accurate in the tail of the distribution.


3

3 BEAUFORT AND CHUKCHI SEAS: MULTI-YEAR FLOES

In the Beaufort and Chukchi Seas, the dominant loads are associated with multi-year floes with embedded ridges. Ice generally moves across the region from east to west and the variation in multi-year ice concentration across the two seas is considerably larger from south to north than the variation from east to west. Figure 3.1 and Figure 3.2 illustrate the strong north-south variation in multi-year concentration over the exploration leases in the two seas. Design loads were calculated for three different ice concentration levels (0.5, 1.5 and 3 tenths), otherwise assuming the same ice characteristics. While there is some reduction in concentration and change in ice characteristics from east to west, this is less critical.

In modeling interactions between multi-year ice and vertically faced structures, the embedded multi-year ridges are idealized as triangular in profile (Figure 3.3a) and impacting with ridge length oriented normal to the direction of motion (Figure 3.4). Failure by crushing is assumed to occur across the complete width of contact. The depth of contact at each penetration is defined by the local thickness of the keel.

The failure strength of the multi-year ice was simulated using a pressure-averaging algorithm that accounts for reductions in peak failure pressure with contact width observed for interactions predominantly involving crushing of ice (Jordaan et al., 2005). The driving force acting on the back of the multi-year floes as a result of ridging of surrounding ice was modeled using the method recommended in ISO 19906; namely the unit driving force FL in MPa/m is given as FL = R h1.25 D-0.54 where h is the level ice thickness of the surrounding ice, D is the diameter of the multi-year floe and R equals 10 MPa / m. The thickness h of the surrounding ice was set equal to the mean monthly average first-year thickness.

For the 100 m conical GBS, the model developed by Wang for infinitely long ridges and referenced in the API RP 2N (API 1995, Wang, 1984, Nevel, 1991) was used to estimate the peak failure force that will occur given sufficient impact momentum and driving force. The force is assumed to increase linearly from one half to all of this maximum value over the width of the ridge. If there is insufficient momentum and driving force, the maximum value will not be achieved. When using the Wang model, the ridges are idealized as being truncated in profile (Figure 3.3b).

Data on multi-year ice features is limited, especially for the Chukchi Sea. For the Chukchi Sea, the same parameters were assumed as for the Beaufort Sea; this is a reasonable approximation as the prevailing currents tend to bring ice into the Chukchi Sea from the Beaufort Sea. From Figure 3.1and Figure 3.2, it is seen that the water depth varies from 30 to 1000 m over the lease area in the Beaufort Sea, but only from 30 to 50 m over the lease area in the Chukchi Sea. A sensitivity


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analysis was conducted to determine if variations in water depth over 30 m influences design loads. As minimal effect was found, only a single set of runs (three sets corresponding to the different multi-year ice concentrations) were conducted for the two regions.

The data inputs for the analysis are shown in Table 3.1 and the resulting load curves are shown in Figure 3.5 through Figure 3.16.


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Base map downloaded from Indian and Northern Affairs site http://www.ainc-inac.gc.ca/nth/og/le/mp/bsmd/beau.pdf

Figure 3.1 Variation in multi-year concentration and water depth over Beaufort Sea lease area

Base map from Proposed Final Program, Outer Continental Shelf, Oil and Gas Leasing Program 2007-2012, April 2007, U.S. Department of the Interior, Minerals Management Service Web site: http://www.mms.gov/5-year/PDFs/MMSProposedFinalProgram2007-2012.pdf

Figure 3.2 Variation in multi-year concentration and water depth over Chukchi Sea lease area


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analysis was conducted to determine if variations in water depth over 30 m influences design loads. As minimal effect was found, only a single set of runs (three sets corresponding to the different multi-year ice concentrations) were conducted for the two regions.



5

Base map downloaded from Indian and Northern Affairs site http://www.ainc-inac.gc.ca/nth/og/le/mp/bsmd/beau.pdf

Figure 3.1 Variation in multi-year concentration and water depth over Beaufort Sea lease area

Base map from Proposed Final Program, Outer Continental Shelf, Oil and Gas Leasing Program 2007-2012, April 2007, U.S. Department of the Interior, Minerals Management Service Web site: http://www.mms.gov/5-year/PDFs/MMSProposedFinalProgram2007-2012.pdf

Figure 3.2 Variation in multi-year concentration and water depth over Chukchi Sea lease area


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Figure 3.3 Multi-year ridge profile options

Figure 3.4 Multi-year ridge approach angle


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Table 3.1 Beaufort and Chukchi Sea ice conditions

Parameter Source Description Level MY ice thickness (m)

Sanderson (1988) Monthly mean values, used for driving force calculation.

MY concentration (tenths)

Based on NIC ice charts

0.5, 1.5 and 3.0 tenths representing different locations (see maps that follow). Sensitivity analysis showed no influence of water depth for water depths greater than 30 m.

MY floe diameter (m) Masterson (2008) Lognormal, = 223 m and = 246 m MY level ice thickness (m)

Masterson (2008) Exponential, = 4.1 m, = 2.3 m, shift = 1.8 m, upper limit 6 m

Proportion of time no movement

Melling and Riedel (2004)

Monthly values ranging from 40% of time in winter to 10% of time in summer. Values for Canadian Beaufort Sea, no data for Chukchi Sea.

Instantaneous drift speed given movement (m/s)


Montly values: gamma distributions with means varying from approximate 0.10 to 0.25 m/s. Values for Canadian Beaufort Sea, no data for Chukchi Sea.

MY ridge spacing Estimate

Lognormal, = 223 m and = 246 m(based on assumption of approximately one ridge per floe) Wadhams & Davy 1986 give a value of 224 based on ULS from submarines

MY keel draft (m) Masterson (2008) Exponential = 8.2 m and = 2.2 m, shift = 5 m.

Keel length (m) Assumed equal to width of floe.

Vertical structure - triangular ridge profile Keel angle (°) ISO/TC 67 / SC 7 30°

Keel width (m) Determined from keel draft and angle based on assumption of triangular ridge

Conical structure - truncated ridge profile Keel width to depth ratio

5 to 1

Keel top to bottom width ratio

1.5 to 1


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Figure 3.3 Multi-year ridge profile options

Figure 3.4 Multi-year ridge approach angle


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Table 3.1 Beaufort and Chukchi Sea ice conditions

Parameter Source Description Level MY ice thickness (m)

Sanderson (1988) Monthly mean values, used for driving force calculation.

MY concentration (tenths)

Based on NIC ice charts

0.5, 1.5 and 3.0 tenths representing different locations (see maps that follow). Sensitivity analysis showed no influence of water depth for water depths greater than 30 m.

MY floe diameter (m) Masterson (2008) Lognormal, = 223 m and = 246 m MY level ice thickness (m)

Masterson (2008) Exponential, = 4.1 m, = 2.3 m, shift = 1.8 m, upper limit 6 m

Proportion of time no movement


Monthly values ranging from 40% of time in winter to 10% of time in summer. Values for Canadian Beaufort Sea, no data for Chukchi Sea.

Instantaneous drift speed given movement (m/s)


Montly values: gamma distributions with means varying from approximate 0.10 to 0.25 m/s. Values for Canadian Beaufort Sea, no data for Chukchi Sea.

MY ridge spacing Estimate

Lognormal, = 223 m and = 246 m(based on assumption of approximately one ridge per floe) Wadhams & Davy 1986 give a value of 224 based on ULS from submarines

MY keel draft (m) Masterson (2008) Exponential = 8.2 m and = 2.2 m, shift = 5 m.

Keel length (m) Assumed equal to width of floe.

Vertical structure - triangular ridge profile Keel angle (°) ISO/TC 67 / SC 7 30°

Keel width (m) Determined from keel draft and angle based on assumption of triangular ridge

Conical structure - truncated ridge profile Keel width to depth ratio

5 to 1

Keel top to bottom width ratio

1.5 to 1


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Figure 3.5 Beaufort & Chukchi Seas: 100 m diameter GBS and 0.5/10ths MY concentration

Figure 3.6 Beaufort & Chukchi Seas: 50 m wide FPSO and 0.5/10ths MY concentration


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Figure 3.5 Beaufort & Chukchi Seas: 100 m diameter GBS and 0.5/10ths MY concentration



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Figure 3.7 Beaufort & Chukchi Seas: 20 m diameter column and 0.5/10ths MY concentration

Figure 3.8 Beaufort & Chukchi Seas: 100 m slope-faced GBS and 0.5/10ths MY concentration


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Figure 3.9 Beaufort & Chukchi Seas: 100m diameter GBS and 1.5/10ths MY concentration



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Figure 3.9 Beaufort & Chukchi Seas: 100m diameter GBS and 1.5/10ths MY concentration



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Figure 3.13 Beaufort & Chukchi Seas: 100m diameter GBS and 3/10ths MY concentration

Figure 3.14 Beaufort & Chukchi Seas: 50 m wide FPSO and 3/10ths MY concentration


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Figure 3.13 Beaufort & Chukchi Seas: 100m diameter GBS and 3/10ths MY concentration

Figure 3.14 Beaufort & Chukchi Seas: 50 m wide FPSO and 3/10ths MY concentration


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Figure 3.15 Beaufort & Chukchi Seas: 20 m diameter column and 3/10ths MY concentration

Figure 3.16 Beaufort & Chukchi Seas: 100 m slope-faced GBS and 3/10ths MY concentration


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4 GRAND BANKS AND LABRADOR SEA: ICEBERGS

On the Grand Banks and in the Labrador Sea, the dominant loads are associated with iceberg impacts in open seas.

The iceberg loads are estimated using a kinetic energy based interaction model. The model takes into account the iceberg shape (global as well as local shape at the point of contact) and the size, drift velocity and wave-induced velocity of the iceberg. The drift and wave-induced velocity are determined based on the sea state and the size of the iceberg. In determining the initial kinetic energy of the iceberg, the hydrodynamic added mass of the iceberg is included. The initial kinetic energy of the iceberg is dissipated through ice crushing and transformation into rotational energy due to the eccentric impact of the iceberg. The force at the point of contact is calculated using a global pressure-area model in conjunction with an area-penetration model. The global pressure-area model is based on a random relationship, as outlined in equation A.8-18 of Section A.8.2.4.3 in ISO/TC 67 / SC 7. The area-penetration model characterizes the contact area between the iceberg and a structure as a function of penetration at the point of contact, with random coefficients for the relationship determined based on an analysis of actual iceberg shapes.

There are several differences in inputs between the Labrador Sea and Grand Banks that affect the calculated loads. For the Grand Banks, platforms located at 46.5N and 48.5W (water depth 95 m) have been considered. For the Labrador Sea, platforms located on the Makkovik Bank (water depth 100 m) have been considered. The areal density of icebergs is significantly higher at the Labrador Sea site (2.0 icebergs per 1000 km2 versus 0.082 for the Grand Banks site). The same iceberg size distribution was assumed for the Labrador Sea as on the Grand Banks (though the icebergs in the Labrador Sea could be slightly larger, there is insufficient data to justify a different distribution given the difference in size).

The data inputs for the Grand Banks analysis are shown in Table 4.1 and the resulting load curves are shown in Figure 4.1 through Figure 4.2. The data inputs for the Labrador Sea analysis are shown in Table 4.2 and the resulting load curves are shown in Figure 4.3 through Figure 4.4. It is seen that the resulting loads are significantly higher for the Labrador Sea. For the Grand Banks site, there are 0.13 impacts per year on average, so the distribution of annual maximum load is scaled down from the parent distribution of loads. For the Labrador site, there are 4.7 impacts per year on average, so the distribution of annual maximum load is shifted to the right of the parent distribution of loads.


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Table 4.1 Grand Banks ice conditions

Parameter Data Source DescriptionAreal density per 1000 km2

Estimated from site specific data

0.08

Waterline length (m) C-CORE (2006) Combination of two exponential distributions Significant wave height (m) AES40 (2000) Site specific empirical distribution Mass (tonnes) C-CORE (2006) M = 1.05L2.68 exp(e), where e = N(0,0.61)Draft (m) C-CORE (2006) D = 3.14L0.68 exp(e), where e = N(0,0.25) Width (m) C-CORE (2006) D = 3.09×L0.490×W 0.215,with R2 = 0.661 Drift speed (m/s) C-CORE (2006) Probabilistic model with drift speed as a function of

length and significant wave height. The mean drift speed for all iceberg sizes and sea states is 0.33 m/s.

‡ see addendum for corrected table


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4 GRAND BANKS AND LABRADOR SEA: ICEBERGS

On the Grand Banks and in the Labrador Sea, the dominant loads are associated with iceberg impacts in open seas.

The iceberg loads are estimated using a kinetic energy based interaction model. The model takes into account the iceberg shape (global as well as local shape at the point of contact) and the size, drift velocity and wave-induced velocity of the iceberg. The drift and wave-induced velocity are determined based on the sea state and the size of the iceberg. In determining the initial kinetic energy of the iceberg, the hydrodynamic added mass of the iceberg is included. The initial kinetic energy of the iceberg is dissipated through ice crushing and transformation into rotational energy due to the eccentric impact of the iceberg. The force at the point of contact is calculated using a global pressure-area model in conjunction with an area-penetration model. The global pressure-area model is based on a random relationship, as outlined in equation A.8-18 of Section A.8.2.4.3 in ISO/TC 67 / SC 7. The area-penetration model characterizes the contact area between the iceberg and a structure as a function of penetration at the point of contact, with random coefficients for the relationship determined based on an analysis of actual iceberg shapes.

There are several differences in inputs between the Labrador Sea and Grand Banks that affect the calculated loads. For the Grand Banks, platforms located at 46.5N and 48.5W (water depth 95 m) have been considered. For the Labrador Sea, platforms located on the Makkovik Bank (water depth 100 m) have been considered. The areal density of icebergs is significantly higher at the Labrador Sea site (2.0 icebergs per 1000 km2 versus 0.082 for the Grand Banks site). The same iceberg size distribution was assumed for the Labrador Sea as on the Grand Banks (though the icebergs in the Labrador Sea could be slightly larger, there is insufficient data to justify a different distribution given the difference in size).

The data inputs for the Grand Banks analysis are shown in Table 4.1 and the resulting load curves are shown in Figure 4.1 through Figure 4.2. The data inputs for the Labrador Sea analysis are shown in Table 4.2 and the resulting load curves are shown in Figure 4.3 through Figure 4.4. It is seen that the resulting loads are significantly higher for the Labrador Sea. For the Grand Banks site, there are 0.13 impacts per year on average, so the distribution of annual maximum load is scaled down from the parent distribution of loads. For the Labrador site, there are 4.7 impacts per year on average, so the distribution of annual maximum load is shifted to the right of the parent distribution of loads.


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0.08

Waterline length (m) C-CORE (2006) Combination of two exponential distributions Significant wave height (m) AES40 (2000) Site specific empirical distribution Mass (tonnes) C-CORE (2006) M = 1.05L2.68 exp(e), where e = N(0,0.61)Draft (m) C-CORE (2006) D = 3.14L0.68 exp(e), where e = N(0,0.25) Width (m) C-CORE (2006) D = 3.09×L0.490×W 0.215,with R2 = 0.661 Drift speed (m/s) C-CORE (2006) Probabilistic model with drift speed as a function of

length and significant wave height. The mean drift speed for all iceberg sizes and sea states is 0.33 m/s.



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‡ see addendum for corrected plot

Figure 4.1 Grand Banks: iceberg interactions with 100 m diameter GBS


Figure 4.2 Grand Banks: iceberg interactions with 50 m wide FPSO


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Table 4.2 Labrador Sea ice conditions



2.0 (Makkovik Bank)

Waterline length (m) C-CORE (2006) Combination of two exponential distributions

Significant wave height (m)

MSC50 (2008), Meteorological Service of Canada

Site specific empirical distribution

Mass (tonnes) C-CORE (2006) M = 1.05L2.68 exp(e), where e = N(0,0.61) Draft (m) C-CORE (2006) D = 3.14L0.68 exp(e), where e = N(0,0.25) Width (m) C-CORE (2006) D = 3.09×L0.490×W 0.215, with R2=0.661 Drift speed (m/s) Labrador Strategic

Environmental Assessment (2008)

Probabilistic model with drift speed as a function of length and significant wave height. The mean drift speed for all iceberg sizes and sea states is 0.25 m/s.



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17




2.0 (Makkovik Bank)

Waterline length (m) C-CORE (2006) Combination of two exponential distributions

Significant wave height (m)

MSC50 (2008), Meteorological Service of Canada

Site specific empirical distribution

Mass (tonnes) C-CORE (2006) M = 1.05L2.68 exp(e), where e = N(0,0.61) Draft (m) C-CORE (2006) D = 3.14L0.68 exp(e), where e = N(0,0.25) Width (m) C-CORE (2006) D = 3.09×L0.490×W 0.215, with R2=0.661 Drift speed (m/s) Labrador Strategic

Environmental Assessment (2008)




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‡ see addendum for corrected plot Figure 4.3 Labrador Sea: iceberg interactions with 100 m diameter GBS

‡see addendum for corrected plot Figure 4.4 Labrador Sea: iceberg interactions with 50 m wide FPSO


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5 SAKHALIN ISLAND: FIRST-YEAR RIDGES

First-year ridges are the dominant loading features off Sakhalin Island. Loads resulting from first-year ridges have been modeled as the sum of the force required to fail the consolidated portion of the ridge (near the surface), and the force required to fail the unconsolidated keel below the consolidated layer.

For ridge interactions with structures having vertical faces, the consolidated layer is assumed to fail by crushing. The failure strength of the consolidated keel was modeled based on the CSA code (CSA, 2004), assuming Zone 2 ice conditions; this model gives consideration to the thickness of ice and the width of the failure contact zone.

For ridge interactions with structures having sloped faces, the consolidated layer is assumed to fail by flexure. The maximum load during an interaction is estimated as the sum of component forces to push the ice sheet through rubble accumulating on the front of the cone; lift and shear ice rubble on top of the sheet; break the consolidated layer by flexure; push the broken ice blocks up the slope through rubble and turn the ice blocks at the top of the slope (assuming the ice impacts a vertical wall or neck). The model is an adaptation of that described in Croasdale et al. (1994).

The loads associated with the unconsolidated layer for structures having either vertical or sloped faces are estimated using the same model. The unconsolidated ice is treated as a Coulomb-Mohr material. At any given penetration the unconsolidated keel may fail by either a local or global plug failure mechanism depending on the local thickness of the unconsolidated layer and the horizontal extent of intact unconsolidated ice still remaining. The pressure required to cause local plug failure is estimated using the Dolgopolov (1975) model and the pressure required to cause global plug failure is estimated using the Croasdale model (1980). The overall model that accounts for both failure mechanisms is described in Brown et al. (1996). The strength of the unconsolidated keel was based on a cohesion of 6000 Pa, an internal friction angle of 40 degrees, a porosity of 0.2, an elastic modulus of 3 GPa and a Poisson ratio of 0.3.

The unit driving force FL (per m of ridge length) acting on the ridge by the surrounding ice was modeled using the method recommended in ISO 19906; namely, FL = R h1.25 L-0.54 where R is uniformly distributed between 2 and 10 MPa / m, h is the level ice thickness of the floe and L is the ridge length.

The data inputs for the analysis are shown in Table 5.1. A water depth of 30 m was assumed. The resulting load curves are shown in Figure 5.1 through Figure 5.4.


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‡ see addendum for corrected plot Figure 4.3 Labrador Sea: iceberg interactions with 100 m diameter GBS

‡see addendum for corrected plot Figure 4.4 Labrador Sea: iceberg interactions with 50 m wide FPSO


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5 SAKHALIN ISLAND: FIRST-YEAR RIDGES

First-year ridges are the dominant loading features off Sakhalin Island. Loads resulting from first-year ridges have been modeled as the sum of the force required to fail the consolidated portion of the ridge (near the surface), and the force required to fail the unconsolidated keel below the consolidated layer.

For ridge interactions with structures having vertical faces, the consolidated layer is assumed to fail by crushing. The failure strength of the consolidated keel was modeled based on the CSA code (CSA, 2004), assuming Zone 2 ice conditions; this model gives consideration to the thickness of ice and the width of the failure contact zone.

For ridge interactions with structures having sloped faces, the consolidated layer is assumed to fail by flexure. The maximum load during an interaction is estimated as the sum of component forces to push the ice sheet through rubble accumulating on the front of the cone; lift and shear ice rubble on top of the sheet; break the consolidated layer by flexure; push the broken ice blocks up the slope through rubble and turn the ice blocks at the top of the slope (assuming the ice impacts a vertical wall or neck). The model is an adaptation of that described in Croasdale et al. (1994).

The loads associated with the unconsolidated layer for structures having either vertical or sloped faces are estimated using the same model. The unconsolidated ice is treated as a Coulomb-Mohr material. At any given penetration the unconsolidated keel may fail by either a local or global plug failure mechanism depending on the local thickness of the unconsolidated layer and the horizontal extent of intact unconsolidated ice still remaining. The pressure required to cause local plug failure is estimated using the Dolgopolov (1975) model and the pressure required to cause global plug failure is estimated using the Croasdale model (1980). The overall model that accounts for both failure mechanisms is described in Brown et al. (1996). The strength of the unconsolidated keel was based on a cohesion of 6000 Pa, an internal friction angle of 40 degrees, a porosity of 0.2, an elastic modulus of 3 GPa and a Poisson ratio of 0.3.

The unit driving force FL (per m of ridge length) acting on the ridge by the surrounding ice was modeled using the method recommended in ISO 19906; namely, FL = R h1.25 L-0.54 where R is uniformly distributed between 2 and 10 MPa / m, h is the level ice thickness of the floe and L is the ridge length.

The data inputs for the analysis are shown in Table 5.1. A water depth of 30 m was assumed. The resulting load curves are shown in Figure 5.1 through Figure 5.4.


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Table 5.1 Sakhalin Island ice conditions

Parameter Source Description

Season length (weeks) Truskov et al. (1999)

Early – mid December to mid – late May (~26 weeks) Model using normal distribution with mean of 180 days and standard deviation of 13 days

Ice concentration Truskov et al. (1999)

During the ice season, there is 9/10ths converage, with open water associated with coastal flaw leads approximately 30 percent of the time. Model using an average value of 0.63.

Level ice thickness (m) Truskov et al. (1999) Truskov indicates level ice thickness up to 1.7 m Model assumes uniform distribution from 0.4 to 1.7 m

Keel draft (m) Truskov et al. (1999) Exponential distribution ( = 7 m, = 2 m, lower cut-off of 5m)

Consolidated layer thickness (m)

Judgment

Model as random factor times times level ice thickness where factor is a triangular distribution from a probability of 1 at 1 m to a probability of 0 at 1.9 m.

Keel angle (°) Wadhams (2000) Model as fixed value of 33°

Keel length (m) Vershinnin et al. (2006) Exponential distribution with mean of 205, standard deviation of 65 and shift of 140 m.

Ridge frequency Truskov et al. (1999) Frequency of 6 ridges per kilometer with keel draft greater than 8.5 m. Modeled frequency determined based on lower draft cut-off and draft distribution.

Instantaneous drift speed (m/s) Bekker et al. (1999)

15% probability of zero velocity (i.e. calm conditions).Instantaneous velocity, when movement modeled as gamma distribution with mean = 0.35 m/s and standard deviation = 0.25 m/s


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Figure 5.1 Sakhalin Island: first-year ridge interactions with 100 m diameter GBS

Figure 5.2 Sakhalin Island: first-year ridge interactions with 50 m wide FPSO


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Table 5.1 Sakhalin Island ice conditions

Parameter Source Description

Season length (weeks) Truskov et al. (1999)

Early – mid December to mid – late May (~26 weeks) Model using normal distribution with mean of 180 days and standard deviation of 13 days

Ice concentration Truskov et al. (1999)

During the ice season, there is 9/10ths converage, with open water associated with coastal flaw leads approximately 30 percent of the time. Model using an average value of 0.63.

Level ice thickness (m) Truskov et al. (1999) Truskov indicates level ice thickness up to 1.7 m Model assumes uniform distribution from 0.4 to 1.7 m

Keel draft (m) Truskov et al. (1999) Exponential distribution ( = 7 m, = 2 m, lower cut-off of 5m)


Judgment


Keel angle (°) Wadhams (2000) Model as fixed value of 33°

Keel length (m) Vershinnin et al. (2006) Exponential distribution with mean of 205, standard deviation of 65 and shift of 140 m.

Ridge frequency Truskov et al. (1999) Frequency of 6 ridges per kilometer with keel draft greater than 8.5 m. Modeled frequency determined based on lower draft cut-off and draft distribution.

Instantaneous drift speed (m/s) Bekker et al. (1999)

15% probability of zero velocity (i.e. calm conditions).Instantaneous velocity, when movement modeled as gamma distribution with mean = 0.35 m/s and standard deviation = 0.25 m/s


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Figure 5.1 Sakhalin Island: first-year ridge interactions with 100 m diameter GBS

Figure 5.2 Sakhalin Island: first-year ridge interactions with 50 m wide FPSO


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Figure 5.3 Sakhalin Island: first-year ridge interactions with 20 m diameter column

Figure 5.4 Sakhalin Island: first-year ridge interactions with 100 m diameter slope-faced GBS


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6 BARENTS SEA: ICEBERGS AND FIRST-YEAR RIDGES

Icebergs and first-year ridges are the dominant loading features in the Barents Sea. While icebergs may potentially impart large loads, they occur relatively infrequently.

Iceberg load distributions were determined using the same models for iceberg loads on the Grand Banks and in the Labrador Sea, but iceberg and environmental inputs appropriate for the Barents Sea. For first-year level ice loads, the same models were used as for first-year ice loads off Sakhalin Island, but with the number and shapes of ridges modeled, the consolidated layer thickness and the surrounding ice thickness appropriate for Barents Sea conditions.

The data inputs for the Barents Sea iceberg analysis are shown in Table 6.1 and the resulting load curves are shown in Figure 6.1 through Figure 6.2. The data inputs for the Barents Sea first-year ridge analysis are shown in Table 6.2 and the resulting load curves are shown in Figure 6.3 through Figure 6.5.


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Figure 5.3 Sakhalin Island: first-year ridge interactions with 20 m diameter column

Figure 5.4 Sakhalin Island: first-year ridge interactions with 100 m diameter slope-faced GBS


23

6 BARENTS SEA: ICEBERGS AND FIRST-YEAR RIDGES

Icebergs and first-year ridges are the dominant loading features in the Barents Sea. While icebergs may potentially impart large loads, they occur relatively infrequently.

Iceberg load distributions were determined using the same models for iceberg loads on the Grand Banks and in the Labrador Sea, but iceberg and environmental inputs appropriate for the Barents Sea. For first-year level ice loads, the same models were used as for first-year ice loads off Sakhalin Island, but with the number and shapes of ridges modeled, the consolidated layer thickness and the surrounding ice thickness appropriate for Barents Sea conditions.

The data inputs for the Barents Sea iceberg analysis are shown in Table 6.1 and the resulting load curves are shown in Figure 6.1 through Figure 6.2. The data inputs for the Barents Sea first-year ridge analysis are shown in Table 6.2 and the resulting load curves are shown in Figure 6.3 through Figure 6.5.


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Table 6.1 Barents Sea iceberg conditions

Parameter Data Source Description Areal density (per 1000 km2) Site specific data 0.05

Waterline length (m) Site specific data Combination of two distributions Significant wave height (m) Site specific data Rayleigh, = 1.76 m and = 0.99 m Mass (tonnes) Loset and Carstens (1996) M = 1.49L2.57 exp(e), where e = N(0,0.43) Draft (m) C-CORE (2006) D = 3.14L0.68 exp(e), where e = N(0,0.25) Width (m) C-CORE (2006) D = 3.09×L0.490×W 0.215, with R2 = 0.661 Drift speed (m/s) Site specific data Gamma, = 0.25 m/s and = 0.20 m/s


25

Figure 6.1 Barents Sea: iceberg interactions with 100 m diameter vertically-sided floater

Figure 6.2 Barents Sea: iceberg interactions with 50 m wide FPSO


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Table 6.1 Barents Sea iceberg conditions

Parameter Data Source Description Areal density (per 1000 km2) Site specific data 0.05

Waterline length (m) Site specific data Combination of two distributions Significant wave height (m) Site specific data Rayleigh, = 1.76 m and = 0.99 m Mass (tonnes) Loset and Carstens (1996) M = 1.49L2.57 exp(e), where e = N(0,0.43) Draft (m) C-CORE (2006) D = 3.14L0.68 exp(e), where e = N(0,0.25) Width (m) C-CORE (2006) D = 3.09×L0.490×W 0.215, with R2 = 0.661 Drift speed (m/s) Site specific data Gamma, = 0.25 m/s and = 0.20 m/s


25

Figure 6.1 Barents Sea: iceberg interactions with 100 m diameter vertically-sided floater

Figure 6.2 Barents Sea: iceberg interactions with 50 m wide FPSO


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Table 6.2 Barents Sea first-year ridge conditions

Parameter Source DescriptionAnnual Pack Ice Occurrence

NIC archived ice charts Pack ice present approximately 3 out of every 10 years

Season length (weeks) NIC archived ice charts Exponential distribution with a mean of 5.6 weeks (39.2 days) corresponding to concentrations greater than 8/10ths

Ice concentration NIC archived ice charts 9/10ths (corresponding to definition of season length)

Level ice thickness (m) Derived from NIC archived ice charts

Exponential distribution with mean 0.56 m, standard deviation 0.26 m, shift 0.3 and upper cut-off 1.5 m.

Keel draft (m) Derived from plot in Naumov et al. (2007)

Gamma distribution with mean 4.8 and standard deviation 2.3.


-


Keel angle (°) Wadhams (2000) Fixed value of 33°

Keel length (m) Derived from plot in Naumov et al. (2007)

Gamma distribution with mean 36.3 m and standard deviation 19.2 m

Ridge frequency Zubakin et al. (2004) 5.1 per km Instantaneous drift speed (m/s)

Zubakin et al. (2004) - 0.2 m/s (assumed same value as for icebergs)


27


Figure 6.3 Barents Sea: first-year ridge interactions with 100 m diameter vertically-sided floater


Figure 6.4 Barents Sea: first-year ridge interactions with 50 m wide FPSO


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Table 6.2 Barents Sea first-year ridge conditions

Parameter Source DescriptionAnnual Pack Ice Occurrence

NIC archived ice charts Pack ice present approximately 3 out of every 10 years

Season length (weeks) NIC archived ice charts Exponential distribution with a mean of 5.6 weeks (39.2 days) corresponding to concentrations greater than 8/10ths

Ice concentration NIC archived ice charts 9/10ths (corresponding to definition of season length)

Level ice thickness (m) Derived from NIC archived ice charts

Exponential distribution with mean 0.56 m, standard deviation 0.26 m, shift 0.3 and upper cut-off 1.5 m.

Keel draft (m) Derived from plot in Naumov et al. (2007)

Gamma distribution with mean 4.8 and standard deviation 2.3.


-


Keel angle (°) Wadhams (2000) Fixed value of 33°

Keel length (m) Derived from plot in Naumov et al. (2007)

Gamma distribution with mean 36.3 m and standard deviation 19.2 m

Ridge frequency Zubakin et al. (2004) 5.1 per km Instantaneous drift speed (m/s)

Zubakin et al. (2004) - 0.2 m/s (assumed same value as for icebergs)


27


Figure 6.3 Barents Sea: first-year ridge interactions with 100 m diameter vertically-sided floater


Figure 6.4 Barents Sea: first-year ridge interactions with 50 m wide FPSO


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Figure 6.5 Barents Sea: first-year ridge interactions with 100 m diameter slope-faced floater


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29

7 CASPIAN SEA: FIRST-YEAR LEVEL ICE

The north-east Caspian Sea is a subarctic region that experiences extensive first-year level ice coverage with a significant degree of rafting. As a result of the shallow water levels (in the order of 5 m), the ice occasionally grounds out, creating stamuki. For vertically-faced structures, the largest loads are associated with crushing of level ice and rafted ice. For sloped structures, the largest loads result from level and rafted ice, either directly as a result of initial ride-up loads, or as a result of transfer of crushing type loads transferred through grounded rubble that subsequently develops in front of structure because of the shallow water depths. While rafted ice is probably significantly weaker than level ice, insufficient strength data on rafted ice was available, so the rafted ice was conservatively treated using the same models and ice strengths as the level ice.

For the analyses, the water depth was set to 5 m and the GBS structures were modeled as square in plan. For the sloped structure, the slope was set to 45 degrees (upward).

Based on an analysis of historical conditions, the number of ice movement events per year was simulated from a normal distribution with a mean of 15 and a standard deviation of 4. Based on observed ice movements and wind duration events, the amount of ice passing a structure during an ice movement was simulated from a lognormal distribution with a mean of 16 km and a standard deviation of 22.5 km.

For the vertically sided structures, ice thickness and crushing pressures were varied during each ice movement event and the peak force during the event determined. Ice thickness was simulated from a distribution representing both level and rafted ice; with rafted ice comprising approximately 30% of the ice passing a structure, based on observation. The ice crushing strength model was derived as a function of level ice thickness using STRICE data collected in the Baltic Sea, for which the crushing strength is believed to be similar. A pressure-averaging method that accounts for the reduction in peak loads with structure width was developed using a similar approach to that developed for multi-year ice crushing loads. The annual maximum force was taken as the maximum of the peak event loads.



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Table 7.1 Caspian Sea ice conditions

Parameter Data Source DescriptionNumber of events per year Site specific data Normal distribution, = 15 and = 4 Event length (km) Site specific data Amount of ice moved past the structure during an

event: Lognormal distribution with = 16 km and = 22.5 km

Ice thickness (m) Site specific data A single distribution representing both level and rafted ice. Rafted ice makes up 30% of the total ice moved past the structure annually. Gamma, = 0.45 m and = 0.089 m

Ice crushing strength (MPa)

Strice data: (Karna and Yan, 2006)

Empirical relationship derived as a function of ice thickness and contact width.

Flexural strength (MPa) Normal distribution, = 0.44 and = 0.13 Rubble porosity Uniform distribution from 0.1 to 0.3 Ice-structure coefficient of friction

Uniform distribution from 0.05 to 0.15

Maximum rubble pile height (m)

Mayne and Brown (2000) 7.59 h0.64 where h is level ice thickness (m)

Rubble cohesion (Pa) 4000Rubble internal angle of friction (deg)

45

Rubble angle of repose Slope – 10 degrees Ice-ice coefficient of friction

0.1


31

Figure 7.1 Caspian Sea: first-year level ice interactions with 100 m wide vertically-faced GBS

Figure 7.2 Caspian Sea: first-year level ice interactions with 20 m diameter column


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Table 7.1 Caspian Sea ice conditions

Parameter Data Source DescriptionNumber of events per year Site specific data Normal distribution, = 15 and = 4 Event length (km) Site specific data Amount of ice moved past the structure during an

event: Lognormal distribution with = 16 km and = 22.5 km

Ice thickness (m) Site specific data A single distribution representing both level and rafted ice. Rafted ice makes up 30% of the total ice moved past the structure annually. Gamma, = 0.45 m and = 0.089 m

Ice crushing strength (MPa)

Strice data: (Karna and Yan, 2006)

Empirical relationship derived as a function of ice thickness and contact width.

Flexural strength (MPa) Normal distribution, = 0.44 and = 0.13 Rubble porosity Uniform distribution from 0.1 to 0.3 Ice-structure coefficient of friction

Uniform distribution from 0.05 to 0.15

Maximum rubble pile height (m)

Mayne and Brown (2000) 7.59 h0.64 where h is level ice thickness (m)

Rubble cohesion (Pa) 4000Rubble internal angle of friction (deg)

45

Rubble angle of repose Slope – 10 degrees Ice-ice coefficient of friction

0.1


31

Figure 7.1 Caspian Sea: first-year level ice interactions with 100 m wide vertically-faced GBS

Figure 7.2 Caspian Sea: first-year level ice interactions with 20 m diameter column


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Figure 7.3 Caspian Sea: first-year level ice interactions with 100 m wide slope-faced GBS


33

8 REFERENCES

API, 1995, API RP 2N Recommended Practice for Planning, Designing, and Constructing Structures and Pipelines for Arctic Conditions

Bekker, A.T., 1999, The Analysis of Ice Loads on "Molikpaq" for Sakhalin Offshore Conditions. ISOPE '99. Brest. May 30-June4.

Brown, T.G., Croasdale, K. R. and Wright, B., 1996, Ice Loads on the Northumberland Strait Bridge Piers – An Approach. Proc. of 6th ISOPE Conference, Los Angeles.

C-CORE 2006 Iceberg Load Software: Theory Manual, C-CORE Report R-05-054-364 Version 3, May 2006.

Croasdale, K.R. 1980. Ice Forces on Fixed Rigid Structures.. IAHR Working Group on Ice Forces on Structures, a State-of-the-Art Report, ed. T. Carstens. CRREL Special Report No.80-26, pp 34-106

Croasdale, K.R., Cammaert, A.B. and Metge, M. 1994. A Method for the Calculation of Sheet Ice Loads on Sloping Structures. Proceedings of the IAHR'94 Symposium on Ice, Vol. 2, pp 874-875, Trondheim, Norway.

Croasdale, K. R., 1997. Ice Structure Interaction: Current State of Knowledge & Implications for Future Developments. ROA Conference, St. Petersburg, Russia.

CSA. 2004. Canadian Standards Association (CSA) CAN/CSA-S.471-04 standard "General Requirements, Design Criteria, the Environment, and Loads (part of the Code for the Design, Construction, and Installation of Fixed Offshore Structures)

Dolgopolov, Y.V., Afanasev, V.A., Korenkov, V.A. and Panfilov, D.F. (1975). Effect of Hummocked Ice on Piers of Marine Hydraulic Structures, Proceedings IAHR Symposium on Ice, pp. 469-478, Hanover, NH, U.S.A.

ISO/TC67/SC7 — Offshore structures for petroleum and natural gas industries. (ISO/TC67/SC7/WG8 — Arctic offshore structures)

Karna and Yan (2006). Analysis of the size effect in ice crushing – edition 2. Internal report, Technical Research Centre for Finland, February 2006.

Loset S.; Carstens T., 1996, Sea ice and iceberg observations in the western Barents Sea in 1987, Cold Regions Science and Technology, Volume 24, Number 4, Dec. 1996 , pp. 323-340(18)

Jordaan, I.J., C. Li, T. Mackey, A. Nobahar, and J. Bruce. 2005. Design Ice Pressure-Area Relationships; Molikpaq Data, Report prepared for Canadian Hydraulics Centre, National Research Council of Canada, Version 2.1

Mayne, D. and Brown, T., 2000, Rubble Pile Observations, Proc. 10th International Offshore and Polar Engineering Conference, Seattle, USA, p 596-599.

Masterson, D., 2008, Personal Communication


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Figure 7.3 Caspian Sea: first-year level ice interactions with 100 m wide slope-faced GBS


33

8 REFERENCES

API, 1995, API RP 2N Recommended Practice for Planning, Designing, and Constructing Structures and Pipelines for Arctic Conditions

Bekker, A.T., 1999, The Analysis of Ice Loads on "Molikpaq" for Sakhalin Offshore Conditions. ISOPE '99. Brest. May 30-June4.

Brown, T.G., Croasdale, K. R. and Wright, B., 1996, Ice Loads on the Northumberland Strait Bridge Piers – An Approach. Proc. of 6th ISOPE Conference, Los Angeles.

C-CORE 2006 Iceberg Load Software: Theory Manual, C-CORE Report R-05-054-364 Version 3, May 2006.


Croasdale, K.R., Cammaert, A.B. and Metge, M. 1994. A Method for the Calculation of Sheet Ice Loads on Sloping Structures. Proceedings of the IAHR'94 Symposium on Ice, Vol. 2, pp 874-875, Trondheim, Norway.

Croasdale, K. R., 1997. Ice Structure Interaction: Current State of Knowledge & Implications for Future Developments. ROA Conference, St. Petersburg, Russia.

CSA. 2004. Canadian Standards Association (CSA) CAN/CSA-S.471-04 standard "General Requirements, Design Criteria, the Environment, and Loads (part of the Code for the Design, Construction, and Installation of Fixed Offshore Structures)

Dolgopolov, Y.V., Afanasev, V.A., Korenkov, V.A. and Panfilov, D.F. (1975). Effect of Hummocked Ice on Piers of Marine Hydraulic Structures, Proceedings IAHR Symposium on Ice, pp. 469-478, Hanover, NH, U.S.A.

ISO/TC67/SC7 — Offshore structures for petroleum and natural gas industries. (ISO/TC67/SC7/WG8 — Arctic offshore structures)

Karna and Yan (2006). Analysis of the size effect in ice crushing – edition 2. Internal report, Technical Research Centre for Finland, February 2006.

Loset S.; Carstens T., 1996, Sea ice and iceberg observations in the western Barents Sea in 1987, Cold Regions Science and Technology, Volume 24, Number 4, Dec. 1996 , pp. 323-340(18)

Jordaan, I.J., C. Li, T. Mackey, A. Nobahar, and J. Bruce. 2005. Design Ice Pressure-Area Relationships; Molikpaq Data, Report prepared for Canadian Hydraulics Centre, National Research Council of Canada, Version 2.1

Mayne, D. and Brown, T., 2000, Rubble Pile Observations, Proc. 10th International Offshore and Polar Engineering Conference, Seattle, USA, p 596-599.

Masterson, D., 2008, Personal Communication


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Melling, H. and D.A. Riedel. 2004. Draft and Movement of Pack Ice in the Beaufort Sea: A Time-Series Presentation April 1990 - August 1999. Canadian Technical Report of Hydrography and Ocean Sciences No. 238.Masterson (2008)

MMS , 2007, Proposed Final Program, Outer Continental Shelf, Oil and Gas Leasing Program,2007-2012, April 2007, MMS Minerals Management Service, U.S. Department of the Interior, Map #4

National Snow and Ice Data Center (NSIDC, 1998), (http://nsidc.org/data/g01360.html)Naumov, A., Gudoshnikov Y., Skutina, E. 2007, Determination of the design ice ridge based on data

of expedition studies in the northeastern Barents Sea. ISOPE Nevel, D.E. 1991. Wang’s Equation For Ice Forces From Pressure Ridges. Int Cold Regions Eng

Conf, pp666-672. Sanderson, T.J.O. 1988. Ice Mechanics: Risks to Offshore Structures. Graham and Trotman Inc.,

Norwell, Massachusetts, 253p. Truskov, P. A., 1999. Metocean, Ice and Seismic Conditions Offshore Northeastern Sakhalin

Island. OTC 10816. Houston, TX, May 3-6. Vershinin, S., Truskov, P. Kuzmichev, K. 2006. Sakhalin Island – Offshore Platform and Influence

of Ice. Institute Giprostroymost. Wadhams, P. 2000. Ice in the ocean. Australia: Gordon and Breach Science Publishers. Wang, Y.S., 1984, Analysis and Model Tests of Pressure Ridges Failing Against Conical Structures,

IAHR Symposium, Hamburg Zubakin, G., Naumov, A, Buzin, I. 2004, Estimates of ice and iceberg spreading in the Barents Sea.

ISOPE

Integrated Ice Management Initiative 2000

Addendum A: Revised Plots for Grand Banks and Labrador Iceberg Loads

and Barents Sea First-Year Ridge Loads


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Melling, H. and D.A. Riedel. 2004. Draft and Movement of Pack Ice in the Beaufort Sea: A Time-Series Presentation April 1990 - August 1999. Canadian Technical Report of Hydrography and Ocean Sciences No. 238.Masterson (2008)

MMS , 2007, Proposed Final Program, Outer Continental Shelf, Oil and Gas Leasing Program,2007-2012, April 2007, MMS Minerals Management Service, U.S. Department of the Interior, Map #4

National Snow and Ice Data Center (NSIDC, 1998), (http://nsidc.org/data/g01360.html)Naumov, A., Gudoshnikov Y., Skutina, E. 2007, Determination of the design ice ridge based on data

of expedition studies in the northeastern Barents Sea. ISOPE Nevel, D.E. 1991. Wang’s Equation For Ice Forces From Pressure Ridges. Int Cold Regions Eng

Conf, pp666-672. Sanderson, T.J.O. 1988. Ice Mechanics: Risks to Offshore Structures. Graham and Trotman Inc.,

Norwell, Massachusetts, 253p. Truskov, P. A., 1999. Metocean, Ice and Seismic Conditions Offshore Northeastern Sakhalin

Island. OTC 10816. Houston, TX, May 3-6. Vershinin, S., Truskov, P. Kuzmichev, K. 2006. Sakhalin Island – Offshore Platform and Influence

of Ice. Institute Giprostroymost. Wadhams, P. 2000. Ice in the ocean. Australia: Gordon and Breach Science Publishers. Wang, Y.S., 1984, Analysis and Model Tests of Pressure Ridges Failing Against Conical Structures,

IAHR Symposium, Hamburg Zubakin, G., Naumov, A, Buzin, I. 2004, Estimates of ice and iceberg spreading in the Barents Sea.

ISOPE


Addendum A: Revised Plots for Grand Banks and Labrador Iceberg Loads

and Barents Sea First-Year Ridge Loads


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A.1 INTRODUCTION

Following the use of the data presented in the body of this report for the calibration analysis, anomalies were found in the results for Grand Banks and Labrador Sea icebergs, and First Year Ridge interactions for the Barents Sea. The data were revised and a new set of load distribution curves were generated. These are presented in this Addendum.


A-3

A.2 REVISED LOAD DISTRIBUTION PLOTS




0.08

Waterline length, L (m) C-CORE (2006) Exponential distribution f(x) = (1/) exp((x-/) = 44 m = 15 m resample if value is greater than 400 m

Significant wave height (m) AES40 (2000) Site specific empirical distribution Mass, M (tonnes) C-CORE (2006) M = 1.05L2.68 exp(e), where e = N(0,0.61)Draft, D (m) C-CORE (2006) D = 3.14L0.68 exp(e), where e = N(0,0.25) Width, W (m) C-CORE (2006) W = 0.005 ×L-2.28×D4.65

Drift speed (m/s) C-CORE (2006) Probabilistic model with drift speed as a function of length and significant wave height. The mean drift speed for all iceberg sizes and sea states is 0.33 m/s.


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A-2

A.1 INTRODUCTION

Following the use of the data presented in the body of this report for the calibration analysis, anomalies were found in the results for Grand Banks and Labrador Sea icebergs, and First Year Ridge interactions for the Barents Sea. The data were revised and a new set of load distribution curves were generated. These are presented in this Addendum.


A-3

A.2 REVISED LOAD DISTRIBUTION PLOTS




0.08


Significant wave height (m) AES40 (2000) Site specific empirical distribution Mass, M (tonnes) C-CORE (2006) M = 1.05L2.68 exp(e), where e = N(0,0.61)Draft, D (m) C-CORE (2006) D = 3.14L0.68 exp(e), where e = N(0,0.25) Width, W (m) C-CORE (2006) W = 0.005 ×L-2.28×D4.65

Drift speed (m/s) C-CORE (2006) Probabilistic model with drift speed as a function of length and significant wave height. The mean drift speed for all iceberg sizes and sea states is 0.33 m/s.


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A-4


A-5




2.0 (Makkovik Bank)


Significant wave height (m) MSC50 (2008) Site specific empirical distribution, Meteorological Service of Canada

Mass, M (tonnes) C-CORE (2006) M = 1.05L2.68 exp(e), where e = N(0,0.61) Draft, D (m) C-CORE (2006) D = 3.14L0.68 exp(e), where e = N(0,0.25) Width, W (m) C-CORE (2006) W = 0.005 ×L-2.28×D4.65

Drift speed (m/s) Labrador Strategic Environmental Assessment (2008)



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A-4


A-5




2.0 (Makkovik Bank)


Significant wave height (m) MSC50 (2008) Site specific empirical distribution, Meteorological Service of Canada

Mass, M (tonnes) C-CORE (2006) M = 1.05L2.68 exp(e), where e = N(0,0.61) Draft, D (m) C-CORE (2006) D = 3.14L0.68 exp(e), where e = N(0,0.25) Width, W (m) C-CORE (2006) W = 0.005 ×L-2.28×D4.65

Drift speed (m/s) Labrador Strategic Environmental Assessment (2008)



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Figure 4.3 Labrador Sea: iceberg interactions with 100 m diameter GBS

Figure 4.4 Labrador Sea: iceberg interactions with 50 m wide FPSO

A-6


Figure 6.3 Barents Sea; first-year ridge interactions with 100 m diameter vertically-sided floater

Figure 6.4 Barents Sea; first-year ridge interactions with 50 m wide FPSO

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Figure 4.3 Labrador Sea: iceberg interactions with 100 m diameter GBS

Figure 4.4 Labrador Sea: iceberg interactions with 50 m wide FPSO

A-6


Figure 6.3 Barents Sea; first-year ridge interactions with 100 m diameter vertically-sided floater

Figure 6.4 Barents Sea; first-year ridge interactions with 50 m wide FPSO

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Addendum B: Response to Comments on ISO/DIS 19906 Calibration Draft Report


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B.1 INTRODUCTION

Some of the comments by TP10 on the report ISO/DIS 19906 Calibration Draft Report May-June, 2009related to inputs provided by C-CORE in an initial report provided in February. Specific answers to those comments are given in this Addendum.


B-3

B.2 RESPONSE TO COMMENTS

Item 4 of Section “Issues that need to be checked and or clarified in the report, perhaps by some re-analysis”

Table 9: the number of MY ice interactions per year for the Beaufort Sea for GV and GC are very different, is there an error in the GC numbers?

As Marc Maes indicated: the number n in Table 9 is not an annual number of ice interactions – these are in Table 8 instead! The n in Table 8 is the sample size and it matches the electronic C-CORE data input sets.

Longer simulations were used for some runs to better define the tails of the some distributions where the relationship between annual maximum load and negative log base 10 of the probability of exceedance appeared to be non-linear.

Section 3 - Item 2 – Key Assumptions that Should be Summarized.

The general shape of the load hazard curve will not substantially change from that reported by C-CORE if different load methods or different input distributions are used.

Yes. A range of load scenarios (regions, ice types and structure types) were considered and current approaches were used to estimate distributions for annual maximum loads. These resulted in action factors of 1.35 or less, with the exception of multi-year impacts with conical structures and first-year ridge loads in the Barents Sea. For multi-year impacts with conical structures, it is believed that present methods are overly conservative because scaling of flexural strength is not taken into consideration. In the case of first-year ridge loads in the Barents Sea, following a number of necessary input modifications, the tails are significantly less ‘heavy’. We cannot guarantee the general shapes of the load hazard curves will not change; but in our judgment, given appropriate models and inputs, the shapes should not change significantly. Reconsideration would be required if fundamentally different assumptions are applied, for example if a load distribution accounting for reduced loads as a result of ice management is considered.

An FPSO was treated as a fixed structure. The flexibility and capacity of the mooring system was not considered.

Yes.

Load on a multi-leg structure was based on simulating a single column. The leg factor was not specified. Jamming between the legs and loading of the base were not considered.

Yes.


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B-2

B.1 INTRODUCTION

Some of the comments by TP10 on the report ISO/DIS 19906 Calibration Draft Report May-June, 2009related to inputs provided by C-CORE in an initial report provided in February. Specific answers to those comments are given in this Addendum.


B-3

B.2 RESPONSE TO COMMENTS

Item 4 of Section “Issues that need to be checked and or clarified in the report, perhaps by some re-analysis”

Table 9: the number of MY ice interactions per year for the Beaufort Sea for GV and GC are very different, is there an error in the GC numbers?

As Marc Maes indicated: the number n in Table 9 is not an annual number of ice interactions – these are in Table 8 instead! The n in Table 8 is the sample size and it matches the electronic C-CORE data input sets.

Longer simulations were used for some runs to better define the tails of the some distributions where the relationship between annual maximum load and negative log base 10 of the probability of exceedance appeared to be non-linear.

Section 3 - Item 2 – Key Assumptions that Should be Summarized.

The general shape of the load hazard curve will not substantially change from that reported by C-CORE if different load methods or different input distributions are used.

Yes. A range of load scenarios (regions, ice types and structure types) were considered and current approaches were used to estimate distributions for annual maximum loads. These resulted in action factors of 1.35 or less, with the exception of multi-year impacts with conical structures and first-year ridge loads in the Barents Sea. For multi-year impacts with conical structures, it is believed that present methods are overly conservative because scaling of flexural strength is not taken into consideration. In the case of first-year ridge loads in the Barents Sea, following a number of necessary input modifications, the tails are significantly less ‘heavy’. We cannot guarantee the general shapes of the load hazard curves will not change; but in our judgment, given appropriate models and inputs, the shapes should not change significantly. Reconsideration would be required if fundamentally different assumptions are applied, for example if a load distribution accounting for reduced loads as a result of ice management is considered.

An FPSO was treated as a fixed structure. The flexibility and capacity of the mooring system was not considered.

Yes.

Load on a multi-leg structure was based on simulating a single column. The leg factor was not specified. Jamming between the legs and loading of the base were not considered.

Yes.


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For the Barents Sea, icebergs and first-year ridges were considered separately. The method of combining the two load hazard curves was not addressed.

Yes. A combined curve could easily be determined assuming iceberg and sea ice loads are essentially independent.

Section 7

Items 3, 4 and 5

Results for Caspian Sea do not appear to reflect the physical limit on ice that is expected and this needs to be addressed (and discussed with C-CORE as needed). For the Caspian, the design ice feature, first year level ice (FYL), has a physical limit to its thickness due to the milder winter air temperature. This limit is not reflected in the curve shown in Figure 5, where the curve increases linearly. Realistically, the Caspian curve should look like the curve for Sakhalin, which clearly shows a physical limit on ice action.

This same comment and question above also applies to Figure 6 that for the conical structure shows a linearly increasing for the Caspian Sea and Sakhalin. As explained above these regions are where there is a physical limit to the ice features.

Ditto for Figures 8 and 9.

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For the Barents Sea, icebergs and first-year ridges were considered separately. The method of combining the two load hazard curves was not addressed.

Yes. A combined curve could easily be determined assuming iceberg and sea ice loads are essentially independent.

Section 7

Items 3, 4 and 5

Results for Caspian Sea do not appear to reflect the physical limit on ice that is expected and this needs to be addressed (and discussed with C-CORE as needed). For the Caspian, the design ice feature, first year level ice (FYL), has a physical limit to its thickness due to the milder winter air temperature. This limit is not reflected in the curve shown in Figure 5, where the curve increases linearly. Realistically, the Caspian curve should look like the curve for Sakhalin, which clearly shows a physical limit on ice action.

This same comment and question above also applies to Figure 6 that for the conical structure shows a linearly increasing for the Caspian Sea and Sakhalin. As explained above these regions are where there is a physical limit to the ice features.

Ditto for Figures 8 and 9.

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Figures 5, 6 and 8 compare loads at different sites for 100 m wide vertically-sided structures, 100 m wide slope-sided structures and 20 m wide vertically-sided structures respectively. The slopes shown reflect the analysis done by C-CORE. Figure 9 compares loads at different sites for multi-legged structures (C-CORE did not explicitly conduct analyses for multi-legged structures).

The reviewer indicates that both the Caspian and offshore Sakhalin regions will be subject to limited ice growth (and hence ice thickness) and should therefore see the tail of the distribution (negative log base 10 probability of exceedence versus annual maximum load) have an increasing downward slope as annual maximum load increases. This is seen only for the 100 m wide vertically-sided structure off Sakhalin. For all three structures in the Caspian and for the slope-faced 100 m wide structure off Sakhalin, the tail of the annual maximum load distribution is linear. For the 20 m wide vertically-sided structure off Sakhalin, the downward slope becomes smaller as annual maximum load increases.

There are several differences in the modeling assumptions and input parameters describing ice conditions used for the Caspian and Sakhalin and the different structures that affect the load distributions:

a) The main loading feature considered for Sakhalin is first-year ridges while in the Caspian; it is first-year level ice. Ice is known to be highly ridged off Sakhalin, whereas in the Caspian, the drafts of ridges are limited by the shallow water depth. This has significant effects on the load curves as discussed below.

b) For the Sakhalin load case, first-year ice thickness was modeled by a rectangular distribution from 0.4 to 1.7 m. The thickness of the consolidated portions of ridges is taken as a multiple of the surrounding level ice thickness; where the multiplier is drawn from a triangular distribution from 1 to 1.9 with the mode at 1. Rafted ice was not included in the distribution. For the Caspian, first-year ice thickness was modeled by a gamma distribution with a mean of 0.45 m and a standard deviation of 0.089 m. The distribution

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included rafted ice, giving the distribution a tail at the upper end. Rafted ice is more extensive in the Caspian than off Sakhalin, where there is more ridging.

c) In the Caspian, level ice interacting with vertically-faced structures is assumed to fail through crushing. The ice crushing model treats the strength as a random parameter that varies with penetration, reduces with ice thickness, and has a reduction in peak strength with contact width. The same strength is assumed (conservatively) for rafted ice as for non-rafted ice. For sloped structures, initial failure is assume to be through ride-up. Once sufficient rubble develops that grounding occurs, subsequent loading is modeled as crushing against the grounded rubble pile and transferred to the structure. The annual maximum loads were found to be associated with the latter mode and the tails of the annual maximum load distributions were linear for all three structures.

d) Sensitivity analyses have been applied for the Caspian 100 m vertically-sided structure. Figure B-1 shows the effect of applying different uniform thickness distributions. It is seen that the slope of the tail of the annual maximum load exceedence curve falls off more quickly for the uniform distributions than the default gamma distribution, but the tails still appear linear. Figure B-2 shows the effect of applying different constant ice strength models. The slopes fall off much more quickly than when a random ice strength model is used, but again the tails are linear. Figure B-3 shows the effect of applying both a uniform thickness distribution and different constant ice strength models. The tails of the distributions are vertical as associated with a constant contact area and constant crushing strength.

e) In modeling ridge interactions with vertically-faced structures offshore Sakhalin, the ridges are idealized as a consolidated layer that fails through crushing and an unconsolidated layer that fails through local and global plug failure. The consolidated layer thickness is modeled by a random factor times the surrounding level ice thickness. The CSA ice crushing strength model is used for the consolidated portion of ridges offshore Sakhalin; this model treats the ice strength as deterministic rather than random, but accounts for lower strengths over large contact widths. The model is an upper bound solution and hence is conservative. Accounting for the randomness in ice strength would tend to make the tail of the annual maximum load linear.

f) For conical structures, the load associated with the consolidated ridge layer is largely influenced by the height of the rubble pile formed. For the 100 m conical structure, this appears to dominate, such that the annual load distribution tail is linear.

g) The failure model for the unconsolidated ridge layer considers the possibility of both local and global plug failure at each penetration. The failure load associated with local plug failure depends largely on the contact width and local ridge thicknesses. The failure load associated with global plug failure depends more on the extent of remaining intact ridge in front of the structure (i.e. the width of the ridge). For narrow structures, the failure load associated with the global plug failure mode of the unconsolidated ridge layer therefore becomes relatively more important, and tends to make the downward slope of the annual load distribution tail increase with annual maximum load.


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Figures 5, 6 and 8 compare loads at different sites for 100 m wide vertically-sided structures, 100 m wide slope-sided structures and 20 m wide vertically-sided structures respectively. The slopes shown reflect the analysis done by C-CORE. Figure 9 compares loads at different sites for multi-legged structures (C-CORE did not explicitly conduct analyses for multi-legged structures).

The reviewer indicates that both the Caspian and offshore Sakhalin regions will be subject to limited ice growth (and hence ice thickness) and should therefore see the tail of the distribution (negative log base 10 probability of exceedence versus annual maximum load) have an increasing downward slope as annual maximum load increases. This is seen only for the 100 m wide vertically-sided structure off Sakhalin. For all three structures in the Caspian and for the slope-faced 100 m wide structure off Sakhalin, the tail of the annual maximum load distribution is linear. For the 20 m wide vertically-sided structure off Sakhalin, the downward slope becomes smaller as annual maximum load increases.

There are several differences in the modeling assumptions and input parameters describing ice conditions used for the Caspian and Sakhalin and the different structures that affect the load distributions:

a) The main loading feature considered for Sakhalin is first-year ridges while in the Caspian; it is first-year level ice. Ice is known to be highly ridged off Sakhalin, whereas in the Caspian, the drafts of ridges are limited by the shallow water depth. This has significant effects on the load curves as discussed below.

b) For the Sakhalin load case, first-year ice thickness was modeled by a rectangular distribution from 0.4 to 1.7 m. The thickness of the consolidated portions of ridges is taken as a multiple of the surrounding level ice thickness; where the multiplier is drawn from a triangular distribution from 1 to 1.9 with the mode at 1. Rafted ice was not included in the distribution. For the Caspian, first-year ice thickness was modeled by a gamma distribution with a mean of 0.45 m and a standard deviation of 0.089 m. The distribution

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included rafted ice, giving the distribution a tail at the upper end. Rafted ice is more extensive in the Caspian than off Sakhalin, where there is more ridging.

c) In the Caspian, level ice interacting with vertically-faced structures is assumed to fail through crushing. The ice crushing model treats the strength as a random parameter that varies with penetration, reduces with ice thickness, and has a reduction in peak strength with contact width. The same strength is assumed (conservatively) for rafted ice as for non-rafted ice. For sloped structures, initial failure is assume to be through ride-up. Once sufficient rubble develops that grounding occurs, subsequent loading is modeled as crushing against the grounded rubble pile and transferred to the structure. The annual maximum loads were found to be associated with the latter mode and the tails of the annual maximum load distributions were linear for all three structures.

d) Sensitivity analyses have been applied for the Caspian 100 m vertically-sided structure. Figure B-1 shows the effect of applying different uniform thickness distributions. It is seen that the slope of the tail of the annual maximum load exceedence curve falls off more quickly for the uniform distributions than the default gamma distribution, but the tails still appear linear. Figure B-2 shows the effect of applying different constant ice strength models. The slopes fall off much more quickly than when a random ice strength model is used, but again the tails are linear. Figure B-3 shows the effect of applying both a uniform thickness distribution and different constant ice strength models. The tails of the distributions are vertical as associated with a constant contact area and constant crushing strength.

e) In modeling ridge interactions with vertically-faced structures offshore Sakhalin, the ridges are idealized as a consolidated layer that fails through crushing and an unconsolidated layer that fails through local and global plug failure. The consolidated layer thickness is modeled by a random factor times the surrounding level ice thickness. The CSA ice crushing strength model is used for the consolidated portion of ridges offshore Sakhalin; this model treats the ice strength as deterministic rather than random, but accounts for lower strengths over large contact widths. The model is an upper bound solution and hence is conservative. Accounting for the randomness in ice strength would tend to make the tail of the annual maximum load linear.

f) For conical structures, the load associated with the consolidated ridge layer is largely influenced by the height of the rubble pile formed. For the 100 m conical structure, this appears to dominate, such that the annual load distribution tail is linear.

g) The failure model for the unconsolidated ridge layer considers the possibility of both local and global plug failure at each penetration. The failure load associated with local plug failure depends largely on the contact width and local ridge thicknesses. The failure load associated with global plug failure depends more on the extent of remaining intact ridge in front of the structure (i.e. the width of the ridge). For narrow structures, the failure load associated with the global plug failure mode of the unconsolidated ridge layer therefore becomes relatively more important, and tends to make the downward slope of the annual load distribution tail increase with annual maximum load.


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h) A large average annual impact rate was modeled for Sakhalin. This had the result that the upper limit for the rectangular distribution has a larger influence in causing the tail of the load distribution to drop off than would be the case if there were fewer impacts. An argument could be made for reducing the number of significant impacts for Sakhalin since many of the floes are quite small and much smaller loads will result if the floes can move around the structure.

In conclusion, the behaviour of the different structures at the two locations appears to result in part because of differences in ice conditions and in part because of differences in model assumptions. In the Caspian, the dominant loads result from level ice, and increased thickness associated with rafting could be an issue if the rafted ice is as strong as non-rafted ice. Because of the shallow water, the peak loads associated with sloped structures will be dominated by crushing against grounded rubble formed in front of the structure (with a portion of the load transmitted to the structure). Random variations in crushing pressure appear to have a larger influence on the shape of the tail than variations in ice thickness.

Offshore Sakhalin, ridged ice is more prevalent. The unconsolidated layer of first-year ridges fails in a different manner than the consolidated layer and may have a greater importance for narrow structures, resulting in differences in the shapes of tails. For sloped structures, the height of rubble formed during ride-up plays an important role. In modeling ice crushing of the consolidated layer for structures off Sakhalin, random variations in ice strength were not considered. This appears to cause the tail of the annual maximum load distribution to have an increasing downward slope as annual maximum load increases. Accounting for random variations in ice strength may result in a more linear tails for the larger diameter structure, and would likely influence the shape of the distribution tail for smaller diameter structures.


Figure B-1 Annual Maximum Load Distribution for 100 m Wide Vertically-Sided Structure in Caspian with Different Thickness Models (Top: Annual Maximum Load; Bottom: Normalized Annual Maximum Load)

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h) A large average annual impact rate was modeled for Sakhalin. This had the result that the upper limit for the rectangular distribution has a larger influence in causing the tail of the load distribution to drop off than would be the case if there were fewer impacts. An argument could be made for reducing the number of significant impacts for Sakhalin since many of the floes are quite small and much smaller loads will result if the floes can move around the structure.

In conclusion, the behaviour of the different structures at the two locations appears to result in part because of differences in ice conditions and in part because of differences in model assumptions. In the Caspian, the dominant loads result from level ice, and increased thickness associated with rafting could be an issue if the rafted ice is as strong as non-rafted ice. Because of the shallow water, the peak loads associated with sloped structures will be dominated by crushing against grounded rubble formed in front of the structure (with a portion of the load transmitted to the structure). Random variations in crushing pressure appear to have a larger influence on the shape of the tail than variations in ice thickness.

Offshore Sakhalin, ridged ice is more prevalent. The unconsolidated layer of first-year ridges fails in a different manner than the consolidated layer and may have a greater importance for narrow structures, resulting in differences in the shapes of tails. For sloped structures, the height of rubble formed during ride-up plays an important role. In modeling ice crushing of the consolidated layer for structures off Sakhalin, random variations in ice strength were not considered. This appears to cause the tail of the annual maximum load distribution to have an increasing downward slope as annual maximum load increases. Accounting for random variations in ice strength may result in a more linear tails for the larger diameter structure, and would likely influence the shape of the distribution tail for smaller diameter structures.


Figure B-1 Annual Maximum Load Distribution for 100 m Wide Vertically-Sided Structure in Caspian with Different Thickness Models (Top: Annual Maximum Load; Bottom: Normalized Annual Maximum Load)

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Figure B-2 Annual Maximum Load Distribution for 100 m Wide Vertically-Sided Structure in Caspian with Different Constant Strength Models (Top: Annual Maximum Load; Bottom: Normalized Annual Maximum Load)

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Figure B-3 Annual Maximum Load Distribution for 100 m Wide Vertically-Sided Structure in the Caspian Sea with Ice Thickness Modeled with a Uniform Distribution from 10 to 75 cm and Different Constant Strength Models (Top: Annual Maximum Load; Bottom: Normalized Annual Maximum Load)

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Figure B-2 Annual Maximum Load Distribution for 100 m Wide Vertically-Sided Structure in Caspian with Different Constant Strength Models (Top: Annual Maximum Load; Bottom: Normalized Annual Maximum Load)

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Figure B-3 Annual Maximum Load Distribution for 100 m Wide Vertically-Sided Structure in the Caspian Sea with Ice Thickness Modeled with a Uniform Distribution from 10 to 75 cm and Different Constant Strength Models (Top: Annual Maximum Load; Bottom: Normalized Annual Maximum Load)

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Annex B

Calibration analysis of action factors for ISO 19906 Arctic offshore structures

Calibration analysis of action factors for ISO 19906 Arctic offshore structures

Final Report submitted to the International Association of Oil and Gas Producers

by Marc A. Maes, Aleatec Advisory Services, October 2009

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Calibration Analysis of Action Factors for ISO 19906 Arctic Offshore Structures Final Report (Draft: April 13, 2009; revised: July 16, 2009; second revision: October 2, 2009) Marc A. Maes, PhD, PEng Aleatec Advisory Services 501, 1731 – 9A Street SW Calgary, Alberta. T2T 3E7 Canada [email protected] Submitted to the: International Association of Oil and Gas Producers Alf Reidar Johansen, OGP Standards Manager Graham AN Thomas, BP, OGP Steering Committee Leader


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Calibration Analysis of Action Factors for ISO 19906 Arctic Offshore Structures Final Report (Draft: April 13, 2009; revised: July 16, 2009; second revision: October 2, 2009) Marc A. Maes, PhD, PEng Aleatec Advisory Services 501, 1731 – 9A Street SW Calgary, Alberta. T2T 3E7 Canada [email protected] Submitted to the: International Association of Oil and Gas Producers Alf Reidar Johansen, OGP Standards Manager Graham AN Thomas, BP, OGP Steering Committee Leader


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Table of Contents Executive Summary 3 1. Background and Objectives 6 2. What is Code Calibration? 7 3. Mandate and Restrictions 9 4. Ultimate Limit States and Abnormal Limit States 11 5. Calibration Procedure 13 6. Probabilistic Models 18 6.1 Resistance R 18 6.2 Permanents Action G 19 6.3 Variable Actions Q 19 6.4 Ice Actions I 21 6.5 Other Environmental Actions E 21 6.6 Action Effect Ratios 23 7. Probabilistic Ice Action Models 24 7.1 Regionalization 24 7.2 (S, H) Tail Models 29 7.3 Ice Action Model Uncertainties 38 8. Action Factors (Environmental and Ice): Results and Verification 40 9. Companion Action Factors (Environmental and Ice): Results and Verification 49 10. Exposure Levels L2 and L3 56 11. Summary of Calibrated Design Check Equations 59 References 60 Acknowledgement 61 Appendix A: Probabilistic Tail Models for Action Effects 62 Appendix B: Region- and Structure Specific Ice Action Effects: Tail Distributions 69 Appendix C: Barents Sea Ice Loads based on Updated C-CORE Data 77


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Table of Contents Executive Summary 3 1. Background and Objectives 6 2. What is Code Calibration? 7 3. Mandate and Restrictions 9 4. Ultimate Limit States and Abnormal Limit States 11 5. Calibration Procedure 13 6. Probabilistic Models 18 6.1 Resistance R 18 6.2 Permanents Action G 19 6.3 Variable Actions Q 19 6.4 Ice Actions I 21 6.5 Other Environmental Actions E 21 6.6 Action Effect Ratios 23 7. Probabilistic Ice Action Models 24 7.1 Regionalization 24 7.2 (S, H) Tail Models 29 7.3 Ice Action Model Uncertainties 38 8. Action Factors (Environmental and Ice): Results and Verification 40 9. Companion Action Factors (Environmental and Ice): Results and Verification 49 10. Exposure Levels L2 and L3 56 11. Summary of Calibrated Design Check Equations 59 References 60 Acknowledgement 61 Appendix A: Probabilistic Tail Models for Action Effects 62 Appendix B: Region- and Structure Specific Ice Action Effects: Tail Distributions 69 Appendix C: Barents Sea Ice Loads based on Updated C-CORE Data 77

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Executive Summary This report describes the results of a calibration of partial action factors for environmental actions in order to provide a basis for determining the action combinations for ISO 19906 Arctic offshore structures. The report also provides detailed guidance on a calibration method should the user of ISO 19906 wish to perform a site-specific or structure-specific calibration using a fully probabilistic approach. This objective is in itself quite important as ISO/DIS 19906:2009 permits such an approach when the potential economic benefits of performing a site-specific calibration are likely to be considerable for large arctic offshore installations (Section 1). The calibration focuses on environmental action factors and various companion action factors for exposure levels L1, L2 and L3. It does not include gravity loads, variable actions, earthquakes or resistance (Section 3). There is considerable emphasis on the modeling and the calibration of ice action processes. The calibration also accounts for the distinction between ultimate limit states (ULS) and abnormal limit states (ALS) as it affects action factors, specified annual probabilities of exceedance, companion factors involving extreme level actions, abnormal level actions, or both, and the inclusion of system robustness/energy dissipation capacity for the abnormal limit states (see Section 4). Two basic sets of design check equations are considered: Set I based on ISO 19902:2007 and Set II based on the current suggestions in ISO/DIS 19906 and CAN/CSA-S471-04 (see Table 1). The calibration involves both a weighted optimization based on getting the logs of limit state failure probabilities to lie as closely as possible to the stated L1, L2 and L3 targets, as well as checks that upper bound failure probability constraints are not violated (see Figures 1a, 1b, and 1c). The calibration accounts for weighted combinations of all action effects in various proportions, for different resistance models, for different levels of action effect model uncertainties, for different levels of statistical and aleatory uncertainty, and for different mean action event occurrence rates. Weights were validated by the ISO panel TP10 of world experts. State-of-the-art probabilistic models (Section 6) are used for various types of load processes, including variable-in-time action effects for variable actions of long/short duration, and environmental actions. Resistance is conservatively based on the use of minimum required design resistance and on a factored design resistance not exceeding the 1%-ile of actual resistance for both ULS and ALS (Section 6.1). Ice actions are regionalized on the basis of uncertainty characterization of extreme action effects (tails and extreme values). This is done with respect to both geographical region and type of structure (Tables 5, 6 and 7). The quantitative probabilistic analysis of ice action effects (Tables 9, 10 and 11) is based on Q-distributions which are parameterized in terms of a slope factor S and a tail heaviness factor H both of which have a direct bearing on ice action factors (Section 7.2 and Appendix A). It is the characterization of the probabilistic ice


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action models and not the actual values of ice actions that govern the partial action factors. Therefore regions with different ice action magnitudes can be considered together if their probabilistic description is similar. Four calibration scenarios are used for ice actions:

– calibration of separate principal ice action factors for each combination of region and type of structure (Table 12).

– calibration of region-wide ice action factors (Table 12 in red).

– calibration of one overall principal ice action factor (Table 12 in

blue).

– inclusion of ice actions in the larger group of all environmental actions.

All four scenarios lead to reasonable action factors that are consistent with ice type and structure type. While for conical structures the 100-year design action effects are considerably less than for vertically sided structures, they increase at a greater rate and therefore require larger principal action factors to meet the reliability targets. Note that this effect disappears for L2 and L3 since the 100-year design action effects are much closer to the minimum required resistance, hence the effects of tail slope and heaviness tend to be less severe (Section 10). The character of the input design action effects for sloping and conical structures merits further investigation. If the results are accepted, then an exception must be made for L1 structure types GC and FC (Table 1) if one is to follow the second or the third calibration scenario above (Table 12). When considering the second calibration scenario above, region-specific action factors are highest for Beaufort-type zones (γI = 1.30), lowest for Sakhalin-type zones (γI = 1.20) and “in-between” for Caspian-type zones (γI = 1.25). Under the third calibration scenario above, the all-ice action factor γI would be 1.30 except that 1.55 should be used for conically sided structures. The calibration of the prescribed annual exceedance probability for the abnormal level ice action PE is very consistent over all regions (Barents, Grand Banks, Labrador), having a value PE = 10-3.8, which corresponds approximately to a 6300 year unfactored design action effect. Various verification and sensitivity studies are performed and shown in this report. A typical two-by-two action effect combination diagram is shown in Figure 24 for Beaufort Sea type ice actions in combination with permanent actions. Minimum required action factors are shown for ULS in Figures 25-27 and for ALS in Figure 28. In all cases the calibrated action factors for both Set I and Set II perform very well with Set I factors being more conservative in load combinations involving small environmental/ice action proportions and Set II failure probabilities more clustered around their ULS and ALS targets.

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The multitude of environmental/ice companion factors (Table 13) is reduced to just 4 companion action factors (Table 14) each of which is subsequently calibrated for L1:

– an ULS companion action factor ψEI for two independent or very weakly correlated continuous environmental processes: 0.60 (calibrated and verified).

– an ULS companion action factor ψED for two strongly dependent or

correlated continuous environmental processes, suggested to be 0.85 (as discussed in Section 9 this companion factor depends strongly on the specific characteristics of the dependency structure between the two actions).

– an ALS companion action factor ψAD involving a discrete principal

process and a continuous companion environmental process which can be treated as independent: 0.35 (best estimate, verified).

– an ALS companion action factor ψAI involving a discrete principal

process and a continuous companion environmental process which are assumed to be strongly dependent: 0.45 (best estimate, verified).

An overview of calibrated action factors and companion factors for L1 is provided in Table 15. A calibration of L2 and L3 factors results in the principal action factors shown in Tables 16 and 17. Environmental and ice action factors decrease to as much as 1.10 (L2) and 0.85 (L3). It is observed that principal ice action factors and principal environmental action factors converge to the same (decreased) values. This is due to the fact that most of the failure probability now accumulates in an area that is much closer to the representative value of the actions (which remains at the 1% annual exceedance level). For the same reason the difference in the ice action factors for vertically sided and conically sided structures also disappears with increasing level of exposure (increasing tolerable risk). A summary of all calibrated design check equations and companion action factors (ULS, ALS, L1, L2, L3) is given in Table 18 for both Set I and Set II.


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action models and not the actual values of ice actions that govern the partial action factors. Therefore regions with different ice action magnitudes can be considered together if their probabilistic description is similar. Four calibration scenarios are used for ice actions:

– calibration of separate principal ice action factors for each combination of region and type of structure (Table 12).

– calibration of region-wide ice action factors (Table 12 in red).

– calibration of one overall principal ice action factor (Table 12 in

blue).

– inclusion of ice actions in the larger group of all environmental actions.

All four scenarios lead to reasonable action factors that are consistent with ice type and structure type. While for conical structures the 100-year design action effects are considerably less than for vertically sided structures, they increase at a greater rate and therefore require larger principal action factors to meet the reliability targets. Note that this effect disappears for L2 and L3 since the 100-year design action effects are much closer to the minimum required resistance, hence the effects of tail slope and heaviness tend to be less severe (Section 10). The character of the input design action effects for sloping and conical structures merits further investigation. If the results are accepted, then an exception must be made for L1 structure types GC and FC (Table 1) if one is to follow the second or the third calibration scenario above (Table 12). When considering the second calibration scenario above, region-specific action factors are highest for Beaufort-type zones (γI = 1.30), lowest for Sakhalin-type zones (γI = 1.20) and “in-between” for Caspian-type zones (γI = 1.25). Under the third calibration scenario above, the all-ice action factor γI would be 1.30 except that 1.55 should be used for conically sided structures. The calibration of the prescribed annual exceedance probability for the abnormal level ice action PE is very consistent over all regions (Barents, Grand Banks, Labrador), having a value PE = 10-3.8, which corresponds approximately to a 6300 year unfactored design action effect. Various verification and sensitivity studies are performed and shown in this report. A typical two-by-two action effect combination diagram is shown in Figure 24 for Beaufort Sea type ice actions in combination with permanent actions. Minimum required action factors are shown for ULS in Figures 25-27 and for ALS in Figure 28. In all cases the calibrated action factors for both Set I and Set II perform very well with Set I factors being more conservative in load combinations involving small environmental/ice action proportions and Set II failure probabilities more clustered around their ULS and ALS targets.

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The multitude of environmental/ice companion factors (Table 13) is reduced to just 4 companion action factors (Table 14) each of which is subsequently calibrated for L1:

– an ULS companion action factor ψEI for two independent or very weakly correlated continuous environmental processes: 0.60 (calibrated and verified).

– an ULS companion action factor ψED for two strongly dependent or

correlated continuous environmental processes, suggested to be 0.85 (as discussed in Section 9 this companion factor depends strongly on the specific characteristics of the dependency structure between the two actions).

– an ALS companion action factor ψAD involving a discrete principal

process and a continuous companion environmental process which can be treated as independent: 0.35 (best estimate, verified).

– an ALS companion action factor ψAI involving a discrete principal

process and a continuous companion environmental process which are assumed to be strongly dependent: 0.45 (best estimate, verified).

An overview of calibrated action factors and companion factors for L1 is provided in Table 15. A calibration of L2 and L3 factors results in the principal action factors shown in Tables 16 and 17. Environmental and ice action factors decrease to as much as 1.10 (L2) and 0.85 (L3). It is observed that principal ice action factors and principal environmental action factors converge to the same (decreased) values. This is due to the fact that most of the failure probability now accumulates in an area that is much closer to the representative value of the actions (which remains at the 1% annual exceedance level). For the same reason the difference in the ice action factors for vertically sided and conically sided structures also disappears with increasing level of exposure (increasing tolerable risk). A summary of all calibrated design check equations and companion action factors (ULS, ALS, L1, L2, L3) is given in Table 18 for both Set I and Set II.


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Background and Objectives

In January 2009, the DIS version of ISO 19906 (2009) was issued. This new standard focuses on action effects typical for arctic offshore structures. It contains normative clauses with respect to reliability, risk and consequences, but it does not provide definitive partial action factors for its limit states design approach. The objective of the work described in this report is to perform a calibration of the environmental action factors for exposure level L1 in order to ensure that the specified target reliability of (1– 10-5) for each ULS and ALS action combination is achieved for circumstances that can reasonably be foreseen. A secondary objective is to also recommend calibrated environmental action factors for L2 and L3. In addition to these objectives, the report provides detailed guidance on a recommended calibration method should the user of ISO 19906 wish to perform a site-specific or structure-specific calibration using a fully probabilistic approach. This objective is in itself quite important as ISO/DIS 19906:2009 permits such an approach when the potential economic benefits of performing a site-specific calibration are likely to be considerable for large arctic offshore installations.

Unique features of the current calibration procedure include:

– the fundamental distinction between ultimate limit states (ULS) and the abnormal limit state (ALS) and the resulting distinctive treatment of extreme and abnormal design actions

– the special emphasis on ice loading and its implication on specific spatial

and temporal modeling issues

– the consideration of arctic offshore regions, of distinct types of ice, and of selected arctic structural systems, and the resulting weighted non-linear constrained optimization that underlies the basic calibration of action factors

– the use of a specified principal/companion action framework for deriving

characteristic values of design actions The present study has been coordinated and supervised by Dr. Marc A. Maes of Aleatec Advisory Services, Calgary, who previously coordinated the calibration of the 1986 and 2003 versions of CSA-S471 (offshore structures), and was involved in the development of ISO 2394, the development of the Joint Committee of Structural Safety (JCSS) probabilistic model code, the calibration and the codification of various LSD standards for tubing and casing design, as well as several site-specific and/or structure-specific load and resistance factor calibrations.

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What is Code Calibration?

Code calibration is based on a standardized process which is outlined in various documents such as ISO 2394 (1998) and several JCSS publications (JCSS, 2001). All aspects of this process have been strictly adhered to. Probabilistic models for load and resistance were based on the “probabilistic model code” (JCSS, 2007) which is available at the international website of the JCSS in Zürich. All modern design codes are based on design check equations on the basis of which a notional reliability verification of a given design can conveniently be performed, using a simple comparison of resistances and loads and/or load effects. Code calibration can be performed by judgment, fitting, optimization or a combination of these (Madsen et al., 1986; Thoft-Christensen and Baker, 1982). Calibration based on professional judgment and proven practice has been the main method until ten-twenty years ago. Fitting of partial safety factors in codes is used when a new code format is introduced and the parameters are then determined such that the same level of safety is obtained as in the old code. The modern version of code calibration is the optimization of a set of design check equations to match, as closely as possible, a specified target reliability level. It is this kind of calibration that is performed here. By means of structural reliability methods the design formats of the new or existing standards, i.e. the design check equations, the characteristic values and partial safety factors may be selected in such a way that the level of reliability of all structures designed according to the standards is homogenous and independent of the choice of material and the prevailing loading, operational and environmental conditions. This process including the choice of the desired level of reliability or “target reliability” is commonly understood as “code calibration”. Reliability based code calibration has been formulated by several researchers, such as Ravindra and Galambos (1978), Ellingwood et al. (1982), Sorensen et al. (1998 and 2001), Maes et al. (2004) and it has therefore been implemented in several new and recent standards. The uncertainties that are to be considered in code calibration are: physical or aleatory uncertainty, and statistical and model uncertainty, also referred to as epistemic uncertainty. The physical uncertainties are typically uncertainties associated with the loading environment, the geometry of the structure and the material properties. The statistical uncertainties arise due to incomplete statistical information e.g. due to a small number of material tests. Finally, the model uncertainties (Section 6.6) must be considered to take into account the uncertainty associated with the idealized descriptions used to approximate the actual physical behaviour of the structure and the loading to which it is subjected. The probabilistic modeling of uncertainties largely rests on a Bayesian statistical interpretation of uncertainties implying that the uncertainty modeling utilizes and facilitates both the incorporation of statistical evidence about uncertain parameters and subjectively assessed uncertainties. Modern methods of reliability and risk analysis allow for a very general representation of these uncertainties ranging from non-stationary stochastic processes and fields to time-invariant

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Background and Objectives

In January 2009, the DIS version of ISO 19906 (2009) was issued. This new standard focuses on action effects typical for arctic offshore structures. It contains normative clauses with respect to reliability, risk and consequences, but it does not provide definitive partial action factors for its limit states design approach. The objective of the work described in this report is to perform a calibration of the environmental action factors for exposure level L1 in order to ensure that the specified target reliability of (1– 10-5) for each ULS and ALS action combination is achieved for circumstances that can reasonably be foreseen. A secondary objective is to also recommend calibrated environmental action factors for L2 and L3. In addition to these objectives, the report provides detailed guidance on a recommended calibration method should the user of ISO 19906 wish to perform a site-specific or structure-specific calibration using a fully probabilistic approach. This objective is in itself quite important as ISO/DIS 19906:2009 permits such an approach when the potential economic benefits of performing a site-specific calibration are likely to be considerable for large arctic offshore installations.

Unique features of the current calibration procedure include:

– the fundamental distinction between ultimate limit states (ULS) and the abnormal limit state (ALS) and the resulting distinctive treatment of extreme and abnormal design actions

– the special emphasis on ice loading and its implication on specific spatial

and temporal modeling issues

– the consideration of arctic offshore regions, of distinct types of ice, and of selected arctic structural systems, and the resulting weighted non-linear constrained optimization that underlies the basic calibration of action factors

– the use of a specified principal/companion action framework for deriving

characteristic values of design actions The present study has been coordinated and supervised by Dr. Marc A. Maes of Aleatec Advisory Services, Calgary, who previously coordinated the calibration of the 1986 and 2003 versions of CSA-S471 (offshore structures), and was involved in the development of ISO 2394, the development of the Joint Committee of Structural Safety (JCSS) probabilistic model code, the calibration and the codification of various LSD standards for tubing and casing design, as well as several site-specific and/or structure-specific load and resistance factor calibrations.

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7

What is Code Calibration?

Code calibration is based on a standardized process which is outlined in various documents such as ISO 2394 (1998) and several JCSS publications (JCSS, 2001). All aspects of this process have been strictly adhered to. Probabilistic models for load and resistance were based on the “probabilistic model code” (JCSS, 2007) which is available at the international website of the JCSS in Zürich. All modern design codes are based on design check equations on the basis of which a notional reliability verification of a given design can conveniently be performed, using a simple comparison of resistances and loads and/or load effects. Code calibration can be performed by judgment, fitting, optimization or a combination of these (Madsen et al., 1986; Thoft-Christensen and Baker, 1982). Calibration based on professional judgment and proven practice has been the main method until ten-twenty years ago. Fitting of partial safety factors in codes is used when a new code format is introduced and the parameters are then determined such that the same level of safety is obtained as in the old code. The modern version of code calibration is the optimization of a set of design check equations to match, as closely as possible, a specified target reliability level. It is this kind of calibration that is performed here. By means of structural reliability methods the design formats of the new or existing standards, i.e. the design check equations, the characteristic values and partial safety factors may be selected in such a way that the level of reliability of all structures designed according to the standards is homogenous and independent of the choice of material and the prevailing loading, operational and environmental conditions. This process including the choice of the desired level of reliability or “target reliability” is commonly understood as “code calibration”. Reliability based code calibration has been formulated by several researchers, such as Ravindra and Galambos (1978), Ellingwood et al. (1982), Sorensen et al. (1998 and 2001), Maes et al. (2004) and it has therefore been implemented in several new and recent standards. The uncertainties that are to be considered in code calibration are: physical or aleatory uncertainty, and statistical and model uncertainty, also referred to as epistemic uncertainty. The physical uncertainties are typically uncertainties associated with the loading environment, the geometry of the structure and the material properties. The statistical uncertainties arise due to incomplete statistical information e.g. due to a small number of material tests. Finally, the model uncertainties (Section 6.6) must be considered to take into account the uncertainty associated with the idealized descriptions used to approximate the actual physical behaviour of the structure and the loading to which it is subjected. The probabilistic modeling of uncertainties largely rests on a Bayesian statistical interpretation of uncertainties implying that the uncertainty modeling utilizes and facilitates both the incorporation of statistical evidence about uncertain parameters and subjectively assessed uncertainties. Modern methods of reliability and risk analysis allow for a very general representation of these uncertainties ranging from non-stationary stochastic processes and fields to time-invariant

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random variables. In most cases it is sufficient to model the uncertain quantities by random variables with given distribution functions and distribution parameters estimated on basis of statistical and/or subjective information. In the probabilistic model code by JCSS (2007) an almost complete set of probabilistic models are given covering most situations encountered in practical engineering problems. Ice action and action effect models however have not been explicitly addressed in code calibration which explains why the present calibration effort focuses heavily on probabilistic aspects of ice actions.

9

Mandate and Restrictions

The present action factor calibration is anchored on the DIS version of ISO 19906 (January 2009) and takes into account the design check equation formats in ISO 19900 as well as the resistance standards ISO 19902, 19903, 19904-1, noting that, in this work, no calibration of partial resistance factors is attempted.

Calibration includes environmental actions only: winds, waves and currents etc. and ice. As ISO 19906 focuses on Arctic offshore structures, there is considerable emphasis on the modeling and the calibration of ice actions. Calibration does not include gravity loads, variable loads, nor earthquakes (ISO 19901-2 and 19902 are deemed to apply). The 19902 partial action factors are used for the actions not being calibrated in this work (gravity loads, variable loads, accidental loads, etc.) at the L1 exposure level. However, the sensitivity of using the current 19906 DIS factors which largely mirror the factors contained in CSA-S471 and which are lower for L1, and the use of lower/calibrated factors for L2 and L3, are investigated. The action factor calibration carefully addresses the regionalization of ice loads, i.e. the spatial partition of design cases on the basis of extreme ice action effect uncertainties (not absolute magnitudes) associated with types of ice (e.g. first-year versus multi-year), geography, frequency of loading, and combinations with other environmental processes (e.g. seismic, waves). In this calibration, 8 geographic ice regions are identified and 8 types of structural systems. The weighting factors were provided by a consensus of the ISO experts, members of TP10, in February 2009. It is essential to realize that “regionalization” refers only to differences in uncertainty modeling/characterization and not to geographical variations in the absolute magnitude of ice actions. Input for this task has been obtained from previously published probabilistic studies and from a substantial C-CORE ice load distribution study (C-CORE, 2009). While the preferred objective is to aim for one ice action factor value for all geographic zones, the possibilities that (1) the ice action factors could be different from the wind/wave/current action factor, and (2) that they could be region-dependent, have been considered in this study. Since regionalization of ice actions shows specific probabilistic features, it was decided that ice action factors should be evaluated for each region and ice type separately so that we develop an understanding of their sensitivities. However, the preferred outcome was agreed to be one ice action factor value for all ice regions and types. As mentioned in Section 1, the other objective of this work is to provide detailed guidance about the calibration process: full documentation and audit trail – data or data sources, and detailed methods. Noting that ISO 19906 allows the user to calibrate site-specific action factors for L1 exposure level and for L2 and L3 exposure levels, the report is to be sufficient to guide users to perform consistent calibrations to the satisfaction of other stakeholders such as regulators. User-

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random variables. In most cases it is sufficient to model the uncertain quantities by random variables with given distribution functions and distribution parameters estimated on basis of statistical and/or subjective information. In the probabilistic model code by JCSS (2007) an almost complete set of probabilistic models are given covering most situations encountered in practical engineering problems. Ice action and action effect models however have not been explicitly addressed in code calibration which explains why the present calibration effort focuses heavily on probabilistic aspects of ice actions.

9

Mandate and Restrictions

The present action factor calibration is anchored on the DIS version of ISO 19906 (January 2009) and takes into account the design check equation formats in ISO 19900 as well as the resistance standards ISO 19902, 19903, 19904-1, noting that, in this work, no calibration of partial resistance factors is attempted.

Calibration includes environmental actions only: winds, waves and currents etc. and ice. As ISO 19906 focuses on Arctic offshore structures, there is considerable emphasis on the modeling and the calibration of ice actions. Calibration does not include gravity loads, variable loads, nor earthquakes (ISO 19901-2 and 19902 are deemed to apply). The 19902 partial action factors are used for the actions not being calibrated in this work (gravity loads, variable loads, accidental loads, etc.) at the L1 exposure level. However, the sensitivity of using the current 19906 DIS factors which largely mirror the factors contained in CSA-S471 and which are lower for L1, and the use of lower/calibrated factors for L2 and L3, are investigated. The action factor calibration carefully addresses the regionalization of ice loads, i.e. the spatial partition of design cases on the basis of extreme ice action effect uncertainties (not absolute magnitudes) associated with types of ice (e.g. first-year versus multi-year), geography, frequency of loading, and combinations with other environmental processes (e.g. seismic, waves). In this calibration, 8 geographic ice regions are identified and 8 types of structural systems. The weighting factors were provided by a consensus of the ISO experts, members of TP10, in February 2009. It is essential to realize that “regionalization” refers only to differences in uncertainty modeling/characterization and not to geographical variations in the absolute magnitude of ice actions. Input for this task has been obtained from previously published probabilistic studies and from a substantial C-CORE ice load distribution study (C-CORE, 2009). While the preferred objective is to aim for one ice action factor value for all geographic zones, the possibilities that (1) the ice action factors could be different from the wind/wave/current action factor, and (2) that they could be region-dependent, have been considered in this study. Since regionalization of ice actions shows specific probabilistic features, it was decided that ice action factors should be evaluated for each region and ice type separately so that we develop an understanding of their sensitivities. However, the preferred outcome was agreed to be one ice action factor value for all ice regions and types. As mentioned in Section 1, the other objective of this work is to provide detailed guidance about the calibration process: full documentation and audit trail – data or data sources, and detailed methods. Noting that ISO 19906 allows the user to calibrate site-specific action factors for L1 exposure level and for L2 and L3 exposure levels, the report is to be sufficient to guide users to perform consistent calibrations to the satisfaction of other stakeholders such as regulators. User-

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calibration and the subsequent application of user-developed site-specific partial action factors are suggested and permitted in the following clauses:

[ISO/DIS 19906:2009, clause 7.1.1] Partial factors for action combinations associated with ULS and ALS shall be in accordance with Table 7-4 or, if adequate data are available, may be specifically calibrated to achieve the reliability target (see 7.2.6) for the structure or the component. [ISO/DIS 19906:2009, clause 7.1.6] Alternative des ign methods may be us ed, pr ovided t hat c onformance w ith t he U LS a nd A LS l imit s tates reliability targets set out in 7.2.6 is demonstrated. [ISO/DIS 19906:2009, clause 7.2.6] The partial action factors specified in Table 7-4 have been der ived so that when applied to ULS and ALS design checks for exposure level L1 arctic offshore structures and their components within the scope of this International Standard, the reliability targets given in Table 7-5 are deemed to be satisfied. Alternatively, i f adequate data are available, par tial action factors may be der ived by performing reliability analyses taking account of the probabilistic descriptions of actions and resistances, specific to the relevant action combinations and exposure l evels. D ue account s hall be t aken of r elevant r esistance f actors. The reliability targets given in Table 7-5 are provided to enable the calibration of action factors on a c onsistent basis with those presented in Table 7-4. These reliability targets, expressed as maximum acceptable annual failure probabilities, are consistent with the intent of ISO 19902, ISO 19903 and ISO 19904-1. The targets in Table 7-5 are for single causes, i.e. for each action combination in isolation.


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calibration and the subsequent application of user-developed site-specific partial action factors are suggested and permitted in the following clauses:

[ISO/DIS 19906:2009, clause 7.1.1] Partial factors for action combinations associated with ULS and ALS shall be in accordance with Table 7-4 or, if adequate data are available, may be specifically calibrated to achieve the reliability target (see 7.2.6) for the structure or the component. [ISO/DIS 19906:2009, clause 7.1.6] Alternative des ign methods may be us ed, pr ovided t hat c onformance w ith t he U LS a nd A LS l imit s tates reliability targets set out in 7.2.6 is demonstrated. [ISO/DIS 19906:2009, clause 7.2.6] The partial action factors specified in Table 7-4 have been der ived so that when applied to ULS and ALS design checks for exposure level L1 arctic offshore structures and their components within the scope of this International Standard, the reliability targets given in Table 7-5 are deemed to be satisfied. Alternatively, i f adequate data are available, par tial action factors may be der ived by performing reliability analyses taking account of the probabilistic descriptions of actions and resistances, specific to the relevant action combinations and exposure l evels. D ue account s hall be t aken of r elevant r esistance f actors. The reliability targets given in Table 7-5 are provided to enable the calibration of action factors on a c onsistent basis with those presented in Table 7-4. These reliability targets, expressed as maximum acceptable annual failure probabilities, are consistent with the intent of ISO 19902, ISO 19903 and ISO 19904-1. The targets in Table 7-5 are for single causes, i.e. for each action combination in isolation.

11

Ultimate Limit States and Abnormal Limit States

ISO/DIS 19906:2009 identifies three distinct extreme design scenarios. Ultimate limit states (ULS) refer to extreme hazards which any structural member or the structural system as a whole must resist with a specified reliability (10-5 for exposure level L1). Abnormal limit states (ALS) refer to very rare and extremely large natural hazards against which the structure must provide sufficient reserve capacity, ductility and/or energy dissipation capability with the same specified reliability. Essentially, the ALS acts as a guarantee that sufficient robustness is in place to deal with infrequent hazards such as massive earthquakes and icebergs, while tolerating non-critical damage. The third design scenario is a post-disaster design check of a partially damaged structural system. Other than the removal of damaged members, it is treated as a special “load combination” in the ULS (action combination 5) and it therefore requires no separate consideration in this calibration. The distinction between ULS and ALS affects the present calibration in 3 ways:

– it requires a separate calibration of EL and AL actions.

– it requires companion factors to be developed for all combinations of EL and AL (e.g. ice and wind, icebergs and waves) involving both discrete and continuous stochastic load processes. See Section 9.

– it requires the use of extended resistance models for ALS having larger

intrinsic uncertainty than the simpler ULS resistance models. This is because mechanical models for e.g. large displacements, fully plastic behaviour, model ductility, structural crushing and energy dissipation, and nonlinear methods of analysis have, generally speaking, larger coefficients of variation (COV). See Section 6.1.

The following clauses highlight the essential differences between ULS and ALS discussed above:

[ISO/DIS 19906:2009, clause 7.2.1.1] The s tructure s hall be designed f or t he U LS f or s trength and s tiffness, an d c hecked for A LS s o it ha s adequate reserve capacity and energy dissipation capability, for FLS so it has adequate endurance under dynamic action effects, and for SLS so it performs adequately under normal use. [ISO/DIS 19906:2009, clause 7.2.1.2] The ULS requirement ensures that no significant s tructural damage occurs for actions with an acceptably low probability of being exceeded during the design service l ife of the structure. The ULS design condition for ice shall be the extreme-level ice event (ELIE). Both local and global actions shall be considered. [ISO/DIS 19906:2009, clause 7.2.1.5] The A LS r equirement is i ntended t o ensure t hat t he structure and f oundation hav e sufficient r eserve strength, displacement or energy dissipation capacity to sustain large actions and other action effects in the inelastic region without complete loss of integrity. Some structural damage can be allowed for ALS. The ALS design condition for ice shall be the abnormal-level ice event (ALIE). Both local and global actions shall be considered.

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[ISO/DIS 19906:2009, clause 7.2.2.1] For structures in arctic and cold regions environments, design checks shall be carried out for both extreme level (EL) and abnormal-level (AL) events, which include ice actions arising from ELIE and ALIE. [ISO/DIS 19906:2009, clause 7.2.2.3] In the ULS design check, structural members and foundation components should not exceed the ULS strength provisions of this International Standard and its referenced standards. The design procedures shall be b ased pr imarily o n l inear elastic m ethods of structural analysis. S ome l ocalized i nelastic b ehaviour i s acceptable, for example, as permitted in Clause 11 for steel structures. The characteristic value for actions arising from the ELIE shall be determined based on an annual probability of exceedance not greater than 10-2. [ISO/DIS 19906:2009, clause 7.2.2.4] In the ALS design check, non-linear methods of analysis may be used. Structural components are allowed to behave plastically, and foundation piles are allowed to reach axial capacity or develop plastic behaviour. The design check depends on a combination of static reserve strength, ductility, and energy dissipation to resist the ALIE conditions. The representative value for actions arising from the ALIE shall be determined based on an annual probability of exceedance not greater than 10-4 or shall be derived from events with an annual probability of occurrence not greater than 10-4. Iceberg and ice island impact events with an annual probability of occurrence between 10-4 and 10 -5, and with high consequences should be considered in the ALIE design checks to ensure that the reliability target in Table 7-5 is satisfied. [ISO/DIS 19906:2009, clause 7.2.5] For t he U LS, t he characteristic resistances s hall be d ivided by r esistance f actors to obtain t he design resistances. Alternatively, the characteristic material properties shall be divided by material factors to obtain the design material properties. The safety for each ultimate limit state shall be verified by ensuring that the effect of factored actions does not exceed the factored resistance. For the ALS, the resistances shall be derived such that failure or collapse does not occur, and therefore structure and foundation resistance or safety factors may be reduced from their ULS values, or set to unity, as permitted by t his I nternational S tandard and i ts r eferenced documents. H owever c omponents m ay be allowed to behave inelastically (i.e. design resistance may be exceeded) if there is sufficient ductility and i f the overall structural design is adequately robust and provides alternative load-paths to distribute and resist the action effects and dissipate the energy.

13

Calibration Procedure

Code calibration consists of the following basic steps which are discussed in some detail in the subsequent sections of this report: A detailed discussion of each of these steps is given in the following section.

1. identification of design check equations and action combinations

2. identification of the probabilistic limit states

3. probabilistic (time-invariant) and stochastic (time-variant) modeling of all the action effects, action combinations and resistances

4. regionalization of actions based on uncertainty ranges, if required

5. weighting of design check equations, material usage and structural

concept selection within each region and overall in consultation with arctic offshore engineers

6. formulation of the objective functions (based on the specified target

reliabilities) and the calibration constraints

7. constrained optimization of action factors, companion factors and specified exceedance probabilities

8. selection/recommendation of the optimal set of partial action factors and

companion factors with due account of exposure levels, and possible regionalization

9. verification

Note that in the context of calibration we make the following important distinction between limit state function (LSF) and design check equations (DCE) which act as deterministic “controls” of the probabilistic LSF:

– DCE are deterministic equations that provide relations between (specified) representative values of actions and resistances, with the “controls” consisting of action factors, resistance factors, combination factors, and specified annual exceedance probabilities or return periods. DCE are what the user “sees” in a standard without being exposed to probabilistic modeling and safety demonstration.

– LSF are functions of random variables/processes for actions and

resistances which denote the state (safe/failure) of a structural member. By convention they are negatively valued in the failure zone F, so that the failure probability corresponds to the probability of LSF being less than zero.

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[ISO/DIS 19906:2009, clause 7.2.2.1] For structures in arctic and cold regions environments, design checks shall be carried out for both extreme level (EL) and abnormal-level (AL) events, which include ice actions arising from ELIE and ALIE. [ISO/DIS 19906:2009, clause 7.2.2.3] In the ULS design check, structural members and foundation components should not exceed the ULS strength provisions of this International Standard and its referenced standards. The design procedures shall be b ased pr imarily o n l inear elastic m ethods of structural analysis. S ome l ocalized i nelastic b ehaviour i s acceptable, for example, as permitted in Clause 11 for steel structures. The characteristic value for actions arising from the ELIE shall be determined based on an annual probability of exceedance not greater than 10-2. [ISO/DIS 19906:2009, clause 7.2.2.4] In the ALS design check, non-linear methods of analysis may be used. Structural components are allowed to behave plastically, and foundation piles are allowed to reach axial capacity or develop plastic behaviour. The design check depends on a combination of static reserve strength, ductility, and energy dissipation to resist the ALIE conditions. The representative value for actions arising from the ALIE shall be determined based on an annual probability of exceedance not greater than 10-4 or shall be derived from events with an annual probability of occurrence not greater than 10-4. Iceberg and ice island impact events with an annual probability of occurrence between 10-4 and 10 -5, and with high consequences should be considered in the ALIE design checks to ensure that the reliability target in Table 7-5 is satisfied. [ISO/DIS 19906:2009, clause 7.2.5] For t he U LS, t he characteristic resistances s hall be d ivided by r esistance f actors to obtain t he design resistances. Alternatively, the characteristic material properties shall be divided by material factors to obtain the design material properties. The safety for each ultimate limit state shall be verified by ensuring that the effect of factored actions does not exceed the factored resistance. For the ALS, the resistances shall be derived such that failure or collapse does not occur, and therefore structure and foundation resistance or safety factors may be reduced from their ULS values, or set to unity, as permitted by t his I nternational S tandard and i ts r eferenced documents. H owever c omponents m ay be allowed to behave inelastically (i.e. design resistance may be exceeded) if there is sufficient ductility and i f the overall structural design is adequately robust and provides alternative load-paths to distribute and resist the action effects and dissipate the energy.

13

Calibration Procedure

Code calibration consists of the following basic steps which are discussed in some detail in the subsequent sections of this report: A detailed discussion of each of these steps is given in the following section.

1. identification of design check equations and action combinations

2. identification of the probabilistic limit states

3. probabilistic (time-invariant) and stochastic (time-variant) modeling of all the action effects, action combinations and resistances

4. regionalization of actions based on uncertainty ranges, if required

5. weighting of design check equations, material usage and structural

concept selection within each region and overall in consultation with arctic offshore engineers

6. formulation of the objective functions (based on the specified target

reliabilities) and the calibration constraints

7. constrained optimization of action factors, companion factors and specified exceedance probabilities

8. selection/recommendation of the optimal set of partial action factors and

companion factors with due account of exposure levels, and possible regionalization

9. verification

Note that in the context of calibration we make the following important distinction between limit state function (LSF) and design check equations (DCE) which act as deterministic “controls” of the probabilistic LSF:

– DCE are deterministic equations that provide relations between (specified) representative values of actions and resistances, with the “controls” consisting of action factors, resistance factors, combination factors, and specified annual exceedance probabilities or return periods. DCE are what the user “sees” in a standard without being exposed to probabilistic modeling and safety demonstration.

– LSF are functions of random variables/processes for actions and

resistances which denote the state (safe/failure) of a structural member. By convention they are negatively valued in the failure zone F, so that the failure probability corresponds to the probability of LSF being less than zero.

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The design-check equations (DCE) in ISO 19906 are established on the basis of the following clause.

[ISO/DIS 19906:2009, clause 7.2.4] Action c ombinations that shall be considered in de sign ar e s pecified in T able 7 -4 F or eac h ac tion combination, the representative value of an action shall be multiplied by the partial action factor specified in Table 7-4. ISO 19900 provides further information on the classification of types of action. For action combinations where an abnormal or accidental action is the principal action, (action combinations 4 and 6 in Table 7-4), the action effects shall be checked for the ALS only. As an alternative to Table 7-4, for each limit state and for relevant exposure levels, the partial action factors may be calibrated using a full probabilistic approach to achieve the limit state reliability targets (see 7.2.6).

The current DCE action factors in the DIS’s Table 7-4 largely mirror some of the action factors in the current CAN/CSA-S471-04. However, the current calibration first considers another set of factors based on ISO 19902:2007. Hence, two sets of DCE are treated and, in both cases, only the action factors for permanent and variable factors are considered fixed while environmental action factors and companion values are subject to calibration:

– Set I: Permanent and Variable action factors based on ISO 19902:2007

– Set II: Permanent and Variable action factors based on current ISO/DIS 19906:2009 and CAN/CSA-S471-04.

The two sets of basic DCE are shown in Table 1. In Table 1, the following control parameters are subject to calibration in the base case of exposure level L1:

(1) the principal environmental action factor γE in ULS-3; possibly also the principal action factor(s) γI for ice if ice (I) is felt to require separate treatment(s).

(2) the companion environmental action factor γEC in ULS-1 and ULS-2, to

be used in combination with permanent and variable actions; possibly also the companion action factor γIC for ice.

(3) [not shown in Table 1] the minimum required annual exceedance

probability PE at which the abnormal environmental/ice actions are specified in ALS-4. Note that a fixed action factor of 1.0 is used for this abnormal action effect.

(4) [not shown in Table 1] the companion action factors ψij to be used in the

various combinations of principal environmental/ice processes (see Section 9).

For a given exposure level, the calibration of all of the above control parameters which we can denote by θ = { γE, γI, …, γEC, γIC, PE, ψij,…} rests on the following constrained optimization (Madsen et al., 1984; Sørensen et al., 1994; Maes et al., 2004):


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The design-check equations (DCE) in ISO 19906 are established on the basis of the following clause.

[ISO/DIS 19906:2009, clause 7.2.4] Action c ombinations that shall be considered in de sign ar e s pecified in T able 7 -4 F or eac h ac tion combination, the representative value of an action shall be multiplied by the partial action factor specified in Table 7-4. ISO 19900 provides further information on the classification of types of action. For action combinations where an abnormal or accidental action is the principal action, (action combinations 4 and 6 in Table 7-4), the action effects shall be checked for the ALS only. As an alternative to Table 7-4, for each limit state and for relevant exposure levels, the partial action factors may be calibrated using a full probabilistic approach to achieve the limit state reliability targets (see 7.2.6).

The current DCE action factors in the DIS’s Table 7-4 largely mirror some of the action factors in the current CAN/CSA-S471-04. However, the current calibration first considers another set of factors based on ISO 19902:2007. Hence, two sets of DCE are treated and, in both cases, only the action factors for permanent and variable factors are considered fixed while environmental action factors and companion values are subject to calibration:

– Set I: Permanent and Variable action factors based on ISO 19902:2007

– Set II: Permanent and Variable action factors based on current ISO/DIS 19906:2009 and CAN/CSA-S471-04.

The two sets of basic DCE are shown in Table 1. In Table 1, the following control parameters are subject to calibration in the base case of exposure level L1:

(1) the principal environmental action factor γE in ULS-3; possibly also the principal action factor(s) γI for ice if ice (I) is felt to require separate treatment(s).

(2) the companion environmental action factor γEC in ULS-1 and ULS-2, to

be used in combination with permanent and variable actions; possibly also the companion action factor γIC for ice.

(3) [not shown in Table 1] the minimum required annual exceedance

probability PE at which the abnormal environmental/ice actions are specified in ALS-4. Note that a fixed action factor of 1.0 is used for this abnormal action effect.

(4) [not shown in Table 1] the companion action factors ψij to be used in the

various combinations of principal environmental/ice processes (see Section 9).

For a given exposure level, the calibration of all of the above control parameters which we can denote by θ = { γE, γI, …, γEC, γIC, PE, ψij,…} rests on the following constrained optimization (Madsen et al., 1984; Sørensen et al., 1994; Maes et al., 2004):

15

θ: minimize 2*

1)log)((log F

L

jF PPw

j−∑

=

θj (1)

subject to the L constraints: – log PF j (θ) ≥ – log PF

UB (2) where PF j (θ) are the logarithms of the limit state failure probabilities corresponding to j=1, …, L different design check equations and load combinations, wj are the associated weights (Σwj =1) assigned to each of the combinations j, and PF

* is the target probability of failure in the reference period of one year. The additional constraints ensure that no limit state failure probability exceeds a threshold or upper bound PF

UB. Both values are discussed below, see also Figure 1(c) below. The L different design combinations refer to all possible combinations of action effects having different ratios, action COVs, resistance COVs, mean arrival rates, model uncertainty COVs, structure types, regions, etc … The optimal control parameters θ are then obtained by numerical solution of the above constrained optimization. The probability of failure PF j for combination j, given any set of θ values are obtained using well established SORM methods. Optimization is performed using multidimensional gradient search.

As mentioned above, calibration involves a weighted optimization using the objective function (1) and a series of constraints expressed by (2). Figure 1 explains that both actions are required:

– the weighted minimization ensures that the set θ makes the sum of square differences between the logarithms of the various PFj and the target PF

* as small as possible. But this “centering and optimization” action will usually leave some design combinations with an unacceptably high PF as shown in Figure 1(a).

– selecting θ on the basis that all PFj should be forced to be less than an

upper bound value PFUB as shown in Figure 1(b) does resolve the above

problem but PF* ceases to be a true target. Also, this objective is

unrealistic as the entire standard would be dominated by a very small number of exceptional design situations that carry less than 0.1% of the total weight of all design cases. A large majority of cases would result in overdesign.

Accordingly both (1) and (2) are required in a successful calibration, as shown in Figure 1(c). Figure 1(c) is the approach selected in the present analysis. It is consistent with Equations (1) and (2) above.


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10-4

10-5

10-6

ρF

all design cases (a) calibration based on optimizing weighted distances to a target reliability only (blue line)

10-4

10-5

10-6

ρF

all design cases (b) calibration based on a restraining upper bound failure probability (red line)

10-4

10-5

10-6

ρF

all design cases (c) calibration based on restrained optimization using both (a) and (b) Figure 1: Illustration of different calibration objectives.

The DIS standard specifies the values of PF* = 10-5, 10-4 and 10-3 for exposure levels L1, L2 and L3, respectively, as shown in the clauses and tables shown below. The upper bound values of PFUB = 10-4, 10-3 and 10-2 are selected as reasonable and acceptable deviations from the target. This is consistent with previous calibration efforts (e.g. Maes et al., 2004; Sørensen et al., 1994). It must be emphasized that only a very small portion (less than 0.1% in weight) in fact reaches the upper bound PFUB, which occurs typically for load combinations consisting of either pure permanent, pure environmental, and pure operational loading.

[ISO/DIS 19906:2009, clause 7.2.6] The r eliability t argets gi ven i n T able 7-5 are provided t o ena ble t he c alibration o f a ction factors on a consistent basis with those pr esented i n Table 7-4. These reliability targets, expressed as maximum acceptable annual failure probabilities, are consistent with the intent of ISO 19902, ISO 19903 and ISO 19904-1. The targets in Table 7-5 are for single causes, i.e. for each action combination in isolation. [ISO/DIS 19906:2009: Table 7-5] Reliability targets for each limit state action combination

Exposure level Maximum Acceptable Annual Failure Probability L1 1,0 x 10-5 L2 1,0 x 10-4 L3 1,0 x 10-3

17

Table 1 – Design check equations (L1) based on 2 sets of action factors

Set I: Permanent and variable action factors based on ISO 19902:2007 ULS-1 1.30(1.00)G + 1.50Q1 + 1.50Q2 + γECEE

ULS-2 no distinction made

ULS-3 1.10(0.90)G + 1.10(0.80)Q1 + γEEE

ALS-4(†) 1.10(0.90)G + 1.10(0.80)Q1 + 1.00EA

ULS-5(‡) 1.00G + 1.00Q1 + γEDEE (†) this design check is not included in 19902, 19903 or 19904 but it is inferred from their accidental

design check. (‡) represents a damaged state “post ALS” design check. EE: representative value of the extreme-level environmental action having EL as its principal action. EA: representative value of the abnormal-level environmental action having AL as its principal action. Unknown environmental action factors are in red. Principal actions are in bold.

Set II: Permanent and variable action factors based on the current ISO/DIS 19906:2009 and CAN/CSA-S471-04 ULS-1 1.25(0.90)G + 1.45Q1 + 1.20Q2 + γECEE

ULS-2 1.25(0.90)G + 1.15Q1 + 1.70Q2 + γECEE

ULS-3 1.05(0.95)G + 1.15Q1 + γEEE

ALS-4 1.05 (0.95)G + 1.15Q1 + 1.00EA

ULS-5(‡) 1.05(0.95)G + 1.00Q1 + γEDEE (‡) represents a damaged state “post ALS” design check EE: representative value of the extreme-level environmental action having EL as its principal action. EA: representative value of the abnormal-level environmental action having AL as its principal action. Unknown environmental action factors are in red. Principal actions are in bold.


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10-4

10-5

10-6

ρF

all design cases (a) calibration based on optimizing weighted distances to a target reliability only (blue line)

10-4

10-5

10-6

ρF

all design cases (b) calibration based on a restraining upper bound failure probability (red line)

10-4

10-5

10-6

ρF

all design cases (c) calibration based on restrained optimization using both (a) and (b) Figure 1: Illustration of different calibration objectives.

The DIS standard specifies the values of PF* = 10-5, 10-4 and 10-3 for exposure levels L1, L2 and L3, respectively, as shown in the clauses and tables shown below. The upper bound values of PFUB = 10-4, 10-3 and 10-2 are selected as reasonable and acceptable deviations from the target. This is consistent with previous calibration efforts (e.g. Maes et al., 2004; Sørensen et al., 1994). It must be emphasized that only a very small portion (less than 0.1% in weight) in fact reaches the upper bound PFUB, which occurs typically for load combinations consisting of either pure permanent, pure environmental, and pure operational loading.

[ISO/DIS 19906:2009, clause 7.2.6] The r eliability t argets gi ven i n T able 7-5 are provided t o ena ble t he c alibration o f a ction factors on a consistent basis with those pr esented i n Table 7-4. These reliability targets, expressed as maximum acceptable annual failure probabilities, are consistent with the intent of ISO 19902, ISO 19903 and ISO 19904-1. The targets in Table 7-5 are for single causes, i.e. for each action combination in isolation. [ISO/DIS 19906:2009: Table 7-5] Reliability targets for each limit state action combination

Exposure level Maximum Acceptable Annual Failure Probability L1 1,0 x 10-5 L2 1,0 x 10-4 L3 1,0 x 10-3

17

Table 1 – Design check equations (L1) based on 2 sets of action factors

Set I: Permanent and variable action factors based on ISO 19902:2007 ULS-1 1.30(1.00)G + 1.50Q1 + 1.50Q2 + γECEE

ULS-2 no distinction made

ULS-3 1.10(0.90)G + 1.10(0.80)Q1 + γEEE

ALS-4(†) 1.10(0.90)G + 1.10(0.80)Q1 + 1.00EA

ULS-5(‡) 1.00G + 1.00Q1 + γEDEE (†) this design check is not included in 19902, 19903 or 19904 but it is inferred from their accidental

design check. (‡) represents a damaged state “post ALS” design check. EE: representative value of the extreme-level environmental action having EL as its principal action. EA: representative value of the abnormal-level environmental action having AL as its principal action. Unknown environmental action factors are in red. Principal actions are in bold.

Set II: Permanent and variable action factors based on the current ISO/DIS 19906:2009 and CAN/CSA-S471-04 ULS-1 1.25(0.90)G + 1.45Q1 + 1.20Q2 + γECEE

ULS-2 1.25(0.90)G + 1.15Q1 + 1.70Q2 + γECEE

ULS-3 1.05(0.95)G + 1.15Q1 + γEEE

ALS-4 1.05 (0.95)G + 1.15Q1 + 1.00EA

ULS-5(‡) 1.05(0.95)G + 1.00Q1 + γEDEE (‡) represents a damaged state “post ALS” design check EE: representative value of the extreme-level environmental action having EL as its principal action. EA: representative value of the abnormal-level environmental action having AL as its principal action. Unknown environmental action factors are in red. Principal actions are in bold.


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Probabilistic Models

6.1 Resistance R Guidelines for the selection of stochastic models of both actions and resistance can be found in many sources. The Eurocodes, ISO 2394 (1998), and JCSS (2007) make the following recommendations for resistance. Strength / resistance parameters are to be modeled by lognormal distributions. This avoids the possibility of negative realizations. The coefficient of variation varies with the material type considered. Typical values are 5% for steel and reinforcement, 15% for the concrete compression strength and 15-20% for the bending strength of structural timber. The characteristic value is generally chosen as the 5% quantile. It is clear that the modeling of resistance is quite important as it critically effects limit state failure probability, even though in the present work we do not calibrate resistance factors.

A broader range of resistance characteristics was considered in Maes (1986b) including different structural elements such as columns, plates and soils. Statistics were generated for the actual strength of certain structural members as compared with their assumed (factored) design strength. Almost all models found in the literature are therefore based on the assumption that resistance R is a random quantity with a lognormal distribution:

R ~ LN (r, vR) (3) where r and vR are the mean and the COV of the two-parameter LN distribution, respectively. If the mean r is related to the (factored) design resistance rd by a factor kR (often referred to as the resistance bias) by the following equation: r = kR rd’ (4) then the ratio of (actual strength/design strength) has an expected value equal to kR with a COV equal to vR. In order to ensure that comparable levels of reliability exist for different degrees of uncertainty regarding the resistance, the parameters kr and vr are related as follows, regardless of the parameters of the lognormal resistance PDF: 2 1 21 exp( ( ) ln(1 ))R R Rk v vδ−= + −Φ + (5) where Φ-1 is the inverse standard cumulative normal distribution function. A key assumption in this calibration is that the factored design resistance rd defined above corresponds to the 1%-ile of the actual resistance. In other words, on average, in 99 cases out of 100, the actual resistance exceeds the (factored) design resistance. Therefore, when δ = 1%, then the Φ-1 (0.01) = –2.326, and equation (5) requires that kR and vR take on the paired values listed in Table 2.

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19

Table 2 – Values of the k-factor kR of resistance, for different COV values vR, for

δ=1%

There exists plenty of evidence to justify the choice of value δ = 1% (see Maes (1986b, 2003) for R/C beams, R/C beams in flexure, steel beams, columns, plates, and soils). It can also be verified that in many standards, including the current CSA-S471 code, the resistance factors are indeed such that, the probability of R being less than the factored resistance is approximately equal to δ = 1%. Resistance model uncertainty (as embodied, for instance, in the ratio of actual versus predicted strength) is included in the modeling of R. For most structural members and soils, this requires us to consider, in the present calibration, a range of vR values, namely10%, 12%, 15%, 20%, 25% and 30% depending on the type of structures (ranging from steel members to soils) and limit states (bending, shear, sliding, …). Also note that this method of calibration assumes that R is the minimum required design resistance (MRDR). No resistance is “added on” as a result of convenience or material availability, for instance due to standard sizes.

As noted in Section 4, the robustness check involved in the abnormal limit states ALS requires the use of larger resistance COV values due to increased uncertainty regarding failure mechanisms typically associated with abnormal level loads. Values of 20%, 25% and 30% are considered for ALS (all the other assumptions above for ULS are assumed to be applicable – only the overall uncertainty increases). 6.2 Permanent Actions G Dead and deformation loads are generally represented by a normal distribution. The representative value g is related to the mean permanent load by a kG factor similar to the one used for resistance; thus, permanent loads are assumed to be normally distributed with mean kG g and a COV equal to vG

G ~ N (kG g, vG) (6) Land-based structures have used values of permanent action between 0.07 and 0.11. Offshore installations are usually subjected to reasonably rigorous weight audits. Frieze and Plane (1985) adopt vG = 0.075. Anzai et al. (1982) use vG = 0.08 and kG = 1.0, whereas previous Canadian reliability studies have generally used vG = 0.07. The values kG = 1.0 and vG = 0.08 are adopted in this study. 6.3 Variable actions Q The key aspect in the modeling of variable (live) loads is the time variability. In recent code calibrations, these loads are modeled using so-called rectangular

vR 0.10 0.12 0.15 0.20 0.25 0.30 kR 1.267 1.330 1.431 1.616 1.828 2.066


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Probabilistic Models

6.1 Resistance R Guidelines for the selection of stochastic models of both actions and resistance can be found in many sources. The Eurocodes, ISO 2394 (1998), and JCSS (2007) make the following recommendations for resistance. Strength / resistance parameters are to be modeled by lognormal distributions. This avoids the possibility of negative realizations. The coefficient of variation varies with the material type considered. Typical values are 5% for steel and reinforcement, 15% for the concrete compression strength and 15-20% for the bending strength of structural timber. The characteristic value is generally chosen as the 5% quantile. It is clear that the modeling of resistance is quite important as it critically effects limit state failure probability, even though in the present work we do not calibrate resistance factors.

A broader range of resistance characteristics was considered in Maes (1986b) including different structural elements such as columns, plates and soils. Statistics were generated for the actual strength of certain structural members as compared with their assumed (factored) design strength. Almost all models found in the literature are therefore based on the assumption that resistance R is a random quantity with a lognormal distribution:

R ~ LN (r, vR) (3) where r and vR are the mean and the COV of the two-parameter LN distribution, respectively. If the mean r is related to the (factored) design resistance rd by a factor kR (often referred to as the resistance bias) by the following equation: r = kR rd’ (4) then the ratio of (actual strength/design strength) has an expected value equal to kR with a COV equal to vR. In order to ensure that comparable levels of reliability exist for different degrees of uncertainty regarding the resistance, the parameters kr and vr are related as follows, regardless of the parameters of the lognormal resistance PDF: 2 1 21 exp( ( ) ln(1 ))R R Rk v vδ−= + −Φ + (5) where Φ-1 is the inverse standard cumulative normal distribution function. A key assumption in this calibration is that the factored design resistance rd defined above corresponds to the 1%-ile of the actual resistance. In other words, on average, in 99 cases out of 100, the actual resistance exceeds the (factored) design resistance. Therefore, when δ = 1%, then the Φ-1 (0.01) = –2.326, and equation (5) requires that kR and vR take on the paired values listed in Table 2.

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19

Table 2 – Values of the k-factor kR of resistance, for different COV values vR, for

δ=1%

There exists plenty of evidence to justify the choice of value δ = 1% (see Maes (1986b, 2003) for R/C beams, R/C beams in flexure, steel beams, columns, plates, and soils). It can also be verified that in many standards, including the current CSA-S471 code, the resistance factors are indeed such that, the probability of R being less than the factored resistance is approximately equal to δ = 1%. Resistance model uncertainty (as embodied, for instance, in the ratio of actual versus predicted strength) is included in the modeling of R. For most structural members and soils, this requires us to consider, in the present calibration, a range of vR values, namely10%, 12%, 15%, 20%, 25% and 30% depending on the type of structures (ranging from steel members to soils) and limit states (bending, shear, sliding, …). Also note that this method of calibration assumes that R is the minimum required design resistance (MRDR). No resistance is “added on” as a result of convenience or material availability, for instance due to standard sizes.

As noted in Section 4, the robustness check involved in the abnormal limit states ALS requires the use of larger resistance COV values due to increased uncertainty regarding failure mechanisms typically associated with abnormal level loads. Values of 20%, 25% and 30% are considered for ALS (all the other assumptions above for ULS are assumed to be applicable – only the overall uncertainty increases). 6.2 Permanent Actions G Dead and deformation loads are generally represented by a normal distribution. The representative value g is related to the mean permanent load by a kG factor similar to the one used for resistance; thus, permanent loads are assumed to be normally distributed with mean kG g and a COV equal to vG

G ~ N (kG g, vG) (6) Land-based structures have used values of permanent action between 0.07 and 0.11. Offshore installations are usually subjected to reasonably rigorous weight audits. Frieze and Plane (1985) adopt vG = 0.075. Anzai et al. (1982) use vG = 0.08 and kG = 1.0, whereas previous Canadian reliability studies have generally used vG = 0.07. The values kG = 1.0 and vG = 0.08 are adopted in this study. 6.3 Variable actions Q The key aspect in the modeling of variable (live) loads is the time variability. In recent code calibrations, these loads are modeled using so-called rectangular

vR 0.10 0.12 0.15 0.20 0.25 0.30 kR 1.267 1.330 1.431 1.616 1.828 2.066


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pulse or Ferry-Borges & Castanheta (FBC) models. This means that a load history is schematised as a series of independent rectangular pulses with “presence” period np (number of days the process is “active” per year) and “renewal” nR (number of times the process renews during these np days). This is illustrated in Figure 2(a) and 2(b).

actio

n ef

fect

one year

np days

nR1

2…

time Figure 2(a) Long duration variable action Q1.

actio

n ef

fect

time1

one year

2

3

...

...

Σ=np days

nR -1 nR

Figure 2(b) Short duration variable action Q2.

For calibration purposes, we distinguish between long-duration and short-duration variable actions, Q1 and Q2, respectively:

– the variable action Q1 of long duration is always active: it is modeled as a load that is renewed (on average) 3 times a year for a full period of 1/3 year. This corresponds to np = 365 days and nR = 3. Alternative values of nR = 12 and 1 are also considered.

– the variable action Q2 of short duration is considered to be refreshed

every day, but is only present for 50 days during that year. This corresponds to np = 50 days and nR = 50. Alternative values of np = 5 days and nR = 5 are also considered.

The distinction between variable actions of long duration Q1 (LD) and short duration Q2 (SD) is quite relevant for the design of offshore installations, since structural members are variously subjected to action effects produced by different types of operations such as:

– drilling operations (LD or SD) – long-term storage of materials and equipment (LD)

21

– storage of liquids (SD or LD) – storage of high-temperature substances (SD or LD) – crane operations (SD) – helicopter landings (SD) – fendering and mooring of supply vessels (SD) – variable hydrostatic pressure and ballast (LD)

Clearly, the action effects associated with these operations have very different temporal and spatial characteristics. The distinction between SD and LD suggests the use of different partial action factors and action combination factors for each category of action effects as in Set II (Section 5).

With respect to the one-year extreme value distribution of variable actions, many kQ factors (the kQ is the ratio between the mean and the representative value of Q) less than unity have been reported in literature, i.e. actual annual extremes are usually less than their representative value. This observation is related to the fact that design live loading is usually overestimated since its definition calls for the most severe of the maximum or minimum combined variable actions, which is a value that is likely greater than the one-year (maximum) action on which calibration is based. Some values of the variable action COV encountered in literature, are vQ = 0.07…0.80 (Fjeld, 1978), 0.03 (Baker and Wyatt, 1979), 0.10 (Frieze and Plane, 1985) and 0.14 (Anzai et al., 1982). For the present calibration, the recommendation of the JCSS (2007) to use a Gumbel distribution for the annual extreme of operational load, is followed

Q ~ Gumbel (kQ q, vQ) (7) where q is the representative action value, where kQ = 0.85, on account of the conservatism that is inherent in the prescription of the characteristic variable action as a maximum, and vQ depends on whether the variable action has LD, in which case vQ = 0.15, or SD, for which vQ = 0.25. Alternative values of 0.20, 0.30 (LD), and 0.45, 0.60 (SD) are also considered. As the present calibration also accounts for the combination of environmental load and companion LD variable action (and vice versa), we require the use of the aforementioned FBC models as defined in Figure 2(a). 6.4 Ice Actions I Ice actions I are the focus of this calibration. Their probabilistic characterization is discussed in detail in the separate Sections 7.1 and 7.2. Ice action model uncertainties are discussed in Section 7.3. 6.5 Non-Ice Environmental Actions E An overview of annual COV-values for wind, wave, current actions is given in Maes (2003). Values of 20% to 40% include uncertainties associated with the transformation of event to action effect, and other action model uncertainties. These annual maximum COVs are for typical world-wide offshore metocean


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pulse or Ferry-Borges & Castanheta (FBC) models. This means that a load history is schematised as a series of independent rectangular pulses with “presence” period np (number of days the process is “active” per year) and “renewal” nR (number of times the process renews during these np days). This is illustrated in Figure 2(a) and 2(b).

actio

n ef

fect

one year

np days

nR1

2…

time Figure 2(a) Long duration variable action Q1.

actio

n ef

fect

time1

one year

2

3

...

...

Σ=np days

nR -1 nR

Figure 2(b) Short duration variable action Q2.

For calibration purposes, we distinguish between long-duration and short-duration variable actions, Q1 and Q2, respectively:

– the variable action Q1 of long duration is always active: it is modeled as a load that is renewed (on average) 3 times a year for a full period of 1/3 year. This corresponds to np = 365 days and nR = 3. Alternative values of nR = 12 and 1 are also considered.

– the variable action Q2 of short duration is considered to be refreshed

every day, but is only present for 50 days during that year. This corresponds to np = 50 days and nR = 50. Alternative values of np = 5 days and nR = 5 are also considered.

The distinction between variable actions of long duration Q1 (LD) and short duration Q2 (SD) is quite relevant for the design of offshore installations, since structural members are variously subjected to action effects produced by different types of operations such as:

– drilling operations (LD or SD) – long-term storage of materials and equipment (LD)

21

– storage of liquids (SD or LD) – storage of high-temperature substances (SD or LD) – crane operations (SD) – helicopter landings (SD) – fendering and mooring of supply vessels (SD) – variable hydrostatic pressure and ballast (LD)

Clearly, the action effects associated with these operations have very different temporal and spatial characteristics. The distinction between SD and LD suggests the use of different partial action factors and action combination factors for each category of action effects as in Set II (Section 5).

With respect to the one-year extreme value distribution of variable actions, many kQ factors (the kQ is the ratio between the mean and the representative value of Q) less than unity have been reported in literature, i.e. actual annual extremes are usually less than their representative value. This observation is related to the fact that design live loading is usually overestimated since its definition calls for the most severe of the maximum or minimum combined variable actions, which is a value that is likely greater than the one-year (maximum) action on which calibration is based. Some values of the variable action COV encountered in literature, are vQ = 0.07…0.80 (Fjeld, 1978), 0.03 (Baker and Wyatt, 1979), 0.10 (Frieze and Plane, 1985) and 0.14 (Anzai et al., 1982). For the present calibration, the recommendation of the JCSS (2007) to use a Gumbel distribution for the annual extreme of operational load, is followed

Q ~ Gumbel (kQ q, vQ) (7) where q is the representative action value, where kQ = 0.85, on account of the conservatism that is inherent in the prescription of the characteristic variable action as a maximum, and vQ depends on whether the variable action has LD, in which case vQ = 0.15, or SD, for which vQ = 0.25. Alternative values of 0.20, 0.30 (LD), and 0.45, 0.60 (SD) are also considered. As the present calibration also accounts for the combination of environmental load and companion LD variable action (and vice versa), we require the use of the aforementioned FBC models as defined in Figure 2(a). 6.4 Ice Actions I Ice actions I are the focus of this calibration. Their probabilistic characterization is discussed in detail in the separate Sections 7.1 and 7.2. Ice action model uncertainties are discussed in Section 7.3. 6.5 Non-Ice Environmental Actions E An overview of annual COV-values for wind, wave, current actions is given in Maes (2003). Values of 20% to 40% include uncertainties associated with the transformation of event to action effect, and other action model uncertainties. These annual maximum COVs are for typical world-wide offshore metocean


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conditions and we assume they also apply to the subset of Arctic and sub-Arctic sea/ocean conditions considered in this study (again, the absolute values may differ but the probabilistic characterizations should be similar). It should be noted that the above COV values include modeling uncertainty (environmental process, process-to-action, process-to-action-effect). In view of the definitions of the representative action E as the 99% percentile of the one-year maximum environmental load distribution, it is sufficient to select the value of COV in order to fix the remaining extremal parameter of the assumed Gumbel probability distribution, namely:

E ~ Gumbel (kE Eq, ve) (8) where the kE factor, defined as the ratio of mean annual extreme load to the representative action Eq at a specified annual probability of exceedance equal to q, is the following function of vE: 1

1 3.137EE

kv

=+

(9)

In Table 3, the values of kE, and the derived normalized extremal parameters a/E and b/E can be found for a selected reference value of vE = 0.35. Alternative values of 0.20, 0.30 and 0.40 are also considered.

Table 3 – Parameters of the probabilistic model for frequent environmental load

vE kE a/E b/E 0.35 0.477 0.4017 0.1301

For inter-environmental action combinations and environmental variable action combinations, frequent load effect processes are modeled as FBC processes similar to Figure 2(a) with nP = 365, nR = 365/3 (waves, winds, currents) and nP = 200 days, nR = 200 for certain seasonal actions. Bracketing values are also considered. Abnormal level loads are modelled as Poisson pulse processes with variable intensity and occurrence as shown in Figure 3. Their representative value is determined at an annual exceedance probability PE.

23

(1)….(2)

(1): Occurrence of events: Poisson with variable arrival rate

(2): Intensity is represented using an (S,H) tail model

Load

effe

ct

Time

Figure 3: Stochastic model used for abnormal environmental action effects. 6.6 Action Effect Ratios It is important to realize that the DCEs for both Set I and Set II (Table 1) are all symbolic equations, i.e. the relative proportion of each contributing load effect is varied from 0 to 100%. As certain combinations ratios of actions are not as likely as others, the following weights are applied as shown in Table 4 and used in Equation (1). The values were obtained by consensus of the TP10 experts.

Table 4 – Relative weight associated with the action effect ratios E/(E+P+Q) and I/(I+P+Q)

Action effect ratio E/(E+P+Q) 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Relative weight (%) 1 4 5 5 5 5 15 20 20 15 5


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conditions and we assume they also apply to the subset of Arctic and sub-Arctic sea/ocean conditions considered in this study (again, the absolute values may differ but the probabilistic characterizations should be similar). It should be noted that the above COV values include modeling uncertainty (environmental process, process-to-action, process-to-action-effect). In view of the definitions of the representative action E as the 99% percentile of the one-year maximum environmental load distribution, it is sufficient to select the value of COV in order to fix the remaining extremal parameter of the assumed Gumbel probability distribution, namely:

E ~ Gumbel (kE Eq, ve) (8) where the kE factor, defined as the ratio of mean annual extreme load to the representative action Eq at a specified annual probability of exceedance equal to q, is the following function of vE: 1

1 3.137EE

kv

=+

(9)

In Table 3, the values of kE, and the derived normalized extremal parameters a/E and b/E can be found for a selected reference value of vE = 0.35. Alternative values of 0.20, 0.30 and 0.40 are also considered.

Table 3 – Parameters of the probabilistic model for frequent environmental load

vE kE a/E b/E 0.35 0.477 0.4017 0.1301

For inter-environmental action combinations and environmental variable action combinations, frequent load effect processes are modeled as FBC processes similar to Figure 2(a) with nP = 365, nR = 365/3 (waves, winds, currents) and nP = 200 days, nR = 200 for certain seasonal actions. Bracketing values are also considered. Abnormal level loads are modelled as Poisson pulse processes with variable intensity and occurrence as shown in Figure 3. Their representative value is determined at an annual exceedance probability PE.

23

(1)….(2)

(1): Occurrence of events: Poisson with variable arrival rate

(2): Intensity is represented using an (S,H) tail model

Load

effe

ctTime

Figure 3: Stochastic model used for abnormal environmental action effects. 6.6 Action Effect Ratios It is important to realize that the DCEs for both Set I and Set II (Table 1) are all symbolic equations, i.e. the relative proportion of each contributing load effect is varied from 0 to 100%. As certain combinations ratios of actions are not as likely as others, the following weights are applied as shown in Table 4 and used in Equation (1). The values were obtained by consensus of the TP10 experts.

Table 4 – Relative weight associated with the action effect ratios E/(E+P+Q) and I/(I+P+Q)

Action effect ratio E/(E+P+Q) 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Relative weight (%) 1 4 5 5 5 5 15 20 20 15 5


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Probabilistic Ice Action Models

7.1 Regionalization As explained in Section 3, we wish to explore the need and the effect of identifying separate ice action classes based on their probabilistic extreme action behaviour (their “tail”). At this stage it is unclear if certain ice actions behave more like wind actions, wave actions, or other types of actions. To provide more insight, 8 geographic zones and 8 arctic structural systems were identified in consultation with TP10. This is shown in Table 5. “Regionalization” is based only on differences in uncertainty modeling and characterization and not on geographical variations in the absolute magnitude of ice actions. Quantitative input for this task has been obtained from previously published probabilistic studies and from a substantial C-CORE ice load distribution study (C-CORE, 2009). Clearly not all structures qualify as possible design solutions for all types or regions. This specificity is shown in Table 6 where weights are assigned by the ISO TP10 experts per zone so that the sum of weights is 100% in each zone. Weights wj are used in Equation (1) to reflect frequency of use (past, present, and future) and to provide a measure of “importance” in the calibration. Table 7 similarly shows estimates of weights for each region also assigned by expert members of the technical panel TP10. It can be seen that the (global) Beaufort Sea zone including Southern and Northern Chukchi Sea, Baffin Bay, Labrador, Laptev Sea, NE Greenland, and Arctic Islands are contributing 40% of the total geographical weight. Within each cell of Table 5 the ice regime can still vary considerably. This affects the tail behaviour of the extreme action effect probability distribution as discussed in Section 7.2 and Appendix A. Table 8 shows the different values of the mean number of ice loading events per year provided by C-CORE, considered in the calibration. The values in bold refer to the base case for each combination of zone and structure; this base case value is used in the various ice action tail plots shown in Section 7.2. It should be noted that the mean number of ice events (the “arrival rate”) includes all ice-structure interactions of any level of significance ranging from tiny action effects to very large action effects. Subsequent values in each cell of Table 8 indicate alternative values considered in the calibration. Values in red reflect the use of ice management and disconnection in the case of floaters. The values in brackets denote the relative weights assigned to each scenario.

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25

Table 5 – Zones and structural systems

MYI 0.5 multi-year ice: 0.5 tenths MYI 3.0 multi-year ice: 3.0 tenths FYR first-year ridges FYL first-year level ice IB icebergs

GV vertically sided GBS GC conically sided GBS FV vertically sided floater FC conically sided floater FP floating production storage offloading unit PC single vertical piled column ML multi-legged structure MI man-made island

Structural system

Region Ice environment GV GC FV FC FP PC ML MI

Beaufort Sea Southern Chukchi Sea Baffin Bay Labrador Laptev Sea

MYI 0.5

Beaufort Sea NE Greenland Northern Chukchi Sea Arctic Islands

MYI 3.0

Sakhalin Cook Inlet Sea of Okhotsk Kara Sea

FYR

Barents Sea Bering Sea

FYR

Caspian Sea Baltic Sea Bohai Sea

FYL

Barents Sea

IB

Grand Banks

IB

Labrador Baffin Bay NE Greenland

IB


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Probabilistic Ice Action Models

7.1 Regionalization As explained in Section 3, we wish to explore the need and the effect of identifying separate ice action classes based on their probabilistic extreme action behaviour (their “tail”). At this stage it is unclear if certain ice actions behave more like wind actions, wave actions, or other types of actions. To provide more insight, 8 geographic zones and 8 arctic structural systems were identified in consultation with TP10. This is shown in Table 5. “Regionalization” is based only on differences in uncertainty modeling and characterization and not on geographical variations in the absolute magnitude of ice actions. Quantitative input for this task has been obtained from previously published probabilistic studies and from a substantial C-CORE ice load distribution study (C-CORE, 2009). Clearly not all structures qualify as possible design solutions for all types or regions. This specificity is shown in Table 6 where weights are assigned by the ISO TP10 experts per zone so that the sum of weights is 100% in each zone. Weights wj are used in Equation (1) to reflect frequency of use (past, present, and future) and to provide a measure of “importance” in the calibration. Table 7 similarly shows estimates of weights for each region also assigned by expert members of the technical panel TP10. It can be seen that the (global) Beaufort Sea zone including Southern and Northern Chukchi Sea, Baffin Bay, Labrador, Laptev Sea, NE Greenland, and Arctic Islands are contributing 40% of the total geographical weight. Within each cell of Table 5 the ice regime can still vary considerably. This affects the tail behaviour of the extreme action effect probability distribution as discussed in Section 7.2 and Appendix A. Table 8 shows the different values of the mean number of ice loading events per year provided by C-CORE, considered in the calibration. The values in bold refer to the base case for each combination of zone and structure; this base case value is used in the various ice action tail plots shown in Section 7.2. It should be noted that the mean number of ice events (the “arrival rate”) includes all ice-structure interactions of any level of significance ranging from tiny action effects to very large action effects. Subsequent values in each cell of Table 8 indicate alternative values considered in the calibration. Values in red reflect the use of ice management and disconnection in the case of floaters. The values in brackets denote the relative weights assigned to each scenario.

7

25

Table 5 – Zones and structural systems



Structural system



MYI 0.5


MYI 3.0


FYR


FYR


FYL

Barents Sea

IB

Grand Banks

IB


IB


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Table 6 – Relative weights of structural systems used in a specific region/ice environment



Structural system

Region Ice environment GV GC FV FC FP PC ML MI Σ


MYI 0.5 60 15 5 5 15 100%


MYI 3.0 70 30 100%


FYR 30 10 20 20 20 100%


FYR 33 33 33 100%


FYL 25 5 15 15 40 100%

Barents Sea

IB 50 50 100%

Grand Banks

IB 50 50 100%


IB 90 10 100%

27

Table 7 – Relative weights of zones and ice environments

Region

MYI 0.5 multi-year ice: 0.5 tenths MYI 3.0 multi-year ice: 3.0 tenths FYR first-year ridges FYL first-year level ice IB icebergs Ice environment Relative weight (%)


MYI 0.5 20


MYI 3.0 20


FYR 15


FYR 5

Caspian Sea Baltic Sea Bohai Bay

FYL 20

Barents Sea IB 5 Grand Banks IB 12.5 Labrador Baffin Bay NE Greenland

IB 2.5

Σ = 100%


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Table 6 – Relative weights of structural systems used in a specific region/ice environment



Structural system

Region Ice environment GV GC FV FC FP PC ML MI Σ


MYI 0.5 60 15 5 5 15 100%


MYI 3.0 70 30 100%


FYR 30 10 20 20 20 100%


FYR 33 33 33 100%


FYL 25 5 15 15 40 100%

Barents Sea

IB 50 50 100%

Grand Banks

IB 50 50 100%


IB 90 10 100%

27

Table 7 – Relative weights of zones and ice environments

Region

MYI 0.5 multi-year ice: 0.5 tenths MYI 3.0 multi-year ice: 3.0 tenths FYR first-year ridges FYL first-year level ice IB icebergs Ice environment Relative weight (%)


MYI 0.5 20


MYI 3.0 20


FYR 15


FYR 5


FYL 20

Barents Sea IB 5 Grand Banks IB 12.5 Labrador Baffin Bay NE Greenland

IB 2.5

Σ = 100%


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Table 8 – Mean number of ice loading events per year, their range, and the effect of ice management/

disconnection


GV vertically sided GBS FV vertically sided floater FP FPSO unit ML multi-legged structure

GC conically sided GBS FC conically sided floater PC vertical piled column MI man-made island

Structural system

Region Ice GV GC FV FC FP PC ML MI

Beaufort Sea S. Chukchi Baffin Bay Labrador Laptev Sea

MYI 0.5 700(25%) 350(25%)

70(25%) 7(25%)

700(25%) 350(25%)

70(25%) 7(25%)

600(25%) 300(25%)

60(25%) 6(25%)

525(25%) 262(25%)

52(25%) 6(25%)

700(25%) 350(25%)

70(25%) 7(25%)

Beaufort Sea NE Greenl. N. Chukchi Arctic Islands

MYI 3.0 4200(25%) 2100(25%) 420(25%)

42(25%)

4200(25%) 2100(25%) 420(25%)

42(25%)


FYR 7600(20%) 7600(20%) 4700(20%) 2800(20%) 4000(20%) 1520(20%) 1520(20%) 940(20%) 560(20%) 800(20%) 3040(20%) 3040(20%) 1880(20%) 1120(20%) 1600(20%) 4560(20%) 4560(20%) 2820(20%) 1680(20%) 2400(20%) 6080(20%) 6080(20%) 3760(20%) 2240(20%) 3200(20%)


FYR 650(40%) 650(40%) 320(40%) 130(60%) 130(60%) 64(60%)


FYL 15(50%) 15(50%) 15(50%) 15(50%) 15(50%) 50(20%) 50(20%) 50(20%) 50(20%) 50(20%) 100(30%) 100(30%) 100(30%) 100(30%) 100(30%)

Barents Sea IB 0.0067(10%) 0.0044(10%) 0.0003(90%) 0.0002(90%)

Grand Banks IB 0.126 0.084 (5%) 0.0042(95%)

Labrador Baffin Bay NE Greenl.

IB 5(25%) 3 (25%) 20(25%) 12(2.5%) 50(25%) 30(2.5%) 100(25%) 60(2.5%) 0.15(22.5%) 0.6 (22.5%) 1.5 (22.5%)

Note: In this Table, the bold values indicate the base case mean annual numbers of ice load events which includes all interactions of any level of significance. The annual extreme ice load probability distribution is based on this value. Subsequent values in each cell indicate alternative values considered in the calibration analysis (if any). Values in brackets denote the relative weights in % associated with these cases (their sum is 100% for each cell). Values in red apply to ice management and disconnection.


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Table 8 – Mean number of ice loading events per year, their range, and the effect of ice management/

disconnection


GV vertically sided GBS FV vertically sided floater FP FPSO unit ML multi-legged structure

GC conically sided GBS FC conically sided floater PC vertical piled column MI man-made island

Structural system

Region Ice GV GC FV FC FP PC ML MI

Beaufort Sea S. Chukchi Baffin Bay Labrador Laptev Sea

MYI 0.5 700(25%) 350(25%)

70(25%) 7(25%)

700(25%) 350(25%)

70(25%) 7(25%)

600(25%) 300(25%)

60(25%) 6(25%)

525(25%) 262(25%)

52(25%) 6(25%)

700(25%) 350(25%)

70(25%) 7(25%)

Beaufort Sea NE Greenl. N. Chukchi Arctic Islands

MYI 3.0 4200(25%) 2100(25%) 420(25%)

42(25%)

4200(25%) 2100(25%) 420(25%)

42(25%)


FYR 7600(20%) 7600(20%) 4700(20%) 2800(20%) 4000(20%) 1520(20%) 1520(20%) 940(20%) 560(20%) 800(20%) 3040(20%) 3040(20%) 1880(20%) 1120(20%) 1600(20%) 4560(20%) 4560(20%) 2820(20%) 1680(20%) 2400(20%) 6080(20%) 6080(20%) 3760(20%) 2240(20%) 3200(20%)


FYR 650(40%) 650(40%) 320(40%) 130(60%) 130(60%) 64(60%)


FYL 15(50%) 15(50%) 15(50%) 15(50%) 15(50%) 50(20%) 50(20%) 50(20%) 50(20%) 50(20%) 100(30%) 100(30%) 100(30%) 100(30%) 100(30%)

Barents Sea IB 0.0067(10%) 0.0044(10%) 0.0003(90%) 0.0002(90%)

Grand Banks IB 0.126 0.084 (5%) 0.0042(95%)

Labrador Baffin Bay NE Greenl.

IB 5(25%) 3 (25%) 20(25%) 12(2.5%) 50(25%) 30(2.5%) 100(25%) 60(2.5%) 0.15(22.5%) 0.6 (22.5%) 1.5 (22.5%)

Note: In this Table, the bold values indicate the base case mean annual numbers of ice load events which includes all interactions of any level of significance. The annual extreme ice load probability distribution is based on this value. Subsequent values in each cell indicate alternative values considered in the calibration analysis (if any). Values in brackets denote the relative weights in % associated with these cases (their sum is 100% for each cell). Values in red apply to ice management and disconnection.

29

7.2 (S, H) Tail Models In order to effectively analyze the tail behaviour of extreme actions we use the Q-distribution. Appendix A provides a detailed description of the use and the benefits of Q-distributions. They can be applied to arbitrary actions in terms of a non-dimensional variable η defined in Section A.3 which enables a fair probabilistic extreme value comparison between all types of actions. It is anchored on a representative value xq, the action with an annual probability of exceedance equal to q. The Q-distribution is defined in terms of two parameters:

– the tail slope S: see Figure A2(a)

– the tail heaviness H: see Figure A2(b) Important advantages of using dedicated tail models such as the Q-distribution for extreme action effects include:

– due to their reliance on the fundamental concept of tail distribution, they can be used for any type of data set.

– they provide very simple plots, so called (η, L*) tail plots that easily

explain the tail behaviour of a specific action. These figures can also be used to compare different actions in terms of their tail behaviour.

– they can be used to model the extreme value behaviour of continuous

environmental processes, discrete environmental processes such as ice action effects, intermittent processes and variable action processes.

– Q-distributions can easily be adjusted to arbitrary arrival rates for discrete

action processes. This is shown in Section A.4 and Figure A3.

– the factors S and H provide a direct link with the required action factors. This feature is of course very useful in calibration (see Section A.3).

– Q-distributions are mathematically convenient in the analysis of limit

state failure probabilities (see Section A.3).

– Q-distribution tail models can easily be adjusted for model/epistemic uncertainty, simply by adjusting tail heaviness. This is shown in Section A.7, Figure A5 and Section 7.3.

– the process of fitting a Q-distribution to an actual data set is very

straightforward and is explained in Section A.1. A full tail analysis of ice action effect data supplied by C-CORE (2009) is performed. Tables 9 and 10 show the result of this analysis. The central part of both tables lists sample values as provided by C-CORE. Blank lines indicate that some combinations of zones and actions were not modeled but their tail behaviour has been inferred from similar zones and structures. The right hand side of both Table 9 and 10 list the parameters of the Q-distribution: the


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anchoring points (either 10-2 or 10-4), the tail slope S and the tail heaviness H. Also mentioned is the reference value of the mean number of action events per year discussed in Section 7.1, Table 8. Note that in Table 9 all values apply to the annual extreme ice action effect while in Table 10 they apply to the action given an impacting iceberg. The values of S and H are also summarized in Table 11 to provide a clearer contrast between the different zones and structures (the footnotes are self explanatory). Appendix B is an extensive case by case representation of ice action effects per zone and per region. Light tails and heavy tails (depending on the case) can be observed. It can also be seen that the tail slope S varies considerably. However, there are certain commonalities. In order to detect them we consider three sets of figures:

– annual extreme ice actions classified per type of structure: Figures 5-10.

– all iceberg-structure interaction loads for all regions (per impact):

Figure 11.

– annual extreme ice actions classified per region for each of the 5 non-iceberg regions: Figures 12-16.

In browsing these figures and Table 11 it is important to keep in mind that S and H are directly related to the minimum required action factor γ as explained in Section A.3. In general, the steeper a tail “dips” (small S), the smaller γ. Also, the greater the upward curvature of the tail (the larger H), the greater γ. It is useful to contrast the above ice action tails (as represented by their respective Q-distributions with specific tail parameters S and H) with tails of the annual extreme environmental actions associated with continuous processes such as waves and winds. This is shown in Figure 17 where ice actions I are contrasted with wave/wind/current extreme actions E in the same tail plot. Bracketing values of νE are shown in the legend. It can be seen that some zones/structures should require larger action factors than the environmental action factor γE while others need smaller action factors.

31

Table 9: Tail analysis of ice action effects (data and Q-distribution model)

n mean sd CoV x 0.1 x 0.01 x 0.0001 x max q S H λ ref

Location Ice type Structure [ - ] [MN] [MN] [ - ] [MN] [MN] [MN] [MN] [ - ] [ - ] [ - ] [1/year]GV 23,940 612.8 105.5 0.172 751 938 1394 1441 10-2 0.087 0.030 697.0GC 10,000 395.2 106.5 0.269 528 767 1602 1602 10-2 0.157 0.141 697.0FP 26,241 402.1 67.9 0.169 490 613 903 925 10-2 0.090 0.047 589.0PC 28,037 213.5 37.0 0.173 262 329 486 496 10-2 0.090 0.030 524.0MI 10-2 0.100 0.030 700.0GV 26,978 760.3 106.3 0.140 899 1100 1453 1664 10-2 0.081 0.008 4183.0GC 10,000 547.2 131.2 0.240 711 1011 1654 1654 10-2 0.137 0.047 4184.0GV 30,000 286.0 13.3 0.046 304 321 343 347 10-2 0.019 -0.145 7588.0GC 30,000 140.1 14.1 0.101 159 183 232 242 10-2 0.055 0.000 7588.0FP 30,000 163.3 5.3 0.032 169 182 210 218 10-2 0.032 0.061 4742.0PC 30,000 67.6 3.6 0.053 72 81 107 111 10-2 0.059 0.157 2822.0ML 10-2 0.030 0.000 4000.0FV 40,000 42.6 67.8 1.591 157 199 264 309 10-2 0.057 0.092 654.0FC 40,000 16.8 27.0 1.606 61 85 186 238 10-2 0.144 0.156 637.0FP 213,605 27.0 42.2 1.563 98 114 157 370 10-2 0.034 0.331 321.3GV 99,997 61.1 6.7 0.109 70 81 104 113 10-2 0.061 0.005 15.0GC 93,042 55.9 4.8 0.085 62 70 87 95 10-2 0.049 0.012 12.6PC 99,993 18.5 2.1 0.114 21 25 32 36 10-2 0.062 -0.001 15.0ML 10-2 0.062 0.000 15.0MI 10-2 0.062 0.010 15.0

Tail analysis of the annual extreme ice load effect

MYI 0.5/10ths

Annual extreme sample values

MYI 3.0/10ths

Beaufort Sea

Sakhalin FYR

Barents Sea FYR

Caspian Sea FYL

Table 10: Tail analysis of iceberg action effects (data and Q-distribution model)

n mean sd CoV x 0.1 x 0.01 x 0.0001 x max q S H λ ref *Location Ice type Structure [ - ] [MN] [MN] [ - ] [MN] [MN] [MN] [MN] [ - ] [ - ] [ - ] [1/year]

FV 500,000 11.0 29.8 2.721 26 122 891 2150 10-4 0.394 0.375 0.0067FP 500,000 12.7 32.7 2.581 30 134 881 2565 10-4 0.370 0.349 0.0044GV 250,000 15.2 30.8 2.029 35 136 756 1409 10-4 0.333 0.307 0.1263FP 500,000 15.0 33.5 2.231 35 140 897 2187 10-4 0.368 0.348 0.0839GV 5,000,000 9.5 23.8 2.511 23 101 606 2867 10-4 0.347 0.320 4.69FP 5,000,000 9.7 25.5 2.637 23 105 675 3335 10-4 0.362 0.338 2.96

Labrador IB

Icebergs: Sample values (per impact) Tail analysis (per impact)

IBBarents Sea

* for annual extreme

Grand Banks IB


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anchoring points (either 10-2 or 10-4), the tail slope S and the tail heaviness H. Also mentioned is the reference value of the mean number of action events per year discussed in Section 7.1, Table 8. Note that in Table 9 all values apply to the annual extreme ice action effect while in Table 10 they apply to the action given an impacting iceberg. The values of S and H are also summarized in Table 11 to provide a clearer contrast between the different zones and structures (the footnotes are self explanatory). Appendix B is an extensive case by case representation of ice action effects per zone and per region. Light tails and heavy tails (depending on the case) can be observed. It can also be seen that the tail slope S varies considerably. However, there are certain commonalities. In order to detect them we consider three sets of figures:

– annual extreme ice actions classified per type of structure: Figures 5-10.

– all iceberg-structure interaction loads for all regions (per impact):

Figure 11.

– annual extreme ice actions classified per region for each of the 5 non-iceberg regions: Figures 12-16.

In browsing these figures and Table 11 it is important to keep in mind that S and H are directly related to the minimum required action factor γ as explained in Section A.3. In general, the steeper a tail “dips” (small S), the smaller γ. Also, the greater the upward curvature of the tail (the larger H), the greater γ. It is useful to contrast the above ice action tails (as represented by their respective Q-distributions with specific tail parameters S and H) with tails of the annual extreme environmental actions associated with continuous processes such as waves and winds. This is shown in Figure 17 where ice actions I are contrasted with wave/wind/current extreme actions E in the same tail plot. Bracketing values of νE are shown in the legend. It can be seen that some zones/structures should require larger action factors than the environmental action factor γE while others need smaller action factors.

31

Table 9: Tail analysis of ice action effects (data and Q-distribution model)

n mean sd CoV x 0.1 x 0.01 x 0.0001 x max q S H λ ref

Location Ice type Structure [ - ] [MN] [MN] [ - ] [MN] [MN] [MN] [MN] [ - ] [ - ] [ - ] [1/year]GV 23,940 612.8 105.5 0.172 751 938 1394 1441 10-2 0.087 0.030 697.0GC 10,000 395.2 106.5 0.269 528 767 1602 1602 10-2 0.157 0.141 697.0FP 26,241 402.1 67.9 0.169 490 613 903 925 10-2 0.090 0.047 589.0PC 28,037 213.5 37.0 0.173 262 329 486 496 10-2 0.090 0.030 524.0MI 10-2 0.100 0.030 700.0GV 26,978 760.3 106.3 0.140 899 1100 1453 1664 10-2 0.081 0.008 4183.0GC 10,000 547.2 131.2 0.240 711 1011 1654 1654 10-2 0.137 0.047 4184.0GV 30,000 286.0 13.3 0.046 304 321 343 347 10-2 0.019 -0.145 7588.0GC 30,000 140.1 14.1 0.101 159 183 232 242 10-2 0.055 0.000 7588.0FP 30,000 163.3 5.3 0.032 169 182 210 218 10-2 0.032 0.061 4742.0PC 30,000 67.6 3.6 0.053 72 81 107 111 10-2 0.059 0.157 2822.0ML 10-2 0.030 0.000 4000.0FV 40,000 42.6 67.8 1.591 157 199 264 309 10-2 0.057 0.092 654.0FC 40,000 16.8 27.0 1.606 61 85 186 238 10-2 0.144 0.156 637.0FP 213,605 27.0 42.2 1.563 98 114 157 370 10-2 0.034 0.331 321.3GV 99,997 61.1 6.7 0.109 70 81 104 113 10-2 0.061 0.005 15.0GC 93,042 55.9 4.8 0.085 62 70 87 95 10-2 0.049 0.012 12.6PC 99,993 18.5 2.1 0.114 21 25 32 36 10-2 0.062 -0.001 15.0ML 10-2 0.062 0.000 15.0MI 10-2 0.062 0.010 15.0

Tail analysis of the annual extreme ice load effect

MYI 0.5/10ths

Annual extreme sample values

MYI 3.0/10ths

Beaufort Sea

Sakhalin FYR

Barents Sea FYR

Caspian Sea FYL

Table 10: Tail analysis of iceberg action effects (data and Q-distribution model)

n mean sd CoV x 0.1 x 0.01 x 0.0001 x max q S H λ ref *Location Ice type Structure [ - ] [MN] [MN] [ - ] [MN] [MN] [MN] [MN] [ - ] [ - ] [ - ] [1/year]

FV 500,000 11.0 29.8 2.721 26 122 891 2150 10-4 0.394 0.375 0.0067FP 500,000 12.7 32.7 2.581 30 134 881 2565 10-4 0.370 0.349 0.0044GV 250,000 15.2 30.8 2.029 35 136 756 1409 10-4 0.333 0.307 0.1263FP 500,000 15.0 33.5 2.231 35 140 897 2187 10-4 0.368 0.348 0.0839GV 5,000,000 9.5 23.8 2.511 23 101 606 2867 10-4 0.347 0.320 4.69FP 5,000,000 9.7 25.5 2.637 23 105 675 3335 10-4 0.362 0.338 2.96

Labrador IB

Icebergs: Sample values (per impact) Tail analysis (per impact)

IBBarents Sea

* for annual extreme

Grand Banks IB


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Table 11 – Extreme ice load probability distributions: tail slope and tail heaviness factors



Structural system

Region Ice environ-ment

GV GC FV FC FP PC ML MI


MYI 0.5

0.087 0.157 0.090 0.090 0.100 0.030 0.141 0.047 0.030 0.030


MYI 3.0 0.081 0.137

0.008 0.047


FYR 0.019 0.055 0.032 0.059 0.030 -0.145 0.000 0.061 0.157 0.000


FYR 0.057 0.144 0.034 0.092 0.156 0.331


FYL 0.061 0.049 0.062 0.062 0.062 0.005 0.012 -0.001 0.000 0.010

Barents Sea IB 0.394 0.370 0.375 0.349

Grand Banks IB 0.333 0.368 0.307 0.348


IB 0.347 0.362 0.320 0.338

Note: Tail slope (TS) factors and tail heaviness (TH) factors are based on a tail-equivalent generalized Pareto distribution (Q-distrbution). In the above rows the first values in red is TS and the second value in blue is TH. TS is an average measure of slope of the upper tail quantiles. TH is a measure of tail heaviness: TH > 0 signifies heavy tail behaviour TH < 0 signifies light tail behaviour TH ≈ 0 signifies Gumbel extreme value type behaviour

33

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5

η based on q=0.01

Exce

edan

ce P

roba

bilit

y

Beaufort Sea MYI 0.5 GV


Sakhalin Island FYR GV

Caspian Sea FYL GV

Figure 5: Annual extreme ice load tail plots: classification according to type of structure: vertically sided GBS.

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5

η based on q=0.01

Exce

edan

ce P

roba

bilit

y

Beaufort MYI 0.5 GC

Beaufort MYI 3.0 GC

Sakhalin Island FYR GC

Caspian Sea FYL GC

Figure 6: Annual extreme ice load tail plots: classification according to type of structure: conically sided GBS.

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5

η based q=0.01

Exce

edan

ce P

roba

bilit

y

Beaufort MYI 0.5 FP

Sakhalin Island FYR FP

Barents Sea FYR FP

Figure 7: Annual extreme ice load tail plots: classification according to type of structure: floating production storage offloading unit.


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Table 11 – Extreme ice load probability distributions: tail slope and tail heaviness factors



Structural system

Region Ice environ-ment

GV GC FV FC FP PC ML MI


MYI 0.5

0.087 0.157 0.090 0.090 0.100 0.030 0.141 0.047 0.030 0.030


MYI 3.0 0.081 0.137

0.008 0.047


FYR 0.019 0.055 0.032 0.059 0.030 -0.145 0.000 0.061 0.157 0.000


FYR 0.057 0.144 0.034 0.092 0.156 0.331


FYL 0.061 0.049 0.062 0.062 0.062 0.005 0.012 -0.001 0.000 0.010

Barents Sea IB 0.394 0.370 0.375 0.349

Grand Banks IB 0.333 0.368 0.307 0.348


IB 0.347 0.362 0.320 0.338

Note: Tail slope (TS) factors and tail heaviness (TH) factors are based on a tail-equivalent generalized Pareto distribution (Q-distrbution). In the above rows the first values in red is TS and the second value in blue is TH. TS is an average measure of slope of the upper tail quantiles. TH is a measure of tail heaviness: TH > 0 signifies heavy tail behaviour TH < 0 signifies light tail behaviour TH ≈ 0 signifies Gumbel extreme value type behaviour

33

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5

η based on q=0.01

Exce

edan

ce P

roba

bilit

y




Caspian Sea FYL GV

Figure 5: Annual extreme ice load tail plots: classification according to type of structure: vertically sided GBS.

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5

η based on q=0.01

Exce

edan

ce P

roba

bilit

y

Beaufort MYI 0.5 GC

Beaufort MYI 3.0 GC


Caspian Sea FYL GC

Figure 6: Annual extreme ice load tail plots: classification according to type of structure: conically sided GBS.

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5

η based q=0.01

Exce

edan

ce P

roba

bilit

y

Beaufort MYI 0.5 FP


Barents Sea FYR FP

Figure 7: Annual extreme ice load tail plots: classification according to type of structure: floating production storage offloading unit.


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1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

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Beaufort Sea MYI 0.5 PC

Sakhalin Island FYR PC

Caspian Sea FYL PC

Figure 8: Annual extreme ice load tail plots: classification according to type of structure: single vertical piled column.

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Sakhalin Island FYR ML

Caspian Sea FYL ML

Figure 9: Annual extreme ice load tail plots: classification according to type of structure: multi-legged structure.

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Beaufort Sea MYI 0.5 MI

Caspian Sea FYL MI

Figure 10: Annual extreme ice load tail plots: classification according to type of structure: man-made island.


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Beaufort Sea MYI 0.5 PC


Caspian Sea FYL PC

Figure 8: Annual extreme ice load tail plots: classification according to type of structure: single vertical piled column.

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Caspian Sea FYL ML

Figure 9: Annual extreme ice load tail plots: classification according to type of structure: multi-legged structure.

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Beaufort Sea MYI 0.5 MI

Caspian Sea FYL MI

Figure 10: Annual extreme ice load tail plots: classification according to type of structure: man-made island.

35

1.E-06

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Barents Sea IB FV

Barents Sea IB FP

Grand Banks IB GV

Grand Banks IB FP

Labrador IB GV

Labrador IB FP

Figure 11: Iceberg-structure interaction loads (per impact) for all regions.

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Beaufort MYI 0.5 GV

Beaufort MYI 0.5 GC

Beaufort MYI 0.5 FP

Beaufort MYI 0.5 PC

Beaufort MYI 0.5 MI

Figure 12: Annual extreme ice load tail plots: classification according to region and type of ice: Beaufort Sea MYI 0.5.

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Beaufort MYI 3.0 GV

Beaufort MYI 3.0 GC

Figure 13: Annual extreme ice load tail plots: classification according to region and type of ice: Beaufort Sea MYI 3.0.


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1.E-05

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Figure 14: Annual extreme ice load tail plots: classification according to region and type of ice: Sakhalin Island FYR.

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Barents Sea FYR FV

Barents Sea FYR FC

Barents Sea FYR FP

Figure 15: Annual extreme ice load tail plots: classification according to region and type of ice: Barents Sea FYR.

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Caspian Sea FYL GV

Caspian Sea FYL GC

Caspian Sea FYL FP

Caspian Sea FYL ML

Caspian Sea FYL MI

Figure 16: Annual extreme ice load tail plots: classification according to region and type of ice: Caspian Sea FYL.

37

1.E-05

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Beaufort Sea MYI 0.5 GCSakhalin Island FYR GCBarents Sea FYR FPAnnual Environmental Action COV = 0.2Annual Environmental Action COV = 0.3Annual Environmental Action COV = 0.4

Figure 17: Comparison of (η, L*) tail plots: ice actions compared with other continuous environmental processes such as waves, winds, currents. The COV values in the legend refer to the annual extreme COV associated with wave/winds/currents which is specific with regards to metocean conditions and type of structure.


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1.E-05

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Figure 14: Annual extreme ice load tail plots: classification according to region and type of ice: Sakhalin Island FYR.

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Barents Sea FYR FV

Barents Sea FYR FC

Barents Sea FYR FP

Figure 15: Annual extreme ice load tail plots: classification according to region and type of ice: Barents Sea FYR.

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Caspian Sea FYL GV

Caspian Sea FYL GC

Caspian Sea FYL FP

Caspian Sea FYL ML

Caspian Sea FYL MI

Figure 16: Annual extreme ice load tail plots: classification according to region and type of ice: Caspian Sea FYL.

37

1.E-05

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Beaufort Sea MYI 0.5 GCSakhalin Island FYR GCBarents Sea FYR FPAnnual Environmental Action COV = 0.2Annual Environmental Action COV = 0.3Annual Environmental Action COV = 0.4

Figure 17: Comparison of (η, L*) tail plots: ice actions compared with other continuous environmental processes such as waves, winds, currents. The COV values in the legend refer to the annual extreme COV associated with wave/winds/currents which is specific with regards to metocean conditions and type of structure.


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7.3 Ice Action Model Uncertainties This section focuses on model and epistemic uncertainties associated with ice action and ice action effects. Resistance model uncertainties are discussed in Section 6.1 and are included in the probabilistic modeling of resistance. Wave, wind and current action uncertainties are discussed in Section 6.5 and are included in the probabilistic characterization of environmental action processes discussed in that section. The present section applies to ice actions. Clearly, the calibration must account for ice action model uncertainties including:

– statistical uncertainties such as caused by lack or absence of environmental and ice data

– statistical uncertainties due to choice of probability distributions

– assumptions and simplifications related to the physical environment

– ice action model unverified assumptions

– ice action model simplifications

– ice/structure/soil interaction uncertainties

– ice action to ice action effect uncertainties

– uncertainties related to global/local ice action spatial effects

– uncertainties related to temporal effects (e.g. occurrence of peak load

during an interaction) Many aspects of load modeling can be uncertain including basic assumptions, incomplete or simplified mathematical/mechanical models, idealizations and the use of insufficiently tested or calibrated variables. A typical example is the assumption of an ice pressure versus area relationship for a specific structure at a specific site – an assumption which in principle can only be verified by a dedicated series of full-scale ice load measurements. While it is generally agreed that these uncertainties must be accounted for in the formulation of design criteria and, by extension, in the calibration of action factors, good practice is for the designer-analyst to adopt a “cautious” deterministic approach using appropriately conservative assumption (Jordaan, 2009). In other words, we should expect users to act responsibly and professionally in selecting load models that have significant impact on the environmental design actions. Another key aspect of action uncertainty analysis is that one must respect and account for the proper hierarchy of uncertainties (Maes, 1991, Nessim et al., 1995, Nishijima et al., 2008). While aleatory uncertainties may or may not vary from load event to load event (depending on their spatial and temporal context) the model uncertainties in the loading models supersedes these uncertainties as

39

shown schematically in the hierarchy of Figure 17-bis. It can be seen that the individual loading events, while conditionally independent given model uncertainty, are in fact correlated due to the shared upper-level model uncertainty. Incorrectly including the top-level uncertainties in the lower-level uncertainties or vice versa, clearly affects extreme values and distribution tails, characteristic values, return periods, design criteria, and any attempt at optimal decision making as shown quantitatively in Maes, 1991, Nessim et al., 1995 and Nishijima et al., 2008.

Figure 17-bis: Hierarchy of load and load model uncertainties. As it is impossible to deal specifically with the large variety of ice action effect models, it is assumed that all aleatory uncertainties are properly accounted for in the ice action probability distributions (specifically in this case, the C-CORE ice action samples). The model/epistemic uncertainties are “added” as per Figure 17-bis using the values given below. It should be stressed that a considerable reduction in model/epistemic uncertainties can be expected for site-specific, metocean-specific, and structure-specific conditions where the different uncertainties can be clearly identified, resulting in better (optimized) custom-tailored action factors. Ice action model uncertainty is included in the present study by adjusting the (S, H) parameters in the Q-distributions as shown in Appendix A, section A.7. The case of zero additional model uncertainty νθ = 0 corresponds to the base case C-CORE ice action probability distributions in the previous sections 7.1 and 7.2. Table 11-bis shows the different νθ values assumed in the analysis together with their estimated weights. No bias was used, only COV. Table 11-bis – Relative weight associated with additional ice action model/epistemic

uncertainty

Ice action model uncertainty COV νθ (*) 0% 5% 10% 15% 20%

Relative weight (%) 20 20 30 20 10 (*) additional to that contained in the input C-CORE ice action effect statistics.

MODEL (EPISTEMIC) UNCERTAINTIES load or load-effect model uncertainties, model assumptions, model simplifications, statistical uncertainties

ALEATORY UNCERTAINTIES 1


ALEATORY UNCERTAINTIES n

interaction #1 interaction #2 interaction #n

model

load interaction events

… …


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shown schematically in the hierarchy of Figure 17-bis. It can be seen that the individual loading events, while conditionally independent given model uncertainty, are in fact correlated due to the shared upper-level model uncertainty. Incorrectly including the top-level uncertainties in the lower-level uncertainties or vice versa, clearly affects extreme values and distribution tails, characteristic values, return periods, design criteria, and any attempt at optimal decision making as shown quantitatively in Maes, 1991, Nessim et al., 1995 and Nishijima et al., 2008.

Figure 17-bis: Hierarchy of load and load model uncertainties. As it is impossible to deal specifically with the large variety of ice action effect models, it is assumed that all aleatory uncertainties are properly accounted for in the ice action probability distributions (specifically in this case, the C-CORE ice action samples). The model/epistemic uncertainties are “added” as per Figure 17-bis using the values given below. It should be stressed that a considerable reduction in model/epistemic uncertainties can be expected for site-specific, metocean-specific, and structure-specific conditions where the different uncertainties can be clearly identified, resulting in better (optimized) custom-tailored action factors. Ice action model uncertainty is included in the present study by adjusting the (S, H) parameters in the Q-distributions as shown in Appendix A, section A.7. The case of zero additional model uncertainty νθ = 0 corresponds to the base case C-CORE ice action probability distributions in the previous sections 7.1 and 7.2. Table 11-bis shows the different νθ values assumed in the analysis together with their estimated weights. No bias was used, only COV. Table 11-bis – Relative weight associated with additional ice action model/epistemic

uncertainty

Ice action model uncertainty COV νθ (*) 0% 5% 10% 15% 20%

Relative weight (%) 20 20 30 20 10 (*) additional to that contained in the input C-CORE ice action effect statistics.

MODEL (EPISTEMIC) UNCERTAINTIES load or load-effect model uncertainties, model assumptions, model simplifications, statistical uncertainties



ALEATORY UNCERTAINTIES n

interaction #1 interaction #2 interaction #n

model

load interaction events

… …


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Action Factors (Environmental and Ice): Results and Verification

The calibration process described in Section 5 is now used to optimize the various factors and parameters θ in both sets of design check equations (Section 5). For environmental actions E other than ice, the L1 principal action factor γE applicable to the 100-year action effect is optimized to be 1.35 for both Set I (ISO 19902) and Set II (CSA-S471) factors. The environmental companion factor γEC in the permanent/variable action design check equations is found to be 0.70. The abnormal action needs to be specified at an annual exceedance probability equal to 10-4. In the following two sections we use “action combination diagrams” to illustrate and verify some of the results of the calibration. It is felt that, in order to appreciate and test the performance of the optimized calibration parameters, two-by-two combinations of various action effects are most effective. Combinations of three, four, or more loads are very hard to visualize; on the other hand, two-by-two action combinations represent “worst-case” scenarios in the sense that if all combinations check out to be satisfactory for all possible contributions of either action effect, then the inclusion of additional action affects cannot decrease the reliability associated with the two-by-two combination. Recall also that all of the verification checks presented in this section are based on the minimum required design resistance. This, again, is a “worst-case” scenario from the point of view of structural safety. In reality, structural components will have “better” limit state reliability values than those shown in the two-by-two load combination diagrams. In the following two-by-two action combination diagrams, the horizontal axis denotes the ratio of one of the two load effects divided by the total load effect. This ratio, called “α” in the subsequent figures, varies from 0 to 100% and therefore, the very left-hand and right-hand sides of the diagram represent each load effect acting individually. Consider for instance Figure 18 which is a combination diagram for permanent load G and environmental load E. The right-hand side of Figure 18 shows the need for the factor γE = 1.35 for structural members dominated by environmental loading. It shows that on the other side of the action combination scale a companion factor of γEC as low as 0.7 can be afforded, which is confirmed by the overall calibration. Figure 19 shows the combined action of variable actions Q, of long duration and E. It can be seen in both Figures 18 and 19 that the environmental design check equations govern all design conditions marked by about 15% or more environmental load effect, i.e. the curves to the right of the noticeable discontinuity in slope. Note also that Set II action factors are overall more “conservative”, particularly on the α→0 side (pure G or pure Q1), while Set I and Set II converge for high environmental action ratios since the same action factor γE is used.

8

41

Turning now to ice action effects we make a distinction between the following calibration scenarios as discussed in Section 3:

(a) calibration of separate principal ice action factors γI for each “cell” in Table 5, i.e. for each combination of ice region and structure: the results are shown in Table 12 in black bold font.

(b) calibration of region-specific principal ice action factors γI : the results

are shown in Table 12 in red bold font.

(c) calibration of a principal ice action factor γI for all regions and all types: the result is shown in Table 12 in blue bold font.

(d) calibration of ice as part of all other environmental actions resulting in

an “overall” E and I factor γE = γI = 1.35 (as above) and PE = 10-4 for abnormal level actions.

It should be noted that action factors for conically sided structures (both GBS and floaters) are always larger than for other structures. The reason for this is the larger S (and H) values in the tails shown in the figures of Section 7.2. While the 100-year design action effects for conical structures are considerably less than for vertically sided structures, they increase at a greater rate and therefore require larger action factors to meet the reliability targets. This finding applies only if the input design actions for conical/sloping structures are validated following further investigation. Note that this effect disappears for L2 and L3 since the 100-year design action effects are much closer to the minimum required resistance, hence the effects of tail slope and heaviness tend to be less severe (see Section 10). As a result an exception must be made for structure types GC and FC if one is to follow calibration scenarios (b) and (c) above, as shown in Table 12. In principle, the exception should also show up in (d) but the overall “weight” (importance) of GC and FC when lumped together with all other types of environmental actions becomes almost negligible. When considering calibration scenario (b), region-specific action factors are highest for Beaufort-type zones (γI = 1.30), lowest for Sakhalin-type zones (γI = 1.20) and “in-between” for Caspian-type zones (γI = 1.25). Barents Sea FYR is a bit of an anomaly because of heavier tails (see Figures in Section 7.2) and perhaps this region should be called inconclusive for the time being; as it is now, it requires γI = 1.45. Under calibration scenario (c), the all-ice γI would be 1.30 except that 1.55 should be used for conically sided structures. The calibration of the prescribed annual exceedance probability for the abnormal level ice action PI is very consistent over all regions (Barents, Grand banks, Labrador). The value PI = 10-3.8 emerges, which corresponds approximately to a 6300 year unfactored design action effect. Note that abnormal ice features include icebergs as well as other ice loading events that are rare (such as islands, large MYI floes). The EL factor of 1.35 safely applies to iceberg actions that are “frequent” as in East Baffin Bay as a high annual arrival rate considerably reduces the annual extreme COV.


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Action Factors (Environmental and Ice): Results and Verification

The calibration process described in Section 5 is now used to optimize the various factors and parameters θ in both sets of design check equations (Section 5). For environmental actions E other than ice, the L1 principal action factor γE applicable to the 100-year action effect is optimized to be 1.35 for both Set I (ISO 19902) and Set II (CSA-S471) factors. The environmental companion factor γEC in the permanent/variable action design check equations is found to be 0.70. The abnormal action needs to be specified at an annual exceedance probability equal to 10-4. In the following two sections we use “action combination diagrams” to illustrate and verify some of the results of the calibration. It is felt that, in order to appreciate and test the performance of the optimized calibration parameters, two-by-two combinations of various action effects are most effective. Combinations of three, four, or more loads are very hard to visualize; on the other hand, two-by-two action combinations represent “worst-case” scenarios in the sense that if all combinations check out to be satisfactory for all possible contributions of either action effect, then the inclusion of additional action affects cannot decrease the reliability associated with the two-by-two combination. Recall also that all of the verification checks presented in this section are based on the minimum required design resistance. This, again, is a “worst-case” scenario from the point of view of structural safety. In reality, structural components will have “better” limit state reliability values than those shown in the two-by-two load combination diagrams. In the following two-by-two action combination diagrams, the horizontal axis denotes the ratio of one of the two load effects divided by the total load effect. This ratio, called “α” in the subsequent figures, varies from 0 to 100% and therefore, the very left-hand and right-hand sides of the diagram represent each load effect acting individually. Consider for instance Figure 18 which is a combination diagram for permanent load G and environmental load E. The right-hand side of Figure 18 shows the need for the factor γE = 1.35 for structural members dominated by environmental loading. It shows that on the other side of the action combination scale a companion factor of γEC as low as 0.7 can be afforded, which is confirmed by the overall calibration. Figure 19 shows the combined action of variable actions Q, of long duration and E. It can be seen in both Figures 18 and 19 that the environmental design check equations govern all design conditions marked by about 15% or more environmental load effect, i.e. the curves to the right of the noticeable discontinuity in slope. Note also that Set II action factors are overall more “conservative”, particularly on the α→0 side (pure G or pure Q1), while Set I and Set II converge for high environmental action ratios since the same action factor γE is used.

8

41

Turning now to ice action effects we make a distinction between the following calibration scenarios as discussed in Section 3:

(a) calibration of separate principal ice action factors γI for each “cell” in Table 5, i.e. for each combination of ice region and structure: the results are shown in Table 12 in black bold font.

(b) calibration of region-specific principal ice action factors γI : the results

are shown in Table 12 in red bold font.

(c) calibration of a principal ice action factor γI for all regions and all types: the result is shown in Table 12 in blue bold font.

(d) calibration of ice as part of all other environmental actions resulting in

an “overall” E and I factor γE = γI = 1.35 (as above) and PE = 10-4 for abnormal level actions.

It should be noted that action factors for conically sided structures (both GBS and floaters) are always larger than for other structures. The reason for this is the larger S (and H) values in the tails shown in the figures of Section 7.2. While the 100-year design action effects for conical structures are considerably less than for vertically sided structures, they increase at a greater rate and therefore require larger action factors to meet the reliability targets. This finding applies only if the input design actions for conical/sloping structures are validated following further investigation. Note that this effect disappears for L2 and L3 since the 100-year design action effects are much closer to the minimum required resistance, hence the effects of tail slope and heaviness tend to be less severe (see Section 10). As a result an exception must be made for structure types GC and FC if one is to follow calibration scenarios (b) and (c) above, as shown in Table 12. In principle, the exception should also show up in (d) but the overall “weight” (importance) of GC and FC when lumped together with all other types of environmental actions becomes almost negligible. When considering calibration scenario (b), region-specific action factors are highest for Beaufort-type zones (γI = 1.30), lowest for Sakhalin-type zones (γI = 1.20) and “in-between” for Caspian-type zones (γI = 1.25). Barents Sea FYR is a bit of an anomaly because of heavier tails (see Figures in Section 7.2) and perhaps this region should be called inconclusive for the time being; as it is now, it requires γI = 1.45. Under calibration scenario (c), the all-ice γI would be 1.30 except that 1.55 should be used for conically sided structures. The calibration of the prescribed annual exceedance probability for the abnormal level ice action PI is very consistent over all regions (Barents, Grand banks, Labrador). The value PI = 10-3.8 emerges, which corresponds approximately to a 6300 year unfactored design action effect. Note that abnormal ice features include icebergs as well as other ice loading events that are rare (such as islands, large MYI floes). The EL factor of 1.35 safely applies to iceberg actions that are “frequent” as in East Baffin Bay as a high annual arrival rate considerably reduces the annual extreme COV.


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As a verification, consider the two-by-two combination diagrams for permanent actions G and ice actions I for Beaufort Sea multi-year ice conditions: Figures 20-24. These combination diagrams depend of course on the type of Set used: Set I (ISO 19902) and Set II (CSA-S471) as explained in Section 5. This difference shows up on the left-hand side (α→0) of the diagrams since the permanent action factors are different for each set. It can be seen that, overall, Set I is more “conservative” for action ratios α < 0.3. Also the principal ice design check equations govern designs marked by α-factors exceeding 0.15 to 0.20. Note that in Figures 20-23 the region/structure-specific ice action factors (scenario (a) above) are used while Figure 24 uses region-specific (b) ice action factors. Referring to Figure 1(c) and Section 5, we should recall that the reliability target applies for the weighted results but there is also an “absolute” constraint one order of magnitude greater, and this explains why the figures appear to show that the 10-5 target (for L1) is not met or cannot be met for certain low-probability action combination effect ratios. Consider now the following sensitivity analysis. Suppose a large set of design combinations were considered for each “cell” in Table 12. Each design situation would have a different resistance COV, or a different annual mean ice encounter rate, or different ice action model uncertainty. Now determine, for each case separately, the minimum required ice action factor to achieve target reliability and not exceed the constraints. Each resulting action factor is shown by a “dot” in the Figures 25, 26 and 27. Also shown are bold black, bold red, and bold blue lines which correspond to the Table 12 calibrated values for (a) each region/structure, (b) each region, and (c) ice-overall, respectively. It can be seen that almost all “dots” fall well below their (a) (b) and (c) calibrated values, suggesting the principle discussed in Section 5 that individual limit state failure probabilities should not exceed their target by “too much”. Overall the suggested values in Table 12 for all 4 calibration scenarios are well on the safe side. The same result appears in Figure 28 which shows the sensitivity of PI for abnormal level ice actions.


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As a verification, consider the two-by-two combination diagrams for permanent actions G and ice actions I for Beaufort Sea multi-year ice conditions: Figures 20-24. These combination diagrams depend of course on the type of Set used: Set I (ISO 19902) and Set II (CSA-S471) as explained in Section 5. This difference shows up on the left-hand side (α→0) of the diagrams since the permanent action factors are different for each set. It can be seen that, overall, Set I is more “conservative” for action ratios α < 0.3. Also the principal ice design check equations govern designs marked by α-factors exceeding 0.15 to 0.20. Note that in Figures 20-23 the region/structure-specific ice action factors (scenario (a) above) are used while Figure 24 uses region-specific (b) ice action factors. Referring to Figure 1(c) and Section 5, we should recall that the reliability target applies for the weighted results but there is also an “absolute” constraint one order of magnitude greater, and this explains why the figures appear to show that the 10-5 target (for L1) is not met or cannot be met for certain low-probability action combination effect ratios. Consider now the following sensitivity analysis. Suppose a large set of design combinations were considered for each “cell” in Table 12. Each design situation would have a different resistance COV, or a different annual mean ice encounter rate, or different ice action model uncertainty. Now determine, for each case separately, the minimum required ice action factor to achieve target reliability and not exceed the constraints. Each resulting action factor is shown by a “dot” in the Figures 25, 26 and 27. Also shown are bold black, bold red, and bold blue lines which correspond to the Table 12 calibrated values for (a) each region/structure, (b) each region, and (c) ice-overall, respectively. It can be seen that almost all “dots” fall well below their (a) (b) and (c) calibrated values, suggesting the principle discussed in Section 5 that individual limit state failure probabilities should not exceed their target by “too much”. Overall the suggested values in Table 12 for all 4 calibration scenarios are well on the safe side. The same result appears in Figure 28 which shows the sensitivity of PI for abnormal level ice actions.

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Table 12 – Calibrated principal extreme-level ice action factors and abnormal-level annual exceedance probabilities (L1)

MYI 0.5 multi-year ice: 0.5 tenths

MYI 3.0 multi-year ice: 3.0 tenths FYR first-year ridges FYL first-year level ice IB icebergs

GV vertically sided GBS GC conically sided GBS FV vertically sided floater FC conically sided floater

FP FPSO unit PC vertical piled column ML multi-legged structure MI man-made island

Structural system



MYI 0.5 1.30 1.55 1.30 1.30 1.30†

† except for low MYI encounter rates: 1.35 Region-wide action factor: 1.30 (except for conically sided structures 1.55) Beaufort Sea NE Greenland Northern Chukchi Sea Arctic Islands

MYI 3.0 1.30 1.50

Region-wide action factor: 1.30 (except for conically sided structures 1.50) Sakhalin Cook Inlet Sea of Okhotsk Kara Sea

FYR 1.20 1.45 1.15(?) 1.20 1.25(?)

(?) denotes inconclusive calibration Region-wide action factor: 1.20 (except for conically sided structures 1.45) Barents Sea Bering Sea

FYR 1.35 1.45 1.35(?)

Region-wide action factor: 1.45 Caspian Sea Baltic Sea Bohai Sea

FYL 1.25 1.30 1.25 1.25 1.25

Region-wide action factor: 1.25 Barents Sea IB

10-3.8

10-3.8 Region-wide action factor: All IB types, all structures 10-3.8

Grand Banks IB

10-3.7



IB

10-3.7

10-3.7

Region-wide action factor: All IB types, all structures 10-3.8

All ice regions and types: 1.30 except for conically sided GBS and floaters 1.55; abnormal ice feature actions at 10-3.8

All environmental actions including ice: 1.35 all Note: This table contains 4 sets of ice action factors:

• the black bold-type value in each cell is the action factor for a given structural type in a given region • the red values are region-specific action factor • the blue value in the penultimate row applies to all regions • the green value in the last row is one “global” ice action factor for all environmental actions


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0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Action effect ratio α

Prob

abili

ty o

f Fai

lure

Set I Action Factors (ISO 19902)

Set II Action Factors (CSA S471)

10-5

10-6

10-4

10-7

10-3

Figure 18: Combination of permanent actions (α=0) and all types of environmental actions (α=1) using both set I and Set II action factors for permanent actions, and γE=1.35 and γEC=0.70.

All environmental actions E

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Action effect ratio α

Prob

abili

ty o

f Fai

lure

Set I Action Factors (ISO 19902)

Set II Action Factors (CSA S471)

10-5

10-6

10-4

10-7

10-3

Figure 19: Combination of long duration variable actions (α=0) and all types of environmental actions (α=1) using both set I and Set II action factors for permanent actions, and γE=1.35 and γEC=0.70.

Using Set I Action Factors (ISO 19902) for Permanent Actions

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0


Prob

abili

ty o

f Fai

lure

GV

GC

FP

PC

MI

10-5

10-6

10-4

10-7

10-3

Using region- and structure-specific calibrated action factors

Figure 20: Combination of Permanent Action (α=0) and Ice Action (α=1) for various Beaufort Sea MYI 0.5 structures. The ratio α indicates the relative magnitude of the ice action effect (Set I Factors).

45

Using Set II Action Factors (CSA S471) for Permanent Actions


Prob

abili

ty o

f Fai

lure

GV

GC

FP

PC

MI

10-5

10-6

10-4

10-7

10-3


Figure 21: Combination of Permanent Action (α=0) and Ice Action (α=1) for various Beaufort Sea MYI 0.5 structures. The ratio α indicates the relative magnitude of the ice action effect (Set II Factors).



Prob

abili

ty o

f Fai

lure

GV

GC

10-5

10-6

10-4

10-7

10-3




0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0


Prob

abili

ty o

f Fai

lure

GV

GC

10-5

10-6

10-4

10-7

10-3




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Prob

abili

ty o

f Fai

lure

GV

GC

FP

PC

MI

10-5

10-6

10-4

10-7

10-3





Prob

abili

ty o

f Fai

lure

GV

GC

10-5

10-6

10-4

10-7

10-3




0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0


Prob

abili

ty o

f Fai

lure

GV

GC

10-5

10-6

10-4

10-7

10-3




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Region-wide Weighted Probability of Failure (All Structures)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0


Prob

abili

ty o

f Fai

lure

Beaufort Sea, MYI 0.5, Set II

Beaufort Sea, MYI 0.5, Set I



10-5

10-6

10-4

10-7

10-3

Figure 24: Combination of Permanent Action (α=0) and Ice Action (α=1) for all Beaufort Sea regions using both Set I and Set II action factors for permanent action, and the calibrated region-wide ice action factors. The ratio α indicates the relative magnitude of the ice action effect.

1.00

1.05

1.10

1.15

1.20

1.25

1.30

1.35

1.40

1.45

1.50

1.55

1.60

EL A

ctio

n fa

ctor

MYI 0.5GV

MYI 0.5 FP

MYI 0.5PC

MYI 0.5MI

MYI 3.0GV

MYI 3.0GC

MYI 0.5GC

Figure 25: Minimum required principal extreme-level ice action factor for Beaufort Sea-type regions (Beaufort Sea, Chukchi Sea, Baffin Bay, Labrador, Laptev Sea, NE Greenland, Arctic Islands). Each dot represents a particular combination of mean encounter rate, resistance COV, and level of action model uncertainty. The black, red and blue lines denote the recommended calibrated action factors for each cell (region + structural type), each region, and ice-overall, respectively.

47

1.00

1.05

1.10

1.15

1.20

1.25

1.30

1.35

1.40

1.45

1.50

1.55

1.60

EL A

ctio

n fa

ctor

SAK FYRGV

SAK FYR FP

SAK FYRPC

SAK FYRML

BAR FYRFV

BAR FYRFC

SAK FYRGC

Figure 26: Minimum required principal extreme-level ice action factor for Sakhalin-type and Barents Sea-type regions (Sakhalin, Cook Inlet, Sea of Okhotsk, Kara Sea, Barents Sea, Bering Sea). Each dot represents a particular combination of mean encounter rate, resistance COV, and level of action model uncertainty. The black, red and blue lines denote the recommended calibrated action factors for each cell (region + structural type), each region, and ice-overall, respectively.

1.00

1.05

1.10

1.15

1.20

1.25

1.30

1.35

1.40

1.45

1.50

1.55

1.60

EL A

ctio

n Fa

ctor

CAS FYLGV

CAS FYLPC

CAS FYLML

CAS FYLMI

CAS FYLGC

Figure 27: Minimum required principal extreme-level ice action factor for Caspian Sea-type regions (Caspian Sea, Baltic Sea, Bohai Sea). Each dot represents a particular combination of mean encounter rate, resistance COV, and level of action model uncertainty. The black, red and blue lines denote the recommended calibrated action factors for each cell (region + structural type), each region, and ice-overall, respectively.


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Region-wide Weighted Probability of Failure (All Structures)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0


Prob

abili

ty o

f Fai

lure





10-5

10-6

10-4

10-7

10-3

Figure 24: Combination of Permanent Action (α=0) and Ice Action (α=1) for all Beaufort Sea regions using both Set I and Set II action factors for permanent action, and the calibrated region-wide ice action factors. The ratio α indicates the relative magnitude of the ice action effect.

1.00

1.05

1.10

1.15

1.20

1.25

1.30

1.35

1.40

1.45

1.50

1.55

1.60

EL A

ctio

n fa

ctor

MYI 0.5GV

MYI 0.5 FP

MYI 0.5PC

MYI 0.5MI

MYI 3.0GV

MYI 3.0GC

MYI 0.5GC

Figure 25: Minimum required principal extreme-level ice action factor for Beaufort Sea-type regions (Beaufort Sea, Chukchi Sea, Baffin Bay, Labrador, Laptev Sea, NE Greenland, Arctic Islands). Each dot represents a particular combination of mean encounter rate, resistance COV, and level of action model uncertainty. The black, red and blue lines denote the recommended calibrated action factors for each cell (region + structural type), each region, and ice-overall, respectively.

47

1.00

1.05

1.10

1.15

1.20

1.25

1.30

1.35

1.40

1.45

1.50

1.55

1.60

EL A

ctio

n fa

ctor

SAK FYRGV

SAK FYR FP

SAK FYRPC

SAK FYRML

BAR FYRFV

BAR FYRFC

SAK FYRGC

Figure 26: Minimum required principal extreme-level ice action factor for Sakhalin-type and Barents Sea-type regions (Sakhalin, Cook Inlet, Sea of Okhotsk, Kara Sea, Barents Sea, Bering Sea). Each dot represents a particular combination of mean encounter rate, resistance COV, and level of action model uncertainty. The black, red and blue lines denote the recommended calibrated action factors for each cell (region + structural type), each region, and ice-overall, respectively.

1.00

1.05

1.10

1.15

1.20

1.25

1.30

1.35

1.40

1.45

1.50

1.55

1.60

EL A

ctio

n Fa

ctor

CAS FYLGV

CAS FYLPC

CAS FYLML

CAS FYLMI

CAS FYLGC

Figure 27: Minimum required principal extreme-level ice action factor for Caspian Sea-type regions (Caspian Sea, Baltic Sea, Bohai Sea). Each dot represents a particular combination of mean encounter rate, resistance COV, and level of action model uncertainty. The black, red and blue lines denote the recommended calibrated action factors for each cell (region + structural type), each region, and ice-overall, respectively.


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Spec

ified

AL

annu

al e

xcee

danc

e pr

obab

ility

Bar IBFV

Bar IBFP

GB IBGV

GB IBFP

Lab IBGV

Lab IBFP

-4.0 10

-3.4

10-3.0

10

-3.810

-3.6

-3.210

10

Figure 28: Minimum required specified exceeded probability for the abnormal level ice action loading in the Barents Sea, Grand Banks, Labrador, Baffin Bay, NE Greenland. Each dot represents a particular combination of mean encounter rate, resistance COV, and level of action model uncertainty. The black, red and blue lines denote the recommended calibrated specified annual exceedance probability levels for each cell (region + structural type), each region, and ice-overall, respectively.

49

Companion Action Factors (Environmental and Ice): Results and Verification

ISO 19906 calls for a design companion action format for combinations of environmental actions. The following clauses are relevant:

[ISO/DIS 19906:2009, clause 7.2.3] Representative values for environmental action combinations shall be determined as the combination of the principal action and the factored companion actions.

Action c ombinations for e ach env ironmental a ction shall be derived by c onsidering each E L and A L representative v alue of t he ac tion i n t urn a s a pr incipal a ction. T hese v alues s hall be ac companied by companion environmental actions. I n ea ch case, t he r epresentative v alues of the E L ac tion, suitably factored, should be considered as companion to the EL or AL principal action. The principal and companion EL actions for ice are extreme-level ice events (ELIE). The principal AL action for ice is the abnormal-level ice event (ALIE). Where data are available, a p robabilistic t reatment of joint probabilities should be conducted to determine the magnitude of companion actions. In the absence of specific consideration of joint probabilities, the combination factors provided for companion EL actions in Table 7-3 shall be used. The values specified in Table 7 -3 ar e c onservative t o ac count for a w ide v ariety o f pos sibilities. C onsequently, site-specific dat a should be used and joint probabilities calculated whenever possible.

It appears therefore that we need to focus on the design check equations in Table 13 where it should be stressed that the resulting representative values are unfactored (for ULS this is obviously quite relevant as the principal environmental and the principal ice action factors γE and γI must be applied to EE or IE; for ALS a factor of 1.0 is applied to EA or IA). The number of companion factors ψij in Table 13 is quite staggering if each environmental process should be considered in combination with a different one. Therefore, Table 14 reduces the number of factors to just four:

(i) a ULS companion action factor ψEI for two independent or very weakly correlated continuous environmental processes.

(ii) a ULS companion action factor ψED for two strongly dependent or

correlated continuous environmental processes. (iii) a ALS companion action factor ψAD involving a discrete principal

process and a continuous companion environmental process which can be treated as independent.

(iv) a ALS companion action factor ψAI involving a discrete principal

process and a continuous companion environmental process which are assumed to be strongly dependent.

Consider first the case (i) of two independent or very weakly correlated environmental/ice processes. This case can be calibrated using the variable action FBC probability models described in Sections 6.6 and 6.4.

9


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Companion Action Factors (Environmental and Ice): Results and Verification

ISO 19906 calls for a design companion action format for combinations of environmental actions. The following clauses are relevant:

[ISO/DIS 19906:2009, clause 7.2.3] Representative values for environmental action combinations shall be determined as the combination of the principal action and the factored companion actions.

Action c ombinations for e ach env ironmental a ction shall be derived by c onsidering each E L and A L representative v alue of t he ac tion i n t urn a s a pr incipal a ction. T hese v alues s hall be ac companied by companion environmental actions. I n ea ch case, t he r epresentative v alues of the E L ac tion, suitably factored, should be considered as companion to the EL or AL principal action. The principal and companion EL actions for ice are extreme-level ice events (ELIE). The principal AL action for ice is the abnormal-level ice event (ALIE). Where data are available, a p robabilistic t reatment of joint probabilities should be conducted to determine the magnitude of companion actions. In the absence of specific consideration of joint probabilities, the combination factors provided for companion EL actions in Table 7-3 shall be used. The values specified in Table 7 -3 ar e c onservative t o ac count for a w ide v ariety o f pos sibilities. C onsequently, site-specific dat a should be used and joint probabilities calculated whenever possible.

It appears therefore that we need to focus on the design check equations in Table 13 where it should be stressed that the resulting representative values are unfactored (for ULS this is obviously quite relevant as the principal environmental and the principal ice action factors γE and γI must be applied to EE or IE; for ALS a factor of 1.0 is applied to EA or IA). The number of companion factors ψij in Table 13 is quite staggering if each environmental process should be considered in combination with a different one. Therefore, Table 14 reduces the number of factors to just four:

(i) a ULS companion action factor ψEI for two independent or very weakly correlated continuous environmental processes.

(ii) a ULS companion action factor ψED for two strongly dependent or

correlated continuous environmental processes. (iii) a ALS companion action factor ψAD involving a discrete principal

process and a continuous companion environmental process which can be treated as independent.

(iv) a ALS companion action factor ψAI involving a discrete principal

process and a continuous companion environmental process which are assumed to be strongly dependent.

Consider first the case (i) of two independent or very weakly correlated environmental/ice processes. This case can be calibrated using the variable action FBC probability models described in Sections 6.6 and 6.4.

9


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The optimal companion factor for this combination scenario is ψEI = 0.6. Note that this result should also be directly applicable to L2 and L3, although this was not explicitly verified. Figures 29-31 show different values of the combination factor ΨE1 for two stochastically independent environmental load processes. The presence and renewal parameters in the FBC pulse action models were varied to verify deviations from this diagram. In all cases differences of less than 5% were found on the –log PF scale. Three cases are shown in Figures 29-31: E1 + E2, E + IB and E + IC where IB and IC are Beaufort Sea-type ice and Caspian Sea-type ice, respectively (see footnotes to these three figures). The latter has a presence of ice (modeled as np in the FBC probability model) which is much lower than IB. However, the combination diagrams show little difference, since the factors γE and γI are different and so are of course the design actions themselves. Next consider the more difficult case (ii) of combining two strongly dependent or correlated continuous environmental/ice processes E1 and E2 and the required companion factor ψED (see Table 14). Existing standards would tend to suggest that the value of ψED is equal to 1.0 for this case meaning that one adds up the extreme action effects for both processes at their full individual 100-year return level. This would obviously be correct if process E2(t) were to be equal to kE1(t) for all points in time t where k is a constant, but this is a really farfetched and extreme case of correlation. The problem with ψED is that we can distinguish so many types of “dependence” between two environmental processes such as (Wen, 1990):

– within-load dependencies (same correlation structures)

– within-cluster dependence (e.g. action effects during weather bursts)

– dependence in the intensities of E1 and E2

– dependence in the occurrence rates of E1 and E2

– dependence in the duration of coincidence of E1 and E2

– various forms of spatial correlation

– cross-correlation within short-term metocean states (e.g. wind and waves in a given sea state

– correlation between long-term metocean states

Accordingly, it is virtually impossible to optimize one single generic factor ψED to reflect all of the above situations. Without doing the actual number-crunching but merely based on site-specific experience, I would suggest ψED = 0.85 with the caveat to optimize such a factor once specific environmental conditions are known for a given site and structure.

51

The third companion factor ψAI for case (iii) and Table 14 denotes which fraction of a continuous extreme level environmental action should be used in conjunction with the (principal value of the) abnormal level ice load, assuming these two processes to be independent. As an example consider iceberg actions and deepwater current actions. The first thing to realize is that AL in Table 13 is an enormously large action effect and one would expect the companion value of an independent environmental action process to be quite small. In fact, the companion action should be based on its point-in-time probability distribution and not its annual extreme value distribution, since the former expresses what can be observed at an arbitrary point in time, which is the time when the abnormal event occurs given the assumption of independence. In order to investigate this combination, the companion process is modeled using the FBC rectangular pulse process technique described in Section 6.4 using various realistic values of np and nR. In all cases the annual extreme pdf is determined together with the corresponding representative action EL at the 100-year return value. Then, a relationship is established between EL and the q-quantile of the point-in-time pdf. Their ratio is the resulting value of ψAI and, depending on the arrival rate of extreme events (which determines q) and depending on the presence and renewal parameters of the companion process, it varies between 0.075 and 0.375. The value ψAI = 0.35 is recommended. Finally, the case (iv) companion factor ψAD in Table 14 is considered. As for the case of ψED we face the question of what exactly is to be understood by “dependence”; e.g. in combining an abnormal level principal iceberg action effect I with a wind or wave action effect E, what are the exact characteristics of the joint probabilistic behaviour of I and E? Following a Bayesian argument, the companion value of E should be based on the following PDF: =)causingevent abnormal|( IEf ÷=∩= )eventtheofintensityevent abnormalanofoccurrence|( IEf (10) )()occurrence|AL()|eventabnormalanofoccurrencePr( EfEIfE ∩=÷ where f(E) is the point-in-time pdf of the continuous companion event E. It appears that two effects show up in (10): the iceberg impact probability can be a function of E and, given an impact, there is also some correlation between the intensity of the iceberg action effect I and the intensity of the environmental action. Assuming both to be linear functions of E then the probabilistic parameters of the pdf of E given I can be updated according to (10). Simulation over a wide set of simple FBC processes using a procedure similar to the above case of ψAI, yields ψAD values that are between 1.05 and 1.25 higher than ψAI. Hence a value ψAD = 0.45 is recommended. The environmental and ice action factors (Section 8) and companion action factors (Section 9) are summarized in Table 15 below.


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The optimal companion factor for this combination scenario is ψEI = 0.6. Note that this result should also be directly applicable to L2 and L3, although this was not explicitly verified. Figures 29-31 show different values of the combination factor ΨE1 for two stochastically independent environmental load processes. The presence and renewal parameters in the FBC pulse action models were varied to verify deviations from this diagram. In all cases differences of less than 5% were found on the –log PF scale. Three cases are shown in Figures 29-31: E1 + E2, E + IB and E + IC where IB and IC are Beaufort Sea-type ice and Caspian Sea-type ice, respectively (see footnotes to these three figures). The latter has a presence of ice (modeled as np in the FBC probability model) which is much lower than IB. However, the combination diagrams show little difference, since the factors γE and γI are different and so are of course the design actions themselves. Next consider the more difficult case (ii) of combining two strongly dependent or correlated continuous environmental/ice processes E1 and E2 and the required companion factor ψED (see Table 14). Existing standards would tend to suggest that the value of ψED is equal to 1.0 for this case meaning that one adds up the extreme action effects for both processes at their full individual 100-year return level. This would obviously be correct if process E2(t) were to be equal to kE1(t) for all points in time t where k is a constant, but this is a really farfetched and extreme case of correlation. The problem with ψED is that we can distinguish so many types of “dependence” between two environmental processes such as (Wen, 1990):

– within-load dependencies (same correlation structures)

– within-cluster dependence (e.g. action effects during weather bursts)

– dependence in the intensities of E1 and E2

– dependence in the occurrence rates of E1 and E2

– dependence in the duration of coincidence of E1 and E2

– various forms of spatial correlation

– cross-correlation within short-term metocean states (e.g. wind and waves in a given sea state

– correlation between long-term metocean states

Accordingly, it is virtually impossible to optimize one single generic factor ψED to reflect all of the above situations. Without doing the actual number-crunching but merely based on site-specific experience, I would suggest ψED = 0.85 with the caveat to optimize such a factor once specific environmental conditions are known for a given site and structure.

51

The third companion factor ψAI for case (iii) and Table 14 denotes which fraction of a continuous extreme level environmental action should be used in conjunction with the (principal value of the) abnormal level ice load, assuming these two processes to be independent. As an example consider iceberg actions and deepwater current actions. The first thing to realize is that AL in Table 13 is an enormously large action effect and one would expect the companion value of an independent environmental action process to be quite small. In fact, the companion action should be based on its point-in-time probability distribution and not its annual extreme value distribution, since the former expresses what can be observed at an arbitrary point in time, which is the time when the abnormal event occurs given the assumption of independence. In order to investigate this combination, the companion process is modeled using the FBC rectangular pulse process technique described in Section 6.4 using various realistic values of np and nR. In all cases the annual extreme pdf is determined together with the corresponding representative action EL at the 100-year return value. Then, a relationship is established between EL and the q-quantile of the point-in-time pdf. Their ratio is the resulting value of ψAI and, depending on the arrival rate of extreme events (which determines q) and depending on the presence and renewal parameters of the companion process, it varies between 0.075 and 0.375. The value ψAI = 0.35 is recommended. Finally, the case (iv) companion factor ψAD in Table 14 is considered. As for the case of ψED we face the question of what exactly is to be understood by “dependence”; e.g. in combining an abnormal level principal iceberg action effect I with a wind or wave action effect E, what are the exact characteristics of the joint probabilistic behaviour of I and E? Following a Bayesian argument, the companion value of E should be based on the following PDF: =)causingevent abnormal|( IEf ÷=∩= )eventtheofintensityevent abnormalanofoccurrence|( IEf (10) )()occurrence|AL()|eventabnormalanofoccurrencePr( EfEIfE ∩=÷ where f(E) is the point-in-time pdf of the continuous companion event E. It appears that two effects show up in (10): the iceberg impact probability can be a function of E and, given an impact, there is also some correlation between the intensity of the iceberg action effect I and the intensity of the environmental action. Assuming both to be linear functions of E then the probabilistic parameters of the pdf of E given I can be updated according to (10). Simulation over a wide set of simple FBC processes using a procedure similar to the above case of ψAI, yields ψAD values that are between 1.05 and 1.25 higher than ψAI. Hence a value ψAD = 0.45 is recommended. The environmental and ice action factors (Section 8) and companion action factors (Section 9) are summarized in Table 15 below.


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Table 13 – Companion environmental actions

+ denotes a (symbolic) combination of action effects

ULS EE representative value of the total extreme-level environmental action (before

applying the action factor) ELi representative value of the extreme-level environmental action i ψEji companion action factor when environmental action j acts as a companion to

the principal extreme-level action i

EE = ELi + ψEji ELj

ALS EA representative value of the total abnormal-level environmental action ALi representative value of the abnormal-level environmental action i ELj representative value of the extreme-level environmental action j ψAji companion action factor when environmental action j acts as a companion to

the principal abnormal-level action i

EA = ALi + ψAji ELj

53

Table 14 – Various types of companion action factors

ELi principal action i

ELj individual companion actions j

ULS applicable companion action factor ψEji in Table 7

ALS applicable companion action factor ψAji in Table 7

WA WI, CW, IW ψED ψAD WA CO, IL, SW ψEI ψAI SW WA, WI, CW, CO, IL ψEI - WI WA, CW, IH, IL, IW ψED ψAD WI SW, CO ψEI ψAI CO IL ψED - CO WA, SW, WI ψEI - IH WI, CW, CO ψED ψAD IL WI, CW, CO ψED ψAD IL WA, SW ψEI ψAI IW WI, WA, CW ψED - ID WI, CW, WA - ψAD ID CO, SW - ψAI WA WI CW CO SW IH IL IW ID ψEI ψED ψAD ψAI

Actions: wave actions wind actions current action (wind-driven) current action (other, such as tidal, deepwater) swell sea ice actions (high concentration ≥ 8/10) sea ice actions (low concentration ≤ 8/10) ice actions which increase as a result of increasing wave actions large discrete ice feature actions, large iceberg actions Companion action factors: companion action factor for two independent or very weakly correlated continuous environmental processes companion action factor for two strongly dependent or correlated continuous environmental processes companion action factor involving a discrete principal process and a continuous companion environmental process which can be treated as independent companion action factor involving a discrete principal process and a continuous companion environmental process which are assumed to be strongly dependent


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Table 13 – Companion environmental actions

+ denotes a (symbolic) combination of action effects

ULS EE representative value of the total extreme-level environmental action (before

applying the action factor) ELi representative value of the extreme-level environmental action i ψEji companion action factor when environmental action j acts as a companion to

the principal extreme-level action i

EE = ELi + ψEji ELj

ALS EA representative value of the total abnormal-level environmental action ALi representative value of the abnormal-level environmental action i ELj representative value of the extreme-level environmental action j ψAji companion action factor when environmental action j acts as a companion to

the principal abnormal-level action i

EA = ALi + ψAji ELj

53

Table 14 – Various types of companion action factors

ELi principal action i

ELj individual companion actions j

ULS applicable companion action factor ψEji in Table 7

ALS applicable companion action factor ψAji in Table 7

WA WI, CW, IW ψED ψAD WA CO, IL, SW ψEI ψAI SW WA, WI, CW, CO, IL ψEI - WI WA, CW, IH, IL, IW ψED ψAD WI SW, CO ψEI ψAI CO IL ψED - CO WA, SW, WI ψEI - IH WI, CW, CO ψED ψAD IL WI, CW, CO ψED ψAD IL WA, SW ψEI ψAI IW WI, WA, CW ψED - ID WI, CW, WA - ψAD ID CO, SW - ψAI WA WI CW CO SW IH IL IW ID ψEI ψED ψAD ψAI

Actions: wave actions wind actions current action (wind-driven) current action (other, such as tidal, deepwater) swell sea ice actions (high concentration ≥ 8/10) sea ice actions (low concentration ≤ 8/10) ice actions which increase as a result of increasing wave actions large discrete ice feature actions, large iceberg actions Companion action factors: companion action factor for two independent or very weakly correlated continuous environmental processes companion action factor for two strongly dependent or correlated continuous environmental processes companion action factor involving a discrete principal process and a continuous companion environmental process which can be treated as independent companion action factor involving a discrete principal process and a continuous companion environmental process which are assumed to be strongly dependent


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Table 15 – Overview of calibrated environmental/ice action factors and AL exceedance probabilities for exposure level L1

(valid for both Set I and Set II)

principal environmental action factor γE 1.35 companion environmental action factor γEC 0.70 AL environmental annual exceedance probability PE 10-4

principal ice action factor γI (a) calibration per region and per structure type from 1.20 to 1.55, as per Table 12 (b) calibration per region from 1.20 to 1.55, as per Table 12 (c) all ice 1.30 exception conically sided structures 1.55 (d) ice is included in all environmental actions 1.35 AL ice annual exceedance probability 10-3.8

companion factor ψEI (Tables 13, 14) 0.60 companion factor ψED (Tables 13, 14) 0.85 companion factor ψAI (Tables 13, 14) 0.35 companion factor ψAD (Tables 13, 14) 0.45


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Table 15 – Overview of calibrated environmental/ice action factors and AL exceedance probabilities for exposure level L1

(valid for both Set I and Set II)

principal environmental action factor γE 1.35 companion environmental action factor γEC 0.70 AL environmental annual exceedance probability PE 10-4

principal ice action factor γI (a) calibration per region and per structure type from 1.20 to 1.55, as per Table 12 (b) calibration per region from 1.20 to 1.55, as per Table 12 (c) all ice 1.30 exception conically sided structures 1.55 (d) ice is included in all environmental actions 1.35 AL ice annual exceedance probability 10-3.8

companion factor ψEI (Tables 13, 14) 0.60 companion factor ψED (Tables 13, 14) 0.85 companion factor ψAI (Tables 13, 14) 0.35 companion factor ψAD (Tables 13, 14) 0.45

55

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0


Prob

abili

ty o

f Fai

lure

companion action factor = 0.5



10-5

10-6

10-4

10-7

10-3

Figure 29: Combination of two independent environmental action processes A and B (both np = 365 days, nR = 365/3), using max [γE(EA+ψEB), γE(ψEA+EB)] where γE = 1.35.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0


Prob

abili

ty o

f Fai

lure




10-5

10-6

10-4

10-7

10-3

Figure 30: Combination of an environmental action process A (np = 365 days, nR = 365/3) and an independent Beaufort Sea region ice action process B (np = 100 days, nR = 30), using max [γE(EA+ψEB), γI(ψEA+EB)] where γE = 1.35 and γI = 1.30. The action effect ratio α=1 for pure A and α=0 for pure B.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0


Prob

abili

ty o

f Fai

lure




10-5

10-6

10-4

10-7

10-3

Figure 31: Combination of an environmental action process A (np = 365 days, nR = 365/3) and an independent Caspian Sea region ice action process B (np = 30 days, nR = 30), using max [γE(EA+ψEB), γI(ψEA+EB)] where γE = 1.35 and γI = 1.25. The action effect ratio α=1 for pure A and α=0 for pure B.


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Exposure Levels L2 and L3

Exposure levels L2 and L3 are associated with different levels of target reliability and different upper bound failure probabilities as discussed in section 5. This is the only difference in the calibration process outlined in the preceding sections. The representative values of all actions remain the same and it is only the unknown set of control parameters θ defined in section 5 that will be different as a result of a new optimization using the L2 and L3 risk targets. As an example, we considered the action factors in Set II (only). This is because their permanent and variable action factors are already available for the so-called Safety-Class II in CSA-S471. No such factors are available for Set I based on ISO 19902. As a complete calibration against L2 and L3 targets was not included in the scope of the present work, we examined and verified only the following specific aspects of the calibration:

1. the principal environmental action factor (all loads) for L2 and L3 2. the region- and structure-specific principal ice action factors for L2 and

L3 only for Beaufort Sea multi-year ice 0.5 and 3.0 tenths conditions (these represent 40% of the total calibration weight and also they resulted in the largest L1 action factors, so that the present analysis for L2 and L3 should be conservative)

3. an overall weighted region-specific principal ice action factor for all Beaufort Sea conditions (L2 and L3)

4. the specified exceedance probabilities for abnormal level ice loads for class L2. (Note that L3 does not consider abnormal actions.)

The results are shown in Tables 16 and 17. We observe that the principal ice action factors and the principal environmental action factors converge to the same (decreased) values. This is due to the fact that most of the failure probability now accumulates in an area that is much closer to the representative value of the actions (which remains at the 1% annual exceedance level). Therefore the effect of tail slope S weakens considerably with respect to L1 (see also Section 7.2). It can also be seen that the action factor for conically sided structures which for L1 was considerably greater than for all other types of structures (1.55 versus 1.30) also tends to converge to the value for the other types of structures. Table 17 shows that it is 1.20 (versus 1.10) and Table 18 shows no further difference between vertically and conically sided structures (1.10 for all). The reason for this is exactly the same as in the preceding paragraph. The tail effect disappears gradually. Note that environmental companion factors for L2 and L3 remain approximately the same as for L1 (see Section 9).

10

57

Table 16 – Calibrated principal extreme-level ice action factors and abnormal-level annual exceedance probabilities for exposure level L2 (Beaufort Sea and icebergs only)




Structural system



MYI 0.5 1.10 1.20 1.10 1.10 1.10†


MYI 3.0 1.10 1.20

Region-wide action factor: 1.10 (except for conically sided structures 1.20) Barents Sea IB

10-2.9


Grand Banks IB

10-2.8



IB

10-2.8

10-2.8


All ice regions and types: 1.10 except for conically sided GBS and floaters 1.20; abnormal ice feature actions at 10-3.0 Note that these values are verified for all Beaufort Sea conditions but are deemed to be safe for all regions (bullet #2, section 10) All environmental actions including ice: 1.10 all Note: This table contains 4 sets of ice action factors:



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Exposure Levels L2 and L3

Exposure levels L2 and L3 are associated with different levels of target reliability and different upper bound failure probabilities as discussed in section 5. This is the only difference in the calibration process outlined in the preceding sections. The representative values of all actions remain the same and it is only the unknown set of control parameters θ defined in section 5 that will be different as a result of a new optimization using the L2 and L3 risk targets. As an example, we considered the action factors in Set II (only). This is because their permanent and variable action factors are already available for the so-called Safety-Class II in CSA-S471. No such factors are available for Set I based on ISO 19902. As a complete calibration against L2 and L3 targets was not included in the scope of the present work, we examined and verified only the following specific aspects of the calibration:

1. the principal environmental action factor (all loads) for L2 and L3 2. the region- and structure-specific principal ice action factors for L2 and

L3 only for Beaufort Sea multi-year ice 0.5 and 3.0 tenths conditions (these represent 40% of the total calibration weight and also they resulted in the largest L1 action factors, so that the present analysis for L2 and L3 should be conservative)

3. an overall weighted region-specific principal ice action factor for all Beaufort Sea conditions (L2 and L3)

4. the specified exceedance probabilities for abnormal level ice loads for class L2. (Note that L3 does not consider abnormal actions.)

The results are shown in Tables 16 and 17. We observe that the principal ice action factors and the principal environmental action factors converge to the same (decreased) values. This is due to the fact that most of the failure probability now accumulates in an area that is much closer to the representative value of the actions (which remains at the 1% annual exceedance level). Therefore the effect of tail slope S weakens considerably with respect to L1 (see also Section 7.2). It can also be seen that the action factor for conically sided structures which for L1 was considerably greater than for all other types of structures (1.55 versus 1.30) also tends to converge to the value for the other types of structures. Table 17 shows that it is 1.20 (versus 1.10) and Table 18 shows no further difference between vertically and conically sided structures (1.10 for all). The reason for this is exactly the same as in the preceding paragraph. The tail effect disappears gradually. Note that environmental companion factors for L2 and L3 remain approximately the same as for L1 (see Section 9).

10

57





Structural system



MYI 0.5 1.10 1.20 1.10 1.10 1.10†


MYI 3.0 1.10 1.20

Region-wide action factor: 1.10 (except for conically sided structures 1.20) Barents Sea IB

10-2.9


Grand Banks IB

10-2.8



IB

10-2.8

10-2.8


All ice regions and types: 1.10 except for conically sided GBS and floaters 1.20; abnormal ice feature actions at 10-3.0 Note that these values are verified for all Beaufort Sea conditions but are deemed to be safe for all regions (bullet #2, section 10) All environmental actions including ice: 1.10 all Note: This table contains 4 sets of ice action factors:



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Structural system



MYI 0.5 0.85 0.85 0.85 0.85 0.85

Region-wide action factor: 0.85 (all structures) Beaufort Sea NE Greenland Northern Chukchi Sea Arctic Islands

MYI 3.0 0.85 0.85

Region-wide action factor: 0.85 (all structures) Barents Sea IB

N/A

N/A Region-wide action factor: All IB types, all structures N/A

Grand Banks IB

N/A



IB

N/A

N/A

Region-wide action factor: All IB types, all structures N/A

All ice regions and types: 0.85 all; abnormal ice feature actions are not considered for L3 Note that these values are verified for all Beaufort Sea conditions but are deemed to be safe for all regions (bullet #2, section 10) All environmental actions including ice: 0.85 all Note: This table contains 4 sets of ice action factors:


59

Summary of Calibrated Design Check Equations

The calibration of the environmental/ice action factors, companion action factors and the specified AL exceedance probabilities in ISO/DIS 19906:2009 results in the design check equations shown in Table 18. Table 18 – Calibrated design check equations for exposure levels L1, L2 and L3

EXPOSURE LEVEL L1 – using Set I action factors (ISO 19902)

ULS-1 (L1) 1.30G + 1.50Q1 +1.50Q2 + 0.70EE

ULS-3 (L1) 1.10G + 1.10Q1 + 1.35EE

ULS-3 Ice (L1) 1.10G + 1.10Q1 + γI IceE where γI is given by Table 12 ALS-4 (L1) 1.00G + 1.00Q1

+ 1.00EA(10-4) ALS-4 Ice (L1) 1.00G + 1.00Q1 + 1.00IceA(PE) where PE is given by Table 12 EXPOSURE LEVEL L1 – using Set II action factors (ISO 19906)

ULS-1 (L1) 1.25G + 1.45Q1 +1.20Q2 + 0.70EE

ULS-2 (L1) 1.25G + 1.15Q1 +1.70Q2 + 0.70EE

ULS-3 (L1) 1.05G + 1.15Q1 + 1.35EE


+ 1.00EA(10-4) ALS-4 Ice (L1) 1.05G + 1.15Q1 + 1.00IceA(PE) where PE is given by Table 12 COMPANION ACTION FACTORS – Both Set I and set II companion factor ψEI: companion factor ψED: companion factor ψAI: companion factor ψAD:

use 0.60 in Table 13 and 14 use 0.85 in Table 13 and 14 use 0.35 in Table 13 and 14 use 0.45 in Table 13 and 14

EXPOSURE LEVEL L2 – using Set II action factors (ISO 19906)

ULS-3 (L2) 1.05G + 1.00Q1 + 1.10EE

ULS-3 Ice (L2) 1.05G + 1.00Q1 + 1.10IceE†

ALS-4 (L2) 1.05G + 1.00Q1 + 1.00EA(10-3)

ALS-4 Ice (L2) 1.05G + 1.00Q1 + 1.00IceA(10-3)

all companion factors ψij are the same as for L1 † except 1.20 for conically sided structures EXPOSURE LEVEL L3 – using Set II action factors (ISO 19906)

ULS-3 (L3) 1.05G + 0.90Q1 + 0.85EE

ULS-3 Ice (L3) 1.05G + 0.90Q1 + 0.85IceE all companion factors ψij are the same as for L1

11


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Structural system



MYI 0.5 0.85 0.85 0.85 0.85 0.85

Region-wide action factor: 0.85 (all structures) Beaufort Sea NE Greenland Northern Chukchi Sea Arctic Islands

MYI 3.0 0.85 0.85

Region-wide action factor: 0.85 (all structures) Barents Sea IB

N/A


Grand Banks IB

N/A



IB

N/A

N/A

Region-wide action factor: All IB types, all structures N/A

All ice regions and types: 0.85 all; abnormal ice feature actions are not considered for L3 Note that these values are verified for all Beaufort Sea conditions but are deemed to be safe for all regions (bullet #2, section 10) All environmental actions including ice: 0.85 all Note: This table contains 4 sets of ice action factors:


59

Summary of Calibrated Design Check Equations

The calibration of the environmental/ice action factors, companion action factors and the specified AL exceedance probabilities in ISO/DIS 19906:2009 results in the design check equations shown in Table 18. Table 18 – Calibrated design check equations for exposure levels L1, L2 and L3

EXPOSURE LEVEL L1 – using Set I action factors (ISO 19902)

ULS-1 (L1) 1.30G + 1.50Q1 +1.50Q2 + 0.70EE

ULS-3 (L1) 1.10G + 1.10Q1 + 1.35EE


+ 1.00EA(10-4) ALS-4 Ice (L1) 1.00G + 1.00Q1 + 1.00IceA(PE) where PE is given by Table 12 EXPOSURE LEVEL L1 – using Set II action factors (ISO 19906)

ULS-1 (L1) 1.25G + 1.45Q1 +1.20Q2 + 0.70EE

ULS-2 (L1) 1.25G + 1.15Q1 +1.70Q2 + 0.70EE

ULS-3 (L1) 1.05G + 1.15Q1 + 1.35EE


+ 1.00EA(10-4) ALS-4 Ice (L1) 1.05G + 1.15Q1 + 1.00IceA(PE) where PE is given by Table 12 COMPANION ACTION FACTORS – Both Set I and set II companion factor ψEI: companion factor ψED: companion factor ψAI: companion factor ψAD:

use 0.60 in Table 13 and 14 use 0.85 in Table 13 and 14 use 0.35 in Table 13 and 14 use 0.45 in Table 13 and 14

EXPOSURE LEVEL L2 – using Set II action factors (ISO 19906)

ULS-3 (L2) 1.05G + 1.00Q1 + 1.10EE

ULS-3 Ice (L2) 1.05G + 1.00Q1 + 1.10IceE†

ALS-4 (L2) 1.05G + 1.00Q1 + 1.00EA(10-3)

ALS-4 Ice (L2) 1.05G + 1.00Q1 + 1.00IceA(10-3)

all companion factors ψij are the same as for L1 † except 1.20 for conically sided structures EXPOSURE LEVEL L3 – using Set II action factors (ISO 19906)

ULS-3 (L3) 1.05G + 0.90Q1 + 0.85EE

ULS-3 Ice (L3) 1.05G + 0.90Q1 + 0.85IceE all companion factors ψij are the same as for L1

11


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References Anzai T., Bryant, L.M. and F.B. Pedersen (1982) “Comparison of a Limit State Design

Code with API RP 2A”, Proc. OTC, 4191. Boos, D.D. (1984) “Using Extreme Value Theory to Estimate Large Percentiles”,

Technometrics, Vol. 2, No. 1, pp. 33-39. API RP2N-2001 (2001) “Recommended Practice for Planning, Designing, and

Constructing Structures and Pipelines for Arctic Conditions”, American Petroleum Institute, 2nd edition.

CAN/CSA-S471-04 (2004) “General Requirements, Design Criteria, the Environment, and Loads (Offshore Structures)”.

C-CORE (2009) “Development of Ice Design Loads and Criteria for Various Arctic Regions”, R08-654, report submitted to OGP February.

Ellingwood, B., J.G. MacGregor, T.V. Galambos and C.A. Cornell (1982) “Probability Based Load Criteria: Load Factors and Load Combinations”, ASCE, Journal of the Structural Division, Vol. 108, N0.ST5, 1982, pp. 978-997.

ISO (1998) “ISO2394 General Principles on Reliability for Structures”. ISO/DIS 19906:2009 (2009) “Arctic Offshore Structures” JCSS, the Joint Committee for Structural Safety (2007) “Probabilistic model code”,

available at http://www.jcss.ethz.ch/. Jordaan, I.J. (2009) “Informal notes on model uncertainty for ISO 19906”, personal

communication. Madsen, H.O., S. Krenk and N.C. Lind (1986) “Methods of Structural Safety”, Prentice-

Hall. Maes, M.A. (1986a) “A Study of a Calibration of the New CSA Code for Fixed Offshore

Structures”, Technical Report No. 9, Ottawa: Canada Oil and Gas Lands Administration, Environmental Protection Branch, March, 1986.

Maes, M.A. (1986b) “Calibration of Design Criteria in the New CSA Standard for Fixed Offshore Structures”, Technical Report No. 9, Ottawa: Canada Oil and Gas Lands Administration, Environmental Protection Branch, October, 1986

Maes, M.A. (1990) “The Influence of Uncertainties on the Selection of Extreme Values of Environmental Loads and Events”, Civil Engineering Systems, June, Vol. 7, No.2, pp. 115-124.

Maes, M.A. and Breitung, K. (1993) “Reliability-Based Tail Estimation”, Proceedings, IUTAM Symposium on Probabilistic Structural Mechanics (Advances in Structural Reliability Methods), San Antonio, Texas, June, pp. 335-346.

Maes, M.A. (1995) “Tail Heaviness in Structural Reliability”, Proceedings of the 7th International Conference on Applications of Statistics and Probability in Civil Engineering Reliability and Risk Analysis, Eds. M. Lemaire et al., Paris, July 1995, Vol. 2, pp. 997-1002.

Maes, M.A. (2003) “Extrapolation into the Unknown: Modeling Tails, Extremes, and Bounds”, chapter in Reliability- Based Design and Optimization, RBO'03, editors S. Jendo and K. Dolinski, Lecture Notes 16, Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw, Poland, pp. 177-210.

Maes, M.A., Abdelatif, S. and Frederking, R. (2004) “Recalibration of partial load factors in the Canadian offshore structures standard CAN/CSA-S471”, Canadian Journal of Civil Engineering, Vol. 31, pp. 684-694.

Masterson, D.M., Frederking, R.M.W. and Truskov, P.A. (2000) “Ice Force and Pressure Determination by Zone”, Proceedings of the 6th International Conference on Ships and Marine Structures in Cold Regions (ICETECH 2000), St. Petersburg, Russia, September 12-14, 2000.

Nessim, M.A., Hong, H.P. and Jordaan, I.J. (1995) “Environmental load uncertainties for offshore structures”, J. OMAE, November, 117, pp. 245-251.

Nishijima, K., Faber, M.H. and Maes, M.A. (2008) “Probabilistic assessment of extreme events subject to epistemic uncertainties”, Proc. 27th OMAE Conference, Estoril, Portugal, OMAE 2008-57172.


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References Anzai T., Bryant, L.M. and F.B. Pedersen (1982) “Comparison of a Limit State Design

Code with API RP 2A”, Proc. OTC, 4191. Boos, D.D. (1984) “Using Extreme Value Theory to Estimate Large Percentiles”,

Technometrics, Vol. 2, No. 1, pp. 33-39. API RP2N-2001 (2001) “Recommended Practice for Planning, Designing, and

Constructing Structures and Pipelines for Arctic Conditions”, American Petroleum Institute, 2nd edition.

CAN/CSA-S471-04 (2004) “General Requirements, Design Criteria, the Environment, and Loads (Offshore Structures)”.

C-CORE (2009) “Development of Ice Design Loads and Criteria for Various Arctic Regions”, R08-654, report submitted to OGP February.

Ellingwood, B., J.G. MacGregor, T.V. Galambos and C.A. Cornell (1982) “Probability Based Load Criteria: Load Factors and Load Combinations”, ASCE, Journal of the Structural Division, Vol. 108, N0.ST5, 1982, pp. 978-997.

ISO (1998) “ISO2394 General Principles on Reliability for Structures”. ISO/DIS 19906:2009 (2009) “Arctic Offshore Structures” JCSS, the Joint Committee for Structural Safety (2007) “Probabilistic model code”,

available at http://www.jcss.ethz.ch/. Jordaan, I.J. (2009) “Informal notes on model uncertainty for ISO 19906”, personal

communication. Madsen, H.O., S. Krenk and N.C. Lind (1986) “Methods of Structural Safety”, Prentice-

Hall. Maes, M.A. (1986a) “A Study of a Calibration of the New CSA Code for Fixed Offshore

Structures”, Technical Report No. 9, Ottawa: Canada Oil and Gas Lands Administration, Environmental Protection Branch, March, 1986.

Maes, M.A. (1986b) “Calibration of Design Criteria in the New CSA Standard for Fixed Offshore Structures”, Technical Report No. 9, Ottawa: Canada Oil and Gas Lands Administration, Environmental Protection Branch, October, 1986

Maes, M.A. (1990) “The Influence of Uncertainties on the Selection of Extreme Values of Environmental Loads and Events”, Civil Engineering Systems, June, Vol. 7, No.2, pp. 115-124.

Maes, M.A. and Breitung, K. (1993) “Reliability-Based Tail Estimation”, Proceedings, IUTAM Symposium on Probabilistic Structural Mechanics (Advances in Structural Reliability Methods), San Antonio, Texas, June, pp. 335-346.

Maes, M.A. (1995) “Tail Heaviness in Structural Reliability”, Proceedings of the 7th International Conference on Applications of Statistics and Probability in Civil Engineering Reliability and Risk Analysis, Eds. M. Lemaire et al., Paris, July 1995, Vol. 2, pp. 997-1002.

Maes, M.A. (2003) “Extrapolation into the Unknown: Modeling Tails, Extremes, and Bounds”, chapter in Reliability- Based Design and Optimization, RBO'03, editors S. Jendo and K. Dolinski, Lecture Notes 16, Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw, Poland, pp. 177-210.

Maes, M.A., Abdelatif, S. and Frederking, R. (2004) “Recalibration of partial load factors in the Canadian offshore structures standard CAN/CSA-S471”, Canadian Journal of Civil Engineering, Vol. 31, pp. 684-694.

Masterson, D.M., Frederking, R.M.W. and Truskov, P.A. (2000) “Ice Force and Pressure Determination by Zone”, Proceedings of the 6th International Conference on Ships and Marine Structures in Cold Regions (ICETECH 2000), St. Petersburg, Russia, September 12-14, 2000.

Nessim, M.A., Hong, H.P. and Jordaan, I.J. (1995) “Environmental load uncertainties for offshore structures”, J. OMAE, November, 117, pp. 245-251.

Nishijima, K., Faber, M.H. and Maes, M.A. (2008) “Probabilistic assessment of extreme events subject to epistemic uncertainties”, Proc. 27th OMAE Conference, Estoril, Portugal, OMAE 2008-57172.

61

Ravindra, M.K. and T.V. Galambos (1978) “Load and Resistance Factor Design for Steel”, ASCE, Journal of the Structural Division, Vol. 104, N0.ST9, 1978, pp. 1337-1353.

SAKO (1999) “Probabilistic Calibration of Partial Safety Factors in the Eurocodes”. Sørensen, J.D., I.B. Kroon and M.H. Faber (1994) “Optimal Reliability-Based Code

Calibration”, Structural Safety, Vol.14, 1994, pp. 197-208. Sørensen, J.D., S.O. Hansen and T. Arnbjerg Nielsen (2001) “Calibration of Partial

Safety Factors for Danish Structural Codes”, Proc. IABSE Conf. Safety, Risk and Reliability – Trends in Engineering, Malta, 2001, IABSE, Zürich, pp. 179-184.

STRUREL (1998) Version 6.1, Theoretical, Technical and Users manual, RCP-GmbH, Munich.

Stuckey, P.D., Ralph, F.E. and Jordaan, I.J. (2008) “Iceberg Design Load Methodology”, ICETECH 2008, Proceedings of the International Conference and Exhibition on Performance o Ships and Structures in Ice (ICETECH 2008), Banff, Canada, July 20-23, 2008.

Thoft Christensen, P., and M. Baker (1982) “Structural Reliability Theory and its Applications”, Springer Verlag.

Wen Y.-K. (1990) “Structural Load Modeling and Combination for Performance and Safety Evaluation”, Elsevier Publishers.

Acknowledgement The author wishes to acknowledge the expert input of the TP10 committee members with regards to ice loading. The assistance of Markus R. Dann, PhD student at the University of Calgary, is greatly appreciated.


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Appendix A: Probabilistic Tail Models for Action Effects

A.1 The concept of tail equivalence and the Q-distribution Risk analysis, reliability-based design and code calibration share the fact that they are critically dependent on the modeling of extreme events having very small probabilities of occurrence. The quality of the analysis depends entirely on how well and how careful we manage to model low-probability events that are unlikely to have been observed in the past. An essential tool in dealing with what may otherwise appear to be a shaky extrapolation into the unknown, is the use of probability distributions specifically dedicated to tails and extremes as opposed to traditional models that are mostly focused on representing the “central” or normal behaviour of a population. A key concept in tail modeling is that of “tail equivalence”. It provides a criterion for the quality of approximating a distribution function F by another distribution G in its tail region. If we consider two distribution functions F(x) and G(x), these distribution functions are called tail equivalent (at the right) if

1)(1)(1lim =

−−

∞→ xFxG

x (A1)

This means that, asymptotically, the relative error of approximating the small exceedance probability 1 – F(x) by 1 – G(x) approaches zero as x increases. The idea is now to replace G(x) in (A1) by the empirical distribution function associated with a data set and to “fit” it to a suitable family of “tail” distributions F(x) such that tail-equivalence exists between the two. The most effective choice for a flexible set of tail models with distribution F(x) is the so-called Quantile Anchored Generalized Pareto distribution or Q-distribution. Details of this tail model can e.g. be found in Maes (1995), Maes and Breitung (1993), and Maes (2003). The essential steps of the Q-distribution technique are reproduced here in order to allow investigation and analysis for arbitrary extreme load data sets. Consider an ordered data set x of n (load) values x1 ≤ x2 ≤ … ≤ xn. Define the Lx

* function of a random variable X as the logarithm of the exceedance probability: ))(1ln()(* xFxL xx −= (A2) where Fx(x) is the cumulative distribution function. Lx

* is therefore a negative-valued function that can only decrease. Its negative L = – L* is commonly used by statisticians and has the advantage that it is positive and increasing but engineers are more familiar with and better served by an L* versus x plot.

A

63

Step one is the anchoring of the data: assign an equal weight of 1/(n+1) to each xi in the data set and select and compute the empirical q-quantile xq of the tail of interest, where q is a selected exceedance probability for this quantile. For instance in a data set of 10,000 simulated load data for which we wish to construct a right (upper) tail model we can consider q to be 10-2 and therefore xq will be the 9900th value in the ordered set x. If the data set is smaller, then q can be 10-1 or any other value. Note that, if needed, the anchor can be changed subsequently once the tail-model has been fitted. Step two is to transform the anchored data set x into a non-dimensional data set η using the transformation:

q

q

xxx

x−

=→η (A3)

so that η = 0 has an exceedance probability of q. Subsequently, determine and plot the empirical L*(η) function of the data set which results in n data points (ηi, Li

*) where

)1

1ln()(*

+−=

niL ii η (A4)

Now, as described in the above references, this (upper) L*- plot “amplifies” the upper tail of the probability distribution in a way that is entirely consistent with the principle of tail equivalence (A1) because vertical distances ΔL* in the (η, L*) plot correspond to the required relative errors in the exceedance probability:

FF

FFFL

−−∆

=−∆−

=−∆=∆1

)1(1

)1(ln(* (A5)

and these are precisely the errors involved in achieving tail equivalence between two distributions based on (A1). This is shown in Figure A1.

0-0.1 +0.1

ln q

q

q

xxx −

=η

HS

ΔL*

L*

Figure A1: Typical (η, L*) tail plot showing tail-equivalence between a data-based empirical distribution function (shown by dots) and a Q-distribution function.


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Appendix A: Probabilistic Tail Models for Action Effects

A.1 The concept of tail equivalence and the Q-distribution Risk analysis, reliability-based design and code calibration share the fact that they are critically dependent on the modeling of extreme events having very small probabilities of occurrence. The quality of the analysis depends entirely on how well and how careful we manage to model low-probability events that are unlikely to have been observed in the past. An essential tool in dealing with what may otherwise appear to be a shaky extrapolation into the unknown, is the use of probability distributions specifically dedicated to tails and extremes as opposed to traditional models that are mostly focused on representing the “central” or normal behaviour of a population. A key concept in tail modeling is that of “tail equivalence”. It provides a criterion for the quality of approximating a distribution function F by another distribution G in its tail region. If we consider two distribution functions F(x) and G(x), these distribution functions are called tail equivalent (at the right) if

1)(1)(1lim =

−−

∞→ xFxG

x (A1)

This means that, asymptotically, the relative error of approximating the small exceedance probability 1 – F(x) by 1 – G(x) approaches zero as x increases. The idea is now to replace G(x) in (A1) by the empirical distribution function associated with a data set and to “fit” it to a suitable family of “tail” distributions F(x) such that tail-equivalence exists between the two. The most effective choice for a flexible set of tail models with distribution F(x) is the so-called Quantile Anchored Generalized Pareto distribution or Q-distribution. Details of this tail model can e.g. be found in Maes (1995), Maes and Breitung (1993), and Maes (2003). The essential steps of the Q-distribution technique are reproduced here in order to allow investigation and analysis for arbitrary extreme load data sets. Consider an ordered data set x of n (load) values x1 ≤ x2 ≤ … ≤ xn. Define the Lx

* function of a random variable X as the logarithm of the exceedance probability: ))(1ln()(* xFxL xx −= (A2) where Fx(x) is the cumulative distribution function. Lx

* is therefore a negative-valued function that can only decrease. Its negative L = – L* is commonly used by statisticians and has the advantage that it is positive and increasing but engineers are more familiar with and better served by an L* versus x plot.

A

63

Step one is the anchoring of the data: assign an equal weight of 1/(n+1) to each xi in the data set and select and compute the empirical q-quantile xq of the tail of interest, where q is a selected exceedance probability for this quantile. For instance in a data set of 10,000 simulated load data for which we wish to construct a right (upper) tail model we can consider q to be 10-2 and therefore xq will be the 9900th value in the ordered set x. If the data set is smaller, then q can be 10-1 or any other value. Note that, if needed, the anchor can be changed subsequently once the tail-model has been fitted. Step two is to transform the anchored data set x into a non-dimensional data set η using the transformation:

q

q

xxx

x−

=→η (A3)

so that η = 0 has an exceedance probability of q. Subsequently, determine and plot the empirical L*(η) function of the data set which results in n data points (ηi, Li

*) where

)1

1ln()(*

+−=

niL ii η (A4)

Now, as described in the above references, this (upper) L*- plot “amplifies” the upper tail of the probability distribution in a way that is entirely consistent with the principle of tail equivalence (A1) because vertical distances ΔL* in the (η, L*) plot correspond to the required relative errors in the exceedance probability:

FF

FFFL

−−∆

=−∆−

=−∆=∆1

)1(1

)1(ln(* (A5)

and these are precisely the errors involved in achieving tail equivalence between two distributions based on (A1). This is shown in Figure A1.

0-0.1 +0.1

ln q

q

q

xxx −

=η

HS

ΔL*

L*

Figure A1: Typical (η, L*) tail plot showing tail-equivalence between a data-based empirical distribution function (shown by dots) and a Q-distribution function.


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A.2 The two tail parameters S and H The family of quantile anchored generalized Pareto distributions (Q-distributions) has the following cumulative distribution function FQ(η) for the transformed variable η:

=

−−

≠

+−

=

−

)0(exp1

)0(11),,|(

/1

Q

HS

q

HSHq

HSqF

H

η

ηη (A6)

having the following L* function (A2):

=−

≠

+−

=)0(ln

)0(1ln1ln),,|(Q

*

HS

q

HSH

Hq

HSqLη

ηη (A7)

where q is the selected anchor point and S and H are two fundamental non-dimensional tail parameters which play a role similar to the first two central moments (the mean and the variance) when the central part of a data set is modeled. S is the (non-dimensional) tail slope at the anchor q, defined as

0* )/(

1

=

−=

ηηddLS (A8)

which is the negative of the tangent of the angle shown in Figure A1. H is the so-called tail heaviness (Boos, 1984; Maes, 1995) and is a direct measure of the curvature of the L* function:

22*

2*2 1')1()/(

/ffF

ddLdLdH −−

−==ηη (A9)

where f and f’ denote the PDF and its first derivative. It can now be checked that the Q-distribution has a constant tail heaviness H for any value of η. In fact it is the only type of distribution to possess this property. It can also be seen from (A7) that a zero tail heaviness (H=0) corresponds to a straight line with slope -1/S in the (η, L*) plot. Small positive or negative H values will cause this function to become slightly concave (heavy tail) or convex (light tails suggestive of upper bounds), respectively. As shown in Figure A2, the parameters S and H fully characterize the critical behaviour of tails and extremes. In order to fit a Q-distribution to the empirical L*(ηi) function associated with a specific data set x, it suffices to minimize the following sum of tail-weighted square errors SSE with respect to H and S:

65

( )∑=

−=n

iiii HSqLLSH

1

2*Q

* ),,|()(),(SSE ηη (A10)

where Li

* is given by (A4) and *QL by (A7). Parameter uncertainty on S and H

can be taken into account by standard likelihood methods as described in Maes and Breitung (1993).

S3 < S2 < S1

L*

η

S3 S2

S1

L*

η

H1>0

H3<0H2=0

(a) same H, different S (b) same S, different H

0 0

q q

Figure A2: Illustration of the effect of the two tail model parameters S and H. A.3 How S and H are related to action factor calibration The values of H and S are also very important when it comes to calibration. When partial action factors γ are applied to actions having a specified exceedance probability equal to q, the failure probability is in fact governed by the behaviour of the (η, L*) plot just to the right of the anchor point. Therefore, in order to achieve the same target failure probability;

(a) for given H: the smaller the slope factor S, the smaller the minimum required action factor γmin. In Figure A2(a) for instance, since S3 < S2 < S1 the corresponding action factors will be ranked as follows: γ3 < γ2 < γ1.

(b) For given S: the lighter the tail, the smaller the minimum required action factor γmin. In Figure A2(b) the values H1 > H2 =0 > H3 will result in γ1 > γ2 > γ3.

The non-dimensional representation of probability distribution tails in an (η, L*) plot has the benefit that different loads or types of loads may be compared with respect to differences in their tail behaviour. This is amply illustrated in this report as far as ice loads are concerned. A.4 Role of the mean action event occurrence rate λ A fair comparison of tails associated with different action effect processes must be based on a common time reference period. This is usually considered to be one year so that the load X represents the annual (maximum) load or load effect. For a discrete stochastic process such as ice loading, the load X arises as the maximum of an uncertain number N of discrete ice load events. Assuming N to be Poisson distributed with an average number of load events λ per year, then the annual


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A.2 The two tail parameters S and H The family of quantile anchored generalized Pareto distributions (Q-distributions) has the following cumulative distribution function FQ(η) for the transformed variable η:

=

−−

≠

+−

=

−

)0(exp1

)0(11),,|(

/1

Q

HS

q

HSHq

HSqF

H

η

ηη (A6)

having the following L* function (A2):

=−

≠

+−

=)0(ln

)0(1ln1ln),,|(Q

*

HS

q

HSH

Hq

HSqLη

ηη (A7)

where q is the selected anchor point and S and H are two fundamental non-dimensional tail parameters which play a role similar to the first two central moments (the mean and the variance) when the central part of a data set is modeled. S is the (non-dimensional) tail slope at the anchor q, defined as

0* )/(

1

=

−=

ηηddLS (A8)

which is the negative of the tangent of the angle shown in Figure A1. H is the so-called tail heaviness (Boos, 1984; Maes, 1995) and is a direct measure of the curvature of the L* function:

22*

2*2 1')1()/(

/ffF

ddLdLdH −−

−==ηη (A9)

where f and f’ denote the PDF and its first derivative. It can now be checked that the Q-distribution has a constant tail heaviness H for any value of η. In fact it is the only type of distribution to possess this property. It can also be seen from (A7) that a zero tail heaviness (H=0) corresponds to a straight line with slope -1/S in the (η, L*) plot. Small positive or negative H values will cause this function to become slightly concave (heavy tail) or convex (light tails suggestive of upper bounds), respectively. As shown in Figure A2, the parameters S and H fully characterize the critical behaviour of tails and extremes. In order to fit a Q-distribution to the empirical L*(ηi) function associated with a specific data set x, it suffices to minimize the following sum of tail-weighted square errors SSE with respect to H and S:

65

( )∑=

−=n

iiii HSqLLSH

1

2*Q

* ),,|()(),(SSE ηη (A10)

where Li

* is given by (A4) and *QL by (A7). Parameter uncertainty on S and H

can be taken into account by standard likelihood methods as described in Maes and Breitung (1993).

S3 < S2 < S1

L*

η

S3 S2

S1

L*

η

H1>0

H3<0H2=0

(a) same H, different S (b) same S, different H

0 0

q q

Figure A2: Illustration of the effect of the two tail model parameters S and H. A.3 How S and H are related to action factor calibration The values of H and S are also very important when it comes to calibration. When partial action factors γ are applied to actions having a specified exceedance probability equal to q, the failure probability is in fact governed by the behaviour of the (η, L*) plot just to the right of the anchor point. Therefore, in order to achieve the same target failure probability;

(a) for given H: the smaller the slope factor S, the smaller the minimum required action factor γmin. In Figure A2(a) for instance, since S3 < S2 < S1 the corresponding action factors will be ranked as follows: γ3 < γ2 < γ1.

(b) For given S: the lighter the tail, the smaller the minimum required action factor γmin. In Figure A2(b) the values H1 > H2 =0 > H3 will result in γ1 > γ2 > γ3.

The non-dimensional representation of probability distribution tails in an (η, L*) plot has the benefit that different loads or types of loads may be compared with respect to differences in their tail behaviour. This is amply illustrated in this report as far as ice loads are concerned. A.4 Role of the mean action event occurrence rate λ A fair comparison of tails associated with different action effect processes must be based on a common time reference period. This is usually considered to be one year so that the load X represents the annual (maximum) load or load effect. For a discrete stochastic process such as ice loading, the load X arises as the maximum of an uncertain number N of discrete ice load events. Assuming N to be Poisson distributed with an average number of load events λ per year, then the annual


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66

extreme load distribution Fx(x) and its L* function L*(x) are clearly a function of this mean arrival rate λ. Now it can easily be verified that changing the value of λ to an alternative value λA – a case that could for instance arise from a change in site or a change of arctic-marine variables – would result in the new LA* function to be shifted parallel upwards by an amount ln(λ / λA), the well known logarithmic shift of extreme values. This is shown in Figure A3.

L*

x

ln(λA/λ)

xq

ln q

xqA

λA

λ Figure A3: Shift in the annual extreme L* function as a result of changing the average annual number of encounters from λ to λA.

In the above Q-distribution model, a change from an annual rate λ to λA has the following effect:

1. the anchor changes from the q-quantile xq to xqA, where

=

+=

≠

−

+=

)0(ln1

)0(11

HSx

HHSx

xA

q

HA

q

qA

λλλλ

(A11)

because the 1/q-year load is changed;

2. the slope factor S decreases from S to SA, where:

=+

=

≠

−

+

=

)0(ln1

1

)0(

11

HS

S

H

HS

S

S

A

HA

HA

A

λλ

λλ

λλ

(A12)

3. the tail heaviness remains unchanged: HA=H

4. the resulting updated annual extreme load XA continues to have a Q-

distribution tail model for the non-dimensional load ηA = (xA-xqA)/xqA given by F(ηA | q, SA, H).

67

A.5 Other quantiles The exceedance probability of any other extreme action value γxq where xq is the anchoring quantile and γ is an action factor greater than 1, can easily be determined from the distribution function (A6):

=

−−

≠

−+

=−>=>

−

)0()1(exp

)0()1(1)1Pr()Pr(

1

HS

q

HSHq

xX

H

qγ

γγηγ (A13)

The above result also allows re-anchoring of the Q-distribution in case this is more convenient for practical reasons, e.g. when the specified annual representative action is changed from say the 100-year action to the 10,000 year action. It also comes in handy in manipulating expressions for simple limit state failure probabilities such as PF = Pr(X ≥ R) = ∫ Pr(η > γρ–1 | ρ)f(ρ)dρ where ρ= R/rd with R equal to the resistance random variable, rd the factored design resistance and γ the action factor in the design check equation γxq ≥ rd. A.6 Using the Q-distribution for other environmental action processes Not just ice actions but all other types of environmental action effects can be represented and/or fitted using a Q-distribution tail model. A typical and common example concerns an environmental action from a continuous stochastic process such as waves or winds, that has an annual maximum action effect E with a Gumbel or a double exponential distribution with a coefficient of variation equal to vE. It is then convenient to use the representative 1/q = 100-year action effect eq as the anchoring quantile for the corresponding Q-distribution formulation FQ(ηE|q, SE, HE) where:

0

ln577.06

1

=

−−=

−=

−

E

EE

q

qE

H

qv

S

eeE

π

η

(A14)

This is illustrated in the (η, L*) plot Figure A4 for q = 0.01 and typical values of the COV vE.


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67

A.5 Other quantiles The exceedance probability of any other extreme action value γxq where xq is the anchoring quantile and γ is an action factor greater than 1, can easily be determined from the distribution function (A6):

=

−−

≠

−+

=−>=>

−

)0()1(exp

)0()1(1)1Pr()Pr(

1

HS

q

HSHq

xX

H

qγ

γγηγ (A13)

The above result also allows re-anchoring of the Q-distribution in case this is more convenient for practical reasons, e.g. when the specified annual representative action is changed from say the 100-year action to the 10,000 year action. It also comes in handy in manipulating expressions for simple limit state failure probabilities such as PF = Pr(X ≥ R) = ∫ Pr(η > γρ–1 | ρ)f(ρ)dρ where ρ= R/rd with R equal to the resistance random variable, rd the factored design resistance and γ the action factor in the design check equation γxq ≥ rd. A.6 Using the Q-distribution for other environmental action processes Not just ice actions but all other types of environmental action effects can be represented and/or fitted using a Q-distribution tail model. A typical and common example concerns an environmental action from a continuous stochastic process such as waves or winds, that has an annual maximum action effect E with a Gumbel or a double exponential distribution with a coefficient of variation equal to vE. It is then convenient to use the representative 1/q = 100-year action effect eq as the anchoring quantile for the corresponding Q-distribution formulation FQ(ηE|q, SE, HE) where:

0

ln577.06

1

=

−−=

−=

−

E

EE

q

qE

H

qv

S

eeE

π

η

(A14)

This is illustrated in the (η, L*) plot Figure A4 for q = 0.01 and typical values of the COV vE.


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1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50

Environmental Action Factor

Prob

abili

ty o

f Fai

lure

Annual Environmental Action (non-ice) COV = 0.4



Figure A4: Comparison of tail models for 3 annual continuous environmental action processes.

A.7 Accounting for model uncertainties Another very convenient property of Q-distribution tail models is that they can easily be adjusted to account for model tail uncertainty. As can be expected the consideration of additional uncertainty in the slope factor S as shown in Figure A5 results in an overall “heavier” tail. To demonstrate this fact, consider the additional variable θ in the expression of the Q-distribution pdf fQ(η|q, S/θ, H) where θ is a random variable with mean 1 and COV vθ. The variable θ reflects model uncertainty in the tail model, which may be due to statistical uncertainty caused by insufficient or untrustworthy data or common model uncertainty (e.g. for ice actions, uncertainty regarding the pressure-area relationship). The “all-inclusive” tail distribution can now be found by integrating fQ over the pdf f(θ) of the model uncertainty variable θ, as sketched in Figure A5. It can be shown that this updated tail distribution is itself a new Q-distribution tail model anchored on its new q-quantile with distribution function FQ(η|q, Sθ, Hθ) where the relationship between the new Sθ, Hθ and the original S, H are as follows:

+== −

2

2

θθ

θθ

vHHSqS v

(A15)

This shows that the additional “weight” on the tail is in fact proportional to the square of the model uncertainty COV vθ

2.

model uncertainty

…

10-1

10-2

10-3

10-4

10-5

10-6

Load effect

Exc

eeda

nce

prob

abilit

y model uncertainty

…

10-1

10-2

10-3

10-4

10-5

10-6

Load effect

Exc

eeda

nce

prob

abilit

y

tail (S,H) before model uncertainty

tail (S*,H*) including model uncertainty

10-1

10-2

10-3

10-4

10-5

10-6

Load effect

Exc

eeda

nce

prob

abilit

y

Figure A5: Illustration of the increase in tail heaviness due to model uncertainty.


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1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50

Environmental Action Factor

Prob

abili

ty o

f Fai

lure




Figure A4: Comparison of tail models for 3 annual continuous environmental action processes.

A.7 Accounting for model uncertainties Another very convenient property of Q-distribution tail models is that they can easily be adjusted to account for model tail uncertainty. As can be expected the consideration of additional uncertainty in the slope factor S as shown in Figure A5 results in an overall “heavier” tail. To demonstrate this fact, consider the additional variable θ in the expression of the Q-distribution pdf fQ(η|q, S/θ, H) where θ is a random variable with mean 1 and COV vθ. The variable θ reflects model uncertainty in the tail model, which may be due to statistical uncertainty caused by insufficient or untrustworthy data or common model uncertainty (e.g. for ice actions, uncertainty regarding the pressure-area relationship). The “all-inclusive” tail distribution can now be found by integrating fQ over the pdf f(θ) of the model uncertainty variable θ, as sketched in Figure A5. It can be shown that this updated tail distribution is itself a new Q-distribution tail model anchored on its new q-quantile with distribution function FQ(η|q, Sθ, Hθ) where the relationship between the new Sθ, Hθ and the original S, H are as follows:

+== −

2

2

θθ

θθ

vHHSqS v

(A15)

This shows that the additional “weight” on the tail is in fact proportional to the square of the model uncertainty COV vθ

2.

model uncertainty

…

10-1

10-2

10-3

10-4

10-5

10-6

Load effect

Exc

eeda

nce

prob

abilit

y model uncertainty

…

10-1

10-2

10-3

10-4

10-5

10-6

Load effect

Exc

eeda

nce

prob

abilit

y

tail (S,H) before model uncertainty

tail (S*,H*) including model uncertainty

10-1

10-2

10-3

10-4

10-5

10-6

Load effect

Exc

eeda

nce

prob

abilit

y

Figure A5: Illustration of the increase in tail heaviness due to model uncertainty.

69

Appendix B: Region- and Structure Specific Ice Action Effects: Tail Distributions

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6

η based on q=0.01

Exce

edan

ce P

roba

bilit

y

Empirical

Tail model

Figure B1: (η, L*) tail plot of the annual extreme ice action effect for: Beaufort Sea, Southern Chukchi Sea, Baffin Bay, Labrador, and Laptev

Sea, multi-year ice 0.5 tenths, vertically sided GBS. The S and H values are shown in Table 9.

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

η based on q=0.01

Exce

edan

ce P

roba

bilit

y

Empirical

Tail model


Sea, multi-year ice 0.5 tenths, conically sided GBS. The S and H values are shown in Table 9.

B


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1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6

η based on q=0.01

Exce

edan

ce P

roba

bilit

y

Empirical

Tail model


Sea, multi-year ice 0.5 tenths, floating production storage offloading unit. The S and H values are shown in Table 9.

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6

η based on q=0.01

Exce

edan

ce P

roba

bilit

y

Empirical

Tail model


Sea, multi-year ice 0.5 tenths, single vertical piled column. The S and H values are shown in Table 9.

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6

η based on q=0.01

Exce

edan

ce P

roba

bilit

y

Empirical

Tail model

Figure B5: (η, L*) tail plot of the annual extreme ice action effect for: Beaufort Sea, NE Greenland, Northern Chukchi Sea, and Arctic Islands,

multi-year ice, 3.0 tenths, vertically sided GBS. The S and H values are shown in Table 9.


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70

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6

η based on q=0.01

Exce

edan

ce P

roba

bilit

y

Empirical

Tail model


Sea, multi-year ice 0.5 tenths, floating production storage offloading unit. The S and H values are shown in Table 9.

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6

η based on q=0.01

Exce

edan

ce P

roba

bilit

y

Empirical

Tail model


Sea, multi-year ice 0.5 tenths, single vertical piled column. The S and H values are shown in Table 9.

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6

η based on q=0.01

Exce

edan

ce P

roba

bilit

y

Empirical

Tail model


multi-year ice, 3.0 tenths, vertically sided GBS. The S and H values are shown in Table 9.

71

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

η based on q=0.01

Exce

edan

ce P

roba

bilit

y

Empirical

Tail model


multi-year ice, 3.0 tenths, conically sided GBS. The S and H values are shown in Table 9.

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10

η based on q=0.01

Exce

edan

ce P

roba

bilit

y

Empirical

Tail model

Figure B7: (η, L*) tail plot of the annual extreme ice action effect for: Sakhalin, Cook Inlet, Sea of Okhotsk, and Kara Sea, first year level ice,

vertically sided GBS. The S and H values are shown in Table 9.

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4

η based on q=0.01

Exce

edan

ce P

roba

bilit

y

Empirical

Tail model


conically sided GBS. The S and H values are shown in Table 9.


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1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20

η based on q=0.01

Exce

edan

ce P

roba

bilit

y

Empirical

Tail model


floating production storage offloading unit. The S and H values are shown in Table 9.

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4

η based on q=0.01

Exce

edan

ce P

roba

bilit

y

Empirical

Tail model


single vertical piled column. The S and H values are shown in Table 9.

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6

η based on q =0.01

Exce

edan

ce P

roba

bilit

y

Empirical

Tail model

Figure B11: (η, L*) tail plot of the annual extreme ice action effect for: Barents Sea and Bering Sea, first year ridges, vertically sided floater. The S and H values are shown in Table 9.

73

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

η based on q =0.01

Exce

edan

ce P

roba

bilit

y

Empirical

Tail model

Figure B12: (η, L*) tail plot of the annual extreme ice action effect for: Barents Sea and Bering Sea, first year ridges, conically sided floater. The S and H values are shown in Table 9.

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-0.2 0.0 0.2 0.4 0.6 0.8 1.0

η based on q=0.01

Exce

edan

ce P

roba

bilit

y

Empirical

Tail model

Figure B13: (η, L*) tail plot of the annual extreme ice action effect for: Barents Sea and Bering Sea, first year ridges, floating production storage

offloading unit. The S and H values are shown in Table 9.

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4

η based on q=0.01

Exce

edan

ce P

roba

bilit

y

Empirical

Tail model

Figure B14: (η, L*) tail plot of the annual extreme ice action effect for: Caspian Sea, Baltic Sea, and Bohai Bay, first year level ice, vertically

sided GBS. The S and H values are shown in Table 9.


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72

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20

η based on q=0.01

Exce

edan

ce P

roba

bilit

y

Empirical

Tail model


floating production storage offloading unit. The S and H values are shown in Table 9.

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4

η based on q=0.01

Exce

edan

ce P

roba

bilit

y

Empirical

Tail model


single vertical piled column. The S and H values are shown in Table 9.

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6

η based on q =0.01

Exce

edan

ce P

roba

bilit

y

Empirical

Tail model

Figure B11: (η, L*) tail plot of the annual extreme ice action effect for: Barents Sea and Bering Sea, first year ridges, vertically sided floater. The S and H values are shown in Table 9.

73

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

η based on q =0.01

Exce

edan

ce P

roba

bilit

y

Empirical

Tail model

Figure B12: (η, L*) tail plot of the annual extreme ice action effect for: Barents Sea and Bering Sea, first year ridges, conically sided floater. The S and H values are shown in Table 9.

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-0.2 0.0 0.2 0.4 0.6 0.8 1.0

η based on q=0.01

Exce

edan

ce P

roba

bilit

y

Empirical

Tail model

Figure B13: (η, L*) tail plot of the annual extreme ice action effect for: Barents Sea and Bering Sea, first year ridges, floating production storage

offloading unit. The S and H values are shown in Table 9.

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4

η based on q=0.01

Exce

edan

ce P

roba

bilit

y

Empirical

Tail model

Figure B14: (η, L*) tail plot of the annual extreme ice action effect for: Caspian Sea, Baltic Sea, and Bohai Bay, first year level ice, vertically



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74

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4

η based on q=0.01

Exce

edan

ce P

roba

bilit

y

Empirical

Tail model

Figure B15: (η, L*) tail plot of the annual extreme ice action effect for: Caspian Sea, Baltic Sea, and Bohai Bay, first year level ice, conically


1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5

η based on q=0.01

Exce

edan

ce P

roba

bilit

y

Empirical

Tail model

Figure B16: (η, L*) tail plot of the annual extreme ice action effect for: Caspian Sea, Baltic Sea, and Bohai Bay, first year level ice, single vertical

piled column. The S and H values are shown in Table 9.

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-1.0 -0.5 0.0 0.5 1.0 1.5


Exce

edan

ce P

roba

bilit

y

Empirical

Tail model

Figure B17: (η, L*) tail plot of iceberg ice actions (given impact) for: Barents Sea, icebergs, vertically sided floater. The S and H values are shown in Table 10.

75

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0


Exce

edan

ce P

roba

bilit

y

Empirical

Tail model

Figure B18: (η, L*) tail plot of iceberg ice actions (given impact) for: Barents Sea, icebergs, floating production storage offloading unit. The S and H values are shown in Table 10.

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-1.0 -0.5 0.0 0.5 1.0


Exce

edan

ce P

roba

bilit

y

Empirical

Tail model

Figure B19: (η, L*) tail plot of iceberg ice actions (given impact) for: Grand Banks, icebergs, vertically sided GBS. The S and H values are shown in Table 10.

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-1.0 -0.5 0.0 0.5 1.0 1.5


Exce

edan

ce P

roba

bilit

y

Empirical

Tail model

Figure B20: (η, L*) tail plot of iceberg ice actions (given impact) for: Grand Banks, icebergs, floating production storage offloading unit. The S and H values are shown in Table 10.


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74

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4

η based on q=0.01

Exce

edan

ce P

roba

bilit

y

Empirical

Tail model

Figure B15: (η, L*) tail plot of the annual extreme ice action effect for: Caspian Sea, Baltic Sea, and Bohai Bay, first year level ice, conically


1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5

η based on q=0.01

Exce

edan

ce P

roba

bilit

y

Empirical

Tail model

Figure B16: (η, L*) tail plot of the annual extreme ice action effect for: Caspian Sea, Baltic Sea, and Bohai Bay, first year level ice, single vertical

piled column. The S and H values are shown in Table 9.

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-1.0 -0.5 0.0 0.5 1.0 1.5


Exce

edan

ce P

roba

bilit

y

Empirical

Tail model

Figure B17: (η, L*) tail plot of iceberg ice actions (given impact) for: Barents Sea, icebergs, vertically sided floater. The S and H values are shown in Table 10.

75

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0


Exce

edan

ce P

roba

bilit

y

Empirical

Tail model

Figure B18: (η, L*) tail plot of iceberg ice actions (given impact) for: Barents Sea, icebergs, floating production storage offloading unit. The S and H values are shown in Table 10.

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-1.0 -0.5 0.0 0.5 1.0


Exce

edan

ce P

roba

bilit

y

Empirical

Tail model

Figure B19: (η, L*) tail plot of iceberg ice actions (given impact) for: Grand Banks, icebergs, vertically sided GBS. The S and H values are shown in Table 10.

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-1.0 -0.5 0.0 0.5 1.0 1.5


Exce

edan

ce P

roba

bilit

y

Empirical

Tail model

Figure B20: (η, L*) tail plot of iceberg ice actions (given impact) for: Grand Banks, icebergs, floating production storage offloading unit. The S and H values are shown in Table 10.


©OGP

76

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0


Exce

edan

ce P

roba

bilit

y

Empirical

Tail model

Figure B21: (η, L*) tail plot of iceberg ice actions (given impact) for: Labrador, Baffin bay, and NE Greenland, icebergs, vertically sided GBS. The S and H values are shown in Table 10.

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

η based on q =0.0001

Exce

edan

ce P

roba

bilit

y

Figure B22: (η, L*) tail plot of iceberg ice actions (given impact) for: Labrador, Baffin bay, and NE Greenland, icebergs, floating production

storage offloading unit. The S and H values are shown in Table 10.

Empirical

Tail model

77

Appendix C: Barents Sea Ice Loads Based on Updated C-CORE Data

This Appendix is dated October 2, 2009. On August 17, 2009 C-CORE issued a memo to OGP-JIP25 (report number R/P-09-027-654 v. 1.0) which contains 3 new/updated ice load exceedance probability plots for Barents Sea: FV, FC and FP. In the calibration based on the original C-CORE Barents Sea data, the tails of all three ice load zones/types were irregular and slightly heavy (more so for FC and FP). This resulted in a region-wide action factor of 1.45 (see Table 12) for the Barents/Bering seas. The new data show a more regular tail behavior having nearly zero tail heaviness factors (near-Gumbel like behavior) which suggests that the region is now close to Beaufort or even Caspian behavior with respect to extreme ice load probabilistic behavior. The new C-CORE information does not justify a new overall calibration as (1) the weight contribution of Barents FV, FC, FP is only 5% of the total weight (see Table 7), and (2) the decrease in tail heaviness of the Barents types has a positive effect on the overall calibration. If anything, the recommended overall 1.35 action factor would show an insignificant decrease, but I would expect that the overall picture (Table 12) remains largely unaffected. The region-specific action factors for Barents Sea FV, FC and FP on the other hand, would decrease to new values in the range 1.30, 1.25 or 1.20 but a new calibration of this site-specific region would have to be performed in order to pinpoint the optimal factor for Barents Sea structures .

C


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77

Appendix C: Barents Sea Ice Loads Based on Updated C-CORE Data

This Appendix is dated October 2, 2009. On August 17, 2009 C-CORE issued a memo to OGP-JIP25 (report number R/P-09-027-654 v. 1.0) which contains 3 new/updated ice load exceedance probability plots for Barents Sea: FV, FC and FP. In the calibration based on the original C-CORE Barents Sea data, the tails of all three ice load zones/types were irregular and slightly heavy (more so for FC and FP). This resulted in a region-wide action factor of 1.45 (see Table 12) for the Barents/Bering seas. The new data show a more regular tail behavior having nearly zero tail heaviness factors (near-Gumbel like behavior) which suggests that the region is now close to Beaufort or even Caspian behavior with respect to extreme ice load probabilistic behavior. The new C-CORE information does not justify a new overall calibration as (1) the weight contribution of Barents FV, FC, FP is only 5% of the total weight (see Table 7), and (2) the decrease in tail heaviness of the Barents types has a positive effect on the overall calibration. If anything, the recommended overall 1.35 action factor would show an insignificant decrease, but I would expect that the overall picture (Table 12) remains largely unaffected. The region-specific action factors for Barents Sea FV, FC and FP on the other hand, would decrease to new values in the range 1.30, 1.25 or 1.20 but a new calibration of this site-specific region would have to be performed in order to pinpoint the optimal factor for Barents Sea structures .

C


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Annex C

Tails of probability distributions for structures with sloping and conical vs vertical sides

Tails of probability distributions for structures with sloping and conical vs vertical sides

Report submitted to Technical Panel TP10 by Ian Jordaan and Associates Inc, December 2009

156


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Tails of Probability Distributions for Structures with Sloping and Conical vs. Vertical Sides

REPORT

Submitted to: Technical Panel TP10

ISO 19906

By: Ian Jordaan and Associates Inc.

7 East Middle Battery Road

St. John’s, NL

Canada A1A 1A3

December 11, 2009


©OGP



Report

Submitted to: Technical Panel TP 10 ISO 19906 Submitted by: Ian Jordaan & Associates Mark Fuglem, C-CORE Ian Jordaan, Ian Jordaan and Associates Ken Croasdale, K.R. Croasdale and Associates Jonathon Bruce, C-CORE December 11, 2009


©OGP



Report

Submitted to: Technical Panel TP 10 ISO 19906 Submitted by: Ian Jordaan & Associates Mark Fuglem, C-CORE Ian Jordaan, Ian Jordaan and Associates Ken Croasdale, K.R. Croasdale and Associates Jonathon Bruce, C-CORE December 11, 2009


©OGP

SummaryThe report is concerned with the question of action factors for sloping and conical structures, both fixed and floating. In the C-CORE (2009) report in which probability distributions for design loads were simulated, it was found that the probability content of the tails of the extremal distributions for these kinds of structures was high. This resulted initially in recommendations of higher action factors for these types of structures for the ELIE condition (e.g. up to 1.55 for a conical GBS in the Beaufort Sea), as against the value of 1.35 for other structures. An in-depth investigation has been performed of the simulations and associated data analyses leading to the tail distributions noted above. This included consideration of failure models for multiyear ridges, and for failure of first year ice against cones and sloping structures (including consideration of rubble formation, ride-up and keel interaction in the latter case). The study has shown for multiyear ridges that the Wang and the beam-on-elastic-foundation models do result in tails in the extremal probability distribution with high probability content (fat tails). This has been found to be related to the nature of the models; it has been found that the loads are proportional to the keel depth to a power of 2 to 2.5. This is to be contrasted with the models for vertical structures, in which the exponent is of the order of unity. The models are based on plasticity (conservative) or elasticity assumptions, with no scale effect. In reality, the failure of a large multiyear ice feature against a cone would result in extensive crushing, which shows a scale effect, as well as scale effects related to flexural failure. The effect of size (scale effect) on the flexural strength, associated with brittle failure, has been reviewed. This is the observed tendency for failure to occur at lower stress depending on the size of the specimen. Weibull “weakest-link” theories provide excellent descriptions of the behaviour and are briefly reviewed. Experimental results have generally indicated a scale effect. These have been obtained in tests on carefully prepared beam specimens cut from ice obtained in the field or manufactured in the laboratory. Specimens made in this way will not reflect the effect of randomness of the morphology of multiyear ridges in nature. Scale effects for actual field conditions are consequently expected to be even more significant. The conclusion is that a scale effect related to fracture processes and flexural failure would be of the order of (dimension)–1 or greater. It is recognized that almost no full scale data on failure of multi-year ice against sloping structures are available. Data from level first year ice in the field suggest an exponent closer to unity of the scale relation, that is, the strength scales according to (thickness)–1. The inclusion of a scale effect of this order results in a reduction of the exponent from the range 2 – 2.5 noted above, to between 1 and 1.5. This would in effect bring the tail of the distribution into agreement with the results for vertical structures.

4

The model for first year ice has been checked thoroughly and improvements and corrections have been made in the investigation reported here. As a result it is found that the distribution in the tail has a similar form to those for vertical structures. Based on the present investigation, it is recommended that the load factor of 1.35 be applied for all structures. This recommendation is made in recognition of the fact that the input to the calibration for sloping structures should include the scale effect for flexural failure (fracture).


©OGP

SummaryThe report is concerned with the question of action factors for sloping and conical structures, both fixed and floating. In the C-CORE (2009) report in which probability distributions for design loads were simulated, it was found that the probability content of the tails of the extremal distributions for these kinds of structures was high. This resulted initially in recommendations of higher action factors for these types of structures for the ELIE condition (e.g. up to 1.55 for a conical GBS in the Beaufort Sea), as against the value of 1.35 for other structures. An in-depth investigation has been performed of the simulations and associated data analyses leading to the tail distributions noted above. This included consideration of failure models for multiyear ridges, and for failure of first year ice against cones and sloping structures (including consideration of rubble formation, ride-up and keel interaction in the latter case). The study has shown for multiyear ridges that the Wang and the beam-on-elastic-foundation models do result in tails in the extremal probability distribution with high probability content (fat tails). This has been found to be related to the nature of the models; it has been found that the loads are proportional to the keel depth to a power of 2 to 2.5. This is to be contrasted with the models for vertical structures, in which the exponent is of the order of unity. The models are based on plasticity (conservative) or elasticity assumptions, with no scale effect. In reality, the failure of a large multiyear ice feature against a cone would result in extensive crushing, which shows a scale effect, as well as scale effects related to flexural failure. The effect of size (scale effect) on the flexural strength, associated with brittle failure, has been reviewed. This is the observed tendency for failure to occur at lower stress depending on the size of the specimen. Weibull “weakest-link” theories provide excellent descriptions of the behaviour and are briefly reviewed. Experimental results have generally indicated a scale effect. These have been obtained in tests on carefully prepared beam specimens cut from ice obtained in the field or manufactured in the laboratory. Specimens made in this way will not reflect the effect of randomness of the morphology of multiyear ridges in nature. Scale effects for actual field conditions are consequently expected to be even more significant. The conclusion is that a scale effect related to fracture processes and flexural failure would be of the order of (dimension)–1 or greater. It is recognized that almost no full scale data on failure of multi-year ice against sloping structures are available. Data from level first year ice in the field suggest an exponent closer to unity of the scale relation, that is, the strength scales according to (thickness)–1. The inclusion of a scale effect of this order results in a reduction of the exponent from the range 2 – 2.5 noted above, to between 1 and 1.5. This would in effect bring the tail of the distribution into agreement with the results for vertical structures.

4

The model for first year ice has been checked thoroughly and improvements and corrections have been made in the investigation reported here. As a result it is found that the distribution in the tail has a similar form to those for vertical structures. Based on the present investigation, it is recommended that the load factor of 1.35 be applied for all structures. This recommendation is made in recognition of the fact that the input to the calibration for sloping structures should include the scale effect for flexural failure (fracture).


©OGP

5

1 Background In the calibration of ISO 19906 (C-CORE, 2009; Maes, 2009), the probability content of the tails of the extremal distributions for conical and sloping structures was found to be relatively large (situation B in Figure 1); as compared to the tails for other types of structures (situation A in Figure 1). This resulted in initial recommendations of higher action factors for the conical and sloping types of structures for the ELIE condition (e.g. up to 1.55 for a conical GBS in the Beaufort Sea), as against the value of 1.35 for other structures. It is noted that Maes (2009) found that action factors less than 1.35 in some cases.

0 20 40 60 80 100 120 140 160 180 20010-6

10-5

10-4

10-3

10-2

10-1

100

Maximum Load (MN)

Exc

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Pro

babi

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Parent A

Annual maximum A – Small tail content

Parent B

Annual maximum B – Large tail content

0 20 40 60 80 100 120 140 160 180 20010-6

10-5

10-4

10-3

10-2

10-1

100

Maximum Load (MN)

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Parent A


Parent B


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Parent A


Parent B


Figure 1 Schematic illustration of different tail behaviour in the extreme Ice failure is a complex process and in practice it is best to rely on measured data as far as is possible. The results for vertical sided structures are based on probabilistic analysis of measured data generally for ice crushing. We are confident that these results capture the main features of the process. In the case of multiyear ice acting on structures with sloping and conical faces, there is no full scale data base. There is very good data for the case of first-year ice from the Confederation Bridge and the Kemi 1 lighthouse. These have been used for various inputs into the modelling but need to be developed further into comprehensive probabilistic models. To date, we have adopted models accepted in the literature and these were used in deriving the C-CORE inputs for probability distributions of extreme loads. The models include:

1. Wang model for failure of large multi-year ridges against conical structures (flexural failure only),

2. Croasdale beam on elastic foundation model for failure of large multi-year ridges against conical structures (flexural failure only), and


©OGP

5

1 Background In the calibration of ISO 19906 (C-CORE, 2009; Maes, 2009), the probability content of the tails of the extremal distributions for conical and sloping structures was found to be relatively large (situation B in Figure 1); as compared to the tails for other types of structures (situation A in Figure 1). This resulted in initial recommendations of higher action factors for the conical and sloping types of structures for the ELIE condition (e.g. up to 1.55 for a conical GBS in the Beaufort Sea), as against the value of 1.35 for other structures. It is noted that Maes (2009) found that action factors less than 1.35 in some cases.

0 20 40 60 80 100 120 140 160 180 20010-6

10-5

10-4

10-3

10-2

10-1

100

Maximum Load (MN)

Exc

eede

nce

Pro

babi

lity

Parent A


Parent B


0 20 40 60 80 100 120 140 160 180 20010-6

10-5

10-4

10-3

10-2

10-1

100

Maximum Load (MN)

Exc

eede

nce

Pro

babi

lity

Parent A


Parent B


0 20 40 60 80 100 120 140 160 180 20010-6

10-5

10-4

10-3

10-2

10-1

100

Maximum Load (MN)

Exc

eede

nce

Pro

babi

lity

Parent A


Parent B


Figure 1 Schematic illustration of different tail behaviour in the extreme Ice failure is a complex process and in practice it is best to rely on measured data as far as is possible. The results for vertical sided structures are based on probabilistic analysis of measured data generally for ice crushing. We are confident that these results capture the main features of the process. In the case of multiyear ice acting on structures with sloping and conical faces, there is no full scale data base. There is very good data for the case of first-year ice from the Confederation Bridge and the Kemi 1 lighthouse. These have been used for various inputs into the modelling but need to be developed further into comprehensive probabilistic models. To date, we have adopted models accepted in the literature and these were used in deriving the C-CORE inputs for probability distributions of extreme loads. The models include:

1. Wang model for failure of large multi-year ridges against conical structures (flexural failure only),

2. Croasdale beam on elastic foundation model for failure of large multi-year ridges against conical structures (flexural failure only), and

6

3. Croasdale ride-up model for failure of first-year ridges interacting with sloped structures for Sakhalin and Barents Sea.

The C-CORE results indicated different “tail” behaviours in the case of the conical and sloped structures as compared to vertically sided structures. Comments on the assumptions involved in these models with regard to multiyear ridge failure are as follows. The Wang model is based on plasticity theory, with the formation of three plastic hinges to form a mechanism. Croasdale proposed models based on beam-on-elastic-foundation theory, essentially a formulation based on elasticity theory. This is considered more appropriate than the plasticity-based theory, since ice is an extremely brittle material, and will fail by fracture rather than the formation of plastic hinges. In the Croasdale ride-up model, the load due to a first-year ridge on a sloped structure is considered. There are two main parts to the model: in the first part, the ride-up forces associated with the consolidated portion of the ridge are calculated and in the second part, local and global plug failure of the unconsolidated keel portion of the ridge are calculated. The ride-up model deals with the force components associated with flexure failure of the consolidated layer, pushing the layer forward through accumulated rubble, lifting and shearing rubble, pushing the broken pieces of ice up the slope and turning blocks of ice at the top of the slope. The plug models deal with shear failure of the unconsolidated keel, treated as a Coulomb-Mohr material.

2 Review of Scale Effect of Fracture Processes and Flexural Strength The present analysis is concentrated on structures placed in the field, since this is the endpoint under consideration. The use of laboratory data does not cover what is intended. The key point is that naturally occurring materials contain flaws such as cracks and inhomogeneities such as grain boundaries. The analysis of data is complicated by the fact that usually an investigator in the field will choose ice that “looks competent”; it is rare to find a series of tests on specimens chosen “at random” spatially. In particular, laboratory specimens will generally be manufactured so as to minimize the variations in structure, and achieve a uniform grain size Dieter (1986) well outlines the physical situation associated with the scale effect. The analysis of brittle materials such as glass, ceramics or ice shows variability of results requiring statistical analysis. As a result, probabilistic modeling is required. Early manifestations of the scale effect were found in testing different diameters of glass rods. The strength was found to decrease with diameter; further, if the tested piece was broken into fragments and the fragments tested, these would in turn yield increased strengths. A key to the problem is the approach by Weibull and related studies. In this the idea of the “weakest-link” is introduced. Elements containing flaws of different size are included in the analysis and failure follows when the weakest element fails. The results show statistical variation, and the scale effect results from the fact that larger volumes of


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material have a larger probability of containing a critical flaw (see Jordaan, 2005, for a summary of the theory). The basic relationship can be written as

,1ασ

−∝V

Equation 1 where V is the stressed volume and α the scaling constant. Length ℓ can be considered by inserting V = ℓ3 in Equation 1 with a revised exponent 3/α. If α = 3, scaling of ℓ–1 results, or an inverse length scaling. Experimental results have generally indicated a scale effect. These have been obtained in tests on carefully prepared beam specimens cut from ice obtained in the field or manufactured in the laboratory. Specimens made in this way will not reflect the effect of randomness of the morphology of multiyear ridges in nature. As noted above, carefully made laboratory specimens will not show a scale effect similar to that found in naturally formed ice. For elastic materials, flexural strength would be expected to scale in a similar way to tensile strength. Sanderson (1988) references small scale tensile tests on ice where tensile strength scaled inversely with the volume to a power α between 1 and 2 (Jellinek, 1958). A variety of other results, some with higher values of α, others with values similar to those just quoted are found in the literature (Sanderson, 1988). The importance of the scale effect on tensile strength was recognized by Croasdale and results of field work by Croasdale and coworkers (personal communication, 2003; see also Gladwell, 1977) are shown in Figure 2. It is noteworthy that the arctic sea ice was first year ice of low salinity in the Mackenzie Delta. These results show a significant scale effect. Bruce (2009) shows based on loads during ship rams with heavy multi-year ice that flexural strength is significantly less than would be implied by small scale tests. In reality, failure of a large multiyear ridge on a conical structure will involve significant crushing to obtain the forces required for flexural failure, and these crushing processes will also be subject to a scale effect in addition to that of flexural failure. Määttanen and Hoikkanen, (1996) found that for first year level ice, a scaling of bending strength proportional to (thickness)1 rather than (thickness)2 was suggested by the data. This suggests again a scaling proportional to (thickness)–1. Sanderson (1988) suggests a scale effect, based on Weibull theory, of the order of (dimension)–1. His work was focussed on compressive failure but it would be expected that a greater scale effect would exist in flexure-crushing of multiyear features as compared to compressive failure. The key conclusion of the above is the fact that fracture processes are scale-dependent. The Wang plasticity and the Croasdale beam-on-elastic-foundation models are continuum models without such an effect, but can be modified to account for scale. The larger the ice feature, the smaller the stress at failure as a result of the greater chance of encountering a larger flaw. A scaling proportional to (thickness)–1 will be considered in the following.


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material have a larger probability of containing a critical flaw (see Jordaan, 2005, for a summary of the theory). The basic relationship can be written as

,1ασ

−∝V

Equation 1 where V is the stressed volume and α the scaling constant. Length ℓ can be considered by inserting V = ℓ3 in Equation 1 with a revised exponent 3/α. If α = 3, scaling of ℓ–1 results, or an inverse length scaling. Experimental results have generally indicated a scale effect. These have been obtained in tests on carefully prepared beam specimens cut from ice obtained in the field or manufactured in the laboratory. Specimens made in this way will not reflect the effect of randomness of the morphology of multiyear ridges in nature. As noted above, carefully made laboratory specimens will not show a scale effect similar to that found in naturally formed ice. For elastic materials, flexural strength would be expected to scale in a similar way to tensile strength. Sanderson (1988) references small scale tensile tests on ice where tensile strength scaled inversely with the volume to a power α between 1 and 2 (Jellinek, 1958). A variety of other results, some with higher values of α, others with values similar to those just quoted are found in the literature (Sanderson, 1988). The importance of the scale effect on tensile strength was recognized by Croasdale and results of field work by Croasdale and coworkers (personal communication, 2003; see also Gladwell, 1977) are shown in Figure 2. It is noteworthy that the arctic sea ice was first year ice of low salinity in the Mackenzie Delta. These results show a significant scale effect. Bruce (2009) shows based on loads during ship rams with heavy multi-year ice that flexural strength is significantly less than would be implied by small scale tests. In reality, failure of a large multiyear ridge on a conical structure will involve significant crushing to obtain the forces required for flexural failure, and these crushing processes will also be subject to a scale effect in addition to that of flexural failure. Määttanen and Hoikkanen, (1996) found that for first year level ice, a scaling of bending strength proportional to (thickness)1 rather than (thickness)2 was suggested by the data. This suggests again a scaling proportional to (thickness)–1. Sanderson (1988) suggests a scale effect, based on Weibull theory, of the order of (dimension)–1. His work was focussed on compressive failure but it would be expected that a greater scale effect would exist in flexure-crushing of multiyear features as compared to compressive failure. The key conclusion of the above is the fact that fracture processes are scale-dependent. The Wang plasticity and the Croasdale beam-on-elastic-foundation models are continuum models without such an effect, but can be modified to account for scale. The larger the ice feature, the smaller the stress at failure as a result of the greater chance of encountering a larger flaw. A scaling proportional to (thickness)–1 will be considered in the following.

8

0.1 1 10 1000

50

100

150

200

250

300

350

400

450

500

Area 0.5 (inches)

Flex

ural

Stre

ngth

(psi

)

Arctic First Year IceArctic Multi Year Ice

Figure 2 Field results of Croasdale showing size effect on flexural strength. Lines through the points indicate trends

3 Effect of Key Model Parameters in Multi-year Ridge Load Analysis Load distributions were determined in the C-CORE analysis for ISO by running the load models within a probabilistic (Monte Carlo) framework in which key parameters were treated probabilistically in terms of appropriate probability distributions. While the variance in all of the parameters considered will have some influence on the shape of the load distribution, and the Monte-Carlo models included limits on the loads associated with available driving forces, it is instructive to further consider the effect of key parameters on the loads. In the Monte-Carlo analyses used for the C-CORE ISO analysis, a probability distribution was defined for keel draft, and fixed ratios between the ridge top and bottom widths were assumed. The models used for the ridge loads assume infinitely long ridges (though length distributions were defined when considering available driving forces). The keel dimension, denoted x, was found to have the largest influence on loads, and its influence on estimated loads is investigated further here. Four models are considered as follows. Models 1 and 3 were used in the C-CORE analysis for the ISO code; models 2 and 4 are also considered in this work for comparison.

1) The Wang model for interaction of multi-year ridges with conically shaped structures, in which the ice is treated as an elastic-perfectly plastic material.

2) The Croasdale beam on elastic foundation model for multi-year ridges interacting with conically shaped structures.

3) A ‘pressure-averaging’ (PA) model for crushing failure of a multiyear ridge against a vertically sided structure. The crushing pressure is considered to vary randomly with penetration, with independent random values at each meter of


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penetration. Different mean crushing strengths are chosen for each feature and the variance in crushing pressure is considered to be reduced with contact width.

4) The CSA model for crushing failure of a multiyear ridge against a vertically sided structure. The crushing pressure is considered to be constant for a given contact area, with the pressure based on contact area and aspect ratio.

The influence of ridge dimension on loads is summarized as follows. Details on the evaluation of key parameters for the different models are given in Appendix A. The power on ridge dimension represents an estimate of the power Q in the approximate relationship

H = KxQ

Equation 2 between the maximum horizontal force H and ridge dimension x for typical large ridges. The ridge keel depth would be the dimension of most interest. Table 1 shows the main results for the Wang and Croasdale models. Table 1 Results for power Q (Equation 2)

Model Power on Ridge Dimension Wang 2.5 Croasdale beam on elastic foundation 2.25 Pressure-averaging slightly greater than 1 CSA 0.83 The above analyses confirm that estimates of loads for multi-year ridges impacting cones as determined using the Wang model will have a significantly greater probability content in the tail as compared to the models for loads on vertical structures. To check if this was an artifact of the Wang model, the model for an elastic beam on an elastic foundation, as developed by Hetenyi and applied to ice by Croasdale, was also considered. The Hetenyi model results in a similar increase in probability content in the tail, although the loads overall are substantially lower than those estimated using the Wang model. As noted above, a key issue is that in both the Wang and Croasdale beam on elastic foundation models, the effect of scale on fracture and flexural strength is not considered. Data noted above suggest that the scale effect is of the order of (length)-1. Consequently, the power for sloped and conical structures will be much closer to that for the models for vertically sided structures. Analysis of the model for first year loads is given in the following and for first year and multiyear models in the Appendices.

5 First-year Ridge Loads In reviewing the shapes of first-year load distributions, we found a discrepancy in the previous Barents Sea load trace and have obtained new results for the 100 m sloped structure, that we believe resulted from a previous input error. The updated load distribution for the Barents Sea 100 m diameter conical structures is shown in Figure 3. The semi-log relationship between load and probability of exceedance is now more linear

10

whereas it previously curved toward higher loads at low probabilities (previously closer to Type B in Figure 1).

Figure 3 Load distributions for the Barents Sea 100 m diameter conical structure. Blue curve is the annual maximum extremal distribution Discussion of Analysis of First-year Ridge Loads In the Monte-Carlo analyses used for the C-CORE ISO work, first-year ridges were idealized in terms of a consolidated layer that breaks in crushing or flexure depending on whether the structure has a vertical or sloping face, and an unconsolidated keel below the consolidated layer that fails in shear like a Coulomb-Mohr material. Three key parameters are found to have a significant influence on first-year ridge loads: the thickness of the ridge consolidated layer, the thickness of the unconsolidated and, in the case of sloped structures, the height of the rubble pile that develops due to ice riding up the slope. The influence of these parameters has been considered for the following model components:

1) Croasdale ride-up model for failure of the consolidated layer against sloped structures. The model accounts for a number of different load components associated with bending failure, pushing ice through rubble, pushing ice up slope through rubble and overturning ice blocks at top of slope.

2) Local (Dolgopolov) plug failure model for failure of the unconsolidated portion of the keel impacting vertical and sloped structures.

3) Global plug failure model for the unconsolidated portion of keels impacting vertical and sloped structures.

4) A ‘pressure-averaging’ (PA) model for crushing failure of consolidated layer of first-year ridges against a vertically sided structure. The crushing pressure is


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penetration. Different mean crushing strengths are chosen for each feature and the variance in crushing pressure is considered to be reduced with contact width.

4) The CSA model for crushing failure of a multiyear ridge against a vertically sided structure. The crushing pressure is considered to be constant for a given contact area, with the pressure based on contact area and aspect ratio.

The influence of ridge dimension on loads is summarized as follows. Details on the evaluation of key parameters for the different models are given in Appendix A. The power on ridge dimension represents an estimate of the power Q in the approximate relationship

H = KxQ

Equation 2 between the maximum horizontal force H and ridge dimension x for typical large ridges. The ridge keel depth would be the dimension of most interest. Table 1 shows the main results for the Wang and Croasdale models. Table 1 Results for power Q (Equation 2)

Model Power on Ridge Dimension Wang 2.5 Croasdale beam on elastic foundation 2.25 Pressure-averaging slightly greater than 1 CSA 0.83 The above analyses confirm that estimates of loads for multi-year ridges impacting cones as determined using the Wang model will have a significantly greater probability content in the tail as compared to the models for loads on vertical structures. To check if this was an artifact of the Wang model, the model for an elastic beam on an elastic foundation, as developed by Hetenyi and applied to ice by Croasdale, was also considered. The Hetenyi model results in a similar increase in probability content in the tail, although the loads overall are substantially lower than those estimated using the Wang model. As noted above, a key issue is that in both the Wang and Croasdale beam on elastic foundation models, the effect of scale on fracture and flexural strength is not considered. Data noted above suggest that the scale effect is of the order of (length)-1. Consequently, the power for sloped and conical structures will be much closer to that for the models for vertically sided structures. Analysis of the model for first year loads is given in the following and for first year and multiyear models in the Appendices.

5 First-year Ridge Loads In reviewing the shapes of first-year load distributions, we found a discrepancy in the previous Barents Sea load trace and have obtained new results for the 100 m sloped structure, that we believe resulted from a previous input error. The updated load distribution for the Barents Sea 100 m diameter conical structures is shown in Figure 3. The semi-log relationship between load and probability of exceedance is now more linear

10

whereas it previously curved toward higher loads at low probabilities (previously closer to Type B in Figure 1).

Figure 3 Load distributions for the Barents Sea 100 m diameter conical structure. Blue curve is the annual maximum extremal distribution Discussion of Analysis of First-year Ridge Loads In the Monte-Carlo analyses used for the C-CORE ISO work, first-year ridges were idealized in terms of a consolidated layer that breaks in crushing or flexure depending on whether the structure has a vertical or sloping face, and an unconsolidated keel below the consolidated layer that fails in shear like a Coulomb-Mohr material. Three key parameters are found to have a significant influence on first-year ridge loads: the thickness of the ridge consolidated layer, the thickness of the unconsolidated and, in the case of sloped structures, the height of the rubble pile that develops due to ice riding up the slope. The influence of these parameters has been considered for the following model components:

1) Croasdale ride-up model for failure of the consolidated layer against sloped structures. The model accounts for a number of different load components associated with bending failure, pushing ice through rubble, pushing ice up slope through rubble and overturning ice blocks at top of slope.

2) Local (Dolgopolov) plug failure model for failure of the unconsolidated portion of the keel impacting vertical and sloped structures.

3) Global plug failure model for the unconsolidated portion of keels impacting vertical and sloped structures.

4) A ‘pressure-averaging’ (PA) model for crushing failure of consolidated layer of first-year ridges against a vertically sided structure. The crushing pressure is


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considered to vary randomly with penetration, with independent random values at each meter of penetration. Different mean crushing strengths are chosen for each feature and the variance in crushing pressure is considered to be reduced with contact width.

5) CSA model for crushing failure of consolidated layer of first-year ridges against a vertically sided structure. The crushing pressure is considered to be constant for a given contact area, with the pressure based on contact area and aspect ratio.

For the C-CORE ISO analyses, structures with vertical sides were modeled using the pressure-averaging crushing model for the consolidated layer, and the local and global plug failure models for the unconsolidated layer. Structures with sloped sides were modeled using the Croasdale model for ride-up of the consolidated layer, and the local and global plug failure models for failure the unconsolidated layer. The CSA model was included here for comparison. For the ride-up model, the rubble pile is assumed to grow in height in proportion to the consolidated layer thickness to the power 0.64 (see Appendix B). The influence of the key parameters on loads is given in Table 2. This summarizes the effect of various terms in the models on loads. Details of the various terms and the evaluation of key parameters for the different models are given in Appendix B. The table shows the power on the different additive terms contributing to the load, and for the Croasdale ride-up model also shows the proportions directly related to the rubble pile height. Table 2 Sensitivity of first-year ridge model components in terms of the power Q (Equation 2)

Model component Powers on

ConsolidatedLayer Thickness

for Additive Terms

ProportionRelated to

Rubble Pile Height

Powers on Unconsolidated

Layer Thickness for

Additive Terms Croasdale ride-up modelHr Ride up 1.64, 1.28 100%, 50%

Hl Lift rubble 1.28, 0.64, 1.0 100%, 100%, 100%

Hb Break ice 2.0, 1.25 0%, 0% Ht Turn blocks 2.0 0% Hp Push through rubble 1.28 100%

Local plug failure 1, 2, 3 Global plug failure 1, 2, 3

PA crushing slightly greater than 1

CSA crushing 0.83 The different load components for the Croasdale ride-up model are shown in order of decreasing magnitude as shown in Appendix B. The ride-up load is predominantly a result of the terms HR and HL which are largely dependent on the height of the rubble

12

pile. There is currently considerable uncertainty regarding rubble heights for different structures and ice thicknesses. The plug models include components related to unconsolidated keel thickness to the first, second and third powers. Based on the analyses, for typical large ridges the lower power terms dominate. As shown in Appendix B, for sloped structures the local and global plug load components are dominated by the ride-up component at lower exceedance probabilities. The consolidated layer thickness is closely related to level ice thickness, and both of these depend on the number of cumulative freezing degree days and have a steep drop in probability of occurrence above certain limits defined by the regional climate. This has a significant effect on the shapes of the tails. The conclusion is that the terms with lower powers dominate in the determination of extreme loads.

6 Recommendation The study has shown that the Wang and the beam-on-elastic-foundation models do result in tails in the extremal probability distribution with high probability content (fat tails). This has been found to be related to the nature of models; it has been found that the loads are proportional to the keel depth to a power of 2 to 2.5. This is to be contrasted with the models for vertical structures, in which the exponent is of the order of unity. The models are based on plasticity (conservative) or elasticity assumptions, with no scale effect. It is recognized that almost no full scale data on failure of multi-year ice against sloping structures are available. Data from level ice suggest scale effect proportional to strength scales according to (thickness)–1. This value is supported by other analyses given in section 2 above, considering fracture and flexural failure. This results in a reduction of the exponent of keel depth to between 1 and 1.5, from the range 2 to 2.5 given in the preceding pararaph. This would in effect bring the tail of the distribution into agreement with the results for vertical structures. The model for first year ice has been checked thoroughly and improvements and corrections have been made in the investigation reported here.. As a result it is found that the distribution in the tail has a similar form to those for vertical structures. This does not include a scale effect on flexural strength. It is recommended that the load factor of 1.35 be applied for all structures. This recommendation is made in recognition of the fact that the input to the calibration for sloping structures should include the scale effect for fracture processes and flexural failure.


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considered to vary randomly with penetration, with independent random values at each meter of penetration. Different mean crushing strengths are chosen for each feature and the variance in crushing pressure is considered to be reduced with contact width.


For the C-CORE ISO analyses, structures with vertical sides were modeled using the pressure-averaging crushing model for the consolidated layer, and the local and global plug failure models for the unconsolidated layer. Structures with sloped sides were modeled using the Croasdale model for ride-up of the consolidated layer, and the local and global plug failure models for failure the unconsolidated layer. The CSA model was included here for comparison. For the ride-up model, the rubble pile is assumed to grow in height in proportion to the consolidated layer thickness to the power 0.64 (see Appendix B). The influence of the key parameters on loads is given in Table 2. This summarizes the effect of various terms in the models on loads. Details of the various terms and the evaluation of key parameters for the different models are given in Appendix B. The table shows the power on the different additive terms contributing to the load, and for the Croasdale ride-up model also shows the proportions directly related to the rubble pile height. Table 2 Sensitivity of first-year ridge model components in terms of the power Q (Equation 2)

Model component Powers on

ConsolidatedLayer Thickness

for Additive Terms

ProportionRelated to

Rubble Pile Height

Powers on Unconsolidated

Layer Thickness for

Additive Terms Croasdale ride-up modelHr Ride up 1.64, 1.28 100%, 50%

Hl Lift rubble 1.28, 0.64, 1.0 100%, 100%, 100%

Hb Break ice 2.0, 1.25 0%, 0% Ht Turn blocks 2.0 0% Hp Push through rubble 1.28 100%

Local plug failure 1, 2, 3 Global plug failure 1, 2, 3

PA crushing slightly greater than 1

CSA crushing 0.83 The different load components for the Croasdale ride-up model are shown in order of decreasing magnitude as shown in Appendix B. The ride-up load is predominantly a result of the terms HR and HL which are largely dependent on the height of the rubble

12

pile. There is currently considerable uncertainty regarding rubble heights for different structures and ice thicknesses. The plug models include components related to unconsolidated keel thickness to the first, second and third powers. Based on the analyses, for typical large ridges the lower power terms dominate. As shown in Appendix B, for sloped structures the local and global plug load components are dominated by the ride-up component at lower exceedance probabilities. The consolidated layer thickness is closely related to level ice thickness, and both of these depend on the number of cumulative freezing degree days and have a steep drop in probability of occurrence above certain limits defined by the regional climate. This has a significant effect on the shapes of the tails. The conclusion is that the terms with lower powers dominate in the determination of extreme loads.

6 Recommendation The study has shown that the Wang and the beam-on-elastic-foundation models do result in tails in the extremal probability distribution with high probability content (fat tails). This has been found to be related to the nature of models; it has been found that the loads are proportional to the keel depth to a power of 2 to 2.5. This is to be contrasted with the models for vertical structures, in which the exponent is of the order of unity. The models are based on plasticity (conservative) or elasticity assumptions, with no scale effect. It is recognized that almost no full scale data on failure of multi-year ice against sloping structures are available. Data from level ice suggest scale effect proportional to strength scales according to (thickness)–1. This value is supported by other analyses given in section 2 above, considering fracture and flexural failure. This results in a reduction of the exponent of keel depth to between 1 and 1.5, from the range 2 to 2.5 given in the preceding pararaph. This would in effect bring the tail of the distribution into agreement with the results for vertical structures. The model for first year ice has been checked thoroughly and improvements and corrections have been made in the investigation reported here.. As a result it is found that the distribution in the tail has a similar form to those for vertical structures. This does not include a scale effect on flexural strength. It is recommended that the load factor of 1.35 be applied for all structures. This recommendation is made in recognition of the fact that the input to the calibration for sloping structures should include the scale effect for fracture processes and flexural failure.


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References API 1995. API RP 2N Recommended Practice for Planning, Designing, and Constructing

Structures and Pipelines for Arctic Conditions Bruce, J. 2009. Level Ice Interaction with Conical and Sloping Offshore Structures,

M.Eng. Thesis, Memorial University of Newfoundland C-CORE 2009. Development of Ice Design Loads and Criteria for Various Arctic

Regions. Report R-09-27-654, Prepared for OGP JIP25 Committee. CSA. 2004. Canadian Standards Association (CSA) CAN/CSA-S.471-04 Standard,

General Requirements, Design Criteria, the Environment, and Loads (part of the Code for the Design, Construction, and Installation of Fixed Offshore Structures)

Croasdale, K.R. 1975. Ice Forces on Marine Structures. Proceedings IAHR Ice Symposium., Pt. 1, pp 315-338.


Croasdale, K.R. 2003. Personal Communication. Croasdale, K.R. and R. W. Marcellus. 1981. Ice Forces On Large Marine Structures

IAHR Symposium, Quebec City, pp. 755 – 770 Croasdale, K.R., Cammaert, A.B. and Metge, M. 1994. A Method for the Calculation of

Sheet Ice Loads on Sloping Structures. Proceedings of the IAHR'94 Symposium on Ice, Vol. 2, pp 874-875, Trondheim, Norway.

Dieter, G.E. 1986. Mechanical Metallurgy. McGraw-Hill. Dolgopolov, Y.V., Afanasev, V.A., Korenkov, V.A. and Panfilov, D.F. (1975). Effect of

Hummocked Ice on Piers of Marine Hydraulic Structures, Proceedings IAHR Symposium on Ice, pp. 469-478, Hanover, NH, U.S.A..

Gladwell, R.W. 1977. Field Studies of the Strength and Physical Properties of a Multi-year Ice Pressure Ridge in the Southern Beaufort Sea. APOA Project 91, Imperial Oil Ltd., Report Number IPRT-3ME-77.

Hetenyi, M., Beams on elastic foundation. 1946. Scientific series, 1946.The University of Michigan Press, University of Michigan Studies, Ann Arbor.

Jellinek, Jordaan, I.J. 2005. Decisions under Uncertainty. Cambridge University Press. Jordaan, I.J., C. Li, T. Mackey, A. Nobahar, and J. Bruce. 2005. Design Ice Pressure-

Area Relationships; Molikpaq Data, Report prepared for Canadian Hydraulics Centre, National Research Council of Canada, Version 2.1


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References API 1995. API RP 2N Recommended Practice for Planning, Designing, and Constructing

Structures and Pipelines for Arctic Conditions Bruce, J. 2009. Level Ice Interaction with Conical and Sloping Offshore Structures,

M.Eng. Thesis, Memorial University of Newfoundland C-CORE 2009. Development of Ice Design Loads and Criteria for Various Arctic

Regions. Report R-09-27-654, Prepared for OGP JIP25 Committee. CSA. 2004. Canadian Standards Association (CSA) CAN/CSA-S.471-04 Standard,

General Requirements, Design Criteria, the Environment, and Loads (part of the Code for the Design, Construction, and Installation of Fixed Offshore Structures)

Croasdale, K.R. 1975. Ice Forces on Marine Structures. Proceedings IAHR Ice Symposium., Pt. 1, pp 315-338.


Croasdale, K.R. 2003. Personal Communication. Croasdale, K.R. and R. W. Marcellus. 1981. Ice Forces On Large Marine Structures

IAHR Symposium, Quebec City, pp. 755 – 770 Croasdale, K.R., Cammaert, A.B. and Metge, M. 1994. A Method for the Calculation of

Sheet Ice Loads on Sloping Structures. Proceedings of the IAHR'94 Symposium on Ice, Vol. 2, pp 874-875, Trondheim, Norway.

Dieter, G.E. 1986. Mechanical Metallurgy. McGraw-Hill. Dolgopolov, Y.V., Afanasev, V.A., Korenkov, V.A. and Panfilov, D.F. (1975). Effect of

Hummocked Ice on Piers of Marine Hydraulic Structures, Proceedings IAHR Symposium on Ice, pp. 469-478, Hanover, NH, U.S.A..

Gladwell, R.W. 1977. Field Studies of the Strength and Physical Properties of a Multi-year Ice Pressure Ridge in the Southern Beaufort Sea. APOA Project 91, Imperial Oil Ltd., Report Number IPRT-3ME-77.

Hetenyi, M., Beams on elastic foundation. 1946. Scientific series, 1946.The University of Michigan Press, University of Michigan Studies, Ann Arbor.

Jellinek, Jordaan, I.J. 2005. Decisions under Uncertainty. Cambridge University Press. Jordaan, I.J., C. Li, T. Mackey, A. Nobahar, and J. Bruce. 2005. Design Ice Pressure-

Area Relationships; Molikpaq Data, Report prepared for Canadian Hydraulics Centre, National Research Council of Canada, Version 2.1

14

Määttanen, M and Hoikkanen, J. 1996. Ice failure and ice loads on a conical structure—Kemi-I cone full scale ice force measurement data analysis, proceedings 13th IAHR Int. Symp. On Ice, Vol. 1 pp 8-16.

Maes, M.A. 2009. Calibration of Action Factors in ISO DIS 19906: 2009 prepared for International Association of Oil and Gas Producers.

Nevel, D.E. 1991. Wang’s Equation For Ice Forces From Pressure Ridges. Int Cold Regions Eng Conf, pp666-672.

Sanderson, T.J.O. 1988. Ice Mechanics: Risks to Offshore Structures. Graham and Trotman Inc., Norwell, Massachusetts, 253p.

Wang, Y.S., 1984, Analysis and Model Tests of Pressure Ridges Failing Against Conical Structures, IAHR Symposium, Hamburg


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APPENDIX A – EFFECT OF KEY PARAMETERS FOR MULTI-YEAR LOADS Wang Model for Multi-year Ridges Impacting Conical Structures The Wang model, as defined by Nevel in API RP-2N, calculates the maximum horizontal force H as

))arctan(tan(3

)(2

µασ

+−

= ba BFAFhH

where

h is the ridge draft, σ is the ridge flexural strength, α is the structure slope, µ is the ice-structure coefficient of friction, and Fa, Fb, A, and B are non-dimensional parameters.

While Fa, Fb, A, and B are non-dimensional parameters, they do vary in different ways with the ridge dimensions. As B is zero for the large ridges considered, consideration is given to Fa and A. Fa is the sum of two terms, the first (Fa1) varies in proportion to Bt

2 / h, where Bt is the width of the ridge, and the second (Fa1) is independent of the ridge dimensions. The term A is proportional to one over the square root of Fa.

Figure 4 shows how the terms vary with keel draft given a typical values for other parameters. The term Fa1 is much larger than Fa2, so Fa will, to close approximation, increase in proportion to the ridge dimension x and the force H predicted using the Wang model, to close approximation, will be proportional to x5/2. Figure 4 shows how the force varies with keel depth, given a typical set of ridge parameters.

16

5 10 15 20 25 300

10

20

30

Keel Draft (m)

Fa1

5 10 15 20 25 301.5417

1.5417

1.5417

1.5417

1.5417

Keel Draft (m)

Fa2

5 10 15 20 25 305

10

15

20

25

Keel Draft (m)

Fa

5 10 15 20 25 300.2

0.4

0.6

0.8

1

Keel Draft (m)

A

5 10 15 20 25 304

6

8

10

Keel Draft (m)

AFa

Figure 4 Magnitude of Wang Components as a Function of Keel Draft for a Representative Beaufort Multi-year Ridge

5 10 15 20 25 300

500

1000

1500

2000

Keel Depth (m)

Hor

izon

tal F

orce

(MN

)

Figure 5 Horizontal Force Determined using Wang model as a Function of Keel Depth for Representative Beaufort Multi-year Ridges


©OGP

15

APPENDIX A – EFFECT OF KEY PARAMETERS FOR MULTI-YEAR LOADS Wang Model for Multi-year Ridges Impacting Conical Structures The Wang model, as defined by Nevel in API RP-2N, calculates the maximum horizontal force H as

))arctan(tan(3

)(2

µασ

+−

= ba BFAFhH

where

h is the ridge draft, σ is the ridge flexural strength, α is the structure slope, µ is the ice-structure coefficient of friction, and Fa, Fb, A, and B are non-dimensional parameters.

While Fa, Fb, A, and B are non-dimensional parameters, they do vary in different ways with the ridge dimensions. As B is zero for the large ridges considered, consideration is given to Fa and A. Fa is the sum of two terms, the first (Fa1) varies in proportion to Bt

2 / h, where Bt is the width of the ridge, and the second (Fa1) is independent of the ridge dimensions. The term A is proportional to one over the square root of Fa.

Figure 4 shows how the terms vary with keel draft given a typical values for other parameters. The term Fa1 is much larger than Fa2, so Fa will, to close approximation, increase in proportion to the ridge dimension x and the force H predicted using the Wang model, to close approximation, will be proportional to x5/2. Figure 4 shows how the force varies with keel depth, given a typical set of ridge parameters.

16

5 10 15 20 25 300

10

20

30

Keel Draft (m)

Fa1

5 10 15 20 25 301.5417

1.5417

1.5417

1.5417

1.5417

Keel Draft (m)

Fa2

5 10 15 20 25 305

10

15

20

25

Keel Draft (m)

Fa

5 10 15 20 25 300.2

0.4

0.6

0.8

1

Keel Draft (m)

A

5 10 15 20 25 304

6

8

10

Keel Draft (m)

AFa

Figure 4 Magnitude of Wang Components as a Function of Keel Draft for a Representative Beaufort Multi-year Ridge

5 10 15 20 25 300

500

1000

1500

2000

Keel Depth (m)

Hor

izon

tal F

orce

(MN

)

Figure 5 Horizontal Force Determined using Wang model as a Function of Keel Depth for Representative Beaufort Multi-year Ridges


©OGP

17

Elastic Beam on Elastic Foundation Model for Multi-year Ridges Impacting Conical Structures Because the Wang model is based on plasticity theory and for the most part for the conditions considered ice fails as a brittle material, an alternative model applied by Croasdale (1975) based on Hetenyi (1946) has been considered here for comparison with the Wang model. For an infinitely long beam, Hetenyi’s solution predicts that a centerline crack will form first, then two hinge cracks, one on each side of the centerline crack. The horizontal load H associated with the formation of the two hinge cracks (assumed to form simultaneously) is

αµααµασ

sincoscossin17.6⋅−⋅+

⋅⋅

⋅⋅=

lyI

H f

where I is the cross-sectional moment of inertia, fσ is the flexural strength, y is the distance from the neutral axis to the top or bottom of the ice, and l is the ridge characteristic length, given as

25.0

4⎟⎟⎠

⎞⎜⎜⎝

⎛=

gbEIl

wρ, and

µ is the coefficient of friction.

If, for example, a rectangular cross-section is assumed, then 12/3bdl = and y = d/2 where d is the depth of the rectangle. Assuming b and d both increase proportionally to ridge dimension x, then it is seen that H increases as x9/4. The power 9/4 is reasonably close to power 5/2 determined for the Wang model. Pressure-Averaging Model for Multi-Year Ridges Impacting a Vertically Faced Structure For vertical structures, the ice is assumed to fail in crushing over the nominal contact area. For a given crushing strength, the load will be proportional to the ridge depth times the contact width. Assuming extreme events fail across the whole with of the structure, the load will be increase in proportion with ridge depth. In the ‘pressure-averaging’ model used for the ISO Monte-Carlo analyses, nominal ice crushing strength is assumed to vary randomly with penetration. For a given floe, a constant mean strength, drawn from a distribution based on full scale data, is assumed. The crushing strength at each meter of penetration is chosen independently from a normal distribution that has a variance that decreases with contact width (reference). For an impact with a ridge that is wider than the structure and has a truncated shape, the contact area will be constant for a significant portion of the impact, and the maximum load to close approximation will equal the maximum of the random loads at each meter of

18

penetration over this distance. The characteristic extreme value of a quantity defined by an extreme value distribution is N standard deviations above the mean, where (Jordaan, 2005, page 491)

( )2/1

2/1

)ln2(24lnlnln)ln2(

nnnN π+

−=

Given an independent random pressure chosen at each meter of penetration, then n is roughly equal to the ridge width. Figure 6 shows the relationship for a typical set of parameters; the pressure varies as the feature width to a low power. The horizontal force F = PA, assuming that the contact width limited by the width of the structure, will therefore increase at a rate slightly greater than x1.

0 20 40 60 80 1000.37

0.38

0.39

0.4

0.41

0.42

0.43

0.44

0.45

0.46

Feature Width (m)

Cha

ract

eris

tic E

xtre

me

Pre

ssur

e (M

Pa)

Figure 6 Approximate Relationship Between Characteristic Extreme Pressure and Ridge Width CSA Model for Multi-year Ridges Impacting Vertical Structures. The CSA model for ice crushing has been considered for comparison with the pressure-averaging model. The crushing pressure is treated as constant for a given contact area, with pressure based on contact area and aspect ratio. For thick multi-year ridges, the aspect ratio will typically be low (<10), but the equations provided for low aspect ratios have only been validated for contact areas up to 50 m2. The equation for aspect ratios from 10 to 80 has been applied; namely:

P = 1.5 CP h-0.174.

The horizontal force is then F = PA. Considering large ridges such that the contact width is determined by the width of the structure, the load will be proportional to x0.83.


©OGP

17

Elastic Beam on Elastic Foundation Model for Multi-year Ridges Impacting Conical Structures Because the Wang model is based on plasticity theory and for the most part for the conditions considered ice fails as a brittle material, an alternative model applied by Croasdale (1975) based on Hetenyi (1946) has been considered here for comparison with the Wang model. For an infinitely long beam, Hetenyi’s solution predicts that a centerline crack will form first, then two hinge cracks, one on each side of the centerline crack. The horizontal load H associated with the formation of the two hinge cracks (assumed to form simultaneously) is

αµααµασ

sincoscossin17.6⋅−⋅+

⋅⋅

⋅⋅=

lyI

H f

where I is the cross-sectional moment of inertia, fσ is the flexural strength, y is the distance from the neutral axis to the top or bottom of the ice, and l is the ridge characteristic length, given as

25.0

4⎟⎟⎠

⎞⎜⎜⎝

⎛=

gbEIl

wρ, and

µ is the coefficient of friction.

If, for example, a rectangular cross-section is assumed, then 12/3bdl = and y = d/2 where d is the depth of the rectangle. Assuming b and d both increase proportionally to ridge dimension x, then it is seen that H increases as x9/4. The power 9/4 is reasonably close to power 5/2 determined for the Wang model. Pressure-Averaging Model for Multi-Year Ridges Impacting a Vertically Faced Structure For vertical structures, the ice is assumed to fail in crushing over the nominal contact area. For a given crushing strength, the load will be proportional to the ridge depth times the contact width. Assuming extreme events fail across the whole with of the structure, the load will be increase in proportion with ridge depth. In the ‘pressure-averaging’ model used for the ISO Monte-Carlo analyses, nominal ice crushing strength is assumed to vary randomly with penetration. For a given floe, a constant mean strength, drawn from a distribution based on full scale data, is assumed. The crushing strength at each meter of penetration is chosen independently from a normal distribution that has a variance that decreases with contact width (reference). For an impact with a ridge that is wider than the structure and has a truncated shape, the contact area will be constant for a significant portion of the impact, and the maximum load to close approximation will equal the maximum of the random loads at each meter of

18

penetration over this distance. The characteristic extreme value of a quantity defined by an extreme value distribution is N standard deviations above the mean, where (Jordaan, 2005, page 491)

( )2/1

2/1

)ln2(24lnlnln)ln2(

nnnN π+

−=

Given an independent random pressure chosen at each meter of penetration, then n is roughly equal to the ridge width. Figure 6 shows the relationship for a typical set of parameters; the pressure varies as the feature width to a low power. The horizontal force F = PA, assuming that the contact width limited by the width of the structure, will therefore increase at a rate slightly greater than x1.

0 20 40 60 80 1000.37

0.38

0.39

0.4

0.41

0.42

0.43

0.44

0.45

0.46

Feature Width (m)

Cha

ract

eris

tic E

xtre

me

Pre

ssur

e (M

Pa)

Figure 6 Approximate Relationship Between Characteristic Extreme Pressure and Ridge Width CSA Model for Multi-year Ridges Impacting Vertical Structures. The CSA model for ice crushing has been considered for comparison with the pressure-averaging model. The crushing pressure is treated as constant for a given contact area, with pressure based on contact area and aspect ratio. For thick multi-year ridges, the aspect ratio will typically be low (<10), but the equations provided for low aspect ratios have only been validated for contact areas up to 50 m2. The equation for aspect ratios from 10 to 80 has been applied; namely:

P = 1.5 CP h-0.174.

The horizontal force is then F = PA. Considering large ridges such that the contact width is determined by the width of the structure, the load will be proportional to x0.83.


©OGP

19

Comparisons

Load exceedance curves are presented for the above models in Figure 7. The loads were determined using a first-order reliability method (FORM). Only key parameters were treated probabilistically and limits on the loads were not included. The keel depth was treated probabilistically in all cases, and for the probabilistic-averaging method, additional parameters defining the mean ridge crushing strength and extreme value were treated probabilistically. The exponential increase in load with logarithm of probability of exceedance in the Wang and Croasdale models in Figure 7 demonstrate the cause of the high action factors. This is not considered a realistic extrapolation without accounting for a size effect on flexural failure.

Figure 7 Approximate analyses of multi-year ridge loads using FORM: (top) Exceedance probability of load given an impact (bottom) Curves normalized to 10-2 values

20

APPENDIX B – EFFECT OF KEY PARAMETERS FOR FIRST-YEAR LOADS

First-year Ridge Loads Three key parameters may have a significant influence on first-year ridge loads: the thickness hC of the ridge consolidated layer, the unconsolidated layer thickness hU, and, in the case of sloped structures, the height hR of the rubble pile that forms on the structure. The ridge consolidated layer thickness and unconsolidated layer thickness have been assumed independent. The height of the rubble pile has been modelled as the following function of the consolidated layer thickness, based on data from the Confederation Bridge:

hR = KR x 7.59 x hC0.64 , where KR is a random quantity.

The following model components have been considered:

1) A ‘pressure-averaging’ model for crushing failure of consolidated layer of first-year ridges against a vertically sided structure. The crushing pressure is considered to vary randomly with penetration, with independent random values at each meter of penetration. Different mean crushing strengths are chosen for each feature and the variance in crushing pressure is considered to be reduced with contact width.


3) Croasdale model for failure of consolidated layer against sloped structures. The model accounts for load components associated with bending failure, pushing ice through rubble, pushing ice up slope through rubble and overturning ice blocks at top of slope.

4) Local plug failure (Dolgopolov) model for unconsolidated keel impacting vertical or sloped structure.

5) Global plug failure model for unconsolidated keel impacting vertical or sloped structure.

For the C-CORE ISO analyses, structures with vertical sides were modeled using the pressure-averaging crushing model for the consolidated layer, and the local and global plug failure models for the unconsolidated layer. Structures with sloped sides were modeled using the Croasdale model for ride-up of the consolidated layer, and the local and global plug failure models for failure the unconsolidated layer. The CSA crushing model has been added for comparison.


©OGP

19

Comparisons

Load exceedance curves are presented for the above models in Figure 7. The loads were determined using a first-order reliability method (FORM). Only key parameters were treated probabilistically and limits on the loads were not included. The keel depth was treated probabilistically in all cases, and for the probabilistic-averaging method, additional parameters defining the mean ridge crushing strength and extreme value were treated probabilistically. The exponential increase in load with logarithm of probability of exceedance in the Wang and Croasdale models in Figure 7 demonstrate the cause of the high action factors. This is not considered a realistic extrapolation without accounting for a size effect on flexural failure.

Figure 7 Approximate analyses of multi-year ridge loads using FORM: (top) Exceedance probability of load given an impact (bottom) Curves normalized to 10-2 values

20

APPENDIX B – EFFECT OF KEY PARAMETERS FOR FIRST-YEAR LOADS

First-year Ridge Loads Three key parameters may have a significant influence on first-year ridge loads: the thickness hC of the ridge consolidated layer, the unconsolidated layer thickness hU, and, in the case of sloped structures, the height hR of the rubble pile that forms on the structure. The ridge consolidated layer thickness and unconsolidated layer thickness have been assumed independent. The height of the rubble pile has been modelled as the following function of the consolidated layer thickness, based on data from the Confederation Bridge:

hR = KR x 7.59 x hC0.64 , where KR is a random quantity.

The following model components have been considered:

1) A ‘pressure-averaging’ model for crushing failure of consolidated layer of first-year ridges against a vertically sided structure. The crushing pressure is considered to vary randomly with penetration, with independent random values at each meter of penetration. Different mean crushing strengths are chosen for each feature and the variance in crushing pressure is considered to be reduced with contact width.


3) Croasdale model for failure of consolidated layer against sloped structures. The model accounts for load components associated with bending failure, pushing ice through rubble, pushing ice up slope through rubble and overturning ice blocks at top of slope.

4) Local plug failure (Dolgopolov) model for unconsolidated keel impacting vertical or sloped structure.

5) Global plug failure model for unconsolidated keel impacting vertical or sloped structure.

For the C-CORE ISO analyses, structures with vertical sides were modeled using the pressure-averaging crushing model for the consolidated layer, and the local and global plug failure models for the unconsolidated layer. Structures with sloped sides were modeled using the Croasdale model for ride-up of the consolidated layer, and the local and global plug failure models for failure the unconsolidated layer. The CSA crushing model has been added for comparison.


©OGP

21

Crushing models The pressure-averaging and CSA models are the same as for multi-year ridges, except that the ice thickness is reduced significantly and the ice crushing strength may be smaller. Croasdale ride-up model

The Croasdale ride-up model determines the horizontal force H as the sum of the following five components: H = Hb+Hr+Ht+Hl+Hp where:

Hp is the force to push the consolidated layer through the rubble to the slope Hl is the force to lift and shear the rubble on top of the consolidated layer, Hb is the force to break the ice, Hr is the force to push the broken blocks of ice up the slope through the

rubble, Ht is the force turn ice blocks at top of slope,

To first approximation, the components vary as follows as a function of the consolidated layer thickness hC and the height of the rubble pile hR as follows: Hb increases as hC

1.25 + k1 hC2

Hr increases as hR2 + k2 hR hC , or equivalently, hC

1.28 + k2 hC1.64

Ht increases as hC2

Hl increases as hR2 + k3 hR, or equivalently, hC

1.28 + k3 hC0.64

Hp increases as hR2, or equivalently, hC

1.28 The different terms and total force are plotted as a function of the consolidated layer thickness in Figure 8. It is seen that the most significant component is the force to push the ice up the slope through the rubble.

22

Figure 8 Variation in ride-up force with consolidated layer thickness Local and global plug failure models As a ridge advances, the unconsolidated keel is assumed to fail locally until the remaining unconsolidated ice that has not failed is reduced in extent to the point that global plug failure occurs (Figure 9).

Ice movement

Failure volume shown in red

Local passive failure Dolgopolov et al. (1975)

Global plug failureCroasdate (1980)

Ice movement


Ice movement




Ice movement

Failure volume shown in red Figure 9 Plug failure models The force associated with local plug failure is given as


©OGP

21

Crushing models The pressure-averaging and CSA models are the same as for multi-year ridges, except that the ice thickness is reduced significantly and the ice crushing strength may be smaller. Croasdale ride-up model

The Croasdale ride-up model determines the horizontal force H as the sum of the following five components: H = Hb+Hr+Ht+Hl+Hp where:

Hp is the force to push the consolidated layer through the rubble to the slope Hl is the force to lift and shear the rubble on top of the consolidated layer, Hb is the force to break the ice, Hr is the force to push the broken blocks of ice up the slope through the

rubble, Ht is the force turn ice blocks at top of slope,

To first approximation, the components vary as follows as a function of the consolidated layer thickness hC and the height of the rubble pile hR as follows: Hb increases as hC

1.25 + k1 hC2

Hr increases as hR2 + k2 hR hC , or equivalently, hC

1.28 + k2 hC1.64

Ht increases as hC2

Hl increases as hR2 + k3 hR, or equivalently, hC

1.28 + k3 hC0.64

Hp increases as hR2, or equivalently, hC

1.28 The different terms and total force are plotted as a function of the consolidated layer thickness in Figure 8. It is seen that the most significant component is the force to push the ice up the slope through the rubble.

22

Figure 8 Variation in ride-up force with consolidated layer thickness Local and global plug failure models As a ridge advances, the unconsolidated keel is assumed to fail locally until the remaining unconsolidated ice that has not failed is reduced in extent to the point that global plug failure occurs (Figure 9).

Ice movement




Ice movement


Ice movement




Ice movement

Failure volume shown in red Figure 9 Plug failure models The force associated with local plug failure is given as


©OGP

23

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛+= pe

peffe

e

eeLP Kch

KhDh

DH 226

12γ

where

De is the contact width, he is the effective maximum unconsolidated keel draft, defined as ecke DShHh +−= , Hk is the local ridge thickness (consolidated layer plus unconsolidated keel), hc is the thickness of the consolidated layer, S is a user defined ‘surcharge’ factor that quantifies the effect of additional

buoyancy due to ice accumulated below the keel as a result of the interaction (see comments below),

γeff is the buoyant density of the unconsolidated keel accounting for keel porosity,

Kp is the passive pressure coefficient of the unconsolidated keel,

)sin(1)sin(1

φφ

−+

=pK ,

φ is the internal friction angle of the unconsolidated keel and c is the cohesion of the unconsolidated keel.

Assuming that the ridge always advances to the point that the maximum unconsolidated thickness hu is reached (this may not be the case), then

33

221 uuuLP hkhkhkH ++∝

The term that dominates will depend on the values of k1, k2 and k3 for typical large ridges. Global plug failure will occur once the local plug failure force is greater than the force to shear a global plug along vertical planes from the sides of the structure through the remaining unconsolidated ridge and a horizontal plane extending between the two vertical planes, between the consolidated and unconsolidated layers. The shear strength along each increment dA of area on the shear planes is modeled as the sum of cohesive and frictional components. The cohesive component equals the cohesive strength times the area, where cohesion may be considered either constant or a function of depth, and in the ISO analyses, was modeled as constant. For large ridges wider than the structure, the force to overcome cohesion on the top plane then increases as the width of the ridge. The force to overcome cohesion on the side planes increases as the width of the ridge times the depth of the ridge. The frictional component over a small increment dA of area equals the tangent of the friction angle times the buoyant pressure resulting from the ice underneath, times the passive pressure coefficient. On the top shear plane, the buoyant pressure is proportional to the depth of the unconsolidated layer below, so the required force to shear the plane is proportional to the ridge width times the unconsolidated layer thickness. On the side

24

shear planes, the buoyant pressure at a given height is proportional to the distance to the bottom of the keel, so the required force to shear the plane is proportional to the ridge width times the square of the unconsolidated layer thickness. The force HGP associated with global plug failure is therefore proportional to

36

254 uuuGP hkhkhkH ++∝

The term that dominates will depend on the values of k4, k5 and k6 for typical large ridges.

Comparisons Load exceedance curves are presented for the above models in Figure 10. The loads were determined using FORM. The figure shows the distribution of loads given an impact. Only key parameters were treated probabilistically. The thickness of the unconsolidated layer was treated probabilistically for global and local plug failure. For crushing and ride-up of the consolidated layer, the thickness of the consolidated layer was modeled as the thickness of the surrounding ice (treated as a random quantity) times the ratio between consolidated and level ice thickness (also treated as a random quantity). When modeling crushing using the probabilistic-averaging method, the mean ridge crushing strength, width of the ridge (assumed proportional to the thickness of the unconsolidated layer) and the extreme value parameter were treated probabilistically. The graph shows the contribution of the individual components to the total load. For instance “Global plug” indicates the load associated with this term, “Ride-up’ shows the contribution of the ride-up term, and so on. An additional case was run in which the force was considered to consist of the forces required for ride-up and failure of the unconsolidated keel according to global plug failure model. The global and local plug loads are dominated by lower power terms. The final curves in Figure 3 above are a combination of the inputs shown below, and blend the high- and low-power terms to give a result that has a well-behaved tail.


©OGP

23

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛+= pe

peffe

e

eeLP Kch

KhDh

DH 226

12γ

where

De is the contact width, he is the effective maximum unconsolidated keel draft, defined as ecke DShHh +−= , Hk is the local ridge thickness (consolidated layer plus unconsolidated keel), hc is the thickness of the consolidated layer, S is a user defined ‘surcharge’ factor that quantifies the effect of additional

buoyancy due to ice accumulated below the keel as a result of the interaction (see comments below),

γeff is the buoyant density of the unconsolidated keel accounting for keel porosity,

Kp is the passive pressure coefficient of the unconsolidated keel,

)sin(1)sin(1

φφ

−+

=pK ,

φ is the internal friction angle of the unconsolidated keel and c is the cohesion of the unconsolidated keel.

Assuming that the ridge always advances to the point that the maximum unconsolidated thickness hu is reached (this may not be the case), then

33

221 uuuLP hkhkhkH ++∝

The term that dominates will depend on the values of k1, k2 and k3 for typical large ridges. Global plug failure will occur once the local plug failure force is greater than the force to shear a global plug along vertical planes from the sides of the structure through the remaining unconsolidated ridge and a horizontal plane extending between the two vertical planes, between the consolidated and unconsolidated layers. The shear strength along each increment dA of area on the shear planes is modeled as the sum of cohesive and frictional components. The cohesive component equals the cohesive strength times the area, where cohesion may be considered either constant or a function of depth, and in the ISO analyses, was modeled as constant. For large ridges wider than the structure, the force to overcome cohesion on the top plane then increases as the width of the ridge. The force to overcome cohesion on the side planes increases as the width of the ridge times the depth of the ridge. The frictional component over a small increment dA of area equals the tangent of the friction angle times the buoyant pressure resulting from the ice underneath, times the passive pressure coefficient. On the top shear plane, the buoyant pressure is proportional to the depth of the unconsolidated layer below, so the required force to shear the plane is proportional to the ridge width times the unconsolidated layer thickness. On the side

24

shear planes, the buoyant pressure at a given height is proportional to the distance to the bottom of the keel, so the required force to shear the plane is proportional to the ridge width times the square of the unconsolidated layer thickness. The force HGP associated with global plug failure is therefore proportional to

36

254 uuuGP hkhkhkH ++∝

The term that dominates will depend on the values of k4, k5 and k6 for typical large ridges.

Comparisons Load exceedance curves are presented for the above models in Figure 10. The loads were determined using FORM. The figure shows the distribution of loads given an impact. Only key parameters were treated probabilistically. The thickness of the unconsolidated layer was treated probabilistically for global and local plug failure. For crushing and ride-up of the consolidated layer, the thickness of the consolidated layer was modeled as the thickness of the surrounding ice (treated as a random quantity) times the ratio between consolidated and level ice thickness (also treated as a random quantity). When modeling crushing using the probabilistic-averaging method, the mean ridge crushing strength, width of the ridge (assumed proportional to the thickness of the unconsolidated layer) and the extreme value parameter were treated probabilistically. The graph shows the contribution of the individual components to the total load. For instance “Global plug” indicates the load associated with this term, “Ride-up’ shows the contribution of the ride-up term, and so on. An additional case was run in which the force was considered to consist of the forces required for ride-up and failure of the unconsolidated keel according to global plug failure model. The global and local plug loads are dominated by lower power terms. The final curves in Figure 3 above are a combination of the inputs shown below, and blend the high- and low-power terms to give a result that has a well-behaved tail.


©OGP

25

Figure 10 Approximate analyses of first-year ridge loads using FORM: (top) Exceedance probability of load given an impact (bottom) Curves normalized to 10-2 values

For further information and publications, please visit our website at

www.ogp.org.uk

25

Figure 10 Approximate analyses of first-year ridge loads using FORM: (top) Exceedance probability of load given an impact (bottom) Curves normalized to 10-2 values

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