IMO GOAL-BASED NEW SHIP CONSTRUCTION STANDARDS. Linkage between FSA and GBS

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1 INTERNATIONAL MARITIME ORGANIZATION E IMO MARITIME SAFETY COMMITTEE 81st session Agenda item 6 MSC 81/INF.6 7 February 2006 ENGLISH ONLY GOAL-BASED NEW SHIP CONSTRUCTION STANDARDS Linkage between FSA and GBS Submitted by the International Association of Classification Societies (IACS) Executive summary: Action to be taken: Paragraph 9 Related documents: SUMMARY This document includes an example of how structural design rules are derived and justified, based on internationally agreed and standardized methods and tools commonly referred to as Structural Reliability Analysis (SRA) and limit state design. MSC 80/6/6, MSC 80/24, MSC 79/23, MSC 79/6/15, MSC 79/INF.5 General 1 Both at MSC 79 and MSC 80 there was considerable debate relating to the understanding of the relation between GBS and FSA, and for issues relating to hull structures there have been debates relating to the relation between Structural Reliability Analysis (SRA) and GBS. 2 IACS wishes to contribute to the understanding by providing an example of how these issues fits together if a standard risk based approach is applied. The approach used demonstrates how FSA, including cost effectiveness assessment may be used to derive target reliabilities (Tier I) for the various failure modes (limit states (Tier II)). SRA is further used to derive and justify the partial safety factors and exact Rule formulation (Tier IV). Whilst a Rule itself may be very difficult to verify against the underlying parameters, the FSA/SRA analyses may be subjected to review and verified. The example therefore also provides a proposal for how to verify (Tier III) the Tier IV rules. 3 The example demonstrates the use of standard SRA to derive a Rule formulation. The Hull Girder Ultimate Capacity is an explicit control of the most critical failure mode for double hull tankers. The criterion for the ultimate strength of the hull girder is given in a partial safety factor format, and has been calibrated using SRA. The example would correspond to a Rule Commentary in SRA jargon. The basic terminology was explained in document MSC 80/6/6, and, as stated therein, the terminology is standardized across industries. For reasons of economy, this document is printed in a limited number. Delegates are kindly asked to bring their copies to meetings and not to request additional copies.

2 - 2-4 The advantage with the approach is that it links the resulting rule (Tier IV) and structural dimension to the level of safety or risk involved (the goal in Tier I). In developing the analysis, all basic assumptions, mechanical models, uncertainties and variabilities are documented and may therefore be subjected to review (Tier III). Therefore, the attached analysis, whereby the rules are derived and justified, can be verified by experts with the relevant background. 5 IACS is not suggesting that all rules should necessarily be justified by the use of SRA. Many rules are based on experience, and have provided the industry with safe ships for a large number of years. The suggestion is to use SRA for the most safety critical rules, when these rules are updated. Furthermore, for innovative ship types or in other cases where no experience exists, SRA should always be used. 6 It is important to note that safety factors are a result of SRA, including physical models, statistical data, uncertainties and calibration procedure. The resulting safety factors therefore belong to the Rules, and should not be subject to arbitrary modifications. The target reliability may be decided by IMO based on considerations of consequences. However, the attached example also demonstrates that the target reliability can be derived by cost effectiveness analysis using the acceptance criteria used in FSA studies. 7 Figure A.14 shows the relation between target reliability and the life cycle cost, and demonstrates that an optimum can be identified. In Figure A.14 the value of averting the loss of life and environmental pollution is not included. This is done in Figure A.15 and A.16. In Figure A.15 the results are given as function of the acceptance criterion on the cost of averting fatalities, and the commonly used $3 million is market by a horizontal line. In Figure A.15 there is no value put on averting pollution. This is done in figure A.16, where a Cost of Averting a Ton of oil Spilled (CATS) is included. 8 As in the attached example, the main content of a rule commentary generally is: Definition of the scope of the rule The specification of examples to be used in the code calibration The limit state formulation The methodology The mechanical model used The environmental loads The load and response model The uncertainties and variabilities (distributions and distribution parameters) The code formulation, including the definition of characteristic values The reliability results with sensitivity The target reliability and how this is derived (from the accident scenarios/fsa) The resulting code (calibrated partial safety factors). Action requested of the Committee 9 The Committee is invited to consider the attached example in the development of goalbased new ship construction standards during its deliberations. ***

3 EXAMPLE; HULL GIRDER ULTIMATE STRENGTH FOR DOUBLE HULL TANKERS 1 INTRODUCTION 1 The Hull Girder Ultimate Capacity is an explicit control of the most critical failure mode for double hull tankers. The criterion for the ultimate strength of the hull girder is given in a partial safety factor format, and has been calibrated using Structural Reliability Analysis (SRA). 2 The hull girder ultimate capacity check is categorized as an Ultimate Limit State (ULS) and is included in the first step in the design verification. Scantlings required will be used as input to the later steps, e.g. a FEM strength assessment. Failure in sagging is identified as the most critical failure mode for double hull tankers. The approach is quite similar to the approach described in Skjong and Bitner Gregersen (2002). The example is also based on work in the JTP, and an earlier version is publicly available at However, the example is extended with cost benefit assessment and cost effectiveness assessment. This is done in order to document the relation between structural dimensions and the associated costs and benefits in terms of improved ship safety, crew safety and protection of the marine environment. 2 SCOPE 3 The present example covers a design rule for determining the hull girder ultimate strength for: (a) (b) Oil tankers equal to or greater than 150 m in length Sagging condition only The example is simplified compared to a real, complete calibration study, and references to some of the analysis carried out have been removed, or just briefly mentioned. 4 The load effect considered is vertical bending moment due to still water and wave loads. North Atlantic environmental conditions are used as basis. Abnormal (freak, rogue) waves are not considered. The net thickness approach, which represents a corroded condition is applied with the ultimate capacity checked with 50% t corr applied to all structural members, where t corr is the corrosion addition. 5 Five test vessels are used, and a summary of vessel particulars are given in Table A. 1. This set of vessels is assumed to span the scope of the Rules. Table A. 1: Test vessels Case Vessel type Lpp (m) Breadth (m) Depth (m) 1 Suezmax Product/Chemical Carrier VLCC VLCC Aframax

4 Page 2 3 METHODOLOGY 3.1 Structural Reliability Analysis 6 SRA has been used as a tool to calibrate a design rule for hull girder ultimate strength. The aim is to obtain a rule that ensures that a sufficient and appropriate safety level is obtained for the structures and structural components covered by the rule. 7 In the SRA the randomness in environment, structural load effects and strength parameters are accounted for. Uncertainties in the prediction models are also considered. The aim of the SRA is to represent the physics of the problem as realistically as possible, reflecting the uncertainty involved at the same time as excessive conservatism is avoided. The main result is a prediction of the nominal annual probability of failure together with the sensitivity of this result with respect to the various parameters. Effects of gross error are not considered in a SRA, as minor changes in structural dimensions generally are an inadequate risk control option in cases of gross errors; reference is made to the Fundamental Postulate in Structural Safety (Ditlevsen, 1981). 8 The rule analysis is a deterministic analysis following a well defined procedure. This procedure should be practical to use in design and approval of the ship. The SRA is a probabilistic analysis used to calibrate the Rule, so whilst the resulting Rule itself looks deterministic it has been based on risk concepts and such Rules are therefore commonly referred to as risk based. 9 The safety level obtained using the rule depends on how the characteristic values are defined and the magnitude of the partial safety factors. It is assumed that the same target safety level is applicable for this ULS for all ships to be covered by the rule. 10 An illustration of calibration is given in Figure A.1. The partial safety factors are calculated as the ratio between the design point values (the most likely values of the stochastic variables at failure) and the characteristic values for cases where the target reliability level is fulfilled. This is straightforward when considering a single case only. However, when more cases and variations in the designs are considered it becomes more complex since such ratios will usually vary between cases. This leads to the problem of code calibration (Madsen, et al; 1986), or optimization (Ronold and Skjong, 2002). 11 In a calibration the magnitudes of the partial safety factors are optimized to provide a consistent reliability level for the test set spanning the scope of the rule; i.e. avoiding significant under-design and excessive over-design. The definition of the characteristic values may in principle also be considered in this optimization. However, characteristic values are often defined in domain standards and the introduction of redefined characteristic values in a Rule may result in misunderstandings. 12 Whereas Figure A.1 illustrates a single test case calibration, Figure A.2 illustrates a more general procedure that has been implemented and applied in the calibration. The steps involved are described as follows: (a) Start out with the characteristic values for the still water bending moment and the wave moment together with initial trial partial safety factors. Results obtained from a single test case calibration, as illustrated in Figure A.1 may be used as guidance to select the initial trial safety factors.

5 Page 3 (b) (c) (d) Apply the rule criteria to compute the required characteristic capacity. This may represent a structural design that differs from the initial design. The difference is defined in terms of a parametric mosel. The parametric model is a deck area scaling factor following a defined procedure on how to modify the deck (stiffener size and plate thickness) in order to increase (or decrease) the capacity relatively to the initial design. The loads are assumed to be unaffected by the design modification. Determine the probability of failure corresponding to the resulting design from step (b), and find its deviation from the specified annual target probability of failure. Evaluate whether the optimum set of partial safety factors are obtained; i.e. minimizing the deviation from the target, considering all cases in the test set. Modify the safety factors and recalculate from (b) if necessary.

6 Page 4 Figure A.1: Calibration single test case illustration Criterion: Rule γ M S SW + γ M W WV M γ U R Criterion: Limit state: Reliability Analysis P f P f, t arget g=m u -M S -M W Still water moment, M SW Rule value, empirical Actual loading condition Other Probability Density - actual loading - model uncertainty M S distribution γ S = M S, DP M SW M S, DP M S Wave moment, M WV Rule value, empirical Direct calculation - Detailed recipe wrt. kind of analysis, environmental conditions, probability level etc. Other Probability Density - joint environmental model - hydrodynamic analysis - model uncertainty annual extreme response γ W = M W, DP M WV M W, DP M W Moment capacity, M U E.g. incremental iterative method Material strength Other Probability Density - random material - geometrical uncertainty - model uncertainty capacity distribution γ R M = M U U, DP M U, DP M u Safety factors, γ S, γ W, γ R Design Points (DP)

7 Page 5 Figure A.2: Calibration, applied procedure, using a parametric models or a Design Modification Factor (DMF) a Characteristic values, M SW & M WV Initial trial safety factors M U,C DMF b M Design analysis, U = ( γ S M SW + γ W MWV )/ γ R? minimum DMF -log(pf) Target c Reliability of design, deviation from target Modify safety factors DMF d e Optimum values of safety factors? YES Calibration completed NO I.e. avoid serious underdesign and excessive over-design by minimising deviation from target probability 3.2 Rule criteria 13 The design format is defined as: M U γ S M SW + γ W M WV γ R Where: M SW is the characteristic still water sagging vertical moment γ S is the partial safety factor for the sagging still water bending moment M WV is the characteristic sagging vertical wave moment γ W is the partial safety factor for the sagging wave bending moment covering environmental, wave load and vertical wave bending moment prediction uncertainties M U is the characteristic vertical hull girder bending moment capacity γ R is the partial safety factor for the vertical hull girder bending moment capacity covering material, geometric and strength prediction uncertainties

8 Page Characteristic load Still water moment 14 The characteristic still water moment used for the purpose of calibration is here defined as the maximum sagging value from any seagoing condition given in the loading manual, but not less than 90% of JTP minimum requirement 1. The minimum requirement for all the 5 cases is higher than the maximum value of the loading manual, but well below the given permissible value taken from the drawing. The values used from the 5 sample ships are included in Table A Wave moment 15 The characteristic wave bending moment is calculated according to Section 7 of the IACS common structural rules for double hull oil tankers, and the values are included in Table A.2. Table A.2: Characteristic still water moment and wave moment (knm) SUEZMAX PRODUCT VLCC 1 VLCC 2 AFRAMAX Still water moment, maximum in load manual Still water moment, JTP minimum requirement Still water moment, permissible from drawing. (Not used) Wave moment, IACS formula 3.4 Characteristic moment capacity The characteristic bending moment capacity may, in principle, be calculated according to any selected computational methods. The characteristic capacities used in this requirement are calculated according to a single step method; here after called HULS-1 for convenience, see Appendix A/2 of the IACS common structural rules for double hull oil tankers. In this method the area of each stiffened panel in the deck from the initial design A net50 is reduced to A eff, based on the ratio between its ultimate capacity σ U calculated using the advanced buckling approach and the yield stress σ yd ; i.e.: σ U A eff = A σ yd net50 17 The sectional properties of the hull girder are modified correspondingly, and the ultimate moment capacity is nominally computed to correspond to initial yield in the deck of the modified section. 1 The final IACS common structural rules for double hull oil tankers were updated on this point, and now have two discrete checks; one using the full permissible still water bending value with a lesser partial safety factor with respect to the wave load.

9 Page 7 4 INITIAL DESIGN AND PARAMETRIC MODEL 18 The net thickness approach is applied using t net50 for all members. 19 In the calibration, as illustrated in Figure A.2, a parametric model is applied as a means of adjusting the moment capacity. The following assumptions are made: (e) (f) The hull girder moment capacity is adjusted by modifying the deck design only, keeping dimensions of sides, bulkheads and bottom structure constant. The change in the deck design is implemented by changing the size of the stiffeners and the plate thickness only, keeping the spacing and the number of stiffeners constant. (g) The change in stiffener size follows a smoothed curve fitted to available profile sizes. (h) (i) The thickness of the deck plating is assumed to change in proportion to the change in thickness of the stiffener flange. Loads are assumed remain unchanged by the design modification. 20 The outlined procedure for deck modification is simple, and does not necessarily lead to optimum designs. For small variations around the initial design, it is considered a reasonable approach for the purpose of calibration. 21 The implemented design modification factor represents relative changes in the gross area of the deck following the recipe outlined in paragraph 0. The capacity determined using the single step procedure (IACS common structural rules for double hull oil tankers, Appendix A/2) is illustrated in Figure A.3 as a function of DMF.

10 Page Figure A.3: Characteristic capacity as a function of DMF Capacity (knm) SUEZMAX PRODUCT VLCC 1 VLCC 2 AFRAMAX Design Modification Factor 5 RELIABILITY ANALYSIS 22 In a SRA the design criterion may be stated by requiring the probability of failure to be less than the target probability of failure. Failure is defined as the state when the load exceeds the capacity, where the uncertainties in both load and capacity are accounted for. 23 The setup of the analysis is illustrated in Figure A.4, and described further in the following subsections. The probability of failure is calculated by the general probabilistic analysis program PROBAN (1996), using the First Order Reliability Method (FORM). Figure A.4: Hull girder collapse, outline of the reliability analysis Load Analysis Reliability Analysis Capacity Analysis Hydrodynamic analysis Transfer functions for wave moment Joint environment Geometry & material PROBAN Load > Capacity Still water moment Geometry, material Panel buckling analysis Dummy load P f Importance Sensitivity Capacity

11 Page 9 6 UNCERTAINTY MODELLING 6.1 Environmental conditions 24 A joint environmental model; i.e. a probabilistic model for the significant wave height and the zero-crossing period, for the North Atlantic environmental conditions is used. This model is developed from the scatter diagram used as basis for developing loads in the IACS common structural rules for double hull oil tankers (Section 2/ ), and implies some smoothing and extrapolation to unobserved conditions. The significant wave height H s of a 3-hours sea state is modelled as a 3-parameter Weibull distribution: f H s β hs ( hs ) = α γ α hs γ exp α β 1 β with scale parameter α=2.721m, shape parameter β=1.401 and location parameter γ=0.866m. 25 The zero-crossing wave period T z is conditional on the significant wave height, and a lognormal distribution has been applied: f T H z s ( t z h s ) = 1 2πσt z exp ( ln t µ ) z 2σ 2 2 Where: µ = σ = E 6.2 Wave moment ( lnt z ) = hs hs Var( lnt z ) = e 26 The structural response due to waves is based on the linear hydrodynamic analysis results for the five test vessels. Results in terms of transfer functions for the selected midship bending moment are used. The long-term response is computed in PROBAN. The basic assumption is a narrow banded Gaussian response in each sea state. This assumption implies Rayleigh distributed maxima for a given sea state, for which a Gumbel type extreme value distribution can be derived. Finally, the annual extreme value distribution is obtained assuming independence between sea states. This approach to use transfer functions with PROBAN is documented by Mathisen and Birknes (2003). 27 The distribution using this approach has been verified versus a conventional Weibull distribution as obtained based on the standard long term response calculation procedure as used for deriving wave load values, see JTP Rule (Section 2/ ). 28 The probability of sagging failure in ballast condition may be neglected since the still water moment in ballast generally gives hogging and leads to a significant reduction in the total sagging moment, see paragraph 0. The loaded conditions at sea are considered, and wave loads corresponding to scantling draught are used. The annual probability of failure is calculated taking into account the relevant fraction of the year for which the vessel is assumed to be in loaded condition at sea; i.e. 42.5% of the year as defined. The ship is in port or sailing in ballast the rest of the time.

12 Page Here focus is on hull girder collapse in heavy weather at sea, and in such severe conditions the ship is most likely to operate in head sea, or nearly head sea. In extreme sea states the waves tend to be more long-crested; e.g. cos 4 directional function or with an even higher exponent. 30 Some test runs for calculation of the wave moment distribution were carried out. A triangular distribution of the main heading between 150º and 210º (head sea defined as 180º) was assumed together with a cos 4 spreading function. This was found to be almost equivalent to head sea and a spreading using cos 2. For this reason, the SRA is carried out for head sea with a shortcrested representation corresponding to cos The Pierson Moskowitz (PM) spectrum has been applied in the analyses. Some sensitivity results using the Jonswap wave spectrum have been carried out. All results are for zero ship speed. 32 A model uncertainty for the response calculation has been applied in terms of a normally distributed uncertainty factor with a mean value of 1.0 and a coefficient of variation of 0.1. This uncertainty is assumed to cover the uncertainty in the linear results itself, including the effect of uncertainty in the wave spectrum. Reference is made to DNV (1992). 33 Furthermore, to use a linear analysis for the bending moment response in extreme weather is a simplification that is difficult to justify. ISSC(2000a) discusses direct calculation procedures for extreme wave loads on ship hull girders. It is stated that: (j) (k) (l) No robust and exact non-linear hydrodynamic wave load procedure exists today, and almost all ship motion and wave load codes rely on potential theory. The validity of linear potential theory is well documented and it is widely used for both ships and offshore structures, and is accurate up to fairly large wave slopes. The difficulties arise in extreme seas. 34 The problems are inherently non-linear dealing with large-amplitude non-linear wave fields and the variable geometry of the ship s hull as it comes in and out of the water as well as with, slamming, wave breaking and green water on deck. Results concerning comparative calculations using different simplified non-linear analyses methods are discussed for a test container ship (Ref: S175). For the present work, considering tankers over 150m and zero speed, there appears not to be any directly applicable results in terms of nonlinear correction factors. 35 Other sources have been investigated in order to find a measure for non-linear correction on the linear results. Results show a large scatter. In ISSC (1991) a bias factor of 1.15 is suggested for sagging (0.85 for hogging) and with a rather low standard deviation of Hovem and Aasbø (1999) show a comparison of results using a non-linear strip theory program (NV 1418) and a linear 3D sink-source theory program (WADAM). Results are calculated for a 125dwt tanker, dwt VLCC and a dwt Bulk Carrier. Nonlinear correction factors near unity are obtained for the tankers; i.e. between 0.97 and 1.05, and between 0.91 and 0.96 for the Bulk carrier. The design wave amplitude has been varied (9.8m-11.8m), and the lowest corrections factors are obtained for the higher wave amplitudes. Also the DNV (1992) has been reviewed, where a general bias of 0.92 is given.

13 Page Pastoor et al (2002) provides some results showing that the non-linear effect first increases with increasing severity of the weather, but may then decrease again when the severity further increases beyond some limit. Numerical results applicable for the tankers studied in the present project are not available, but the tendency of first increasing then decreasing is interesting. 37 From the available data it is difficult to conclude on a correct model uncertainty to account for non-linear effects. A wide scatter in the results appears. An uncertainty factor with a mean value of 1.0 and a coefficient of variation of 0.1 has been applied in the present analyses, applied to the total wave bending moment. Sensitivity analyses have been performed to show the effect of different assumptions, but not included in herein. 6.3 Still water moment 38 In general for tankers ballast conditions represent hogging and loaded conditions represent sagging. Also, the wave induced moment has been found to be greater in loaded than in ballast condition. For this reason the chance of sagging failure in ballast condition has been ignored. 39 The calibration has been performed using the assumptions as outlined below. (m) (n) (o) Identify all seagoing loaded conditions in the loading manual. Emergency ballast and segregated/transitory/group load conditions (that often gives hogging) are omitted. Calculate the mean value and the standard deviation based on numbers for the identified conditions, assuming equal weight for each condition. This has been done for the five test vessels together with three additional vessels, and the results are included in Table A.3. Table A.3: Still water statistic for the 5 test vessels and additional 3 vessels. Moments in MNm Mean Std.dev. Max Mean/max Std.dev/Max. (Max-mean)/ Std.dev SUEZMAX % 9 % 1.64 PRODUCT % 25 % 1.63 VLCC % 18 % 1.77 VLCC % 20 % 2.07 AFRAMAX % 25 % 1.66 AFRAMAX (2) % 22 % 1.30 PRODUCT (2) % 31 % 1.45 PRODUCT (3) % 35 % 1.46 Average 63 % 23 % 1.62

14 Page It is seen that the mean value is between 49% and 85% of the maximum value of the conditions identified. When the mean value is relatively high, the standard deviation is relatively small. There is a tendency for the shorter vessels to have a relatively lower mean and a higher standard deviation than the longer vessels. 41 On average, the maximum value is 1.6 standard deviations above the mean value. A conventional definition of a characteristic value is to use a consistent fractile of its associated distribution. For example the characteristic yield stress is usually defined as the 5% fractile of its distribution which, corresponds to 1.64 standard deviations below the mean value, if a normal distribution is used. 42 The model that is used in the present work assumes that the still water moment is normally distributed with a mean value of 0.7 times the maximum value in the loading manual, and with a standard deviation of 0.2 times the maximum value. This distribution has been applied in the analyses of the 5 test vessels. No upper threshold to the distribution has been implemented. In other words, there is a chance that the still water moment may attain a value that exceeds the maximum value in the loading manual, although the probability of this is small; i.e. 7%. 43 A model uncertainty factor on the still water moment has also been applied in terms of a normally distributed variable with a mean value of 1.0 and a coefficient of variation of Combination of wave and still water moment 44 The still-water bending moment will be added to the wave moment by linear superposition. Two different combinations, following Turkstra s combination rule, Tursktra (1970), are evaluated: (p) (q) An annual extreme value of the wave induced moment with a random value of the still water moment. An annual extreme value of the still water moment together with an extreme value of the wave moment during one voyage. 45 Depending on the magnitude, the variability and the duration of a voyage, either of these combinations may be governing. However, for the present tanker study, it appears that the extreme wave load is dominating, and combination 1 is governing for the probability of failure. This has also been found in the present study and in other studies (Bach-Gansmo and Lotsberg, 1989; Kaminski, 1997). 6.5 Moment capacity 46 The physical model applied in the capacity calculation is similar to the model used for the computation of the characteristic capacity as defined in paragraph 0; i.e. the HULS-1 model. The uncertainties accounted for are the yield strength, which is modelled by a lognormal distribution, and a model uncertainty to reflect uncertainty in the calculation model. Geometrical dimensions are modelled as deterministic values. 47 The results are conditional on the applied net thicknesses, hence, time variant corrosion is not considered. Initial imperfections are not modelled as such, but accounted for in the applied model uncertainty. The stiffness is modelled as a deterministic value since the associated uncertainty is rather small and has negligible influence on the results.

15 Page The distribution of the yield strength is derived from its characteristic value defined as the lower 5% fractile. A coefficient of variation of 0.08 is used for normal grade steel (used for the Product tanker), and 0.06 has been applied for high strength steel used in the remaining cases. These values are taken from the DNV (1992) and Skjong et al (1995), and are commonly applied. 49 In ISSC (2000b) comparable coefficients of variation of 0.09 and 0.07 are given respectively. The distribution parameters are included in Table A.4. The spatial variation of the material strength has not been considered. There is likely to be some averaging effects since one would expect some degree of independency in the steel properties for different plates and stiffeners around the hull section. For this reason, the applied distribution model is likely to be somewhat pessimistic. 50 The magnitude of the model uncertainty is chosen with some basis in the obtained nonlinear finite element analysis results for the Suezmax, Törnqvist (2004). The HULS-1 prediction model provides comparable results to the non-linear analysis when rather pessimistic imperfections are applied. Somewhat higher capacity is obtained when a more realistic imperfection model is applied ( hungry horse ). These results are summarized in Table A The numbers indicated a model uncertainty factor with a bias higher than 1.0. A value of 1.05 with a standard deviation of 0.1 has been applied, assumed to reflect the difference between the HULS-1 model and the non-linear result as well as the difference between the nonlinear result and real life. 52 Additional non-linear analyses results for other vessels are demanded in order to gain further confidence in the simplified approach.

16 Page 14 Table A.4: Comparison of non-linear ABAQUS analyses results and HULS-1 calculations (GNm), from Törnqvist (2004) 50% t " as built" corr Initial Change - Change - Change - 3 relative to scantlings, 1 yield 2 yield small scantlings "as built" gross stress 235 stress 355 stiffener Fixed deck area = Initial scantlings, gross Huls ABAQUS: Imp. model Imp. model Imp. model Imp. model Imp. model Imp. model Imp. model Abaqus/Huls-1 Imp. model Imp. model Imp. model Imp. model Imp. model Imp. model Imp. model Note ABAQUS imperfection model. 1. deck and ship side - harmonic and regular up-down (eigenmode close), - tolerance level 2. deck only - harmonic and regular up-down (eigenmode close)- tolerance level 3. deck plate hungry horse plate short waved harmonic- tolerance level 4. deck and ship side - Global single span, tolerance level 5. perfect 6. Hungry Horse - 50% of tolerance level 7. Hungry Horse - 200% of tolerance level 6.6 Summary of the uncertainties 53 Summary of the applied uncertainties is included in Table A.5.

17 Page 15 Table A.5: Summary of applied uncertainties Variable name Distribution Parameters Response variables: Significant wave height Weibull Ref 0 Zero-crossing wave period Log-normal Function of H s, ref. 0 Short term extreme wave moment Gumbel Function of sea state Annual extreme wave moment Numerically Ref. 0 computed Still water moment Normal Mean=0.7 times max of manual Std.dev=0.2 times max of manual Capacity variables: Yield strength (normal grade) Lognormal Mean=269MPa, CoV=0.08, Low limit=0 Yield strength (High strength) Lognormal Mean=348MPa, CoV=0.06, Low limit=0 Model uncertainties: Wave moment, unc. in linear Normal Mean=1.0, Std.dev.=0.1 result Wave moment, nonlinear effects Normal Mean=1.0, Std.dev.=0.1 (+ sensitivity) Still water moment Normal Mean=1.0, Std.dev.=0.1 Capacity calculation Normal Mean=1.05, Std.dev.=0.1 7 CALIBRATION RESULTS 54 First, the annual probability of failure was calculated for the initial design. Analyses using gross and net scantlings with both (t=t off -0.5t corr ) and (t=t off -1.0t corr ) applied to all structural members were performed. 55 The results are illustrated in Figure A.5. The following notes are made: (a) (b) The probability of failure increases by a factor near 10 going from gross to net scantling (t=t off -0.5t corr ), and another factor near 10 to net scantlings with (t=t off -1.0t corr ). The highest consequence of corrosion on the reliability is seen in the PRODUCT tanker. This is reasonable since it has the lowest plate thickness, and consequently the highest relative reduction in steel area due to t corr deduction. Considering net scantling (t=t off -0.5t corr ) for which the rule applies, the lowest probability of failure is obtained (2x10-4 ) for the Product tanker, and the highest (1.5x10-3 ) for Suezmax. 56 Please note that for overall hull girder strength the degradation of properties associated with 100% t corr is not permitted; repair is required when the overall hull girder strength degradation of properties reaches those associated with 50% t corr.

18 Page 16 Figure A.5: Annual probability of failure (-log(pf)), initial scantling, gross and net 5.0 -log(pf) SUEZMAX PRODUCT VLCC 1 VLCC 2 AFRAMAX 1.0 Gross Gross - 50% tcorr Structural condition Gross - 100% tcorr 57 Thereafter, the probability of failure was calculated using net scantling (t=t off -0.5t corr ) with varying design modification factors. These results are illustrated in Figure A.6 Figure A.6: Probability of failure as a function of design modification factor 5.0 -log(pf) SUEZMAX PRODUCT VLCC 1 VLCC 2 AFRAMAX Design Modification Factor Note: The Design Modification Factor (DMF) represents the ratio between actual crosssectional area of the deck and the initial cross-sectional area using gross values. The procedure for deck modification is described in Design points values versus characteristic values 58 The design point values come from the SRA when a First Order or Second Order Reliability Method is used (FORM or SORM), and represent the most likely outcome of variables at failure. Corresponding to the design point values for the still water, wave moment and the moment capacity, partial safety factors are computed for each individual case in the test set, according to the illustration given in Figure A.1. This has been done for different values of the design modification factor, and the results are illustrated in Figure A.7 as function of the annual probability of failure. 59 The results provided in the figure indicate reasonable partial safety factors; however, the procedure illustrated in Figure A.2 will be used for the final calibration.

19 Page Comments to the Figure A.7: (a) (b) (c) The partial safety factors for the still water bending moment in Figure A.7 appear to be less than unity, and show some scatter between the various cases. The physical interpretation of this is that the characteristic value (maximum in the loading manual but not less than 90% of the JTP minimum permissible) is higher than the value that is most likely to occur at failure. A slight increase with increasing target level is seen. The Suezmax and the Aframax cases show the lowest partial safety factors, which can be explained by the relatively high value of the minimum permissible still water bending moment compared to the values in the loading manual for these cases, see Table A.2. To conform to normal practice and an intuitive understanding of partial safety factors, it may be wise to set this partial safety factor to unity, although the results indicate a lower value. The partial safety factors for the capacity are near 1.1 at target probability levels between 10-3 and 10-4 and the scatter between the cases is small. This result indicates that the randomness in the capacity is less than in the wave moment; i.e. the lower tail of the capacity distribution has a smaller area than the upper tail of the wave load distribution. The partial safety factors for the wave moment show some scatter between the cases, and are increasing more than the other safety factors with increasing safety level. Figure A.7: Partial safety factors as a function of target probability of failure, based on single test case calibration as outlined in Figure A.1 Partial safety factor WAVE CAPACITY STILL WATER log(pf) SUEZMAX gamma_sw SUEZMAX gamma_wv SUEZMAX gamma_r PRODUCT gamma_sw PRODUCT gamma_wv PRODUCT gamma_r VLCC 1 gamma_sw VLCC 1 gamma_wv VLCC 1 gamma_r VLCC 2 gamma_sw VLCC 2 gamma_wv VLCC 2 gamma_r AFRAMAX gamma_sw AFRAMAX gamma_wv AFRAMAX gamma_r 7.2 Partial safety factors 61 In this section partial safety factors obtained following the procedure as outlined in Figure A.2 are reported. In this optimization the deviation in annual failure probability from target is computed. This deviation is squared, and summed over the test set according to the objective function given in the equation below. This sum is minimized in the calibration by changing the safety factors.

20 Page This type of objective function implies a very high penalty on under-design. The N value may also serve as a weight factor if one wishes to assign different weight to the various cases in the test set. Here the same weight is assumed for each of the 5 vessels in the test set. N r r ( P, γ ) = γ T Where: ( PT Pi ( )) i= 1 2 P r γ T P i N is the target annual probability of failure is the vector of partial safety factors subjected to calibration is the annual probability of failure for case i associated with the calibrated partial safety factors the number of cases included in the calibration analysis 63 The partial safety factors following the single test case procedure in Figure A.1 are included in Figure A.7 for several target safety levels. Here the safety factor for the still water moment is set to 1.0, to conform to normal practice. A value from 1.1 or 1.15 has then been set for the capacity, based on the results provided in Figure A.7. Finally, the safety factor for the wave moment is optimized using the penalty function as given above. The results are included in Table A.6. Two alternative sets of partial safety factors are given at the target safety level of Table A.6: Calibrated partial safety factors Target P f γ SW γ WV γ R x10-4 (i) x10-4 (ii) Figure A.8: Probability of failure obtained after calibration log(pf) SUEZMAX PRODUCT VLCC 1 VLCC 2 AFRAMAX Initital design Pf,target=0.001 Pf,target= (i) Pf,target= (ii)

21 Page Figure A.8 shows the resulting probability of failure for the various cases in the test set when the rule criteria is applied using the partial safety factors as reported in Table A.6. The reliability of the initial design (initial scantlings 50% tcorr) is included for reference. 7.3 Consequence evaluations 65 The consequences of the proposed hull girder ultimate strength requirement have been evaluated against the initial scantlings. The changes have been evaluated in terms of: (a) (b) Required ultimate moment capacity by the hull girder ultimate strength criterion, Figure A.9. Required change in the deck cross-sectional area to achieve the required ultimate moment capacity in a), Figure A Figure A.9 shows the required M U in percentage of M U for initial scantling corresponding to the target safety level of The required M U is evaluated for the: (a) (b) design point (most likely value) from the reliability analysis at target probability of failure (first column in group) calibrated rule requirement (second column in group). 67 The safety factors applied in the rule check are taken from Table A The required M U, at target level 10-3, for the Suezmax and VLCC 2 cases is equal to or higher than M U corresponding to initial scantlings, whereas the M U for initial scantlings is more than sufficient for the remaining cases. The deviation between the first column (design point at target P f ) and the second column indicates how well the rule performs relative to the target safety level. E.g., it may be seen that the two VLCC cases and the Aframax are slightly over-designed, which correspond to the results in Figure A.8 where these cases show lower probability of failure than the annual target P f = Figure A.10 shows comparable results as those in Figure A.9. Here the required value of the DMF is given rather than the required change in M U. In the cases where DMF is less or equal to unity, the hull girder ULS check is not governing; i.e. the initial scantlings meet the requirement. 70 In the cases where DMF is greater than unity, a reinforcement of the deck relative to the initial design is required to meet the criteria. The first column for each case indicates DMF at the target reliability level based on the reliability analysis results. The second column shows the DMF obtained when the rule check using the calibrated partial safety factors is performed. 71 If the rule column is greater than the design point, the rule provides a conservative design, which is most significant for the two VLCC cases (as also mentioned above when comparing M U ). 72 By comparing Figure A.9 and Figure A.10 it may be seen that the required change in percentage of M U can be obtained by changing the deck cross-sectional area with almost the same percentage.

22 Page 20 Figure A.9: Required M U at target P f and by rule (P f,target =10-3 ). Relative to M U for initial scantling. 120 % 115 % Mu_rule/Mu_target _scantling 110 % 105 % 100 % 95 % 90 % 85 % 80 % SUEZMAX PRODUCT Mu_dpt/Mu_target scantling Mu_c/Mu_target scantling Target scantling VLCC 1 VLCC 2 AFRAMAX Figure A.10 Required DMF at target P f and by rule (P f,target =10-3 ). Relative to DMF for initial scantling DMF at target Pf DMF after calibration 1.10 Target scantling DMF SUEZMAX PRODUCT VLCC 1 VLCC 2 AFRAMAX 7.4 Target reliability level 73 In the previous section, partial safety factors are calibrated for different target probabilities. A target level based on existing structures should be between 10-3 and A target level based on tabulated values, such as those used in DNV Classification Note 30.6 or Denmark et al (2004) indicates a stricter target level. One should, however, keep in mind that the calculated probability of failure is a nominal value which is sensitive to the reliability model and uncertainties applied. It should also be kept in mind that the probability of failure using net thickness is near 10 times higher than the gross result. 75 North Atlantic environmental conditions are more severe than most other environmental conditions, and any benefit of weather routing has not been considered. 76 A review of historical data may add some value to the discussion around target, but this has not yet been performed.

23 Page Cost Benefit and Cost Effectiveness Evaluation 77 The selection of target safety level may be more rationally selected based on cost benefit analysis or presentation of cost effectiveness criteria (Skjong, 2002). This would make the analysis more consistent with the FSA approach (IMO; 2002). The idea is then to identify the optimum safety level considering the cost of marginally increasing the net scantling and the risk reduction effect this would have in term of improved safety, reduced risk of environmental damage and reduced risk of property loss. The question is simply how much money should be invested into the initial design compared with the chance of failure and its associated costs. The cost effectiveness analysis takes into consideration the safety of life, and the net cost of averting a fatality (NCAF) has been calculated. Hull girder collapse is the most critical failure mode for a tanker. It is assumed to lead to a total loss of the ship, and the chance of loss of crew must be taken into consideration as well as the risk to the environment. 78 The historical data for loss of tankers due to hull girder collapse in sagging in severe weather are scarce. In the cost benefit and cost effectiveness analysis the calculated nominal probability of failure has been applied with a frequency interpretation. This should be done with care. 79 The calculated annual probability of failure is a higher value than what has been observed in reality. This can have several reasons that can be associated with the modelling assumptions and data: (r) (s) (t) The basis for the calculation is North Atlantic environmental condition which is more severe than a world wide model. No tanker operates in the North Atlantic environment for her entire service life. If a World Wide environment was used the annual probability of failure is reduced to 7% of the annual probability corresponding to the North Atlantic Environment. Ships generally avoid the most severe weather by weather routing. Often the steel strength is significantly higher than the specification. 80 It should therefore be noted that the cost benefit and cost effectiveness analysis are conditional on the assumptions and distribution models applied for the computation of the annual probability of failure, and can only be interpreted with this in mind. The advantage with the approach is to link the resulting scantling requirements to the safety targets. 81 An overview of costing assumptions are as follows: (a) The new-building price of the ship and the value reduction as the ship ages is taken into account in order to have an estimate of the costs related to loss of the ship. This is linked to the probability of failure; which increases with increasing ship age. (b) Failure is also assumed to imply loss of the 1/5 of the cargo, at it is assumed that there is a 10% chance of polluting the shore. According to Sørgård et al (1999), the likelihood of polluting the shores, in cases of structural failure is 9.23%. As this failure mode is likely to occur in extreme weather condition, and far from shorelines the use of 10% is judged conservative. The failure mode subjected to analysis is failure in sagging condition, which corresponds to loaded condition of

24 Page 22 the ship. The Cost of Averting a Ton of oil Spilled (CATS), is taken from Skjong et al (2004), CATS = $60,000. This cost is higher than the value of the lost cargo and the cost of cleanup. (c) (d) (e) (f) Opportunity cost (delay related to temporary replacement until a new ship is available) has not been considered in the present analysis. The lost opportunity for one operator represents a new opportunity for another operator and can therefore be excluded if we consider costs to the society at large. These costs are in any case low compared with the other costs. Costs of salvage, search and rescue have been ignored. Cost of strengthening the structure against hull girder collapse. This cost is modelled as the difference compared to the cost of the initial design, and is based on unit weight steelwork prices considering the ship deck over the extension of 0.4 L amidships. Depreciation of future costs is at 5% annually, which is considered comparable to a risk free rate of return as suggested in document MSC 72/ The assumed new price of a ship is taken from Drewry (2000), and has been adjusted to 2005 prices. The replacement cost of the ship is assumed to follow a linear reduction from new to scrapping value over the lifetime of 25 years. The scrapping value has been estimated according to Stopford (1997), where a value of $200 per light weight ton is used. 83 With the assumptions described in Chapter 0 the change in steel weight has been calculated, assuming that the modification is implemented over 0.4L amidships. A unit price for steelwork has been assumed; i.e. $2.5/kg. This value varies significantly between different locations; e.g. values between $1/kg (China) and $4/kg (EuroMed) are listed by Drewry (2004). 84 Further effort for optimizing the design has not been performed, and it may be possible that increased strength can be obtained using less steel than the above assumptions give. With this in mind, the costs related to strengthening the design are likely to be to the conservative side. Some conservatism can also be associated to the fact that the marginal additional cost related to steelwork is likely to be less than the overall unit cost, since the structure is to be welded anyway. The relationship between costs and safety level is illustrated in Figure A.11. The lines cross zero at the safety level corresponding to initial design. The slope of the curve indicates costs per unit safety, and is seen to be lower for a small ship (Product) than for a large ship (VLCC).