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SUB-COMMITTEE ON STABILITY AND LOAD LINES AND ON FISHING VESSELS SAFETY 55th session Agenda item 7

SLF 55/INF.7

14 December 2012 ENGLISH ONLY

REVISION OF THE DAMAGE STABILITY REGULATIONS

FOR RO-RO PASSENGER SHIPS

The GOAL based Damage Stability project (GOALDS) – Derivation of updated probability distributions of collision and grounding

damage characteristics for passenger ships

Submitted by Denmark and the United Kingdom

SUMMARY

Executive summary: This document contains a report on collision and grounding damage statistics of the GOAL based Damage Stability project (GOALDS)

Strategic direction: 5.1

High-level action: 5.1.1

Planned output: 5.1.1.5

Action to be taken: Paragraph 27

Related documents: SLF 45/3/3; SLF 46/INF.6; SLF 52/11/1; MSC 84/22/12; SLF 52/WP.3 and MSC 91/7/2

Introduction 1 This document provides information on the results of the "GOAL based Damage Stability" project (GOALDS). 2 The study has been partially funded by the European Commission under the 7th research Framework Programme Theme "Sustainable Surface Transport". 3 In the framework of the GOALDS project, the database created in the HARDER project has been enhanced by collecting additional collision and grounding accident data and new statistical analyses have been carried out. The casualty data were mainly derived from classification societies (DNV, GL and LR) damage files covering the condition of water ingress as a consequence of the casualty. The casualty data collected in GOALDS have made it possible to supplement the HARDER database of collision and grounding damages significantly.

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Background 4 MSC 84 agreed to include a new item on "Damage stability regulations for ro-ro passenger ships" in the Sub-Committee's work programme. 5 The Sub-Committee, at its fifty-second session, discussed in detail the impact of the SOLAS 2009 amendments on the damage stability requirements for ro-ro passenger ships after the presentation of three European Union funded research projects (GOALDS, FLOODSTAND and EMSA2), and whether in this regard any amendment to SOLAS should be considered. 6 The Sub-Committee noted the general view of the SDS Working Group that more research and the evaluation of further studies were important and necessary before considering any possible additional measures. Following a request by the Sub-Committee, MSC 89 agreed to extend the target completion year for this item to 2013. 7 The Sub-Committee at its fifty-third session, instructed the SDS Correspondence Group to further consider the impact of the SOLAS 2009 amendments on ro-ro passenger ships, as compared to the SOLAS 1990 regulations in association with the Stockholm Agreement, taking into account document SLF 52/WP.3, and any further relevant research results as they become available. Main contents of the GOALDS project 8 The GOALDS research project contained the following main sub-projects:

.1 extending the formulation introduced by resolution MSC.216(82) for the assessment of the probability of survival of passenger ships in damaged condition, based on the results of extensive numerical simulations;

.2 performing comprehensive model tests to investigate the process of ship

stability deterioration in damaged condition and to provide a basis for the validation of the numerical simulation results;

.3 compiling damage statistics and probability functions for the damage

location, length, breadth and penetration in case of a collision/grounding accident, based on a thorough review of available information regarding these accidents over the past 60 years worldwide;

.4 formulating a new probabilistic damage stability concept for passenger

ships, incorporating collision and grounding damages, along with an alternative method for the calculation of ship survival probability;

.5 establishing new risk-based damage stability requirements for passenger

vessels based on a cost-benefit analysis to establish the highest level for the required subdivision index;

.6 to demonstrate that a commercially viable passenger vessel could be built

to a significantly higher Attained Index than set forth by current requirements; and

.7 investigating the impact of the new formulation for the probabilistic damage

stability evaluation of passenger ships on the design and operational characteristics of a typical set of ROPAX and cruise vessel designs (case studies).

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Main findings and achievements of the GOALDS project Casualty data collection 9 Part of the project was to collect new casualty data for collision and groundings to combine the data with the data collected during the European Union research project HARDER. Within the HARDER project data from IMO damage cards, damage repair reports from classification societies and damage reports from the former GDR register have been considered. The HARDER database has been rechecked and, where available, additional data have been added. 10 New casualty data (after 2000) have been identified by searching Lloyd's Register Fairplay casualty database (LRF). LRF cases that were identified as serious have been selected and sorted with respect to the classing of involved ships in an IACS society. Cases identified to be in relation to consortium members (DNV, GL and LR) have been processed. 11 Within the GOALDS project 348 cases of collisions, groundings and contacts have been identified. Together with the redefined HARDER dataset, a number of 1527 cases formed a casualty database used for statistical analysis in the GOALDS project (table 1).

Table 1: Contribution of the two projects to the casualty database

Collision Grounding Contact HARDER 832 312 35 1179 GOALDS 184 160 4 348 1016 472 39 1527

Collision casualty data analysis 12 The new casualty data collected during the GOALDS project were submitted from the classification societies that are members of the consortium and some additional data were derived from internet search. To check whether damage dimensions vary with intervals of the casualty date or building year, a sensitivity analysis was conducted. However, it became apparent that the data sample size was very small especially for passenger ships, when the sample period was limited to the last 20 years. Therefore, it was decided to use the complete data, independently of ship type and accident period, in evaluating the damage dimensions of passenger ships. 13 A sensitivity analysis regarding the change of rules that have influenced the construction of ships has been carried out with no significant findings. Neither classification rules nor SOLAS amendments were identified to have changed the construction significantly in this short time period. Such changes can be identified in damage dimensions within decades only, analogous to the increasing number of newbuildings designed according to the new rules.

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Figure 1 – Comparison of mean value of damage length as a function of the ship length between the GOALDS database, HARDER data and SOLAS distribution

14 Figure 1 shows a comparison of the average damage length as a function of the ship length between current SOLAS 2009 assumptions, HARDER data and data of the present GOALDS database (HARDER+GOALDS updates). 15 It can be seen that now the average damage length as obtained from the enhanced GOALDS database is consistently smaller and close to the SOLAS assumption. However, from the statistical point of view, observed differences are within confidence intervals (dashed lines) for the estimated mean which, particularly in the region of long ships, are rather wide (lack of sufficient sample data). Grounding casualty data analysis 16 During the evaluation of the grounding casualties, some groundings had multiple damage penetrations recorded. Several cases were identified with up to 16 penetrations of the bottom shell plating. As many of those damages are small but widely spread over the ship's bottom it was decided to replace the multiple damages of each case by one equivalent damage. 17 An equivalent damage covers the length of the damaged area, its area is equal to the sum of all individual damages and has a mean width (considering the mean width of all observed case damage widths). Proceeding like this ensures that the small damage lengths will not be wrongly represented in the damage statistics.

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Figure 2 – Comparison between vertical damage penetration and minimum SOLAS requirements for double bottom height

18 The available grounding data were analysed to determine whether the observed damage penetrations reported in the database could have pierced the inner bottom if it is designed to the minimum SOLAS requirements. 19 Figure 2 shows a scatter plot of measured damage penetration as a function of the ship breadth and the minimum double bottom height requirements as specified in SOLAS regulation II-1/9 in general and for longer lower holds RoPax designs. Table 2 - Probability of penetration exceeding SOLAS minimum double bottom height

20 The analysis leading to the estimations in table 2 used the whole set of data. However, figure 2 appears to suggest that the actual probability of exceeding the SOLAS minimum double bottom height could be dependent on the ship size, with higher probability for smaller ships and lower probability for larger ships. General comments on quality of data 21 A general note concerning the quality of the available accidents database is absolutely necessary.

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22 Despite all the efforts spent on removing duplications, wrong cases, and so on, the quality of the data cannot be said to be high, but rather average to low. The reasons are to be found in the fact that the reporting and storing process of accident data is uncertain and confusing, often leading to incomplete data, prone to confusion, mistakes and contradiction. In particular, the lack of sufficient information for each damage case often required interpretation based on subjective judgment. Filtering of data on the basis of clear mathematical relationships was often difficult, again, due to the fact that not all accident records contained all the necessary data. It was also impossible to keep only a set of fully consistent data, as the sample would have become extremely small otherwise. It is, therefore, suggested that more efforts should be spent in the future in improving the recording and processing of accident data. If not, it is expected that similar significant difficulties will be experienced in future revisions and updating of damage statistics for design and/or regulatory purposes. However, it should be noted that the resulting GOALDS database is the most comprehensive database yet in existence. Comments on quality of collision data 23 The data added in GOALDS do not affect extreme values, which remain with those observed in the HARDER database. Consequently, the agreement of high percentile levels with SOLAS assumptions has not significantly changed. The problem of large uncertainty in the region of large ships has not (and could not have) been resolved due to the lack of data (rare events). 24 On the basis of the performed comparisons, and in view of the analysis of the data of the updated database in GOALDS, it can be said that the present SOLAS distributions for the damage length due to ship-ship collision can still be considered a reasonable tool for engineering/regulatory application. This tool seems to embed a certain level of conservativeness. 25 The non-negligible level of uncertainty in the statistical estimators due to the limited number of data, and the average quality of the database suggest that any modification of present SOLAS assumptions concerning the damage length is premature and not strongly supportable from the statistical point of view. Specific indications for passenger vessels cannot be obtained due to the limited number of available data. Comments on quality of grounding data 26 On the basis of the findings from the analyses carried out in GOALDS it is possible to provide some recommendations for the way forward. There are two ways for implementing the results (with further refinements):

.1 Probabilistic approach – A fully probabilistic model for grounding damage characteristics, conceptually similar to that presently in SOLAS 2009 for side damages. Such an approach has been formulated in GOALDS conceptually, but presently it cannot be implemented to ship-like forms. Thus the fully probabilistic approach to bottom damages for regulatory purposes is at this stage not possible.

.2 Deterministic approach – A deterministic approach modifying assumptions

of regulation II-1/9. This "global" approach could be more robust than the fully probabilistic approach and less affected by the problems identified in the analyses. Probabilities of exceeding the SOLAS bottom damage characteristics have been found to be, overall, quite in line with those estimated at the time of development of regulation II-1/9. Therefore, the

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present analyses would not call for revisions of regulation II-1/9, unless different acceptable levels of probabilities of exceedance are set. There are some indications that the present regulation II-1/9 requirements are more conservative for large ships and less conservative for small ships, and this aspect deserves additional attention. However, the statistical uncertainty, especially for large ships, is quite high due to the limited number of data.

Action requested of the Sub-Committee 27 The Sub-Committee is invited to note the research carried out by the GOALDS project and included as annexes 1 and 2 to this document, and to consider its findings within its work on the item on "Revision of damage stability regulations for passenger ships".

***

GOALDS-D-3.1-GL- Collision Damage Characteristics – rev1 Page 1 of 90

Grant Agreement No: 233876 Project Acronym: GOALDS Project Title: GOAL based Damage Stability

Deliverable D 3.1

Report detailing derivation of updated probability distributions of collision

damage characteristics for passenger ships

Document Id. GOALDS-D-3.1-GL- Collision Damage Characteristics – rev1

Due date of Deliverable: 2010-05-31 Actual Submission Date: 2011-09-15 Gabriele Bulian (DINMA) Christian Mains (GL) -document author/s- Alberto Francescutto (DINMA)

final

-document approved by- -revision type- 2011-09-15

CO 1

-date of last update- -distribution level-

1 dissemination level PU Public PP Restricted to Program Participants (including Commission Services) RE Restricted to a group specified by the Consortium (including Commission Services) CO Confidential, only for members of the consortium (including Commission Services)

ANNEX 1 SLF 55/INF.7

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Disclaimer

The information contained in this report is subject to change without notice and should not be construed as a commitment by any members of the GOALDS Consortium or the authors. In the event of any software or algorithms being described in this report, the GOALDS Consortium assumes no responsibility for the use or inability to use any of its software or algorithms. The information is provided without any warranty of any kind and the GOALDS Consortium expressly disclaims all implied warranties, including but not limited to the implied warranties of merchantability and fitness for a particular use. (c) COPYRIGHT 2009 The GOALDS Consortium This document may be not copied and reproduced without written permission from the GOALDS Consortium. Acknowledgement of the authors of the document shall be clearly referenced. All rights reserved.

Document History Document ID. Date Description GOALDS-PR-09/2009-to-03/2010-WP 3.1/2-Progress-Report–rev0 2010-03-24 Draft

GOALDS-PR-09/2009-to-03/2010-WP 3.1Progress-Report final–rev0 2010-09-03 Final draft

GOALDS-PR-09/2009-to-03/2010-WP 3.1Progress-Report final–rev1 2010-10-08 Final

GOALDS-D-3.1-GL- Collision Damage Characteristics – rev1 2011-09-15 final

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Document Control Sheet Title: Collision Damage Characteristics Abstract In the framework of GOALDS "Task 3.1 - Collision Damage Characteristics" collision accidents data have been collected and statistically analysed, critically considering the strength and weaknesses of this approach. The casualty data was mainly derived from classification societies damage files under the condition of water ingress as a consequence of the casualty. The casualty data collected in GOALDS allowed to increase the database of HARDER collision data by about 29% compared to the original HARDER database. For the statistical analysis ships subject to SOLAS have been filtered. Furthermore a criterion to identify struck vessels has been used similar to the HARDER project to achieve comparable results. In general, the statistical analysis verifies the HARDER data and the probabilistic formulae stipulated in the SOLAS 2009, and the outcomes from the new analysis do not provide strong justifications for changing present SOLAS2009 regulations concerning side damages as a consequence of data added in GOALDS. On the basis of the performed comparisons, and in view of the analysis of the data of the updated database in GOALDS, it can be said that, although with a series of reported remarks, present SOLAS distributions for the damage length due to ship-ship collision can still be considered a reasonable tool for engineering / regulatory application. This tool seems to embed a certain level of conservativeness. The not negligible level of uncertainty in the statistical estimators due to the limited number of data, and the average quality of the database suggest that any modification of present SOLAS assumption concerning the damage length can be considered premature and not strongly supportable from the statistical point of view. Specific indications for passenger vessels cannot be obtained due to the limited number of available data.

Deliverable D 3.1


Summary Report: Introduction In accordance with the GOALDS project description, the focus of Task 3.1 was on collision damage characteristics, work that started but was never completed in project HARDER. The expected main goal of Task 3.1 was the statistical description of collision damage characteristics in accordance with collected data, with particular attention, but not limited to, the case of passenger vessels. The collected data have been carefully scrutinized in order to remove, as far as feasible, double entries, mistyped data, etc. Such checking has been carried out partially manually and partially automatically. A statistical analysis has been carried out using the "clean" database addressing different aspects of the collision problem. In particular, the statistical analysis was aimed at: a) Describing collision damage position and dimensions b) Checking the SOLAS 2009 probabilistic formulae c) Checking the applicability on passenger ships In carrying out the analysis of damage dimensions and position, particular attention has been given to the determination of specific information for passenger vessels. Due to the lack of specific data for passenger vessels a general damage analysis has been carried out. The comparison with the actual SOLAS and HARDER formulations has shown good correspondence. State of the Art The SOLAS II-1 damage stability requirements guarantee an equivalent level of safety for different kind of ships in case of collisions. The newly collected casualty data and its analysis has been used to verifying the probabilistic approach, especially damage location and length. Value added to GOALDS This task delivers one of the main inputs to the project. The statistical analysis of these collision data and its further interpretations will direct the project’s recommendation to regulatory institutions and will provide input for risk modelling, experimental tests, etc. Achievements The major achievements from Task 3.1 are detailed in the present deliverable and associated annexes. However, they can be very briefly summarised as follows: 1) Creation of a reference database for collision damage characteristics. This database can be used for further and more refined statistical analyses. 2) Statistical analysis of collision damages has shown good correspondence with the probabilistic SOLAS formulae. 3) The analysis of the data has shown that the collected data during the GOALDS project (from classification damage files) tend to smaller damages assuming hull penetration. Input from other Deliverables None How the results relate to the overall goals of GOALDS The obtained results are fully integrated with the overall GOALDS project. The collected data clearly indicates that the sample of passenger ships is to small to develop a separate approach of probabilistic damages stability requirements as stated in the task description. However, the analysis has verified the SOLAS damage stability requirements in general.

This executive summary may be published outside the GOALDS consortium. No

Deliverable D 3.1


Work carried out by Approved by

Sigmund Rusaas, DNV Odd Olufsen, DNV Spyros Hirdaris, LR Henrik Erichsen, LR Gabriele Bulian, DINMA Alberto Francescutto, DINMA Christian Mains, GL Alberto Francescutto, DINMA

- signature on file - - signature of internal reviewer and date of acceptance -

Dracos Vassalos

- signature on file -

- signature of external reviewer and date of acceptance -

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Table of contents

1 PARTICIPATION IN PROJECT MEETINGS, WORKSHOPS AND OTHER EVENTS .................. 7 2 REPORT OF ACTIVITIES ........................................................................................................................ 7 3 MAJOR ACHIEVEMENTS WITHIN THE SCOPE OF THE PROJECT............................................ 8

3.1 DATA COLLECTION...................................................................................................................................... 8 4 COLLISION CASUALTIES..................................................................................................................... 10 5 STATISTICAL ANALYSIS COLLISION .............................................................................................. 11 6 MAJOR PROBLEMS................................................................................................................................ 13 7 RESULTS.................................................................................................................................................... 13

7.1 LONGITUDINAL POSITION OF THE CENTRE OF DAMAGE XDAM:............................................................................... 13 7.2 LONGITUDINAL DAMAGE EXTENT LX: .............................................................................................................. 13 7.3 ADDITIONAL NOTES ................................................................................................................................... 14

8 DISSEMINATION ACTIVITIES ......................................................................................................................... 14 9 OTHER COMMENTS ...................................................................................................................................... 14 REFERENCES.................................................................................................................................................... 15 LIST OF ANNEXES........................................................................................................................................... 15 ANNEX 1: OVERVIEW OF THE GOALDS DATABASE ............................................................................ 16 ANNEX 2: COLLECTING COLLISION DATA ............................................................................................ 18 ANNEX 3: EXPLORATORY DATA ANALYSIS OF SHIP-SHIP COLLISION DATA FROM THE UPDATED GOALDS DATABASE................................................................................................................... 41

SUMMARY ......................................................................................................................................................... 42 INTRODUCTION.................................................................................................................................................. 43 STATISTICAL ANALYSIS ..................................................................................................................................... 44

General information..................................................................................................................................... 44 Distribution of ship dimensions.................................................................................................................... 46 Longitudinal position of damage.................................................................................................................. 46 Longitudinal extent of damage ..................................................................................................................... 55 Damage penetration..................................................................................................................................... 67

CONCLUSIONS ................................................................................................................................................... 76 ACKNOWLEDGMENTS ........................................................................................................................................ 79 REFERENCES...................................................................................................................................................... 79 NOMENCLATURE ............................................................................................................................................... 81 APPENDIX 1: THE "POTENTIAL" DAMAGE LENGTH............................................................................................. 82

Introduction.................................................................................................................................................. 82 Derivation of the cumulative distribution of the potential damage length ................................................... 84 An example of derivation of the distribution of the potential damage length............................................... 88

APPENDIX 2: MARGINAL DISTRIBUTION OF THE DIMENSIONLESS DAMAGE PENETRATION ................................. 89

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1 Participation in project meetings, workshops and other events List of project meetings, workshops and other events with names of participants Meeting Place Dates Names of participants WP 3.1,3.2 GL-HO, Hamburg 11-12./03.2010 Nikolaos Tsakalakis, SSRC

Sigmund Rusaas, DNV Spyros Hirdaris, LR Henrik Erichsen, LR Gabriele Bulian, DINMA Rainer Hamann, GL Christian Mains, GL

2 Report of activities Part of task 3.1 and 3.2 was to collect new casualty data for collision and groundings to combine the data with the data collected during the EU research project HARDER. Within the HARDER project data from IMO damage cards, classification societies damage repair reports and damage reports from the former GDR register have been considered. The HARDER database has been rechecked and if available, additional data has been implemented. New casualty data (after 2000) has identified by searching Lloyd’s Register Fairplay casualty database (LRF). LRF cases that were identified as serious have been selected and sorted with respect to the IACS society. Cases identified for consortium members have been submitted to DNV, GL and LR. From these classification societies’ data has been delivered. An attempt was made to gain additional data from ABS, BV and RINA which results in no further data. ABS had legal restrictions. BV and RINA did not reply on the inquiry. The definition of serious is quite open according to LRF database. It seems not only depending on fatalities/injuries but will be judged by the reporting party (e.g. stranding of tanker without oil outflow is reported as serious case). Having had a close look into LRF more serious casualties as non serious were found. During the collection of data from the consortium members it turned up that not all identified serious LRF cases were showing penetrations of the hull. That is the reason for the small number of casualties implemented compared to the identified numbers. It was agreed during the kick off meeting in Athens that only cases with hull penetrations shall be collected and used for further analysis. The collected casualty data has been filtered according to the following conditions:

1) doublets have been deleted; missing main dimensions are implemented 2) all passenger ships and others with Lpp > 40.0 m (refer to GT > 500) 3) all penetrations of the hull 4) for collisions the struck criterion has been calculated to (X-l/2)/Lpp < 0.95

(aft end of the damage is located forward of the collision bulkhead) 5) for groundings multiple damages of one casualty have been substituted by one equivalent damage

Three kinds of casualties have been identified: collision, grounding and contact. The selected datasets have been statistically analysed in depth.

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3 Major achievements within the scope of the project

3.1 Data Collection Actually 1527 cases have been identified for collision, grounding and contact within the database. This data set has been used to start the statistical analysis (see item 3.2). Collision Grounding Contact HARDER 832 312 35 1179 GOALDS 184 160 4 348 database 1016 472 39 1527

The distribution of the ship types within the database involved in collision, grounding and contact are shown in figure 1. Due to the small number of identified contact cases no analysis has been performed.

GOALDS database - ship types

Bulk Carrier7%

Container11%

General Cargo47%

Passenger/RoRo7%

Tanker24%

other4%

Figure 1: Distribution of the GOALDS database ship types Compared to the world wide fleet (source: World Fleet Structure per Class (Fairplay) 2010-02-01) and to ships classed with IACS societies the general cargo ships are overrepresented within the casualty database (see figure 2). Ship type world wide fleet IACS database seagoing 02/2010 02/2010 1944 - 2009 Bulk Carrier 8182 6346 103Container 4739 4438 164General Cargo 21430 6771 728Passenger/RoRo 8095 2668 110Tanker 14037 8833 359other 55073 15458 63Total 111556 44514 1527

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World wide fleet - database4,

2

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world wide fleetIACSdatabase

Figure 2: Comparism between the world wide fleet, IACS classed fleet and the GOALDS database For 639 casualties the selected dataset contains information about the building year. Ship type Year of building seagoing 1944 - 1988 1989 - 2009 Bulk Carrier 43 29 72Container 32 132 164General Cargo 184 66 250Passenger/RoRo 50 10 60Tanker 48 28 76other 14 3 17Total 371 268 639

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Figure 3: Building date of ship types within the GOALDS database

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For 954 casualties the selected dataset contains information about the casualty date. Ship type Date of casualty seagoing 1944 - 1988 1989 - 2009 Bulk Carrier 7 74 81Container 6 164 170General Cargo 110 312 422Passenger/RoRo 21 71 92Tanker 41 101 142other 19 28 47Total 204 750 954

Date of Casualty

7 6

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Bulk Carrier

Container

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Passenger/RoRo

Tankerother

[N]

1944 - 19881989 - 2009

Figure 4: Casualty date of ship types within the GOALDS database

4 Collision casualties The new casualty data collected during the GOALDS project was submitted from the classification societies that are member of the consortium and some additional data were derived form internet search. To check whether damage dimensions vary with intervals of the casualty date or building year several charts have been plotted in the interim report. When limiting the casualty date to the last 20 years it turned out that especially for passenger ships the sample date is small. Therefore, it was decided to use the complete sample data. Investigation about change of rules that have influenced the construction of ships has been carried out with no significant findings. Neither classification rules nor SOLAS amendments were identified to have changed the construction significantly in a short time period. Such changes can be identified in damage dimensions within the decades, only, analogous to the increasing number of newbuildings designed according to the new rules. Comparing the damage dimensions of all casualty data (see figure 5 data set A) with the data of the last 20 years (see figure 5 data set B) shows a tendency to smaller dimensions for the last 20 years. Reasons for that will be discussed below.

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A (710) vs. B (199) - 1.2 Damage length

0.0

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0.000.100.200.300.400.500.600.700.800.901.00

F(x)PDF-A

PDF-B

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Figure 5: Comparism of damage length between all casualties (A) and casualties of the last 20 years (B) Checking the casualty data it turned out that the damage dimensions of collected cases within the GOALDS project are smaller than that collected during the HARDER project. Especially the damage length is significantly smaller. Having a look into the HARDER data most of the casualties were reported by the IMO damage cards. These cards have to be filled in if there was a significant damage according to the instruction. The data collected within the GOALDS project was mainly delivered by class societies searching their damage and repair files with the objective collision with hull breach. While the IMO damage cards might have for greater hull penetrations the class damage and repair files have recorded any small breach of the hull. This might be major reason for the tendency to smaller damage dimensions. Another reason worth mentioning is that the type of steel for ships’ constructions has been changed within the last 20 years from mild to high tensile steel. The greater yield stress of high tensile steel leads to more energy absorption (greater deformation) before breakage. PDF and CDF Charts of the selected casualties are shown in the annex 2.

5 Statistical analysis collision The statistical analysis has been carried out by DINMA.. Here only some major results are reported, while all the details are reported in Annex 3. Figure 6 shows a comparison of the average damage length as a function of the ship length between SOLAS assumptions, HARDER data and data of the present GOALDS database (HARDER+GOALDS updates). It can be seen that now the average damage length as obtained from the whole database is systematically smaller that the SOLAS assumption. However, from the statistical point of view, differences are still comparable with confidence intervals (dashed lines) for the estimated mean which, particularly in the region of long ships, are significantly wide.

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Figure 6: Comparison of mean value of damage length as a function of the ship length between global database, HARDER data and SOLAS distribution. It is now worth checking the behavior of the average dimensionless damage penetration Ly/B as a function of the ship breadth, and how much this quantity changes when data having penetrations bigger than half the ship breadth are neglected. Results of the sliding window analysis are shown in figure 7. It can be seen that the average dimensionless damage penetration is almost constant (or slightly increasing) up to a breadth of about 20m, after which it drops significantly. The effect of neglecting cases with Ly>B/2 is visible only up to a breadth of about 30m, with a corresponding decrease in the average dimensionless damage penetration of about 0.041 B on average, which corresponds to about 20% of the mean damage penetration presently assumed by SOLAS for "long" damages (i.e. damages with Lx/LShip ≥ 1/30). The addition of GOALDS data, due to the limited number of added cases, has a negligible effect on the behavior of the database.

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Figure 7: Behaviour of average dimensionless damage penetration as a function of the ship breadth.

6 Major problems Prior to the statistical analysis, the casualty data was filtered in the same way as during the HARDER project. This has been done with similar filter criteria because the origin ones used during the HARDER project were not available anymore. A general note concerning the quality of the available accidents database is absolutely necessary. Despite all the efforts spent to remove doublets, wrong cases, etc. it is not possible to say that the quality of the data is high, but rather average to low. The reasons are to be found in the fact that the reporting and storing process of accidents data is often partial, prone to mistypes and confusions. In particular, the lack of information for each damage case often required subjective judgment. Filtering of data on the basis of clear mathematical relationships was often difficult, again, due to the fact that not all accidents contained all the necessary data. It was also impossible to keep only a set of fully consistent data, otherwise the sample would have become extremely small. It is therefore suggested that more efforts should be spent in the future in order to improve the recording and processing of accidents data, otherwise it is expectable that not negligible difficulties will arise in possible future tentative revisions of damage statistics for design and/or regulatory purposes.

7 Results

7.1 Longitudinal position of the centre of damage Xdam: There are not significant differences between the distributions of Xdam/Lpp for ships between about 100m and 200m in length. Some differences are indicated in case of longer and shorter ships. However, differences in the mean value of Xdam/Lpp and in several percentile levels are not large. Therefore considering the same distribution of Xdam/Lpp for any ship length could be considered acceptable from the engineering point of view, especially taking into account the fact that a clear trend in the dependence of the distribution of Xdam/Lpp from Lpp cannot be observed.

7.2 Longitudinal damage extent Lx: Additional GOALDS data are, on average, associated with relatively small damages for what concerns the longitudinal damage length.

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As a consequence the percentile levels and the mean value of damage length for different ship lengths tend to be shifted towards smaller damage length when comparing the HARDER data and the updated HARDER+GOALDS database. A comparison between percentile levels obtained from the HARDER data and SOLAS distributions shows a good agreement. The agreement is worse in case of high (97.5%) and small (2.5%) percentile levels as well as in the case of large ships, but in these cases it is necessary to take into account the large uncertainty involved, which precludes any firm conclusion. In general, it seems that present SOLAS distributions are a sufficient approximation of the HARDER data. Since data added in GOALDS do not affect extreme values, which remain those observed in the HARDER database, the agreement of high percentile levels with SOLAS assumptions is not significantly changed. The problem of large uncertainty in the region of large ships has not been solved. On the basis of the performed comparisons, and in view of the analysis of the data of the updated database in GOALDS, it can be said that, although with a series of reported remarks, present SOLAS distributions for the damage length due to ship-ship collision can still be considered a reasonable tool for engineering / regulatory application. This tool seems to embed a certain level of conservativeness. The not negligible level of uncertainty in the statistical estimators due to the limited number of data, and the average quality of the database suggest that any modification of present SOLAS assumption concerning the damage length can be considered premature and not strongly supportable from the statistical point of view. Specific indications for passenger vessels cannot be obtained due to the limited number of available data.

7.3 Additional notes Finally, it is important to underline that present SOLAS regulation provides a probabilistic approach for what concerns the upper edge of the damage through the so called v-factor. However, SOLAS does not provide any probabilistic approach for the description of the position of the lower edge of damage, and a worst-case approach is presently used to deal with the lower damage edge. This matter needs further attention and the available database can help in developing a suitable distribution also for the position of the lower edge of damage.

8 Dissemination activities Dissemination during the GOALDS workshop in Glasgow form 2010-09-08 to 2010-09-09

9 Other comments None

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References 1. HARDER casualty database 2. FAIRPLAY, World Fleet Structure per Class 2010 3. GOALDS casualty database 4. IMO, "SOLAS Consolidated Edition 2009", London, 2009

List of Annexes

• Annex 1 - "Overview of the GOALDS database", Christian Mains, GL • Annex 2 - "PDF and CDF charts from the database", Christian Mains, GL • Annex 3 – “Exploratory data analysis of ship-ship collision data from the updated GOALDS

database”, Gabriele Bulian and Alberto Francescutto, DINMA

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Annex 1: Overview of the GOALDS database Christian Mains, GL The casualty data collected during the GOALDS project have been merged with the HARDER database. Whilst during the HARDER project several sources like IMO damage cards, DSRK (former GDR) damage files and classification damage files the GOALDS data were retrieved from classification damage files and some rare casualty reports. A GOALDS dataset contains 91 fields of information. Six of these fields contain information to identify the vessel which are not shown in the database version delivered to project for legal reasons. Furthermore, information about the two involved ships (collision) like main dimensions, ship type building year, operational condition before and after casualty, casualty date, - place and - category as well as dimensions and location of the damage. Additional information form reports, internet, sea court cases which have been rarely found was filed but has not been considered within the statistical analysis. The complete list of data fields with description can be found in the file GOALDS-C-3.1_3.2¬database-field-description rev1.pdf delivered to the project. During the project task 3.1 and 3.2 DINMA and GL also worked on the data quality of the database in order to avoid double consideration of casualties, unrealistic casualties in view of damage dimensions. To overcome some missing but important data like struck or striking ship a criterion was applied that was agreed among the task members. However, such procedure could not be applied for all necessary but missing data. Other missing data like main dimensions, building year which could be found in public reliable databases have been added. The most reliable data fields are: Year of building Year of building year of the building completion (delivery) (1st

ship) Lpp Lpp length between perpendiculars, [m] (1st ship)

Loa Loa length over all, [m] (1st ship)

B B breadth moulded, [m] (1st ship)

D D depth moulded, [m] (1st ship)

Year of building 2 Year of building (from 2nd ship)

year of the building (2nd ship)

Lpp 2 Lpp (from 2nd ship) length between perpendiculars, [m] (2nd ship)

Loa 2 Loa (from 2nd ship) length over all, [m] (2nd ship)

B 2 B (from 2nd ship) breadth moulded, [m] (2nd ship)

D 2 D (from 2nd ship) depth moulded, [m] (2nd ship)

Type 1 Type of ship (left field) type of the ship ### validity rule ### category ###

Subtype 1 - - '' - - (right field) details to the type of the ship

Place of casualty place of casualty (left field)

place of the casualty ### validity rule ### category ###


Subtype 1 - - '' - - (right field) details to the type of the ship

Place of casualty place of casualty (left field)

place of the casualty ### validity rule ### category ###

Type of casualty Type of damage (left field)

nature of the damage ### validity rule ### category ###

Type of casualty 2 - - '' - - (right field) details to the damage of the casualty

Nature of casualty Nature of casualty (left field)

nature of the casualty ### validity rule ### category ###

Nature of casualty 2 - - '' - - (right field) details to the nature of the casualty

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Ship side ship side damaged ship side ### validity rule ### category ###

X X the horizontal distance from the AP to the centre of damage, [m]

Z Z

Collision: the vertical distance from baseline to the lowest point of the damage, [m] Grounding: not applicable

l l the maximum longitudinal damage length, [m]

h/w Height if collision/

Width if grounding

Collision: the maximum vertical damage height measured up from Z, [m] Grounding: the maximum transverse damage width, [m]

Area Area damage area, in square meters

Penetration

penetration depth, if collision / penetration height, if grounding

Collision: the maximum transverse penetration of damage, [m] Grounding: the maximum vertical penetration of damage, [m]

Within the statistical analysis prepared by DINMA ("Exploratory data analysis of grounding data fromthe updated GOALDS database and assessment of requirements and assumptions in SOLAS Ch. II-1 Part B-2 Regulation 9", Gabriele Bulian and Alberto Francescutto, DINMA) the reliability can be judgedby the number of samples contributing to the analysis.

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Annex 2: Collecting collision data Christian Mains, GL Data has been delivered by the consortium members DNV, LR and GL. The request from ABS, BV and RINA results in no further data. ABS has legal restrictions. BV and RINA did not answer the inquiry. The collected casualty data has been filtered according to the following conditions:


(aft end of the damage is located forward of the collision bulkhead) Number of collisions 848 (128 GOALDS, 720 HARDER) Charts of the data are presented according to the following matrix scheme: Data is being differentiated between all data (1944 – 2009) as set A and data of the latest 20 years (1989 – 2009) as set B. The charts of consistent data for set B have not been plotted due to the small number of cases. Collision struck (calculated)

all ships passenger-/roro ships Bulker/Tanker Gen. Cargo/

Container all consistent all consistent all consistent all consistent

X 1.1 n.a. 3.1 n.a. 5.1 n.a. 7.1 n.a. l 1.2 2.2 3.2 4.2 5.2 6.2 7.2 8.2 h 1.3 2.3 3.3 4.3 5.3 6.3 7.3 8.3

A 1944-2009

d 1.4 2.4 3.4 4.4 5.4 6.4 7.4 8.4 X 1.1 n.a. 3.1 n.a. 5.1 n.a. 7.1 n.a. l 1.2 n.a. 3.2 n.a. 5.2 n.a. 7.2 n.a. h 1.3 n.a. 3.3 n.a. 5.3 n.a. 7.3 n.a.

B 1989-2009

d 1.4 n.a. 3.4 n.a. 5.4 n.a. 7.4 n.a. For collisions the categories all ships, passenger ships, tankers and bulk carriers as well as general cargo and container ships have been plotted on the next pages. For these 4 categories all available data will be compared with data sets were the damage dimensions are complete - further referred to as consistent (l, h and d is available for one casualty). The charts show probability density and cumulative distribution functions.

X damage location (Nx := number of casualties) l damage length h damage height d penetration depth

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A-1.1 Damage location (719)

0,0

0,5

1,0

1,5

2,0

2,5

-0,1 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 1,1

X/Lpp

f(x)

0

20

40

60

80

100

120

140

160

Nx

PDFNx


0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

-0,1 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 1,1

X/Lpp

f(x)

0

2

4

6

8

10

12N

x

PDFNx

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0,0

0,5

1,0

1,5

2,0

2,5

-0,1 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 1,1

X/Lpp

f(x)

0

5

10

15

20

25

30

35

40

45

Nx

PDFNx


0,0

0,5

1,0

1,5

2,0

2,5

-0,1 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 1,1

X/Lpp

f(x)

0

10

20

30

40

50

60

70

80

90N

x

PDFNx

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A-1.2 Damage length (710)

0,0

2,0

4,0

6,0

8,0

10,0

12,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

l/Lpp

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20

F(x)

PDFCDF


0,0

2,0

4,0

6,0

8,0

10,0

12,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

l/Lpp

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20F(

x)

PDFCDF

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0,0

2,0

4,0

6,0

8,0

10,0

12,0

14,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

l/Lpp

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20

F(x)

PDFCDF


0,0

2,0

4,0

6,0

8,0

10,0

12,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

l/Lpp

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20F(

x)

PDFCDF

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A-1.3 Damage height (554 / 440 up to h/D=1)

0,0

0,5

1,0

1,5

2,0

2,5

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

h/D

f(x)

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

F(x)

PDFCDF


0,0

0,5

1,0

1,5

2,0

2,5

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

h/D

f(x)

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70F(

x)

PDFCDF

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0,0

0,5

1,0

1,5

2,0

2,5

3,0

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

h/D

f(x)

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

F(x)

PDFCDF


0,0

0,5

1,0

1,5

2,0

2,5

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

h/D

f(x)

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80F(

x)

PDFCDF

Deliverable D 3.1


A-1.4 Penetration depth (390 / 364 up to d/B=0.5)

0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

d/B

f(x)

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

F(x)

PDFCDF

A-3.4 Penetration depth (34 / 33 up to d/B=0.5))

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

d/B

f(x)

0.00

0.20

0.40

0.60

0.80

1.00

1.20F(

x)PDFCDF

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0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

8,0

9,0

10,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

d/B

f(x)

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

F(x)

PDFCDF


0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

d/B

f(x)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00F(

x)PDFCDF

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A-2.2 Damage length (consistent data 334)

0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

8,0

9,0

10,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

l/Lpp

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20

F(x)

PDFCDF


0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

l/Lpp

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20F(

x)PDFCDF

Deliverable D 3.1



0,0

2,0

4,0

6,0

8,0

10,0

12,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

l/Lpp

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20

F(x)

PDFCDF


0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

8,0

9,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

l/Lpp

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20F(

x)PDFCDF

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A-2.3 Damage height (consistent data 334 / 252 up to h/D=1)

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

h/D

f(x)

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

F(x)

PDFCDF


0,0

0,2

0,4

0,6

0,8

1,0

1,2

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

h/D

f(x)

0,00

0,10

0,20

0,30

0,40

0,50

0,60F(

x)

PDFCDF

Deliverable D 3.1



0,0

0,5

1,0

1,5

2,0

2,5

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

h/D

f(x)

0,00

0,10

0,20

0,30

0,40

0,50

0,60

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0,80

0,90

1,00

F(x)

PDFCDF


0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

h/D

f(x)

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80F(

x)

PDFCDF

Deliverable D 3.1


A-2.4 Penetration depth (consistent data 334 / 319 up to d/B=0.5)

0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

d/B

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20

F(x)

PDFCDF

A-4.4 Penetration depth (consistent data 29/28 up to d/B=0.5)

0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

d/B

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20F(

x)PDFCDF

Deliverable D 3.1



0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

8,0

9,0

10,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

d/B

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20

F(x)

PDFCDF


0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0

4,5

5,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

d/B

f(x)

0,00

0,10

0,20

0,30

0,40

0,50

0,60

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0,80

0,90

1,00F(

x)PDFCDF

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B-1.1 Damage location (601)

0.0

0.5

1.0

1.5

2.0

2.5

-0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

X/Lpp

f(x)

0

20

40

60

80

100

120

140

Nx

PDFNx


0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

-0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

X/Lpp

f(x)

0

1

1

2

2

3

3

4

4

5N

x

PDFNx

Deliverable D 3.1



0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

-0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

X/Lpp

f(x)

0

2

4

6

8

10

12

Nx

PDFNx


0.0

0.5

1.0

1.5

2.0

2.5

-0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

X/Lpp

f(x)

0

5

10

15

20

25

30N

x

PDFNx

Deliverable D 3.1


B-1.2 Damage length (199)

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

l/Lpp

f(x)

0.00

0.20

0.40

0.60

0.80

1.00

1.20

F(x)

PDFCDF


0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

l/Lpp

f(x)

0.00

0.20

0.40

0.60

0.80

1.00

1.20F(

x)

PDFCDF

Deliverable D 3.1


B-5.2 Damage length 45)

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

l/Lpp

f(x)

0.00

0.20

0.40

0.60

0.80

1.00

1.20

F(x)

PDFCDF


0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

l/Lpp

f(x)

0.00

0.20

0.40

0.60

0.80

1.00

1.20F(

x)

PDFCDF

Deliverable D 3.1


B-1.3 Damage height (119 / 111 up to h/D=1)

0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

h/D

f(x)

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

F(x)

PDFCDF


0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

h/D

f(x)

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

F(x)

PDFCDF

Deliverable D 3.1



0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

h/D

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Annex 3: Exploratory data analysis of ship-ship collision data from the updated GOALDS database

Gabriele Bulian ([email protected]), Alberto Francescutto ([email protected]) Department of Mechanical Engineering and Naval Architecture - University of Trieste

Document history Revision Date Corresponding author Description

00 17 June 2010

G. Bulian ([email protected]) First draft

01 09

August 2010

G. Bulian ([email protected])

Second draft - Updated extraction of passenger vessels data (5 additional cases) and corrected relevant figures / data

- Added analysis of /x pp ppE L L L

- Improved comments in the text - Editorial corrections

02 30

August 2010


Draft Final Version - Editorial corrections - Corrected mistype in the reporting of definition of struck vessel from Ref. [2] - Corrected text labels for Figure 14 - Corrected text labels for Figure 29 - Updated Figure 26 - Added acknowledgments - Changed "draught during casualty" to "draught before casualty" according to the revised description of fields from GL (30 August 2010)

mailto:[email protected]





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Summary This document contains an exploratory data analysis carried out on the collision database updated in the course of the GOALDS project (WP3). Ship-ship collisions have been taken into account, trying to filter from the database damaged ship which can be identified as struck vessels. The attention has been focalised on two main aspects. On one side the statistics coming from the updated database have been compared with present SOLAS assumptions which originated from the HARDER project in order to assess whether the additional data gathered in the GOALDS project could indicate the necessity of a modification of present SOLAS regulations concerning side damage due to ship-ship collision. On the other side particular attention has been given to, and specific analyses (when feasible) have been carried out on passenger vessels, as required in the GOALDS Task 3.1 - "Collision Damage Characteristics". Attention has also been given to some theoretical issues which were identified in the development of the SOLAS regulations, and which were several times remarked in the scientific literature. When possible and reasonable the effect of the additional data collected in the framework of GOALDS has been assessed by comparison with analyses carried out using only previous HARDER data. The main conclusions obtained from the analysis are summarised as follows, while more detailed information are given in the paper:

- The number of data from passenger ships is too limited to allow any determination of specific damage distribution for this ship type.

- Data in the range of long ships (about above 200m) are still very limited and the statistical uncertainty precludes any firm conclusion when directly analysing damage characteristics.

- In general data collected in GOALDS did not significantly change the statistics of the database, with the exception of the damage length which, with the addition of GOALDS data, showed a tendency towards a reduction.

- The suitability of the SOLAS dimensionless approach for the damage position is supported by the data.

- SOLAS assumptions concerning damage length seem to be in line with HARDER data, and conservative with respect to the updated GOALDS database.

- The SOLAS dimensionless approach for the damage penetration is supported by the data up to ship breadths of about 20m. For larger breadths this approach seems to be conservative, and it seems that a dimensional approach could be more consistent with the data. However, the data available in the range of large breadth are limited, and the statistical uncertainty is high.

- The influence of considering or neglecting, in line with SOLAS assumptions, damages penetrating the ship for more than B/2 cannot be considered negligible.

- When neglecting, consistently with SOLAS, damages penetrating the ship for more than B/2, the SOLAS approach is suitable up to about a breadth of 20m and conservative for larger breadths. If damages exceeding B/2 in penetration are not neglected, SOLAS is not conservative for small breadths and conservative for large breadths. Some analysis have been carried out taking into account the effect of the limitation of the aspect ratio of the dimensionless damage, as presently inherent in SOLAS rules.

- In general, despite all the efforts spent to remove doublets, wrong cases, etc. it is not possible to say that the quality of the data is high, but rather average to low. Sufficiently large subsets of fully consistent data are particularly missing. It is therefore suggested that more efforts should be spent in the future in order to improve the recording and processing of accidents data, otherwise it is expectable that not negligible difficulties will arise in possible future tentative revisions of damage statistics for design and/or regulatory purposes.

- Present SOLAS regulation provides a probabilistic approach for what concerns the upper edge of the damage through the so called v-factor. However, SOLAS does not provide any probabilistic approach for the description of the position of the lower edge of damage, and a worst-case approach is presently used to deal with the lower damage edge. This matter needs further attention and the available database can help in developing a suitable distribution also for the position of the lower edge of damage.

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Introduction The analyses of the data shown in this report are based on the GOALDS database of damage characteristics [1]. Before going to the statistical analysis it is worth reporting how the global database has been filtered in order to obtain the working set of data assumed to belong to ship-ship collisions where the ship is the struck vessel. The filtering of data has been carried out in five different levels

Level 01. Collision casualties have been extracted on the base of the field "Nature of Casualty" available in the database.

Level 02. Some inconsistent cases have been identified and removed. In particular o For what concern the longitudinal extension of damage: IDs 977, 2352. o For what concerns the damage penetration: IDs 137, 684, 2922, 2924, 2975, 2985,

3007. Level 03. A subsequent series of filtering have been performed in order to retain only ship-ship

collisions where the damaged ship is the struck ship (for consistency with HARDER project and SOLAS). Therefore only data associated with a field "Ship to ship" having value different from "FALSE" were selected. The filtering based on "Ship to ship" different from "FALSE" was used instead of a filtering based on "Ship to ship" equal to "TRUE" because some cases have an empty cell for this field. Cases with an empty cell for the field "Ship to Ship" have hence been considered/assumed as ship-ship collision. In addition cases associated with "Nature of casualty 2" equal to "contact" (only ID 833 at this level) have been eliminated. According to this filtering the used set of data could contain also collisions which are not ship-ship collisions. A stricter filtering was not used in order not to reduce too much the available sample.

Level 04. A further filtering has been performed in order to remove all those cases having a reported vertical position of the lower edge of the damage (Z) above the waterline. To do so, firstly a reference draught has been determined, where possible. This reference draught was considered equal to the draught amidships before casualty (field "d mid"), if present. As a second priority option, the reference draught was considered equal to the draught calculated amidships before casualty (field "d calc mid"), if present. Then the calculated reference draught was compared with the vertical distance from baseline to the lowest point of the damage (field "Z"), and all cases having a lower edge of damage above the reference waterline have been eliminated. All the other cases not fulfilling the previous condition have been retained, this meaning both cases having a lower edge of damage below the waterline, and cases for which the lower edge of damage was not reported or the reference draught could not be calculated due to missing draught information. According to this filtering it is possible that the used set of data could contain also damages having lower edge of damage above water. A stricter filtering was not used in order not to reduce too much the available sample.

Before going to the description of the final filtering level (Level 05), it is necessary to make a small introduction. The final filtering level is intended to remove from the database damaged ships which are likely to be striking ships. On this topic, there are two document which are relevant for consistency purposes with past analyses, namely: 1) §3.1 in HARDER 1-11-D-2001-01-1 [2]: in this reference the definition of "striking vessel" is

based on the position of the aft end of the damage. A ship is considered as "striking" when the position of the aft end of damage is positioned forward with respect to 0.975 ppL⋅ from

the aft perpendicular. 2) §12.1 in HARDER 2-22-D-2001-01-4 [3]: in this reference it seems that all cases having a

centre of damage forward of the estimated position of the collision bulkhead have been neglected (see also §7.2.2 in [4]). The collision bulkhead has been assumed in [3][4] to be at 0.05 ppL aft of the forward perpendicular for 200mppL ≤ , and at 10m aft of the forward

perpendicular for 200 . ppL m>The first definition, based on [2] seems more reasonable to identify striking vessels, and it has therefore been used here. Hence:

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Filtering 05. This filtering level is intended to remove damages associated with striking vessels. A ship is considered to be a striking vessel when, from the data in the database, it is possible to check that the aft end of damage is positioned forward with respect to 0.975 ppL⋅ from the

aft perpendicular. In addition to the filtering reported above, some cases have also been found to be inconsistent with respect to draught before casualty and depth. In particular, for IDs 4022, 593 and 297 the draught before casualty was reported to be larger than the ship depth, and hence these two data (draught and depth) have been removed. The statistical analysis has been carried out on the database filtered at Level 05. Further filtering of data has been carried out when necessary, and it will be clearly reported in the subsequent sections if necessary. As a general note it must be said that data collected in GOALDS are, in the large majority of cases, missing information on the ship draught.

Statistical analysis

General information The total number of data in the global GOALDS database [1] and in the database used as a basis for ship-ship collision analysis is reported in Table 1. It can be seen that GOALDS project contributed with more than 20% of data of the global database, with a similar percentage also when considering the reduced set of data identified as ship-ship collisions with the damaged ship not being the striking vessel. When limiting our attention to ship-ship collisions involving not striking passenger vessels, the total number of entries drops significantly, and also the relative contribution of the GOALDS data to the total number of cases reduces. Passenger vessels have been identified from the database using fields "Type 1" and "Subtype 1" and this category contains also RoPax vessels. In order to extract data unambiguously associated with passenger vessels, only those cases explicitly reporting the indication of ship carrying passengers in fields "Type 1" or "subtype 1" have been used.

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Table 1: Number of data in the database.

Total entries HARDER GOALDS Global Database 1527 (100%) 1179 (77%) 348 (23%)

Ship-ship collision Damage starting below waterline

Not striking vessel 668 (100%) 519 (78%) 149 (22%)

Ship-ship collision Damage starting below waterline

Not striking vessel Passenger ship

35 (100%) 31 (89%) 4 (11%)

The main goals of the present analysis are, in principle:

- To determine, on the base of the additionally collected data with respect to HARDER project, whether there is any strong justification for an update of the present SOLAS damage stability regulation concerning collision damages;

- To determine specific indications for passenger ships. Already at this stage it can be concluded that, due to the limited number of data for collisions involving passenger ships (only 35 cases as reported in Table 1) any robust statistical analysis is precluded. As it is well known, present SOLAS damage stability regulation has been developed using the results of the HARDER project as a basis. Hence, for what concerns the analysis of the suitability of present SOLAS regulations, the available set of data will be (partially) analysed in a way consistent with the HARDER analysis, when necessary. In particular, for those casualties resulting in multiple damages along the ship, each damage will be considered as a separate case. This approach is of course questionable, since, from the point of view of static ship stability (not from the point of view of time domain characteristics of the flooding process), what is important is the flooded region in the hull, and not how many breaches actually led to such flooding. Despite recognising the limit of this approach, it has been used for consistency reasons. In the following, the sample of data will be analysed using a sliding window technique already used in the past [5]. The idea behind this technique is to avoid any parameterisation of the underlying set of data, unless necessary. The main goal of this type of analysis is to determine whether there is any significant dependence between two random variables, and if this dependence is found, the aim of the analysis is to provide indications for a proper modelling of this dependence. Two generic random variables are considered, say X and Y with a set of samples N( ), 1,...,i ix y i N= . The analysis considers a series of subsets, obtained by filtering on the basis

of appropriate intervals (windows) for the variable X . The generic k th− subset , associated

with the window , is defined as:

kΩ

min, max,,k kx x⎤⎦ ⎤⎦

( ) min, max, , : , k i i i k kx y x x x⎤ ⎤Ω = ∈⎦ ⎦ (1)

A detailed (conditional) statistical analysis is then performed on the samples of the random variable Y belonging to each subset kΩ , addressing the mean and maximum values of Y ,

different percentile levels, estimated cumulative distribution, etc. The generic statistical estimator for the variable Y (e.g. the mean value of Y ) is finally reported as a function of the mean value of the random variable X for those samples belonging to the subset kΩ . By proper sliding of the

window , it is possible to identify tendencies for the statistical characteristics of the

considered random variable Y as a function of the random variable

min, x,ma,kx x⎤⎦ k ⎤⎦X .

All the statistical analysis has been carried out under MATLAB® environment.

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Distribution of ship dimensions In order to correctly interpret the results of the statistical analysis, and in particular the limited significance of statistical estimators in certain ranges, it is important to analyse the sample of data from the point of view of the main ship dimensions. Figure 1 reports the cumulative distributions of main ship dimensions (when known) for the ships available in the sample considered for the analysis. It can be seen that the percentage of ships in the range of large and small ships is, of course, limited. In particular, if we consider percentiles 5% and 95% as references, they correspond for the whole sample, to 50.0m 258.1mppL = , 8.5m 32.3mB = and

3.7m 20.2mD = . The interval between the 5% and the 95% levels shrinks when looking at

passenger ships, particularly for what concerns the ship length. The ship length between perpendiculars of passenger ships in the database ranges from 67.5m to 258.75m. It is therefore expectable that the limited number of data in the range of large and small ships will render the statistical estimator in those ranges quite uncertain. It is worth recalling here that present SOLAS damage "stability requirements in parts B-1 through B-4 shall apply to cargo ships of 80 m in length (L) and upwards and to all passenger ships regardless of length but shall exclude those cargo ships which are shown to comply with subdivision and damage stability regulations in other instruments developed by the Organization" [6], where the length L to be compared with the 80m limit is the ship length according to the International Convention on Load Lines in force. Data obtained in the range of short cargo ships shall therefore be considered with this limit in mind. It is also worth underlining that the reference length used in SOLAS damage stability requirements is the subdivision length of the ship, while here we refer to the ship length between perpendiculars, which is usually smaller than the subdivision length.

Figure 1: Cumulative distribution of main dimensions of ships available for the analysis.

Longitudinal position of damage The longitudinal position of centre of damage is presently considered in SOLAS as uniformly distributed along the ship. A scatter plot of the database is shown in Figure 2, where cases collected in the GOALDS project are highlighted, as well as those cases involving passenger ships. Consistently with the discussion concerning the distribution of ship dimensions, and in particular with the cumulative distribution for passenger ships shown in Figure 1, the majority of passenger vessels concentrates approximately in the range 100m-150m in length.

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Figure 2: Scatter plot of longitudinal position of the centre of damage as a function of the ship length

between perpendiculars. From the scatter plot in Figure 2 there is a clear clustering of damage centre in the forward part of the ship. An analysis of different percentile levels and mean value for the quantity /dam ppX L as a

function of is shown in ppL Figure 3. The analysis has been carried out using windows having 50m

width, starting from ] ]0 ,50ppL m m∈ up to ] ]200 , 250ppL m m∈ with 5m steps. An additional

window has been used, namely ] ]250 ,350m mppL ∈ , in order to take into account the limited

number of cases in the range of long ships. The total number of samples in each window is shown in Figure 4. It can be seen from Figure 4 that the number of samples for each window significantly drops in the range of large ships, and also in the range of small ships. This is a natural consequence of the already discussed distributions of ship dimensions. In the region of ship lengths where the number of points in each window is large, the percentile levels as well as the mean level, are quite constant. This indicates an independence of the distribution of the damage location /dam ppX L

/dam

from the ship

length. The situation is, instead, uncertain for what concern the distribution of ppX L in case

of large and small ships. However, as pointed out, in these ranges the number of samples in each window is much smaller, and therefore it is necessary to appropriately take into account the confidence intervals associated with the statistical estimators before coming to definite conclusions.

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Figure 3: Sliding window analysis of longitudinal position of the centre of damage as a function of the

ship length between perpendiculars.

Figure 4: Total number of samples for each window used in Figure 3.

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Figure 5 shows, as an example, the average value of /dam ppX L estimated for each window, as

well as the corresponding 95% confidence intervals. It can be seen that the width of the confidence intervals significantly increases when large ships are considered. On the other hand, in case of small ships, despite the reduction in the number of point in each window, the confidence intervals remain quite limited in width, thanks to a reduction of the standard deviation of the sample which counteracts the reduction in the number of data points. Looking at Figure 5 it could be concluded that the number of points in the range of large ships are too few to say anything concerning the variations of the mean (and also of the percentile levels) observed in Figure 3. On the other hand some indication of difference in the distribution of longitudinal position of damage between small ships and medium size ships could be more supportable.

Figure 5: Average dimensionless position of centre of damage /dam ppX L with 95% confidence

intervals. Figure 6 shows the results of a two samples Kolmogorov-Smirnov test applied by considering every possible couple of considered windows to test the null hypothesis of equal CDF among different windows. It can be seen that the tests indicates statistically significant differences especially for what concerns small ships and medium size ships. Although there seems to be a statistically significant difference also between large ships and medium size ships, in such case the pattern is less clear due to the limited number of data.

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Figure 6: Results of window-to-window two samples Kolmogorov-Smirnov test.

Therefore, results shown in Figure 6 indicate that the distributions of /dam ppX L are not

significantly different for ships between about 100m and 200m in length. However, some differences are highlighted in case of longer and shorter ships. Nevertheless, differences in the mean value of /dam ppX L

dam

and several percentile levels are not large, and therefore considering the

same distribution of / ppX L for any ship length could be considered acceptable from the

engineering point of view, especially taking into account the fact that a clear trend in the dependence of the distribution of /dam ppX L from cannot be observed and also taking into

account the fact that it is not easy to find a clear physical reason for the dependence of the position of damage from the actual ship size which can be consistent with the data.

ppL

It is at this point necessary to discuss the actual shape of the distribution of /dam ppX L . In this

context it is necessary to recall that, according to [3][4], the analysis of the dimensionless damage position /dam ppX L seems to have been carried out after removing all damages having damX

forward of the estimated position of the collision bulkhead. The collision bulkhead has been

estimated to be positioned at a distance equal to min 0.05 ,10ppL m aft of the forward

perpendicular. It is understandable that the result of such a filtering is the removal of forward damages. This was evident from the results reported in the past in [3][4] and the same, expectable, behaviour is again visible when analysing the new database, as shown in Figure 7. It must be underlined that the total number of available data is reduced from 668 to 484 due to the removal of the forward damages.

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Figure 7: Effect of filtering of cases having centre positioned forward of the estimated position of the

collision bulkhead. It is obvious that the removal of forward damage has an influence on the average position of damage. To assess this effect, the same analysis already performed in Figure 3 is now carried out

after removing all cases having min 0.05 ,10dam pp ppX L L> −

/dam pp

m , and the results are shown in

Figure 8. The interesting consequence of the removal of the forward damages is a reduced dependence of the percentile levels and of the mean of X L from . This seems to be

due to the fact that, according to the available data, forward damages are more likely in case of ships of medium size, as can be understood from percentile levels in

ppL

Figure 3.

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Figure 8: Sliding window analysis of longitudinal position of the centre of damage as a function of the

ship length between perpendiculars. Forward damages removed. It is now worth considering whether the addition of the new GOALDS data has any significant influence on the distribution of /dam ppX L , and also whether the distribution assumed in

SOLAS2009 can be considered sufficiently accurate from the statistical and/or engineering point of view. First of all, in Figure 9, we compare the distribution of /dam ppX L considering only GOALDS data

and only HARDER data, without removing forward damages. It can be seen that the confidence interval in the distribution estimated from GOALDS data are larger due to the reduced number of data points. There seems to be a tendency in GOALDS data to have damages located more towards the aft of the ship with respect to HARDER data. However, a two samples Kolmogorov-Smirnov test applied on the data does not reject the hypothesis of equal CDF at 5% significance level. Therefore, from the statistical point of view, the two distributions cannot be considered significantly different. When forward damages are removed, as shown in Figure 10, distributions for /dam ppX L from GOALDS and HARDER data become more equal, and also in this case,

although different, they are not considered significantly different from a statistical point of view.

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Figure 9: Distribution of /dam ppX L . Comparison between HARDER data and GOALDS data. All

cases.

Figure 10: Distribution of /dam ppX L . Comparison between HARDER data and GOALDS data.

Forward damages removed.

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By joining HARDER and GOALDS data and removing forward damages it is now possible to compare the distribution of /dam ppX L with the uniform distribution assumed in present SOLAS.

Since present SOLAS formulation has been developed from the results of HARDER project, a comparison is carried out here under the same assumption, only in order to assess whether the addition of new data significantly changed the database characteristics. Results of the analysis are shown in Figure 11. From the comparison it can be seen that:

- The additional GOALDS data did not significantly change the behaviour of the database. - As a consequence, if the approximation of the HARDER distribution with a uniform

distribution was considered appropriate at the time of development of SOLAS, there is no justification for not considering it appropriate from an engineering point of view also on the basis of the present updated database.

- The uniform SOLAS distribution slightly overestimates the probability of damages located in the aft part of the ship.

- The uniform distribution does not reflect the presence of a mode in the probability density function of /dam ppX L close to .5/ 0dam ppX L ≈ . This modal value is evident in Figure 7,

and can be seen also in Figure 11 as the point of maximum derivative of the estimated CDF.

- The probability density function obtained from the data in the database can be fitted better with a linear or piecewise-linear function of /dam ppX L , similar to that used in the

regulation SOLAS A.265.

Figure 11: Distribution of /dam ppX L . Comparison between HARDER data, HARDER+GOALDS

data and uniform distribution as considered in SOLAS. Forward damages removed. It is however important to underline that a not negligible uncertainty in the selection of the appropriate distribution for /dam ppX L arises from the decision of removing (or not removing)

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forward damages, since the removal of forward damages basically removes a modal value of the probability density function of /dam ppX L close to the forward end of the ship. This difficulty is

likely connected with the difficulty in separating striking ships from struck ships in a robust way.

Finally, it is now worth showing, in Figure 12, a comparison of ( )/dam ppCDF X L between

passenger ships data and other ships data. It is evident that the limited number of passenger ships in the sample does not allow any statistically significant conclusion to be drawn, although there seems to be some indication for a tendency of damages in passenger ships to be located more forward with respect to other ship typologies.

X /dam ppLFigure 12: Distribution of . Comparison between passenger ships data and non-passenger

ships data. All cases.

Longitudinal extent of damage A scatter plot of the longitudinal damage extent as available from the database is shown in Figure 13. In the figure, data collected in GOALDS and data for passenger vessels are highlighted. In addition, a series of IDs are reported, referring to a series of cases which are worth some comment.

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Figure 13: Scatter plot of longitudinal damage extent as a function of the ship length between

perpendiculars. By looking at the scatter plot in Figure 13 it can be seen that GOALDS additional data tend to be in the region of small damages. Passenger ships distribute quite evenly in the region of medium size ships, apart from a few cases. The region of lengths above 200-250m clearly shows, again, a scarcity of data. It is worth noticing that IDs 4032 and 4033, which represent very long damages, actually belong to the same casualty reported to have occurred in 1994 to an oil tanker in open sea. Similarly, also IDs 4438 and 4437 represent multiple hull breaches recorded in occasion of the same casualty occurred in 2009 to a container vessels. In the case of the tanker the two damages do not overlap, and overall the breakage covers 73% of the ship length, which seems to be an extremely unlikely case tractable as outlier. In the casualty involving the container vessel, there is an overlapping of the two damaged longitudinal regions of the ship. Moreover, in case of ID 4438 the damage is extremely likely to be above the waterline, but since the ship draught was not available in the database, for methodological reasons, the case was kept in the database due to the impossibility of clearly checking the bottom position of the damage with respect to the ship waterline. In case of ID 107 a very limited amount of data is available concerning the damage characteristics (only the length). The ID 316 is indicated only as reference since the damage length in this case is larger than the maximum damage length of 60m which SOLAS considers for ships above 198m in length. In line with the discussion carried out in the section concerning the longitudinal position of damage, we are here interested in identifying the effect of removal of "forward damage cases", i.e. those cases having centre position forward of the estimated position of the collision bulkhead. Figure 14 identifies damages having centre positioned forward of the estimated position of the collision bulkhead. It can be seen that this subset of data is in line with the global database, and it is therefore expectable that the removal of these cases will not have a great influence on the statistics.

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Figure 14: Scatter plot of longitudinal damage extent as a function of the ship length between

perpendiculars. Identification of forward damage cases. A series of percentile levels as well as the mean damage length have been analysed considering different subsets. Similarly to what has been done in case of longitudinal position of damage, the analysis has been carried out using windows having 50m width, starting from ] ]0 ,50ppL m∈ m up

to ] ]200 , 250ppL m∈ m with 5m steps. An additional window has been used, namely

] ]250 ,350ppL m m∈ , in order to take into account the limited number of cases in the range of

long ships. First of all we have considered the global effect of the addition of GOALDS data to the HARDER basic database, and the results are shown in Figure 15. As a consequence of the already discussed fact that damages collected in GOALDS are in general relatively small in length, it follows that percentile levels of damage length distribution are shifted by the addition of GOALDS data towards smaller damages. It must also be noted that GOALDS data do not affect the envelope of maximum values of damage lengths, because the extreme cases are all (with the exception of ID 4438) coming from HARDER data.

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Figure 15: Percentile levels of damage length distribution. Comparison between HARDER database

and updated HARDER+GOALDS database. As a measure of direct comparison, the average damage length as a function of the ship length between perpendicular is shown in Figure 16 together with 95% confidence intervals. A zoom of the same figure is shown in Figure 17 in order to better see the variation in the mean. A clear and, most important, systematic reduction in the average damage length can be observed for all ship lengths as a consequence of the addition of GOALDS collected damage cases. Still, however, confidence intervals in the region of large ships are very wide due to the limited and dispersed data set. As a support for the following discussion, Figure 18 shows the behaviour of the dimensionless average damage length /x ppL L as a function of the ship length between

perpendiculars. When considering the complete database (HARDER and GOALDS data) a

systematic reduction of /x ppE L L ppL as the ship length increases can be noticed, while this

reduction is still visible, but less evident, when considering only HARDER data.

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Figure 16: Average damage length. Comparison between HARDER database and updated

HARDER+GOALDS database.

Figure 17: Average damage length. Comparison between HARDER database and updated

HARDER+GOALDS database. Zoom.

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Figure 18: Average dimensionless damage length. Comparison between HARDER database and

updated HARDER+GOALDS database. Zoom. It is now interesting to see also the effect of the removal of "forward damages" on the mean damage length. Figure 19 compares the estimated average measured damage length as a function of the ship length between perpendiculars when considering the whole database and when removing cases having centre of damage forward of the estimated position of collision bulkhead. It is evident that the removal of "forward damages" has a very limited and not systematic effect. It follows that it can be considered reasonable to analyse the whole database and to compare the results with SOLAS requirements even without removing forward damages.

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Figure 19: Average damage length. Effect of removal of "forward damages".

From Figure 15, Figure 16, Figure 17 and Figure 18, there are indications that a pure dimensionless approach for the distribution of the longitudinal damage extent cannot be considered appropriate for representing the data. The inappropriateness of a purely nondimensional approach can be appreciated in particular when looking at Figure 18, where the average dimensionless damage length is shown as a function of the ship length between

perpendiculars. There is, indeed, a systematic reduction of /x pp ppE L L L as the ship length

increases, which is particularly evident when considering the whole available database. This aspect was also discussed in [5] and present SOLAS requirements actually partially deal with this matter by providing a distribution of damage length which modifies its properties as the ship length (the subdivison ship length in SOLAS) changes. Indeed, up to a ship length of 198m the distribution of the dimensionless damage length /x shipL L is kept constant, while for ships above

260m in length it is the distribution of the dimensional damage length xL which is kept constant.

For intermediate values of ship length a gradual modification of the distribution is considered in order to blend the purely dimensionless approach and the purely dimensional approach. It is therefore interesting to see the level of agreement of present SOLAS distributions with respect to data in the updated database created in GOALDS. For sake of consistency with the analysis carried out in the framework of the development of SOLAS regulation, here we will compare the characteristics of the distribution of the measured damage length as reported in the database with the underlying distributions in SOLAS regulation. It must however be underlined that this comparison is, from the theoretical point of view, incorrect, although numerical differences induced by a more theoretically correct method are small. The theoretical incorrectness of a direct comparison of such quantities is discussed in [7][8], and some more detail on this point is given in Appendix 1. The problem is that the measured damage length from accidents, which is reported in the database, cannot be considered independent of the damage position. Indeed, the measured damage length is geometrically limited by the aft and

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forward end of the ship. While this geometrical limitation is relatively unimportant when the damage centre is positioned close to amidships, the importance of this limitation increases as the centre of the damage shifts towards the aft and forward ends of the ship. The effect of geometrical limitations on damage length given by the forward and aft end of the ship is evident in the SOLAS regulation, since different formulae are present for the probability of flooding of end compartments. In the development of the SOLAS the distribution of the damage length as measured from accidents has been used directly as if it were what in [7][8] is called the "conditional distribution" of damage length, or what, for sake of clarity, we prefer to term as the "distribution of the potential damage length" (see Appendix 1). Fortunately, thanks to the fact that the majority of damages have a longitudinal extent that is significantly shorter than the ship length, and thanks to the fact that from statistics the centre of the damage is quite evenly distributed along the ship length, differences between the distribution of damage length as measured from statistics (which is available) and the distribution of the "potential damage length" (which must be inferred starting from theoretical assumptions) are relatively small. As a consequence a direct comparison between SOLAS formulation and data from the analysis of database is reasonable from the engineering/numerical point of view. Figure 20 reports, for reference, some main characteristics of the SOLAS distribution for the damage length, namely a series of percentile levels, the mean damage length and the maximum damage length. It is also worth recalling that the SOLAS distribution for damage length is a bi-linear function (see [3][4][5][6]).

Figure 20: Some main characteristics of SOLAS distribution of damage length: percentile levels, mean

value and maximum value. A first comparison between percentile levels obtained from the HARDER data and SOLAS distributions is shown in Figure 21 from which a fairly good agreement can be seen. The agreement is worse in case of high (97.5%) and small (2.5%) percentile levels as well as in the case of large ships, but in these cases it is necessary to take into account the large involved

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uncertainty, which precludes any firm conclusion. In general it seems that present SOLAS distributions is a sufficient approximation of the HARDER data. From the results reported in Figure 15, Figure 16 and Figure 17 and from the good agreement observed in Figure 21 between SOLAS and HARDER data it is expectable that SOLAS assumptions will be conservative with respect to the data in the global database. This idea is confirmed in Figure 22, where it can be seen that percentile levels of the longitudinal damage length are in general associated with smaller damages with respect to what considered in SOLAS.

Figure 21: Comparison of percentile levels and mean value of damage length as a function of the ship

length between HARDER data and SOLAS distribution.

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Figure 22: Comparison of percentile levels and mean value of damage length as a function of the ship

length between global database and SOLAS distribution. In order to better quantify the level of conservativeness which seems to be present in SOLAS assumptions with respect to the updated database, Figure shows a comparison of the average damage length as a function of the ship length between SOLAS assumptions, HARDER data and data of the present GOALDS database (HARDER+GOALDS updates). It can be seen that now the average damage length as obtained from the whole database is systematically smaller that the SOLAS assumption. However, from the statistical point of view, differences are still comparable with confidence intervals for the estimated mean which, particularly in the region of long ships, are significantly wide.

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Figure 23: Comparison of mean value of damage length as a function of the ship length between global

database, HARDER data and SOLAS distribution. It is now worth checking whether there is any significant difference between the probability distribution of damage length between passenger ships and other ships. As it is evident from Figure 13, the number of sample data for passenger vessels is limited, and the available data for passenger ships are concentrated in the region of medium size ships. Figure 24 shows the number of data concerning all ships and passenger vessels available in each window: it is clear from this plot that any quantitative analysis based on such a limited number of points for passenger vessels is statistically questionable, especially if the intention is to extrapolate the results in the range of small and large ships.

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Figure 24: Number of vessels for each tested window.

For sake of qualitative comparison, the cumulative distribution of damage length for the window

] ]100 ,150ppL m m∈ is determined for passenger ships only and for all the other ships separately.

The result of the comparison is shown in Figure 25. It can be seen that the confidence intervals for the CDF of damage length in case of passenger ships are very wide, due to the limited sample. There seems to be a tendency, for this window, to have damages for passenger vessels which are longer than damages for other ships. However, a two-sample Kolmogorov-Smirnov test does not reject the hypothesis of equal distribution among the two groups at 5% significance level. The number of data is insufficient to draw any definite strongly supportable conclusion even for this single window where passenger ships samples are maximum, and the situation is worse for other ranges of dimensions.

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Figure 25: Comparison of CDF of damage length for passenger ships and other ships in the ship length

window between 100m and 150m. On the basis of the performed comparisons, and in view of the analysis of the data of the updated database in GOALDS, it can be said that, although with a series of reported remarks, present SOLAS distributions for the damage length due to ship-ship collision can still be considered a reasonable tool for engineering / regulatory application. This tool seems to embed a certain level of conservativeness. The not negligible level of uncertainty in the statistical estimators due to the limited number of data, and the average quality of the database suggest that any modification of present SOLAS assumption concerning the damage length can be considered premature and not strongly supportable from the statistical point of view. Specific indications for passenger vessels cannot be obtained due to the limited number of available data.

Damage penetration

Notes on the SOLAS distribution for damage penetration Before going to the statistical analysis of available data it is worth recalling present assumptions in SOLAS concerning the distribution of the damage penetration. In present SOLAS regulation the dimensionless damage penetration is considered to have a distribution which is

independent of the actual ship dimension. SOLAS also assumes a limited dependence between the dimensionless damage penetration and the dimensionless damage length

/yL B

/yL B /x shipL L

/

in case

of short damages, in the form of a sort of limiting aspect ratio for the damage. This dependence is the reason for the presence of the factor in SOLAS regulation for the calculation of the coefficient . In particular SOLAS assumes that the CDF of conditional to

Gr /yL B x shipL L is as

follows:

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( )2

1 2

max

1 2

max

0 if 0

if 02

1 if

24 16 ; ; ; 5 5

1min ,152

y x

ship

cdf c c

L L c cB L

η

ηmaxη λ η η

η η

η λ

η λ

<⎧⎪⎪= ⋅ + ⋅ ≤ <⎨⎪

≥⎪⎩

= = = − =

⎧ ⎫= ⎨ ⎬⎩ ⎭

η

(2)

From (2) it can be seen that, when 1

30x

ship

LL

≥ , the distribution of the dimensionless damage

penetration is independent of /yL B /x shipL L , and the maximum damage penetration is equal to

half the ship breadth. For damages shorter than 1

30x

ship

LL

= a dependence is assumed between

and /yL B /x shipL L in the form of a truncation of the "long damages CDF" at a value

15y x

ship

LLB L

= ⋅ . The truncation of the CDF is accompanied by the necessary addition of a

singularity at 15y x

ship

LLB L

= ⋅ in order to obtain a total unitary value of the area under the PDF. It

is clear that this sort of truncation with the addition of a corrective singularity has mostly a mathematical background, which renders the mathematical form (2) more easily implementable in the analytical calculation of the coefficient. At the same time it is not physically supportable.

However, a better, physically sounder, mathematical description of

ry x

ship

L LcdfB L

⎛ ⎞⎜⎜⎝ ⎠

⎟⎟

30

, having a

similar behaviour as (2), would probably increase the complexity of the analytical formulation but would not have a great impact on the final numerical value of , and, in particular, in the final value of the attained subdivision index. It is worth noticing here that, when the

average damage penetration can be calculated from

r/ 1/x shipL L ≥

(2) and it is

/ /y x shipL L 1/ 30E L B ≥ = 0.2 .

According to the conditional distribution (2), the cumulative distribution of the dimensionless damage length shall be obtained, in principle, from the knowledge of the probability density function of the dimensionless damage length as:

( ) ( ) ( )max

0

; y x

ship

cdf cdf pdf d

L LB L

λ

η η λ λ λ

η λ

= ⋅

= =

∫ (3)

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Statistical analysis First of all Figure 26 reports a scatter plot of the available data. It can be seen that data added in the framework of GOALDS containing usable data in this context represent a very limited percentage of the total available cases (6 cases over a total of 276 cases). Additional GOALDS data concentrate in the region of breadth over 20m with small damage penetration, which is consistent with what has been observed in case of GOALDS data concerning damage length. Samples associated with passenger ships are only 20, and are concentrated in the region of breadths between around 15m and 21m.

Figure 26: Scatter plot of damage penetration as a function of the ship breadth.

From the scatter plot in Figure 26 it is expectable that the addition of GOALDS data will have some (minor) effect only in the range of large breadths. A first analysis concerning percentile levels and average damage penetration is shown in Figure 27 using the complete set of data available from the database. The analysis has been carried out using 5m wide windows, starting from ] ]5 ,10B m m∈ up to ] ]30 ,35B m m∈ with 5m steps. Two

additional windows have been used, namely ] ]35 , 45B m m∈ and ] ]40 ,60B m∈ m , in order to

take into account the limited number of cases in the range of wide ships. For sake of comparison the maximum damage penetration and the average damage penetration as assumed in SOLAS when the dimensionless damage length is larger than 1/30 are also reported.

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Figure 27: Percentile and average damage penetration as a function of the ship breadth. Complete

database. From Figure 27 it can be seen that percentile levels and average damage penetration tends to increase almost proportionally to the ship breadth up to about 20-22m, which would suggest the suitability of the dimensionless approach for the damage breadth. For larger breadths, up to about 30m, there seems to be a sort of saturation which would suggest that a constant dimensional approach for the distribution of the damage penetration should be considered between 20 and 30m in breadth. In case of breadths larger than 30m the behaviour is not clear due to the very limited sample, although an average tendency in keeping a constant distribution for the damage penetration could be guessed. When comparing SOLAS requirements and data from the database we see that the measured average damage penetration tends to be larger than the SOLAS assumption, and the same could be said for the maximum damage penetration. However, it must be emphasized that in the development of SOLAS regulation, damages penetrating the ship for more than half the breadth were omitted. If we repeat the analysis in Figure 27 following the same approach we obtain the results in Figure 28. It can be seen that neglecting cases having maximum penetration larger than half the ship breadth leads to a set of data which is more consistent with SOLAS assumptions. Still, however, there is a tendency towards a saturation of the distribution of the dimensional damage penetration for ship breadths above about 20m. From the available database we can find 24 cases having on a total 276 available samples. / 2yL B>

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Figure 28: Percentile and average damage penetration as a function of the ship breadth. Cases with

penetration larger than B/2 omitted. It is now worth checking the behaviour of the average dimensionless damage penetration

as a function of the ship breadth, and how much this quantity changes when data having penetrations bigger than half the ship breadth are neglected. Results of the sliding window analysis are shown in

/yL B

/ 2

Figure . It can be seen that, consistently with the previous analysis, the average dimensionless damage penetration is almost constant (or slightly increasing) up to a breadth of about 20m, after which it drops significantly. The effect of neglecting cases with is

visible only up to a breadth of about 30m, with a corresponding decrease in the average dimensionless damage penetration of about

yL B>

0.041B on average, which corresponds to about 20% of the mean damage penetration presently assumed by SOLAS for "long" damages (i.e. damages with ). / 1/x shipL L ≥ 30The addition of GOALDS data, due to the limited number of added cases, has a negligible effect on the behaviour of the database, as can be seen from the example analysis of the average damage penetration in Figure 30. It is also worth noticing in Figure 30 the significant width of the confidence intervals for the mean when the ship breadth exceeds about 20-25m.

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Figure 29: Behaviour of average dimensionless damage penetration as a function of the ship breadth.

Figure 30: Effect of data added in GOALDS on the average damage penetration as a function of the

ship breadth.

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On the base of the analysis of the database carried out so far for what concerns damage penetration, it seems that the effect of considering/neglecting cases with penetration exceeding

/ 2B could deserve some additional attention. It seems also that the use of a dimensionless approach is questionable in case of ship breadths larger than about 20-25m. However in the range of breadth above 20-25m the available data are relatively few, and hence the uncertainty is large. When taking into account cases with penetration larger than / 2B it seems that present SOLAS assumptions are not conservative for ships having breadth below about 20-25m, while the assumption are conservative for ships with larger breadths. If cases with penetration larger than

/ 2B are neglected, SOLAS assumptions are in line with data for ships up to about 20-25m in breadth, and the SOLAS assumptions are conservative for wider ships. From the analysis carried out so far it seems that the distribution of the dimensionless damage penetration is not significantly dependent on the ship breadth up to a ship breadth of about 20-25m. On the basis of this consideration, we have collected all the data for ships having breadth not larger than 22m and we have compared the distribution of the dimensionless damage penetration

with present SOLAS distribution of damage penetration for "long damages" (1

30x

ship

LL

≥ ). Results

of the comparison are shown in Figure 31, from which it can be seen that the SOLAS assumption looks as a good representation of the data when damages with penetration larger than half the ship breadth are neglected.

Figure 31: Comparison of dimensionless damage penetration between data and SOLAS neglecting

aspect ratio limitations. However, it must be said that the comparison in Figure 31, although consistent with the work which was carrier out in HARDER, does not really reflect the present underlying SOLAS assumptions for what concerns the damage penetration, since it neglects that the damage penetration and the damage length are assumed in SOLAS to be not independent due to the

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introduction of a maximum aspect ratio for the dimensionless damage. The correct cumulative distribution to be compared with data from the database should not be that neglecting aspect ratio effects, but, instead, the marginal distribution obtained from (2)-(3). Some more mathematical details are given in Appendix 2. The comparison, taking into account aspect ratio effects, is shown in Figure 33, from which it is clear that the probability of smaller damage penetrations is now increased if the limitation in the aspect ratio is taken into account. In Figure 33 calculations accounting for the aspect ratio limitations have been carried out for a ship length of 105m and a ship breadth of 15m which are representative of the underlying sample of data from which the empirical cumulative distribution of dimensionless damage penetration has been determined.

Figure 32: Comparison of dimensionless damage penetration between data and marginal distribution from SOLAS considering aspect ratio limitations. Only cases with penetration less than half the ship

breadth. It is now worth analysing whether some specific behaviour can be observed in case of passenger vessels. From the scatter plot in Figure 26 it can be seen that most of the passenger ships available in the database which are relevant to the present analysis have a beam of less than about 22m. In addition, as already said, from the analysis carried out so far it seems that the distribution of the dimensionless damage penetration is not significantly dependent on the ship breadth up to a ship breadth of about 20-25m. On the basis of these considerations we have compared, in Figure 33, the CDF of the dimensionless damage penetration for passenger

vessels with that of other ships having breadth not larger than 22m. It can be seen that the available sample of passenger vessels is too small to draw any conclusion from the analysis.

/yL B

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Figure 33: Cumulative distribution of dimensionless damage penetration for ships having breadth not

larger than 22m. Comparison between passenger ships and other ships.

Relation between damage length and damage penetration Before concluding the statistical analysis of damage penetration it is worth having a look at the mutual relation between damage penetration and damage length, since under SOLAS assumptions these two quantities are not independent, as already discussed when presenting the SOLAS CDF of the dimensionless damage penetration in (2) and as discussed in Appendix 2. SOLAS assumes, indeed, a sort of limiting aspect ratio for the dimensionless damage, i.e.

/15

/y y ship

x ship x

L B L LL L L B

= ⋅ ≤ (4)

Limiting the aspect ratio of the dimensionless damage is physically questionable. Indeed it would be physically sounder to consider a limiting aspect ratio for the dimensional damage, i.e. a limit on the quantity , in the range of small damages where the limiting factors are not the main

ship dimension. Fortunately, for standard ships, the ratio shows not a large variation. As

a consequence, if we take the average value of as a reference, we have

/yL Lx

B/shipLB/shipL

limitlimit

//y y

x ship x

L B L LE

L L L B⎛ ⎞ ⎛ ⎞ ⎧ ⎫

≈ ⋅⎜ ⎟ ⎨ ⎬⎜ ⎟⎜ ⎟ ⎩ ⎭⎝ ⎠⎝ ⎠

ship (5)

which can be compared with SOLAS assumptions. From the data in the database which are relevant to this section the average ratio is about 6.7. /ppL B

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Figure 34 shows scatter plots of available data in terms of damage penetration and damage aspect ratio as a function of the damage length. We can see that the large majority of recorded damages have aspect ratios below , and all recorded damages have aspect ratio below 5.5. Damage cases associated with penetration larger than B/2 are also highlighted in order to show their relative position in the scatter plot, as well as cases added in GOALDS.

2 3÷

Figure 34: Scatter plots of damage penetration and damage aspect ratio as a function of the damage

length.

Conclusions On the basis of the available data and of the statistical analysis carried out, a series of comments can be made and the following conclusions can be drawn. General comments:

1) The number of data concerning ship-ship collisions involving passenger ships identified not to be striking vessels (35 cases) is too limited to develop specific indications concerning damage characteristics.

Concerning the longitudinal position of the centre of damage damX :

1) There are not significant differences between the distributions of /dam ppX L for ships

between about 100m and 200m in length. Some differences are indicated in case of longer and shorter ships. However, differences in the mean value of /dam ppX L and in several

percentile levels are not large, and therefore considering the same distribution of /dam ppX L for any ship length could be considered acceptable from the engineering point

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of view, especially taking into account the fact that a clear trend in the dependence of the distribution of /dam ppX L from ppL cannot be observed.

2) The addition of GOALDS data to the database did not significantly change the distribution of the damage location with respect to HARDER data. As a consequence, if the approximation of the HARDER distribution with a uniform distribution was considered appropriate at the time of development of SOLAS, there is no justification for not considering it appropriate from an engineering point of view also on the basis of the present updated database.

3) A non-negligible uncertainty in the selection of the appropriate distribution for /dam ppX L

arises from the decision of removing or not removing forward damages, since the removal of forward damages basically removes a modal value of the probability density function of

/dam ppX L close to the forward end of the ship. This difficulty is likely connected with the

difficulty in separating striking ships from struck ships in a robust way. Concerning the longitudinal damage extent xL :

1) Additional GOALDS data are, on average, associated with relatively small damages for what concerns the longitudinal damage length.

2) As a consequence the percentile levels and the mean value of damage length for different ship lengths tend to be shifted towards smaller damage length when comparing the HARDER data and the updated HARDER+GOALDS database.

3) A clear and, most important, systematic reduction in the average damage length can be observed for all ship lengths as a consequence of the addition of GOALDS collected damage cases. Still, however, confidence intervals in the region of large ships are very wide due to the limited and dispersed data set.

4) The effect of the removal of "forward damages" has a very limited and not systematic effect on the mean damage length as a function of the ship length. It follows that it can be considered reasonable to analyse the whole database and to compare the results with SOLAS requirements even without removing forward damages.

5) Some theoretical issues have been underlined which were already identified in the past in the public literature concerning the way SOLAS distributions have been developed. These theoretical issues have been thoroughly discussed in a separate appendix, and a numerical example has been provided to see the effects of a more consistent determination of relevant damage distributions. However, the quantitative influence is limited, and can be considered negligible from an engineering point of view, also in view of the global level of uncertainty and approximation involved in the whole process of developing the distributions.

6) A comparison between percentile levels obtained from the HARDER data and SOLAS distributions shows a fairly good agreement. The agreement is worse in case of high (97.5%) and small (2.5%) percentile levels as well as in the case of large ships, but in these cases it is necessary to take into account the large uncertainty involved, which precludes any firm conclusion. In general it seems that present SOLAS distributions are a sufficient approximation of the HARDER data.

7) SOLAS distribution of damage length is conservative with respect to data obtained from the updated database. In particular the conservativeness is evident for percentile levels up to about 75% and for the average damage length. Since data added in GOALDS do not affect extreme values, which remain those observed in the HARDER database, the agreement of high percentile levels with SOLAS assumptions is not significantly changed. The problem of large uncertainty in the region of large ships has not been solved.

8) The average damage length as obtained from the whole database is systematically smaller that the SOLAS assumption. However, from the statistical point of view, differences are still comparable with confidence intervals for the estimated mean which, particularly in the region of long ships, are significantly wide.

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9) The number of accidents data for passenger ships is too limited to allow any quantitative statistically significant firm conclusion on a specific distribution of damage characteristics for this type of ships. An example has been carried out in the window

] ]100 ,150ppL m∈ m where passenger ship data are maximum. The result of the

comparison of the CDF of damage length between passenger ships and other ships shows a tendency, for this window, to have damages for passenger vessels which are longer than damages for other ships. However, a two-sample Kolmogorov-Smirnov test does not reject the hypothesis of equal distribution among the two groups at 5% significance level. The number of data is insufficient to draw any definite strongly supportable conclusion even for this single window where passenger ships samples are maximum, and the situation is worse for other ranges of dimensions.

10) On the basis of the performed comparisons, and in view of the analysis of the data of the updated database in GOALDS, it can be said that, although with a series of reported remarks, present SOLAS distributions for the damage length due to ship-ship collision can still be considered a reasonable tool for engineering / regulatory application. This tool seems to embed a certain level of conservativeness. The not negligible level of uncertainty in the statistical estimators due to the limited number of data, and the average quality of the database suggest that any modification of present SOLAS assumption concerning the damage length can be considered premature and not strongly supportable from the statistical point of view. Specific indications for passenger vessels cannot be obtained due to the limited number of available data.

Concerning the damage penetration : yL

1) Additional GOALDS data are, on average, associated with relatively small damages for what concerns the longitudinal damage length, and they are in very limited number (only 6). The global effect of cases added in GOALDS is negligible.

2) A total of only 20 data concerning passenger vessels are available, and they are mostly concentrated in the region of breadths between around 15m and 21m.

3) A dimensionless approach for the damage penetration, as presently considered in SOLAS, is supported by the data up to a ship breadth of about 20. For larger ship breadths the dimensionless approach seems to be questionable and conservative, and a dimensional approach seems to be more consistent with the data.

4) If damage penetrations larger than B/2 are kept in the database the average damage penetration in the region of small breadth is underestimated by the SOLAS assumptions. However, if, consistently with HARDER analysis and SOLAS assumptions, damages associated with penetrations larger than B/2 are neglected, SOLAS average damage penetration agrees well with the available database up to a breadth of about 20m. For larger breadths the SOLAS approach seems conservative. It seems that the effect of considering or neglecting cases with penetration exceeding / 2B could deserve some additional attention.

5) Neglecting cases associated with damage penetrations larger than B/2 leads to a variation in the average damage penetration from the database of about 0.041B in the range of ship breadths up to about 30m, and no variation for larger breadths. This variation corresponds to about 20% of the average damage penetration presently assumed by SOLAS for "long" damages (i.e. damages with 30 ). / 1/x shipL L ≥

6) When taking into account cases with penetration larger than / 2B it seems that present SOLAS assumptions are not conservative for ships having breadth below about 20-25m, while the assumption are conservative for ships with larger breadths. If cases with penetration larger than / 2B are neglected, SOLAS assumptions are in line with data for ships up to about 20-25m in breadth, and the SOLAS assumptions are conservative for wider ships.

7) Comparisons have been carried out using the SOLAS cumulative distribution for damages not affected by limitations in the aspect ratio. However, a more rigorous analysis should be

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carried out taking into account the effects of the limitation of the aspect ratio of dimensionless damage as inherent in present SOLAS rules. An example of this comparison has been shown, but a systematic application of the method is not straightforward due to the effect of the ship length, for ships above 198m in length, on the results.

8) The sample of passenger vessels is too small to draw any conclusion concerning any specific characteristic of damage penetration distribution for this ship type.

9) The damage aspect ratio /y xL L has been found to be always smaller than about 5.5 and

in the large majority of cases below 2-3. A general note concerning the quality of the available accidents database is absolutely necessary. Despite all the efforts spent to remove doublets, wrong cases, etc. it is not possible to say that the quality of the data is high, but rather average to low. The reasons are to be found in the fact that the reporting and storing process of accidents data is often partial, prone to mistypes and confusions. In particular, the lack of information for each damage case often required subjective judgement. Filtering of data on the basis of clear mathematical relationships was often difficult, again, due to the fact that not all accidents contained all the necessary data. It was also impossible to keep only a set of fully consistent data, otherwise the sample would have become extremely small. It is therefore suggested that more efforts should be spent in the future in order to improve the recording and processing of accidents data, otherwise it is expectable that not negligible difficulties will arise in possible future tentative revisions of damage statistics for design and/or regulatory purposes. Finally, it is important to underline that present SOLAS regulation provides a probabilistic approach for what concerns the upper edge of the damage through the so called v-factor. However, SOLAS does not provide any probabilistic approach for the description of the position of the lower edge of damage, and a worst-case approach is presently used to deal with the lower damage edge. This matter needs further attention and the available database can help in developing a suitable distribution also for the position of the lower edge of damage.

Acknowledgments The authors are grateful to those GOALDS partners that provided literature, corrections and suggestions for the improvement of the present paper, in particular: Det Norske Veritas (DNV), Germanischer Lloyd AG (GL), Lloyds Register of Shipping (LR), National Technical University of Athens (NTUA), University of Strathclyde (SSRC).

References [1] Mains, C., "WP3 Database of damage characteristics - File: GOALDS-database-rev3.xls",

GOALDS , 8 June 2010. [2] Mains, C., "Updated damage statistics on collision and grounding", HARDER Document 1-

11-D-2001-01-1, 12 July 2001 [3] Lützen, M., "Damage Distributions", HARDER Document 2-22-D-2001-01-4, 29 July 2002 [4] Lützen, M., "Ship Collision Damages", PhD Thesis, Department of Mechanical Engineering,

Technical University of Denmark, December 2001 [5] Bulian, G., Francescutto, A., "Some considerations on the probability distributions for the

damage length and damage penetration based on a re-analysis of recorded ship collisions data", International Shipbuilding Progress, Vol. 52, No. 4, 2005, pp. 325-356.

[6] IMO, "SOLAS Consolidated Edition 2009", London, 2009

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[7] Pawłowski, M., "Subdivision and damage stability of ships", Euro-MTEC book series, Foundation for the Promotion of Maritime Industry, Gdansk, ISBN 83-919488-6-2, 2004, 311 pp.

[8] Pawłowski, M., "Probability of flooding a compartment (the pi factor) – a critique and a

proposal", Proceedings of the Institution of Mechanical Engineers, Part M: J. Engineering for the Mari-time Environment, 2005, Vol. 219, pp. 185–201.

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Nomenclature Quantity Units Definition x axis− -- Axis in longitudinal ship

direction, directed from stern to bow. 0x = at aft perpendicular.

y axis− -- Axis in transversal ship direction. Directed from starboard to portside. at centreplane.

0y =

z axis− -- Axis in vertical ship direction. Directed upwards. on the baseline.

0z =

damX [ ]m Longitudinal position of centre of damage.

xL [ ]m Dimensional damage length along x axis−

yL [ ]m Dimensional damage length along y axis− . In case of collision this is the damage penetration. In case of grounding this is the damage width.

zL [ ]m Dimensional damage length along z axis− . In case of collision this is the damage height. In case of grounding this is the damage penetration.

ppL [ ]m Ship length between perpendiculars

B [ ]m Moulded ship breadth

D [ ]m Moulded ship depth

CDF (or cdf ) [ ]− Cumulative distribution function

PDF (or pdf ) [ ]− Probability density function

ID Identification number of damage case according to GOALDS database

.coll bhX [ ]m Estimated reference position of collision bulkhead as

min 0.05 ,10pp ppL L− ⋅ m

Deliverable D 3.1


Appendix 1: The "potential" damage length

Introduction In [7][8] some theoretical concerns have been expressed regarding the determination of distribution of damage characteristics, particularly the damage length, starting from data available from the collision database. The problem has been addressed on the basis of mathematical considerations related to the domain/support of the random variables involved in the determination of the probability of flooding of a given set of compartments. The intention of this appendix is to provide a sort of "idealised physical model" on the basis of which the same results of [7][8] can be obtained. An example assessment of the influence of a more correct derivation of damage characteristics on the basis of [7][8] is also reported. We start from the simple idealised case in Figure A1.1, where a ship is struck by another ship, and the damage created by the striking vessel on the struck vessel is completely internal, i.e. the aft and forward end of the damage are internal with respect to the limits of the struck vessel. In this case the damage length that will be reported in a hypothetical database of collisions is simply the length of the damage caused on the hull of the struck vessel. In this case we say that the measured damage length is equal to the "potential damage length". In order to clarify what the potential damage length is intended to be, we refer to the case shown in Figure A1.2.

Figure A1.1: Idealised "internal" damage case.

Deliverable D 3.1


Figure A1.2: Idealised "aft" damage case.

In the idealised case shown in Figure A1.2 we see that the collision occurred in the aft part of the struck vessel. We can see that a certain damage length could be measured on the side of the struck vessel, and reported in a hypothetical database. Again, this is the "measured damage length". However, we can imagine that, if the striking vessel had collided with the struck vessel in a position sufficiently shifted forward with respect to the position reported in Figure A1.2, and assuming the same penetration, a longer damage could have been measured. The maximum damage length which could have been measured if the striking position had been different is indicated in Figure A1.2 as the "potential damage length". The situation is almost identical in case of "forward" damages. In case of aft damages, the forward end of the "measured damage length" coincides with the forward end of the "potential damage length", while in case of forward damages the aft end of the "measured damage length" coincides with the aft end of the "potential damage length". Let us now assume, just for idealisation purposes, that the "measured damage length" as reported in the database is the result of a large number of random collisions of the type shown in Figure A1.1 and Figure A1.2. The "measured damage length" embeds the characteristics of the distribution of the "potential damage length" as well as the limiting effects of the aft and forward end of the struck ship. Given the longitudinal position of the measured centre of damage damX ,

the following simple relation holds between the measured damage length xL , the "potential"

damage length ,x pL and the ship length:

,max , ,max

, ,max ,

,max

Zone "E":

Zone "I":

min 2 ,2 2

x x p x x

x p x x x p

x dam ship dam

L L L L

L L L L

L X L

< ⇒ =

≤ ⇒ =

= ⋅ ⋅ − ⋅ X

(A1.1)

The transformation of variables in (A1.1) is easily understandable using the usual Wendel diagram as shown in Figure A1.3.

Deliverable D 3.1


Basically, the relation (A1.1) provides a direct transformation from the unknown random variable

,x pL and the measurable random variable xL , where the random variable xL (measured damage

length) is obtained as a truncation of the random variable ,x pL (potential damage length), and this

truncation depends on the ship length and on another (measured/measurable) random variable

damX . In "Zone E", the too long, and hence not physically measurable, variable ,x pL is truncated

and transformed to the value . ,maxxL

Figure A1.3: Different truncation zones for the potential damage length.

It is not possible, for geometrical reasons, to consider the position of the centre of the measured damage damX and the measured damage length as independent, because the latter is

geometrically limited by the former. It is on the other hand more supportable, although approximate/idealised, to consider/assume the position of the centre of the measured damage

damX length and the "potential damage length" ,x pL as independent. The independence of such

variables is important for an easier determination of the "p-factors" in the way it has been done in the development of SOLAS.

Derivation of the cumulative distribution of the potential damage length Let us then consider the following three assumptions:

1) The random variable damX (measured) and the random variable ,x pL (not measurable)

are independent. 2) The random variable xL (measurable) is obtained from ,x pL (not measurable) through

(A1.1).

Deliverable D 3.1


3) The maximum value of the random variable ,x pL (not measurable) is smaller than the ship

length. On the basis of the reported three assumptions it is possible to determine the cumulative distribution of ,x pL starting from the knowledge of the measured distributions for damX and xL .

To describe how, we exploit Figure A1.4.

Figure A1.4: Different truncation zones for the potential damage length.

Let us assume xq to be a generic value for the damage length. The probability that a measured

damage length is smaller than or equal to the value xq can be expressed in terms of the joint

probability of ,x pL and damX , in general, as follows:

( ) ( )

( ) ( ) ( ) ( ) ( ) ( )

( ) ( )

Pr

Pr Pr

Pr Pr

Pr Pr

; ; 2 2

x x

x x dam A x dam A x

x x A x dam F x A x dam F x

x x F x dam F x dam

x xx ship A x F x ship

L q

L q X x q X x q

L q x q X x q x q X x q

L q x q X x q X

q qq L x q x q L

≤ =

= ≤ ≤ ⋅ ≤ +

+ ≤ < ≤ ⋅ < ≤

+ ≤ < ⋅ <

≤ = = −

+ (A1.2)

However, for geometrical reasons, since the measured damage length in the aft and forward part of the ship is limited by damX , it follows that:

Deliverable D 3.1


( ) ( )

Pr 1

Pr 1x x dam A x

x x F x dam

L q X x q

L q x q X

≤ ≤

≤ <

=

= (A1.3)

i.e. when ( )dam A xX x q≤ or ( )F x damx q X< the measured damage length xL is always smaller

than the value xq .

In the internal zone, where ( ) ( )A x dam F xx q X x q< ≤

,

, the truncation (A1.1) does not affect the

damage length, and hence in this region it is x x pL L≡ , hence:

( ) ( ) ( ) ( ) ,Pr Prx x A x dam F x x p x A x dam F xL q x q X x q L q x q X x q≤ < ≤ ≡ ≤ < ≤ (A1.4)

It is now useful to use the assumption of independence between the random variable damX and

the random variable ,x pL , according to which the conditional probability involving the potential

damage length in (A1.4) is equal to the marginal probability as:

( ) ( ) ,Pr Pr ,x p x A x dam F x x p xL q x q X x q L q≤ < ≤ = ≤ (A1.5)

By using (A1.5) and (A1.3), and substituting into (A1.2), we obtain:

( )

( ) ( ) ( )

,

Pr

Pr

Pr Pr

Pr

x x

dam A x

x p x A x dam F x

F x dam

L q

X x q

L q x q X x q

x q X

≤ =

= ≤ +

+ ≤ ⋅ < ≤

+ <

+

+

(A1.6)

By definition of cumulative distribution, equation (A1.6) can be rewritten as

( )( )( )

( ) ( )( ) ( )( )( )( )

,

1

x

dam

x p dam dam

dam

L x

X A x

L x X F x X A x

X F x

cdf q

cdf x q

cdf q cdf x q cdf x q

cdf x q

=

= +

⎡ ⎤+ ⋅ −⎣ ⎦⎡ ⎤+ −⎣ ⎦

(A1.7)

And finally, equation (A1.7) can be simplified to

( ) ( )

( ) ( ),

11

2 2

x

x p

dam dam

L xL x

xX F x ship X A x

cdf qcdf q

qcdf x q L cdf x q

−= −

⎛ ⎞ ⎛= − − =⎜ ⎟ ⎜⎝ ⎠ ⎝

xq ⎞⎟⎠

(A1.8)

In those cases where the probability density function of damX can be sufficiently approximated by

an, at most, linear function, the expression (A1.8) further simplifies and becomes independent of the actual distribution of damX . Indeed, if the probability density function of damX is linear:

Deliverable D 3.1


( ) 2 2

1 2 with 0, and ,2dam

shipX ship

2

ship ship ship

Lpdf x k x x L k

L L L⎡ ⎤⎛ ⎞

⎡ ⎤= + ⋅ − ∈ ∈ −⎢ ⎥⎜ ⎟ ⎣ ⎦⎢ ⎥⎝ ⎠ ⎣ ⎦

(A1.9)

it follows that, for whatever acceptable value of the angular coefficient , we have that: k

( ) ( )

( )2

2

2 2

1

dam dam

xship

dam

x

x xX F x ship X A x

qL

xX

q ship

q qcdf x q L cdf x q

qpdf x dxL

−

⎛ ⎞ ⎛= − − =⎜ ⎟ ⎜⎝ ⎠ ⎝

= = −∫

⎞ =⎟⎠

(A1.10)

and finally (A1.8) simplifies to (Pawłowski, M., 2009 - personal communication):

( ) ( ),

11

1

x

x p

L xL x

x

ship

cdf qcdf q q

L

−= −

−

(A1.11)

The relation (A1.8) is exactly the same, although in dimensional form, of the dimensionless relations in [7][8] (see, e.g., eq. (4) in [8]). From the application point of view the relation (A1.8) allows to obtain the not directly measurable cumulative distribution of the potential damage length ( ) starting from the distributions of

the measurable quantities ,x pLcdf

xL and damX .

It is important to state at this stage that all the developments reported here are based on an idealisation that, although it can be physically interpreted, is mostly mathematical in nature. The definition of the potential damage and the used assumptions are reasonable and have direct important implications. Indeed, this idealisation is extremely useful because:

It allows to develop a model for a random variable, the potential damage length ,x pL ,

which, by definition, is independent of the damage centre position damX .

The independence between ,x pL and damX can significantly simplify analytical

integration of probabilities as well as direct generation of damages according to the specified characteristics.

The correct application and use of the distribution of ,x pL , as obtained from (A1.8),

and of damX , as obtained from the statistics of damage, allow to get results (e.g. p-

factors) which are consistent with the distribution of the measured damage length xL .

A theoretical criticism which should be done to the development of p-factors in SOLAS, as pointed out in [8], is that the distribution as obtained from the damage statistics has been used as if

it were the distribution . As a consequence, present formulations for p-factors in SOLAS are

not fully consistent with the statistics of damage.

xLcdf

,x pLcdf

On the other hand, the numerical difference induced by this misuse of is likely small thanks

to the fact that the majority of damage lengths are usually not large in relation to the ship length. The next section shows an example of application of the reported procedure in order to compare

and .

xLcdf

xLcdf,x pLcdf

Deliverable D 3.1


An example of derivation of the distribution of the potential damage length Here we will show how much the cumulative distribution of the damage length and the cumulative distribution of the potential damage length can differ in a realistic case. We will consider that the probability density function of damX is sufficiently well approximated by an at most linear function,

and therefore we will use the relation (A1.11). In order to have a sufficient set of data we will consider ships having length 100 , and in order to collect data together we will

first approach the problem in dimensionless form by rewriting

150ppm L m< ≤(A1.11) as:

( ) ( )

,

11

1

;

p

x p xp

ship ship

cdfcdf

L LL L

λλ

λΛ

Λ

−= −

−

Λ = Λ = (A1.12)

which is consistent with [8], although it represents a small "stretching" of the idealised modelling referred above. As reference ship length we will use the ship length between perpendiculars. Results of the calculation are shown in Figure A1.5, from which it is clear that differences between

and cdfΛ pcdfΛ , and hence between and , are small. Moreover, as expectable from

the physics/mathematics of the problem, the distribution of the potential damage length is shifted towards longer damages with respect to measured damages which are necessarily smaller as a consequence of the truncation according to

xLcdf,x pLcdf

(A1.1).

Figure A1.5: Distribution of dimensionless potential damage length estimated from the cumulative

distribution of measured damage length for ships between 100m and 150m in length.

Deliverable D 3.1


Appendix 2: Marginal distribution of the dimensionless damage penetration It has been already reported that present SOLAS inherently assumes a maximum allowable ratio between the dimensionless damage penetration and the dimensionless damage length. We repeat here, for sake of easier reference, the assumed SOLAS conditional distribution of dimensionless damage penetration:

( )2

1 2

max

1 2

max

0 if 0

if 02

1 if

24 16 ; ; ; 5 5

1min ,152

y x

ship

cdf c c

L L c cB L

ηη

maxη λ η η

η η

η λ

η λ

<⎧⎪⎪= ⋅ + ⋅ ≤ <⎨⎪

≥⎪⎩

= = = − =

⎧ ⎫= ⎨ ⎬⎩ ⎭

η

(A2.1)

And the marginal distribution of the dimensionless damage penetration can be obtained by means of the following integration:

( ) ( ) ( )max

0

; y x

ship

cdf cdf pdf d

L LB L

λ

η η λ λ λ

η λ

= ⋅

= =

∫ (A2.2)

By combining (A2.1) and (A2.2) we can see that

( ) 212 161 15 15 5 5ship shipcdf cdf L cdf Lη ηη λ λ ηΗ Λ Λ

⎛ ⎞⎛ ⎞ ⎛ ⎞ η⎡ ⎤= = + − = ⋅ − ⋅ + ⋅⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎢ ⎥⎣ ⎦⎝ ⎠ ⎝ ⎠⎝ ⎠ (A2.3)

where the subscripts have been added to avoid confusions between the cumulative distribution of the dimensionless damage length and penetration. It is worth noticing that the cumulative distribution of the dimensionless damage length depends on the ship length, and for this reason this dependence has been highlighted explicitly in (A2.3). It must however be underlined that it is not clear, from the public documentation available concerning the development of the SOLAS, whether the limitation in the aspect ratio has been embedded in the factor using the "potential damage length" or using the damage length already considered truncated at the ends of the ship ("measured damage length"). For this reason the formula in

r

(A2.3) should be considered with caution, and the proper cumulative distribution for the dimensionless damage length should be used. If, in the development of SOLAS, the limiting aspect ratio was based on the cumulative distribution of the "potential damage length", then in (A2.2) and (A2.3) the underlying SOLAS distribution for the damage length should be used (because it is, or better it has been used as, a "potential damage length" distribution). On the other hand, if the SOLAS formulation took into account the limiting aspect ratio using the truncated damage length at the aft and forward part of the ship, the equations (A2.2) and (A2.3) should take into account the cumulative distribution of the truncated

Deliverable D 3.1


("measured") dimensionless damage length. It is however possible to exploit the results in Appendix 1 to rewrite (A2.3) in this case as

( )

2

1 1 115 15

12 161 115 15 5 5

p

p

ship

ship

cdf cdf L

cdf L

η ηη λ

η η λ η η

Η Λ

Λ

⎡ ⎤⎛ ⎞⎛ ⎞ ⎛ ⎞= − − = ⋅ − +⎢ ⎥⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠⎝ ⎠⎣ ⎦⎛ ⎞⎛ ⎞ ⎛ ⎞ ⎡+ − = ⋅ − ⋅ − ⋅ + ⋅⎜ ⎟ ⎜ ⎟⎜ ⎟

⎤⎢ ⎥⎝ ⎠ ⎣⎝ ⎠⎝ ⎠ ⎦

(A2.4)

However, since the difference between the cumulative distribution of the "potential damage length" and of the "measured damage length" are relatively small, as shown in Appendix 1, also the differences between the two approaches (A2.3) and (A2.4) are quantitatively small. This can be seen in the example shown in Figure A2.1. It can be seen that the effect of the limitation in the maximum aspect ratio for the dimensionless damage characteristics increases the probability of damages with small penetration.

Figure A2.1: Example of cumulative distributions of damage penetration.

ANNEX 2 SLF 55/INF.7

Grant Agreement No: 233876 Project Acronym: GOALDS Project Title: GOAL based Damage Stability

Deliverable D 3.2

Report detailing derivation of probability distributions of grounding damage characteristics for passenger ships

Document Id. GOALDS-D-3.2-GL- Grounding Damage Characteristics –rev1

Due date of Deliverable: 2010-05-31 Actual Submission Date: 2011-03-02 Christian Mains (GL) Gabriele Bulian (DINMA) -document autho /s-r Alberto Francescutto

final

-document approved by- -revision type- 2011-03-02

CO 1

-date o last updatef - t -distribu ion level-

1 dissemination level PU Public PP Restricted to Programme Participants (including Commission Services) RE Restricted to a group specified by the Consortium (including Commission Services) CO Confidential, only for members of the consortium (including Commission Services)

GOALDS-D-3.2-GL- Grounding Damage Characteristics –rev1 Page 1 of 21

Deliverable D3.2 Disclaimer

The information contained in this report is subject to change without notice and should not be construed as a commitment by any members of the GOALDS Consortium or the authors. In the event of any software or algorithms being described in this report, the GOALDS Consortium assumes no responsibility for the use or inability to use any of its software or algorithms. The information is provided without any warranty of any kind and the GOALDS Consortium expressly disclaims all implied warranties, including but not limited to the implied warranties of merchantability and fitness for a particular use. (c) COPYRIGHT 2009 The GOALDS Consortium This document may be not copied and reproduced without written permission from the GOALDS Consortium. Acknowledgement of the authors of the document shall be clearly referenced. All rights reserved.

Document History Document ID. Date Description GOALDS-PR-09/2009-to-03/2010-WP 3.1/2-Progress-Report–rev0 2010-03-24 Draft

GOALDS-PR-09/2009-to-03/2010-WP 3.2 Report final–rev0 2010-09-03 Final draft

GOALDS-PR-09/2009-to-03/2010-WP 3.2 Report final–rev1 2010-10-28 Final

GOALDS-D-3.2-GL- Grounding Damage Characteristics –rev1 2011-03-02 Final


Deliverable D3.2 Document Control Sheet Title: Grounding Damage CharacteristicsAbstract In the framework of GOALDS "Task 3.2 - Grounding Damage Characteristics" grounding accidents data have been collected and statistically analysed, critically considering the strength and weaknesses of this approach. The casualty data was mainly derived from classification societies damage files with under the condition of water ingress as a consequence of the accident. The casualty data collected in GOALDS allowed to increase the database of HARDER grounding data by about 51% compared to the original HARDER database. Grounding damage characteristics for those accidents resulting in hull penetration have been statistically analysed with the aim of: a) describing grounding damage position and dimensions, and b) evaluating present SOLAS minimum double bottom height requirements and deterministic bottom damage requirements. In the analysis of grounding damage characteristics, full and not full hull forms have been dealt with separately in order to highlight possible different behaviours. SOLAS requirements have been assessed by estimating the probability of penetrating a double bottom constructed in marginal compliance of SOLAS standards and by calculating the probability of exceedance of bottom damage dimensions as specified by SOLAS. The obtained probabilities of exceedance of bottom damage dimensions have been compared with known figures available from IMO documentation. In the course of the work, a statistical analysis has also been performed on the ship speed at the moment of grounding. Summary Report: Introduction In accordance with the GOALDS project description, the focus of Task 3.2 was on grounding damage characteristics, work that started but was never completed in project HARDER. The expected main goal of Task 3.2 was the statistical description of grounding damage characteristics in accordance with collected data, with particular attention, but not limited to, the case of passenger vessels. To achieve this target, grounding accidents data have been initially collected. The collected data have been carefully scrutinized in order to remove, as far as feasible, double entries, mistyped data, etc. Such checking has been carried out partially manually and partially automatically. A statistical analysis has been carried out using the "clean" database addressing different aspects of the grounding problem. In particular, the statistical analysis was aimed at:

a) Describing grounding damage position and dimensions b) Evaluating present SOLAS minimum double bottom height requirements and deterministic bottom damage requirements.

In carrying out the analysis of damage dimensions and position, particular attention has been given to the determination of specific information for passenger vessels. Due to the lack of specific data for passenger vessels, however, a broader category of vessels has eventually been considered, i.e. the category of "not full hull forms", to which passenger ships typically belong. During the analysis it was indeed shown that the behaviour observed for damages to "not full hull forms" could be considered representative also for passenger vessels. The category of "full hull forms", to which tankers and bulk carriers typically belong, has been considered alongside. Some differences in terms of damage position and dimensions have been highlighted between the two considered groups. In the evaluation of present SOLAS minimum double bottom height requirements and deterministic bottom damage requirements, all ships, with the exception of tankers and fishing vessels, have been considered. The analysis was aimed at obtaining mainly two type of information using grounding data collected in GOALDS. Firstly, the SOLAS minimum double bottom height requirements were considered. The probability of penetrating the inner bottom plating has been


Deliverable D3.2

estimated, using the collected data, in the case of grounding accident if the ship is constructed in marginal compliance with SOLAS minimum double bottom height requirements. Secondly, the probabilities have been estimated that damage dimensions resulting from a grounding accident are larger than the bottom damage dimensions specified by SOLAS Chapter II-1 - Part B-2 - Regulation 9 in case of ships with alternative double bottom arrangements. The obtained probability levels have been compared with those reported in the IMO document SLF47/INF.4, which is part of the background for the development of Regulation 9. State of the Art Presently IMO SOLAS regulations try to guarantee a sufficient level of safety in case of grounding accident by specifying minimum double bottom height requirements or, in case of ships (partially) not fulfilling such requirements, by requiring the ship capability of withstanding deterministic bottom damage with specified dimensions and position. Such requirements were developed using a limited set of data and during HARDER project grounding damages were not thoroughly analysed. It is therefore necessary to clarify whether, on the basis of newly collected data, there is any need to revise such requirements. Moreover, a quantitative, accepted, probabilistic description of grounding damage characteristics is, in general, not available from for use in risk models and/or probabilistic approaches at industrial, regulatory and research level. Value added to GOALDS This task delivers one of the main inputs to the project. The statistical analysis of these grounding data and its further interpretations will direct the project’s recommendation to regulatory institutions and will provide input for risk modelling, experimental tests, etc. Achievements The major achievements from Task 3.2 are detailed in the present deliverable and associated annexes. However, they can be very briefly summarised as follows:

1) Creation of a reference database for grounding damage characteristics. This database can be used for further and more refined statistical analyses.

2) Statistical description of grounding damage characteristics by separately considering full from not full hull forms. The obtained results can be used to develop probabilistic as well as deterministic (minor damage) approaches for grounding survivability.

3) Statistical description of the speed of the ship at the moment of grounding. The obtained results can be used in risk models and/or direct numerical simulations.

4) Estimation of the probability of penetration of inner bottom during a grounding accident in case of construction marginally compliant with SOLAS minimum double bottom height requirements. The obtained results can be used to assess the appropriateness of present SOLAS standards and provide quantitative background for possible correction actions if deemed necessary.

5) Estimation of the probability of exceedance of grounding damage dimensions specified by SOLAS in case of alternative double bottom arrangements. The obtained results can be used to assess the appropriateness of present SOLAS standards and provide quantitative background for possible correction actions if deemed necessary.

Not achieved …. Input from other Deliverables None How the results relate to the overall goals of GOALDS The obtained results are fully integrated with the overall GOALDS project. Indeed, data collected in this task and the associated statistical analysis represent a probabilistic description of grounding damage extent and position. From such a description, specific mathematical models can be developed for the distributions of damage dimensions and position. Such information can be used, in principle, to set-up a fully probabilistic approach for the survivability to grounding damages. In


Deliverable D3.2

addition, or as an alternative, the obtained distributions allow to determine, in principle, deterministic (minor damage) requirements after specifying acceptable exceedance probability levels. The generality of the obtained results make them an important background for further development in the direction of both probabilistic and/or deterministic approaches to grounding damage survivability assessment. In addition, the obtained results, possibly combined with the associated mathematical modelling, can be used to update IMO requirements for minimum double bottom height and/or deterministic bottom damage requirements, if deemed necessary, after specifying acceptable probability levels. All these aspects are strongly related with the overall goals of GOALDS.

This executive summary may be published outside the GOALDS consortium. NO

Work carried out by Approved by

Sigmund Rusaas, DNV Odd Olufsen, DNV Spyros Hirdaris, LR Henrik Erichsen, LR Gabriele Bulian, DINMA Alberto Francescutto, DINMA Christian Mains, GL.

Alberto Francescutto

- signature on file - - signature of internal reviewer and date of acceptance -

Dracos Vassalos

- signature on file -

- signature o external reviewer and date of acceptancef -


Deliverable D3.2 Table of contents

1 INTRODUCTION........................................................................................................................................ 7 2 IDENTIFICATION AND COLLECTION OF CASUALTIES ............................................................... 7

2.1 DATABASE ............................................................................................................................................. 7 2.2 GROUNDING CASUALTIES ....................................................................................................................... 8

3 STATISTICAL ANALYSIS GROUNDING............................................................................................ 11 4 MAJOR PROBLEMS................................................................................................................................ 14 5 RESULTS OF THE STATISTICAL ANALYSIS................................................................................... 14

5.1 GENERAL COMMENTS........................................................................................................................... 14 5.2 LONGITUDINAL POSITION OF THE CENTRE OF DAMAGE XDAM ................................................................ 15 5.3 LONGITUDINAL DAMAGE EXTENT LX .................................................................................................... 15 5.4 TRANSVERSAL POSITION OF THE DAMAGE............................................................................................ 16 5.5 TRANSVERSAL DAMAGE EXTENT LY ..................................................................................................... 16

5.5.1 Analysis of not-full ships ................................................................................................................. 16 5.5.2 Analysis of full ships........................................................................................................................ 17

5.6 DAMAGE PENETRATION LZ ................................................................................................................... 18 6 CONCLUSIONS AND RECOMMENDATIONS ................................................................................... 18 REFERENCES.................................................................................................................................................... 21 LIST OF ANNEXES........................................................................................................................................... 21


Deliverable D3.2

1 Introduction This task will focus on grounding damage characteristics, work that started but was never completed in project HARDER; moreover, the emphasis will now be placed on passenger ships. To this end, starting with the GL HARDER database, all available information on grounding accidents around the world for the past 30-50 years will be collated, and analyzed. There is a critical mass of stakeholders in the project to ensure that such information shall be made available, namely Classification Societies, Ship Owners and National Administrations. Such data, with additional data sought form other sources (e.g., P&I Clubs) will be gathered, scrutinised for quality and consistency and further analysis. Such analysis will target appropriate distributions of grounding damage characteristics, similar to collision damages. In case where available data is not sufficient, appropriate numerical studies will again be undertaken and verified to fill any gaps. In particular, it is anticipated to encounter some problems in substantiating models of penetration depth and ensuing effective damage length (the actual length which results in major compartments flooding beyond double bottom) with statistical information alone. In this case, simplified models with verification by FEM studies will need to be deployed to develop suitable formulations for probability distributions of grounding damages for passenger ships, appropriate to serve as international regulatory instrument. Efforts will be expended to ascertain compatibility of these methods with the formulations adopted by IMO in Resolution MSC 216 (82) on Dec 2006 and entering into force on 1 January 2009.

2 Identification and collection of casualties Part of task 3.1 and 3.2 was to collect new casualty data for collision and groundings to combine the data with the data collected during the EU research project HARDER. Within the HARDER project data from IMO damage cards, classification societies damage repair reports and damage reports from the former GDR register have been considered. The HARDER database has been re-checked and if available, additional data has been implemented. New casualty data (after 2000) has identified by searching Lloyd’s Register Fairplay casualty database (LRF). LRF cases that were identified as serious have been selected and sorted with respect to the IACS society. Cases identified for consortium members have been submitted to DNV, GL and LR. From these classification societies’ data has been delivered. An attempt was made to gain additional data from ABS, BV and RINA, which results in no further data. ABS had legal restrictions. BV and RINA did not reply on the inquiry. The definition of serious is quite open according to LRF database. It seems not only depending on fatalities/injuries but will be judged by the reporting party (e.g. stranding of tanker without oil outflow is reported as serious case). Having had a close look into LRF more serious casualties as non serious were found. During the collection of data from the consortium members, it turned up that not all identified serious LRF cases were showing penetrations of the hull. That is the reason for the small number of casualties implemented compared to the identified numbers. It was agreed during the kick off meeting in Athens that only cases with hull penetrations shall be collected and used for further analysis.

2.1 Database The collected casualty data has been filtered according to the following conditions:



Three kinds of casualties have been identified: collision, grounding and contact.


The selected datasets have been statistically analysed in depth.

Deliverable D3.2 Actually, 1527 cases have been identified for collision, grounding and contact within the database. This data set has been used to start the statistical analysis (see item 3.2). Collision Grounding Contact HARDER 832 312 35 1179GOALDS 184 160 4 348database 1016 472 39 1527



Bulk Carrier7%

Container11%

General Cargo47%

Passenger/RoRo7%

Tanker24%

other4%

Figure 1: Distribution of the GOALDS database ship types

2.2 Grounding casualties The new casualty data collected during the GOALDS project was submitted from the classification societies that are member of the consortium and some additional data were derived form internet search. To check whether damage dimensions vary with intervals of the casualty date or building year several charts have been plotted in the interim report. When limiting the casualty date to the last 20 years it turned out that especially for passenger ships the sample date is small. Therefore, it was decided to use the complete sample data. Investigation about change of rules that have influenced the construction of ships has been carried out with no significant findings. Neither classification rules nor SOLAS amendments were identified to have changed the construction significantly in a short time period. Such changes can be identified in damage dimensions within the decades, only, analogous to the increasing number of newbuildings designed according to the new rules. During the evaluation of the grounding casualties, multiple damages for one grounding case were found. This is often the case when ships are grounding on rocks. Several cases were identified with up to 16 penetrations of the bottom shell plating. Figure 5 is showing the non-dimensional longitudinal location and damage length of the multiple damage case 2473 over the number of penetrations. The horizontal bars are representing middle of the penetration’s longitudinal location of the penetration and the small vertical lines are representing the non-dimensional damage length.


Deliverable D3.2


Case 2473

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

#

X/Lp

p, l/

Lpp

Figure 5: Case 2473 with 15 penetrations of the bottom shell As many of those damages are small but widely spread over the ships bottom it was decided among the WP 3.2 partners (during the Hamburg meeting March 2010) to exchange the multiple damages of each case by one equivalent damage. An equivalent damage covers the length of the damaged area and has a mean width (considering the mean width of all given width). Proceeding like this ensures that the small damage lengths (see figure 8 and 9) will not be overestimated. In two cases were the damage length is greater than the distance between the longitudinal location of the damages the damage length was calculated by addition of the given damages lengths. The longitudinal location of the equivalent damage was adjusted to the middle of the damage lengths resulting in a shift of the damage location (see figure 6 and 7) to the forward part of the ship. Data with regard to the transverse offset coordinate is not available for the bottom damages. Considering this, the mean value of all given damage widths were considered as substitute.

Grounding data (org vs. equiv)

0,00,20,40,60,81,01,21,41,61,8

-0,1 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 1,1

X/Lpp

PDF

pdf - orgpdf - equiv

Figure 6: Comparison between PDF (X/Lpp) considering all cases as single versus equivalent

Deliverable D3.2



0,00,10,20,30,40,50,60,70,80,91,0

-0,1 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 1,1

X/Lpp

CDF

cdf -orgcdf - equiv

Figure 7: Comparison between CDF (X/Lpp) considering all cases as single versus equivalent


0,0

2,0

4,0

6,0

8,0

10,0

12,0

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

l/Lpp

PDF

pdf - orgpdf - equiv

Figure 8: Comparison between PDF (l/Lpp) considering all cases as single versus equivalent


0,00,10,20,30,40,50,60,70,80,91,0

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

l/Lpp

CDF

cdf -orgcdf - equiv

Figure 9: Comparison between CDF (l/Lpp) considering all cases as single versus equivalent The casualty database substituting the multiple damages cases with the equivalent grounding damage cases have been used for the statistical analysis. PDF and CDF Charts of the selected casualties with and without multiple damages are shown in annex 1.

Deliverable D3.2

3 Statistical analysis grounding The statistical analysis has been carried out by DINMA (see Annex 3). An extract from this analysis is shown below. One of the most significant differences between vessel types can be found in the longitudinal centre of damage Xdam if the vessels will be grouped into 2 categories. Looking at typical bottom lines (see figure 10) the category of full vessels will be represented by tanker and bulk carriers and the category of not-full vessels will be represented by general cargo, container and passenger vessels.

Figure 10: Typical bottom lines For sake of direct comparison, figure 12 reports the cumulative distribution of the non-dimensional position of the centre of damage for full ships and for not-full ships. In addition, also the cumulative distribution for the same quantity has been estimated using the whole set of data (i.e. full and not full ships together). Similarly, a direct comparison of histograms of relative frequency is proposed in figure 11.

FP

Container Ship


Deliverable D3.2


Figure 11: Comparison of histogram of relative frequency of Xdam/Lpp in case of full ships, not full ships and in

case of using the complete database.

Figure 12: Comparison of estimated CDF(Xdam/Lpp) in case of full ships, not full ships and in case of using the

complete database By looking at figure 11 and 12 it can be seen that, of course, the distribution obtained by using the whole set of data is a sort of weighted average between the distribution of full ships and not-full ships, with a tendency towards that of not-full hull forms due to the larger number of data. Before closing the exploratory data analysis on Xdam it is worth comparing, only for qualitative indication, the cumulative distribution of Xdam/Lpp as obtained for passenger ships, with those obtained for full and not full ships. Figure 13 contains this comparison. Of course, the limited number of passenger vessels available in the database prevents any statistically significant conclusion, however it seems that the distribution observed for passenger vessels is more similar to, and could therefore be represented by the distribution obtained from the set of data for not-full hull forms.

Deliverable D3.2


Figure 13: Comparison of CDF(Xdam/Lpp) between passenger ships, not full ships and full ships. Looking at the non-dimensional longitudinal extent of the damage versus the ship’s length (see figure 14) the relative damage length of ships with a length of 100m and more is located between 0.15 and 0.25 Lpp.

Figure 14: ELx/Lpp | Lppfor full ships and not-full ships A clear tendency of smaller damage length for full ships can be observed up to a ship length of 150 m. Considering that the number of observed bottom damages for not-full ships is decreasing from about 30 for 150 m ships down to below 10 for 200 m ships and that there are practically no further statistical relevant damage cases for not-full ships beyond 200 m (see figure 15) the results of the statistical analysis for ships greater than 200 m should observed cautiously.

Deliverable D3.2


Figure 15: Number of points in each window for the analyses.

4 Major problems A general note concerning the quality of the available accidents database is necessary to be implemented within the final report of the project. Despite all the efforts spent to remove doublets, wrong cases, etc. it is not possible to say that the quality of the data is high, but rather average to low. The reasons can be found in the fact that the reporting and storing process of accidents data is often partial, prone to mistypes and confusions. In particular, the lack of information for each damage case often required subjective judgement. Filtering of data based on clear mathematical relationships was often difficult, again, because not all accidents contained all the necessary data. It was also impossible to keep only a set of fully consistent data, otherwise the sample would have become extremely small. It is therefore suggested that more efforts should be spent in the future in order to improve the recording and processing of accidents data, otherwise it is expectable that not negligible difficulties will arise in possible future tentative revisions of damage statistics for design and/or regulatory purposes.

5 Results of the statistical analysis

5.1 General comments • Due to the very limited number of samples (only 22) in the database that are associated to

passenger vessels, it is in general not possible to draw specific conclusions associated with this ship type with a reasonable level of confidence. For this reason, any indication for this ship type, when derived from the statistical analysis, is to be considered with extreme caution bearing in mind the very limited sample of data.

• Data for "full hull forms", i.e. tankers and bulk carriers, are 138, while "not-full hull forms" represent 221 entries in the database, with a resulting ratio of 1.6. It follows that in the analyses involving all data, the final results could be mainly driven by the sample of not-full hull forms. However, according to the availability of data, this ratio changes depending on the particular analysis. Therefore, the dominant subset, if any, depends of the specific quantity under analysis.

• The majority of not-full ships belong to the range of the relatively short lengths (small ship sizes), while full ships belong in the majority of cases to the range of long ships lengths (large ship sizes). Any comparison between the two classes of ships should therefore be considered

Deliverable D3.2 with caution, because full ships are mainly governed by the behaviour of large ships, while not-full ships are mainly governed by the behaviour of smaller ships.

• There are indications that data coming from the HARDER database could have not been in all cases correctly identified as multiple damages belonging to the same casualty.

5.2 Longitudinal position of the centre of damage Xdam • For both full and not-full ships it seems justifiable, from the engineering point of view, to use

a unique distribution for the non-dimensional longitudinal position of the centre of damage Xdam/Lpp irrespective of the ship dimensions.

• The distributions of Xdam/Lpp in case of full ships and in case of not-full ships show some differences. In particular, the centre of damage tends to occur with higher probability in the forward part of the ship for full ships, while not-full ships tend to have a centre of damage shifted towards the central part of the hull.

• Of course, the limited number of passenger vessels available in the database prevents any statistically significant conclusion. However, it seems that the distribution of Xdam/Lpp observed for passenger vessels is more similar to, and could therefore be represented by, the distribution obtained from the set of data for not-full hull forms.

• A statistical analysis has also been performed for the non-dimensional position of the forward end of damage, i.e. XF, dam/Lpp. According to the obtained results it could be said that, overall, the variable XF, dam/Lpp seems to show less systematic dependence of the characteristics of its distribution from the ship length. In this respect it could be considered more appropriate / manageable than the variable Xdam/Lpp for characterising the position of bottom damages along the ship.

• The probability density function of XF, dam/Lpp tends to have a prominent peak in the forward region of the ship (say forward of about 0.9 Lpp), both in case of full hull forms and in case of not-full hull forms, and the peak is more evident in case of full hull forms.

• The magnitude of the forward peak of the probability density function of XF, dam/Lpp can be quantitatively appraised by reporting that 50% of the damages have a forward end of damage XF, dam which is forward of about 0.75 Lpp for not-full hull forms and forward of 0.87 Lpp for full hull forms. While 30% of the damages have a forward end which is forward of 0.89 Lpp for not-full hull forms, and forward of 0.94 Lpp for full hull forms.

5.3 Longitudinal damage extent Lx • There are 309 cases reporting the longitudinal extent of damage Lx. In this sample, 131 cases

belong to full hull forms, while 178 cases belong to not-full hull forms. For what concerns specifically passenger vessels, 17 reported cases, on a total of 22 passenger vessels in the database, contain information on the longitudinal damage extent.

• For not-full ships, apart from the region of small ships, with length around 50m-70m, is not strongly dependent on the ship length, and it tends to become almost constant, or slightly increasing as the ship length increases. Short ships show a smaller conditional average non-dimensional damage length. At the same time the median value of Lx./Lpp tends to systematically increase as the ship length (and hence the ship size) increases.

• For full ships there is a clear tendency of Lx./Lpp to increase, almost linearly, as the ship length increases up to about 150m, whereas for longer ships Lx./Lpp becomes almost constant. A very similar behaviour is evident also for the median value of Lx./Lpp.

• In the region of lengths between 50m and 100m the distributions of Lx./Lpp for full ships and not-full ships are significantly different, with full ships showing smaller damages. In the region of ship lengths between 125m and 175m the obtained distributions of Lx./Lpp for the two subsets are close, and differences are small.

• From a systematic application of a two-sample Kolmogorov-Smirnov test for different ranges of ship length, it has been observed that differences in the distribution of Lx./Lpp between full ships and not-full ships are statistically significant mainly in the range between, roughly, about 60m and 120m. Outside these range differences among the distributions are statistically not significant. This is partially because the distributions are actually similar, but also to the fact


Deliverable D3.2 that there is a lack of data for both full and not-full ships in the small length range and, particularly, a lack of data for not-full ships in the range of large lengths. We could roughly say that differences in the distributions for the dimensionless damage length between full and not-full ships should be considered not negligible below a ship length of about 120m and negligible for longer ships.

• There is a good agreement between the distribution of Lx./Lpp obtained for all passenger vessels and that obtained using all ships not shorter than 80m. At the same time the maximum observed dimensionless damage length for passenger vessels is smaller than that observed in the sample of all ships not smaller than 80m. However, the number of data for passenger vessels is too limited to draw any conclusion and the hypothesis of equal distributions is not rejected by a two-sample Kolmogorov-Smirnov test at 5% significance level.

• In a tentative of explanation of the differences observed for the behaviour of CDF(Lx/Lpp I Lpp) between small ship lengths and large ship lengths for full ships, an analysis of the database has been carried out separating the available data based on their source as reported in the database. The length of about 150m, which has been observed to mark, approximately, a change of behaviour in CDF(Lx/Lpp I Lpp) for full ships from ship-size-dependent (small ships) and ship-size-independent (large ships), well agree with a sharp separation of the data among two main sources, namely "DNV_IMO" and "IMO". A similar sharp separation among different data sources is not present in case of not-full ships. Although the analyses carried out cannot be considered to represent a proof of a link between the source of the data and the differences in the behaviour of CDF(Lx/Lpp I Lpp) observed between small and large ship lengths for full ships, this point should deserve some more attention and further analysis.

5.4 Transversal position of the damage The database does not contain any information concerning the transversal position of bottom damages. In absence of such information, it could be assumed that the centre of the damage is uniformly distributed in transversal direction.

5.5 Transversal damage extent Ly • A total of 210 cases, i.e. 58.5% of the total entries in the database, contain information on

the damage width, with 41 cases added in the framework of GOALDS (19.5% of data), and 169 cases, 80.5% of the sample, coming from the HARDER project. Of the total 210 cases, 112 (53.3%) belong to full ships, while 98 (46.7%) belong to not-full ships.

• Only 13 cases, namely less than 6.2% of the total 210 data containing the damage width, belong to passenger vessels. It is therefore clear that any derivation of specific information for passenger vessels on the basis of only 13 points is impossible due to the excessive uncertainty in the statistical estimators.

• The analysis of data has been split in two separate parts: analysis of not-full ships and analysis of full ships.

5.5.1 Analysis of not-full ships • Data are available mainly in the range of breadths below 20m-25m. In particular there are no

data for post-panamax vessels. • There is an evident difference between the population collected in GOALDS and the other

data, with GOALDS data belonging all to the region of (very) small ratios Ly/B. • The analysis of ELy/B I B and of the percentile levels of CDF(Ly/B I B) seems to indicate the

suitability of a ship-size independent model, at least from ship breadths up to 20m. For larger ship breadths, the situation is very doubtful, with a significant effect of damages collected in GOALDS, which are mainly of small size, and which lead to a significant shift of the distribution of Ly/B towards smaller values of dimensionless damage width as the ship breadth increases above about 20m.

• The sharp shifting of the distribution towards smaller damages in the region governed by data collected in GOALDS is quite doubtful. This behaviour seems especially doubtful when looking at the final windows for the extreme breadths, where GOALDS data are accompanied by data


Deliverable D3.2 from other sources, and consequently, the characteristics of damage tend to shift again towards larger dimensionless widths.

• It is difficult to provide a definite conclusion without the availability of additional data, however it seems reasonable to keep the indication given by data for B ≤ 20 m, i.e. the indication of the suitability for a common distribution of Ly/B independent of the actual ship breadth (size). On the basis of this assumption (that, however, needs more data to be fully justified or rejected) a common cumulative distribution CDF(Ly/B) for not-full ships has been estimated from the database, with an average damage width of about 0.1 B, and precisely

[ ]95%/ 0.1062 0.0740,0.1384y CI

E L B =.

5.5.2 Analysis of full ships • There is a sharp separation in terms of ships size between data coming from different sources,

particularly "IMO" and "DNV_IMO", with this latter data mainly belonging to the range of breadths above 25m and the former being associated mainly with the range of smaller breadths. This aspect has been found to significantly drive the statistical estimators.

• GOALDS data are mostly in the region of breadths below 28m. • The behaviour of the dimensionless damage width Ly/B seems to change abruptly when

moving from small breadths, below about 25m, to large breadths, above about 25m. In both ranges, a non-dimensional approach for the damage width seems to be appropriate; however, the characteristics of the distribution in the two ranges are significantly different, with a significant shift towards large dimensionless damage widths in the range of large ship breadths.

• The quite sharp separation between the two behaviours seems to be related to the effect of the two main sources of data, namely "IMO" and "DNV_IMO". A series of checks concerning this aspect have been carried out, as well as a check of the dependence of the average dimensionless damage width on the data source. The finding is that the influence of the data source seems not negligible, and the largest ELy/B is obtained in case of source "DNV_IMO".

• According to the available data, two options have been considered suitable for the modelling of the distribution of the dimensionless measured damage width. As an interim, to some extent questionable, solution, it could be decided to use all the data for developing a reference CDF(Ly/B) irrespective of the ship size. The alternative would be the creation of two separate cumulative distributions for the region of large breadths and for the region of small breadths, with a blending in the intermediate zone. These two options, apart from the blending, have been analysed, and the corresponding distributions have been estimated. The estimation for the cumulative distribution of Ly/B) by separating ships with B ≤ 25 m from ships with B > 25 m allowed to clarify that the differences in the two distributions are significant.

• When considering a single distribution CDF(Ly/B) for full ships, then

[ ]95%/ 0.2028 0.1509,0.2547y CI

E L B =.

• When considering a separation of full ships for B ≤ 25 m and B > 25 m, the average dimensionless damage widths are significantly different, with

[ ]95%/ 25 0.0920 0.0565,0.1274y CI

E L B B m≤ = and

[ ]95%/ 25 0.2693 0.1924,0.3461y CI

E L B B m> =.

• Comparisons have been carried out between the distributions of dimensionless damage width

as obtained for full and not-full ships. If a single distribution for Ly/B, irrespective of the ship size, is considered for each category, it can be seen that full ships show significantly larger damage widths than not-full ships, with an average dimensionless damage width for full ships which is almost twice as the value for not-full ships. However, when separating full ships into two groups, i.e. B ≤ 25 m and B > 25 m, it can be seen that the cumulative distribution of Ly/B for not-full ships and that for full ships with breadths not larger than 25m are quite


Deliverable D3.2 comparable, as well as the mean values. Whilst the distribution of Ly/B for full ships with B > 25 m is significantly different and strongly shifted towards wider dimensionless damages.

5.6 Damage penetration Lz • Data available for Lz (125 cases) mainly belong to the class of full ships (83 cases), with not-

full ships representing a minority (42 cases). • The available data for full and not-full ships are not evenly distributed in the range of ship

sizes. Indeed, data for full ships mainly belong to the range of ship lengths above 150m (about 82% of full ships data), while data for not-full ships are almost completely belonging to ships having less than 150m in length (about 91% of not-full ships data). A similar situation occurs in terms of ship breadth, with about 90% of cases for not-full ships being associated with breadths smaller than 20m, and about 82% of cases of full ships being associated with breadths above 20m. This situation creates difficulties in obtaining directly comparable statistics between full and not-full ships in similar regions of ship size.

• Only 3 cases reporting Lz are available for passenger vessels, and therefore it is impossible to provide any statistics for this specific ship type for what concerns bottom damage penetration.

• In all but two cases, penetrations are smaller than 4.2m, and only one reported case has a penetration of 7m.

• The analysis of the average dimensional and dimensionless damage penetration as a function of the ship breadth does not indicate significant differences between full ships and not-full ships in the range of ship breadths where the two categories can be compared. Therefore, for what concerns the damage penetration, the same distributions could be used for both full and not-full ships. More precisely, there is no evidence for the necessity of considering different distributions for full and not-full ships.

• The behaviour of the distribution of the bottom damage penetration Lz is not simple, and cannot be perfectly represented for any generic ship size neither with a dimensional approach using CDF(Lz) nor with a non-dimensional approach using CDF(Lz /B). However, among these two extreme possibilities, it seems that a completely dimensional approach, based on a common CDF(Lz) irrespective of the ship size, could provide a quite good agreement with the distributions of damage penetration obtained in different ranges of ship breadths. This agreement can be considered more robust than what has been observed when trying to use a common distribution for CDF(Lz /B) irrespective of the ship size. It seems therefore that a fully dimensional approach for any ship size, with CDF(Lz) obtained from the available data, and a maximum damage penetration of the order of 5m, could be a good balance between simplicity and accuracy. However, this selection depends on the range of application in terms of ship dimensions: by limiting the range of ship dimensions, more accurate, and still simple, approximations can likely be found.

6 Conclusions and recommendations The analysis of grounding data carried out in Task 3.2 is quite extensive. Detailed information can be found in this document and in the associated annexes. It is however possible to provide an extreme summary of the main findings:

1) The statistical analysis of grounding damages has been carried out separating "full ships" (tankers and bulk carriers) from "not full ships" (all the other ships). It has been found that the behaviour of passenger vessels, for which very few data are available, can be represented by that of "not full ships".

2) For what concerns grounding damage dimensions and position: a. There are no information in the database concerning the transversal position of

damage. b. The distribution of the position of damage is different between full and not full ships,

with a tendency for full ships to suffer damages more forward with respect to not full ships.

c. The longitudinal position of the forward end of damage seems to be a better variable for describing the positioning of the damage in comparison with longitudinal position


Deliverable D3.2 of the centre of damage. The distribution of the longitudinal position of the forward end of damage has a significant peak in the forward part of the ship.

d. The distribution of damage penetration has a complex behaviour requiring more investigation (see Task 3.4).

e. The distribution of the damage length seems to be not significantly different between full and not full ships.

f. The distribution of the transversal damage extent is significantly different between full and not full ships.

g. Statistical dependencies among different variables characterising the damage position and dimensions have been identified.

h. The distribution of the ship speed at the moment of grounding has been analysed separately for full and not full ships showing some differences in the behaviour, with a tendency for full ships to suffer grounding at lower speeds with respect to not full ships.

3) The assessment of SOLAS Chapter II-1 - Part B-2 - Regulation 9 requirements and assumptions has been carried out omitting tankers and fishing vessels. The collected data and the performed analysis allowed to obtain the following estimations:

a. The probability that, in case of grounding, the inner bottom is penetrated if it is constructed according to minimum required SOLAS double bottom height.

b. The probability that, in case of grounding, the damage extent is larger than that assumed by SOLAS.

4) The probability that, in case of grounding, the inner bottom is penetrated if it is constructed according to minimum required SOLAS double bottom height has been determined as follows:

a. In case of standard ships: [ ]95%27.3% 16.1%,41.0%

CI

b. In case of passenger ships with large lower holds: [ ]95%14.5% 6.5%,26.7%

CI

5) The probabilities of exceedance of bottom damage characteristics assumed in SOLAS as estimated in this Task are overall in line with those reported in the IMO Document SLF47/INF.4 containing proposals very close to what is presently implemented in the definitions in Regulation 9. A strictly exact comparison between present analysis and SLF47/INF.4 was not possible due to the slightly different definitions of the events under analysis. However, some indicative comparison between probability levels were possible with reference to standard requirements:

a. Exceedance of SOLAS bottom damage length: This analysis: - SLF47/INF.4: 43% [ 95%

54.6% 47.6%,61.6%CI]

]

]

b. Exceedance of SOLAS bottom damage width: This analysis: - SLF47/INF.4: about 38%-40% [ 95%

18.2% 11.5%,26.7%CI

c. Exceedance of SOLAS bottom damage penetration: This analysis: - SLF47/INF.4: about 26%. [ 95%

29.1% 17.6%,42.9%CI

The obtained probability levels are, overall, quite in line with those in SLF47/INF.4 (damage width is an exception), with the probability of exceeding the SOLAS bottom damage length being larger in the present analysis, the probability of exceeding the SOLAS damage width being significantly smaller, and with comparable probability levels for what concerns damage penetration. This means that probabilities of exceedance of SOLAS bottom damage dimensions have been found to be, overall, quite in line with those estimated, and implicitly agreed at IMO, at the time of development of Regulation 9.

6) In general, despite all the efforts spent to remove doublets, wrong cases, etc. it is not possible to say that the quality of the database is high. Sufficiently large subsets of fully consistent data are particularly missing. Some differences have also been highlighted between previous data (HARDER) and data collected in GOALDS, which call for further attention. It is therefore suggested that more efforts should be spent in the future in order to improve the recording and processing of accidents data, otherwise it is expectable that not negligible difficulties will arise in possible future tentative revisions of damage statistics for design and/or regulatory purposes.


Deliverable D3.2 On the basis of the findings from the analyses carried out in this Task it is possible to provide some recommendations for the proceeding of the work. There are indeed, basically, two ways for implementing the results (with further refinements) of this task:

• Probabilistic approach. A fully probabilistic model for grounding damage characteristics, conceptually similar to that presently in SOLAS2009 for side damages. Such an approach could be derived in the framework of research applications on the basis of available data. The quality of the database seems to be not sufficiently high for deriving a robust detailed fully probabilistic approach for bottom damage for regulatory purposes at this stage. Further clarifications are needed concerning grey areas identified in the analyses before proceeding along this way.

• Deterministic approach. A deterministic approach modifying Reg.9 assumptions. This “global” approach could be more robust than the fully probabilistic approach and less affected by the problems identified in the analyses. Probabilities of exceedance of SOLAS bottom damage characteristics have been found to be, overall, quite in line with those estimated at the time of development of Reg. 9. Hence, the present analyses would not call for strong revisions of Reg.9, unless different acceptable probabilities of exceedance are set. There are some indications that the present Reg.9 requirements could be more conservative for large ships and less conservative for small ships, and this aspect deserves additional attention. However, the statistical uncertainty is quite large due to the limited number of data, and therefore it is difficult to arrive at robust conclusions on this particular point.

In general it seems that, for research purposes, the probabilistic approach could be suitable and should be pursued in the framework of GOALDS project, and possibly, in the long term, for regulatory implementation. The possibility of using direct Monte Carlo simulations in a probabilistic framework should also be considered as a step forward with respect to present formulations based on p-factors. On the other hand, for a possible regulatory implementation, it seems that the second approach, the deterministic one, could be more feasible in a short term framework, of course if the modification of Regulation 9 will be deemed necessary.


Deliverable D3.2

References 1. HARDER casualty database

2. FAIRPLAY, World Fleet Structure per Class 2010

3. GOALDS casualty database

4. IMO, "SOLAS Consolidated Edition 2009", London, 2009

5. IMO Document SLF47/INF.4, "Bottom damage statistics for draft regulation 9", Submitted by

Germany and Norway, London, UK, 9 June 2004

List of annexes The following annexes are reported at the end of this main text:

• Annex 1 - "Overview of the GOALDS database", Christian Mains, GL • Annex 2 - "PDF and CDF charts from the database", Christian Mains, GL • Annex 3 - "Exploratory data analysis of grounding data from the updated GOALDS database

and assessment of requirements and assumptions in SOLAS Ch. II-1 Part B-2 Regulation 9", Gabriele Bulian and Alberto Francescutto, DINMA


Deliverable D3.2 - Annex 1

GOALDS-D-3.2-GL- Grounding Damage Characteristics –rev1 - ANNEX 1 Page 1 of 3

Annex 1 – Overview of the GOALDS database Christian Mains, GL



Overview of the GOALDS database Christian Mains, GL The casualty data collected during the GOALDS project have been merged with the HARDER database. Whilst during the HARDER project several sources like IMO damage cards, DSRK (former GDR) damage files and classification damage files the GOALDS data were retrieved from classification damage files and some rare casualty reports. A GOALDS dataset contains 91 fields of information. Six of these fields contain information to identify the vessel which are not shown in the database version delivered to project for legal reasons. Furthermore, information about the two involved ships (collision) like main dimensions, ship type building year, operational condition before and after casualty, casualty date, - place and - category as well as dimensions and location of the damage. Additional information form reports, internet, sea court cases which have been rarely found was filed but has not been considered within the statistical analysis. The complete list of data fields with description can be found in the file GOALDS-C-3.1_3.2-database-field-description rev1.pdf delivered to the project. During the project task 3.1 and 3.2 DINMA and GL also worked on the data quality of the database in order to avoid double consideration of casualties, unrealistic casualties in view of damage dimensions. To overcome some missing but important data like struck or striking ship a criterion was applied that was agreed among the task members. However, such procedure could not be applied for all necessary but missing data. Other missing data like main dimensions, building year which could be found in public reliable databases have been added. The most reliable data fields are: Year of building Year of building year of the building completion (delivery) (1st ship) Lpp Lpp length between perpendiculars, [m] (1st ship) Loa Loa length over all, [m] (1st ship) B B breadth moulded, [m] (1st ship) D D depth moulded, [m] (1st ship) Year of building 2 Year of building (from

2nd ship) year of the building (2nd ship)

Lpp 2 Lpp (from 2nd ship) length between perpendiculars, [m] (2nd ship) Loa 2 Loa (from 2nd ship) length over all, [m] (2nd ship) B 2 B (from 2nd ship) breadth moulded, [m] (2nd ship) D 2 D (from 2nd ship) depth moulded, [m] (2nd ship) Type 1 Type of ship (left field) type of the ship ### validity rule ### category

### Subtype 1 - - '' - - (right field) details to the type of the ship Place of casualty place of casualty

(left field) place of the casualty ### validity rule ### category ###


Subtype 1 - - '' - - (right field) details to the type of the ship Place of casualty place of casualty

(left field) place of the casualty ### validity rule ### category ###

Type of casualty Type of damage (left field)

nature of the damage ### validity rule ### category ###

Type of casualty 2 - - '' - - (right field) details to the damage of the casualty Nature of casualty Nature of casualty

(left field) nature of the casualty ### validity rule ### category ###

Nature of casualty 2 - - '' - - (right field) details to the nature of the casualty Ship side ship side damaged ship side ### validity rule ###

category ### X X the horizontal distance from the AP to the centre

of damage, [m] Z Z Collision:



the vertical distance from baseline to the lowest point of the damage, [m] Grounding: not applicable

l l the maximum longitudinal damage length, [m] h/w Height if collision/

Width if grounding Collision: the maximum vertical damage height measured up from Z, [m] Grounding: the maximum transverse damage width, [m]

Area Area damage area, in square meters Penetration penetration depth, if

collision / penetration height, if grounding

Collision: the maximum transverse penetration of damage, [m] Grounding: the maximum vertical penetration of damage, [m]

Within the statistical analysis prepared by DINMA ("Exploratory data analysis of grounding data from the updated GOALDS database and assessment of requirements and assumptions in SOLAS Ch. II-1 Part B-2 Regulation 9", Gabriele Bulian and Alberto Francescutto, DINMA) the reliability can be judged by the number of samples contributing to the analysis.



Annex 2 – PDF and CDF charts from the database

Christian Mains, GL



PDF and CDF charts from the database (Christian Mains, GL) Data has been delivered by the consortium members DNV, LR and GL. The request from ABS, BV and RINA results in no further data. ABS has legal restrictions. BV and RINA did not answer the inquiry. 1. Database

The collected casualty data has been filtered according to the following conditions:



Three kinds of casualties have been identified: collision, grounding and contact. The selected datasets have been statistically analysed in depth. Actually, 1527 cases have been identified for collision, grounding and contact within the database. This data set has been used to start the statistical analysis (see item 3.2). Collision Grounding Contact HARDER 832 312 35 1179GOALDS 184 160 4 348database 1016 472 39 1527



Bulk Carrier7%

Container11%

General Cargo47%

Passenger/RoRo7%

Tanker24%

other4%

Figure 1: Distribution of the GOALDS database ship types



Compared to the world wide fleet (source: World Fleet Structure per Class (Fairplay) 2010-02-01) and to ships classed with IACS societies the general cargo ships are overrepresented within the casualty database (see figure 2). Ship type world wide fleet IACS database seagoing 02/2010 02/2010 1944 - 2009 Bulk Carrier 8182 6346 103Container 4739 4438 164General Cargo 21430 6771 728Passenger/RoRo 8095 2668 110Tanker 14037 8833 359other 55073 15458 63Total 111556 44514 1527

World wide fleet - database

4,2

19,2

7,3

12,6

5,7

4,0 6,

1

2,4

7,9

13,9

6,7

10,7

47,7

7,2

23,5

4,17,

3

49,4

0

10

20

30

40

50

Bulk Carrier

Container

General Cargo

Passenger/RoRo

Tankerother

[%]

world wide fleetIACSdatabase

Figure 2: Comparism between the world wide fleet, IACS cassed fleet and the GOALDS database For 639 casualties the selected dataset contains information about the building year. Ship type Year of building seagoing 1944 - 1988 1989 - 2009 Bulk Carrier 43 29 72Container 32 132 164General Cargo 184 66 250Passenger/RoRo 50 10 60Tanker 48 28 76other 14 3 17Total 371 268 639



Year of building43

32

184

50 48

14

29

132

66

10

28

3

0

50

100

150

200

Bulk Carrier

Container

General Cargo

Passenger/RoRo

Tankerother

[N]

1944 - 19881989 - 2009

Figure 3: Building date of shiptypes within the GOALDS database For 954 casualties the selected dataset contains information about the casualty date. Ship type Date of casualty seagoing 1944 - 1988 1989 - 2009 Bulk Carrier 7 74 81Container 6 164 170General Cargo 110 312 422Passenger/RoRo 21 71 92Tanker 41 101 142other 19 28 47Total 204 750 954

Date of Casualty

7 6

110

21

41

19

74

164

71

101

28

0

50

100

150

200

250

300

Bulk Carrier

Container

General Cargo

Passenger/RoRo

Tankerother

[N]

1944 - 19881989 - 2009

Figure 4: Casualty date of shiptypes within the GOALDS database



2. Grounding data The collected casualty data has been filtered according to the following conditions:

a) doublets have been deleted; missing main dimensions are implemented b) all passenger ships and others with Lpp > 40.0 m (refer to GT > 500) c) all penetrations of the hull

Number of groundings 457 (148 GOALDS, 309 HARDER) Charts of the data is presented according to the following matrix scheme: Grounding

all ships passenger-/roro ships Bulker/Tanker Gen. Cargo/

Container X 1.1 3.1 5.1 7.1 l 1.2 3.2 5.2 7.2 h 1.3 3.3 5.3 7.3

A 1944-2009

d 1.4 3.4 5.4 7.4 For groundings the categories all ships, passenger ships, tankers and bulk carriers as well as general cargo and container ships have been plotted on the next pages. Due to lack of passenger ship groundings data has been combined with groundings of general cargo and container ships as bottom line characterristics of these ships are similar. To check the influence of multiple damages charts have been drawn up with and without multiple damages.

X damage location (Nx := number of casualties) l damage length w damage width d penetration depth

Additionally the grouping of ships with similar bottom lines should show if this will result in different distributions of the damage location (see bottom lines below).

Container Ship

FP


A-1.1 Damage location without multiple cases (291)

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

-0,1 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 1,1

X/Lpp

f(x)

0

10

20

30

40

50

60

Nx

f(x)Nx


0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

-0,1 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 1,1

X/Lpp

f(x)

0

10

20

30

40

50

60

70

Nx

f(x)Nx




0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

-0,1 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 1,1

X/Lpp

f(x)

0

1

2

3

4

5

6

7

8

9

Nx

f(x)Nx


0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

-0,1 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 1,1

X/Lpp

f(x)

0

1

2

3

4

5

6

7

8

9

10

Nx

f(x)Nx




0,0

0,5

1,0

1,5

2,0

2,5

-0,1 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 1,1

X/Lpp

f(x)

0

5

10

15

20

25

30

Nx

f(x)Nx


0,0

0,5

1,0

1,5

2,0

2,5

-0,1 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 1,1

X/Lpp

f(x)

0

5

10

15

20

25

30

35

Nx

f(x)Nx




0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

2,0

-0,1 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 1,1

X/Lpp

f(x)

0

5

10

15

20

25

Nx

f(x)Nx


0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

-0,1 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 1,1

X/Lpp

f(x)

0

5

10

15

20

25

30

35

Nx

f(x)Nx



A-3.1+A-7.1 Damage location without multiple cases (153)

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

-0,1 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 1,1

X/Lpp

f(x)

0

5

10

15

20

25

30

Nx

f(x)Nx

A-3.1+A-7.1 Damage location (246)

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

-0,1 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 1,1

X/Lpp

f(x)

0

5

10

15

20

25

30

35

40

Nx

f(x)Nx



A-1.2 Damage length without multiple cases (258)

0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

8,0

9,0

10,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

l/Lpp

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20

F(x)

f(x)F(x)


0,0

2,0

4,0

6,0

8,0

10,0

12,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

l/Lpp

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20

F(x)

f(x)F(x)




0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

8,0

9,0

10,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

l/Lpp

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20

F(x)

f(x)F(x)


0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

8,0

9,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

l/Lpp

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20

F(x)

f(x)F(x)




0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

8,0

9,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

l/Lpp

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20

F(x)

f(x)F(x)


0,0

2,0

4,0

6,0

8,0

10,0

12,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

l/Lpp

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20

F(x)

f(x)F(x)




0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

8,0

9,0

10,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

l/Lpp

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20

F(x)

f(x)F(x)


0,0

2,0

4,0

6,0

8,0

10,0

12,0

14,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

l/Lpp

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20

F(x)

f(x)F(x)



A-3.2+A-7.2 Damage length without multiple cases (139)

0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

8,0

9,0

10,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

l/Lpp

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20

F(x)

f(x)F(x)

A-3.2+A-7.2 Damage length (196)

0,0

2,0

4,0

6,0

8,0

10,0

12,0

14,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

l/Lpp

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20

F(x)

f(x)F(x)



A-1.3 Damage width without multiple cases (192)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

w/B

f(x)

0.00

0.20

0.40

0.60

0.80

1.00

1.20

F(x)

f(x)F(x)

A-1.3 Damage width (266)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

w/B

f(x)

0.00

0.20

0.40

0.60

0.80

1.00

1.20F(

x)

f(x)F(x)




0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

w/B

f(x)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

F(x)

f(x)F(x)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

w/B

f(x)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

F(x)

f(x)F(x)




0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

w/B

f(x)

0.00

0.20

0.40

0.60

0.80

1.00

1.20

F(x)

f(x)F(x)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

w/B

f(x)

0.00

0.20

0.40

0.60

0.80

1.00

1.20

F(x)

f(x)F(x)




0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

w/B

f(x)

0.00

0.20

0.40

0.60

0.80

1.00

1.20

F(x)

f(x)F(x)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

w/B

f(x)

0.00

0.20

0.40

0.60

0.80

1.00

1.20

F(x)

f(x)F(x)



A-3.3+A-7.3 Damage width without multiple cases (86)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

w/B

f(x)

0.00

0.20

0.40

0.60

0.80

1.00

1.20

F(x)

f(x)F(x)

A-3.3+A-7.3 Damage width (132)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

w/B

f(x)

0.00

0.20

0.40

0.60

0.80

1.00

1.20

F(x)

f(x)F(x)



A-1.4 Penetration depth without multiple cases (121 / 119 up to d/D=0.5)

0,0

2,0

4,0

6,0

8,0

10,0

12,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

d/D

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20

F(x)

f(x)F(x)

A-1.4 Penetration depth (121 / 119 up to d/D=0.5)

0,0

2,0

4,0

6,0

8,0

10,0

12,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

d/D

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20

F(x)

f(x)F(x)



A-3.4 Penetration depth without multiple cases (3)

0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

d/D

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20

F(x)

f(x)

A-3.4 Penetration depth (3)

0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

d/D

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20

F(x)

f(x)



A-5.4 Penetration depth without multiple cases (84 / 82 up to d/D=0.5)

0,0

2,0

4,0

6,0

8,0

10,0

12,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

d/D

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20

F(x)

f(x)F(x)

A-5.4 Penetration depth (84 / 82 up to d/D=0.5)

0,0

2,0

4,0

6,0

8,0

10,0

12,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

d/D

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20

F(x)

f(x)F(x)



A-7.4 Penetration depth without multiple cases (31)

0,0

2,0

4,0

6,0

8,0

10,0

12,0

14,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

d/D

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20

F(x)

f(x)

A-7.4 Penetration depth (31)

0,0

2,0

4,0

6,0

8,0

10,0

12,0

14,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

d/D

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20

F(x)

f(x)



A-3.4+A-7.4 Penetration depth without multiple cases (34)

0,0

2,0

4,0

6,0

8,0

10,0

12,0

14,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

d/D

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20

F(x)

f(x)

A-3.4+A-7.4 Penetration depth (34)

0,0

2,0

4,0

6,0

8,0

10,0

12,0

14,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50

d/D

f(x)

0,00

0,20

0,40

0,60

0,80

1,00

1,20

F(x)

f(x)


Annex 3 - Exploratory data analysis of grounding data from the updated GOALDS database and assessment of requirements and assumptions in

SOLAS Ch. II-1 Part B-2 Regulation 9

Gabriele Bulian and Alberto Francescutto, DINMA



Exploratory data analysis of grounding data from the updated GOALDS database and assessment of

requirements and assumptions in SOLAS Ch. II-1 Part B-2 Regulation 9

Gabriele Bulian ([email protected]), Alberto Francescutto ([email protected]) Department of Mechanical Engineering and Naval Architecture - University of Trieste

Document history Revision Date Corresponding

author Description

00 29 June 2010

G. Bulian ([email protected]) First draft

01 09

August 2010


Second draft - Updated extraction of passenger vessels data (5 additional cases) and corrected relevant figures / data - Improved comments in the text - Editorial corrections

02 30

August 2010


Draft Final Version - Editorial corrections - Added Table 8. - Added a note concerning the possibility of using the transformed variable /zL Bα to obtain distributions with less dependence on the ship size. - Added acknowledgments








Summary This document contains an exploratory data analysis carried out on the grounding damages database as updated in the course of the GOALDS project (WP3). Damages due to grounding have been taken into account. The present analysis can be split in two main parts:

- An exploratory data analysis of grounding damage characteristics. - An assessment of the probabilities of exceedance of SOLAS minimum double bottom height and

SOLAS bottom damage characteristics as reported in SOLAS Chapter II-1, Part B-2, Regulation 9 for passenger and cargo ships other than tankers.

The exploratory data analysis has been focalised on the determination of the behaviour of the distributions of grounding damage characteristics. The following characteristics have been analysed: longitudinal position of damage, vertical damage extent (damage penetration), longitudinal damage extent (damage length), and transversal damage extent (damage width). Most of the attention has been given to the description and analyses of marginal distributions for the reported quantities. However, despite the limited available amount of data, a series of (mostly qualitative) analyses have been carried out in order to highlight statistical dependencies among variables. In addition, also the distribution of the ship speed at the moment of grounding has been analysed. Wherever possible, the analyses have been carried out separately for the category of "full ships" (tankers and bulk carriers) and for the category named here "not full ships" (all the other data). The intention of the separation was to identify possible differences in the behaviour of grounding damage characteristics between ships with high block coefficient and the other vessels. Due to the limited number of data concerning passenger vessels it was not possible to derive any quantitative indication for this ship type, however, when possible, mainly qualitative analyses have been carried out to check the coherence in the behaviour of passenger vessels with "not full ships", or with the complete database, as appropriate. For what concerns the assessment of requirements and assumptions in SOLAS Chapter II-1 - Part B-2 - Regulation 9 "Double bottoms in passenger ships and cargo ships other than tankers", the analysis in this paper has been devoted at the estimation, from the data in the database, of the probabilities of:

- Exceedance of the SOLAS double bottom requirements by the grounding damage penetration. - Exceedance of bottom damage characteristics as assumed by SOLAS.

A series of conclusions could be drawn from all the analyses, which are extensively reported at the end of the paper. Some of the main conclusion are however reported here only as major indications, and the reader is referred to the complete analysis and set of conclusions for a thorough discussion. Concerning the database:

- The sample for passenger vessels is very small. It is therefore impossible to draw any quantitative robust conclusion for this ship type.

- There are indications that data coming from the HARDER database could have not been in all cases correctly identified as multiple damages belonging to the same casualty.

- There seems to be a not negligible influence of the source of data in the database on some damage characteristics.

Concerning the distributions of the damage characteristics and of the ship speed at the moment of grounding: - The database does not contain any information concerning the transversal position of the damage. In

absence of such information it could be assumed that the centre of the damage is uniformly distributed in transversal direction.

- For both full and not full ships it seems justifiable to use a unique distribution for the nondimensional longitudinal position of damage irrespective of the ship dimensions, although this distribution could differ between full and not full ships.

- The forward end of damage seems to be a better variable for the description of the longitudinal location of bottom damage than the centre of damage. The probability density function for the forward end of damage has a significant peak in the forward region of the ship, which is more evident for full hull forms.

- In all but two cases penetrations are smaller than 4.2m, and only one reported case has a penetration of 7m, and there are not significant differences in the distribution of the damage penetration between full and not full ships.

- The behaviour of the distribution of the bottom damage penetration is not simple, and cannot be perfectly represented for any generic ship size neither with a dimensional approach nor with a nondimensional approach. However, among these two extreme possibilities, it seems that a completely dimensional approach could provide a better agreement with data than a nondimensional approach. It seems therefore that a fully dimensional approach for any ship size and type, with distribution of


Deliverable D3.2 - Annex 3 damage penetration obtained from the available data, and a maximum damage penetration of the order of 5m, could be a good balance between simplicity and accuracy.

- For not full ships the distribution of the dimensionless damage length seems to be not strongly dependent on the ship length, while some dependence is more visible in case of full ships. However, it seems that it could be possible to consider, as a working tool, a unique distribution for the dimensionless damage length for full and not full ships irrespective of the ship size. This distribution for the dimensionless damage length could be estimated from the available data for ships of 80m in length and over, and could represent a good balance between accuracy, simplicity and conservativeness. It must be underlined that some concerns are reported in the paper regarding a possible influence of the source of data on the characteristics of the damage length.

- The analysis of the transversal damage extent showed not negligible differences between full ships and not full ships, with full ships showing not negligibly wider damages in nondimensional form. In case of not full ships the analysis of data seems to indicate the suitability of a nondimensional approach for the transversal damage extent, although there is a quite large uncertainty in the range of ship breadths above 20m. In case of characteristics of damage width distribution for full ships, a sharp separation has been identified between two different ranges of ship dimensions (small / large ships), which seems to be correlated with different sources of data. Taking the two ranges separately, a dimensionless approach seems to be applicable for each range. Two options have been considered for an appropriate distribution for the dimensionless damage width for full ships, a conservative one and an "average" one. However further clarifications seem to be necessary.

- Statistical dependencies among different variables characterising the damage position and dimensions have been identified. In general, the damage width and penetration tend to be smaller when the damage length decreases. It is not clear at this stage whether neglecting these dependencies in a search for a simple modelling could have significant effects on the determination of the probability of flooding of specific spaces in a ship.

- The well known and unavoidable statistical dependence between damage length and position, which is governed by the geometrical limitation induced by the extreme forward and aft ends of the ship, has been shown. In this context the theoretical bases have been described for a procedure for the creation of a virtual random variable (the "potential damage length") independent of the damage position, and it has been shown that the required assumptions for the application of this procedure seems to be approximately fulfilled by the available data. It must be underlined that a similar procedure should be applied also in case of the transversal damage extent since also the transversal damage extent is geometrically limited by the extreme portside and starboard limits of the ship.

- Separate analyses of the distribution of ship speed at the moment of grounding have been carried out for full and not full ships. In case of full ships the distribution of the ship speed at the moment of grounding has been found to be approximately independent of the ship size. For not full ships the distribution of the ship speed at the moment of grounding has been found to be slightly dependent on the ship size, with a small tendency towards an increase of the speed as the ship length increases. However, the increase, although systematic, is relatively small and a saturation is expected to occur in the range of long ships where, unfortunately, there are not sufficient data available from the database.

Concerning the assessment of SOLAS Chapter II-1 - Part B-2 - Regulation 9 requirements and assumptions: - The analysis concerning SOLAS Regulation 9 has been carried out omitting data associated with

tankers and fishing vessels. - Available data are limited, in the very large majority and depending on the particular variable of

interest, to panamax breadth (32.2m), and hence the range of post-panamax vessels is almost not covered.

- The available number of data for passenger vessels is too limited to draw any specific conclusion for this ship type on the basis of the corresponding sample. As a consequence, the complete database relevant to the analysis of SOLAS requirements has been used also to check requirements which, in principle, are relevant only for passenger vessels.

- The probability of damage penetration exceeding the minimum double bottom height required by SOLAS has been estimated, considering all data pertinent to this analysis, as

[ ]95%27.3% 16.1%,41.0%

CI . - The probability of damage penetration exceeding the minimum double bottom height required by

SOLAS for passenger ships with large lower holds has been estimated, considering all data pertinent to this analysis, as [ ]95%

14.5% 6.5%,26.7%CI .

- There seems to be some indication that there could be a dependence between the ship size and the probability that the bottom damage penetration could exceed SOLAS minimum double bottom height


Deliverable D3.2 - Annex 3 requirements. In particular, there seems to be some indication that the probability of penetrating a double bottom marginally compliant with SOLAS requirements is larger for small ships and smaller for large ships. This trend is less visible when considering specific requirements for passenger ships with large lower holds.

- The probabilities of exceeding (each/at least one/all) assumed SOLAS dimensions for bottom damage have been estimated as follows:

o Considering standard requirements: Exceedance of SOLAS bottom damage length: [ ]95%

54.6% 47.6%,61.6%CI ;

Exceedance of SOLAS bottom damage width: [ ]95%18.2% 11.5%,26.7%

CI ;

Exceedance of SOLAS bottom damage penetration: [ ]95%29.1% 17.6%,42.9%

CI ;

Exceedance of all SOLAS bottom damage dimensions: [ ]95%11.1% 3.7%,24.1%

CI ;

Exceedance of at least one SOLAS bottom damage dimension: [ ]95%64.4% 48.8%,78.1%

CI ;

o Considering an increased bottom damage penetration min /10,3B m relevant for passenger ships with large lower holds (first two values reported again only for reference): Exceedance of SOLAS bottom damage length: [ ]95%

54.6% 47.6%,61.6%CI ;

Exceedance of SOLAS bottom damage width: [ ]95%18.2% 11.5%,26.7%

CI ;

Exceedance of SOLAS bottom damage penetration: [ ]95%14.5% 6.5%,26.7%

CI ;

Exceedance of all SOLAS bottom damage dimensions: [ ]95%8.9% 2.5%,21.2%

CI ;

Exceedance of at least one SOLAS bottom damage dimension: [ ]95%CI

- It is important to underline that the probabilities of exceedance of bottom damage characteristics assumed in SOLAS as estimated in this paper are in line with those reported in the IMO Document SLF47/INF.4 containing proposals very close to what is presently implemented in the definitions in Regulation 9. A strictly exact comparison between present analysis and SLF47/INF.4 is not possible due to the slightly different definitions of the events under analysis. However, some indicative comparison between probability levels is possible with reference to standard requirements:

60 ; .0% 44.3%,74.3%

o Exceedance of SOLAS bottom damage length: This paper: 54.6% - SLF47/INF.4: 43%

o Exceedance of SOLAS bottom damage width: This paper: 18.2% - SLF47/INF.4: about 38%-40%

o Exceedance of SOLAS bottom damage penetration: This paper: 29.1% - SLF47/INF.4: about 26%.

- Trends have been investigated in order to see whether the probability of exceeding SOLAS bottom damage characteristics could be dependent on the ship size. Despite the large uncertainty associated with the limited number of data some trends have been observed. There seems to be a small trend towards an increase of the probability of exceeding SOLAS damage length as the ship length increase up to about 80m, for longer ships this probability seems to be not strongly dependent on the ship length. The probability of exceeding the SOLAS reference bottom damage width seems to be almost constant for ships up to a length of about 125m, and decreasing for longer ships, but the confidence intervals are too wide to definitely consider this decrease as significant. There seems to be a systematic tendency towards a decrease of the probability of exceeding the assumed SOLAS bottom damage penetration as the ship length (size) increases, and this could mean that SOLAS damage assumptions could be, for what concerns the damage penetration, more conservative for large ships and less conservative for small ships. The obtained result seems to be consistent with the observed suitability of a common distribution for the dimensional vertical damage extent independent of ship size, while SOLAS bottom damage penetration is proportional to the ship breadth (with a maximum at 2m or 3m for passenger ships with long lower holds) and hence to the ship size.

It seems that effective use of the information in this paper, as well as of the updated GOALDS database, in the frame of development/update of relevant regulatory frameworks could be done following, mainly, two ways, namely:

- Development of a fully probabilistic approach for bottom damage, similar to the one already in use for side damage, by exploiting, but not necessarily limiting to, the distributions described in this paper, after proper explicit mathematical modelling/fitting.


Deliverable D3.2 - Annex 3 - Development/update of bottom damage characteristics and/or double bottom height requirements by

specifying a-priori appropriate acceptable levels for the probabilities of exceedance, and determining the corresponding double bottom requirements / damage characteristics.

The first approach would be the more physical one, though also the more complex both from the application and from the mathematical points of view. Typical issues that could be foreseen in the development of such an approach could mainly come from the fitting process of the obtained distributions, from the embedding (if considered necessary) of dependence among variables, from the analytical integration of the integrals required for the development of so-called "p-factors". In particular the selection of the fitting procedure, or, better, of the type of fitting functions for the obtained empirical distributions is strictly related to the necessity of obtaining analytically integrable functions in the development of so-called "p-factors". Indeed, the selection of the functions for the fitting of the distributions would be limited to those classes of functions allowing the subsequent required analytical integrations. This would certainly limit the possibility of obtaining accurate fittings of the empirical distributions. Moreover, it is expected that the obtained formulations for the p-factors will be valid only for volumes having cuboid shapes, and in case of more complex subdivisions appropriate transformation into (approximate) sets of cuboids would be necessary. The second approach would be a more pragmatic one, and would be a simplification of the real problem, but would be easier to apply from the design point of view, and could be tuned to embed a specified level of conservativeness. The limited availability of data in the database could however lead to a not negligible level of uncertainty in the determination of the reference damage characteristics, and this aspect should be borne in mind. However, a third alternative could also be envisaged, which is mainly an alternative to the first considered approach. It could indeed be possible to simply clearly specify the (joint if necessary) probability density functions of the variables describing the location and the dimensions of the damage, and then consider the application of such distributions in a Monte-Carlo (possibly with variance reduction techniques) approach to the bottom damage, or, if possible, through direct deterministic numerical integration. This type of approach would be extremely flexible in terms of possible future updates, because it would not require a re-calculation of formulae for p-factors, or a re-determination of reference bottom damage characteristics, but the update would just be a re-specification of the (joint) probability density functions to be used in the generation of damages. Moreover, this approach could partially avoid foreseeable problems associated with the application of classical p-factors to complex not cuboid internal volumes, a problem which is presently evident in case of application of side damage p-factors to certain complex subdivisions. Finally, it is worth reporting that, in general, despite all the efforts spent to remove doublets, wrong cases, etc. it is not possible to say that the quality of the database is high. Sufficiently large subsets of fully consistent data are particularly missing. Some differences have also been highlighted between previous data and data collected in GOALDS, which call for further attention. It is therefore suggested that more efforts should be spent in the future in order to improve the recording and processing of accidents data, otherwise it is expectable that not negligible difficulties will arise in possible future tentative revisions of damage statistics for design and/or regulatory purposes.



Introduction The analyses of the data shown in this report are based on the GOALDS database of damage characteristics [1]. Before going to the statistical analysis it is worth reporting how the global database has been filtered in order to obtain the working set of data assumed to belong to damages due to grounding accidents, excluding contact accidents. The filtering of data has been carried out in four levels as follows:

Level 01. Grounding damages have been initially extracted according to the field "Nature of casualty" retaining only those cases associated with grounding.

Level 02. At this level, following the indications in [2], casualties reported to have resulted in multiple holes have been substituted by their corresponding "equivalent" damages according to the characteristics derived in [3]. In this process the Casualty ID 2367 has been updated with respect to [3], incorporating a missing hole, but the result of the update has been simply a very small difference in damage width (from to 0.039 to 0.032m). Moreover, for the Casualty ID 2392 the ship type has been corrected from "container" to "general cargo". Some fields for equivalent damages in [3] have been found to be empty (e.g. the field "side"). When possible without ambiguities, these fields have been filled taking into account the information reported for the original single holes from which the equivalent damages were derived in [3]. The Casualty ID for the equivalent damages has been taken as the Casualty ID corresponding to the original holes, while the ID of each equivalent damage has been arbitrarily set equal to the Casualty ID multiplied by -1.

Level 03. The scope of the filtering at this level was the identification and removal of "inconsistent" cases, i.e. cases containing characteristics which are likely to indicate errors in reporting the data. In particular, a damage case has been flagged as inconsistent when any of the following conditions was fulfilled:

o The forward end of damage is forward of 1.10 , i.e.: ppL⋅

, 1.102

xF dam dam pp

LX X L= + > ⋅

o The aft end of damage is aft of , i.e.: 0.10 ppL− ⋅

, 0.102

xA dam dam pp

LX X L= − < − ⋅

o The damage length is larger than 1.20 ppL⋅ , i.e.: 1.20x pL L> ⋅ p

o The transversal extent of damage is larger than the ship breadth, i.e.: yL B>From the analysis of the database, the following IDs have been found to be "inconsistent" according to the reported definition:

o , 1.102

xF dam dam pp

LX X L= + > ⋅ : IDs 1674, 3106, 3108

o , 0.102

xA dam dam pp

LX X L= − < − ⋅ : ID 2947

o : None 1.20x pL > ⋅ pLo : ID 240 yL B>

In addition, the IDs 3075 and -2356 (an equivalent damage) have been found to report a damage width equal to zero: for these IDs the damage width has been removed. Finally, a column has been added (field "Speed DINMA") containing a modification of the original field "shipspeed v1". The modification of some of the data in the original field "shipspeed


Deliverable D3.2 - Annex 3 v1" has been necessary because in some cases these field originally contained non-numeric values like, e.g., "DEAD SLOW", "1-2", etc. Level 04. At this filtering level, cases identified as "contacts" according to the field

All ed at the filtering level

e analyses that will follow, ships in the database will often be divided in two groups,

ull forms: all cases associated with accidents occurred to tankers or bulk carriers

ng cases. g that the ship length between perpendiculars

pap

Statistical analysis of damage characteristics

General information analysis, see Table 1, come from the database of damage

"nature of casualty 2" have been removed (IDs 234, 1189, 1414). the analyses reported in this paper are based on the data as obtain

04. In thnamely:

Full h(according to the field "Type 1"). Not full hull forms: all the remaini

It is important to underline at the very beginninppL , which is available from the GOALDS database, and which will be used throughout this

er as reference ship length does not coincide, in general, with the ship length considered in SOLAS regulations [4]. Indeed, damage stability requirements in SOLAS refer mostly to the "subdivision length", while requirements for double bottom and bottom damage are based on the ship length according to the International Convention on Load Lines in force. However, in this paper, this difference has been neglected.

Data used in the presentcharacteristics as updated in GOALDS [1] after the filtering procedure reported in the introduction. The contribution to the sample of grounding damages from data collected in GOALDS is 16.2%. It is worth mentioning that the number of entries should be considered with caution, since multiple damages which occurred in the same casualty have been transformed into "equivalent damages" for the purpose of this analysis [3]. Moreover, the actual number of available samples for each different analysis carried out in this paper is always smaller than the number of samples reported in Table 1, since in the large majority of cases not all damage characteristics are available for each collected casualty. Passenger vessels have been identified from the database using fields "Type 1" and "Subtype 1" and this category contains also RoPax vessels. In order to extract data unambiguously associated with passenger vessels, only those cases explicitly reporting the indication of ship carrying passengers in fields "Type 1" or "Subtype 1" have been used.



Table 1: Number of data in the database.

Total entries HARDER GOALDS

Global updated GOALDS database

Total cases 1527 (100.0%)

1179 (77.2%)

348 (22.8%)

Total cases* 359 (100.0%)

301 (83.8%)

58 (16.2%)

Passenger vessels* 22 (6.1%)

21 (5.8%)

1 (0.3%)

Full hull forms (bulk carriers and tankers)*

138 (38.4%)

120 (33.4%)

18 (5.0%)

Gro

undi

ng d

ata

afte

r fil

terin

g pr

oced

ure

Not full hull forms* 221 (61.6%)

181 (50.4%)

40 (11.1%)

(*): Percentages are with respect to total grounding cases The main goals of this paper are, in principle: - To analyse the characteristics of grounding damage characteristics. In particular for what

concerns differences between full and not full hull forms, and also in terms of suitability of dimensional/non-dimensional/ship-size-dependent approaches for the underlying distributions of damage characteristics.

- To assess, on the basis of available data, the probability of exceedance of present SOLAS requirements for what concerns double bottom height and reference bottom damage characteristics for passenger and cargo vessels other than tankers lacking (part of) double bottom or having unusual double bottom arrangements.

From the number of samples reported in Table 1, we can see that the number of passenger vessels is extremely limited. Therefore, it can be said, already at this stage, that it is in general not possible to draw specific conclusions associated with this ship type with a reasonable level of confidence. For this reason, any indication for this ship type, when derived in the present paper, is to be considered with extreme caution bearing in mind the very limited sample. For what concerns the split of the complete database into "full hull forms" (bulk carriers and tankers) and "not full hull forms", it can be seen that these latter are the majority (221 vs. 138, i.e. a ratio of 1.6). It follows that in the analyses involving all data, the final results could be mainly driven by the sample of not full hull forms. However, the actual ratio between data for full and not full hull forms depends on the variable(s) under analysis, and therefore the class driving the statistics could change from analysis to analysis. The database does not contain any information concerning the transversal position of the damage. In absence of such information it could be assumed that the centre of the damage is uniformly distributed in transversal direction. It is also worth at this stage to compare the distribution of the ship length between perpendiculars for the two considered classes of ships. Figure 1 shows for the subset of full ships, the subset of not full ships, and for the complete database. It can be seen that the majority of not full ships belong to the range of relatively small lengths (and therefore small ship sizes). On the other hand full ships belong in the majority of cases to the range of large ship lengths (and therefore large ship sizes). According to Figure 1 any comparison between the two classes of ships should therefore be considered with caution, because full ships are mainly governed by the behaviour of large ships, while not full ships are mainly

( ppCDF L )


Deliverable D3.2 - Annex 3 governed by the behaviour of smaller ships. This aspect will be repeatedly addressed throughout the paper in different occasions.

Figure 1: Cumulative distribution of length between perpendiculars. Comparison between full ships, not

full ships and complete database. In the following, the sample of data will be analysed using a sliding window technique already used in the past [5]. The idea behind this technique is to avoid any parameterisation of the underlying set of data, unless necessary. The main goal of this type of analysis is to determine whether there is any significant dependence between two random variables, and if this dependence is found, the aim of the analysis is to provide indications for a proper modelling of this dependence. Two generic random variables are considered, say X and Y with a set of samples N( ), 1,...,i ix y i N= . The analysis considers a series of subsets, obtained by filtering on the basis of appropriate intervals (windows) for the variable X . The generic subset k th− kΩ ,

associated with the window , is defined as: min, max,,k kx x⎤⎦ ⎤⎦

( ) min, max, , : , k i i i k kx y x x x⎤ ⎤Ω = ∈⎦ ⎦ (1) A detailed (conditional) statistical analysis is then performed on the samples of the random variable belonging to each subset Y kΩ , addressing the mean and maximum values of Y , different percentile levels, estimated cumulative distribution, etc. The generic statistical estimator for the variable Y (e.g. the mean value of Y ) is finally reported as a function of the mean value of the random variable X for those samples belonging to the subset . By kΩ


Deliverable D3.2 - Annex 3 proper sliding of the window , it is possible to identify tendencies for the statistical characteristics of the considered random variable Y as a function of the random variable

min, max,,k kx x⎤⎦ ⎤⎦

X . All the statistical analyses have been carried out under MATLAB® environment. In some cases the text will contain sets expressed in compact notation. For example [ ]1,5,10,11:1:15

is a compact notation for the set 1,5,10,11,12,13,14,15 .

Longitudinal position of damage

Introduction The first variable under analysis is the longitudinal position of the damage. Typically the longitudinal position of damage, damX , is identified as the position of the centre of damage (see, e.g., [4]). The use of the centre of the longitudinal extent of damage is physically reasonable when thinking of collision, since in the simplified case of a collision at right angle between two ships the centre of the damage could be thought to roughly correspond to the centreline of the ramming ship. However, if we concentrate on the specific case of grounding, the physics is likely different. The typical archetypal model for a grounding damage would likely consider a ship moving forward with a certain speed hitting some obstacle on the seabed, as, e.g., a rock. In this simplified case it is expectable that the grounding damage has a starting point located forward, and then extends towards the aft part of the ship as the ship reduces its speed as a consequence of the grounding. Of course this is a simplified case, because in some cases grounding accidents occur when the ship is drifting in dead condition against the rocks, and in these cases this idealised model is not applicable. However, having this simplified archetypal modelling in mind, it can be understood that the centre of damage is a less natural variable to be considered than the forward end of damage (say, the start of damage according to the model). It will therefore be interesting to analyse the location of the collected grounding damages both in terms of the "more standard" centre of damage and also in terms of the forward position of damage. The forward position, of damage can be calculated when the position of the centre of damage

,F damX

damX as well as the longitudinal extent of damage xL are known:

, 2x

F dam damLX X= + (2)

Since the original database contains damX and not , and since ,F damX damX and xL are not always both known in all cases, it follows that the number of available samples concerning

is equal to the number of samples for which ,F damX damX and xL are known, and it is necessarily less than the minimum between the number of samples containing damX and those containing xL . The available set of data where damX is known comprises 309 samples, with 132 cases belonging to full hull forms and 177 cases belonging to not full hull forms. The ratio is thus

which is not extremely different from what can be obtained from the global set of data according to Table 1, i.e. 138132 /177 0.75=

/ 221 0.62= .


Deliverable D3.2 - Annex 3 When considering , the available sample reduces to 263 cases, with 125 cases belonging to full ships and 138 cases belonging to not full ships. The higher reduction in the available samples is observed, then, for the subset of not full ships. In case of the sample used for the analyses of , the ratio between full and not full hull forms modifies to

.

,F damX

,F damX125/138 0.91=

Longitudinal position of the centre of damage damX

The first point to be addressed is whether there is any dependence between the longitudinal position of the damage, made non-dimensional by using the ship length between perpendiculars , and the actual ship size. ppLFigure 2 shows a scatter plot of as a function of the ship length. Data are separated into full ships and not full ships. It can be seen that, according to the results already reported in Figure 1, the sample of full ships populates mainly the range of large ships, while not full ships are mostly concentrated in the range of smaller ship size.

/dam ppX L

Figure 2: Scatter plot of nondimensional centre of damage as a function of the ship length.

In order to check for the possible dependence on the ship length of the distribution of the nondimensional position of the centre of damage, we have carried out a sliding window analysis for full ships and not full ships separately. The average value and different percentile levels have been calculated by sliding different windows for the length between perpendiculars . ppL

In case of full ships, 50m wide windows have been considered from ] ]0 ,50ppL m∈ m up to

] ]290 ,340ppL m m∈ with 5m steps, and a final window ] ]300 ,355ppL m m∈ has been


Deliverable D3.2 - Annex 3 considered to take into account the longest available ship (350.5m between perpendiculars). The results of the analysis are shown in Figure 3, where each quantity is reported as a function of the average value of the length between perpendiculars inside each window. The number of points in each window used for the analysis in Figure 3 is reported in Figure 4.

Figure 3: Sliding window analysis for percentile levels of the distribution of the nondimensional damage

centre and for the average value of as a function of the ship length between

perpendiculars . Full ships.

/dam ppX L /dam ppX L

ppL



Figure 4: Number of points in each window for the analysis in Figure 3.

By looking at Figure 3, taking into account Figure 4, it can be seen that, for full ships, there seems not to be any systematic dependence of the average value /dam pp ppE X L L and of the

highest percentile levels of ( /dam pp ppCDF X L L ) on the ship length, although some slight

tendency towards a decrease of the 97.5% and the 75% percentile levels as the ship length increases seems visible. Some erratic and not systematic behaviour of the 25% percentile level and of the 2.5% level can be seen. It must however be borne in mind that, although not explicitly reported, estimated percentile levels are associated with a statistical uncertainty. To check for the possible presence of significant differences of ( )/dam pp ppCDF X L L among

different windows, a systematic application of a two-samples Kolmogorov-Smirnov test for testing the hypothesis of equal CDF among two different windows has been carried out. The results are shown in Figure 5.



Figure 5: Results of window-to-window two-sample Kolmogorov-Smirnov test of hypothesis for equal

( /dam pp ppCDF X L L ) among different windows. Full ships.

From what is reported in Figure 5 it seems that in the majority of the comparisons among different windows, the differences among ( )/dam pp ppCDF X L L have been found to be

statistically not significant according to the considered test, and the hypothesis of equal CDF among windows has not been rejected. A limited exception are the comparisons between windows with centre in the range of 220m-250m and in the range 150m-200m. These ranges can be identified in Figure 3 as those ranges with the stronger variation of, particularly, the 25% percentile level. However, from the obtained results, it seems justifiable, from the engineering point of view, to consider a unique average distribution for the nondimensional position of the centre of damage which is independent of the ship length. Such distribution is shown in Figure 6, while the corresponding histogram of the relative frequency of for full ships is shown in Figure 7.

/dam ppX L



Figure 6: Estimated cumulative distribution for in case of full ships. /dam ppX L

Figure 7: Relative frequency histogram for in case of full ships. /dam ppX L


Deliverable D3.2 - Annex 3 Considering Figure 6, and using Figure 7 as a guide, it can be seen that, for full ships, about 60% of the damages have a centre positioned forward of 0.7 ppL⋅ . There is therefore a clear tendency for full ships to have damages with centre located in the forward part of the ship. Nevertheless an interesting quite localised peak in the histogram in Figure 7 is visible close to the central part of the ship. A similar analysis has been carried out also in case of not full ships. As shown in Figure 1, not full ships are mainly concentrated in the region of relatively small lengths, therefore the range of very long vessels cannot be covered appropriately because data are few or missing. In case of not full ships, 50m wide windows have been considered from ] ]0 ,50ppL m∈ m up

to ] ]150 ,200ppL m m∈ . Two additional windows, namely ] ]175 ,250ppL m m∈ and

] ]225 ,350ppL m m∈ , have been considered but basically only for sake of completeness, recognising the lack of data in those ranges. The analysis of /dam pp ppE X L L and of percentile levels for ( )p in case

of not full ships is shown in Figure 8, while the number of available points in each window for not full ships is shown in Figure

/dam pp pCDF X L L

9.



perpendiculars . Not full ships.

/dam ppX L /dam ppX L

ppL



Figure 9: Number of points in each window for the analysis in Figure 8.

Results reported in Figure 8 indicate a tendency for high percentile levels and for the mean value to slightly shift towards the aft part of the ship as the ship length increases. The more visible trend towards the aft part of the ship is on the 75% percentile level. The behaviour of the considered percentile levels, as well as the behaviour of the mean is quite regular up to an average length between perpendiculars in the window of about 160m-180m. When moving to larger ship lengths, the behaviour is more irregular with a jump in case of the last window

] ]225 ,350ppL m∈ m which is likely due to the limited number of available data points (see Figure 9), with a consequent quite high uncertainty in the estimators. Similarly to Figure 5, also in this case a systematic application of a two-sample Kolmogorov-Smirnov test has been carried out between samples in different windows, and results are shown in Figure 10.



Figure 10: Results of window-to-window two-sample Kolmogorov-Smirnov test of hypothesis for equal

( /dam pp ppCDF X L L ) among different windows. Not full ships.

According to Figure 10 some statistically significant difference among ( )/dam pp ppCDF X L L

can be seen when comparing ships of about 60m-80m with ships of about 130m-140m. The obtained statistically significant difference is reasonable in view of the observed tendency in the 75% percentile level in Figure 8 and in view of the availability, in these ranges, of not small samples (see Figure 9). However, in the majority of the remaining comparisons, significant differences could not be observed. Hence, in absence of more data, and considering especially that the mean value and the median value in Figure 8 are quite independent of the ship length, it seems reasonable, from the engineering point of view, to use, also for not full hull forms, a unique distribution, independent of the ship size, for the nondimensional position of the centre of damage. The estimated together

with an histogram of the relative frequency of are shown in Figure 11 and Figure 12 respectively.

( /dam ppCDF X L )/dam ppX L



Figure 11: Estimated cumulative distribution for in case of not full ships. /dam ppX L

Figure 12: Relative frequency histogram for in case of not full ships. /dam ppX L


Deliverable D3.2 - Annex 3 Looking at Figure 11 and Figure 12 it can be seen that, in comparison to the case of full ships (see Figure 6 and Figure 7), a larger percentage of cases have now a centre of damage which is shifted towards the central part of the ship. For sake of direct comparison, Figure 13 reports the cumulative distribution of the nondimensional position of the centre of damage for full ships and for not full ships. In addition, also the cumulative distribution for the same quantity has been estimated using the whole set of data (i.e. full and not full ships together). Similarly, a direct comparison of histograms of relative frequency is proposed in Figure 14.

Figure 13: Comparison of estimated ( )/dam ppCDF X L in case of full ships, not full ships and in case of

using the complete database.



Figure 14: Comparison of histogram of relative frequency of in case of full ships, not full ships

and in case of using the complete database. /dam ppX L

By looking at Figure 13 and Figure 14 it can be seen that, of course, the distribution obtained by using the whole set of data is a sort of weighted average between the distribution of full ships and not full ships, with a tendency towards that of not full hull forms due to the larger number of data. Before closing the exploratory data analysis on damX it is worth comparing, only for qualitative indication, the cumulative distribution of as obtained for passenger ships, with those obtained for full and not full ships. Figure 15 contains this comparison. Of course the limited number of passenger vessels available in the database prevents any statistically significant conclusion, however it seems that the distribution observed for passenger vessels is more similar to, and could therefore be represented by, the distribution obtained from the set of data for not full hull forms.

/dam ppX L



Figure 15: Comparison of between passenger ships, not full ships and full ships. ( /dam ppCDF X L )

Longitudinal position of the forward end of damage ,F damX

As anticipated, the forward end of damage could be, in the context of grounding, a more physical reference for the description of the damage. It is therefore worth also considering this variable in a way which is similar to that used for the analysis of the position of the centre of damage. By definition of forward end of damage , see eq. (2), and because of its geometrical meaning, it is obvious that the distribution of will be shifted towards the forward end of the ship with respect to the distribution of the damage centre

,F damX

,F damX

damX . A view of the available data is given in Figure 16 and Figure 17, and in Figure 17 full ships and not full ships are highlighted, as well as data added in GOALDS.



Figure 16: Scatter plot of and as function of . , /F dam ppX L /dam ppX L ppL

Figure 17: Scatter plot of the nondimensional damage extent as function of . ppL


Deliverable D3.2 - Annex 3 The analysis of mean and percentile levels has been carried out also for separately for full ships and not full ships. Results are shown in Figure 18 and Figure 19.

, /F dam ppX L



perpendiculars . Full ships. , /F dam ppX L , /F dam ppX L

ppL





perpendiculars . Not full ships. , /F dam ppX L , /F dam ppX L

ppL Comparing Figure 18 with Figure 3 it seems that in case of full hull forms both the nondimensional centre of damage and the nondimensional forward end of damage have distributions not strongly dependent from the ship size (measured here by the length between perpendiculars). When using the centre of damage as reference, there is a small tendency in Figure 3 to have damages shifted towards the aft part of the ship as the length increases, while when using the forward end of damage as reference point, there seems to be in Figure 18 a slightly opposite tendency, i.e. a small tendency to have damages with forward end shifted a little bit forward as the ship length increases. However, in both cases the tendency is quite small and could be neglected. Comparing Figure 19 with Figure 8 it seems that the variable shows a smaller dependence from the ship length. In Figure 8 a tendency towards a shifting aft of the centre of damage was detectable, while in Figure 19 this tendency, although still visible, seems to be less marked.

, /F dam ppX L

It could therefore be said that, overall, the variable seems to show a smaller/less systematic dependence of the characteristics of its distribution on the ship length. In this respect the variable could be considered more appropriate / manageable than the variable for characterising the position of bottom damages along the ship.

, /F dam ppX L

, /F dam ppX L/dam ppX L

Neglecting the dependence of the distribution of on the ship length, the

cumulative distribution has been estimated for full ships, not full ships, , /F dam ppX L

( , /F dam ppCDF X L )GOALDS-D-3.2-GL- Grounding Damage Characteristics –rev1 - ANNEX 3

Page 26 of 107

Deliverable D3.2 - Annex 3 and for the complete database. Results of the estimation of ( ), /F dam ppCDF X L are shown in Figure 20, while histograms of relative frequency are shown in Figure 21 and Figure 22 for full and not full ships respectively. Figure 23 finally compares relative frequency histograms for full ships, not full ships and the complete database.

Figure 20: Comparison of estimated ( ), /F dam ppCDF X L in case of full ships, not full ships and in case of

using the complete database.



Figure 21: Relative frequency histogram for in case of full ships. , /F dam ppX L

Figure 22: Relative frequency histogram for in case of not full ships. , /F dam ppX L



Figure 23: Comparison of histogram of relative frequency of in case of full ships, not full

ships and in case of using the complete database. , /F dam ppX L

According to Figure 21, Figure 22 and Figure 23, the probability density function of would tend to have a prominent peak in the forward region of the ship (say forward of about

), both in case of full hull forms and in case of not full hull forms, but the peak is more evident in case of full hull forms. When looking at Figure 20 it can be seen that in case of not full hull forms 50% of the cases have a forward end of damage which is forward of (i.e. a "grounding damage which starts forward of") about 0.75

,F damX

0.9 ppL⋅

ppL⋅ , while in case of full hull forms 50% of the cases have a forward end of damage which is forward of (i.e. a "grounding damage which starts forward of") about 0.87 ppL⋅ . It is also very interesting to note that 30% of the damages have a forward end of damage forward of 0.89 ppL⋅ in case of not full hull forms, and forward of 0.94 in case of full hull forms. ppL⋅As a final qualitative analysis, similarly to Figure 15, we compare in Figure 24 the cumulative distribution of as obtained from the very limited sample of passenger vessels (only 15 from which can be calculated), with the distributions obtained from the subsets of full and not full hull forms: there seems to be again a better agreement between passenger vessels data and data from not full hull forms, but it is impossible to go beyond a qualitative indication due to the limited sample of data associated with passenger vessels.

, /F dam ppX L

, /F dam ppX L



Figure 24: Comparison of between passenger ships, not full ships and full ships. ( , /F dam ppCDF X L )

Damage penetration For bottom damages, the damage penetration is intended as the vertical damage extent zL , i.e. the extent of damage along the z-axis. The available database contains a total of 125 reported cases with information concerning the vertical extent of damage zL . Of these 125 cases, 83 cases belong to the class of full hull forms, while the remaining 42 cases belong to the class of not full hull forms. It is interesting to see that in the analysis of damage penetration the ratio between full and not full hull forms (83/ 42 1.98= ) is completely different from the ratio between data belonging to the class of full hull forms and the class of not full hull forms in the whole database (according to Table 1 this ratio is 138/ 221 0.62= ). According to the reported numbers, the sample of data is quite limited, and this should be borne in mind when looking at the following analyses where ships are separated between full and not full hull forms. In addition, only 3 cases reporting zL are available for passenger vessels, and therefore it is impossible to provide any statistics for this specific ship type for what concerns bottom damage penetration. First of all we report scatter plots of the available data concerning zL as function of the ship length between perpendiculars (Figure 25) and as function of the ship breadth.



Figure 25: Scatter plot of damage penetration zL as function of . ppL

Figure 26: Scatter plot of damage penetration zL as function of B .


Deliverable D3.2 - Annex 3 From Figure 25 it can be seen that the range of ship lengths above about 150m is almost completely governed by data associated with full hull forms, while not full hull forms mainly concentrate in the region of smaller ship lengths, with a limited number of exceptions. Some full ships are present also in the range of small lengths, but their number is significantly smaller than the number of not full ships in the same range of ship lengths. Indeed, with respect to data relevant to this section, 91% of not full ships have less than 150m in length, while about 82% of the full hull forms have more than 150m in length. The situation is, of course, not very different when looking at Figure 26, where it can be seen that the majority of not full ships (90%) have breadths smaller than 20m, while the majority of full ships data (82%) are associated with breadths larger than 20m. It will therefore be difficult to obtain directly comparable statistics for full and not full hull forms due to the lack of a sufficiently large overlapping region of ship sizes. In addition, it is expectable that statistical estimators for full ships will be less reliable in the range of relatively small lengths, while statistical estimators for not full ships will be statistically almost meaningless above the length of about 150m. From Figure 25 and Figure 26 we can also see that in all but two cases penetrations are smaller than 4.2m, and only one reported case has a penetration of 7m. The limited availability of data and their uneven distribution among different ship sizes preclude the possibility of an extensive analysis of percentile levels of the distribution of the damage penetration as a function of the ship size. We will therefore investigate only the behaviour of the average damage penetration as a function of the ship size. For this purpose a sliding window approach will be used, and windows will be adapted taking into account the availability of data. The analyses will be performed using the ship breadth as the reference measure for the ship size, because bottom damage penetration requirements, as in SOLAS [4], are generally linked to the ship breadth. In case of full hull forms, lower bounds for the windows have been defined, in terms of breadth, as [ ]5,10,20 :1:30,35,40,45 m , while upper bounds have been taken as

[ ]10,20,25:1:35,45,50,60 m . It can be seen that, when feasible, 5m wide windows in terms of ship breadth have been used, otherwise larger windows have been considered in order to have a sufficient number of points. In case of not full ships, lower bounds have been set as [ ]5:1:15,20 m and upper bounds have been set to [ ]10 :1: 20,60 m . It is clear that the last

window used in case of not full ships, i.e. ] ]20,60B∈ m is questionable, but it was not possible to find a better solution due to the limited number of data for breadths above 20m. The results of the analysis are reported in Figure 27, where the conditional average zE L B is shown as a function of the ship breadth for full ships and not full ships. In addition an analysis has been carried out on full ships after removing the ID 3109, which corresponds to the largest penetration in the database, i.e. 7zL m= .



Figure 27: Behaviour of the average of damage penetration conditional to the ship breadth, zE L B ,

for not full ships and full ships. From the curves in Figure 27 it can be seen that, in the region where results from full ships and not full ships are directly comparable, i.e. below about 20-25m, the differences between the conditional averages for the two classes of ships are negligible. For what concerns the general behaviour of zE L B , there seems to be an initial tendency for a constant average dimensional damage penetration, say up to about 20m in breadth. For larger breadths, there seems to be a tendency towards an increasing of the average damage penetration as the ship dimensions, here measured by the ship breadth, increase. It must however be borne in mind that the confidence intervals for the estimated mean values are very wide, and this renders relative comparisons between means in different windows of limited statistical significance. The reported effect of the removal of the largest observed penetration ( 7zL m= ), i.e. the ID

3109, is also instructive. Indeed, the effect of this removal on zE L B in the last two windows associated with the largest breadths is not small, and it can be seen that keeping or removing just one point can create different impressions for what concerns the trend of zE L B (a similar problem was addressed in [5]).

The analysis carried out in dimensional form in Figure 27 has also been carried out in terms of nondimensional damage penetration, by checking the behaviour of /zE L B B , as shown in Figure 28.



Figure 28: Behaviour of the average dimensionless damage penetration conditional to the ship breadth,

/zE L B B , for not full ships and full ships.

From Figure 28 it can be seen, for both full and not full ships, an initial decreasing of the average conditional nondimensional damage penetration /zE L B B as the ship breadth increases, and this is consistent with the almost constant conditional average value of the dimensional damage penetration zE L B observed in Figure 27. For breadth larger than, say

20m-25m, /zE L B B becomes almost constant, or slightly decreasing, which is consistent

with the increase of zE L B observed in Figure 27. According to Figure 27 and Figure 28 it seems that, in the range below a breadth of about 25m, where full and not full ships can be compared, the behaviours of the corresponding average dimensional and dimensionless damage penetrations are not significantly different. Therefore, for what concerns the damage penetration, a separation between full ships and not full ships seems to be not necessary, or, better, there is no evidence for the necessity of considering different distributions for full and not full ships. Again referring to Figure 27 and Figure 28 it is not clear whether it is more appropriate to apply a purely dimensional or a purely nondimensional approach for the damage penetration. From the behaviour of the mean it seems that neither of the two is strictly correct. At the same time, looking at Figure 25 and Figure 26, it seems that the maximum observed damage penetration is not significantly dependent from the ship size, apart from the presence of the ID 3109 that could be considered also as an outlier. The independency of the maximum observed damage penetration of the ship size, as well as the almost constant zE L B observed in Figure 27 for relatively small breadths, would indicate a preference towards the use of a GOALDS-D-3.2-GL- Grounding Damage Characteristics –rev1 - ANNEX 3

Page 34 of 107

Deliverable D3.2 - Annex 3 purely dimensional approach, at least in the region of breadths below, say, 20m-25m. However, the slight increase of zE L B observed in Figure 27 for larger breadths, combined with the almost constant maximum observed damage penetration would call for the necessity for a ship-size dependent characterisation of the distribution of the damage penetration. Since purely dimensional or purely nondimensional approaches for the damage characteristics are much more easily manageable, it is therefore interesting to check whether, under a certain level of approximation, it is acceptable to use a purely dimensional or a purely nondimensional approach independent of the ship size. It is expectable for a purely dimensional approach based on the available database to be slightly conservative for small ships and slightly not conservative for large ships (here the wording "conservative" is used in a mostly qualitative way, and is basically limited to considerations based on the average damage penetration). On the other hand a purely nondimensional approach could be expected to be significantly not conservative for small ships and conservative for large ships. Taking into account the fact that we have not noticed significant differences between full and not full ships, we will use the complete database to compare dimensional and nondimensional approaches. We have therefore split our sample of data on the basis of the ship breadth in three classes having about the same number of samples for zL :

- The first class, 0 16−Ω , is ] ]0 ,16B m m∈ with 41 cases

- The second class, 16 27−Ω , is ] ]16 ,27B m∈ m with 42 cases

- The third class, 27 60−Ω is ] ]27 ,60B m∈ m with 42 cases

The estimated cumulative distributions ( )z sCDF L Ω and ( /zCDF L B Ω )s (with

'0 16', '16 27', '27 60's = − − − ) have been determined for each class and compared. In

addition, the cumulative distributions ( )zCDF L and ( )/zCDF L B obtained for the whole sample have been calculated and reported. In the comparisons the influence of the ID 3109 has also been explicitly taken into account by either considering or removing this case. Figure 29 and Figure 30 show the results of the dimensional approach, with and without the ID 3109 respectively, while Figure 31 and Figure 32 show the results of the nondimensional approach, with and without ID 3109 respectively.



Figure 29: Comparison of ( z sCDF L Ω ) for the three considered subsets and for the entire sample.

Figure 30: Comparison of ( z sCDF L Ω ) for the three considered subsets and for the entire sample. ID

3109 removed.



Figure 31: Comparison of ( /zCDF L B )sΩ for the three considered subsets and for the entire sample.

Figure 32: Comparison of ( /zCDF L B )sΩ for the three considered subsets and for the entire sample.

ID 3109 removed.


Deliverable D3.2 - Annex 3 Looking at the dimensional analyses in Figure 29 and Figure 30, it can be seen that the effect of the removal of the ID 3109 associated with a damage penetration of 7m is more evident than in case of the nondimensional analyses in Figure 31 and Figure 32. When considering the dimensional approach in Figure 29, and, particularly in Figure 30 after removing ID 3109, it can be seen that there are, as expectable, some differences in the cumulative distributions among different subsets, with a tendency towards bigger damages in larger ships. However the differences are quite limited in comparison with the confidence intervals from the estimations, which are quite large due to the limited number of samples. For the subsets ] ]0 ,16B m m∈ and ] ]16 ,27B m∈ m we have that ( )0 16zCDF L −Ω and

( 16 27zCDF L −Ω ) are very close, while for ] ]27 ,60B m∈ m there is a tendency for

( 27 60zCDF L −Ω ) to shift towards larger damages, which is consistent with the analysis of the conditional average damage penetration in Figure 27. When considering the cumulative distribution of the damage penetration obtained for the whole database, , it can be seen that this distribution is a quite good, overall, approximation for all the cumulative distributions based on the three subsets, namely

( )zCDF L

( )0 16zCDF L −Ω , ( )16 27zCDF L −Ω and

( 27 60zCDF L −Ω ) . The presence of the outlier ID 3109 poses some difficulties in discussing a reasonable upper limit for the maximum damage penetration. However, the 99% percentile of all available damage penetrations (considering ID 3109) corresponds to about 4.9m, and therefore a maximum damage penetration could be considered as 5m. It must however be recalled that the determination of such high percentile level is associated with a large uncertainty. When looking at the nondimensional approach analysed in Figure 31 and Figure 32, it can be seen that the cumulative distribution of the nondimensional damage penetration for ships in the subset of smaller breadths, ] ]0 ,16B m m∈ , is significantly different from the distributions

of /zL B in the other two considered subsets ( ] ]16 ,27B m∈ m and ] ]27 ,60B m∈ m ). On the

other hand, ( )16 27/zCDF L B −Ω and ( )27 60/zCDF L B −Ω are very similar when ID 3109 is not removed, while, when ID 3109 is removed, there seems to be a systematic shift of

( /zCDF L B Ω )s towards larger nondimensional damages as the ship breadth decreases, with this shifting becoming very evident in the region of smaller breadths. The cumulative distribution ( )/zCDF L B as obtained from the whole database seems to be not capable of

providing a good representation of ( )0 16/zCDF L B −Ω . Summarising this discussion, it seems that the behaviour of the distribution of the bottom damage penetration zL is not simple, and cannot be perfectly represented for any generic ship

size neither with a dimensional approach using ( )zCDF L nor with a nondimensional

approach using ( )/zCDF L B . However, among these two extreme possibilities, it seems that

a completely dimensional approach, based on a common ( )zCDF L irrespective of the ship size, could provide a quite good agreement with the distributions of damage penetration obtained in different ranges of ship breadths, and that this agreement can be considered more robust than what has been observed when trying to use a common distribution for

( )/zCDF L B irrespective of the ship size. It seems therefore that a fully dimensional


Deliverable D3.2 - Annex 3 approach irrespective of the ship size, with ( )zCDF L obtained from the available data, and a maximum damage penetration of the order of 5m, could be a good balance between simplicity and accuracy. However, this selection depends on the range of application in terms of ship dimensions: by limiting the range of ship dimensions, more accurate, and still simple, approximations can likely be found. In addition, in view of the obtained results in Figure 27 (with a tendency towards an increase of zE L B as B increases) and Figure 28 (with a

tendency towards a decrease of /zE L B B as B increases), there are indications that

considering the variable /zL Bα could lead to distributions less dependent on the ship size. From some preliminary calculations it seems that a value of 0.5α ≈ could be considered as a first rough approximation. This idea requires, however, better fitting and further investigation.

Longitudinal extent of damage There are 309 cases reporting the longitudinal extent of damage xL . In this sample, 131 cases belong to full hull forms, while 178 cases belong to not full hull forms, giving a ratio of

which is not very far from what can be obtained from the global set of data according to Table 1, i.e. 138131/178 0.74=

/ 221 0.62= . Looking at the number of available samples in Table 1, it can be seen that the large majority of reported cases belonging to full hull forms in the database contain information on the damage length (131/138 0.95= ), while in case of not full hull forms this ratio drops to 178/ 221 0.81= . For what concerns specifically passenger vessels, 17 reported cases, on a total of 22 passenger vessels in the database, contain information on the longitudinal damage extent, corresponding to a ratio of 17 / 22 0.77= which is similar to that seen, in general, for not full hull forms. The available data are shown in Figure 33 in terms of dimensionless damage length as a function of the ship length between perpendiculars.

/x pL L p



Figure 33: Scatter plot of as function of /x pL L p ppL

Similarly to what has already been observed in case of the analysis of the damage penetration, also in Figure 33 it is evident that the domain is almost split in two parts: in the range of large

there are mainly full ships, while below there are mainly not full ships. Passenger ships are few and in all but one case they are below 180m. When analysing the behaviour of

ppL

xL it will be in principle difficult to obtain reliable data for full ships in the range of small lengths and, particularly, for not full ships in the range of large lengths. Percentile levels and conditional average for the dimensionless damage length have been estimated by sliding window analyses. In case of not full ships, 50m wide windows have been considered from

/x pL L p

] ]0 ,50ppL m∈ m up to ] ]150 ,200ppL m∈ m . Two additional windows,

namely ] ]175 ,250ppL m m∈ and ] ]225 ,350ppL m m∈ , have been considered but basically only for sake of completeness, recognising the lack of data in that range. On the other hand, in case of full ships, 50m wide windows have been considered from ] ]0 ,50ppL m∈ m up to

] ]290 ,340ppL m∈ m , with a final window ] ]300 ,355ppL m∈ m to keep also the longest ship (350.4m between perpendiculars). Results for not full ships and for full ships are shown in Figure 34 and Figure 35 respectively, while Figure 36 shows the number of points in each window used in the analyses.



Figure 34: Percentile levels and /x pp ppE L L L . Not full ships.

Figure 35: Percentile levels and /x pp ppE L L L . Full ships.



Figure 36: Number of points in each window for the analyses in Figure 34 and Figure 35.

By looking at the analysis for not full ships in Figure 34 there seems to be a slight tendency for the nondimensional measured damage length towards a shifting in the direction of longer damages as the ship length increases. This tendency is more evident especially because in the region of smallest ships, around 50m in length, the estimated conditional average nondimensional damage length is clearly smaller than in case of longer ships. However, if we do not consider the region of very small lengths, then

/x pL L p

/x pp ppE L L L is not strongly

dependent on the ship length, and it tends to become almost constant. At the same time the median value of tends to systematically increase as the ship length (and hence the ship size) increases, indicating a variation in the shape of the distribution.

/x pL L p

If we now concentrate on Figure 35 for full ships, we can see a clear tendency for

/x pp ppE L L L to increase, almost linearly, as the ship length increases up to about 150m.

For longer ships /x pp ppE L L L becomes almost constant. A very similar behaviour is

evident also for the median value of . /x pL L p

In order to better compare the behaviour of full and not full ships, Figure 37 shows

/x pp ppE L L L with 95% confidence intervals for the two subsets. In addition, the result of

the analysis of /x pp ppE L L L using the whole set of available data, with the same

windowing used for full ships, is also reported.



Figure 37: /x pp ppE L L L for full ships and not full ships.

Looking at Figure 37 it seems that differences between full ships and not full ships are evident in the range of smaller ship lengths, say below 100m-120m. At the same time differences in

/x pp ppE L L L reduce significantly for longer ships. In the region of lengths close to 140-

150m there seem not to be significant differences, also in view of the relatively large confidence intervals. It is interesting to note that, when the complete database is considered, the average dimensionless damage length is almost independent of the ship length, with some tendency towards decreasing in the range of very small ships, say below about 60m-80m. To further investigate the observed different behaviour for the average value, and hence the distribution, of , we have directly compared the estimated cumulative distributions of

for full ships and not full ships in two different ranges of ship lengths. Results of the comparison are shown in Figure 38.

/x pL L p

p/x pL L



Figure 38: Comparison between estimated cumulative distributions for for full and not full ships

in two ranges of ship lengths. /x pL L p

From Figure 38 we can see that, in the range ] ]50 ,100ppL m∈ m

p

there is a clear and also statistically significant difference between the cumulative distribution of for full ships, showing smaller nondimensional damages, and not full ships, showing significantly larger nondimensional damages. However, when we move to the interval

/x pL L

] ]125 ,175ppL m∈ m , differences between full and not full ships become smaller and statistically not significant, also in view of the limited sample of not full vessels. It seems therefore that, in principle,

( /x pp ppCDF L L L ) should be different between full ships and not full ships, with not full

ships showing larger damages, in the region of small , while in the region of large it seems possible to use the same distribution both for full and not full ships. In order to better identify the region where the cumulative distributions of the nondimensional damage length between full and not full ships are significantly different from the statistical point of view, we have carried out a systematic set of two-sample Kolmogorov-Smirnov tests, as shown in Figure 39.

ppL ppL



Figure 39: Determination of ranges of ship lengths where the distribution of is significantly

different between full and not full hull forms. /x pL L p

From the results in Figure 39 it seems that, apart from the region of ship lengths between about 60m and 120m, for all the remaining ship lengths the distribution ( )/x pp ppCDF L L L is

not significantly different between full and not full ships. In general, however, it must be said that in the range of small lengths there is a lack of data for both full and not full ships, which renders differences in the distributions statistically not significant even when large. Similarly, in the range of large lengths there is a lack of data for not full ships, and this lack of data renders even large differences between distributions statistically not significant. The range between roughly 70m and 170m of average ship length inside the testing window seems to be the most appropriate for a discussion of the results, because in this range there are a sufficient number of points both for full and not full ships (see Figure 36), although this number is not always large. Accordingly, and extrapolating the results of the hypothesis test (this operation cannot be, however, strongly justified), we could roughly say that differences in the distributions for the dimensionless damage length between full and not full ships should be considered not negligible below a ship length of about 120m and negligible for longer ships. It is clear that the observed differences in the behaviour of between full and not full

ships would call for a model of the distribution

/x pL L p

( )/x pp ppCDF L L L which differs for the two

subsets. In case of not full ships it seems that, with a sufficient approximation, a purely dimensionless model independent of the ship length could be applicable:

( ) ( ) ( ),1 ,2 ,1 ,2, / / /pp pp x pp pp x pp pp x ppL L CDF L L L CDF L L L CDF L L∀ = = . On the other hand it

seems that for full ships a ship-size-dependent model for ( )/x pp ppCDF L L L would be


Deliverable D3.2 - Annex 3 needed, with a shifting of dimensionless damages towards larger sizes as the ship length increases from 0m to about 150m, while a dimensionless ship-size independent model could be appropriate for longer ships. In addition it seems that the same dimensionless model could be applicable for not full ships irrespective of the length and for full ships above about 150m in length (see Figure 38). It must also be noted that this model for the distribution of can be expected to be conservative when compared to the model that would probably be required for full ships of small length.

/x pL L p

p

p

Recognising all the above, but in view of the search for a simplification of the problem embedding a good balance between simplicity, accuracy and approximation of data, we test here the idea of using the same model for the distribution of irrespective of the ship type (full / not full ships) and irrespective of the ship length. Two models will be considered:

/x pL L

1) We will determine the distribution of for all ships irrespective of the ship

length, i.e.

/x pL L

( )/x ppCDF L L ;

2) We will determine the distribution of for all ships having length above 80m,

i.e.

/x pL L p

( )/ 8x pp ppCDF L L L m≥ 0 ;

It is expected that ( / 8x pp ppCDF L L L m≥ )0 will be more conservative than ( )/x ppCDF L L

because small full and not full ships typically show smaller nondimensional damage lengths. The obtained distributions, as well as the mean value and some references percentile levels are shown in Figure 40.

Figure 40: Estimated cumulative distribution for dimensionless damage length using all ships and using

all ships with length between perpendiculars not less than 80m.


Deliverable D3.2 - Annex 3 From the distributions shown in Figure 40 it can be seen that the effect of ships below 80m in length is quite limited. As expected, ( )/ 8x pp ppCDF L L L m≥ 0 is slightly biased towards

larger dimensionless damage lengths than ( )/x ppCDF L L , however the difference is small and statistically not significant. Confidence intervals for the average value have been reported, while the magnitude of the confidence intervals for percentile levels can be deduced from the reported confidence intervals for the estimated cumulative distribution. It can be seen that the average values obtained in Figure 40 are in line with those obtained for not full ships above 60m-80m and are in line with the average nondimensional damage length observed for full ships above about 150m (see Figure 37). The same can also be said concerning the percentile levels (see Figure 34 and Figure 35). Thanks to the small difference observed in Figure 40, and for sake of conservativeness, we could consider

( / 8x pp ppCDF L L L m≥ )0

p

as a reference distribution which is sufficiently accurate for

describing the average behaviour of for not full ships above 60m-80m and for full

ships above about 150m. For smaller lengths

/x pL L

( )/ 8x pp ppCDF L L L m≥ 0 is on average

conservative both for full and not full ships. It can therefore be considered that using

( / 8x pp ppCDF L L L m≥ )0 as a working tool irrespective of the actual ship length could be a

good balance between accuracy, simplicity and conservativeness. In order to better understand the relation between the percentile levels inherent in

( / 8x pp ppCDF L L L m≥ )0 , as well as the mean value, in comparison with those actually

estimated for full ships and not full ships as function of the ship length, Figure 41 and Figure 42 provide a graphical representation. The agreement can be considered sufficiently good in the region of lengths where a nondimensional approach is assumed to be acceptable for full and not full ships, also in view of the fact that the percentile levels estimated by the sliding window technique have quite large confidence intervals due to the limited number of samples in each window. The conservativeness in the range of small ship lengths, in particular for what concerns full ships, is now, hopefully, more clear.



Figure 41: Comparison between percentile levels and mean value given by ( )/ 8x pp ppCDF L L L m≥ 0

with those estimated for ( )/x pp ppCDF L L L . Full ships.



Figure 42: Comparison between percentile levels and mean value given by ( )/ 8x pp ppCDF L L L m≥ 0

with those estimated for ( )/x pp ppCDF L L L . Not full ships.

Going now to the specific case of passenger ships, Figure 43 compares

( / 8x pp ppCDF L L L m≥ )0

p

with data coming from passenger vessels. There is a good

agreement between the distribution of obtained for all passenger vessels and that obtained using all ships not shorter than 80m. At the same time the maximum observed dimensionless damage length for passenger vessels is smaller than that observed in the sample of all ships not smaller than 80m. However, the number of data for passenger vessels is too limited to draw any conclusion and the hypothesis of equal distributions is not rejected by a two-sample Kolmogorov-Smirnov test at 5% significance level.

/x pL L



Figure 43: Comparison between distribution of dimensionless damage length for passenger vessels and

( )/ 8x pp ppCDF L L L m≥ 0 based on all ships.

Before closing this section, however, it is worth to provide some additional comment on the different behaviour observed for full hull forms when moving from small ship lengths to large ship lengths. Indeed, the difference in the behaviour of the dimensionless damage length distribution is qualitative and not only quantitative. In a tentative of explanation, we have tried to find some quantity in the present database which could be correlated with this difference, and the attention was captured by the field reporting the source of data in the used database [1]. In Figure 46 a scatter plot of the dimensionless damage length as a function of the ship length is shown, with data separated according to their source. Data added in GOALDS are also highlighted.



Figure 44: Ratio as a function of the ship length with points separated into different categories

on the basis of the source of data. Full ships. /x pL L p

m

From Figure 44 it is evident that, for ships below about 150m in length, the majority of data come from the source "IMO". On the other hand, for ships longer than about 150m in length the majority of data has "DNV_IMO" as source. The separation is quite sharp, and the separation point, i.e. corresponds approximately to the length where the qualitative change in the behaviour of the distribution of the dimensionless damage length has been observed in this section.

150ppL ≈

As a comparison, the same analysis has been performed also for not full ships, as shown in Figure 45. In this case data with source "DNV_IMO" are missing and the set of data does not show any sharp separation between different sources.



Figure 45: Ratio as a function of the ship length with points separated into different categories

on the basis of the source of data. Not full ships. /x pL L p

The analyses in Figure 44 and Figure 45 cannot be considered to represent a proof of a link between the source of the data and the differences in the behaviour of ( )/x pp ppCDF L L L

observed between small and large ship lengths for full ships. However this point is worth some more attention and further analysis.

Transversal damage extent

Introduction Grounding data containing information on the transversal damage extent (the damage "width") are in total 210, i.e. 58.5% of the total entries in the database. Of these 210 cases, 41 cases have been added in the framework of GOALDS ( 41/ 210 19.5%= of data), while the remaining 169, i.e. 80.5% of the cases, come from the HARDER project. Of the total 210 cases, 112, i.e. about 53.3%, belong to the class of full ships, while the remaining 98 (46.7%) belong to the class of not full ships. It can be seen, then, that almost half of the data belong to full ships, and the remaining half of the data belong to not full ships. In total, only 13 cases, less 6.2% of the data containing the damage width, belong to passenger vessels. It is therefore clear that any derivation of specific information for passenger vessels on the basis of only 13 samples is impossible due to the excessive uncertainty in the statistical estimators. The scatter plot of available data for the dimensionless damage width is reported in Figure 46 as function of the ship breadth, and in Figure 47 as function of the ship length between perpendiculars.

/yL B

GOALDS-D-3.2-GL- Grounding Damage Characteristics –rev1 - ANNEX 3

Page 52 of 107


Figure 46: Scatter plot of dimensionless damage width, , as a function of the ship breadth. /yL B

Figure 47: Scatter plot of dimensionless damage width, , as a function of the ship length. /yL B


Deliverable D3.2 - Annex 3 Again, full ships mainly populate the region of large breadths and lengths, while not full ships mainly populate the region of small breadths and lengths. In addressing the statistics of damage widths it has been decided to separate full and not full ships in two sections as a consequence of some difficulties, which will be clarified in the relevant section, in the analysis of data belonging to full ships.

Transversal damage extent for not full ships Not full ships have been extracted from the database and the dimensionless damage width has been analysed. A scatter plot of the available data is shown in Figure 48, where the source of the data is also highlighted by separating points in different categories. In addition, data collected in the GOALDS project are also identified. It can be seen that the majority of available data belong to the region of breadths below about 20m-25m (about 80% of data have , while almost 90% of data have 21B ≤ m m25B ≤ ). A limited set of data is available in the range of large breadths, with a significant part of data coming from the GOALDS project. In addition, it can be seen that a large part of the GOALDS data is represented by equivalent damage characteristics, i.e. characteristics of virtual equivalent damages intended to substitute a set of multiple holes in the same casualty [3].

Figure 48: Scatter plot of as function of with indication of data source. Not full ships. /yL B ppL

From Figure 48 it can be seen that there is a limited availability of data in the range of large breadths, and in particular there are no data in case of post-panamax vessels, since the maximum breadth for which data are available is 32.25m. There is an evident difference between the population collected in GOALDS and the other data. In particular GOALDS data belong all to the region of (very) small ratios . As /yL B


Deliverable D3.2 - Annex 3 consequence it is expectable that the statistics for 20 22B m m≤ − and the statistics for larger breadths will show significant differences connected to the data source. A sliding window analysis has been carried out on the data reported in Figure 48 for percentile levels and mean value. The windows used in the analysis are 5m large (in breadth) starting from ] ]5 ,10B m m∈ up to ] ]25 ,30B m∈ m with 1m steps. A final window has been

used for ] ]26 ,35B m∈ m . The results of the analysis are reported in Figure 49, while the number of points in each window is shown in Figure 50.

Figure 49: Percentile levels and /yE L B B . Not full ships.



Figure 50: Number of points in each window used in the analysis reported in Figure 49.

As expected, in correspondence with the change of data source moving from small to large breadths, the distribution ( /yCDF L B B) shifts significantly towards smaller damages as the

ship breadth increases. In the region where more data are available, i.e. below about a breadth of about 20m, it seems that the average value /yE L B B as well as the percentile levels of

( /yCDF L B B)

m

are quite constant, indicating the suitability of a common distribution for

independent on the ship breadth. The sharp shifting of the distribution towards smaller damages in the region governed by GOALDS collected data is quite doubtful. This behaviour looks especially doubtful when looking at the final windows for the extreme breadths, where GOALDS data are accompanied by data from other sources, and, as a consequence, the characteristics of damage tend to shift again towards larger dimensionless widths.

/yL B

It is difficult to provide a definite conclusion. However, it seems reasonable that the minimum, close to 25B ≈ , in the graph of the mean and some percentile levels observed in Figure 49 is a spurious effect, and it seems reasonable to keep the indication given by data for

, i.e. the indication of the suitability for a common distribution of independent of the actual ship breadth (size).

20B ≤ m /yL B

On the basis of this assumption (that, however, needs more data to be fully justified or rejected) a common cumulative distribution ( )/yCDF L B for not full ships has been estimated from the database, and is reported in Figure 51. Figure 51, for sake of reference, also reports the estimated average value of the dimensionless transversal damage extent, which is slightly larger than , with the associated 95% confidence intervals. 0.1B GOALDS-D-3.2-GL- Grounding Damage Characteristics –rev1 - ANNEX 3

Page 56 of 107


Figure 51: Estimated distribution ( )/yCDF L B for not full ships.

Transversal damage extent for full ships Full ships have been extracted from the database and the dimensionless damage width has been analysed. A scatter plot of the available data is shown in Figure 52, where the source of the data is also highlighted by separating points in different categories. In addition, data collected in GOALDS project are also identified. It can be seen that, similarly to what happened in the analysis of the dimensionless damage length for full ships (see Figure 44), there is a sharp separation between data coming from source "IMO" and data coming from source "DNV_IMO", and here the separation is at a breadth of about 25m. The dimensionless damage widths associated with the source "DNV_IMO", which form the large majority of the sample in the range of larger breadths (above 25m), seem to be systematically larger than the dimensionless widths associated with the source "IMO", which instead form more than half of the sample in the range of breadths below 25m. This characteristic is expected to have a not negligible influence on the statistical analysis when moving from below to above 25m in breadth. GOALDS data belong to the range of small dimensionless damage widths, and this characteristic is similar to what has been observed in case of not full ships in Figure 48. In addition, GOALDS data are mostly in the region of breadths below 28m.



Figure 52: Scatter plot of as function of with indication of data source. Full ships. /yL B ppL

A sliding window analysis ha been performed, with windows 5m wide ranging from

] ]5 ,10B m m∈ up to ] ]40 ,45B m∈ m with 1m steps, and additionally with windows 10m wide

from ] ]41 ,51B m m∈ up to ] ]50 ,60B m∈ m at 1m steps. The analysis of conditional percentile levels and mean provides the results shown in Figure 53, while Figure 54 shows the number of points in each window used in the analysis.



Figure 53: Percentile levels and /yE L B B . Not full ships.

Figure 54: Number of points in each window in the analysis reported in Figure 53.


Deliverable D3.2 - Annex 3 Looking at the behaviour of conditional percentile levels and mean in Figure 53, it can be seen that initially, for breadths below about 20m-23m, both the mean and the percentile levels are quite constant, indicating the suitability of a nondimensional approach for the cumulative distribution of in this range. If the ship breadth increases, however, a sharp increase in the mean and in the percentile levels is observed in a very small range of breadths, but this increase stops quite suddenly, and for breadths above about 25m again percentile levels and mean value tend to remain quite constant as the ship breadth increases, indicating the suitability of a nondimensional approach for breadths above about 25m. However, the distribution for to be associated with the range of small breadths, and the distribution of the same quantity in the range of large breadths would be quite different, with this latter being shifted towards larger damages and the former being shifted towards smaller damages. The sharp separation between the two observed behaviours was to some extent expected, according to the discussion already done with reference to Figure 52, and the range of change of behaviour for the distribution of agrees quite well with the range where data from source "IMO" ends and data from the source "DNV_IMO" starts.

/yL B

/yL B

/yL B

In order to check the influence of different data sources, we have therefore repeated the analysis of the mean performed in Figure 53 but now we have omitted, in a first case, data coming from source "IMO", and in a second case we have omitted data coming from the source "DNV_IMO". The results are shown in Figure 55, where different windows have been used in order to adapt them to the reduced sets of data in the range of either small or large breadths.

Figure 55: Effect on the estimated /yE L B B of the removal of data according to data source. Full

ships. From Figure 55 it can be seen that it is difficult to obtain reliable estimates in the range of large breadths when data from the source "DNV_IMO" are removed, and conversely it is GOALDS-D-3.2-GL- Grounding Damage Characteristics –rev1 - ANNEX 3

Page 60 of 107

Deliverable D3.2 - Annex 3 difficult to obtain reliable estimations in the range of small breadths when data from source "IMO" are removed. Nevertheless there seems to be an indication that data from the source "DNV_IMO" are associated with dimensionless widths which are not negligibly larger than average dimensionless widths associated with the remaining data sources, and due to the condensation of "DNV_IMO" in the range of large breadths, this is creating the sharp change in the behaviour of the distribution of which is seen above 25m of breadth. It can be

seen in Figure 55 that when "DNV_IMO" data are removed

/yL B

/yE L B B calculated on the

basis of the remaining set of data does not increase as the ship breadth increases and it even decreases. For sake of reference Table 2 reports the calculated average dimensionless damage width separating data according to the data source, from which it can be seen that data from source "DNV_IMO" are those associated with the largest estimated average dimensionless damage width. Negative values in the lower bounds of some confidence intervals for

/yE L B B are of course meaningless because is always a positive quantity. However

they are reported in Table 2 only for sake of completeness in order to provide a complete quantitative measure of uncertainty for the mean, i.e. the width of the confidence interval, being comparable for all data sources.

/yL B

Table 2: Average dimensionless damage width for full ships according to data source.

Full ships

Source Number of samples

/yE L B with 95% confidence intervals

GL Schaka 2 0.0161 [-0.0340,0.0661]95%CIIMO 29 0.1072 [0.0641,0.1502]95%CI

DNV_IMO 61 0.3054 [0.2209,0.3900]95%CIDNV 4 0.0089 [-0.0049,0.0227]95%CILR 6 0.0289 [-0.0007,0.0586]95%CI

Equivalent 10 0.0732 [-0.0163,0.1627]95%CI It is hence difficult to model the behaviour of the distribution of the dimensionless damage width. The data obtained so far indicate the suitability of a dimensionless approach. However the dimensionless approach should be developed separately for ships below 25m in breadth and ships above 25m in breadth. This behaviour seems to be not very supportable from the physical point of view, and some indications have been found that the sharp variation could be associated with a difference in the source of data. However, it is not possible to arrive at any conclusion without further investigating this matter having at disposal additional information. For the time being it seems that the indication of the suitability, in principle, of the nondimensional approach could be accepted. As an interim solution it could therefore be decided to use all the data for developing a reference ( )/yCDF L B irrespective of the ship size. Of course the suitability of such a single distribution for the dimensionless damage width could be questionable. According to the available data, the alternative would be the creation of two separate cumulative distributions for the region of large breadths and for the region of small breadths, with a blending in the intermediate zone.


Deliverable D3.2 - Annex 3 Figure 56 shows the distribution ( )/yCDF L B considering all the data together. It can be seen

that a singularity is visible at /yL B 1= , corresponding to a jump in the CDF, because there are 6 cases having exactly among the available data. /yL B =1

Figure 56: Estimated distribution ( )/yCDF L B for full ships.

Figure 57 compares the cumulative distributions of the dimensionless damage width estimated from the database for ships having breadth larger than 25m and for ships with breadth not larger than 25m. A large difference in the distributions is evident, and also, as a consequence, in the mean values. It is interesting to see that the average dimensionless damage width for ships with is quite in line with what has been observed for not full ships (see Figure 51).

25B ≤ m



Figure 57: Estimated distributions ( )/ 25yCDF L B B m≤ and ( )/ 25yCDF L B B m> for full ships.

Additional notes

By comparing the cumulative distribution ( )/yCDF L B estimated for not full ships in Figure 51 and for full ships in Figure 56, it is evident that full ships have a distribution shifted towards larger dimensionless damage widths. The average dimensionless damage width for full ships is [ ]95%

0.2028 0.1509,0.2547CI which is almost twice as high as the average value

observed for not full ships, i.e. [ ]95%0.1062 0.0740,0.1384

CI . Although this difference could be due to a tendency for full ships to suffer wider bottom damages, it is still important to consider that this difference could also be partially due to the different geometry of the bottom of full and not full ships. Since the bottom of full ships is, on average, wider than the bottom of not full ships (see Figure 58), and since the measured damage width is always geometrically limited by the width of the bottom in the region affected by the bottom damage, it is possible that the slenderness of bottom waterlines in not full ships could also have had some influence on the statistics of the measured damage width as reported in the database. This aspect, however, must be considered with caution, due to the observed significant difference between the cumulative distribution of the dimensionless damage width for full ships below and above 25m in breadth (see Figure 57). Indeed, considering ships with

, the statistics of L B for full ships are more in line with those observed for not full ships that are mostly below 25m in breadth.

yL

25B ≤ m /y



Figure 58: Typical bottom lines for different ship typologies [6].

It is then worth comparing the distributions for full ships and not full ships as obtained in Figure 51, Figure 56 and Figure 57 in order to clarify the differences. This comparison is carried out in Figure 59. It can be seen that in the range of small breadths the distributions of full and not full ships are not significantly different, although some difference is visible especially in the range of maximum dimensionless widths, with the not full ships showing larger maxima (which is in contrast with the discussion above on the shape of bottom lines). It must however be borne in mind that the sample of not full ships contains also some cases with breadths larger than 25m. It is also evident that, when considering the remaining distributions, the differences between full and not full ships are not negligible.



Figure 59: Comparison between different distributions for obtained from the database. /yL B

Analysis of statistical dependence between damage characteristics

Introduction In the preceding analyses the main damage characteristics, namely the longitudinal position of centre of damage damX (or forward end of damage ), the vertical extent of damage ,F damX zL (damage penetration), the longitudinal extent of damage xL (damage length) and the transversal damage extent (damage width) have been analysed separately, and, when possible, appropriate marginal distributions in dimensional or nondimensional form, depending on the quantity, have been estimated, discussed and reported. It is the intention of this section to address and qualitatively characterise possible dependencies among the variables. Due to the fact that the majority of cases available in the database do not contain all the geometrical characteristics of the damage, the number of available points for the following analyses of statistical dependence will be limited. For this reason the analyses reported in this section will be mainly qualitative in nature, with the intention of providing qualitative indications for the process of development, if necessary, of appropriate modelling for the random variables involved in grounding damages. Moreover, all the analyses will be carried out considering all the ships together. This choice allows increasing the sample of points, although it can be questionable since it can merge, in some cases, different underlying behaviours. However, due to the qualitative nature, as already said, of this section, the need for increasing the sample points has been considered of higher importance, and hence ships have not been separated into different categories.

yL


Deliverable D3.2 - Annex 3 Longitudinal damage position damX (or ,F damX ) and longitudinal damage extent xL

The measured longitudinal position of the centre of damage damX and the measured longitudinal extent of damage xL cannot be independent due to the geometrical limitations given by the finite longitudinal extension of the hull (a similar situation would arise when considering the transversal damage extent and the transversal position of damage). Indeed, assuming that the hull extends from 0X = to shipX L= , it follows that

min 2 , 2 1x dam dam

ship ship ship

L X XL L L

⎧ ⎫⎛ ⎞⎪ ⎪≤ ⋅ ⋅ −⎜ ⎟⎨ ⎬⎜ ⎟⎪ ⎪⎝ ⎠⎩ ⎭ (3)

Therefore damX and xL must necessarily be statistically dependent. In general, then, the distribution of the longitudinal extent of damage should always be considered as a conditional distribution with respect to the damage position, i.e. ( )x damCDF L X . This point has been addressed in the past in [7][8] from the point of view of the definition of suitable distributions for the longitudinal damage extent (see also [9]). It is however possible, under certain assumptions [7][8], to define a virtual random variable (called in [9] the "potential damage length" in ship-ship collisions) which, after the truncation induced by the random variable defining the position of the damage, reduces to the actual measured damage length xL . Similarly to (3), if the forward end of damage is considered as the random variable defining the damage position, xL and cannot be statistically independent because the following relation must hold:

,F damX

,F damx

ship ship

XLL L

≤ (4)

and therefore, the distribution of the longitudinal damage extent should always be considered as conditional to the position of the forward end of damage, i.e. ( ),x F damCDF L X . A methodology similar to that in [7][8][9], and based on the same assumptions, can be applied starting from (4) in order to develop a distribution for a random variable, say the "potential bottom damage length", which, after the truncation induced by , provides a distribution which is coherent with the observed distribution of the measured damage length

,F damX

xL . It can indeed be proved, in a way similar to [7][8][9], that, if the distribution of is

independent of in the interval

/x shiL L p

, /F dam shipX L ,0, /x F dam shipL X L⎡ ⎡∈ ⎣ ⎣ and a singularity occurs

along to fulfil the condition of unitary integral under the (conditional) probability density function, then it is possible to define a random variable, called here the "potential bottom damage length" , having distribution given by:

, /x F dam shipL X L=

,x pL

( ) ( ) ( )( )

,

,

,

,,

,1x F dam

x p

F dam

L x x X F dam xL x p x

X F dam x

cdf L q cdf X qcdf L q

cdf X q

= − == =

− =(5)

GOALDS-D-3.2-GL- Grounding Damage Characteristics –rev1 - ANNEX 3

Page 66 of 107

Deliverable D3.2 - Annex 3 From (5) it follows that it must be ( ) ( )

,0, 0

x F damx L x X xq cdf q cdf q∀ ≥ − ≥

m

. However, this

follows from the fact that it is always ,x F daL X≤ for geometrical reasons (at least assuming the x-axis to start from the extreme aft end of the ship). Moreover, the numerator in (5) is always not larger than the denominator due to fact that the cumulative distribution is, by definition, not larger than one. Under the already reported assumption, the virtual random variable defined through its distribution in (5) can be considered independent of the position of the forward end of damage . The random variable

,x pL

,F damX xL obtained from the truncation of according to ,x pL

, , ,

, , ,

if // if /

x p x p F dam shipx

F dam ship x p F dam ship

L L XL

X L L X L≤⎧

= ⎨ >⎩

L (6)

is expected to have (approximately) the same conditional distribution ( ),x F damCDF L X as observed from the actual measured damage length. When the centre of damage damX is used instead of the forward end of damage then the formulae already known for the collision case [7][8][9] can be used directly:

,F damX

( ) ( )

( ) ( ),

11

2 2

x

x p

dam dam

L xL x

x xX F x ship X A x

cdf qcdf q

q qcdf x q L cdf x q

−= −

⎛ ⎞ ⎛= − − =⎜ ⎟ ⎜⎝ ⎠ ⎝

⎞⎟⎠

p

(7)

From a practical point of view, in order to use (5), or (7), it is necessary that, basically, with good approximation, the percentile levels of can be considered independent of

or , inside the allowable regions defined by (4), or (3). It is important to underline that it is

/x shiL L

, /F dam shipX L /dam shipX Lnot the conditional average which must remain constant (since it does

not remain constant under the reported theoretical modelling), but are the percentile levels of the distribution which should remain independent from the damage position in order to use (5) or (7). Figure 60 and Figure 61 show the scatter plots of the available data in the planes ( )/ , /dam pp x ppX L L L and ( respectively, with in addition the estimated conditional mean and conditional median (i.e. the 50% percentile level) calculated by a sliding window analysis based on windows having width of 0.1 from

), / , /F dam pp x ppX L L L

] ]0.05,0.05− up to

] ]0.95,1.05 with steps of 0.01 in both cases.



Figure 60: Scatter plot of as function of with estimated /x pL L p /dam ppX L / /x pp dam ppE L L X L

and median value.

Figure 61: Scatter plot of as function of with estimated /x pL L p /dam ppX L ,/ /x pp F dam ppE L L X L

and median value.


Deliverable D3.2 - Annex 3 It can be seen that some of the points in Figure 60 and Figure 61 fall outside the geometrical limits based on . This is not an error, instead this is a natural and expected consequence of the fact that the actual overall ship length is different from the ship length between perpendiculars, and therefore in some cases, the damage extends aft or forward of the perpendiculars.

ppL

As anticipated, the application of (5), or (7), would require an independence of the percentile levels of the distribution of the (dimensionless) damage length from the (dimensionless) damage position. Looking in Figure 60 at the behaviour of the median value, i.e. the 50% percentile level, it can be seen that, inside the acceptable region given by (3), there is a quite large flat region for the median indicating the desired independence. As the interval shifts towards the aft and forward ends of the ship, however, the median tends to reduce, and therefore the independence is partially lost. Nevertheless it seems that the assumptions required by (7) are, at least approximately, reflected by the data. It is worth underlining that the conditional mean value in Figure 60 does not have, and it is not required/expected to have, any flat region, because the conditional average of the measured damage length is necessarily dependent on the damage location. Looking now at the alternative representation in Figure 61, it can be seen that the conditional median value has a significantly large flat region starting from about up to the forward end of the ship. This characteristic is in line with the required assumptions for the application of (5). Also in this case, it can be seen that the conditional mean value of the damage length is not independent of the damage position, and neither was it expected to be. Indeed the measured damage length is on average larger when the damage has a forward end located in the forward part of the ship, and necessarily smaller, for geometrical reasons, when the forward end of the damage is located in the aft part of the ship.

, / 0F dam ppX L ≈ .3

It is interesting to note that the graphical representation based on the position of the forward end of damage (Figure 61) seems to be much more readily understandable than the corresponding representation based on the centre of damage (Figure 60). Moreover, the possible definition of characteristic damage dimensions seems to be more natural by using the representation in Figure 61 than the representation in Figure 60. In addition it is extremely important to note that the numerical value of the estimated conditional average damage length is significantly dependent on whether the statistics is considered conditional to the position of the centre of damage or to the position of the forward end of damage, although, of course, the marginal average dimensionless damage length is the same for both Figure 60 and Figure 61. It is therefore important to clearly define how the conditional mean is to be calculated with reference to the way the damage position is defined. Finally, it is worth underlining again that the procedure reported in this section for the determination of the "potential damage length" should be applied in principle also in case of the measured transversal damage extent with reference to the transversal position of damage (not available in the database) because, also in such case, the measurable transversal damage extent is geometrically limited by the extreme portside and starboard limits of the ship, and therefore the measured transversal damage extent and the transversal position of damage (not available from the database) cannot be considered independent.

yL

Longitudinal damage extent xL and vertical damage extent zL

Here we will analyse the dependence between the damage length xL and the damage penetration zL . In particular we will try to provide some basis for trying answering the GOALDS-D-3.2-GL- Grounding Damage Characteristics –rev1 - ANNEX 3

Page 69 of 107

Deliverable D3.2 - Annex 3 question whether it is likely or not to have, e.g., very short (dimensionless) damages with very large penetration. Since in the analysis of marginal distribution it was considered that the dimensionless damage length , as well as the dimensional damage penetration /x pL L p zL , could be suitable for describing the damage characteristics as the ship size changes, we have used these two variables for an analysis on their possible dependence. Figure 62 shows a scatter plot of zL as a function of together with the estimated conditional mean and median using sliding windows with widths adapted to the data, particularly in the range of very small .

/x pL L p

p/x pL L

Figure 62: Scatter plot of dimensional damage penetration zL as function of dimensionless damage length

with estimated conditional mean /x pL L p /z x ppE L L L and median.

From the result in Figure 62 it can be seen that, for dimensionless damage lengths above about 0.1 both the mean and the median are quite constant, indicating (though not proving) a possible independence of zL from if . However, for shorter dimensionless damage lengths there is a visible decrease of the average damage penetration, indicating that damages with small dimensionless damage length also show small dimensional damage penetrations. Differently from the mean, the median does not show such a visible decrease, and remains more constant in almost the whole range of , although, in the region of very small dimensionless damage lengths, below about 0.05, also the median value tends to decrease.

/x pL L p .1

p

/ 0x ppL L >

/x pL L


Deliverable D3.2 - Annex 3 If this dependence is neglected by considering zL independent of , it is likely to model a probability of occurrence of short (in terms of ) and deep (in terms of

/x pL L p

p/x pL L zL ) damages which is higher than the corresponding probability as estimable from the database. It is not clear at this stage, however, whether this difference can be considered negligible or not.

Longitudinal damage extent xL and transversal damage extent yL

Here we will analyse whether the dependence between the damage length xL and the damage width . In particular we will try to provide some basis for trying answering the question whether it is likely or not to have, e.g., very short (dimensionless) but wide (dimensionless) damages.

yL

Since in the analysis of marginal distribution it was considered that the dimensionless damage length , as well as the dimensionless damage width , could be suitable for describing the damage characteristics as the ship size changes, we have used these two variables for an analysis on their possible dependence.

/x pL L p

p

p

/yL B

Figure 63 shows a scatter plot of as a function of together with the estimated conditional mean and median using sliding windows with widths adapted to the data, particularly in the range of very small .

/yL B /x pL L

/x pL L

Figure 63: Scatter plot of dimensionless damage width as function of dimensionless damage length

with estimated conditional mean

/yL B

/x pL L p / /y x pE L B L L p and median.

It can be seen from the analysis reported in Figure 63 that the dimensionless damage width tends to reduce as the dimensionless damage length reduces, i.e. damages which are short in dimensionless form are also characterised, on average, by a small dimensionless width. A


Deliverable D3.2 - Annex 3 particular decrease in both the conditional average and the conditional mean can be seen for damages having dimensionless length shorter than about 0.1, and this behaviour mimic, to some extent, the behaviour observed in Figure 62 for the damage penetration. From the performed analyses there is therefore some evidence of dependence between dimensionless damage length and dimensionless damage width, with damages having small dimensionless damage length being characterised also by small dimensionless damage width. If this dependence is neglected by considering independent of , it is likely to model a probability of occurrence of short (dimensionless) and wide (dimensionless) damages which is higher than the corresponding probability as estimable from the database. It is not clear at this stage, however, whether this difference can be considered negligible or not.

/yL B /x pL L p

Transversal damage extent yL and vertical damage extent zL

The analysis of a possible dependence between the transversal damage extent and the vertical damage extent

yL

zL has been carried out both in partially dimensionless form in the

plane ( / , )y zL B L , and in fully dimensional form in the plane ( ),y zL L .

Results of the analysis in the plane ( )/ ,y zL B L are shown in Figure 64, while those for the

analysis in the plane ( are shown in Figure 65. ),y zL L

Figure 64: Scatter plot of dimensional damage penetration zL as function of dimensionless damage width

with estimated conditional mean /yL B /z yE L L B and median.



Figure 65: Scatter plot of dimensional damage penetration zL as function of dimensional damage width

with estimated conditional mean yL z yE L L and median.

For both the analyses shown in Figure 64 and Figure 65, there seems to be a dependence between the damage width and the damage penetration, with larger dimensional damage penetrations associated with larger dimensional/dimensionless damage widths.

Additional analyses

Distribution of ship speed in grounding accidents The available database contains some information also regarding the ship speed at the time of the accident. It is therefore interesting to statistically analyse this quantity because, in principle, the dimension of the bottom damage in grounding should be associated with the kinetic energy of the ship at the moment of grounding and, hence, to the ship speed. The total number of data with speed available and usable is 122, with 43 cases (35%) belonging to full ships and 79 cases (65%) belonging to not full ships. Data added in GOALDS are 8 (7%) and data belonging to passenger vessels are in total 12 (10%), although it seems that two cases reported as different accidents, namely ID 1088 and 1089, are very likely to be different holes associated with the same casualty, and therefore it is possible that one of the data for passenger vessels should actually be considered as a repetition. Figure 66 shows a scatter plot of the ship speed at the moment of grounding as a function of the ship length, while Figure 67 shows the same data but in terms of Froude number.



Figure 66: Ship speed at the moment of grounding.

Figure 67: Froude number at the moment of grounding.


Deliverable D3.2 - Annex 3 From the data in Figure 66 it is not possible to see strong evident trends for the ship speed, while in case of Figure 67 it is evident that the Froude number at the moment of accident is dependent on the ship length, with a significant reduction of the Froude number at the moment of grounding for long ships. According to these premises, we have carried out a sliding window analysis on the data in Figure 66 separating full and not full ships, in order to check whether it is possible to assume a constant distribution for the ship speed at the moment of grounding, or whether it is necessary to link the speed with the ship length. For not full ships, 50m wide windows have been taken from ] ]0 ,50ppL m∈ m up to

] ]125 ,175ppL m m∈ at 5m steps, with final window ] ]130 ,225ppL m m∈ . The results of the analysis are shown in Figure 68.

Figure 68: Estimated ship ppE V L and percentile levels of ( )ship ppCDF V L . Not full ships.

The analysis of conditional average and percentile levels in Figure 68 indicates that there is a slight trend towards the increase of the speed at the moment of grounding as the ship length increases for not full ships. Unfortunately, available data do not allow to cover sufficiently the range of large ships and therefore the extrapolation is quite doubtful. Confidence intervals for the mean are quite large due to the large dispersion and limited number of data, but the behaviour is quite systematic, and therefore should be taken into account. However, it must be borne in mind that, the increasing behaviour observed in Figure 68 for conditional mean and percentile levels is expected, at some stage, to saturate, due to the limited maximum speed of large ships of the world fleet. In order to analyse the modifications the distribution of ship speed undergoes when changing the ship length, Figure 69 compares the estimated distribution of the ship speed at the moment GOALDS-D-3.2-GL- Grounding Damage Characteristics –rev1 - ANNEX 3

Page 75 of 107

Deliverable D3.2 - Annex 3 of grounding for three different example ranges of lengths, namely ] ]40 ,80ppL m∈ m ,

] ]80 ,120ppL m m∈ and ] ]120 ,160ppL m m∈ .

Figure 69: Comparison between estimated cumulative distributions of ship speed at the moment of

grounding for different ranges of ship lengths. Not full ships. It can be seen that all the estimated cumulative distributions in Figure 69 are almost linear, and this would correspond to a uniform distribution of ship speed in a proper range (not necessarily starting from zero speed). A better agreement with the estimated distributions can likely be obtained by using cubic polynomials. If, however, the tendency observed in Figure 68 is considered negligible, then a common distribution for the ship speed at the moment of grounding relevant to not full ships can be estimated from the whole set of not full ships data, as shown in Figure 70.



Figure 70: Estimated ( )shipCDF V for not full ships irrespective of the ship dimensions.

Comparing Figure 70 and Figure 69 it can be seen that the assumption of a unique distribution as in Figure 70 would provide a good agreement for ships above 80m, while, for smaller ship lengths, the distribution in Figure 70 would overestimate the probability of high speeds at the moment of grounding, and could therefore be considered conservative for small vessels since it is expectable for the grounding damage extent to be an increasing (or at least not decreasing) function of the ship speed at the moment of grounding. We go now to the analysis of full ships, approaching the problem in a way similar to that used for not full ships. Figure 71 shows the results of the sliding window analysis for full ships, where intervals in have been used starting from ppL ] ]25 ,75ppL m∈ m up to

] ]200 ,250ppL m m∈ with 5m steps. An additional interval has been considered with

] ]200 ,300ppL m∈ m to take into account the longest full ship containing information for the speed at the moment of grounding.



Figure 71: Estimated ship ppE V L and percentile levels of ( )ship ppCDF V L . Full ships.

The limited number of available data for full ships reflects in larger confidence intervals for the estimated conditional mean ship ppE V L in Figure 71, as well as in larger uncertainty in

the estimated percentile levels (not reported). Moreover, the increased uncertainty is likely the cause for the irregular behaviour of ship ppE V L and estimated percentile levels of

( )ship ppCDF V L in Figure 71. Despite the large statistical noise, it seems that there is a very

small tendency towards a decrease of the ship speed at the moment of grounding as the ship length increases. However this tendency seems very small, and can probably be neglected. The largest observed speeds for full ships in Figure 71 are in line with typical maximum speeds for bulk carrier and tankers, i.e. in the range of 14knots-16knots. According to Figure 71 it could therefore be considered acceptable to use a common distribution for the ship speed at the moment of grounding for full ships irrespective of the ship length. This distribution has been estimated from the available data and is reported in Figure 72, and, according to its shape, it could be fitted, as a first (rough) approach, by a uniform distribution in an appropriate range of speeds (not necessarily starting from zero speed), but a better approximation could be obtained by an appropriate cubic polynomial.



Figure 72: Estimated ( )shipCDF V for full ships irrespective of the ship dimensions.

It is also instructive to directly compare the distributions ( )shipCDF V as estimated for full (Figure 70) and not full (Figure 72) ships, as done in Figure 73, from which the larger probability of high grounding speeds for not full ships are more evident.

Figure 73: Comparison between ( )shipCDF V estimated for full and not full ships.


Deliverable D3.2 - Annex 3 SOLAS requirements for double bottom height and bottom damage characteristics for passenger and cargo ships other than tankers

Introduction In Chapter II-1 - Part B-2 - Regulation 9 "Double bottoms in passenger ships and cargo ships other than tankers" the SOLAS convention [4] contains requirements for minimum double bottom height (paragraph 2) and for bottom damage characteristics to be considered in specific calculations in case of absence of double bottom or in case of unusual double bottom arrangements (paragraph 8). In addition, in paragraph 9 of the same regulation, specific requirements are considered for passenger ships with large lower holds (LLH). Summarising the SOLAS requirements (refer to the complete text in SOLAS [4] for details):

The double bottom height shall be not less than the following value

S2009 max min ,2 ,0.7620BDBH m m⎧ ⎫⎧ ⎫= ⎨ ⎨ ⎬

⎩ ⎭⎩ ⎭⎬ (8)

In case of large lower holds in passenger ships, the Administration may require an

increased double bottom height. The maximum increased minimum double bottom height is:

S2009,LLH max min ,3 ,0.7610BDBH m m⎧ ⎫⎧ ⎫= ⎨ ⎨ ⎬

⎩ ⎭⎩ ⎭⎬ (9)

Actually Regulation 9.9 does not explicitly specify the minimum value of 760mm as reported in (9). However, since it is expected that the intention of the regulator is to increase the double bottom height in case of presence of large lower holds, for consistency with (8), the 760mm limit has been considered in (9).

In case of absence of double bottom in (part of) the ship and/or in the case of unusual bottom arrangements in a passenger ship or a cargo ship it shall be demonstrated that the ship is capable of withstanding bottom damages with characteristics as specified in Table 3. In Table 3 a vertical extent of damage ( ) is also reported in case of passenger ships with larger lower holds. This quantity is actually not explicitly specified in SOLAS. However, it has been assumed here as a reasonable logical consequence of increased minimum double bottom height requirements for passenger ships with large lower holds (Regulation 9.9).

,S2009-LLHzL



Table 3: Bottom damage characteristics according to SOLAS Ch.II-1, Part B-2, Regulation 9.

For 0.3 shipL from the forward

perpendicular of the ship

Any other part of the

ship

Longitudinal extent ,S2009xL [ ]m 2/31min ,14.53 shipL m⎧ ⎫

⎨ ⎬⎩ ⎭

Transverse extent ,S2009yL [ ]m min ,106B m⎧ ⎫

⎨ ⎬⎩ ⎭

min ,56B m⎧ ⎫

⎨ ⎬⎩ ⎭

Vertical extent, measured from the keel line ,S2009zL [ ]m min , 2

20B m⎧ ⎫

⎨ ⎬⎩ ⎭

Vertical extent, measured from the keel line in case of passenger ships

with large lower holds - ASSUMED as reference on the

basis of Reg.9.9

,S2009-LLHzL [ ]m min ,310B m⎧ ⎫

⎨ ⎬⎩ ⎭

The origin of the SOLAS requirements reported in Table 3 can be sought in [10]. Indeed the document [10] contains proposals very close to the formulas presently implemented in SOLAS and reported in Table 3. The sample of data used for the analysis in [10] is represented by a subset of data coming from the HARDER project. The intention of this section is to assess the probability of exceedance of SOLAS requirements using data available in the updated GOALDS database of grounding damages. Since SOLAS Regulation 9 explicitly excludes tankers, in the following the analyses will be carried out excluding accidents involving tankers from the analysed data. This is also in line with the original sample of ships used in [10]. It is however important to underline that the exclusion of data coming from accidents occurred to tankers significantly limits the database population in the range of large ships. The basic GOALDS-updated database also contains a limited number of accidents, in total six, involving fishing vessel which have also been neglected in this section.

Information on available data Available data used in this section come from the GOALDS database [1] after the filtering procedure described in the introduction of this paper, and after removing, as already said in the previous section, data associated with tankers and fishing vessels. It is worth therefore to describe the content of the database, as shown in Table 4. From Table 4 it can be seen that the majority of the data is associated with not full hull forms (87.0% of entries), and passenger ships represent a minority of the sample (8.9%). Data added in GOALDS represent 20.7% of the total available set of data. It is also worth mentioning that there is a significant difference between the number of "equivalent" damages coming from GOALDS data and the number of those coming from the HARDER project. "Equivalent damages" have been introduced in GOALDS, on the basis of expert judgement [3], in order to transform multiple holes reported for a single accident, into a single damage, considered "equivalent", in terms of flooded region of the hull. This way of defining the "equivalent damage" is of course relevant only for what concerns stability related problems, and cannot be considered appropriate for, e.g.,


Deliverable D3.2 - Annex 3 structural considerations. According to Table 4, grounding accidents (relevant to this section) collected in GOALDS and resulting in multiple damages represent 54.9% of the total sample of GOALDS data (relevant to this section). On the other hand, the analysis of HARDER data highlighted only 1.5% of total HARDER cases (relevant to this section) which were associated with multiple damages in the same accident. The enormous difference between HARDER and GOALDS data in the relative proportion of casualties reported to result in multiple damages after grounding calls for thorough attention. It seems that data coming from the HARDER database could have not been in all cases correctly identified as multiple damages belonging to the same casualty.

Table 4: Content of the database used in the comparison with SOLAS requirements for double bottom height and SOLAS assumptions for bottom damage.

Total number of entries: 247 (100%)

Data added in GOALDS: 51 (20.7%) Equivalent damages: 28 (11.3%) Original single hole damages: 23 (9.3%)

Data from HARDER:196 (79.4%) Equivalent damages: 3 (1.2%) Original single hole damages: 193 (78.1%)

Passenger ships: 22 (8.9%)

Full hull forms (only bulk carriers, since tankers have been removed):

32 (13.0%) GOALDS: 11 (4.5%) HARDER: 21 (8.5%)

Not full hull forms:215 (87.0%) GOALDS: 40 (16.2%) HARDER: 175 (70.9%)

Double bottom height requirements Starting from the available data we have analysed whether the observed damage penetrations reported in the database could have exceeded the inner bottom if the ceiling of the double bottom had been designed at a position corresponding with minimum SOLAS requirements. Figure 74 shows a scatter plot of measured damage penetration as a function of the ship breadth. Minimum double bottom height requirements as specified in (8) and (9) are reported in order to check whether the inner bottom could have been penetrated if the ship double bottom were built according to minimum SOLAS standards. Moreover, data coming from passenger ships are also highlighted (only three cases).



Figure 74: Comparison between vertical damage penetration and minimum SOLAS requirements for

double bottom height. From the analysis of Figure 74 it can be seen that the available data are limited to panamax breadth (32.2m), and hence the range of post-panamax vessels is not covered. For what concerns passenger vessels, the number of data (only three) is too limited to draw any specific conclusion for this ship type. The obtained estimated probability that the damage penetration is larger than the SOLAS minimum double bottom height is reported in Table 5, together with 95% confidence intervals and information on number of samples. It must be said that the estimation of S2009-LLHPr zL DBH> is not fully consistent, because in principle it should have been based only on data associated with passenger ships. However, due to the very limited number of such data (see Figure 74) this is impossible, hence it has been decided to use the whole set of data associated with passenger and cargo ships other than tankers relevant to this section.

Table 5: Probability of penetration exceeding SOLAS minimum double bottom height.

S2009Pr zL DBH> [ ]95%27.3% 16.1%,41.0%

CI Samples: 55, Exceeding: 15

S2009-LLHPr zL DBH> [ ]95%14.5% 6.5%,26.7%

CI Samples: 55, Exceeding: 8 The analysis leading to estimations in Table 5 considers the whole set of data together. However, looking at Figure 74 there seems to be some indication that the actual probability of exceedance of SOLAS minimum double bottom height could be dependent on the ship size, with higher probability in the range of small ships, and smaller probability in the range of large ships. In order to check this possibility, the ratio has been reported as a function of the ship length between perpendiculars in Figure 75. Together with the raw data, a

S2009/zL DBH


Deliverable D3.2 - Annex 3 sliding window calculation of the mean has also been applied. Intervals of length between perpendiculars 50m wide ranging from ] ]0 ,50ppL m∈ m to ] ]100 ,150ppL m∈ m at 5m steps

have been considered, with the addition of two final intervals, namely ] ]150 ,250ppL m m∈

and ] ]200 ,350ppL m m∈ . The obtained conditional mean is reported in Figure 75 together with 95% confidence intervals. From the results it seems there is a decrease of the average ratio as the ship length increases, which is stronger when moving from very small ships (around 50m in length) to small/average size ships (around 80m-100m in length), while it is less clear for larger ships. This behaviour could be linked with a possible reduction of the probability of exceedance of minimum double requirements as the ship length increases. It must however be underlined that, due to the limited number of available data, confidence intervals for the mean are quite wide, and it is therefore difficult to draw firm conclusions.

S2009/zL DBH

Figure 75: Ratio as a function of the length between perpendiculars and conditional mean S2009/zL DBH

S2009/z pE L DBH L p .

The same type of analysis has also been carried out considering the requirements on minimum double bottom height for passenger ships, and hence the ratio . Also in this case, due to the limited number of data associated with passenger ships, the whole set of data (which excludes tankers and fishing vessels, but retain bulk carriers) has been considered. Results are shown in Figure 76, where the same windows for used in Figure 75 have been used in the sliding window analysis. As expectable due to the functional relation between

and (see (8) and (9)), also in this case there is a tendency towards a

S2009-LLH/zL DBH

ppL

S2009-LLHDBH S2009DBH


Deliverable D3.2 - Annex 3 decrease of the ratio as the ship length increases from small ships up to about 80m-100m, while a more stable behaviour is visible for longer ships. However, also in this case, due to the limited number of available data, confidence intervals for the mean are quite wide.

S2009-LLH/zL DBH

Figure 76: Ratio as a function of the length between perpendiculars and conditional

mean

S2009-LLH/zL DBH

S2009-LLH/z pE L DBH L p .

The trends in Figure 75 and Figure 76 for the conditional averages S2009/z pE L DBH L p and

S2009-LLH/zE L DBH Lpp are quite systematic. However, this does not necessarily mean that there must be a corresponding trend also for what concerns the conditional exceedance probabilities S2009Pr z ppL DBH L> and S2009-LLHPr z ppL DBH L> . In order to estimate the behaviour of the probability of exceedance of SOLAS reference bottom damage dimensions, the sliding window approach has been applied to the data in Figure 75 and Figure 76 in order to estimate S2009Pr z ppL DBH L> and S2009-LLHPr z ppL DBH L> from the database. The results of the application are shown in Figure 77.



Figure 77: Dependence between ship length and estimated probability of exceeding minimum double

bottom height according to SOLAS. The estimations in Figure 77 are associated with quite wide confidence intervals due to the limited amount of available data. Nevertheless it seems that trends are quite visible and systematic, and to some extent in line with the indications given by the conditional averages in Figure 75 and Figure 76. It seems, indeed, that S2009Pr zL DBH L> pp shows a systematic tendency towards a decreasing as the ship length increases, and this could mean that SOLAS minimum double bottom height could be more conservative for large ships and less conservative for small ships. A similar behaviour seems to be present in case of S2009-LLHPr zL DBH L> pp . However, in this case, a tendency seems visible towards a sort of stabilization of

S2009-LLHPr zL DBH L> pp as the ship length exceeds about 80m-100m. The number of data is however insufficient to draw any firm conclusion.

Bottom damage characteristics According to SOLAS Ch.II-1, Part B-2, Regulation 9.8 (and, partially, Regulation 9.9), unusual double bottom arrangements or (partial) dispensation from fitting of double bottom can be accepted by the Administration, if the ship is able to withstand a bottom damage assumed at any position along the ship's bottom and with an extent specified according to dimensions reported in Table 3 (the assumptions done in this paper concerning in Table 3 must be borne in mind).

,S2009-LLHzL


Deliverable D3.2 - Annex 3 It is therefore the intention of this section to quantify the probability of exceedance of bottom damage dimensions presently assumed in SOLAS. In particular, the following probabilities have been estimated from the damages in the database:

a) The probability that the longitudinal extent of damage exceeds the value prescribed by SOLAS, i.e. ,S2009Pr x xL L> ;

b) The probability that the transverse extent of damage exceeds the value prescribed by SOLAS, i.e. ,S2009Pr y yL L> ;

c) The probability that the vertical extent of damage exceeds the value prescribed by SOLAS, i.e. ,S2009Pr z zL L> ;

d) The probability that all damage dimensions prescribed by SOLAS are exceeded, i.e. ( ) ( ) ( ) ,S2009 ,S2009 ,S2009Pr x x y y z zL L L L L L> ∧ > ∧ > ;

e) The probability that at least one of the damage dimensions prescribed by SOLAS is exceeded, i.e. ( ) ( ) ( ) ,S2009 ,S2009 ,S2009Pr x x y y z zL L L L L L> ∨ > ∨ > ;

The same probabilities have also been calculated considering the assumed vertical damage extent in case of large lower holds in passenger ships as shown in Table 3. Due to the limited number of available accidents involving passenger ships, the complete database (with the exception of accidents occurred to tankers and fishing vessels), as in the previous section, have been used. The obtained results are shown in Table 6 and Table 7. Of course probabilities related only to the longitudinal extent of damage

,S2009-LLHzL

xL or to the transverse extent of damage do not differ between Table 6 and Table 7 since the presence of large lower holds is assumed to modify requirements only for the vertical extent of damage.

yL

Table 6: Exceedance probabilities (with 95% confidence intervals) for bottom damage characteristics as

prescribed in SOLAS.

,S2009Pr x xL L> [ ]95%54.6% 47.6%,61.6%

CI Samples:205, Exceeding:112

,S2009Pr y yL L> [ ]95%18.2% 11.5%,26.7%


,S2009Pr z zL L> [ ]95%29.1% 17.6%,42.9%


( )( )( )

,S2009

,S2009

,S2009

Prx x

y y

z z

L L

L L

L L

⎧ ⎫> ∧⎪ ⎪⎪ ⎪∧ > ∧⎨ ⎬⎪ ⎪∧ >⎪ ⎪⎩ ⎭

[ ]95%11.1% 3.7%,24.1%


( )( )( )

,S2009

,S2009

,S2009

Prx x

y y

z z

L L

L L

L L

⎧ ⎫> ∨⎪ ⎪⎪ ⎪∨ > ∨⎨ ⎬⎪ ⎪∨ >⎪ ⎪⎩ ⎭

[ ]95%64.4% 48.8%,78.1%




Table 7: Exceedance probabilities (with 95% confidence intervals) for bottom damage characteristics in case of large lower holds. Dimensions based on SOLAS according to assumptions in Table 3.

,S2009Pr x xL L> [ ]95%54.6% 47.6%,61.6%


,S2009Pr y yL L> [ ]95%18.2% 11.5%,26.7%


,S2009-LLHPr z zL L> [ ]95%14.5% 6.5%,26.7%


( )( )( )

,S2009

,S2009

,S2009-LLH

Prx x

y y

z z

L L

L L

L L

⎧ ⎫> ∧⎪ ⎪⎪ ⎪∧ > ∧⎨ ⎬⎪ ⎪∧ >⎪ ⎪⎩ ⎭

[ ]95%8.9% 2.5%,21.2%


( )( )( )

,S2009

,S2009

,S2009-LLH

Prx x

y y

z z

L L

L L

L L

⎧ ⎫> ∨⎪ ⎪⎪ ⎪∨ > ∨⎨ ⎬⎪ ⎪∨ >⎪ ⎪⎩ ⎭

[ ]95%60.0% 44.3%,74.3%


The probability levels considered in [10] are not fully comparable with those obtained in this section due to some differences in the methodology of analysis. A comparison is nevertheless possible, at least in terms of orders of magnitude, if we bear in mind that this comparison is approximate in nature. For what concerns the longitudinal damage extent, xL , we refer here to §4.3 in [10]. It seems (the sentence in §4.3 in [10] is not very clear), that the exceedance probability

2/31Pr min ,14.53xL L⎧ ⎫⎧>⎨ ⎨

⎩ ⎭⎩ ⎭m⎫⎬⎬ was identified as about 43% (complement of 57% to 100%). In

the present analysis the same probability is identifiable as ,S2009Pr x xL L> and it has been

estimated as [ ]95%54.6% 47.6%,61.6%

CI (see Table 6 or Table 7), hence higher than the value in §4.3 in [10]. For what concerns the damage width , §4.5 in [10] indicates a probability of about 60%-62% that the damage width is less than with a maximum damage width varying between 5m and 10m. This probability corresponds to an exceedance probability of about 38%-40%. Thanks to the small variation of this probability when varying the maximum width between 5m and 10m, it is possible to compare this latter exceedance probability coming from information reported in [10], with the estimated

yL/ 6B

,S2009Pr y yL L> . According to Table 6 (or

Table 7), we have estimated [ ],S2009 95%Pr 18.2% 11.5%,26.7%y y CI

L L> = , which is significantly smaller than the level 38%-40% coming from [10]. Going now to the damage penetration zL , we have estimated an exceedance probability of

SOLAS bottom damage requirements as [ ],S2009 95%Pr 29.1% 17.6%,42.9%z z CI

L L> = . Looking at §4.8 in [10], it can be seen that the probability of exceedance of a penetration equal to was about 26%, which is comparable with the estimation in this paper. / 20BFinally, a summary of the approximate comparison between the present analysis and data available in [10] is shown in Table 8. GOALDS-D-3.2-GL- Grounding Damage Characteristics –rev1 - ANNEX 3

Page 88 of 107

Deliverable D3.2 - Annex 3 Table 8: Approximate comparison of probabilities of exceedance. Present analysis and information from

SLF47/INF.4 [10].

Present analysis Approximate reference value from SLF47/INF.4

,S2009Pr x xL L> [ ]95%54.6% 47.6%,61.6%

CI 43 % (Ref: §4.3)

,S2009Pr y yL L> [ ]95%18.2% 11.5%,26.7%

CI about 38%-40% (Ref: §4.5)

,S2009Pr z zL L> [ ]95%29.1% 17.6%,42.9%

CI 26% (Ref: §4.8) Results shown in Table 6 and Table 7 are however overall results not taking into account possible differences in the probability of exceeding SOLAS damage dimensions among different ship sizes. In order to disclose possible dependencies of the considered probability from the ship size, it is useful to have at disposal a scatter plot of the population of data in terms of ratios , , , as functions of the ship length, which is representative of the ship overall dimensions. The exceedance of a value of one by any of the considered ratios (with caution on which is actually an assumption in this paper) indicates an exceedance of SOLAS assumptions concerning damage extent. Appropriate scatter plots are show in Figure 78. For each scatter plot the average value of the relevant ratio based on a sliding window analysis is also reported in order to identify possible trends, with windows adapted to the available data. For the ratios and

the used windows are 50m wide starting from

,S2009/x xL L ,S2009/y yL L ,S2009/z zL L ,S2009-LLH/z zL L

,S2009-LLH/z zL L

,S2009/x xL L

,S2009/y yL L ] ]0 ,50ppL m∈ m to

] ]200 ,250ppL m m∈ at 5m steps, with the addition of one final interval ] ]200 ,350ppL m m∈ . In case of ratios and the windows are the same already used in Figure 75 and Figure 76.

,S2009/z zL L ,S2009-LLH/z zL L


Deliverable D3.2 - Annex 3 Figure 78: Ratio between measured damage dimensions from the database and SOLAS requirements as

function of the ship length between perpendiculars. From the results in Figure 78 it can be seen that trends are different for the different ratios. In order to have a better view of such trends, Figure 79 shows the estimated conditional expected value of the considered ratios as a function of the ship length between perpendiculars.

Figure 79: Conditional average ratio between measured damage dimensions from the database and

SOLAS requirements as function of the ship length between perpendiculars. According to Figure 79, the average value of the ratio shows a tendency towards increasing as the ship length increases up to about 120m-150m. For longer ships there seems to be an almost constant or even slightly decreasing tendency. On the other hand the average value of the ratio seems to be almost independent of the ship length, with a slight decreasing tendency as the ship length increases. For what concerns the average values of the ratios and , the observed trends tend confirm the discussion already done for what concerns minimum double bottom height (see Figure 75 and Figure 76), with a decreasing tendency of

,S2009/x xL L

,S2009/y yL L

,S2009/z zL L ,S2009-LLH/z zL L

,S2009/z z ppE L L L and ,S2009-LLH/z z ppE L L L as the ship length

increases. However, it must be said that a trend of the average value is not necessarily associated with a trend of the probability of exceedance of a given value, because this quantity depends on percentile levels, which can be dependent on the ship length in a way not necessarily consistent with the mean. It is therefore interesting to analyse directly the estimated probability of exceedance of reference SOLAS bottom damage characteristics as the ship length is changed, as shown in Figure 80.



Figure 80: Modification of exceedance probability of reference SOLAS bottom damage dimensions as a

function of the ship length between perpendiculars. From the results in Figure 80, different trends are observed. For what concerns the longitudinal damage extent xL , it can be seen that the estimated probability of exceedance of the reference SOLAS bottom damage length , i.e. ,S2009xL

,S2009Pr x x ppL L L> , increases when the ship length increases from about 45m to about 80m.

For longer ships there is a slight tendency towards the increase of the exceedance probability, but the variations are small and it can be said that the exceedance probability is almost constant when . 80ppL m>

In case of the transverse damage extent , the value of yL ,S2009Pr y y ppL L L> does not change

significantly from about up to 50ppL ≈ m m125ppL ≈ . For longer ships there seems to be a

quite sudden decrease of ,S2009Pr y y ppL L L> . However, the confidence intervals are too

wide to definitely consider this change as significant, and more data would be needed. Going now to ,S2009Pr z z ppL L L> , despite the large confidence intervals, which are

consequence of the limited sample of data, there seems to be a systematic tendency towards a decreasing of ,S2009Pr z z ppL L L> as the ship length increases, and this could mean that

SOLAS damage assumptions could be, for what concerns the damage penetration, more conservative for large ships and less conservative for small ships. A similar behaviour seems to be present in case of ,S2009-LLHPr z z ppL L L> . However, in this

case, a tendency seems visible towards a sort of stabilization of ,S2009-LLHPr z z ppL L L> as the

ship length exceeds about 80m-100m. The wide confidence intervals, however, suggest that the number of data is insufficient to draw firm conclusions.


Deliverable D3.2 - Annex 3 The obtained results for ,S2009Pr z z ppL L L> and ,S2009-LLHPr z z ppL L L> are in line with

what has been found in Figure 77 for S2009Pr z ppL DBH L> and S2009-LLHPr z ppL DBH L> . This was actually expectable, and expected, due to the very similar mathematical formulation for (eq. (8)) and (see Table 3), and for (eq. (9)) and (see Table 3).

S2009DBH ,S2009zL S2009-LLHDBH ,S2009-LLHzL

Conclusions General comments:

1) Due to the very limited number of samples (only 22) in the database which are associated with passenger vessels, it is in general not possible to draw specific conclusions associated with this ship type with a reasonable level of confidence. For this reason, any indication for this ship type, when derived in the present paper, is to be considered with extreme caution bearing in mind the very limited sample of data.

2) Data for "full hull forms", i.e. tankers and bulk carriers, are 138, while "not full hull forms" represent 221 entries in the database, with a resulting ratio of 1.6. It follows that in the analyses involving all data, the final results could be mainly driven by the sample of not full hull forms. However, according to the availability of data, this ratio changes depending on the particular analysis. Therefore the dominant subset, if any, depends of the specific quantity under analysis.

3) The majority of not full ships belong to the range of the relatively short lengths (small ship sizes), while full ships belong in the majority of cases to the range of long ships lengths (large ship sizes). Any comparison between the two classes of ships should therefore be considered with caution, because full ships are mainly governed by the behaviour of large ships, while not full ships are mainly governed by the behaviour of smaller ships.

4) There are indications that data coming from the HARDER database could have not been in all cases correctly identified as multiple damages belonging to the same casualty.

For what concerns the transversal position of the damage:

1) The database does not contain any information concerning the transversal position of the damage. In absence of such information it could be assumed that the centre of the damage is uniformly distributed in transversal direction.

For what concerns the longitudinal position of damage:

1) For both full and not full ships it seems justifiable, from the engineering point of view, to use a unique distribution for the nondimensional longitudinal position of the centre of damage irrespective of the ship dimensions. /dam ppX L

2) The distributions of in case of full ships and in case of not full ships show some differences. In particular, the centre of damage tends to occur with higher probability in the forward part of the ship for full ships, while not full ships tend to have a centre of damage shifted towards the central part of the hull.

/dam ppX L

3) Of course the limited number of passenger vessels available in the database prevents any statistically significant conclusion. However it seems that the distribution of

observed for passenger vessels is more similar to, and could therefore be represented by, the distribution obtained from the set of data for not full hull forms.

/dam ppX L


Deliverable D3.2 - Annex 3 4) A statistical analysis has also been performed for the nondimensional position of the

forward end of damage, i.e. . According to the obtained results it could be said that, overall, the variable seems to show a smaller/less systematic dependence of the characteristics of its distribution from the ship length. In this respect it could be considered more appropriate / manageable than the variable

for characterising the position of bottom damages along the ship.

, /F dam ppX L

, /F dam ppX L

/dam ppX L5) The probability density function of tends to have a prominent peak in the

forward region of the ship (say forward of about , /F dam ppX L

0.9 ppL⋅ ), both in case of full hull forms and in case of not full hull forms, and the peak is more evident in case of full hull forms.

6) The magnitude of the forward peak of the probability density function of can be quantitatively appreciated by reporting that 50% of the damages have a forward end of damage which is forward of about 0.75

, /F dam ppX L

,F damX ppL⋅ for not full hull forms, and forward of 0.87 for full hull forms, while 30% of the damages have a forward end which is forward of 0.89

ppL⋅

ppL⋅ for not full hull forms, and forward of 0.94 for full hull forms.

ppL⋅

For what concerns the damage penetration:

1) Data available for zL (125 cases) mainly belong to the class of full ships (83 cases), with not full ships representing a minority (42 cases).

2) The available data for full and not full ships are not evenly distributed in the range of ship sizes. Indeed, data for full ships mainly belong to the range of ship lengths above 150m (about 82% of full ships data), while data for not full ships are almost completely belonging to ships having less than 150m in length (about 91% of not full ships data). A similar situation occurs in terms of ship breadth, with about 90% of cases for not full ships being associated with breadths smaller than 20m, and about 82% of cases of full ships being associated with breadths above 20m. This situation creates difficulties in obtaining directly comparable statistics between full and not full ships in similar regions of ship size.

3) Only 3 cases reporting zL are available for passenger vessels, and therefore it is impossible to provide any statistics for this specific ship type for what concerns bottom damage penetration.

4) In all but two cases penetrations are smaller than 4.2m, and only one reported case has a penetration of 7m.

5) The analysis of the average dimensional and dimensionless damage penetration as a function of the ship breadth, zE L B and /zE L B B , does not indicate significant differences between full ships and not full ships in the range of ship breadths where the two categories can be compared. Therefore, for what concerns the damage penetration, the same distributions could be used for both full and not full ships. More precisely, there is no evidence for the necessity of considering different distributions for full and not full ships.

6) The behaviour of the distribution of the bottom damage penetration zL is not simple, and cannot be perfectly represented for any generic ship size neither with a dimensional approach using ( )zCDF L nor with a nondimensional approach using


Deliverable D3.2 - Annex 3 ( )/zCDF L B . However, amo two extreme possibilities, it seems that a

mensional approach, based on a common

ng these

completely di ( )zCDF L irrespective of the ship size, could provide a quite good agreement with the distributions of damage penetration obtained in different ranges of ship breadths, and that this agreement can be considered more robust than what has been observed when trying to use a common distribution for ( )/zCDF L B irrespective of the ship size. It seems therefore that a

fully dimensiona for any ship size, with l approach ( )zCDF L obtained from the available data, and a maximum damage penetration of the order of 5m, could be a good balance between simplicity and accuracy. However, this selection depends on the range of application in terms of ship dimensions: by limiting the range of ship dimensions, more accurate, and still simple, approximations can likely be found.

at concerns the longitudinal damage extent:

or whF 1) There are 309 cases reporting the longitudinal extent of damage xL . In this sample,

2)

131 cases belong to full hull forms, while 178 cases belong to not full hull forms. For what concerns specifically passenger vessels, 17 reported cases, on a total of 22 passenger vessels in the database, contain information on the longitudinal damage extent. For not full ships, apart from the region of small ships, with length around 50m-70m,

/x pp ppE L L L is not strongly dependent on the ship length, and it tends to become

, or slightly increasing as the ship length increases. Short ships show a smaller conditional average nondimensional damage length. At the same time the median value of /x ppL L tends to systematically increase as the ship length (and hence the ship size) incrFor full ships there is a c

almost constant

eases. 3) lear tendency for /x pp ppE L L L to increase, almost linearly,

, whereas for longer ships as the ship length increases up to about 150m

/x pp ppE L L L becomes almost constant. A very similar behaviour is evident also for

e of /x ppL L . In the region of leng twthe median valu

4) ths be een 50m and 100m the distributions of p for full

5) ferent

range b

/x pL Lships and not full ships are significantly different, with full ships showing smaller damages. In the region of ship lengths between 125m and 175m the obtained distributions of /x ppL L for the two subsets are close, and differences are small. From a systematic application of a two-sample Kolmogorov-Smirnov test for difranges of ship length, it has been observed that differences in the distribution of

/x ppL L between full ships and not full ships are statistically significant mainly in the etween, roughly, about 60m and 120m. Outside these range differences among

the distributions are statistically not significant. This is partially due to the fact that the distributions are actually similar, but also to the fact that there is a lack of data for both full and not full ships in the small length range and, particularly, a lack of data for not full ships in the range of large lengths. We could roughly say that differences in the distributions for the dimensionless damage length between full and not full ships should be considered not negligible below a ship length of about 120m and negligible for longer ships.



( )/ 80x pp ppCDF L L L m≥ as estimated from the 6) It could be possible to consider

available database as a reference sufficiently accurate for describing the average behaviour of x pp above 60m-80m and for

full ships above about 150m. For r lengths

distribution which is L L for not full ships

smalle

/

( )/ 80x pp ppCDF L L L m≥ is on

average conservative both for full and not full ships. Summarising, it can therefore be considered that using the estimated ( )

accuracy, simplicity and7)

for pa

8)

/ 80x pp ppCDF L L L m≥ from the data, i.e.

basically a nondimensional approach, as a working tool irrespective of the actual ship length could be a good balance between conservativeness. There is a good agreement between the distribution of /x ppL L obtained for all passenger vessels and that obtained using all ships not shorter than 80m. At the same time the maximum observed dimensionless damage length ssenger vessels is smaller than that observed in the sample of all ships not smaller than 80m. However the number of data for passenger vessels is too limited to draw any conclusion and the hypothesis of equal distributions is not rejected by a two-sample Kolmogorov-Smirnov test at 5% significance level. In a tentative of explanation of the differences observed for the behaviour of

( )/CDF L L L between small shipx pp pp

analys base has been carried out separating the available data on the basis eported in the database. The length of about 150m, which has been

observed to mark, approximately, a change of behaviour in

lengths and large ship lengths for full ships, an

is of the dataof their source as r

( )/x pp ppCDF L L L for full

ships from ship-size-dependent (small ships) and ship-size-indepe ships), well agree with a sharp separation of the data among tw namely "DNV_IMO" and "IMO". A similar sharp separation among different data sources is not present in case of not full ships. Although the analyses carried out cannot be considered to represent a proof of a link between the source of the data and the differences in the behaviour of

ndent (largeo main sources,

( )/x pp ppCDF L L L observed between small and large

ship lengths for full ships, this point should dese ve some more attention and further analysis.

at concern

r

For wh s the transversal damage extent:

1) A total of 210 cases, i.e. 58.5% of the total entries in the database, contain information in the framework of GOALDS (19.5% of

2) elong to passenger vessels. It is therefore clear that any derivation of specific

3)

lable mainly in the range of breadths below 20m-25m. In ax vessels.

on the damage width, with 41 cases addeddata), and 169 cases, 80.5% of the sample, coming from the HARDER project. Of the total 210 cases, 112 (53.3%) belong to full ships, while 98 (46.7%) belong to not full ships. Only 13 cases, namely less than 6.2% of the total 210 data containing the damage width, binformation for passenger vessels on the basis of only 13 points is impossible due to the excessive uncertainty in the statistical estimators. The analysis of data has been split in two separate parts: analysis of not full ships and analysis of full ships.

4) For what concerns the analysis of not full ships: a) Data are avai

particular there are no data for post-panamGOALDS-D-3.2-GL- Grounding Damage Characteristics –rev1 - ANNEX 3

Page 95 of 107

Deliverable D3.2 - Annex 3 b) There is an evident difference between the population collected in GOALDS

and the other data, with GOALDS data belonging all to the region of (very)

c) of

small ratios /yL B .

The analysis / B B and of the percentile levels of ( )/CDF L B B yE L y

the suitabili el, at least fromto 20m. For

d) in GOALDS is quite doubtful. This behaviour

e) onable to keep the indication given by

seems to indicate ty of a ship-size independent mod ship breadths up larger ship breadths the situation is very doubtful, with a significant effect of damages collected in GOALDS, which are mainly of small size, and which lead to a significant shift of the distribution of /yL B towards smaller values of dimensionless damage width as the ship breadth increases above about 20m. The sharp shifting of the distribution towards smaller damages in the region governed by data collected seems especially doubtful when looking at the final windows for the extreme breadths, where GOALDS data are accompanied by data from other sources, and, as a consequence, the characteristics of damage tend to shift again towards larger dimensionless widths. It is difficult to provide a definite conclusion without the availability of additional data, however it seems reasdata for 20B m≤ , i.e. the indication of the suitability for a common distribution of /yL B independent of the actual ship breadth (size). On the basis of thi tion (that, however, needs more data to be fully justified or rejected) a comm mulative distribution

s assumpon cu ( )/yCDF L B for not full ships has

been estimated from the database, with an average damage width of about 0.1B , and precisely [ ]95%

/ 0.1062 0.07y CIE L B = .

at concerns the analysis of ful ships: 40,0.1384

5) For wh la) There is a sharp separation in terms of ships size between data coming from

nd "DNV_IMO", with this latter data

b) c) seems to change

25m, to large siona

d)

different sources, particularly "IMO" amainly belonging to the range of breadths above 25m and the former being associated mainly with the range of smaller breadths. This aspect has been found to significantly drive the statistical estimators. GOALDS data are mostly in the region of breadths below 28m. The behaviour of the dimensionless damage width /yL Babruptly when moving from small breadths, below about breadths, above about 25m. In both ranges a nondimen l approach for the damage width seems to be appropriate, however the characteristics of the distribution in the two ranges are significantly different, with a significant shift towards large dimensionless damage widths in the range of large ship breadths. The quite sharp separation between the two behaviours seems to be related to the effect of the two main sources of data, namely "IMO" and "DNV_IMO". A series of checks concerning this aspect have been carried out, as well as a check of the dependence of the average dimensionless damage width on the data source. The finding is that the influence of the data source seems not negligible, and the largest /yE L B is obtained in case of source "DNV_IMO".


Deliverable D3.2 - Annex 3 e) two optio

dimAccording to the available data, ns have been considered suitable for the modelling of the distribution of the ensionless measured damage width. As an interim, to some extent questionable, solution, it could be decided to use all the data for developing a reference ( )/yCDF L B irrespective of the ship size. The alternative would be the creation of two separate cumulative distributions for the region of large breadths and for the region of small breadths, with a blending in the intermediate zone. These two options, apart from the blending, have been analysed, and the corresponding distributions have been estimated. The estimation for the cumulative distribution of /yL B by separating ships with 25B m≤ from ships with 25B m> allowed to clarify that the differences in the two distributions are significant. When considering a single d ribution f) ist ( )/yCDF L r full ships, then

B fo

[ ]95%CI

g) When considering a separation of full ship m/ 0.2028 0.1509,0.2547yE L B = .

25B and 25B m> , the ≤s foraverage dimensionless damage widths are significantly different, with

[ ]95%/ 25 0.0920 0.0565,0.1274y CI

E L B B m≤ = and

[ ]95%CI

6) Comparisons have been carried out between the distributwidth as obtained for full and not full ships. If a single distribution for

verag

For wh

/ 25 0.2693 0.1924,0.3461yE L B B m> = .

ions of dimensionless damage /yL B ,

irrespective of the ship size, is considered for each category, it can be seen that full ships show significantly larger damage widths than not full ships, with an a e dimensionless damage width for full ships which is almost twice as the value for not full ships. However, when separating full ships into two groups, i.e. 25B m≤ and

25B m> , it can be seen that the cumulative distribution of /yL B for not full ships and that for full ships with breadths not larger than 25m are quite comparable, as well

ean values, while the distribution of /yL B for full with 25B m> is significantly different and strongly shifted towards wider dimensionless damages.

at concerns the analysis of statistical dependence among different variables:

as the m ships

Statistical dependence between longitudinal damage extent x1) L and longitudinal position of damages (centre, damX , or forward end, ,F damX ):

a. The longitudinal damage extent xL and the longitudinal position of centre of damage damX cannot dependent, for gebe in ometrical reasons. The same holds for xL and the longitudinal position of the forward end of damage ,F damX . This is verified by the analysis of the data. Under certain assumptions it is possible to define a virtual rando riable, named here the "potential bottom damage length" , which is by assumption

b. m va,x pL

independent of the damage location. The actual "measured" damage length xL is, by construction, obtained as a truncation of ,xL epending on the damage location, and it is this truncation that re-create the dependence between the damage location and x

p d

L . Under the required assumptions, the distribution of


Deliverable D3.2 - Annex 3 ,x pL can be obtained from the distribution of xL and the distribution of the

location of damage available from the database. According to the data it seems the required assumptions are approximately f lfilled, and therefore it is in

principle possible to determine the distribution of the virtual auxiliary random variable ,x pL . The representation and the analysis of data seem to be much more natural when the dime

that u

c. nsionless damage length p is reported as a function of the

be pre

d. inciple also in case of the measured transversal

avai

2) Statisti

/x pL Ldimensionless position of the forward end of damage , /F dam ppX L . It seems, therefore, that this representation should ferred with respect to the more usual one based on the centre of damage, which is likely more appropriate for ship-ship collision damages. The procedure reported for the determination of the "potential damage length"

,x pL should be applied in prdamage extent yL with reference to the transversal position of damage (not

lable in the database) because, also in that case, the measurable transversal damage extent is geometrically limited by the extreme portside and starboard limits of the ship, and therefore the measured transversal damage extent and the transversal position of damage (not available from the database) cannot be considered independent. cal dependence between longitudinal damage extent xL and vertical damage

zextent L :

a. A scatter plot in the ( )/ ,x pp zL L L plane has been analysed by using a sliding window analysis in terms of conditional mean and conditional median.

age lengthb. For dimensionless dam s above about 0.1 both the conditional mean and the conditional median for zL are quite constant, indicating (though not proving) a possible independence of zL from /x ppL L if / 0.1x ppL L > . For shorter dimensionless dama lengths there is a visible decrease of the average damage penetration, indicatin that da wit ens

c. geg mages h small dim ionless

d.

damage length also show small dimensional damage penetrations. Differently from the mean, the median does not show such a visible decrease, and remains more constant in almost the whole range of /x ppL L , although, in the region of very small dimensionless damage lengths, below about 0.05, also the median value tends to decrease. If this dependence is neglected by considering zL independent of /x ppL L , it is likely to model a probability of s of p ) and occurrence of short (in term /x pL Ldeep (in terms of zL ) damages which is higher than the co ding probability as can be estimated from the database. It is not clear a stage, however, whether this ifference can be considered negligible or not. cal dependence between longitudinal damage extent x

rrespont this

d3) Statisti L and transversal

extent yL : damage

a. A scatter plot in the ( )/ , /L L L B plane has been analysed by using a sliding wind

x pp y

ow analysis in terms of conditional mean and conditional median.


Deliverable D3.2 - Annex 3 b. The dimensionless dam tends to reduce as the dimensionless

damage length /x ppL L reduces, this meaning that damages which are short inage width

harac

c.

/yL B

dimensionless form are also c terised, on average, by a small dimensionless width. A particular decrease in both the conditional average and the conditional mean can be seen for damages having about / 0.1x ppL L < ,

The behaviour is similar to the behaviour observed in the plane ( )/ ,x pp zL L L when analysing the dimensional damage penetration as a f function o the

4) Statistiextent

dimensionless damage length. cal dependence between transversal damage extent yL and vertical damage

zL :

a. Scatter plots in the partially dimensionless plane ( ),/y zL B L and in the fully

mdi ensional plane ( ),y zL L have been analysed in terms of conditional mean

/E L L B or z y z y values. b. es ther

width and the damage ensional damage

For what conc

E L L and conditional median For both the analys e seems to be a dependence between the damage

penetration, with larger dimpenetrations associated with larger dimensional/dimensionless damage widths.

erns the ship speed at the moment of grounding: ip speed at the moment of grounding has been analysed. The total number of 1) The sh

2)

ndent on the ship length, with a tendency towards an increase of the speed

b.

or instance, cubic

c.

d.

data with speed available and usable is 122, with 43 cases (35%) belonging to full ships and 79 cases (65%) belonging to not full ships. Data added in GOALDS are 8 (7%) and data belonging to passenger vessels are in total 12 (10%), although it seems that two cases reported as different accidents, namely ID 1088 and 1089, are very likely to be different holes associated with the same casualty, and therefore it is possible that one of the data for passenger vessels should actually be considered as a repetition. For not full ships:

a. The distribution of the ship speed at the moment of grounding is slightly depeat the moment of grounding as the ship length increases. However, the tendency, although clearly systematic, is not very strong. It seems reasonable to use a uniform distribution for the ship speed at the moment of grounding (not necessarily starting from zero speed). However, better agreement can likely be obtained through, fpolynomials. Unfortunately available data do not comprise the range of long ships, and the analysis cover up to maximum ship length of about 150m-160m. Extrapolation for longer ships is uncertain, but a saturation could be expectable in the range of large ships as a consequence of the limited maximum speed of larger ships in the world fleet. If the tendency towards a shifting of the speed at the moment of grounding is considered negligible, then a ship-size independent distribution for the ship speed at the moment of grounding for not full ships can be estimated from the whole set of data. The estimated cumulative distribution could be approximated by a uniform distribution (linear CDF , constant PDF ) in an


Deliverable D3.2 - Annex 3 appropriate range (not necessarily starting from zero speed), however better approximations could likely be obtained by the use of, for instance, cubic polynomials. If a common ship-size independent distribution for the speed at the moment of grounding is assumed and estimated from the database for not full ships, this distribution is

e.

a good description of the actual distributions observed for ships

3) For fula.

rtain. Despite the large statistical noise, it seems that a very small tendency towards a decrease of the ship speed at the

b.

in an appropriate range of speeds (not necessarily starting from

For what conc

above 80m in length, while for ships below 80m such a common distribution would overestimate the occurrence of high speeds, and could therefore be considered conservative. l ships: The number of available data is quite limited and therefore ship-size dependent estimations are quite uncethere ismoment of grounding as the ship length increases. However this tendency seems very small, and can probably be neglected. It could therefore be considered acceptable to use a common distribution for the ship speed at the moment of grounding for full ships irrespective of the ship length.

c. Such distribution has been estimated from the available data and, according to its shape, it could be approximated, as a first approach, by a uniform distribution zero speed), but a better approximation could be obtained by an appropriate cubic polynomial.

erns SOLAS requirements related to double bottom in passenger and cargo ships, in general:

1) The analysis has been carried out omitting all data coming from accidents involving

accidents resulting in multiple damages and collected in GOALDS project

e other hand, the analysis of HARDER data highlighted

3)

ships imposed to use all the available data (i.e. also data

For wh

tankers and fishing vessels. 2) Grounding

represent 54.9% of the total sample of data collected in GOALDS and used to check SOLAS requirements. On thonly 1.5% of total HARDER cases used in the same context which were associated with multiple damages in the same accident. The enormous difference between HARDER and GOALDS data in the relative proportion of casualties reported to result in multiple damages after grounding call for thorough attention. Available data are limited, in the very large majority and depending on the particular variable of interest, to panamax breadth (32.2m), and hence the range of post-panamax vessels is almost not covered.

4) The available number of data for passenger vessels is too limited to draw any specific conclusion for this ship type. Moreover, the limited number of data related to accidents involving passenger coming from non-passenger vessels, with the exclusion of data associated with tankers and fishing vessels accidents) in the assessment of requirements specific for passenger vessels with large lower holds. Accordingly, results shall be considered with caution.

at concerns SOLAS requirements for double bottom height in passenger and cargo ships other than tankers:

1) The probability of damage penetration exceeding the minimum double bottom height, S2009Pr zL DBH> , has been estimated as [ ]95%

27.3% 16.1%,41.0%CI .


Deliverable D3.2 - Annex 3 2) The probability of damage penetration exceeding the minimum double bottom height

specified for passenger ships with large lower holds, S2009-LLHz

estim [Pr L DBH> , has been

ated as ]95%14.5% 6.5%,26.7%

CI 3) There are quite systematic trends for the conditional averages of the ratios between the

vertical damage penetration and the required SOLAS minimum double bot om height, t S/z pE L DBH L and 2009 p S2009-LLHz pp

creasing of these average values as the ship length increases from the

wide due to the limite ber of available data. 4)

/E L DBH L . The tendency, in both cases, is towards a derange of small ships up to about 80m-100m in length, after which a sort of stabilization is visible. Confidence intervals on the mean values are however quite

d numThere seems to be some indication that there could be a dependence between the ship size and the probability that the bottom damage penetration could exceed SOLAS minimum double bottom height requirements. In particular, there seems to be some indication that the probability of penetrating a double bottom marginally compliant with SOLAS requirements is larger for small ships and smaller for large ships. Indeed, the estimated S2009Pr z ppL DBH L> shows a systematic tendency towards a decreasing as the ship length increases. A similar behaviour is visible for

S2009-LLHPr z ppL DBH L> . However, in this case there seems to be a tendency

towards a sort of stabilization of S2009-LLH ppDBH L> as the ship length exceeds about 80m-100m. The number of data is however insufficient to draw any firm conclusion.

at concerns SOLAS requirements ottom damage in passenger

Pr zL

For wh for the extent of double band cargo ships other than tankers showing unusual double bottom arrangements:

The probability of exceeding assumed SOLAS dimensions for bottom damage has been estimated as follows:

1)

a) Probability ,S2009Pr x xL L> that the longitudinal extent of damage exceeds

the value prescribed by SOLAS: [ ]95%CI

b) Probability 54.6% 47.6%,61.6% ;

Pr yL > ,S2009yL that the transverse extent of damage exceeds the

ibed by SOLAS:value prescr [ ]95%18.2% 11.5%,26.7%

CI ;

Probability c) ,S2009Pr z zL L> that ma the vertical extent of da ge exceeds the

value prescribed by SOLAS: [ ]95%29.1% 17.6%,42.9%

CI ;

Probability ( ) ( ) ( ) ,S2009 S2009Pr x xL L> ,S2009 ,y y z zL L L L∧ > ∧ > that that all

dimensions p

d)

damage rescribed by SOLAS are exceeded: [ ]95%

11.1% 3.7%,24.1%CI ;

( ) ( ) ( ) ,S2009 ,S2009 ,S2009Pr x x y y z zL L L L L L> ∨ > ∨ > e) Probability that at least one

of the damage dimensions prescribed by SOLAS is exceeded: [ ]95%

64.4% 48.8%,78.1%CI ;

2) An approximate comparison with exceedance probability levels of bottom damage characteristics as reported in [10] showed the following indications:


Deliverable D3.2 - Annex 3 ,S2009Pr x xL L>a) The estimated probability in this paper

( [ ]95%54.6% 47.6%,61.6%

CI ) seems to be larger than the level considered in §4.3 in [10] (43%);

b) The estimated probability ,S2009Pr y yL L> in this paper

[ ]( 95%18.2% 11.5%,26.7%

CI ) seems to y smaller than the level considered in §4.5 in [10] (about 38%-40%); T bility

be significantl

c) he estimated proba ,S2009Pr z zL L> in this paper

[( ]95%29.1% 17.6%,42.9%

CI ) seems to be e level considered in §4.8 in [10] (26%);

mparison is approximate in nature since the events ted with the estimated probability levels are n

comparable with th

It must be borne in mind that this coassocia ot exactly the same in all cases, but nevertheless, they are quite comparable. In order to draw ait sconside d as reference acceptable not to ls, appropriate acceptable levels should be

3)

ny conclusion, however, hould be clarified whether the probability levels reported in [10] are to be

re levels of exceedance or not, and if these levels are be considered as acceptable leve

identified before deciding on whether or not present SOLAS assumptions for bottom damage characteristics are sufficient. In case of passenger ships with large lower holds, the Administration may require an increased vertical extent of bottom damage for demonstrating compliance with Regulation 9.8. Here the increased bottom damage has been assumed equal to

min /10,3B m , consistently with increased double bottom height requirements.

When considering an increase in the bottom damage penetration up to 4) min /10,3B m the following probabilities are obtained, which are to be deemed relevant to the case of passenger ships with large lower holds:

a) Probability ,S2009Pr x xL L> : [ ]95%54.6% 47.6%,61.6%

CI ;

ity b) Probabil ,S2009y yPr L L> : [ ]95%CI

c) Probabi ity 18.2% 11.5%,26.7% ;

l ,S2009-LLHPr z zL L> : [ ]95%14.5% 6.5%,26.7%

CI ;

d) Probability ( ) ( ) ( ) ,S2009 ,S2009Pr x x y yL L L L> ∧ > ,S2009-LLHz zL L∧ > :

[ ]95%8.9% 2.5%,21.2%

CI ;

) (e) Probability ( ) ( ) ,S2009 ,S2009 ,S2009-LLHPr x x y y z zL L L L L L> ∨ > > : ∨

[ ]95%60.0% 44.3%,74.3%

CI ;

wh ,S2009Pr y yL L> ere ,S2Pr x xL L> 009 and have been reported again only for sakof completeness since the presence of large lower holds only influences the assumed vertical extent of damage.

5) The average value of the ratio shows a tendency towards increasing as thship length increases up to about 120m-150m. For longer ships there seems to be an almost constant or even slightly decreasing tendency.

6) The average value of the ratio seems to be almost independent of the ship length, with a slight decreasing tendency as the ship length increases.

e

,S2009/x xL L e

,S2009/y yL L


Deliverable D3.2 - Annex 3 7) at concerns the a values of the r

8)

out 80

For wh verage atios ,S2009/z zL L and ,S2009-LLH/z zL L , there is a decreasing tendency as a function of the ship length. The probabilities of exceedance of the SOLAS bottom damage dimensions have been analysed as functions of the ship length. The number of data is not large, and therefore confidence intervals for the estimations are quite wide, particularly in case of large ships. Some trend, however, seems to be visible. In particular:

b m a) For ships longer than a it seems that ,S2009Pr x x ppL L L> is almost

constant. For shorter ships ,S2009Pr x x ppL L L> seems to be an increasing

m damage width, function of the ship length.

b) The probability of exceeding the SOLAS reference botto

,S2009Pr y y ppL L L> , seems to be almost constant for ships up to a length of

about 125m. For longer ships there seems to be a quite sudden decrease of

,S2009Pr y y ppL L L> . However, the confidence intervals are too wide to

more data would bc) stematic tendency towards a decreasing of

definitely consider this change as significant, and e needed. There seems to be a sy

,S2009Pr z z ppL L L> as the sh ld mean that ip length increases, and this cou

e oships. A similar

SOLAS damage assumptions could be, for what concerns the damage pen tration, more c nservative for large ships and less conservative for small

behaviour seems to be present in case of

,S2009-LLHPr z z ppL L L> . However, in this case, a tendency seems visible

towards a sort of stabilization of ,S2009-LLHPr z z ppL L L> as the ship length

exceeds about 80m-100m. The number of data is however insufficient to draw . The obtained results could mean that SOLAS damage be, for what concerns the damage penetration, more

conservative for large ships and less conservative for small ships. The observed behaviour for

any firm conclusionassumptions could

,S2009Pr z z ppL L L> and ,S2009-LLHPr z z ppL L L>

seems to be consisten with the observed suitability of a common ship-size tindependent distribution ( )CDF L for the dimensional vertical damage extent, while SOLAS bottom dama ortional to the ship breadth (with a maximum at 2m or 3m for passenger ships with long lower holds).

ffective use of the information in this paper, as well as of the update GOALDS e frame of development/up , mainly, two ways, namelypment of a fully probabilistic approach for bottom damage, similar to the one in use for side damage, b ting, but not necessarily limiting to, the tions described in this paper, after proper explicit mathematical

ing/fitting. pment/update of bottom damage characteristics and/or double bottom height ments by

z

ge penetration is prop

It seems that edatabase, in th date of relevant regulatory frameworks could bedone following :

- Develoalready y exploidistribumodell

- Develorequire specifying a-priori appropriate acceptable levels for the probabilities


Deliverable D3.2 - Annex 3 of exceedance, and determining the corresponding double bottom requirements / damage characteristics.

The first approach would be the more physical one, though also the more complex both from the appin the obtainevariabl cal integration of the integrals required for the development of so-call fitting obtainiIndeed tions for the fitting of the distributions would be limited to

a Monte-

probability density

lication and from the mathematical point of view. Typical issues that could be foreseen development of such an approach could mainly come from the fitting process of the d distributions, from the embedding (if considered necessary) of dependence among es, from the analyti

ed "p-factors". In particular the selection of the fitting procedure, or, better, of the type of functions for the obtained empirical distributions is strictly related to the necessity of ng analytically integrable functions in the development of so-called "p-factors". , the selection of the func

those classes of functions allowing the subsequent required analytical integrations. This would certainly limit the possibility of obtaining accurate fittings of the empirical distributions. Moreover, it is expected that the obtained formulations for the p-factors will be valid only for volumes having cuboid shapes, and in case of more complex subdivisions appropriate transformation into (approximate) sets of cuboids would be necessary. The second approach would be a more pragmatic one, and would be a simplification of the real problem, but would be easier to apply from the design point of view, and could be tuned to embed a specified level of conservativeness. The limited availability of data in the database could however lead to a not negligible level of uncertainty in the determination of the reference damage characteristics, and this aspect should be borne in mind. However, a third alternative could also be envisaged, which is mainly an alternative to the first considered approach. It could indeed be possible to simply clearly specify the (joint if necessary) probability density functions of the variables describing the location and the dimensions of the damage, and then consider the application of such distributions inCarlo (possibly with variance reduction techniques) approach to the bottom damage, or, if possible, through direct deterministic numerical integration. This type of approach would be extremely flexible in terms of possible future updates, because it would not require a re-calculation of formulae for p-factors, or a re-determination of reference bottom damage characteristics, but the update would just be a re-specification of the (joint)functions to be used in the generation of damages. Moreover, this approach could partially avoid foreseeable problems associated with the application of classical p-factors to complex not cuboid internal volumes, a problem which is presently evident in case of application of side damage p-factors to certain complex subdivisions. Finally, it is worth reporting that, in general, despite all the efforts spent to remove doublets, wrong cases, etc. it is not possible to say that the quality of the database is high. Sufficiently large subsets of fully consistent data are particularly missing. Some differences have also been highlighted between previous data and data collected in GOALDS, which call for further attention. It is therefore suggested that more efforts should be spent in the future in order to improve the recording and processing of accidents data, otherwise it is expectable that not negligible difficulties will arise in possible future tentative revisions of damage statistics for design and/or regulatory purposes.

Acknowledgments The authors are grateful to those GOALDS partners that provided literature, corrections and suggestions for the improvement of the present paper, in particular: Det Norske Veritas (DNV), Germanischer Lloyd AG (GL), Lloyds Register of Shipping (LR), National Technical University of Athens (NTUA), University of Strathclyde (SSRC).


Deliverable D3.2 - Annex 3 References [1] Mains, C., "WP3 Database of damage characteristics - File: GOALDS-database-

, 8 June 2010. .1, WP3.2 Technical meeting - Meeting date: 2010-03-11/12",

2010.

., Francescutto, A., "Some considerations on the probability distributions for

uilding Progress, Vol. 52, No. 4, 2005, pp. 325-

[6] 10

-919488-

[9] n, G., Francescutto, A., "Exploratory data analysis of ship-ship collision data

eristics, Rev.0, 17 June 2010, 50pp.

rev3.xls", GOALDS[2] Mains, C., "WP 3

GOALDS Document Id GOALDS-A-Hamburg-2010-03-11-GL-rev0, Prepared 2010-04-14, 4pp.

[3] Mains, C., Bulian, G., "Equivalent grounding damage characteristics - File: GOALDS-ground-multipl_equivalent2010-06-22_rev2.xls", GOALDS , 22 June

[4] IMO, "SOLAS Consolidated Edition 2009", London, 2009 [5] Bulian, G

the damage length and damage penetration based on a re-analysis of recorded ship collisions data", International Shipb356. Mains, C., "GOALDS WP3, T3.2 – groundings, check of influence of multiple cases", 03 March 20

[7] Pawłowski, M., "Subdivision and damage stability of ships", Euro-MTEC book series, Foundation for the Promotion of Maritime Industry, Gdansk, ISBN 836-2, 2004, 311 pp.

[8] Pawłowski, M., "Probability of flooding a compartment (the pi factor) – a critique and a proposal", Proceedings of the Institution of Mechanical Engineers, Part M: J. Engineering for the Mari-time Environment, 2005, Vol. 219, pp. 185–201. Buliafrom the updated GOALDS database", GOALDS Interim Report - Task 3.1: Collision Damage Charact

[10] IMO Document SLF47/INF.4, "Bottom damage statistics for draft regulation 9", Submitted by Germany and Norway, London, UK, 9 June 2004



Nomenclature Quantity Units Definition

x axis− -- Axis in longitudinal ship direction, directed from stern to bow. 0x = at aft perpendicular.

y axis− -- Axis in transversal ship direction. Directed from starboard to portside. 0y = at centreplane.

z axis− -- Axis in vertical ship direction. Directed upwards. 0z = on the baseline.

damX [ ]m Longitudinal position of centre of damage.

,F damX [ ]m Longitudinal position of the forward end of damage.

xL [ ]m Dimensional damage length along x axis−

yL [ ]m Dimensional damage length along y axis− . In case of collision this is the damage penetration. In case of grounding this is the damage width.

zL [ ]m Dimensional damage length along . In case of collision this is the damage height. In case of grounding this is the damage penetration.

z axis−

ppL [ ]m Ship length between perpendiculars

shipL [ ]m Generic ship length (e.g. the subdivision length according to SOLAS or the ship length according to the International Convention on Load Lines)

B [ ]m Moulded ship breadth

D [ ]m Moulded ship depth

shipV [ ]/m s or

[ ]knots

Ship speed (at the moment of grounding)

CDF (or ) cdf [ ]− Cumulative distribution function

PDF (or pdf ) [ ]− Probability density function

.E depends on variable

Expected value of a random variable

ID Identification number of damage case according to GOALDS database

Casualty ID Number identifying a specific casualty according to GOALDS database. Note that different IDs can be associated with the same "Casualty ID".



Quantity Units Definition

S2009DBH [ ]mMinimum double bottom height according to SOLAS2009 for passenger and cargo ships other than tankers (Ch.II-1, Part B-2, Regulation 9.2)

S2009,LLHDBH [ ]mMaximum value of the increased minimum double bottom height the Administration may require according to SOLAS2009 for passenger ships with large lower holds (Ch.II-1, Part B-2, Regulation 9.9).

,S2009xL [ ]m Longitudinal extent of bottom damage according to SOLAS2009, (Ch.II-1, Part B-2, Regulation 9.8)

,S2009yL [ ]m Transverse extent of bottom damage according to SOLAS2009, (Ch.II-1, Part B-2, Regulation 9.8)

,S2009zL [ ]mVertical extent of bottom damage, measured from the keel line, according to SOLAS2009, (Ch.II-1, Part B-2, Regulation 9.8)

,S2009-LLHzL [ ]mASSUMED vertical extent of bottom damage, measured from the keel line, according to SOLAS2009, (Ch.II-1, Part B-2, Regulation 9.8) for passenger ships with large lower holds (Ch.II-1, Part B-2, Regulation 9.9)


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