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CRITERIA FOR SURVIVAL IN DAMAGED

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D. Vassalos, M. Pawlowski" and O. Turan

Department of Ship and Marine Technology, University of Strathclyde, Glasgow, UK Visiting Research Fellow, Gdansk Technical University, Poland

SUMMARY

Buildinc on earlier developments under the UK RoRo Research Programme, the focus of the effort during the North West

European Joint R&D Project has been on improving and validating comprehensively an exisring theoretical model,

capaOle of predicting the capsizal resistance of a damaged vessel in realistic environmental conditions wniisr accounting for progressive floocing. Having successfully fulfilled this task, the Strathc!yde University Ship Stability (SUSS) Research Group has subsequently undertaken a systematic parametric investigation aiming to identity the key factors influencing the vessel's ability to survive a said damage as well as representative parameters characterising uniquely this ability for any vessel type. form, size and compartmentation as a function of sea state with the view to using these as a basis tor

developing rational survival criteria. In their quest to meeting these goals, the Strathclyde team achieved a major

breakthrough which is likely to serve as a key contribution to new 1MO regulations, for assessing the damage survivablilty of passenger/RoRo vessais, and to facilitate the harmonisation of probabilistic stability standards.

AUTHORS' BOGRAPHES

Dracos Vassalos is a Professor in the Department of Ship and Marine Technology at the University of Strathclyde and

the leader of the Stability Research Group, con'iorising some 12 researchers and research students dealing with all

aspects of stability of ships and ocean vehicles. He has been involved with stability research for over 18 years and has

served as a Principal Investigator in a numoer of major research projects including: SAFESHIP, PRESS, UK RoRo

Research Programme, Stability of High Speed Twin-Hull Craft. MOD Trimaran Programme ana the Joint North West

European Project. Professor Vassaios is the overall co-ordinator of a major EU initiative on the safety of RoRo vessels involving S Universities and over 30 companies and research institutes from 11 European Nations an a member of the UK delegation to 1MO for ship stability.

Maciej Pawlowski is a visiting Research Feilow in the Department of Ship and Marine Technology at the University of

Strathclyde since July 1995 involved the development of probabilistic damage stability cnteria within the North West

European R&D Project. Maciej Pawlowski is a Professor in the Department of Ocean Engineering and Shipbuilding at

the Technical University of Gdansk. specialising on ship statics and, in particular. the probabilistic assessment of ship safety in damaged condition. In connection with the latter Professor Pawiowski has since 1972 been very active in the

SLF Sub-Committee at 1MO where he has made significant contributions to the prooabilistic subdivision regulations. Osman Turan is a Research Fellow in the Department of Ship and Marine Technology at the University of Strathclyde and a key member of the Stability Research Group. Dr. Turan is involved with theoretical, experimental and rule development

work concerning RoRo vessels as well as general stability problems of ships and advanced marine vehicles. After

completing his PhD at Strathclvde on the "Dynamic Stability Assessment of Damaged Passenger Ships Using a Time

Simulation Aoroach" and working as a research assistant on damage stability related projects he took up a lectureship post at Yildiz Technical University in Turkey. He rejoined the Strathciyoe team in February 1995.

1. INTRODUCTION

The limited understanding of the complex dynamic

behaviour of a damaged vessel and the progression of flood water through the ship in a random sea state has,

to date, resulted in

approaches for assessing the

damage survivability of ships that

rely mainly on

hydrostatic properties.

Furthermore, in case of serious flooding of ships with

large undivided deck spaces. such as RoRo vessels, the

loss could be catastrophic as a result of rapid capsize,

rendering evacuation of passengers and crew im practical, with disastrous (unacceptable) consecuences. Trie tragic accidents of the Herald of Free

Enterprise and more recently

of

Estonia were the

strongest indicators yet of the existing gaps in assessing damage survivability in a flooded condition particularly for this class of vessels.

Following the tragic capsize of the Herald of Free

Enterprise in March 1987 and realising this

unsatisfactory state of affairs, the UK Department of

Transport initiated an

extensive RoRo Research

Programme, comprising a number of studies

into

damage survivability of these ships, including model tests n waves, [1] to [4] and numerical simulations, [5],

[6.

The Strathclyde team was charged with the responsibility of developina and validating a theoretical capsize model

which could predict the minimum stability needed by a

damaged vessel to resist capsizing in a given sea state. This responsibility was successfully discharged in 1992,

[1. With the Estonia tragedy shaking once more the

foundations of shipping, it forced the profession to seek soiutions urgently and, in attempting to do so, to use the

right expertise and experience to

provide the right

capsize safety has suddenly reached the deserved and

lonc overdue intensity. The Nordic countries reacted

quickly in undertaking this responsibility leading to a

wider-based project, known as the North West European Research arid Development Project (Joint R&D Project), aiming to ensure "passenger survival" irrespective of the

degree of damage and severity of sea state RoRo

vessels are likely to encounter.

Deriving from the success demonstrated by the SUSS Group during the

UK RoRo research and taken into consideration that the

UK had already commissioned Phase lIA of the RoRo Survivability Research. focusing on the mathematical model developed at the University of Strathclyde, the

Group was invited to participate in this Joint R&D Project.

The intention was, following a process of

further

development and validation of the existing simulation

program, to apply it to different vessel types, forms, sizes

and compartmentation and to representative damage scenarios and environments with a view to verifying its

general applicability to assessing the capsize safety of a

damaged ship in a given sea state and to using it as a basis for developing new survival criteria for ships in

damaged condition.

This work formed Task 5 of the

Project

The focus in this paoer will be on the development of new survival criteria. Full details of ail the work undertaken at Strathclyde under the Joint R&D Project can be found in

(81.

2. BACKGROUND

2.1 THE ORIGINAL SURVIVAL FACTOR

At about the same time as the 1974 SOLAS Convention was introduced, the International Maritime Organisation

(1MO), published Resolution A265 (VIII), [9]. These

regulations used a probabilistic approach to assessing

damage location and extent drawing upon statistical data to derive estimates for the likelihood of particular damage

cases.

The method consists of the calculation of an Attained

Index of Subdivision, A, for the ship which must be

greater than or equal to a Required Subdivision Index, R, which is

a function of ship length, passenger/crew

numbers and lifeboat capacity, Index "A" is in turn a

function of three different probabilities, "a", "p" and "s". Factor "a" accounts for the probability of damage as related to the position of the compartment in the ship's

length: "p"

reflects the effect

of variation on the

longitudinal

extent of damage: "s" represents the

probability of survival given

the damage under

consideration.

The total attained index is the sum of the products of "ai",

"p«' and "s" for each of

the compartment and

compartment groups. i. within the ship. lt is the survival factor s, where attention was focused in Task 5.

lt is true to state that the ship damage stability problem has not received much research attention in the past

mainly because a meaningful treatment of it, particularly one involving progressive flooding in a random seaway,

was perceived to be too difficult an undertaking by

theoretical/numerical means.

For this reason an

experimental approach was adopted aiming to establish

a simplified relationship berveen environmental and

stability-related parameters for a damaged ship and

hence determine capsizal resistance in a given sea. On the basis of limited model tests carried out separately in

the United Kingdom, (10], and the USA, [11] such a

relationship was established between critical metacentnc heights (GM ) - limit of capsizal resistance- and vessel freeboard in a given critical sea state, characterised by the significant wave height. (H0 ). From the results of these tests it was decided to use flooded metaceritric

height (GM) and effective freeboard (Fe) rather than the

restoring (GZ ) curve ana GZ curve characteristics to

judge capsizal resistance. Suoolernentary model tests

have shown that for a given freeboard in any given sea state the critical GM is proportional to the beam of the

vessel, (B). Consequently, the following relationship was invoked:

(H3) _cntc = f (GM1" FelS) (1)

Deriving from the above, the probability "s" that a snip with a given value of the damage stability parameter

(GM1" F018) will survive damage in a given sea state will

be equal to the probability of not exceeding (H0 )cntj Therefore, the probability "s" can be derived from the

significant wave height distribution relevant to the area of the particular accident in conjunction with the relationship indicated in (1), i.e.:

0=F[H0(GM+" Fe/B)] (2)

A graph of this probability as a function of the damage

stability parameter is shown in Figure 1 below, obtained by using data given in [9] & [10].

0.8 3.6

0.4

02

001 02 003 0.04 (m

Figure 1: The probability of collision survival s

a: based on model tests and sea state distribution(10],

(11];

b: based on a comparative method [121; C: approximation adopted by 1MO

A reasonable approximation of this function is s = t7 (GMf Fe/B) 1/6 = (x/x1 ) 1/6 ₍₃₎

for S C (0,1), where x is the damage stability parameter in metres and x1 (= 0.0416 m) is a vaiue of x yielding

s =

1. 1MO approximates this probability

with a

considerable underestimation, as shown in Figure 1,

using the equation:

- C (0,1). If s is less than 0.6, which happens with

.o15 m, then 1MO requires s to be taken as zero [9],

rflectiflg the lack of confidence

in

the quality

of

for small s factors. In this range. a good

approx mat 0fl can be obtained for the s factor by using

bear interpolation between s = 0.6 for x = 0.015 m and

s = i for x = 0.04 m.

UK RaRo RESEARCH PROGRAMME

A new attempt to generalise the results of model

exoeriments and numerical simulations of the extensive RoRo research programme undertaken in the UK in the wake of the Herald of Free Enterprise disaster has been proposed in the form of a relationship between the ratio

HJF

and the non-dimensional flooded metacentric

height OM , defined as follows:

GMfC5Tf

B2 (5)

where, L. f ) volume of displacement of the vessel together with the flooded water block coefficient of the vessel to the damaged waterline

T >

draught of the vessel in the flooded

condition

L5 z) length between perpendiculars

with the other parameters as defined earlier. The

non-dimensional flooded metacentnc height

is defined

basicaily as the ratio GM1 / BM, where BM. is the

metacentric radius in the flooded condition. However, this

type of boundary survivability curve could not be

generaiised either as GMf and Fe do not reflect, for

example, the effect of different structural arrangements on the vehicle deck that can be used for enhancing the

damage survivability of RoRo vessels. For this purpose, the definition of the effective freeboard would have to be much more intricate.

Damage stability is a complex problem involving a large number of variables and with results only from one or two

given shapes it is difficult to identity the significant

Parameters governing the problem.

An extensive Investigation can, of course, be undertaken by using

numerical simulations, provided the latter are of the same

accuracy as the model tests. Full benefit from these

results will not be derived, however, until a consistent theory is developed which will enable the results to be generalised to other ship forms, sizes, and subdivision arrangements, thus leading to a definition of a unique

boundary survivability curve valid for

ail vessels, as

explained in the following.

This goal is essentially synonymous with the

development of rational survival criteria.

BOUNDARY

SURV1VABL1TY

CURVE

lt is generally acknowledged that the critical sea state a

Ship with a given loading condition and compartment

3

flooaed can withstand, cannot be determined uniquely.

This is

not because of inaccuracies

in the model

experiments or numerical simulations, nor because of limited duration of test runs, but simply because of the

random nature of the critical sea state, characterised by a certain distribution. Hence, any boundary survivability curve is a fuzzy curve, indicative only of the mean values

of the critical significant wave heights, characterising such sea states. Therefore, to define the distribution of

critical sea states (and its mean or median value), a

given flooding scenario will need to be repeated many times with different initial conditions. A boundary curve

cannot be defined by just one irial". This dependence of capsize boundaries on initial conditions is characteristic

of the non-linear nature of the problem at hand but has only recently been appreciated. The probability s that a ship with a given loading condition and compartment flooded will not capsize after damage is equal to the mean probabiiity that the critical significant wave height

related to this case is not exceeded:

s = [HF(HS) (H5) dH5 (7)

f(H5 ) z) probability density function of

critical sea states for a ship with a given loading condition and compartment flooded

The range of change of F(H5) for moderate and higher

critical sea states is small, as can be seen in [9], whereas

for low critical sea states (when damaged stability is deficient) the range of variation of critical sea states is

narrow. Therefore, by virtue of the mean value theorem, equation (7) yields:

SF[(Hs)me1

(8)

This implies that,

in

practice, the s factor can be

calculated as if the critical sea states were of binary

nature, cut oft at the mean value. As can be seen, of prime importance for the determination of the s factor, and thus for the whole method, is the basic expression for the s factor, given by equation (8), that requires the

critical sea state (Hs)mean to be known tor each damage case, denoted in the following simply by H5. However, to obtain this basic factor, it will be necessary to determine

H5 without the

aid

of model tests

or numerical

simulations, as these are not suited and intended for

routine applications. For this purpose, a simple but

meaningful procedure must be developed which can be verified by previous and new results, preferably based on

the theory underlying the numerical simulations, [5].

Before proceeding with the description

of such a

procedure, a

brief outline of the development and

validation of the numerical simulation program will first be given, highlighting some of the deficiencies still in need of further attention and development.

3. MATHEMATICAL MODELLING

To study effectively damage survivabiiity one needs to put together a highly non-linear six-dearees-of-freecom

where F (H5 z) cumulative distribution

function

of sea states at the

seakeeping model (that allows the vessel to dritt as well

as changes in

its mass, centre of mass and mean

attitude relative to the mean waterplane with time - the

same dependence of environmental excitation and

hydrodynamic reaction forces on the changing

underwater volume of the vessel must also be catered for), a water ingress model (that allows for

multiple-compartment flooding in the presence of oscillatory flows in extreme wave conditions and at times of shear flows),

a sloshing model (that allows for random inflow and

outflow through multiple openings), together with their

interaction.

An attempt in

this direction represents ongoing efforts among the SUSS Group [13] This is a top-down approach to solving this problem. The use of

such a

tool" in

its complete form, however, for

parametric investigations and routine design applications is outwith reach at present.

The state-of-the art,

currently represented by the

numerical model developed at Strathclyde, relates to a three-degree-of-freedom non-linear seakeeping model (allowing for change of vessel mass and heave and roil

restoring that take

into account ship motions,

trim,

sinkage and heel) and a hydraulic water ingress model (allowing for water inflow and outflow and associated

gravitational forces in a semi-empirical manner,

applicable to multiple-compartment flooding and to any vessel subdivision and deck arrangement). Flood water s assumed to move in phase with the ship roll motion with an instantaneous free-surface parailel to the mean waterplane. This is the model developed during the UK

RoRo research following a bottom-up approach and

formed also the basis for the Joint R&D Project. The

numerical model has undergone vigorous validation by means of supporting model experiments using three

different RoRo vessels tested

by three

different

organisations (British Maritime Technology Ltd. [7], and Danish Maritime Institute and M.ARINTEK, [8]), providing

strong evidence that this relatively simpler model can

describe adequately the behaviour of a damaged vessel

subjected to large scale flooding, thus allowing for

determination of a capsizal boundary with

sufficient engineering accuracy. Typical comparisons between

theoretical and experimental results are shown in Figure 2, taken from [8]. In this respect, this model serves an

extremely useful purpose.

lt must be understood. however, that damaged vessels

could in theory capsize in a mode still dominated by

vessel and flood water dynamics and in some cases in a very unpredictable manner, characteristic of highly non-linear systems. Furthermore, the emphasis in studying

damage survivability need not focus necessarily

in

determining the capsizal boundary. For example, the

actual time taken for the vessel to capsize (survival

time), knowledge of which is absolutely vital to ensure

successful mustering and evacuation of passengers and

crew, requires a more accurate modelling of the whole

dynamic process.

This forms the focus

of a new

research effort, supported yet again by the Manne Safety Agency of the UK Department of Transport, undertaken jointly by the University of Strathciyde and BMT Ltd.

4. _{DEVELOPMENT OF SURVIVAL CRITERIA} 4.1. SENSITIVITY STUDY

In order to identity the most influential parameters for the

stability and survivability of a damaged ship, a series of

parametric studies have been carried out using the

developed numerical simulation program.

For this

purpose a matrix which combines different damaged

freeboards, vehicle deck subdivisions, loading conditions, damage location, vessel size and sea states

has been tested. The parametric investigation began

with a sensitivity study of the two ships used in the Joint R&D Project which were tested extensively for software

verificationlvaíidation purposes. SHIP i was also used

during the UK RoRo Research Programme whilst SHiP 2

is representative of a modem passenger/RoRo Vessel

with improved stability characteristics. Full details of this

investigation can be found in [8]. Some information of

the ships and damaged conditions used in the sensitivity

study are given here, followed by presentation and

discussion of only the results which are directly related to the development of survival criteria.

SHIP i drausnt d Disniacernent. Block Coetfc,ent. C5 Intact Freeboard. F 6. IDo I 12.4000 tonnes 0.582 I 1.68 n

Table 1:

Principal Design Particulars of SHiP i

Table 2: Sensitivity Study Test Matrix for SHIP I

As can be seen there are 60 test conditions and for each condition a minimum of four different sea states has been considered.

The sea states were tested to Q.25rP

resolution (i.e. sea states were increased progressivelY

by 0.25m intervals). Where necessary, several n.in5

were carried out for the same conditions to ensure

statistical consIstency of the results. All condition5

address midship damage and the derived results refer tO 100% SOLAS damage opening, as defined in [7].

Model Scaje 42.05I

Lensth. L 3100mI

Bearn.B 2600mj

Deoth to Buikheao DecK. D 780m I Deoth to Uouer Most Corrnnuous Deck 18 0to I

OPEN DECK CENTRAL

CASING CASINGS

OFEN DECK -TRANS VESSE 8ULKHE..DS KG Oanaed F (mi Damaged F (rai Oarriased F (ml Damaged F 1m) (m l0.2110.571L02 O.2210.37IL0210.2115.37i 1.02 0.2119.5711.02I

9.0

NIX X XIXlX

xixix

XIX

X

10.0

lxix

x

xIxIxI

XXI

xFxlx

X

11.0

IXIX xjxIXlXi XXIX

lxix

X

12.0

XIX

X XIXXI XjXI

xxix

X

Table 3 Damaged Conditions for SHIP i

Table 5: Sensitivity Study Test Matrix for SHIP

As shown in the table above, the sensitivity study matrix

for SHIP 2 covers 72 different test conditions, for which

the limtting sea states were found. Similar to SHIP 1, sea

states were tested to 0.25m resolution.

Again all

conditions refer to midship damage and to 100% SOLAS damage opening unless stated otherwise.

Table 4: Principal Design Particu'ars of SHIP 2

Table 6: Damaged Conditions for SHIP 2

The wave environment used in model tests was also

Used to _{undertake the numerical simulations.} lt is

representative of the North Sea and is modelled by using JONSWAP spectra. Details for this and of the vehicle deck Subdivision arrangements used for the two ships

are given in [8}.

D

4.2 SENSITIVITY OF VESSEL SURVIVAL ON GM

AND OTHER RESiDUAL STABILITY

PARAMETERS

If different subdivisions of the

vehicle deck are

contemplated, then clearly GM1 cannot be considered as

a representative parameter to characterise the damage

suniivabiUty of passenger/RoRo vessels. However, GM

in itself is

the key opening the door to

the most successful characteristic property of a vessel's ability to

resist capsize in any condition and environment, namely, the restoring curve. Even if one does not support this

view, any results that this route is likely to yield, offer two distinct advantages: simplicity and applicability. It was

attempted initially, therefore,

to express the survival

factor "s" as a function of residual stability characteristics,

judiciously chosen (e.g. systematic parametric

investigations, regression analyses, experiential

judgement, etc.) to

enable such a factor to be

generalised for application to

all vessel types and

compartnientation.

A first exploration in this direction met with a problem that needed careful thinking. Damage stability calculations for

vessels damaged both above and below the bulkhead

deck would require, according to MO, that the water

level in each damaged compartment open to the sea

must be at the same level as the sea i.e. final equilibrium be reached. However, the O-Z curves derived on the

basis of this approach, simply fail to offer any useful

information.

The principal reason lies on the wrong

assumption that water is free-flooding the deck in these calculations. Taking heed from this and from the fact that water on deck is a dominant parameter affecting damage survivability, as earlier experience amply demonstrated,

it was decided to attempt to quantify the critical amount

of water on deck as a matter of top priority. The first

important step was to achieve a good understanding of

what is meant by critical amount of water on deck and to develop a practical method of quantifying this.

4.3 CRITICAL AMOUNT OF WATER ON

DECK - "THE POINT OF NO-RETURN" The effect of random waves on the rolling motion of a

damaged ship appears to be rather small and for capsize to occur in a "pure" dynamic mode should be regarded as the exception rather than the rule. The main effect of the

waves, therefore, is to exacerbate flooding. In this

respect, the effect of heave motion

in reducing the damaged freeboard is as important as the roil motion.

Model experiments and numerical simulations have

clearly demonstrated that the dominant factor determining the behaviour of the vessel is the amount of flood water accumulating on the vehicle deck. In case of large scale flooding,

the vessel motions become

subdued with the mean heel angle increasing sIowly until

a critical

value is

reached beyond which heeling

increases exponentially and the vessel caosizes very

rapidly. In this context, the term "point of no return" is

used as indicative of the fate of the vessel when this critical heel angle is attained. Put differently, the flood water on the vehicle deck increases slowly, deoending on the vessel and environmental conditions, until the

amount accumulated reached a level that cannot be supported by the vessel/environment and the vessel

Modi Scsie j 34 66

130 on

255m

Dectho3uikheadDedD 335m

to Lpoer Most Conunuous Deck 7 10m

575m

DtsvIacement. 5 1200.0 tonnes Block CociScoent. C0 0 612

lrxtactFretboard.F 26m

OPEN DECK OE'TrRAI._{CASDG CASC1OS}ama

OPENDECK"

TRE

KO DamaacsF(mliDan,a2edF(mlI Dom3Funl DooraeaF(mi

nu 11.0 1.0 0.5 0.5 1.0 LS 0.5 LOI LO (LS LO I .0

91)

'XIXIX xIXIX XIXrXIXIXIX

9-.)

XX1X X1X1X XIXI X IX!XIXI

0.5

XIXIXIXIXJXI X

Xi X

lxi

XIX

1.5

'(IXIX XIXIXI XXIX Xi XIX

LO

Xl XIX XI XI XI XI XIX

xIx

X

13.0 IXIXIX XIXIXIXIXIXIXIXiXI

Damaeco Comparunent Lenonh 1m) ' Daxnagec Freeboard (ml Intact KM (ml Damaged KM (ml 2405 1.5 14.22 I 13.46 3243 1.0 4.22 I 14.48 4025 0 5 1422 14.59 02 1795 13 SS

Damaged Intact Damaged Freeboard (rn) KM (m KM 1m)

1395 14.34 0.55

13,95 I 14.74

capsizes very rapidly _{as a result. The amount of flood} water when the point of no-return is reached is the critical amount of water on deck. _{In relation to this, two points} deserve emphasis: _{This amount is substantially}

less than the amount of water_{just before the vessel actually}

caosizes but is in excess of the amount required to

statically capsize the ship. _{In this respect, the energy}

input on account of the waves help the vessel sustain a

larger amount of water than what her static restoring

characteristics appear to dictate. Because of the nature of the capsize mode when serious flooding of the vehicle deck takes place, it is not difficuft to estimate the critical

amount of water on deck at the point of no-return from

experimental or numerical simulation records considering

either the flood water

_{on the vehicle deck or the roil}

motion of vessel. This is _{demonstrated in Figure 3 with}

some summary results shown in Figure 5, using SHIP 2. 4.4 _{STATIC EQUIVALENT METHOD}

Careful examination of the numerical simulation results,

such as those shown in Figure 3, led to the following

observations and developments:

The point of no return _{occurs at a heeling angle}

very close to 8m' where the

_{GZ curve is at}

maximum. This angie, in the majority of cases

examined, is less then 10_{degrees. Reference is}

made here to the

GZ curve

_calculated

traditionally, usina the

_{constant displacement}

method and allowing fer

_{free-flooding}

_{of the}

vehicle deck when the deck edge is submerged. s _{This fact, coupled with observations from physical}

model experiments and the experience amassed

from studying large numbers of numerical tests led to the development of an "Static Equivalent Method" which allows for the calculation of the

critical amount of water

_{on deck from statical}

stability calculations.

_{To this end, a floocing}

scenario is considered,

_{in which the ship is}

damaged only below the _{vehicle deck but with a} certain amount of water on the (undamaged) deck

inside the upper (intact)

_{part of the ship. The}

critical

_{amount of water on deck}

_{is then}

determined by the amount causing the ship to

assume an angle of loll (angle of_{equilibrium) 8e}

that equals the angle

_{8m' determined}

previously.

Strictly speakinc, the

_{GZ curve should be}

calculated by considering a freely floating ship, to

allow for the trimming moment produced by the

amount of water on deck at the point of no-return.

The scenario described above scenario

is

depicted in Figure 4, believed to represent closely

observations of the flooding process near the capsize boundary or when a stationary (steady)

state is reached with the water ori elevated at an average height above the mean water plane, as a result of the wave action and vessel motions.

3

Figure 4: Stability of

_{a damaged ship with water}

accumulated on deck

(Static Equivalent Method)

In the process of seeking a generalized damaged

stabil-ity cnterion, the quantities considered to describe the

above scenario at the point of no return are h and f _as

defined in Figure 4. Due to the dynamic action of waves, the flooded water accumulates on deck causing the ship to heel and trim and, when the deck edge becomes sub-merged, the water continues _{to elevate above the sea}

level until it reached a height h, depending on the sea

state, at which inflow and outflow of water through the

opening is balanced, maintaining the amount of trapped water on the deck constant _{over some ceriod of time as}

if the upper part of the

_{ship were intact. The ship} assumes then a heel angle at which the heeling moment due to the accumulated water on deck is balanced by the restoring moment. _{This quasi-static heel angle}

deter-mines in turn the mean roll angle about which the ship

oscillates - _{statically, this cannot be greater than the}

angle 8max

4.5 _{A RATIONAL BOUNDARY SURVIVABILITY} CUR VE

Deriving from the above and adopting the philosophy outlined in (14], efforts at this stage concentrated on

investigating whether a similar damage stability cnterion (boundary survivability curve), will be valid for any ship of

any size, loading condition, damage scenario and

subdivision arrangement. _{The relationship presently} considered is in the form

h/i-I5 = f(fl)

₍₉₎

where, h and f are the two quantities derived readily by

the static equivalent method

_{and H5 is the average}

significant wave height characterising a critical sea state,

found with the aid of numerical _{simulations. Preceding}

the examination of uniqueness of equation (9), was

obtaining evidence on the validity of the static equivalent method. which is described next.

(a) _{Comparison between numerical simulation}

and 'static equivalent method"

_results

r 4.

were performed between the static and dynamic

ecicdcn5 of the critical amount of water on deck for

SHIP 2. considering the test matrix of Table 5.

The parameter used for comparason is the critical amount of

water on the vehicle deck as derived from numerical si1uladofl and the stic equivalent method. Additional

icuIabOflS were also camed out for SHIP 1, considering

o-ity an open deck arrangement. Typical results are

presented in Figure

5, demonstrating the excellent

agreement achieved in all

the cases considered,

parbculariy so for the operational range of KG values. lt

should be noted that, in accordance with the nature of a critical sea state, the critical amount of water on deck is

aise a random quantity.

(b) Uniqueness

To validate the above considerations concerning

uniqueness of the boundary survivability curve, the three

mcortant quantities

h, f and critical H3

have been calculated for SHIP i and SHIP 2, for as many as 126

cases, including results from two scaled versions of SHIP (scales 1.5 and 2/3). The results of calculations are

lotted in Figures 6 to 9, using H5 instead of H3, where

sr is a modied significant wave height. accounting in a

ay for the relative motion between the vessel and

iaves at the damage opening. The points in the two

gures are differentiated only according to

different amage freeboards, denoted by F. Based on the results

btained, the following observations are note worthy:

Contrary to expectations, the immersion of the

deck edge at the damage opening, f, is irrelevant

concerning the capsizing

resistance of the

damaged ship and can be disregarded from

further considerations. This is clearly demonstrated in Figures 6 and 7. The immersion

of

the deck edge at

the

opening can be

interpreted as a negative freeboard and this is

likely to be the case considering the mode of

capsize described

in the foregoing in the

presence of large scale flooding. When the deck s above the sea level, i.e. freeboard is positive,

the situation is different. Naturally, in this case,

both the flooding process threshold and the

amount of kinetic energy of waves that

is

available to sustain the water accumulated on the

deck at a given level would be affected by the

freeboard.

The above observation leads directly to the very important conclusion that the elevation of water

on deck above the sea level, h, is the unique

measure of ship survival in the damaged condition

(the higher the water elevation at the point of no

return, the higher the sea state needed to elevate

water to this level and the higher the capsizal

resistance of the ship. lt follows, therefore, that

the relationship between h and H3 ¡s unique for a given ship, irrespective of subdivision

arrangements and loading conditions,

as it

depends primarily on the relative motion between the vessel and waves at the opening. lt would be

very surprising, if that were not the case. Other

effects, such as shape and size of the damage or

type of ship, are marginal. The relationship can

7

only be affected by the dynamic properties of the

ship

(primarily heave motion) and sea state

characteristics.

s Surprisingly, the size of the ship has little or no

effect on the survival capability. Figure 8 clearly

confirms this conclusion.

The reason for this

derives from the fact that the effect of ship size is

largely accounted for by the modified significant

wave height H3r. Moreover, a change of H5 with

ship size is associated with a change of wave

period T that depends on ship size in such a

manner that the resulting effect is neutralised.

The location of the compartment along the ship length has no effect on the survival capability of the ship provided that the static calculations are performed accounting for the trimming moment

due to water elevated on deck.

s The smallest scatter of points in Figures 6 and 7

is obtained for

H_sr- H_s1.3 (10)

s The average value of h /H equals then 0.085 for

both test ships. Hence, the sought boundary

survivability curve may take the form: h = 0.085 H513 (11)

This equation provides on the whole an excellent prediction, with deviations in the majority of cases

less than the sea state resolution used to derive

Hs. This impressive result can be observed in

Figures 8 and 9. Eleven points derived from the

model experiments undertaken during the Joint

R&D Project are also incorporated ¡n the sample data presented in Figure 8 which appear to fit the theoretical prediction very well.

(c) Practical application

This boundary survivability curve in the form of equation (11) could not be simpier for practical

applications.

For this purpose, for a given

compartment group it is necessary to calculate only the measure of damage stability, i.e. the elevation of flooded water on deck h at the point of no return, equalling the angle 6m' The mean

critical sea state is then given as

H3=( h

(12)

\0.o851

s Having determined the critical sea state H3 for a given damage, the factor s can be easily obtained

from the sea state distribution occurring at the moment of collision F = F (H3 ), as explained in the foregoing. For purposes of illustration alone, the sea state distribution proposed by 1MO, [9],

could be used, as shown in Figure iO.

lt is

noteworthy that the distribution of sea states at the moment of collision is different from the sea state distribution, obtained from regular weather

statistics. In a large majority of cases, collisions

happen in the proximity of ports,

in confined

in a similar manner to that previously used for the damage stability parameter GMf"FJB. A graph of

this probability is shown in Figure 11, using the

sea state distribution, shown in

Figure 10, in

association with the boundary survivabiHty curve,

given by equation (12).

A very good approximation of this function for h up

to 0.6 metres is given by

s _{{h/0.6+h(0.6-h) (ah2+b hc)]1"4 (14)}

for he0, 0.6, with a

= 11.7; b = -16.9; c = 8.40. For h greater than 0.6 m, s = 1.

Specific applications ought to consider actual

distribu-tions. characterising the area of operation, as described in paper 6.

5. _{CONCLUDING REMARKS}

Based on the research work described in the foregoing

the following concluding remarks can be made:

A numerical simulation model has been

developed, capable of predicting with good

engineering accuracy, the capsizal resistance of a damaged ship, of any type and

compartrnentation, in a seaway whilst accounting for progressive ffooding.

A comprehensive _{calibration/validation}

programme has ailowed for sufficient confidence

to be built up, rendering the developed model a

valuable design "tool".

A systematic

parametric investigation has

produced valuable results, showing a clear way

forward in the development of survival criteria for

passenger/RoRo vessels within a probabilistic framework as well as offering sound knowledge

and design ideas for improving their damage

survivability.

Finally and, most importantly, a damage stability criterion

has been proposed deriving

from physical considerations, based on model

experiments and numerical simulations.

lt

uniquely represents ships of any form, s;ze and

subdivision arrangement, and can be readily

implemented n practice. This major achievement offers a real opportunity for rationalising damage stability assessment. There is, therefore, hofle

that this fully rationai criterion can be approved by 1MO in a short time scale.

PUCILL, K F and VELSCHOU, S:

_"RoRo

Passenger Ferries Safety Studies _{Model Tests}

for a Typical Ferry", Proc., RINA and DoT Int.

Symp. on the Safety of RoRo Passenger Ships,

RINA, London, April 1990, paper No. 7.

Dand, I. W: 'Experiments with a Flooded Model

of

_{a RoRo Passenger Ferry",}

_{Proc., 2nd}

Kummerman mt. Conf. on RoRo Safety

and

Vulnerability n The Way Ahead, RINA, London,

April 1991, paper No. 11.

[31 _{VELSCHOU. S and SCHINDLER. M: "RoRo}

Passenger Ferry Damage Stability Studies

- A

Continuation of Model Tests for a Typical Ferry", Proc.,

_{The RINA Symp. on RoRo Ship's}

Survivability - Phase 2. RINA, London, Nov. 1994, paper No. 5.

DAND, I W: 'Factors Affecting the Capsize of

Damaged RoRo Vessels in Waves", Proc., The

RINA Symp. on RoRo Ship's Survivability* Phase

2, RINA, London, 25 November 1994, paper No.

3.

VASSALOS, D: "Capsizal Resistance Prediction of a Damaged Ship in a Random Sea", Proc., The RINA Symp. on RoRo Ship's Survivability - Phase 2, RINA, London, Nov. 1994, paper No. 2; also in: Trans. RINA, Vol. 138, 1995.

[61

VASSALOS, D and TURAN, O:

_{"A Realistic}

Approach to Assessing the Damage Survivability

of Passenger Ships", Trans. SNAME, Vol. 102,

1994.

VASSALOS, D and TURAN. O: "Development of

Survival Criteria for RoRo Passenger Ships - A

Theoretical Approach", Final Report on the RoRo Damage Stability Programme. Phase II,

Department of Ship and Marine Technology,

University of Strathciyde, December 1992. VASSALOS, D, PAWLOWSKI, M and TURAN, O:

"A Theoretical

Investigation on the Capsizal

Resistance of Passenger/RoRo Vessels and

Proposal of Survival Criteria", Final Report, Task 5. The North West European R&D Project, March

1996.

INTERNATIONAL MARITIME ORGANISATION

(1MO): "Regulation on Subdivision and Stability o"

Passenger Ships (as an Equivalent to Part B of

Chacter II

of the 1974 SOLAS

_{Convention)",}

waters and in fog, typically associated with calm

weather. lt is understandable that

in such

6. _{ACKNOWLEDGEMENTS}

circumstances sea states are on the wnole lower

than at the

open

sea or

under normal operating The_{financial support of the UK Department of Transport}

conditions.

As the critical sea state H

is a

_{and of the Joint R&D Project is gratefully acknowledged.}

function of h,

_{the factor s can be directly}

We should also like to record our appreciation to ail our

expressed as a composite function of the

_{colleagues in the Marine Safety Agency and}

in the

measure of damage stability, h _{Project for their help, contribution and support in} more ways than one,

s = F [H (h)] (13)

[10]

1MO, London, 1974, 114 pp. This publication

contains IMO resolutions A.265

(VIII), A.266 (VIII), and explanatory notes.

61RO, H, and BROWNE, R P: "Damage Stability

Model Experiments", Trans. RINA, Vol.

116.

1974, pp. 69-91; also in:

The N.

Architect, October 1974, ibid.

MIDOLETON, E H, and NUMATA, E: "Tests of a

Damaged Stability Model in Waves", SNAME

Spring Meeting, April

1970, Washington DC,

paper No. 7.

i 2] PAWLOWSKI, M: "Bezpieczenstwo Niezatapiainosciowe Statkow (Safety of Ships n the Damaged Condition)", OSc thesis, Zeszyti

Naukowe "Sudownictwo Okretowe", No. 392142. Journal of Technical University of Gdansk, 1985.

SAFER-EURORO: "An Integrated Approach to

Safer European RoRo Ferry Design",

BRITE-EURAM Clustered Research Programme proposai, April 1996.

HUTCHISON, B L: "Water On-Deck Accumulation

Studies by the SNAME Ad Hoc RoRo Safety

Panel", Workshop on Numerical and Physical

Simulation of Ship Capsize in Heavy Seas, Ross Priory, 24-25 July 1995, University of Strathclyde, Glasgow, UK.

=

> o 1 2 5 Intact GM (m) O o

Freeboard= 0.50 m

2 3

05

1.5 2 25 3 ntact GM (ni)

Figure 2: SHIW2

- SIDE CAS[NQSI-

Comparison between theoretical and

experimental results

IMARINTEK- CAPSIZE DMARINTE(-NOCAPSIZE ASTRATHCI.YDE -CAPS STRATh1CLY0E- NO CAPSIZE GOMI-NO CAPS OMI-CAPSIZE R o

I

_G R D Intct GM (ni)

Freeboard= 1.0 m

8 7 R IMARINTE<- CAPSIZE

6

_I

DMAIEK -NO CAPSIZE

E o _{ASATdCLYOE - CAPSIZE} O, o ASTRATHCI.YDE - NO CAPSIZE G 2 40Ml- CAPSZE 00Ml-NO CAPSIZE

Freeboard =1.5 m

O 8

I

_{IMAi1NTEX- CAPSZE} 7

u

D _{DMARIEX -NO CAPSIZE}

R

=4

ASTRAT1-CLYDE -CAPSIZE 2 STRATHCL'YDE - NO CAPSIZE O 4 5 6 5

C C o C C o 6000 5000 4000 3000 2000 1000 o -1000 4000 3000 2000 1000 O -1000

Sea State : 3.Om

WATER ON VEHICLE DECK

TIME (nec)

WATER ON VEHICLE DECK

TIME (nec) KG: 12.5m 5000-4000 3000 o 2000 -1000 0

Freeboard : 1.5m Sea State : 2.75m

WATER ON VEHICLE DECK

TIME (nec)

WATER ON VEHICLE DECK

TIME (eec)

KG: 13.Om

Figure 3:

Evaluation of critical amount of water on deck at "the point of no-relulIl''

(SI lIP 2, Open Deck, I)eck Area = 3,000

m2) Freeboard : 1.5m

i )l($)p

$4 -_100 150

200_250

3_

g 10Q 200

3qQ.4pQ

.600 10000 6000

WATER ON VEHICLE DECK

6000

WATER ON VEHICLE DECK

C C 6000 o 4000 o 6000 C C 4000 2000 O -2000 2000 TIME (nec) 100 2 0 400 TIME (nec) Sea State : 4.5m KG : 9.Om

Freeboard : 1.5m Sea State : 4.25m

KG 9,5m

Freeboard : t5m

Sea Stato : 4.75m

KG: 105m

Freeboard 1.5m Sea Stato : 3.5m

KG : 11.5m Freeboard : 1.5m C 2500 2000 1500 1000 500 o -500

co;

2 6cC 0

2cm

iaco

1J

14cc 12cc

ic

sco

4m

20C o 8.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 -9.0 10.0

Freeboard 1.5m

KG (m)

Freeboard 1.Om

11.0

K(rn)

Freeboard O.5m

140 Dynamic Static

Fiure 5:

Critical amount of water on deck for SHIP 2 with operi deck - comparison

between numerical simulation and static equivalent method

12.0 13.0 14.0

Dynamic

Static

Dynamic

0.12 0.10 0.08 0.06 0.04 0.02 0.00 h/Hsr 0.14

Figure 6: Boundary survivability curve for SBIP2 (total 85 cases)

F = 1.5 m, midship and forv.'ard damage, scales: 1 and 1.5

F = 1.0 m, midship and forward damage, scales: 1, 1.5 and 2/3

F = 0.5 m, midship damage, scales: 1, 1.5 and 2/3

Figure 7: Boundary survivability

_{curve for SI-11F i (all 36 cases)}

13 VHs r

o F= 1.5m

F 1.0 m

F=0.5

m

D D

OiOo1

D D D o

o

g

_o,Ç!

D o Q O 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.00 0.10 0.20 0.30 0.40 0i4 0.12 0.10 0.08 0.06 0.04 0.02 0.00 F = 1.06

m

F = 0.56 m F= 0,22 m VHs r

1.2

-1.0 0.8 f

0.6

0.4

-02

0.0 1.0 0.8 0.6 0.4 0.2 0.0 h O 2 4 6 ₈ 10 C

o F1.5m

F=1.Om

F0.5m

-Trend

xD

MARNTEK 12 0 2 4 6 8 10 12

Figure 8: Boundary survivability curve for SHIP 2 (total 90 + 11 cases)

Minimum mailtude of water elevation h versus modifed wave height H57.

F = 1.5 m, midship and forward damage, scales: 1, 1.5 and 2/3

F = 1.0 m, midship and forward damage, scales: 1, 1.5 and 2/3

F = 0.5 m, midship damage, scales: 1, 1.5 and 2/3

h

o F=1.06m

F=0.56m

F0.22m

-Trend

Hsr

Fi2ure 9: Boundary survivability curve for SHIP 1 (all 36 cases)

H57-1.0 0.9 0.8 o C, C o 0.5 u,

ö0.4

0.3

1.0

0.9 0.8 0.7 0.6 0.5 0.4 0,3 O L

"0.6

I C I j 0.1 0.2 0.3

Sgnñcnt wave height H, metres

1EJetion of water h, meters

0.4 0.5 0.6

Fin-ure 11: The probability of collision survivaJ

_{- the survival factor s as a fiinction of}

water on deck elevation h

15

0.0 1.0 2.0 3.0 4.0

Fiaure 10: Distribution of seastates occurring at the

moment of collision according to