Characterisation of the flooding process of a damaged Ro-Ro vessel

CHARACTERISATION OF THE FLOODING PROCESS OF A DAMAGED

g

_{RO-RO VESSEL}

0e

0G

by

. 4 Prof. D. Vassalos& Dr. L. Letizia

The Ship Stability Research Centre, Department of Ship and Marine Technology,

t.3oa

'1

. University of Strathciyde, Glasgow, UK

a

_SUMMARY

Recent research at the University of Strathclyde culminated in the development of a numerical procedure for assessing the damage survivability of damaged Ro-Ro vessels and, using this as a basis, new survival criteria have been proposed and submitted to

TIMO for consideration by the international shipping community. This paper presents

the results of a fundamental study aimed at enhancing the insight into one of the most dominant parameters affecting the survival of a Ro-Ro vessel, the water accumulation on the vehicle deck. The investigation represents an attempt to identi the most important contributing factors to the flooding process by performing a series of

experiments using a scaled model of a typical Ro-Ro vessel. The matrix considered

involves a range of ship design and environmental parameters in a number of simplified

damage scenarios, building up to the more realistic damages in a way that allows for isolation of individual contributions to the water accumulation on the Ro-Ro deck.

The results of the experiments, supplemented by and contrasted with results of

numerical simulations, are presented and discussed, leading to recommendations for

characterising the flooding process for general assessment of damage survivability.

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 with potentially serious consequences concerning the loss of

life and property whilst endangering the environment. The tragic accidents of the

Herald of Free Enterprise and more recently of Estonia were the strongest indicators yet of the magnitude of the problem at hand. particularly when water enters the deck of ships with large undivided spaces, such as Ro-Ro vessels. The ship loss could be

catastrophic as a result of rapid capsize, rendering evacuation of passengers and crew impractical, with disastrous (unacceptable) consequences. Concerted action to address the water-on-deck problem in the wake of these led to the proposal of new stability requirements, known as the Stockholm Regional Agreement, or more commonly as SOLAS '9050, pertaining to compliance of existing Ro-Ro vessels with SOLAS '90 requirements whilst accounting for the presence of a maximum 0.5 m height of water on the vehicle deck. In view of the uncertainties in the current state of knowledge concerning the ability of a vessel to survive damage in a given sea state, an alternative route has been allowed which provides a non-prescriptive way of ensuring compliance and one hopes enhanced survivability, namely the "Equivalence" route, by performing model experiments in accordance with the requirements of the SOLAS regulation II-1/8. In response to these developments, the shipping industry, slowly but steadily,

appears to be favouring the model experiments route, implicitly demonstrating mistrust

towards deterministic regulations which, admittedly, lack solid _{foundations. An}

attractive alternative route to tackling the water-on-deck _{problem in a way that allows}

for a systematic identification of the most cost-effective and _{survivability-effective}

solutions has been introduced by the Ship Stability Research Centre _{(SSRC) at the}

University of Strathclyde, by making use of a mathematicallnumerical model,

developed and validated over the past nine years, describing the dynamic behaviour of a damaged ship in seaway whilst subjected to progressive flooding. This model was

made the basis during the Joint North West European Project

_{(INWEP) for}

formulating and proposing rational survival criteria _{to deal with water on deck as part}

of the probabilistic procedure for assessing damage stability, [1]. A relevant paper was

submitted to TIMO and is currently being considered by the working group on

harmonisation of probabilistic standards. In both the developed mathematical model and the ensuing criteria the process of water accumulation on the Ro-Ro deck as well as the actual amount of water are dominant features. In this respect, an acceptably

accurate model of water inress/egress

is a prerequisite to undertaking any

investigations on damage survivability.

Deriving from the above, this paper attempts to elucidate some of the basic

characteristics of the flooding process considering

a typical Ro-Ro vessel, by

presenting and discussing preliminary results

from an

extensive experimental

programme aimed at enhancing understanding and insight

of this

complex

phenomenon. Firstly, a brief introduction is of the state-of-the-art mathematical _model

presently undergoing validation at the SSRC. MATEIIEMATTCAL MODEL

To study effectively damage survivability one needs to put togethera non-linear

six-degrees-of-freedom seakeeping model. (that allows the vessel to drift

_{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 hydrodynamir

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 on-going efforts at SSRC. [2]. The use of such a "tool" in its complete form, however, for parametric

investigations and routine design applications is not within reach at present. The model that has been the focus of research developments by the Strathclyde team during

the recent past and is currently undergoing validation, allows for a vessel drifting with the centre of gravity updated instantaneously during progressive flooding. It is a

non-linear, coupled six-degrees-of-freedom model comprising the following:

{±w (t)]±[]} {

_}+{[(t)+]

Vo} {

}±f

{K(t

[

JMw (t)]

-{F }

{F } WOD

Convolution integral ,representing radiation damping

Various generalised force vectors comprising wave (ist and 2nd

order), wind and current excitation as well as restoration and

gravitational effects. All these are updated instantaneously as a function of the vessel attitude relative to the mean waterplane by

using a database which spans the whole practical range of interest concerning heel, trim, sinkage, heading and frequency. The same applies to the hydrodynamic reaction forces. Excitation from shifting

of cargo can also be considered.

This force vector is now comprised of dynamic effects of flood water in contrast to its counterpart in the previous model which involves

only gravitational effects.

The phase/amplitude difference between vessel roll and flood water motions will be determined by building a comprehensive database through a systematic series of model

experiments using a sway-heave-roll bench test apparatus. In case the dynamic behaviour of the flood water is considerable and could prove to be dominating or

heavily influencing the vessel behaviour, the dynamic system of vessel-flood water must be treated as two separate worlds interacting, using CFD techniques to describe

flood water sloshing, as indicated above.

MODELLHG IHt WATER DIGRESS

The correct modelling of the inflow/outflow of water through the damage opening is

naturally of primary importance for a reliable simulation of the progress of events

during the flooding process. Quantities like time to capsize depend in fact critically on

the evolution of this phenomenon. On the basis of the assumption that a simplified technique can be acceptably accurate if supported by experimental evidence, the

formulation attempted here does not diverge drastically from those employed by other

researchers. However, it attempts to offer credibility to the adopted, approach by

providing a solid theoretical and experimental background.

In this respect, the

experimental investigation focuses mainly on the fundamental nature of the flooding process and attempts to elucidate the main contributing factors to its evolution, It is

readily accepted that a characterisation of the flooding of damaged ship compartments in a random sea is a highly complicated problem, in need of strong assumptions, unless

employing complex CFD techniques. Within the frame of the dynamic model presented

here this route is clearly impractical, thus leading to the semi-empirical approach as the only viable alternative. In the approximate method adopted in the models described in

Generalised mass matrix.

Flood water moving independently of the vessel but with an

instantaneous free surface parallel to the mean waterpiane. Generalised added mass matrix (asymptotic values)

Rate of flood water matrix (acting as damping).

the foregoing, water iness is _{treated as an intermittent probabilistic event based on}

the calculation of the relative position between wave elevation and dama2e location. The mode of flow is affected larely by the hydrostatic _{pressure head and the area of}

the damage hole but this _{is influenced by dynamic}

effects, edge effect, shape of

opening, wave direction and profile,

water elevation on either side of the openina and dama e location. The methodology proposed here leads to specific equations for the

rate of flooding through the damage _{opening whilst offering flooding}

coefficients

expressly measured experimentally_{for use with the derived}

equations. Considering, for

example, damage below the bulkhead deck, _{a flooding scenario is depicted by the} simplified picture shown in Figure _{1, with the sea treated}

as a reservoir and the

pressure distribution in the hold assumed_{hydrostatic. If Bernoulli's equation}

is applied

at sections A and B, assuming that the total pressure head is maintained constant and the velocity is zero in the reservoir, the inflow velocity at point P can be calculated _as follows:

h011±

±O=h±

:

vt2g(h0h1)

dQ = _{K,j2g(h0 - hth)dA}

This expression reduces to the general_{form of those used for free-discharng}

orifices

and notches when either h _{or hrn is negative, if the following limits are set:}

I h =_{O if h} O

lhoutO if

h0O

Fiure 1: Water Inress Main _Parameters

This takes care of those situations in which water is present only on one side of the dama2e. Of course, when h is less than hrn. _{the flow becomes negative, and water is}

expected to flow out of the compartment and into the sea. To accommodate for this the pressure head equation is _{put into the form:}

Q(t) = KJ

_{sign(h0 _h).J2gh0 h}

Damage .dA (6)

Considering that h0

-

_{represents the instantaneous down flooding distance}

which is relatively easy to _{compute, the problem of progressive flooding reduces to the}

evaluation of the coefficient K which can be done _{experimentally, i.e., K can be}

assumed to be an empirical function of relevant parameters to suite a more realistic

case in which incident, di.ffl-acted and radiating waves _{as well as sloshing of the flood}

water are present. _{Preliminary experimental research, [2], demonstrated}

that the

present formulation describes sufficiently _{well the trend of the}

rate of flooding with time as results in Figure 2 show. Deriving from these results, it is worth noting _also

that the rate of flooding depends _{maihiy on the relative water elevation as deduced}

from the argument presented _{in the foregoing and}

not the wave height itself A second observation shows that the mean value of K appears to fall as soon as water is present on both sides of the damage opening. As a result of this, it would be to reasonable to adopt two coefficients intended for use according to the particular case encountered.

The mean value for the flooding _{coefficient when pure inflow}

occurs (water only

present external to the ship) is almost _{1 .4, whilst with water present on both sides it} reduces to 0.8 when the damage opening faces the oncoming _{waves. If the damage} opening is away from the oncoming waves, the correspondin values of the flooding

coefficient appear to be approximately the same and close to 1.0.

Foodn0 Rt ,n3/ec) _{v CIo.ed RooQnç Raie}

.0030

.0024

0012

- (Ir',k,M

-10 30 30 40 50

ooQ,ç _{Md v CItd FooOn5 Rt}

(1 O z 2.0 cm)

1.050 cm)

10 00 30 40 50

(',L-n4.M

T c)

dQ

_{K.sign(h0 - h).2gh0}

_{- h}

_{.dA, with the}

same limits as above (5)

The rate of flooding and hence the time history of the flood water can be found _by integrating dQ over the damage_{opening height, i.e.}

Flood,,0 Rate oonl , ed Flood, Rate

flnie l,ec

Msuri

Floodn9 Rate lni.eo) P4.aooed vn Calo.ted Floodng Rate,,

r,08 , ev3.O oo te0.8 50 ao3Q )

50 30 40 50 60 70 80

FloOdnç Rote lnimObooc Meoredvn C o.iated Flood,,9 Rate

.0030 24, .5018 .0012 I I

--.

0.0000 °. 10 20 30 40 59 60 70 80

floode; Rate Im3l,,.eci Mnan.rn0vnCated Floodng Rate

140.8 liZ ovl.0 ctn) 1140.6 liZ 040.0 otn)

.0024 .0018! .0012 00000 20 30 40 Time teevl

Time sect Tin,,, toed

50 80 70 80 90

Finure 2: Experimental Flooding Curves

EXPERIMENTAL PROGRAM.MIE Dama2e Scenarios and Test Conditions

To foster a better understanding of the water accumulation on Ro-Ro vehicle decks, a

series of experiments has been planned and is taking place at the University of

Strathclvde.

In this paper the results of the first series of tests are presented,

concerning mean asymptotic height of flood water on the vehicle deck h, as a function of wave and damage opening characteristics. The model used in these experiments is

described in [3] and is a 1:42 scale model of a typical Ro-Ro vessel, the main

particulars

of which are shown in

Table 1. The model accommodates two

compartments open to the sea: the first extending from the double bottom to the

bulkhead deck and from 526m to 659m from the aft perpendicular, giving a damaged freeboard of 1.OSm and the second, - on the vehicle deck - extending from 22.25m to

97.25m from the aft perpendicular.

.0030 .0024° .0018 I .0012 ¡T Ca1

¡L-''

90080

Table 1: Main Particulars of the Ro-Ro Vessel Used in the Experimental Investigation

The parameters investigated so far cover a range of regular and irregular waves as shown in Tables 2 and 3 and a number of damage scenarios as illustrated in Figure 3. These scenarios attempt to isolate the various contributions to the floodingprocess, as explained next:

Scenario 1, describes damage of the vehicle deck only

Scenario 2 _{describes damage both above and below the bulkhead deck but without}

penetration

Scenario 3 is the same as scenario 2 but with penetration, allowing water to flow

between the two compartments

All three scenarios were tested with a fixed and a heaving model to allow for an evaluation of the contribution of heave motion to the flooding process and of the

interaction between the two processes. The damage opening in these scenarios was modelled according to a 100% SOLAS, i.e., damage length at the waterline equal to

(O.O3L5 + 3.0) metres or 11 metres, whichever is less, using a trapezoidal opening

with sides at 150 to the vertical.

Scenarios 4 to 6, refer to different shapes of the damage opening, all satisfying SOLAS requirements, with scenario 6 in particular attempting to duplicate the side damage suffered by the European Gateway following collision with Speedlink Vanguard in 1982. Roll motion, freeboard and KG are the parameters currently being investigated

and the results will be published in the near future.

Table 2: Reu1ar Wave Parameters

WavelleightH(m)

2.0,3.0,4.0,5.0

Wave Period T(sec) 2.50, 1.25, 1.00, 0.83, 0.62

Table 3: Irregular Wave Parameters (JONS WAP Spectrum)

LBP (length between perpendiculars) =

1310m

B (breadth) = 26.Om

T (desin draught) = 610m

D (depth to uppermost continuous deck) = 18.8m

D (depth to bulkhead deck) = 78m

Ddb (depth to double bottom) = 16m

(displacement) = 12200 tonnes

Cb (block coefficient) = 0.582

Significant Wave Height H (ni) Zero Crossing Period T0 (sec)

2.0 4.42

3.0 _5.42

4.0 _6.25

Presentation of Results and Discussion

The results derived from testing in regular waves are shown in Figures 4 (heaving model) and 5 (fixed model). With reference to the asymptotic height of water on the

vehicle deck, the following observations can be made:

h is clearly a function of both T and H. The variation of h, _{however, becomes more}

pronounced with the heaving model. _{This latter phenomenon is}

a direct result of the

tuning/de-tuning between wave and heave motion. _{It would be reasonable, for} example, to expect a reduction in _{flooding when the model moves in phase with the} waves, whereas the reverse will be true when the model heaves in anti-phase _with the waves. In addition, heave motion affects directly the flooding process both in

terms of influencing the relative _{water elevation directly as well as causing water to}

be sucked into the damaged compartments as the model heaves downwards whilst giving rise to something of a "pumping" action, causing water to flood the vehicle deck through the triangular opening between the two _compartments

The shape of the damage opening has a clear influence _{on h.}

It is worth noting that the water ingress and _{egress are fundamentally different flows.}

Water eress has

_{more of a constant nature,}

depending mainly on h, whilst water

inress is intrinsically intermittent, especially for larger _{freeboards. As the flooding} process evolves a steady (or stationary) state may be reached when the _{integral of the} sum of inflow and outflow functions _{oscillates around}

zero, i.e. when, on the _average,

inflow and outflow neutralise _{each other. This leads to larger h values with increasing}

wave heights and decreasing wave periods, as a larger number of _{higher crests would} reach the deck level. It has been observed though, that steep

_{waves tend to di.act}

and break against the model side giving rise to highly distorted _{crests which carry}

considerably less water. _{This is the reason why there seems to be}

an optimal wave

frequency for flooding even in the case of the fixed model.

As a direct consequence of the observations noted _{above, two important}

conclusions

can be drawn. _{Firstly, the vessel motion}

influences considerably and directly the flooding process and conversely,

flooding affects both the vessel motion and her

attitude. _{It is essential, therefore, to take both phenomena into}

consideration when

studying the evolution of either. _{Secondly, since flooding and ship motion are two} compounded processes, testing in regular waves will be unsuitable as it can lead _to deceptive results. This second _{conclusion can be better appreciated by considering that} for long wave periods the vessel will be heaving in phase with the waves, hence the distance between sea water and vehicle deck will be nearly _{constant and flooding will} be impaired. Furthermore, a comparison of the average height of_{water accumulated} on deck between Figures 4, 5 (regular _{waves) and Finure 6 (irreular}

waves) clearly

reveals that h is generally smaller in the presence of irregular waves, _{even though} similarity in trends is evident. Finally, it may be observed _{that the amount ofwater}

accumulated in on deck in_{scenarios i and 2 is generally greater than the corresponding}

amount in scenario 3. _{This difference is attributed to the down flooding of} water

through the triangular

_{penetration notch, from the vehicle deck to the lower}

compartment.

NUMERICAL SIMTTLATION RESULTS

Considering the findings described _{in the foregoing, a number of numerical tests were}

also undertaken for comparison purposes and to further enhance the insight_{into some}

of the interesting observations in the experimental results, _{considering damage}

scenarios 1, 2 and 3, for

_{a free drifting vessel.}

Unlike the model used in the

experiments, the ship employed in the numerical analysis

_{is free to}

_{move and its}

behaviour is estimated in 3D in accordance with the _{model described above. The}

numerical model of a Ro-Ro vessel readily available _{was used for the purpose, the}

main particulars of which _{are given in Table 4. More details can be found in [4]. The}

damage scenario investigated considers a large _{compartment (comp. 1) and the car}

deck (comp. 2)

_{open to the sea through}

a SOLAS trapezoidal damage opening

amidships. The open deck extends longitudinally for _{75.Om from -41 .8m forward and} transversely from side to side. The lower compartment occupies the space between double bottom and bulkhead deck for a length of 27.7m, from -19.Om forward. This

Table 4: Main Particulars of the Ro-Ro Vessel

Used in Numerical Investination

In the numerical simulation, the damaged

compartments are considered to be empty initially for damage scenarios 2 and 3 whilst in the _{case of scenario I}

some 4,000.0

tonnes of water is allowed _{in intact compartment i}

in order to achieve the same

freeboard as in the other conditions. Once _{simulation begins, flooding of the damaged} compartments is triggered twenty seconds later. _{This artifice allows for}

dynamic and

numerical transients _{to die out before flooding starts, rendering}

it independent from_the

particular initial conditions _chosen.

All tests were performed with irregular _waves using a JONSWAP spectrum, with constant _{values of Eis and KG, which were set}

to

2.45 m and 9.86 m, respectively. These define

a point on the survivability boundary as

determined by the model experiments [4]. This choice _{was aimed at amplifying the}

possible effects of the various parameters investigated.

In accordance with_{the experimental results, numerical simulations}

were also successful

in demonstrating the importance of the triangular penetration _{notch between the two} compartments in reducing the chance of water accumulation on the _{vehicle deck. In} fact, in a fully dynamic case, flood water hardly

ever manages to build up when this opening is accounted _{for and down flooding to the lower}

compartment is allowed. Unlike the experiments, however, the numerical _{simulations reveal}

a new aspect

concerning the influence

of different damage openings on the behaviour_{of a damaged} vessel. _{It becomes evident from Figures 7}

(scenario 1) and 8 _{(scenario 2) that the}

major difference between_{the output of these two damage conditions is that in}

scenario

1, the amount of _{water trapped in compartment I makes the vessel}

inherently more

stable than when this _{space is open to the sea. This enhances the ability of}

the vessel to

sustain a considerably _{larger amount of}

water on deck than the

_{amount normally}

sufficient to lead _{to capsize. This observation is supported by the trends of the flood}

water realisation shown in Figure_{8, which indicate}

how flood water in _{compartment i}

tends to flow out

_{as the ship heels before}

capsizing. _{This, of course, is hardly}

surprising but it

certainly helps further understanding on how important the

interactions between vessel motion and water ingress and accumulation _are.

_{It is}

interesting to note, along the same lines, how_{well correlated the roll,}

heave and flood

water realisations _{are in Figure 7 as indeed the}

only tangible accumulation of water on

deck appearing in Figure 9 occurs in the presence of_{concurrent large heave and roll}

motions.

(length between perpendiculars) _{= 1261m}

B _(breadth)

= _227m

T _{(design drau2ht)}

= _5.625m

D _{(depth to uppermost continuous deck)}

= _126m

Phd

Ddb _{(depth to double bottom)}

= _1.2m (displacement) ₌ 8807 tonnes Cb (block coefficient) ₌ 0.53 KG _{(design KG)} = _1010m KM _{(intact KIM)} 1162m

CONCLUDING REMARKS

The evidence presented in this paper offers important clues concerning _specific contributions to the water accumulation

_{on the Ro-Ro vehicle deck and}

the

characterisation of the flooding _{process. It also demonstrates that there}

are good

reasons to solicit due consideration of the shape _{and configuration of the damage} openings in determining the amount of water accumulating on vehicle decks and

discourage apparently innocuous simplifications often adopted to tackle the problem assessing the damage survivability of this type of vessels [5]. _{Considering, however,} that modelling a damage opening in a way that reproduces reality exactly will not be possible and, in fact, not relevant, it will be particularly helpful for all concerned _to appreciate that all that is necessary to progress further in this field is the _{definition of a} generalised damage opening, based on acceptable statistical data. that is universally accepted and used in testing for damage survivability in both physical _{and numerical} model tests. _{Thankfully, such convergence is becoming evident with the}

use of the

opening described here_{as scenario 4.}

It also very important to emphasise that the study of damage _{survivability involves two} distinct but intrinsically interrelated and highly interacting processes, namely, ship motion and flooding. _{The non-stationarity in the vessel motion introduced by the} water accumulation coupled with the intermittence of the flooding process itself and the severe non-linearities in the_{ensuing dynamic systezm demand great care in dealing}

with the many issues of this complex problem.

REFERENCES

Vassalos, D., Pawlowski, M. and Turan, O.: "A Theoretical Investigation _{on the}

Capsi:al Resistance of

_{Passenger/Ro-Ro Vessels and Proposai of Survival} Criteria", Final Report, Task 5, The Joint North West European R&D Project, March 1996.

Letizia, L.: 'Damage Survivabili _{of Passenger Ships in a Seaway", Ph.D.}

Thesis, Department of Ship and Marine Technology, University of Strathclyde.

November 1996.

DM1 88116: 'RO-RO Passenger Ferry Safety Studies Model Test

_{for FlU}

-Final Report of Phase I",

_{DM11 Project Report}

_{to the UK Department of}

Transport, 1990.

Dand, I.W.: "Experiments with a Flooclable Model of a RO-RO Passenger

Ferry ", _{MT Project Report to the Department of Transport,}

IBMT Fluid

Mechanics Ltd, 1990.

The Glosten Associates, inc.: " _{Water Accumulationon the Deck of a Stati onarv} Ship "- SNAME Ad Hoc RO-RO _{Safety Panel, Annex A, FileNo. 94209.01}

- 8 February 1995.

c 2 4 ₅ 16.2 PWd 16.2

Fiure 4: Asymptotic Height of Water on the Vehicle in Regular Waves

(Heaving Model)

Damage Scenario i Damage Scenario 4

Damage Scenario 2 Damage Scenario 5

Figure 5: Asymptotic Height of Water on the Vehicle in Regular Waves

(Fixed Model)

Damage Scenario i _{Damage Scenario 4}

Damage Scenario 2 Damage Scenario 5

0.6 < O.4 1.2 0.2 02 o Hsm) Heaving Model Fixed Model o 1.5 2 2.5 3 3.5 4 4.5 5 5.5 + Damage Scenario i 0Damage Scenario 2 *Damage Scenario 3 + Damage Scenario i 4-- Damage Scenario 2 *--Damage Scenano 3

Ficure 6: Variation of the Asymptotic Height of Flood Water on the Vehicle Deck with Significant Wave Height and Damage Condition

1.5 2 2.5 3.5 4 4.5 5 5.5 Hs (m)

4.00 2.00 0.00 -2.0W -4.00 -6.00

5

= -8.00 o -10.00 -12.00 -14.00 4.50 4.00

'3.50

3.00 o s 2.50 2.00 ' 1.50 C., >1.00 0.50 o oo 0.00 Hs = 2.45 m; To = 6.0 sec KG = 9.86 m; Freeboard = 0.7 m Time (sec)

Ijlir

9 t

fIll

'lifIlI'IIILì

4500.00 -.4000.00 C,, 3500.00 3000.00 2500.00 C) 2000.00 1500.00 1000.00 u-0.00 200.00 400.00 600.00 800.00 1000.00 Time (sec)

Fiqure 7: Simulation Results - Damage Scenario 1.

.00

Comp. i

Comp. 2

200.00 400.00 600.00 800.00 1000.00

6.00 ..5.00 4.00 3.00 2.00 C., > ( 1.00 4500.00 4000.00 3500.00 3000.00 .2500.00 2000.00 1500.00 Hs = 2.45 m; To = 6.0 sec: KG 9.86 m; Freeboard = 0.7 m 5.00 0.00 -5.0.00 100.00 200.30 300.00 400.00 .,-10.00 '-15.00 -20.00 -25.00 -30.00 -35.00 -40.00 -45.00 Time (sec) hl!lllIi!?!JIl'!f _{rÌ1Ii1!th1;f1} 0.00 0.00 100.00 200.00 300.00 400.00 500.00 600.00 700.00 800.00 Time (sec) I II' 'IT?!!? Li& r 1000.00 500.00 0.00-

- -.

-500.O.00 200,00 400.00 600.00 800.00 Time (sec)

Fiaure 8: Simulation Results - Damage Scenario 2.

Comp. 1 Comp. 2

3.00 2.00 1.00 0.00 o 2 -2.00 -3.00 -4.00 -5.00 6.00 .E5.00 4.00 3.00 2.00 > ( 1.00 o 0.00 0.00 4500.00 4000.00 13500.00 3000.00 2500.00 2000.00 1500.00 1000.00 500.00 0.00 -500 .0.00 Hs = 2.45 m; To = 6.0 sec: KG = 9.36 m: Freeboard = 0.7ni 200.00 Time (sec) 400.00 600.00 Time (sec) 200.00 400.00 600.00 800.00 1000.00 Time (sec)

FiQur6 9: Simulation Results- Damage Scenario 3.

800.00 1000.00

Comp. i