Collision Analysis for MS DEXTRA Abstract 1 Introduction

P. T. Pedersen & S. Zhang, Technical University of Denmark: Collision Analysis for MS DEXTRA___________________________________________________________________________________

__________________________________________________________________________________Paper number (2) SAFER EURORO Spring meeting, NANTES 28 April 1999 1

Collision Analysis for MS DEXTRABy

Preben Terndrup Pedersen and Shengming ZhangDepartment of Naval Architecture and Offshore Engineering

Technical University of DenmarkBuild. 101E, DK-2800 Lyngby

AbstractIt is a major challenge to for the maritime community to develop probability-basedprocedures for design against collision and grounding events. To quantify the risksinvolved in ship traffic in specific geographic areas implies that probabilities as wellas inherent consequences of various collision and grounding events have to beanalysed and assessed.The present paper outlines such a rational procedure for evaluation of the probabilisticdistribution of damages caused by collisions against other ships for a specific ship ona specific route.The work described in the paper constitutes a step towards the more long term goal todevelop probability-based codes for design against collision and grounding events,similar to the present development towards the use of reliability-based procedures forstrength design of ships subjected to the traditional environmental loads.

1 Introduction

The present paper describes part of the research work performed in the project Designfor Structural Safety under Extreme Loads (DEXTREMEL). The project partners areGermanischer Lloyd (Project Coordinator), Technical University of Denmark,Maritime Research Institute Netherlands, National Technical University of Athens,SIREHNA, University of Newcastle upon Tyne, and Astilleros Españoles. The projectis supported by the Commission of European Countries as project BE97-4375.

DEXTREMEL addresses three extreme load scenarios, which must be investigatedprior to the evaluation of residual structural integrity of RoRo ferries in adverseconditions. These scenarios include structural damage due to 1) collision andgrounding loads, 2) bow door loads, and 3) green water loads.

The present paper deals with the work done during the first 16 months on theprobabilistic prediction of the frequency of collisions and the spatial probabilisticdistribution of collision damages.

This part of the research is divided in the following subtasks:1.0 Definition of relevant design cases1.1 Development of probabilistic models for collision event



1.2 Development of models for external ship collision dynamics1.3 Development of models for internal ship collision dynamics1.4 Establishment of damage probability distributions

So far the effort has been concentrated on Tasks 1.0 - 1.3.

During the subtask 1.0 the participants identified a relatively fast (26 knots) RoRoferry with a length between perpendiculars equal to 173 m, breadth of 26 m, and 6.5m draught, see Arias (1998). The project ship, named MS DEXTRA, will during theproject be analysed for two different routes; one of them is between Cadiz inmainland Spain and the Canary Islands.

Fig. 1.1. A schematic illustration of steps in collision analysis

The contents of the remaining four subtasks 1.1- 1.4 are illustrated graphically in Fig.1.1.

Subtask 1.1 is devoted to a methodology for calculation of the probability of ship-shipcollisions for a ship on a given route where the marine traffic is known. Steps in theprocedure for this analysis are indicated in the upper part of Fig.1.1.

For each individual collision scenario the subsequent analysis procedure is dividedinto two tasks:



• The external dynamics, and• The internal mechanics.

The external dynamics deal with the energy released for crushing of the involved shipstructures and the impact impulse of the collision by analyzing the rigid body motionsof the colliding ships taking into account the effect of the surrounding water.

The internal mechanics deals with the structural response and damage caused by theenergy released to be dissipated by crushing of the ship structures during the collision.

These two tasks can in most cases be treated independently.

A complete probabilistic collision analysis as the one indicated in Fig. 1.1 involvesanalysis of several thousands of collision scenarios. Therefore, for practical use inprobabilistic models it is necessary that each individual collision analysis can beperformed by relatively fast procedures and thus in most cases simple procedures. Ofcourse, since simplified structural analysis procedures rely on a number of simplifyingassumptions these must be validated by either experiments or detailed Finite ElementAnalysis procedures. The following paper by Samuelidis will describe such a detailedfinite element analysis performed for validation of the simplified methods to bedescribed in the present paper.

2. Collision probability analysis

In recent years there has been a rapid development of new navigational systems. Agrowing number of VTS systems are established around the world. Extensive trialshave been carried out with sole lookout during night on ship bridges. IMO hasintroduced requirements for new ships to fulfil particular manoeuvrability criteria[IMO Resolution A 751]. And a new generation of large fast ferries has emerged. It isgenerally agreed that all these activities have considerable influence on the probabilityof ship accidents in the form of collisions and grounding. But so far no rationalanalysis tools to quantify the effect of these changes have been available. Insteadnearly all research on ship accidents has been devoted to analysis of consequences ofgiven accident scenarios. It is with this background that the work in this project,Hansen and Pedersen (1998), on a rational model for determination of the probabilityfor ship accidents has been carried out.

The main principle behind the most commonly used risk models is to determine thenumber of possible ship accidents Na, i.e. the number of collisions if no aversivemanoeuvres are made. This number Na of possible accidents is then multiplied by acausation probability Pc in order to find the actual accident frequency. The causationprobability Pc is the fraction of the accident candidates that result in an accident.

For calculation of the number of possible ship collision candidates Na we shallconsider two crossing waterways where the ship traffic is known and has beengrouped into a number of different ship classes according to vessel type, dead weighttonnage or length, loaded or ballasted, with or without bulbous bow etc.



Fig. 2.1 shows such two crossing waterways. In Pedersen (1995) is presented acalculation model for the number Na of possible events where two ships will collide inthe overlapping area Ω if no aversive manoeuvres are made. The result from thisreference is that by summing all the class "j" ships of waterway 2 on collision coursewith all relevant class "i" ships during the time ∆t the following expression can beapplied:

Fig. 2.1. Crossing waterways with risk area of ship-ship collision.

t dA D V )z(f )z(f V V

Q Q = N ijijj

(2) ji

(1) i(2)

j(1)i

(2)j

(1)i

)zz(jia

ji

∆∫ ∫∑∑Ω

(2.1)

Here Qj(α) is the traffic flow (i.e. number of ships per unit time) of ship class j in

waterway no. α, Vj(α) is the associated speed. The lateral distribution of the ship traffic

of class j in waterway α is denoted fj(α),, Dij is the geometrical collision diameter

defined in Fig. 2.2, and finally the relative velocity is denoted Vij .



Fig. 2.2. Definition of geometrical collision diameter Dij.

The expected number of ship-ship collisions is then determined as

N P = N acship-ship (2.2)

Here the causation probability Pc can be estimated on the basis of available accidentdata collected at various locations and then transformed to the area of interest.Another approach is to analyse the cause leading to human inaction or externalfailures and set up a fault-tree procedure. In the present work we have applied a newprocedure based on a Bayesian Network procedure for calculation of Pc presented inHansen and Pedersen (1998).

The methodology for the developed procedure is based on the assumption that theship and crew characteristics and the navigational environment mainly determine thecollision probability. That is, technical failures such as engine failure and rudderfailure play a minor role.

The most important ship and crew characteristics are taken to be: ship speed, shipmanoeuvrability, the layout of the navigational bridge, the radar system, the numberand the training of navigators, the presence of a look out etc. The main parametersaffecting the navigational environment are ship traffic density, probabilitydistributions of wind speeds, visibility, rain and snow.

With knowledge of the ship characteristics and a study of the human failureprobability, i.e. a study of the navigator's role in resolving critical situations, a set ofcausation factors Pc has been derived.

By application of the Bayesian Network procedure for estimation of the causationprobability, it is possible through future research to examine the beneficial effect of



new bridge procedures, of improved manoeuvring capability, of having a pilot onboard, or of introducing a VTS system in certain geographical areas.

Based on the mathematical model for estimation of collision probabilities describedabove a computer program has been written for calculation of collision probabilitiesin specific waterways where the ship traffic distribution is known.

Fig 2.3 MS DEXTRA chosen as design case for DEXTREMEL

The basic idea behind the procedure is that one specific Ro-Ro passenger vessel (MSDEXTRA see Fig. 2.3) is making round trips on a specific route between Cadiz andthe Canary Islands.

On this route there is further a given distribution of other types of vessels such thatthree in principle different types of collisions can occur. One type of collision is ahead-on induced collision due to two-way traffic in the straight waterway segments.Another type of collision on the Ro-Ro waterway occurs at bends where two straightroute segments intersects. At such an intersection a ship can become a collisioncandidate if the course is not changed at the intersection. This probability of omissionP0 is taken as 0.01.

Finally, the model calculates the probability for collisions due to an arbitrary numberof crossing routes, as indicated in Fig. 2.1. These crossing routes are defined to haveone-way traffic only and have a specified distribution of the types of vessels. Thus, iftwo-way traffic exists in the crossing route, the route must be included twice, one foreach direction of the traffic. This strategy is adopted to allow for different trafficdistribution in the two directions.

For each waterway segment the number of collision candidates related to head-on,intersections, and crossing situations is calculated for each vessel type. Theprobabilities of collision is then estimated by multiplication with the causation factorsverified by the Bayesian Network procedure

P[head on] = 4.9⋅10-5

P[intersection] = 1.3⋅10-4

P[crossing] = 1.3⋅10-4



The overall ship traffic in the considered geographical area is divided into differentvessel types and into different size categories. For each of these vessel classes acertain fraction is assumed to be in ballast condition and the remaining vessels fullyloaded. Similarly, the fraction of vessels without bulbous bows has to be specified

The striking vessels are grouped in the following categories:• Bulk carriers• Chemical tankers• Container vessels• Gas tankers• Oil tankers• Other vessels• Passenger vessels• Ro-Ro vessels

Each of the categories contains a number of vessels. Each vessel is defined by thefollowing properties:• Length• Breadth• Depth

And, for both loaded and ballast conditions:• Speed• Draught• Displacement• Height of deck• Height of bulb

Finally the database has data for probability of the vessel:• Being in a loaded condition• Being in a ballast condition• Having a bulbous bow

Among the routes intended for the RoRo vessel MS DEXTRA is the traffic betweenCadiz in mainland Spain and Las Palmas and Tenerife on the Canary Islands. Themain traffic routes in this area are shown in Fig 2.4.



Figure 2.4: Ship Traffic between Cadiz and the Canary Islands.

The geographical position of the six geographical fix-points in Fig. 2.4 is found to be:

1. Cadiz 36o30' N ; 06o20' W2. Turning 28o28' N3. L Palmas 28o05'.N ; 15o27' W4. Tenerife 28o28' N ; 16o15' W5. Europe 36o07' N ; 05o21' W6. C Vinc. 37o00 N ; 09o.00' W

According to Spanish port statistics the total annual traffic to the harbours in Tenerifeand in Las Palmas is 8647 and 8012 ships per year, respectively. The annual shiptraffic out of and into the Gibraltar Straight was according to "COAST 301" in 1987in total 51138 ship passages. Recently, i.e. 10. Dec. 1998 the total traffic for 1997became available. Now the traffic has increased to 65597 ships. But since thecomposition of the ship traffic in 1997 is not available we have in Hansen andPedersen (1998) applied the COST data.

The result of the numerical calculations is a complete distribution of collisionscenarios as indicated in the upper part of Fig 1.1. The integrated result is that theannual probability of collision involving MS DEXTRA is .042. That is, a collision isexpected to take place with a return period of 24 years.



3. External Dynamics

3.1 IntroductionKnowing the probabilistic distribution of collision scenarios the next step is todetermine the consequences of these collisions. Here the first step is to determine thefraction of the available kinetic energy that is released for crushing of the involvedship structures.

For this, an analytical method for the energy loss and the impact impulse has beendeveloped for arbitrary ship-ship collisions, see Pedersen and Zhang (1999). At thestart of the calculation, the ships are supposed to have surge motion and sway motion,and the subsequent sliding and rebounding in the plane of the water surface during thecollision are analyzed. The energy loss for dissipation by structural deformations ofthe involved structures is expressed in closed-form expressions. The procedure isbased on rigid body mechanics, where it is assumed that there is negligible strainenergy for deformation outside the contact region and that the contact region is localand small. This implies that the collision can be considered as instantaneous and eachbody is assumed to exert an impulsive force on the other at the point of contact. Themodel includes friction between the impacting surfaces so those situations withglancing blows can be identified.

3.2 Theoretical Analysis ModelTo illustrate the assumptions behind the method we shall consider a striking ship (A),which sails at a forward speed of Vax and a speed of Vay in the sway direction andcollides with a struck ship (B), sailing at a forward speed of Vb1 and a sway speed ofVb2 . An XYZ-coordinate system is fixed to the sea bottom. The Z-axis points in adirection out of the water surface, the X-axis lies in the symmetry plane of the strikingship pointing towards the bow, and the origin of the XYZ-system is placed so that themidship section is in the YZ-plane at the moment 0=t . The origin of a ξ η -systemis located at the impact point C, the ξ - direction is normal to the impact surface, theangle between the X-axis and the η -axis is α , and the angle between the X-axis andthe 1-axis is β , see Fig. 3.1.



Fig. 3.1. The coordinate system used for analysis of ship-ship collisions.

The equations of motion of the striking ship (A) due to the impact force componentsξF in the ξ - direction and ηF in the η - direction can be expressed as

M m v F Fa ax ax( ) sin cos1 + = − −•

ξ ηα α (3.1)

M m v F Fa ay ay( ) cos sin1 + = − +•

ξ ηα α (3.2)

M R j F y x x

F y x x

a a a a c c a

c c a

2 1( ) [ sin ( ) cos ]

[ cos ( ) sin ]

+ = − −

+ + −

•ω α α

α α

ξ

η

(3.3)

Here Ma is the mass of the striking ship, ( , , )v vax ay a

• • •ω denote the accelerations

during the collisions of the striking ship in the X- and Y-directions and the rotationaround the center of gravity, respectively. The radius of the ship mass inertia aroundthe center of gravity is aR , the coordinate of the center of gravity of the striking shipis ( , )xa 0 , the coordinate of the impact point is ( , )x yc c , the added mass coefficientfor the surge motion is axm , the added mass coefficient for the sway motion is aymand the added mass coefficient of moment for the rotation around the center of thegravity is aj .

Similarly the motions of the struck ship can be expressed as

M m v F Fb b b( ) sin( ) cos( )1 1 1+ = − − + −•

ξ ηβ α β α (3.4)

M m v F Fb b b( ) cos( ) sin( )1 2 2+ = − + −•

ξ ηβ α β α (3.5)

M R j F y y x x

F y y x x

b b b b c b c b

c b c b

2 1( ) [( ) sin ( ) cos ]

[( ) cos ( ) sin ]

+ = − − − −

− − + −

•ω α α

α α

ξ

η

(3.6)



The added mass coefficients m m jax ay a, , and m m jb b b1 2, , , taking into account the

interaction effects between the ships and the surrounding water, depend on the hullform of the ships and the impact duration etc. For simplicity, Minorsky (1959)proposed to use a constant value of the added mass coefficients of ships for the swaymotion:

may = 0 4.

Motora et al. (1978) conducted a series of model tests and a hydrodynamic analysison the added mass coefficient for the sway motion. They found that the added masscoefficient varies during the collision, the value is in the range of 3.1~4.0=aym . Thelonger the duration, the larger the value of the coefficient. However, if the collisionduration is very short, the value of may = 0 4. assumed by Minorsky may be correct. InPetersen and Pedersen (1981), it is shown that the added mass coefficient for the swaymotion can be estimated from

)]()0([)( ∞−+∞= mmkmmay

where )(∞m and )0(m are the threshold values of the added mass coefficient for thesway motion when the frequency of the collision approaches infinity or zero,respectively. The value of the factor k is a function of the duration of the collisionand the ship draught.

The added mass coefficient max related to the forward motion is small compared withthe mass of the ship. It is found to be

07.002.0 tomax =

The added mass coefficient for the yaw motion of the ship, aj , is (Pedersen et al.,1993):

21.0=aj

For simplicity, in the examples of the present calculations, the added masscoefficients are taken to be

05.01 == bax mm (for the surge motion)85.02 == bay mm (for the sway motion)

21.0== ba jj (for the yaw motion)

In the examples of the present calculations, the radius of inertia is taken to be aquarter of the ship length: 4/aa LR = and 4/bb LR = .



By a transformation of the Eqs. (3.1) - (3.6) to the moving ξ - η coordinate systemfollowed by an integration of the relative equations of motion with respect to time, theimpact impulse in the ξ - direction and in the η - direction can be obtained as

ξηηξ

ηηξξ

ηξKDKD

DeKdtFI

T

⋅−⋅−+

==••

∫)0()1)(0(

00

ξηηξ

ξξηη

ξηKDKD

eKDdtFI

T

⋅−⋅+−

==••

∫)1)(0()0(

00

Here the coefficients Dξ , K ξ , Dη , Kη are algebraic expressions involving the massesof the vessels, e is the coefficient of restitution, the added masses and geometricalparameters describing the location of the impact point, see Pedersen and Zhang(1999).

The ratio of the impact impulses, expressed as

)0()1)(0(

)1)(0()0(

0

0••

••

−+

+−==

ηξ

ξηµ

ηη

ξξ

ξ

η

DeK

eKDII

(3.7)

determines whether the ships will slide against each other or the collision point will befixed.

In the case where the ships sticks to each other at the collision point the energyreleased in the ξ - direction ξE can be expressed as

2

0

)0(1

21max •

⋅+== ∫ ξ

µξ

ηξ

ξ

ξξ

DDdFE (3.8)

and the energy released in the η - direction ηE can be expressed as

2

0

)0(1

121max •

+⋅== ∫ η

µ

ηηξ

η

ηη

KKdFE (3.9)

where maxξ and maxη are the penetrations in the ξ - direction and in the η - direction atthe end of the collision. The total released energy is the sum of the energy released inthe ξ - direction and in the η - direction: E E Etotal = +ξ η .

Similar equations have been derived for the case where the ships slide against eachother.



3.3 Verification of Simplified External Dynamics Model

For verification of the procedure let us first consider an example from Brach (1993)using a slender rod (free in air) impacting a surface. The problem is illustrated in Fig.3.2. The physical parameters are presented in Table 3.1. A comparison of the presentresults with Brach's results is given in Table 3.2. In the example, the initial velocity of

the rod in the normal direction of the surface is 0.1)0( =•ξ m/s. The initial rotational

velocity of the rod is zero and the initial velocities in the direction parallel to the

surface are 0.0)0( =•η m/s, -0.2 m/s, -0.6m/s, and 1.0 m/s, respectively. The

coefficients of restitution are 5.0=e and 05.0 , respectively.

The comparison shows that the present results and Brach’s results agree quite well.

Rod

α L ξ C

η

Fig. 3.2. Diagram of a slender rod striking a massive plane at the point C.

Table 3.1. Physical parameters of the slender rod. Mass M=1.0 kg Length (m) L=1.0 m Moment of inertia 2

121 MLI =

Impact angle α o 45 deg.

Initial velocities (m/s) ξ ω

η

•

•

= =

= − −

( ) . , ( ) ;

( ) . , . , , .

0 10 0 0

0 0 2 0 6 0 10



Table 3.2 Comparison of the present results with Brach’s results.

Normal impulse

I Nmξ ( )%100⋅

energyInitiallossEnergyInitial

velocity η

•( )0

Coefficientofrestitution

eT

= −•

•ξ

ξ

( )

( )0

Impulseratio

µPresent Brach Present Brach

0.0 5.0=e 0.600# 0.938 0.938 46.9 46.9 05.0=e 0.600# 0.656 0.656 62.3 62.3

-0.2 5.0=e 0.507# 0.862 0.862 33.1 33.3 05.0=e 0.462# 0.581 0.580 47.9 47.9

-0.6 5.0=e 0.263# 0.712 0.732 17.9 17.9 05.0=e 0.043# 0.431 0.569 29.3 29.3

1.0 5.0=e 0.905# 1.313 1.395 92.2 92.1 05.0=e 0.988# 1.031 1.031 99.9 99.6

# Critical value which just causes the glancing to stop.

The second verification example is taken from Petersen (1982) and Hanhirova (1995).The results presented by Petersen were calculated by time simulations and the resultsobtained by Hanhirova were calculated by an analytical method. The case was acollision between two similar ships. The main dimensions of the ships are given inTable 3.3.

Firstly, we use the same assumption as used by Petersen. That is an entirely plasticcollision where the two ships are locked together after the collision. The presentcalculation results and the existing results are presented in Table 3.4 where d is theimpact location measured from the centre of the struck ship. From Table 3.4 it is seenthat good agreement is achieved except in case No. 4. We cannot explain thedifference in case No. 4, except that the high value given by Petersen for this casedoes not seem reasonable.

Table 3.3. Main dimensions of the ships used for validation.Length 116.0mBreadth 19.0mDraught 6.9mDisplacement 10 340tRadius of the ship inertia 29.0m



Table 3.4. Comparison of results for the energy loss in collisions.

Parameters V m s([ ] / )= E MJξ ( ) E MJη ( )

Case Va Vb α β= d Present Petersen Hanhirova (1982) (1995)

Present Petersen Hanhirova (1982) (1995)

1 4.5 0 90 0 70.1 69.6 54.4 0.0 0.0 0.02 4.5 4.5 90 0 70.1 64.1 54.4 21.4 24.7 41.53 4.5 4.5 60 0 35.3 29.8 28.3 0.2 5.2 15.84 4.5 4.5 30 0 7.4 71.9 4.0 0.0 49.3 7.25 4.5 4.5 120 0 64.9 60.5 41.7 90.4 93.1 115.06 4.5 4.5 120 L/3 42.9 49.2 74.1 85.4 90.7 102.07 4.5 4.5 120 L/6 60.0 64.9 60.6 92.3 91.6 110.08 4.5 4.5 120 -L/3 30.8 26.3 74.1 68.0 86.7 102.013 4.5 0 120 0 50.1 54.0 40.9 15.0 9.8 14.014 4.5 2.25 120 0 57.5 60.3 42.8 45.1 40.7 51.515 4.5 9.5 120 0 81.4 50.7 28.6 245.3 258.0 347.0

Secondly, we consider the ships sliding against each other. The coefficient of frictionbetween the two ships is assumed to be µ0 0 6= . , and the calculation results arepresented in Table 3.5. The results show that when the ships slide against each other,the energy to be dissipated by the crushing structures is decreased in comparison withthe case where the ships are locked together.

Table 3.5. Comparison of results obtained by the present method for the energy lossin cases of ships being locked together or sliding against each other.

Parameters V m s([ ] / )= E MJξ ( ) E MJη ( ) η•( )( / )T m s

Case Va Vb α β= d Plastic µ0 0 6= . Plastic µ0 0 6= . Plastic µ0 0 6= .1 4.5 0 90 0 70.1 70.1 0.0 0.0 0.0 0.002 4.5 4.5 90 0 70.1 70.1 21.4 21.4 0.0 0.003 4.5 4.5 60 0 35.3 35.3 0.2 0.2 0.0 0.004 4.5 4.5 30 0 7.4 7.4 0.0 0.0 0.0 0.005 4.5 4.5 120 0 64.9 53.6 90.4 84.1 0.0 -3.446 4.5 4.5 120 L/3 42.9 28.9 85.4 54.4 0.0 -5.487 4.5 4.5 120 L/6 60.0 45.6 92.3 77.8 0.0 -4.348 4.5 4.5 120 -L/3 30.8 24.9 68.0 44.2 0.0 -4.7613 4.5 0 120 0 50.1 50.1 15.0 15.0 0.0 0.0014 4.5 2.25 120 0 57.5 53.6 45.1 43.9 0.0 -1.1915 4.5 9.5 120 0 81.4 53.6 245.3 166.6 0.0 -8.44

3.3 External Dynamics Examples involving MS DEXTRAAs a first example it is assumed that an 86 m long high-speed craft strikes MSDEXTRA at different collision angles and locations. The main dimensions of the twovessels are presented in Table 3.6. Before the collisions, the speed of the striking craftis 32 knots (full service speed) and MS DEXTRA is also sailing at its full speed of 27knots.



Table 3.6. Main dimensions of the striking craft and MS DEXTRACraft MS DEXTRA

Lpp (m) 86.5 173Breadth (m) 17.4 26.0Depth (m) * 15.7Draught (m) 3.6 6.5Displacement (ton) 500 16,073

The calculated results for the total kinetic energy loss are shown in Fig. 3.3. It is seenfrom the results that the effect of the collision angle on the energy loss is significant,but the collision location has very weak influence on the energy loss. The reason isthat the mass of MS DEXTRA is very large compared with the mass of the strikingcraft. During the collision, the induced sway motions of MS DEXTRA are very small.

Fig.3.3. Energy loss of an 86 m craft striking with MS DEXTRA vessel at differentcollision angles and locations.

As a second example involving MS DEXTRA we shall consider a 180 m RoRo ferrystriking MS DEXTRA at different collision angles and collision positions. Thebreadth of the RoRo ferry is 31.5 m, the depth is 9.3 m, the draught is 7.3 m, and thedisplacement is 27,000 tons. It is assumed that the 180 m RoRo ferry strikes MSDEXTRA with a speed of 10 knots, while MS DEXTRA is sailing at a speed of 10knots.

The energy loss in these collisions is shown in Fig. 3.4. The results show that both thecollision angles and collision locations have significant influence on the energy loss.It is also noted that the energy loss is large if the collision is in fore part of the struckMS DEXTRA.

86m craft (32kn) strikes with MS Dextra (27kn)

0

50

100

150

200

250

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

Collision locations (d/L)

Ene

rgy

loss

(MJ)

30 deg.60 deg.90 deg.120 deg.150 deg.



Fig.3.4. Energy loss of an 180 m RoRo ferry striking with MS DEXTRA at differentcollision angles and locations.

4 Simplified methods for analysis of the internal dynamics

4.1 IntroductionKnowing the energy released for crushing in a specific collision scenario the next stepin the present rational collision analysis procedure is to determine the resultingstructural damage.

During this first phase of DEXTREMEL simplified methods for calculating thecollision force and the resulting hole in the ship structures has been established. At thesame time a comprehensive finite element model has been established to verify thesimplified method, see the following paper by Samuelidis.

The side structure of ships is very complex. The deformed, destroyed and crushedmodes of side structures are also very complex. However, a ship may be viewed as anassembly of plated structures such as shell plating, transverse frames, horizontal decksand bulkheads are built in various plates. Observations from full-scale ship accidentsand model experiments reveal that the primary energy absorbing mechanisms of theside structure are

• Membrane deformation of shell plating and attached stiffeners• Folding and crushing of transverse frames and longitudinal stringers• Folding, cutting and crushing of horizontal decks• Cutting or crushing of ship bottoms• Crushing of bulkheads

180m RoRo vessel (10kn) strikes with MS Dextra (10kn)

0

50

100

150

200

250

300

350

400

450

500

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

Collision locations (d/L)

Ene

rgy

loss

(MJ)

30 deg.

60 deg.

90 deg.120 deg.

150 deg.



By analysing damage of each basic structures and adding their contributions together,the total collision resistance and dissipated energy can be determined, Zhang (1999).

The simplified method (or the limit analysis) is widely used in engineering analysisand design. It has been proved that the method is valuable for estimating the collapseload of a structure subject to extreme loads. The collapse load so obtained can be usedas a realistic basis for design. However, it should be emphasised that the limit analysisis an approximate method. A basic assumption is that the material is perfectly plasticwithout strain hardening or softening.

Most of the simplified methods are based on the upper bound plasticity theorem:If the work rate of a system of applied loads during any kinematically admissiblecollapse of the structure is equated to the corresponding internal energy dissipationrate, then the system of loads will cause collapse or be at the point of collapse.

The upper-bound method was used by Wierzbicki and Abramowicz (1983) for axialcrushing of plate intersections and plate cutting, by Abramowicz (1994) and Amdahl(1983) for axial crushing of −L , −T and −X type elements, by Kierkegaard (1993)for ship bow crushing, by Paik and Pedersen (1995a) for plate element crushing, andby Simonsen (1997) for ship grounding. In the MIT - Industry Joint Program onTanker Safety the method was applied thoroughly to analysis of the damage of shipgrounding. It was shown that the theoretical results are quite close to experimentalresults.

4.2 Formulation of the Upper-bound MethodThe equilibrium for the external energy rate and the internal energy dissipation ratecan be expressed as

int

••=⋅ EF δ (4.1)

where F is the external force, •δ is the velocity at the force action point, int

•E is the

internal energy rate.

For a general solid body, the internal energy rate int

•E can be expressed as

∫••

=V

ijij dVE εσint (4.2)

where ij

•ε is the rate of the strain tensor, V is the volume of the solid body. By use of

von Mises' flow theory, the rate of plastic energy dissipation is given as

∫••

=V

e dVE εσ0int (4.3)



where )(32

ijije

•••= εεε and 0σ is the flow stress.

For a plane stress condition, the von Mises yield condition gives

20

222 3 σσσσσσ =+−+ xyxxxxyyxx (4.4)

For a deforming plate, the rate of internal plastic energy dissipation can be written asthe sum of the bending and the membrane energy dissipation rate:

•••+= mb EEE int (4.5)

The bending energy rate can be expressed as

∑∫=

•••+=

n

iiii

A

b lMdAkME1

0 θαβαβ , ( 2,1, =βα ) (4.6)

where A is the plate area, αβk is the curvature of the plating, and iθ and il are the

rotation and the length of the ith plastic hinge line, respectively. αβM is the bending

moment tensor, 0M is the fully plastic bending moment )4/)(3/2( 200 tM σ= , and t

is the plate thickness. It is seen from the expression that the bending energy containsthe continuous deformation field and the plastic hinge lines. In some practicalapplications, simplified velocity fields are assumed so that only the plastic hinge linesare considered and the continuous deformation of the curvature is neglected. In thiscase the bending energy is simplified as

∑=

••=

n

iiiib lME

10 θ (4.7)

The membrane energy rate of a deforming plate can be calculated from

∫••

=A

m dANE αβαβ ε , ( 2,1, =βα ) (4.8)

where αβN is the membrane force tensor, αβε•

is the strain rate tensor. By use of vonMises' yield criterion, the membrane energy rate can be expressed as

∫••••••

+++=A

xyyyxxyyxxm dxdytE 2220

32 εεεεεσ (4.9)

In the limit analysis method, a key point is the construction of a kinematicallyadmissible velocity and displacement field. This is mainly based on observations fromexperimental tests, full-scale accidents and existing analysis work.



4.3 Rupture of Ship Structural ElementsWhen a structure has been deformed to its limit, it will rupture and be exposed tofailure. It is an extremely complex problem to predict the rupture of structuresaccurately. Different loads may cause different failure modes. Jones (1989) discussedthe rupture criteria of ductile metal beams subjected to large dynamic loads. Threemajor failure criteria of the metal beams were discussed. The first is the tensiletearing failure mode, which occurs when the maximum strain equals the criticalrupture strain of the material, and the beam ruptures. Thus

cεε =max

The second failure model is the transverse shear failure mode, which develops in abeam when large transverse shear deformations occur within a very short region ofthe plastic beam. When the total transverse shear displacement sW in a particularlocation equals a critical value, the beam ruptures.

The third failure criterion is the energy density failure mode. It is assumed thatrupture occurs in a rigid-plastic structure when the absorption of plastic work per unitvolume reaches the critical value cΘ :

cΘ=Θ

As Simonsen (1997) mentioned, the simplified methods are based on overalldeformation mechanisms. It is not possible to trace the strain history of materialelements at a very detailed level. Therefore, as many authors did, e.g. Wang (1995)and Paik and Pedersen (1995b), we use the maximum strain failure criteria. That iswhen the maximum strain in a structure reaches a critical strain, the structure ruptures.

In practical calculations, we need to know the critical strain of a material to predictthe structural failure. Generally, this depends on axial tensile experiments.

Experiments conducted by Wen and Jones (1993) and Amdahl (1992) showed that thetensile ductility of mild steel is in the range of 20.0 to 35.0 . Amdahl (1995) pointedout that due to scale effects and material imperfections, this value is far too large inthe assessment of full-scale collisions. The critical strain value suggested by Amdahl(1995) for side collisions is between %5 to %10 .

In the minor collision analyses performed by McDermott et al. (1974), the criticalrupture strain for mild steel material in side collisions is evaluated from

)32.0

(10.0 fc

εε ⋅= (4.10)

where fε is the tensile ductility. It has been indicated by McDermott et al. that thisformula may give reasonable agreement with experimental results in the deformationof shell plating. So in this work, we either uses McDermott's formula, if the tensileductility of the material is known, or assume a value (say %10~%5=cε for mildsteel) for the critical rupture strain in side collisions.



When the critical rupture strain is known, the critical deflection or penetration of theshell plating can be determined. For example, a point load acting in the middle of aplate strip with a span of b2 , the strain in the plate strip due to transverse deflectioncan be calculated from

22 )(21

1)(1bbδδε ≈−+= (4.11)

where δ is the deflection at the middle point.

When the deflection is large enough, the strain in the plate strip reaches the criticalrupture value. The critical rupture deflection or penetration is then determined from

cc b εδ 2⋅= (4.12)

If the critical strain is %10=cε , then the critical penetration is bc 447.0=δ .

4.4 Crushing of Stiffened Decks and BottomsObservations from collision accidents show that the damage modes of ship decks arefolding, crushing and tension rupture. Some illustrations of damaged decks fromcollision accidents are shown in Fig. 4.1.

Fig. 4.1. Illustrations of deck damages observed in collision accidents.



Fig. 4.1 shows the analysis model of a bow crushing into the side of a struck ship. Thestiffened decks or bulkheads are divided into different elements (L-, T-, and X-elements), that are crushed by the striking bow. With further penetration, more andmore elements are crushed and destroyed. Typical axial crushing modes of L -, T -and X - elements are shown in Fig. 4.2.

Fig. 4.2. A striking bow crushes the deck structures and the side of a struck ship.

Fig. 4.3. Axial crushing modes of L-, T- and X- elements.

Many authors have investigated axial crushing of the basic elements, using theoreticalmethods and experimental methods. Amdahl (1983), Wierzbicki and Abramowicz(1983), Kierkegaard (1993), Abramowicz (1994), Paik and Pedersen (1995a) didcomprehensive work on the element axial crushing. Paik and Wierzbicki (1997)carried out a benchmark study on the crushing strength by comparing the existingtheoretical formulas and experimental results. Due to the simplicity of the expressionof we have in DEXTREMEL chosen to use Abramowicz's formula to calculate thedeck crushing resistance. The expression is

)263.3)(1.22.1( 33.067.10 ctnnnF XTL σ++= (4.13)



For the initial collision phase, it is reasonable to assume that the deck fails in thefolding deformation. The collision location is assumed to be in the middle betweentwo web frames. The collision situation is shown in Fig. 4.3.

Fig. 4.4. Initial deformation of the deck folding.

For the initial crushing of the deck the authors have derived the following theformulas for the mean crushing force:

>

≤=

Hbt

HbtF

d

d

2....................................77.6

2...................................33.4

33.067.10

33.067.10

δσ

δσ (4.14)

where

δ is the penetration, 31

2 )(8383.0 dtbH = , dt is the thickness of the deck plate and b2is the spacing between heavy transverse stiffeners.

When the striking bow touches the heavy stiffeners of the deck, as shown in Fig. 4.5,crushing of the deck structure (such as the basic elements L-, T- and X-) will happen.Then Abramowicz's formula Eq. (4.13) is employed for analyzing the crushing force.It is assumed that the basic elements are not deformed and crushed until the strikingbow pushes them directly. The deck plate between the touching point and the non-deformed stiffener suffers tension and bending deformation. Its behaviour is similar toweb folding. Therefore, the collision force for the further deck crushing can beexpressed as

33.4)263.3)(1.22.1( 33.067.10

33.067.10

1idiiXTL

N

i

btctnnnFdeck

σσ +++= ∑=

(4.15)



where Ln , Tn , Xn are the numbers of the L -, T - and X -elements crushed in eachdeck, it is the average thickness of the basic elements in deck i , ic is the averagecross-sectional length of an element in the deck i , dt is the thickness of the deckplate, ib is the distance between the touching point and the non-deformed stiffenersand deckN is the number of crushed decks.

Fig. 4.5. Further crushing of ship decks.

5 Preliminary Collision Analyses for MS DEXTRA

In this section, we shall demonstrate the outer dynamics procedure described inSection 3 and the inner mechanics procedure briefly presented in Section 4 to analysea few collision scenarios where a 160 m long conventional merchant vessel strikesMS DEXTRA. The main particulars of the conventional striking ship are presented inTable 5.1. It is assumed that the striking ship collides with the ferry at a forward speedof 4.0 m/s. Two cases are calculated here. One is when the struck MS DEXTRA sailswith a forward speed of 4.0 m/s, the other is when the speed of MS DEXTRA is zero



(V=0). We shall assume that the bow of the striking vessel is considerably strongerthan the side structure of MS DEXTRA.

Table 5.1. Main particulars of the conventional striking ship.Length(m)

Breadth(m)

Depth(m)

Deckheight (m)

Draught(m)

Bow angleθ2

(degrees)

Stemangleϕ(degrees)

160 24.6 13.3 16.3 5.5 80 70

Outer Dynamics: First the collision energy to be dissipated by destroying the struckMS DEXTRA is calculated. Fig. 5.1 shows the energy loss with various collisionangles where the collision position is located at the centre of the struck ship. Fig. 5.2presents the collision energy loss with different collision locations where the collisionis perpendicular to the struck ship. The results show that both the collision angle andthe collision location influence the energy loss significantly. For the centralperpendicular collision, the energy loss is 39.4 MJ when the speed of the struck shipis zero, and the energy loss is 50.2 MJ when the speed of the struck ship is 4.0 m/s.

Fig. 5.1. Energy loss as function of collision angle when the impact is at the centre ofthe struck ship.



Fig. 5.2. Energy loss as function of collision location, when the collision isperpendicular to the side of the struck vessel.

Inner Mechanics: When the energy loss to be dissipated by destroying the sidestructure is known, the subsequent damages to the struck MS DEXTRA can becalculated using the procedure briefly described in Section 4. The analysis procedureis as follows:

It is here assumed that the collision position is located in the middle between twotransverse frames of the midship, see Fig. 5.3. In the initial phases of the collision, theshell plating of the struck ship is subjected to tension. With increasing penetration, thestriking bow comes into contact with frames, stringers and horizontal decks. Theframes, the stringers and the decks are then subsequently crushed. It is assumed thatframes, stringers and decks are not deformed and crushed until the striking bowtouches them directly. By calculation of the resistance of deformed shell plating,frames and decks etc, the collision resistance and the absorbed energy are obtained.When the calculated absorbed energy is equal to the energy loss, determined from theouter analysis procedure, the calculation stops. After the maximum penetration hasbeen determined, the size of a hole in the shell plating created by the striking bow iscalculated.



Fig. 5.3. Collision position for a conventional ship striking the DEXTREMEL vessel.

Fig. 5.4 shows the calculated energy dissipated by the struck ship for variouspenetrations when the speed of the struck ship is zero and the collision angle is 90degrees. It is seen from the results that when the penetration of the striking bow intothe side of the struck ship is 5.0 m, the energy dissipated by the struck ship is 39.3MJ. All the energy loss is dissipated by the struck ship at this penetration (the strikingbow is as mentioned above to be rigid). This means that the indentation stops at thispenetration. The damage length is 8.38 m. The ratio between the damage length andthe vessel length is 4.8%.



Fig. 5.4. Dissipated energy of the struck ship as function of penetrationswhen the speed of the struck ship is zero.

Fig. 5.5 shows the energy absorbed by the struck ship as function of the penetrationwhen the speed of the struck ship is 4.0 m/s and the collision angle is 90 degrees. Thepenetration is measured along the penetration angle 1352/90 =+= αβ degrees.When the penetration reaches 7.85 m, the energy dissipated by the struck ship is 50.3MJ. The struck ship at this penetration dissipates all the energy loss. Therefore, thepenetration stops and the max collision penetration is 7.85 m in this case. Theperpendicular indentation is approximately 55.5)135sin(85.7 =⋅ o m. The damagelength is 10.5 m. The ratio between the damage length and the ship length is 6.1%.This result indicates that when a struck ship has forward speed, the collision energyloss and the resulting damage are larger than when the speed of the struck ship is zero.

Fig. 5.5. Dissipated energy of the struck ship as function of penetration when thestruck ship has a forward speed of 4.0 m/s and the collision angle is 90 degrees.



6 Conclusions

One of the goals of the Brite-Euram project DEXTREMEL is to quantify the risksinvolved in ship traffic in specific geographical areas. To do this rational risk analysisprocedures must be developed. This implies that probabilities as well as inherentconsequences of various collision and grounding events have to be analysed andassessed.

The present paper outlines a method for evaluation of the probability of ship-shipcollisions. The main benefit of the method is that it makes it possible to comparevarious navigation routes and procedures by assessing the relative frequency ofcollisions.

The paper also outlines methods for estimating the structural damage that may resultfrom collision events. These procedures are based on mathematical models for theoverall motions of the involved ships for determination of those energies that must beabsorbed by crushing of the involved ship structures.

Thus, at this stage most of the elements in a reliability-based procedure for theevaluation of the collision probability and the consequences of ship collisions for agiven ship on a given route have been derived.

7 References

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(2) Amdahl, J. (1983): "Energy Absorption in Ship-Platform Impact", NorwegianInstitute of Technology, Report No. UR-83-34.

(3) Amdahl, J. (1995): "Side Collision", 22nd WEGEMT Graduate School, TechnicalUniversity of Denmark.

(4) Amdahl, J. and Kavlie, D. (1992): "Experimental and Numerical Simulation ofDouble Hull Stranding", DNV-MIT Work Shop on Mechanics of Ship Collisionand Grounding, DNV, Norway.

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(8) Hansen, P. F. and Pedersen, P.T. (1998): "Collision Probability Analysis"Dextremel Report No. DTR-1.1-DTU-11.98.

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(10) Kierkegaard, H. (1993b): "Ship Bow Response in High Energy Collisions",Marine Structures, No. 6.

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(19) Pedersen, P. T., Valsgaard, S., Olsen D. and Spangenberg, S. (1993): "ShipImpacts: Bow Collisions", Int. J. of Impact Engineering, Vol. 13, No. 2, pp.163-187.

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(24) Wang, G. (1995): "Structural Analysis of Ship Collision and Grounding", Ph.D.thesis, University of Tokyo.

(25) Wen, H. M and Jones, N. (1993): "Experimental Investigation of the ScalingLaws for Metal Plates Struck by Large Masses", Int. J. Impact Engineering,Vol. 13, No. 3, pp. 485-505.

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(27) Wierzbicki, T. and Simonsen, B. C. (1996): "Global Structural Model of BowIndentation into Ship Side", MIT Rupture Analysis of Oil Tankers in SideCollision, Report No. 2.

(28) Zhang, S. (1999): "The Mechanics of Ship Collisions", Ph.D. Dissertation,Department of Naval Architecture and Offshore Engineering, TechnicalUniversity of Denmark.

Collision Analysis for MS DEXTRA Abstract 1 Introduction

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