61
1 INTRODUCTION
Maritime traffic volumes and ship dimensions are
expected to increase further, requiring fairway and
port designs being adapted to the new situation. In
general, these design processes should be
accompaniedbyanassessmentoftheriskofcollision
andgrounding.
AccordingtoIMO(2007),“risk”isdefinedasthe
combinat
ionof number of occurrences per time unit
and the severity of their consequences. The
occurrencemightbeacollisionoragroundingevent.
Itsconsequenceise.g.anoilleakageorasinkingship,
whichismostlymeasuredinmonetaryvalues.Thus,
itimpliesthecommonriskdefinitionasprobabilit
yof
a collision multiplied by its expected damage
(Pedersen2010).
Toquantifytherisk,theInternationalAssociation
of Marine Aids to Navigations and Lighthouse
Authorities IALA recommends a probabilistic
methodology based on frequency modeling (IALA
2009). Basically, the methodology distinguishes
collisions between ships underway and grounding,
which includes collisions between ships and fixed
objects (in the following, “collision” includes
grounding events, as they are methodologically
similartocollisionswithfixedobjects).
However,inthi
sspecificcasetheriskofmooring
dolphins in relation to an anchorage has to be
assessed. While the former is clearly a fixed object,
vessels lying at an anchorage are neither underway
nor complet
ely fixed objects. Thus, the anchorage’s
riskisdifficulttodeterminewiththeproposedIALA
methodology.
Basedonariskassessmentformulainsection2,a
brief review of frequency modeling’s theory and
consequencecalculationaregiveninsection3and4.
The collision type “ship‐anchorage” is defined in
section 5, for which a frequency and a consequence
model are derived in section 6 and 7 in line with
current ma
ritime risk models. Section 8 applies the
models on an example scenario and compares the
results with alternative modeling based on current
methodology.Insection9conclusionsaredrawn.
ABSTRACT:Thispa
perproposesacollisionmodelforshipsunderwayandtemporaryobjectsasanextension
to state‐of‐the‐art maritime risk assessment like IALA iWrap MkII. It gives a brief review of frequency
modeling’s and consequence calculation theory as well as its applicat
ions, before it analogously derives a
modeltoassesstheriskofanchorageareas.Subsequently,itsbenefitisdemonstratedbyanexamplescenario.
Assessing the Frequency and Material Consequences
of Collisions with Vessels Lying at an Anchorage in
Line with IALA iWrap MkII
H.‐C.Burmeister,L.Walther,C.Jahn&S.Töter
FraunhoferCenterforMaritimeLogisticsandServicesCML,Hamburg,Germany
J
.Froese
HamburgUniversityofTechnologyTUHH–InstituteofMaritimeLogistics,Hamburg,Germany
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 8
Number 1
March 2014
DOI:10.12716/1001.08.01.07
62
f
i
(z)
f
j
(z)
Object
z
max
z
min
B
i
Q
i
Q
j
B
j
Center of shipping lane
Figure1.Head‐onandfixed objectcategoryIsituation(basedonPedersen1995)
2 THEORYOFRISKASSESSMENT
Referringtothedefinitionoftheterm“risk”insection
1,theriskiscomposedofthefrequencyorprobability
P
ithataconsequenceCiresultsfromthehazardHias
well as an utility function U converting the
consequence to a monetary value. The risk can be
formulatedas(Pedersen2010,IMO2007):
,
iii i
i
R
isk P H C U C
(1)
3 THEORYOFFREQUENCYMODELS
Collision probabilities are mostly determined by
frequency models, which are based on the work of
Macduff(1974),Fujii(1983)andPedersen(1995).The
methodologyhasbeenappliedinseveralanalysese.g.
in the Canary Islands (Otto et al. 2002), in the
Øresund (Rambøll 2006) or in the Gul
f of Finland
(Kujalaetal.2009,Hänninenetal.2012).
Inthesemodels,thefrequencycorrespondstothe
number of collision events N in a specific time. In
principle, this number is calculated by multiplying
the number of collision candidates N
a with the
causationprobabilityP
C:
Ca
NPN
(2)
3.1 Collisioncandidate
A“collisioncandidate”isasituation,whichresultsin
a collision, if no av
ersive maneuvers are made. For
vesselsunderway,itsnumberiscalculated based on
the geometric specification of the investigated sea
area, the traffic volumes, vessel specifications and
their lateral distribution under the assumption of
“blindnavigation”.Thel
atterimplies,thatinitiallya
vessel choses its route independently of the current
situation.Dependingonthetypeofmeeting situation:
Passing afixedobject,
Head‐onmeeting,
Overtaking,
Crossingor
Merging
differentmodelsarecommonlyacceptedtodetermine
the number of collision candidates (Pedersen 2010,
IALA 2012). In case of object collisions, Pedersen
(1995)proposesfourcategoriestofurtherclassifythe
typeofaccident:
1 Ordinary,directrouteatnormalspeed,
2 Failtochangecourseatgiventurningpoint,
3 Collisionasresultofevasiveact
ionsor
4 Other(e.g.drifting).
Thesituationofthefirstcategoryisdisplayedon
the bottom of figure 1. According to basic statistics,
the number of collision candidates in a specific
timeframeforthistypecanbeestimatedby:
2
2
i
max
i
min
B
z
I
ai i
i
B
z
NQ fzdz
(3)
given that Q
i represents the number of passing
vessels of type i in this time, B
i is the breadth of
vessels of type i, f
i(z) stands for their lateral
distribution and z
min and zmax characterizes the
dimensionsofthefixedobject.
Thenumberofhead‐oncollisioncandidatescanbe
estimatedinasimilarwayby:
,
,
ij
head head
aW ijij
ij
ij
vv
NL QQP
vv
(4)
withjrepresentingtypesofmeetingvessels,v
iisthe
speedofvesselsoftypeiandL
Wisthelengthofthe
route or fairway, where head‐on meetings are
63
expected (see also figure 1). Finally, the probability
P
i,j
head
formeetingvesselscanbecalculatedby:
iij
iij
zBB/2
head
i,j i i j j
zBB/2
Pfzfzdz
j
i
dz
(5)
Analogously, estimation for the further types of
collision can be derived, but as they are not further
neededinthiswork,itisreferredtoPedersen(1995).
3.2 Causationprobability
Thecausationprobabilityisdefinedasthefractionof
collision candidates that results in a collision. In
general, these factors differ depending on the
situation types and are mainly derived from
analyt
icalmethodsorBayesiannetworks.
As this paper focuses on collision candidate
determination and not on causation probability
modelingin the context of frequency modeling,it is
referredtoe.g.IMO(2007),Hänninen&Kujala(2010),
Pedersen (2010) and IALA (2012) for furt
her
information. For grounding and object collisions,
IALA (2012) suggests a default causation factor of
1.6
10
‐4
.
4 THEORYOFCONSEQUENCECALCULATION
Consequences of ship collisions can generally be
relatedtodamagedmaterialevenleadingtoasinking
ship, environmental damages mainly due to an oil
leakageaswellasfatalities.
As this paper only focusseson material damages
as possible consequences, collision problems can be
divided in the external dynamics and the int
ernal
mechanics of the collision. The external dynamics
considers the global motion of the vessels and the
interaction with the surrounding water, while the
internal mechanics deals with the response of the
shipsʹ structure (Lützen 2001). Thus, the internal
mechanics refers to the deformation of the colliding
vessels.
Methods to analyze the external dynamics of
collisionsrangefromempirical oranalyt
icalsolutions
thus closed form solutions, to time‐stepped
simulations (Brown 2002). In the context of risk
analysis, a great variety of collision scenarios is
considered,forwhichreason analyticalsolutionsare
mostlyfavoredoverti
me‐steppedsimulations.
The internal mechanics can be studied by two
classesoftheoreticalmethods:Finiteelementmethods
as well as analytical methods (Lützen 2001). Finite
element methods allow calculating the internal
mechanics by detailed modeling of ship structures
thatcanbeinvolvedinthecollision,suchasthebow
of the striking vessel and the lat
eral ship hull
structure of the struck vessel (Zhang 1999). Due to
very different types of ships and the resulting
inhomogeneousdistributionofbowshapesandsteel
structures,analyticalmethodsareagainfavoredover
finite element methods for application in maritime
riskassessment.
Theanalyticala
pproachtodeterminethedamaged
materialvolume,consideringbothexternaldynamics
andinternalmechanics,generallyrelatesthedamage
sizetothedissipatedkineticenergyandlinksittoa
monetaryvalue(e.g.Pedersen2010).
4.1 AbsorbedEnergy
The amount of kinetic energy absorbed by the
deformation of the ships’ hulls can be calculated
assuming a tota
lly inelastic collision (Brown 2002,
Minorsky 1959, Zhang 1999). Although the impact
responseisusuallyneithertotallyinelasticnortotally
elastic, a more exact calculation requires detailed
knowledge and modeling of ship structures.
Assuming that the maximum possible percentage of
the initial kinetic energy is absorbed by the ships’
hulls in a tota
lly inelastic collision, it presents a
conservativeapproach.
The absorbedenergy can, thus, be obtained from
the difference between the initial kinetic energy of
bothshipsbeforethecollisionandthekineticenergy
in the system after the collision. The energies are
calculated based on the principle of energy
conservationandthemomentumequation.R
otational
energiesarenotconsidered.
The absorbed energy can be derived using the
ships‘displacements∆
iand∆j,velocitiesviandvjand
addedmass coefficients m
axand mayconsideringthe
water in surge or sway motion due to the ship’s
motion,aswellastheangleofencounter
:
22
22 22
2
1
1
2
2cos
1
(1 )
2
11
ax i i j j
ii jj ii jj
ax
ax i ay j
Emvv
vv vv
m
mm
(6)
The index i indicates the striking ship, while j
standsforthestruckship.
4.2 DamageSize
Thedamagesizeorvolumeofdestroyedmaterialcan
berelatedtotheabsorbedenergy.Themostcommon
empirical approach for ships on crossing routes
considering external dynamics and internal
mechanics has been developed by Minorsky (Brown
2002,Zha
ng1999).
Minorsky(1959)examineddatafrom26full‐scale
ship collisions, where vessel speed, angle of
encounter and damage size were known. For wider
applicability as well as greater accuracy, this linear
approach has been modified several times and has
been developed further amongst others by Pedersen
&Zha
ng(2000):
0.67
00
0,77 3.5
Cj i
t
ER R
d
(7)
64
The first term describes the damage of the
ruptured or tensioned side structure, thus the
damagedmaterialvolumeofthestruckshipR
i,taking
intoaccounttheflowstressofthematerialσ
0andthe
criticalrupturestrainε
c.Thesecondtermreferstothe
damagedmaterialvolume atthebowof thestriking
shipR
iassuming acrushingorfoldingdamagetype.
Itincludesthe averagethicknessofcrushed plates
and the average width of the plates in the cross
section
(Zhang1999).
4.3 MonetaryValue
In the third step, the damaged material volume is
translated into a monetary value. The repair costs
C
Materialnotonlydependonthe damagedvolumesRi
andR
j,thedensityofsteelρandthecostsforatypical
repairjobC
Repair,butalsoonthelocationoftherepair
yardleadingtocostsforthevoyagetotheyardC
Yard
andtheprobabilitythatarepairinayardisrequired
P
Yard:
()
M
aterial i j Repair Yard Yard
CRRCCP
(8)
P
Yard amounts to zero in case of low energy
collisions,andtooneforhighenergycollision.Incase
of low energy collisions the ship’s hull is only
deformedbutnotruptured.Thus,itisassumedthata
ship’sclassificationcertificatecanbemaintainedand
a stay at a yard is not required. This depends on a
crit
icalkineticenergy,whichcanbederivedfromthe
ship’sdisplacementandacriticalspeed.
Incasetheresultingmonetaryvalueishigherthan
thebuildingcosts,totallosscanbeassumed.
5 RISKFACTORANCHORAGE
Anchoragesposearisktonavigationalsafety,asthere
oftenanchorvessels,whichthenareanobstacletha
t
others might collide with.Notwithstanding
improving navigational aids and crew qualification,
collisionsstilloccur,likee.g.thecollisionbetweenthe
“Katharina Siemer” and anchoring “Angon” on the
Elbe River in November 2012 or between
“Jinggangshan” and anchoring “Aeolos” near
Gibraltar in May 2011. Thus, an a
ppropriate
consideration of anchorages during maritime risk
assessmentsshouldbeaspired.
5.1 Anchoragecharacteristics
An anchorage is a limited area that is suitable for
vesselstoanchor.Thoseareasarehighlightedinsea
charts and might also be marked with buoys (BSH
2011).However,iftheanchorageisnotinuse,itisnot
an obstacle for shipping as it normally does not
necessi
tateanyfixedinfrastructure(exceptinthecase
ofbuoys).
The actual obstacles are the vessels lying at an
anchorage,whichonemaycollidewith.Incontrastto
a berthed ship, those ones change their position by
swinging at anchor depending on wind, waves and
ti
de.
5.2 Collisiontypesonananchorage
Types of collision that may occur in relation to an
anchoragearecollisionsbetween:
1 Anchoredvessels,
2 Anchoredvesselandvesselunderway(e.g.witha
transitingvessel),
3 Vessels underway (e.g. transiting vessel and a
vesselleavingtheanchorage)or
4 Other(e.g.drifting).
While the collision candidates for the thi
rd type
can be determined with the help of a crossing or
merging model, none is available for the upper
categories, as the anchored vessels are neither fixed
objectsnorpermanentobstacles.Inthefollowing,the
first one is called “anchorage‐“ and the second one
“ship‐anchorage‐collision”.
f
i
(z)
z
max
z
min
B
i
Q
i
Center of shipping lane
⚓
⚓
f
a
(z)
d
a
Anchorage
⚓
⚓
⚓
Figure2:Ship‐anchorage‐collision
6 PROBABILITYOFSHIP‐ANCHORAGE‐
COLLISION
6.1 Mathematicalmodelforcollisioncandidates
Todeterminetheship‐anchoragecollisioncandidates
similarto (3)and (4) firstall meetingsituationsin a
given timeframe must be calculated. If
use,a is the
fractionoftimethattheanchorageisusedbyatleast
one vessel of type a and Q
a is the mean number of
vessels of type a, which lay at the anchorage at the
same time, then the total number of collision
candidatesisgivenby:
,,
,
SA SA
aiuseaaia
ia
NQQP
(9)
wherethefirstthreeelementsdeterminethenumber
ofallmeetingsituations.
Afterwards,theprobabilit
yP
i,j
S‐A
oftheunderway
vessel heading towards an anchored ship has to be
calculated. This is done by f
a(z), which is the
probability density function of the anchoring ship’s
distance to the center of the shipping lane, and d
a
representing its obstacle dimensions including paid
out anchor chain perpendicular to the other vessel’s
moving direction (see also figure 2). If the vessels
65
underway are described as in (3), then the collision
candidatescanbeestimatedsimilarto(4)by:
/2
SA
,a
/2
iia
iia
zBd
iiiaaai
zBd
Pfzfzdzdz
(10)
6.2 Causationprobability
Thisworkfocusesprimarilyonmodelingofcollision
candidates. Thus, in the first instance the causation
probabilitiesforfixedobjectcollisioncouldbeusedas
an approximation for calculating the number of
collisionevents.
6.3 Modelvariables
Of course, the different types of anchoring vessels
allow modeling different sizes of ships. However, it
furthermore allows incorporat
ing swinging circle
effects,asd
aand fa(z)dependon theactualweather
andtidalconstraints.Therefore,theshipoftypeais
split into several types with different obstacle
characteristics, while its likelihood is controlled by
use,a, which is set according to the tidal conditions’
fractionoftime.
As the boundaries z
min and zmax of the anchorage
arenotpartofthemodel,ithastobeensuredbythe
chosen distribution function that the anchoring
vessels are positioned within the anchorage area.
However, the tails of f
a(z) outside the anchorage
could be used to model meeting situations between
vessels underway and ships adrift because of a
brokenanchororwithshipsswingingatanchorinto
theshippinglane.
7 CONSEQUENCEOFSHIP‐ANCHORAGE‐
COLLISION
In order to estimate the consequences of ship‐
anchoragecollisionsswingingcircleeffectshavetobe
ta
ken into account. Due to the varying angle of
encounter, ship‐ship collisions can be orthogonal,
parallel or in between, thus leading to bow‐side‐
structurecollisions,head‐oncollisionsorintermediate
encounters.
Moreover, the speed of the anchored ship is
assumed to be zero. Based on formula (6) the
ab
sorbed energy for orthogonal collisions of two
vesselscanbecalculatedby:
222
2
(1 )
11
1
22
11
ax i i
ax i i
ax i ay j
mv
Emv
mm
(11)
In contrast to orthogonal collisions, where the
struck ship is assumed not only to have a forward
speed but also a sway velocity after the collision,
head‐oncollisionswithanangleofencounterof0°or
180°principally onlylead to a surge motion of both
ships. Hence, only the added ma
ss coefficient for
surgemotion has to be considered when calculation
the absorbed energy resulting in the following
expressionbasedon(6):
2
1
1
2
ij
ax i
ij
Em v
(12)
8 RISKASSESSMENTEXAMPLE
Due to confident
iality reasons the original case that
inspired the extension can’t be presented here.
However,asimplifiedvirtualdecisionsituationshall
demonstratetheutilityoftheship‐anchorage‐collision
model.
8.1 Decisionalternatives
In an area of restricted tidal waters short‐term
berths are needed for ships wait
ing e.g. for a free
berthatthepieroralocking.However,itisdiscussed
toeitherdisplayanarrowanchoragearea nexttothe
fairwayortoconstructseveraldolphinsallowingfor
short‐term moorings. As the second option is more
costlyitssafetybenefitsshouldbeanalyzed.
8.2 Frequencymod
elingasship‐anchorage‐collision
The principal layout of the dolphin alternative
correspondstofigure1andtheoneoftheanchorage
to figure 2. Table 1 gives an overview about the
scenario variables. It is assumed that during 75% of
thetimetheanchorageareaorthedolphinsareinuse.
Furthermore, the berths at the dolphins are on the
fairwayside,thustheobstacledimensionsincreaseif
avesselismoored.Ifthereareseveralships,theyare
moored in series; consequently the obstacle
dimensionsstayconstant.
Table1.Scenariovariablesforfrequencymodeling.
_______________________________________________
VariableAnchorageMooringdolphins
_______________________________________________
Q1,Q2 20,000 Ships/a 20,000 Ships/a
B
1,B2 20 m20 m
f
1(z) N(50,50
2
)N(50,50
2
)
f
2(z) N(‐50,50
2
)N(‐50,50
2
)
z
min 150 m300* m
z
max 450 m305 m
τ
use,a 0.75‐0.75 ‐
Q
a2.5Ships 2.5Ships
_______________________________________________
* zmin=280mfordolphinsifshipsaremoored
Duetoti
dalwaters,theanchoringvesselsswingat
the anchor thus having different obstacle positions
and dimensions over time. The latter strongly
dependsonthevesselsangletothefairway.Iffurther
weather effects are neglected and a tidal current
parallelto the fairway is assumed, then the obstacle
dimension of the anchoring vessel (perpendicular to
the fairway) over ti
me follows approximately the
solidlineinfigure3.
Itcanbe seen, that shortly after slack tide, when
the dotted current line crosses the axis of abscissae,
thechangingcurrentdirectionturnsaroundthevessel
66
untilitlaysagainparalleltothefairwayaccordingto
the new tide. During this time, the obstacle
dimensions are of course much higher than in the
dolphin case, where the vessels stay parallel
independentlyofthetide.
Within this example, a turning rate of 5 degrees
per minute is assumed and the turni
ng process is
divided into three different relations. Their
characteristicsaregivenintable2consideringthatthe
likelihoodofanchoredvesselsoutsidetheanchorage
(e.g. due to drifting because of broken anchor) is
below 1.0%. In reality, the position distribution as
well as the lateral dimension should of course be
derivedbyav
ailableinformation,ase.g.datafromthe
AutomaticInformationSystemAIS.
Table2.Obstacledimensionsinanchoragescenario
_______________________________________________
RelationOrthogonal Inbetween Parallel
_______________________________________________
Fractionoftime 0.040.060.90
d
a 100 m 60 m 20 m
f
a(z)N(300,40
2
) N(300,20
2
) N(300,10
2
)
_______________________________________________
8.3 Frequencymod
elingasfixed‐object‐collision
Even though anchoring vessels do not fit the
definition of fixed object collision models, two
alternativesarepresentedbasedonthemethodology
described in Pedersen (1995) to allow for a
comparisonwiththeproposedmodel.
In the first alternative“Fixed Object: Anchorage”
thewholeanchorageismodeledasanobjectfor75%
of the ti
me, while the second one “Fixed Object:
Anchoredvessel” assumes that all obstacles lay in a
row in the middle of the anchorage similar to the
dimensions in table 2. Of course, the latter implies
thatnotthewholeanchorageareaisused.
8.4 Comparisonoffrequency mod
elingresults
Table3 shows the estimated collision candidates for
thedecisionalternatives.Using(3),theestimationof
the collision candidates for the dolphin scenario can
be performed directly according to accepted
methodologyandresultsin0.084collisioncandidates
perannum.
Indeed, it is observable tha
t the results for the
anchorage scenario widely differ depending on the
chosen model. If e.g. the whole anchorage area is
modeled as a fixed object, then this results in 540
estimated collision candidates. This seems to be a
very conservative approach as underway vessels
traveling through this area are not necessarily on
collisioncoursewithananchoringship.
Table3.Collisioncandidateresultsofexample
_______________________________________________
ModelCollisioncandidates
_______________________________________________
Ship‐Anchorage‐Collision 2.472 p.a.
FixedObject:Anchorage 540.040 p.a.
FixedObject:Anchoredvessel0.111 p.a.
_______________________________________________
FixedObject:Mooringdolphins 0.084 p.a.
_______________________________________________
Figure3.Lateraldimensionofanchoringvessel(idealized)
In contrast to that assuming a fixed anchoring
position might be toosubjective due to the fact that
thechosenpositioncouldstronglybiastheresults.As
commonly used lateral probability distributions
decline in the tails, assuming a more distant
anchoring position would strongly affect the
calculated collision candidates, and thus the risk
assessment. If it is e.g. a
nticipated in this example,
thatallanchoringvesselslaynexttothefairway‐side
border of the anchorage, the expected number of
collisioncandidateswouldbeclosetotheoneinthe
“Fixedobject:Anchorage”case.
Astheresultreactsverysensitivetotheassumed
anchoring position, it can be considered to be the
mostobjectivewaytoincludetheprobabilit
ydensity
functionf
a(z)oftheanchoringpositiondirectlyinthe
risk assessment by using the proposed model.
Therefore, frequency distributions derived from
recorded AIS‐data provide an accurate base to
determinetherequiredfunctionsf
a(z)andfi(z).
8.5 Consequencecalculation
On the basis of the frequency modeling results the
consequences are calculated for ship‐anchorage‐
collisionsincomparisontothedolphinscenario.For
thecalculation,ashipwiththedimensionsintable4
and building costs of around 16.78 million € is
assumed. The ship at the anchorage or mooring
dolphinshasthesamedimensions.
Typicalrepaircostsareassumedas6,000€/
t(Otto
etal.2002),whichincludethefullrepairprocess,such
as cutting‐building‐fitting of the damaged volume.
Furthermore, costs for the voyage to the shipyard
C
Yardofabout50,000€/repairjobincludingfuel,crew
andtugcostsareadded(Ottoetal.2002).Costsfora
damaged mooring dolphin are approximated with
200,000€.
Regardingthecalculationofthedamagedmaterial
volume of both vessels using formula (7) normal
strengthhullstructuralsteelisusedwithaflowstress
σ
0of460N/mm²andadensityρ of 7.85 t/m³.For
thecriticalrupturestrainε
cameanvalueforstiffened
andunstiffenedplatesof7%isassumedaccordingto
Paik & Pedersen (1996). The relation of average
thickness of crushed plates to average width of the
67
plates in the cross section
is 1/83 referring to
(Zhang1999).
Table4.Scenariovariablesforconsequencecalculation.
_______________________________________________
VariableAnchorageMooringdolphin s
_______________________________________________
L1,L2 120 m120 m
B
1,B2 20 m20 m
T
1,T2 8 m8 m
∆
1,∆2 15,700 t15,700 t
v
1,v2 8;0kn8;0kn
C
Ship1,CShip2 16.78 mil€ 16.78 mil€
C
Dolphin 200,000 €
ε
c7 %7 %
σ
0460 N/mm² 460 N/mm²
t/d1/831/83
ρ7.85t/m³ 7.85t/m³
_______________________________________________
Table5summarizestheresultsoftheconsequence
calculationbasedonthethree‐stepapproachrelating
thedamagedmaterialvolumetotheabsorbedenergy
and linking it to a monetary value. The results are
onlyshownforship‐anchoragecollisions comparedto
themooringdolphinscenario.
Table5.Consequenceresultsofexample
_______________________________________________
ModelConsequence
_______________________________________________
Ship‐Anchorage‐Collision139,828€
FixedObject:Mooringdolphins 264,042€
_______________________________________________
Taking into account the fraction of time for
orthogonal, parallel and in between collision
situationsas wellas thefractionof time particularly
the dolphins are in use, it can be seen that the
consequencesareonaveragealmosttwiceashighfor
themooringdolphinscenariothanfor
ship‐anchorage
collisions.
Ontheonehandthiscanbeexplained by higher
energiestobeabsorbedincase ofmooring dolphins
as the moored vessels cannot experience a surge or
sway motion after the collision, but needs to absorb
the energy that could stay in the system due to the
motion.
On the other hand, even more significant is the
influenceofthecostsincaseonemooringdolphinis
damagedbyashipcrushinghead‐onintoit,because
thereisnoshipatthemooringdolphinsatthepoint
intimeofthecollision.
8.6 Riskassessment
According
to the definition of risk, the risk of the
ship‐anchorage scenario and the mooring dolphin
scenariocanbederivedfromthecollisioncandidates
or probabilities and the consequences using (1). The
resultsarelistedinTable6.
Table6.Riskresultsofexample
_______________________________________________
ModelRisk
_______________________________________________
Ship‐Anchorage‐Collision55.31 €p.a.
FixedObject:Mooringdolphins3.55 €p.a.
_______________________________________________
The results emphasize the importance of risk
assessment besides frequency modeling and
consequence calculation. In this example the
consequence results indicate that an anchorage area
should be favored over mooring dolphins. Only
looking at the frequencies, in contrast would give
impression vice versa. The risk assessment relates
bothproviding
thebasisforasounddecision.
Furthermore, the analysis of the different
anchoringsituationscouldalsobeofhelpbyfinding
highriskysituations.Table7showsthepartialresults
oftheship‐anchorage‐collision‐modelinthisexample
and it can be observed, that nearly all collision
candidates are expected
during the orthogonal
situation.
Table7.Collisioncandidates’situationdependingontide
_______________________________________________
RelationOrthogonalInbetween Parallel
_______________________________________________
Fractionoftime0.040.060.90
Collisioncand.2.2570.1080.107
Consequence 145,871€ 89,239€ 63,625€
Risk52.67€ 1.55€1.09€
_______________________________________________
9 CONCLUSION
Withinthisworkadditionalcollisiontypesthanthose
used in IALA (2012) have been defined, which are
related to anchorage areas. A model for estimating
collision candidates between vessels underway and
vessels lying at an anchorage has been proposed,
which is capable of taking into account information
on
the anchoring position’s frequency distribution.
Notwithstanding,theproposedmodelsufferssimilar
drawbacks as frequency models in general, e.g. that
vesselmovementsarenottakenintoaccountandthat
information about the exact collision situations is
missing(Goerlandt&Kujala2011).
Nevertheless, the proposed model goes in line
with state‐of‐
the‐art frequency models for collisions
betweenshipsorshipsandfixedobjectstoallowfor
comparison with other collision types. The method
hasbeenappliedonanexamplecasederivedfroma
realproblemtodemonstratetheshortageofmodeling
anchorageareas as fixed obstacles. Additionally,the
proposed model is
capable to roughly consider
swingingcircleeffects.
Tofullyassesstheriskinducedbyananchorageit
can be seen that the consequences need to be
evaluated. An analytical approach considering
external dynamics and internal mechanics based on
threestepsrelating thedamaged material volumeto
theabsorbedenergyand
subsequentlylinkingittoa
monetaryvaluehasbeenapplied.
Although the approach assumes totally inelastic
behavior besides other simplifications, such as
neglecting rotational energies, it can be used for
maritime risk assessment based on a variety of
collision scenarios and ship types. Nevertheless, the
approach only gives a rough estimation
of the
consequences.Wherepossible,additionalinformation
onthecollidingvesselsormoredetailedmodelingof
ship structures should be integrated in the
consequencecalculation.
68
Indeed, further adjustments are necessary to
establishafullriskmodelforanchorages.Nexttothe
proposed geometric model, a deeper analysis of
causationfactorsshouldbeconductedforthistypeof
accidents. Moreover, consequences not only refer to
damaged material, but also to environmental
damages, fatalities or loss of
earnings (Pedersen
2010).However, thisrequiresfurtherinvestigationfor
ship‐anchorage‐collisions.
Consideringthementionedadjustmentsthispaper
presented a way to more accurately assess an
anchorage’sriskinlinewithIALAiWrapMkII.
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