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Statistical Design of Fender for Berthing Ship
Shigeru Ueda
Tottori University, Tottori, Japan
Toshihiko Hirano
Tottori University, Graduate School, Tottori, Japan
Satoru Shiraishi, Shuji Yamamoto
Independent Administrative Port and Airport Research Institute, Kanagawa, Japan
Seigi Yamase
Bridgestone Corporation (Yokohama Factory), Kanagawa, Japan
ABSTRACI
Fender is commonly used for the purpose to absorb berthing energy
and to decrease impact of berthing ship. Ships berthing energy is
proportional to virtual mass of ship and square of approach velocity,
however it was reduced by rotational motion caused by eccentric
berthing. Currently, fender is designed by calculating berthing energy
for the maximum size ship and/or standard size ship considering ship
mass, virtual mass factor, design approach velocity and eccentricity
factor. Then select suitable fender to absorb ships berthing energy.
Recently, ship size increases so fast. For instance, size of modem
container ships became more than 100,000 DWT. At some port, no
berth is constructed to meet above those ships in full laden. As the
result, ships larger than design ship is to be obliged lightening its draft
at berthing. Even if the berth water depth is secured, virtual approach
velocity must be decreased than design approach velocity.
Some of the present authors had attempted to design a fender for
berthing ship by means of statistical method and presented the results
of the analysis to the llth ISOPE (Ueda and et al 2001). While in the
previous paper, the probability of failure and safety factor on fender
design for container ships were calculated, in this paper, analysis was
made for conventional cargo ships by use of statistical data of arriving
ships in some major port in Japan.
KEY
WORDS:
rubber fender, statistical design, berthing ship,
approach velocity, ship displacement, virtual mass factor, eccentricity
factor
1. INTRODUCTION
When ships berth for loading and unloading, fender is used fo
the purpose to absorb berthing energy and to decrease impact o
berthing ship. Because of its purpose, fender should be designed tha
ships berthing energy does not exceed energy absorption of fender.
Ships berthing energy is calculated for the maximum size shi
and/or standard size ship considering ship mass, virtual mass factor
design approach velocity and eccentricity factor. But ship size
generally registered by dead weight tonnage
(DWT)
for container ships
cargo ships and others. Therefore, those factors necessary in calculation
of berthing energy such as ship mass, virtual mass factor, design
approach velocity and eccentricity factor are to be derived from
D WT.
In the current Design Standard for Port and Harbour Facilities
Japan (1999), factors concerning berthing energy are determined
accordance with either 75% or 95% confidence level.
As those factor
are not fixed but variable, and different for those entrance ships of sam
DWT, there is a possibility that ships berthing energy exceed th
energy absorption of design fender.
In this paper, all factors were treated as variable. And th
probability of failure of fender designed according to the current design
standard was calculated by statistical method. Then the authors wi
propose the statistical design method of fenders for berthing ships.
2. PROCEDURE OF THIS STUDY
In this study, fender is designed by statistical method as follow
(refer to Figure-l).
@ Give ship size
D WT
for analysis.
Proceedings of The Twelfth (2002) International Offshore and Polar Engineering Conference
Kitakyushu, Japan, May 2631, 2002
Copyright 2002 by The International Society of Offshore and Polar Engineers
ISBN 1-880653-58-3 (Set); ISSN 1098-6189 (Set)
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Analyze the relation between
DWT
and V,(approach velocity),
C,(virtual mass factor), C,(eccentricity factor). Then, calculate
those values such as
V,,,
C,,,, C,. (see section 3.1)
Analyze Z the ratio of energy absorption of fender against
catalogue value
Ecu,.
Then, obtain the energy absorption of design
fender Ef (see section 3.2)
Obtain ships berthing energy Es.
Compare the ships berthing energy
Es
and the energy absorption
of design fender Ey
Calculate the probability of exceedance of the ships berthing
energy over the energy absorption of design fender. (see section
4)
Calcu1at.e the energy absorption of fender and the safety factor
which satisfies the required probability of exceedance.
Figure-l Procedure of This Study
Where, specified failure function G is defined as following equation.
G=E, -Es
E,: Energy absorption of fender, E,: Ships berthing energy
Z Fender factor, EC,,: Catalogue value
M Ships mass (Displacement tonnage), V,: Approach velocity
C,: Virtual mass factor, C,: Eccentricity factor
1)
3. CHARACTERISTIC OF FACTORS CONCERNING
FENDER DESIGN
3.1 Factors Concerning Ship s Berthi ng Energy (Ueda et al. 2001)
In this chapter, the relation is shown between DWT and factors of
ships berthing energy. All factors such as ship mass, approach velocity,
virtual mass factor, eccentricity factor are treated as random variables.
Those values are regressed to linear on co-natural logarithms
And it is assumed that those values above mentioned as normally
distributed on regression lines (refer to Figure. 2).
In this study, object of analysis is not only a container ship b
also a cargo ship. Therefore the relation between
DWT
and
DT a
shown for container ships and cargo ships. The relation between
DW
and other factors concerning energy absorption of fender were alread
presented in the paper submitted to the llth ISOPE, however thos
relations are shown again (Figures.4-6).
Design Ship Size
ln DWT)
Figure-2 Explanation of Relation between DWT
and Factors of Ships Berthing Energy
a) Ship Mass (Ship Di splacement Tonnage), DT
Figure-3 shows the relation between DWT and displacement
tonnage
DT
for ships listed in Lloyd Registered of Shipping an
Registered Ship in Japan analyzed by Akakura and et al. (1998). This
the relation of container ship for ships full laden.
200,000
5
& 150,000
3
r
2 100,000
E
8
m
.g 50,000
.P
a
0
-I
0
20,000 40,000 60,000 80,000 100,000 120,000
Dead Weight Tonnage (DFV)
0
- 50% confidence
0 - 75% confidence
0
____ 90
confidence
@I I-~- 95% confidence
50 confidence DT =2.203.DWT0.
75 confidence DT =2.317.DWT3
90 confidence DT =2.425 .DWT s3
95 confidence DT =2.492.DWTQ
Figure-3 Relation between D WT and DT for Container Ship
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Regression Equations between DWT and DT for Cargo Ship under
10,OOODWT are as follows.
50 confidence DT = 3.327. D WTQ.899
75 confidence DT = 3.548. DWT.g99
2)
90
confidence DT = 3.767. D WT.899
95 confidence DT = 3.899. DWT.899
Regression Equations between
DWT
and DT for Cargo Ship over
10,OOODWT
re as follows.
50 confidence DT = 3.119. DWT.93
75% confiaence DT = 3.373. DWTa.93
(3)
90
confidence DT = 3.614. DWT.93
95 confidence DT = 3.767. DWT0.93
b) Approach Veloci V,
Ship shall touch the quay at either bow or stem at first impact,
then touch at the opposite side alternatively. According to the
observation by Moriya et al. (199 1 , it is found that approach velocities
in bow berthing are rather larger than those at stem berthing, however
there are several occasions in stem berthing which are rather larger than
those of at bow berthing. Therefore, analysis was made with the data
including approach velocities at bow and stem berthing, and the
relation between DWT and approach velocities was obtained as shown
in Figure-4.
0.25
g 0.20
x
; 0.15
s
f 0.10
41
8 0.05
0.00
(j) ~ 50% confidence
@ - 75% confidence
(3 - 90% confidence
@ ,--x~.- 95% contidence
9
\
50%cotidence V, =1.925.DWT~.*
@&- 75%conftience Vb=2.422.DWTmo338
90%confdence V, = 2.977. DwTm338
95%mnfiience V, =3.369. DWlmo.8
0 10000 20000 30000 40000
50000
Dead Weight Tonnage (D WT)
Figure-4 Relation between
D
WT and
V,
c) Vi rtual Mass Facto*, C,,,
Virtual mass factor is calculated by means of Uedas formula
(1981) for those ships listed in Lloyd Registered of Shipping and
Registered Ship in Japan. Figure-5 shows the relation between DWT
and virtual mass factor.
c, =l+Lxd
2C, B
(4)
Where,
C,: Virtual mass factor, C,: Block coefftcient
d: Full load draft, B: Breadth extreme
ah----
50% confidence
@----
90% confidence
@ - 75% confidence
@ -..95% confidence
2.2
50%confidence C,=1.490~DCYT0.**
75% confidence C =1.527~DcYT~0218
90%confidence
cl cl.56 1.DwP8
95 %confidence
c, =1.68 1~DwP*
0
20,000 40,000 60,000
80,000
100,000 120,000
Dead Weight Tonnage (D WT)
Figure-5 Relation between DWT and C,
d) Eccentr icity Factor, C,
Eccentricity factor is given by the following formula which
derived considering energy dissipation after the berthing with t
rotational motion around the contact point either at bow or stem. B
use of those data above mentioned, the relation between
DWT
a
eccentricity factor is obtained as follows.
1
ce = 1 + z/u)
Where,
I: the distance from the contact point to center of gravity of berthin
ship measured parallel to the quay line
r: radius of gyration
CD----
50% confidence
@ - 75% confidence
0 -- 90% confidence @ ^.~.I.. I.~5% confidence
0.60 ,
1
a 0.55
B
d
.& 0.50
2
I2 0.45
fi o.40 iiii. ~~~~~
0 20,000 40,000 60,000 80,000
100,000 120,000
Dead Weight Tonnage (DWT)
Figure-6 Relation between
D WT
and C,
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3.2 Factor Concerning Energy Absorption
Fender factor Z is the factor of energy absorption of fender
against catalogue value Ecar For instance, factor Z4.0 means that the
energy absorption of fender is equal to that of catalogue value and
ZxO.9 is regarded to 10% reduction to E,,,. Probability density function
fit well to normal distribution of which mean ~~0.997 and standard
deviation d z= 0.03 1 as shown in Figure-7.
Measured Value
II Normal Distribution
Fender Factor Z
Figure-7 Frequency Distribution and Expectation of Factor 2
4. PROBABILITY OF EXCEEDANCE FOR THE
CURRENT DESIGN METHOD
4.1 Example
of
Designed Fender
In this chapter, probability of exceedance was calculated for
designed fender by current method.
Fender was designed in cases where those values of 75%, 90%,
95% confidence levels for those items concerning ships berthing
energy as ship mass, virtual mass factor and eccentricity factor. Table-l
lists the condition of each case and energy absorption of fender in each
case.
Table-l Examples of Designed Fender Capacity
vb
DT,C,,C,
Effective Fender Capacity (kNm)
(Confidence (Confidence
35,OOODWTII 5,000DWT11 5,OOODWT
Level)
Level)
Ibontainer Shill1 Cargo Shin 11Cargo Shin 1
I 75%
11 128.8 11
izi
4.2 Calculati on Method
Based on statistical characteristics of factors, probability
exceedance that the ships berthing energy excess the effectiv
designed fender capacity was calculated. Calculation method is t
following two methods.
(a) Monte-Calm Simulation
Random numbers of the statistical characteristics of factors abov
mentioned were occurred and simulated. Where, number of simulation
trial was 10,000. As an instance, Figure-8 (a)-(d) show the number
occurrence and theoretical probability distribution of ship mas
approach velocity, virtual mass factor, eccentricity factor f
35,000DWT
container ship.
3000
2500
2000
; 1500
2 1000
z
F+ 500
0
:
P
;:
El
:
z
z
,
z m
z
: :
m
z m E
:
(a) Frequency of Distribution of DT
3000
2500
2000
; 1500
2 1000
2
Lr, 500
0
(b) Frequency of Distribution of V,,
3000
2500
(c) Frequency of Distribution of C,
2500
2000
; 1500
5 1000
rA 500
0
(d) Frequency of Distribution of C,
Figure-8 Calculation Results of Each Random Number
(Des&r Shin Size 35.000DKContainer Shin)
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(b) Second-Moment Method
Factors concerning ships berthing energy are treated as
logarithmic normal distribution. However, if all factors concerning
specified failure function G are assumed normal distribution, meanp G
and standard deviation bG of specified failure function G is obtained
from the following equation.
Where,
,U G: mean of specified failure function G
c G: standard deviation of specified failure function G
bGo)=P,-
,~2F33.P4P5J2
p I: mean of Z, ,U z: mean of DT,
,U + mean of V,,
p 4: mean of Cm p 5: mean of C,
c I: standard deviation of E,,,,
d z: standard deviation of DT,
d 3: standard deviation of V,,
d I: standard deviation of C,,
c + standard deviation of C,
Therefore, probability of exceedance is calculated by the following
equation.
For example, when design ship size is 35,OOODWT container ship and
catalogue value of fender is 128.8kNm, mean and standard deviation
are calculated as p G =69.395kNm and c G =72.252kNm. Thus,
probability of exceedance is calculated as 0.168 by equation (8).
4.3 Result of Probabil i@ of Exceedance
(a) Probability of Exceedance for Container Ship
In case of container ship of 35,OOODWT, Figure-9 shows the
probability of exceedance that the ships berthing energy exceed the
energy absorption of designed fender calculated by means of two
methods.
From the results, results of those two methods i.e. Monte-Calro
simulation and Second-Moment method are different in case of low
probability of exceedance. This may be caused by the difference of
assumption of statistical characters, i.e. Monte-Calro simulation
assumed logarithmic normal distribution but Second-Moment method
assumed normal distribution. It is obvious that there is a different in th
foot of distribution (refer to Figure-lo). Factors concerning ship
berthing energy are assumed normal distribution on natural logarithms
i.e. logarithmic normal distribution. Therefore, logarithmic norma
distribution for Monte-Calro simulation is better than norma
distribution for Second-Moment method. As the result, hereafter th
analysis is made by Monte-Calro simulation. Where, fender factor Z
treated as variable.
0.20
0.1 5
x
ii
m
iii
::
UJ 0.10
>,
.e
z
2
9
CL
0.05
Monte-Cairo Simulation Second-Moment Method
V,=75% confidence
V,=90% confidence
V,,=75% confidence
,
V,=90% confidence :
DT,CM.cC DT,CM.Ce DT.Ch+,Ce
DT.CM.Ce DT.cM,Ce
DT.CM,Ce
75XcMlfidence 9C coniidence 95Uconfiden.x 75Xconfidence 9O confidence 95Xconfiden
level
level
level level
level level
Figure-9 Probability of Exceedance for 35,000DWT Container Ship
-Logarithmic Normal
Distribution
.mw+-Normal Distribution
Ships erthing nergy (kNm)
Figure-10 Ships Berthing Energy of 35,000DWT Container Ship
by Two Methods
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(b) Probability of Exceedance for Cargo Ship
Furthermore, the probability of exceedance is calculated for
cargo ships. Figure-11-12 show the results of probability exceedance
for cargo ship by Monte-Calro simulation.
Vh=75% confidence
. ..---*..
Vb=90? confidence :
Vb=95% confident
DT,Cm,Ce
DT,Cm,Ce
75%confidence
90%confidence
level
level
DT,Cm,Ce
95%confidence
level
Figure- 11 Probability of Exceedance for
5,000D WT
Cargo Ship
0.20 r-
-I
Vb=75% confidence
5 11 - . . . . . . . . .
x
Vb=90% confidence 1
a
,
0.00
I
DT,Cm,Ce
DT,dm,Ce
DT,Cm,Ce
75%confidence
90%confidence
95%confidence
level
level
level
Figure-l 2 Probability of Exceedance for 10,OOODWT Cargo Ship
From the results, when confidence level of approach velocity is
raised, probability of exceedance is lower than other factors. It is found
out that the ships berthing energy is most influenced by the approach
velocity. It is the reason that ships berthing energy is proportional to
square of approach velocity and standard deviation of approach
velocity is maximum value in those factors.
5. FENDER DESIGN OF STATISTICAL METHOD
It can be said that probability of exceedance is seemed rathe
high for the fender designed according to the current design method. I
this chapter, the energy absorption for the required probability
exceedance is calculated for container ship and cargo ship, and then th
safety factor against effective designed fender capacity according to th
current design method is calculated.
The safety factor is defined by the following equation.
E, =Z-EC,, >y-Ed
9)
Where,
E,: Guaranty energy absorption of fender (kNm)
Z Ratio of energy absorption of fender catalogue value EcO,
EC,,:
Catalogue value of energy absorption of fender
Eg
Effective designed fender capacity according to the current desig
method (kNm), y : safety factor
Effective designed fender capacity Ed is calculated in accordance
with the current design method by use of 75% confidence level for sh
size, virtual mass factor and eccentricity factor, and 95% confidence
level for approach velocity.
Calculation of the safety factor was made by the following
method.
0 Calculate the energy absorption of fender Ed, by use of curren
design method.
@ Calculate the catalogue value of fender.
(Ecat=y *EJ .Z)
@ Energy absorption of the selected fender is obtained as
EFZ*E,,,=
Y *EF
@ Then, design ship size (DWT) is converted to DT.
@ And, calculate ships berthing energy
E,
for each trial.
@ Compare
Ef
and
E,.
If
E>Ep
regard that ships berthing energ
exceed energy absorption of fender.
@ Count the number of such occurrence among 10,000 trial, an
obtain the probability of exceedance.
@ Change safety factor y and calculate energy absorption an
repeat the steps from @ to @ until energy absorption satisfie
the required probability of exceedance.
Figure-13 show the result for
35,000DWT
container ship. In ca
when the factor Z was fixed as 0.9, and Ed is calculated by use of Vb
confidence level and DT, C,, C, of 75% confidence level. The result
safety factor was already presented in the paper submitted to the 1
ISOEP. In this paper, safety factor is calculated when factor Z
variable too. Furthermore, analysis is made for cargo ships. Figures
14-15 show those results on the condition that Z is variable.
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..-a-- Safety Factor
Current 0.01 0.006 0.004 0.002
Design Required Probability of Exceedance
Figure-13 Energy Absorption and Safety Factor for Required
Probability of Exceedance (35,OOODWTContainer Ship)
a
2 600
Required Energy
-.-~---Safety Factor
[ 3.0
Current 0.01
0.006
0.004 0.002
Design
Required Probability of Exceedance
Figure-14 Energy Absorption and Safety Factor for Required
Probability of Exceedance (5,OOOOwTCargo Ship)
Required Energy -s--Safety Factor
Current 0.01 0.006 0.004 0.002
Design
Required Probability of Exceedance
Figure-l 5 Energy Absorption and Safety Factor for Required
Probability of Exceedance (10,OOODwT Cargo Ship)
2.5
2.0
;;
1.5 z
2
x
1.0 e
0.5
0.0
Figure-13-15 show the required energy and safety factor f
required probability of exceedance. For example, when require
probability of exceedance is 0.01, safety factor is about 1.4, i.e. energ
absorption of fender is required about 1.4 times energy of designed
fender by current method.
These results are shown the necessity that factors considering
design of fender are treated as variable and fender is designed b
statistical design method.
6. CONCLUSION
(1) Ships berthing energy is greatly influenced by approach velocity
This is the reason that berthing energy is proportional to square
approach velocity and standard deviation of approach velocity
is maximum value in those factors.
(2) Factors concerning berthing energy not fixed but variable. Thu
even if entrance ship is the same as design ship size, it is possible
that ships berthing energy exceed energy absorption of fender.
(3) When a fender is designed by current design method, it
necessary to consider the safety factor for fender design.
(4) In this study, it is suggested that factors considering design
fender are treated as variable.
(5) This must be said not only for fender design but also for planning
port facilities in consideration of movement of conditions such
increment of ship size.
ACKNOWLEDGEMENT
The authors express sincere appreciation to the Yokohama
Investigation and Design Offlice, Second District Port Construction
Bureau,
Ministry of Transport (Now, Ministry of Land an
Transportation) for their kind cooperation to analyze the approach
velocity.
REFERENCES
1.
Ueda Shigeru et al (2001): Statistical Design of Fenders f
Berthing Ship, 1 tb ISOPE, pp.583-588.
2. Coastal Development Institute of Technology (1999): Technica
Standards for Port and Harbour Facilities in Japan, pp.48-55.
3. Akakura Yasuhiro et al (1998): Statistical Analysis of Shi
Dimensions for the Size of Design Ship, report of Port an
Harbour Research Institute, No.9 10, ~23.
4. Moriya Kazuyoshi et al (1991): Field Investigation of Approach
Velocity of Berthing Ships, Proceedings of Coastal Engineering
Japan, Vo1.38, pp.751-755.
5. Ueda Shigeru (1981): Study on Berthing Impact Force of Ver
Large Crude Oil Carriers, Report of Port and Harbour Research
Institute, Vo1.20, No.2, pp.169-209.
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