Post on 22-Nov-2014
description
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Shigeru Ueda
Seigi Yamase
Tatsuhiko Okada
Reliability Design of Fender Systems and Mooring Facilities
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Preface Review of fender design
Reliability design method
Appropriate confidence level , safety factor , and probability of failure
Conclusion and recommendation
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Fender
Absorb ship’s berthing energy andreduce berthing impact force
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Tanker ship and FenderTanker Ship vs. Fender
0
10
20
30
40
50
60
1940 1950 1960 1970 1980 1990year
ESSO PACIFIC (51.6)
GLOBTIC TOKYO 48.5)
THE OKINOSHIMA MARU( 25.4)
THE IDEMITU MARU(20.9)
THE TOKYO MARU( 15.9)
THE TOKYO MARU(13.9)
(2.8)
CYLINDRICAL SUPER ARCH
SUPER CELL
SUPER M
CELL
HYPER CELL
DYNA ARCH
Increase of ship size requires more energy absorption
Figure 3 Load-Deflection Characteristics of Rubber Fender
0
100
200
300
400
500
600
0 10 20 30 40 50Compression Strain(% )
Reac
tion
Forc
eN)
(k
SUC1000HRH
Deflection against
Steady force 10% Allowable Deflection 35%
Rated Deflection
S. UEDA
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National Oil Stockpiling Kamigotoh Base
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Ship‘s Berthing Energy
csemd CCCCMvE 2
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dE
(kNm)energy berthing sship':dEin ton)ent (displacem mass ship:M
(m/s)velocity approach :v
factor softness:sC
factor mass virtual:mCfactorty eccentrici:eC
factorn cofigulatoberth :cC
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Deterministic Method (conventional)
Maximum or Standard Ship size: Mass of ship Design approach velocity :observed data ex: design approach velocity of some berth ;20cm/s maximum observed approach velocity was 13cm/s among 788 sets of data Virtual mass fcator, eccentricity factor : analysis Where, each factor is dealt equally weighted. But, approach velocity have greater influence to the berthing energy than the other factors.
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Approach Velocity
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Probability Distribution Function (Regression for any Confidence Level)
Confidence 50%
Confidence 75%
Probability of exceedance
0
5
10
0 10
ln(DWT)
ln(F
acto
r for
Ber
thin
g En
ergy
)
.
Table 1.Relation between Normalized Variable and Confidence LevelConfidenntial Level 50% 75% 90% 95%
Normal Value 0 0.647 1.283 1.645
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Table 2.Regression of Variables vs DWT
Table 2.Regression of Variables Vs to DWT
X X Displacementby Akakura (
)ln(953.0)ln( ln DWTPDT DT DT =0.754DT )ln(953.0874.0)ln( DWTDT Approach Velocityby Moriya (
bV )ln(338.0)ln( ln DWTPV Vbb Vb =0.655 Vb )ln(338.0215.1)ln( DWTVb Approach Velocityby Yamase (
bV )ln(419.0)ln( ln DWTPV Vbb Vb =1.326 Vb )ln(419.0531.2)ln( DWTVb Approach Velocityby Yamase (
bV )ln(128.0)ln( ln DWTPV VBb Vb =-3.772Vb )ln(128.0987.2)ln( DWTVb Virtual Mass Factorby Akakura (
mC )ln(022.0)ln( ln DWTPC Cmm Cm =0.399 Cm )ln(022.0445.0)ln( DWTCm Eccentricity Factorby Akakura (
eC )ln(015.0)ln( ln DWTPC Cee Ce =-0.477Ce )ln(015.0427.0)ln( DWTDT Approach Velocityby Yamase (
bA )ln(590.0)ln( ln DWTPA Abb Ab =3.843Ab )ln(590.0023.6)ln( DWTAb Approach Velocityby Yamase (
bA )ln(047.0)ln( ln DWTPA Abb Ab =-0.0873Ab )ln(0470.08453.1)ln( DWTAb Table 2.Regression of Variables Vs to DWT
X X Displacementby Akakura (
)ln(953.0)ln( ln DWTPDT DT DT =0.754DT )ln(953.0874.0)ln( DWTDT Approach Velocityby Moriya (
bV )ln(338.0)ln( ln DWTPV Vbb Vb =0.655 Vb )ln(338.0215.1)ln( DWTVb Approach Velocityby Yamase (
bV )ln(419.0)ln( ln DWTPV Vbb Vb =1.326 Vb )ln(419.0531.2)ln( DWTVb Approach Velocityby Yamase (
bV )ln(128.0)ln( ln DWTPV VBb Vb =-3.772Vb )ln(128.0987.2)ln( DWTVb Virtual Mass Factorby Akakura (
mC )ln(022.0)ln( ln DWTPC Cmm Cm =0.399 Cm )ln(022.0445.0)ln( DWTCm Eccentricity Factorby Akakura (
eC )ln(015.0)ln( ln DWTPC Cee Ce =-0.477Ce )ln(015.0427.0)ln( DWTDT Approach Velocityby Yamase (
bA )ln(590.0)ln( ln DWTPA Abb Ab =3.843Ab )ln(590.0023.6)ln( DWTAb Approach Velocityby Yamase (
bA )ln(047.0)ln( ln DWTPA Abb Ab =-0.0873Ab )ln(0470.08453.1)ln( DWTAb
Variables Regression Formula and 95% Confidence Value X X
Regression )ln(953.0)ln( ln DWTPDT DT Displacement
by Akakura ( DT ) 95% confidence )ln(953.0874.0)ln( DWTDT DT =0.754
DT =0.073
Regression )ln(338.0)ln( ln DWTPV Vbb Approach Velocity
by Moriya (bV ) 95% confidence )ln(338.0215.1)ln( DWTVb
Vb =0.655
Vb =0.340
Regression )ln(419.0)ln( ln DWTPV Vbb Approach Velocity
by Yamase (bV ) N port 95% confidence )ln(419.0531.2)ln( DWTVb
Vb =1.326
Vb =0.733
Regression )ln(128.0)ln( ln DWTPV VBb Approach Velocity
by Yamase (bV ) M port 95% confidence )ln(128.0987.2)ln( DWTVb
Vb =-3.772
Vb =0.477
Regression )ln(022.0)ln( ln DWTPC Cmm Virtual Mass Factor
by Akakura (mC ) 95% confidence )ln(022.0445.0)ln( DWTCm
Cm =0.399
Cm =0.036
Regression )ln(015.0)ln( ln DWTPC Cee Eccentricity Factor
by Akakura (eC ) 95% confidence )ln(015.0427.0)ln( DWTDT
Ce =-0.477
Ce =0.030
Regression )ln(590.0)ln( ln DWTPA Abb Approach Velocity
by Yamase (bA ) N port 95% confidence )ln(590.0023.6)ln( DWTAb
Ab =3.843
Ab =1.325
Regression )ln(047.0)ln( ln DWTPA Abb Approach Velocity
by Yamase (bA ) M port 95% confidence )ln(0470.08453.1)ln( DWTAb
Ab =-0.0873
Ab =1.1748
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Load-Deflection Characteristics of Rubber Fender
Fender Performance Curve
0.00.2
0.40.60.8
1.01.2
0 10 20 30 40 50 60 70Compression strain (%)
Rea
ctio
n Fo
rce
0.00.4
0.81.21.6
2.02.4
Ener
gyA
bsor
ptio
n
Mavimum Reaction Force
MaxumumEnergy Absorptoin
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Energy Absorption of Fender
0
5
10
15
0.90
0.92
0.94
0.96
0.98
1.00
1.02
1.04
1.06
1.08
1.10
Factor Z
Freq
uenc
yMeansurement Value Normal Distribution
μ Z=0.997
σ Z=0.031
Example of fender performance distribution
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FIRST ORDER RELIABILITY DESIGN METHOD AND THE SAFETY INDEX
Target Safety Index and Partial Safety Factor Nagao, Okada and Ueda (2003) applied the First Order Reliability Method to fender design for berthing ship
288.022/1 kDWTCePCMPVbPDTPcatkZ DWTPPPPEZGkCekCMkVbkDT
k
XXTXX X
V i
)1(
The partial safety factor of each item related to the ship berthing energy
)(2XXX
αis the sensitive factor of the variable Χ
.
0.1)( 2 X
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PROBABILITY DISTRIBUTION FUNCTION AND THE PROBABILITY OF FAILURE
Generally it is difficult to calculate the probability of failure pf precisely.
It is important for the reliability design to establish the allowable probability of failure or target Pfa, , safety index βT.
The probability of failure pf is calculated by the following equation.
dssp f )(1
z
zzs
Where, )(s is the standard normal distribution.
Monte-Carlo simulation method is employed to calculate the probability of failure pf .
Comparison is made beween MSC and FORM.
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Sensitive factorSensitive factor for approach velocity is most influential
Sensitive factor for ship size (DWT) is also influential
shi p si zeDWT Z P DT P Vb P CM P Ce DWT10,000 -0.26715,000 -0.23320,000 -0.27535,000 -0.194
-0.051 -0.044
sensitive factor α X
0.044 -0.103 -0.961
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Table 3. Partial Safety Factor
μ X σ X VX α X β T γ X β TO γ XOZ 0.997 0.031 0.031 0.044 0.997 0.996
P DT 2.131 0.156 0.073 -0.103 1.017 1.020P Vb 2.040 0.714 0.350 -0.961 1.741 1.875P Cm 1.491 0.054 0.036 -0.051 1.004 1.005P ce 0.621 0.019 0.030 -0.044 1.033 1.003
DWT(35,000) 30265 15117 0.499 -0.194 1.214 1.252
2.203 2.600
Fender is designed in accordance with the current design method and its energy absorption is 317kNm for the 35,000 container ship.
γ : partial safety factor
This is a instance and is not be applicable to a ll berth
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MONTE-CARLO SIMULATION
Monte-Carlo Simulation was done by use of probability density distribution functions mentioned above. The probability of failure is given by following equation.
NqPf
Where, q : the number of trails when the performance function becomes zero and or negative
N : number of trials.
,
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Comparison the Results by FORM and Monte Carlo Simulation
Table 4. Comparison of the Results by FORM and Monte Carlo simulation.
γ
p f
FORM 1.613 0.0147MCS 1.644 0.0168
Where , γ is the ratio of required energy absorption to meet the failure probability against a fender designed by conventional method for a 35,000 container ship to absorp 317kNm. (95% confidence level )
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Comparison the Results by FORM and Monte Carlo Simulation
Largest 1.25Smallest 1.75Largest 1.5Smallest 2
1.752.0 or
Factor for Abnormal Berthing Impact(Cab) -Safety Factor
General CargoRo-Ro and Ferry
Tanker andBulk
Container
Table 5. Factor for Abnormal Berthing Impact PIANC2002,
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SAFETY FACTOR OF ENERGY ABSORPTION
0100200300400500600700800900
CurentDesign
0.01 0.006 0.004 0.002
Required Probability of Exceedance
Req
uire
d E
nerg
yA
bsor
ptio
n of
Fen
der
(kN
m)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Saf
ety
Fact
or
RequiredEnergyAbsorption ofFender (kNm)
Safety Factor
Figureure.4 Probability of Failure and the Safety Factor
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Importance measuring approach velocity at each berth
Approach Velocity is the most important factor and
it is influenced by following factors
Ship size Location and condition of basin (exposed or sheltered) Berthing manoeuvring Tug assistance Use of ship’s thruster
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Automatic Berthing System (RTK-GPS)
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CONCLUSIONS
Reliability design method would be established through intensive effort of field data collection.
Application of numerical simulation method to obtain the probability of failure is useful.
Data collection of appraoch velosity is strongly recommended.
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Acknowledgement
Thank you very much for your kind cooperation!!