1

Shigeru Ueda

Seigi Yamase

Tatsuhiko Okada

Reliability Design of Fender Systems and Mooring Facilities

2

Preface Review of fender design

Reliability design method

Appropriate confidence level ， safety factor ， and probability of failure

Conclusion and recommendation

3

Fender

Absorb ship’s berthing energy andreduce berthing impact force

4

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

6

National Oil Stockpiling Kamigotoh Base

7

Ship‘s Berthing Energy

csemd CCCCMvE 2

21

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

8

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.

9

Approach Velocity

11

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

12

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 )

21

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!!