CDIT Library No.1

Guidelines for Design and Testingof
Rubber Fender Systems

June 2019

Coastal Development Institute of Technology

Foreword to the English Edition

The fender system plays a key role in the safe berthing of a vessel and stable loading/unloading as
auxiliary equipment at the mooring facility. “The Technical Standards and Commentaries for Port and Harbor
Facilities in Japan” provide the design method and “the Standard Specifications for Port & Harbor Projects”
provide the specifications and testing methods of rubber fender system. Although a change in performance of
rubber fender due to differences in berthing speed and environmental conditions was not considered in thedesign of fender systems according to above, knowledge of the effect of performance changes taking thecharacteristics of rubber into consideration is increasing in recent years.
Rubber is a material which has viscosity and elasticity and works as a shock absorber for huge, heavy andhard materials like concrete and steel. On the other hands, it is known that the performance of rubber fenderis sensitive to using condition and environment.
Accordingly, in order to provide accurate and advanced design and testing methods of rubber fenders
system, it was decided to draw up new practical guidelines for more logical design and testing methods of therubber fenders system indicating the methods of evaluating the effects of performance changes due toberthing speed and environmental conditions. Collaborative research by the Coastal Development Institute ofTechnology and major five manufacturers of the rubber fender system in Japan started in August 2015. Anexpert committee was established in fiscal 2017 where discussions had been made on the draft guidelines
prepared by collaborative research, which is now finalized and published as the Guidelines for the Design
and Testing of Rubber Fender Systems. These guidelines are intended to be specific and easy to understandwith many graphical references and design examples of rubber fenders system in the Appendices.
It is my great pleasure to publish the English Edition of this guideline and I hope this will be widely
disseminated and contribute the technology of rubber fender in ports around the world.

Shigeo Takahashi, President
Coastal Development Institute of Technology
August, 2019

Editorial Committee (Original as of 2018)
Committee Chairman:

Shigeru Ueda, Professor Emeritus, Tottori University

Committee member:

Satoru Shiraishi, Professor, Hokkaido University of Science
Mitsuru Kawamata, Deputy Director, Engineering Administration Office, Engineering
Planning Division, Port and Harbor Bureau, Ministry of Land,
Infrastructure, Transport and Tourism,
Masafumi Miyata, Head, Port Facilities Division, National Institute for Land andInfrastructure Management, Ministry of Land, Infrastructure, Transport
and Tourism
Haruo Yoneyama, Director, Coastal and Ocean Engineering Department, Port and Airport
Research InstituteToshio Endo,
Director of Yokohama Port and Airport Technical Research Office,Kanto Regional Development Bureau, Ministry of Land, Infrastructure,
Transport and Tourism
Takashi Masaoka, Former General Manager, Planning Department, Yokohama-Kawasaki
International Port Corporation
Kousuke Shibazaki, Manager, Engineering, Planning Department, Yokohama-Kawasaki
International Port Corporation

Secretariat Office:Shuji Yamamoto, Councilor, Coastal Development Institute of Technology
Yoshiyuki Ozawa, Chief Reaeacher, Research Department, Coastal Development
Institute of Technology
Yuusuke Motomizu, Former Researcher, Research Department, Coastal Development
Institute of Technology

Working Group Members: Hitoshi Akiyama, General Manager, Fender Department, Bridgestone Corporation
Motohiro Yasui, Manager, Marine Fender Department, Bridgestone Corporation
Hiroyoshi Izunome, General Manager, Marine & Civil Products, Industrial Rubber
Products Division, Meiji Rubber & Chemical Co.,Ltd
Yuuji Shiki, General Manager, Engineering department, Meiyu Kohan Co., Ltd.
Hiroaki Koda, General Manager, Production Engineering Section, Shibata Industrial
Co.,Ltd
Masamitsu Ikebe, Senior Manager, Marine Engineering Section, Shibata Industrial
Co.,Ltd
Masanori Nakagaki, Counselor, Engineering Team, Tokyo Engineering Group,Engineering Department, Seibu Polymer Corporation.
Yohei Watari, Chief, Engineering Team, Tokyo Engineering Group, Engineering
Department, Seibu Polymer Corporation.
Hiroshi Noiri, Manager, Infrastructure Products Business Unit, Hybrid Rubber Products
HQS., Sumitomo Rubber Industries, Ltd.
Tatsuya Maruyama, Chief, Infrastructure Products Business Unit, Hybrid Rubber
Products HQS., Sumitomo Rubber Industries, Ltd.

Guidelines for Design and Testing of Rubber Fender Systems
CONTENTS
1

Preface・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 1

2Nomenclature・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 2

3Role of rubber fenders and their types・・・・・・・・・・・・・・・・・・・・・・・・ 5
3.1 General・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 5
3.2 Role of rubber fenders・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 5
3.3 Rubber fenders with fender panels・・・・・・・・・・・・・・・・・・・・・・・ 7
3.4 Rubber fenders without fender panels・・・・・・・・・・・・・・・・・・・・・・ 8
References ・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 10

4

Performance of rubber fenders・・・・・・・・・・・・・・・・・・・・・・・・・・ 11
4.1 General・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 11
4.2 Influence factors・・・・・・・・・・・・・・・・・・・・・・・・・・・・・
11
4.2.1 Coefficient of production tolerance: CP・・・・・・・・・・・・・・・・・・・ 12
4.2.2 Coefficient of angular berthing: Ca・・・・・・・・・・・・・・・・・・・・・ 13
4.2.3 Velocity factor: VF・・・・・・・・・・・・・・・・・・・・・・・・・・・ 16
4.2.4 Temperature factor: TF・・・・・・・・・・・・・・・・・・・・・・・・・ 21
4.2.5 Ageing factor: Cag・・・・・・・・・・・・・・・・・・・・・・・・・・・ 24
4.2.6 Repetition factor: Cr・・・・・・・・・・・・・・・・・・・・・・・・・・・ 26
4.2.7 Creep characteristic・・・・・・・・・・・・・・・・・・・・・・・・・・・ 27
References ・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 28

5

Design・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 30
5.1 General・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 30
5.2 Design procedure of rubber fender・・・・・・・・・・・・・・・・・・・・・・・ 30
5.3 Effective berthing energy・・・・･･･・・・・・・・・・・・・・・・・・・・・
31
5.4 Influence factors・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 34
5.4.1 Condition from design background・・・・・・・・・・・・・・・・・・・・・ 34
5.4.2 Patterns of influence factors・・・・・・・・・・・・・・・・・・・・・・・・ 35
5.4.3 Example of managing the influence factors and their patterns・・・・・・・・・・ 36
5.5 Determination of influence factors・・・・・・・・・・・・・・・・・・・・・・・ 39
5.5.1 Calculation of design energy absorption: EA－・・・・・・・・・・・・・・・・・ 39
5.5.2 Calculation of design reaction force: R+・・・・・・・・・・・・・・・・・・・ 40
5.5.3 Calculation of design factors for mooring analysis・・・・・・・・・・・・・・・ 40
5.5.4 Consideration of number and length of fenders・・・・・・・・・・・・・・・・ 41
5.6 Arrangement of rubber fenders・・・・・・・・・・・・・・・・・・・・・・・・ ・ 41
5.6.1 Installation pitch of fenders・・・・・・・・・・・・・・・・・・・・・ ・・・ 42
5.6.2 Vertical installation of fenders・・・・・・・・・・・・・・・・・・・・・・・ 44
5.7 Detailed design and consideration・・・・・・・・・・・・・・・・・・・・・・・ 46
5.7.1 Allowable hull pressure・・・・・・・・・・・・・・・・・・・・・・・・・・ 46
5.7.2 Load cases for fender panel・・・・・・・・・・・・・・・・・・・・・・・・ 47
5.7.3 Design considerations・・・・・・・・・・・・・・・・・・・・・・・・・・ 48
5.7.4 Load cases for regions surrounding fender panel and chains・・・・・・・・・・・ 49

5.8 Corrosion protection of steel parts・・・・・・・・・・・・・・・・・・・・・・・ 54
5.8.1 Painting・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 55
5.8.2 Plating・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 55
5.9 Allowable stress of steel material ・・・・・・・・・・・・・・・・・・・・・・・ 56
References ・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 57
6

Testing・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 58
6.1 General・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・58
6.2 Test classification by purpose・・・・・・・・・・・・・・・・・・・・・・・・・ 58
6.3 Development test・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 59
6.3.1 Static compression test (Standard compression test)・・・・・・・・・・・・・・ 59
6.3.2 Angular compression test・・・・・・・・・・・・・・・・・・・・・・・・・ 61
6.3.3 Velocity dependency test・・・・・・・・・・・・・・・・・・・・・・・・・ 64
6.3.4 Temperature dependency test・・・・・・・・・・・・・・・・・・・・・・・ 72
6.3.5 Relationship between temperature factor and velocity factor・・・・・・・・・・・ 78
6.3.6 Material test・・・・・・・・・・・・・・・・・・・・・・・・・・・ ・・・80
6.4 Authentication tests・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 81
6.4.1 Durability・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 81
6.4.2 Other authentication tests・・・・・・・・・・・・・・・・・・・・・・・・ 82
6.5 Quality verification test・・・・・・・・・・・・・・・・・・・・・・・・・・・ 82
6.5.1 Static compression test・・・・・・・・・・・・・・・・・・・・・・・・・・ 82
6.5.2 Material test・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 85
6.6 Influence factors and classification of tests・・・・・・・・・・・・・・・・・・・ 87
6.7 Similarity rules in scale model testing・・・・・・・・・・・・・・・・・・・・・・88
References・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 94
Appendices ・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 95
A.1 General ・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 95
A.2 Pattern A: Manufacturing tolerance ・・・・・・・・・・・・・・・・・・・・・・ 95
A.2.1 General cargo vessel of 5,000 DWT: Without fender panel ・・・・・・・・・・・ 95
A.2.2
Allowable berthing velocity of oversized vessel for existing fender・・・・・・・ 97
A.3 Pattern B: Considering major influence factors ・・・・・・・・・・・・・・・・・ 98
A.3.1 General cargo vessel of 30,000 DWT: Without fender panel ・・・・・・・・・・ 98
A.3.2 Tanker of 100,000 DWT: With fender panel・・・・・・・・・・・・・・・・ 103
A.3.3 Long distance ferry of 10,000 DWT: With large fender panel・・・・・・・・・・ 108
A.4 Pattern C: Fender design via mooring analysis ・・・・・・・・・・・・・・・・・ 114
A.5 Calculation example: Effective berthing energy ・・・・・・・・・・・・・・・・ 122
References ・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・・ 126

Chapter 1

PrefaceA rubber fender is a shock absorber installed on a wharf to absorb the berthing energy of a vessel to relieve impact. In
the past, timber and old tires were used before rubber fenders capable of efficiently absorbing the berthing energy weredeveloped. As vessels became larger, the rubber fenders were enhanced in terms of performance and size. A criticalfactor regarding the selection of rubber fenders is the effective berthing energy of the vessel. With increase in the vessel
size, the rubber fenders are required to absorb a large amount of energy, and buckling-type rubber fenders, in which thereaction force does not increase considerably, have been widely used.
In Japan, the design method for rubber fenders is specified by the Technical Standards and Commentaries of Portsand Harbour Facilities in Japan 1), and the specifications and test methods are specified by the Standard Specifications
for Ports and Harbour Works 2). In contrast, overseas, the British Standard 3), PIANC (the World Association for
Waterborne Transport Infrastructure) Report 4) and PIANC Guidelines 5) regulations are widely applied. The PIANC
Guidelines 5), issued in 2002, propose a design method that takes into account the operational conditions and naturalenvironment and their influence on the rubber fender performance in terms of, for example, the berthing velocity andtemperature. In Japan, for a long time, only production tolerance has been considered as a performance influence factor;
however, overseas, the design and test methods are expected to incorporate the influence of the berthing velocity andtemperature. In addition, it is necessary to consider the ageing performance of the rubber fenders to make effective useof existing facilities and prolong the service life.
Considering this background, this guideline is designed in accordance with the PIANC Guidelines 5) forbuckling-type rubber fenders, with the objective of taking into consideration factors such as the ageing of rubber
fenders and providing a test method for the design factors. In the design method, in addition to the production tolerance
conventionally considered in Japan, the influence factors of rubber fenders, such as the berthing angle, berthing velocity,temperature, repetition fatigue, ageing and the effect of creep characteristics, are considered. Furthermore, criticalpoints regarding the installation distance and height of fenders and design methods for fender panels and chains that areoften installed in the case of large rubber fenders are presented. Furthermore, as the test method, we propose a standard
method for appropriately evaluating the performance of rubber fenders required for the given design method. The
design case study is presented as an appendix.

[References]
1) Ports and Harbours Association of Japan (PHAJ): Technical Standards and Commentaries of Ports and Harbour
Facilities in Japan, pp. 1262-1268, 2018
2) Ports and Harbour Bureau, Ministry of Land, Infrastructure, Transport and Tourism (MLIT): Standard Specifications
for Ports and Harbor Works, Vol.1, pp.71-72, 20173) British Standard: Maritime Structures-Part 4 Code of Practice for Design of Fendering and Mooring Systems, 2014
4) PIANC: Report of the International Commission for Improving the Design of Fender Systems, Bulletin No.45, 1984
5) PIANC: Guidelines for the Design of Fenders System, Report of Working Group 33 of the Maritime Navigation
Commission, 2002

1

Chapter 2
Nomenclature

SymbolExplanation

A
Asway
B

：
：
：

Effective contact area of fender panel
Lateral wind pressure area of vessel
Beam of vesselCa：

Coefficient of angular berthing

CaE：

Energy coefficient of angular berthing

CagR

：

Reaction force coefficient of ageing

CagE

：

Energy coefficient of ageing

CaR：

Reaction force coefficient of angular berthing

CaR(ε)：

Reaction force coefficient of angular berthing at strain ε

Cb：Block coefficient

Cc：

Berth configuration factor

Ce
Cm

：
：

Eccentricity factor
Virtual mass factor

Cp：

Coefficient of production error

Cr：

Coefficient of repetition

Cre

：

Cs

：

Coefficient of recovery
Softness factor

Cw：

Wind drag coefficient of vesselCΦ:

Coefficient of angular compression directiond：Draught of vessel

D：

Allowable deflection of fender

DS：

Height of vesselDT：

Displacement tonnage of vessel (t)e：Ratio of fender spacing to perpendicular length

E：

Young’s modulus

EA：

Energy absorption (standard value in catalogue)

EAag

：

Energy coefficient of ageing

EAT：

Energy absorption at temperature T

EAθ

：Energy absorption at berthing angle θ

EAV
Eb

：
：

Energy absorption at berthing velocity V
Effective berthing energy

f
F

：
：

Freeboard height of vessel
Berthing force

Fj：

External force vector of moored vessel

Fm
FR
FR
H

：
：
：
：

Reaction force of scale model
Reaction force of actual-size fenderWind drag on vessel
Fender height

HF：

Height of fender panel

2

Symbol

Explanation

HFe：

Effective height of fender panel

Hp：

Allowable hull pressure

h
k

：
：

Residual height of fender after compression
Parameter for berthing point between fenders

Kij：

Restoration coefficient matrix of moored vessel

Kr：

Radius of vessel rotation

L：

Distance between contact point and fender centre

Lf：

Length of fender

Lc：

Length of chain

Lij：

Delay function of moored vessel

Loa
Lpp

：

Overall length of vessel
Length between perpendiculars

Ly
mij

：
：

Contact length of V-type fender
Additional mass matrix of moored vessel

M：

Mass of vessel

Mｆ：

Rotational moment at fender top

Mij

：

Nij

：

Mass matrix of moored vessel
Dumping coefficient matrix of moored vessel

P
R

：
：

Average hull pressure
Reaction force of fender

RR：

Standard reaction force of fender (catalogue value)RF1(ε)：

Reaction force at strain ε under static compression loading

RF2(ε)：

Reaction force at strain ε under static unloading

Rr：

Radius of hull curvature at berthing point

RS：

Distance between berthing point and vessel gravity centre parallel to berth line

RV：

Reaction force of fender at compression speed V

RV(ε)

：

Reaction force at compression speed V and strain εRT：Reaction force of fender at temperature T

RT(ε)
R(ε)

：
：

Reaction force of fender at temperature T and strain ε
Reaction force of fender at strain εRθ：Reaction force at berthing angle θ

Rθ(ε)

：

Reaction force at berthing angle θ and strain ε

S
T
TF

：
：
：

Installation spacing of fenders; scale of modelling
Tension of chain
Temperature factor

TFR：

Temperature factor of reaction force

TFE：

Temperature factor of energy absorption

TFR(ε)：

Temperature factor of reaction force at strain εTFE(ε)：

Temperature factor of energy absorption at strain ε

Ua
V

：
：

Wind speed
Compression speed (Strain rate)

VB：

Berthing velocity (Speed)

VF：

Velocity factor：

3

Symbol

Explanation

VFR：

Velocity factor of reaction force

VFE：

Velocity factor of energy absorption

VFE(ε)：

Velocity factor of energy absorption at strain ε

VFR(ε)：

Velocity factor of reaction force at strain εV0：Static compression speed (V0=0.01–0.3%/s)

WF：

Width of fender panel

WFe：

Effective width of fender panel

WW
x

：
：

Weight of fender panel
Displacement of vessel in sway

Xi(t)

：

Displacement vector of vessel centre at time t

α
β

：
：

γ

：

δ

：

δ0

：

δ1
ε
η
θ
θa
θW
μ
μV
ρ
σ
τ
φ

：
：
：
：
：
：
：
：
：
：
：
：

Ratio of parallel bar length to perpendicular length of vessel
Angle between chain and fender panel
Angle between velocity vector and line connecting berthing point and centre ofgravity of vessel
Deflection of fender
Deflection at fender centre when vessel contacts the full surface of fender panel
during angular berthing
Virtual displacement of origin under catalogue value of angular performance
Strain (deflection) of object (fender)
Viscosity coefficient of rubber
Berthing angle; angle of berthing point
Wind incident angle to vessel
Wave incident angle to vessel
Friction coefficient
Average berthing velocity
DensityStandard deviation; stressStress due to viscosity of rubber
Angle of compression direction

4Chapter 3
Role of rubber fenders and their types
3.1 General
A rubber fender is a shock absorber installed on a wharf to absorb the berthing energy of a vessel to be berthed andmoored. Since various types of rubber fenders are manufactured according to the application, it is necessary to selectand design fenders appropriately according to the ship type and berth type. This document focuses on buckling-type
rubber fenders because of their large ratio of energy absorption to reaction force for ship berthing. The purpose, type,requirements and buckling-type performance of rubber fenders are described in the following subsections.
The following types of rubber fenders are also used in ports; however, they are not described in this document
because they differ from buckling-type rubber fenders.
(1) Rubber fenders with gradually increasing reaction force, such as cylindrical rubber fenders(2) Pneumatic fenders (for details, readers can refer to ISO 17357-1)(3) Rotary fenders(4) Shock absorbers such as square-type, D-type and ladder fenders(5) Rubber net and corner protection material(6) Rubber fenders applied in facilities other than ship mooring facilities, such as bridge piers, canals and locks

3.2 Role of rubber fenders
A rubber fender is a shock absorber installed on a wharf to absorb the berthing energy of a vessel. Timber and old tires
were used as shock absorbers until the first rubber fenders were developed in the 1950s. The concept of the role ofrubber fenders in the berthing process is illustrated in Figure 3.2.1.

Here,

Eb ：Effective berthing energy (kNm)
M : Mass of vessel (＝Displacement tonnage: DT, t)
VB : Berthing velocity (m/s)
Ce : Eccentricity factor
Cm : Virtual mass factor
Cc : Berth configuration factor
Cs : Softness factor
Fig. 3.2.1 Concept of berthing
As shown in Fig. 3.2.1, the effective berthing energy Eb is the multiplication product of the normal kinetic energy ofvessel: 1/2・M・VB2 and the coefficients (Ce, Cm, Cc, and Cs), as defined in equation (5.3.1) in Chapter 5. Furthermore, as
shown in Fig. 3.2.2, the area between the reaction force curve and deflection amount in the x-axis corresponds to theamount of absorbed energy. Thus, for fenders, the absorbed energy EA must be equal to or more than the effective
berthing energy Eb of the vessel.

5Fig. 3.2.2 Performance curve of buckling-type rubber fender
The reaction force R of a fender acts as a horizontal force on the wharf or on the side hull of the berthing vessel; thus,
it is desirable that the reaction force is as small as possible. In contrast, a larger energy absorption EA is desirable.
Therefore, as shown in Fig. 3.2.2, the reaction force curve of the fender exhibits a high spring constant at the initial stageof compression and a constant portion later at higher deflection. Such characteristics are a result of the buckling
deformation of the rubber fenders. The initial stage of compression corresponds to a high spring constant; however, oncethe peak of reaction force is exceeded, the spring constant decreases due to buckling, and as compression progresses, thevalue of the spring constant increases again, exceeding the value of the previous peak. Assuming that the point at which
the reaction force exceeds the peak again is the maximum deflection, and the reaction force RR at the peak point is the
maximum reaction force; if the compression is within the maximum deflection, the reaction force is the maximum
horizontal force to the wharf and vessel hull. This mechanism corresponds to the buckling-type performance, and it iscurrently the mainstream concept for the design of rubber fenders. In the PIANC Guidelines 1), the coefficient obtainedby dividing the energy absorption EA by the maximum reaction force RR is known as the fender factor. In terms of fender
design, maximizing the fender factor is considered essential to ensure efficient performance. For the same type of rubber
fenders, if performance fluctuations exist due to the design condition, the maximum reaction force and the maximum
deflection in the design condition are considered to be the design reaction force and design deflection, respectively. This
aspect is explained in detail in Chapter 4.
With increase in the size of vessels, the requirements for rubber fenders have diversified; furthermore, it has become
necessary to increase the area contacting the vessel hull to reduce the contact pressure, taking into account the hullstrength. To this end, a configuration in which a fender panel is fixed to the front of a rubber fender is widely used. In
particular, fender panels are attached to most rubber fenders for large vessels. Rubber fenders without fender panels areprimarily used for medium- or small-sized vessels for which the hull pressure is not a design issue. Thus, a rubber fenderthat satisfies the given requirements can be selected. The fender performance can also be adjusted by changing therubber material, that is, by using materials with a different performance grade or rubber grade.
Fenders also play a crucial role in mooring. A situation in which a ship is moored on a quay is shown in Fig. 3.2.3. In
this case, the fender acts when the vessel approaches the quay, whereas the tension of the mooring ropes is the acting
force when the vessel moves farther.

Fig. 3.2.3 Concept of vessel moored using fenders and ropes

63.3 Rubber fenders with fender panels
A fender panel is a frame made primarily of steel, which is fixed to the front of a rubber fender to lower the averageface pressure. A rubber fender with a panel has the disadvantages of complex design due to the increase in the number ofsystem parts such as the panel, pads and chains; however, it also has several advantages, as listed. With the increase in
the size of vessels, several large fenders have been equipped with fender panels.
(1) The average hull pressure can be adjusted.
(2) The rubber is not in direct contact with the vessel hull.
(3) The system demonstrates satisfactory performance, even in the case of partial contact with projections on thehull.
(4) It is possible to adjust the panel length and number of fenders per panel.
A typical installation of rubber fenders with panels (vertical cylinder type, rectangular type) is shown in Fig. 3.3.1.1 andFig. 3.3.1.2.

Fig. 3.3.1.1 Rubber fenders with panel（vertical cylinder type）

Fig. 3.3.1.2 Rubber fenders with panel（rectangular type）

The shape of rubber fenders varies depending on the manufacturer. Several examples are shown in Fig. 3.3.2 to Fig.
3.3.6. A special type of V-type fender can have a panel fixed on the top, as shown in Fig. 3.3.6.

Fig. 3.3.2 Vertical cylinder typeFig. 3.3.3 Cone type7

Fig. 3.3.4 Rectangular column(one-piece)

Fig. 3.3.5 Rectangular column(Separated element)

Fig. 3.3.6 V-type fender with panel
There are no specific criteria regarding whether a rubber fender should be fitted with fender panels. Panels are often
installed if there is an allowable limit for the hull pressure. The considerations for hull pressure are described in Section
5.7.1 in Chapter 5. Even if there is no restriction regarding the hull pressure, a fender panel may be required when a large
contact area is required, for example, in the case of fenders for ferries.

3.4 Rubber fenders without fender panels
In this section, V-type rubber fenders are considered as rubber fenders without fender panels. A V-type rubber fender
has a V-shaped cross section with steel plates embedded in the fixing flange portion for installation. The fender has thesame cross-sectional shape in the longitudinal direction. Since the rubber comes in direct contact with the vessel hull,
partial damage is likely to occur. Energy absorption occurs only due to the contact length, and the contact pressure ishigh. Although these are notable disadvantages, V-type rubber fenders have the following advantages.
(1) The application range is wide because the length can be adjusted.
(2) Since such fenders exhibit buckling-type performance, the energy absorption is large even for small-sized
fenders.
V-type rubber fenders were widely used as the first rubber fenders with buckling-type performance. The typicalcross-sectional shapes and installation of V-shaped rubber fenders are shown in Fig. 3.4.1.

8

Fig. 3.4.1 V-type fender: Section and installation
This type of rubber fender has had a long development history; first, a flange integrated-type fender was developed,
as shown in Fig. 3.4.2. Since then, various shapes have been developed, which have been incorporated in V-type rubber
fenders.

Fig. 3.4.2 Flange integrated

Fig. 3.4.3 Centre supported

Fig. 3.4.4 With resin pad

V-type rubber fenders can be widely applied according to the conditions of ports and vessels by changing the lengthand mounting arrangement. Typical mounting arrangements and features are presented in Table 3.4.1. For example, if theship has a belt on the hull, the effective berthing energy can be absorbed by the horizontal fenders, although the hull belt
may ride on the fender and damage it. Furthermore, in the case of vertical installation, if a horizontal hull belt is present,
the load is concentrated since contact occurs only at the intersection. In such a case, alternate vertical and horizontal
installation can be employed; the effective berthing energy is absorbed by the horizontal fenders, while the verticalfenders prevent the belt from being lifted. Alternatively, the rubber fenders with panels, as described in the previous
section, can be applied.
Moreover, as shown in Fig. 3.4.5, a rubber fender shaped such that the V-shaped cross-section is pivoted is alsoavailable. The length of such fenders cannot be changed; however, such fenders are nondirectional to angular and shear
deformations.

Fig. 3.4.5 Pivoted V-type fender9

Table 3.4.1 Typical arrangements and features of V-type rubber fender[References]
1) PIANC: Guidelines for the Design of Fenders System, Report of Working Group 33 of the Maritime Navigation
Commission, 2002

10

Chapter 4
Performance of rubber fenders
4.1 GeneralIn the design process, the performance of rubber fenders is considered in terms of the deflection–reaction force
characteristics at compression and the energy absorption calculated from these characteristics. Rubber has visco-elastic
properties, and its performance is affected by the natural environment and conditions of use. Factors that affect theperformance are called influence factors, and they must be taken into consideration when designing rubber fenders. In
the PIANC Guidelines 1), factors such as temperature and the influence of berthing speed are specifically defined. The
performance under deceleration from the berthing velocity is called the rated performance as it is similar to that during
actual berthing. This book defines the standard performance as one that is more manageable and demonstrable while
being consistent with the guidelines. In addition, other influence factors introduced in the Technical Standards andCommentaries of Ports and Harbour Facilities in Japan 2), 3), which include the angle, repetition fatigue, ageing, andcreep, are also considered.

4.2 Influence factors
The Technical Standards and Commentaries of Ports and Harbour Facilities in Japan 2), 3) introduce the following
seven factors that affect the performance of rubber fenders. In this book, the standard conditions for each factor are set
as follows. The concept of influence coefficients and their effect on the fender design are clarified in Sections 4.2.1 to
4.2.7.
Influence factor(1) Production tolerance: CP(2) Angular factor: Ca(3) Velocity factor: VF(4) Temperature factor: TF(5) Ageing: Cag(6) Repetition fatigue: Cr(7) Creep characteristics

Standard condition
1.0 (Standard value)Standard angle θ0 = 0°
Standard strain rate V0 = 0.01 to 0.3%/sStandard temperature T0 = 23°C
0 years after production (in principle, within 6 months)
1.0 (Standard value: the first performance value after fender has been compressed
3 times or more and left for one hour or more)
1.0 (No steady load)

A factor influencing the performance can be expressed as in equation (4.2.1) or equation (4.2.2) in terms of thecorresponding ratio to the standard performance. The standard performance refers to the basic performance described in
manufacturers’ catalogues, and it pertains to the performance when all influence factors (1) to (7) correspond to thestandard conditions. The performance pertaining to actual design conditions is known as the design performance.

Influence factor of reaction force =Reaction force under influence factor
Reaction force pertaining to standard performance(4.2.1)

Influence factor of energy absorption=

Energy absorption under influence factor
Energy absorption pertaining to standard performance(4.2.2)

Regarding the velocity factor, the PIANC Guidelines 1) specify the rated performance as corresponding todecelerating compression from the initial speed of 0.15 m/s. However, in this document, apart from the rated
performance, the performance at a sufficiently slow speed is specified as the standard performance. This definition is11

simply a matter of convenience and ability of the test facility. Although the rated performance should be exhibited in
actual berthing, the demonstrable performance is regarded as the standard performance. The practical design is expected
to correspond to the design performance based on design conditions.
Since the influence coefficients change because of compressive strain, equations (4.2.1) and (4.2.2) can be obtained
individually for each strain. The final value obtained at the design strain is termed as the influence factor, and a value at
any other strain is known as a strain-specific influence factor. When the performance curve exhibits a shape similar(within 3% of error) to that of the variation of the influence factor, the influence factor is constant regardless of thestrain. In such a case, the influence coefficients of the reaction force and energy absorption are also equivalent. Whenselecting a rubber fender, it is not necessary to determine strain-specific values, and determining only the coefficient at
the design strain is sufficient. Thus, the strain-specific influence factors are considered only when required.
4.2.1 Coefficient of production tolerance: CP
The ratio of static compression test results of an individual fender to the standard performance (catalogue value) isdefined as the coefficient of production tolerance, Cp, and it can be defined as in equations (4.2.3) and (4.2.4).
Production tolerance of reaction force:
Production tolerance of energy absorption:

CpR ＝ R
CpE ＝ E

／
／

RR
EA

(4.2.3)(4.2.4)

Here,

CpR
R
RR
CpE
E
EA

：
：
：
：
：
：

Production tolerance of reaction force
Reaction force during compression test under standard condition
Standard reaction force (catalogue value)
Production tolerance of energy absorption
Energy absorption during compression test under standard condition
Standard energy absorption (catalogue value)

Rubber fenders are made primarily of natural rubber produced from sap and synthetic rubber made from petroleum;
the rubber is mixed with chemicals, such as sulfur and carbon, and subsequently vulcanized by heat and pressure.
Therefore, the fender performance is different under various conditions such as seasonal variations and differences in
the manufacturing processes. Fig. 4.2.1 shows an example of the frequency distribution of the ratios of the test values tothe catalogue values of the energy absorption (CpE) of various rubber fenders pertaining to different manufacturers 4).
According to Fig. 4.2.1, the production tolerance generally falls within ± 10%. Furthermore, since the change in shapesof performance due to the production tolerance is nearly negligible, the coefficients of reaction force and energy
absorption may be equivalent (Cp = CpR = CpE).

12

Fig. 4.2.1 Distribution of production tolerance 4)
4.2.2 Coefficient of angular berthing: Ca
When a rubber fender is angularly compressed, the following two types of inclination angles can be considered. Notethat the angular compression described in case (2) is not the same as angular berthing. The inclination angle in case (1)is the angle between the side of the vessel hull and the rubber fender in contact with the vessel, and the inclination angle
in case (2) is the angle of the berthing velocity vector with respect to the centreline of the fender (which corresponds tothe berthing direction). In general, the berthing angle is often referred to as the ship-side angle in case (1).
(1) Case when the hull of a berthing vessel is inclined to the berth line.
Fig. 4.2.2 shows the case when the vessel side is horizontally inclined and the compression direction isparallel to the fender axis. However, as shown in Fig. 4.2.3, this state also occurs when the flared portion of thehull contacts the fender under a vertical inclination.

Fig. 4.2.2 Angular berthing (Horizontal)

Fig. 4.2.3 Berthing with flare angle (Vertical)

The berthing angle θ represents the angle between the vessel side and fender that is in contact with the vessel.
It is considered that the same phenomenon occurs when the hull exhibits a flare angle in the vertical direction,
as shown in Fig. 4.2.3. Although the actual hull shape curves in three dimensions, it is assumed that the contact
area of the hull is straight with a constant flare angle. The reaction force when a rubber fender is compressed at
an angle θ ° is slightly lower than that at θ = 0 °, as shown in Fig. 4.2.4 for various values of θ.

13

Fig. 4.2.4 Fender performance under angular berthing
The performance under angular compression is subject to the complex effects of the inclination angle andpanel size, as described in the following section. If the rubber fender has a panel, as shown in Fig. 4.2.2 or Fig.
4.2.3, the vessel hull will hit the edge of the panel and rotate the panel. When the angle of panel rotation
becomes θ, the panel comes into full contact with vessel hull, owing to which the panel and head of the rubber
fender stop rotating, and the fender is compressed to the maximum deflection with angle θ. Fig. 4.2.5 and Fig.
4.2.6 show conceptual diagrams of the performance curve.

Fig. 4.2.5 Angular performance for various θ(Constant contact point: L)

Fig. 4.2.6 Angular performance for various L(Constant berthing angle: θ)

In Fig. 4.2.5, when the hull contacts the fender at an angle θ, the reaction force increases linearly due to theforce that rotates the panel to cause a small displacement; further, the reaction force increases when the entire
panel contacts the vessel hull. The yellow triangles in Fig. 4.2.5 and Fig. 4.2.6 are considered to correspond to
the energy absorbed by the rotation of the panel. Thus, with increase in the angle θ, the area of the yellow
triangle increases. Furthermore, as shown in Fig. 4.2.6, when the angle θ is constant and the size of the panel
increases, the contact point moves farther (Llarge), and the area of the yellow triangle increases. Because thisenergy absorption is small and depends on the angle and size of the panel, the angular performance defined in
the manufactures’ catalogues may not consider this energy. It is assumed that the displacement at which thereaction force increases is δ0 because the rotation angle of the panel and the inclination angle θ on the ship side14

become equal. This value also differs depending on the angle and size of the panel. The performance curve
shown in Fig. 4.2.4 assumes the displacement δ1 that intersects the horizontal axis of the figure as the origin,disregarding the portion due to the rotation of the panel. However, since the angle does not change in Fig. 4.2.6,
the reaction force curve of the angular compression has the same shape if the virtual displacement δ1 is theorigin and the design reaction force Rθ is constant, regardless of the berth position L.
The allowable displacement in angular compression is determined by the manufacturer, taking into accountthe deformation of the product. For example, at high angles, the outer surface of the fender may beover-compressed before reaching the design-allowable deflection. In such a case, the allowable deflection
specified in the catalogue may be smaller than the design deflection determined considering the angularperformance.
The performance of angular compression is often presented in manufacturers’ catalogues or technicaldocuments. In the case of small rubber fenders such as V-type fenders without panels, it may not be necessary
to consider the angular coefficients, as summarized in Table 5.4.4 in Chapter 5 5.4. The performance of V-type
rubber fenders without panels also varies depending on the direction of inclination. If the inclination is in thewidth direction of the fender, the performance must be in accordance with that defined in the manufacturers’
catalogues or technical documents. The angular performance in the longitudinal direction can be approximatedby assuming that only the contact portion generates a reaction force. The details regarding this aspect arepresented in equation 5.6.7, in Section 5.6.2 in Chapter 5.
The influence of the angular compression on the performance is defined as the angular coefficient Ca. In
design, the angular coefficient Ca at the angle θ of the design condition is employed with the catalogue value ofthe standard condition to obtain the design performance.
Angular coefficient of reaction force:
Angular coefficient of energy absorption:

CaR ＝ Rθ／RR
CaE ＝ EAθ／EA(4.2.5)(4.2.6)

Here,

CaR
Rθ
RR
CaE
EAθ
EA

：
：
：
：
：
：

Angular coefficient of reaction force
Reaction force at angle θStandard reaction force at angle 0°
Angular coefficient of energy absorption
Energy absorption at angle θStandard energy absorption at angle 0°

The fender can be selected by obtaining the reaction force and the energy absorption using equations (4.2.5)
and (4.2.6), respectively. The reaction force performances at various angles do not exhibit similar shapes, as
shown in Fig. 4.2.4; thus, their values cannot be obtained by simply applying a constant Ca to the reaction force
value for each deflection of the standard performance. To obtain the angular reaction force for each deflection,an angular coefficient for each deflection is required, as shown in equation 4.2.7.
Angular coefficient of reaction force at deflection ε (％)： CaR(ε) ＝ Rθ(ε)／R(ε)(4.2.7)Here,

CaR(ε) ： Angular coefficient of reaction force at deflection ε (%)Rθ(ε) ： Reaction force at deflection ε (%) and angle θR(ε) ： Standard reaction force at deflection ε (%) and angle 0°
The reaction force corresponding to the deflection is necessary, for example, when considering theperformance of rubber fenders in terms of horizontal force characteristics such as in single pile dolphins andflexible piers, or when using fender as a mooring spring for calculating the motion of a moored vessel. To
obtain the coefficient CaE (ε) of energy absorption by deflection, it is possible to calculate the reaction force by15

deflection by using the angular coefficient of equation (4.2.7) in the process of integrating the reaction force
from 0% to deflection ε. The integrated value up to the design deflection is the coefficient of energy absorption
CaE.
The procedure of determining the angular coefficient to be used for design from the results of the angulartest is explained in Section 6.3.2 in Chapter 6.
(2) Case when the direction of berthing vessel is not parallel to the compression axis of the fenderFig. 4.2.7 shows the case in which a vessel is moving forward and the berth direction is at an angle to thecompression axis of the rubber fender. In this case, the compression angle φ is the angle between the berth
direction of the vessel and compression axis of the fender. At this time, friction is generated between thesurface of the fender panel and hull of the vessel, and the balance with the shear reaction force of the rubber
fender causes shaking due to the phenomena of following and sliding. In normal berthing, vessels are supposed
to stop moving forward before they compress the fenders; therefore, angular berthing in the design of rubber
fenders corresponds to the case shown in Fig. 4.2.2, and the shear compression is not considered unless certain
specific conditions exist. Under special circumstances, for example, when there is no assistance from tugboats
and the forward speed cannot be eliminated, or compression with sharp angles is required such as in the case ofbridge protection, canals, locks, etc., the manufacturer's technical data or individually scaled model testing may
be necessary. When the shear displacement is large, in addition to the frictional force, excessive shear
deformation can be suppressed by the tension of the shear chain, as shown in Fig. 4.2.7. Similar to that of theangular compression, the influence of the berthing direction on the performance is defined as the angularcoefficient C, which can be defined as in equation (4.2.8) and equation (4.2.9).

Fig. 4.2.7 Berthing along with angle of direction
Angular coefficient of reaction force:
CφR ＝ Rφ／RR
Angular coefficient of energy absorption :CφE ＝ EAφ／EA
Here,
CφR ： Angular coefficient of reaction force
Rφ ： Reaction force at direction angle φ
RR ： Standard reaction force at direction angle of 0°
CφE ： Angular coefficient of energy absorption
EAφ ： Energy absorption at direction angle φ
EA： Standard energy absorption at direction angle of 0°(4.2.8)(4.2.9)4.2.3 Velocity factor: VF(1) Constant Velocity (CV) and Decreasing Velocity (DV)
Since rubber has visco-elastic properties, the reaction force of a rubber fender changes depending on thecompression speed. Generally, a higher deformation speed corresponds to a higher reaction force. However, in
actual berthing, compression initiates at the berthing velocity and decelerates as the berthing energy isabsorbed, finally coming to a stop. In the PIANC Guidelines 1), the initial berthing velocity is set as 0.15 m/s,
and decelerating compression that nearly stops at the maximum deflection is specified. This performance is16

termed as the rated performance. Since it is difficult to reproduce such conditions when using a real-sized
fender, an alternative method is proposed. First, a scale model is compressed at a constant speed under various
strain rates, and the velocity factor for each constant speed is determined; subsequently, the performance forthe decelerating compression is estimated via calculations to determine the rated performance. Since thepurpose of both the methods is to obtain the rated performance, the method for determining the deceleration(DV) performance from constant speed compression (CV) is introduced.
(2) Constant Velocity (CV)Fig. 4.2.8 shows the concept of reaction force performance under constant speed compression (CV) when thestrain rate is changed. With increase in the strain rate, the reaction force increases. The velocity factor forconstant velocity (CV) can be defined as in equation (4.2.10) and equation (4.2.11).
Velocity factor of reaction force: VFR ＝ RV／RR
Velocity factor of energy absorption: VFE ＝ EAV／EA
Here,
VFR ： Velocity factor of reaction force
RV ： Design reaction force under constant velocity (CV)RR ： Standard reaction force under standard velocity
VFE ： Velocity factor of energy absorption
EAV ： Design energy absorption under constant velocity (CV)EA ： Standard energy absorption under standard velocity(4.2.10)(4.2.11)

Fig. 4.2.8 Performance under different compression velocities (CV)In Fig. 4.2.8, at standard performance (V=V0), the peak reaction force at approximately 25% and the reaction
force at the design deflection have the same value, and the design reaction force RV in this case becomes RR. At
V = 1%/s, since the reaction force at the design deflection is larger than the peak reaction force, the reaction
force at the design deflection becomes the design reaction force RV. Conversely, at V = 15%/s, since thereaction force at the design deflection is smaller than the peak reaction force, the peak reaction force becomes
the design reaction force RV. When the compression speed is extremely large such as V = 50%/s, the reaction
force may monotonously increase without exhibiting a local peak. In such a case, the reaction force at adeflection that involves the standard energy absorption is set as the design reaction force RV. The PIANC
Guidelines 1) prescribe that the reaction force at 35% deflection is used, but depending on the type of fender,

17

the design reaction force may be underestimated, which is a risk condition. The relationship between the strain
rate V and the velocity coefficient VFR of reaction force determined using equation (4.2.10) is shown in Fig.
4.2.9.

Fig. 4.2.9 Velocity factor and strain rate: Constant velocity (CV)(3) Decreasing Velocity (DV)
Since the compression speed decreases in actual berthing, the compression type that simulates it is termed
deceleration compression (DV). In the PIANC Guidelines 1), the standard initial velocity is 0.15 m/s, themethod of deceleration is approximated via a straight line or cosine waveform, and the final performance atwhich the effective berthing energy is absorbed and the vessel stops is defined as the rated performance. The
reaction force at this instant is termed as the rated reaction force, the deflection amount is the rated deflection,and the energy absorption is the rated energy absorption when the other factors correspond to the standard
condition. The method of correcting the fender performance by employing the velocity factor of the berthingvelocity for the design condition based on the rated performances has been specified. As explained in Section
6.7 in Chapter 6, the velocity factors of rubber fenders are similar in terms of the strain rate rather than theactual velocity. Therefore, if the horizontal axis in Fig. 4.2.9 is the actual velocity, the velocity factor must be
different depending on the size of the rubber fender. However, in this document, the strain rate (V0=0.01 to
0.3%/s) is sufficiently low, as V0 in Fig. 4.2.9 is defined as the standard velocity and the velocity factor is 1.0.
The relationship between the strain rate and velocity factor can be defined in a size-independent manner,
making it easy to use for design.
Two methods exist for determining the decelerating compression performance: one in which thedecelerating compression is determined by changing the initial speed in a scale model or a small-sized actual
fender, and another in which it is calculated using the velocity factor of constant speed compression, as shownin Fig. 4.2.9. Here, an example of the latter calculation method is demonstrated. Fig. 4.2.10 shows an
explanatory view of the principle of determining the performance of decelerating compression from thevelocity factor of constant speed compression. Consider a rubber fender (1000 H) having a height of 1 m, andassume an initial velocity (berthing velocity) of 0.15 m/s, which corresponds to a strain rate of 15%/s. Whenthe velocity decelerates from 15%/s → 12%/s → 5%/s → 1%/s → 0%/s, as shown in the upper figure in Fig.
4.2.10, the reaction force curve at the speed after deceleration traces the progress of the compression, as
indicated by the red line in the lower figure of Fig. 4.2.10, and subsequently, the deceleration performance canbe determined.

18

Fig. 4.2.10 Procedure to estimate DV performance from CV performances
If the shape of the reaction force curve changes at a remarkably high compression speed, as in V = 50%/s inFig. 4.2.10, it is necessary to use a strain-specific velocity factor. However, in the considered example, thebuckling-type performance is exhibited at V = 15%/s or less, and thus, the velocity coefficient of Fig. 4.2.9
may be used assuming that the shapes of the curves are similar. The energy absorption can be determined byintegrating the reaction force curves with respect to the displacement (deflection); however, if the curves are
similar in shape, the velocity factor of energy absorption is equal to the velocity factor of the reaction force.
Since there are several patterns of deceleration, such as linear deceleration, deceleration with a cosine
waveform, or deceleration by absorbing effective berthing energy, it is necessary to specify which deceleration
type is employed. The test results of deceleration compression (DV) at an initial compression speed of 0.15 m/s
and the deceleration performance determine from the CV performance under different velocities are comparedin Fig. 6.3.8 in Section 6.3.3 in Chapter 6,.
The comparison of the DV (deceleration) performance conforming to the PIANC Guidelines 1) under
different initial speeds is shown in Fig. 4.2.11. As shown in Fig. 4.2.11, the rated performance is obtained at an
initial velocity of 0.15 m/s, while the conditions other than those for speed are standard conditions. In an actual
compression test, if the compression speed is zero, the reaction force becomes unstable due to stress relaxation ;thus, the PIANC Guidelines 1) define the final speed as 0.05 m/s or less.

19

Fig.4.2.11 Fender performances under decreasing strain rates: DV
Fig. 4.2.12 shows the velocity factor of decelerating compression determined using the strain rate as
described above and compared with CV in Fig. 4.2.9. This value is smaller than the constant speed
performance under a constant initial speed because at the deflection for which the reaction force is the
maximum, certain deceleration has already occurred. Because this deceleration performance is used directly inthe selection of fenders, it is necessary to mention at least this aspect of deceleration performance in the
catalogue. If the difference between the reaction force and energy absorption is small (within 3%), the same
numerical value can be used for the velocity factor. The range is also shown in Figure 4.2.12.

Fig. 4.2.12 Velocity factor and strain rate: decreasing velocity (DV) and constant velocity (CV)(1) Comparison with PIANC Guidelines 1)
Table 4.2.1 presents a comparison of the proposed method and that specified by the PIANC Guidelines 1)
regarding the concept of velocity factor. The main difference is that the values used for the denominators of20

equation (4.2.10) and (4.2.11) in the proposed method are different from those used in the PIANC Guidelines 1).
Even if the coefficients change, the implication of the final result is the same, and thus, the two methods can beconsidered to be consistent.
Table 4.2.1 Comparison of the velocity factor obtained using the proposed method
and that defined by the PIANC Guidelines.
1）

M ethod defined in this bookM ethod in PIANC guideline

Dominant performancefor velocity factors

Standard performance:
CV performance under constant strain rate 0.01%/s to 0.3%/s

Rated performance:
DV performance under initial speed 0.15m/s

Test and specimen

CV(Constant speed) or DV (Decreasng speed)

DV (Decreasing speed) testfor velocity factor

Scale model or real size product

Scale model or real size product

M ethod to obtain

Calculate DV performance using CV test results.
(Or direct DV test)

Direct DV test

DV performance
Velocity factor formula
Design reaction force forfenders without buckling

Pros

＝

Calculated or tested DV performance
CV performance under constant strain rate 0.01%/s to 0.3%/s

Reaction force at deflection at which standard energy is absorbed.

＝

DV performance under actual berthing speed
DV performance under initial speed 0.15m/s
Reaction force at 35% deflection

・Standard performance can be demonstrated by product tests.

・Can use DV test performance directly for design.

・Velocity (Strain rate)does not depend on fender size

・Energy absorption value will be slightly higher.

・Energy absorption value is slightly lower.
Cons・Calculation required to obtain DV from CV.

・Large test facility is required.
・Several cases of velocity must be considered for each size.

Since a velocity factor for each deflection is required to obtain a detailed reaction force curve, VF is
considered as a function of deflection ε, as shown in equation (4.2.12). When the energy absorption factor VFE(ε) for each deflection is required, the reaction force for each deflection obtained using the velocity factor of
equation (4.2.12) is integrated from 0% to the design deflection. Details regarding this aspect are presented in
Chapter 6, Section 6.3.3.
Velocity factor of the reaction force at deflection ε %:VFR (ε)＝ RV (ε）／ R(ε)
Here,
VFR(ε) ： Velocity factor of reaction force at deflection ε
RV (ε) ： Reaction force at deflection ε with velocity V
R(ε) ： Standard reaction force at deflection ε(4.2.12)In the selection of ordinary rubber fenders, if a velocity factor for decelerating compression exists, thefactors for constant velocity and strain-specific velocity factor are not required; thus, the design can be realizedeven if the values are not listed in the catalogue. However, since the value is required in the calculation
methods of the velocity factor, the motion analysis of moored vessels, and the special design of flexible
structures such as single-pile dolphins, it is desirable that the values are presented as technical data.
When the fender height is small, such as in the case of scale model testing, the standard strain rate of
0.01%/s to 0.3%/s may be difficult to realize owing to the limitations of the testing facility. In such a case, areaction force compressed at an actual speed of 0.01 to 1.3 mm/s may be used.

4.2.4 Temperature factor: TF
The performance of rubber fenders also varies with temperature. Normally, the reaction force of rubber fenders
increases when the temperature decreases; thus, it is necessary to verify the minimum energy absorption at hightemperatures and the maximum reaction force at low temperatures. A conceptual diagram is shown in Fig. 4.2.13. The

21

temperature factor TF can be defined as the ratio of the standard reaction force RR at the standard temperature of 23°C
to a reaction force RT at the temperature corresponding to design conditions. When determining the temperature factor
specific to a deflection, TF(ε) is defined as a function of deflection ε.

Fig. 4.2.13 Conceptual diagram of temperature dependency of fender performance
The temperature factor TF is defined as in equation (4.2.13) and equation (4.2.14). The conditions for the temperature
test and specific calculation examples for the temperature factor are presented in Chapter 6, Section 6.3.4.
Temperature factor of reaction force:
TFR ＝ RT／RR
Temperature factor of energy absorption: TFE ＝EAT／EA(4.2.13)(4.2.14)

Here,
T

:
Temperature (°C)
ε-10 : Design deflection (%) at which the standard energy absorption occurs at low temperature of -10°C
ε23 : Standard deflection (%) at standard temperature of 23°C
ε40
: Design deflection (%) at high temperature of 40°C
εT
: Arbitrary deflection temperature factor of energy absorption (%) at temperature T°C
TFR : Temperature factor of reaction force
RT: Reaction force at temperature T°C
R-10 : Design reaction force at temperature of -10°C (at deflection ε-10, as shown in Fig. 4.2.13)
RR: Standard reaction force (Standard conditions)
TFE : Temperature factor of energy absorption
EAT : Energy absorption at temperature T°C
EA-10 : Design energy absorption at temperature -10°C
EA: Standard energy absorption (Standard conditions)
EA40 : Design energy absorption at temperature 40°C
An example of the temperature factor for the reaction force and energy absorption is shown in Fig. 4.2.14. The same
temperature factor may be used if the difference in the values of the reaction force factor and energy absorption factor iswithin 3%. However, the range within 3% varies depending on the type of rubber fender and rubber grade, and thus, this
aspect must be specified in the catalogue.

22

Fig. 4.2.14 Temperature factors of fender performance
The temperature factor for each deflection is required to determine the performance curve. In this case, TFR(ε) is
considered as a function of deflection ε, as given in equation (4.2.15).
Temperature factor of the reaction force at deflection ε (%):

TFR (ε)= RT (ε）／ R(ε)(4.2.15)

Here,

TFR (ε) : Temperature factor of reaction force at deflection ε (%)
RT (ε) : Reaction force at temperature T and deflection εR(ε) : Standard reaction force at deflection ε at standard temperature
The energy absorption factor for each deflection TFE (ε) can be calculated by integrating the reaction force for eachdeflection determined by the temperature factor of equation (4.2.15) from 0% to each deflection. The integrated value
up to the design deflection is TFE. When the temperature becomes extremely low, the reaction force curve continues toincrease without exhibiting a peak due to buckling, as shown at T=−10°C in Fig. 4.2.13. In such a case, the maximum
reaction force at which standard energy absorption at a standard temperature of 23°C occurs is considered the design
reaction force at that temperature. The normal design does not require the use of a temperature factor per deflection ;however, at extremely low temperatures, the fenders may not be able to demonstrate a buckling-type performance. Thus,
it is desirable to use a deflection-specific temperature factor for evaluating the motion of moored vessels or designingflexible quays such as single-pile dolphins. Conversely, if the temperature is high (approximately 40°C), the standard
energy may not be absorbed at the standard temperature. In this case, the size must be reselected in the catalogue.
To set the temperature as a design condition, the statistical records of the maximum (and minimum) daily averagetemperatures of the JMA (Japan Meteorological Agency), which are near to those at the use site may be considered if
there is no record of actual measurements at the use site. However, it is desirable to use these values after correction via
certain field observations. Rubber has a low heat transfer coefficient, and it takes approximately 1.2 days to stabilize thetemperature at a depth of approximately 15 cm (refer to equation (6.3.1) in Chapter 6, Section 6.3.1). Simply applying
the instantaneous maximum and minimum temperatures may result in an overestimation of the temperature dependence;
therefore, it is practical to use the abovementioned daily average maximum and minimum temperatures. In addition, theTechnical Standards and Commentaries of Ports and Harbour Facilities in Japan -II Marine storage base facility 3)
specifies a temperature factor of 0.95 to 1.25.
Furthermore, rubber materials are visco-elastic, and there exists a relationship between the speed dependence andtemperature dependence, as defined by the WLF equation 5). This equation can be used to verify whether the velocity
factors and temperature factors are measured suitably (details are provided in Chapter 6).

23

4.2.5 Ageing factor: Cag
Rubber fenders deteriorate due to the influence of heat, ultraviolet light, oxygen, etc. An oxidation reaction, in which
oxygen molecules form radicals (free radicals) may occur, leading to cleaving of the molecules by extracting hydrogenfrom the molecular chains of rubber; this reaction softens the rubber, and the fender reaction force is reduced. In
contrast, sulphur molecules bridge the linear molecules of rubber, although the unbonded sulphur bonds slowly even atroom temperature; this reaction cures the rubber, and the fender reaction force increases. Therefore, the ageing reactionof rubber coexists with the softening and hardening reactions. In a survey of the materials used to manufacture rubber
fenders, it was noted that the rate of hardening reaction was slightly higher, and the fender reaction force gradually
increased with the service life 6). As shown in equation (4.2.16), the ratio of the standard reaction force at the beginningof service life to that after ageing is defined as the ageing factor CagR, and it is applied to the performance value as an
influence factor. Ageing is not considered in the PIANC Guidelines 1), and Cag is considered to be 1.0 in general fender
design. However, since the reaction force of rubber fenders tends to increase with the number of service years, it isdefined as an influence factor so that it can be evaluated when necessary to consider long-term use and deterioration ofa quay.
Ageing factor of reaction force：

CagR＝Rag ／RR(4.2.16)

The energy absorption is considered to increase with increase in the reaction force; therefore, it is not necessary toconsider this aspect in design; however, since there exist cases in which the reaction force decreases with service life,
the energy absorption can be considered as defined in equation (4.2.17).
Ageing factor of energy absorption：

CagE ＝EAag／EA(4.2.17)

Here,

Rag :

Reaction force after ageing
RR : Standard reaction force before service
EAag : Energy absorption after ageing
EA : Standard energy absorption before service
The factor of ageing is not usually taken into consideration in the design of fenders for general berths; however, it isnecessary to focus on the increase in the reaction force in the case of high temperature environments or when theapplication involves places or structures in which replacement is difficult. The reaction force of thick-walled rubber
fenders gradually increases with age; however, it has been noted that the deterioration of rubber is concentrated near thesurface7). Cag differs depending on the product, material and environment, and it must be estimated according to the
expected service life. In the Technical Standards and Commentaries of Ports and Harbour Facilities in Japan -II Marine
storage base facility 3), the increase in reaction force with CagR = 1.0 to 1.05 is considered. The actual ageing coefficient
can be obtained using equation (4.2.16) by performing the compression test of an old fender collected from the site ofuse; however, some studies have reported on estimation performed using scale models by employing the Arrhenius
method, among other methods 6), 8).
Fig. 4.2.15 shows an example of the ageing factor and service years of used vertical cylinder (CELL) rubber fenders
returned from harbours. The figure also shows an example of the ageing factor of scale models after they underwent
heat-accelerated ageing, as determined using the Arrhenius method. However, the Arrhenius method of ageing prediction
is likely to cause a large error when considering the activation energy; thus, its validity must be examined by evaluating
the products returned from actual sites 8). The scale model demonstrates good agreement with the old fenders, as shownin Fig. 4.2.15. However, sufficient information regarding the secular change of rubber fenders may not be available, and
it is necessary to enhance the investigation of different types and rubber grades.

24

Fig. 4.2.15 Ageing factor of rubber fender and scale model (CELL type)(Catalogue data used for year 0)
The ageing factor of rubber fenders usually does not take into consideration the reaction force of the firstpre-compression; however, if the fender is not compressed for a long period, such as when it is in-stock, re-hardening
occurs and ageing is affected. Subsequently, it was found that the fender may be cured to achieve a performance better
than the first compression performance after manufacturing 7), 8). After this reaction force recovery, if the fender iscompressed even once, the reaction force becomes stable and only the influence of ageing remains. However, caution
must be exercised because the increase in reaction force affects the strength of the structure, even if it occurs only once.
Re-hardening of the rubber material was the focus of a report by Mullins et al. 10). Rubber is a visco-elastic material; thus,
when rubber is unloaded after being subjected to deformation, the complete recovery of the residual strain does not occur,
although the strain remains when the rubber is deformed again, and the resilience of rubber decreases. It is believed thatco-existing phenomena occur in which recovery is delayed due to viscosity and molecular breakage occurs due todeformation, which cannot be reversed. The reaction force returns to the original performance with time; however, therecovery due to viscosity is relatively fast and occurs almost completely in a few hours to approximately a day after
unloading; the material in this case does not cure to exhibit a performance better than the original one. Furthermore, therecombination of broken molecules takes time, and curing gradually continues on a yearly basis; in some cases, as withageing, curing may result in the rubber exhibiting more than the original reaction force. In this document, the recovery of
the reaction force due to viscosity of the former is termed "recovery", and the recovery of the reaction force due to therecombination of broken molecules is termed "re-hardening".
Fig. 4.2.16 shows an example of the variation in the performance relative to the performance before unloading, withchange in the standing time (un-loaded time). The performance was approximated using two types of regression methods
before and after 1000 days. When rubber fenders with extremely low frequency of berthing or rubber fenders that havebeen kept in stock for a long duration are used, it is necessary to consider the re-hardening characteristics. The
re-hardening characteristics depend on the shape and material of the rubber fender. Table 4.2.2 presents an example of
the re-hardening correction factor Cre. For convenience, the coefficients are organized by stages. If the number of daysleft to stand is large, re-hardening can be taken into account using the ageing correction factor Cag, by considering there-hardening factor Cre presented in Table 4.2.2, as obtained from equation (4.2.18).

25

Ageing correction factor Cag obtained using re-hardening factor Cre

Cag (after correction) ＝ Cag (before correction)× Cre (re-hardening factor)(4.2.18)

According to Table 4.2.2, the re-hardening factor is not required to be considered if berthing occurs one or more times
in 10 days. It is not necessary to consider re-hardening in common mooring facilities, as it is estimated that the berthinginterval is often less than a week in normal ports. However, if the frequency of use is extremely low, if the fender is not
used for an extended period, or if rubber fenders that have been stocked for a long time are to be reused, the re-hardening
factor should be considered in the design reaction force. Alternatively, countermeasures such as limiting the first berthing
condition to a smaller value or reapplying a stress relaxation compression may be adopted.
In addition, such re-hardening may occur even in a working fender if the compression deflection due to berthing isalways small. Although an example was presented in Table 4.2.2 and Fig. 4.2.16 owing to the importance of this factor,
the chemical behaviour of material must be clarified, and the accuracy of the factor must be improved.
Table 4.2.2 Example for re-hardening factor Cre
Standing period
Re-hardening factor Cre
10 days or less
1.00
10–100 days
1.07
100–1000 days
1.09
1000–10000 days
1.25

Fig. 4.2.16 Example of re-hardening factor: Cre
4.2.6 Repetition factor: Cr
Because a rubber fender is repeatedly compressed, its reaction force decreases due to fatigue. Extreme decrease in thereaction force against the motion of a moored ship or floating structure during stormy weather is a matter of concern.
The ratio of the reaction force before repetition fatigue (standard performance) to that after repetition fatigue is definedas the repetition factor Cr. In the Technical Standards and Commentaries of Ports and Harbour Facilities in Japan -II
Marine storage base facility 3), Cr with a value of 0.9 to 1.0 is considered as the repetition factor of the reaction force. In
the design of a normal fender for berthing, it is considered that the vessel will be evacuated during a storm, and thus,
continuous repetitive compression to the same rubber fender does not occur; in other words, the repetition factor could
be Cr = 1.0 for both the reaction force and the absorbed energy.
As mentioned in Section 4.2, the standard repetition factor is Cr=1.0, which corresponds to the performance of thefender after being compressed three times or more and left for one hour or more. This aspect is defined by the quality
control test conducted on rubber fenders after production, and it is different from that for repeated fatigue due to normal

26

port operation.
In the same manner as for ageing, sufficient information pertaining to repetition fatigue is not yet available. Fig. 4.2.17
shows the results of a fatigue test conducted by Ueda et al. 11) as an example. As the number of repetitions increases to
100 and subsequently 1000, the reaction force decreases, as does the reduction rate, which appears saturated. If
compression continues further, the fender will eventually break and lose its functionality. When a rubber fender isdamaged due to fatigue, a sharp decrease in the reaction force occurs, as shown in Fig. 4.2.17; at this instant, anothervisual symptom is a crack that penetrates the main body, and the number of compressions at which either one is observed
is defined as breakage.
According to the PIANC Guidelines 2) and Standard Specifications for Ports and Harbour Works 9), it is required thatrubber fenders do not break even if they are subjected to 3000 cycles of continuous compression to the design
deflection. This aspect corresponds to a certification test for confirming the durability, considering that rubber fenders
are subjected to large compression strains of 50% to 70%. To date, the value of Cr is rarely used in design because thedegradation of performance by the fatigue tests are not used in design.
However, to predict the life of rubber fenders, repeated fatigue and ageing, as described in the previous section, areimportant factors. Akiyama 8) conducted fatigue tests pertaining to the heat-accelerated degradation of scaled models
based on Arrhenius's law and reported that the fatigue failure was accelerated remarkably by degradation due to ageing.
In the future, it is expected that rational life prediction in design may be realized by additional research.

Fig. 4.2.17 Repetition fatigue test of vertical cylindrical fender (CELL-type)10)(Initial value: Average of 2nd and 3rd compression)

4.2.7 Creep characteristic
Deflection advances with time if a constant compression load is applied to the rubber fenders; this phenomenon iscalled creep. The reaction force decreases when a rubber fender buckles, and if the load is continued to be applied, there
is a risk that the compression will lead to the designed deflection instantaneously. The results of the constant load test ofa vertical cylindrical rubber fender (CELL-type) is shown in Fig. 4.2.18 as an example. Even when the initial deflection
is continuously applied for a load of 8% or 10% for 10 h, the deflection saturates and approaches a constant value;
however, at a load of 12%, the deflection gradually progresses. Since the deflection corresponding to the peak reaction
force of this rubber fender is approximately 25%, 52.5% of the designed deflection is reached instantaneously when theload reaches its peak at 25%; such conditions should be avoided in the long-term mooring of vessels.

27

Fig. 4.2.18 Example of creep test
Such a phenomenon is not required to be considered during the design for berthing; however, if there is a possibility
that the wind load during mooring may increase, it is necessary to ensure that the rubber fenders do not buckle
unexpectedly. In the Technical Standards and Commentaries of Ports and Harbour Facilities in Japan -II Marine storage
base facility 3), the wind pressure is recommended to be within the steady force equivalent to 10% of the deflection of therubber fender, as shown in equation (4.2.19).
Steady external force to rubber fenders＜

Reaction force at deflection

ε＝10％(4.2.19)

It is also necessary to confirm whether 10% is appropriate as the initial strain for rubber fenders other than that
corresponding to Figure 4.2.18. The creep property should be considered as an initial strain due to a steady external
force, and it is not used as an influence factor leading to an enhancement or degradation in the performance. The creep
is used as a safety standard for fenders that does not cause self-buckling because the displacement progresses
temporally to the external force applied constantly. Appendix 4 shows an example of the verification of the wind load in
the mooring analysis of a vessel under stormy conditions.

[References]
1) PIANC: Guidelines for the Design of Fenders System, Report of Working Group 33 of the Maritime Navigation
Commission, 2002
2) Ports and Harbours Association of Japan (PHAJ): Technical Standards and Commentaries of Ports and Harbour
Facilities in Japan, pp.1262-1268, 2018
3) Ports and Harbours Association of Japan (PHAJ): Technical Standards and Commentaries of Ports and Harbour
Facilities in Japan -II Marine storage base facility, pp.127, 1980
4) Ueda, S., Hirano, T., Shiraishi, S., Yamamoto, S., and Yamase, S.: Reliability Design Method of Fender for Berthing
Ship, PIANC2002, 30th International Navigation Congress, S4B P56.doc, pp. 692-707, 2002
5) Williams, M. L., Landel, R. F., Ferry, J. D.: The Temperature Dependence of Relaxation Mechanisms in Amorphous
Polymers and Other Glass-forming Liquids, Am. Chem.Soc., Vol.77, p.3701,1955
6）Akiyama, H., Shiomi, T., Omura, A., Yamamoto, S., Ueda, S., Kamada, T.: Method to Estimate the Aging of Large
Rubber Marine Fender, Proceedings of the 27th International Ocean and Polar Engineering Conference,
pp.1459-1466, 20177）Akiyama, H., Shimizu, K., Ueda, S., Kamada, T.: Investigation on Service Years of Large Rubber Marine Fenders ,Journal of JSCE, Vol.5, pp.392-401, 201728

8) Akiyama, H. (2018): Study on Aging of Circular Hollow Rubber Fender in Long Term Usage, Osaka University
Doctoral Thesis (in Japanese)9) Mullins, L: Effect of stretching on the properties of rubber, Journal of rubber research, 16, P275-289, 1947
10) Ueda, S., Shiraishi, S., Maruyama, T., Uezono, A., Takasaki, M., Yamase, S.: Properties of Rubber fender in use of
Mooring for Floating Bridge, Proceedings of the 14th Symposium of Ocean Engineering, SNAJ, pp.359-364, 1998
(in Japanese)
11）Ports and Harbour Bureau, Ministry of Land, Infrastructure, Transport and Tourism (MLIT): Standard Specifications
for Ports and Harbor Works, Vol.1, pp.71-72, 2017

29

Chapter 5
Design5.1 General
When designing rubber fenders considering the various effects of use conditions and the environment, fenders that
can absorb more energy than the effective berthing energy must be selected; furthermore, the maximum reaction force
should be safe for mooring facilities. The surface pressure towards the vessel hull should be within the allowable hullpressure of the vessel. In addition, the fender, including the peripheral parts, must be designed to function as a safe
system under the considered design conditions.

5.2 Design procedure of rubber fender
Since rubber fenders vary in size and performance in terms of those for leisure boats to those for super-tankers, it isnecessary to design fenders that are appropriate for a given condition. In particular, the effective berthing energy is
initially calculated, and the type and size of rubber fenders are selected accordingly. Next, the factors affecting theperformance are considered. To select the appropriate factor pattern, the design conditions of the mooring facilities andthe allowable hull pressure, as a representative of the vessel side strength, are compared with the corresponding
performance of the rubber fenders. Rubber fenders are selected considering the influence factors, and a detailed design
process that accounts for installation, pitch spacing, fender panel, chain, etc. is performed. Fig. 5.2.1 shows the design
process flow of rubber fenders.

Fig. 5.2.1 Process flow for fender design

30

The classification of factor patterns is described in Chapter 5, Table 5.4.4, and design examples are presented in the
Appendix.

5.3 Effective berthing energy
The effective berthing energy to be absorbed by the rubber fender can be calculated using equation (5.3.1).

1
Effective berthing energy:

Eb =

2

・ M ・ V B ・ C e ・ C m・ C c ・ C s

2(5.3.1)

Here,

Eb : Effective berthing energy (kNm=kJ)
M : Mass of vessel (＝Displacement tonnage: DT, t)
VB : Berthing velocity (m/s)
Ce : Eccentricity factor
Cm : Virtual mass factor
Cc : Berth configuration factor
Cs : Softness factor
The key variables and coefficients in equation (5.3.1) can be described as follows:(1) Berthing velocity: VB
As given in equation (5.3.1), since the berthing velocity is squared when calculating the effective berthing
energy, it exerts more influence than other coefficients do. The berthing velocity is affected by the type of ship,loading condition, location and structure of mooring facilities, weather and sea conditions, presence/absence oftug boats, etc. Vessels have evolved over time, and the measured data and standards of berthing velocity havebeen updated accordingly 1), 2), 3). In actual design, it is desirable to set these parameters appropriately based on
local measurement data and the latest statistics along with the abovementioned information.
(2) Eccentricity factor: Ce
As shown in Fig. 5.3.1, in most berthing vessels, the hull contacts a fender at berthing angle θ and starts torotate. As a result, a part of the kinetic energy (berthing energy) is consumed by the rotation. The remaining
energy can be determined by performing correction using the eccentricity factor Ce. The eccentricity factor Ce
can be expressed using the equation (5.3.2) when the berthing direction is perpendicular to the berth.

Fig. 5.3.1 Eccentrically berthing vessel

Ce=

Kr 2
2

Kr +Rs2=

1
Rs 2
1+ ( )
Kr
31(5.3.2)

Here,Kr :Gyration radius of vessel (m)Kr=(0.19 Cb+0.11) Lpp

Cb :(5.3.3)Block coefficient

Cb =

DT

(5.3.4)

Lpp ∙B∙d∙ρDT : Displacement tonnage (t)Lpp : Length between perpendicular (m)B : Beam of vessel (m)d : Draught of vessel (m)ρ : Density of water (Sea water: 1.025 t/m3)
Rs : Distance between berthing point and vessel gravity centre parallel to berth line (m)If accurate information is not available, or if only a preliminary review is conducted, the values in Table
5.3.1 may be used.
Table 5.3.1 Preliminary review of eccentric factor using berthing methods
Berthing method

Ce

Schematic view
1/4 Lpp

1/4 point(Continuous berth)

0.5

1/3 Lpp

1/3 point(Dolphin)

0.7

Stern
(Roll on Roll off)

1

In Fig. 5.3.1, it is assumed that a rubber fender is present at the contact point of the vessel; however, in reality, rubber
fenders are attached at a certain interval S; in addition, as shown in Fig. 5.3.2, there exists a case in which the vessel
makes contact between two fenders.
In the Technical Standards and Commentaries of Ports and Harbour Facilities in Japan 2), the eccentricity coefficient Ce
at this instant is obtained by determining Rs, as defined in equation (5.3.2). As shown in Fig. 5.3.2, Rs is the distancefrom the contact point to the centre of gravity of the vessel, and it is measured parallel to the berth line. When the hullof the vessel approaches the berth and contacts two rubber fenders F 1 and F2, Rs can be determined using equations(5.3.5) and (5.3.6). Here, Rs is R1 when k > 0.5 and R2 when k <0.5; when k = 0.5, Rs is assigned the value of either R1and R2 that corresponds to a larger value of Ce.

R1＝｛0.5α ＋ e（1－k）｝Lpp cosθ

(5.3.5)32

R2＝｛0.5α － e k｝Lpp cosθ

(5.3.6)

Here,k ：A parameter that represents the closest point of the vessel and berth between fenders F1 and F2.
k is 0 <k <1; in general, k is approximately 0.5
R1 ：Distance (m) from the berthing point to the centre of gravity (CG) of vessel, measured parallel to thewharf as the vessel contacts fender F1R2 ：Distance (m) from the berthing point to the centre of gravity (CG) of vessel, measured parallel to thewharf as the vessel contacts fender F2
θ ：Berthing angle (°)
e ：Ratio of fender spacing S measured in the longitudinal direction of the vessel to the length between
perpendiculars Lpp
α ：Ratio (parallel coefficient) of the length of parallel line at the berthing position to the length between
perpendiculars Lpp
The eccentricity factor Ce is determined by substituting the Rs obtained using the abovementioned process into
equation (5.3.2).

Fig. 5.3.2 Vessel berthing between fenders(3) Virtual mass factor: Cm
Several formulas have been used to determine the virtual mass (added mass coefficient, hydrodynamic mass),
and it has been researched extensively. The following two formulas are recommended in the PIANC Guidelines
4).
1) Ueda's formulaUeda's formula was proposed in 1981 and is based on model experiments and field observations. It canbe presented as equation (5.3.7).
Cm = 1+πd∙2∙Cb B：Side berthing(5.3.7)

Here,

Cb: Block coefficient (equation (5.3.4))

2) Vasco Costa’s formula
In this formula, it is assumed that a certain amount of water mass (d·d·Lpp) is added at the time ofberthing. The total added mass is 2 d·d·Lpp because the phenomenon occurs on both sides of vessel. In

33

addition, the mass of the vessel is Lpp·B·d. Therefore, the virtual mass at the time of berthing can beobtained using equation (5.3.8) by adding the two defined masses.

Volume = Lpp ∙B∙d+2∙d2 ∙Lpp = Lpp ∙B∙d× (1+

2∙d
B

)

(5.3.8)Fig. 5.3.3 Virtual mass of vessel (Vasco Costa)
Subsequently, the virtual mass factor (Cm) can be calculated using equation (5.3.9)

Cm = 1+

2∙d：Side berthingB(5.3.9)

Here,

Lpp
B
d

: Length between perpendiculars (m): Beam of vessel (m): Draught of vessel (m)This formula is considered to be effective only under the following conditions; Ueda’s equation should
be used in all other cases (5.3.7).
・ The bottom clearance of the vessel is 0.1×d or more.
・ Berthing speed is 0.08 m/s or more.
3) Bow and stern berthing
For bow and stern berthing (roll on roll off), as described in the PIANC Guidelines 4), a value of 1.1
should be adopted. The British Standard 5) advocates a value of 1.0. Here, the larger value is selected.

Cm = 1.1:

Bow and stern berthing(5.3.10)(4) Berth configuration factor: Cc and softness factor: Cs
The berth configuration factor Cc is thought to be applicable in the case of permeable (such as apile-supported pier) and non-permeable structures (a quay); when there is no escape for water, the water acts asa cushion and absorbs a certain amount of energy. The softness factor Cs considers energy absorption by elastic
deformation of a vessel hull plate. Although both factors represent rational concepts, presently, the value of 1.0
is adopted because no research has yet demonstrated empirical evidence for the determination of numericalvalues.

5.4 Influence factors
5.4.1 Conditions from design background
The influence factors for rubber fenders must be determined in accordance with the use conditions and purpose.
When making a decision, the following aspects must be considered from the viewpoint of strength of the mooring
facility and vessel.

34

(1) Structure of mooring facility
A mooring facility with earth pressure behind a gravity type, sheet pile type or shelf type wall is stableagainst an external force such as a berthing force or wave force. In a basic design, the inertial forces at the timeof an earthquake often dominate in the horizontal direction. Therefore, the reaction force of a fender isrelatively small at the time of berthing, and the influence factors are not significant. In these construction types,
the strength of the mooring facility is usually sufficient, and the influence factor of rubber fender performancedoes not need to be considered. However, in the case of piers supported by piles such as single-pile dolphinsand jackets, the influence of horizontal force, such as the reaction force of fenders at the time of berthing,cannot be ignored.
(2) Allowable hull pressure of vessel
It is considered that small vessels, such as fishing boats, leisure boats, small barges, small cargo vessels, andfloating piers, are less affected by the reaction of fenders against the strength on the hull side. However, with
the increase in vessel size, such as in the case of container ships, large tankers, etc., the strength on the side of
the vessel becomes relatively important. In such cases, the pressure (face pressure) exerted on the vessel sidefrom the fender is limited. Therefore, when a design limit of allowable hull pressure exists, it is necessary toconsider the influence factors of the fender reaction force. In the PIANC Guidelines 4), the maximum value ofthe allowable hull pressure is 700 kN/m2, and thus, this value is used for reference.
(3) Fender design by mooring analysis
In case a vessel is moored in a port facing the open ocean, and in the case of long-term mooring vessels, inwhich mooring is required even in stormy weather due to the presence of waves and wind, the maximum
compression of rubber fenders by the collision force may exceed the design values under the berthing condition.
To enable fender design considering such conditions, it is necessary to perform mooring simulations to analyse
the motion of the vessels. For general cargo ships and tankers, Ueda and Shiraishi 6) considered the simulation
results of several movements observed according to vessel type, wave direction and wave period and proposed
the ratio E/δ pertaining to the ratio of the energy absorption of rubber fenders to the compression deflection δ.
E/δ can be used as a reference to evaluate conditions that require the consideration of motion during mooring in
the fender design process.
In addition, in the case in which undulating waves enter from the open ocean, the amount of vessel motion
increases, and it may not be possible to satisfy the required rate of cargo handling operations. In such cases, it
may be necessary to investigate a mooring system consisting of rubber fenders and a mooring line from theviewpoint of securing the necessary cargo handling operations. Ueda et al. 7) proposed allowable wave heights
in various wave directions and wave periods for typical mooring conditions for various vessel types, and thesevalues can be used as a reference when determining conditions that require this type of analysis.
5.4.2 Patterns of influence factors
For the design of rubber fenders, the influence factors are considered according to the conditions of mooring facilities
and vessels. The treatment for the design of influence factors described in Chapter 4, Section 4.2 can be classified into
the following three patterns.
(1) Pattern A
When the strength of the mooring facility has sufficient tolerance for horizontal force—as in the case of agravity type wall, sheet pile type wall or shelf type quay—and the vessel has no restrictions pertaining to thehull pressure (or the hull pressure is more than 700 kN/m2), the effects of natural environment and conditionsof use are considered to be small, and the performance of rubber fenders involves the consideration of only the
production tolerance. However, even in the case of gravity type quays, the allowable horizontal force may need
to be considered in cases involving ageing or conditions in which the influence of temperature is large, such as
in a cold region; under such circumstances, the influence of the actual conditions should be consideredappropriately according to the evaluation of the designer.

35

(2) Pattern B
If the horizontal strength of a mooring facility is affected by fender performance, such as in the case of pilepiers, dolphins and jackets, or if the vessel is restricted to a hull pressure of less than 700 kN/m2, the influenceof temperature must be considered as a natural condition, and the berthing angle and velocity must be
considered as use conditions. However, in the case of a pile-supported jetty for fishing boats and small boats, if
the berth force is sufficiently smaller than the horizontal load capacity of the mooring facility, coefficientpattern A may be adopted according to the judgment of the designer.
(3) Pattern C
When vessels are moored on a quay during stormy weather, when moored vessels are affected by swells or
long-period waves, or when using rubber fenders for mooring of floating structures, rubber fender performanceis different than under berthing conditions; furthermore, the influence of motion on the fender performance iscomplex. Therefore, it is necessary to carefully consider the influence factors in conditions involving, forexample, repetitive fatigue; creep characteristics and hysteresis characteristics as well as other factors mustalso be considered extensively.
The concept of patterns for considering the influence of various factors is summarized in Table 5.4.4.
5.4.3 Example of managing the influence factors and their patterns
The influence factors for designing rubber fenders are set as follows according to catalogues and technical data. Notethat the catalogue display examples are presented in Tables 5.4.1 to 5.4.3; however, these values should not be used in
actual design because they are numerical values used only for explanation. Please refer to the manufacturers’ catalogues
and technical data for the actual design process.
(1) Production tolerance factor: Cp-

The production tolerance factor has a maximum value of CpR + = 1.1 and minimum value of Cp E = 0.9 unlessotherwise specified, and these values can be used for cases of both the reaction force and energy absorption.
(2) Angular factor: Ca
The angular factor may be considered in a different manner depending on the manufacturer and type, as
described in Chapter 4, Section 4.2.2. Generally, the values for this factor are displayed in the form of a table,
as given in Table 5.4.1. At the angle corresponding to the design conditions, the largest reaction force CaR + andthe smallest energy absorption factor CaE− are taken into account in the design. At a small angle, the reaction
force may slightly increase, and some reaction force factors may exceed 1.00.
Table 5.4.1 Example of catalogue display of angular factor
Angle

Design deflection

Angular factor of reaction force

Angular factor of energy absorption

(°)

(%)

CaR

CaE

0
3
5
8
10
15
20

52.5
51.9
51.3
49.8
48.8
45.5
41.3

1.00
1.01
1.01
1.01
0.99
0.98
0.92

1.00
1.00
0.99
0.95
0.94
0.86
0.71

(3) Velocity factor: VF
The velocity factor used for design involves decelerating compression DV with the berthing velocity taken

36

as the initial speed. This factor is represented in the form of a numerical table, such as in the example shown in
Fig. 4.2.12 in Chapter 4, Section 4.2.3 or Table 5.4.2. At the strain rate obtained by dividing the design berthingvelocity by the fender height, the largest factor of reaction force (VFR+) and smallest factor of energy absorption-(VFE ) is considered in the design. In the case of an intermediate strain rate, a linear interpolation can be used.
Since nearly equivalent factors (within 3%) may use common values, in this example, if the initial velocity is
within 0.1%/s, the influence of the velocity can be neglected and assigned a value of 1.0. In some cases, it may
be possible to simplify the process by using a common factor between rubber grades and between the reaction
force and energy absorption.
Table 5.4.2

Example of catalogue display of velocity factor (DV)

Grade A

Rubber grade

Grade B

Strain rate

Reaction

Energy(%/S)

force VFR

absorption VFE

Reaction

30
20
10
5
1.00
0.50
0.10
0.05
0.01

1.23
1.20
1.17

1.18
1.17
1.14

force

Grade C

EnergyVFR

Reactionabsorption VFE

1.21
1.18

force

1.18
1.15

EnergyVFRabsorption VFE

1.20
1.17

1.17
1.14

1.15

1.14

1.13
1.06

1.10
1.05
1.04
1.00

(4) Temperature factor: TF
The temperature factor is represented by a numerical table, such as in the example shown in Fig. 4.2.14 inSection 4.2.4 in Chapter 4 or Table 5.4.3. In the design, TFR+, which is the maximum value in the temperature-

range of the design conditions, is considered for the factor of reaction force, and the factor TFE , which is theminimum value at the highest temperature, is considered for energy absorption. Since the values are common
in the same manner as the velocity factor, in this example, the temperature effect is considered negligible from
23°C to 30°C.
Table 5.4.3
Rubber grade

Example of catalogue display of temperature factor

Grade A

Temperature

Reaction

Energy(℃)

force VFR

absorption VFE

Grade B
Reaction
force

VFR

Grade C

EnergyReaction

Energyabsorption VFEforce VFR

absorption VFE

-30

2.28

1.75

1.84

1.69

1.78

-20

1.77

1.49

1.52

1.44

1.47

-10

1.39

0

1.30

1.26

1.16

1.13

10

1.06

23

1.00

30

1.00

40

0.94

0.99

0.95

50

0.85

1.00

0.90

1.00

0.96
0.91

(5) Overall influence factor
The factors resulting from the consideration of performance influence are not strictly independent but
related; for example, it is considered that the velocity factor could be affected by temperature and ageing. It is37

assumed that the overall influence factor may be predicted by performing superposition by multiplication, as
shown in equations (5.4.1) and (5.4.2).
Final reaction force＝Standard reaction force (Catalogue) ×CpR×CaR×VFR×TFR×Cr×CagR
Final energy absorption＝Standard energy absorption (Catalogue)
×CpE×CaE×VFE×TFE×Cr×CagE(5.4.1)(5.4.2)(6) Influence factor by factor pattern
The influence factors obtained in the manner described above are allocated to the factor patterns classified in
Section 5.4.2. Specifically, the categorization is performed as presented in Table 5.4.4.
Table 5.4.4 Factors influencing performance of rubber fender
Pattern B
Factor pattern
Pattern A
Pattern C
Consideration of major
Influence factors
Production tolerance
Mooring analysis
factors
Production
tolerance
Cp
AngularfactorCa
VelocityfactorVF
TemperaturefactorTF

Ageingfactor Cag

Repetition
factorCr

Reaction force
CpR
Energyabsorption CpE
Reaction force
CpR
Energyabsorption CpE
Reaction force
CpR
Energyabsorption CpE
Reaction force
CpR
Energyabsorption CpE
Reaction force
CpR
Energyabsorption CpE
Reaction force
CpR
Energyabsorption CpE
Creep

*1
*2

Maximum CpR+=1.1

Maximum CpR+=1.1

Maximum CpR+=1.1

Minimum CpE－=0.9

Minimum CpE－=0.9

Minimum CpE－=0.9

Maximum

CaR＋

Minimum

CaE－

No consideration orMaximum CaR(ε)＋
Minimum CaR(ε)－
Or by deflection*2

Maximum

VFR＋

Minimum

VFE－*3

Maximum

TFR＋

Minimum

TFE－

No consideration

No consideration

No consideration*4

No consideration orMaximum VFR(ε)＋,
Minimum VFR(ε)－
Or by deflection *2
No consideration orMaximum TFR(ε)＋,
Minimum TFR(ε)－
Or by deflection *2
No consideration orMaximum *4 CagR＋ or
1.0–1.05

No consideration

No consideration

No consideration

No consideration

No consideration or
0.9–1.0

No consideration

No consideration

Wind force＜Reaction
force at 10%*5

Index + indicates the maximum value,- denotes the minimum value
In the consideration of the influence of angle and velocity in the calculation for a mooring vessel with factor
pattern C, the angle and speed during mooring fluctuate instantaneously, and it is difficult to perform an accurate
simulation unless the influence factor is incorporated into the calculation program. Therefore, the maximum
reaction force and amount of maximum motion may be evaluated by analysing two cases involving the maximum
and minimum values of factors. (Refer to Section 5.5.3) Additionally, when the reaction force characteristics
change in extremely low temperatures, the performance of each deflection must be considered.

38

*3
*4
*5

Under normal circumstances, the velocity factor VFE－ of energy absorption can take the value of the deceleration
velocity, which is not a standard velocity; in this case, VFE =VFE－=VFE+.
Although sufficient survey results 8) pertaining to ageing have not been obtained, they are listed as items because
they are expected to be addressed in the future.
The vertical cylindrical rubber fenders (CELL) lead to 10% deflection. The deflections due to other rubber fenders
must be individually determined by testing.

5.5 Determination of influence factors
Since the influence factors affect the performance of rubber fenders, the rubber fenders should be selectedconsidering these factors. At the time of selection, the performance value is multiplied by the influence factors to reduce
the standard energy absorption EA in the catalogue to the minimum value EA－ so that the effective berthing energy Ebsatisfies the relationship given in equation (5.5.1).

E A－

≧

Eb

(5.5.1)For the reaction force, the product of the standard reaction force R in the catalogue and the influence factor must be R＋
to satisfy both conditions specified in equation (5.5.2).

R＋

≦
≦

Design horizontal force to mooring facility(Allowable hull pressure × Effective area of fender panel)(5.5.2)The suffix + indicates the maximum value, and －indicates the minimum value.
When it is certain that the ship will contact several rubber fenders, the total energy absorption of the fenders may beconsidered as EA. However, it is necessary to determine the minimum value EA- of the sum of the respective energy
absorptions and the maximum value R+ of the sum of reaction forces to determine the curvature radius of the vessel hullat the berthing point and the spacing (installation pitch) between fenders.
5.5.1 Calculation of design energy absorption: EA－
The minimum value EA－of the design energy absorption is determined using equation (5.5.3).

EA－= EA× CpE－× CaE× VFE × TFE－× CagE－(5.5.3)where

E A－ :EA:
CpE－ :CaE :VFE :TFE－ :
CagE－ :

Minimum design energy absorption (kNm)Standard energy absorption (catalogue value)
Minimum factor of production tolerance (0.9)
Angular factor of energy absorption
Velocity factor of energy absorption (decreasing velocity from berthing velocity)
Minimum temperature factor of energy absorption (highest temperature)
Ageing factor of energy absorption

For angular berthing, geometric checks are also required; for instance, the end of the fender panel must not touch thequay during the absorption of berthing energy.

39

5.5.2 Calculation of design reaction force: R+
The maximum design reaction force R+ considering the influence factor of design condition can be obtained using
equation (5.5.4).

R＋ = RR × CpR＋× CaR＋× VFR ×TFR＋ ×CagR＋(5.5.4)

Here,

R＋ :
RR
:
CpR＋ :
CaR＋ :VFR :TFR＋ :
CagR＋ :

Maximum design reaction force (kN)Standard reaction force (catalogue)
Maximum factor of production tolerance (1.1)
Angular factor of reaction force or 1.0 (larger value)
Velocity factor of reaction force (decreasing velocity from berthing velocity)
Maximum temperature factor of reaction force (lowest temperature)
Ageing factor of reaction force

5.5.3 Calculation of design factors for mooring analysis
In the motion calculation of the moored vessel, it is necessary to express the performance of rubber fenders as
accurately as possible. The compression (loading) performance RF1 and the return (unloading) performance RF2 aredifferent, as shown in Fig. 5.5.1, resulting in energy loss. This loss is known as the hysteresis loss, and a considerable
amount of this energy is converted to heat. Assuming that this hysteresis loss is expressed as shown in Fig. 5.5.1, let R (ε)
be an approximate function of the reaction force by the deflection, which is expressed by a regression equation or
numerical table. The maximum and minimum factors can be calculated using equations (5.5.5) to (5.5.8).

Fig. 5.5.1 Loading and unloading performance of rubber fender
Maximum performance: RF1(ε)＋＝

RF1(ε) × CpR＋× VFR(ε) × TFR(ε)＋ × CagR＋(5.5.5)

Unloading : RF2(ε)＋
Minimum performance＝RF2(ε) × CpR＋× VFR(ε) × TFR(ε)＋ × CagR＋(5.5.6): RF1(ε)－＝

RF1(ε) × CpR－× CaR(ε)－× TFR(ε)－× Cr × CagR－(5.5.7)

Unloading : RF2(ε)－＝

RF2(ε) × CpR－× CaR(ε)－× TFR(ε)－× Cr × CagR－(5.5.8)

Loading

LoadingHere,
RF1(ε), RF2(ε): Standard reaction force for loading and unloading at deflection εRF1(ε)＋, RF1(ε)－ : Maximum and minimum reaction force at deflection ε during loading
RF2(ε)＋, RF2(ε)－ : Maximum and minimum reaction force at deflection ε during unloading
CaR(ε)－: Minimum angular factor of reaction force at deflection ε
CpR＋, CpR－
: Maximum and minimum production tolerance factors of reaction force (0.9, 1.1)
VFR(ε): Velocity factor of reaction force at deflection ε
TFR(ε)＋, TFR(ε)－ : Maximum and minimum temperature factors of reaction force at deflection ε

40

CrR
CagR＋,CagR－: Repetition factor of reaction force: Ageing factor of reaction force

The expressions in equations (5.5.5) to (5.5.8) are used as the performance functions of rubber fenders for themooring simulation of vessels. The angle coefficient CaR, velocity coefficient VFR, and repetition factor CrR are difficult
to take into consideration when performing the simulation because the angle and speed change constantly, and repetition
fatigue accumulates. As a countermeasure, the coefficients may be substituted by performing the calculation using only
the maximum and minimum values of the performance. Furthermore, a complex behaviour is exhibited in which thevelocity changes in the middle of compression, and this phenomenon cannot be reproduced without employing amethod such as a hybrid simulation 9). However, as shown in Fig. 5.5.1, approximations can be made in which the upperand lower connections are established using linear spring constants of the initial deflection. In the design of fenders, thegenerated reaction force when the maximum factors are adopted is the design load to the structure, and the maximum
deflection when the analysis is performed using the lower limit of each factor is the allowable design deflection. In thesimulation, the specifications of the rubber fender are determined by trial and error to be within the design limits.
5.5.4 Consideration of number and length of fenders
The performance of a rubber fender with a fender panel can be modified by attaching multiple fenders to one panel.
However, as shown in Fig. 5.5.2, if two rubber fenders are attached to one panel, although the energy absorption EA will
be doubled, the reaction force R will also be doubled. Furthermore, the performance of the rubber fender is related tothe size; when the size is doubled, the reaction force becomes 22 = 4 times, and the energy absorption becomes 23 = 8
times. In other words, if one rubber fender having a size (height) of approximately 1.26 times is attached, the reaction
force can be suppressed to 1.6 times while realizing two times the energy absorption. Therefore, no restrictions exist,
such as in terms of the installation space of the quay or maximum height, and the efficiency of energy absorption (EA /R) is the maximum when using a single fender. However, when a large panel is required, several fenders may be used toensure the stability of the system. Considering the length, as shown in Fig. 3.3.4 to Fig. 3.3.6 in Chapter 3, an adjustable
type fender can also help modify the performance by increasing the length instead of changing the height. As describedabove, although various responses are possible depending on the application, when the length is less than the height, thecompression mode may change due to the influence of both ends. In addition, it should be noted that the influence of theangle increases with increase in the installation pitch.

Fig. 5.5.2 Performance comparison of single and multiple fenders for fender panels
When upgrading existing facilities or dealing with larger vessels, the restriction of rubber fender height to theoverhang of loading cranes, compatibility of size and pitch of fixing bolts, etc. are also important considerations.

5.6 Arrangement of rubber fenders
In the arrangement of rubber fenders, the effective berthing energy must be able to be absorbed, even in the worst
situation, by taking into consideration the installation pitch, shape of the vessel, position of mooring facility, tidal leve ls,

41and draft; moreover, crashes should be avoided, and concerns must be clarified and addressed by adopting suitablecountermeasures. In certain circumstances, it is difficult to obtain the curvature of the ship hull, which is necessary to
determine the installation pitch; thus, this document does not specify the determination method and provides only
reference examples.
5.6.1 Installation pitch of fenders
When installing a large number of rubber fenders at a constant pitch on a long quay, the determination of theinstallation pitch becomes important. As shown in Fig. 5.6.1.1 and Fig. 5.6.1.2, when multiple rubber fenders are
installed at a pitch S on a quay, and the pitch S is shorter than the curvature radius of the vessel hull, multiple rubber
fenders will be compressed. The installation pitch of rubber fenders needs to be determined so that the part of the hullclosest to the quay wall does not make contact when the effective berthing energy is absorbed by the fenders. Several
methods of determining the pitch S are proposed as a reference in this subsection. If the installation position is fixed at
the existing mooring facilities and it is difficult to shorten the installation pitch, measure s such as raising the rubber
fender by the base and advancing the berthing line can be adopted.
(1) Design calculation method for example of harbour structure 3):
Pitch: S ≦ 1/5 to 1/6 times the length perpendicular of vessel (αLppcosθ) (α: see Fig. 5.3.2)(2) British Standard 5): Pitch S ≦ 0.150.15Loa（Loa: Overall length of vessel）(3) Method to determine pitch from the hull radius of vessel: equation (5.6.1)
Assuming that the hull shape at the berthing part is a cylinder with a radius of hull curvature Rr, and assuming that achord is present between two fenders separated by pitch S, as shown in Fig. 5.6.1.2, the pitch can be calculated
according to equation (5.6.1) using the residual height h when the fender is compressed to its design deflection and theestimated values of hull radius Rr.
𝑆 = 2√𝑅𝑟 2 − （𝑅𝑟 − ℎ)2(5.6.1)Here,
S : Fender pitch (m)Rr : Hull radius of vessel at berthing point (m)H : Residual height when fender is compressed to design deflection (m)Fig. 5.6.1.1 Berthing at centre of three fenders

Fig. 5.6.1.2 Berthing between two fenders

Assuming that two rubber fenders are compressed, as shown in Fig. 5.6.1.2, and assuming that the curvature radius of
the hull is Rr, the local angle θ on the contact point can be estimated using equation (5.6.2).

42θ=sin-1 (

S
)
2Rr

(5.6.2)

Often, the installation pitch cannot be changed if the quay structure is based on the existing quay wall. In the case of
replacement of the existing rubber fenders, it may be difficult to raise the height by a base or spacer.
The curvature radius Rr of the hull is often not available. In such a case, it may be assumed using equation (5.6.3).

Rr =B Lpp 2+
4 16B

(5.6.3)Here,

B : Beam of vessel (m)Lpp : Length between perpendiculars (m)Equation (5.6.3) can be employed under the assumptions of quarter point berthing; furthermore, as shown in Fig.
5.6.2, if a circle passes through the three red points, the relationship presented in equation (5.6.4) holds. If thisexpression is calculated around Rr, equation (5.6.3) can be obtained.

Rr 2 = (Rr－B/2)2 + (Lpp/4)2(5.6.4)

Fig. 5.6.2 Assumption of hull radius at berthing point
When a vessel comes in contact with multiple fenders, it is possible to use the sum of the reaction force and energy
absorption of the respective fenders in contact. However, in reality, the shape data of a vessel hull is difficult to obtain,
and thus, accurate confirmation is difficult. Therefore, if the radius of curvature cannot be obtained, it can be assumed
using equation (5.6.3). In contrast, it is necessary to accurately determine the reaction force when the vessel contacts
two fenders, as shown in Fig. 5.6.1.2, and when vessel contacts three fenders in the centre and on both sides, as shownin Figure 5.6.1.1. When the range of the vessel size is large, it is not economical to arrange the rubber fenders for large
ships at the pitch calculated using the hull radius Rr of small vessels. In such a case, V-type rubber fenders for small
vessels are sometimes placed in the middle of rubber fenders for large vessels. In addition, since the vessel hull above
the fender level has a larger flare angle, it is also necessary to consider the contact of the vessel hull with the upper edgeof the quay. Depending on the location, the flare angle may exceed the berthing angle by three to four times 10).
However, it is difficult to obtain hull shape data for a modern vessel, and thus, the flare angles corresponding todifferent vessel types and sizes are not available. In principle, as large flares on the hull can cause damage to port
facilities, berthing should be controlled to be parallel to the berth line, and large berthing angles should be avoided. In
addition, the hull radius is considered to be smaller on the stern side than on the bow side; thus, when considering
berthing at the stern side, it is reasonable to assume that a shingle fender must absorb the effective berthing energy.

43

5.6.2 Vertical installation of fenders(1) Installation of V-type rubber fender
As shown in Fig. 5.6.3, V-type rubber fenders without fender panels do not contact at the full length forcertain vessel positions, and rubber fenders can perform only in the length contacted. It is necessary to estimate
the minimum contact length from the minimum deck height, draft, tidal level, etc. and select the length suchthat the effective berthing energy Eb can be absorbed. This phenomenon is called partial compression, and theperformance can be evaluated using equation (5.6.5).
(Energy absorption by partial compression)=(Energy absorption per meter)×(Contact length)(5.6.5)In the case of rubber fenders with a constant cross-section (for example, V-type rubber fenders) for which theperformance can be modified by changing the length, if the length is shorter than the height, the length ratio isaffected by both the ends. The length ratio in this case may not correspond to the performance being proportional
to the length. The contact length of a rubber fender relates to not only the length of the rubber fender but also theinstallation position. The installation considerations for V-type rubber fenders are listed as follows, and Fig.
5.6.3 provides an explanatory view of the aspects to be considered.
・ The flare of a large vessel should not contact the edge of the quay, even when the rubber fender is compressed.
・ It is desirable that the top head of fender is always visible and not be submerged in water.
・ The necessary concrete coverage should be secured over the anchor bolts
・ The effective berthing energy must be absorbed by the length in contact with the rubber fenders

Fig. 5.6.3 Considerations for vertical installation of V-type rubber fender
As shown in Fig. 5.6.3, when the flare of a large vessel comes in contact with a vertically installed V-type
rubber fender, the fender is subjected to vertical angular compression. Generally, the angular performance ofV-type rubber fenders described in catalogues is the angular performance in the width direction, and thelongitudinal angular performance is often not defined because it changes depending on the length of the rubber
fender. In such a case, the performance can be determined in the following manner.
The performance curve of the energy absorption EA of a V-type rubber fender is defined as in equation (5.6.6)
as a function of the deflection x by considering a polynomial function or numerical values in a table.

44

EA

=

f(x）

Continuous functions such as polynomials(5.6.6)

If variables are defined as shown in Fig. 5.6.4 for the condition shown in Fig. 5.6.3, the angular reaction force
of a rubber fender can be estimated using equation (5.6.7) by integrating the reaction force of the compressed
part.
Ly

EAθ = ∫y＝0 f(D-y tanθ) dy
L= ∑ y f(D-y tanθ)
y＝ 0

Here,
EAθ
Ly
D
θ
y

:
:
:
:
:

Continuous function
Discrete data

(5.6.7)

Energy absorption at simulated angular compression (kNm)Contact length (m)Design deflection of V-type fender (m)Flare angle
Variable from fender top (m)The maximum reaction force to the quay is larger when the entire surface is compressed at an angle of 0°; thus,
a reaction force with an angle of 0° is used.

Fig. 5.6.4 Angular compression by hull flare to V-type rubber fender
Since the amount of compression by the hull flare, as calculated using equation (5.6.7), is small, the fender
may not be able to absorb the effective berthing energy of a large vessel. In such a case, horizontal installation oralternate vertical and horizontal installation of V-type rubber fenders can be realized. Alternatively, rubber
fenders with fender plates may be used.
(2) Installation of rubber fender with panel
Even in the case of rubber fenders with panels, it is necessary to perform a geometric investigation of theminimum vessel freeboard, draft and lowest tidal level. In such cases, the panel, chain, etc. need to be consideredin the system, as described in the next section.

45

5.7 Detailed design and considerations
In the next step for the selection of a rubber fender, the design of parts such as fender panels, chains and fixings isrequired for the fender system. In particular, in the case of rubber fenders with panels, the design of these parts is avaluable aspect that determines the final size, rubber grade and cost. After the selection, based on the effective berthing
energy, if the design of a fender panel or chain for the selected rubber fender is not suitable, the designer may overlook
the inherent hazards of the system. It is necessary to perform the design appropriately in accordance with theengineering principle and confirm the results with the purchaser. The actual design calculations may be left to
manufacturers because the details of these design procedures vary by type, size, and manufacturer. Therefore, the basic
concepts of the fundamental balance of forces and moments are presented here.

5.7.1 Allowable hull pressure
The fender panel should be joinable with the rubber fender body, and its size should be larger than the required
contact area for the allowable average hull pressure. The average hull pressure P on the panel is determined by dividing
the design reaction force by the effective panel area, as shown in equation (5.7.1), to determine the size of the fender
panel.

P 

R
A

 Hp

(5.7.1)

where

P:
R:
A:
Hp :
WF :
HF :

Average hull pressure(kN/m2 = kPa)
Design reaction force(kN)
Effective contact area of fender panel(A = WFe x HFe：m2)
Allowable hull pressure (kN/m2 = kPa)
Width of fender panel(WFe = Effective width：m)Height of fender panel(HFe = Effective height：m)Table 5.7.1 presents the values of the maximum allowable hull pressure recommended for each type of vessel in the
PIANC Guidelines s) amended with an example of the domestic results. According to the Technical Standards andCommentaries of Ports and Harbour Facilities in Japan 2), the recommended hull pressure is 200 to 400 kN/m2 on thepremise of the frame (ribs) coming into contact on the vessel side. The effective width and effective height of the fender
panel may not include the oblique chamfer portion of the end in the area but may include the gaps between the resin
pads. This configuration is shown in Fig. 5.7.1.

Fig. 5.7.1 Effective size of fender panel46

Although the hull pressure is restricted by the strength on the vessel side, the hull pressure is not uniform because thereinforcement on the hull is not uniform. The allowable hull pressure is the average face pressure, used as a standard for
determining the size of the fender panel. However, in certain locations, the pressure is higher than the average hullpressure at the reinforcing rib of the vessel side. Furthermore, the contact pressure is zero on the indented area. In
addition, in the case of angular berthing, the contact of the panel in the initial stage of berthing is a point or line contact,
and the contact area cannot be calculated. Although the hull pressure is usually referred to as the contact pressure, here,
it is termed as the average hull pressure to distinguish it from the local contact pressure. Moreover, since this pressure
has a large value in a rubber fender without a panel, the panel is often required when the hull pressure is limited.
Table 5.7.1 Guide of allowable hull pressure
Allowable hull pressure（kN/m2）

Type of vesselContainer vessel
1st and 2nd generation *1
3rd generation (Panamax 1700–2500 TEU)*1
4th generation (3600–4800 TEU)*1
5th and 6th generation (SuperPanamax, 4900 TEU) *1

<400
<300
<250
<200

Recent examples in Japan *2<200–290

General cargo vessel≦20,000 DWT＞20,000 DWT<400–700<400

Oil tanker≦60,000 DWT＞60,000 DWTVLCC (Very large oil tanker)

<350
＜300
<150–200

Recent examples in Japan *2<200

Gas carrier(LNG/LPG)<200

Recent examples in Japan (LNG) *2<130–134

Recent examples in Japan (LPG)*2<245

Bulk carrier
Recent examples in Japan (Ore carrier)

<200
*2

<280–320

SWATH (Small-waterplane-area twin hull)

Hull pressure is not considered
for vessels with belt protection.

RO-RO (Roll On Roll Off ) vessel
Passenger vessel

Notes: * 1 The TEU of each generation of container vessels is based on Tanaka et al. 11).
* 2 Amended PIANC Guidelines 4) based on examples corresponding to Japan.

5.7.2 Load cases for fender panel
The bending moment applied to the fender panel should be carefully considered according to the manner in which theberth force is applied, as shown in Fig. 5.7.2.
1)
2)
3)
4)
5)

Point load: Corner contact at the initial stage of berthing, etc.
Line load: Angular berthing, contact of hull flare, etc.
Two line loads: Contact of vessel with belted hull
Central line load: Contact with the centre of two or more vertical fenders
Distributed load: Full contact or partial contact with fender panel

47

Fig. 5.7.2 Load cases for fender panel

5.7.3 Design Considerations
When designing fender panels and chains, the berthing and cargo handling operations can affect the durability offenders and the safety of operations. Some representative examples are as follows:(1) Prevention of breakage due to hooking of mooring ropes
As shown in the left figure in Fig. 5.7.3, the case in which a low freeboard vessel performs berthing lower
than a rubber fender is called low contact. In this case, a tension chain is often installed at the upper end of thefender panel; since this chain is connected to the eye plate on the top of panel, as shown in Fig. 5.7.3, the chain
can prevent the ropes coming between the quay and fender panel and being hooked when the mooring rope
loosens. This consideration is important to ensure that a mooring rope caught on the fender panel does notinterfere with rope management or cause an accident. In many cases, rope wear is reduced by covering thechain with a rubber hose or rope guard and processing the corners of the eye plate (chain hanger) to be smooth.
Similar to a rope guard, a guard exists that extends the bar from the lower end of the panel to the water toprevent the penetration of the mooring rope underneath the fender. In addition, sharp corners must be removed
in locations in which the rope is likely to be caught and to keep the upper end of the panel at a position lower
than that of the quay top.
(2) Preventing hooking on the hull belt
As shown in the right figure in Fig. 5.7.3, if the vessel has a belt that extends from the hull, installing a wing
to prevent hooking by producing an inclined portion at the upper and lower ends of fender panel is effective. In
addition, if such a protrusion is present on the vessel side, the resin pad on the surface of the panel may bedamaged rapidly; thus, a resin pad should not be used when constantly receiving loads such as those of a ferry.

Fig. 5.7.3 Design considerations for areas surrounding fender panel

48

5.7.4 Load cases for regions surrounding fender panel and chains
The basic concept of each load case occurring in the fender panel is described below. Since these calculations assume
rubber fenders acting as spring elements as a function of deflection, the calculation process is often left to the
manufacturer. However, it is desirable to be able to verify whether the results are correct based on basic principles.
(1) Line load cases
As shown in Fig. 5.7.4, equation (5.7.2), and equation (5.7.3), when the hull contacts the rubber fender at anangle and is compressed with the line load F, the rubber fender generates a reaction force R by deflection δ1
and the rotational moment Mf that resists the rotational angle θ. Although shear resistance is also generated, it isignored because its value is small. The bending moment and chain tension generated in the fender panel can be
determined from the balance of forces and rotational moments. When the rotational angle becomes θ, the vessel
hull and the fender panel come into full contact, and the pressure distribution is as shown in Fig. 5.7.8.
Therefore, Fig. 5.7.4 can be considered to represent the state immediately before full contact.

Fig. 5.7.4 Line load by angular berthing: Single fender with chains
In Fig. 5.7.4, the balance between the forces applied to the fender panel and the rotational moments, as wellas the geometric relationship between the displacements, are as shown in equation (5.7.2).

R=F+T
M f = TL2 － FL1
δ1＝δ0 － L1tanθ

(5.7.2)Here,

R : Reaction force of fender (kN)
Mf : Rotational moment of fender (kN･m)
F : Berthing force (kN)
T : Chain tension (kN)
δ0 : Deflection at berthing point (m)δ1 : Deflection at fender centre (m)θ : Berthing angle (°)
If no chain is present, Fig. 5.7.4 changes to Fig. 5.7.5, and the balance between the force and rotational
moment can be expressed as in equation (5.7.3).

R=F
M f = FL1
δ1＝δ0 － L1 tanθ

(5.7.3)49

Fig. 5.7.5 Line load by angular berthing: Single fender without chain
If the compression deflection δ1 (displacement amount / height, %) and the inclination angle θ aredetermined, the reaction force R and the rotational moment Mf of the rubber fender can be determined using apolynomial function or data table. However, the method of determination differs depending on the type of
product and manufacturer, and thus, it is not mentioned in this document. In particular, in the case of multiple
fenders, the rotational moment of fenders is often omitted. The reaction force of the fenders and the tension ofchains can be obtained from equation (5.7.2) by varying the berthing point deflection δ0 from 0 in appropriate
increments. The strength of the fender panel can be obtained by calculating the generated bending moment andthe section modulus of the panel. However, since the structure of the fender panel also differs depending on the
manufacturer, this aspect is not considered herein, and only the balance of the loads is demonstrated.
If two rubber fenders are present on a single fender panel, the condition is as shown in Fig. 5.7.6, and thebalance between the force and rotational moment can be expressed as in equation (5.7.4).
R(1)＋R (2) = F + T
M f (1)＋M f (2) = T（L1 + L2＋L3）－ R (1) L1 － R (2) （L1 + L2）(5.7.4)

Assuming a chain does not stretch, the geometric relationship of the deflections of the two fenders and theberthing point is as shown in equation (5.7.5).
δ1＝δ0 ―
δ2＝δ1 ―

L1 tanθL2 tanθ(5.7.5)In addition, in this case, if the deflection δ0 at the berthing point is changed from 0 to a certain value inappropriate increments, the deflection of each fender can be determined using equation (5.7.5), and theberthing force F and chain tension T can be determined using equation (5.7.4). The energy absorption can beobtained by integrating the berthing force F from the deflection δ=0 to the design deflection δmax, as given inequation (5.7.6).
δmax

Ea = ∫δ＝0 F(δ) dδ= ∑δδmaxF(δ)＝0𝐹(𝛿): Continuous function
𝐹(𝛿): Discrete data

50

(5.7.6)

F

L3
L2
R(2)

L１
R(1)
δ

T

θ
M(2)
M(1)

δ
δ
Fig. 5.7.6 Line load by angular berthing: Two fenders with chain(2) Point load case
When a vessel contacts the fender panel at a three-dimensional angle, it is initially a point load. As the hull
approaches further, it becomes a line load and eventually contacts the entire surface of the panel. When several
fenders are attached to a single large fender panel or the angle of the vessel hull is large, the point load statecontinues for a large duration. It should be noted that the maximum bending moment may act on the panel inthis state, or maximum chain tension may occur. A point contact with a fender system with an arbitrary numberof rubber fenders is illustrated in Fig. 5.7.7, and the state is expressed in equation (5.7.7). The number of
equations and number of unknown variables increase; however, if there exists a function of reaction force R(i,j)
for the deflection of each fender, the bending moments and chain tension can be determined via numericalcalculations. The energy absorption can be obtained using equation (5.7.6). Note that if the fender panel is large
and the panel edge contacts the quay before the design deflection of the fender, the fender must be able toabsorb the effective berthing energy up to that point. Equation (5.7.7) has several unknown variables, and thus,
it needs to be solved using numerical calculations, such as Newton's method. The validity of the result can be
confirmed by substituting it into the left side of equation (5.7.7) and ensuring that the right side becomes zero.

Fig. 5.7.7 Point load by angular berthing: Multiple fenders n×m

51

F+T+ ∑ni=1 ∑m
j=1 R(i,j) =0n∑m
i=1 {X(i)∙ ∑j=1 R(i,j)}+X(m+1)∙T=0(5.7.7)∑nj=1 {Y(j)∙ ∑m
i=1 R(i,j)}+Y(n+1)∙T=0
Here,
X(i) :
Y(j) :n :m :R(i,j) :X coordinate of the i-th rubber fender in X direction (m)Y coordinate of the j-th rubber fender in Y direction (m)Number of fenders in the Y direction
Number of fenders in the X direction
Reaction force of fender (i,j) (kN)

Here, the rotational moment of the rubber fender is ignored. Additionally, the geometric relationship ofthe deflection is as given in equation (5.7.8).
Under such a point load condition, when the deflection of the rubber fender reaches the design deflection, or
the fender panel comes into contact with the quay, the chain tension may increase to the design limit. As aresult, the link may become too large to be selected. According to the PIANC Guidelines 4), the safety factor ofa normal chain is set between 3 and 5, and a safety factor of 2.0 may be adopted when the chain load isincreased due to an abnormal berth. As described above, it is acceptable to reduce the safety factor to 2.0 when
one chain is subjected to a large tension in a short period.
δ(1,1)＝δ0 － X(1) tanθX － Y(1) tanθY・δ(i, j)＝δ0 － X (i) tanθX － Y (j) tanθY・・・δ(m,n)＝δ0 － X (m) tanθX － Y (n) tanθY(5.7.8)(3) Distributed load case
When an angled hull contacts the fender panel, and the entire surface touches the vessel side after the point
load and line load, a distributed load is considered to occur, as shown in Fig. 5.7.8.

Fig. 5.7.8 Distributed load by angular berthing: Single fender
At this time, the balance between the forces and rotational moment around the fender panel is as given inequation (5.7.9).

52

L

R = ∫𝑥＝0 ω(x) dx
L

Mf ＝ ∫x＝0 ω(x)∙x dx-R∙L１(5.7.9)In equation (5.7.9), R is a reaction force for each deflection at the time of angular compression at angle θ. Mf
is a rotational moment at the deflection and angle at that instant, which varies depending on the product but isrequired to determine the slope of the distributed load ω(x). The distributed load may be an equal distribution
load for angle=0, or a slope distribution load for angle=θ, as shown in Fig. 5.7.8. However, in fact, the shape ofthe distribution depends on the position of the frame (rib) on the vessel hull, and thus, it is difficult todetermine the distribution shape. The distributed load in Fig. 5.7.8 is an example for a case in which a linear
inclination is assumed. Normally, the strength obtained by the point load or line load is often used, but the
distribution load can be used when the angle is unknown, and the state of point load or line load cannot be set.
As described above, the bending moment generated at each position of the fender panel can be calculated
from the load balance condition in accordance with the berthing conditions. Subsequently, the maximum
bending moment can be determined, and the generated stress can be calculated from the section modulus of thefender panel. This stress must be within the allowable bending stress.
(4) Chain design
Chains are used to restrain undesirable deformations of rubber fenders. Chains may be classified into thefollowing categories according to their functions, and they are designed as needed.
1) Tension chain (Fig. 5.7.9)
・ To control the stretching of the rubber fender・ To control the rotation of the fender panel.

Fig. 5.7.9 Role of tension chain2) Weight chain (Fig. 5.7.10)
・ To control the front drooping of the fender・ A tension chain is needed to control the tipping forward of the fender panel if the weight chain is
attached to the lower part of the panel.

53

Fig. 5.7.10 Role of weight chain3) Shear chain (Fig. 5.7.11)
・ To control shearing of the rubber fenderFig. 5.7.11 Role of shear chain4) Example of friction coefficient μ
In Fig. 5.7.11, μ is the friction coefficient between the fender panel surface and the vessel hull. The
following values are often used as an example of the friction coefficient.
Fender panel (resin pad) and vessel hull (Steel): 0.2 to 0.25
Fender panel (Steel) and vessel hull (Steel): 0.3 to 0.35
Rubber and vessel hull (Steel): 0.3 to 0.4
In most cases, the chain tension is calculated in the process of obtaining the bending moment of the fender
panel, as explained in the previous section. The load conditions must be set appropriately, and the maximum
tension generated must be determined and ensured to be less than or equal to the design tension of the chain.
Not all cases of fenders with panels require chains. The requirement of chains should be carefully considered,as the installation of chain often requires that the fender panel has additional strength.

5.8 Corrosion protection of steel parts
Although it depends on the environment and use conditions, the service life of corroded steel is generally shorter thanthe life of a rubber body if no measures are adopted. Therefore, when using steel parts, it is necessary to provide
appropriate corrosion protection in accordance with the coastal environment. Two primary types of corrosion protection
methods exist: cathodic protection and anticorrosion coatings. The Technical Standards and Commentaries of Ports andHarbour Facilities in Japan 2) recommends that the cathodic protection method should be adopted in cases involving
water levels equivalent to or lower than the mean low water level (MLWL), and anticorrosion coatings should be
adopted in cases involving water levels higher than 1 m less than the low water level (LWL-1 m). Data regarding
corrosion protection and repair of steel structures in ports and harbours are described in detail in, for example, theManual for Corrosion Protection and Repair of Steel Structures in Ports and Harbours 12). In this work, the54considerations for coating and plating commonly used for bolts and chains are presented. If part or all of the fender
panel falls below the average low water level, coating protection and cathodic protection may be used in combination ;for details, the reader may refer to the Manual for Corrosion Protection and Repair of Steel Structures in Ports andHarbors 12).
With steel materials such as fender panels and chains used for rubber fenders, it is necessary to properly perform
maintenance and control together with the adoption of anticorrosion measures and partial replacement based on the stateof deterioration. The cycle of replacement is considerably affected by maintenance measures such as touch-up painting.
To evaluate the degree of deterioration, one may refer to the Guidelines for the Maintenance of Rubber Fender Systems
13).
5.8.1 Painting
Fender panels are mainly protected by painting. An example of the paint specification is described. Because a fender
panel can be checked and replaced on a regular basis, in contrast to other steel structures used in mooring facilities, theneed for long-term corrosion protection is not as high as for permanent steel structures. However, the environment
involves a splash zone with the influence of ultraviolet rays, and thus, a maintenance plan should be carefully
considered with equal focus on the economic aspects. According to the Manual for Corrosion Protection and Repair of
Steel Structures in Ports and Harbors 12), as given in Table 5.8.1, the useful life is 10 to 15 years for both heavy
protection grade-1 and heavy protection grade-2 paints.
The corrosion rate of steel after deterioration of the paint film is defined in Technical Standards and Commentaries ofPorts and Harbour Facilities in Japan 2) as follows.
H. W. L or higher: 0.3 mm/y
H. W. L to L. W. L-1 m: 0.1 to 0.3 mm/y
It is necessary to consider the abovementioned corrosion allowance assuming that the paint has deteriorated and lostits effect. As specified in the Technical Standards and Commentaries of Ports and Harbour Facilities in Japan 2), thecorrosion countermeasure, which is based solely on the additional thickness, should not be applied. Therefore, if
painting is performed properly and maintenance is possible, it is not necessary to incorporate the corrosion allowance inthe strength design unless extraordinary circumstances exist. However, in a case in which the paint on the front face ofthe fender panel wears away due to the belt of the vessel, such as in the case of ferries, the corrosion allowance of 0.3
mm/year must be considered in the stress design, and the strength after wear should correspond to the yield point of thesteel material.
Table 5.8.1 Corrosion protection for fender plate using paint
Paint spec.
Substrate adjustment

PrimerTop coat
Total film thickness

Heavy protection grade-1

Heavy protection grade -2

Degree of adjustment:

Degree of adjustment:

Sa 2-1/2 or more

Sa 2-1/2 or moreThin film organic (Epoxy)Thin film organic (Epoxy)

Thick film organic (Epoxy)

Zinc rich primer: 20 μm

Zinc rich primer: 20–30 μm

Zinc rich primer: 60–70 μm

Tar epoxy substitute resin paint

Epoxy resin paint

Epoxy resin paint

300 μm

430 μm390 μm

320 μm450 μm

5.8.2 Plating
Plating protection is applied at locations involving metal-to-metal contact such as for chains and shackles. The
plating specification of a chain generally has a molten zinc adhesion amount of 550 g/m 2 or more or a thickness of 76

55

μm or more. However, to secure engagement, the threaded portion is not limited to the above values.
Bolts and nuts are often made of stainless steel or plated steel depending on the conditions. Surface treatment
according to the material is described in Table 5.8.2.

Material

Table 5.8.2 Surface treatment for bolts and nuts
Surface treatment/Remarks

SS400

Galvanization

SUS304

When the material is subjected to hot forging after solution
heat treatment, solution heat treatment is performed again;
subsequently, passivation film formation treatment such as acidwashing is performed.

SUS316

5.9 Allowable stress of steel material
The allowable stress of steel materials is presented in Table 5.9.1. Because the allowable stress varies depending on
the plate thickness, steel plates of 16 mm or more and stainless-steel materials are considered, for example, as specified
in the Design Standard for Steel Structures 14) of the Architectural Institute of Japan.
Table 5.9.1 Allowable stress of steel material (Thickness less than 16 mm)

Allowable stress(N/mm2)

Structural steel

Technical Standards and Commentaries of Ports and Harbour
Facilities in Japan, 1989

SS400

400

Yield stress or
70% of tensilestress245

SM490A

490

325

Tensilestrength

Allowabletensile stress

Allowable
shear stress

140

80

190

110

Based on the type and strength of the chain, the following Japanese Industrial Standards can be referred to.
Japanese Industrial Standard JIS F-3303-2010, “Flash butt welded anchor chain":
The breaking load and bearing load capacity of the stud-link and normal link chains are defined. The
bearing load is the load at which the material begins to undergo plastic deformation, and its value isapproximately 1/1.4 of the breaking load for a chain with a stud and 1/2 for a chain without a stud.
Japanese Industrial Standard JIS F-2106-2013, “Marine General Purpose Chains":
The bearing load and working load are defined for a studless chain; the working load is approximately
1/2.5 of the bearing load.
Assuming that the safety factor is the ratio of the breaking load to the working load, the safety factor is 5.0 for
studless chains and 3.5 for stud-link chains. Moreover, in the PIANC Guidelines 4), the safety factor of the chain ranges
between 3 and 5, and it is considered to be 2.0 in the case of abnormal berthing. With reference to these values, in thecase of a chain for rubber fenders with a fender panel, a safety factor of at least 3.0 should be considered when a load isalways applied similar to a weight chain. In addition, as described in Section 5.7.4, when point loads occur in a shortperiod in one chain due to angular berthing, the safety factor may be considered as 2.0.

56

〔References〕
1) Murakami, K., Takenobu, M., M. Miyata, M., Yoneyama, H.: A Fundamental Analysis on the Characteristics ofBerthing Velocity of Ships for Design of Port Facilities, Technical Note of National Institute for Land andInfrastructure Management, National Institute for Land and Infrastructure Management, No.864, p.54, 2015 (inJapanese)2) Ports and Harbours Association of Japan (PHAJ): Technical Standards and Commentaries of Ports and Harbour
Facilities in Japan, 2018
3) Ports and Harbours Association of Japan (PHAJ): Design example of port structure, Vol. 1, 1992 (in Japanese)
4) PIANC: Guidelines for the Design of Fenders System, Report of Working Group 33 of the Maritime Navigation
Commission, 2002
5) British Standard: Maritime works-Part 4 Code of Practice for Design of Fendering and Mooring Systems, BS 6349-4,
20146) Ueda, S., Shiraishi, S.: On the Design of Fenders Based on the Ship Oscillations Moored to Quay Walls, Technical
Note of the Port and Harbour Research Institute, No.729, pp.1-55, 1992 (in Japanese)
7) Ueda, S., Shiraishi, S., Oshima, H., Asano, K.: Allowable Wave Height and Warf Operation Efficiency Based on theOscillations of Ships Moored to Quay Walls, Technical Note of the Port and Harbour Research Institute, No.779,
pp.1-44, 1994 (in Japanese)
8) Akiyama, H.: Study on Aging of Circular Hollow Rubber Fender in Long Term Usage, Osaka University Doctoral
Thesis, 2018 (in Japanese)
9) Oda, K., Maruyama, T., Tanaka, H., Nagata, S., Yamase, S.: Hybrid Simulation for a New Movable Floating Bridge,
Proc. Of the 6th East Asia-Pacific Conference on Structural Engineering and Construction, pp.435-441, 1998
10) Yamase, S., Ueda, S.: Berthing Energy Absorption for Large Container Vessel, Proc. of 16th ISOPE, Vol. 3，
pp.689-894，2006
11) Tanaka, Y., Yamaguchi, N., Aoyagi, A.: Technical Trend of Large Container Ship, Mitsubishi Heavy Industries
Technical Report, Vol.34, No.5, pp.306-309, 1997 (in Japanese)
12) Coastal Development Institute of Technology (CDIT): Manual on Corrosion Prevention and Repair for Ports andHarbor Steel Structure, No.35, 2009 (in Japanese)
13) Coastal Development Institute of Technology (CDIT): Maintenance Guidelines for Maritime Fender Systems(Ver.2), No.40, 2013 (in Japanese)
14) Architectural Institute of Japan: Design Standard for Steel Structures－Based on Allowable Stress Concept, 2005

57

Chapter 6
Testing

6.1 General
Rubber is a visco-elastic material that exhibits complicated characteristics. To conduct performance testing of arubber fender, it is necessary to set appropriate conditions and control them properly to ensure that the test is conductedaccording to the given conditions. In this book, the tests are classified as follows according to the purpose: adevelopment test, an authentication test, and a quality verification test. Management and operation are performed
according to the classified purposes.

6.2 Test classification by purpose
The tests for rubber fenders can be classified into the following three types according to the purpose of the test.
(1) Development test
A series of tests is conducted by the manufacturer for the development of rubber fenders; among these, thetests that are the basis of catalogue values and technical data are called development tests. Such tests are often
implemented under various conditions to cover all possible situations. Normally, reproduction istime-consuming and costly and may not be released, as it is a proprietary technology of the manufacturer.
Technical documents or catalogues must clarify details regarding the parameters of the tests as much as
possible.
(2) Authentication test
A test commissioned by a third party to conduct a type approval or an objective evaluation on a specific itemof the fender is known as an authentication test. Several methods of authentication testing exist: for instance,
when a sample or an actual product is submitted for testing, and a test is conducted by a third party who issues
a certificate; when the test is conducted by the manufacturer in the presence of a third party; or when the test is
conducted by the manufacturer and the certificate is issued by a third party upon the submission of the test
report.
(3) Quality verification test
A test performed by a manufacturer to confirm the quality of a product before shipping is known as a quality
verification test. This test is carried out for all or extracted samples as needed, and the inspection results arereported to the purchaser. The purchaser or agent may also be present during testing. A quality verification test
includes the quality control test defined in the Standard Specifications for Ports and Harbor Works, 1) and thecontrol test is internally conducted by the manufacturer.
Table 6.2.1 summarizes the abovementioned test classifications. The method and purpose differ depending on the testclassification; therefore, even the same test should be conducted in an appropriate manner in line with the purpose.

58

Table 6.2.1 Classification of rubber fender test
Definition

Development
test

Authentication
test

Qualityverification
test

Tests conducted bymanufacturers during
development of rubber
fenders based on
catalogue data, etc.

Testing mainly entrusted
to third parties to obtain
type approval andobjective evaluation of
specific items
Test performed bymanufacturer to confirm
product quality before
shipping for all or
extracted samples

Test type

Method of disclosure

Practitioner

Standard compression
test; test for influence ofangle, velocity andtemperature; material
test; durability test;
repetition test; creep
property, etc. as required

Manufacturer’s own
disclosures, catalogues,
website; however,some information may
not be disclosed due toit being proprietary
technology, or the tests
may take excessive
time and cost to
reproduce

Manufacturers or
their third party
agentsTests that can be
performed by third
parties (Durability tests
can also be performed bymanufacturers)

Certification
documents designatedby third parties

Third party.
Durability test
can also be
performed by the
manufacturerStandard compression
test, material test

Test report by
manufacturer or
third-party who can
perform testing

Manufacturer:(Shipment test)
Purchaser:(Acceptance test)

6.3 Development test
The development test is a test carried out by the manufacturer during the development of rubber fenders for the
improvement of product quality and the formation of a technical basis including catalogue data, etc. The following is an
explanation of the major development tests, in particular, the test methods concerning the influence factors, dataprocessing, catalogue entry items, etc., and their examples. As these example figures are only for the purpose of
explanation, they should not be used in actual design, and data from the manufacturers' catalogues, technical documents,
etc. must be referred to.
6.3.1 Static compression test (Standard compression test)
The static compression test is an index that represents the basic performance of rubber fenders. In addition to being adevelopment test, it is also performed as an authentication test and a quality verification test, and it is performed widelyfor actual products to scale models. Although large-scale actual fender tests depend on the scale of the testing facility,
manufacturers must be able to carry out this test internally or externally for all types, sizes, and performance grades
manufactured in-house. The specific test method can be described as in the following steps according to the PIANC
Guidelines 2).
(1) Temperature stabilization of test piece and environment
Since the performance of rubber fenders is affected by the temperature, the test should be conducted in atemperature-controlled environment at the target temperature. The target temperature for measuring thestandard performance is 23±5°C (standard temperature), and the static compression performance at thistemperature is known as the standard compression performance. It is desirable to conduct the static
compression test in an environment having a temperature within the target temperature of ±15°C, even under59

conditions in which it is difficult to maintain constant temperature. Specifically, the following two methods
exist.
1) Temperature control before test
Proper temperature control should be realized by storing rubber fenders in an environment such asthat of a temperature-controlled room at a target temperature of ±5°C for a necessary time until
stabilization. The number of days required to stabilize the temperature of the entire rubber body can be
determined using equation (6.3.1).
Days for thermal stabilization＝20·(Maximum rubber thickness(m))1.5(6.3.1)After the fender is moved out of the temperature-controlled room, if the test environment is out of
the range of the target temperature ±5°C, the total test time including the preliminary test should bewithin 2 h to reduce its influence on performance. Additionally, in case temperature correction isrequired later, the environmental temperature at which the rubber fender is placed should be recorded
throughout the test.
2) Temperature correction as an alternative to temperature control:
In the case of large-sized fenders, it is difficult to maintain the fender at the target temperature ±5°C
in advance; furthermore, when the test time including the preliminary compression after taking thesample out of the temperature-controlled room becomes 2 h or more, the temperature is correctedusing the average value of the recorded environmental temperature. The correction is performed bymultiplying the temperature factor with respect to the time average of the recorded environmental
temperature (equation (6.3.1)) with the target temperature. Even in such cases, it is desirable that thetest environment is within the range of the target temperature ±15°C. Even when the test room itself istemperature-controlled or when the environmental temperature change is within the target temperature±5°C, it is recommended that the environmental temperature at which the rubber fender is placed isrecorded throughout the test.
(2) Preliminary compression
Compression is performed three or more times depending on the manufacturer's recommendation up to thedesign deflection or more. Although methods to consider the compression residual strain, compression rate,compression interval, etc. are not specified, it is desirable to unify these concepts. It is recommended that the
number of compressions and performance values are recorded.
(3) Main compression (Static)
The sample is maintained at the target temperature ±5°C for 1 h or more after the preliminary compression,and compression is performed one more time to the design deflection or more; the corresponding performanceis the static compression performance. To eliminate the residual strain of pre-compression, the initial deflection
point at which the reaction force increases is the zero deflection. The compression rate is within the range ofstandard strain rate (0.01 to 0.3%/s or 0.3 to 1.3 mm/s), and if the compression rate in this range cannot be
determined due to size restrictions, etc., the results are corrected considering the velocity factor. In accordancewith the capability of the testing facility, it is possible to realize decelerating compression DV from a highinitial velocity and determine the performance, including the influence of velocity. The corresponding
performance is called the decelerating compression performance, and it is different from the static compression
performance. In the case of velocity reduction compression, the initial speed and reduced speeds are also
recorded. In addition, when storage cannot be performed at the target temperature ±5°C, the result istemperature-corrected using the average value of the recorded environmental temperatures.
(4) Open leg V-type rubber fenders are fixed to the base plate of the machine so that the legs do not open.

60

(5) Energy absorption is obtained by integrating the reaction force with respect to the deflection up to the
maximum deflection. The integration can be numerical, such as trapezoidal integration, and the step size of thedeflection is within 5%.
6.3.2 Angular compression test
For the test of angular dependence, a real-size fender or scale model can be used. As shown in Fig. 6.3.1, theinclination angle θ is the angle between the rubber fender top surface and compression plate of the tester, and thecompression direction is the axial direction of the rubber fender.

Fig. 6.3.1 Angular compression test
(1) Specimen
When using a scale model, a height of 100 mm or more should be considered.
(2) Temperature stabilization
The specimen is thermally stabilized to a standard temperature of 23±5°C. The stabilizing time pertains to
the number of days equal to or greater than that obtained using equation (6.3.1). When the temperature cannot
be maintained constant, the temperature history of the stabilization time may be recorded, and the performance
may be corrected using the temperature factor.
(3) Preliminary compression
Compression should be performed at least 3 times up to the design deflection or more at an angle of 0± 1°.
Methods to consider the residual deflection, compression speed, compression interval, etc. are not specified;
however, it is desirable to unify these concepts. It is also recommended that the number of times and reaction
force data are recorded.
(4) Thermal stabilization
After preliminary compression, the sample is thermally stabilized at a standard temperature of 23±5°C for 1
h or more.
(5) Main compression
Main compression is performed once to the design deflection or more at an inclination angle θ°± 1°. The
compression rate is in the range of strain rate of 0.01 to 0.3%/s or rate of 0.3 to 1.3 mm/s.
(6) In angular compression testing, although the angular test of one specimen for one type of angle is ideal, whenusing the same specimen repeatedly at different angles, countermeasures to minimize the influence of thehistory should be used. For example, when the specimen is rotated 180° after the angular test, the reaction force
tends to increase due to the history, and when the same specimen is tested at the same angle, the reaction force
decreases. To this end, one can use a reference model having the same history as a comparison or eliminate the61influence of the history by averaging and/or maintaining the specimen at the reference temperature of 23±5°C
for 2 h or more for recovery. It is desirable to adopt these measures to reduce the effects of history and record
the procedures performed.
(7) The ratio of performance at angle 0° to the performance obtained during compression at the set angle isdetermined. The ratio of the reaction force at the design deflection or the ratio of the maximum reaction force
until then is referred to as the angular factor. The ratio of the reaction force to deflection of 5% is referred to as
the deflection-specific angular factor.
(8) In angular compression, when the centre of the rubber fender is compressed to the design deflection, the end
may exceed the compression limit and part of the body may be damaged. The allowable deflection is set so thatthe body is not damaged, and the face plates of the tester are not in contact with each other.
(9) V-type rubber fenders with open legs should be fixed so that the legs do not open.
(10) The compression plate of the tester should be made of steel, and water, oil and other substances that change
the friction coefficient must be removed from the surface.
(11) The energy absorption is obtained by integrating the reaction force with respect to the deflection up to the
maximum deflection. The integration can be numerical, such as trapezoidal integration, and the step size of thedeflection is within 5%.
(12) Definition of angular factor
The angular factor is obtained from equation (6.3.2), assuming Rθ (θ: angle) is the reaction force at angle θ.

Angular factor of reaction force
Angular factor of energy absorption
Here,
CaR
Rθ
RR
CaE
EAθ
EA

：
：
：
：
：
：

:
:

CaR ＝ Rθ / RR
CaE ＝ EAθ / EA

(6.3.2)

Angular factor of reaction force
Reaction force at angle θ°Standard reaction force (θ=0°)
Angular factor of energy absorption
Energy absorption at angle θ°Standard energy absorption (θ=0°)(13) Example of handling angular test data
The test data processing method for the angular test is described by taking an example of a scale model of avertical cylindrical rubber fender. Fig. 6.3.2 shows the result data.

62

Fig. 6.3.2 Example data of angular test result
As explained in Fig. 4.2.4 in Chapter 4, Section 4.2.2, the example test data corresponds to that after origin
adjustment, in which the virtual displacement δ1 is obtained by neglecting the data before the full contact at low
deflection. In the catalogue performance, the reaction force is also zero at a deflection of 0%, but the value isretained as in Fig. 6.3.2. The data processing is summarized in Table 6.3.1.
Table 6.3.1 Example of angular test data processing
Angle θ ＝0°
Reaction force

Deflection Reaction force(nonData (kN)
dimension)
ε
③

④＝③／①

0.0%
5.0%
10.0%
15.0%
20.0%
25.0%
30.0%
35.0%
40.0%
45.0%
50.0%
52.5%
55.0%

0
1.82
3.37
4.49
4.91
5.00
4.94
4.86
4.81
4.81
4.86
5.00
5.32

0
0.36
0.67
0.90
0.98
1.00
0.99
0.97
0.96
0.96
0.97
1.00
1.06

Angle θ ＝5°
Angular factor
EnergyEnergyReaction force(Reaction
absorption
absorption
Data (kN)force)
factorfactor

⑤

0
0.01
0.03
0.07
0.12
0.17
0.22
0.27
0.32
0.37
0.41
0.44
0.46

⑥

0.25
1.69
3.30
4.40
4.93
5.05
4.98
4.88
4.83
4.85
5.00
5.20
5.56

Standard reaction force
Deflection at
5.00 kN E A absorbed
R R ①＝
Standard energy absorption factor
E A ②=

Angle θ ＝10°

0.44

Maximum
reaction force
factor

⑦=⑥/①

0.05
0.34
0.66
0.88
0.99
1.01
1.00
0.98
0.97
0.97
1.00
1.04
1.11

50.6%
1.01

⑧

0
0.01
0.03
0.07
0.12
0.17
0.22
0.27
0.32
0.37
0.42
0.44
0.47
Angularfactor of R
Ca R ＝
Angularfactor of E
Ca E =

Angularfactor(Energyabsorption)

Reactionforce Data
(kN)

⑩

⑨＝⑧/②

0.00
0.02
0.08
0.17
0.27
0.39
0.50
0.61
0.72
0.83
0.95
1.00
1.07

0.49
1.63
3.12
4.23
4.80
4.95
4.90
4.82
4.82
4.97
5.33
5.66

1.01

Deflection at
E A absorbed

0.96

Maximum
reaction force
factorAngularfactor(Reaction
force)

⑪=⑩/①

0.10
0.33
0.62
0.85
0.96
0.99
0.98
0.96
0.96
0.99
1.07
1.13

45.5%
1.00

Angle

Energyabsorption
factorAngular factor(Energyabsorption)

Reactionforce Data
(kN)

⑫

⑬＝⑫/②

⑭

0
0.01
0.03
0.07
0.12
0.16
0.21
0.26
0.31
0.36
0.41
0.44

Angular factor
of R Ca R ＝
Angular factorof E Ca E =

0.00
0.02
0.08
0.16
0.26
0.38
0.49
0.60
0.71
0.82
0.94
1.00

0.97
2.00
3.24
4.09
4.49
4.60
4.62
4.70
5.12
6.38

Angular factor(Reaction force)

⑮=⑫/①

0.19
0.40
0.65
0.82
0.90
0.92
0.92
0.94
1.02
1.28

θ ＝20°
Energyabsorption
factorAngular factor(Energyabsorption)

⑯

⑰＝⑮/②

0
0.01
0.04
0.08
0.12
0.17
0.21
0.26
0.31
0.37

0.00
0.03
0.09
0.18
0.27
0.38
0.48
0.59
0.70
0.83

1.00

Deflection at
E A absorbed

38.6%

Angular factor
of R Ca R ＝

1.00

0.83

Maximum
reaction force
factor

1.00

Angular factorof E Ca E =0.67

As shown in Chapter 4, Section 4.2.2, it is possible to consider the deflection at the fender panel end andcreate Table 6.3.1 to determine the performance including the initial rotation (yellow part in Fig. 4.2.5 and Fig.
4.2.6). In Table 6.3.1, the standard reaction force at an angle of 0° is 5.00 kN ①. The reaction force data (③,⑥, ⑩, ⑭) is divided by the standard reaction force ① to obtain a dimensionless reaction force (④, ⑦, ⑪, ⑮),
which is integrated to obtain the dimensionless energy absorption (⑤, ⑧, ⑫, ⑯). The same process isperformed for angles of 5°, 10° and 20°. At an angle of 5°, the maximum reaction force at a deflection of 25%
increases by approximately 0.01. At an angle of 5°, 50.6% of the reaction force at a deflection of 25% becomes
the same value in the high deflection region, and it becomes 0.96 when the non-dimensional energy absorption63

up to this deflection is obtained using linear interpolation. These values become the angular factors CaR and CaEof the reaction force and the energy absorption at an angle of 5°. At an angle of 10°, the reaction force at the
deflection of 45.5% at which the standard reaction force is absorbed becomes larger than the maximum
reaction force at the strain of 25%; thus, the energy absorption factor (0.83) up to this deflection becomes theangular factor CaE. Similarly, at an angle of 20°, the maximum reaction force (1.00) generates a deflection of
38.6%, and the energy absorption until this point is 0.67. If other angles are similarly processed, the angularfactors obtained are as listed in Table 6.3.2.1. If the factor variation within 3% is common, its values can belisted as in Table 6.3.2.2; thus, if the angle is 4° or less, the influence of compression angle can be ignored. It is
desirable to present either Table 6.3.2.1 or Table 6.3.2.2 in the catalogue of rubber fenders. However, since thereaction force curve is not similar to that of the angles, the factors of reaction force and energy absorption canbe shared only for angles of 4° or less.
Table 6.3.2.1 Example of angular factor
Angles
(°)
0
3
4
5
6
10
15
20

Angular factor ofreaction force
Ca R
1.00
1.02
1.02
1.01
1.01
1.00
1.00
1.00

Table 6.3.2.2 Example of angular factor (Simplified)Angular factor ofenergy absorption
Ca E
1.00
1.01
0.99
0.96
0.95
0.83
0.74
0.67

Angles
(°)
0
3
4
5
6
10
15
20

Angular factor ofreaction force
Ca R

Angular factor ofenergy absorption
Ca E

1.00

1.00

0.96
0.95
0.83
0.74
0.67

(14) Shear compression
When performing shear compression, as described in Chapter 4, Section 4.2.2, a tester capable of measuring
the displacement and load in two axial directions as shown in Fig. 6.3.3.1 is required; however, as shown in Fig.
6.3.3.2, compression is possible using only a single axial tester if an angular jig is used.

Fig. 6.3.3.1 Shear compression test (2-axis)

Fig. 6.3.3.2 Shear compression test (1-axis with jig)(15) Angular performance of V-type rubber fender
V-type rubber fenders can also be subjected to the angular compression test by employing theabovementioned method; however, two angular directions are present: in the width and longitudinal directions.
The value for the longitudinal direction can be obtained by performing calculations using equation (5.6.7) in
Chapter 5, Section 5.6.2.

6.3.3 Velocity dependency test
Two types of velocity dependent tests exist: CV constant velocity compression that involves compression at aconstant velocity, and DV deceleration compression, at which the velocity becomes zero (5 mm/s at PIANC Guidelines

64

2)

at the design deflection. Although it is ideal to perform DV deceleration compression directly, the relationshipbetween the actual berthing velocity and fender height is diverse; therefore, after performing CV tests under various
strain rates, the DV deceleration performance can be calculated based on the CV results. This section describes the CV
test method, data processing, and calculation procedure to obtain the DV performance.
(1) Specimen
When using a scale model, a height of 100 mm or more should be employed.
(2) Temperature stabilization
The specimen is thermally stabilized to a standard temperature of 23±5°C. The stabilizing time corresponds
to the number of days equal to or greater than that specified in equation (6.3.1).
(3) Preliminary compression
Compression should be performed at least 3 times up to the design deflection or more. The consideration ofresidual deflection, compression speed, compression interval, etc. is not specified; however, it is desirable tounify these concepts. It is also recommended that the number of times and reaction force data is recorded.
(4) Thermal stabilization
After preliminary compression, the specimen is thermally stabilized at a standard temperature of 23±5°C for
1 h or more.
(5) Main compression
Main compression is performed once to the design deflection or more. The strain rate is in the range of 0.01
to 50%/s for at least three different strain rates.
(6) When the same specimen is used repeatedly, it is necessary to adopt measures to minimize the influence of thecompression history. For example, the specimen can be maintained at a standard temperature of 23 ± 5°C. for atime of 2 h or more. Alternatively, the same historical reference model can be used as a comparison reference.
As an alternative, the influence of history can be minimized by averaging. In all these cases, it is advisable torecord the procedures employed.
(7) The ratio between the performance at standard (static) compression speed to that obtained during compression
at the target speed is determined. The ratio of the design reaction force or the maximum reaction force up tothat deflection is used as a velocity factor, and the ratio of the reaction force for every 5% of the deflection is
known as the deflection-specific velocity factor.
(8) The energy absorption is obtained by integrating the reaction force with respect to the deflection up to thedesign deflection. The integration can be numerical such as trapezoidal integration, and the step size ofdeflection is within 5%. An example of the test conditions is presented in Table 6.3.3.

65

Table 6.3.3 Example of velocity test conditions

Specimen

Preliminary
compression

Items
Type of fender
Performance grade （Rubber）

Conditions
V
3 gradesHighest, Middle and Lowest

Number of specimens per grade

More than one/Grade

Specimen:1 and reference:1 piece

Size (height ×length)

Larger than 100mmｘ100mm

Consider ends effectNumber of compressions
Final deflection（Rated deflection+α）

More than 3 times
More than rated deflection

Stabilizing temperature before test

23℃

Tolerance of stabilizing temperature before test

±5℃

Stabilizing temperature during test

23℃

Tolerance of stabilizing temperature during test

±5℃

Number of compressions

1 or more

Temperature during compression

23±5℃

Final deflection（Rated deflection+α）
Main compression

RemarksMore than rated deflection

Stabilizing temperature before test

23℃

Tolerance of stabilizing temperature before test

±5℃
±5℃

Tolerance of ambient temperature during test
Interval of compression
Temperature of storage after test

Constant interval
23±5℃

Measures to negate When one specimen is used in multiple velocity conditions, use reference model of same history of standard velocity or averaged
history effectresults of different test order to minimize history influence.

(9) Example of handling of constant velocity (CV) test results
The velocity factor in the CV test is defined as in equation (6.3.3).
Velocity factor of reaction force: VFR ＝ RV／RR
Velocity factor of energy absorption : VFE ＝ EAV／EA
Here,
VFR ：
RV ：
RR ：
VFE ：
EAV ：
EA ：

(6.3.3)

Velocity factor of reaction force
Design reaction force at constant velocity V (CV)Standard reaction force at standard (static) velocity
Velocity factor of energy absorption
Design energy absorption at constant velocity V (CV)Standard energy absorption at standard (static) velocity

The results of constant velocity (CV) test of the scale model of a vertical cylinder rubber fender are presented
as follows as an example of the data processing method. Fig. 6.3.4 shows an example of the result data.

66

Fig. 6.3.4 Example data of constant velocity (CV) test result
The test results and calculation of each velocity factor is explained in Table 6.3.4.
Table 6.3.4 Example of constant velocity (CV) test data processing
Strain rate V ＝0.044%/sDeflection
ε
0.0%
5.0%
10.0%
15.0%
20.0%
25.0%
30.0%
35.0%
40.0%
45.0%
50.0%
52.5%
55.0%

Reactionforce Data
(kN)

③

0
1.82
3.37
4.49
4.91
5.00
4.94
4.86
4.81
4.81
4.86
5.00
5.32

Reaction force(non-dimension)

④＝③／①

0
0.36
0.67
0.90
0.98
1.00
0.99
0.97
0.96
0.96
0.97
1.00
1.06

Strain rate V ＝30%/s

Energyabsorption
factorReactionforce Data
(kN)

⑤

⑥

0
0.01
0.03
0.07
0.12
0.17
0.22
0.27
0.32
0.37
0.41
0.44
0.46

Standard reaction force
5.00 kN
R R ①＝
Standard energy absorption factor
E A ②=

0.44

0.00
2.17
4.02
5.48
6.17
6.33
6.18
6.03
5.94
5.90
5.97
6.07
6.25

Velocityfactor(Reaction
force)

⑦=⑥/①

0
0.43
0.80
1.10
1.23
1.27
1.24
1.21
1.19
1.18
1.19
1.21
1.25

Strain rate V ＝10%/s

Energyabsorption
factorVelocity factor
of R at eachdeflection

Velocity factor of
E A at eachdeflection

⑧

⑨=⑦/④

⑩＝⑧/⑤

0
0.01
0.04
0.09
0.15
0.21
0.27
0.33
0.39
0.45
0.51
0.54
0.57

1.00
1.19
1.19
1.22
1.26
1.27
1.25
1.24
1.24
1.23
1.23
1.21
1.18

Reactionforce Data
(kN)⑪

Velocityfactor(Reaction
force)
⑫=⑪/①

0.00
2.11
3.85
5.24
5.84
5.96
5.85
5.71
5.62
5.60
5.67
5.78
6.00

0.00
0.42
0.77
1.05
1.17
1.19
1.17
1.14
1.12
1.12
1.13
1.16
1.20

1.00
1.19
1.19
1.20
1.22
1.23
1.24
1.24
1.24
1.24
1.24
1.23
1.23

Energyabsorption
factor
⑬

0
0.01
0.04
0.09
0.14
0.20
0.26
0.32
0.37
0.43
0.49
0.51
0.54

Strain rate V ＝1%/s⑮＝⑬/⑤

Reactionforce Data
(kN)⑯

Velocityfactor(Reaction
force)
⑰=⑯/①

1.00
1.16
1.15
1.15
1.16
1.17
1.17
1.18
1.18
1.17
1.17
1.17
1.17

0.00
1.87
3.52
4.76
5.27
5.39
5.31
5.21
5.15
5.14
5.19
5.32
5.56

0.00
0.37
0.70
0.95
1.05
1.08
1.06
1.04
1.03
1.03
1.04
1.06
1.11

Velocity
Velocity factor
factor of R atof E A at each
each
deflection
deflection

⑭=⑫/④

1.00
1.16
1.14
1.17
1.19
1.19
1.18
1.18
1.17
1.17
1.17
1.16
1.13

Energyabsorption
factor
⑱

0
0.01
0.04
0.08
0.13
0.18
0.23
0.29
0.34
0.39
0.44
0.47
0.50

Velocity
Velocity factor offactor of R at
E A at each
each
deflection
deflection

⑲=⑰/④

⑳＝⑱/⑤

1.00
1.03
1.05
1.06
1.07
1.08
1.08
1.07
1.07
1.07
1.07
1.06
1.05

1.00
1.03
1.04
1.05
1.05
1.06
1.06
1.07
1.07
1.07
1.07
1.07
1.07

Deflection at E A
absorbed

43.85%

Velocity factor
of R VF R ＝

1.27

Deflection at E A
absorbed

45.82%

Velocityfactor of R
VF R ＝

1.19

Deflection at E A
absorbed

49.68%

Velocityfactor of R
VF R ＝

1.08

Maximum reaction force
factor at E A absorbed

1.27

Velocity factorof E A VF E =1.23

Maximum reaction force
factor at E A absorbed

1.19

Velocityfactor of E A
VF E =

1.17

Maximum reaction force
factor at E A absorbed

1.08

Velocityfactor of E A
VF E =

1.07

In the data presented in Table 6.3.4, the standard reaction force at standard speed (0.044%/s) is 5.00 kN (①).
The reaction force data is divided by the standard reaction force to obtain a dimensionless reaction force (④),
which is integrated to obtain a dimensionless standard energy absorption value (②). Table 6.3.4 presents thesame processing at compression rates of 30%/s, 10%/s and 1%/s. At a compression rate of 30%/s, anon-dimensional standard energy absorption of 0.44 kN∙m can be realized at a deflection of 43.85%. The
maximum reaction force until then is the peak reaction force at a deflection of 25%. For this fender, themaximum reaction force is a peak value at a deflection of 25% at any speed, and the buckling typecharacteristics are maintained. Since the standard reaction force RR is non-dimensional, the maximum reaction
force at each velocity becomes the velocity factor VFR, and the energy absorption up to the deflection at which
the same reaction force as the peak value is generated in the high deflection region is VFE. In Fig. 6.3.5, thevelocity factor of the reaction force and energy absorption are plotted in relation to the strain rate. Note that thestrain rate is logarithmic.

67

Fig. 6.3.5 Example of velocity factor and strain rate (CV)(10) Example of processing constant velocity (CV) results into decelerating velocity (DV) factor
Since the velocity factor directly used for design is a factor corresponding to the decelerating velocity (DV)performance, it is calculated as follows using the factors of the CV test described above. The conceptual
diagram is shown in Chapter 4, Fig. 4.2.10, and a concrete calculation example is demonstrated here.
In deceleration compression (DV), as the deflection progresses from the initial velocity, the velocity
decelerates and becomes close to zero at the design deflection. The PIANC Guidelines 2) proposes linear
deceleration, cosine waveform, etc. as the modes of deceleration. Deceleration by a cosine waveform is a modein which 0% of the deflection is considered as 1.0 in equation (6.3.4), and a coefficient of cosine that becomes
π/2 in the design deflection is calculated under the initial velocity.
V = VBcos(πδ/2D)(6.3.4)Here,
V ：Strain rate (%/s)
VB ：Initial strain rate (＝Berthing velocity / Fender height) (%/s)δ ：Deflection (%)
D ：Design deflection of fender (%)
As an example, the decelerating performance for each deflection of the rubber fender with a standard
reaction force RR = 2327 (kN) at a height of 2 m (2000 H) is presented in Table 6.3.5. Table 6.3.5 indicates theperformance at cosine deceleration. The velocity factor VFR used in this case is a coefficient of the CV
performance demonstrated in Fig. 6.3.5. From Table 6.3.5, the velocity factors of the deceleration performancecan be calculated as follows.
Initial berthing velocity:
Velocity factor of reaction force at decelerating performance (DV):
Velocity factor of energy absorption at decelerating performance (DV):VB ＝7.5 (%/s)＝0.15 (m/s)
VFR＝2670／2327＝1.15
VFE＝2315／2043＝1.13

Since the initial velocity is 0.15 m/s, the design reaction force is 2670 kN, and the design energy absorption
is 2315 kN∙m. In the above example, the difference between the velocity factor of the reaction force andabsorbed energy is approximately 2% because, as seen in Fig. 6.3.4, the buckling type characteristic ismaintained with respect to the change in velocity, and the reaction force curve has a substantially similar shape.

68

Table 6.3.5 Example of processing CV results into DV performance
Performance by deflection
Displace
Deflection ment
ε(m)
δ (%)

Velocity
(m/s)

δ ×H

Strain rate
V （％/ｓ）

Velocityfactor of CV
VF R
Fig.6.3.5
1.17
1.17
1.16
1.16
1.15

0
5
10
15
20

0
0.1
0.2
0.3
0.4

equation(6.3.4)
0.150
7.50
0.148
7.42
0.144
7.20
0.136
6.82
0.126
6.31

25
30
35
40
45
50
52.5
55

0.5
0.6
0.7
0.8
0.9
1
1.05
1.1

0.113
0.098
0.081
0.062
0.042
0.021
0.011
0.000

5.67
4.91
4.05
3.12
2.11
1.07
0.54
0.00

Standard Standard energy Reaction forceof DV
reactionabsorbtion
force （kN)
(kN×m)R V (ε )＝

1.15
1.14
1.13
1.12
1.11
1.08
1.05
1.00

Energyabsorption of
DV (kN×m)

0
845
1566
2088
2287

0
42
163
346
564

0
985
1822
2421
2639

=∫ R V (ε )dε
0
49
190
402
655

2327
2300
2262
2237
2237
2262
2327
2473

795
1026
1254
1479
1703
1928
2043
2163

2670
2621
2559
2510
2487
2443
2435
2473

920
1185
1444
1697
1947
2194
2315
2438

R R (ε )EA

R R (ε )×VF R

A size of 2000H was assumed in the above example; however, since the velocity factors are based on thestrain rate, the values do not depend on the size of fenders. By changing the initial strain rate and performing
the same processes with other performance grades, the velocity factor table is similar to Table 6.3.6.
Table 6.3.6 Example of DV velocity factor for cosine deceleration(catalogue display, before simplification)
Performance
grade
Strain rate
(%/S)
30
20
10
5
1.00
0.50
0.10
0.05
0.01

Grade A
Reactionforce VF R
1.23
1.20
1.17
1.13
1.06
1.04
1.01
1.00
1.00

Grade B

EnergyReactionabsorption
force VF R
VF E
1.18
1.21
1.17
1.18
1.14
1.15
1.11
1.12
1.06
1.06
1.05
1.04
1.01
1.01
1.00
1.00
1.00
1.00

Grade C

EnergyReactionabsorption
force VF R
VF E
1.18
1.20
1.15
1.17
1.13
1.14
1.10
1.11
1.05
1.05
1.04
1.04
1.01
1.00
1.00
1.00
1.00
1.00

Energyabsorption
VF E
1.17
1.14
1.12
1.09
1.05
1.04
1.00
1.00
1.00

In Table 6.3.7, differences within 3% are standardized. It is desirable that the catalogue displays the data asgiven in Table 6.3.6 or Table 6.3.7 or as a graph shown in Fig. 6.3.6. In the case of only a graph display, it isnecessary to display the approximate coefficients of the formula to ensure that the numerical values used forthe design can be determined.

69

Table 6.3.7 Example of DV velocity factor for cosine deceleration(catalogue display, after simplification)
Performance
grade
Strain rate
(%/S)
30
20
10
5
1.00
0.50
0.10
0.05
0.01

Grade A
Reactionforce VF R

Energyabsorption
VF E
1.18
1.17
1.14

Grade B

Grade C

EnergyEnergyReactionabsorption
absorption
force VF R
VF E
VF E
1.21
1.18
1.20
1.17
1.18
1.15
1.17
1.14
1.15
1.14
1.10
1.05
1.04

Reactionforce VF R

1.23
1.20
1.17
1.13
1.06

1.00

Fig. 6.3.6 Sample graph of DV velocity factor for cosine deceleration(11) Mode of velocity reduction
Although the above description is based on deceleration corresponding to a cosine curve, the deceleration
mode is not particularly defined and may be linear. The deceleration mode in actual berthing can be estimatedas follows by obtaining the remaining amount of effective berthing energy. As another example, let the fender
have a height of 1000 mm. We attempt to determine the mode of deceleration at the initial velocity of 0.15 m/s,
as used in the PIANC Guidelines 2). Since the initial berthing velocity corresponds to 15%/s, the initial velocity
factor is VFR (V = 15%/s), and the initial deflection of the fender, for example, the reaction force at the standard
compression velocity at a deflection of 5% is R5 (V = V0); the reaction force R5 (V = 15) at a velocity of 0.15m/s is as shown in equation (6.3.5).
R5(V=15)=R5(V=V0)×VFR (V=15)(6.3.5)The energy ΔE absorbed up to a strain of 5% is the area of a triangle surrounded by the reaction force of astrain rate of 0% and 5% and the horizontal axis, and it can be expressed as in equation (6.3.6).

70

ΔE = R5(V=15)×ε(=0.05 m) / 2(6.3.6)The effective berthing energy Eb can be calculated using equation (5.3.1) in Chapter 5, that is

Eb 

M
2
VB  Ce  Cm  Cc  Cs
2

(5.3.1)

Here,

Eb : Effective berthing energy（kNm=kJ）
M : Mass of vessel (＝Displacement tonnage: DT, t)
VB : Berthing velocity (（m/s)
Ce : Eccentricity factor
Cm : Virtual mass factor
Cc : Berth configuration factor
Cs : Softness factor
Next, we summarize the coefficients, and define Ctotal as follows.
Ctotal=Ce  Cm  Cc  Cs

(6.3.7)The effective berthing energy Eb can be determined using equation (6.3.8).

Eb 

M
2
 VB  Ctotal
2(6.3.8)The compression speed is reduced from V0 to V5, as shown in equation (6.3.9) since ΔE is absorbed at adeflection of 5%.

V5
=
V0

Eb‐E
Eb

(6.3.9)If the velocity factor VFR at the compression velocity V10 is determined and the same calculations are repeatedwith increased deflection, the deceleration performance (DV) by energy absorption can be obtained. It is also
possible to compress the scale model fender by assuming the mode of deceleration to be a cosine waveform or astraight line to obtain the deceleration performance; however, it is expected that in actual berthing, the mode of
deceleration is as shown in equation (6.3.9). Fig. 6.3.7 compares the linear deceleration, cosine waveform
deceleration, and energy absorption deceleration according to equation (6.3.9). The decelerating velocity due toenergy absorption is similar to that for the cosine waveform at low deflection; however, it increases at highdeflection. Additionally, if the velocity factor VFR is expressed in terms of the deflection and the factor at eachvelocity and each deflection is used, it is possible to obtain the DV performance in each deceleration mode. In
this manner, the decelerating performance calculated using the CV performance and the test results of actual
compression under a cosine waveform from the initial speed of 0.15 m/s can be determined, as shown in Fig.
6.3.8. In all cases, the maximum value of reaction force increases by approximately 20% at an initial velocity of
0.15 m/s (here, 15%/s) compared with the static performance. The difference among the deceleration methods
and that between the test value and the calculated value appear in the high deflection area; however, thedifferences are small. The reason the test value is higher in the high deflection region is the deference of stressrelaxation of the rubber due to the difference between the compression time at a constant velocity and reduced
time owing to deceleration from a large initial velocity. Although the energy absorption is slightly larger at thetest value than at the calculated value, the calculation method involving the CV performance is considered toensure safety in fender design. To summarize, the influence of velocity on the reaction force is large(approximately 20%) and needs to be considered in fender design; however, since the influence of the mode of
deceleration is small, it does not lead to a considerable difference in the design.

71Fig. 6.3.7 Deceleration modes of decreasing velocity (DV)Fig. 6.3.8 Performances of decelerating test and calculation (DV)

6.3.4 Temperature dependency test
The test of temperature dependency involves measuring the temperature dependency of the elastic modulus of thematerial and directly measuring the temperature dependency of rubber fenders (real product or scale model). Because
testing rubber fenders is time consuming and costly, it is acceptable to perform testing at only representative
temperatures (e.g., -30°C, 0°C, 23°C, 50°C) and estimate the factors at other intermediate temperature by interpolating
the material test results, as described later.
(1) Temperature dependency test of rubber fenders
1) Specimen
When using a scale model, a height of 100 mm or more should be employed.

722) Temperature stabilization
The specimen is thermally stabilized to a target temperature ±5°C. The stabilizing time corresponds tothe number of days equal to or greater than that specified in equation (6.3.1).
3) The temperature range is measured every 10°C from -30°C to 50°C, and a standard temperature of 23°C isused instead of 20°C.
4) Preliminary compression
Compression is performed at least 3 times up to the design deflection or more. The consideration ofresidual deflection, compression speed, compression interval, etc. is not specified; however, it is desirable
to unify the concepts. It is also recommended that the number of times and reaction force data are recorded.
5) Thermal stabilization
After preliminary compression, the specimen is thermally stabilized at a target temperature ±5°C for 1 h
or more.
6) Main compression
Main compression is performed once to the design deflection or more. The compression rate should be
set in the range of strain rate of 0.01 to 0.3%/s or speed of 0.3 to 1.3 mm/s.
7) The reaction force at the design deflection at the target temperature or its maximum value (design reaction
force) up to that point is divided by the reaction force at the standard temperature of 23°C, and the resulting
value is known as the temperature factor. The ratio between the reaction forces for every 5% deflection tothat at the standard temperature is called the deflection-specific temperature factor. When the reaction force
increases monotonously and does not have a peak point, the reaction force at the time of standard energy
absorption at the standard temperature of 23°C is adopted as the design reaction force.
8) If the same specimen is to be used at different temperatures, measures must be adopted to minimize theeffects of the compression history. To this end, the specimen can be placed in a constant temperature room
for the temperature stabilization time plus 2 hours or more; alternatively, a specimen having the same
compression history can be used as a reference, or the results can be averaged to negate the influence ofhistory.
9) The energy absorption is obtained by integrating the reaction force with respect to the deflection up to thedesign deflection. The integration can be numerical such as trapezoidal integration, and the step size ofdeflection is within 5%.
An example of the test conditions is presented in Table 6.3.8

73

Table 6.3.8 Example of temperature test conditions

Specimen

Preliminary
compression

Items
Type of fender
Performance grade （Rubber）

Conditions
V
3 gradesHighest, Middle and Lowest

Number of specimens per grade
Size (height ×length)More than one/Grade
Larger than 100mmｘ100mm

Specimen:1 and reference:1 piece
Consider ends effectNumber of compressions
Final deflection（Rated deflection+α）

More than 3 times
More than rated deflection

Stabilizing temperature before test

23℃

Tolerance of stabilizing temperature before test

±5℃

Stabilizing temperature during test

23℃

Tolerance of stabilizing temperature during test

±5℃

Number of compressions
Compression speed
Final deflection（Rated deflection+α）

1 or more
0.01 to 0.3%/s or 0.3 to 1.3mm/s.
More than rated deflection

Standerd compression speed

Temperature stabilizing time ：T1

20×(Thickness)１.5/24 or longer

equation (6.3.1)

Recovery time after compression：T2
Main compression

2 hours or longer

Compression interval：T=T1+T2

T=T1+T2 or longer

Stabilizing temperature before test
Tolerance of stabilizing temperature before test

Target temperature±5℃±5℃

Tolerance of ambient temperature during test

23℃±5℃

Temperature of storage after test

±3℃

Tolerance of heat chamber
Measures to negate
history effectRemarks

When one specimen is used in multiple velocity conditions, use reference model of same history of standard velocity or averaged
results of different test order to minimize history influence.

10) Temperature factor: TF
The temperature factor TF is defined as in equations (6.3.10) and (6.3.11).
Temperature factor of reaction force: TFR ＝ RT／RR
Temperature factor of energy absorption : TFE ＝ EAT／EA
Here,
TFR
: Temperature factor of reaction force
RT: Design reaction force at design temperature: T°C
RR: Standard reaction force at standard temperature: 23°C
TFE
: Temperature factor of energy absorption
EAT: Design energy absorption at design temperature: T°C
EA: Standard energy absorption at standard temperature: 23°C

(6.3.10)(6.3.11)When TFR (ε) is determined separately for deflection, TFR is considered as a function of deflection ε, asin equation (6.3.12).
Temperature factor of reaction force at deflection ε% :TFR (ε）=

RT (ε）/RR(ε)(6.3.12)Here,
TFR (ε） : Temperature factor of reaction force at deflection ε%
RT (ε): Design reaction force at design temperature at deflection ε%RR(ε): Standard reaction force at standard temperature at deflection ε%11) Handling example of temperature test data
The test data processing method of the temperature test is described by taking an example of a scalemodel of vertical cylinder rubber fenders. Fig. 6.3.9 shows the result data.

74

Fig. 6.3.9 Example data of temperature dependency test
The results are presented in Table 6.3.9.
Table 6.3.9 Example of processing of temperature dependency test data
Standard temperature T ＝23℃
Deflection Reaction force Reaction force
Data (kN) (non-dimension)
ε
③
④＝③／①

Energyabsorption
factor⑤

Cold temperature T ＝ -20℃
Temperature
Reaction force
factorData (kN)(Reaction
force)⑥⑦=⑥/①

Cool temperature

Energyabsorption
factorT emperaturefactor of R at eachdeflection

T emperaturefactor of E A ateach deflection

⑧

⑨=⑦/④

⑩＝⑧/⑤

Reactionforce Data(kN)⑪

Temperaturefactor(Reaction
force)⑫=⑪/①

Energyabsorption
factor⑬

T＝0℃

T emperaturefactor of R at
each
deflection⑭=⑫/④

Hot temperature
T emperaturefactor of E A ateach deflection⑮＝⑬/⑤

Reactionforce Data
(kN)⑯

Velocityfactor(Reaction
force)⑰=⑯/①

Energyabsorption
factor⑱

T＝40℃

Velocityfactor of R at
each
deflection⑲=⑰/④

Velocity factorof E A at eachdeflection

⑳＝⑱/⑤

0.0%
5.0%
10.0%
15.0%
20.0%
25.0%
30.0%
35.0%
40.0%

0
1.82
3.37
4.49
4.91
5.00
4.94
4.86
4.81

0
0.36
0.67
0.90
0.98
1.00
0.99
0.97
0.96

0
0.01
0.03
0.07
0.12
0.17
0.22
0.27
0.32

0.00
2.86
4.82
6.22
6.72
6.87
6.93
7.04
7.25

0.00
0.57
0.96
1.24
1.34
1.37
1.39
1.41
1.45

0.00
0.01
0.05
0.11
0.17
0.24
0.31
0.38
0.45

1.00
1.57
1.43
1.39
1.37
1.37
1.40
1.45
1.51

1.00
1.57
1.51
1.45
1.42
1.41
1.40
1.41
1.42

0.00
2.17
3.83
5.00
5.41
5.48
5.45
5.41
5.42

0.00
0.43
0.77
1.00
1.08
1.10
1.09
1.08
1.08

0.00
0.01
0.04
0.08
0.14
0.19
0.25
0.30
0.35

1.00
1.19
1.14
1.11
1.10
1.10
1.10
1.11
1.13

1.00
1.19
1.17
1.14
1.13
1.12
1.12
1.11
1.12

0.00
1.62
3.12
4.24
4.71
4.84
4.80
4.72
4.67

0.00
0.32
0.62
0.85
0.94
0.97
0.96
0.94
0.93

0.00
0.01
0.03
0.07
0.11
0.16
0.21
0.26
0.30

1.00
0.89
0.93
0.95
0.96
0.97
0.97
0.97
0.97

1.00
0.89
0.91
0.92
0.94
0.94
0.95
0.95
0.96

45.0%

4.81

0.96

0.37

7.64

1.53

0.53

1.59

1.44

5.53

1.11

0.41

1.15

1.12

4.65

0.93

0.35

0.97

0.96

50.0%
52.5%
55.0%

4.86
5.00
5.32

0.97
1.00
1.06

0.41
0.44
0.46

8.22
8.76
9.62

1.64
1.75
1.92

0.60
0.65
0.69

1.69
1.75
1.81

1.46
1.47
1.49

5.74
6.00
6.47

1.15
1.20
1.29

0.47
0.50
0.53

1.18
1.20
1.22

1.12
1.13
1.13

4.68
4.80
5.09

0.94
0.96
1.02

0.40
0.42
0.45

0.96
0.96
0.96

0.96
0.96
1.02

Deflection at E A absorbed

39.17%

Standard reaction force
5.00 kN
R R ①＝
Standard energy absorption factor
E A ②=

0.44

Maximum reaction force
factor at E A absorbed

1.44

T emperaturefactor of R
TF R＝
T emperaturefactor of E A
TF E =

Deflection at E A
absorbed

1.44
1.47(=1.00 at E A
is absorbed)

Maximum reaction force
factor at E A absorbed

48.00%

1.13

T emperaturefactor of R
TF R ＝
T emperaturefactor of E A
TF E =

1.13

Deflection at E A
absorbed

1.13
Maximum reaction force(=1.00 at E A
factor at E A absorbed
is absorbed)

54.33%

1.00

T emperaturefactor of R
TF R ＝
T emperaturefactor of E A

1.00

0.96

TF E =In Table 6.3.9, similar to the test results of other influencing factors, a dimensionless performance iscalculated by dividing the reaction force data by the standard reaction force of 5.00 kN (①) at a deflectionof 25% under the standard temperature of 23°C. The value is integrated with respect to the deflection todetermine the non-dimensional energy absorption (②). The same treatment is performed at temperatures of-20°C, 0°C and 40°C. However, at a temperature of −20°C, the reaction force does not have a local peakvalue and increases monotonically; therefore, the reaction force at the deflection at which standard energy
absorption occurs (②) is determined via linear interpolation (TFR =1.44). Note that the energy absorption
has a design deflection value of 52.5% (TFE =1.47), which means that it is 47% larger than the standard
energy absorption, while the reaction force is 75% larger than the standard value. Therefore, at extremely
low temperatures, although the fender performance is higher than that in the design condition, it is not used
due to it exceeding the required value. Furthermore, at a temperature of 40°C, the energy absorption at thedesign deflection decreases to TFE = 0.96. Therefore, one should be careful as the temperature affects thesize selection of the fender.
If the other temperatures are similarly organized, they can be presented as in Table 6.3.10.1. As withother factors, the factors that can be shared within 3% are as given in Table 6.3.10.2. In the range of 10°C to
30°C, the difference due to the performance grade is negligible; however, since the performance curve is75not similar in shape at low temperatures, the range in which the value can be shared is limited. It is
desirable to use deflection-specific performance curves, especially when performing mooring analysis using
Grade A rubber fenders in cold climates.
Table 6.3.10.1 Example of temperature factors (catalogue display, before simplification)
Performanc
e gradeStrain rate
(%/S)
-30
-20
-10
0
10
23
30
40
50

Grade A

Grade B

Grade C

Reaction Energy Reaction
Energy Reaction Energy
force absorption
force
absorption
force absorption
TF R
TF E
TF R
TF E
TF R
TF E
2.28
2.29
1.75
1.84
1.69
1.78
1.77
1.76
1.49
1.52
1.44
1.47
1.39
1.40
1.30
1.30
1.26
1.26
1.16
1.18
1.16
1.16
1.13
1.13
1.04
1.07
1.06
1.06
1.06
1.06
1.00
1.00
1.00
1.00
1.00
1.00
0.99
0.98
1.00
1.00
1.00
1.00
0.97
0.94
0.99
0.95
1.00
0.96
0.87
0.85
1.00
0.90
1.00
0.91

Table 6.3.10.1 Example of temperature factor (catalogue display, after simplification)
Performanc
e gradeStrain rate
(%/S)
-30
-20
-10
0
10
23
30
40
50

Grade A

Grade B

Grade C

Reaction Energy
Reaction
EnergyReaction Energy
force absorption
force
absorption
force absorption
TF R
TF E
TF R
TF E
TF R
TF E
2.28
1.75
1.84
1.69
1.78
1.77
1.49
1.52
1.44
1.47
1.30
1.26
1.39
1.16
1.13
1.06
1.00
1.00
0.99
0.95
0.96
0.97
0.94
1.00
1.00
0.90
0.91
0.87
0.85

Fig. 6.3.10 Example of temperature factor (catalogue display, graph)76

These tendencies are shown in Fig. 6.3.10. The rubber fender catalogue should preferably present either
Table 6.3.10.1, Table 6.3.10.2 or Fig. 6.3.10. When only a graph is shown, it is desirable to present anapproximate expression and its coefficients so that it can be used for design.
(1) Temperature dependency test of rubber
The temperature dependency of fenders is due to the temperature dependency of rubber. Therefore, testing
the temperature dependency of rubber is useful in complementing the temperature dependency of the fender.
1) Specimen
A dumbbell or ring must be used, as specified in JIS K6250.
2) Temperature stabilization
The specimen is thermally stabilized in a thermostatic chamber. The temperature stabilizing time is 1 hor more at the target temperature ± 3°C.
3) Tests
The stress, tensile strength, and elongation in increments of 10% tensile strain (10% to 100%) aremeasured, and the hardness is measured separately.
4) Test conditions
The temperature range is measured every 10°C for -30°C to 50°C, and a standard temperature of 23°C
is employed instead of 20°C.
5) Representative value
A representative value for determining the temperature factor is employed. Here, we present an
example in which the tensile stress (Md100) at a strain of 100% is used, and the ratio of Md100(T=23°C) to the corresponding value at the target temperature is considered. The representative value
does not have to be Md100, but it is desirable to use a representative value that reflects the changes in
the reaction force of the rubber fender.
The temperature dependence of a sample material is as shown in Fig. 6.3.11.

Fig. 6.3.11 Concept of temperature test results for rubber
In Figure 6.3.11
Md100 (T=23): Tensile stress (kPa) at 100% strain at target temperature 23°C
Md100 (T= 0) : Tensile stress at 100% strain at a temperature of 0°C (kPa)
Md100 (T=10): Tensile stress at 100% strain at a temperature of 10°C (kPa)77Md100 (T=30): Tensile stress at 100% strain at a temperature of 30°C (kPa)
Md100 (T=50): Tensile stress at 100% strain at a temperature of 50°C (kPa)
Md100 is selected for the temperature closest to that corresponding to the temperature factor of the rubber fender(real product or scale model), and the temperature factor of a rubber fender is estimated by interpolation, taking the ratioof Md100 between previous and next temperature. For example, assuming that temperature factors of -30°C, 0°C, 23°C
and 50°C are available, the temperature factor TF (T=10) and TF (T=30) of the rubber fender at temperatures of 10°C
and 30°C can be obtained by linear interpolation using equation (6.3.13). The method of interpolation can be selected
appropriately according to the tendency of the data.
𝑇𝐹(𝑇 = 10) = 𝑇𝐹(𝑇 = 23) +(𝑇𝐹(𝑇=0)−𝑇𝐹(𝑇=23))・(Md100(𝑇=10)−Md100(𝑇=23))(Md100(𝑇=0)−Md100(𝑇=23))(6.3.13)
𝑇𝐹(𝑇 = 30) = 𝑇𝐹(𝑇 = 50) +(𝑇𝐹(𝑇=23)−𝑇𝐹(𝑇=50))・(Md100(𝑇=30)−Md100(𝑇=50))( Md100(𝑇=23)−Md1+00(𝑇=50) )6.3.5 Relationship between temperature factor and speed factor
Rubber is a visco-elastic material, and a relationship between speed dependency and temperature dependency exists.
This relation was reported by Williams, Landel & Ferry (WLF) 3) and can be used to verify whether the data are
accurately measured. In the case of shortage of data, a reasonable estimation can be made based on the nature of therubber, and this method is better than general interpolation or extrapolation. The formula of WLF is as shown inequation (6.3.14).

log10aT  

c1 T  Ts 
c2  T  Ts 

(6.3.14)

αT ： Shift factor
T： Temperature (°C)
TS
: Standard temperature TS≒Tg＋50°C
Tg: Glass transition point of rubber
c1 ： Coefficient: 8.86
c2 ： Coefficient: 101.6
The verification of correlation of temperature factor and speed factor can be performed as follows.
STEP-1: First, plot the temperature factor and speed factor, as shown in Fig. 6.3.12.1 and Fig. 6.3.12.2. It is noteasy to change the compression speed when using large test equipment, and the temperature is easier tochange than the compression speed. Here, it is assumed that 9 temperature factors and 4 speed factors havebeen measured.

78

Fig. 6.3.12.1 Example of temperature factor

Fig. 6.3.12.2 Example of velocity factor

STEP-2: Next, the horizontal axis of each graph is displayed logarithmically. At this time, the X axis oftemperature T substitutes the test temperature in equation (6.3.14) and becomes αT. The initial value of Ts is
50°C, as shown in Fig. 6.3.13. The speed factor is shown in Fig. 6.3.14 with the logarithm of the strain rateon the X axis.

Fig. 6.3.13 Temperature factor (log)Fig. 6.3.14 Velocity factor (log)STEP-3: Overlay both graphs. The velocity factor and temperature factor are plotted on the same Y-axis; αT andlog velocity are plotted on the same X-axis. Since changing the value of Ts changes the value of αT, thevalue of Ts is adjusted so that the plots of the velocity factor and the temperature factor overlap. The
temperature factor may be approximated and the value of Ts may be determined using an Excel Solver
function or similar approaches to minimize the residual sum of squares to the velocity factor.
Both the graphs should have curves of similar shapes, and if the curves are not similar, the test results may
have errors. The state of superposition is shown in Fig. 6.3.15. The temperature factor (blue circle) and the velocity
factor (red X point) are almost identical. The orange square point denotes the standard conditions (V0=0.01 to
0.3%/s at temperature 23°C) and its value is 1.0. In this manner, while interpolating between test data, factors atvery low and high velocities can be rationally estimated by superposing the temperature factors.

79

Fig. 6.3.15 Overlapping of temperature factor and velocity factor

6.3.6 Material tests
The quality of rubber materials is important because rubber fenders are often subjected to high strain. Althoughmaterial testing may be carried out not only in development tests but also in authentication tests and quality verification
tests, it is desirable that all tests are conducted following the same procedure.
For rubber materials, (1) to (4) must be satisfied as basic requirements.
(1) A vulcanized product must be obtained by mixing natural or synthetic rubber containing carbon black or whitecarbon.
(2) The material must have ageing resistance, seawater resistance, ozone resistance, abrasion resistance, etc.
(3) The material must be homogeneous and free from foreign matter, bubbles, scratches, cracks and other harmful
defects.
(4) Embedded steel plate for installation flange must be covered and firmly cured by vulcanization; furthermore, it
should not be exposed.
In addition, in the Standard Specifications for Ports and Harbor Works 1), the standard physical property values ofrubber used for rubber fenders are defined, as given in Table 6.3.11.
Table 6.3.11 Physical properties of rubber for fenders
Material test
Ageing method
Accelerated
ageingRequirement

Heat ageing JIS K 6257 Accelerated ageing (AA-2), 70℃±1℃ｘ96 +0/-2 hours

Tensile strength

Not less than 80% of original value
Tensile test JIS K 6251

Elongation at break
Hardness

Ozone
resistance

Test standard

Static ozone
degradation

Not less than 80% of original value
Durometer hardness（Type-A)
JIS K 6253-3 （ISO 7619-1)
JIS K 6259 (ISO1431-1)50±5pphm, 20±2% elongation, 40±2℃ｘ72hours

80

Must not exceed +8 point of originalvalue
No visible cracks after 72 hours

6.4 Authentication test
The authentication test is a test entrusted to a third party to obtain an objective evaluation, and the following
durability test is currently prescribed by the Standard Specifications for Ports and Harbor Works 1). The specificprocedure is described in detail, for example, in the Standard Procedure to Durability Test for Rubber Fender Units 4).
6.4.1 Durability test
Fatigue deterioration in a durability test is not similar to that of a scale model; therefore, commercially available
products are used as test specimens. The available size is selected by a manufacturer according to the capacity of thetest facility. Because of the difference in heat generation and heat dissipation, larger sized fenders exhibit a larger
increase in rubber temperature due to continuous compression. However, since actual fenders in ports are notcompressed continuously, time for heat dissipation and recovery is available. Although recognizing the influence ofsuch aspects, a durability test is the most direct test method to evaluate the basic durability of rubber fenders, and thistest must be performed as an authentication test to validate the durability.
(1) Temperature stabilization
The specimen is thermally stabilized to a standard temperature of 23±5°C. The stabilizing time corresponds
to the number of days equal to or greater than that obtained using equation (6.3.1).
(2) Preliminary compression
Compression is performed at least 3 times up to the design deflection or more. The consideration of residual
deflection, compression speed, compression interval, etc. is not specified, but it is desirable to unify theseconcepts and record the number of times and reaction force data.
(3) Static compression for pre-test performance
After preliminary compression, the specimen is thermally stabilized at a standard temperature of 23±5°C for
1 h or more. Next, the specimen is compressed again to its design deflection or more at a strain rate ranging
from 0.01 to 0.3%/s.
(4) Durability test
The durability test consists of 3,000 compression cycles to a design deflection or more at a constant speed(CV) or deceleration (DV) with the period of one compression cycle not exceeding 150 s. The waveform ofdeceleration (DV) is not specified, but the compression and unloading start positions should be fixed.
(5) Visual check
Visually confirm that no cracks or defects are visible to the naked eye after the durability test.
(6) Static compression for post-test performance
Within 24 hours after the durability test, the specimen is compressed again until the design deflection or
more, and its performance is considered as the static compression performance after the durability test. At thetime of testing, it is desirable to record the temperature of the environment in which the rubber fender is placed.
Examples of durability test results are given in Table 6.4.1.

81

Table 6.4.1 Example of durability test result
Rubber fender

Sample: 600H

No. Sam001

Test dateDec., 1st, 2016

Pre-test
performance

Energy absorption

196.7 kN∙m

Post-test
performance
Visual check

Reaction force

429.5 kN

Test dateFeb.,6th, 2016

Durability test end dateFeb.,5th, 2016 18:15

Energy absorption

176.2kN∙m

Post-test compression start dateFeb.,6th, 2016 06:15

Reaction force

392.3 kN

Recovery time

12 hours

Defects

None

Judgement

Satisfactory

The durability test is also called the repetition fatigue test when compression is continued until failure, and an
example is shown in Fig. 4.2.17 in Chapter 4. It is desirable that the fatigue characteristics are presented in the technicaldata as needed, even if they are not presented in the catalogue.
6.4.2 Other authentication tests
Static compression tests ((3) and (6) in 6.4.1) before and after the durability test and material tests are also required,as specified in the Standard Procedure to Durability Test for Rubber Fender Units 4). These tests are equivalent to thestatic compression test described in Section 6.3.1 and the material test described in Section 6.3.6.

6.5 Quality verification test
The quality verification test is used by manufacturers to ensure product quality. The test is conducted on the premisethat products to be delivered are individually implemented, and the results are presented to the purchaser. Specifically,
the test should be conducted based on the agreement between the purchaser and manufacturer. Generally, static
compression tests and material tests are required to be performed. The test methods are the same as those for thedevelopment test; however, they are described in detail in this section because the test results are accompanied by apass/fail judgment of products before delivery to customer.
6.5.1 Static compression test
The static compression test leads to an index that represents the basic performance of rubber fenders. Furthermore,
the test is performed as a development test and an authentication test in addition to the quality verification test , and it isperformed widely for specimens ranging from actual products to scale models. Although large-scale actual fender tests
depend on the scale of the testing facility, manufacturers must be able to carry out this test internally or externally for all
types, sizes, and performance grades manufactured in-house. The specific test method is carried out in the following
steps according to the PIANC Guidelines 2).
(1) Temperature stabilization of test piece and environment
Since the performance of rubber fenders is affected by the temperature, the test should be conducted in atemperature-controlled environment at the target temperature. The target temperature for measuring thestandard performance is 23±5℃ (standard temperature), and it is desirable to conduct the static compression
test in an environment within the target temperature ±15°C even in an environment where it is difficult tomaintain constant temperature. Specifically, the following two methods can be employed.
1) Temperature control before test
Proper temperature control should be performed by storing rubber fenders in an environment suchas that of a temperature-controlled room at a target temperature of ±5°C for a necessary period until
the fenders are stabilized. The number of days required to stabilize the temperature of entire rubber

82

body is determined using equation (6.3.1).
Days for thermal stabilization＝20·(Maximum rubber thickness(m))1.5(6.3.1)After taking the fender out of the temperature-controlled room, if the test environment is out of therange of the target temperature ±5°C, the total test time including the preliminary test should be within
2 hours to reduce performance influence. Additionally, for the case temperature correction is needed
later, the environmental temperature at which rubber fender is placed should be recorded throughout
the test.
2) Temperature correction as alternative of temperature control:
As in the case of large sized fenders, when it is difficult to maintain the fender at the target
temperature ±5°C in advance, or when the test time including preliminary compression after the
specimen has been taken out of the temperature-controlled room is more than 2 h, the temperature iscorrected using the average value of the recorded environmental temperature. The correction is
performed by multiplying the temperature factor with respect to the time average of the recorded
environmental temperature (equation (6.3.1)) with the target temperature. Even in such a case, it isdesirable that the test environment is within the temperature range of target temperature ±15°C. Even
when the test room itself is temperature-controlled or when the ambient temperature change is within
the target temperature ±5°C, it is recommended that the ambient temperature at which the rubber
fender is placed throughout the test is recorded.
(2) Preliminary compression
Compression must be performed three or more times upon the manufacturer's recommendation up to thedesign deflection or more. The consideration of compression residual strain, compression rate, compressioninterval, etc. is not specified; however, it is desirable to unify these concepts. It is recommended that the
number of compressions and performance values are recorded.
(3) Main compression (Static)
Leave the specimen at the target temperature ±5°C for 1 h or more after preliminary compression andcompress the specimen again to the design deflection or more; the corresponding performance is the static
compression performance. To eliminate the residual strain of preliminary compression, the initial deflection
point at which the reaction force starts to increases is the origin of the deflection axis. The compression rate iswithin the range of the standard strain rate (0.01 to 0.3%/s or 0.3 to 1.3 mm/s), and if the compression rate inthis range is difficult to be realized due to size restrictions, etc., correct the result using the velocity factor. In
accordance with the capability of the testing facility, it is possible to execute decelerating compression DV
from a high initial velocity to measure the performance including the influence of velocity. This performance is
known as the decelerating compression performance, and it is different from the static compression
performance. In the case of velocity reduction compression, the initial speed and reduced speeds are also
recorded. In addition, when storage cannot be performed at the target temperature ±5°C, the result istemperature-corrected using the average value of the recorded ambient temperatures.
(4) Number of samplings for quality confirmation test
The quality confirmation test includes a sampling test and a 100% test. The frequency of the sampling test is
set at a rate of 1 unit if the number of fenders is 10 or less, and 1 unit per 10 units if more than 10 units areused; the fraction value is rounded up.
(5) Treatment at time of failure in quality confirmation test
If a failure occurs in the 100% test, it is rejected. If a rejection occurs in a sampling test, the rejected sample
is removed and the number of samplings for the remaining products is doubled (1 unit for 5 units, 2 units for83

group of less than 5 units) for the additional tests. If failure still occurs, 100% inspection is conducted and thefailed products are rejected.
(6) Break-in compression
The rubber fenders for which the effect of reaction force on the safety of a structure cannot be ignored, inother words, for which the design condition is other than the influence factor pattern A specified in Table 5.4.4
in Chapter 5, Section 5.4, are compressed to the design deflection or more at least once after being
manufactured. This compression is expected to remove the first high reaction force of virgin products and is
known as break-in compression. This process must be performed even for the products that are not selected for
quality confirmation tests.
(7) V-type rubber fenders of open leg type are fixed to the base plate of the tester to ensure that the legs do not
open.
(8) Energy absorption is obtained by integrating the reaction force with respect to the deflection up to the
maximum deflection. The integration can be numerical such as trapezoidal integration, and the step size ofdeflection is within 5%.
An example of a static compression test for quality verification is presented in Table 6.5.1.

84

Table 6.5.1 Example of static compression test for quality verification
Compression performance (Test result)
Product

Sample 1000H
Sample1

Product No.

Start: 24℃

Temperature

Reaction force

Deflection
（1）

(%)

（2）

Test dateFeb., 6th, 2017

Grade A

Main compression

11：30,Feb., 7th, 2017(kN)

Preliminary compression（mm）Rubber grade
Finish:24℃（3）

End time

Main compression

13:00

(4)

Energy absorption（kN∙m）

0

0

0.0

0.0

0.0

0.0

50

5

201.0

168.0

165.0

173.0

4.3

100

10

336.0

291.0

286.0

300.0

16.2

150

15

452.0

384.0

376.0

395.0

33.5

200

20

538.0

440.0

428.0

451.0

54.7

250

25

578.0

458.0

442.0

468.0

77.7

300

30

579.0

448.0

432.0

457.0

100.8

350

35

549.0

429.0

413.0

437.0

123.2

400

40

508.0

413.0

398.0

421.0

144.7

450

45

474.0

404.0

390.0

412.0

165.6

500

50

450.0

402.0

390.0

411.0

186.2

525

52.5

443.0

420.0

406.0

429.0

196.7

550

55

454.0

456.0

448.0

470.0

207.9

Reaction force

Standard

ResultDeviation

at 52.5% (kN)

437+10%429.5-1.72%

Energy absorption
(kN)

0.0

Standard

ResultDeviation

192-10%

196.7

2.45%

Reaction force

Performance curve

Energy absorption
250

450

Reaction force（ ｋ N)

400

200

350
300

150

250
200

100

150
100

Energy absorption（ ｋ N・ m)

500

50

50

0

0

0

10

20

30

40

50

60

Deflection（ ％）6.5.2 Material tests
The quality of rubber materials is important because rubber fenders are often subjected to high strain. Althoughmaterial testing may be carried out not only in quality verification tests but also in authentication tests and development
tests, it is desirable that all tests are conducted following the same procedure.
For rubber materials, (1) to (4) must be satisfied as basic requirements.
(1) A vulcanized product must be obtained by mixing natural or synthetic rubber containing carbon black or whitecarbon.

85

(2) The material must have ageing resistance, seawater resistance, ozone resistance, abrasion resistance, etc.
(3) The material must be homogeneous and free from foreign matter, bubbles, scratches, cracks and other harmful
defects.
(4) Embedded steel plate for installation flange must be covered and firmly cured by vulcanization; furthermore, it
should not be exposed.
In addition, in the Standard Specifications for Ports and Harbor Works 1), the standard physical property values ofrubber used for rubber fenders are defined as given in Table 6.5.2. Rubber exerts its physical properties by means of avulcanization reaction caused by heat and pressure. The method of applying pressure and temperature differs dependingon the product because thick materials such as rubber fenders require a long time for the internal part to be affected. The
process is a unique expertise of each manufacturer. Even if the material test sheet is selected from the same mixing lot
as the product, the time to reach the heat of vulcanization is different depending on the depth from the surface of
product; thus, it is impossible to match the history of the temperature for any part of product. In the product, any
physical property is distributed naturally. Therefore, it must be noted that the material test described here is theconfirmation of the standard value necessary to reliably exhibit the required performance when the material constitutes
a rubber fender, and it is not always necessary to ensure the same physical properties everywhere.
Table 6.5.2 Physical properties of rubber for fender (Same as Table 6.3.11)
Material test
Ageing method
Accelerated
ageingRequirement

Heat ageing JIS K 6257 Accelerated ageing (AA-2), 70℃±1℃ｘ96 +0/-2 hours

Tensile strength

Not less than 80% of original value
Tensile test JIS K 6251

Elongation at break
Hardness

Ozone
resistance

Test standard

Static ozone
degradation

Not less than 80% of original value
Durometer hardness（Type-A)
JIS K 6253-3 （ISO 7619-1)
JIS K 6259 (ISO1431-1)50±5pphm, 20±2% elongation, 40±2℃ｘ72hours

Must not exceed +8 point of originalvalue
No visible cracks after 72 hours(1) Batch and lot in quality verification test of material
In principle, the test pieces to be subjected to material testing involve one set of samples taken from thesame lot as the product. The rubber material is prepared as raw rubber before vulcanization, which is used forthe product in the kneading step. One batch of the material obtained in one kneading step, and the total of eachbatch continuously produced with the same composition is called a lot. For large products, multiple batches
may be used for one product, and depending on the amount of rubber, multiple lots may be used. The same lot
to be subjected to the material test refers to the material extracted from any batch in the kneading lot of thematerial used for the product. In addition, when the material is used for multiple different products from one lot,
the material extracted from the batch is used for the target product.
(2) Response to failure in quality verification test
If the quality verification test does not meet the requirement values specified in Table 6.5.2, retesting is
performed using two more sets of samples from the same kneading lot. If all the samples pass, and if the
products that use the same lot pass the other quality verification tests, it is acceptable to assume that the
product can pass the quality verification test.
(3) Submission of used material sample (for ingredient confirmation)
Although the material sample to be subjected to the test must be from the same mixing lot, it may be difficult
to prove this aspect to a third party due to the nature of the production process. The purchaser can request the
manufacturer to submit the material sample used in the quality verification test. The purchaser can retrieve thesample and store them, and he/she can independently confirm the identity of the basic component with the86delivered product at any time and method using a third-party organization.
An example of the material test result for the quality verification test is given in Table 6.5.3.
Table 6.5.3 Example of material test result

Physical property test report(1) Hardness
Method: JIS K 6253-3
Accelerated Aging: JIS K 6257
Condition: 70℃±1℃ｘ96 +0/-2 hours
Before ageng

After ageing

Difference

Requirement

Judgement

56

62

+6

Not more than +8

Satisfactory(2) Tensile test
Method: JIS K 6251
Accelerated Aging: JIS K 6257
Condition: 70℃±1℃ｘ96 +0/-2 hours
Tensile strength (kN)
Before ageng

After ageing

Ratio

Requirement

Judgement

16.7

15.8

95%

Not less than 80% of
before aging

Satisfactory

After ageing

Ratio

Requirement

Judgement89%

Not less than 80% of
before aging

Satisfactory

Elongation at break (%)
Before ageng
540

480

(3) Ozone resistance
Method: JIS K 6259-1
Condition: 50±5pphm ozone, 20±2% elongation, 40±2℃ｘ72hours
Results
No cracks

Requirement

Judgement

No visible cracks
after 72 hours

Satisfactory

6.6 Influence factor and classification of tests
The various tests described in the previous section differ in terms of the classification of tests to be performed
considering the performance influencing factors defined in Chapter 5, Section 5.4. The test classification is presented inTable 6.6.1.

87

Table 6.6.1 Performance influencing factors and types of tests
Production tolerance only

Major influence factors

Mooring analysis（Pattern A）（Pattern B）（Pattern C）（Delivery test）

Quality verification test
（Sampling）

Quality verification test
（Sampling）

Quality verification test
（100%）

Material test

Quality verification test

Quality verification test

Quality verification test

Authentication test

Authentication test

Authentication test

Angular compression

N/A

Development test

Development test

Velocity dependency

N/A

Development test

Development test

Temperature dependency

N/A

Development test

Development test

Aging

N/A

N/A

Development test /reseach

Repetition fatigue

N/A

N/A

Development test

Creep characteristic

N/A

N/A

Development test

Influence factor
Static compression

Durability test
（3000 cycle）(1) The quality verification tests (static compression test and material test) and authentication tests (durability test),
which are listed in Table 6.6.1 are defined in the Standard Specifications for Ports and Harbor Works 1).
(2) The durability test is also a development test; however, since it has already been established as anauthentication test and is defined in the Standard Specifications for Ports and Harbor Works 1), the 3000-cycle
durability test was classified as an authentication test.
(3) In several cases, it is difficult to reproduce a development test as an authentication test under the same
conditions at a third party premises, to ensure the results in the presence of a third party such as for a quality
verification test or to submit the used sample after testing. Therefore, manufacturers should explain the test
contents using technical documents.
(4) The research for ageing is still under development, and presently, its testing requires a large duration. However,certain information in terms of test data for used fenders 6) and accelerated ageing testing of scale models 7) isavailable; thus, one may refer to the technical data of the manufacturer, if necessary.
(5) Repetition fatigue and creep characteristics tests are conducted using the manufacturer's technical data, if
necessary 7).

6.7 Similarity rules in scale model testing
Rubber fenders are large in size, and it is sometimes difficult to conduct various tests on an actual product. In suchcases, a scaled model is used. The model test of rubber fenders employs a scale model, which is smaller than the
product, and has the same material as that of an actual fender.
The size of an actual fender is indexed by R and that of the model is represented by m; the scale S is defined using
equation (6.7.1).

Ｓ ＝ HR/Hm(6.7.1)Here,

Ｓ ： Scale
ＨR： Height of fender
Ｈm： Height of scale model

88

Since the exact match between a scale model and actual product is reflected only in a full-scale test, the physicalquantity of interest must ideally be similar. For example, in a hydraulic experiment, both the product and model must
use water, and the gravitational acceleration must be the same as well. Therefore, the material property and time must be
adjusted to match the Froude number to ensure that the flow field is similar to the free surface. Furthermore, inexperiments involving pipe flows around obstacles, the physical property values and time must be adjusted to match the
Reynolds numbers.
The characteristics of deflection and reaction force of rubber fenders do not approximate such motions; however, thestress and strain generated in rubber must be similar. To make the concept easy to understand, assume a cubic rubberblock, as shown in Fig. 6.7.1. Furthermore, assume that the size of the model for the test is one-third that of the product,
and both the model and product are made of the same material. It can be seen that the physical quantities in Fig. 6.7.1
are scaled down, as defined in equation (6.7.2).
Height ：HR/Hm＝S＝3
Deflection ：dR/dm＝S＝3
Area ：AR/Am ＝ S2 ＝ 9
Volume ：VR/Vm ＝ S3 ＝ 27
Weight ：WR/Wm ＝ S3＝ 27
Strain ε(-) ：（dR/HR）/（dm/Hm）＝（dR/dm）/(Hm/HR）＝S×1/S ＝1
Reaction force at strain ε ：FR/Fm ＝S2 ＝ 9

Area: AR
Volume: VR
Weight: WR(6.7.2)

Area: AR
Volume: VR
Weight: WR
Fig. 6.7.1 Cubic fender and 1/3 scale model

If it takes tR seconds to compress the real cubic fender by dR, equation (6.7.3) can be used to obtain the time tm
required for compression of the model to the same deflection.
(HR/dR)／tR＝ (Hm/dm)／tm
Considering(6.7.3)

HR/dR＝ Hm/dm,
tR=tm(6.7.4)89

The following five mechanical quantities are considered to discuss the validity of the abovementioned similarity
rules.
1) Elastic force: Linear force proportional to strain (Hooke's law)2) Viscous force: Force proportional to deformation speed (Newton's viscosity)
3) Friction force: Force proportional to and perpendicular to vertical load (Coulomb friction)4) Weight: Downward force by gravity
5) Inertial force: Product of mass and acceleration (Newton's law of inertia)(1) Elastic force
Assuming that the stress is σ, strain is ε, and Young's modulus is E, equation (6.7.5) holds.
σ＝εE(6.7.5)

Considering a rubber block having a spring constant K, according to Hooke's law, if the compression
displacement is δ and elastic force is F, equation (6.7.6) holds.
F =Kδ

(6.7.6)

Assuming that the representative area (cross-sectional area) of this rubber block is A, and the representative
length (height) is H, the spring constant K can be expressed using equation (6.7.7).
K=EA／H(6.7.7)

As shown in Fig. 6.7.1, the real product is represented by R, and the model is represented by the subscript m.
According to equations (6.7.6) and (6.7.7),
Real product : F R＝KR  δR＝(ERAR／HR)δR
Scale model : F m＝Km  δm＝(EmAm／Hm)δm(6.7.8)Assuming that the product and model are made of the same material, ER=Em. The elastic force ratio FR / F m
is
F R／F m＝(ERAR／HR)δm／{(EmAm／Hm)δR}＝(AR /Am)( Hm/ HR)( δR/δm)(6.7.9)Substituting AR /Am=S2, Hm/ HR=1/S, and δR/δm=S from equation (6.7.2) in equation (6.7.9),
F R／F m＝S2

(6.7.10)

Therefore, the elastic force is considered to be proportional to the square of the scale as well as the area.
(2) Viscous force
The performance of rubber fenders is affected by the compression speed, due to the viscosity of rubber. The
stress τ due to viscosity is proportional to the strain rate dε / dt, and equation (6.7.11) holds if the proportional
constant η is considered as the viscosity coefficient.
τ= η  (dε/dt)(6.7.11)The viscosity coefficient η is a physical property value of the material, and it is not influenced by thedimensions of the object. When the area is multiplied by equation (6.7.11), the viscous force F is obtained, and90

when the real product is represented by R and the model is represented by the subscript m, the viscous force canbe obtained using equation (6.7.12).
Real product : F R＝ηR  AR  (dεR/dtR)
Scale model : F m＝ηm  Am  (dεm/dtm)（6.7.12）The strain rate is dimensionless, and it can be considered that εR = εm. Therefore, the ratio of viscous force
F due to viscosity can be determined using equation (6.7.12).
F R／F m＝(ηR  AR  tm)／(ηm  Am  tR)(6.7.13)

From equation (6.7.2), AR /Am=S2
F R／F m＝S2  (ηR ／ηm)  (tm ／tR)

(6.7.14)

If both the real product and model are made of the same material, ηR =ηm; thus, equation (6.7.14) becomes
F R／F m＝S2  (tm ／tR)

(6.7.15)

Therefore, from equation (6.7.4), if tm =tR, the viscous force is considered to be proportional to the squareof the scale, similar to the elastic force.
(3) Friction force
The frictional force F is proportional to the vertical load R, and when the proportional constant is μ (friction
coefficient), the frictional force can be expressed using equation (6.7.16).
F ＝ μ R(6.7.16)

The suffix R corresponds to the real product, and m corresponds to the scale model. The ratio of friction forces
is as given in equation (6.7.17).
F R ／F m＝(μR  R R )／(μm  R m)

(6.7.17)

If the same material is used for the product and model, the friction coefficients are equal. Furthermore, if μm=μR, the ratio of friction forces becomes the same as the ratio of the reaction forces, and equation (6.7.18)
holds.
F R ／F m＝R R／R m＝S2

(6.7.18)

Therefore, it is considered that the friction force is also proportional to the square of the scale, similar to theforce due to elasticity and viscosity.
(4) Weight
Although it is considered that the elastic force, viscous force, and friction force are all proportional to thesquare of the scale, this similarity rule does not hold for the weight even though the dead weight is a downward
force. Assuming that the weight of a rubber fender is W, the density is ρ, and the volume is V, the weight can becalculated using equation (6.7.19).
W＝ ρV

(6.7.19)

91

The real product is represented by R, and the model is represented by m. The ratio of the self weights of the
product and model is as shown in equation (6.7.20).
W R ／W m＝(ρR  V R )／(ρm  V m)

(6.7.20)

Since VR / Vm = S3 from equation (6.7.2), it is necessary to satisfy ρR / ρm = 1 / S to ensure that the weight W
is proportional to the square of the scale along with the elastic force, viscous force and friction force. To thisend, it is necessary to use a material having a density S times more than that of the model, which is impossible
when using the same material. Table 6.7.1 presents an example of the self-weight and reaction force of fenders
as reference for comparing the error.

Fender size: H
100H (Model)
1000H
3000H

Table 6.7.1 Self weight and reaction force of fenders
Self-weight: W (kg)Reaction force: R (kN)
W / R (%)
0.79
57
0.014
700
568
1.21
16600
5670
2.87

Since rubber fenders are attached horizontally, the reaction force and the weight are orthogonal; although theweight does not necessarily act as an error of the reaction force directly, the error is larger for larger sizes, as
shown in Table 6.7.1. It can be seen that even the largest rubber fenders have a weight that is less than 3% of
the reaction force. A larger sized fender is more likely to be deformed by its own weight (front drooping) andneeds to be supported by the weight chain.
(5) Inertial force
The inertial force F is expressed as a product of the mass and acceleration, as given in equation (6.7.21),
where M is the mass and x is the displacement.
F ＝ M  (d2x /dt2)(6.7.21)

Assuming that the acceleration is an average value, the real product is represented by R, and the model isrepresented by a subscript m, the ratio of inertial forces is defined as in equation (6.7.22).
FR／Fm＝(MR  xR／tR2 )／(Mm  xm／tm2)= (MR／Mm)  (xR／xm)  (tm／tR)2(6.7.22)Since the mass is proportional to volume, equation (6.7.23) is obtained from equation (6.7.21) if MR / Mm =S and xR / xm = S.
3

FR ／Fm＝S4  (tm／tR)2(6.7.23)

Therefore, for the ratio FR／Fm of the inertial forces to be a square of the scale along with the elastic force,viscous force, and friction force, it is necessary to satisfy equation (6.7.24). To this end, the model must deform
S times faster.
tR／tm＝S(6.7.24)

This aspect contradicts the expression of the viscous force with tR / tm = 1; for S=1, i.e., at full size, theviscous force and inertial force are similar simultaneously.
As a reference, let us estimate the inertia force and reaction force at the time of berthing of a rubber fender.
Assuming that the compression is performed at an initial velocity V and stopped at 50% deflection, the time t at92

this point can be expressed using equation (6.7.25).
t＝0.5H／V(6.7.25)

Assuming that the average acceleration is V／t＝V 2／(0.5H) and the mass moved by compression is one
half the weight of the rubber fender, the inertial force F can be expressed using equation (6.7.26).
F＝W/(2g)V 2／(0.5H）(6.7.26)

The estimated results are as presented in Table 6.7.2. It can be seen that the influence of the inertial force isnegligibly small compared to that of the self-weight of the fender.
Table 6.7.2 Inertial force and reaction force of rubber fender at berthing
Fender size: H

Velocity:
V (m/s)Self-weight:
W (kg)

Inertial force
F (kN)

Reaction force:
R (kN)

F/R(%)

100H (Model)
1000H
3000H

0.01
0.1
0.3

0.79
700
16600

8.05E-05
0.71
50.76

57
568
5670

1.41E-04
0.13
0.90

The above aspects can be summarized as follows. It should be noted that similarity rules do not hold for these
physical quantities.
(1) Deflection by self weightThe deflection of a fender by its self-weight does not become similar in scale (S) because its own weight is(S 3) and reaction force is (S 2). No major impact on performance is noted as the direction is different withrespect to the berthing.
(2) Inertial force due to fender deformation
The inertial force generated by the deformation of rubber fenders is not similar because it is related to theweight of the rubber; however, its influence during actual berthing is small.
(3) Temperature
The heat generation is proportional to the volume (S 3), heat conduction is proportional to the distance (S),and heat dissipation is proportional to the surface area (S 2); therefore, the similarity does not hold. It is thus
necessary to focus on repetition fatigue tests involving heat generation.
(4) Error in production
In addition to the difference in the accuracy between the dimensions of the actual product and scale model,
heat transfer between the actual product and scale model cannot be made similar; therefore, the curingconditions are not exactly the same, and the thickness distribution of rubber properties is slightly different evenwhen the same materials are used. Although the model vulcanization conditions are devised to obtain aperformance close to that of the actual product, the methods often correspond to a manufacturer's own
technology.
To minimize the effects of these errors, it is desirable that the test results of the scaled model use coefficients with thetest data at the standard conditions of the model rather than scaling up the model data. Such an additional form is calleda reference model.

93

〔References〕
1）Ports and Harbour Bureau, Ministry of Land, Infrastructure, Transport and Tourism (MLIT): Standard Specifications
for Ports and Harbour Works, Vol.1, pp.71-72, 2017
2) PIANC: Guidelines for the Design of Fenders System, Report of Working Group 33 of the Maritime Navigation
Commission, 2002
3) M. L. Williams, R. F. Landel, J. D. Ferry, J.: The Temperature Dependence of Relaxation Mechanisms in Amorphous
Polymers and Other Glass-forming Liquids, Am. Chem. Soc., Vol.77, p.3701, 1955
4) Service Center of Port Engineering (SCOPE) (2012): Standard Procedure to Durability Test for Rubber Fender
Units5) Ueda, S., Shiraishi, S., Maruyama, T., Uezono, A., Takasaki, M., Yamase, S.: Properties of Rubber fender in use of
Mooring for Floating Bridge, Proceedings of the 14th Symposium of Ocean Engineering, SNAJ, pp.359-364, 1998
(in Japanese)
6) Akiyama, H., Shimizu, K., Ueda, S., Kamada, T.: Investigation on Service Years of Large Rubber Marine Fenders,
Journal of JSCE, Vol.5, pp.392-401, 2017
7) Akiyama, H.: Study on Aging of Circular Hollow Rubber Fender in Long Term Usage, Osaka University Doctoral
Thesis, 2018 (in Japanese)

94AppendicesA.1 General
The impact of the proposed rubber fender design on the conventional design specifications is as follows.
(1) When considering only manufacturing tolerance: Pattern A
No impact, as there is no change in the design method employed in Japan.
(2) When considering the major influence factors: Pattern B
This pattern is equivalent to the PIANC Guidelines 1). The variations in the performance, particularly when thereaction force is redesigned at the berthing velocity (deceleration) and/or low temperature, may meet therequirements of energy absorption even with slightly smaller sizes or performance grades, while the reaction
force and hull pressure may increase slightly.
(3) When designing fenders through mooring analysis involving numerical calculation: Pattern C
No influence, as the design method is different depending on the case, and it has been studied independently.
The following sections present examples of design considering each factor pattern proposed in this document. The
performance data and influence factors used here are samples for explaining the design process, and thus, they are
different from actual data. When designing, please refer to the manufacturers’ catalogues and technical data and use datathat matches the product and performance grade.

A.2 Pattern A: Manufacturing tolerance
A.2.1 General cargo vessel of 5,000 DWT: Without fender panel
We consider the trial design of fenders expected to receive 5,000 DWT cargo ships on a gravity quay. Since norestriction of allowable surface pressure exists and the quay is gravity type with earth pressure behind, the design
example presented is of a case in which the allowable horizontal load is sufficiently large with respect to the reaction
force of the rubber fender.
(1) Design conditions
The vessel specifications are listed in Table A.2.1. When the target vessel is known, the vessel statement andthe latest statistics 2) can be used. In this case, it is assumed that the data in Table A.2.1 is available.
Table A.2.1 Vessel data
Items
Condition Unit
Type of vessel
General cargo
Dead weight tonnage：DWT

5,000 tGross tonnage：GT

2,645 tLength between perpendiculars：Lpp

99.46 mBeam of vessel：B

16.96 mFull draught of vessel：ｄ

6.44

Berthing velocity：VB

0.2 m/s95m

(2) Effective berthing energy
The effective berthing energy is calculated as presented in Table A.2.2.
Table A.2.2 Effective Berthing energy(Equation (5.3.1), Section 5.3, Chapter 5.3)
Displacement tonnageDT5,870 tBlock coefficient

Cb

0.53

Virtual mass factor

Cm

2.13

Eccentricity factor

Ce

0.50

Softness factor

Cs

1.00

Berth configuration factor

Cc

1.00

Effective berthing energy

Eb

125 kNm(＝kJ)(3) Selection of rubber fenders
Since the mooring facilities are gravity type, they correspond to factor pattern A specified in Table 5.4.4 in
Chapter 5, and it is sufficient to consider only the manufacturing tolerance as the influence factor for the
standard performance. Therefore, from the manufacturer’s catalogue, a size corresponding to an energy
absorption of 139 kN·m, as obtained by increasing the effective berthing energy 125 kN·m by 10% is selected.
Rubber fenders are usually selected with alternative choices of size and performance grade. For example,
considering V-type fenders, candidates that satisfy the abovementioned energy absorption for 500H, 600H, and800H can be selected as shown in Tables A.2.3, A.2.4, and A.2.5, respectively.
Table A.2.3 Catalogue example: V-type fender 500H
Performance Grades

Grade A

Grade B

Design deflection
Performance
Length1000mm
1500mm
2000mm
2500mm
3000mm45%

45%

Reaction force
(kN)
460
689
919
1149
1379

Energy absorption(kN・m）
81
121
161
202
242

Reaction force
(kN)
383
575
766
958
1149

Grade C
45%

Energy absorption(kN・m）
67
101
135
168
202

Reaction force
(kN)
306
460
613
766
919

Energy absorption(kN・m）
54
81
108
135
161

Table A.2.4 Catalogue example: V-type fender 600H
Performance Grades

Grade A

Grade B

Design deflection

45%

45%

Performance

Grade C
45%

1000mm
1500mm
2000mmReaction force
(kN)
552
828
1104

Energy absorption(kN・m）
117
175
234

Reaction force
(kN)
460
690
920

Energy absorption(kN・m）
97146
1952500mm

1380

292

1150

3000mm

1656

350

1380

LengthReaction force
(kN)
368
552
736

Energy absorption(kN・m）
78
117
156

243

920

195

292

1104

234

Table A.2.5 Catalogue example: V-type fender 800H
Performance Grades
Design deflection
Performance
Length1000mm
1500mm
2000mm
2500mm
3000mmGrade A
45%
Reaction force Energy absorption(kN)(kN・m）
707
189
1061
283
1414
377
1768
471
2121
566

Grade B
45%
Reaction force
Energy absorption(kN)(kN・m）
589
157
884
236
1179
314
1473
393
1768
471

96

Grade C
45%
Reaction force
Energy absorption(kN)(kN・m）
471
126
707
189
943
251
1179
314
1414
377

In Tables A.2.3, A.2.4, and A.2.5, the red boxes are candidates for the effective berthing energy. If the fender
length can be adjusted every 100 mm, it is possible to determine the optimum length by proportioning theenergy absorption surrounded by two red frames to the length. The sizes and performance grades presented inTable A.2.6 can be selected.
Table A.2.6 Selected V-type fender for each performance grade
Performance Grades
Performance
Size
500H
600H
800H

Length
(mm)
1800
1200
800

Grade A
Reaction force
(kN)
827
662
566

Energy absorption(kN・m）
145
140
151

Length
(mm)
2100
1500
900

Grade B
Reaction force
(kN)
804
690
530

Energy absorption(kN・m）
141
146
141

Length
(mm)
2600
1800
1200

Grade C
Reaction force
(kN)
797
662
566

Energy absorption(kN・m）
140
140
151

The choice of size from Table A.2.6 is determined by the installation and other considerations, as describedin Chapter 5, Section 5.6. For example, when the difference in water levels or the difference in the vertical
position of the vessel berthing points is large, the size can be small, for example, 500H×2600 mm for a low
performance grade fender with long length. However, the fender may slightly long with respect to the height.
Conversely, when the height must be increased due to the restrictions of installation pitch, etc., 800H×800 mm
can be selected. However, if the length is less than the height, a certain minimum length is necessary because
the deformation mode may change due to the influence of both ends of the rubber fender. For lengths not
specified in the catalogue, it is necessary to ask the manufacturer for the possibility of adjusting the length. In
this case, V-type 600H×1.5 m (grade B) is selected from the catalogue as a rubber fender capable of absorbing
the effective berthing energy of the vessel.
<Standard performance>
Size: V type 600H × 1500L (performance grade B)
Design deflection: Within 45.0 (%)
Reaction force: Standard RR=690, Max. R+=760 (+ 10%) (kN)
Energy absorption: Standard EA=146, Min. EA－=132 (-10%) > 125 (kN·m)(4) Arrangement of rubber fenders (reference)
The rubber fenders can be considered to be installed vertically, horizontally, in an alternating manner (in thevertical and horizontal directions), etc. In this case, the most commonly used configuration, that is, verticalinstallation is chosen, and the recommended installation pitch S is calculated. First, the curvature radius Rr of
the hull of the 5,000 DWT cargo vessel is obtained as follows using equation (5.6.3) of Section 5.6.1, Chapter
5.
Rr = B/4 + Lpp2 / (16B) = 40.7 (m)Therefore, the installation pitch S can be determined as follows using equation (5.6.1) of Section 5.6.1, Chapter 5.
𝑆 = 2 × √40.72 − (40.7 − 0.6 × 0.55)2 = 10.3(m)

A.2.2 Allowable berthing velocity of oversized vessel for existing fender
Assuming that a full-load 10,000 DWT passenger vessel berths to the quay of the 5,000 DWT cargo vessel designed
in A.2.1, The allowable conditions for berthing are as follows.
(1) Design conditions
Table A.2.7 presents the specifications of the vessels expected to berth on this quay. In this case, thefollowing restrictions other than the effective berthing energy are not considered; however, that these aspects
need to be checked and considered in actual cases.

971) Limitations of water depth and loaded draft (Bottom clearance)2) Restriction of protrusion of fender line
3) Presence or absence of hull fenders (Belted hull)4) Considerations stated in Chapter 5 (e.g., Fig. 5.6.3)
Table A.2.7 Vessel data
Item
Condition
Unit
Type of vessel
Passenger
Dead weight tonnage：DWT

10,000t

Gross tonnage：GT

89,390t

Length between perpendiculars：Lpp

271 m

Beam of vessel：B

32.4

m

Full draught of vessel：d

8.11

m

Displacement tonnage：DT

51,220t

Block coefficient：Cb

0.53

Virtual mass factor：Cm

1.787

Eccentricity factor：Ce

0.5

Softness factor：Cs

1.0

Berth configuration factor：Cc

1.0(2) Calculation of limit value of the berthing speed
From the previous section, the details of existing rubber fenders are as follows, and the minimum value ofenergy absorption EA－ is 132 kN·m.
<Standard performance>
Size: V type 600H × 1500L (performance grade B)
Design deflection: Within 45.0 (%)
Reaction force: Standard RR=690, Max. R+=760 (+ 10%) (kN)
Energy absorption: Standard EA=146, Min. EA－=132 (-10%) > 125 (kN·m)
The berthing velocity VB at which the effective berthing energy of the passenger vessel in Table A.2.7 is 132
kN·m is as follows when the factors are summarized, and Ctotal can be defined as follows from equation (5.3.1)
in Chapter 5.
Ctotal ＝ Ce  Cm  Cc  Cs ＝ 0.5×1.787×1.0×1.0＝0.8936
The allowable berthing velocity can be calculated as follows:

VB 

2  EA2  132 0.076
M  Ctotal
51220 0.8936（m/s）

Therefore, for a 10,000 DWT passenger vessel, it is necessary to carefully control the berthing velocity to beless than 0.076 m/s.

A.3 Pattern B: Considering major influence factors
A.3.1 General cargo vessel of 30,000 DWT: Without fender panel
In this case, a 30,000 DWT cargo vessel berths to a quay that is a pile type pier, and the reaction force of the fender is98considered as a horizontal load to the quay. The rubber fender design corresponds to Pattern B, in which the influence
factors must be considered.
(1) Design conditions
It is assumed that the specifications of the vessel are as listed in Table A.3.1.1. If these data are unknown, theTechnical Note of National Institute for Land and Infrastructure Management 3) may be helpful.
Table A.3.1.1 Vessel data
Item
Condition
Unit
Type of vessel
General cargo
Gross tonnage：GT

15,870 t

Dead weight tonnage：DWT

30,000 t

Displacement tonnage：DT

35,220 t

Length between perpendiculars：Lpp

171.00 m

Beam of vessel：B

28.30 mFull draught of vessel：d

16.22

m

1) Berthing conditions
Table A.3.1.2 Berthing conditions
Berthing velocity：VB

0.10 m/s

Berthing angle：θ

5.00 °

Installation pitch：S

12.0

m

2)

Quay structure:

Pile supported

3)

Allowable hull pressure:4)

Temperature: 4℃–34℃ (Lowest and highest of daily average)

Not specified(2) Effective berthing energy
Table A.3.1.3 Effective berthing energy(Equation (5.3.1), Section 5.3, Chapter 5.3）
Block coefficient

Cb

0.673

Virtual mass factor

Cm

1.870

Eccentricity factor

Ce

0.553

Effective berthing energy

Eb

182 kNm(＝kJ)(3) Selection of rubber fender
An example of a catalogue for a rubber fender that can absorb the effective berthing energy of vessel is given
in Table A.3.1.4.

99

Table A.3.1.4 Catalogue example: V-type fender 800H
Performance Grades
Design deflection
Performance
Length1000mm
1500mm
2000mm
2500mm
3000mmGrade A
45%
Reaction force Energy absorption(kN)(kN・m）
707
189
1061
283
1414
377
1768
471
2121
566

Grade B
45%
Reaction force Energy absorption(kN)(kN・m）
589
157
884
236
1179
314
1473
393
1768
471

Grade C
45%
Reaction force Energy absorption(kN)(kN・m）
471
126
707
189
943
251
1179
314
1414
377

From Table A.3.1.4, V-type 800H×1400L (Grade B) is selected. The selected size is determined in proportion
to the numbers in the red frame for a length of 1400 mm.
<Standard performance>
Deflection: Within 45.0 (%)
Reaction Force: R= 825 (kN) (less than + 10%)
Energy absorption: EA= 220 (kN∙m) (-10% or more)
Because the quay is a pile pier, it is necessary to consider the influence factors of fender performance; thus,
factor pattern B is focused on. Each factor of pattern B is determined as follows using the manufacturer's
catalogue or technical data.
1) Manufacturing tolerance: Cp
Manufacturing tolerance is usually described along with the performance in the catalogue.
Lower limit: Cp－＝0.90, Upper limit: Cp＋＝1.10
2) Angular factor: Ca
The angular factor is given, for example, as shown in Table A.3.1.5. The angular factors for a berthing
angle of 5° are CaR＝1.01 for the reaction force and CaE＝0.99 for energy absorption.
Table A.3.1.5 Example of angular factor
Angular factor of Angular factor ofAngle
reaction force
energy absorption
(°）
CaR
CaE
0
1.00
1.00
3
1.01
1.00
5

1.01

0.99

8
10
15
20

1.01
0.99
0.98
0.92

0.95
0.94
0.86
0.71

3) Velocity factor: VF
The velocity factor VFR of the reaction force varies depending on the shape and material of the rubber
fender, and is displayed as shown in, for example, Fig. A.3.1.1. If the graph and the polynomial are
displayed as shown in Fig. A.3.1.1, the velocity factor can be calculated if the coefficients of thepolynomial are given. If the velocity is displayed in the number table, one can read from the number tableand prorate as needed. Although the display mode (graph or table or figures) may differ depending on the
manufacturer, the factor must be catalogued in a manner that allows data to be extracted for design.
Since the size of the rubber fender is 800H, the berthing velocity of 10 cm/s has a strain rate of 12.5%

100

/s. From the table on the right of Fig. A. 3.1.1, VFR can be prorated as in equation (A.3.1.1).
At strain rate 12.5%/s: VFR＝(12.5－10)／(20－10)×(1.25－1.21)＋1.21＝1.22

1.5

Performance grade
Strain rate(%/s)
Grade A Grade B
Grade C

Grade A ：VF=a 1・logV B 3+a 2・logV B 2+a 3・logV B +a 4
Grade C ：VF=c 1・logV B 3+c 2・logV B 2+c 3・logV B +c 4

1

0.5
0.1

1
Strain rate (%/s)

10

100

0.01
0.02
0.05
0.1
0.2
0.5
1
2
5
10
20
50
100

0.94
0.96
0.98
1.01
1.03
1.07
1.11
1.15
1.20
1.25
1.30
1.38
1.44

0.95
0.97
0.99
1.01
1.03
1.07
1.09
1.13
1.17
1.21
1.25
1.31
1.35

0.97
0.98
1.00
1.02
1.03
1.06
1.08
1.11
1.15
1.18
1.22
1.27
1.31

Fig. A.3.1.1 Example of velocity factor (decreasing velocity) of reaction force
The velocity factor VFE of energy absorption is displayed, for example, as shown in Fig. A.3.1.2. The
VFE of deceleration compression at a strain rate of 12.5% /s, by interpolation, becomes VFE = 1.21,
similar to that obtained using equation (A.3.1.1).
Strain rate
(%/s)

1.5
3

2

Grade A ：VF=a 1・logV B +a 2・logV B +a 3・logV B +a 4
Grade B ：VF=b 1・logV B 3+b 2・logV B 2+b 3・logV B +b 4
3

2

Grade C ：VF=c 1・logV B +c 2・logV B +c 3・logV B +c 4

Velocity factor: VFE

Velocity factor: VFR

Grade B ：VF=b 1・logV B 3+b 2・logV B 2+b 3・logV B +b 4

0.01

(A.3.1.1)

1.0

0.5
0.01

0.1

1
Strain rate (%/s)

10

100

0.01
0.02
0.05
0.1
0.2
0.5
1
2
5
10
20
50
100

Performance grade
Grade A Grade B Grade C
0.93
0.94
0.96
0.95
0.96
0.97
0.97
0.98
0.99
1.00
1.00
1.00
1.02
1.02
1.02
1.06
1.06
1.05
1.10
1.08
1.07
1.13
1.11
1.10
1.19
1.16
1.13
1.24
1.20
1.17
1.29
1.24
1.20
1.36
1.29
1.26
1.42
1.34
1.30

Fig. A.3.1.2 Example of velocity factor (decreasing velocity) of energy absorption
As mentioned above, the velocity factors of reaction force and energy absorption often change by only
approximately 1%; therefore, some manufacturers may use a common factor; however, the original data
are used in this case.
4) Temperature factor: TF
The temperature factor varies depending on the shape and material of the rubber fender. The reaction
force and energy absorption are displayed, for example, as shown in Fig. A.3.1.3 and Fig. A. 3.1.4,
respectively. Thus, if a graph and a polynomial are displayed, the temperature factor can be calculated if
the coefficients of the polynomial are given. If the factor is displayed in a number table, one may read the101

value from the table in the same manner as the velocity factor and prorate as needed.
From Fig. A.3.1.3 and Fig. A.3.1.4, the temperature factor TF is as follows.
Temperature factor of reaction force TFR：1.12 (4°C)–0.97 (34°C)
Temperature factor of energy absorption TFE：1.11 (4°C)–0.96 (34°C)
Therefore, the maximum value TFR+ = 1.12 is adopted for the reaction force, and the minimum value
TFE ｰ = 0.96 is adopted for the energy absorption.
Similar to the velocity factor, the temperature factor for the reaction force and energy absorptionchanges by only approximately 1%, and simplification can be performed by using a common temperaturefactor; however, the original data is used in this example.

3.0

Temperature factor: TFR

Grade A ：TF =A 1・T 3+A 2 ・T 2+A 3 ・T +A 4
2.5

Grade B ：TF =B 1・T 3+B 2・T 2+B 3 ・T +B 4
Grade C ：TF =C 1・T 3+C 2 ・T 2+C 3・T +C 4

2.0

1.5
1.0
0.5

0.0
-30

-20

-10

0

10

20

30

40

50

Performance grade

Temperature(℃)

Grade A

Grade B

Grade C

-30
-20
-10
0
10
20
30
40
50

2.45
1.86
1.46
1.21
1.08
1.01
0.98
0.93
0.84

2.16
1.68
1.36
1.17
1.06
1.01
0.98
0.95
0.88

1.93
1.56
1.31
1.15
1.06
1.01
0.98
0.95
0.90

Temperature （℃）

Fig. A.3.1.3 Example for temperature factor of reaction force

Temperature factor: TFE

3.0

Grade A ：TF =A 1・T 3+A 2 ・T 2+A 3 ・T +A 4

2.5

Grade B ：TF =B 1・T 3+B 2・T 2+B 3 ・T +B 4
2.0

Grade C ：TF =C 1・T 3+C 2 ・T 2+C 3・T +C 4

1.5
1.0
0.5
0.0
-30

-20

-10

0

10

20

30

40

50

Performance grade

Temperature(℃)

Grade A

Grade B

Grade C

-30
-20
-10
0
10
20
30
40
50

2.43
1.84
1.45
1.20
1.07
1.00
0.97
0.92
0.83

2.13
1.67
1.35
1.16
1.05
1.00
0.97
0.94
0.87

1.91
1.54
1.29
1.14
1.05
1.00
0.97
0.94
0.89

Temperature （℃）

Fig. A.3.1.4 Example for temperature factor of energy absorption
From the above examples, the design performance of the selected rubber fender V-type 800H × 1400L(grade B) is as follows.
5) Design reaction force
R＋＝RR×Cp＋×CaR×VFR×TFR＋＝825×1.1×1.01×1.22×1.12＝1252 (kN)102

R＋ : Design reaction force after considering influence factors (kN)
RR : Standard reaction force (kN)
Cp＋: Production tolerance (1.1)
CaR : Angular factor of reaction force (CaR＝1.01：Angle 5° from Table A.3.1.5)
VFR : Velocity factor of reaction force (VFR＝1.22, DV of 12.5%/s, from Fig. A.3.1.1)
TFR＋: Maximum temperature factor (TF＋＝1.12 at 4℃ from Fig. A.3.1.3)
6) Design energy absorption
EA－＝EA×Cp-×CaE ×VFE×TFE－＝220×0.9×0.99×1.21×0.96＝227.7(kN･m) ≧ 182(kN･m)
EA－ : Design energy absorption after considering influence factors (kN･m)
EA : Standard energy absorption (kN･m)
Cp－ : Production tolerance (0.9)
CaE : Angular factor of energy absorption (CAe＝0.99 at angle 5°, from Table A.3.1.5)
VFE : Velocity factor of energy absorption (VFE＝1.21, DV of 12.5%/s from Table A.3.1.5)
TFE－ : Minimum temperature factor (TFE－＝0.96 at 34°C, from Fig. A.3.1.4)
The effective berthing energy of the vessel can be absorbed even when considering the influence of the temperatureand berthing angle. The lower limit value of the velocity factor VFE of the abovementioned energy absorption adopts thevalue of the deceleration (DV) performance at V = 12.5%/s. For example, as discussed in section A.2.2, when large
vessels are expected to berth at a slow berthing velocity, it is better to adopt the static performance instead of the DV
deceleration performance (VFE－ = 1.0). Even in this case, the energy absorption EA is 188 kN·m, and the required
performance can be satisfied.
As described above, it is possible to design a V-type rubber fender having no fender panel for a 30,000 DWT classvessel; however, it is premised that no limitation on the hull pressure exists. When a V-type rubber fender is selected,
the maximum average hull pressure is assumed if the contact width of the fender head is considered to be 0.6 m.
1252 kN / (0.6 m × 1.4 m) = 1491 (kN/m2)
This value is considerably large, and in case such a value cannot be managed, one must change the value to select thefender panel. In addition, a vessel having no restriction on the allowable hull pressure may have a belt (continuous
fender protruding from hull), and the contact surface may be partially lost by the belt impacting the rubber. Thus, afender panel with wings may also be considered, as shown in Fig. 5.7.3 in Chapter 5, Section 5.7.3.

A.3.2 Tanker of 100,000 DWT: With fender panel
Rubber fenders for tankers are often installed on pile-type dolphins, and a hull pressure restriction exists on the vessel
side. Therefore, it is necessary to carefully estimate the maximum reaction force. This section presents an example ofthe design of a rubber fender with a panel in which the influence factor of pattern B is considered assuming thefollowing case.
(1) Design conditions
No hull fenders exist for a tanker, and the vessel often makes full contact with the fender panel. In addition,although the berthing velocity is well-managed because tugboat assistance can be realized, the safety
considerations are important because the load involves hazardous material.
1) It is assumed that the following constraints exist on the size of the rubber fenders.
Allowable average hull pressure: 200 (kN/m2)

103

Horizontal load capacity of quay (dolphin): 3000 (kN) (per rubber fender)
Installation space in front of the dolphin: Horizontal 6 m × vertical 5 m
Fender height: Within 2.5 m from quay line including the fender panel2) The vessel specifications are presented in Table A.3.2.1.
Table A.3.2.1 Vessel data
Item

Condition

Type of vessel

Unit

TankerDead weight tonnage：DWT

100,000

Gross tonnage：GT

53,500 t

Length between perpendiculars：Lpp

238.35 m

Beam of vessel：B

42.72 mFull draught of vessel：d14.75 mBerthing angle：

θBerthing velocity：t

5.00 °
0.15 m/s

VB3) Temperature: 5°C–31°C (Lowest and highest of daily average from field measurement)(2) Effective berthing energy
The calculation results for the effective berthing energy are presented in Table A.3.2.2, and the berthing
condition is shown in Fig. A.3.2.1.
Table A.3.2.2 Berthing data(from equation (5.3.1) of Section 5.3 in Chapter 5)
Displacement tonnage

DT

123,500 t

Block coefficient

Cb

0.80

Virtual mass factor

Cm

1.68

Eccentricity factor

Ce

0.61

Softness factor

Cs

1.00

Berth configuration factor

Cc

1.00

Effective berthing energyEb1421 kNm(＝kJ)

104

Fig. A.3.2.1 Berthing of tanker to dolphin(3) Selection of rubber fenderA rubber fender of the vertical cylinder type with the configuration of 2000H (grade B) can absorb theeffective berthing energy of the vessel. The standard performance from the catalogue is as follows.
<Standard performance>
Size:
2000H × 1 × 1 (Grade B)
Reaction force RR: 1750 (kN)
Energy absorption EA: 1540 (kNm)
Considering the factor of influence for pattern B, the values for each factor are as follows, as obtained fromthe manufacturers’ catalogues or technical data.
Manufacturing tolerance : Cp－＝0.9、Cp+＝1.1
Angular factor: CaR＝1.00、CaE＝0.96 (from Table 6.3.2.2 in Chapter 6; for angle of 5°)
Velocity factor: VFR＝VFE＝1.125 (from Table 6.3.7 in Chapter 6; 0.15 m/s＝7.5%/s)
Temperature factor: TFE－＝1.00, TFR＋＝1.11 (from Table 6.3.10.2 in Chapter 6; 31°C–5°C)
In this case, the influence factors of the reaction force and energy absorption are common.
1) Design reaction force
R＋＝RR×Cp＋×CaR×VFR×TFR＋＝1750×1.1×1.00×1.125×1.11＝2404 (kN)
R＋ : Design reaction force after considering influence factors (kN)
RR : Standard reaction force (kN)
Cp＋: Production tolerance (1.1)
CaR : Angular factor of reaction force
VFR : Velocity factor of reaction force
TFR＋: Maximum temperature factor
2) Design energy absorption

105

EA－＝EA×Cp－×CaE ×VFE×TFE－＝1540×0.9×0.96×1.125×1.00＝1497(kN･m) ≧ 1421(kN･m)
EA－ : Design energy absorption after considering influence factors (kN･m)
EA : Standard energy absorption (kN･m)
Cp－ : Production tolerance (0.9)
CaE : Angular factor of energy absorption
VFE : Velocity factor of energy absorption (DV, Common with VFR)
TFE－ : Minimum temperature factor(4) Detail design
1) Required area of fender panel
As explained in Chapter 5, Section 5.7.1, the required effective area A of the allowable surfacepressure HP to the fender panel is as follows.
A ＝ R＋ ／ HP ＝ 2404／200 ＝ 12.02 (m2)The size of the fender panel is determined by the number and spacing of the resin pads placed on thecontact surface. Although these values differ depending on the manufacturer, the following fender panel isconsidered as an example.
Horizontal direction: 3560 (mm) (including both side chamfers of 100 mm)
Vertical direction: 3940 (mm) (including upper chamfer of 100 mm)
Thickness: 330 (mm) (including resin pad of 30 t)
Weight: 3698 (kg)
Average hull pressure: 186 (kN/m2) (except peripheral chamfers of 100 mm)
2) Strength of fender panel
For the bending moment generated in the horizontal direction of the fender panel, consider the
distributed load to be as shown in Fig. 5.7.8 in Chapter 5. The data generated by fender compression to
the design deflection at an angle of 5° are as follows. Please note that since this calculation was performed
using a software owned by a manufacturer, the detailed calculation steps are omitted.
Berthing point displacement δ0 : 1.15 (m)Fender centre displacement δ:
1.02 (m) (Central deflection 51%,
At this time, deflection of the end becomes 55% the limit)+
Design reaction force of fender R : 2404 (kN)
Rotational moment of fender Mf : -13.84 (kN∙m)Distance from fender centre to berthing point L1 : 1.68 (m) (except end chamfer of 100 mm)
Distributed load on the fender panel:
ω(x)＝－4.378x + 722.8（kN/m）Distance from the end of panel x: See Fig. 5.7.8 in Chapter 5 (m)Horizontal bending moment generated in panel: 1023.5 (kNm)
Horizontal section modulus of panel: 10.821 (m 3)
Horizontal bending stress: 94.58 (kN/m2)
In the case of a tanker, since the vertical angle is due to the rolling of the vessel, it is often sufficiently
safe if the vertical strength is the same as the horizontal strength. However, in the case of berthing at theflare part of the hull or in the case of a vertically long panel, the vertical strength is dominant.
3) Weight chain106

To support the weight of the fender panel, two chains are installed: one each on the left and right sidesof the fender body, as shown on the right in Fig. 5.7.10 in Chapter 5. The tension T applied to the chain
can be obtained by equation (A.3.2.1), assuming that the angle of elevation of the chain is β.
T ＝ (μR+＋WW)／cos(β) ＝ 619 (kN)（309 kN/chain）
Here,
μ : Friction coefficient between fender panel (resin pad) and vessel hull (＝0.2)
β： Angle between chain and fender panel(A.3.2.1)(＝sin−1 {(𝐻 − 𝛿)／𝐿𝑐 })R+ ： Design reaction force (2404 kN)
H ： Fender height (2000 mm)
δ ： Deflection of fender (500 mm at maximum reaction force)
Lc ： Length of chain (2730 mm; calculated length +1 to +3%)
WW ： Weight of fender panel (3698 kg)4) Space for rubber fender installation
The condition in which the rubber fender is attached to the quay is shown in Fig. A.3.2.2. Usually, thedesign of the dolphins is performed prior to the selection of rubber fenders, or often, the dolphin has
already been constructed. In Fig. A.3.2.2, both the rubber fenders and chains are contained in the quay
mounting space. However, if the top of the quay is low, it will not be possible to secure a concrete
thickness commensurate with the embedded depth of the U-shaped anchor. Generally, it is recommended
that the concrete is secured with the same thickness as the embedding depth assuming a 45° cone failure;
however, this aspect is difficult to be realized when the quay top is excessively low. Fig. A.3.2.3 shows anexample of the countermeasure when the concrete cover cannot be secured. A corresponds to the methodof bevelling the space for the U-shaped anchor at the corner of the quay to ensure oblique embedding. B
corresponds to the method of lowering the position of the weight chain; in this case, the fender panel may
incline forward, and thus, the upper end needs to be tensioned using a tension chain (see Chapter 5, Fig.
5.7.10). C shows the method of building a post on the quay top to ensure attachment for the weight chain
when other methods are not sufficient. As described above, it is desirable to consider not only fixing bolts
for installation but also employing various chain arrangement in advance in the space.
The specifications of the weight chain are determined by the fender size and weight of the fender panel.
It is necessary to consider this aspect, as judgment criteria exist for each rubber fender and manufacturer.

Plain view

Side viewFig. A.3.2.2 Installation of rubber fender to dolphin (2000H×1×1)

107

A: Chamfered quay top

B: Lowering weight chain

C: Chain post on the top

Fig. A.3.2.3 Possible countermeasures for weight chain arrangement
A.3.3 Long distance ferry of 10,000 DWT: With large fender panel
Rubber fenders for ferries are often attached to a large-sized panel and installed on a parapet on the quay. The quay is
expected to possess a sufficiently large horizontal strength against an earthquake if it is a gravity type; however, it isnecessary to carefully estimate the maximum reaction force when it is necessary to install the chain on the front of aparapet.
This section presents a design example in which the influence factor pattern B is considered assuming theabovementioned case.
(1) Design conditions
1) The vessel data is presented in Table A.3.3.1.
Table A.3.3.1 Vessel data
Item

Condition

Type of vessel

UnitLong distance ferry

Dead weight tonnage：DWT

10,000t

Gross tonnage：GT

23,520t

Length between perpendiculars：Lpp

182.70m

Beam of vessel：B

28.20

m

Full draught of vessel：d

2.27

m

6.00

°

0.15

m/s

Berthing angle：

θBerthing velocity：

VB2) It is assumed that the following constraints exist on the size of the rubber fender.
Allowable average hull pressure: No limit
Horizontal load capacity of quay (Parapet): 2000 (kN) (per fender system)
Minimum size of fender panel: 4 m × 4 m or more
Maximum height: Within 1.2 m including fender panel
In the case of a ferry, hull belts exist, and the vessel hull rarely makes full contact with the fender panel.
However, the tugboat assistance is often not available, a wide fender panel is preferred as the target, and108

berthing velocity can also be high. Furthermore, in several cases, height restrictions exist to ensureboarding and deboarding of passengers.
3) Temperature: 5°C–30°C(2) Effective berthing energy
The calculation results for the effective berthing energy are presented in Table 3.3.2.
Table 3.3.2 Berthing data(from equation (5.3.1) of Section 5.3 in Chapter 5)
Displacement tonnageDT29,165 t

Block coefficient

Cb

0.50

Virtual mass factor

Cm

1.25

Eccentricity factor

Ce

0.50

Softness factor

Cs

1.00

Berth configuration factor

Cc

1.00

Effective berthing energyEb

206 kNm(=kJ)(3) Selection of rubber fenders
A vertical cylinder type rubber fender with a size of 1000H (performance grade: standard) is capable ofabsorbing the effective berthing energy of vessels. The standard performance from the catalogue is as follows.
<Standard performance>
Size: 1000H × 1 × 1 (single unit)
Reaction force：625 (kN) (+10%)
Energy absorption ：224 (kN･m) (-10%)
However, using only one 1000H unit on a 4 m × 4 m fender panel leads to poor balance. Therefore, if twounits are arranged vertically and horizontally, the required amount of absorbed energy per unit becomes 206 / 4= 51.5 (kN･m), and the rubber fender is downsized to 630H. The standard performance of the 630H fender is
as follows.
<Standard performance>Size: 630H × 2 × 2 (4 unit)
Reaction force：249×4＝996 (kN) (+10%)
Energy absorption ：56.3×4＝225.2 (kN･m) (-10%)
However, the above selection is based on the premise that the vessel hull is in full contact with the fender
panel at an angle of 0° in the abovementioned cases. In fact, when the vessel is berthing at an angle of 6°, thetime of point contact at the corner may be more than that of the full contact. It is thus necessary to select afender considering this aspect as well, as the fender will absorb less energy than a standard fender.
If corner point contact is assumed, the balance between force and bending moment must be considered, as
described in Fig. 5.7.7 in Chapter 5, Section 5.7.4. The correct size is required to be determined via trial anderror; however, assuming that the rubber fender has a size of 800H, the arrangement is as shown in Fig.
A.3.3.1.

109

Fig. A.3.3.1 Fender system concept (800H×2×2 for ferry)
The equations of balance between the forces and bending moments, from equation (5.7.7) in Chapter 5,
Section 5.7.4, are as follows. Please note that the rotational moments of the rubber fenders are ignored.
𝐹 + 𝑇 + ∑2𝑖=1 ∑2𝑗=1 𝑅(𝑖, 𝑗) = 0(A.3.3.1)∑2𝑖=1{𝑋(𝑖) ∙ ∑2𝑗=1 𝑅(𝑖, 𝑗)} + 𝑋(3) ∙ 𝑇 = 0(A.3.3.2)∑2𝑗=1{𝑌(𝑗) ∙ ∑2𝑖=1 𝑅(𝑖, 𝑗)} + 𝑌(3) ∙ 𝑇 = 0(A.3.3.3)

Here,
X(i) : X coordinate of i-th rubber fender in X direction (i = 3 is chain position)
Y(j) : Y coordinate of j-th rubber fender in Y direction (j = 3 is chain position)
R(i,j) : Reaction force of rubber fender (i,j) （kN）
It is desirable that the reaction force R (i, j) of the rubber fender for any displacement δ is represented as apolynomial in the manufacturer's catalogue or technical data. Additionally, the geometric relationships of thedisplacement amounts are as follows.
δ(1,1)＝δ0 － X(1)tanθX － Y(1)tanθYδ(1, 2)＝δ0 － X (1)tanθX － Y (2)tanθYδ(2, 1)＝δ0 － X (2)tanθX － Y (1)tanθYδ(2, 2)＝δ0 － X (2)tanθX － Y (2)tanθYθX and θY are angles of the horizontal and vertical directions of the fender panel, respectively.
The standard performance of the vertical cylinder fender 800H is as follows.
<Standard performance>
Size: 800H × 2 × 2
Design deflection : Within 55%(4 units, Grade A)

110(A.3.3.4)

Reaction force: 280×4＝1120 (kN)
Energy absorption : 104×4＝416 (kN･m)
Considering the influence factor in Pattern B, the velocity factor and temperature factor are obtained fromthe manufacturer's catalogue or technical data as follows.
Manufacturing tolerance: Cp－＝0.9, Cp+＝1.1
Angular factor: 1.00 (Berthing angle 6°; however, it is not considered as the inclination to 6° is gradual)
Velocity factor: VFR＝1.20, VFE＝1.17(DV deceleration performance with V = 18.75%/s; refer to Chapter 6, Table 6.3.7)
Temperature factor: TFR＝TFE＝1.00–1.11 (30℃–5℃; see Chapter 6, Table 6.3.10.2)
Therefore, the maximum reaction force acting on the parapet is 1120 × 1.1 × 1.20 × 1.11 = 1641 kN (410 kN
per unit). The angular factor is assumed to 1.0 because the angle changes according to the process ofcompression. The performance curve of the fender unit is as shown in Fig. A.3.3.2. Since the compression
velocity varies depending on the position, the minimum value of velocity factor (1.0) is assumed. Thus, theminimum value of the design reaction force is 1120 × 0.9 × 1.0 × 1.0 = 1008 kN (252 kN per unit).

Fig. A.3.3.2 Performance of vertical cylinder 800H (Single unit)
If the reaction force of the rubber fender in Fig. A.3.3.2 is substituted into a mathematical expression as

R(i,j) in equation (A.3.2.1), the berthing point displacement δ0, berthing force F, and chain tension T can becalculated numerically. The solution of equations (A.3.3.1) to (A.3.3.4) for the system in Fig. A.3.3.1 ispresented below. Table A.3.3.3 and Table A.3.3.4 respectively present the results for the maximum andminimum values of the reaction force.

111

Table A.3.3.3 Performance of each fender and total system (maximum influence factors)
Total system
Displace Horrizontal Verticalmentangle ofangle of
δ0
panel
panel
mm
0
59
118
177
236
295
354
413
472
531
590

Chain
tensionT

Fender ( 1, 1)

Fender ( 1, 2)

Fender ( 2, 1)

Fender ( 2, 2)

Berthing
EnergyReaction
Energy Deflectio Reaction Energy
Reaction Energy
Reaction Energy
Deflection
Deflection
Deflection
force
absorption
force
absorptionnforce
absorption
force absorption
force absorption
δ
δ
δ
F
E
R
E
δ
R
E
R
E
R
E

deg

deg

kN

kN

kN×m

%

kN

0
-0.44
-0.89
-1.33
-1.78
-2.22
-2.67
-2.75
-3.55
-4.00
-4.44

0
-0.44
-0.89
-1.33
-1.78
-2.22
-2.67
-3.47
-3.55
-4.00
-4.44

0
178.42355.37500.59606.50677.89723.91752.49772.26786.44804.700217.47421.65568.72656.06699.70718.46724.85727.23729.55751.61

0
6.29
25.37
54.90
91.29
131.45173.37216.00258.88301.82345.33

0
5.43
10.87
16.30
21.74
27.17
32.61
38.04
43.47
48.91
54.34

0
155.94291.01369.72398.40398.97391.56386.22383.90386.61416.71

kN×m
0
3.33
13.22
27.80
44.64
62.03
79.22
96.11
112.84129.55146.83

%

kN

0
3.49
6.99
10.48
13.97
17.47
20.96
22.87
27.95
31.44
34.93

0
98.90
199.31
283.12343.09379.42396.57400.06398.04393.14388.82

kN×m
0
1.35
5.54
12.33
21.14
31.29
42.17
48.26
64.51
75.56
86.49

%

kN

0
3.49
6.99
10.48
13.97
17.47
20.96
26.04
27.95
31.44
34.93

0
98.90
199.31
283.12343.09379.42396.57400.06398.04393.14388.82

kN×m
0
1.35
5.54
12.33
21.14
31.29
42.17
58.41
64.51
75.56
86.49

%

kN

0
1.55
3.11
4.66
6.21
7.76
9.32
10.87
12.42
13.97
15.53

0
42.16
87.38
133.35177.99219.77257.66291.01
319.50343.09361.96

kN×m
0
0.26
1.06
2.43
4.37
6.84
9.81
13.22
17.02
21.14
25.52

Table A.3.3.4 Performance of each fender and total system (minimum influence factors)
Total system
Displace Horrizontal Verticalmentangle ofangle of
δ0
panel
panel
mm
0
59
118
177
236
295
354
413
472
531
590

deg

deg

0
-0.44
-0.89
-1.33
-1.78
-2.22
-2.67
-2.75
-3.55
-4.00
-4.44

0
-0.44
-0.89
-1.33
-1.78
-2.22
-2.67
-3.47
-3.55
-4.00
-4.44

Fender ( 1, 1)

ChaintensionT

Berthing
force
F

EnergyReaction
Deflection
absorption
force
δ
E
R

kN

kN

kN×m

%

kN

0
112.41223.88315.37382.10427.07456.06474.07486.52495.46506.960
137.01265.64358.29413.32440.81452.63456.65458.16459.62473.51

0
3.96
15.98
34.58
57.51
82.81
109.22136.08163.09190.15217.56

0
5.43
10.87
16.30
21.74
27.17
32.61
38.04
43.47
48.91
54.34

0
98.24
183.34232.92250.99251.35
246.68243.32241.86243.56262.53Fender ( 1, 2)
EnergyReaction
Deflection
absorption
force
δ
E
R
kN×m
0
2.10
8.33
17.51
28.12
39.08
49.91
60.55
71.09
81.62
92.50

%

kN

0
3.49
6.99
10.48
13.97
17.47
20.96
22.87
27.95
31.44
34.93

0
62.31
125.57178.37216.15239.03249.84252.04250.77247.68244.96

Fender ( 2, 1)
EnergyReaction
Deflection
absorption
force
δ
E
R
kN×m
0
0.85
3.49
7.77
13.32
19.71
26.57
30.40
40.64
47.60
54.49

%

kN

0
3.49
6.99
10.48
13.97
17.47
20.96
26.04
27.95
31.44
34.93

0
62.31
125.57178.37216.15239.03249.84252.04250.77247.68244.96

Fender ( 2, 2)
EnergyReaction
Deflection
absorption
force
δ
E
R
kN×m
0
0.85
3.49
7.77
13.32
19.71
26.57
36.80
40.64
47.60
54.49

%

kN

0
1.55
3.11
4.66
6.21
7.76
9.32
10.87
12.42
13.97
15.53

0
26.56
55.05
84.01
112.13138.46162.33
183.34201.28216.15228.03

The final performance at the corner point berthing is as follows.
<Corner point berthing performance>
Size:
800H × 2 × 2
Final displacement at berthing point: 590 (mm)Reaction force at berthing point:
752 (kN)
from Table A.3.3
Total energy absorption:
218 (kN･m) ≧206from Table A.3.3.4
Tension of chain:
805 (kN)
from Table A.3.3.3
Final fender panel angle:
4.4° (common to vertical and horizontal) <design condition 6°
The performance curve for the entire system is shown in Fig. A.3.3.3.

112

Energyabsorption
E
kN×m
0
0.16
0.67
1.53
2.75
4.31
6.18
8.33
10.72
13.32
16.08

Fig. A.3.3.3 Performance of fender system: vertical cylinder 800H × 2 × 2
Since the fender panel angle (4.44°) is less than the berthing angle (6°), the berthing energy is absorbed
during point contact at the corner of the fender panel. Although this system is not an efficient one from theviewpoint of energy absorption, it can be a rational system in view of the requirements of fenders for ferries.
As seen in Fig. A.3.3.3, the curve of berthing force considering the angle differs from the standard performance.
For example, when the fender is in contact with a location at which the vessel has a flare angle, it is moreaccurate to use the reaction force by deflection, as shown in Fig. A.3.3, for a mooring simulation. Suchconsideration is possible when the flare angle of the contact point is known.
(4) Weight chain
The tension of the weight chain is calculated as follows. Assuming that the friction coefficient μ between thehull and fender panel is 0.3 when the fenders are compressed uniformly and the hull moves downward, thetension T applied to weight chain is as shown in Fig. A.3.3.4. The tension T is obtained using equation(A3.3.5).
T ＝ [𝜇 {∑2𝑖=1 ∑2𝑗=1 𝑅(𝑖, 𝑗)} + 𝑊𝑊 ]／𝑐𝑜𝑠(𝛽) ＝ 544 (kN) (272 kN per chain)Here,μ(A.3.3.5): Friction coefficient μ between hull and fender panel (=0.3)
Because ferries often have a hull belt, which comes into contact with the steel plate without resin
pads on the fender panel, μ was set to 0.3.

β ： Angle between chain and fender panel(＝sin−1 {(𝐻 − 𝛿)／𝐿𝑐 })H ： Height of fender (800 mm)
Strictly, the height of the fender depends on the position of the eye plate and U-shaped anchor;
thus, this height is the centre-to-centre distance of the shackle pin.
δ ： Design deflection of fender (440 mm)
Lc ： Length of chain (1200 mm)
WW ： Weight of fender panel (4000 kg)∑2𝑖=1 ∑2𝑗=1 𝑅(𝑖, 𝑗) ： Total reaction force of fenders (1600 kN)

113

Fig. A.3.3.4 Weight chain design
As a result, the maximum tension occurred at 55% of the fender height with a value of 272 kN per chain. In
such a system, the tension is high. In particular, since a tension chain is subjected to a tension of 805 kN, it ispossible that the number of links cannot be secured. In this case, it is necessary to review the entire system. The
allowable tension of the tension chain can be considered as a short-term load, as described in Chapter 5.9, andthe safety factor can be set as 2. In weight chain design, the long-term load (safety factor 3.0 or more)considering the panel weight and the short-term load during shear compression (safety factor 2.0 or more)calculated using equation (A.3.3.5) are compared, and design is performed considering severe conditions.

A.4 Pattern C: Fender design by mooring analysis
When using factor pattern C, in certain cases, a floating structure such as a floating pier, floating oil storage, or
floating bridge is permanently moored, or a vessel is moored to a quay during a storm or long-period wave. In this work,
as an example of rubber fender design considering the vessel motion, a numerical simulation is performed to estimate
whether the vessel can be safely moored under rough weather conditions by rubber fenders and mooring ropes.
Normally, during stormy weather such as a typhoon, ships evacuate offshore; however, depending on the situation, theships may remain moored to the wharf to allow the alleviation of congestion in the water area. The process flow of thisinvestigation is shown in Fig. A.4.1.

114

Fig. A.4.1 Flow of fender design by mooring simulation
The example vessel is assumed to be a medium-sized container vessel of approximately 10,000 DWT, as shown in
Fig. A.4.2. It is assumed that the rubber fenders selected considering the effective berthing energy are already installedin the same manner as described in this book, and whether the fender will be compressed beyond the design deflection
in rough weather has been confirmed via mooring simulation.

Fig. A.4.2 Birds-eye view of moored medium-sized container vessel(1) Motion equation of moored vessel
The equation of motion for the moored vessel as shown in Fig. A.4.2 can be written as equation (A.4.1) 1).

115

6

6

6

ｔ

∑{𝑀𝑖𝑗 + 𝑚𝑖𝑗 (∞)}𝑋̈𝑖 (𝑡) + ∑ { ∫ 𝐿𝑖𝑗 (t − τ)𝑋̇𝑖 (τ)dτ + 𝑁𝑖𝑗 (t)𝑋𝑖 (𝑡)
i=1

i=1

−∞

} + ∑(𝐾𝑖𝑗 + 𝐺𝑖𝑗 )𝑋𝑖 (𝑡)＝ 𝐹𝑗 (𝑡)𝑖=1(A.4.1)Here,
Mij : Mass matrix of moored vesselｍij(∞) : Additional mass matrix of moored vessel
Xi(t) : Displacement vector of vessel centre at time t
Lij(t) : Delay function of moored vessel at time t
Nij(t) : Dumping coefficient matrix of moored vessel at time t
Kij : Restoration coefficient matrix of moored vessel
Gij : Mooring force matrix
Fj(t) : External force vectori と j : Mode of vessel motion (i,j＝1–6)
The delay function and additional mass can be expressed as follows:
𝐿𝑖𝑗 =

2 ∞
∫ 𝐵𝑖𝑗 (𝜎) cos 𝜎𝑡𝑑𝜎𝜎 0

1

(A.4.2)∞

𝑚𝑖𝑗 (∞) = 𝐴𝑖𝑗 (𝜎) + ∫0 𝐿𝑖𝑗 (𝑡) sin 𝜎𝑡𝑑𝑡
𝜎(A.4.3)Here
Aij(σ) : Additional mass at σ
Bij(σ) : Dumping coefficient at σ
σ : Angular frequency
The solution of equation (A.4.1) is complicated, and it is more convenient to use commercially available
software than a newly developed one. Several programs are available; however, it is desirable that programs
verified using hydraulic experiments or field measurement are used, if possible.
(2) Input data
When designing rubber fenders by using mooring simulations, the most crucial step is the setting of theconditions and calculation cases for the simulation. Hereinafter, calculation examples are described along withthe procedure.
1) Natural conditions
In principle, natural conditions that are severe and occur frequently for rubber fenders should beselected based on local survey results. In this work, two types of conditions are assumed: one involving
strong wind as a condition of stormy weather (denoted as strong wind), and another involving long period
swells, in which the wave height and period are set to be large and long, respectively. To set severe
conditions for rubber fenders, the wind is considered to be offshore wind blowing perpendicular to thelong axis of the vessel, and the waves are at 45° from the short axis of the vessel to the stern, considering
the compression of the rubber fender by vessel yawing. It is assumed that this condition corresponds tothat shown in Fig. A.4.3. It was assumed that no current was present.
A list of natural conditions is presented in Table A.4.1.

116

Table A.4.1 Natural conditions
Significant wave height
0.5 m
0.8 m
Wave period
6s
10 s
Wave spectrum
Bretschneider–Mitsuyasu
45°
45°
Wave direction：θｗ
Average wind speed (10 min)25 m/s
15 m/sWind spectrum
Davenport
Wind friction coefficient
0.003
Wind drag coefficient
0.898Wind direction: θa0°0°2) Berth layout
Fig. A.4.3 shows the berth layout in plain view. In the two cases—10,000 DWT medium-sized container
vessel and 5,000 DWT small-sized container vessel—full loading and empty loading are considered. It iseasy to believe that the smaller ship is safer; however, it is necessary to confirm the more severe condition
because only 2 units are in contact with the 5,000 DWT, while 3 rubber fenders come in contact with the
10,000 DWT. The cross-section is as shown in Fig. A.4.4.

Fig. A.4.3 Berth layout: Plain view

Medium container vessel 10,000 DWT

Small container vessel 5,000 DWT

Fig. A.4.4 Berth layout: Cross-section

1173) Vessel data
Table A.4.2 presents the vessel data of the medium and small-sized container vessels. The vessel data
are derived primarily from the Technical Standards and Commentaries of Ports and Harbour Facilities inJapan 4) and the latest statistics 3); however, some data must be investigated or assumed. In Table A.4.2, theyellow highlighted red numbers within the bold frame are less common and must be researched. The
overall height D (type depth) is also often omitted in recent statistics.
In berthing design, it is often not necessary to consider the ballast condition because the mass of anempty vessel is considerably less. However, when mooring, the ballast is susceptible to the wind when thevessel is empty and has a wider area exposed to the wind. This situation is difficult for the fenders. The
deflection of rubber fenders at the ballast condition is usually large and severe in the medium-sized
vessel; thus, calculations for the small vessel were performed considering only the ballast condition.
Table A.4.2 Vessel data for container

Data
Effective berthing energy(kN·m)
Dead Weight tonnage : DWT
Displacement tonnage: DT
Gross tonnage : GT
Length between perpendiculars: Lpp (m)Beam ： B (m)Height ： D s (m)Draught ： d (m)Freeboard ： f (m)Water depth (m)KG (m)GMT (m)GML (m)Radius of Gyration-Roll (m)Radius of Gyration-Pitch (m)Radius of Gyration-Yaw (m)Center of floatation*1 (m)Medium-Full
162.3
10,00015,0178,820
131.83
22.4
20
8.02
12
15
8.18
1.73
172.5
7.84
32.96
32.96
0.53

Wind pressure area-Surge (m2)

409.9

2

Vessel size-Draught
Medium-Ballast Small-Ballast
162.3
84.6
10,000
5,000
6,184
3,217
8,820
4,410
131.83
99.8
22.4
18.37
20
9
4
3.25
16
5.75
15
15
8.18
7.03
3.63
2.92
172.5
120.82
7.84
6.49
32.96
24.96
32.96
324.96
0.528
0.459
499.6

1882.82410.9Wind pressure area-Sway (m )Natural period-Roll (s)
11.95
8.25
*1 Distance from center of floatation to center of gravity in surge direction329
1480.8
7.62(3) Selection of rubber fenders and determination of influence factors
The influence factors of rubber fender performance described in Chapter 4 were selected as follows, and the
maximum and minimum values of the influence factors were estimated.
Manufacturing tolerance : Cp－＝0.9、Cp+＝1.1
Angular factor: Maximum angle: 10°(CaR－＝0.98), Minimum angle: 0°(CaR+＝1.0)
Velocity factor: Velocity changes during mooring. Here, it is assumed that one deflection cycle is55%×4 and takes 6 s (Wave period), and the average strain rate is estimated as 30%/s.
The velocity factors are VFR－＝1.0, VFR+＝1.236.
Temperature factor: Temperature ranges from 0℃ to 30℃; thus, the temperature factors are TFR－＝
0.984、TFR+＝1.116
Ageing factor: From the Technical Standards and Commentaries of Ports and Harbour Facilities in118

Japan-II Floating Oil Storage Facility 5), the ageing factors are Cag－＝1.0、Cag+＝1.05
Repetition fatigue: From the Technical Standards and Commentaries of Ports and Harbour Facilities inJapan-II Floating Oil Storage Facility 5), the repetition factors are Cr-＝0.9、Cr+＝
1.0
Creep characteristic: It was confirmed that the average value of wind pressure was within the reaction
force of 10% deflection as follows.
Wind pressure:
Fw＝0.5×ρ×Ua2×Cw×Asway＝ 277 (kN) (Medium-Ballast, 3 fenders)< 299 (kN) (1000H at 10%), 323 (kN) (1250H at 10%)(A.4.4)Here,
Fw: Wind pressure (kN)
ρ : Air density (=0.00123 t/m3)
Ua: Wind speed (=25 m/s)
Cw: Wind drag coefficient of sway (from Table A.4.1, Cw =0.898)
Asway: Wind pressure area of sway (from Table A.4.1, Medium-Ballast: Asway =2411 m2)
The performance curves of the rubber fender assumed in this case is shown in Fig. A.4.5, and thespecifications are listed in Table A.4.3. The minimum value of energy absorption and the maximum reaction
force are considered to realize the absorption of the effective berthing energy. When designed at berthing withan angle of 10°, the berthing energy can be sufficiently absorbed if the fenders have a size of 1000H; however,calculation for the vessel motion at mooring indicates that larger fenders (1250H) are necessary. Since themooring simulation is a type of numerical experiment, the appropriate size and performance cannot be obtained
unless trial and error is performed. In this case, two types of sizes are examined assuming that the rubber
fender is required to be eventually increased in size to 1250H. As shown in Fig. A. 4.5, the reaction force ofover-compression is assumed to exhibit a linear increase to ensure the accuracy above the allowable deflectionof rubber fender is low.

Fig. A.4.5 Performance curve of rubber fenders

119

Table A.4.3 Design performance of fenders and influence factors
Fender size
1000H
1250H
Remarks
Performance grade
Grade A
Grade B
Allowable deflection: 55％
Unit3
3
Allowable deflection: 55％
0° Normal performanceStandard reaction force

568kN

614kN

Minimum reaction force

453kN

489kN

Maximum reaction force

905kN

979kN

Influence factor
C p － (0.9)ｘC aR － (0.98)ｘVF R － (1.0)ｘ
TF R － (0.984)ｘC r (0.9)ｘC ag － (1.0)
C p + (1.1)ｘC aR ＋(1.0)ｘVF R ＋(1.236)ｘTF R +(1.116)ｘC r (1.0)ｘC ag (1.05)

10°Angular performanceStandard reaction force

643kN

589kN

Minimum reaction force

506kN

547kN

Maximum reaction force

927kN

1003kN

Minimum energy absorption

182kNm246kNmInfluence factor
C p － (0.9)ｘC aR － (0.98)ｘVF R － (1.0)ｘ
TF R － (0.984)ｘC r (0.9)ｘC ag － (1.0)
C p + (1.1)ｘC aR ＋(1.0)ｘVF R ＋(1.236)ｘTF R +(1.116)ｘC R (1.0)ｘC ag (1.05)
C p － (0.9)ｘC aE － (0.98)ｘVF E － (1.0)ｘ
TF E － (0.984)ｘC r (0.9)ｘC ag － (1.0)(4) Mooring rope
Along with rubber fenders, mooring ropes also have a substantial impact on vessel motion. However, thetension generated in the mooring rope is small because the wind and waves are directed from the offshore toevaluate the safety of fenders in this case. Therefore, the mooring ropes were of the following types with a totalof four ropes: one bowline, one stern line, and two spring lines were deployed, as shown in Fig. A.4.3. The
specifications of the ropes are as follows:
Rope specification: 2 strands Nylon φ60
Breaking load: 920 (kN)(5) Result of mooring simulation
The simulation results are presented in Table A.4.4. The calculation cases are as follows: 2 cases for different
natural conditions (strong wind, long wave), 3 cases for different ship specifications (medium size-full draught,
medium size ballast and small size-ballast), 2 cases for different sizes of rubber fenders (1000H and 1250H),
and in total, 24 preliminary calculation cases with maximum and minimum reaction forces. First, two caseswith 1000H rubber fenders were calculated, and in Case 2 (Ballast), fender No. 1 was overcompressed,
exceeding the allowable deflection. Therefore, the size of rubber fenders was changed to 1250H, andsubsequently, the calculation was performed for seven optimized cases listed in Table A.4.4. Each calculation
was performed for 100 waves (600 s, 1000 s) in increments of 0.1 s. The Technical Standards andCommentaries of Ports and Harbour Facilities in Japan 4) recommends a calculation time corresponding to morethan 100 waves. In addition, the standard deviations were obtained from the calculation results of the fenderdeflection and reaction force, and the expected value for 1000 waves was also calculated.
First, no problems were encountered because the maximum deflection of the rubber fender is 26% and the
expected value of the 1000 wave simulation is 43% when calculated considering the medium-sized vessel fulldraught and strong wind conditions in Case 1. However, when the ballast is loaded as in Case 2, the120

corresponding value is 63% and the fender is overcompressed. Although the size of 1000H (height of 1 m) was
sufficient for berthing, it is insufficient for mooring in stormy weather. Therefore, after Case 3, the size offender was increased to 1250 H (1.25 m in height) and the rubber was downgraded (Grade A to Grade B);
moreover, the fender reaction force adopted the minimum value of the influence factors. The result of Case 3
corresponds to less than the allowable deflection; however, in case 4, which involves ballast loading, the value
for fender 1 is 51%, which is close to the limit (55%), and the 1000 wave expected value is 56%, which isslightly more than 55%. In the ballast case of a small vessel of Case 5, the maximum value is 51%, and the
expected value of 1000 waves is 53%; both these values are within the limit of allowable deflection. The
maximum deflection for the case of a medium-sized vessel-full draught with a wave having a height and periodof 0.8 m and 10 s in Case 6 is 36%; however, the 1000 wave expected value is 57%, which slightly exceeds theallowable deflection. It is necessary to ensure that severe conditions are not overlooked, since the motion of themoored vessel changes in a complex manner with change in the condition. It is up to the designers to make thefinal decision. The maximum reaction force generated is in case 4 in which a medium-sized vessel is ballast
loaded under strong wind conditions. Case 7 corresponded to the same conditions except that the fenders had ahigh reaction force. As a result, the maximum value was 979 kN, and the expected value of 1000 waves was1804 kN. If this value exceeds the allowable horizontal force of the quay structure, it is necessary to recalculate
using a different performance grade of a larger sized fender with a lower reaction force.
Table A.4.4 Final result for mooring simulation
Case

Case 1Case 2

Case 3

Case 4

Case 5

Case 6

Case 7Naturalcondition

Strongwind

Strongwind

Strongwind

Strongwind

Strong
wind

Long
wave

Strong
wind

Note:
Red

VesselRubber fender

Fender Deflection (%)

Reaction force (kN)Maximum

1/1000expected value

Maximum

1/1000expected value

1

26%

43%

453ｋN

860ｋN

2

22%

32%

448ｋN

788ｋN

3

22%

26%

448ｋN

707ｋN

1

63%

107%

1048ｋN

687ｋN

2

43%

64%

453ｋN

453ｋN

3

37%

42%

453ｋN

451ｋN

1

21%

36%

482ｋN

895ｋN

2

18%

27%

465ｋN

771ｋN

3

18%

22%

458ｋN

685ｋN

Vessel condition Direction

Maximum
motionFenderspecification

Fender
No.

SURGE
SWAY
HEAVE
ROLL
PITCH
YAW
SURGE
SWAY
HEAVE
ROLL
PITCH
YAW
SURGE
SWAY
HEAVE
ROLL
PITCH
YAW
SURGE
SWAY
HEAVE
ROLL
PITCH
YAW
SURGE
SWAY
HEAVE
ROLL
PITCH
YAW
SURGE
SWAY
HEAVE
ROLL
PITCH
YAW
SURGE
SWAY
HEAVE
ROLL
PITCH
YAW

0.16m
0.24m
-0.03m
1.21°
0.18°
0.20°
0.20m
0.43m
-0.05m-3.24°
0.23°
0.66°
0.16m
0.25m
-0.03m
1.29°
0.18°
0.21°
0.18m
0.40m
-0.05m-3.43°
0.23°
0.71°
0.16m
0.52m
-0.09m
-4.98°
0.47°
0.70°
0.38m
-0.34m-0.31m-4.53°-0.91°
0.65°
0.16m-0.18m-0.31m-0.05°
0.24°
0.60°

1000HMinimum

MediumFull draught

MediumBallastMediumFull draught

MediumBallastSmall
BallastMediumFull draught

MediumBallast

1000HMinimum
1000HMinimum
1000HMinimum
1000HMinimum
1000HMinimum
1250HMinimum
1250HMinimum
1250HMinimum
1250HMinimum
1250HMinimum
1250HMinimum

1

51%

56%

489ｋN

547ｋN

2

30%

43%

489ｋN

489ｋN

3

31%

43%

489ｋN

489ｋN

1250HMinimum

1

51%

53%

489ｋN

934ｋN

1250HMinimum

2

37%

48%

489ｋN

937ｋN

1

26%

40%

489ｋN

489ｋN

2

28%

31%

489ｋN

489ｋN

3

36%

57%

489ｋN

556ｋN

1

34%

36%

979ｋN

1804ｋN

2

13%

16%

813ｋN

1149ｋN

3

21%

28%

972ｋN

1647ｋN

1250HMinimum
1250HMinimum
1250HMinimum
1250HMaximum
1250HMaximum
1250HMaximum

Fender deflection is close to allowable limit (50 - 55%).
Fender deflection is over allowable limit (more than 55%).

121

Mooring rope
Specification

Rope No.

Maximumtension2 strands
Nylon φ60
2 strands
Nylon φ60
2 strands
Nylon φ60
2 strands
Nylon φ60
2 strands
Nylon φ60
2 strands
Nylon φ60
2 strands
Nylon φ60
2 strands
Nylon φ60
2 strands
Nylon φ60
2 strands
Nylon φ60
2 strands
Nylon φ60
2 strands
Nylon φ60
2 strands
Nylon φ60
2 strands
Nylon φ60
2 strands
Nylon φ60
2 strands
Nylon φ60
2 strands
Nylon φ60
2 strands
Nylon φ60
2 strands
Nylon φ60
2 strands
Nylon φ60
2 strands
Nylon φ60

1
2
3
4

10ｋN
14ｋN
18ｋN
13ｋN

Not tensed
1
2
3
4

11ｋN
15ｋN
29ｋN
22ｋN

Not tensed
1
2
3
4

10ｋN
14ｋN
18ｋN
13ｋN

Not tensed
1
2
3
4

11ｋN
15ｋN
30ｋN
24ｋN

Not tensed
1
2
3
4

10ｋN
15ｋN
17ｋN
33ｋN

Not tensed
1
2
3
4

20ｋN
23ｋN
46ｋN
35ｋN

Not tensed
1
2
3
4

20ｋN
23ｋN
46ｋN
35ｋN

Not tensed

As described above, it is important to set suitable calculation cases without overlooking the key conditions
that are critical to the design. While trying to cover all possible conditions consumes many person-hours andtime, excessive risk of overlooking critical phenomena exists if this process is omitted. It is recommended thatthe initial estimation is performed under typical conditions, and the cases are gradually modified duringconsideration.

A.5 Calculation example: Effective berthing energy
The effective berthing energy needs to be calculated each time according to the type and size of vessel, method ofberthing, berthing velocity, etc., as shown in equation 5.3.1 in Chapter 5. When studying the outline of rubber fenders, it
is helpful a rough indication depending on target vessel is present. The following example corresponds to thecalculation of the effective berthing energy after setting the typical conditions.
The conditions for calculation can be set as follows.
(1) Vessel data
1) Displacement tonnage: DT
Estimated dead weight tonnage (DWT) and gross tonnage (GT) of full draught condition with reference
to the Technical Note of The Port and Airport Research Institute 2), based on values with 75% coverage.
2) Eccentricity factor: Ce, virtual mass factor: Cm
From the Technical Note of National Institute for Land and Infrastructure Management 3), the survey
results (cover rate 75%) for the length between perpendiculars (Lpp), width (B) and full draught (d) wereused. The eccentricity factor (Ce), gyration radius (Kr), block coefficient (Cb) and virtual mass factor (Cm)are calculated using equations (5.3.2), (5.3.3), (5.3.4), and (5.3.7), respectively.
(2) Berthing method:

Assuming 1⁄4 point berthing:(3) Berthing velocity:Three typical values are used: VB = 0.1 m/s、0.15 m/s、0.20 m/s.

RS＝1/4×Lpp, as shown in Fig. 5.3.1

Tables A.5.1 to A.5.10 present the calculation results for the effective berthing energy for different types of vessel.

122

Tables A.5.1 Effective berthing energy: General cargo vessel
DT (75%)=2.92 ×DWT ^ 0.924

LengthDead weight Displacement
betweentonnagetonnageperpendiculars
DWT (t)DT (t)Lpp (m)
700
1,000
2,000
3,000
5,000
10,00012,00018,00030,00040,00055,00070,00090,000120,000
150,000
200,000
250,000
300,000
400,000

1,242
1,727
3,277
4,767
7,642
14,50017,161
24,96140,01752,20270,06187,549110,434
144,061
177,048
230,959
283,844335,925
438,214

Full
draught
d (m)

Beam
B (m)

53
57
71
81
95
118
125
141
166
181
200
216
234
256
274
300
319
324
353

9.6
10.4
12.8
14.3
16.6
20.3
21.4
24.0
27.9
30.3
32.3
32.3
38.2
41.5
44.3
48.1
56.2
57.3
65.0

Eccentricity
factorCe

Virtualmass
factor
Cm

0.49
0.51
0.51
0.51
0.51
0.51
0.51
0.52
0.52
0.52
0.53
0.55
0.52
0.52
0.52
0.53
0.50
0.52
0.53

1.75
1.73
1.74
1.77
1.77
1.78
1.77
1.77
1.78
1.78
1.78
1.78
1.78
1.79
1.78
1.79
1.78
1.75
1.69

3.3
3.7
4.6
5.3
6.2
7.7
8.1
9.2
10.8
11.8
13.0
14.0
15.1
16.6
17.7
19.4
20.8
22.0
23.1

Effective berthing energy (kN·m)
Velocity V B

Velocity V B

Velocity V B

0.10m/s

0.15m/s

0.20m/s

5.37
7.6
14.5
21.4
34.5
65.9
78.0
114.2
184
241
329
428
513
673
827
1084
1271
1543
1949

12.08
17.2
32.7
48.2
77.5
148
175
257
414
541
740
963
1155
1514
1861
2439
2859
3471
4386

21.5
30.5
58.2
85.6
138
263
312
457
735
962
1316
1712
2053
2691
3309
4335
5083
6170
7798

Tables A.5.2 Effective berthing energy: Container vessel
DT (75%)=1.634 ×DWT ^ 0.986

LengthDead weight Displacement
betweentonnagetonnageperpendiculars
DWT (t)DT (t)Lpp (m)5,000
10,00020,00030,00040,00050,00060,000100,000
140,000
165,000
185,000
200,000

7,252
14,36328,44942,432
56,34970,216
84,044139,076
193,791
227,872
255,084
275,466

101
130
165
190
215
255
272
322
353
360
382
382

Beam
B (m)
18.3
22.2
27.0
30.3
31.8
32.3
35.5
45.3
48.5
52.0
59.4
59.4

Full
draughtd (m)Eccentricity
factorCe

Virtualmass
factor
Cm

6.0
7.9
10.2
11.9
11.9
12.8
13.5
14.6
15.8
16.2
16.2
16.2

0.46
0.45
0.45
0.45
0.48
0.47
0.46
0.46
0.49
0.50
0.48
0.50

1.81
1.91
1.97
2.02
1.87
1.96
1.95
1.79
1.73
1.67
1.63
1.59

123

Effective berthing energy (kN·m)
Velocity V B

Velocity V B

Velocity V B

0.10m/s

0.15m/s

0.20m/s

30.2
61.9
126
192
251
320
375
575
815
947
993
1087

68.0
139
284
431
565
720
843
1294
1833
2131
2234
2447

121
248
505
767
1004
1281
1499
2300
3259
3789
3971
4350

Remarks
TEU(Coverage:
25～75％）
400～500
200～1000
1100～1800
1900～2700
2800～3500
3600～4400
4500～5300
7900～8700
11400～12100
13500～14300
16300～18200
17800～19700

Tables A.5.3 Effective berthing energy: Tanker
DT (75%)=1.688 ×DWT ^ 0.976

LengthDead weight Displacement
betweentonnagetonnageperpendiculars
DWT (t)DT (t)Lpp (m)
1,000
2,000
3,000
5,000
10,00015,00020,00030,00050,00070,00090,000100,000
150,000
300,000

1,430
2,813
4,179
6,880
13,532
20,102
26,61839,54165,09890,404
115,535
128,048
190,212374,147

Beam
B (m)

57
72
84
100
128
148
164
168
193
213
228
235
263
322

Full
draughtd (m)Eccentricity
factorCe

Virtualmass
factor
Cm

4.1
5.0
5.6
6.4
7.8
8.8
9.5
10.6
12.3
13.5
14.5
14.9
16.7
22.1

0.44
0.45
0.46
0.47
0.47
0.48
0.48
0.53
0.53
0.57
0.52
0.53
0.55
0.54

2.08
2.03
2.01
1.96
1.93
1.92
1.90
1.77
1.72
1.69
1.67
1.66
1.62
1.68

10.2
12.4
13.9
16.1
19.7
22.1
24.0
26.9
32.9
32.9
43.5
43.5
48.9
60.2

Effective berthing energy (kN·m)
Velocity V B

Velocity V B

Velocity V B

0.10m/s

0.15m/s

0.20m/s

6.53
12.9
19.2
31.4
61.8
92.2
122
184
296
435
499
563
842
1700

14.7
29.0
43.1
70.7
139
208
274
413
666
978
1122
1266
1894
3824

26.1
51.6
76.6
126
247
369
488
735
1184
1739
1995
2251
3367
6799

Tables A.5.4 Effective berthing energy: Roll On Roll Off vessel
DT (75%)=8.728 ×DWT ^ 0.79

LengthDisplacement
Gross tonnage
betweentonnageGT (t)
perpendiculars
DT (t)Lpp (m)3,000
5,000
10,00015,00020,00040,00060,0004,873
7,296
12,616
17,37921,81437,71751,958

110
131
161
161
181
191
191

Beam
B (m)

Full
draughtd (m)Eccentricity
factorCe

Virtualmass
factor
Cm

5.6
6.2
7.0
7.6
7.9
9.1
9.9

0.36
0.35
0.36
0.38
0.42
0.47
0.52

2.14
2.11
2.01
1.86
1.83
1.68
1.58

19.0
22.2
27.4
30.3
27.3
31.5
34.2

Effective berthing energy (kN·m)
Velocity V B

Velocity V B

Velocity V B

0.10m/s

0.15m/s

0.20m/s

18.7
27.3
45.0
61.9
84.4
150
212

42.1
61.3
101.3
139
190
337
478

Remarks

74.9 Japanese gross
109.0
tonnage
180(Japanese ship248
statement）
338 International gross600
tonnage
850 （Lloyd's data）

Tables A.5.5 Effective berthing energy: Car carrier (PCC) vessel
DT (75%)=Gross tonnage
GT (t)
3,000
5,000
40,00012,00020,00030,00040,00060,00070,0001.946 ×DWT ^ 0.898

LengthDisplacement
betweentonnageperpendiculars
DT (t)Lpp (m)
2,580
4,081
26,411
8,959
14,173
20,39826,41138,01243,656

106
130
192
136
151
164
174
192
220

Beam
B (m)
17.3
21.2
33.1
24.0
26.3
28.3
31.4
33.3
33.3

Full
draughtd (m)Eccentricity
factorCe

Virtualmass
factor
Cm

5.0
6.1
10.2
6.5
7.0
7.5
9.2
10.2
10.9

0.30
0.28
0.36
0.36
0.40
0.43
0.41
0.43
0.42

2.65
2.91
2.22
2.03
1.84
1.73
1.90
1.85
1.96

124

Effective berthing energy (kN·m)
Velocity V B

Velocity V B

Velocity V B

0.10m/s

0.15m/s

0.20m/s

10.14
16.5
104
33.0
52.3
76.4
102
152
179

22.8
37.1
234
74.1
118
172
230
341
402

Remarks

40.5 Japanese gross
65.9
tonnage
416(Japanese ship
132
209
International gross306
tonnage409（Lloyd's data）
606
715

Tables A.5.6 Effective berthing energy: LPG carrier
DT (75%)=4.268 ×DWT ^ 0.914

LengthDisplacement
Gross tonnage
betweentonnageGT (t)
perpendiculars
DT (t)Lpp (m)3,000
5,000
10,00020,00040,00050,000

6,432
10,25819,33036,422
68,62984,156

92
106
130
159
219
219

Beam
B (m)

Full
draughtd (m)Eccentricity
factorCe

Virtualmass
factor
Cm

6.0
7.0
8.6
10.5
12.2
12.2

0.49
0.50
0.51
0.52
0.47
0.53

1.83
1.82
1.80
1.77
1.76
1.62

16.2
18.5
22.3
26.7
37.3
37.3

Effective berthing energy (kN·m)
Velocity V B

Velocity V B

Velocity V B

0.10m/s

0.15m/s

0.20m/s

28.6
46.3
88.3
169
287
363

64.4
104.1
199
380
647
818

Remarks

114.5
185International gross353
tonnage675（Lloyd's data）
1150
1454

Tables A.5.7 Effective berthing energy: LNG carrier
DT (75%)=Gross tonnage
GT (t)
20,00030,00050,00080,000100,000
130,000
160,000

1.601 ×DWT ^ 0.97

LengthDisplacement
betweentonnageperpendiculars
DT (t)Lpp (m)23,79035,25357,86291,283
113,342
146,190
178,808

159
183
217
255
275
301
333

Beam
B (m)

Full
draughtd (m)Eccentricity
factorCe

Virtualmass
factor
Cm

8.0
8.9
10.1
11.5
12.2
13.1
13.8

0.48
0.48
0.49
0.50
0.50
0.50
0.48

1.69
1.66
1.62
1.59
1.58
1.57
1.57

26.8
30.6
36.0
41.9
45.0
48.9
54.6

Effective berthing energy (kN·m)
Velocity V B

Velocity V B

Velocity V B

0.10m/s

0.15m/s

0.20m/s

96.1
141
230
361
447
575
680

216
318
517
811
1005
1293
1529

Remarks384
565
920 International gross
tonnage
1442
1786 （Lloyd's data）
2299
2719

Tables A.5.8 Effective berthing energy: Passenger carrier
DT (75%)=2.73 ×DWT ^ 0.871

LengthDisplacement
Gross tonnage
betweentonnageGT (t)
perpendiculars
DT (t)Lpp (m)3,000
5,000
10,00020,00030,00050,00070,000100,000
130,000
160,000

2,916
4,550
8,321
15,21821,66433,80445,31561,82577,698
93,100

81
96
122
155
178
213
239
270
297
311

Beam
B (m)

Full
draughtd (m)Eccentricity
factorCe

Virtualmass
factor
Cm

4.2
4.8
5.7
6.4
6.9
7.6
8.0
8.4
8.8
9.1

0.41
0.41
0.42
0.44
0.45
0.46
0.49
0.50
0.51
0.52

1.79
1.78
1.77
1.67
1.63
1.59
1.54
1.50
1.48
1.45

16.5
18.5
21.8
25.5
28.0
32.3
32.3
35.6
38.5
41.0

Effective berthing energy (kN·m)
Velocity V B

Velocity V B

Velocity V B

0.10m/s

0.15m/s

0.20m/s

10.56
16.7
30.7
55.9
79.7
123
172
233
290
348

23.8
37.5
69.1
125.9
179
276
387
524
653
783

Remarks

42.3
66.7
122.8
224 International gross319
tonnage491（Lloyd's data）
688
932
1162
1392

Tables A.5.9 Effective berthing energy: Middle distance (less than 300 km) ferry
DT (75%)=4.98 ×DWT ^ 0.855

LengthDisplacement
Gross tonnage
betweentonnageGT (t)
perpendiculars
DT (t)Lpp (m)
400
700
1,000
3,000
7,000
10,00013,000

836
1,348
1,829
4,679
9,656
13,09916,393

46
58
67
104
145
167
186

Beam
B (m)
11.6
13.2
14.4
18.6
22.6
24.6
26.1

Full
draughtd (m)Eccentricity
factorCe

Virtualmass
factor
Cm

2.8
3.3
3.6
4.7
5.8
6.4
6.8

0.42
0.41
0.41
0.40
0.40
0.40
0.40

1.69
1.75
1.76
1.79
1.81
1.84
1.84

125

Effective berthing energy (kN·m)
Velocity V B

Velocity V B

Velocity V B

0.10m/s

0.15m/s

0.20m/s

2.99
4.86
6.59
16.9
35.0
47.7
59.7

6.73
10.94
14.8
38.0
78.8
107
134

11.96
19.5
26.3
67.5
140
191
239

Remarks

Japanese gross
tonnage(Japanese ship
statement））

Tables A.5.10 Effective berthing energy: Long distance (more than 300 km) ferry
DT (75%)=15.409 ×DWT ^ 0.735
LengthDisplacement
Full
Eccentricity
Gross tonnage
betweenBeam
tonnagedraught
factorGT (t)
perpendiculars B (m)DT (t)d (m)Ce
Lpp (m)
6000
9,220
136
22.5
6.2
0.39
10000
13,421
162
25.9
6.2
0.40
15000
18,080
187
27.6
6.9
0.40
20000
22,337
207
27.6
7.4
0.41

VirtualEffective berthing energy (kN·m)
mass
Velocity V B Velocity V B Velocity V B
factor0.10m/s
0.15m/s
0.20m/s
Cm
1.91
34.4
77.5
138
1.75
47.3
106.4
189
1.79
64.8
146
259
1.82
83.0
187
332

Remarks

Japanese gross
tonnage(Japanese ship
statement））〔References〕
1) PIANC: Guidelines for the Design of Fenders System, Report of Working Group 33 of the Maritime Navigation
Commission, 2002
2) Yoneyama, H.: Proposal of Regression Equations for Displacement Tonnage of Ships, Technical Note of The Portand Airport Research Institute, No. 1340, 2018 (in Japanese)3) Iwasaki, K., Yamagata, S.: Study on Ship Dimensions by Statistical Analysis, Technical Note of National Institute forLand and Infrastructure Management, No. 991, 2017 (in Japanese)
4) Ports and Harbours Association of Japan (PHAJ): Technical Standards and Commentaries of Ports and Harbour
Facilities in Japan, pp.1262-1268, 2018 (in Japanese)5) Ports and Harbours Association of Japan (PHAJ): Technical Standards and Commentaries of Ports and Harbour
Facilities in Japan-II Floating Oil Storage Facility, pp.127, 1980 (in Japanese)

126

CDIT Library No. 1
Guidelines for Design and Testing of Rubber Fender systems
June 2019

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