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Technical standards and commentaries for port and harbour facilties in japan

Technical standards and commentaries for port and harbour facilties in japan

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    • The Overseas Coastal Area Development Institute of Japan3-2-4 Kasumigaseki, Chiyoda-ku, Tokyo, 100-0013, JapanCopyright © 2002 by The Overseas Coastal Area Development Institute of JapanPrinted by Daikousha Printing Co., Ltd.All rights reserved. No part of this publication may be reproduced, stored in a retrieval systems,transmitted in any form or by any means, electric, mechanical, photocopying, recording or otherwise,without the prior written permission of the publisher.Original Japanese language edition published by the Japan Ports and Harbours Association.Printed in Japan
    • PREFACE-i-PrefaceThis book is a translation of the major portion of the Technical Standards and Commentaries of Portand Harbour Facilities in Japan (1999 edition) published by the Japan Port and Harbour Association,stipulated by the Ordinance of the Minister of Transport, which was issued in April 1999. The translationcovers about two thirds of the Japanese edition.Japanese islands have a long extension of coastline, measuring about 34,000 km, for the total land areaof some 380,000 square kilometers. Throughout her history, Japan has depended on the ports and harborson daily living and prosperity of people there. Japan did not develop extensive inland canal systems asfound in the European Continent because of its mountainous geography, but rather produced many harborsand havens along its coastline in the past. Today, the number of officially designated commercial ports andharbors amounts to about 1,100 and the number of fishing ports exceeds 3,000.After 220 years of isolation from the world civilization from the 17th to 19th centuries, Japan began tomodernize its society and civilization rapidly after the Meiji revolution in 1868. Modern technology of portand harbor engineering has been introduced by distinguished engineers from abroad and learned by manyambitious and capable young engineers in Japan. Ports of Yokohama, Kobe, and others began toaccommodate large ocean-going vessels in the late 19th century as the Japanese economy had shown arapid growth.Japanese engineers had drafted an engineering manual on design and construction of port and harborfacilities as early as in 1943. The manual was revised in 1959 with inclusion of new technology such asthose of coastal engineering and geotechnical engineering, which were developed during the SecondWorld War or just before it. The Japanese economy that was utterly destroyed by the war had begun torebuild itself rapidly after the 1950s. There were so many demands for the expansion of port and harborfacilities throughout Japan. Engineers were urged to design and construct facilities after facilities. Japanhas built the breakwaters and the quays with the rate of about 20,000 meters each per year throughout the1960s, 1970s, and 1980s.Such a feat of port development was made possible with provision of sound engineering manuals. TheMinistry of Land, Infrastructure and Transport (formerly the Ministry of Transport up to January 2001)which was responsible for port development and operation, revised the basic law on ports and harbors in1974 so as to take responsibility for provision of technical standards for design, construction, andmaintenance of port and harbor facilities. The first official technical standards and commentaries for portand harbor facilities were issued in 1979, and published by the Japan Port and Harbour Association forgeneral use. The technical standards were prepared by a technical committee composed of governmentengineers within the former Ministry of Transport, including members of the Port and Harbour ResearchInstitute and several District Port Construction Bureaus that were responsible for design and constructionin the field. Its English version was published by the Overseas Coastal Area Development Institute in1980, but it introduced only the skeleton of the Japanese version without giving the details.The Technical Standards and Commentaries for Port and Harbor Facilities in Japan have been revisedin 1988 and 1999, each time incorporating new technological developments. The present Englishtranslation endeavors to introduce the newest edition of 1999 to the port and harbor engineers overseas. Itis a direct translation of essential parts of Japanese edition. Many phrases and expressions reflect thecustomary, regulatory writings in Japanese, which are often awkward in English. Some sentences aftertranslation may not be fluent enough and give troubles for decipher. The editors in charge of translationrequest the readers for patience and generosity in their efforts for understanding Japanese technology inport and harbor engineering.With the globalization in every aspect of human activities, indigenous practices and customs are forcedto comply with the world standards. Technology by definition is supposed to be universal. Nevertheless,each country has developed its own specialty to suit its local conditions. The overseas readers may findsome of Japanese technical standards strange and difficult for adoption for their usage. Such conflicts intechnology are the starting points for mutual understanding and further developments in the future. Theeditors wish wholeheartedly this English version of Japanese technical standards be welcomed by theoverseas colleagues and serve for the advancement of port and harbor technology in the world.January 2002Y. Goda, T. Tabata and S. YamamotoEditors for translation version
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-ii-
    • CONTENTS-iii-CONTENTSPrefacePart I GeneralChapter 1 General Rules.................................................................................................................................................11.1 Scope of Application .............................................................................................................................11.2 Definitions ...............................................................................................................................................21.3 Usage of SI Units...................................................................................................................................2Chapter 2 Datum Level for Construction Work.........................................................................................................4Chapter 3 Maintenance....................................................................................................................................................5Part II Design ConditionsChapter 1 General .............................................................................................................................................................7Chapter 2 Vessels..............................................................................................................................................................92.1 Dimensions of Target Vessel...............................................................................................................92.2 External Forces Generated by Vessels ...........................................................................................162.2.1 General .....................................................................................................................................162.2.2 Berthing.....................................................................................................................................16[1] Berthing Energy..................................................................................................................16[2] Berthing Velocity ................................................................................................................17[3] Eccentricity Factor..............................................................................................................20[4] Virtual Mass Factor ............................................................................................................212.2.3 Moored Vessels .......................................................................................................................22[1] Motions of Moored Vessel..................................................................................................22[2] Waves Acting on Vessel.....................................................................................................22[3] Wind Load Acting on Vessel ..............................................................................................23[4] Current Forces Acting on Vessel........................................................................................24[5] Load-Deflection Characteristics of Mooring System ..........................................................252.2.4 Tractive Force Acting on Mooring Post and Bollard..................................................................25Chapter 3 Wind and Wind Pressure ..........................................................................................................................283.1 General..................................................................................................................................................283.2 Wind.......................................................................................................................................................293.3 Wind Pressure......................................................................................................................................30Chapter 4 Waves..............................................................................................................................................................324.1 General..................................................................................................................................................324.1.1 Procedure for Determining the Waves Used in Design.............................................................324.1.2 Waves to Be Used in Design ....................................................................................................324.1.3 Properties of Waves..................................................................................................................33[1] Fundamental Properties of Waves.....................................................................................33[2] Statistical Properties of Waves...........................................................................................37[3] Wave Spectrum..................................................................................................................384.2 Method of Determining Wave Conditions to Be Used in Design .................................................404.2.1 Principles for Determining the Deepwater Waves Used in Design ...........................................404.2.2 Procedure for Obtaining the Parameters of Design Waves ......................................................414.3 Wave Hindcasting................................................................................................................................424.3.1 General .....................................................................................................................................424.3.2 Wave Hindcasting in Generating Area......................................................................................424.3.3 Swell Hindcasting......................................................................................................................464.4 Statistical Processing of Wave Observation and Hindcasted Data.............................................474.5 Transformations of Waves .................................................................................................................494.5.1 General .....................................................................................................................................494.5.2 Wave Refraction........................................................................................................................494.5.3 Wave Diffraction........................................................................................................................52[1] Diffraction ...........................................................................................................................52[2] Combination of Diffraction and Refraction..........................................................................694.5.4 Wave Reflection........................................................................................................................70
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-iv-[1] General .............................................................................................................................. 70[2] Reflection Coefficient......................................................................................................... 71[3] Transformation of Waves at Concave Corners, near the Heads of Breakwaters,and around Detached Breakwaters ................................................................................... 724.5.5 Wave Shoaling.......................................................................................................................... 744.5.6 Wave Breaking ......................................................................................................................... 754.6 Wave Runup, Overtopping, and Transmission............................................................................... 804.6.1 Wave Runup............................................................................................................................. 804.6.2 Wave Overtopping .................................................................................................................... 844.6.3 Wave Transmission .................................................................................................................. 904.7 Wave Setup and Surf Beat................................................................................................................ 914.7.1 Wave Setup .............................................................................................................................. 914.7.2 Surf Beat................................................................................................................................... 924.8 Long-Period Waves and Seiche ....................................................................................................... 934.9 Waves inside Harbors ........................................................................................................................ 944.9.1 Calmness and Disturbances..................................................................................................... 944.9.2 Evaluation of Harbor Calmness ................................................................................................ 944.10 Ship Waves .......................................................................................................................................... 94Chapter 5 Wave Force................................................................................................................................................. 1005.1 General ...............................................................................................................................................1005.2 Wave Force Acting on Upright Wall ...............................................................................................1005.2.1 General Considerations..........................................................................................................1005.2.2 Wave Forces of Standing and Breaking Waves .....................................................................101[1] Wave Force under Wave Crest........................................................................................101[2] Wave Force under Wave Trough..................................................................................... 1055.2.3 Impulsive Pressure Due to Breaking Waves ..........................................................................1065.2.4 Wave Force on Upright Wall Covered with Wave-Dissipating Concrete Blocks.....................1095.2.5 Effect of Alignment of Breakwater on Wave Force ................................................................. 1105.2.6 Effect of Abrupt Change in Water Depth on Wave Force ....................................................... 1105.2.7 Wave Force on Upright Wall near Shoreline or on Shore........................................................111[1] Wave Force at the Seaward Side of Shoreline .................................................................111[2] Wave Force at the Landward Side of Shoreline ...............................................................1115.2.8 Wave Force on Upright Wave-Absorbing Caisson ..................................................................1115.3 Mass of Armor Stones and Concrete Blocks................................................................................ 1125.3.1 Armor Units on Slope.............................................................................................................. 1125.3.2 Armor Units on Foundation Mound of Composite Breakwater ............................................... 1175.4 Wave Forces Acting on Cylindrical Members and Large Isolated Structures ......................... 1195.4.1 Wave Force on Cylindrical Members...................................................................................... 1195.4.2 Wave Force on Large Isolated Structure ................................................................................1215.5 Wave Force Acting on Structure Located near the Still Water Level........................................ 1225.5.1 Uplift Acting on Horizontal Plate near the Still Water Level ....................................................122Chapter 6 Tides and Abnormal Water Levels.......................................................................................................1276.1 Design Water Level...........................................................................................................................1276.2 Astronomical Tide .............................................................................................................................1286.3 Storm Surge.......................................................................................................................................1286.4 Tsunami ..............................................................................................................................................1306.5 Seiche ................................................................................................................................................. 1336.6 Groundwater Level and Permeation ..............................................................................................135Chapter 7 Currents and Current Force...................................................................................................................1387.1 General ...............................................................................................................................................1387.2 Current Forces Acting on Submerged Members and Structures ..............................................1387.3 Mass of Armor Stones and Concrete Blocks against Currents .................................................140Chapter 8 External Forces Acting on Floating Body and Its Motions ...........................................................1428.1 General ...............................................................................................................................................1428.2 External Forces Acting on Floating Body ......................................................................................1438.3 Motions of Floating Body and Mooring Force............................................................................... 145Chapter 9 Estuarine Hydraulics ................................................................................................................................1489.1 General ...............................................................................................................................................148Chapter 10 Littoral Drift ..................................................................................................................................................15410.1 General ...............................................................................................................................................15410.2 Scouring around Structures.............................................................................................................16110.3 Prediction of Beach Deformation....................................................................................................163
    • CONTENTS-v-Chapter 11 Subsoil...........................................................................................................................................................16711.1 Method of Determining Geotechnical Conditions.........................................................................16711.1.1 Principles.................................................................................................................................16711.1.2 Selection of Soil Investigation Methods ..................................................................................16811.1.3 Standard Penetration Test ......................................................................................................16811.2 Physical Properties of Soils .............................................................................................................16811.2.1 Unit Weight of Soil...................................................................................................................16811.2.2 Classification of Soils ..............................................................................................................16911.2.3 Coefficient of Permeability of Soil ...........................................................................................16911.3 Mechanical Properties of Soils........................................................................................................17011.3.1 Elastic Constants ....................................................................................................................17011.3.2 Consolidation Properties.........................................................................................................17011.3.3 Shear Properties .....................................................................................................................17311.4 Angle of Internal Friction by N-value ..............................................................................................17511.5 Application of Soundings Other Than SPT....................................................................................17611.6 Dynamic Properties of Soils.............................................................................................................17811.6.1 Dynamic Modulus of Deformation...........................................................................................17811.6.2 Dynamic Strength Properties ..................................................................................................180Chapter 12 Earthquakes and Seismic Force...........................................................................................................18212.1 General................................................................................................................................................18212.2 Earthquake Resistance of Port and Harbor Facilities in Design................................................18212.3 Seismic Coefficient Method .............................................................................................................18412.4 Design Seismic Coefficient ..............................................................................................................18412.5 Seismic Response Analysis.............................................................................................................19012.6 Seismic Deformation Method ..........................................................................................................192Chapter 13 Liquefaction .................................................................................................................................................19513.1 General................................................................................................................................................19513.2 Prediction of Liquefaction.................................................................................................................19513.3 Countermeasures against Liquefaction .........................................................................................199Chapter 14 Earth Pressure and Water Pressure ...................................................................................................20014.1 Earth Pressure ...................................................................................................................................20014.2 Earth Pressure under Ordinary Conditions ...................................................................................20014.2.1 Earth Pressure of Sandy Soil under Ordinary Conditions.......................................................20014.2.2 Earth Pressure of Cohesive Soil under Ordinary Conditions ..................................................20114.3 Earth Pressure during Earthquake .................................................................................................20214.3.1 Earth Pressure of Sandy Soil during Earthquake....................................................................20214.3.2 Earth Pressure of Cohesive Soil during Earthquake...............................................................20414.3.3 Apparent Seismic Coefficient..................................................................................................20414.4 Water Pressure..................................................................................................................................20514.4.1 Residual Water Pressure ........................................................................................................20514.4.2 Dynamic Water Pressure during Earthquake..........................................................................205Chapter 15 Loads.............................................................................................................................................................20715.1 General................................................................................................................................................20715.2 Deadweight and Surcharge .............................................................................................................20715.3 Static Load..........................................................................................................................................20715.3.1 Static Load under Ordinary Conditions ...................................................................................20715.3.2 Static Load during Earthquake................................................................................................20815.3.3 Unevenly Distributed Load......................................................................................................20815.3.4 Snow Load ..............................................................................................................................20815.4 Live Load ............................................................................................................................................20915.4.1 Train Load...............................................................................................................................20915.4.2 Vehicle Load ...........................................................................................................................20915.4.3 Cargo Handling Equipment Load............................................................................................20915.4.4 Sidewalk Live Load .................................................................................................................209Chapter 16 Coefficient of Friction................................................................................................................................21016.1 General................................................................................................................................................210Part III MaterialsChapter 1 General .........................................................................................................................................................2111.1 Selection of Materials........................................................................................................................211
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-vi-1.2 Safety of Structural Elements.......................................................................................................... 211Chapter 2 Steel...............................................................................................................................................................2122.1 Materials .............................................................................................................................................2122.2 Steel Meterial Constants Used in Design Calculation.................................................................2122.3 Allowable Stresses............................................................................................................................ 2122.3.1 General ...................................................................................................................................2122.3.2 Structural Steel .......................................................................................................................2122.3.3 Steel Piles and Steel Pipe Sheet Piles ...................................................................................2132.3.4 Steel Sheet Piles ....................................................................................................................2142.3.5 Cast Steel and Forged Steel...................................................................................................2142.3.6 Allowable Stresses for Steel at Welded Zones and Spliced Sections ....................................2142.3.7 Increase of Allowable Stresses...............................................................................................2152.4 Corrosion Control ..............................................................................................................................2162.4.1 General ...................................................................................................................................2162.4.2 Corrosion Rates of Steel Materials .........................................................................................2162.4.3 Corrosion Control Methods.....................................................................................................2172.4.4 Cathodic Protection Method ...................................................................................................217[1] Range of Application........................................................................................................217[2] Protective Potential..........................................................................................................218[3] Protective Current Density...............................................................................................2192.4.5 Coating Method ...................................................................................................................... 220[1] Extent of Application ........................................................................................................220[2] Applicable Methods..........................................................................................................220[3] Selection of Method .........................................................................................................220Chapter 3 Concrete....................................................................................................................................................... 2213.1 General ...............................................................................................................................................2213.2 Basics of Design Based on the Limit State Design Method.......................................................2213.3 Design Based on Allowable Stress Method..................................................................................2233.4 Concrete Materials............................................................................................................................ 2243.5 Concrete Quality and Performance................................................................................................ 2253.6 Underwater Concrete .......................................................................................................................227Chapter 4 Bituminous Materials................................................................................................................................2284.1 General ...............................................................................................................................................2284.2 Asphalt Mat ........................................................................................................................................2284.2.1 General ...................................................................................................................................2284.2.2 Materials ................................................................................................................................. 2284.2.3 Mix Proportioning....................................................................................................................2294.3 Paving Materials................................................................................................................................2294.4 Sand Mastic Asphalt.........................................................................................................................2294.4.1 General ...................................................................................................................................2294.4.2 Materials ................................................................................................................................. 2304.4.3 Mix Proportioning....................................................................................................................230Chapter 5 Stone ............................................................................................................................................................. 2315.1 General ...............................................................................................................................................2315.2 Rubble for Foundation...................................................................................................................... 2315.3 Backfilling Materials ..........................................................................................................................2315.4 Base Course Materials of Pavement .............................................................................................232Chapter 6 Timber ...........................................................................................................................................................2336.1 Quality of Timber...............................................................................................................................2336.1.1 Structural Timber ....................................................................................................................2336.1.2 Timber Piles............................................................................................................................ 2336.2 Allowable Stresses of Timber..........................................................................................................2336.2.1 General ...................................................................................................................................2336.2.2 Allowable Stresses of Structural Timber.................................................................................2336.3 Quality of Glued Laminated Timber ...............................................................................................2336.3.1 Allowable Stress for Glued Laminated Timber .......................................................................2336.4 Joining of Timber...............................................................................................................................2336.5 Maintenance of Timber.....................................................................................................................233Chapter 7 Other Materials...........................................................................................................................................2347.1 Metals Other Than Steel ..................................................................................................................2347.2 Plastics and Rubbers........................................................................................................................2347.3 Coating Materials ..............................................................................................................................236
    • CONTENTS-vii-7.4 Grouting Materials .............................................................................................................................2377.4.1 General ...................................................................................................................................2377.4.2 Properties of Grouting Materials .............................................................................................237Chapter 8 Recyclable Resources .............................................................................................................................2388.1 General................................................................................................................................................2388.2 Slag......................................................................................................................................................2388.3 Coal Ash..............................................................................................................................................2398.4 Crashed Concrete .............................................................................................................................240Part IV Precast Concrete UnitsChapter 1 Caissons.......................................................................................................................................................2411.1 General................................................................................................................................................2411.2 Determination of Dimensions ..........................................................................................................2421.3 Floating Stability ................................................................................................................................2421.4 Design External Forces ....................................................................................................................2431.4.1 Combination of Loads and Load Factors ................................................................................2431.4.2 External Forces during Fabrication .........................................................................................2491.4.3 External Forces during Launching and Floating......................................................................2491.4.4 External Forces during Installation..........................................................................................2501.4.5 External Forces after Construction..........................................................................................250[1] Outer Walls.......................................................................................................................250[2] Bottom Slab......................................................................................................................251[3] Partition Walls and Others................................................................................................2531.5 Design of Members ...........................................................................................................................2541.5.1 Outer Wall ...............................................................................................................................2541.5.2 Partition Wall...........................................................................................................................2541.5.3 Bottom Slab.............................................................................................................................2541.5.4 Others .....................................................................................................................................2551.6 Design of Hooks for Suspension by Crane ...................................................................................255Chapter 2 L-Shaped Blocks........................................................................................................................................2562.1 General................................................................................................................................................2562.2 Determination of Dimensions ..........................................................................................................2562.3 Loads Acting on Members ...............................................................................................................2572.3.1 General ...................................................................................................................................2572.3.2 Earth Pressure ........................................................................................................................2582.3.3 Converted Loads for Design Calculation.................................................................................2582.4 Design of Members ...........................................................................................................................2592.4.1 Front Wall................................................................................................................................2592.4.2 Footing ....................................................................................................................................2592.4.3 Bottom Slab.............................................................................................................................2592.4.4 Buttress...................................................................................................................................2602.5 Design of Hooks for Suspension by Crane ...................................................................................260Chapter 3 Cellular Blocks............................................................................................................................................2613.1 General................................................................................................................................................2613.2 Determination of Dimensions ..........................................................................................................2613.2.1 Shape of Cellular Blocks.........................................................................................................2613.2.2 Determination of Dimensions..................................................................................................2613.3 Loads Acting on Cellular Blocks......................................................................................................2623.3.1 General ...................................................................................................................................2623.3.2 Earth Pressure of Filling and Residual Water Pressure..........................................................2623.3.3 Converted Loads for Design Calculation.................................................................................2643.4 Design of Members ...........................................................................................................................2643.4.1 Rectangular Cellular Blocks....................................................................................................2643.4.2 Other Types of Cellular Blocks................................................................................................265Chapter 4 Upright Wave-Absorbing Caissons......................................................................................................2674.1 General................................................................................................................................................2674.2 External Forces Acting on Members ..............................................................................................2674.3 Design of Members ...........................................................................................................................269Chapter 5 Hybrid Caissons.........................................................................................................................................2705.1 General................................................................................................................................................2705.2 Determination of Dimensions ..........................................................................................................270
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-viii-5.3 Design External Forces....................................................................................................................2715.4 Design of Members...........................................................................................................................2715.4.1 Section Force..........................................................................................................................2715.4.2 Design of Composite Slabs ....................................................................................................2715.4.3 Design of SRC Members ........................................................................................................2715.4.4 Design of Partitions................................................................................................................. 2715.4.5 Design of Corners and Joints .................................................................................................2715.4.6 Safety against Fatigue Failure................................................................................................ 2725.5 Corrosion Control ..............................................................................................................................272Part V FoundationsChapter 1 General .........................................................................................................................................................273Chapter 2 Bearing Capacity of Shallow Foundations ........................................................................................2742.1 General ...............................................................................................................................................2742.2 Bearing Capacity of Foundation on Sandy Ground.....................................................................2742.3 Bearing Capacity of Foundation on Clayey Ground.................................................................... 2752.4 Bearing Capacity of Multilayered Ground ..................................................................................... 2762.5 Bearing Capacity for Eccentric and Inclined Loads.....................................................................277Chapter 3 Bearing Capacity of Deep Foundations .............................................................................................2803.1 General ...............................................................................................................................................2803.2 Vertical Bearing Capacity................................................................................................................. 2803.3 Lateral Bearing Capacity..................................................................................................................281Chapter 4 Bearing Capacity of Pile Foundations ................................................................................................ 2844.1 Allowable Axial Bearing Capacity of Piles..................................................................................... 2844.1.1 General ...................................................................................................................................2844.1.2 Standard Allowable Axial Bearing Capacity............................................................................2844.1.3 Ultimate Axial Bearing Capacity of Single Piles......................................................................2854.1.4 Estimation of Ultimate Axial Bearing Capacity by Loading Tests ...........................................2854.1.5 Estimation of Ultimate Axial Bearing Capacity by Static Bearing Capacity Formulas ............ 2864.1.6 Examination of Compressive Stress of Pile Materials ............................................................2884.1.7 Decrease of Bearing Capacity Due to Joints ..........................................................................2884.1.8 Decrease of Bearing Capacity Due to Slenderness Ratio ......................................................2884.1.9 Bearing Capacity of Pile Group ..............................................................................................2884.1.10 Examination of Negative Skin Friction ....................................................................................2904.1.11 Examination of Settlement of Piles .........................................................................................2914.2 Allowable Pulling Resistance of Piles ............................................................................................2914.2.1 General ...................................................................................................................................2914.2.2 Standard Allowable Pulling Resistance ..................................................................................2924.2.3 Maximum Pulling Resistance of Single Pile............................................................................2924.2.4 Examination of Tensile Stress of Pile Materials......................................................................2934.2.5 Matters to Be Considered for Obtaining Allowable Pulling Resistance of Piles......................2934.3 Allowable Lateral Bearing Capacity of Piles .................................................................................2934.3.1 General ...................................................................................................................................2934.3.2 Estimation of Allowable Lateral Bearing Capacity of Piles .....................................................2954.3.3 Estimation of Pile Behavior Using Loading Tests ...................................................................2954.3.4 Estimation of Pile Behavior Using Analytical Methods ...........................................................2954.3.5 Consideration of Pile Group Action.........................................................................................3014.3.6 Lateral Bearing Capacity of Coupled Piles .............................................................................3014.4 Pile Design in General...................................................................................................................... 3044.4.1 Load Sharing ..........................................................................................................................3044.4.2 Load Distribution.....................................................................................................................3054.4.3 Distance between Centers of Piles.........................................................................................3054.4.4 Allowable Stresses for Pile Materials......................................................................................3054.5 Detailed Design ................................................................................................................................. 3064.5.1 Examination of Loads during Construction .............................................................................3064.5.2 Design of Joints between Piles and Structure ........................................................................3074.5.3 Joints of Piles..........................................................................................................................3084.5.4 Change of Plate Thickness or Materials of Steel Pipe Piles................................................... 3084.5.5 Other Points for Caution in Design .........................................................................................308Chapter 5 Settlement of Foundations .....................................................................................................................3105.1 Stress in Soil Mass ...........................................................................................................................3105.2 Immediate Settlement.......................................................................................................................310
    • CONTENTS-ix-5.3 Consolidation Settlement .................................................................................................................3105.4 Lateral Displacement ........................................................................................................................3125.5 Differential Settlements ....................................................................................................................312Chapter 6 Stability of Slopes......................................................................................................................................3146.1 General................................................................................................................................................3146.2 Stability Analysis................................................................................................................................3156.2.1 Stability Analysis Using Circular Slip Surface Method ............................................................3156.2.2 Stability Analysis Assuming Slip Surfaces Other Than Circular Arc Slip Surface...................316Chapter 7 Soil Improvement Methods.....................................................................................................................3187.1 General................................................................................................................................................3187.2 Replacement Method........................................................................................................................3187.3 Vertical Drain Method .......................................................................................................................3187.3.1 Principle of Design ..................................................................................................................3187.3.2 Determination of Height and Width of Fill................................................................................319[1] Height and Width of Fill Required for Soil Improvement ..................................................319[2] Height and Width of Fill Required for Stability of Fill Embankment..................................3197.3.3 Design of Drain Piles...............................................................................................................319[1] Drain Piles and Sand Mat.................................................................................................319[2] Interval of Drain Piles .......................................................................................................3207.4 Deep Mixing Method .........................................................................................................................3227.4.1 Principle of Design ..................................................................................................................322[1] Scope of Application.........................................................................................................322[2] Basic Concept ..................................................................................................................3237.4.2 Assumptions for Dimensions of Stabilized Body.....................................................................323[1] Mixture Design of Stabilized Soil......................................................................................323[2] Allowable Stress of Stabilized Body.................................................................................3247.4.3 Calculation of External Forces ................................................................................................3257.5 Lightweight Treated Soil Method ....................................................................................................3267.5.1 Outline of Lightweight Treated Soil Method ............................................................................3267.5.2 Basic Design Concept.............................................................................................................3267.5.3 Mixture Design of Treated Soil................................................................................................3277.5.4 Examination of Area to Be Treated.........................................................................................3287.5.5 Workability Verification Tests..................................................................................................3287.6 Replacement Method with Granulated Blast Furnace Slag........................................................3287.6.1 Principle of Design ..................................................................................................................3287.6.2 Physical Properties of Granulated Blast Furnace Slag ...........................................................3287.7 Premixing Method..............................................................................................................................3297.7.1 Principle of Design ..................................................................................................................329[1] Scope of Application.........................................................................................................329[2] Consideration for Design..................................................................................................3297.7.2 Preliminary Survey..................................................................................................................3297.7.3 Determination of Strength of Treated Soil...............................................................................3307.7.4 Mixture Design of Treated Soil................................................................................................3307.7.5 Examination of Area of Improvement......................................................................................3317.8 Active Earth Pressure of Solidified Geotechnical Materials........................................................3337.8.1 Scope of Application ...............................................................................................................3337.8.2 Active Earth Pressure .............................................................................................................333[1] Outline..............................................................................................................................333[2] Strength Parameters ........................................................................................................334[3] Calculation of Active Earth Pressure................................................................................334[4] Case of Limited Area of Subsoil Improvement.................................................................3357.9 Sand Compaction Pile Method (for Sandy Subsoil).....................................................................3367.9.1 Principle of Design ..................................................................................................................3367.9.2 Sand Volume to Be Supplied ..................................................................................................3367.9.3 Design Based on Trial Execution............................................................................................3387.10 Sand Compaction Pile Method (for Cohesive Subsoil) ...............................................................3397.10.1 Principle of Design ..................................................................................................................339[1] Scope of Application.........................................................................................................339[2] Basic Concept ..................................................................................................................3397.10.2 Strength and Permeability of Sand Piles.................................................................................3397.10.3 Shear Strength of Improved Subsoil .......................................................................................3397.10.4 Stability Analysis .....................................................................................................................3407.10.5 Examining Consolidation.........................................................................................................341
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-x-Part VI Navigation Channels and BasinsChapter 1 General .........................................................................................................................................................345Chapter 2 Navigation Channels ................................................................................................................................3462.1 General ...............................................................................................................................................3462.2 Alignment of Navigation Channel ..................................................................................................3462.3 Width of Navigation Channel........................................................................................................... 3472.4 Depth of Navigation Channel ..........................................................................................................3482.5 Length of Navigation Channel at Harbor Entrance......................................................................3482.6 Calmness of Navigation Channel ...................................................................................................348Chapter 3 Navigation Channels outside Breakwaters .......................................................................................3503.1 General ...............................................................................................................................................3503.2 Width of Navigation Channel........................................................................................................... 3503.3 Depth of Navigation Channel ..........................................................................................................350Chapter 4 Basins............................................................................................................................................................3514.1 General ...............................................................................................................................................3514.2 Location and Area of Basin .............................................................................................................3514.2.1 Location ..................................................................................................................................3514.2.2 Area of Basin Used for Anchorage or Mooring .......................................................................3514.2.3 Area of Basin Used for Ship Maneuvering..............................................................................352[1] Turning Basin...................................................................................................................352[2] Mooring / Unmooring Basin .............................................................................................3534.3 Depth of Basin ...................................................................................................................................3534.4 Calmness of Basin............................................................................................................................ 3534.5 Timber Sorting Pond.........................................................................................................................354Chapter 5 Small Craft Basins.....................................................................................................................................355Chapter 6 Maintenance of Navigation Channels and Basins..........................................................................3556.1 General ...............................................................................................................................................355Part VII Protective Facilities for HarborsChapter 1 General .........................................................................................................................................................3571.1 General Consideration .....................................................................................................................3571.2 Maintenance.......................................................................................................................................357Chapter 2 Breakwaters ................................................................................................................................................3582.1 General ...............................................................................................................................................3582.2 Layout of Breakwaters...................................................................................................................... 3582.3 Design Conditions of Breakwaters .................................................................................................3592.4 Selection of Structural Types ..........................................................................................................3592.5 Determination of Cross Section ......................................................................................................3622.5.1 Upright Breakwater................................................................................................................. 3622.5.2 Composite Breakwater ........................................................................................................... 3632.5.3 Sloping Breakwater................................................................................................................. 3632.5.4 Caisson Type Breakwater Covered with Wave-Dissipating Concrete Blocks ........................3642.6 External Forces for Stability Calculation........................................................................................3642.6.1 General ...................................................................................................................................3642.6.2 Wave Forces...........................................................................................................................3652.6.3 Hydrostatic Pressure ..............................................................................................................3652.6.4 Buoyancy................................................................................................................................3652.6.5 Deadweight.............................................................................................................................3652.6.6 Stability during Earthuakes.....................................................................................................3652.7 Stability Calculation...........................................................................................................................3652.7.1 Stability Calculation of Upright Section...................................................................................3652.7.2 Stability Calculation of Sloping Section ..................................................................................3692.7.3 Stability Calculation of Whole Section ....................................................................................3692.7.4 Stability Calculation for Head and Corner of Breakwater .......................................................3692.8 Details of Structures .........................................................................................................................3702.8.1 Upright Breakwater................................................................................................................. 3702.8.2 Composite Breakwater ........................................................................................................... 3712.8.3 Sloping Breakwater................................................................................................................. 372
    • CONTENTS-xi-2.8.4 Caisson Type Breakwater Covered with Wave-Dissipating Concrete Blocks.........................3722.9 Detailed Design of Upright Section.................................................................................................3722.10 Breakwaters for Timber-Handling Facilities ..................................................................................3722.10.1 Breakwaters for Timber Storage Ponds and Timber Sorting Ponds .......................................3722.10.2 Fences to Prevent Timber Drifting ..........................................................................................3732.11 Storm Surge Protection Breakwater...............................................................................................3732.12 Tsunami Protection Breakwater......................................................................................................373Chapter 3 Other Types of Breakwaters ..................................................................................................................3763.1 Selection of Structural Type.............................................................................................................3763.2 Gravity Type Special Breakwaters..................................................................................................3773.2.1 General ...................................................................................................................................3773.2.2 Upright Wave-Absorbing Block Breakwater............................................................................378[1] General.............................................................................................................................378[2] Crest Elevation.................................................................................................................378[3] Wave Force......................................................................................................................3793.2.3 Wave-Absorbing Caisson Breakwater ....................................................................................379[1] General.............................................................................................................................379[2] Determination of Target Waves to Be Absorbed..............................................................380[3] Determination of Dimensions for Wave-Absorbing Section .............................................380[4] Wave Force for Examination of Structural Stability..........................................................380[5] Wave Force for Design of Structural Members ................................................................3803.2.4 Sloping-Top Caisson Breakwater............................................................................................380[1] General.............................................................................................................................380[2] Wave Force......................................................................................................................3813.3 Non-Gravity Type Breakwaters .......................................................................................................3823.3.1 Curtain Wall Breakwater .........................................................................................................382[1] General.............................................................................................................................382[2] Wave Force......................................................................................................................384[3] Design of Piles .................................................................................................................3843.3.2 Floating Breakwater ................................................................................................................384[1] General.............................................................................................................................384[2] Selection of Design Conditions ........................................................................................385[3] Design of Mooring System ...............................................................................................385[4] Design of Floating Body Structure....................................................................................386Chapter 4 Locks..............................................................................................................................................................3884.1 Selection of Location.........................................................................................................................3884.2 Size and Layout of Lock ...................................................................................................................3884.3 Selection of Structural Type.............................................................................................................3894.3.1 Gate ........................................................................................................................................3894.3.2 Lock Chamber.........................................................................................................................3894.4 External Forces and Loads Acting on Lock...................................................................................3894.5 Pumping and Drainage System ......................................................................................................3894.6 Auxiliary Facilities..............................................................................................................................389Chapter 5 Facilities to Prevent Shoaling and Siltation.......................................................................................3905.1 General................................................................................................................................................3905.2 Jetty .....................................................................................................................................................3905.2.1 Layout of Jetty.........................................................................................................................3905.2.2 Details of Jetty.........................................................................................................................3915.3 Group of Groins .................................................................................................................................3925.4 Training Jetties...................................................................................................................................3925.4.1 Layout of Training Jetties........................................................................................................3925.4.2 Water Depth at Tip of Training Jetty .......................................................................................3935.4.3 Structure of Training Jetty.......................................................................................................3935.5 Facilities to Trap Littoral Transport and Sediment Flowing out of Rivers.................................3935.6 Countermeasures against Wind-Blown Sand...............................................................................3945.6.1 General ...................................................................................................................................3945.6.2 Selection of Countermeasures................................................................................................394Chapter 6 Revetments..................................................................................................................................................3966.1 Principle of Design ............................................................................................................................3966.2 Design Conditions .............................................................................................................................3966.3 Structural Stability..............................................................................................................................3986.4 Determination of Cross Section ......................................................................................................3986.5 Details..................................................................................................................................................398
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-xii-Part VIII Mooring FacilitiesChapter 1 General .........................................................................................................................................................4011.1 General Consideration .....................................................................................................................4011.2 Maintenance of Mooring Facilities..................................................................................................401Chapter 2 Dimensions of Mooring Facilities..........................................................................................................4022.1 Length and Water Depth of Berths.................................................................................................4022.2 Crown Heights of Mooring Facilities...............................................................................................4052.3 Ship Clearance for Mooring Facilities ............................................................................................4052.4 Design Water Depth .........................................................................................................................4052.5 Protection against Scouring.............................................................................................................4062.6 Ancillary Facilities..............................................................................................................................406Chapter 3 Structural Types of Mooring Facilities ................................................................................................ 407Chapter 4 Gravity Type Quaywalls ..........................................................................................................................4084.1 Principle of Design............................................................................................................................ 4084.2 External Forces and Loads Acting on Walls.................................................................................4084.3 Stability Calculations.........................................................................................................................4104.3.1 Items to Be Considered in Stability Calculations .................................................................... 4104.3.2 Examination against Sliding of Wall........................................................................................4104.3.3 Examination Concerning Bearing Capacity of Foundation ..................................................... 4114.3.4 Examination Concerning Overturning of Wall......................................................................... 4114.3.5 Examination on Soft Foundation............................................................................................. 4114.4 Stability Calculations of Cellular Concrete Blocks .......................................................................4124.5 Effects of Backfill...............................................................................................................................4134.6 Detailed Design ................................................................................................................................. 414Chapter 5 Sheet Pile Quaywalls ...............................................................................................................................4155.1 General ...............................................................................................................................................4155.2 External Forces Acting on Sheet Pile Wall ...................................................................................4155.2.1 External Forces to Be Considered..........................................................................................4155.3 Design of Sheet Pile Wall ................................................................................................................4175.3.1 Setting Level of Tie Rod .........................................................................................................4175.3.2 Embedded Length of Sheet Piles ...........................................................................................4175.3.3 Bending Moment of Sheet Piles and Reaction at Tie Rod Setting Point ................................4185.3.4 Cross Section of Sheet Piles ..................................................................................................4195.3.5 Consideration of the Effect of Section Rigidity of Sheet Piles ................................................4195.4 Design of Tie Rods ...........................................................................................................................4245.4.1 Tension of Tie Rod ................................................................................................................. 4245.4.2 Cross Section of Tie Rod........................................................................................................4245.5 Design of Wale ..................................................................................................................................4255.6 Examination for Circular Slip........................................................................................................... 4255.7 Design of Anchorage Work..............................................................................................................4265.7.1 Selection of Structural Type of Anchorage Work.................................................................... 4265.7.2 Location of Anchorage Work ..................................................................................................4265.7.3 Design of Anchorage Work.....................................................................................................4275.8 Detailed Design ................................................................................................................................. 4285.8.1 Coping ....................................................................................................................................4285.8.2 Fitting of Tie Rods and Wale to Sheet Piles ...........................................................................4295.8.3 Tie Rod ...................................................................................................................................4295.8.4 Fitting of Tie Rods to Anchorage Work...................................................................................4295.9 Special Notes for Design of Sheet Pile Wall on Soft Ground.....................................................429Chapter 6 Sheet Pile Quaywalls with Relieving Platform .................................................................................4316.1 Scope of Application.........................................................................................................................4316.2 Principles of Design ..........................................................................................................................4316.3 Determination of Height and Width of Relieving Platform ..........................................................4316.4 Earth Pressure and Residual Water Pressure Acting on Sheet Piles ......................................4326.5 Design of Sheet Pile Wall ................................................................................................................4326.5.1 Embedded Length of Sheet Piles ...........................................................................................4326.5.2 Cross Section of Sheet Piles ..................................................................................................4336.6 Design of Relieving Platform and Relieving Platform Piles........................................................4336.6.1 External Forces Acting on Relieving Platform ........................................................................4336.6.2 Design of Relieving Platform ..................................................................................................4336.6.3 Design of Piles........................................................................................................................434
    • CONTENTS-xiii-6.7 Examination of Stability as Gravity Type Wall ..............................................................................4346.8 Examination of Stability against Circular Slip................................................................................435Chapter 7 Steel Sheet Pile Cellular-Bulkhead Quaywalls ................................................................................4367.1 Principle of Design ............................................................................................................................4367.2 External Forces Acting on Steel Sheet Pile Cellular-Bulkhead Quaywall ................................4377.3 Examination of Wall Width against Shear Deformation ..............................................................4387.3.1 General ...................................................................................................................................4387.3.2 Equivalent Width of Wall .........................................................................................................4397.3.3 Calculation of Deformation Moment........................................................................................4397.3.4 Calculation of Resisting Moment.............................................................................................4407.4 Examination of Stability of Wall Body as a Whole........................................................................4437.4.1 General ...................................................................................................................................4437.4.2 Modulus of Subgrade Reaction...............................................................................................4437.4.3 Calculation of Subgrade Reaction and Wall Displacement.....................................................4437.5 Examination of Bearing Capacity of the Ground ..........................................................................4487.6 Examination against Sliding of Wall ...............................................................................................4487.7 Examination of Displacement of Wall Top.....................................................................................4487.8 Examination of Stability against Circular Slip................................................................................4497.9 Layout of Cells and Arcs ..................................................................................................................4497.10 Calculation of Hoop Tension............................................................................................................4497.11 Design of T-Shaped Sheet Pile.......................................................................................................4507.11.1 General ...................................................................................................................................4507.11.2 Structure of T-Shaped Sheet Pile ...........................................................................................4507.12 Detailed Design..................................................................................................................................4517.12.1 Design of Pile to Support Coping............................................................................................4517.12.2 Design of Coping.....................................................................................................................451Chapter 8 Steel Plate Cellular-Bulkhead Quaywalls ..........................................................................................4528.1 Scope of Application .........................................................................................................................4528.2 Placement-Type Steel Plate Cellular-Bulkhead Quaywalls........................................................4528.2.1 Principle of Design ..................................................................................................................4528.2.2 External Forces Acting on Steel Plate Cellular-Bulkhead .......................................................4538.2.3 Examination of Wall Width against Shear Deformation ..........................................................4538.2.4 Examination of Stability of Wall Body as a Whole...................................................................4548.2.5 Examination of Bearing Capacity of the Ground.....................................................................4558.2.6 Examination of Stability against Circular Slip..........................................................................4558.2.7 Determination of Thickness of Steel Plate of Cell Shell..........................................................4558.2.8 Layout of Cells and Arcs .........................................................................................................4568.2.9 Detailed Design.......................................................................................................................4568.3 Embedded-Type Steel Plate Cellular-Bulkhead Quaywalls........................................................4568.3.1 Principle of Design ..................................................................................................................4568.3.2 External Forces Acting on Embedded-Type Steel Plate Celluler-Bulkhead............................4578.3.3 Examination of Wall Width against Shear Deformation ..........................................................4578.3.4 Examination of Stability of Wall Body as a Whole...................................................................4588.3.5 Examination of Bearing Capacity of the Ground.....................................................................4588.3.6 Examination against Sliding of Wall........................................................................................4588.3.7 Examination of Displacement of Wall Top ..............................................................................4588.3.8 Examination of Stability against Circular Slip..........................................................................4588.3.9 Layout of Cells and Arcs .........................................................................................................4588.3.10 Determination of Plate Thickness of Cell Shell and Arc Section.............................................4588.3.11 Joints and Stiffeners................................................................................................................4598.3.12 Detailed Design.......................................................................................................................459Chapter 9 Open-Type Wharves on Vertical Piles................................................................................................4609.1 Principle of Design ............................................................................................................................4609.2 Layout and Dimensions....................................................................................................................4629.2.1 Size of Deck Block and Layout of Piles...................................................................................4629.2.2 Dimensions of Superstructure.................................................................................................4629.2.3 Arrangement of Fenders and Bollards ....................................................................................4639.3 External Forces Acting on Open-Type Wharf...............................................................................4639.3.1 Design External Forces...........................................................................................................4639.3.2 Calculation of Fender Reaction Force.....................................................................................4649.4 Assumptions Concerning Sea Bottom Ground.............................................................................4649.4.1 Determination of Slope Inclination ..........................................................................................4649.4.2 Virtual Ground Surface............................................................................................................4659.5 Design of Piles ...................................................................................................................................465
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-xiv-9.5.1 General ...................................................................................................................................4659.5.2 Coefficient of Horizontal Subgrade Reaction..........................................................................4659.5.3 Virtual Fixed Point...................................................................................................................4669.5.4 Member Forces Acting on Individual Piles..............................................................................4669.5.5 Cross-Sectional Stresses of Piles...........................................................................................4689.5.6 Examination of Embedded Length for Bearing Capacity ........................................................4689.5.7 Examination of Embedded Length for Lateral Resistance......................................................4689.5.8 Examination of Pile Joints.......................................................................................................4689.5.9 Change of Plate Thickness or Material of Steel Pipe Pile ......................................................4689.6 Examination of Earthquake-Resistant Performance ...................................................................4699.6.1 Assumption of Cross Section for Earthquake-Resistant Performance Examination ..............4709.6.2 Examination Method of Earthquake-Resistant Performance..................................................4709.6.3 Determination of Seismic Motion for Examination of Earthquake-Resistant Performance.....4719.6.4 Examination of Load Carrying Capacity Using Simplified Method..........................................4739.6.5 Examination of Load Carrying Capacity Using Elasto-Plastic Analysis .................................. 4759.7 Design of Earth-Retaining Section .................................................................................................4779.8 Examination of Stability against Circular Slip ............................................................................... 4779.9 Detailed Design ................................................................................................................................. 4789.9.1 Load Combinations for Superstructure Design.......................................................................4789.9.2 Calculation of Reinforcing Bar Arrangement of Superstructure..............................................4789.9.3 Design of Pile Head ................................................................................................................478Chapter 10 Open-Type Wharves on Coupled Raking Piles............................................................................... 48010.1 Principle of Design............................................................................................................................ 48010.2 Layout and Dimensions....................................................................................................................48110.2.1 Size of Deck Block and Layout of Piles ..................................................................................48110.2.2 Dimensions of Supersutructure ..............................................................................................48110.2.3 Arrangement of Fenders and Bollards....................................................................................48110.3 External Forces Acting on Open-Type Wharf on Coupled Raking Piles.................................. 48110.3.1 Design External Forces ..........................................................................................................48110.3.2 Calculation of Fender Reaction Force ....................................................................................48110.4 Assumptions Concerning Sea Bottom Ground.............................................................................48110.4.1 Determination of Slope Inclination .......................................................................................... 48110.4.2 Virtual Ground Surface ........................................................................................................... 48110.5 Determination of Forces Acting on Piles and Cross Sections of Piles .....................................48110.5.1 Horizontal Force Transmitted to Heads of Coupled Raking Piles...........................................48110.5.2 Vertical Load Transmitted to Heads of Coupled Raking Piles ................................................48310.5.3 Pushing-In and Pulling-Out Forces of Coupled Raking Piles .................................................48310.5.4 Cross-Sectional Stresses of Piles...........................................................................................48310.6 Examination of Strength of Wharf in the Direction of Its Face Line ..........................................48410.7 Embedded Length of Raking Pile...................................................................................................48410.8 Design of Earth-Retaining Section .................................................................................................48410.9 Examination of Stability against Circular Slip ............................................................................... 48410.10 Detailed Design ................................................................................................................................. 484Chapter 11 Detached Pier.............................................................................................................................................48511.1 Scope of Application.........................................................................................................................48511.2 Principle of Design............................................................................................................................ 48511.3 Design of Detached Pier ..................................................................................................................48511.3.1 Layout and Dimensions ..........................................................................................................48511.3.2 External Forces and Loads.....................................................................................................48511.3.3 Design of Piers .......................................................................................................................48611.3.4 Design of Girder...................................................................................................................... 48611.4 Ancillary Equipment..........................................................................................................................48611.5 Detailed Design ................................................................................................................................. 48611.5.1 Superstructure ........................................................................................................................48611.5.2 Gangways..............................................................................................................................486Chapter 12 Floating Piers..............................................................................................................................................48712.1 Scope of Application.........................................................................................................................48712.2 Principle of Design............................................................................................................................ 48812.3 Design of Pontoon.............................................................................................................................48812.3.1 Dimensions of Pontoon........................................................................................................... 48812.3.2 External Forces and Loads Acting on Pontoon ......................................................................48812.3.3 Stability of Pontoon................................................................................................................. 48812.3.4 Design of Individual Parts of Pontoon..................................................................................... 48912.4 Design of Mooring System...............................................................................................................490
    • CONTENTS-xv-12.4.1 Mooring Method ......................................................................................................................49012.4.2 Design of Mooring Chain.........................................................................................................490[1] Design External Forces....................................................................................................490[2] Setting of Chain................................................................................................................490[3] Diameter of Chain ............................................................................................................49012.4.3 Design of Mooring Anchor.......................................................................................................492[1] Design External Forces....................................................................................................492[2] Design of Mooring Anchor................................................................................................49212.5 Design of Access Bridge and Gangway ........................................................................................49212.5.1 Dimensions and Inclination .....................................................................................................49212.5.2 Design of Access Bridge and Gangway..................................................................................49312.5.3 Adjusting Tower ......................................................................................................................493Chapter 13 Dolphins........................................................................................................................................................49413.1 Principle of Design ............................................................................................................................49413.2 Layout..................................................................................................................................................49413.3 External Forces Acting on Dolphins ...............................................................................................49513.4 Pile Type Dolphins ............................................................................................................................49513.5 Steel Cellular-Bulkhead Type Dolphins .........................................................................................49513.6 Caisson Type Dolphins.....................................................................................................................496Chapter 14 Slipways and Shallow Draft Quays......................................................................................................49714.1 Slipways..............................................................................................................................................49714.1.1 Principle of Design ..................................................................................................................49714.1.2 Location of Slipway .................................................................................................................49714.1.3 Dimensions of Individual Parts................................................................................................497[1] Elevations of Individual Parts ...........................................................................................497[2] Slipway Length and Background Space...........................................................................498[3] Water Depth .....................................................................................................................498[4] Gradient of Slipway ..........................................................................................................498[5] Basin Area........................................................................................................................49814.1.4 Front Wall and Pavement........................................................................................................499[1] Front Wall.........................................................................................................................499[2] Pavement .........................................................................................................................49914.2 Shallow Draft Quay ...........................................................................................................................499Chapter 15 Air-Cushion Vehicle Landing Facilities ...............................................................................................50015.1 Principle of Design ............................................................................................................................50015.2 Location...............................................................................................................................................50115.3 Air-Cushion Vehicle Landing Facilities...........................................................................................50115.4 Dimensions of Individual Parts........................................................................................................501Chapter 16 Mooring Buoys and Mooring Posts......................................................................................................50216.1 Mooring Buoys ...................................................................................................................................50216.1.1 Principle of Design ..................................................................................................................50216.1.2 Tractive Force Acting on Mooring Buoy..................................................................................50316.1.3 Design of Individual Parts of Mooring Buoy ............................................................................504[1] Mooring Anchor................................................................................................................504[2] Sinker and Sinker Chain...................................................................................................504[3] Ground Chain...................................................................................................................505[4] Main Chain .......................................................................................................................506[5] Floating Body ...................................................................................................................50716.2 Mooring Posts ....................................................................................................................................507Chapter 17 Other Types of Mooring Facilities.........................................................................................................50817.1 Quaywall of Wave-Absorbing Type ................................................................................................50817.1.1 Principle of Design ..................................................................................................................50817.1.2 Determination of Structural Form............................................................................................50817.2 Cantilever Sheet Pile Quaywall.......................................................................................................50917.2.1 Principle of Design ..................................................................................................................50917.2.2 External Forces Acting on Sheet Pile Wall..............................................................................51017.2.3 Determination of Cross Section of Sheet Piles .......................................................................51117.2.4 Determination of Embedded Length of Sheet Piles ................................................................51117.2.5 Examination of Displacement of Sheet Pile Crown.................................................................51117.2.6 External Forces during Construction.......................................................................................51217.2.7 Detailed Design.......................................................................................................................51217.3 Sheet Pile Quaywall with Batter Anchor Piles ..............................................................................51217.3.1 Principle of Design ..................................................................................................................512
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-xvi-17.3.2 External Forces Acting on Sheet Pile Wall with Batter Anchor Piles ......................................51317.3.3 Calculation of Horizontal and Vertical Forces Acting on Connecting Point ............................51317.3.4 Determination of Cross Sections of Sheet Pile and Batter Anchor Pile.................................. 51317.3.5 Determination of Embedded Lengths of Sheet Pile and Batter Anchor Pile...........................51317.3.6 Detailed Design ...................................................................................................................... 51317.4 Sheet Pile Quaywall with Batter Piles in Front .............................................................................51417.4.1 Principle of Design..................................................................................................................51417.4.2 Layout and Dimensions ..........................................................................................................51517.4.3 Design of Sheet Pile Wall .......................................................................................................51517.4.4 Design of Open-Type Superstructure ..................................................................................... 51517.4.5 Embedded Length ..................................................................................................................51617.4.6 Detailed Design ...................................................................................................................... 51617.5 Double Sheet Pile Quaywall............................................................................................................51617.5.1 Principle of Design..................................................................................................................51617.5.2 External Forces Acting on Double Sheet Pile Quaywall ......................................................... 51717.5.3 Design of Double Sheet Pile Quaywall ...................................................................................517Chapter 18 Transitional Parts of Quaywalls ............................................................................................................51918.1 Principle of Design............................................................................................................................ 51918.2 Transitional Part Where Frontal Water Depth Varies..................................................................51918.3 Transitional Part Where Quaywalls of Different Type Are Connected .....................................51918.4 Outward Projecting Corner..............................................................................................................519Chapter 19 Ancillary Facilities...................................................................................................................................... 52019.1 General ...............................................................................................................................................52019.2 Mooring Equipment...........................................................................................................................52019.3 Mooring Posts, Bollards, and Mooring Rings ............................................................................... 52019.3.1 General ...................................................................................................................................52019.3.2 Arrangement of Mooring Posts, Bollards and Mooring Rings.................................................52119.3.3 Tractive Force of Vessel .........................................................................................................52119.3.4 Structure ................................................................................................................................. 52219.4 Fender System ..................................................................................................................................52219.4.1 General ...................................................................................................................................52219.4.2 Arrangement of Fenders.........................................................................................................52319.4.3 Berthing Energy of Vessel ......................................................................................................52319.4.4 Selection of Fender................................................................................................................. 52319.5 Safety Facilities ................................................................................................................................. 52519.5.1 General ...................................................................................................................................52519.5.2 Skirt Guard..............................................................................................................................52519.5.3 Fence and Rope .....................................................................................................................52519.5.4 Signs or Notices...................................................................................................................... 52519.5.5 Curbing ...................................................................................................................................52519.5.6 Fire Fighting Equipment and Alarm Systems ......................................................................... 52519.6 Service Facilities ...............................................................................................................................52519.6.1 General ...................................................................................................................................52519.6.2 Lighting Facilities ....................................................................................................................52519.6.3 Facilities for Passenger Embarkation and Disembarkation ....................................................52519.6.4 Vehicle Ramp .........................................................................................................................52619.6.5 Water Supply Facilities ........................................................................................................... 52619.6.6 Drainage Facilities ..................................................................................................................52619.6.7 Fueling and Electric Power Supply Facilities ..........................................................................52619.6.8 Signs or Notices...................................................................................................................... 52719.7 Stairways and Ladders.....................................................................................................................52719.8 Lifesaving Facilities...........................................................................................................................52719.9 Curbing ...............................................................................................................................................52719.10 Vehicle Ramp.....................................................................................................................................52719.11 Signs, Notices and Protective Fences...........................................................................................52719.11.1 General ...................................................................................................................................52719.11.2 Provision of Signs ...................................................................................................................52719.11.3 Types and Location of Signs ..................................................................................................52819.11.4 Position of Sign.......................................................................................................................52819.11.5 Structure of Sign .....................................................................................................................52919.11.6 Materials ................................................................................................................................. 53019.11.7 Maintenance and Management ..............................................................................................53019.11.8 Protective Fences ...................................................................................................................53019.11.9 Barricades...............................................................................................................................531
    • CONTENTS-xvii-19.12 Lighting Facilities ...............................................................................................................................53119.12.1 General ...................................................................................................................................53119.12.2 Standard Intensity of Illumination............................................................................................531[1] Definition ..........................................................................................................................531[2] Standard Intensity of Illumination for Outdoor Lighting ....................................................531[3] Standard Intensity of Illumination for Indoor Lighting .......................................................53219.12.3 Selection of Light Source ........................................................................................................53219.12.4 Selection of Lighting Equipment..............................................................................................534[1] Outdoor Lighting...............................................................................................................534[2] Indoor Lighting..................................................................................................................53419.12.5 Design of Lighting ...................................................................................................................53519.12.6 Maintenance and Management...............................................................................................537[1] Inspections .......................................................................................................................537[2] Cleaning and Repair.........................................................................................................538Chapter 20 Aprons ...........................................................................................................................................................54020.1 Principle of Design ............................................................................................................................54020.2 Type of Apron.....................................................................................................................................54020.2.1 Width ......................................................................................................................................54020.2.2 Gradient ..................................................................................................................................54020.2.3 Type of Pavement...................................................................................................................54020.3 Countermeasures against Settlement of Apron............................................................................54020.4 Load Conditions.................................................................................................................................54120.5 Design of Concrete Pavement ........................................................................................................54120.5.1 Design Conditions...................................................................................................................54120.5.2 Composition of Pavement.......................................................................................................54220.5.3 Joints.......................................................................................................................................54520.5.4 Tie-Bar and Slip-Bar................................................................................................................54720.5.5 End Protection.........................................................................................................................54720.6 Design of Asphalt Pavement ...........................................................................................................54720.6.1 Design Conditions...................................................................................................................54720.6.2 Composition of Pavement.......................................................................................................54820.6.3 End Protection.........................................................................................................................55120.7 Design of Concrete Block Pavement..............................................................................................55120.7.1 Design Conditions...................................................................................................................55120.7.2 Composition of Pavement.......................................................................................................55220.7.3 Joints.......................................................................................................................................553Chapter 21 Foundation for Cargo Handling Equipment.......................................................................................55421.1 Principle of Design ............................................................................................................................55421.2 External Forces Acting on Foundation...........................................................................................55421.3 Design of Foundation with Piles......................................................................................................55521.3.1 Concrete Beam .......................................................................................................................55521.3.2 Bearing Capacity of Piles........................................................................................................55521.4 Design of Foundation without Piles ................................................................................................55621.4.1 Examination of Effects on Wharf.............................................................................................55621.4.2 Concrete Beam .......................................................................................................................556Part IX Other Port FacilitiesChapter 1 Port Traffic Facilities .................................................................................................................................5591.1 General................................................................................................................................................5591.1.1 Scope of Application ...............................................................................................................5591.1.2 Operation and Maintenance of Facilities for Land Traffic........................................................5591.2 Roads ..................................................................................................................................................5591.2.1 General ...................................................................................................................................5591.2.2 Design Vehicles ......................................................................................................................5591.2.3 Roadways and Lanes..............................................................................................................5591.2.4 Clearance Limit .......................................................................................................................5601.2.5 Widening of Roads at Bends...................................................................................................5611.2.6 Longitudinal Slope...................................................................................................................5611.2.7 Level Crossings.......................................................................................................................5621.2.8 Pavement................................................................................................................................5621.2.9 Signs .......................................................................................................................................5631.3 Car Parks............................................................................................................................................5641.3.1 General ...................................................................................................................................564
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-xviii-1.3.2 Size and Location ...................................................................................................................5641.4 Railways .............................................................................................................................................5671.5 Heliports..............................................................................................................................................5671.6 Tunnels ...............................................................................................................................................5671.6.1 General ...................................................................................................................................5671.6.2 Principle of Planning and Design............................................................................................5671.6.3 Depth of Immersion ................................................................................................................5681.6.4 Structure and Length of Immersed Tunnel Elements .............................................................5681.6.5 Ventilation Towers ..................................................................................................................5681.6.6 Access Roads.........................................................................................................................5691.6.7 Calculation of Stability of Immersed Tunnel Section .............................................................. 5691.6.8 Design of Immersed Tunnel Elements....................................................................................5691.6.9 Joints ...................................................................................................................................... 5701.6.10 Control and Operation Facilities .............................................................................................5701.7 Bridges................................................................................................................................................5701.7.1 General ...................................................................................................................................5701.7.2 Design Requirements .............................................................................................................5701.7.3 Structural Durability ................................................................................................................5711.7.4 Fender System .......................................................................................................................571Chapter 2 Cargo Sorting Facilities ...........................................................................................................................5732.1 General ...............................................................................................................................................5732.2 Cargo Sorting Areas .........................................................................................................................5732.3 Quay Sheds .......................................................................................................................................5732.4 Cargo Handling Equipment .............................................................................................................5732.4.1 General ...................................................................................................................................5732.4.2 Oil Handling Equipment..........................................................................................................5742.4.3 Operation and Maintenance of Cargo Handling Equipment ................................................... 5742.5 Timber Sorting Areas........................................................................................................................5742.6 Sorting Facilities for Marine Products ............................................................................................5752.7 Sorting Facilities for Hazardous Cargo.......................................................................................... 575Chapter 3 Storage Facilities.......................................................................................................................................5763.1 General ...............................................................................................................................................5763.2 Yards for Dangerous Cargo and Oil Storage Facilities...............................................................5763.3 Other Storage Facilities....................................................................................................................576Chapter 4 Facilities for Ship Services .....................................................................................................................5774.1 General ...............................................................................................................................................5774.2 Water Supply Facilities.....................................................................................................................577Chapter 5 Facilities for Passenger...........................................................................................................................5785.1 Facilities for Passenger Boarding...................................................................................................5785.1.1 General ...................................................................................................................................5785.1.2 Structural Types...................................................................................................................... 5785.1.3 Design of Facilities for Passenger Boarding...........................................................................5785.1.4 Ancillary Facilities ...................................................................................................................5785.2 Passenger Building...........................................................................................................................5795.2.1 General ...................................................................................................................................5795.2.2 Design of Passenger Buildings...............................................................................................5795.2.3 Ancillary Facilities ...................................................................................................................579Part X Special Purpose WharvesChapter 1 Container Terminals ................................................................................................................................. 5811.1 Principle of Design............................................................................................................................ 5811.2 Design of Mooring Facilities ............................................................................................................5821.2.1 Length and Water Depth of Berths .........................................................................................5821.2.2 Mooring Equipment................................................................................................................. 5821.2.3 Fender System .......................................................................................................................5831.3 Design of Land Facilities..................................................................................................................5831.3.1 Apron ...................................................................................................................................... 5831.3.2 Container Cranes....................................................................................................................5831.3.3 Container Yard........................................................................................................................5831.3.4 Container Freight Station........................................................................................................5831.3.5 Maintenance Shop..................................................................................................................583
    • CONTENTS-xix-1.3.6 Administration Building............................................................................................................5831.3.7 Gates.......................................................................................................................................5831.3.8 Ancillary Facilities....................................................................................................................583Chapter 2 Ferry Terminals ..........................................................................................................................................5842.1 Principle of Design ............................................................................................................................5842.2 Design of Mooring Facilities.............................................................................................................5852.2.1 Length and Water Depth of Berths..........................................................................................5852.2.2 Mooring Equipment.................................................................................................................5852.2.3 Fender System........................................................................................................................5862.2.4 Protection Works against Scouring.........................................................................................5862.3 Design of Vehicle Ramp...................................................................................................................5862.3.1 Width, Length, Gradient, and Radius of Curvature .................................................................5862.3.2 Ancillary Facilities and Signs...................................................................................................5862.3.3 Design of Moving Parts...........................................................................................................5862.4 Facilities for Passenger Boarding...................................................................................................5862.4.1 Width, Length, Gradient, and Ancillary Facilities.....................................................................5872.4.2 Design of Moving Parts...........................................................................................................5872.5 Design of Other Facilities.................................................................................................................5872.5.1 Roads......................................................................................................................................5872.5.2 Passageways..........................................................................................................................5872.5.3 Car Parks ................................................................................................................................5872.5.4 Passenger Terminals ..............................................................................................................5882.5.5 Safety Equipment....................................................................................................................588Part XI MarinasChapter 1 Introduction..................................................................................................................................................589Chapter 2 Main Dimensions of Target Boats ........................................................................................................590Chapter 3 Navigation Channels and Basins..........................................................................................................5913.1 General................................................................................................................................................5913.2 Navigation Channels.........................................................................................................................5913.3 Mooring Basins ..................................................................................................................................591Chapter 4 Protective Facilities ...................................................................................................................................592Chapter 5 Mooring Facilities.......................................................................................................................................5935.1 General................................................................................................................................................5935.2 Design Conditions for Mooring Facilities .......................................................................................5935.3 Floating Piers .....................................................................................................................................5955.3.1 General ...................................................................................................................................5955.3.2 Structure..................................................................................................................................5955.3.3 Examination of Safety .............................................................................................................5955.3.4 Structural Design.....................................................................................................................5965.3.5 Mooring Method ......................................................................................................................5965.3.6 Access Bridges .......................................................................................................................5965.4 Ancillary Facilities..............................................................................................................................5975.5 Lifting / Lowering Frame Facilities ..................................................................................................597Chapter 6 Facilities for Ship Services......................................................................................................................5986.1 General................................................................................................................................................5986.2 Land Storage Facilities .....................................................................................................................598Chapter 7 Land Traffic Facilities................................................................................................................................599INDEX
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-xx-
    • Part I General
    • PART I GENERAL-1-Part I GeneralChapter 1 General Rules1.1 Scope of ApplicationThe Ministerial Ordinance stipulating the Technical Standards for Port and Harbour Facilities(Ministry of Transport Ordinance No. 30, 1974; hereafter referred to simply as the Ministerial Ordinance)and the Notification stipulating the Details of Technical Standards for Port and Harbour Facilities(Ministry of Transport Notification No. 181, 1999; hereafter referred to simply as the Notification), both ofwhich have been issued in line with Article 56-2 of the “Port and Harbour Law”, shall be applied to theconstruction, improvement, and maintenance of port and harbor facilities.[Commentary](1) The Ministerial Ordinance and the Notification (hereafter collectively referred to as the Technical Standards)apply not to the port and harbor facilities stipulated in Article 2 of the “Port and Harbour Law”, but rather tothe port and harbor facilities stipulated in Article 19 of the Port and Harbour Law Enforcement Order.Accordingly the Technical Standards also apply to facilities like navigation channels, basins, protectivefacilities and mooring facilities of the marinas and privately owned ports, which are found in outside of thelegally designated port areas.(2) Since the Technical Standards covers a wide rage of facilities, there will be cases where the items shown in theTechnical Standards may be inadequate for dealing with planning, designing, constructing, maintaining orrepairing of a particular individual structure of a port or harbor. There is also possibility that new items may beadded in the future in line with technical developments or innovations. With regard to matters for which thereare no stipulations in the Technical Standards, appropriate methods other than those mentioned in the TechnicalStandards may be adopted, after confirming the safety of a structure in consideration using appropriate methodssuch as model tests or trustworthy numerical calculations (following the main items of the Technical Standards).(3) Figure C- 1.1.1 shows the statutory structure of the Technical Standards.Fig. C- 1.1.1 Statutory Structure of the Technical Standards for Port and Harbour Facilities(4) This document is intended to help individuals concerned with correct interpretation of the Technical Standardsand to facilitate right application of the Ministerial Ordinance and the Notification. This document is made up ofthe main items, along with reference sections marked Commentary and Technical Notes, which supplementthe main items. The texts in large letters are the main items that describe the parts of the Notification and thebasic items that must be obeyed, regarding the items related to the Notification. The sections markedCommentary mainly give the background to and the basis for the Notification, etc. The sections markedTechnical Notes provide investigation methods and/or standards that will be of reference value, when executingactual design works, specific examples of structures, and other related materials.(5) Design methods can be broadly classified into the methods that use the safety factors and the methods that usethe indices based on probability theory, according to the way of judging the safety of structures.A safety factor is not an index that represents the degree of safety quantitatively. Rather, it is determinedthrough experience to compensate for the uncertainty in a variety of factors. In this document, the safety factorsindicate values that are considered by experience to be sufficiently safe under standard conditions. Dependingon the conditions, it may be acceptable to lower the values of safety factors, but when doing so it is necessary tomake a decision using prudent judgement based on sound reasoning.In the case that the probability distributions of loads and structure strengths can be adequately approximated,it is possible to use a reliability design method. Unlike the more traditional design methods in which safetyfactors are used, a reliability design method makes it possible to gain a quantitative understanding of thePort and Harbour Law Enforcement Order Port and Harbour Law EnforcementRegulationsThe NotificationPort and Harbour Law[Article 56-2](technical standards forport and harbour facilities)Port and Harbour LawEnforcement Order[Article 19](stipulation of facilities covered)Port and Harbour LawEnforcement Regulations[Article 28](stipulation of facilities excludedfrom coverage)The Technical StandardsThe Ministerial Ordinance
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-2-likelihood of the failure of structure in question and then to keep the likelihood below a certain allowable value.With a reliability design method, design is carried out by using the partial safety factors and reliability indices.Formally speaking, the limit state design method can be classified as one form of reliability design method.1.2 DefinitionsThe terms used in the Notification are based on the terminology used in the Ministerial Ordinance; inaddition, the meanings of the following terms as stipulated in the law or notification are cited.(1) Dangerous articles: This term refers to those that are designated in the Notification stipulating the“Types of Hazardous Goods” for the “Port Regulation Law Enforcement Regulations” (Ministryof Transport Notification No. 547, 1979).(2) Datum level for construction work: This is the standard water level used when constructing,improving or maintaining port and harbor facilities, and is equal to the chart datum level (specificallythe chart datum for which the height is determined based on the provisions of Article 9 (8) of the“Law for Hydrographic Activities” (Law No. 102, 1950)). However, in the case of port and harborfacilities in lakes and rivers for which there is little tidal influence, in order to ensure the safe use ofthe port or harbor in question, the datum level for construction work shall be determined whileconsidering the conditions of extremely low water level that may occur during a drought season.[Commentary]In addition to the terms defined above, the meanings of the following terms are listed below.(1) Super-large vessel: A cargo ship with a deadweight tonnage of 100,000 t or more, except in the case of LPGcarriers and LNG carriers, in which case the gross tonnage is 25,000 t or more.(2) Passenger ship: A vessel with a capacity of 13 or more passengers.(3) Pleasure boat: A yacht, motorboat or other vessel used for sport or recreation.1.3 Usage of SI Units[Commentary]In line with the provisions in the “Measurement Law” (Law No. 51, May 20, 1992), with the aim of executing asmooth switchover to SI units, the Ministry of Agriculture, Forestry and Fisheries, the Ministry of Transport and theMinistry of Construction have concluded to use the International System of Units in their public work projectsstarting from April 1999.
    • PART I GENERAL-3-Table C- 1.3.1 Conversion Factors from Conventional Units to SI UnitsNumber Quantity Non-SI units SI units Conversion factor1 Length µ m 1µ = 1µm2 Mass kgf•s2/m kg 1kgf•s2/m = 9.80665kg3 Acceleration Gal m/s2 1Gal = 0.01m/s24Forcekgf N 1kgf = 9.80665N5 dyn N 1dyn = 10µN6 Moment of a force kgf•m N•m 1kgf•m = 9.80665N•m7Pressurekgf/cm2PaN/mm21kgf/cm2= 9.80665 × 104Pa= 9.80665 × 10-2MPa1kgf/cm2= 9.80665 × 10-2N/mm28 mHg Pa 1mHg = 133.322kPa9 Stress kgf/cm2PaN/mm21kgf/cm2= 9.80665 × 104Pa= 9.80665 × 10-2MPa1kgf/cm2= 9.80665 × 10-2N/mm210Work (energy)kgf•m J 1kfg•m = 9.80665J11 erg J 1erg = 100nJ12 PowerPSHPW1PS = 735.499W1HP = 746.101W13 Quantity of heat calJW•s1cal = 4.18605J1cal = 4.18605W•s14Thermalconductivitycal/(h•m•ºC) W/(m•ºC)1cal/(h•m•ºC)= 0.001163W/(m•ºC)15Heat conductioncoefficientcal/(h•m2•ºC) W/(m2•ºC)1cal/(h•m2•ºC)= 0.001163W/(m2•ºC)16Specific heatcapacitycal/(kg•ºC) J/(kg•ºC)1cal/(kg•ºC)= 4.18605J/(kg•ºC)17 Sound pressure level - dB 1phon = 1dB
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-4-Chapter 2 Datum Level for Construction Work[Commentary]The datum level for port and harbor construction work is the standard water level that shall form the basisfor the planning, design, and construction of facilities. The chart datum level shall be used as the datumlevel for construction work.[Technical Notes](1) Chart Datum LevelThe chart datum level is set as the level below the mean sea level by the amount equal to or approximatelyequivalent to the sum of the amplitueds of the four major tidal constituents (M2, S2, K1, and O1 tides), which areobtained from the harmonic analysis of tidal observation data. Here M2 is the principal lunar semi-diurnal tide,S2 is the principal solar semi-diurnal tide, K1 is the luni-solar diurnal tide, and O1 is the principal lunar diurnaltide.Note that the heights of rocks or land marks shown on the nautical charts are the elevation above the meansea level, which is the long-term average of the hourly sea surface height at the place in question. (In the casethat the observation period is short, however, corrections for seasonal fluctuations should be made whendetermining the mean sea level.) The difference in height between the chart datum level and the mean sea levelis referred to as Z0.(2) International Marine Chart DatumThe International Hydrographic Organization (IHO) has decided to adopt the Lowest Astronomical Tide (LAT)as the international marine chart datum, and issued a recommendation to this effect to the HydrographicDepartments in various countries throughout the world in June 1997. The LAT is defined as the lowest sea levelthat is assumed to occur under the combination of average weather conditions and generally conceivableastronomical conditions. In actual practice, tide levels for at least 19 years are calculated using harmonicconstants obtained from at least one year’s worth of observations, and then the lowest water level is taken as theLAT.However, in the case of Japan, the chart datum level is obtained using the old method described in (1) above(approximate lowest water level). There will be no switchover to the LAT in the near future in Japan, but it isplanned to meet the IHO recommendation by stating the difference between the LAT and the chart datum levelin tide tables published by the Hydrographic Department of Maritime Safety Agency, Ministry of Land,Infrastructure, and Transport, Japan.
    • PART I GENERAL-5-Chapter 3 MaintenanceIn order to maintain the functions of port and harbor facilities at a satisfactory service level and to preventdeterioration in the safety of such facilities, comprehensive maintenance including inspections,evaluations, repairs, etc. shall be carried out, in line with the specific characteristics of the port or harbor inquestion.[Commentary](1) “Maintenance” refers to a system consisting of a series of linked activities involving the efficient detection ofchanges in the state of serviceability of the facilities and the execution of effective measures such as rationalevaluation, repair, and reinforcement.(2) Port and harbor facilities must generally remain in service for long periods of time, during which the functionsdemanded of the facilities must be maintained. It is thus essential not only to give due consideration wheninitially designing the structures in question, but also to carry out proper maintenance after the facilities havebeen put into service.(3) A whole variety of data concerning maintenance (specifically, inspections, checks, evaluations, repair,reinforcement work, etc.) must be recorded and stored in a standard format. Maintenance data kept in goodsystematic order is the basic information necessary for carrying out appropriate evaluation of the level ofsoundness of the facilities in question, and executing their maintenance and repairs. At the same time themaintenace data is useful when taking measures against the deterioration of the facilities as a whole and wheninvestigating the possibility in the life cycle cost reduction of the facilities.(4) When designing a structure, it is necessary to give due consideration to the system of future maintenance and toselect the types of structures and the materials used so that future maintenance will be easily executed, whilereflecting this aspect in the detailed design.•[Technical Notes](1) The concepts of the terms relating to maintenance are as follows:(2) With regard to the procedure for maintenance, it is a good idea to draw up a maintenance plan for each structurewhile considering factors like the structural form, the tendency to deteriorate and the degree of importance, andthen to implement maintenance work based on this plan.(3) For basic and common matters concerning maintenance, refer to the “Manual for Maintenance and Repair ofPort and Harbor Structures”.MaintenanceInspection / checking:• • • •Activities to investigate the state of a structure, the situationregarding damage and the remaining level of function, along withrelated administrative work: mainly composed of periodic andspecial inspectionsEvaluation: • • • • • • • • • • • • • • • Evaluation of the level of soundness based on the results ofinspection / checking, and judgement of the necessity or otherwiseof repairs etc.Maintenance: • • • • • • • • • • • • •Activities carried out with the aim of holding back the physicaldeterioration of a structure and keeping its function withinacceptable levels.Repair / reinforcement: • • Activities in which a structure that has deteriorated physically and/or functionally is partially reconstructed in order to restore therequired function and/or structure.
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-6-
    • Part II Design Conditions
    • PART II DESIGN CONDITIONS-7-Part II Design ConditionsChapter 1 GeneralIn designing port and harbor facilities, the design conditions shall be chosen from the items listed below bytaking into consideration the natural, service and construction conditions, the characteristics of materials,the environmental impacts, and the social requirements for the facilities.(1) Ship dimensions(2) External forces produced by ships(3) Winds and wind pressure(4) Waves and wave force(5) Tide and extraordinary sea levels(6) Currents and current force(7) External forces acting on floating structures and their motions(8) Estuarine hydraulics and littoral drift(9) Subsoil(10) Earthquakes and seismic force(11) Liquefaction(12) Earth pressure and water pressure(13) Deadweight and surcharge(14) Coefficient of friction(15) Other necessary design conditions[Commentary]The design conditions should be determined carefully, because they exercise great influence upon the safety,functions, and construction cost of the facilities. The design conditions listed above are just those that have a largeinfluence on port and harbor facilities. They are generally determined according to the results of surveys and tests.Thus, the design conditions should be precisely determined upon full understanding of the methods and results ofsuch investigations and tests. In the case of temporary structures, the design conditions may be determined whileconsidering also the length of service life.[Technical Notes](1) In designing port and harbor facilities, the following matters should be taken into consideration.(a) Functions of the facilitiesSince facilities often have multiple functions, care should be exercised so that all functions of the facilities willbe exploited fully.(b) Importance of the facilitiesThe degree of importance of the facilities should be considered in order to design the facilities by takingappropriate account of safety and broad economic implications. The design criteria influenced by importanceof facilities are those of environmental conditions, design seismic coefficient, lifetime, loads, safety factor,etc. In determining the degree of importance of the facilities, the following criteria should be taken intoconsideration.• Influence upon human lives and property if the facilities are damaged.• Impact on society and its economy if the facilities are damaged.• Influence upon other facilities if the facilities are damaged.• Replaceability of the facilities.(c) LifetimeThe length of lifetime should be taken into account in determining the structure and materials of the facilitiesand also in determining the necessity for and extent of the improvement of the existing facilities. Lifetime ofthe facilities should be determined by examinig the following:• Operational function of the facilitiesThe number of years until the facilities can no longer be usable due to the occurrence of problems in termsof the function of the facilities, for example the water depth of a mooring basin becoming insufficient owingto the increase in vessel size.• Economic viewpoint of the facilitiesThe number of years until the facilities become economically uncompetitive with other newer facilities(unless some kind of improvements are carried out).
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-8-• Social function of the facilitiesThe number of years until the functions of the facilities that constituted the original purpose becomeunnecessary or until different functions are called for the facilities due to new port planning etc.• Physical property of the facilitiesThe number of years until it is no longer possible to maintain the strength of materials composing thestructures at the specified level due to processes such as corrosion or weathering of these materials.(d) Encounter probabilityThe encounter probability is intimately linked with the lifetime length. The encounter probability E1 isobtained using equation (1.1.1) 1)(1.1.1)whereL1: lifetime length: return period(e) Environmental conditionsNot only the wave, seismic, topographical and soil conditions, which have direct influences on the design ofthe facilities, but also the water quality, bottom material, animal and plant life, atmospheric conditions andrising sea level due to global warming should be taken into consideration.(f) MaterialsIt is necessary to consider the physical external forces, deterioration, lifetime, structural type, constructionworks, cost, and influence on the environment and landscape when selecting the materials. It is most importantto ensure the reguired quality. In recent years, in addition to more traditional materials, new materials such asstainless steels, titanium and new rubbers, and recycled materials such as slag, coal ash and dredged sedimenthave begun to be used.(g) Construction methodIn order to carry out design rationally, it is necessary to give sufficient consideration to the constructionmethod.(h) Work accuracyIt is necessary to carry out design considering the accuracy of construction works that can be maintained inactual projects.(i) Construction periodIn the case that the construction period is stipulated, it is necessary to give consideration both to the design andthe construction method, in order that it will be possible to complete construction work within the stipulatedperiod. The construction period is generally determined by things like the availability of the materials, theconstruction equipment, the degree of difficulty of construction, the opening date and the natural conditions.(j) Construction costs etc.Construction costs consist of the initial investment costs and maintenance costs. All of these costs must beconsidered in design and construction. When doing this, it is necessary to consider the early use of thefacilities and to secure an early return on investment. There is also a design approach that the facilities are putinto service step by step as the construction progresses, while ensuring the safety of service / construction.Note also that the initial investment costs mentioned here include compensation duties.When carrying out design etc., due consideration must be given to things like the structural type and theconstruction method, since the construction costs will depend on these things.[Reference]1) Borgman, L. E.: “Risk criteria”, Proc. ASCE, Vol. 89, No. WW3, 1963, pp.1-35.E1 1 1 1 T1¤–( )L1–=T1
    • PART II DESIGN CONDITIONS-9-Chapter 2 Vessels2.1 Dimensions of Target Vessel (Notification Article 21)The principal dimensions of the target vessel shall be set using the following method:(1) In the case that the target vessel can be identified, use the principal dimensions of that vessel.(2) In the case that the target vessel cannot be identified, use appropriate principal dimensions determinedby statistical methods.[Technical Notes](1) Article 1, Clause 2 of the Ministerial Ordinance stipulates that the “target vessel” is the vessel that has thelargest gross tonnage out of those that are expected to use the port or harbor facilities in question. Accordingly,in the case that the target vessel can be identified, the principal dimensions of this vessel should be used.(2) In the case that the target vessel cannot be identified in advance, such as in the case of port and harbor facilitiesfor public use, the principal dimensions of the target vessel may be determined by referring to Table T- 2.1.1. Inthis table, the tonnages (usually either gross or deadweight tonnage) are used as representative indicators.(3) Table T- 2.1.1 lists the “principal dimensions of vessels for the case that the target vessel cannot be identified”by tonnage level. These values have been obtained through methods such as statistical analysis 1),2), and theymainly represent the 75% cover ratio values for each tonnage of vessels. Accordingly, for any given tonnage,there will be some vessels that have principal dimensions that exceed the values in the table. There will also bevessels that have a tonnage greater than that of the target vessel listed in the table, but still have principaldimensions smaller than those of the target vessel.(4) Table T- 2.1.1 has been obtained using the data from “Lloyd’s Maritime Information June ’95” and “NihonSenpaku Meisaisho” (“Detailed List of Japanese Vessels”; 1995 edition). The definitions of principaldimensions in the table are shown in Fig. T- 2.1.1.(5) Since the principal dimensions of long distance ferries that sail over 300km tend to have different characteristicsfrom those of short-to-medium distance ferries, the principal dimensions are listed separately for “long distanceferries” and “short-to-medium distance ferries.”(6) Since the principal dimensions of Japanese passenger ships tend to have different characteristics from those offoreign passenger ships, the principal dimensions are listed separately for “Japanese passenger ships” and“foreign passenger ships”.(7) The mast height varies considerably even for vessels of the same type with the same tonnage, and so whendesigning facilities like bridges that pass over navigation routes, it is necessary to carry out a survey on the mastheights of the target vessels.(8) In the case that the target vessel is known to be a small cargo ship but it is not possible to identify precisely thedemensions of the ship in advance, the principal dimensions of “small cargo ships” can be obtained by referringto Table T- 2.1.2. The values in Table T- 2.1.2 have been obtained using the same kind of procedure as those inTable T- 2.1.1, but in the case of such small vessels there are large variations in the principal dimensions and soparticular care should be exercised when using Table T- 2.1.2.(9) TonnageThe definitions of the various types of tonnage are as follows:(a) Gross tonnageThe measurement tonnage of sealed compartments of a vessel, as stipulated in the “Law Concerning theMeasurement of the Tonnage of Ships”. The “gross tonnage” is used as an indicator that represents the sizeof a vessel in Japan’s maritime systems. Note however that there is also the “international gross tonnage”,which, in line with the provisions in treaties etc., is also used as an indicator that represents the size of a vessel,but mainly for vessels that make international sailings. The values of the “gross tonnage” and the“international gross tonnage” can differ from one another; the relationship between the two is stipulated inArticle 35 of the “Enforcement Regulations for the Law Concerning the Measurement of the Tonnage ofShips” (Ministerial Ordinance No. 47, 1981).(b) Deadweight tonnageThe maximum weight, expressed in tons, of cargo that can be loaded onto a vessel.(c) Displacement tonnageThe amount of water, expressed in tons, displaced by a vessel when it is floating at rest.(10) For the sake of consistency, equation (2.1.1) shows the relationship between the deadweight tonnage (DWT) andthe gross tonnage (GT) for the types of vessels that use the deadweight tonnage as the representative indicator 1).For each type of vessels, the equation may be applied if the tonnage is within the range shown in Table T- 2.1.1.
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-10-Cargo ships: GT = 0.541DWTContainer ships: GT = 0.880DWTOil tankers: GT = 0.553DWTRoll-on/roll-off vessels: GT = 0.808DWTwhereGT : gross tonnageDWT : deadweight tonnage(11) Tables T-2.1.3 to T-2.1.6 list the frequency distribution of the principal dimensions of general cargo ships, bulkcargo carriers, container ships, and oil tankers, which were analyzed by the Systems Laboratory of Port andHarbour Research Institute (PHRI) using the data from “Lloyd’s Maritime Informations Services (June ’98)”.Fig. T- 2.1.1 Definitions of Principal Dimensions of VesselTable T- 2.1.1 Principal Dimensions of Vessels for the Case That the Target Vessel Cannot Be Identified1. Cargo ships2. Container shipsDeadweight tonnage (DWT) Length overall (L) Molded breadth (B) Full load draft (d)1,000 ton2,0003,0005,00010,00012,00018,00030,00040,00055,00070,00090,000100,000150,00067 m839410913714416118520021823324925628610.9 m13.114.616.819.921.023.627.529.932.332.338.139.344.33.9 m4.95.66.58.28.69.611.011.812.913.714.715.116.9Deadweight tonnage (DWT) Length overall (L) Molded breadth (B) Full load draft (d)30,000 ton40,00050,00060,000218 m24426628630.2 m32.332.336.511.1 m12.213.013.8(2.1.1)64748FullloaddraftLength overallLoad water lineLength between perpendicularsAfter perpendicular Fore perpendicularMoulded breadthMouldeddepth
    • PART II DESIGN CONDITIONS-11-3. Ferries3-A Short-to-medium distance ferries (sailing distance less than 300km)3-B Long distance ferries (sailing distance 300km or more)4. Roll-on/roll-off vessels5. Passenger ships5-A Japanese passenger ships5-B Foreign passenger ships6. Pure car carriersGross tonnage (GT) Length overall (L) Molded breadth (B) Full load draft (d)400 ton7001,0002,5005,00010,00050 m637210413614811.8 m13.514.718.321.623.03.0 m3.43.74.65.35.7Gross tonnage (GT) Length overall (L) Molded breadth (B) Full load draft (d)6,000 ton10,00013,00016,00020,00023,000142 m16718519219220022.3 m25.227.328.228.228.26.0 m6.46.86.86.87.2Deadweight tonnage (DWT) Length overall (L) Molded breadth (B) Full load draft (d)400 ton1,5002,5004,0006,00010,00075 m9711513415418213.6 m16.418.520.722.925.911.1 m4.75.56.37.07.4Gross tonnage (GT) Length overall (L) Molded breadth (B) Full load draft (d)2,000 ton4,0007,00010,00020,00030,00083 m10713014718821715.6 m18.521.223.227.530.44.0 m4.95.76.66.66.6Gross tonnage (GT) Length overall (L) Molded breadth (B) Full load draft (d)20,000 ton30,00050,00070,000180 m20724827825.7 m28.432.335.28.0 m8.08.08.0Gross tonnage (GT) Length overall (L) Molded breadth (B) Full load draft (d)500 ton1,5003,0005,00012,00018,00025,00070 m9411413016518420011.8 m15.718.821.527.030.032.33.8 m5.05.86.68.08.89.5
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-12-7. Oil tankersTable T- 2.1.2 Principal Dimensions of Small Cargo ShipsTable T-2.1.3 Frequency Distributions of Principal Dimensions of General Cargo Ships(a) DWT - Length overall(b) DWT - Breadth(c) DWT - Full load draftDeadweight tonnage (DWT) Length overall (L) Molded breadth (B) Full load draft (d)1,000 ton2,0003,0005,00010,00015,00020,00030,00050,00070,00090,00061 m768710212714415818021123525410.2 m12.614.316.820.823.625.829.232.338.041.14.0 m4.95.56.47.98.99.610.912.613.915.0Deadweight tonnage (DWT) Length overall (L) Molded breadth (B) Full load draft (d)500 ton70051 m579.0 m9.53.3 m3.4L*@
    • PART II DESIGN CONDITIONS-13-Table T-2.1.4 Frequency Distributions of Principal Dimensions of Bulk Cargo Carriers(a) DWT - Length overall(b) DWT - Breadth(c) DWT - Full load draftL*@
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-14-Table T-2.1.5 Frequency Distributions of Principal Dimensions of Container Ships(a) DWT - Length overall(b) DWT - Breadth(c) DWT - Full load draft(d) DWT - TEUL*dunknownunknown
    • PART II DESIGN CONDITIONS-15-Table T-2.1.6 Frequency Distributions of Principal Dimensions of Oil Tankers(a) DWT - Length overall(b) DWT - Breadth(c) DWT - Full load draftL*@
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-16-2.2 External Forces Generated by Vessels2.2.1 GeneralThe external forces acting on the mooring facilities when a vessel is berthing or moored shall bedetermined using an appropriate method, considering the dimensions of the target vessel, the berthingmethod and the berthing velocity, the structure of the mooring facilities, the mooring method and theproperties of the mooring system, along with the influence of things like the winds, waves and tidalcurrents.[Commentary](1) The following loads acting on mooring facilities should be considered when a vessel is berthing or moored:a) Loads caused by berthing of a vesselb) Loads caused by motions of a moored vesselWhen designing mooring facilities, the berthing force must be considered first. Then the impact forces andtractive forces on the mooring facilities due to the motions of the moored vessel, which are caused by the waveforce, wind force and current force, should be considered. In particular, for the cases of the mooring facilities inthe ports and harbors that face out onto the open sea with long-period waves expected to come in, of thoseinstalled in the open sea or harbor entrances such as offshore terminals, and of those in the harbors where vesselsseek refuge during storms, the influence of the wave force acting on a vessel is large and so due considerationmust be given to the wave force.(2) As a general rule, the berthing forces acting on the mooring facilities should be calculated based on the berthingenergy of the vessel and using the load-deflection characteristics of the fenders.(3) As a general rule, the tractive forces and impact forces generated by the motions of a moored vessel should beobtained by carrying out a numerical simulation of vessel motions taking into account the wave force acting onthe vessel, the wind force, the current force, and the load-deflection characteristics of the mooring system.2.2.2 Berthing[1] Berthing Energy (Notification Article 22, Clause 1)It shall be standard to calculate the external force generated by berthing of a vessel with the followingequation:(2.2.1)In this equation, , , V, , , , and represent the following:: berthing energy of vessel (kJ = kN•m): mass of vessel (t)V: berthing velocity of vessel (m/s): eccentricity factor: virtual mass factor: softness factor (standard value is 1.0): berth configuration factor (standard value is 1.0)[Commentary]In addition to the kinetic energy method mentioned above, there are also other methods of estimating the berthingenergy of a vessel: for example, statistical methods, methods using hydraulic model experiments, and methods usingfluid dynamics models 3). However, with these alternative methods, the data necessary for design are insufficient andthe values of the various constants used in the calculations may not be sufficiently well known. Thus, the kineticenergy method is generally used.[Technical Notes](1) If it is assumed that a berthing vessel moves only in the abeam direction, then the kinetic energy is equal to. However, when a vessel is berthing at a dolphin, a quaywall, or a berthing beam equipped withfenders, the energy absorbed by the fenders (i.e., the berthing energy of the vessel) will becomeconsidering the various influencing factors, where .(2) The vessel mass is taken to be the displacement tonnage (DT) of the target vessel. In the case that the targetvessel cannot be identified, equation (2.2.2) 1) may be used to give the relationship between the deadweighttonnage (DWT) or the gross tonnage (GT) and the displacement tonnage (DT).EfMsV22-------------è øæ öCeCmCsCc=Ef Ms Ce Cm Cs CcEfMsCeCmCsCcEsMsV2( ) 2¤Ef Es f´f Ce Cm´ Cs´ Cc´=Ms
    • PART II DESIGN CONDITIONS-17-Cargo ships (less than 10,000DWT): log (DT) = 0.550 + 0.899 log (DWT)Cargo ships (10,000DWT or more): log (DT) = 0.511 + 0.913 log (DWT)Container ships: log (DT) = 0.365 + 0.953 log (DWT)Ferries (long distance): log (DT) = 1.388 + 0.683 log (GT)Ferries (short-to-medium distance): log (DT) = 0.506 + 0.904 log (GT)Roll-on/roll-off vessels: log (DT) = 0.657 + 0.909 log (DWT)Passenger ships (Japanese): log (DT) = 0.026 + 0.981 log (GT)Passenger ships (foreign): log (DT) = 0.341 + 0.891 log (GT)Car carriers: log (DT) = 1.915 + 0.588 log (GT)Oil tankers: log (DT) = 0.332 + 0.956 log (DWT)whereDT: displacement tonnage (amount of water, in tons, displaced by the vessel when fully loaded)GT: gross tonnageDWT: deadweight tonnage(3) The softness factor represents the ratio of the remaining amount of the berthing energy after energyabsorption due to deformation of the shell plating of the vessel to the initial berthing energy. It is generallyassumed that no energy is absorbed in this way and so the value of is often given as 1.0.(4) When a vessel berths, the mass of water between the vessel and the mooring facilities resists to move out andacts just as if a cushion is placed in this space. The energy that must be absorbed by the fenders is thus reduced.This effect is considered when determining the berth configuration factor . It is thought that the effectdepends on things like the berthing angle, the shape of the vessel’s shell plating, the under-keel clearance, andthe berthing velocity, but little research has been carried out to determine it.[2] Berthing VelocityThe berthing velocity of a vessel shall be determined based on the measurement in situ or past data ofsimilar measurements, considering the type of the target vessel, the extent to which the vessel is loaded, theposition and structure of the mooring facilities, weather and oceanographic conditions, and the availabilityor absence of tugboats and their sizes.[Technical Notes](1) Observing the way in which large cargo ships and large oil tankers make berthing, one notices that such vesselscome to a temporary standstill, lined up parallel to the quaywall at a certain distance away from it. They are thengently pushed by several tugboats until they come into contact with the quay. When there is a strong windblowing toward the quay, such vessels may berth while actually being pulled outwards by the tugboats. Whensuch a berthing method is adopted, it is common to set the berthing velocity to 10 ~ 15 cm/s based on past designexamples.(2) Special vessels such as ferries, roll-on/roll-off vessels, and small cargo ships berth under their own powerwithout assistance of tugboats. If there is a ramp at the bow or stern of such a vessel, the vessel may line upperpendicular to the quay. In these cases, a berthing method different from that for larger vessels described in (1)may be used. It is thus necessary to determine berthing velocities carefully based on actualy measured values,paying attention to the type of berthing method employed by the target vessel.(3) Figure T- 2.2.1 shows the relationship between the vessel handling conditions and berthing velocity by vesselsize 4); it has been prepared based on the data collected through experience. This figure shows that the larger thevessel, the lower the berthing velocity becomes; moreover, the berthing velocity must be set high if the mooringfacilities is not sheltered by breakwaters etc.(4) According to the results of surveys on berthing velocity 5),6), the berthing velocity is usually less than 10 cm/s forgeneral cargo ships, but there are a few cases where it is over 10 cm/s (see Fig. T- 2.2.2). The berthing velocityonly occasionally exceeds 10 cm/s for large oil tankers that use offshore terminals (see Fig. T- 2.2.3). Even forferries which berth under their own power, the majority berth at the velocity of less than 10 cm/s. Nevertheless,there are a few cases in which the berthing velocity is over 15 cm/s and so due care must be taken whendesigning ferry quays (see Fig. T- 2.2.4). It was also clear from the above-mentioned survey results that thedegree to which a vessel is loaded up has a considerable influence on the berthing velocity. In other words, if avessel is fully loaded, meaning that the under-keel clearance is small, then the berthing velocity tends to belower, whereas if it is lightly loaded, meaning that the under-keel clearance is large, then the berthing velocitytends to be higher.64444744448(2.2.2)CsCsCc
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-18-Fig. T- 2.2.1 Relationship between Vessel Handling Conditions and Berthing Velocity by Vessel Size 4)Fig. T- 2.2.2 Berthing Velocity and Displacement Tonnage for General Cargo Ships 5)Fig. T- 2.2.3 Berthing Velocity and Displacement Tonnage for Large Oil Tankers 6)Fig. T- 2.2.4 Berthing Velocity and Displacement Tonnage for Longitudinal Berthing of Ferries 5)DifficultexposedGood berthingexposedEasy berthingexposedDifficult berthingshelteredGood berthingshelteredDifficultyofhandlingvessel/mooringfacilitiesbeingshelterdornot Berthing velocity (cm/s)Open type quayWall type quay (sheet pile, gravity types)Berthingvelocity(cm/s)Displacement tonnage ,6 (tons)Displacement tonnage ,6 (10,000 tons)Berthingvelocity(cm/s)Displacement tonnage ,6 (tons)Berthingvelocity(cm/s)Stern berthingBow berthing
    • PART II DESIGN CONDITIONS-19-According to the survey by Moriya et al., the average berthing velocities for cargo ships, container ships, andpure car carriers are as listed in Table T- 2.2.1. The relationship between the deadweight tonnage and berthingvelocity is shown in Fig. T- 2.2.5. This survey also shows that the larger the vessel, the lower the berthingvelocity tends to be. The highest berthing velocities observed were about 15 cm/s for vessels under 10,000 DWTand about 10 cm/s for vessels of 10,000 DWT or over.Table T- 2.2.1 Deadweight Tonnage and Average Berthing Velocity(5) Figure T- 2.2.6 shows a berthing velocity frequency distribution obtained from actual measurement records atoffshore terminals used by large oil tankers of around 200,000 DWT. It can be seen that the highest measuredberthing velocity was 13 cm/s. If the data are assumed to follow a Weibull distribution, then the probability ofthe berthing velocity below the value 13 cm/s would be 99.6%. The mean µ is 4.41 cm/s and the standarddeviation s is 2.08 cm/s. Application of the Weibull distribution yields the probability density function asexpressed in equation (2.2.3):(2.2.3)whereV: berthing velocity (cm/s)From this equation, the probability of the berthing velocity exceeding 14.5 cm/s becomes 1/1000. The offshoreterminals where the berthing velocity measurements were taken had a design berthing velocity of either 15 cm/sor 20 cm/s 7).(6) Small vessels such as small cargo ships and fishing boats come to berths by controlling their positions undertheir own power without assistance of tugboats. Consequently, the berthing velocity is generally higher than thatfor larger vessels, and in some cases it can even exceed 30 cm/s. For small vessels in particular, it is necessary tocarefully determine the berthing velocity based on actually measured values etc.(7) In cases where cautious berthing methods such as those described in (1) are not used, or in the case of berthingof small or medium-sized vessels under influence of currents, it is necessary to determine the berthing velocitybased on actual measurement data etc., considering the ship drift velocity by currents.(8) When designing mooring facilities that may be used by fishing boats, it is recommended to carry out designworks based on the design standards for fishing port facilities and actual states of usage.Deadweight tonnage(DWT)Berthing velocity (cm/s)Cargo ships Container ships Pure car carriers All vessels1,000 class5,000 class10,000 class15,000 class30,000 class50,000 class8.16.75.04.53.93.5-7.87.24.94.13.4--4.64.74.4-8.17.25.34.64.13.4All vessels 5.2 5.0 4.6 5.0Dead weight tonnage (DWT)Cargo shipsContainer shipsPure car carriersV(cm/s)Poisson distribution m = 3Poisson distribution m = 4Weibull distributionNormal distributionV (cm/s)N=738NFig. T- 2.2.5 Relationship between DeadweightTonnage and Berthing VelocityFig. T- 2.2.6 Frequency Distribution ofBerthing Velocity 10)f V( )f V( )V0.8------- V1.25–( )exp=
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-20-[3] Eccentricity Factor (Notification Article 22, Clause 2)The eccentricity factor shall be calculated by the following:(2.2.4)where l and r represent the following:l: distance from the point where the vessel touches the mooring facilities to the center of gravity ofthe vessel as measured along the face line of the mooring facilities (m)r: radius of gyration around the vertical axis passing through the center of gravity of the vessel (m)[Technical Notes](1) When a vessel is in the middle of berthing operation, it is not aligned perfectly along the face line of the berth.This means that after it comes into contact with the mooring facilities (fenders), it starts yawing and rolling. Thisresults in some of the vessel’s kinetic energy being used up. The amount of energy used up by rolling is smallcompared with that by yawing and can be ignored. Equation (2.2.4) thus only considers the amount of energyused up by yawing.(2) The radious of gyration r relative to Lpp is a function of the block coefficient of the vessel and can beobtained from Fig. T- 2.2.7 8). Alternatively, one may use the linear approximation shown in equation (2.2.5) .(2.2.5)wherer: radius of gyration; this is related to the moment of inertia around the vertical axis of the vessel bythe relationship: length between perpendiculars (m): block coefficient; = /( Bd) ( : Volume of water displaced by the vessel (m3), B: mouldedbreadth (m), d: draft (m))(3) As sketched in Fig. T- 2.2.8, when a vessel comes into contact with the fenders F1 and F2 with the point of thevessel closest to the quaywall being the point P, the distance l from the point of contact to the center of gravity ofthe vessel as measured parallel to the mooring facilities is given by equation (2.2.6) or (2.2.7); l is taken to bewhen k < 0.5 and when k > 0.5. When k = 0.5, l is taken as whichever of or that gives the highervalue of in equation (2.2.4).(2.2.6)(2.2.7)Ce11lr--è øæ ö2+--------------------=Cbr 0.19Cb 0.11+( )Lpp=IzIz Msr2=LppCb Cb Ñ Lpp ÑL1 L2 L1 L2CeθQGBBAAPF2F1eLppcosθkeLppcosθLppαLppRadiusofgyrationinthelongitudinaldirection(r)Lengthbetweenperpendiculars(Lpp)Block coefficient CbFig. T- 2.2.7 Relationship between the Radius of Gyrationaround the Vertical Axis and the BlockCoefficient (Myers, 1969) 7)Fig. T- 2.2.8 Vessel BerthingL2 0.5a e 1 k–( )+ Lpp qcos=L1 0.5a ek–( )Lpp qcos=
    • PART II DESIGN CONDITIONS-21-where: distance from the point of contact to the center of gravity of the vessel as measured parallel to themooring facilities when the vessel makes contact with fender F1: distance from the point of contact to the center of gravity of the vessel as measured parallel to themooring facilities when the vessel makes contact with fender F2q: berthing angle (the value of q is set as a design condition; it is usually set somewhere in the range0 ~ 10º)e: ratio of the distance between the fenders, as measured in the longitudinal direction of the vessel, to thelength between perpendicularsa: ratio of the length of the parallel side of the vessel at the height of the point of contact with the fender tothe length between perpendiculars; this varies according to factors like the type of vessel, and the blockcoefficient etc., but is generally in the range 1/3 ~ 1/2.k: parameter that represents the relative location of the point where the vessel comes closest to the mooringfacilities between the fenders F1 and F2 ; k varies between 0 and 1, but it is generally taken at k = 0.5.[4] Virtual Mass Factor (Notification Article 22, Clause 3)It shall be standard to calculate the virtual mass factor using the following equations:where Cb,Ñ, Lpp, B, and d represent the following:: block coefficient: volume of water displaced by the vessel (m3): length between perpendiculars (m)B: moulded breadth (m)d: full load draft (m)[Technical Notes](1) When a vessel berths, the vessel (which has mass ) and the water mass surrounding the vessel (which hasmass ) both decelerate. Accordingly, the inertial force corresponding to the water mass is added to that of thevessel itself. The virtual coefficient is thus defined as in equation (2.2.9).(2.2.9)where: virtual mass factor: mass of vessel (t): mass of the water surrounding the vessel (added mass) (t)Ueda 8) proposed equation (2.2.8) based on the results of model experiments and field observations. The secondterm in equation (2.2.8) corresponds to in equation (2.2.9).(2) As a general rule, the actual values of the target vessel are used for the length between perpendiculars ( ), themoulded breadth (B), and the full load draft (d). But when one of the standard ship sizes is used, one may use theprincipal dimensions given in 2.1 Dimensions of the Target Vessel. Regression equations have been proposedfor the relationships between the deadweight tonnage, the moulded breadth and the full load draft 1). It is alsopossible to use equations (2.2.10), which give the relationship between the deadweight tonnage (DWT) or thegross tonnage (GT) and the length between perpendiculars for different types of vessel 1).Cargo ships (less than 10,000 DWT): log (Lpp) = 0.867 + 0.310 log (DWT)Cargo ships (10,000 DWT or more): log (Lpp) = 0.964 + 0.285 log (DWT)Container ships: log (Lpp) = 0.516 + 0.401 log (DWT)Ferries (long distance, 13,000 GT or less): log (Lpp) = log (94.6 + 0.00596GT)Ferries (short-to-medium distance, 6,000 t or less): log (Lpp) = 0.613 + 0.401 log (GT)Roll-on/roll-off vessels: log (Lpp) = 0.840 + 0.349 log (DWT)Passenger ships (Japanese): log (Lpp) = 0.679 + 0.359 log (GT)Passenger ships (foreign): log (Lpp) = 0.787 + 0.330 log (GT)Car carriers: log (Lpp) = 1.046 + 0.280 log (GT)Oil tankers: log (Lpp) = 0.793 + 0.322 log (DWT)L1L2Cm 1p2Cb---------+dB---´=64748(2.2.8)CbÑLppBd---------------=CbÑLppMsMwCmMs Mw+Ms---------------------=CmMsMwMw Ms¤Lpp64444744448(2.2.10)
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-22-(3) The volume of water displaced by the vessel is determined by dividing the displacement tonnage DT by thedensity of seawater (1.03 t/m3)2.2.3 Moored Vessels[1] Motions of Moored Vessel (Notification Article 23)As a general rule, the external forces generated by the motions of a moored vessel shall be calculated bycarrying out a numerical simulation of vessel motions, with the wave force acting on the vessel, the windforce, the current force due to water currents, etc. being set appropriately.[Commentary](1) Vessels moored at mooring facilities situated in the open sea or near to harbor entrances, or at mooring facilitiesinside harbors for which long-period waves are expected to come in, along with vessels moored during stormyweather, are liable to be moved under the influence of loads due to waves, winds, currents, etc. In some cases,the kinetic energy due to such motions can exceed the berthing energy. In such cases, it is thus advisable to givefull consideration to the tractive forces and impact forces caused by the motions of vessels when designingbollards and fenders 10).(2) As a general rule, the external forces generated by the motions of a vessel should be obtained by carrying out anumerical simulation of vessel motions, based on the factors such as the wave force acting on the vessel, thewind force, the current force due to currents, and the load-deflection characteristics of the mooring system.[Technical Notes](1) As a general rule, the motions of a moored vessel should be analyzed through numerical simulation, withconsideration given to the random variations of the loads and the nonlinearity of the load-deflectioncharacteristics of the mooring system. However, when such a numerical simulation of vessel motions is notpossible, or when the vessel is moored at a system that is considered to be more-or-less symmetrical, one mayobtain the displacement of and loads on the mooring system either by using frequency response analysis forregular waves or by referring to results of an motion analysis on a floating body moored at a system that hasload-deflection characteristics of bilinear nature 11).(2) The total wave force acting on the hull of a vessel is analyzed by dividing it into the wave exciting force due toincident waves and the radiation force that is generated as the vessel moves. The wave exciting force due toincident waves is the wave force calculated for the case that motions of the vessel are restrained. The radiationforce is the wave force exerted on the hull when the vessel undergoes a motion of unit amplitude for each modeof motions. The radiation force can be expressed as the summation of a term that is proportional to theacceleration of the vessel and a term that is proportional to the velocity. Specifically, the former can be expressedas an added mass divided by acceleration, while the latter can be expressed as a damping coefficient divided byvelocity 12). In addition, a nonlinear fluid dynamic force that is proportional to the square of the wave height actson the vessel (see 8.2 External Forces Acting on Floating Body).(3) For vessels that have a block coefficient of 0.7 ~ 0.8 such as large oil tankers, the ship hull can be representedwith an elliptical cylinder, allowing an approximate evaluation of the wave force 13).(4) For box-shaped vessels such as working craft, the wave force can be obtained by taking the vessel to be either afloating body with a rectangular cross section or a floating body of a rectangular prism.[2] Waves Acting on VesselThe wave force acting on a moored vessel shall be calculated using an appropriate method, considering thetype of vessel and the wave parameters.[Commentary]The wave force acting on a moored vessel is calculated using an appropriate method, for example the strip method,the source distribution technique, the boundary element method, or the finite element method; the most commonmethod used for vessels is the strip method.[Technical Notes](1) Wave Force by the Strip Method 11), 12)(a) Wave force of regular waves acting on the hullThe wave force acting on the hull is taken to be the summation of the Froude-Kriloff force and the force by thewaves that are reflected by the hull (diffraction force).Ñ
    • PART II DESIGN CONDITIONS-23-(b) Froude-Kriloff forceThe Froude-Kriloff force is the force derived by integrating the pressure of progressive waves around thecircumference of the hull. In the case of a moored vessel in front of a quaywall, it is taken to be the summationof the force of the incident waves and the force of the reflected waves from the quaywall.(c) Diffraction forceThe diffraction force acting on a vessel is the force that is generated by the change in the pressure field whenincident waves are scattered by the vessel’s hull. As an estimate, this change in the pressure field can bereplaced by the radiation force (the wave making resistance when the vessel moves at a certain velocitythrough a calm fluid) for the case that the hull is moved relative to fluid. It is assumed that the velocity of thevessel in this case is equal to the velocity of the cross section of the hull relative to the water particles in theincident waves. This velocity is referred to as the “equivalent relative velocity”.(d) Total force acting on the hull as a wholeThe total wave force acting on the hull as a whole can be obtained by integrating the Froude-Kriloff force andthe diffraction force acting on a cross section of the hull in the longitudinal direction from to.(2) Waves Forces by Diffraction Theory 13)In the case that the vessel in question is very fat (i.e., it has a block coefficient of 0.7 ~ 0.8), there are noreflecting structures such as quaywalls behind the vessel, and the motions of the vessel are considered to be verysmall, the vessel may be represented with an elliptical cylinder and the wave force may be calculated using anequation based on a diffraction theory 13).[3] Wind Load Acting on VesselThe wind load acting on a moored vessel shall be determined using an appropriate calculation formula.[Commentary]It is desirable to determine the wind load acting on a moored vessel while considering the temporal fluctuation of thewind velocity and the characteristics of the drag coefficients, which depend on the cross-sectional form of the vessel.[Technical Notes](1) The wind load acting on a vessel should be determined from equations (2.2.11) ~ (2.2.13), using the dragcoefficients and in the X and Y directions and the pressure moment coefficient about the midship.(2.2.11)(2.2.12)(2.2.13)where: drag coefficient in the X direction (from the front of the vessel): drag coefficient in the Y direction (from the side of the vessel): pressure moment coefficient about the midship: X component of the wind force (kN): Y component of the wind force (kN): moment of the wind load about the midship (kN•m): density of air; (t/m3)U: wind velocity (m/s): front projected area above the water surface (m2): side projected area above the water surface (m2): length between perpendiculars (m)(2) It is desirable to determine the wind force coefficients , , and through wind tunnel tests or water tanktests on a target vessel. Since such experiments require time and cost, it is acceptable to use the calculationequations for wind force coefficients 14),15) that are based on wind tunnel tests or water tank tests that have beencarried out in the past.(3) The maximum wind velocity (10-minute average wind velocity) should be used as the wind velocity U.(4) For the front projected area above the water surface and the side projected area above the water surface, it isdesirable to use the values for the target vessel. For standard vessel sizes, one may refer to regressionequations 1).(5) Since the wind velocity varies both in time and in space, the wind velocity should be treated as fluctuating in thex Lpp– 2¤=x Lpp 2¤=CbCX CY CMRX12---raU2ATCX=RY12---raU2ALCY=RM12---raU2ALLppCM=CXCYCMRXRYRMra ra 1.23 10 3–´=ATALLppCX CY CM
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-24-analysis of the motions of a moored vessel. Davenport 16) and Hino have proposed the frequency spectra for thetime fluctuations of the wind velocity. The frequency spectra proposed by Davenport and Hino are given byequations (2.2.14) and (2.2.15), respectively./where: frequency spectrum of wind velocity (m2•s): average wind velocity at the standard height 10 m (m/s): friction coefficient for the surface defined with the wind velocity at the standard height; over theocean, it is considered that = 0.003 is appropriate.a: exponent when the vertical profile of the wind velocity is expressed by a power lawz: height above the surface of the ground or ocean (m)m: correction factor relating to the stability of the atmosphere; m is taken to be 2 in the case of a storm.[4] Current Forces Acting on VesselThe flow pressure force due to tidal currents acting on a vessel shall be determined using an appropriatecalculation formula.[Technical Notes](1) Current Pressure Force Due to Currents Coming onto the Bow of VesselThe current pressure force on the vessel due to currents coming onto the bow of a vessel may be calculated usingequation (2.2.16).(2.2.16)where: current pressure force (kN)S: wetted surface area (m2)V: flow velocity (m/s)(2) Current Pressure Force Due to Currents Coming onto the Side of VesselThe current pressure force due to a current coming onto the side of a vessel may be calculated using equation(2.2.17).(2.2.17)whereR: current pressure force (kN): density of seawater (t/m3) (standard value: = 1.03 t/m3)C: current pressure coefficientV: flow velocity (m/s)B: side projected area of hull below the waterline (m2)(3) The current pressure force due to tidal currents can in principle be divided into frictional resistance and pressureresistance. It is thought that the resistance to currents coming onto the bow of a vessel is predominantlyfrictional resistance, whereas the resistance to currents coming onto the side of a vessel is predominantlypressure resistance. However, in practice it is difficult to rigorously separate the two resistances and investigatethem individually. Equation (2.2.16) is a simplification of the following Froude equation with = 1.03,t = 15ºC and l = 0.14:(2.2.18)where: current pressure force (N): specific gravity of seawater (standard value: = 1.03)g: gravitational acceleration (m/s2)t: temperature (ºC)S: wetted surface area (m2)f Su f( ) 4KrU102 X21 X2+( )4 3¤----------------------------=(2.2.14)64748X 1200f= U10Su f( ) 2.856KrU102b--------------- 1fb---è øæ ö2+î þí ýì ü5– 6¤=(2.2.15)64748b 1.169 10 3–U10aKr-------------è øç ÷æ ö z10------è øæ ö2ma 1–´=Su f( )U10KrKrU z 10¤( )aµ[ ]Rf 0.0014SV2=RfR 0.5r0CV2B=r0 r0rwRf rwgl 1 0.0043 15 t–( )+{ }SV1.825=Rfrw rw
    • PART II DESIGN CONDITIONS-25-V: flow velocity (m/s)l: coefficient (l = 0.14741 for a 30m-long vessel and l = 0.13783 for a 250m-long vessel)(4) The current pressure coefficient C in equation (2.2.17) varies according to the relative current direction q; thevalues obtained from Fig. T- 2.2.9 may be used for reference purposes.(5) Regarding the wetted surface area S and the side projected area below the waterline B, one may use valuesobtained from a regression equations 3) that have been derived by statistical analysis.Fig. T- 2.2.9 Current Pressure Coefficient C[5] Load-Deflection Characteristics of Mooring SystemWhen performing a motion analysis of a moored vessel, the load-deflection characteristics of the mooringsystem (mooring ropes, fenders, etc.) shall be modeled appropriately.[Technical Notes]The load-deflection characteristics of a mooring system (mooring ropes, fenders, etc.) is generally nonlinear.Moreover, with regard to the load-deflection characteristics of a fender, they may show hysteresis, and so it isdesirable to model these characteristics appropriately before carrying out the motion analysis of a moored vessel.2.2.4 Tractive Force Acting on Mooring Post and Bollard (Notification Article 79)(1) It shall be standard to take the values listed in Table 2.2.1 as the tractive forces of vessels acting onmooring posts and bollards.(2) In the case of a mooring post, it shall be standard to assume that the tractive force stipulated in (1) actshorizontally and a tractive force equal to one half of this acts upwards simultaneously.(3) In the case of a bollard, it shall be standard to assume that the tractive force stipulated in (1) acts in alldirections.Table 2.2.1 Tractive Forces of Vessels (Notification Article 79, Appended Table 12)Gross tonnage (GT) ofvessel (tons)Tractive force acting on amooring post (kN)Tractive force acting on abollard (kN)200 < GT ≦ 500 150 150500 < GT ≦ 1,000 250 2501,000 < GT ≦ 2,000 350 2502,000 < GT ≦ 3,000 350 3503,000 < GT ≦ 5,000 500 3505,000 < GT ≦ 10,000 700 50010,000 < GT ≦ 20,000 1,000 70020,000 < GT ≦ 50,000 1,500 1,000Currentpressurecoefficient+Relative current direction ( )G1.57.0Water depth Ddraft @ = 1.1
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-26-[Commentary](1) “Mooring posts” are installed away from the waterline, either on or near to the mooring facilities, close to theboth ends of a berth so that they may be used for mooring a vessel in a storm. “Bollards”, on the other hand, areinstalled close to the waterline of the mooring facilities so that they may be used for mooring, berthing, orunberthing a vessel in normal conditions.(2) Regarding the layout and names of mooring ropes to moor a vessel, see Part ⅧⅧⅧⅧ, 2.1 Length and Water Depthof Berths.(3) Regarding the layout and structure of mooring posts and bollards, see Part ⅧⅧⅧⅧ , 19.3 Mooring Posts, Bollards,and Mooring Rings.[Technical Notes](1) It is desirable to calculate the tractive force acting on a mooring post and a bollard based on the breakingstrength of the mooring ropes possessed by a vessel arriving at the berth, the meteorological and oceanographicconditions at the place where the mooring facilities are installed, and the dimensions of vessels, and if necessaryalso considering the force due to a berthing vessel, the wind pressure on a moored vessel, and the force due tomotions of a vessel 9), 11). Alternatively, it is also possible to determine the tractive force acting on a mooringpost and a bollard in accordance with (2) ~ (6) below.(2) In the case that the gross tonnage of a vessel exceeds 5,000 tons and there is no risk of more than one mooringrope being attached to a bollard that is used for spring lines at the middle of mooring facilities for which thevessel’s berth is fixed, the tractive force acting on a bollard may be taken as one half of the value listed in Table2.2.1.(3) The tractive force due to a vessel whose gross tonnage is no more than 200 tons or greater than 100,000 tons(i.e., a vessel that is not covered in Table 2.2.1) should be calculated by considering the meteorological andoceanographic conditions, the structure of the mooring facilities, past measurement data on tractive force, etc.The tractive force on mooring facilities at which vessels are moored even in rough weather or mooring facilitiesthat are installed in waters with severe meteorological / oceanographic conditions should also be calculated byconsidering these conditions.(4) The tractive force acting on a mooring post has been determined based on the wind pressure acting on a vessel insuch a way that a lightly loaded vessel should be able to moor safely even when the wind velocity is 25 ~ 30m/s, with the assumption that the mooring posts are installed at the place away from the wharf waterline by theamount of vessel’s width and that the breast lines are pulled in a direction 45º to the vessel’s longitudinalaxis 17),18). The tractive force so obtained corresponds to the breaking strength of one to two mooring ropes,where the breaking strength of a mooring rope is evaluated according to the “Steel Ship Regulations” by theNippon Kaiji Kyokai. For a small vessel of gross tonnage up to 1,000 tons, the mooring posts can withstand thetractive force under the wind velocity of up to 35 m/s.The tractive force acting on a bollard has been determined based on the wind pressure acting on a vessel insuch a way that even a lightly loaded vessel should be able to moor using only bollards in a wind of velocity up to15 m/s, with the assumption that the ropes at the bow and stern are pulled in a direction at least 25º to the vessel’saxis. The tractive force so obtained corresponds to the breaking strength of one mooring rope for a vessel ofgross tonnage up to 5,000 tons and two mooring ropes for a vessel of gross tonnage over 5,000 tons, where thebreaking strength of a mooring rope is evaluated according to the “Steel Ship Regulations” by the Nippon KaijiKyokai.The tractive force for a bollard that is used for spring lines and is installed at the middle of a berth, for whichthe vessel’s berthing position is fixed, corresponds to the breaking strength of one mooring rope, where thebreaking strength of a mooring rope is evaluated according to the “Steel Ship Regulations” by the Nippon KaijiKyokai. Note however that, although there are stipulations concerning synthetic fiber ropes in the “Steel ShipRegulations” by the Nippon Kaiji Kyokai with regard to nylon ropes and type B vinylon ropes (both of whichare types of synthetic fiber rope), the required safety factor has been set large owing to the factors such that thereis little data on the past usage of such ropes and their abrasion resistance is low, and so both the required ropediameter and the breaking strength are large. Accordingly, in the case of berths for which the mooring vesselsuse only nylon ropes or type B vinylon ropes, it is not possible to apply the stipulations in (2) above.In the above-mentioned tractive force calculations, in addition to the wind pressure, it has been assumed thatthere are tidal currents of 2 kt in the longitudinal direction and 0.6 kt in the transverse direction.(5) When determining the tractive force from a small vessel of gross tonnage no more than 200 tons, it is desirableto consider the type of vessel, the berthing situation, the structure of the mooring facilities, etc. During actual50,000 < GT ≦ 100,000 2,000 1,000Gross tonnage (GT) ofvessel (tons)Tractive force acting on amooring post (kN)Tractive force acting on abollard (kN)
    • PART II DESIGN CONDITIONS-27-design of mooring posts and bollards for vessels of gross tonnage no more than 200 tons, it is standard to takethe tractive force acting on a mooring posts to be 150 kN and the tractive force acting on a bollard to be 50 kN.(6) When calculating the tractive force in the case of vessels such as ferries, container ships, or passenger ships,caution should be exercised in using Table 2.2.1, because the wind pressure-receiving areas of such vessels arelarge.[References]1) Yasuhiro AKAKURA, Hironao TAKAHASHI, Takashi NAKAMOTO: “Statistical analysis of ship dimensions for the size ofdesign ship”, Tech. Note of PHRI, No. 910, 1998 (in Japanese).2) Yasuhiro AKAKURA and Hironao TAKAHASHI: “Ship dimensions of design ship under given confidence limits”, TechnicalNote of P.H.R.I., September 1998.3) PIANC: “Report of the International Commission for Improving the Design of Fender Systems”, Supplement to Bulletine No.45, 1984.4) Baker, A. L. L.: “The impact of ships when berthing”, Proc. Int’l Navig. Congr. (PIANC), Rome, Sect II, Quest. 2, 1953, pp.111-142.5) Masahito MIZOGUCHI, Tanekiyo NAKAYAMA: “Studies on the berthing velocity, energy of the ships”, Tech. Note ofPHRI, No. 170, 1973 (in Japanese).6) Hirokane OTANI, Shigeru UEDA, Tatsuru ICHIKAWA, Kensei SUGIHARA: “A study on the berthing impact of the bigtanker”, Tech. Note of PHRI, No. 176, 1974 (in Japanese).7) Shigeru UEDA: “Study on berthing impact force of very large crude oil carriers”, Rept. of PHRI, Vol. 20, No. 2, 1981, pp.169-209 (in Japanese).8) Myers, J.: “Handbook of Ocean and Underwater Engineering”, McGraw-Hill, New York, 1969.9) Shigeru UEDA, Eijiro OOI: “On the design of fending systems for mooring facilities in a port”, Tech. Note of PHRI, No. 596,1987 (in Japanese).10) Shigeru UEDA, Satoru SHIRAISHI: “On the design of fenders based on the ship oscillations moored to quaywalls”, Tech.Note of PHRI, No. 729, 1992 (in Japanese).11) Shigeru UEDA: “Analytical method of motions moored to quaywalls and the applications”, Tech. Note of PHRI, No. 504,1984 (in Japanese).12) Shigeru UEDA, Satoru SHIRAISI: “Method and its evaluation for computation of moored ship’s motions”, Rept. of PHRI,Vol. 22, No. 4, 1983 pp. 181-218 (in Japanese).13) Yoshimi GODA, Tomotsuka TAKAYAMA, Tadashi SASADA: “Theoretical and experimental investigation of wave forceson a fixed vessel approximated with an elliptic cylinder”, Rept of PHRI, Vol. 12, No. 4, 1994, pp. 23-74 (in Japanese).14) R. M. Isherwood: “Wind resistance of merchant ships”, Bulliten of the Royal Inst. Naval Architects, 1972, pp. 327-338.15) Shigeru UEDA, Satoru SHIRAISHI, Kouhei ASANO, Hiroyuki OSHIMA: “Proposal of equation of wind force coefficientand evaluation of the effect to motions of moored ships”, Tech. Note of PHRI, No. 760, 1993 (in Japanese).16) Davenport, A. G.: “Gust loading factors”, Proc. of ASCE, ST3, 1967, pp. 11-34.17) Hirofumi INAGAKI, Koichi YAMAGUCHI, Takeo KATAYAMA: “Standardization of mooring posts and bollards forwharf”, Tech. Note of PHRI, No. 102, 1970 (in Japanese).18) Iaso FUKUDA, Tadahiko YAGYU: “Tractive force on mooring posts and bollards”, Tech. Note of PHRI, No. 427, 1982 (inJapanese).
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-28-Chapter 3 Wind and Wind Pressure3.1 GeneralWhen designing port and harbor facilities, meteorological factors such as winds, air pressure, fog, rainfall,snow depth, and air temperature should be considered.[Commentary]The effects that meteorological factors exert on the design of port and harbor facilities are as follows:(1) Air pressure and its distribution are the factors that govern the generations of winds and storm surge.(2) Wind is a factor that governs the generations of waves and storm surge, it exerts external forces on port andharbor facilities and moored vessels in the form of wind pressure, and it can disrupt port and harbor works suchas cargo handling.(3) Rainfall is a factor that determines the required capacity of drainage facilities in ports and harbors, and rain canalso disrupt port and harbor works such as cargo handling.(4) Fog is a factor that is an impediment to the navigation of vessels when they are entering or leaving a harbor, andalso decreases the productivity of port and harbor facilities.(5) In some cases, snow load is considered as a static load acting on port and harbor facilities.(6) Air temperature affects the stress distribution within structures of port and harbor facilities and may lead to theoccurrence of thermal stress in these structures.[Technical Notes](1) In calculations concerning the generation of storm surge or waves due to a typhoon, it is common to assume thatthe air pressure distribution follows either Fujita’s equation (3.1.1) or Myers’ equation (3.1.2); the constants inthe chosen equation are determined based on actual air pressure measurements in the region of typhoons.(Fujita’ formula) (3.1.1)(Myers’ formula) (3.1.2)wherep: air pressure at a distance r from the center of typhoon (hPa)r: distance from the center of typhoon (km): air pressure at the center of typhoon (hPa): estimated distance from the center of typhoon to the point where the wind velocity is maximum (km): air pressure drop at the center of typhoon (hPa);: air pressure at (hPa);The size of a typhoon varies with time, and so and must be determined as the functions of time.(2) With regard to wind, see 3.2 Wind.(3) Rain is generally divided into the rain of thunderstorms that have heavy rainfall in a short period of time and therain that continues for a prolonged period of time (rain by a typhoon is a representative example of the latter).When designing drainage facilities, it is necessary to determine the intensity of rainfall both for the case wherethe amount of runoff increases very rapidly and for the case where the runoff continues for a prolonged period.In the case of sewage planning whereby the intensity of rainfall during a thunderstorm is a problem, Sherman’sformula or Talbot’s formula is used.(Sherman’s formula) (3.1.3)(Talbot’s formula) (3.1.4)whereR: intensity of rainfall (mm/h)t: duration of rainfall (min)a, b, n: constants(4) With regard to snow load acting upon port and harbor facilities, see 15.3.4 Snow Load.p p¥Dp1 r r0¤( )2+--------------------------------–=p pc Dpr0r----–è øæ öexp+=pcr0Dp Dp p¥ pc–=p¥ r ¥= p¥ pc Dp+=r0 DpRatn----=Rat b+-----------=
    • PART II DESIGN CONDITIONS-29-3.2 Wind (Notification Article 3, Clause 1)It shall be standard to set the wind characteristics for wave estimations and the wind characteristics as thecause of an external force on port and harbor facilities as stipulated in the following:(1) When calculating the wind velocity and wind direction used in estimations of waves and storm surges,either the actual wind measurements or the calculated values for gradient winds are to be used, withall necessary corrections having been made for the heights of measurements, etc.(2) The velocity of the wind acting on port and harbor facilities shall be set based on statistical data for anappropriate period in line with the characteristics of the facilities and structures.[Technical Notes](1) Gradient Winds(a) The velocity of the gradient wind can be expressed as a function of pressure gradient, radius of curvature ofisobars, latitude, and air density as in equation (3.2.1).(3.2.1)where: velocity of gradient wind (cm/s); in the case of an anticyclone, equation (3.2.1) gives a negative valueand so the absolute value should be taken.: pressure gradient (taken to be positive for a cyclone, negative for an anticyclone) (g/cm2/s2)r: radius of curvature of isobars (cm): angular velocity of Earths rotation ( );: latitude (º): density of air (g/cm3)Before performing the calculation, measurement units should first be converted into the CGS units listedabove. Note that 1º of latitude corresponds to a distance of approximately 1.11 × cm, and an air pressureof 1.0 hPa is g/cm/s2.(b) A gradient wind for which the isobars are straight lines (i.e., their radius of curvature in equation (3.2.1) isinfinite) is called the geostrophic wind. In this case, the wind velocity is .(2) The actual sea surface wind velocity is generally lower than the value obtained from the gradient wind equation.Moreover, although the direction of a gradient wind is parallel to the isobars in theory, the sea surface windblows at a certain angle a to the isobars as sketched in Fig. T- 3.2.2. In the northern hemisphere, the windaround a cyclone blows in a counterclockwise direction and inwards, whereas the wind around an anticycloneblows in a clockwise direction and outwards. It is known that the relationship between the velocity of gradientwinds and that of the actual sea surface wind varies with the latitude. The relationship under the averageconditions is summarized in Table T- 3.2.1. However, this is no more than a guideline; when estimating seasurface winds, it is necessary to make appropriate corrections by comparing estimations with actualmeasurements taken along the coast and values that have been reported by vessels out at sea (the latter arewritten on weather charts).Table T- 3.2.1 Relationship between Sea Surface WindSpeed and Gradient Wind SpeedFig. T- 3.2.2 Wind Direction for aCyclone (Low) and anAnticyclone (High)(3) When selecting the design wind velocity for the wind that acts directly on port and harbor facilities and mooredvessels, one should estimate the extreme distribution of the wind velocity based on actual measurement datataken over a long period (at least 30 years as a general rule) and then use the wind velocity corresponding to therequired return period.It is standard to take the wind parameters to be the direction and velocity, with the wind direction beingrepresented using the sixteen-points bearing system and the wind velocity by the mean wind velocity over 10minutes.Latitude 10º 20º 30º 40º 50ºAngle a 24º 20º 18º 17º 15ºVelocity ratio 0.51 0.60 0.64 0.67 0.70Vg rw f 1– 1¶p ¶r¤rarw2 2sin f-----------------------------++è øç ÷æ ösin=Vgp¶r¶-----w s 1– w 7.29 10 5– s¤´=fra107103V ¶p ¶r¤( ) 2rarw fsin( )¤=Low HighVs Vg¤
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-30-In the Meteorological Agency’s Technical Observation Notes No. 34, the expected wind velocities with thereturn periods of 5, 10, 20, 50, 100 and 200 years for 141 government meteorological offices have beenestimated from the ten-minute mean wind velocity data of about 35 years, under the assumption that windvelocity follows a double exponential distribution. For locations with topographical conditions different fromthat of the nearest among the above-mentioned meteorological offices, one should conduct observations for atleast one year and then conduct a comparative investigation on topographical effects in order to make it possibleto use the aforementioned estimation results.(4) Regarding the wind velocity used in estimating storm surges and waves, it is standard to use the value at a heightof 10 m above sea level. The wind velocities obtained at government meteorological offices are the values for aheight of approximately 10 m above the ground level. Accordingly, when attempting to use such observedvalues to estimate sea surface winds, in the case that the elevations of the structural members are considerablydifferent from 10 m, it is necessary to correct the wind velocity with respect to the height. The vertical profile ofthe wind velocity is generally represented with a power law, and so in current design calculations for all kinds ofstructures, a power law is simply used: i.e.,(3.2.2)where: wind velocity at height h (m/s): wind velocity at height (m/s)The value of the exponent varies with the situation with regard to the roughness near to the surface of the groundand the stability of the atmosphere. In structural calculations on land, a value of n = 1/10 ~ 1/4 is used, and it iscommon to use a value of n ≧ 1/7 out to sea.Statistical data on wind velocity usually consider the ten-minute mean wind velocity. However, for somestructures the mean wind velocity over a shorter time period or the maximum instantaneous wind velocity maybe used, in which case it is necessary to gain an understanding of the relationship between the mean windvelocity over a certain time period and the maximum wind velocity, and also the characteristics of the gustfactor.3.3 Wind Pressure (Notification Article 3, Clause 2)The wind pressure shall be set appropriately, giving due consideration to the situation with regard to thestructural types of the facilities and their locations.[Technical Notes](1) When calculating the wind pressure acting on a moored vessel, one should refer to 2.2.3 [3] Wind Load Actingon a Vessel.(2) In the case that there are no statutory stipulations concerning the wind pressure acting on a structure, the windpressure may be calculated using equation (3.3.1).(3.3.1)wherep: wind pressure (N/m2)q: velocity pressure (N/m2)c: wind pressure coefficientEquation (3.3.1) expresses the wind pressure, i.e., the force due to the wind per unit area subjected to the windforce. The total force due to the wind acting on a member or structure is thus the wind pressure as given byequation (3.3.1) multiplied by the area of that member or structure affected by the wind in a plane perpendicularto the direction in which the wind acts.The velocity pressure q is defined as in equation (3.3.2).(3.3.2)whereq: velocity pressure (N/m2): density of air (kg/m3) = 1.23 kg/m3U: design wind velocity (m/s)The design wind velocity should be taken at 1.2 to 1.5 times the standard wind velocity (ten-minute mean windvelocity at a height of 10 m). This is because the maximum instantaneous wind velocity is about 1.2 to 1.5 timesthe ten-minute mean wind velocity.The wind pressure coefficient varies depending on the conditions such as the shape of the member orstructure, the wind direction, and the Reynolds number. With the exception of cases where it is determined bymeans of the wind tunnel experiments, it may be set by referring to the Article 87 of the “Enforcement OrderUh U0hh0-----è øæ ön=UhU0 h0p cq=q12---raU2=ra ra
    • PART II DESIGN CONDITIONS-31-of the Building Standard Law” (Government Ordinance No. 338, 1950) or the “Crane Structure Standards”(Ministry of Labor Notification). With regard to wind direction, it is generally required to consider the winddirection that is most unfavorable to the structure, with the exception of cases where it has been verified thatthere exists an overwhelmingly prevailing direction of winds.
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-32-Chapter 4 Waves4.1 General4.1.1 Procedure for Determining the Waves Used in Design (Notification Article 4, Clause 1)The waves used in the investigation of the stability of protective harbor facilities and other port and harborfacilities, as well as the examination of the degree of calmness of navigation channels and basins shall beset using wave data obtained from either actual wave measurements or wave hindcasting. Wavecharacteristics shall be obtained by carrying out necessary statistical processing and by analyzing wavetransformations owing to sea bottom topography and others. It shall be standard to carry out the wavehindcasting using a method that is based on an appropriate equation for representing the relationshipbetween the wind velocity and the wave spectrum or the significant wave parameters.[Commentary]The size and structural form of facilities are determinedby the factors such as the height and period of the wavesthat act on them. The setting of the wave conditions to beused in design should thus be carried out carefully. Thesetting of wave conditions should be carried outseparately for “ordinary waves” (i.e., waves that occur inordinary conditions: these are required when estimatingthe harbor calmness or the net working rate of cargohandling) and “storm waves” (i.e., waves that occur instorm conditions: these are required when estimating thewave force acting on structures).The waves that are obtained by statistically process-ing data based on either actual measurements or hindcast-ing are generally deepwater waves that are unaffected bythe sea bottom topography. Deepwater waves propagatetowards the coast, and once the waves reach to the waterdepth about one half the wavelength, they start to experi-ence the effects of topography and transform with theresult of wave height change. “Wave transformation”includes refraction, diffraction, reflection, shoaling, andbreaking. In order to determine the wave conditions at theplace where wave data is needed (for instance the placewhere a structure of interest is located), it is necessary togive appropriate consideration to such wave transforma-tions by means of numerical calculations or model exper-iments.In the above-mentioned procedure for setting thewave conditions to be used in design, it is necessary togive sufficient consideration to the irregularity of thewaves and to treat the waves as being of random natureas much as possible.[Technical Notes]A sample procedure for setting the wave conditions to be used in design is shown in Fig. T- 4.1.1.4.1.2 Waves to Be Used in DesignSignificant waves, highest waves, deepwater waves, equivalent deepwater waves and others shall be usedin the design of port and harbor facilities.[Commentary]The waves used in the design of structures are generally “significant waves”. The significant wave is a hypotheticalwave that is a statistical indicator of an irregular wave group. Significant waves have the dimensions that areapproximately equal to the values from visual wave observations, and so they are used in wave hindcasting. It is alsoknown that the period of a significant wave is approximately equal to the period at the peak of the wave spectrum.Because of such advantages, significant waves have been commonly used to represent wave groups. Nevertheless,depending on the purpose, it may be necessary to convert significant waves into other waves such as highest wavesand highest one-tenth waves.Wave data1)Actual measurement data2) Hindcasting valuesStatistical analysis1) Ordinary waves 2) Storm wavesWave occurrence rate ofdeepwater wavesWave transformationWave occurrence rateat the place of interestDesign deepwater wavesWave transformationParameters of design waves1) Significant wave2) Highest wave1)Wave force actingon structures2)Amount of wavesovertopping at seawalland revetments3) Others1) Harbor calmness2) Net working rate,number of working days3)Transport energy ofincoming waves4) OthersFig. T- 4.1.1 Procedure for Settingthe Waves to BeUsed in Design
    • PART II DESIGN CONDITIONS-33-[Technical Notes](1) Definitions of Wave Parameters(a) Significant wave (significant wave height H1/3 and significant wave period T1/3)The waves in a wave group are rearranged in the order of their heights and the highest one-third are selected;the significant wave is then the hypothetical wave whose height and period are the mean height and period ofthe selected waves.(b) Highest wave (highest wave height Hmax and highest wave period Tmax)The highest wave in a wave group.(c) Highest one-tenth wave (H1/10, T1/10)The wave whose height and period are equal to the mean height and period of the highest one-tenth of thewaves in a wave group.(d) Mean wave (mean wave height , mean period )The wave whose height and period are equal to the mean height and period of all of the waves in a wavegroup.(e) Deepwater waves (deepwater wave height H0 and deepwater wave period T0)The waves at a place where the water depth is at least one half of the wavelength; the wave parameters areexpressed with those of the significant wave at this place.(f) Equivalent deepwater wave height (H0¢)A hypothetical wave height that has been corrected for the effects of planar topographic changes such asrefraction and diffraction; it is expressed with the significant wave height.(2) Maximum WaveThe largest significant wave within a series of significant wave data that was observed during a certain period(for example, one day, one month, or one year) is called the “maximum wave”. In order to clearly specify thelength of the observation period, it is advisable to refer to the maximum wave such as the “maximum significantwave over a period of one day (or one month, one year, etc.)”. Moreover, when one wishes to clearly state thatone is referring to the significant wave for the largest wave that occurred during a stormy weather, the term“peak wave” is used (see 4.4 Statistical Processing of Wave Observation and Hindcasted Data). The“maximum wave height” is the maximum value of the significant wave height during a certain period; this isdifferent from the definition of the “highest wave height”.(3) Significance of Equivalent Deepwater WavesThe wave height at a certain place in the field is determined as the result of transformations by shoaling andbreaking, which depend on the water depth at that place, and those by diffraction and refraction, which dependon the planar topographical conditions at that place. However, in hydraulic model experiments on thetransformation or overtopping of waves in a two-dimensional channel or in two-dimensional analysis by wavetransformation theory, planar topographical changes are not taken into consideration. When applying the resultsof a two-dimensional model experiment or a theoretical calculation to the field, it is thus necessary toincorporate in advance the special conditions of the place in question, namely the effects of planar topographicalchanges (specifically the effects of diffraction and refraction), into the deepwater waves for the place inquestion, thus adjusting the deepwater waves into a form whereby they correspond to the deepwater incidentwave height used for the experiment or theoretical calculation. The deepwater wave height obtained bycorrecting the effects of diffraction and refraction with their coefficients is called the “equivalent deepwaterwave height”.The equivalent deepwater wave height at the place for which design is being carried out is given as follows:(4.1.1)whereKr: refraction coefficient for the place in question (see 4.5.2 Wave Refraction)Kd: diffraction coefficient for the place in question (see 4.5.3 Wave Diffraction)4.1.3 Properties of Waves[1] Fundamental Properties of WavesFundamental properties of waves such as the wavelength and velocity may be estimated by means of thesmall amplitude wave theory. However, the height of breaking waves and the runup height shall beestimated while considering the finite amplitude effects.H TH0¢ KdKrH0=
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-34-[Technical Notes](1) Small Amplitude Wave TheoryThe fundamental properties of waves are expressed as the functions of the wave height, period, and water depth.Various characteristics of shallow water waves as obtained as a first approximation by small amplitude wavetheory are listed below. Note that, with regard to the coordinates, the positive x direction is taken in the directionof wave travel and the positive z direction vertically upwards with z = 0 corresponding to the still water level.The water depth h is assumed to be constant and wave characteristics are assumed to be uniform in thetransverse direction (y direction).(a) Surface elevation (displacement from still water level) (m)(4.1.2)whereh: surface elevation (m)H: wave height (m)L: wavelength (m)T: period (s)(b) Wavelength (m)(4.1.3)whereh: water depth (m)g: gravitational acceleration (m/s2)(c) Wave velocity (m/s)(4.1.4)(d) Water particle velocity (m/s)whereu: component of water particle velocity in the x direction (m/s)w: component of water particle velocity in the z direction (m/s)(e) Water particle acceleration (m/s)where: component of water particle acceleration in the x direction (m/s2): component of water particle acceleration in the z direction (m/s2)h x t,( )H2----2pL------x2pT------t–è øæ ösin=LgT22p--------- 2phL----------tanh=CgT2p------ 2phL----------tanhgL2p------ 2phL----------tanh= =(4.1.5)644474448upHT-------=2p z h+( )L-----------------------cosh2phL----------sinh-----------------------------------2pL------x2pT------t–è øæ ösinwpHT-------=2p z h+( )L-----------------------cosh2phL----------sinh-----------------------------------2pL------x2pT------t–è øæ öcos(4.1.6)644474448dudt------2p2HT2-------------–=h2p z h+( )L-----------------------cos2phL----------sinh-----------------------------------2pL------x2pT------t–è øæ öcosdwdt-------2p2HT2-------------–=h2p z h+( )L-----------------------cos2phL----------sinh-----------------------------------2pL------x2pT------t–è øæ ösindudt------dwdt-------
    • PART II DESIGN CONDITIONS-35-(f) Pressure in water when wave acts (N/m2)(4.1.7)wherer0: density of water (1.01~1.05 × 103 kg/m3 for seawater)(g) Mean energy of wave per unit area of water surface (J)(4.1.8)where Ek and Ep are the kinetic and potential energy densities respectively, with Ek = Ep.(h) Mean rate of energy transported in the direction of wave travel per unit time per unit width of wave (N • m/m/s)W = CG E = nCE (4.1.9)CG = nC (4.1.10)whereCG: group velocity of waves (m/s)(4.1.11)(2) Characteristics of Deepwater Waves and Wavelength(a) Deepwater wavesWaves in water with the depth greater than one-half the wavelength (h/L > 1/2) are called the deepwaterwaves. Various characteristics of deepwater waves may be obtained from the equations of small amplitudewave theory by letting h/L ® ∞ . The wavelength L0, wave velocity C0, and group velocity CG for deepwaterwaves thus become as below. Note that the units of period T are seconds (s).L0 = 1.56T 2(m), C0 = 1.56T (m/s)CG= 0.78T (m/s) (4.1.12)= 1.52T (kt)= 2.81T (km/h)As expressed in equation (4.1.12), the wavelength, wave velocity, and group velocity for deepwater wavesdepend only on the period and are independent of the water depth.(b) Wavelength of long wavesWaves for which the wavelength is extremely long compared with the water depth (h/L < 1/25) are called thelong waves. Various characteristics of long waves may be obtained from the equations of small amplitudewave theory by taking h/L to be extremely small. The wavelength, wave velocity, and group velocity for longwaves thus become as follows:(m) (4.1.13)(m/s)(3) Consideration of Finite Amplitude EffectsThe equations shown in (1) are not always accurate for general shallow water waves having a large height, andso it is sometimes necessary to use equations for finite amplitude waves. When carrying out calculations usingfinite amplitude wave equations, one should refer to “Handbook of Hydraulic Formulas” published by the JapanSociety of Civil Engineers. The amount of the errors in calculations that arise from the use of the smallamplitude wave theory varies according to the wave steepness H/L and the ratio of water depth to wavelength. Nevertheless, the error in wave parameters is usually no more than 20 ~ 30% with the exception of thehorizontal water particle velocity u.One of the finite amplitude effects of waves appears on the crest elevation hc relative to the wave height; theratio increases as the wave height increases. The definition of the crest elevation hc is shown at the top of Fig. T-4.1.2. This figure was drawn up based on wave profile records from the field. It shows the ratio of the highestcrest elevation obtained from each observation record to the highest wave height Hmax in that record as thefunction of relative wave height H1/3/h.p12---r0gH2p z h+( )L-----------------------cosh2phL----------cosh-----------------------------------2pL------x2pT------t–è øæ ösin r0gz–=E Ek Ep+18---r0gH2= =n12--- 14phL----------4phL----------sinh---------------------+è øç ÷ç ÷ç ÷æ ö=L T gh=C CG gh= =h L¤
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-36-(4) Types of Finite Amplitude Wave TheoryThe finite amplitude wave theories include the Stokeswave theory, cnoidal wave theory, and others. In theformer, the wave steepness is assumed to be relativelylow, and the wave profile is represented as a series oftrigonometric functions. A number of researchers haveproposed several approximate series solutions. In thistheory, however, convergence of the series becomesextremely poor as the water depth to wavelength ratiodecreases. This means that the theory cannot be applied ifthe water depth to wavelength ratio is too small. On theother hand, the cnoidel wave theory is obtained by a per-turbation expansion method with the water depth towavelength ratio assumed to be extremely small, mean-ing that it is valid when the water depth to wavelengthratio is small. Errors become large, however, when thewater depth to wavelength ratio increases. In addition tothese two theories, there are also the hyperbolic wavetheory, in which a cnoidal wave is approximated as anexpansion of hyperbolic functions, and the solitary wavetheory, which is the asymptotic case of the cnoidal wavetheory when the wavelength approaches to infinity. Withthe exception of solitary wave theory, the equations in allof these finite amplitude wave theories are complicated,meaning that calculations are not easy. In particular, with the cnoidal wave theory, the equations contain ellipticintegrals, making them very inconvenient to handle. If Dean’s stream function method 1), 2) is adopted, then thewave profile and water particle velocity can be obtained with good accuracy right up to the point where the wavebreaks.(5) Application of Finite Amplitude Wave Theories to Structural DesignsNonlinear theories, which include finite amplitude wave theories, are applied to a wide variety of coastalengineering fields. However, there are still a large number of unknowns, and so, in the case of design at present,they are only applied to a limited number of fields such as those discussed below.(a) Maximum horizontal water particle velocity umax at each elevation below the wave crestThis information is vital in the estimation of the wave force on a vertical structural member. The equationsfrom the Stokes wave theory are used when the water depth to wavelength ratio is large, and the equationsfrom solitary wave theory are used when the water depth to wavelength ratio is small. An approximatecalculation may be carried out using the following empirical equation 3):(4.1.14)where the coefficient a is given as listed in Table T- 4.1.2.Table T- 4.1.2 Coefficient a for Calculation of Maximum Horizontal Water Particle Velocity(b) Wave shoalingWave shoaling, which occurs as the water depth decreases, may be calculated using a long wave theory thatincludes nonlinear terms. Alternatively, the cnoidal wave theory or hyperbolic wave theory may be applied tothis phenomenon (see 4.5.5 Wave Shoaling).(c) Rise and drop of the mean water levelThe mean water level gradually drops as waves approach the breaking point and then rises within the breakerzone toward the shoreline, as can be calculated from the theory of nonlinear interference between waves andcurrents. This mean water level change is taken into account for the calculation of the wave height change dueto random wave breaking (see 4.5.6 Wave Breaking).h/L a h/L a0.030.050.070.100.141.501.501.431.250.970.20.30.50.70.680.490.250.27Number ofdata pointsStandarddeviationMeanH1/3 / h(ηc)maxHmaxFig. T- 4.1.2 Relationship between MaximumCrest Elevation (hc)max/Hmax andRelative Wave Height H1/3/humax z( )pHT------- 1 aHh----è øæ ö1 2¤ z h+h-----------è øæ ö3+i hcos 2p z h+( )( ) L¤[ ]2ph( ) L¤[ ]sinh------------------------------------------------------=
    • PART II DESIGN CONDITIONS-37-(d) Air gap of offshore structuresWhen determining the amount of air gap of offshore structures above the still water level, it is advisable toconsider the relative increase in the wave crest elevation due to the finite amplitude effect such as exhibited inFig. T-4.1.12.[2] Statistical Properties of WavesIn the design of port and harbor facilities, it shall be standard to consider the statistical properties of thewaves with regard to wave heights and periods and to use the Rayleigh distribution for the wave heights ofan irregular deepwater wave group.[Commentary]The assumption behind the theory of Rayleigh distribution is a precondition that the wave energy is concentrated inan extremely narrow band around a certain frequency. Problems thus remain with regard to its applicability to oceanwaves for which the frequency band is broad. Nevertheless, it has been pointed out that, so long as the waves aredefined by the zero-upcrossing method, the Rayleigh distribution can be applied to ocean waves as an acceptableapproximation.[Technical Notes](1) Expression of Rayleigh DistributionThe Rayleigh distribution is given by the following equation:(4.1.15)wherep(H/H): probability density function of wave heightsH : mean wave height (m)According to the Rayleigh distribution, the highest one-tenth wave height H1/10, the significant wave height, and the mean wave height H are related to one another by the following equations:(4.1.16)On average, these relationships agree well with the results of wave observations in situ.The highest wave height Hmax is difficult to determine precisely as will be discussed in (2) below, but ingeneral it may be fixed as in the following relationship:~ (4.1.17)The periods are related as follows:≒ ~ (4.1.18)It should be noted however that as waves approach the coast, waves with the heights greater than the breakinglimit begin to break and that their heights are reduced. Thus it is not possible to use the Rayleigh distribution forthe wave heights within the breaker zone.(2) Occurrence Probability of the Highest Wave HeightThe highest wave height Hmax is a statistical quantity that cannot be determined precisely; it is only possible togive its occurrence probability. If the wave height is assumed to follow a Rayleigh distribution, then theexpected value Hmax of Hmax , when a large number of samples each composed of N waves are ensembled, isgiven as follows:(4.1.20)It should be noted, however, that when Hmax is obtained for each of a large number of samples each containingN waves, there will be a considerable number of cases in which Hmax exceeds Hmax. Thus a simple use of Hmaxas the design wave might place structures on a risky side. One can thus envisage the method in which a waveheight (Hmax)m with m = 0.05 or 0.1 is used, where (Hmax)m is set such that the probability of the value of Hmaxexceeding (Hmax)m is m (i.e., the significance level is m). The value of (Hmax)m for a given significance level m isgiven by the following equation:(4.1.21)p H H¤( )p2---HH-----p4---HH-----è øæ ö2–î þí ýì üexp=H1 3¤H1 10¤ 1.27H1 3¤=H1 3¤ 1.60H=Hmax 1.6(= 2.0)H1 3¤Tmax T1 3¤ 1.1(= 1.3)THmax 0.706 lnN0.57722 lnN----------------+è øæ ö H1 3¤=Hmax( )m 0.706H1 3¤ lnNln 1 1 m–( )¤[ ]----------------------------------è øæ ö=678
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-38-Table T- 4.1.4 lists the values obtained from this equation. Because Hmax is not a definite value but rather aprobabilistic variable, the value of Hmax / H1/3 varies greatly with N and m. However, considering the facts that thewave height only approximately follows a Rayleigh distribution and that the wave pressure formula has been derivedwhile containing a certain scatter of experimental data, it is appropriate to use Hmax = (1.6 ~ 2.0) H1/3 by neglectingthe very small or large values in the table.Table T- 4.1.4 Relationship between Highest Wave Height Hmax and Significant Wave Height H1/3[3] Wave SpectrumIn the design of port and harbor facilities, due consideration shall be given to the functional form of thewave spectrum and an appropriate expression shall be used.[Technical Notes](1) General Form of Wave SpectrumThe general form of the wave spectrum is usually represented as in the following equation:(4.1.22)wheref: frequencyq: azimuth from the principal direction of the waveS(f,q): directional spectrumIn the above, S(f) is a function that represents the distribution of the wave energy with respect to frequency; it iscalled the “frequency spectrum”. G(f,q) is a function that represents the distribution of the wave energy withrespect to direction; it is called the “directional spreading function”.The functions expressed in the following equations may be used for S(f) and G(f,q). The frequency spectrumof equation (4.1.23) is called the Bretschneider-Mitsuyasu spectrum, while equation (4.1.24) is called theMitsuyasu type spreading function.(4.1.23)(4.1.24)where G0 is a constant of proportionality that satisfies the following normalization condition:(4.1.25)where qmax and qmin are respectively the maximum and minimum angles of deviation from the principaldirection.The term S in equation (4.1.24) is a parameter that represents the degree of directional spreading of waveenergy. It is given by the following formulas::(4.1.26): ≦where fm is the frequency at which the spectrum peak appears. It may be represented in terms of the significantwave period T1/3 as in the following equation:(4.1.27)If the units of H1/3 and T1/3 are meters and seconds respectively, then the units of S(f,q) are m2•s.Number of wavesNMode(Hmax) mode50% significancelevel(Hmax) 0.5Mean(Hmax)10% significancelevel(Hmax) 0.15% significancelevel(Hmax) 0.05501002005001,0002,0005,00010,0001.40H1/31.52H1/31.63H1/31.76H1/31.86H1/31.95H1/32.05H1/32.12H1/31.46H1/31.58H1/31.68H1/31.81H1/31.91H1/32.00H1/32.10H1/32.19H1/31.50H1/31.61H1/31.72H1/31.84H1/31.94H1/32.02H1/32.12H1/32.19H1/31.76H1/31.85H1/31.94H1/32.06H1/32.14H1/32.22H1/32.31H1/32.39H1/31.86H1/31.95H1/32.03H1/32.14H1/32.22H1/32.30H1/33.39H1/32.47H1/3S f q,( ) S f( )G f q,( )=S f( ) 0.257H1 3¤ T21 3¤ f5–4–1.03 T1 3¤ f( )4––[ ]exp=G f q,( ) G0 i2Sq2---cos=G f q,( ) qdqminqmaxò 1=S Smaxffm-----è øæ ö2.5–= f fm>64748S Smaxffm-----è øæ ö5= f fmfm 1 1.05T1 3¤( )¤=
    • PART II DESIGN CONDITIONS-39-(2) Value of Directional Spreading ParameterIt is standard to take a value of 10 for the maximum value Smax of the directional spreading parameter in the caseof wind waves in deep water. In the case of swell considering the process of wave decay and others, it isappropriate to take a value of 20 or more. Figure T- 4.1.4 shows a graph of approximately estimated values ofSmax against wave steepness. Judging by the value of wave steepness, it can be seen that Smax< 20 for windwaves. This graph may be used in order to set an approximate value for Smax. Goda and Suzuki 4)have proposedusing as the standard values Smax = 10 for wind waves, Smax = 25 for swell during initial decay, and Smax = 75 forswell that has a long decay distance.(3) Change in Smax Due to RefractionThe form of the directional spreading function changes as waves undergo the refraction process. When adiffraction calculation on irregular waves is carried out using waves that have been refracted, it is thus veryimportant to consider such changes in the directional spreading function. Figure T- 4.1.5 shows the values ofSmax after waves have been refracted at a coastline with straight and parallel depth contour lines. In the figure,(ap)0 is the incident angle of the principal wave direction at the deepwater boundary, i.e., the angle between theprincipal wave direction and the line normal to the depth contours.(4) Improved Model for Frequency SpectrumIf waves are generated in a laboratory flume using the Bretschneider-Mitsuyasu spectrum expressed by equation(4.1.23), the significant wave period of the generated waves often deviates from the target significant waveperiod. The reason for such a deviation is that the original equation (4.1.23) is given in terms of the peakfrequency fm, but this is replaced with the significant wave period T1/3 by using equation (4.1.27). Goda 54) hasthus proposed the following standard spectral form for which the significant wave period of the generated wavesdoes not deviate from the target significant wave period.(4.1.28)The peak frequency for equation (4.1.28) is about 8% lower than that for equation (4.1.23), the spectral densityat the peak is about 18% higher, and overall the spectrum is shifted towards the low frequency side. At the veryleast, it is advisable to use the spectral form expressed by equation (4.1.28) for the target spectrum in hydraulicmodel experiments.(5) Relationship between Wave Spectrum and Typical Values of Wave Characteristics(a) Wave spectrum and typical value of wave heightIf the probability density function for the occurrence of a wave height H is assumed to follow the Rayleighdistribution, then the relationship between the mean wave height H and the zeroth moment of the wave(αp)0h/L0SmaxFig. T- 4.1.4 Graph Showing Estimated Valuesof Smax against Wave SteepnessFig. T- 4.1.5 Graph Showing the Changein Smax Due to RefractionS f( ) 0.205H1 3¤ T21 3¤ f5–4–0.75 T1 3¤ f( )4––[ ]exp=
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-40-spectrum m0 is given by equation (4.1.30), where the n-th moment of the wave spectrum is defined as inequation (4.1.29).(4.1.29)≒ (4.1.30)Using the relationship H1/3 = 1.60 , one arrives at the following relationship between the significant waveheight and the spectrum.≒ (4.1.31)According to the results of actual observations, it is often the case that the best relationship is. In the case of wave data from the shallow waters where the wave height is large, the wavesare highly nonlinear and so the relationship is satisfied. In either case, there is a very strongcorrelation between and m0. It is thus acceptable to use equation (4.1.31) and calculate the significantwave height from the spectrum.(b) Wave spectrum and typical value of periodWhen waves are defined using the zero-upcrossingmethod, the mean period Tz is given by the followingequation according to Rice’s theory.(4.1.32)Calculating the mean period using the Bretschneider-Mitsuyasu type spectrum gives the followingrelationship:(4.1.33)Figure T- 4.1.6 shows a comparison between the meanperiods T obtained from actually observed wave profilesand the mean periods Tz estimated from spectrumcalculations. The values of Tz / T are distributed in therange 0.6 ~ 1.0, with the mean being 0.83. In other words,the mean values obtained from wave profiles tend to beabout 20% greater than those calculated from themoments of spectra. The deviation from Rice’s theory isthought to have been caused by the presence of secondorder nonliner components in the high frequency range ofwave spectra.(6) Spectrum for Long-Period WavesThe above explanation concerns the spectra for wind waves and swell components that have a relatively shortperiod. For long-period wave components that have a period of tens of seconds or more, see 4.8 Long-periodWaves and Seiche.4.2 Method of Determining Wave Conditions to Be Used in Design4.2.1 Principles for Determining the Deepwater Waves Used in Design (Notification Article 4, Clause 2)The duration of statistical wave data used in setting the deepwater wave conditions for investigating thestability of the structures of port and harbor facilities etc. shall be determined appropriately, in dueconsideration to the functions of the port and harbor facilities and the characteristics of the structures.[Commentary](1) As for actual measurement data, a relatively long period of measurements (10 years or more) is desirable.However, when there is a lack of such actual measurement data, hindcasted values that have been obtained usingat least about 30 years’ worth of meteorological data should be used, with these being corrected by means of theavailable data of actual wave measurement.(2) When hindcasted values obtained from meteorological data are corrected using actual measurement data, it isnecessary that the measurement data should cover the period of 3 years at the minimum and contain aconsiderable number of cases of large storms. However, if waves were recorded during an extraordinary weatherthat only occurs once every a few tens of years and the values for these waves exceed all the hindcasted values,the observed values may be used to obtain the design deepwater waves.mn f nS f( ) fd0¥ò=H 2pm0= 2.5 m0HH1 3¤ 4.0 m0H1 3¤ 3.8 m0=H1 3¤ 4.0 m0=H1 3¤Mean ; 0.832Standard deviation ; 0.072N = 171 dataFig. T- 4.1.6 Frequency Distribution of theRatio of Mean Period Tz bySpectral Calculation to ActuallyMeasured Mean Period TTz m0 m2¤=Tz 0.74T1 3¤=
    • PART II DESIGN CONDITIONS-41-(3) If there is absolutely no actual measurement data at the site of interest, or if the only measurement data availableis for extremely limited conditions, measurement data for a neighboring place with similar natural conditionsmay be used. In this case, NOWPHAS (Nationwide Ocean Wave Information Network for Ports and Harbors)data may be used.(4) If it is known that an extraordinary storm event occurred in the area before the period for which wavehindcasting using meteorological data is carried out (for example, in a previous decade), the record of such anevent should be taken into consideration.(5) When hindcasted values for a hypothetical typhoon are used, it is advisable to sufficiently investigate themagnitudes of past typhoons and the courses that they followed, and to even include an investigation on theoccurrence probability of such a typhoon.(6) When estimating deepwater waves using actual measurement data, it is neccessary to take into account the factthat the measured wave height has been affected by refraction and shoaling. Thus the wave height of thedeepwater waves should be corrected by dividing the measured height by the refraction coefficient and theshoaling coefficient. In this case, it is also necessary to consider changes in the wave direction.(7) If the significant wave height obtained from actual measurement data is more than one half of the water depth atthe measurement location, it is considered that this wave record has been affected by wave breaking. With suchwave data, the parameters of the deepwater waves should be estimated by means of wave hindcasting. Notehowever that, with regard to the hindcasted deepwater waves, significant waves for the measurement locationshould be estimated as described in 4.5 Transformations of Waves, and a comparison with the actualmeasurement data should be carried out.(8) It is advisable to determine the deepwater waves that will be used in design with consideration of the encounterprobability based on the return period and the lifetime of the structure in question. However, the way in whichthe encounter probability is interpreted will depend on the functions, importance and return on investment of thestructure, and other factors, and so it is not possible to determine it for the general case. It must therefore bedetermined independently for each individual case by the judgement of the engineer in charge. Here, the“encounter probability” means the probability that waves with a height larger than the return wave height for agiven return period occurs at least once during the lifetime of the structure in question.(9) When determing the deepwater waves that will be used in design, it is necessary to examine the external forceson and past damage of existing structures adjacent to the structure under design.(10) It is standard to set deepwater wave parameters separately for each direction of the sixteen-point bearings,although the directions for which the wave height is small and their effects on the structure are readily judged asnegligible may be excluded. The wave direction hereby refers to the direction of the irregular wave componentthat has the highest energy density, in other words, the principal direction. Since the wave force acting on thestructure in question will not change greatly when the wave direction changes by only a few degrees, it isacceptable in design to represent the wave direction using the sixteen-point bearing system.4.2.2 Procedure for Obtaining the Parameters of Design WavesFirst, deepwater waves shall be determined by following 4.2.1 Principles for Determining theDeepwater Waves Used in Design. Then, transformations due to refraction, diffraction, shoaling, andbreaking shall be evaluated. Finally, the waves that have the most unfavorable effects on the structure inquestion or facilities in the hinterland shall be used as the design waves.[Technical Notes]The parameters of the design waves are determined according to the following procedures:(1) The effects of wave transformation such as refraction, diffraction, shoaling, and breaking are applied to thedeepwater waves determined by following 4.2.1 Principles for Determining the Deepwater Waves Used inDesign, in order to determine the parameters of the design waves at the design location.(2) If the location in question is subject to special conditions (for example, disturbances from externally reflectedwaves or an increase in wave height due to concave corners), these should also be taken into account.(3) The wave force and other wave actions on the structure in question such as overtopping are determined for thewaves obtained above.(4) According to the various conditions related to wave actions, there can be cases where the wave force becomeslargest when the water level is low, and so investigations should be carried out for all conceivable water levels.(5) The above calculations are carried out for each possible direction in which the deepwater waves may come in.The deepwater waves for which the wave action is largest or for which the effects on the structure in question orfacilities in the hinterland are most unfavorable are chosen as the design waves.
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-42-4.3 Wave Hindcasting4.3.1 GeneralWave hindcasting shall be carried out by using an appropriate hindcasting method.[Commentary](1) Wave hindcasting should be made in the following two steps:(a) Setting of the wind field(b) Calculation of wave development and attenuation.(2) The field where waves are generated and developed is called the fetch (or wind field), and it is characterized byfour parameters: wind velocity, wind direction, fetch length, and wind duration. Where the wind field is set, thewave development and attenuation should be calculated by using the most appropriate hindcasting method forthe wind field conditions.[Technical Notes]The wind field is to be set according to the following procedures:(a) Collection of surface weather charts and meteorological data.(b) Determination of the duration of hindcasting for each case.(c) Calculation of gradient winds from the surface weather charts.(d) Estimation of the sea surface winds by empirical formulas and data of measurement.(e) Preparation of the wind field chart.4.3.2 Wave Hindcasting in Generating AreaFor the hindcasting of waves in the generating area, the spectrum methods and the significant wavemethods are recommended as standard methods.[Commentary]The reliability of the results of the wave hindcast should be examined through the comparison with the wavemeasurement data.[Technical Notes](1) Spectral Methods(a) GeneralSpectral methods can be classified into the spectral component methods that have been developed byassuming that the components of the spectrum for each frequency and direction develop independently untilsome equilibrium state is reached 6),7), and the parameteric methods that are based on the idea that thedevelopment and decay of a wave spectrum can be described by a certain small number of parameters 8),9),10).With the former, the development of waves is described in terms of the influx of energy from the wind into thecomponent waves that make up the spectrum and the weak nonlinear interaction between component waves.With the latter, development of waves are treated as the overall result of strong nonlinear effects and a kind ofsimilarity mechanism is assumed with introduction of a few parameters. Calculations are carried out byformulating and solving the equations that govern the development and transformation processes of wavesusing the parameters.The accuracy of wave hindcasting by spectral methods has not been sufficiently investigated yet. However,since the accuracy of wave hindcasting depends greatly on the accuracy of estimating ocean winds, at presentit is reasonable to believe that the accuracy of spectral methods is comparable to that of significant wavemethods. Nevertheless, it should be noted that even for the same wave hindcasting model, results can vary by10 ~ 20% due to differences in the matters like the calculation mesh, the boundary conditions or empiricalconstants. Accordingly, it is necessary to investigate the validity and accuracy of hindcasted results bycomparing them with observation values (examples of such comparisons are given in references 6)~11)). Inparticular, an equilibrium spectral form is assigned as the limit of wave development in the current spectralmethods. It is thought that the accuracy of the supposed equilibrium spectrum itself affects the results greatly,and so it is a good idea to investigate the accuracy with regard to the functional forms of frequency spectrumor the directional spectrum. This is because the significant wave height is proportional to the square root of theintegral of the directional spectrum, meaning that the calculation is such that the significant wave height doesnot change very much even if the spectral form itself changes somewhat, and so it is considered that the mostrigorous way of carrying out evaluation is to examine the spectral form.The spectral methods have the following advantages over the significant wave methods.
    • PART II DESIGN CONDITIONS-43-① The effects of the variations of wind speed and direction on wave development are physically welldescribed.② Appropriate estimation results on wave heights and periods are obtained even when the wind field movestogether with wave propagation.③ Wind waves and swell mixed sea conditions can be reproduced in one calculation.Accordingly, if the results of hindcasting using a significant wave method seem dubious, it is a good idea tomake hindcasting again using a spectral method. Incidentally, spectral methods have been researched anddeveloped while primarily focusing on deepwater waves. There are only a few studies concerning shallowwater waves, namely Collins 12), Cavaleri 13), Golding 14) and Yamaguchi et al.(b) Details 6),7)Wave forecasting methods by mean of wave spectrum have been developed by many researchers since the1960s. Those developed by Japanese reserchers include Inoue’s model 6), Isozaki and Uji’s MRI model 7), andYamaguchi and Tsuchiya’s model. The basis of these models is the following energy balance equation:(4.3.1)where: energy density of a two-dimensional wave spectrum: linear amplifying factor in Phillips’ resonance theory 15): exponential amplifying factor in Miles’ theory 16): energy dissipated due to wave breaking: energy loss due to internal friction during wave propagations etc.: energy exchange due to the nonlinear interaction between component waves: component wave frequency and anglet: timex: position vector: group velocity vectorU: wind velocity: differential operator(2) Significant Wave Methods(a) S-M-B method① General 19),20)The S-M-B method is used when the wind field is stationary. The height and period of deepwatersignificant waves are estimated from the wind velocity and wind duration in the fetch and the fetch lengthusing Fig. T- 4.3.1. Of the wave height obtained from the wind velocity and that from the wind duration,the lower one is adopted as the hindcasted value; likewise for the period. Figure T- 4.3.1 has been drawnbased on the relationships by equations (4.3.2), (4.3.3) and (4.3.4), which were rewritten by Wilson 21) in1965.(4.3.2)(4.3.3)(4.3.4)where: significant wave height (m): significant wave period (s)U: wind velocity at 10 m above sea surface (m/s).F: fetch length (m)g: acceleration of gravity (m/s2) (= 9.81 m/s2)t: minimum duration (hr)¶¶t----E f q t x, , ,( ) CG f( )–= ÑE f q t x, , ,( ) a f U,( ) b f U,( )E F q t x, , ,( ) F3 F4 F5+ + + + +E F q t x, , ,( )a f U,( )b f U,( )F3F4F5f q,CG f( )ÑgH1 3¤U2--------------- 0.30 111 0.004gFU2------è øæ ö1 2¤+î þí ýì ü2----------------------------------------------------–=gT1 3¤2pU-------------- 1.37 111 0.008gFU2------è øæ ö1 3¤+î þí ýì ü5----------------------------------------------------–=t iFdCG-------0Fò iFdgT1 3¤ 4p¤------------------------0Fò= =H1 3¤T1 3¤
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-44-Fig. T - 4.3.1 Wave Forecasting Diagram by the S-M-B Method② Handling of the effective fetch lengthWhen the fetch width is small relative to the fetch length (for example, in a long bay), the fetch length isdetermined by the distance to the opposite shore. If the distance to the opposite shore varies greatly whenthe direction is changed only slightly, it is advisable to use the effective fetch length defined by in equation(4.3.5) 22) when hindcasting is made.(4.3.5)where:effective fetch length (km):distance to opposite shore in the i-th direction (km):angle between the direction of Fi and the predominant wind direction (º)(b) Wilson’s method 21), 23)Wilson’s method is an extension of the S-M-B method. It includes improvements that it can be applied even toa moving fetch, for example in the case of a typhoon. Using the H1/3-t-F-T1/3 graph shown in Fig. T- 4.3.2, thepropagation of waves is traced in the F-T plane, while the development of the significant wave height andperiod are traced in the H1/3-t plane and T1/3-t plane, respectively. This figure has been obtained by calculationbased on equations (4.3.2), (4.3.3) and (4.3.4).(c) Hindcasting for shallow water wavesMethods that consider the influence of the water depth on wave development (i.e., the energy loss due tofriction with the sea bottom) include the Sakamoto-Ijima method. It is known from experience that thesignificant wave period and the significant wave height satisfy the following relationship. (Note however thatthis applies only for wind waves within the fetch area.)(4.3.6)where:significant wave height (m):significant wave period (s)WindSpeedH13 (m) T13 (s) t (h) T13H 13( )2= const.FetchFeffSFi2qicosS qicos------------------------=FeffFiqiT1 3¤ 3.86 H1 3¤=H1 3¤T1 3¤
    • PART II DESIGN CONDITIONS-45-Fig. T- 4.3.2 H1/3-t-F-T1/3 Graph (from Wilsons equations (1965))In the Sakamoto-Ijima method, the ideas in Wilson’s method for deep water waves have been incorporatedinto the case for shallow water waves, resulting in an H1/3-t-F-CG graph such as shown in Fig. T- 4.3.3. Withuse of such a graph it possible to carry out the hindcasting of shallow water waves in a variable fetch.Fig. T- 4.3.3 H1/3-F-CG Graph for Shallow Water Waves (Sakamoto-Ijima Method)(A) Note: The numbers on the graphshow wind velocity (m/s),with water depth (m) in brackets
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-46-4.3.3 Swell HindcastingWhen swell hindcasting is necessary, it is standard to use the Bretschneider method.[Commentary]Swell hindcasting methods include the Bretschneider method 24), the P-N-J method 5), and spectral methods. With theBretschneider method, the wave height and period of swell are hindcasted from the parameters of the significantwave. With the P-N-J method, the swell parameters are obtained by estimating the effects of the velocity dispersionand directional spreading of spectral components. With spectral methods as mentioned above, numerical calculationsare used; generally, no distinction is made between waves and swell in the generating area, with calculations for thecomponent waves at all of the different frequencies being carried out simultaneously, and the results being thesignificant wave parameters for the combination of wind waves and swell. If a significant wave method is used in thehindcasting of waves in the generating area, it is necessary to hindcast swell, in which case it is standard to use theBretschneider method, which is relatively simple and easy to use. Note however that the amount of reliableobservation data that has been obtained for swell is insufficient, and so the hindcasting accuracy is lower than that forwaves in the generating area. Accordingly, it is necessary to treat swell hindcast values as representing no more thanapproximate values, and it is advisable to use them only after carrying out a comparative investigation with actualmeasurement data.[Technical Notes]In the Bretschneider method, swell hindcasting is carried out by using Fig. T- 4.3.4.Fig. T- 4.3.4 Swell Hindcasting DiagramThe term Fmin in the diagram is the minimum fetch length, D is the decay distance of the swell, HF and TF are theheight and period of the significant wave at the end of the fetch respectively, and HD and TD are the height and periodof the significant wave at the swell hindcasting point respectively. If the significant wave height and period aredetermined by the wind velocity and the fetch length in the S-M-B method, the minimum fetch length Fmin is equal tothe actual fetch length. If the wave development is governed by the wind duration, then Fmin is the fetch lengthcorresponding to that wind duration and wind velocity.The time t required for waves to propagate over the decay distance D is calculated from the following equation:(4.3.7)where:group velocity corresponding to (m/s)tDCGD-----------4pDgTD-----------= =CGD TD
    • PART II DESIGN CONDITIONS-47-4.4 Statistical Processing of Wave Observation and Hindcasted Data(1) Wave characteristics shall be expressed as joint distributions of wave height and period by wavedirection using the monthly, seasonal, and annual wave data.(2) Storm wave data shall be sorted by the peaks-over-threshold method so as to yield the data set ofextreme wave heights for extreme statistical analysis, and the extreme wave heights shall beexpressed in terms of the return perid.[Commentary](1) The wave distribution characteristics for ordinary conditions are expressed separately for each wave direction asa joint distribution of wave height and period. Observation data are often available for the wave height and theperiod, and so it is standard to use such data. If observation data are not available, then hindcast data is used.Since waves in ordinary conditions are often affected by the local wind, it is necessary to gain a sufficientunderstanding of the local wind characteristics. There is generally not much observation data available for thewave direction, and so it is standard to use hindcasting. It is necessary to give sufficient consideration to theeffects of swell.(2) It is standard to represent the height of waves used in the design of protective facilities as the “return waveheight” for the return period of the “peak waves” using data over a long time period (at least 30 years as ageneral rule). Since there are only a few places at which observation data extending over such a prolonged timeduration are available, generally hindcast data must be used.(3) The peak waves, basic data for estimating the return wave height, are the wave (generally the significant wave)at the time for which the wave height becomes largest during the process of wave development and decay undera certain meteorological condition. It is thought that sampled peak waves are mutually independent in statisticalsense. When estimating the return wave height, it is possible to use the time series of data for which the peakwaves exceed a certain threshold value during the period in question. Alternatively, it is possible to obtain themaximum value of the “peak waves” for each year, and then use the data as the annual maximum wave. In eithercase, the theoretical distribution function of the return wave height is not known, and so one should try to fitseveral distribution functions such as the those of the Gumbel distribution and the Weibull distribution, find thefunctional form that best fits the data, and then extrapolate it in order to estimate the return wave heights for anumber of different return periods (say 50 years, 100 years, etc.). The accuracy of the resulting estimated valuesdepends largely on the reliability of the data used rather than on the statistical processing method. When drawingup the data set of peak waves using wave hindcasting, it is thus necessary to take due care in appropriatelyselecting the hindcasting method and to closely inspect the hindcasted results.(4) With regard to the wave period corresponding to the return wave height, the relationship between the waveheight and the wave period is plotted for the data of peak waves (which have been used in estimating the returnwave height), and then the wave period is determined appropriately based on the correlation between the two.[Technical Notes](1) Estimation of Return Wave HeightDuring statistical processing, the wave heights arerearranged in the descending order, and the probability ofeach value of wave height not being exceeded iscalculated. If there are N data and the m-th largest waveheight is denoted with xm,N, then the probability P that thewave height does not exceed xm,N is calculated using thefollowing equation:≦ (4.4.1)The values used for a and b in this equation depend on thedistribution function. Specifically, values such as those inTable T- 4.4.1 are used. The values used for the Gumbeldistribution were determined by Gringorten 25) in such a way as to minimize the effects of statistical scatter inthe data. The values used for the Weibull distribution were determined by Petruaskas and Aagaard 26) using thesame principle.It is commented that the Thomas plot often used in hydrology corresponds to the case a = 0, b = 1, and theHazen plot corresponds to the case a = 0.5, b = 0.The distribution functions used in hydrology include the Gumbel distribution (double exponentialdistribution), the logarithmic extreme value distribution, and the normal distribution (in the last case, the datamust first be transformed appropriately). Since the data on peak wave heights have not been accumulated over aprolonged period of time, it is not well known which distribution function is most suitable.Table T- 4.4.1 Parameters Used in Calculating theProbability not Exceeding a Certain Wave HeightDistribution function a bGumbel distributionWeibull distribution (k = 0.75)“ (k = 0.85)“ (k = 1.0)“ (k = 1.1)“ (k = 1.25)“ (k = 1.5)“ (k = 2.0)0.440.540.510.480.460.440.420.390.120.640.590.530.500.470.420.37P H[ xm N, ] 1m a–N b+--------------–=
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-48-Following Petruaskas and Aagaard, we thus introduce the method whereby one tries fitting eight distributionfunctions, namely the Gumbel distribution function (equation (4.4.2)) and the Weibull distribution function(equation (4.4.3)) with k = 0.75, 0.85, 1.0, 1.1, 1.25, 1.5 and 2.0; the distribution function that best fits the dataon any particular data set is then selected as the extreme distribution for that data set.≦ (Gumbel distribution) (4.4.2)≦ (Weibull distribution) (4.4.3)In order to fit the data to the distribution function, the “non-exceedance probability” (probability not exceeding acertain wave height) P is transformed into the variable using equation (4.4.4) or (4.4.5).≦ (Gumbel distribution) (4.4.4)≦ (Weibull distribution) (4.4.5)If the data fit equation (4.4.2) or (4.4.3) perfectly, then there will be a linear relationship between x and .Accordingly, the data are assumed to follow the linear relationship shown in equation (4.4.6). The parameters Aand B are determined using the method of least squares, thus giving an equation for estimating the return waveheight.(4.4.6)where and are the estimated values of the parameters A and B in equation (4.4.2) or (4.4.3), respectively.The return period Rp of the wave height H is related to the non-exceedance probability P (H ≦ x) as in thefollowing:or (4.4.7)≦whereK: number of years during the period for which analysis was carried outN: number of data of peak waves(2) Candidate Distribution Functions and Rejection EriteriaGoda has proposed the following method 51) ~ 53), which is a revised version of the method introduced above.(a) Addition of the Fisher-Tippett type II distribution to the candidate distributionsThe Fisher-Tippett type II distribution is given by the following equation.≦ (4.4.8)The following nine functions are employed as the candidate functions to be tried for fitting: the Gumbeldistribution function (equation (4.4.2)), the Weibull distribution function (equation (4.4.3)) with k = 0.75, 1.0,1.4 and 2.0 (four preset values), and the Fisher-Tippett type II distribution function with k = 2.5, 3.33, 5.0 and10.0 (four preset values).In place of the values listed in Table T- 4.4.1, the following equations are used for a and b in equation(4.4.1):For the Gumbel distribution,a = 0.44, b = 0.12 (4.4.9)For the Weibull distribution,(4.4.10)For the Fisher-Tippett type II distribution,(4.4.11)P H[ x]x B–A------------è øæ ö–î þí ýì üexp–exp=P H[ x] 1x B–A------------è øæ ök–î þí ýì üexp–=rv x B–( ) A¤=( )rv ln lnP H[–{–= x]}rv ln 1 P H[–{–[= x]}]1 k¤rvx A= ^ rv Bˆ+ ^A^ Bˆ^RpKN----11 P H x£( )–-------------------------------·=≦P H( x) 1KNRp----------–=P H[ x] 1 x B–( ) kA( )¤+{ }k––[ ]exp=a 0.20 0.27 k+=b 0.20 0.23 k+=a 0.44 0.52 k¤+=b 0.12 0.11 k¤–=
    • PART II DESIGN CONDITIONS-49-(b) Selection of the best function through introduction of rejection criteriaInappropriate functions are rejected by means of two sets of criterion. The first is the REC criterion. For theresidual of the correlation coefficient for each distribution function, the 95% non-exceedance probability levelis determined in advance. If the residual of the correlation coefficient exceeds this threshold value for adistribution function when the extreme value data is fitted to that distribution function, the function in questionis rejected as being inappropriate. The second is the DOL criterion. The maximum value in the data is madedimensionless using the mean and standard deviation for the whole data. If this value is below the 5% orabove the 95% level of the cumulative distriburion of dimensionless deviation of the distribution functionbeing fitted, that function is rejected as being inappropriate. Next, the best function is selected not simplyaccording to the value of the correlation coefficient, but rather according to the MIR criterion, This criteriontakes into account the fact that the mean of the residual of the correlation coefficient relative to 1.0 will varyaccording to the distribution function. The function for which the ratio of the residual of the correlationcoefficient of the sample to the mean residual for the fitted distribution is lowest is judged to be the best fittingdistribution function.4.5 Transformations of Waves4.5.1 General (Notification Article 4, Clause 3)As a general rule, the waves to be considered to exert actions on port and harbor facilities shall be thewaves that are most unfavorable in terms of the structure stability or the usage of the port and harborfacilities. In this consideration, appropriate attention shall be given to wave transformations during thepropagation of waves from deepwater toward the shore, which include refraction, diffraction, shoaling,breaking, and others.4.5.2 Wave RefractionThe phenomenon of wave refraction occurs in intermediate depth to shallow waters. This is due to thechange in local wave velocity caused by the change in water depth. The changes in wave height and wavedirection due to refraction shall be considered.[Technical Notes](1) Refraction Calculations for Regular Waves(a) Refraction phenomenon and refraction coefficient (see Fig. T- 4.5.1)If waves are obliquely incident on a straight boundary where the water depth changes from h1 to h2, waves arerefracted at the boundary due to the change in wave velocity caused by the change in water depth. Supposethat the distance between wave rays changes from b1 to b2 as a result. If the change in the wave ray width isnot so large, it can be assumed that no wave energy flux cuts across the wave ray and flows out. If othersources of energy loss such as the friction along the sea bottom are ignored, then the continuity in the flux ofenergy transport results in the change of the wave height H1 at water depth h1 to the wave height H2 at waterdepth h2 as given by the following equation:(4.5.1)whereCG1 , CG2: group velocities at water depths h1 and h2, respectively (m/s)b1 , b2: distances between wave rays at water depths h1 and h2, respectively (m)In the equation, represents the change in wave heightdue to refraction, while represents the change inwave height due to the change in water depth. Using the shoalingcoefficient (see 4.5.5 Wave Shoaling), can berepresented as = , where Ks1 and Ks2 arethe shoaling coefficients at water depths h1 and h2, respectively.Suppose that the wave ray width, which is b0 for deepwaterwaves, changes to b due to the refraction phenomenon. The ratioof the wave height after the change to the original wave height inthis case is called the “refraction coefficient”. The refractioncoefficient Kr is given by the following equation:(4.5.2)H2H1------CG1CG2----------b1b2-----=water depth h1water depth h2Fig. T- 4.5.1 Schematic Diagramof Wave Refractionb1 b2¤CG1 CG2¤CG1 CG2¤CG1 CG2¤ Ks2 Ks1¤Kr b0 b¤=
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-50-(b) Refraction calculation methodsRefraction calculation methods for regular waves include the wave ray methods in which calculations using acomputer are made possible, and the numerical wave propagation analysis methods 27) in which surface waveequations are solved by computers using finite difference schemes. An appropriate calculation method ischosen in accordance with the situation.Note however that for a coastline for which the depth contours are straight and parallel to one another, thechange in the wave direction and the refraction coefficient can be calculated using the following equations:(4.5.3)(4.5.4)Here, L, a and a0 denote the wavelength at water depth h, the angle of incidence of the wave at water depth h,and the angle of incidence of the wave in deep water, respectively. Figures T- 4.5.2 and T- 4.5.3 show therefraction coefficient and the wave direction, as calculated using equations (4.5.4) and (4.5.3), respectively.(2) Range of Application of Refraction Calculations Using Regular WavesBased on the principles behind calculations for regular waves, such calculations are applicable for waves forwhich there is little directional spreading and the frequency band is narrow; for example, swell-type waves andtsunamis. For waves like wind waves for which there is much directional spreading and the frequency band isbroad, it is necessary to carry out refraction calculations for irregular waves. Nevertheless, comparing the graphsshowing changes in the refraction coefficient and wave direction for regular waves and irregular waves at a coastasin a0sin2phL----------tanh=Kra0cosacos---------------=Fig. T- 4.5.2 Refraction Coefficient of Regular Waves at Coastwith Straight, Parallel Depth ContoursFig. T- 4.5.3 Graph Showing the Change in the Wave Direction of Regular Wavesat Coast with Straight, Parallel Depth Contours
    • PART II DESIGN CONDITIONS-51-with straight, parallel depth contours, it can be seen that there is only a little difference between regular wavesand irregular waves in this case. This means that when the topography of a coastline is monotonous to the extentthat the depth contours are considered to be straight and parallel to the shoreline, the difference between theresults of refraction calculations for regular waves and irregular waves is usually only slight, and so the resultsof refraction calculations using regular waves can be used as a good approximation.(3) Refraction Calculations for Irregular Waves(a) Calculation methodsRefraction calculation methods for irregular waves include the following: ① the component wave method,whereby the directional wave spectrum is divided into an appropriate number of component waves, arefraction calculation is performed for each component wave, and then the refraction coefficient for theirregular wave is evaluated by making a weighted average of the component wave energies; ② methods inwhich the wave energy balance equation 28) or the mild-slope wave equation is solved directly using acomputer with finite difference schemes. As with the component wave method, the energy balance equation isderived by assuming that wave energy does not cut across wave rays and flow out. This means that thetechnique is basically the same in both cases. However, with the energy balance equation method, refractionwithin a small but finite region is calculated, meaning that the refraction coefficient does not become infiniteeven at a point in which two regular wave rays may converge. On the other hand, the mild-slope waveequation method is a strictly analytical method, but it is difficult to apply it to a large region. Whendetermining the refraction coefficient for irregular waves, it is acceptable to use the component wave method,which involves the linear superposition of refraction coefficients for regular waves and is thus simple andconvenient. However, when intersections of wave rays occur during a refraction calculation for a componentwave, the energy balance equation method may be used for practical purposes with the exception of the casethat the degree of intersection is large.(b) Effects of diffractionWhen deepwater waves have been diffracted by an island or a headland, the wave spectrum becomes generallydifferent from a standard form that has been assumed initially. Thus it is necessary to use the spectral formafter diffraction when performing the refraction calculation.(c) Diagrams of the refraction coefficient and angle for irregular waves at a coast with straight, parallel depthcontoursFigures T- 4.5.4 and T- 4.5.5 show the refraction coefficient Kr and the principal wave direction ap,respectively, for irregular waves at a coast with straight, parallel depth contours, with the principal direction ofdeepwater waves (ap)0 as the parameter. The direction (ap)0 is expressed as the angle between the wavedirection and the line normal to the boundary of deepwater. Smax is the maximum value of the parameter thatexpresses the degree of directional spreading of wave energy (see 4.1.3 [3] Wave Spectrum).Fig. T- 4.5.4 Refraction Coefficient of Irregular Waves at Coastwith Straight, Parallel Depth Contours
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-52-Fig. T- 4.5.5 Change Due to Refraction in the Principal Direction ap of Irregular Wavesat Coast with Straight, Parallel Depth Contours(4) At places where the water depth is no more than about one half of the deepwater wave height, waves exhibit thecharacteristics of flow rather than those of undulations. This means that refraction calculations for wavedirections and refraction coefficients can only be applied to the water where the depth is at least one half of thedeepwater wave height.4.5.3 Wave Diffraction[1] DiffractionThe wave height in regions in which waves are anticipated to be greatly affected by the phenomenon ofdiffraction caused by obstacles such as breakwaters or islands shall be calculated using an appropriatemethod.[Commentary]Diffraction is a phenomenon whereby waves wheel into a region that is screened by something like a breakwater. It isthe most important phenomenon when determining the wave height in a harbor. The irregularity of waves should beconsidered in a diffraction calculation. For a harbor within which the water depth is assumed uniform, the diffractiondiagrams for irregular waves with regard to a semi-infinite breakwater or a straight breakwater that has just oneopening have been prepared. The ratio of the wave height after diffraction to the incident wave height is called thediffraction coefficient Kd. In other words, the diffraction coefficient Kd is given by the following equation:(4.5.10)whereHi: incident wave height outside harborHd: height of wave in harbor after diffractionDiffraction diagrams and diffraction calculation methods assume that the water depth within the harbor is uniform. Ifthere are large variations in water depth within the harbor, the errors will become large, in which case it is advisableto investigate the wave height in the harbor by means of either hydraulic scale model tests or else numericalcalculation methods that also take refraction into account.[Technical Notes](1) Diffraction Diagrams for Irregular WavesFigures T- 4.5.6 (a) ~ (c) show the diffraction diagrams by a semi-infinite breakwater for irregular waves withthe directional spreading parameter Smax = 10, 25, and 75. Figures T- 4.5.6 (a) ~ (llll) show the diffractiondiagrams through an opening of B/L = 1, 2, 4, and 8 for irregular waves with Smax = 10, 25, and 75.Kd Hd Hi¤=
    • PART II DESIGN CONDITIONS-53----- Period ratio ─ Diffraction coefficientFig. T - 4.5.6(a) Diffraction Diagram by Semi-infinite Breakwaters (θ= 90º) for Smax = 10Wave directionWave direction
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-54----- Period ratio ─ Diffraction coefficientFig. T - 4.5.6(b) Diffraction Diagram by Semi-infinite Breakwaters (θ= 90º) for Smax = 25Wave directionWave direction
    • PART II DESIGN CONDITIONS-55----- Period ratio ─ Diffraction coefficientFig. T - 4.5.6(c) Diffraction Diagram by Semi-infinite Breakwaters (θ= 90º) for Smax = 75Wave directionWave direction
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-56-Period ratio Diffraction coefficientPeriod ratio Diffraction coefficientFig. T - 4.5.7(a) Diffraction Diagram by Breakwaters with an Opening (B/L= 1.0) for Smax = 10Wave directionWavedirection
    • PART II DESIGN CONDITIONS-57-Period ratio Diffraction coefficientPeriod ratio Diffraction coefficientFig. T - 4.5.7(b) Diffraction Diagram by Breakwaters with an Opening (B/L= 1.0) for Smax = 25Wave directionWave direction
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-58-Period ratio Diffraction coefficientPeriod ratio Diffraction coefficientFig. T - 4.5.7(c) Diffraction Diagram by Breakwaters with an Opening (B/L= 1.0) for Smax = 75Wave directionWave direction
    • PART II DESIGN CONDITIONS-59-Period ratio Diffraction coefficientPeriod ratio Diffraction coefficientFig. T - 4.5.7(d) Diffraction Diagram by Breakwaters with an Opening (B/L= 2.0) for Smax = 10Wave directionWave direction
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-60-Period ratio Diffraction coefficientPeriod ratio Diffraction coefficientFig. T - 4.5.7(e) Diffraction Diagram by Breakwaters with an Opening (B/L= 2.0) for Smax = 25Wave directionWave direction
    • PART II DESIGN CONDITIONS-61-Period ratio Diffraction coefficientPeriod ratio Diffraction coefficientFig. T - 4.5.7(f) Diffraction Diagram by Breakwaters with an Opening (B/L= 2.0) for Smax = 75Wave directionWave direction
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-62-Period ratio Diffraction coefficientPeriod ratio Diffraction coefficientFig. T - 4.5.7(g) Diffraction Diagram by Breakwaters with an Opening (B/L= 4.0) for Smax = 10Wave directionWave direction
    • PART II DESIGN CONDITIONS-63-Period ratio Diffraction coefficientPeriod ratio Diffraction coefficientFig. T - 4.5.7(h) Diffraction Diagram by Breakwaters with an Opening (B/L= 4.0) for Smax = 25Wave directionWave direction
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-64-Period ratio Diffraction coefficientPeriod ratio Diffraction coefficientFig. T - 4.5.7(i) Diffraction Diagram by Breakwaters with an Opening (B/L= 4.0) for Smax = 75Wave directionWave direction
    • PART II DESIGN CONDITIONS-65-Period ratio Diffraction coefficientPeriod ratio Diffraction coefficientFig. T - 4.5.7(j) Diffraction Diagram by Breakwaters with an Opening (B/L= 8.0) for Smax = 10Wave directionWave direction
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-66-Period ratio Diffraction coefficienteriod ratio Diffraction coefficientFig. T - 4.5.7(k) Diffraction Diagram by Breakwaters with an Opening (B/L= 8.0) for Smax = 25Wave directionWave direction
    • PART II DESIGN CONDITIONS-67-Period ratio Diffraction coefficientPeriod ratio Diffraction coefficientFig. T - 4.5.7(llll) Diffraction Diagram by Breakwaters with an Opening (B/L= 8.0) for Smax = 75Wave directionWave direction
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-68-(2) Treatment of Obliquely Incident WavesWhen waves are obliquely incident to a breakwater that contains an opening, it is advisable to obtain thediffraction diagram by means of a numerical calculation. When this is not possible, or when the diffractiondiagram is only required as a rough guideline, the following approximate method may be used instead.(a) Determining the axis of the diffracted waveWhen waves are obliquely incident to a breakwater that contains an opening, the direction q¢ of the axis of thediffracted waves (see Fig. T- 4.5.8) varies slightly from the direction of incidence q. Tables T- 4.5.1 (a) ~ (c)list the direction of the axis of the diffracted waves as a function of the aperture ratio B/L and the direction ofincidence. These tables are used to obtain the direction q¢ of the axis of the diffracted waves, and then thevirtual aperture ratio B¢/L corresponding to q¢ is obtained from the following equation:(4.5.11)Table T- 4.5.1 Angle of Axis of Diffracted Waveθ¢(a) Smax = 10(a) Smax = 25(a) Smax =75Note: Angle in the parentheses is the angle of deflection relative to the angle of incidenceFig. T- 4.5.8 Virtual Aperture B¢ and Angle of Axis of Diffracted Waveθ¢(b) Fitting of a diffraction diagramOut of the diffraction diagrams of normal incidence in Figs. T-4.5.7 (a) ~ (llll), the diffraction diagram that hasan aperture ratio nearly equal to the virtual aperture ratio is selected. This diffraction diagram is next rotateduntil the direction of incidence matches the direction of the axis of the diffracted waves as determined fromTable T- 4.5.1. The diffraction diagram is then copied and taken to be the diffraction diagram for obliquelyB/LAngle between breakwater and incident wave direction q15º 30º 45º 60º1.02.04.053º (38º)46º (31º)41º (26º)58º (28º)53º (23º)49º (19º)65º (20º)62º (17º)60º (15º)71º (11º)70º (10º)70º (10º)B/LAngle between breakwater and incident wave direction q15º 30º 45º 60º1.02.04.049º (34º)41º (26º)36º (21º)52º (22º)47º (17º)42º (12º)61º (16º)57º (12º)54º (9º)70º (10º)67º (7º)65º (5º)B/LAngle between breakwater and incident wave direction q15º 30º 45º 60º1.02.04.041º (26º)36º (21º)30º (15º)45º (15º)41º (11º)36º (6º)55º (10º)52º (7º)49º (4º)66º (6º)64º (4º)62º (2º)B¢ L¤ B L¤( ) q¢sin=Principal direction of incident wavePrincipal direction of diffracted wave
    • PART II DESIGN CONDITIONS-69-incident waves. The errors in this approximate method are largest around the opening in the breakwater; interms of the diffraction coefficient, the maximum error may amount to around 0.1 in the absolute value.(3) Method for Determining Diffraction Coefficient in a HarborThe diffraction coefficient within a complex shape of harbor is generally estimated by numerical computationwith a computer. Diffraction calculation methods include Takayama’s method, which involves linear superposition of analytical solutions for detached breakwaters, and calculation methods that use the Green functions.(4) Directional Spreading MethodWhen the length of an island or the width of the entrance of a bay is at least ten times the wavelength of theincident waves, there will not be a large difference between the wave height estimate by the direct diffractioncalculation and the estimate using the amount of directional wave energy that arrives directly at the point ofinterest behind the island or in the bay; the latter is called the directional spreading method. However, if thepoint of interest is just behind an island or headland, the effects of diffracted waves will be large, and so thedirectional spreading method cannot be applied.(5) Studies Using Hydraulic Model ExperimentsThanks to improvements in multidirectional random wave generating devices, it is easy to reproduce waves thathave directional spreading in the laboratory nowadays, meaning that diffraction experiments can be carried outrelatively easily. When carrying out a model experiment, an opening in the harbor model is set up within theeffective wave making zone, and the wave height is simultaneously measured at a number of points within theharbor. The diffraction coefficient is obtained by dividing the significant wave height in the harbor by thesignificant wave height at the harbor entrance averaged over at least two observation points.[2] Combination of Diffraction and RefractionWhen carrying out diffraction calculations for waves in waters where the water depth varies greatly, waverefraction must also be considered.[Commentary](1) When the water depth within a harbor is made more-or-less uniform by say dredging (this is often the case withlarge harbors), the refraction of waves after diffraction can be ignored. In order to determine the wave height inthe harbor in this case, it is acceptable to first carry out a calculation considering only refraction and breakingfrom the deepwater wave hindcasting point to the harbor entrance. Next, a diffraction calculation for the areawithin the harbor is carried out, taking the incident wave height to be equal to the calculated wave height at theharbor entrance. In this case, the wave height at a point of interest within the harbor is expressed using thefollowing equation:H = Kd Kr Ks H0 (4.5.12)whereKd: diffraction coefficient at the point of interest within a harborKr: refraction coefficient at the harbor entranceKs: shoaling coefficient at the harbor entrance (see 4.5.5 Wave Shoaling)H0: deepwater wave heightThe energy balance equation method or the improved energy balance equation method in which a termrepresenting dissipation due to wave breaking is added is appropriate as the refraction calculation method for theopen sea. Takayama’s harbor calmness calculation method, whereby diffraction solutions for detachedbreakwaters are superimposed in order to obtain the change in the wave height of irregular waves within theharbor due to diffraction and reflection, can be used for the diffraction calculation for the area within the harbor,provided there are no complex topographic variations within the harbor.(2) When there are large variations in water depth even at places screened by a breakwater (this is often the casewith relatively small harbors and coastal areas), it is necessary to simultaneously consider both diffraction andrefraction within the harbor. If ignoring wave reflection and just investigating the approximate change in waveheight, it is possible to carry out refraction and diffraction calculations separately, and then estimate the changein wave height by multiplying together the refraction and diffraction coefficients obtained.Calculation methods that allow simultaneous consideration of refraction and diffraction of irregular wavesinclude a method that uses time-dependent mild-slope irregular wave equations, a method in which theBoussinesq equation is solved using the finite difference method 29), and the multicomponent coupling methodof Nadaoka et al. There are also literatures in which other calculation methods are explained.
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-70-4.5.4 Wave Reflection[1] GeneralIn the design of port and harbor facilities, investigations shall be carried out onto the effects of reflectedwaves from neighboring structures on the facilities in question and also the effects of wave reflection fromthe facilities in question on neighboring areas.[Commentary]It is necessary to take note of the fact that waves reflected from port and harbor facilities can exercise a largeinfluence on the navigation of vessels and cargo handling. For example, waves reflected from vertical breakwaterscan cause disturbances in navigation channels, and multiple-reflected waves from quaywalls can cause agitationswithin harbors.[Technical Notes](1) Composition of Reflected Waves and Incident WavesThe wave height Hs when incident waves and waves reflected from a number of reflective boundaries coexist (atrain of incident waves and those of reflected waves from reflective boundaries are termed the “wave groups”)can be calculated using the following equation:(4.5.13)whereHs: significant wave height when all of the wave groups are taken togetherH1, H2, ¼Hn: significant wave heights of wave groupsNote however that, if the wave action varies with the wave direction, the differences in the wave directions ofvarious wave groups must be considered. The calculated wave height is valid for places that are at least about0.7 wavelengths away from a reflecting boundary.Regarding the diffraction and/or refraction of waves for which wave direction is an important factor, thesignificant wave height is determined separately for each wave group by carrying out whatever calculation isnecessary for that wave group, when the wave directions of various wave groups differ. Then the compositewave height is calculated by putting these significant wave heights into equation (4.5.13). An acceptablealternative is to determine the spectrum for each wave group, add these spectra together in order to calculate thespectral form when the wave groups coexist, and then perform direct diffraction and/or refraction calculationsusing this spectrum.(2) Composition of PeriodsThe significant wave height to be used in calculating the wave force when two wave groups of different periodsare superimposed may be determined by the energy composition method (i.e., equation (4.5.13)). The significantwave period T1/3 may be determined using the following equation 30):(4.5.14)where(4.5.15)(4.5.16)0.632 + 0.144ln RT : 0.1 ≦ RT < 0.80.6 : 0.8 ≦ RT < 1 (4.5.17)13.97 + 4.33ln RT : 0.1 ≦ RT < 0.410.0 : 0.4 ≦ RT < 1 (4.5.18)(4.5.19)(4.5.20)(H1/3)I, (H1/3)II : significant wave heights of wave groups I and II before superimposition, respectively (m)(T1/3)I, (T1/3)II : significant wave periods of wave groups I and II before superimposition, respectively (s)Note that, in the above equations, I is assigned to the wave group with the shorter period and Ⅱto that with thelonger period.Hs H 12H22 ¼ Hn2+ + +=T1 3¤ kH1 3¤( )I2H1 3¤( )II2+H1 3¤( )I2T1 3¤( )I2¤ H1 3¤( )II2T1 3¤( )II2¤+-------------------------------------------------------------------------------------------=k 1.0 a RH m¤( ) 0.121Aln RH m¤( )–+=a 0.08 RTln( )2 0.15 RTln–=mîíì=Aîíì=RH H1 3¤( )IH1 3¤( )II¤=RT T1 3¤( )IT1 3¤( )II¤=
    • PART II DESIGN CONDITIONS-71-(3) Methods for Calculating the Effects of Reflected WavesCalculation methods for investigating the extent of the effects of waves reflected from a structure include thepoligonal island reflection method and a simple method by means of diffraction diagrams.(a) Poligonal island reflection methodIn this calculation method, the theoretical solution that shows the wave transformation around a single convexcorner is separated into three terms, representing the incident, the reflected and the scattered waves,respectively. The term for the scattered waves is progressively expanded to obtain an approximate equation, sothat the method can be applied to the case where there are a number of convex corners. When there are anumber of convex corners, it is assumed as a precondition that the lengths of the sides between convex cornersare at least five times the wavelength of the incident waves, so that the convex corners do not interfere witheach other. It is necessary to take heed of the fact that errors may become large if the sides are shorter thanthis. Since another assumption is made such that the water depth is uniform, the refraction of reflected wavescannot be calculated. In general, it is sufficient for practical purposes if the lengths of the sides betweenconvex corners are at least about three times the wavelength of the incident waves. This calculation methodcan also be applied to the reflection of irregular waves by means of superposing component waves. Althoughthe wave diffraction problems can also be analyzed with this calculation method, there will be large errors if itis applied to the diffraction of waves by thin structures such as breakwaters.(b) Simple method by means of diffraction diagramsExplanation is made for the example shown in Fig.T- 4.5.9. The wave height at a point A on the frontface of an upright detached breakwater is estimatedwhen waves are incident on the detached break-water at an angle a. Instead of the detached break-water, it is supposed that there are two semi-infinitevirtual breakwaters with an opening, such as shownwith dashed lines in Fig. T- 4.5.9. Next, one consid-ers the situation whereby waves are incident on thevirtual opening from both the wave direction of theincident waves and the direction symmetrical to thiswith respect to the detached breakwater (i.e., thedirection shown by the dashed arrow in Fig. T-4.5.9), and draws the diffraction diagram for theopening (dashed lines in Fig. T- 4.5.9). The range ofinfluence of the reflected waves is represented bymeans of the diffraction diagram for the virtualbreakwaters with the opening. Accordingly, supposing that the diffraction coefficient at point A is read off asbeing 0.68, then the wave height ratio with respect to the incident waves at point A is obtained by combiningthis value of 0.68 with a value of 1.0 representing the incident waves; since it is the energies that are added, thewave height ratio becomes . It should be noted, however, that this value of 1.21 representsthe mean value of the wave height ratio around the point A. It is not advisable to use this method for pointswithin 0.7 wavelengths of the detached breakwater, because the errors due to a phase coupling effect will belarge.For the case of wave reflection by a semi-infinite breakwater, the virtual breakwater also becomes a semi-infinite breakwater in the opposite direction, and so the diffraction diagram for a semi-infinite breakwater isused. When the reflection coefficient of the front face of the breakwater is less than 1.0 due to wave-absorbingwork for example, the diffraction coefficient should be multiplied by the reflection coefficient before beingused. For example, if the reflection coefficient of the detached breakwater is 0.4 in the previous example, thewave height ratio at the point A becomes .[2] Reflection CoefficientReflection coefficients shall be determined appropriately based on the results of field observations,hydraulic model experiments, and past data.[Technical Notes](1) Approximate Values for Reflection CoefficientIt is desirable to evaluate the value of reflection coefficient by means of field observations. However, when it isdifficult to carry out observation or when the structure in question has not yet been constructed, it is standard toestimate reflection coefficient by referring to the results of hydraulic model experiments. In this case, it isdesirable to use irregular waves as the test waves. The method by Goda et al. 31) may be used for the analysis ofirregular wave test data.Fig. T- 4.5.9 Sketch Showing the Effectof Reflected Waves1 0.682+ 1.21=1 0.4 0.68´( )2+ 1.04=
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-72-The following is a list of approximate values for the reflection coefficients of several types of structures.Upright wall: 0.7 ~ 1.0(0.7 is for the case of a low crown with much overtopping)Submerged upright breakwater: 0.5 ~ 0.7Rubble mound: 0.3 ~ 0.6Precast wave-dissipating concrete blocks: 0.3 ~ 0.5Upright wave-absorbing structure: 0.3 ~ 0.6Natural beach: 0.05 ~ 0.2With the exception of the upright wall, the lower limits in the above ranges of reflection coefficient correspondto the case of steep waves and the upper limits to waves with low steepness. It should be noted, however, thatwith the upright wave-absorbing structure, the reflection coefficient varies with the wavelength, and the shapeand dimensions of the structure.[3] Transformation of Waves at Concave Corners, near the Heads of Breakwaters, and aroundDetached BreakwatersAround the concave corners of structures, near the heads of breakwaters, and around detachedbreakwaters, the wave height becomes larger than the normal value of standing waves owing to the effectsof diffraction and reflection. This increase in wave height shall be investigated thoroughly. Moreover, theirregularity of waves shall be considered in the analysis.[Technical Notes](1) Influence of Wave IrregularityWhen the wave height distribution near a concave corner or the head of a breakwater is calculated for regularwaves, a distributional form with large undulations is obtained. However, when wave irregularity is incorporatedinto the calculation, the undulated form of the distribution becomes smoothed out, excluding the region withinone wavelength of a concave corner, and the peak value of the wave height becomes smaller. Calculation usingregular waves thus overestimates the increase in the wave height around concave corners and the heads ofbreakwaters.(2) Graphs for Calculating Wave Height Distribution around a Concave CornerWave height distributions for irregular waves near a concave corner are shown in Fig. T- 4.5.10. This figureexhibits the form of the distribution of the maximum value of the wave height, as obtained from numericalcalculations for each principal wave direction. It has been assumed that waves are completely reflected by thebreakwater. In the diagram, Kd is the ratio of the wave height at the front face of the main breakwater to the waveheight of the incident waves. The irregular waves used in the calculation has a spectral form with Smax = 75,which implies a narrow directional spreading. The long dash-dot line in each graph shows the distribution of themaximum value of the wave height at each point as obtained using an approximate calculation. The length l1 isthat of the main breakwater, l2 is that of the wing breakwater, and b is the angle between the main breakwaterand the wing breakwater. This figure may be used to calculate the wave height distribution near a concavecorner. When it is not easy to use the calculation program, the approximate calculation method may be used.(3) Wave-Height-Reducing Effects of Wave-Absorbing WorkWhen a wave-absorbing work is installed in order to suppress the increase in wave height around a concavecorner and if the wave-absorbing work is such that the reflection coefficient of the breakwater becomes no morethan 0.4, it is quite acceptable to ignore the increase in wave height due to the presence of concave corner.However, this is only the case when the wave-absorbing work extends along the whole of the breakwater. If thebreakwater is long, one cannot expect the wave-absorbing work to be very effective unless it is installed alongthe entire length of the breakwater, because the effect of waves reflected from the wing breakwater extend evento places at a considerable distance away from the concave corner. The same can be said for the influence of themain breakwater on the wing breakwater.
    • PART II DESIGN CONDITIONS-73-Fig. T- 4.5.10 Distribution of the Maximum Value of the Wave Height around Concave Corner 32)Computer methodApproximate solution methodComputer methodApproximate solution method
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-74-(4) Increase in Wave Height at the Head of a BreakwaterNear the head of a semi-infinite breakwater or those ofbreakwaters at a harbor entrance (specifically within adistance of one wavelength from the head), wavesdiffracted by breakwaters exercise an effect of local waveheight increase over the normal standing wave heights.Because the wave height distribution has an undulatingform even at the back face of a breakwater, it is necessaryto take heed of the fact that the difference in water levelbetween the inside and the outside of the breakwatergives rise to a large wave force. Figure T- 4.5.11 showsan example of the results of a calculation of the waveforce ratio (i.e., the ratio of the wave force to that of astanding wave) near the head of a breakwater.(5) Increase in Wave Height around Detached BreakwaterAlong a detached breakwater, waves with the height greater than that of normal standing waves are produced,and the wave height distribution takes an undulating form even at the back face of the breakwater. This is due tothe effect of wave diffraction at the two ends of the breakwater 34). The wave force also becomes large due to thedifference between the water levels in the offshore and onshore sides of the breakwater. In particular, it isnecessary to take heed of the fact that, with a detached breakwater, the place where the maximum wave force isgenerated can shift greatly with the wave direction and the ratio of the breakwater length to the wavelength.Figure T- 4.5.12 shows an example of the results of a calculation of the wave force distribution along a detachedbreakwater for unidirectional irregular waves. In this calculation, the wave direction for which the largest waveforce occurrs is a = 30º (i.e., not when the waves are normally incident to the breakwater, but rather whenobliquely incident with a relatively shallow angle).Fig. T- 4.5.12 Wave Force Distribution along a Detached Breakwater4.5.5 Wave ShoalingWhen waves propagate into shallow waters, shoaling shall be considered in addition to refraction anddiffraction. It shall be standard to consider the nonlinearity of waves when calculating the shoalingcoefficient.[Commentary]Shoaling is one of the important factors that lead to changing of the wave height in coastal waters. It exemplifies thefact that the wave height in shallow waters is also governed by the water depth and the wave period. Figure T- 4.5.13has been drawn up based on Shuto’s nonlinear long wave theory. It includes the linearized solution by the smallamplitude wave theory and enables the estimation of the shoaling coefficient from deep to shallow waters. In thediagram, Ks is the shoaling coefficient, H0¢ is the equivalent deepwater wave height, H is the wave height at waterdepth h, and L0 is the wavelength in deepwater.Irregular wavesRegular wavesWaveforceratio0Fig. T- 4.5.11 Wave Force Distribution alonga Semi-Infinite Breakwater 33)WaveforceratioN (m)α=30°45°60°75°90°αN
    • PART II DESIGN CONDITIONS-75-Fig. T- 4.5.13 Graph for Evaluation of Shoaling Coefficient4.5.6 Wave BreakingAt places where the water depth is no more than about three times the equivalent deepwater wave height,changing of the wave height due to wave breaking shall be considered. It shall be standard to consider theirregularity of waves when calculating the change in the wave height due to wave breaking.[Commentary]After the height of waves has increased owing to shoaling, waves break at a certain water depth and the wave heightdecreases rapidly. This phenomenon is called the wave breaking. It is an important factor to be considered whendetermining the wave conditions exercising on maritime structures. For regular waves, the place at which wavesbreak is always the same: this is referred to as the “wave breaking point”. For irregular waves, the location of wavebreaking depends on the height and period of individual waves, and wave breaking thus occurs over a certaindistance: this area is referred to as the “breaker zone”.[Technical Notes](1) Change in Wave Height Due to Wave BreakingThe change in wave height due to wave breaking may be determined using Figs. T- 4.5.14 (a) ~ (e) or Figs. T-4.5.15 (a) ~ (e). These figures show the change in wave height for irregular waves as calculated by Goda 35), 44)using a theoretical model of wave breaking. For the region to the right of the dash-dot line on each graph, thechange in wave height is calculated using the shoaling coefficient (see 4.5.5 Wave Shoaling). For the region tothe left of this dash-dot line, the change in wave height due to wave breaking dominates, and so the wave heightmust be determined using this graph. As for the bottom slope, it is appropriate to use the mean bottom slope overthe region where the water depth to equivalent deepwater wave height ratio h/H0¢ is in the range of 1.5 to 2.5.(2) Scope of Application of Graphs of Wave Height ChangeAt places where the water depth is no more than about one half of the equivalent deepwater wave height, a majorportion of wave energy is converted to the energy of oscillating flows rather than to that of water levelundulation. Therefore, when calculating the wave force acting on a structure in a very shallow water, it isdesirable to use the wave height at the place where the water depth is one half of the equivalent deepwater waveheight, if the facilities in question are highly important.2%decayline000 00 00
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-76-2%decaylineBottom slope00 000h / H0Fig. T- 4.5.14 (a) Diagram of Significant WaveHeight in the Breaker Zonefor Bottom Slope of 1/102%decaylineBottom slope00000Fig. T- 4.5.14 (b) Diagram of Significant WaveHeight in the Breaker Zonefor Bottom Slope of 1/202%decaylineBottom slope000 00Fig. T- 4.5.14 (c) Diagram of Significant WaveHeight in the Breaker Zonefor Bottom Slope of 1/302%decaylineBottom slope000 00Fig. T- 4.5.14 (d) Diagram of Significant WaveHeight in the Breaker Zonefor Bottom Slope of 1/50
    • PART II DESIGN CONDITIONS-77-2%decaylineBottom slope00 000Fig. T- 4.5.14 (e) Diagram of Significant WaveHeight in the Breaker Zonefor Bottom Slope of 1/1002%decaylineBottom slope00 00Fig. T- 4.5.15 (a) Diagram of Highest WaveHeight in the Breaker Zonefor Bottom Slope of 1/102%decaylineBottom slope00 00Fig. T- 4.5.15 (b) Diagram of Highes WaveHeight in the Breaker Zonefor Bottom Slope of 1/202%decaylineBottom slope00 00Fig. T- 4.5.15 (c) Diagram of Highest WaveHeight in the Breaker Zonefor Bottom Slope of 1/30
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-78-(3) Approximate Calculation Formulas for Breaking Wave HeightCalculation of wave height changes based on a theoretical model for wave breaking generally requires use of acomputer. However, considering the variability of the phenomenon and the overall accuracy, it is acceptable tocalculate wave height changes using the following simple formula 35), 44):= (4.5.21)where(4.5.22)The shoaling coefficient Ks is determined using Fig. T- 4.5.13, the operators min{ } and max{ } take theminimum and maximum value of the mulitiple quantities within the braces, respectively, and tanq is the bottomslope.Similarly, an approximate calculation formula for the highest wave height Hmax is given as follows:(4.5.23)where(4.5.24)(4) Graph for Calculating Breaking Wave Height 35)If the maximum value (H1/3)peak of the significant wave height in the breaker zone is taken as representative ofthe breaking wave height, then the breaker index curve becomes as shown in Fig. T- 4.5.16. If the water depth(h1/3)peak at which the significant wave height is a maximum is taken as representative of the breaker depth, thenthe graph for calculating the breaker depth becomes as shown in Fig. T- 4.5.17.2%decaylineBottom slope00 00Fig. T- 4.5.15 (d) Diagram of Highest WaveHeight in the Breaker Zonefor Bottom Slope of 1/502%decaylineBottom slope00 00Fig. T- 4.5.15 (e) Diagram of Highest WaveHeight in the Breaker Zonefor Bottom Slope of 1/100H1 3¤KsH0¢ h L0¤ 0.2³min b0H0¢ b1h+( ) bmaxH0¢ KsH0¢, ,{ } h L0¤ 0.2<≧::{b0 0.028 H0¢ L0¤( ) 0.38– 20 qtan( )1.5[ ]exp=b1 0.52 4.2 qtan[ ]exp=bmax max 0.92 0.32 H0¢ L0¤( ) 0.29– 2.4 qtan[ ]exp,{ }=Hmax =1.8KsH0¢ h L0¤ 0.2³min b0H0¢ b1h+( ) bmaxH0¢ 1.8KsH0¢, ,{ } h L0¤ 0.2<≧* * *::{b0 0.052 H0¢ L0¤( ) 0.38– 20 qtan( )1.5[ ]exp=*b1 0.63 3.8 qtan[ ]exp=*bmax max 1.65 0.53 H0¢ L0¤( ) 0.29– 2.4 qtan[ ]exp,{ }=*6474864748
    • PART II DESIGN CONDITIONS-79-(5) Breaking Wave Height Criterion for Regular WavesFigure T- 4.5.18 shows the breaking wave height criterion for regular waves. This figure can be used tocalculate the breaking wave height criterion in hydraulic model experiments using regular waves. The curves inthe graph can be approximated with the following equation:(4.5.25)where tanq denotes the bottom slope.Figure T- 4.5.18 shows the limiting wave height at the point of first wave breaking. At places where thewater is shallow, the water depth increases owing to the wave setup caused by wave breaking. When estimatingthe limiting wave height in the breaker zone, it is thus necessary to consider this increase in water level.Fig. T- 4.5.18 Breaking Wave Height Criterion for Regular Waves(6) Change in Wave Height at Reef CoastsAt reef coasts where shallow water and a flat sea bottom continue over a prolonged distance, the change in waveheight cannot be calculated directly using Figs. T- 4.5.14 and T- 4.5.15. Instead, the following empiricalequation may be used 36):(4.5.26)Note: (01/3) peak is the maximum valueof 01/3 in the breaker zoneBottomslope00 0Fig. T- 4.5.16 Diagram of Maximum Valueof the SignificantNote: (01/3) peak is the water depth atwhich 01/3 is a maximumin the breaker zoneBottomslope0 00Fig. T- 4.5.17 Diagram of Water Depth at whichthe Maximum Value of the SignificantWave Height OccursHbL0------ 0.17 1 1.5phL0------ 1 15 4 3¤ qtan+( )–î þí ýì üexp–=Bottom slope00HxH0¢-------- B AxH0¢--------è øæ ö–î þí ýì üexp ah h¥+H0¢----------------+=
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-80-whereH0¢: equivalent deepwater wave heightHx: significant wave height at a distance x from the tip of the reefh: water depth over the reef: increase in the mean water level at a place sufficiently distant from the tip of the reefThe coefficients A and a are 0.05 and 0.33, respectively, according to the results of hydraulic modelexperiments. However, it is advisable to use the following values that have been obtained from the data of fieldobservations.The coefficient B corresponds to the bottom slope at the front of the reef. Using Fig. T- 4.5.14, it is obtainedfrom the significant wave height Hx = 0 at water depth h as follows.(4.5.28)The term (h+ )/H0¢ is given by(4.5.29)where b = 0.56. From the continuity of the mean water level at the tip of the reef (x = 0), C0 is given by(4.5.30)The term represents the rise in the mean water level at water depth h, which is controlled by the bottomslope in front of the reef and wave steepness (see 4.7.1 Wave Setup).The calculation method in the above has been derived under the assumption that the water depth h over thereef is small and waves break over the reef. It is thus not possible to apply the method when the water is deepand wave breaking does not occur.Considering the breaking wave height criterion of a solitary wave, the highest wave height Hmax, x at thedistance x from the tip of the reef may be obtained as follows.(4.5.31)where min{a, b} is the smaller value of a or b, and is the rise in the mean water level at the distance x and isgiven by the following equation:(4.5.32)4.6 Wave Runup, Overtopping, and Transmission4.6.1 Wave RunupWave runup shall be calculated appropriately by taking into account the configuration and location of theseawall and the sea bottom topgraphy.[Commentary]The phenomenon of wave runup is dependent upon a whole variety of factors, such as the wave characteristics, theconfiguration and location of the seawall, and the sea bottom topography; thus the runup height varies in a complexway. There are calculation diagrams and equations based on the results of past researches that may be used, althoughthey are applicable only under certain limited conditions. When the seawall and sea bottom are complex in form, it isadvisable to determine wave runup heights by carrying out hydraulic model experiments. When designing seawalls ofgently sloping type and the like, it is advisable to set the crown elevation of the seawall to be higher than the runupheight for regular waves. However, for irregular waves, depending on the wave height, overflow can occur, and soh¥A 0.089H0¢h h¥+---------------- 0.015+=(4.5.27)þïïïýïïïüa0.20 4m H0¢ 2m³>( )0.33 H0¢ 4m³( )îïíïì=BHx 0=H0¢-------------- ah h¥+H0¢----------------–=h¥h h¥+H0¢---------------- C0 138---ba2+è øæ ö¤=C0hx 0= h+H0¢-----------------------è øæ ö238---bHx 0=H0¢--------------è øæ ö2+=hx 0=Hmax x, min 0.78 h hx+( ) 1.8Hx,{ }=hxhx h+H0¢--------------- C038---bHxH0¢--------è øæ ö2–=
    • PART II DESIGN CONDITIONS-81-ultimately the crown elevation and the form of the seawall are determined so as to make the quantity of overtopping(see 4.6.2 Wave Overtopping) no more than a certain permissible value.[Technical Notes]The following is the description of methods for calculating the runup height over smooth impermeable slopes:(1) Simple Cross Section“A simple cross section” refers to the case in which a seawall (including an upright wall) having a front slope ofan uniform gradient a is located at a certain place (of water depth h) on the sea bottom with an almost uniformgradient q.(a) Region of standing wavesTakada has proposed the following equation for determining the runup height when the water depth h at thefoot of the levee is in the range where standing waves exist (i.e., deeper than the depth at the breaker line). Hedealt with two cases separately; i.e., the case where wave breaking does not occur on the front slope and thecase where such wave breaking does occur.Firstly, according to Miche’s equation, the minimum angle of inclination of the slope ac for which wavebreaking does not occur is found as that satisfying the following condition:(4.6.1)Accordingly, when the angle of inclination of the slope is greater than ac, wave breaking does not occur overthe slope, in which case the runup height is given by the following equation:: (4.6.2)where H0¢ is the equivalent deepwater wave height, Ks is the shoaling coefficient, H1 is the wave height at thewater depth at the foot of the slope, hs is the crest elevation, and R is the runup height.Takada used the following equation for hs/H1,which assumes that there is good agreement between thevalue from Miche’s standing wave theory and experimental data.(4.6.3)When the angle of inclination of the slope is smaller than ac, wave breaking does occur on the front slope. Inthis case, it is assumed that the runup height is proportional to tan2/3a, leading to the following equation:Ks : (4.6.4)When the water depth is such that standing waves exist, the runup height can be calculated as above. Themaximum runup height occurs when a = ac, with the runup height decreasing both when the slope is moresteeply inclined than this and when it is more gently inclined.(b) Region where the water is shallower than the breaker depthTakada has given the runup height for regions where the water is sufficiently shallow for wave breaking tooccur as follows:(4.6.5)where R0 is the runup height on the levee body at the shoreline (h = 0).Based on the experimental results of Toyoshima et al., R0/H0¢ is given as follows:: Bottom slope 1/10: Bottom slope 1/20 (4.6.6): Bottom slope 1/30The term hR in equation (4.6.5) is the water depth at the foot of the levee for which the runup height becomeslargest. It is estimated using Fig. T- 4.6.1, which shows the runup height for a vertical wall. The term LR in thefigure is the wavelength at water depth hR, while Rmax is the maximum runup height for the region where thewater depth is such that standing waves exist (i.e., the runup height when h = hR).2acp---------2acsinp----------------H0¢L0--------=RH0¢--------p2a-------hsH1------ 1–+è øæ ö Ks= a ac>hs H1¤ 1 pH1L------ khcoth 134 2khsinh----------------------14 h2 khcos-----------------------–+è øæ ö×+=R H0¢¤p2ac---------hsH1------ 1–è øæ ö+î þí ýì ü=accotacot--------------è øæ ö2 3¤a ac<R H0¢¤ Rmax H0¢¤ R0 H0¢¤–( )hhR----- R0 H0¢¤+=0.18 H0¢ L0¤( ) 1 2¤–R H0¢¤îïíïì= 0.075 H0¢ L0¤( ) 1 2¤–0.046 H0¢ L0¤( ) 1 2¤–
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-82-(2) Complex Cross SectionA “complex cross section” refers to the case wherethe sea bottom topography and the configuration andlocation of the seawall (on the whole) are as shown inFig. T- 4.6.2.(a) When the cross section can be considered to becomplex, the runup height of the seawall isobtained as follows (refer to Fig. T- 4.6.2) 37).① The wave breaking point B is determined fromthe deepwater wave characteristics.② Next, the runup height R is assumed and thepoint A is set at the maximum runup point. Then,the points A and B are joined by a straight line,and the gradient of this line yields the virtualgradient cota.③ The runup height for this virtual gradient iscalculated using Fig. T- 4.6.3, and the calculatedheight is compared with the initially assumedrunup height. If the two do not agree, then a newrunup height is assumed, and the estimation are repeated (i.e., the new runup height is used to give a newvirtual gradient and so on). This iterative process is repeated until convergence is achieved.④ The value so obtained is taken to be the runup height for the complex cross section in question.(b) When the results obtained from this method are compared with actual experimental results for a complex crosssection, it is generally found that there is good agreement between the two, with the error usually being nomore than 10%. However, if the bottom slope is too gentle, the agreement between the two becomes poor, andso this method should only be used when the bottom slope is steeper than 1/30.(c) Figure T- 4.6.4 shows experimental results obtained for a bottom slope of 1/70. This figure provides a usefulreference when estimating the runup height for a complex cross section with a gentle bottom slope.Fig. T- 4.6.2 Complex Cross Section and Virtual GradientFig. T- 4.6.3 Runup Height on a SlopeShoaling coefficient00000Fig. T- 4.6.1 Graph for Estimating hR for a Vertical WallVirtual gradientMaximum runup pointWave breaking pointActual cross section
    • PART II DESIGN CONDITIONS-83-Fig. T- 4.6.4 Runup Height on a Seawall Located Closer to the Land than the Wave Breaking Point(3) Oblique Wave IncidenceFigure T- 4.6.5 shows the relationship between the incident angle coefficient Kb and the angle b. Here, b is theangle between the wave crest line of the incident waves and the centerline of the seawall, and the incident anglecoefficient Kb is the ratio of the runup height for angle b to the runup height when the waves are normallyincident (i.e., when b = 0). This figure can be used to estimate the effect of wave incident angle on the runupheight.(4) Effects of Wave-Absorbing WorkThe runup height can be significantly reduced when the front face of a seawall is completely covered with wave-dissipating concrete blocks. Figure T- 4.6.6 shows an example. However, the effect of the concrete blocksvaries greatly according to the way in which they are laid, and so in general it is advisable to determine the runupheight by means of hydraulic model experiments.(5) Estimation ErrorsIt is important to note that the curves for determining the runup height have been obtained by averagingexperimental data that show a large scatter. It should also be noted that actual wave runup will frequentlyexceeds the design crown height because of wave irregularity when the crown height of a seawall is designedagainst the significant waves, even if the scatter of the experimental data is not considered; in fact, in extremecases as many as about a half of the waves may exceed this height. Accordingly, the crown height of a seawallshould not be decided based purely on the runup height of regular waves; rather, it is necessary to giveconsideration to the quantity of overtopping (see 4.6.2 Wave Overtopping).Holland(Former)Russia0 0Fig. T- 4.6.5 Relationship between Wave IncidentAngle and Runup Height(Full Lines: Experimental Values byPublic Works Research Institute,Ministry of Construction)Surface covered with wave-dissipatingconcrete blocksSmooth surface00 0Fig. T- 4.6.6 Reduction in Runup HeightDue to Wave-Absorbing Work
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-84-4.6.2 Wave OvertoppingFor structures for which the quantity of overtopping is an important design factor, the overtopping quantityshall be calculated by carrying out hydraulic model experiments or by using data from hydraulic modelexperiments carried out in the past. In this case, wave irregularity shall be considered.[Commentary]The “quantity of overtopping” is the total volume of overtopped water. The “rate of overtopping”, on the other hand,is the average volume of water overtopping in a unit time; it is obtained by dividing the quantity of overtopping bythe time duration of measurement. The quantity of overtopping and the rate of overtopping are generally expressedper unit width.If the quantity of overtopping is large, then not only there will be damage to the seawall body itself, but alsodamage by flooding to the roads, houses and/or port and harbor facilities behind the levee or seawall, despite that thelevee or seawall is intended to protect them. There is further a risk to users of water frontage amenity facilities thatthey may be drowned or injured. During design, it is necessary to make the quantity of overtopping no more than acertain permissible value that has been determined in line with the characteristics of structures and the situation withregard to their usage. Furthermore, when estimating the quantity of overtopping by means of experiments, it isdesirable to consider changes in tidal water level, i.e., to carry out experiments for different water levels.[Technical Notes](1) Diagrams for Calculating the Rate of Overtopping 38)For an upright or wave-absorbing seawall that has a simple form (i.e., that does not have anything like a toeprotection mound or a crown parapet), the rate of overtopping may be estimated using Figs. T- 4.6.7 ~ 4.6.10.These graphs have been drawn up based on experiments employing irregular waves. From the results of acomparison between the experiments and field observations, it is thought that the accuracy of the curves givingthe rate of overtopping is within the range listed in Table T- 4.6.1. The rate of overtopping for the wave-absorbing seawall has been obtained under the conditition that the lower armor layer at the crown consists of 2rows of wave-dissipating concrete blocks.Table T- 4.6.1 Estimated Range for the Actual Rate of Overtopping Relative to the Estimated ValueNote that when obtaining rough estimates for the rate of overtopping for irregular waves using Figs. T- 4.6.7 ~4.6.10, the following should be considered:(a) If the actual values of the bottom slope and the deepwater wave steepness do not match any of the values onthe graphs, the graph for which the values most closely match should be used, or alternatively interpolationshould be carried out.(b) The wave-dissipating concrete blocks in the figures are made up of two layers of tetrapods. If a different kindof wave-dissipating concrete block is used, or if the same kind of wave-dissipating concrete block is used butthere are differences in the crown width, in the way in which the tetrapods are laid, or in the form of the toe,then there is a risk that the actual rate of overtopping may considerably differ from the value obtained by thefigures.(c) If the number of rows of concrete blocks at the crown is increased, the quantity of overtopping tends todecrease 39).(d) When there are difficulties in applying the graphs for estimating the rate of overtopping, the approximateequation of Takayama et al. 40) may be used.Upright seawall Wave-absorbing seawall10-210-310-410-50.7 ~ 1.5 times0.4 ~ 20.2 ~ 30.1 ~ 50.5 ~ 2 times0.2 ~ 30.1 ~ 50.05 ~ 10q 2g H0( )3( )¤
    • PART II DESIGN CONDITIONS-85-Fig. T- 4.6.7 Graphs for Estimating the Rate of Overtopping for an Upright Seawall (Bottom Slope 1/30)
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-86-Fig. T- 4.6.8 Graphs for Estimating the Rate of Overtopping for an Upright Seawall (Bottom Slope 1/10)
    • PART II DESIGN CONDITIONS-87-Fig. T- 4.6.9 Graphs for Estimating the Rate of Overtopping for a Wave-Absorbing Seawall (Bottom Slope 1/30)Concrete block00000000Concrete block0 0000000000Concrete block000 00000
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-88-Fig. T- 4.6.10 Graphs for Estimating the Rate of Overtopping for a Wave-Absorbing Seawall (Bottom Slope 1/10)Concrete block0 000 00000Concrete block0 000000Concrete block0000000
    • PART II DESIGN CONDITIONS-89-(2) Permissible Rate of OvertoppingThe permissible rate of overtopping depends on factors such as the structural type of the seawall, the situationwith regard to land usage behind the seawall, and the capacity of drainage facilities; it must be set appropriatelyin line with the individual situation. Although it is thus impossible to give one standard value for the permissiblerate of overtopping, Goda 41) nevertheless gave the values for the damage limit rate of overtopping as listed inTable T- 4.6.2 based on past cases of disasters. Furthermore, Nagai et al. have considered the degree ofimportance of the facilities behind the seawall and have come up with the values for the permissible rate ofovertopping as listed in Table T- 4.6.3, using the results of experiments with regular waves.Table T- 4.6.2 Damage Limit Rate of OvertoppingTable T- 4.6.3 Permissible Rate of Overtopping (m3/m•s) as a Function of the Degree of Importance of the Hinterland(3) Equivalent Crown Height CoefficientThe equivalent crown height coefficient can be used as a guideline when setting the quantity of overtopping fora seawall upon which wave-dissipating concrete blocks are laid or for a seawall of wave-absorbing type withvertical slits. The equivalent crown height coefficient is the ratio of the height of the seawall in question to theheight of an imaginary upright seawall that results in the same quantity of overtopping, where the conditions interms of waves and the sea bottom topography are taken to be the same for the both cases. If the equivalentcrown height coefficient is less than 1.0, this means that the crown of the seawall under study can be loweredbelow that of an upright seawall and still give the same quantity of overtopping; in other words, the seawallunder study has a form that is effective in reducing the quantity of overtopping. Below are the reference valuesfor the equivalent crown height coefficient b for typical types of seawall.Wave-absorbing seawall with concrete block mound 40): ~ 0.7Vertical-slit type seawall 40) :Parapet retreating type seawall 39) : ~ 0.5Stepped seawall 39) : ~ 1.0When the waves are obliquely incident 42) :(q is the angle of incidence of the waves; it is 0º whenthe waves are normally incident on the seawall)(4) Effect of Winds on the Quantity of OvertoppingIn general, winds have a relatively large effect on the quantity of overtopping when it is small, although there isa lot of variation. However, the relative effect of winds decreases as the quantity of overtopping increases.Figure T- 4.6.11 shows the results of an investigation on the wind effect on the quantity of overtopping based onfield observations. The abscissa shows the spatial gradient of the quantity of overtopping, while the ordinateshows the quantity of overtopping per unit area. As can be seen from the figure, when the quantity ofovertopping is small, the larger the wind velocity, the smaller the spatial gradient of the quantity of overtoppingbecomes. When the quantity of overtopping is large, the spatial gradient of the quantity of overtoppingincreases. This shows that, when the quantity of overtopping is small, the distance over which a mass of watersplash strongly affected by the wind velocity, with a larger distance at a higher wind velocity; however, when thequantity of overtopping is large, the difference in the splash distance becomes small.(5) Overtopping of Multidirectional Random WavesIn waters where the multidirectionality of waves is well clarified, the rate of overtopping may be corrected inline with Smax as in reference 42).Type Covering Rate of overtopping (m3/m•s)RevetmentApron pavedApron unpaved0.20.05LeveeConcrete on front slope, crown, and back slopeConcrete on front slope and crown, but no concrete on backslopeConcrete on front slope only0.050.020.005 or lessAreas where there is a high concentration of houses, public facilities etc.behind the seawall, and so it is anticipated that flooding due to overtopping orspray would cause particularly serious damageAbout 0.01Other important areas About 0.02Other areas 0.02 ~ 0.06b 0.9=b 0.6=b 1.0=b 1.7=bîíì=1 2qsin–1 2i30°sin–::q 30°£q 30°>≦þýü
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-90-Fig. T- 4.6.11 Wind Effect on Spatial Gradient of Wave Overtopping Quantity4.6.3 Wave TransmissionIt shall be standard to calculate the height of waves transmitted behind a breakwater by overtopping and/orpermeation through the core or the fundation mound of breakwater by referring to either the results ofhydraulic model experiments or the past data.[Commentary]It is necessary to appropriately estimate the transmitted wave height after waves have overtopped and/or passedthrough a breakwater, because the transmitted waves affect the wave height distribution behind the breakwater.Transmitted waves include waves that have overtopped and/or overflowed, as well as waves that have permeatedthrough a rubble mound breakwater or a foundation mound of composite breakwater. Recently, several breakwatershave been built with caissons (which are originally not permeable) having through-holes in order to enhance theexchange of the seawater within a harbor. In this case, it is necessary to examine the value of wave transmissioncoefficient, because the coefficient serves as an indicator of the efficiency of the exchange of seawater.[Technical Notes](1) Transmission Coefficient for a Composite BreakwaterFigure T- 4.6.12 may be used to calculate the height of waves that are transmitted into a harbor when theyovertop a composite breakwater or permeate through a foundation mound. Even when the waves are irregular,the transmission coefficient agrees pretty well with that shown in Fig. T- 4.6.12. It has also been shown that Fig.T- 4.6.12 is valid not only for the significant wave height, but also for the highest one-tenth wave height and themean wave height.Fig. T- 4.6.12 Graph for Calculating the Wave Height Transmission CoefficientWindvelocityQuantityofovertoppingperunitareaqGradient
    • PART II DESIGN CONDITIONS-91-(2) Period of Transmitted Waves for a Composite BreakwaterThe period of the transmitted waves drops to about 50 ~ 80% of the corresponding incident wave period (this istrue both for the significant wave period and the mean period).(3) Experimental Data on Other Types of BreakwaterFor composite breakwaters covered with wave-dissipating concrete blocks, rubble mound breakwaters armoredwith wave-dissipating concrete blocks, and other such breakwaters, experiments on the transmitted wave heighthave been carried out by the Civil Engineering Research Institute of Hokkaido Development Bureau.(4) Transmission Coefficient for Structures Other than Composite Breakwaters(a) For a porous, water-permeable structure such as a rubble mound breakwater or a wave-dissipating concreteblock type breakwater, Kondo’s theoretical analysis may be referred to. The following empirical equation maybe used to obtain the transmission coefficient of a typical structure.Stone breakwater: (4.6.7)where kt=1.26 (B/d)0.67, B is the crown width of the structure, d is the depth from the water surface to theground surface of the structure, H is the height of incident waves, and L is the wavelength of transmittedwaves.(b) For a curtain wall breakwater, the empirial solutions of Morihira et al. 43) may be used (see Part VII, 3.3.1Curtain Wall Breakwater).(c) For the transmission coefficient of an upright breakwater of permeable type that has slits in both the front andrear walls, the experimental results are available.(d) Types of breakwater aiming to promote the exchange of seawater include multiple-wing type permeablebreakwaters, multiple-vertical cylinder breakwaters, horizontal-plate type permeable breakwaters, and pipetype breakwaters. The transmission coefficients of these types of breakwater have been obtained by hydraulicmodel tests.(5) Transmission Coefficient for a Submerged BreakwaterA submerged breakwater is usually made by piling up natural stones or crushed rock to form a mound, and thencovering the surface with concrete blocks to protect underlayers. For a submerged breakwater of crushed rock, agraph showing the relationship between the crown height of the breakwater and the transmission coefficient isavailable.4.7 Wave Setup and Surf Beat4.7.1 Wave SetupWhen designing structures that will be placed within the breaker zone, it is desirable to consider thephenomenon of wave setup as necessary, which occurs in the breaker zone owing to wave breaking as theyapproach the coast.[Technical Notes](1) Diagrams for Estimating the Amount of Wave SetupThe changes in the mean water level by random wave breaking on the bottom slopes of 1/100 and 1/10 ascalculated by Goda 35), 44) are shown in Figs. T- 4.7.1 and T- 4.7.2. The smaller the wave steepness (H0¢/L0,where H0¢ is the equivalent deepwater wave height and L0 is the wavelength in deepwater ), the larger the rise ofmean water level becomes. Moreover, the steeper the bottom slope, the larger the rise of mean water level.Figure T- 4.7.3 shows the rise of mean water level at the shoreline. The effects of wave steepness and bottomslope on the rise of mean water level are clearly shown. When H0¢/L0 is in the range 0.01 ~ 0.05, with theexception of very steep bottom slope, the rise of mean water level near the shoreline is of the order (0.1 ~0.15)H0¢.(2) Consideration of the Rise in Mean Water Level in DesignA rise of mean water level causes the wave breaking point to shift shoreward and the breaking wave height toincrease. The rise of in mean water level is thus important for the accurate calculation of the design wave heightin shallow waters.KT 1 1 kt H L¤+( )¤=
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-92-4.7.2 Surf BeatIn shallow waters, surf beat with the period of one to several minutes shall be investigated as necessary.[Technical Notes]Goda’s Formula for Estimating Surf Beat AmplitudeBased on the results of field observations of surf beat, Goda has proposed the following relationship 35), 44):(4.7.1)Changeinmeanwaterlevel0000/H0η′/H0h ′Fig. T- 4.7.1 Change in Mean Water Level(Bottom Slope 1/10)Changeinmeanwaterlevel000/H0h ′0η/H0′Fig. T- 4.7.2 Change in Mean Water Level(Bottom Slope 1/100)RiscinmeanwaterlevelWave steepness00 0Fig. T- 4.7.3 Rise in Mean Water Levelat the ShorelineOaraiNiigataMiyazakiNear shoreline Offshore0000zrmshrms( )0---------------------H0¢L0--------- 1hH0¢---------+è øæ ö1 2¤Fig. T- 4.7.4 Ratio of Surf Beat Amplitude toDeepwater Wave Amplitudezrms0.04 hrms( )0H0¢L0-------- 1hH0¢--------+è øæ ö-------------------------------------0.01H0¢H0¢L0-------- 1hH0¢--------+è øæ ö-------------------------------------= =
    • PART II DESIGN CONDITIONS-93-where zrms is the root mean square amplitude of the surf beat wave profile, (hrms)0 is the root mean squareamplitude of the deepwater wave profile, H0¢ is the equivalent deepwater wave height, L0 is the wavelength indeepwater, and h is the water depth.This equation shows that the amplitude of the surf beat is proportional to the deepwater wave height, that itfalls as the water depth increases, and that it increases as the deepwater wave steepness H0¢/L0 decreases. FigureT- 4.7.5 shows a comparison between the estimation by equation (4.7.1) and actual observation values.4.8 Long-Period Waves and SeicheWith regard to long-period waves and seiche in harbors, field observations shall be carried out as far aspossible, and appropriate measures to control them shall be taken based on the results of theseobservations.[Commentary]Water level fluctuations with the period between one and several minutes sometimes appear at observation points inharbors and off the shore. Such fluctuations are called long-period waves. If the period of such long-period waves isclose to the natural period of oscillation of the vibration system made up of a vessel and its mooring ropes, thephenomenon of resonance can give rise to a large surge motion even if the wave height is small, resulting in largeeffects on the cargo handling efficiency of the port. If it is clear from observations that long-period waves ofsignificant wave height 10 ~ 15 cm or more frequently arise in a harbor, it is advisable to investigate either hard orsoft countermeasures.When conspicuous water level fluctuations with the period several minutes or longer occur at an observation pointin a harbor, it can be assumed that the phenomenon of “seiche” is taking place. This phenomenon occurs when smalldisturbances in water level generated by changes in air pressure out at sea are amplified by the resonant oscillationsof the harbor or bay. If the amplitude of such seiche becomes significantly large, inundation at the head of the bay orreverse outflow from municipal drainage channels may occur. Also high current velocities may occur locally in aharbor, resulting in breaking of the mooring ropes of small vessels. When drawing up a harbor plan, it is thusdesirable to give consideration to making the shape of the harbor to minimize the seiche motion as much as possible.[Technical Notes](1) Threshold Height of Long-period Waves for CargoHandling WorksIt is necessary to give due consideration to the factthat long-period waves in front of a quaywall caninduce ship surging with the amplitude of severalmeters through resonance. The threshold height oflong-period waves for smooth cargo handling worksdepends on the factors such as the period of the long-period waves, the dimensions of the vessel inquestion, the mooring situation, and the loadingconditions. Nevertheless, according to fieldobservations carried out in places like TomakomaiBay 46), it corresponds to a significant wave height ofabout 10 ~ 15 cm.(2) Calculating the Propagation of Long-period WavesIt is desirable to calculate the propagation of long-period waves into a harbor by setting up incidentwave boundary out at sea and then using either theBoussinesq equation 29) or a calculation method thatuses long linear wave equations 47).(3) Standard Spectrum for Long-period WavesWhen there has been insufficient field observationdata of long-period waves out at sea and the long-period wave conditions that determine the design external forces have not been established, the standardspectrum shown in reference 48) or its approximate expression may be used. Figure T- 4.8.1 shows a comparisonbetween an observed spectrum and an approximate form of the standard spectrum. The term al in the figure is aparameter that represents the energy level of the long-period waves.(4) Calculation Method for SeicheSee 6.5 Seiche for a calculation method for seiche.Observed spectrumApproximate form ofstandard spectrumFig. T- 4.8.1 Comparison between Standard Spectrumwith Long-period Components andObserved Spectrum
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-94-4.9 Waves inside Harbors4.9.1 Calmness and DisturbancesWhen evaluating the harbor calmness, the factors that give rise to disturbances in the harbor shall be setappropriately.[Commentary]The problem of harbor calmness is extremely complex. It involves not only physical factors such as waves, winds,vessel motions, and the wind- and wave-resistance of working machinery, but also the factors requiring humanjudgement: the latter include the easiness of vessels entering and leaving a harbor, vessel refuge during stormyweather, and the threshold conditions of works at sea. The harbor calmness is further related with the economicfactors, such as the efficiency of cargo handling works, the operating rate of vessels, and the cost of constructing thevarious facilities required to improve the harbor calmness. The factors that lead to wave disturbances in harbors,which form the basis of the criteria for determining the harbor calmness, include the following:(a) Waves penetrating through the harbor entrance(b) Transmission of waves into the harbor over breakwaters(c) Reflected waves(d) Long-period waves(e) SeicheIn large harbors, wind waves generated within the harbor may require attention, and the ship-generated waves bylarger vessels may cause troubles for small vessels.4.9.2 Evaluation of Harbor CalmnessThe harbor calmness shall be evaluated by considering individual wave components estimated separatelyfor respective factors that cause disturbances in the harbor.[Technical Notes]The following method may be used for evaluating the harbor calmness:(1) To estimate the waves in the harbor, first establish the joint distribution of the height and direction of deepwaterwaves.(2) Next, calculate the wave transformations by refraction and breaking that takes place between the deepwaterwave observation and/or hindcasting point and the harbor entrance, using say the energy balance equationmethod, and thus obtain the wave conditions at the harbor entrance.(3) Obtain the wave height in the harbor, focusing mainly on diffraction and reflection. If necessary, carry out aninvestigation on wave transmission at this time.(4) The wave height in the harbor can be estimated by taking the squares of each of the diffracted wave height, thereflected wave height and the transmitted wave height, adding the results, and then taking the square root. Forharbors where the effects of transmitted waves are relatively slight, the wave period in the harbor may be takento be the same as the period of the diffracted waves. Note that the wave height in the harbor should beinvestigated for each wave direction for various classes of wave heights with the occurrence probability outsidethe harbor.(5) It is standard to express the occurrence rate of waves in a harbor as the percentage of the waves exceeding 0.5 mor 1.0 m in height or in terms of the number of days. However, depending on the usage purpose, it is alsoacceptable to take into consideration the exceedance probability for other wave height classes. The harborcalmness is obtained by subtracting from 100% the occurrence probability (in percentage) that the wave heightin the harbor exceeds the threshold level for cargo handling works at the berth in question. It is not possible todetermine a value for the threshold wave height for cargo handling works that is valid universally; rather, itdepends on the purpose for which the wharf facilities are used, the dimensions of vessels, and the period anddirection of waves, etc. Nevertheless, a value of 0.5 to 1.0 m (significant wave height) may be used as areference value. However, it should be noted that the critical wave height for cargo handling is lower for wavesof long-periodicity such as swell 49), and so care is required when evaluating the net working rate for ports andharbors that face out onto the open sea.4.10 Ship WavesIn canals and navigation channels, it is desirable to examine the influence of waves generated by movingvessels.
    • PART II DESIGN CONDITIONS-95-[Technical Notes](1) Pattern of Ship Waves as Viewed from TopIf ship waves are viewed from top, it appears as shown in Fig. T- 4.10.1. Specifically, it is composed of twogroups of waves. One group of waves spread out in a shape like 八 (the Chinese character for 8) from a pointslightly ahead of the bow of the vessel. The other group of waves are behind the vessel and are such that thewave crest is perpendicular to the vessel’s sailing line. The former waves are termed the “divergent waves”,while the latter are termed the “transverse waves”. The divergent waves form concave curves; the closer to thesailing line, the smaller the gap between waves. On the other hand, the transverse waves are approximately arc-shaped, with the gap between waves being constant (i.e., independent of the distance from the sailing line). Indeep water, the area over which the ship waves extend is limited within the area bounded by the two cusplineswith the angles ± 19º28 from the sailing line and starting from the origin (i.e., the point from which the cusplines diverge) lying somewhat in front of the bow of the vessel. The divergent waves cross the transverse wavesjust inside the cusplines; this is where the wave height is largest. The wave steepness is smaller for the transversewaves than for the divergent waves, implying that the transverse waves often cannot be discerned from an aerialphotograph.Fig. T- 4.10.1 Plan View of Ship Waves(2) Wavelength and Period of Ship WavesThe wavelength and period of ship waves differ for the divergent waves and the transverse waves, with the latterhaving both a longer wavelength and a longer period. Amongst the divergent waves, the wavelength and periodare both longest for the first wave and then become progressively shorter.(a) The wavelength of the transverse waves can be obtained by the numerical solution of the following equation,which is derived from the condition that the celerity of the transverse waves must be the same as the velocityat which the vessel is sailing forward.: (provided ) (4.10.1)whereLt: wavelength of transverse waves (m)h: water depth (m)V: sailing speed of vessel (m/s)Note however that when the water is sufficiently deep, the wavelength of the transverse waves is given by thefollowing equation:(4.10.2)whereL0: wavelength of transverse waves at places where the water is sufficiently deep (m)Vk: sailing speed of vessel (kt); Vk = 1.946V (m/s)(b) The period of the transverse waves is equal to the period of progresseive waves with the wavelength Lt (or L0)in water of depth h. It is given by equation (4.10.3) or (4.10.4).(4.10.3)(4.10.4)Vessels sailing linegLt2p------- 2phLt----------tanh V 2= V gh<L02pg------V 2 0.169Vk2= =Tt2pg------Lt2phLt----------è øæ öcoth T02phLt----------è øæ öcoth= =T02pg------V 0.330Vk= =
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-96-whereTt: period of transverse waves in water of depth h (s)T0: period of transverse waves at places where the water is sufficiently deep (s)(c) The wavelength and period of the divergent waves are given by equations (4.10.5) and (4.10.6), which arederived from the condition that the component of the vessel’s speed in the direction of travel of the divergentwaves must be equal to the velocity of the divergent waves.(4.10.5)(4.10.6)whereLd: wavelength of divergent waves as measured in the direction of travel (m)Td: period of divergent waves (s)q: angle between the direction of travel of the divergent waves and the sailing line (º)According to Kelvin’s theory of wave generation at places where the water is sufficiently deep, the angle oftravel q of the divergent waves can be obtained as shown in Fig. T- 4.10.2, as a function of the position of theplace under study relative to the vessel. Note however that for actual vessels the minimum value of q isgenerally about 40º, and q is usually about 50º ~ 55º for the point on a particular divergent wave at which thewave height is a maximum. Note also that, as shown in the illustration in the figure, the angle q directs thelocation of the source point Q from where the divergent wave has been generated; a is the angle between thecusp line and the sailing line.Fig. T- 4.10.2 Wave Direction and Period ofat Places Where the Water is Sufficiently Deep(3) Shoaling Effect on Ship WavesAs common with water waves in general, ship waves are affected by the water depth, and their properties varywhen the water depth decreases relative to the wavelength of ship waves. This shoaling effect on ship wavesmay be ignored if the following condition is satisfied:V ≦ (4.10.7)The critical water depth above which ship waves may be regarded as deepwater waves is calculated by equation(4.10.7), as listed in Table T-4.10.1. As can be seen from this table, the waves generated by vessels in normalconditions can generally be regarded as deepwater waves. Situations in which they must be regarded as shallowwater waves include the following cases: a high-speed ferry travels through relatively shallow waters, amotorboat travels through shallow waters, and ship waves propagate into shallow waters. Note that ship wavesin shallow water have a longer wavelength and period than those generated by the vessel sailing in deep water atthe same speed.Ld Lt2qcos=Td Tt qcos=RatiooftheperiodofthedivergentwavestothatofthetransversewavesTd/T0AnglebetweenthedirectionoftravelofthedivergentwavesandthesailinglineGRelative position of observation point x / s000.7 gh
    • PART II DESIGN CONDITIONS-97-Table T-4.10.1 Conditions under Which Ship Waves Can Be Regarded as Deepwater Waves(4) Height of Ship WavesThe Ship Wave Research Committee of the Japan Association for Preventing Maritime Accidents has proposedthe following equation for giving a rough estimate of the height of ship waves:(4.10.8)whereH0: characteristic wave height of ship waves (m), or the maximum wave height observed at a distance of100 m from the sailing line when a vessel is sailing at its full-load cruising speedLs: length of the vessel (m): full-load cruising speed (kt)EHPW: wave-making power (W)The wave-making power EHPW is calculated as follows.(4.10.9)(4.10.10)(4.10.11)S ≒ (4.10.12)(4.10.13)whereSHPm: continuous maximum shaft power (W)r0: density of seawater (kg/m3); r0 = 1030 (kg/m3)V0: full-load cruising speed (m/s); V0 = 0.514VKCF: frictional resistance coefficientn: coefficient of kinematic viscosity of water (m2/s); n ≒ 1.2 × 10-6 (m2/s)Ñ: full-load displacement of vessel (m3)Equation (4.10.8) has been obtained by assuming that the energy consumed through wave making resistance isequal to the propagation energy of ship waves, while the values of the coefficients have been determined asaverages from the data from ship towing tank tests. The characteristic wave height H0 varies from vessel tovessel, although for medium-sized and large vessels it is about 1.0 ~ 2.0 m. Tugboats sailing at full speedproduce relatively large waves.It is considered that the wave height decays as s-1/3, where s is the distance of the observation point from thesailing line. It is also considered that the wave height is proportional to the cube of the cruising speed of thevessel. Accordingly:(4.10.14)whereHmax:maximum height of ship waves at any chosen observation point (m)s:distance from the observation point to the sailing line (m)Vk:actual cruising speed of the vessel (kt)Equation (4.10.14) cannot be applied if s is too small; specifically, the approximate minimum value of s forwhich equation (4.10.14) can be applied is either the vessel length Ls or 100 m, whichever is the smaller.The upper limit of the height of ship waves occurs when the breaking criterion is satisfied; this criterion isexpresed as the steepness Hmax/Lt of the highest divergent wave being equal to 0.14. If the angle between thewave direction and the sailing line is assumed to be q = 50º at the point on a divergent wave where the waveheight becomes largest, the upper limit of the wave height at any given point is given by equation (4.10.15). Thisalso assumes, however, that the conditions for deepwater waves are satisfied.(4.10.15)whereSpeed of vessel Vk (kt)Water depth h (m) ≧Period of transverse waves T0 (s)5.01.41.77.53.12.510.05.53.312.58.64.115.012.45.017.516.95.820.022.06.625.034.48.330.049.69.9H0Ls100---------è øæ ö1 3¤ EHPW1620LsVK------------------------=VKEHPW EHP EHPF–=EHP 0.6SHPm=EHPF12---rSV03CF=2.5 ÑLsCF 0.075V0Lsn-----------log 2–è øæ ö2¤=Hmax H0100s---------è øæ ö1 3¤ VkVK------è øæ ö3=Hlimit 0.010Vk2=
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-98-Hlimit:upper limit of the height of ship waves as determined by the wave breaking conditions (m)(5) Propagation of Ship Waves(a) Among two groups of ship waves, the transverse waves propagate in the direction of vessel’s sailing line, andcontinue to propagate even if the vessel changes course or stops. In this case, the waves have a typical natureof regular waves (with the period being given by equation (4.10.3), and they propagate at the group velocity,undergoing transformation such as refraction and others. Takeuchi and Nanasawa gave an example of suchtransformations. Note however that as the waves propagate, the length of wave crest spreads out (the wavecrest gets longer), and even when the water is of uniform depth, the wave height decays in a manner inverselyproportional to the square root of the distance traveled.(b) The direction of propagation of a divergent wave varies from point to point on the wave crest. According toKelvin’s theory of wave generation, the angle between the direction of propagation and the sailing line is q =35.3º at the outer edge of a divergent wave. As one moves inwards along the wave crest, the value of qapproaches 90º. The first(c) arriving at a any particular point has the angle q = 35.3º, while q getting gradually larger for subsequentwaves. This spatial change in the direction of propagation of the divergent waves can be estimated using Fig.T- 4.10.2.(d) The propagation velocity of a divergent wave at any point on the wave crest is the group velocitycorresponding to the period Td at that point (see equation (4.10.6)). In the illustration in Fig. T- 4.10.2, thetime needed for a component wave to propagate at the group velocity from the point Q at wave source to thepoint P is equal to the time taken for the vessel to travel at the speed V from the point Q to the point O. Sinceeach wave profile propagates at the wave velocity (phase velocity), the waves appear to pass beyond thecuspline and vanish one after the other at the outer edge of the divergent waves.(6) Generation of Solitary Waves.When a vessel sails through shallow waters, solitary waves are generated in front of the vessel if the cruisingspeed Vk (m/s) approaches . Around the mouths of rivers, there is a possibility of small vessels beingaffected by such solitary waves generated by other large vessels 50).[References]1) Dean, G. R.: “Stream function wave theory and application”, Handbook of Coastal and Ocean Engineering, Volume 1, GulfPub., 1991, pp. 63-94.2) Dean G. R. and R. A. Dalrymple: “Water Wave Mechanics for Engineers and Scientists”, World Scientific, 1991, pp. 305-3093) Goda, Y.: “Wave forces on a vertical circular cylinder: Experiments and proposed method of wave force computation”, Rept.of PHRI, No. 8, 1964, 74 p.4) Yoshimi GODA, Yasumasa SUZUKI: “Computation of refraction and diffraction of sea waves with Mitsuyasu’s directionalspectrum”, Tech. Note of PHRI, No. 230, 1975 (in Japanese).5) Pierson, W. J. Jr., G. Neumann and R. W. James: “Practical methods for observing and forecasting ocean waves by means ofwave spectra and statistics”, U. S. Navy Hydrographic Office, Pub. 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    • PART II DESIGN CONDITIONS-99-22) Saville. T.: “The effect of fetch width on wave generation”, Tech. Memo., B. E. B., No. 70.23) Wilson, B. W.: “Graphical approach to the forecasting of waves in moving fetches”, Tech, Memo., B. E. B., No. 73, 1955.24) Bretschneider. C. L.: “Decay of ocean waves: Fundamentals of ocean engineering - Part 8b”, Ocean Industry, 1968, pp. 45-50.25) Gringorten, I. I.: “A plotting rule for extreme probability paper”, J. Geophysical Res., Vol. 68 No. 3, 1963, pp. 813-814.26) Petruaskas, C. and P. M. Aagaard: “Extrapolation of historical storm data for estimating design wave heights”, Preprints 2ndOTC, No. 1190, 1970, pp. I-409-428.27) Yoshiyuki ITO, Katsutoshi TANIMOTO, Shoichi YAMAMOTO: “Wave height distribution in the region of ray crossing -application of the numerical analysis method of wave propagation -”, Rept of PHRI, Vol. 11, No. 3, 1972, pp. 87-110 (inJapanese).28) Tomotsuka TAKAYAMA, Naota IKEDA, Tetsuya HIRAISHI: “Practical computation method of directional random wavetransformation”, Rept. of PHRI, Vol. 30, No. 1, 1991, pp. 21-67 (in Japanese).29) Tetsuya HIRAISHI, Isao UEHARA, Yasumasa SUZUKI: “Applicability of wave transformation model in boussinesqequation”, Tech. Note of PHRI, No. 814, 1995, 22 p. 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Note of PHRI, No.112, 1971 (in Japanese).34) Yoshimi GODA, Tomotsuka YOSHIMURA: “Wave force computation for structures of large diameter, isolated in theoffshore”, Rept. of PHRI, Vol. 10, No. 4, 1971 (in Japanese).35) Yoshimi GODA: “Deformation of irregular waves due to depth-controlled wave breaking” Rept. of PHRI, Vol. 14, No. 3,1975 (in Japanese).36) Tomotsuka TAKAYAMA, Yutaka KAMIYAMA, Osamu KIKUCHI: “Wave transformation on a reef ”, Tech. Note of PHRI,No. 278, 1977, 32 p. (in Japanese).37) Saville, T. Jr.: “Wave run-up on composite slopes”, Proc. 6th Conf. on Coastal Eng., 1958, pp. 691-699.38) Yoshimi GODA, Yasuharu KISHIRA, Yutaka KAMIYAMA: “Laboratory investigation on the overtopping rate of seawallsby irregular waves”, Rept. of PHRI, Vol. 14, No. 4, 1975, pp. 3-44 (in Japanese).39) Yoshimi GODA, Yasuharu KISHIRA: “Experiments on irregular wave overtopping characteristics of low crest types”, Tech.Note of PHRI, No. 242, 1976, 28 p. (in Japanese).40) Tomotsuka TAKAYAMA, Toshihiko NAGAI, Kazuhiko NISHIDA: “Decrease of wave overtopping amount due to seawallsof low crest types”, Rept. of PHRI, Vol. 21, No. 2, 1982, pp. 151-205 (in Japanese).41) Yoshimi GODA: “Estimation of the rate of irregular wave overtopping of seawalls”, Rept. of PHRI, Vol. 9, No. 4, 1970, pp.3-41 (in Japanese).42) Tetsuya HIRAISHI, Norio MOCHIZUKI, Kazuo SATO, Haruhiro MARUYAMA, Tsuyoshi KANAZAWA, TatsuyaMASUMOTO: “Effect of wave directionality on overtopping at seawall”, Rept. of PHRI, Vol. 35, No. 1, 1996, pp. 39-64 (inJapanese).43) Michio MORIHIRA, Shusaku KAKIZAKI, Yoshimi GODA: “Experimental investigation of a curtain-wall breakwater”,Rept. of PHRI, Vol. 3, No. 1, 1964, pp. 1-27 (in Japanese).44) Yoshimi Goda: “Irregular wave deformation in the surf zone”, Constal Engineering in Japan, JSCE, Vol. 18, 1975, pp. 13-26.45) Kazumasa KATOH, Satoshi NAKAMURA, Naota IKEDA: “Estimation of infragravity waves in consideration of wavegroups - An examination on basis of field observation at HORF -”, Rep. of PHRI, Vol. 30, No. 1, 1991, pp. 137-163 (inJapanese).46) Tetsuya HIRAISHI, Atsuhiro TADOKORO, Hideyoshi FUJISAKU: “Characteristics of long period waves observed in port”,Rept. of PHRI Vol. 35, No. 3, 1996, pp. 3-36 (in Japanese).47) Tomotsuka TAKAYAMA, Tetsuya HIRAISHI: “Amplification mechanism of harbor oscillation derived from fieldobservation and numerical simulation”, Tech. Note of PHRI, No. 636, 1988, 70 p. (in Japanese).48) Tetsuya HIRAISHI, Tokuhiro TADOKORO, Shigenori TAMAKI, Junzo HASEGAWA: “Standard frequency spectrum oflong-period waves for design of port and harbor facilities,” porc. 44th Japanese Coastal Eng. Corof., 1997, pp. 246-250 (inJapanese).49) Shigeru UEDA, Satoru SHIRAISHI, Hiroyuki OSHIMA, Kohei ASANO: “Allowable wave height and wharf operationefficiency based on the oscillations of ships moored to quay walls”, Tech. Note of PHRI, No. 779, 1994, 44 p. (in Japanese).50) Ertekin, R. C., W. C. Webster and J. V. Wehausen: “Ship generated solitions”, Proc. 15th Symp. Nav. Hydrodyn., 1985, pp.347-364.51) Yoshimi GODA: “On the methodology of selecting design wave height”, Proc. 21st Int. Conf. Coastal Eng., ASCE, 1988, pp.899-913.52) Yoshimi GODA and Koji KOBUNE: “Distribution function fitting to storm waves”, Proc. 22nd Int. Conf. Coastal Eng.,ASCE, 1990, pp. 18-31.53) Yoshimi GODA: “Random Waves and Design of Maritime Structures (2nd Edition)”, World Scientific, Singapore, 2000,Chapt. 11 (Statistical Analysis of Extreme Waves).54) Yoshimi GODA: “Statistical variability of sea state parameters as a function of wave spectrum,” Coastal Engineering inJapan, JSCE, Vol. 31, No. 1, 1988, pp. 39-52.
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-100-Chapter 5 Wave Force5.1 General (Notification Article 5, Clause 1)The wave force acting on a structure shall be determined using appropriate hydraulic model experiments ordesign methods described in 5.2 Wave Force Acting on Upright Wall, with the design waves determinedby the procedures described in Chapter 4 Waves.[Commentary](1) Structure Type and Wave ForcesWave forces can be generally classified by the type of structure as follows:(a) Wave force acting on a wall-type structure(b) Wave force acting on armor stones or concrete blocks(c) Wave force acting on submerged members(d) Wave force acting on structures near the water surfaceThe wave force is different for each type of structure. It is thus necessary to use an appropriate calculationmethod in accordance with the structural type. For some types of structures with a few experiences ofconstruction, their wave forces have not been sufficiently elucidated, and therefore it is desirable to carry outstudies including hydraulic model experiments for such structures.(2) Wave Irregularity and Wave ForceSea waves are irregular with the wave height and period varying from wave to wave. Depending on the waterdepth and the topography of the sea bottom, there may appear waves that have not broken, waves that are justbreaking, or waves that have already broken. When calculating the wave force, it is important to include thewaves that cause the severest effect on the structure. It is necessary to give sufficient consideration to waveirregularity and to the characteristics of the wave force being produced in accordance with the type of structure.In general, it may be assumed that the larger the wave height, the greater the wave force becomes. It is thusacceptable to focus on the wave force of the highest wave among a train of irregular waves attacking thestructure. However, with regard to the stabilities of floating structures and cylindrical structures with smallrigidity, and those of concrete blocks or armor stones on the slope, it is desirable to consider the effect of thesuccessive action of the irregular waves.(3) Calculation of Wave Force Using Hydraulic Model ExperimentsWhen studying wave force using hydraulic model experiments, it is necessary to give sufficient consideration tothe failure process of the structure and to use an appropriate measurement method. It is also necessary to givesufficient consideration to the irregularity of waves. In particular, when carrying out experiments using regularwaves, an investigation against the highest wave should be included.5.2 Wave Force Acting on Upright Wall5.2.1 General ConsiderationsThe wave force acting on an upright wall varies with the wave conditions, as well as the tidal level, thewater depth, the sea bottom topography, the cross-sectional form of the structure, and the configuration ofthe alignment of the structure. The wave force acting on an upright wall shall thus be calculatedappropriately while considering these items.An upright wall on a steep seabed or a high mound is often subjected to a strong impulsive wavebreaking force, so that sufficient attention shall be paid to the conditions under which such a force isgenerated when calculating the wave force.[Commentary](1) Parameters Affecting Wave Force on an Upright Wall 1)The major parameters that affect the wave force acting on an upright wall are the wave period, the wave height,the wave direction, the water level, the water depth, the bottom slope, the water depth on and the berm width ofthe mound, the crown height of upright wall, and the water depth at the base of upright wall. In addition, it isalso necessary to consider the effect of the wall alignment. The wave force on an upright wall with a concavedalignment may be larger than that on an upright, straight wall of infinite length. Furthermore, if the front face ofupright wall is covered with a mound of wave-dissipating concrete blocks, the characteristics of these blocks andthe crown height and width of the mound will affect the wave force.(2) Types of Wave ForceThe wave force acting on an upright wall can be classified according to the type of waves as a standing waveforce, a breaking wave force, or a wave force due to a broken wave. It is considered that the wave force changes
    • PART II DESIGN CONDITIONS-101-its type continuously with the variation in the offshore wave height. A standing wave force is produced by waveswhose height is small compared with the water depth, and the change in the wave pressure over time is gradual.As the wave height increases, the wave force also increases. In general, the largest wave force is generated bythe waves breaking just a little off the upright wall. Accordingly, with the exception of very shallow waterconditions, the force exerted by waves breaking just in front of an upright wall is larger than the wave force byhigher waves that have already broken well. It is necessary to note that when breaking waves act on an uprightwall on a steep seabed, or on an upright wall set on a high mound (even if built on a gentle seabed), a very strongimpulsive breaking wave force may be generated.5.2.2 Wave Forces of Standing and Breaking Waves[1] Wave Force under Wave Crest (Notification Article 5, Clause 1, Number 1)(1) Wave Pressure on the Front Face of an Upright WallAssuming a linear distribution of wave pressure with a maximum value p1 at the still water level, 0at the height h* above the still water level, and p2 at the sea bottom, the wave pressure from thebottom to the crown of the upright wall shall be calculated by the following equations:h* (5.2.1)(5.2.2)(5.2.3)(5.2.4)whereh*: height above still water level at which intensity of wave pressure is 0 (m)p1: intensity of wave pressure at still water level (kN/m2)p2: intensity of wave pressure at sea bottom (kN/m2)p3: intensity of wave pressure at toe of upright wall (kN/m2)r0: density of water (t/m3)g: gravitational acceleration (m/s2)b: angle between the line normal to the upright wall and the direction of wave approach.The angle shall be reduced by 15º, but the resultant angle shall be no less than 0º. Thiscorrection provides a safety margin against uncertainty in the wave direction.l1, l2: wave pressure modification factors (1.0 is the standard value)h: water depth in front of upright wall (m)L: wavelength at water depth h used in calculation as specified in the item (3) below (m)HD: wave height used in calculation as specified in the item (3) below (m)(5.2.5)(5.2.6)(5.2.7)wherehb: water depth at an offshore distance of 5 times the significant wave height from theupright wall (m)d: water depth at the crest of either the foot protection works or the mound armoringunits of whichever is higher (m)h¢: water depth at toe of upright wall (m)min {a,b}: smaller value of a or b(2) Uplift beneath Upright WallThe uplift acting on the bottom of an upright wall is described by a triangular distribution, with thepressure intensity at the front toe pu given by the following equation and 0 at the rear toe.(5.2.8)0.75 1 bcos+( )l1HD=p1 0.5 1 bcos+( ) a1l1 a2l22bcos+( )r0gHD=p2p12ph L¤( )cosh----------------------------------=p3 a3p1=a1 0.612---4ph L¤4ph L¤( )sinh---------------------------------î þí ýì ü2+=x2 minhb d–3hb--------------è øæ öHDd-------è øæ ö22dHD-------,î þí ýì ü=a3 1h¢h---- 112ph L¤( )cosh----------------------------------–î þí ýì ü–=pu 0.5 1 bcos+( )a1a3l3r0gHD=
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-102-wherepu: uplift pressure acting at front toe of upright wall (kN/m2)l3: uplift pressure modification factor (1.0 is the standard value)(3) Wave Height and Wavelength Used in the Wave Pressure CalculationThe wave height HD and the wavelength L are the height and wavelength of the highest wave. Thewavelength of the highest wave is that corresponding to the significant wave period, while theheight of the highest wave is as follows:(a) When the upright wall is located off the breaking zone:HD = HmaxHmax = 1.8H1/3whereHmax: highest wave height of incident waves at the water depth at the upright wall (m)H1/3: significant wave height of incident waves at the water depth at the upright wall (m)(b) When the upright wall is located within the breaking zone:HD is the maximum wave height considering the breaking of irregular waves (m)[Commentary]It is standard to calculate the maximum horizontal wave force acting on an upright wall and the simultaneous upliftpressure using the extended Goda equation.The extended Goda pressure formula is that proposed by Goda and modified to include the effects of wavedirection and others. Its single-equation formula enables to calculate the wave force from the standing to breakingwave conditions without making any abrupt transition. However, where the upright wall is located on a steep seabed,or built on a high mound, and is subjected to a strong impulsive wave pressure due to breaking waves, the formulamay underestimate the wave force. It should therefore be carefully applied with consideration of the possibility ofoccurrence of impulsive wave pressure due to breaking waves (see 5.2.3 Impulsive Pressure Due to BreakingWaves).The wave pressure given by the Goda formula takes the hydrostatic pressure at the still water condition as thereference value. Any hydrostatic pressure difference between the offshore and onshore sides of the wall, if presents,should be considered separately. Further, the equation is designed to examine the stability of the whole body ofvertical wall. When breaking wave actions exist, the equation does not necessarily express the local maximum wavepressure at the respective positions; thus such should be considered during examination of the stress of structuralmembers.[Technical Notes](1) Wave Pressure on the Front Face According to the Extended Goda FormulaFigure T- 5.2.1 illustrates the distribution of wave pressure acting on an upright section of a breakwater. Thecorrection to the incident wave angle b is exemplified in Fig. T- 5.2.2.Fig. T- 5.2.1 Wave Pressure Distribution Used in Design Calculation678(5.2.9)BuoyancyF1DFuF2F3D?η@D*
    • PART II DESIGN CONDITIONS-103-Fig. T- 5.2.2 Way of Obtaining the Incident Wave Angle b(2) Highest WaveIn breakwater designs in general, it is necessary to evaluate the largest wave force that can be given by the Godaformula using the highest wave. The appearance of the highest wave in an irregular wave group is probabilistic,and so it is not possible to determine the highest wave explicitly. Nevertheless, after examination of the resultsof applying the current method to breakwaters in the field, it has been made standard to use 1.8 times thesignificant wave height as the height of the highest wave when the upright wall is located off the breaking zone.It has also been made standard to use the wavelength corresponding to the significant wave period as thewavelength of the highest wave.In order to determine whether or not the highest wave is subject to wave breaking, the graphs for determiningthe highest wave height (Fig. T- 4.5.15 (a)~(e) in 4.5.6 Wave Breaking) should be used by referring to thelocation of the peak wave height in the zone in the onshore side of the 2% decay line. It is acceptable to considerthat the highest wave is not subject to wave breaking when the water is deeper than that at the peak height, butthat it is subject to wave breaking when the water is shallower than this. If the highest wave height is to beobtained using the approximate equation (4.5.23) in 4.5.6 Wave Breaking, hb should be substituted as h in thefirst term in the braces { } on the right-hand side of the equation.If using a value other than 1.8 as the coefficient on the right-hand side of equation (5.2.9), it is necessary toconduct sufficient investigations into the occurrence of the highest wave and then choose an appropriate value(see 4.1.3 [2] Statistical Properties of Waves).(3) Correction Factors l1, l2, l3Equations (5.2.1) ~ (5.2.8) are the extended version of the Goda formula. It contains three correction factors sothat it can be applied to walls of different shapes and conditions. For an upright wall, the correction factors are ofcourse 1.0. The wave pressure acting on other types of wall such as a caisson covered with a mound of wave-dissipating concrete blocks or a perforated-wall caisson may be expressed using the extended Goda formula withappropriate correction factors (see 5.2.4 Wave Force on Upright Wall Covered with Wave-DissipatingConcrete Blocks).(4) Application of Other Theoretical and Calculation EquationsWhen the ratio of the wave height to the water depth is small and a standing wave force is obviously exerted ona upright wall, a high-accuracy, standing wave theory may be applied. In this case, however, it is necessary togive sufficient consideration to the irregularity of waves in the field, and to evaluate the force due to the highestwave. Moreover, when the applicability can be verified based on past results for existing breakwaters, theSainflou formula 3) and the Hiroi formula may also be used for a design wave force calculation.(5) Features and Application Limits of the Goda FormulaThe first feature of the Goda formula is that the wave force from standing waves to breaking waves can beevaluated continuously, including the effect of period. The parameter a1 given by equation (5.2.5) expresses theeffect of the period (strictly speaking h/L); it takes the limiting values of 1.1 for shallow water waves and 0.6 fordeepwater waves. The effect of period also appear when evaluating the maximum wave height to be used in thecalculation; for a constant deepwater wave height, the longer the period, the larger the maximum wave height inthe surf zone. Since the Goda formula incorporates the effect of period on the wave pressure as well as on themaximum wave height, it is necessary to take sufficient care when determining the period in the designconditions.Another feature of the Goda formula is that the change in the wave force with the mound height and thebottom slope is considered by means of the parameter a2. As can be seen from equation (5.2.6), as the moundheight is gradually increased from zero (i.e., d = h), a2 gradually increases from zero to its maximum value.After reaching its maximum value, a2 then decreases until it reaches zero again when d = 0. The maximumvalue of a2 is 1.1; combining this with the maximum value of a1 of 1.1, the intensity of the wave pressure p1 atthe still water level is given by 2.2r0gHD.With regard to the effect of the bottom slope, hb within the equation for a2 is taken as the water depth at thedistance of 5 times the design significant wave height from the upright wall. Because of this artifice, a steepbottom slope results in the same effect as having a high mound. The effect of the bottom slope also appear whenevaluating the maximum wave height to be used in the calculation. In the wave breaking zone, the steeper thebottom slope, the larger the wave height, because the wave height used in the calculation is the maximum wavePrincipaldirectionofwaveNormal Line to the alignment90°15°β
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-104-height at the a distance 5H1/3 offshore from the upright wall. The bottom slope thus has a strong influence on thewave force, and so care must be taken when setting the bottom slope in the design conditions.As explained above, the Goda formula considers the effects of the mound height and the bottom slope on thewave pressure. Nevertheless, for an upright wall on a high mound or a steep sea bed, a large impulsive breakingwave force may act, and under such conditions the Goda formula may underestimate the wave force. Whenapplying the Goda formula, it is thus necessary to pay attention to the risk of an impulsive breaking wave forcearising. In particular, with a high mound, it is necessary to consider not only a2 in equation (5.2.6) but also theimpulsive breaking wave force coefficient aI by Takahashi et al. (see 5.2.3 Impulsive Pressure Due toBreaking Waves), and to use aI in place of a2 when aI is the larger of the two.One more problem with the Goda formula concerns its applicability to extremely shallow waters, forexample near to the shoreline. The Goda formula cannot be applied accurately for broken waves. It is difficult,however, to clearly define where the limit of applicability lies. For cases such as the wave force acting on anupright wall near the shoreline, it is advisable to use other calculation equations together with the Goda formula.(see 5.2.7 Wave Force on Upright Wall near Shoreline or on Shore).(6) Modification of the Original Goda Formula for Wave DirectionAlthough results from a number of experiments on the effect of wave direction on the wave force are available,there are still many points that are unclear. Traditionally, for standing waves, no correction has been made forwave direction to the wave force. The effects of wave direction have been considered only for breaking waves,by multiplying the wave force by cos2b, where b is the angle between the direction of wave approach and theline normal to upright wall alignment. However, this has resulted in the irrational situation whereby the breakingwave force is assumed to decrease as the wave angle b increases, reaching zero at the limiting value b = 90º, andyet standing waves are assumed to maintain as the perfect standing wave condition. One explanation is such thatbecause actual breakwaters are finite in extension, when the incident angle is large (i.e., oblique waveincidence), it takes a considerably large distance from the tip of breakwater until the wave height becomes twotimes the incident height. As b approaches to the limiting value of b = 90º, the distance to the place where thewave height becomes two fold tends to go to infinity. In other words, in this case, it is appropriate to considerthat the wave pressure of progressive waves acts on the upright wall. Considering these points and application tobreakwaters in the field, it has been decided to correct equation (5.2.2) for wave direction by multiplying a2(which represents mound effects) with cos2b, and then multiplying the whole term by 0.5(1+cosb).(7) Wave Force and Significant Wave Period for Waves Composed of Two Groups of Different PeriodsExamples of two wave groups of different periods being superimposed are such a case that waves enter a bayfrom the outer sea and another group of waves are generated within the bay by local winds. Another case is thesuperposition of diffracted waves coming from the entrance of a harbor and waves transmitted by means ofovertopping. In such cases, the spectrum is bimodal (i.e., having two peaks), and there are actual cases of suchobservations in the field. Tanimoto et al. 4) carried out experiments on the wave force acting on the uprightsection of a composite breakwater by using waves with a bimodal spectrum, and verified that the Goda formulacan be applied even in such a case. They also proposed a method for calculating the significant wave period tobe used in the wave force calculation (see 4.5.4 Wave Reflection). If each frequency spectrum of the two wavegroups before superimposition can be considered to be a Bretschneider-Mitsuyasu type, the significant waveperiod after superimposition may be obtained using the method by Tanimoto et al. Then this significant waveperiod may be used in wave force calculation.(8) Wave Force for Low Crested Upright WallAccording to results of model experiments, the stability of upright wall tends to increase as the crown height isreduced. Nakata and Terauchi have proposed a method for calculating the wave force for a breakwater with alow crown height. In the method, the horizontal wave pressure and the uplift pressure from the Goda formula aremultiplied by a modification factor lh, thus reducing the wave force.(9) Wave Force for High Crested Upright WallWhen the crown of the upright wall is considerably higher than that for a normal breakwater, there will be noovertopping, meaning that the wave force may be larger than that given by the Goda formula. Mizuno andSugimoto carried out experiments into the wave force acting on a breakwater with a high crown.(10) Wave Force on Inclined WallsWhen the wall is slightly inclined, the horizontal wave force is more-or-less the same as that for a perfectlyupright wall. However, it is necessary to consider the vertical component of the wave force acting on theinclined surface, along with the reduction in uplift pressure and others. Tanimoto and Kimura 5) have carried outexperiments on the wave force for trapezoidal caisson walls, and have proposed a method for calculating thewave force. For a caisson in which the upper part of the upright section is inclined (sloping-top caisson), thehorizontal wave force is reduced not only for the sloping part but also for the vertical part. It is also necessary toconsider the vertical component of the wave force for the sloping part for stability analysis of breakwaters.Morihira et al. were the first to propose a method for calculating the wave force in such a case. Hosoyamada etal. have come up with a method that is based on the approach by Morihira et al., but the method by Hosoyamadais more general and can be applied for a wider variety of sloping-top caissons (see Part VII, 3.2.4 Sloping-TopCaisson Breakwater).
    • PART II DESIGN CONDITIONS-105-(11) Uplift on a Caisson with a FootingWhen a caisson has a footing, a wave force acts downwards onthe upper surface of the footing on the seaside, and an upliftpressure of p¢u acts at the front toe, while the uplift pressure at therear toe is zero. Nevertheless, in general the resultant force is notsignificantly different to that without the footing. It is thusacceptable to ignore the footing, and to assume that the upliftpressure has a triangular distribution as shown in Fig. T- 5.2.3,with the uplift pressure pu at the front toe being given by equation(5.2.8), and the uplift pressure at the rear toe being zero. If thefooting is extremely long, however, it is necessary to calculate theuplift pressure appropriately, considering the change in the upliftpressure p¢u at the front toe of the footing.(12) Wide Mound Berm in Front of the Upright WallThe wave force acting on the upright wall of a composite breakwater varies not only with the mound height butalso with the berm width and the front slope of mound (see 5.2.3 Impulsive Pressure Due to Breaking Waves).As explained, of these three factors, the Goda formula incorporates only the effect of the mound height.Consequently, if the width and/or slope of the mound are considerably different from normal, it is advisable tocarry out studies using hydraulic model experiments. Note however that if the berm is sufficiently wide, it maybe considered as a part of the topography of the sea bottom. Even with the standard formula, if the width is morethan one half of the wavelength, it is thus standard to use the water depth on the mound for evaluation of both thewave height and the wavelength to be used in the wave force calculation.(13) Wave Force Acting on an Upright Wall Comprised of a Row of Vertical CylindersNagai et al. and Hayashi et al. have carried out studies on the wave force acting on an upright wall comprised ofa row of cylinders (a pile breakwater). Through their researches, it has been verified that the wave force is notgreatly different from that acting on an upright wall with a flat face. It is thus acceptable to treat an upright wallcomprised of a row of cylinders as having a flat face and calculate the wave force using the Goda formula.[2] Wave Force under Wave Trough (Notification Article 5, Clause 1, Number 2)The negative wave force at the time of wave trough acting at a wall shall be calculated using eitherappropriate hydraulic model experiments or an appropriate calculation formula.[Commentary]When the trough of a wave is acting at a wall, a negative wave force acts corresponding to the trough depth of thewater surface from the still water level. A “negative wave force” is the force directed seaward. It is necessary to notethat the negative wave force may be comparable in magnitude to a positive wave force when the water is deep and thewavelength is short.[Technical Notes](1) Negative Wave Pressure DistributionThe negative wave pressure acting on an upright wall at the wave trough can be approximately estimated asshown in Fig. T- 5.2.4. Specifically, it can be assumed that a wave pressure acts toward the sea, with themagnitude of this wave pressure being zero at the still water level and having a constant value of pn from a depth0.5HD below the still water level right down to the toe of the wall. Here, pn is given as follows:(5.2.10)wherepn: intensity of wave pressure in constantregion (kN/m2)r0: density of seawater (usually 1.03 t/m3)g: gravitational acceleration (9.81 m/s2)HD: wave height used in design calculation(m)In addition, the negative uplift pressure acting on thebottom of the upright wall can be assumed to act asshown in Fig. T- 5.2.4. Specifically, it can beassumed that an uplift pressure acts downwards withits intensity being pn (as given by equation (5.2.10))at the front toe, zero at the rear toe, and having atriangular distribution in-between. Incidentally, it is necessary to use the highest wave height as the wave heightHD used in the design calculation.Fig. T- 5.2.3 Uplift Pressure WhenThere Is a Footingpn 0.5r0gHD=ShorewardSeaward0.50,T- 5.2.4 Negative Wave Pressure Distribution
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-106-(2) Negative Wave Force by Finite Amplitude Wave TheoryGoda and Kakizaki 6) have carried out a wave force calculation based on the fourth order approximate solutionsof a finite amplitude standing wave theory, and presented calculation diagrams for negative wave pressure. It hasbeen verified that their calculation results agree well with experimental results. When the water is deep andstanding waves are clearly formed, it is acceptable to use the results of this finite amplitude standing wavetheory of higher order approximation. It should be noted that, for a deepwater breakwater, the negative waveforce at the wave trough may become larger than the positive wave force at the wave crest, and that the uprightwall may slide toward offshore.5.2.3 Impulsive Pressure Due to Breaking Waves(1) When it is apprehended that an impulsive pressure due to breaking waves may be generated, a studyincluding hydraulic model experiments shall be carried out as a general rule.(2) It is desirable to avoid the adoption of cross-sectional forms and structure type that may induce thegeneration of large impulsive pressure due to breaking waves. If a large impulsive pressure due tobreaking waves cannot be avoided, it is desirable to redesign the structure such that the wave forcewill be reduced, for example by providing appropriate wave-absorbing works.[Commentary]An impulsive pressure is generated when the wave front of a breaking wave strikes a wall surface. It has been shownfrom model experiments that under certain conditions the maximum wave pressure may rise as much as several tensof times the hydrostatic pressure corresponding to the wave height (1.0r0 gHD). However, such a wave pressure actsonly locally and for a very short time, and even slight changes in conditions lead to marked reduction in the wavepressure. Because of the impulsive nature of the wave force, the effects on stability and the stress in structuralelements vary according to the dynamic properties of the structure. Accordingly, when there is a risk of a largeimpulsive pressure due to breaking waves being generated, it is necessary to take appropriate countermeasures byunderstanding the conditions of the impulsive pressure generation and the wave force characteristics by means ofhydraulic model experiments.[Technical Notes](1) Conditions of Impulsive Pressure Due to Breaking WavesA whole variety of factors contribute to generation of an impulsive pressure due to breaking waves, and so it isdifficult to describe the conditions in general. Nevertheless, based on the results of a variety of experiments, itcan be said that an impulsive pressure is liable to occur in the following cases when the wave angle b is less than20º.(a) Steep bottom slopeWhen the three conditions (the bottom slope is steeper than about 1/30; there are waves that break slightly offthe upright wall; and their equivalent deepwater wave steepness is less than 0.03) are satisfied simultaneously,then an impulsive pressure is liable to be generated.(b) High moundEven if the bottom slope is gentle, the shape of the rubble mound may cause an impulsive pressure to begenerated. In this case, in addition to the wave conditions, the crown height, the berm width and the slopegradient of the mound all play a part, and so it is hard to determine the conditions under which such animpulsive pressure will be generated. In general, an impulsive pressure will be generated when the mound isrelatively high, the berm width is suitably wide or the slope gradient is gentle, and breaking waves form avertical wall of water at the slope or at the top of the mound 7). When the seabed slope is gentler than aboutand the ratio of the depth of water above the top of the mound (including any armor work) to the waterdepth above the seabed is greater than 0.6, it may be assumed that a large impulsive pressure will not begenerated.(2) CountermeasuresIf a large impulsive pressure due to breaking waves acts on an upright wall, the wave force can be greatlyreduced by sufficiently covering the front face with a mound of wave-dissipating concrete blocks. In particular,with a high mound, a sufficient covering with wave-dissipating concrete blocks can stop the occurrence of theimpulsive pressure itself. In some cases the action of an impulsive pressure can also be avoided by using specialcaissons such as perforated-wall caissons or sloping-top caissons 7). The wave direction also has a large effect onthe occurrence of an impulsive pressure, and therefore, one possible countermeasure is to ensure that the wavedirection is not perpendicular to the breakwater alignment.(3) Investigating Wave Force Using Model ExperimentsWhen investigating the wave force using hydraulic model experiments for the case that an impulsive pressuredue to breaking wave acts, it is necessary to give consideration to the response characteristics of the structure to1 50¤
    • PART II DESIGN CONDITIONS-107-the impact force. It is better to study the stability of the upright wall as a whole by sliding tests, and to study thestrength of structural elements such as parapets by stress and strain measurements.(4) Impulsive Pressure Due to Breaking Waves Acting on an Upright Wall on a Steep Seabed.(a) Water depth that produce a maximum wave pressure and the mean intensity of wave pressureMitsuyasu 8), Hom-ma et al., Morihira et al. 9), Goda and Haranaka 10), Horikawa and Noguchi, and Fujisakiand Sasada have all carried out studies on the impulsive pressure due to breaking waves acting on an uprightwall on a steeply sloping sea bottom. In particular, Mitsuyasu carried out a wide range of experiments usingregular waves whereby he studied the breaking wave force acting on an upright wall on uniform slopes ofgradient 1/50, 1/25, and 1/15 for a variety of water depths. He investigated the change in the total wave forcewith the water depth at the location of the upright wall, and obtained an equation for calculating the waterdepth hM at the upright wall for which the impulsive wave force is largest. When the Mitsuyasu equation isrewritten in terms of the deepwater wavelength, it becomes as follows:(5.2.11)where(5.2.12)H0: deepwater wave height (m)L0: deepwater wavelength (m)tanq: gradient of uniform slopeHom-ma, Horikawa and Hase have proposed a slightly different value for CM based on the results ofexperiments with a gradient of 1/15 and other data. In any case, the impulsive wave pressure is largest whenthe structure is located slightly shoreward of the wave breaking point for progressive waves.Figure T- 5.2.5 shows the total wave force when the impulsive wave force is largest for a number of slopegradients, as based on the results of Mitsuyasu’s experiments. In this figure, the mean intensity of the wavepressure p has been obtained and then divided by r0gHD to make it dimensionless; it has then been plottedagainst the deepwater wave steepness. It is possible to gain an understanding of the overall trend from thisfigure. Specifically, it can be seen that the smaller the wave steepness, the larger the impulsive pressure isgenerated. Also, as the slope gradient becomes smaller, the intensity of the maximum impulsive pressuredecreases.(b) Conditions for generation of impulsive breaking wave pressureThe conditions for the occurrence of animpulsive pressure on a steep seabed, asdescribed in (1) (a), have been set by prima-rily employing Fig. T- 5.2.5 as a grossguideline. For irregular waves in the sea,the wave steepness can be evaluated as theratio of the equivalent deepwater waveheight corresponding to the highest waveheight Hmax to the deepwater wavelengthcorresponding to the significant waveperiod: the wave height Hmax is to be evalu-ated at the distance 5H1/3 from the uprightwall. One may refer to Fig. T- 5.2.5 inorder to obtain an approximate estimate ofthe mean intensity of the wave pressure forthis equivalent deepwater wave steepness.In this case, Hb should be taken to be theaforementioned Hmax.One can also envisage an installation of a breakwater at a place where the risk of impulsive pressuregeneration is not large for the design waves. However, when placing an upright wall closer to the shore wherewaves already broken act upon, it becomes important to carry out investigations for waves with a height lesserthan that of the design waves.(c) Impulsive wave force acting on an upright wall on a horizontal floor adjoining a steep slopeTakahashi et al. 11) have carried out studies on the impulsive wave pressure acting on an upright wall on ahorizontal floor that is joined to a steep slope. They employed a horizontal berm connected to a slope ofgradient 1/10 or 3/100 in a wave channel, and then measured the wave pressure that acts on an upright wall ata variety of positions with regular waves. They have proposed an equation (valid for certain wave conditions)for calculating the upright wall position at which the wave force is largest and the maximum wave force in thatcondition.hMH0------ CMH0L0------è øæ ö1 4/–=CM 0.59 3.2 qtan–=Fig. T- 5.2.5 Mean Intensity of Wave Pressurefor the Severest Wave Breaking(Upright Wall on a Steep Slope)
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-108-(5) Impulsive Wave Pressure Acting on a Composite Breakwater(a) Effect of the mound shape (impulsive breaking wave pressure coefficient)Takahashi et al. have proposed, based on the results of sliding experiments 7), the impulsive breaking wavepressure coefficient aI. This is a coefficient that represents the extent of the impulsive pressure due tobreaking waves when the mound is high. It is expressed as the function of the ratio of the wave height to thedepth of water above the mound in front of the caisson H/d, the ratio of the depth of water above the mound tothe original water depth at the upright wall d/h, and the ratio of the berm width of the mound to the wavelengthat this place BM/L. Note that the wave height H is the design wave height (highest wave height).The impulsive breaking wave pressure coefficient aI is expressed as the product of aI0 and aI1 as in thefollowing equations:(5.2.13)(5.2.14)Figure T- 5.2.6 shows the distribution of aI1.It attains the maximum value of 1 when d/his 0.4 and BM /L is 0.12. The impulsive break-ing wave pressure coefficient aI takes valuesbetween 0 and 2; the larger the value of aI,the larger the impulsive breaking wave forceis. When calculating the wave force usingGoda’s formula, one should use aI in place ofa2 (equation (5.2.6)) if aI is larger than a2.Note that equation (5.2.13) for aI has beenderived for the case of H/h being equal to0.60 or greater, based on the results of slidingexperiments. This coefficient aI may be usedwhen examining the sliding of an uprightwall against the waves of relatively largeheight.(b) Effect of the crown height of the upright wallThe higher the crown height, the greater therisk of an impulsive breaking wave forcebeing generated. This is because the steepfront of a breaking wave often takes a nearlyvertical cliff of water above the still waterlevel, and if there is an upright wall at thisplace, the impact of the wave front results inthe generation of an impulsive force. Forexample, Mizuno et al. have pointed out thetendency that, when the crown is high, animpulsive breaking wave force is generatedeven when the mound is relatively low.(c) Effect of the wave directionAccording to the results of the sliding experiments of Tanimoto et al. 7), even if conditions are such that a largeimpulsive pressure is generated when the wave angle b is 0º, there is a rapid drop in the magnitude of the waveforce as b increases to 30º or 45º. By considering the fluctuation in the wave direction, it is reasonable toassume that the condition for the generation of an impulsive wave force is that b is less than 20º.(d) Dynamic response of the upright section to an impulsive force and the sliding of upright sectionWhen an impulsive pressure due to breaking waves acts on an upright section, the instantaneous local pressurecan rise up to several tens of times the hydrostatic pressure corresponding to the wave height, although theduration time of the impulsive pressure is very short. The impulsive peak pressures fluctuate significantly, butthe fluctuations in the impulse are not large. It is necessary to evaluate the contribution of the impulsivebreaking wave force to sliding in terms of the dynamic response, considering deformation of the mound andthe subsoil. Goda 12) as well as Takahashi and Shimosako, have carried out calculations of the shear force atthe bottom of an upright section using dynamic models. Judging by the results of these calculations and theresults of various sliding experiments, it would seem reasonable to take the mean intensity of the wavepressure equivalent to the sliding shear force to be (2.5 ~ 3.0) r0gH. The impulsive breaking wave pressurecoefficient aI has been introduced, based on the results of sliding experiments with consideration of suchdynamic response effects.aI aI0aI1=aI0 =îíìH d¤ H d¤ 2£2 H d¤ 2>::≦00 0.1 0.2 0.3 0.40.20.40.60.81.00.00.90.80.60.40.20.1αI1h – dhBMLBHdαI= αI0αI1αI0=Hd :Hd 22 :Hd ><=2Fig. T- 5.2.6 Impulsive Breaking WavePressure Coefficient aI1
    • PART II DESIGN CONDITIONS-109-5.2.4 Wave Force on Upright Wall Covered with Wave-Dissipating Concrete BlocksThe wave force acting on an upright wall covered with a mound of wave-dissipating concrete blocks shallbe evaluated based on hydraulic model experiments or an appropriate calculation equation, considering thecrown height and width of the wave-absorbing work as well as the characteristics of the wave-dissipatingconcrete blocks.[Commentary]If the front face of an upright wall is covered with a mound of wave-dissipating precast concrete blocks, the featuresof wave force acting on the wall are changed. The extent of this change depends on the characteristics of incidentwaves, along with the crown height and width of the wave-absorbing work, the type of wave-dissipating concreteblocks used, and the composition of the wave-absorbing work. In general, when nonbreaking waves act on an uprightwall, the change in wave force upon the upright wall covered with wave-dissipating blocks is not large. However,when a large impulsive breaking wave force acts, the wave force can be reduced significantly by covering the uprightwall with a mound of wave-dissipating blocks. Nevertheless, such a reduction in the wave force is only achievedwhen the wave-absorbing work has a sufficient width and crown height; in particular, it should be noted that if the topof the wave-absorbing work is below the design water level, the wave-absorbing work often invites an increase in thewave force.[Technical Notes](1) Wave Force Calculation Formula for Upright Wall Sufficiently Covered with Wave-Dissipating Concrete BlocksThe wave force acting on an upright wall covered with a mound of wave-dissipating concrete blocks variesdepending on the composition of the wave-absorbing work, and therefore it should be evaluated using the resultsof model experiments corresponding to the design conditions. However, if the crown elevation of the wave-absorbing work is as high as the top of the upright wall and the wave-dissipating concrete blocks are sufficientlystable against the wave actions, the wave force acting on the upright wall may be calculated using the extendedGoda formula. In this method with the standard formula given in 5.2.2 Wave Forces of Standing and BreakingWaves, the values of h*, p1, and pu given by equations (5.2.1), (5.2.2), and (5.2.8) are used respectively, but it isnecessary to assign appropriate values to the wave pressure modification factors l1, l2, and l3 in accordancewith the design conditions.(2) Modification Factors for the Extended Goda FormulaThe method using the extended Goda formula can be applied by assigning appropriate values to the modificationfactors l1, l2, and l3. Studies have been carried out by Tanimoto et al. 13), Takahashi et al. 14), Sekino andKakuno, and Tanaka and Abe amongst others and have revealed the following:(a) Wave-dissipating concrete blocks cause a considerable reduction in the breaking wave pressure, and so it isgenerally acceptable to set the breaking wave pressure modification factor l2 to zero.(b) The larger the wave height, the smaller the modification factor l1 for standing wave type pressure and themodification factor l3 for uplift pressure become.(c) The larger the ratio of the block mound width to the wavelength, the smaller the modification factors l1 and l3become.(d) If even a small portion of the upper part of the upright section is left uncovered, there is a risk of the waveforce here becoming an impulsive breaking force.Based on such experimental results, Takahashi et al. 14) have summarized that in general, when the upright wallis sufficiently covered with wave-dissipating concrete blocks, the wave pressure reduction factor l2 may betaken to be zero, while the values of l1 and l3 depend primarily on the wave height H (the highest wave height).They have thus proposed the following equations:l1 = (5.2.15)l3 = l1 (5.2.16)l2 = 0 (5.2.17)In the breaker zone, where breakwaters covered with wave-dissipating concrete blocks are generally used, theabove equations give l1 = l3 = 0.8.6781.0 : H/h ≦ 0.31.2 - (2/3)(H/h) : 0.3 < H/h ≦ 0.60.8 : H/h > 0.6
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-110-5.2.5 Effect of Alignment of Breakwater on Wave ForceIn the case when the distribution of wave heights along the face line of a breakwater is not uniform, thewave force shall be calculated by giving appropriate consideration to this aspect of wave heightdistribution.[Commentary]When the extension of breakwater is not infinitely long, the distribution of the wave height along the face line ofbreakwater becomes non-uniform due to the effects of wave reflection and diffraction. Ito and Tanimoto 16) havepointed out that most damaged breakwaters having been struck by storm waves equivalent to design waves show apattern of meandering distribution of sliding distance (they have termed this “meandering damage”), and that one ofthe causes of this type of damage is the differences in the local wave forces induced by the non-uniform wave heightdistribution. The variation of wave heights along the breakwater is particularly prominent when the breakwateralignment contains a corner that is concave with respect to the direction of wave incidence (see 4.5.4 [3]Transformation of Waves at Concave Corners, near the Heads of Breakwaters, and around Detached Break-waters).Variations in wave heights along the breakwater alignment may also occur near the head of the breakwater. Inparticular, for a detached breakwater that extends over a short length only, diffracted waves from the two ends maycause large variations in wave heights 17).[Technical Notes]Wave force calculation methods that consider the effects of the shape of the breakwater alignment have not reached tothe level of reasonable reliability yet. It is thus desirable to carry out an investigation using hydraulic modelexperiments. Nevertheless, there is a good correlation between the increase in the wave height owing to the shape ofthe breakwater alignment and the increase in the wave force. It is thus acceptable to increase the wave height for thedesign calculations in accordance with the extent of the effect of the shape of the breakwater alignment as in equation(5.2.18), and then calculate the wave force based on the standard calculation formula.HD¢ = min {KcHD, KcbHb} (5.2.18)whereHD¢: wave height to be used in the wave force calculation in consideration of the effect of the shape of breakwateralignment (m)Kc: coefficient for the increase in wave height due to the effect of the shape of breakwater alignment; Kc ≧ 1.0Kcb: limit value of the height increase coefficient for breaking limit waves; Kcb ≒ 1.4HD: wave height used in the wave force calculation when the effects of the shape of breakwater alignment arenot considered (m)Hb: breaking wave height at the offshore location with the distance of 5 times the significant height ofprogressive waves from the upright wall (m)The height increase coefficient Kc in equation (5.2.18) is generally expressed as in equation (5.2.19). It should beappropriately determined based on the distribution of the standing wave height (see 4.5.4 [3] Transformation ofWaves at Concave Corners, near the Heads of Breakwaters, and around Detached Breakwaters) along the faceline of breakwater as determined under the condition that the waves do not break.Kc = HS / {HI (1 + KR)} (5.2.19)whereHS: standing wave height along the front wall of breakwater (m)HI: incident wave height (m)KR: reflection coefficient for the breakwater in questionIf the waves are treated as being of regular trains, then the coefficient for wave height increase varies considerablyalong the breakwater. Moreover, the height increase coefficient is very sensitive to the period of the incident wavesand the direction of incidence. It is thus reasonable to consider the irregularity of the period and the direction ofincident wave. It should be noted that the value of Kc obtained in this way varies along the breakwater and that theremay be regions where Kc < 1.0. However, the wave height to be used in design must not be less than the originalincident wave height.The limit value Kcb of the height increase coefficient for breaking waves has not been clarified in details.Nevertheless, it may be considered to be about 1.4 based on experimental results up to the present time.5.2.6 Effect of Abrupt Change in Water Depth on Wave ForceFor an upright wall located in a place where the water depth changes abruptly owing to the presence ofreefs and others, it is desirable to calculate the wave force acting on the upright wall based on hydraulicmodel experiments, by taking the rapid transformation of waves into consideration.
    • PART II DESIGN CONDITIONS-111-[Technical Notes]Ito et al. 18) have carried out experiments on the wave force acting on an upright wall located on or behind a reefwhere the water depth is more-or-less uniform, with the offshore slope of the shoal having a gradient of about 1/10.5.2.7 Wave Force on Upright Wall near Shoreline or on Shore[1] Wave Force at the Seaward Side of ShorelineIt is desirable to calculate the wave force acting on an upright wall in shallow water near the shorelinebased on hydraulic model experiments, considering the effects of water level changes due to surf beat etc.and the complex processes of random wave breaking.[Technical Notes]A number of different wave force formulas have been proposed for upright walls near the shoreline and on shore. It isnecessary to carry out an appropriate wave force calculation in line with the design conditions. Very roughlyspeaking, the standard formula in 5.2.2 Wave Forces of Standing and Breaking Waves are applicable in the regionswhere the seabed slope is gentle and the water is relatively deep. The formula of Tominaga and Kutsumi is applicablein the regions near the shoreline. The formula of Hom-ma, Horikawa and Hase is applicable in the regions where theseabed slope is steep and the water is of intermediate depth.When applying the standard wave pressure formula to the places where the water depth is less than one half theequivalent deepwater wave height, it may be appropriate to use the values for the wavelength and wave height at thewater depth equal to one half the equivalent deepwater wave height in the calculation.[2] Wave Force at the Landward Side of ShorelineIt is desirable to calculate the wave force on an upright wall situated on the landward side of the shorelinebased on hydraulic model experiments, considering increases in the water level due to surf beat and wavesetup as well as wave runup.[Technical Notes]For an upright wall situated on the landward side of the shoreline, the formulas by the US Army Coastal EngineeringResearch Center (CERC) 19) are available. Moreover, one may refer to the research that has been carried out byTominaga and Kutsumi on the wave force acting on an upright wall situated on the landward side of the shoreline.5.2.8 Wave Force on Upright Wave-Absorbing CaissonThe wave force acting on an upright wave-absorbing caisson shall be calculated based on hydraulic modelexperiments or appropriate calculation formulas, considering changes in the wave force due to thestructure of the wave-absorbing compartment.[Commentary]The wave force acting on an upright wave-absorbing caisson (perforated-wall caisson etc.) varies in a complex way.Specifically, it varies with the wave characteristics, the water level, the water depth, the topography of sea bottom andthe shape of the mound as with the case of a normal upright wall, but it also varies with the structure of the wave-absorbing compartment. It is thus difficult to designate a general calculation method that can be used in all cases.Consequently, if the calculation method that is sufficiently reliable for the structure in question has not beenproposed, it is necessary to carry out studies using hydraulic model experiments matched to the individual conditions.It is necessary to sufficiently investigate not only the wave force to be used in the stability investigation but also thewave force acting on structural members. Moreover, it should be noted that the wave force varies significantlyaccording to whether or not the top of wave chamber is covered with a ceiling slab.[Technical Notes](1) Wave Force without a Ceiling Slab in the Wave ChamberThe wave force acting on an upright wave-absorbing caisson varies depending on the structural conditions of thewave-absorbing compartment, and so it is not possible to calculate this wave force for all general cases involved.Nevertheless, for the normal case where there is no ceiling slab in the wave chamber, one can use the extendedGoda formula to calculate the wave force, provided necessary modifications are made. Takahashi et al. 20) havecarried out experiments on a vertical-slit wall caisson, and have presented a method for calculating the wavepressure acting on the slit and rear walls for four representative phases, whereby the wave pressure given by theextended Goda formula is multiplied by a modification factor l for the vertical-slit wall caisson; they givespecific values for the modification factor for the slit and rear walls for each phase. This method can be used to
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-112-give not only the wave force that is severest in terms of the sliding or overturning of the caisson, but also thewave force that is severest in terms of the design of the elements for each wall.(2) Wave Force with a Ceiling Slab in the Wave ChamberWhen the top of the wave chamber is closed off with provision of a ceiling slab, an impulsive pressure isgenerated at the instant when the air layer in the upper part of the wave chamber is trapped in by the rise of watersurface. It is thus necessary to give consideration to this impulsive pressure in particular with regard to the wavepressure used in design of structural elements. This impulsive pressure can be reduced by providing suitable airholes. However, it should be noted that if these air holes are too large, the rising water surface will directly hitthe ceiling slab without air cushion, meaning that the wave force may actually increase 22), 23).5.3 Mass of Armor Stones and Concrete Blocks5.3.1 Armor Units on Slope (Notification Article 48, Clause 5)It shall be standard to calculate the mass of rubble stones or concrete blocks necessary to cover the frontslope of a sloping structure that is subject to wave forces, by means of appropriate hydraulic modelexperiments or the following equation:(5.3.1)whereM: minimum mass of rubble stones or concrete blocks (t)rr: density of rubble stones or concrete blocks (t/m3)H: wave height used in the stability calculation (m)NS: stability numberSr: specific gravity of rubble stones or concrete blocks relative to sea water[Commentary]The armor layer for the slope of a rubble mound breakwater protects the rubble stones in the inside, and so it isnecessary to ensure that an armor unit has a mass sufficient to be stable against wave actions so that it does not scatteritself. The mass required to produce such stability can be calculated using a suitable calculation formula. Forexample, for the armor units on the slope of a rubble mound breakwater, the required mass was calculated in the pastby Hudson’s formula with an appropriate coefficient (KD value), but recently it has become common to use Hudson’sformula with a stability number. The latter is more general in that it can also be applied to other cases, such as thearmor units on the mound of a composite breakwater.[Technical Notes](1) Hudson’s FormulaThe required mass of armor units on a slope can be expressed using the Hudson formula with a stability number(this is also referred to as the generalized Hudson formula) 24) (see equation (5.3.1)).(2) Stability Number and Nominal DiameterThe stability number directly corresponds to the necessary size (nominal diameter) of the armor stones orconcrete blocks for a given wave height. In other words, by introducing the nominal diameter Dn = (M/rr)1/3 andthe term D = Sr - 1 and substituting them into equation (5.3.1), the following relatively simple equation isobtained:H/(DDn) = NS (5.3.2)It can be seen that the nominal diameter is proportional to the wave height with the constant of proportionalitybeing 1/DNS.(3) Design Wave HeightThe Hudson formula was proposed based on the results of experiments that used regular waves. When applyingit to the action of actual waves (which are irregular), there is thus a problem of which defcinition of wave heightsshould be used. However, with structures that are made of rubble stones or concrete blocks, there is a tendencyfor damage to occur not when one single wave having the maximum height H among an irregular wave trainattacks the armor layer, but rather for damage to progress gradually under the continuous action of waves ofvarious heights. Considering this fact and past experiences, it has been decided to make it standard to use thesignificant wave height of incident waves at the place where the slope is located as the wave height H inequation (5.3.1), because the significant wave height is representative of the overall scale of an irregular wavetrain. Consequently, it is also standard to use the significant wave height when using the generalized Hudsonformula. Note however that for places where the water depth is less than one half the equivalent deepwater waveheight, the significant wave height at the water depth equal to one half the equivalent deepwater wave heightshould be used.MrrH3NS3Sr 1–( )3----------------------------=
    • PART II DESIGN CONDITIONS-113-(4) Parameters Affecting the Stability NumberAs shown in equation (5.3.1), the required mass of armor stones or concrete blocks varies with the wave heightand the density of the armor units, and also the stability number NS. The NS value is a coefficient that representsthe effects of the characteristics of structure, those of armor units, wave characteristics and other factors on thestability. The main factors that influence the NS value are as follows.(a) Characteristics of the structure① Type of structure (rubble mound breakwater, breakwater covered with wave-dissipating concrete blocks,composite breakwater, etc.)② Gradient of the armored slope③ Position of armor units (breakwater head, breakwater trunk, position relative to still water level, front faceand top of slope, back face, berm, etc.)④ Crown height and width, and shape of superstructure⑤ Inner layer (its coefficient of permeability, thickness, and degree of surface roughness)(b) Characteristics of the armor units① Shape of armor units (shape of armor stones or concrete blocks; for armor stones, their diameterdistribution)② Placement of armor units (number of layers, regular laying or random placement, etc.)③ Strength of armor material(c) Wave characteristics① Number of waves acting on armor layers② Wave steepness③ Form of sea bottom (bottom slope, existence of reef, etc.)④ Ratio of wave height to water depth (as indices of nonbreaking or breaking wave condition, breaker type,etc.)⑤ Wave direction, wave spectrum, wave grouping characteristics(d) Extent of damage (damage rate, damage level, relative damage)Consequently, the NS value used in design must be determined appropriately based on hydraulic modelexperiments in line with the respective design conditions. By comparing the results of regular wave experimentswith those of irregular wave experiments, it was found that the ratio of the height of regular waves to thesignificant height of irregular waves that gave the same damage ratio (within the error of 10%) varied in therange of 1.0 to 2.0 (depending on the conditions). In other words, there was a tendency for the irregular waveaction to be more destructive than the action of regular waves. It is thus better to employ irregular waves inexperiments.(5) Stability number NS and KD valueIn 1959, Hudson published the so-called Hudson formula 24), replacing the previous Iribarren-Hudson formula.Hudson developed equation (5.3.1) by himself using instead of NS, i.e.(5.3.3)wherea: angle of the slope from the horizontal line (º)KD: constant determined primarily by the shape of the armor units and the damage ratioThe Hudson formula was based on the results of a wide range of model experiments and has proved itself well inusage in the prototype design. In the past, this formula (i.e., the one using the KD value) has thus been used in thecalculation of the required mass of armor units on a slope.However, the generalized Hudson formula that uses the stability number (equation (5.3.1)) has been used forquite a while for calculating the required mass of armor units on the mound of a composite breakwater (to bediscussed later), and is also used for the armor units of other structures such as submerged breakwaters. It is thusnow more commonly used than the old formula with the KD value, and so the generalized Hudson formula withthe stability number can be considered as being the standard equation for calculating the required mass of armorunits on a slope.The stability number NS can be derived from the KD value and the angle a of the slope from the horizontalline by using equation (5.3.3.) There is no problem with this process if the KD value is an established one and theslope angle is within a range of normal design. However, most of the KD values obtained up to the present timehave not sufficiently incorporated various factors like the characteristics of the structure and the waves. Thus,this method of determining the stability number NS from the KD value cannot be guaranteed to yield economicaldesign always. In order to calculate more reasonable values for the required mass, it is thus desirable to use theresults of experiments matched to the conditions in question, or else to use calculation formulas (calculationdiagrams) that include the various relevant factors as described below.KD acotN3SKD acot=
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-114-(6) Van der Meer’s Formula for Armor StonesIn 1987, van der Meer carried out systematic experiments concerning the armor stones on the slope of a rubblemound breakwater with a high crown. He proposed the following calculation formula for the stability number,which considers not only the slope gradient, but also the wave steepness, the number of waves, and the damagelevel 25). Note however that the following formula has been slightly altered in comparison with van der Meer’soriginal one in order to make calculations easier. For example, the wave height H2% for which the probability ofexceedance is 2% has been replaced by H1/20.NS = max {Nspl, Nssr} (5.3.4)Nspl = 6.2CHP 0.18 (S 0.2 / N 0.1) Ir- 0.5 (5.3.5)Nssr = CHP-0.13 (S 0.2 / N 0.1) (cota)0.5IrP (5.3.6)whereNspl: stability number for plunging breakersNssr: stability number for surging breakerIr: Iribarren number (tan a/Som0.5) (also called the surf similarity parameter)Som: wave steepness (H1/3/L0)L0: deepwater wavelength (L0 = gT1/32/2p, g= 9.81m/s2)T1/3: significant wave periodCH: modification factor due to wave breaking [=1.4 / (H1/20/H1/3) ](=1.0 in the region where wave breaking does not occur)H1/3: significant wave heightH1/20: highest one-twentieth wave height (see Fig. T- 5.3.1)a: angle of slope from the horizontal line (º)Dn50: nominal diameter of armor stone (=(M50/rr)1/3)M50: 50% value of the mass distribution curve of an armor stone (required mass of an armor stone)P: permeability coefficient of the inner layer (see Fig. T- 5.3.2)S: deformation level (S = A / Dn502) (see Table T- 5.3.1)A: erosion area of cross section (see Fig. T- 5.3.3)N: number of waves (in storm duration)The wave height H1/20 in Fig. T- 5.3.1 is for a point at a distance 5H1/3 from the breakwater, and H0’ is theequivalent deepwater wave height.The deformation level S is an index that represents the amount of deformation of the armor stones, and it is akind of damage ratio. It is defined as the result of the area A eroded by waves (see Fig. T- 5.3.3) being dividedby the square of the nominal diameter Dn50 of the armor stones. As shown in Table T- 5.3.1, three stages aredefined with regard to the deformation level of the armor stones: initial damage, intermediate damage, andfailure. With the standard design, it is common to use the deformation level for initial damage for N = 1000waves. However, with design where a certain amount of deformation is permitted, usage of the value forintermediate damage can also be envisaged.Table T- 5.3.1 Deformation Level S for Each Failure Stage for a Two-layered Armor(7) Stability Number for Armor Concrete Units of Rubble Mound BreakwaterVan der Meer has carried out model experiments on several kinds of precast concrete blocks, and proposed theformulas for calculating the stability number NS26). In addition, other people are also proceeding with researchinto establishing calculation formulas for precast concrete blocks. For example, Burcharth and Liu 27)haveproposed a calculation formula. However, it should be noted that these are based on the results of experimentsfor a rubble mound breakwater with a high crown.(8) Stability Number for Concrete Units of the Wave-Dissipating Block Mound in Front of Upright Walls (horizontally-composite breakwater)The wave-dissipating concrete block mound of a horizontally-composite breakwater may have various cross-sectional forms. In particular, when all the front face of an upright wall is covered by wave-dissipating concreteblocks, the stability is higher than for the normal case of armor concrete units covering a rubble moundbreakwater because the permeability is high. In Japan, much research has been carried out on the stability ofbreakwaters covered with wave-dissipating concrete blocks. For example, Tanimoto et al. 28), Kajima et al., andHanzawa et al. have carried out systematic research on the stability of wave-absorbing concrete blocks. Inaddition, Takahashi et al. 29)have proposed the following equation for wave-dissipating concrete blocks that arerandomly placed in the mound covering the whole of upright wall.Slope Initial damage Intermediate damage Failure1 : 1.51 : 21 : 31 : 41 : 6222333 ~ 54 ~ 66 ~ 98 ~128 ~1288121717
    • PART II DESIGN CONDITIONS-115-Sea Bottom slope 1/30Sea Bottom slope 1/50Sea Bottom slope 1/100H0′ : Equivalent deepwaterwave heightH0′/L0Fig. T- 5.3.1 Ratio of H1/20 to H1/3 (H1/20 Values are ata Distance 5H1/3 from the Breakwater)h/H0¢Nominal diameter of armor stonesNominal diameter of filter materialNominal diameter of core materialArmorlayerArmorlayerArmorlayerArmorlayerFilter layerFilterlayerImpermeablelayerCoreNo filter, no coreArea of eroded partFig. T- 5.3.3 Erosion Area AFig. T- 5.3.2 Permeability Coefficient P
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-116-(5.3.7)whereN0: relative damage (a kind of damage ratio that represents the extent of damage: it is defined as thenumber of concrete blocks that have moved within a width Dn in the direction of the breakwateralignment, where Dn is the nominal diameter of the concrete blocks: Dn = (M/rr)1/3, where M is themass of a concrete block)CH: modification factor due to wave breaking; CH = 1.4 / (H1/20 / H1/3) (in the region where wave breakingdoes not occur, H1/20 / H1/3 = 1.4, and so CH = 1.0)a, b: coefficients that depend on the shape of the concrete blocks and the slope angle (for concrete blockswith the KD value of 8.3, a = 2.32 and b = 1.33, if cot a = 4/3; a = 2.32 and b = 1.42, if cot a = 1.5)Takahashi et al. 29) have further presented a method for calculating the cumulative relative damage (the expectedrelative damage) over the lifetime of a breakwater. In the future, reliability design methods that consider theexpected relative damage will become important in the advanced design methodology.In the region where wave breaking does not occur, if the number of waves is 1000 and the relative damageN0 is 0.3, the design mass as calculated using the method of Takahashi et al. is more-or-less the same as thatcalculated using the KD value in the past. The value of N0 = 0.3 corresponds to the conventionally-used damageratio of 1%.(9) Breakwater HeadWaves attack the head of a breakwater from a whole angle of directions, and there is a greater risk of the armorunits on the top of the slope falling not so much forward but rather toward the rear side. Stones or concreteblocks to be used at the head of a breakwater must thus have a mass greater than the value given by equation(5.3.1). Hudson suggested to raise the mass by 10% in the case of stones and 30% in the case of concrete blocks.However, it is thought to be insufficient. It would be desirable to use the mass at least 1.5 times the value givenby equation (5.3.1) for both stones and concrete blocks.(10) Submerged Armor UnitsSince the action of waves on a rubble mound breakwater is weaker midwater than around the waterline, stonesor concrete blocks of reduced mass may be used at depths more than 1.5H1/3 below the still water level.(11) Effect of Wave DirectionThe extent to which the incident wave angle affects the stability of the armor stones has not been investigatedsufficiently. Nevertheless, according to the results of experiments carried out by van de Kreeke 30) in which thewave angle was changed between 0º (i.e., direction of incidence is perpendicular to the breakwater alignment),30º, 45º, 60º and 90º, the damage ratio for a wave direction of 45º or smaller is more-or-less the same as thatwhen the wave direction is 0º; when the wave direction is more than 60º, the damage ratio drops. Based on theseresults, it is considered that when the wave angle b (see Fig. T- 5.2.2 in 5.2.2 [1] Wave Force under WaveCrest) is 45º or less, the minimum mass should not be corrected for wave direction. Moreover, Christensen etal. 31) have shown that the stability increases when the directional spreading of random waves is large.(12) Integrity of Concrete BlocksWith a precast concrete block, it is necessary not only to ensure that the block has a mass sufficient to be stableagainst the design waves, but also to confirm that the block itself has sufficient structural strength.(13) Armor Units in Reef AreaIn general, a reef rises up at a steep slope from the relatively deep sea, and forms a relatively flat and shallow seabottom. Consequently, when a large wave arrives at such a reef, it breaks around the tip of the reef, and then theregenerated waves propagate over the reef in the form of surge. The characteristics of waves over a reef arestrongly dependent on not only the incident wave conditions but also the water depth over the reef and thedistance from the tip of the reef. The stability of wave-dissipating concrete blocks situated on a reef also variesgreatly for the same reasons, making the situation more complicated than that in general cases. The stability ofwave-dissipating concrete blocks situated on a reef must thus be investigated based either on model experimentsmatching the conditions in question or on field experiences for sites having similar conditions.(14) Armor Units of Low Crest BreakwaterFor a rubble mound breakwater with a low crown, it is necessary to note that the concrete blocks around itscrown (in particular on the shoreward side) are easily damaged. For example, for detached breakwater composedof wave-dissipating concrete blocks, unlike a caisson breakwater covered with wave-dissipating concreteblocks, there is no supporting wall at the back and the crown is not high. This means that the concrete blocksnear the crown (in particular at the rear) are easily damaged, and indeed such cases of block damage have beenreported.(15) Effect of Steep Slope BedWhen the bottom slope is steep and waves break in plunging form, a large wave force may act on concreteblocks, subject to their shapes. It is thus necessary to carry out appropriate investigations while considering thepossibility of large wave force (see Takeda et al.).NS CH a N0 N0.5¤( )0.2 b+{ }=
    • PART II DESIGN CONDITIONS-117-(16) High-density BlocksThe minimum mass of blocks that are made of high-density aggregate may also be determined using the Hudsonformula with the stability number (equation (5.3.1)). As shown by the equation, high-density blocks have a highstability, so a stable armor layer can be made using relatively small blocks of high density.(17) Effect of PlacementThe stability of wave-dissipating concrete blocks also varies with the method of placement (random placementor regular placement etc.). According to the results of experiments carried out to compare the random placementover the whole cross section and that of regular two-layer placement upon a stone core, the stability of theregular placement with well-interlocking was markedly improved for most of the cases tested. Moreover, thestability is also affected by the crown height and width of the mound of wave-dissipating concrete blocks.According to the results of a number of experiments, for example, there is a tendency of greater stability whenthe crown is high and wide.(18) Standard Method of Hydraulic Model ExperimentsThe stability of concrete blocks is influenced by a very large number of factors, and so it has still not beensufficiently elucidated. This means that it is necessary to carry out studies using model experiments for thedesign of prototype breakwaters, and it is needed to progressively accumulate the results of such experiments.The following points should be noted when carrying out studies using model experiments.(a) It is standard to carry out experiments using irregular waves.(b) For each particular set of conditions, the experiment should be repeated at least three times (i.e., with threedifferent wave trains). However, when experiments are carried out by systematically varying the mass andother factors and a large amount of data can be acquired, one run for each test condition will suffice.(c) It is standard to study the action of 1000 waves in total of three runs for each wave height level. Even for thesystematic experiments, it is desirable to apply more than 500 waves or so.(d) For the description of the extent of damage, in addition to the damage ratio which has been commonly used inthe past, the deformation level or the degree of damage may also be used. The deformation level is suitablewhen it is difficult to count the number of armor stones or concrete blocks that have moved, while the degreeof damage is suitable when one wishes to represent the damage to wave-dissipating concrete blocks. Thedamage ratio is the ratio of the number of damaged armor units in an inspection area to the total number ofarmor units in the same inspection area. The inspection area is taken from the elevation of wave runup to thedepth of 1.5H below the still water level or to the bottom elevation of the armor layer (take a shallower depth),where the wave height H is inversely derived from the Hudson formula with the mass of armor units as theinput. However, for the deformation level and the degree of damage, there is no need to define the inspectionarea. For evaluating the damage ratio, an armor unit is judged to be damaged if it has moved over a distance ofmore than about 1/2 to 1.0 times its height.5.3.2 Armor Units on Foundation Mound of Composite Breakwater (Notification Article 48, Clause 5)It shall be standard to calculate the mass of armor stones or concrete blocks for the foundation mound of acomposite breakwater, by means of appropriate hydraulic model experiments or the following equation:(5.3.1)whereM: minimum mass of rubble stones or concrete blocks (t)rr: density of rubble stones or concrete blocks (t/m3)H: wave height used in the stability calculation (m)NS: stability numberSr: specific gravity of rubble stones or concrete blocks relative to sea water[Commentary]The mass required for an armor unit covering the foundation mound of a composite breakwater varies according tothe wave characteristics, the water depth, the shape of the mound (thickness, berm width, slope angle, etc.), and thetype of armor unit, its placement method, and its position (breakwater head, breakwater trunk, etc.). In particular, theeffects of the wave characteristics and the mound shape are more pronounced than those in the case of the armor unitscovering the surface of sloped breakwater in 5.3.1 Armor Units on Slope. It is thus necessary to appropriatelydetermine the mass, considering the results of past studies, research, and actual experience in the field, and carryingout model experiments if necessary. Moreover, it is necessary to take sufficient heed of the effects of waveirregularity.MrrH3NS3Sr 1–( )3----------------------------=
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-118-Note however that the stability of the armor units covering the foundation mound of a composite breakwater is notnecessarily determined purely by their sizes. Depending on the structure and the layout of armor units, it may bepossible to achieve stability even when the armor units are relatively small.[Technical Notes](1) Generalized Hudson’s Formula for Calculating the Required MassSimilarly with the stable mass of armor units on a slope, the required mass of armor units covering thefoundation mound of a composite breakwater can be calculated using the generalized Hudson formula (theHudson formula with the stability number), i.e., equation (5.3.1). Ever since Brebner and Donnelly 32) used it asthe basic equation for calculating the required mass of the armor stones of the rubble mound for an upright wall,the generalized Hudson formula has been used widely, and in Japan it is also known as the Brebner-Donnellyformula. Because it has a certain degree of validity even from a theoretical standpoint, the generalized Hudsonformula may also be used as the basic formula for calculating the minimum mass of armor units for thebreakwater mound 33). Note however that the stability number NS varies not only with the water depth, the wavecharacteristics, the shape of the mound, and the characteristics of the armor units, but also with their position ofthe placement (breakwater trunk, breakwater head, etc.). It is thus necessary to assign the stability number NSappropriately through model experiments corresponding to the design conditions. Moreover, the wave heightused in the design calculation is generally the significant wave height, and the waves used in the modelexperiments should be irregular.(2) Stability Number for Armor StonesThe stability number NS can be determined using the method of Inagaki and Katayama 34), which is based uponthe work of Brebner and Donnelly and past experience of damage. However, the following formulas byTanimoto et al. 33) are based on the flow velocity near the mound and allow the incorporation of a variety ofconditions, and they have been extended by Takahashi, Kimura, and Tanimoto 35) to include the effects of wavedirection. The extended Tanimoto formulas have thus been made the standard formulas.(a) Extended Tanimoto formulas: (5.3.8)(5.3.9)(5.3.10)(5.3.11)whereh¢: water depth on top of rubble mound foundation (excluding the armor layer) (m) (see Fig. T- 5.3.4)l: in the case of normal wave incidence, the berm width BM (m)In the case of oblique wave incidence, either BM or BM¢, whichever gives the larger value of (k2)B(see Fig. T- 5.3.4)L: wavelength corresponding to the design significant wave period at the water depth h¢ (m)as: correction factor for when the armor layer is horizontal (= 0.45)b: incident wave angle (see Fig. T- 5.3.5)H1/3: design significant wave height (m)The validity of the above formulas have been verified for the breakwater trunk for oblique wave incidencewith an angle of incidence of up to 60º.Fig. T- 5.3.4 Standard Cross Section of a Composite Breakwater and Notations(b) Stability Number When a Certain Amount of Damage is PermittedSudo et al. have carried out stability experiments for the special case such that the mound is low and no wavebreaking occurs. They investigated the relationship between the number of waves N and the damage ratio, andproposed the following equation that gives the stability number NS* for any given number of waves N and anygiven damage ratio DN (%).NS max 1.8 1.31 k–k1 3/------------h¢H1 3¤------------ 1.8 1.5–1 k–( )2k1 3/-------------------h¢H1 3¤------------exp+,î þí ýì ü= BM L¢¤ 0.25<k k1 k2( )B=k14ph¢ L¢¤4ph¢ L¢¤( )sinh------------------------------------=k2( )Bmax as2sin bs2cos 2pl bcos L¢¤( ) 2ba2 2pl bcos L¢¤( )sincos,{ }=hhdB MB MChShorewardSeawardFoot protection blocksFoot protection blocksUprightsectionArmor material Rubble mound Armor material
    • PART II DESIGN CONDITIONS-119-* (5.3.12)where NS is the stability number given by the Tanimoto formula when N = 500 and the damage ratio is 1%. Indesign it is necessary to take N = 1000 considering the progress of damage, while the damage ratio 3% to 5%can be allowed for a 2-layer armoring. If N = 1000 and DN = 5%, then NS* = 1.44NS. This means that therequired mass decreases to about 1/3 of that required for N = 500 and DN = 1%.(3) Stability Number for Concrete UnitsThe stability number NS for concrete blocks varies according to theshape of the block and the method of placement. It is thus desirableto evaluate the stability number by means of hydraulic modelexperiments. When carrying out such experiments, it is best toemploy irregular waves.(4) Conditions for Applying the Stability Number for Armor Stones onFoundation MoundWhen the water above the armor units covering a mound is shallow,wave breaking often causes the armor stones to become unstable. Itis thus appropriate to use the stability number for armor stones on amound only when h¢/H1/3 ≧ 1: when h¢/H1/3<1, it is better to use thestability number for armor stones on a slope of mound breakwater.The validity of the stability number for armor stones in theTanimoto formulas has not been verified experimentally for whenh’/H1/3 is small: when h’/H1/3 is about 1 or less, it is thus desirableto examine the validity using hydraulic model experiments.(5) Armor Layer ThicknessIt is standard to use two layers of armor stones. However, it isacceptable to use only one layer, provided that consideration isgiven to past experiences of breakwaters. In this case, one couldthink of compensating the use of one layer only by setting the damage ratio in the aforementioned equation(5.3.12) to a low value of DN = 1% for N =1000 acting waves. For concrete armor blocks, it is rather standard touse one layer, although two layers may be laid if the shape of the blocks is favorable for two layer placement andthe design wave conditions are severe.(6) Armor Units for Breakwater HeadAt the head of a breakwater, strong currents occur locally near the corners at the edge of the upright section,meaning that the armor units become liable to move. It is thus necessary to verify the extent to which the mass ofarmor units should be increased at the breakwater head by carrying out hydraulic model experiments. Ifhydraulic model experiments are not carried out, it is standard to increase the mass to at least 1.5 times that at thebreakwater trunk.The mass of the armor stones at the breakwater head can also be calculated using the extended Tanimotoformula. Specifically, for the breakwater head, the flow velocity parameter k in equation (5.3.9) should berewritten as follows:k = k 1 (k 2)T (5.3.13)(k2)T = 0.22 (5.3.14)Note however that if the calculated mass turns out to be less than 1.5 times that for the breakwater trunk, it isadvisable to set it to 1.5 times that for the breakwater trunk.5.4 Wave Forces Acting on Cylindrical Members and Large Isolated Structures5.4.1 Wave Force on Cylindrical MembersThe wave force acting on an cylindrical member can be calculated as the sum of a drag force that isproportional to the square of the water particle velocity under waves and an inertia force that isproportional to the water particle acceleration.[Commentary]Structural members such as piles that have a small diameter relative to the wavelength hardly disturb the propagationof waves. The wave force acting on such members can be obtained using the Morison equation, in which the waveforce is expressed as the sum of a drag force that is proportional to the square of the velocity of the water particles andan inertia force that is proportional to the acceleration. Note however that with the Morison equation, it is necessaryto assign accurate values to the water particle velocity and acceleration of the waves, as well as to the wave surfaceelevation. It is also necessary to appropriately evaluate the drag coefficient and the inertia coefficient by means ofmodel experiments or field measurement results. It should further be noted that the impact of the wave front mayNS NS DN 0.3 1 500 N¤–( ){ }exp¤[ ]0.25=BreakwatertrunkBreakwater headFig. T- 5.3.5 Shape of the BreakwaterAlignment and Effects ofWave Direction
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-120-generate an impulsive wave force if the member is located near to the still water level or if breaking waves hit themember, and that a lift force may act upon it, depending on the shape and position of the member.[Technical Notes](1) Morison’s EquationThe wave force acting on a structural member is calculated based on the following equation:(5.4.1)where: force that acts on a small length DS (m) in the axial direction of the member, where the direction ofthis force lies in the plane containing the member axis and the direction of motion of the waterparticles and is perpendicular to the member axis (kN): components of the water particle velocity (m/s) and acceleration (m/s2), respectively, in the directionperpendicular to the member axis that lies within the plane containing the member axis and thedirection of motion of the water particles (i.e., the same direction as ) (these components are forincident waves that are not disturbed by the presence of member): absolute value of (m/s)CD: drag coefficientCM: inertia coefficientD: width of the member in the direction perpendicular to the member axis as viewed from the directionof (m)A: cross-sectional area of the member along a plane perpendicular to member axis (m2)r0: density of seawater (normally 1.03 t/m3)Equation (5.4.1) is a generalized form of the equation presented by Morison et al. 36), to give the wave forceacting on a section of a very small length DS of a member orientated in any given direction. The arrows on top ofsymbols indicate that the force, velocity and acceleration are the components in the direction perpendicular tothe member. The first term on the right-hand side represents the drag force, while the second term represents theinertia force. The water particle velocity and acceleration components in the equation both vary in time andspace. It is necessary to take sufficient heed of these variations, and to investigate the distribution of the waveforce that is severest to the member or structure in question.(2) Water Particle Velocity and Acceleration ComponentsThe components of water particle velocity and acceleration and in equation (5.4.1) represent those of thewater particle motion at the center of the member. These components are in the direction perpendicular to themember axis, and are evaluated under the assumption that waves are not disturbed by the presence of thestructure in question. When calculating the wave force, it is necessary to estimate these components as accurateas possible, based on either experimental dater or theoretical prediction. In particular, the water particle velocitycomponent contributes to the wave force with its second power, meaning that when the wave height is large, anapproximation using small amplitude wave theory becomes insufficient to yield reliable estimate. Moreover,when the member extends above the mean water level, it is necessary to give sufficient consideration to therange over which the wave force acts, i.e., the elevation of wave crest. When evaluating these terms usingtheoretical values, it is desirable to use the finite amplitude wave theory that agrees with the characteristics ofthe design waves, based on 4.1.3 Properties of Waves. Note also that it is necessary to take full account of waveirregularity with regard to the wave height and period used in the wave force calculation, and to study the wavecharacteristics that are severest to the safety of member or structure in question. In general, the highest waveheight and the significant wave period should be used in the analysis for rigid structures.(3) Drag CoefficientIn general, the drag coefficient for steady flow can be used as the drag coefficient CD for wave force. Notehowever that the drag coefficient varies with the shape of the member, the surface roughness, the Reynoldsnumber Re, and the separation distance between neighboring members. It also varies with the Keulegan-Carpenter number (KC number) because the flow is of oscillating nature. It is necessary to consider theseconditions when setting the value of drag coefficient. For a circular cylindrical member, it is standard to set CD =1.0 if the finite amplitude properties of the waves are fully evaluated. For an unmanned structure, a lower valuemay be used if its value is based on the results of model experiments matched to the conditions. Even in thiscase, however, CD should not be set below 0.7. Note also that when estimating the water particle velocity bymeans of an approximate equation, it is necessary to use a value for the drag coefficient that has been adjustedfor the estimation error in the water particle velocity(4) Inertia CoefficientThe calculated value by the small amplitude wave theory may be used for the inertia coefficient CM. Note,however, that the inertia coefficient varies with the shape of the member and other factors such as the Reynoldsnumber, the KC number, the surface roughness, and the separation distance between neighboring members. It isthus necessary to set the value of the inertia coefficient appropriately in line with the given conditions. For auufn12---CDr0 un unDDS CMr0anADS+=ufnuun an,ufnun unufnun uan
    • PART II DESIGN CONDITIONS-121-circular cylindrical member, CM = 2.0 may be used as a standard value, provided the diameter of the member isno more than 1/10 of the wavelength.(5) Lift ForceIn addition to the drag and inertia forces of equation (5.4.1), the lift force acts on an underwater member in thedirection perpendicular to the plane containing the member axis and the direction of the water particle motion. Ingeneral, it is acceptable to ignore this lift force, but it is necessary to take heed of the fact that the lift force maybecome a problem for horizontal members that are placed near to the seabed. Moreover, for long and thinmembers, it is necessary to take heed of the fact that the lift force may induce vibrations.(6) Standard Value for Drag CoefficientWhen the water particle velocity can be calculated accurately, the value of drag coefficient for steady flow suchas those listed in Table T- 7.2.1 in 7.2 Current Forces Acting on Submerged Members and Structures maybe used.(7) Standard Value for Inertia CoefficientWhen the diameter of the object in question is no more than 1/10 of the wavelength, it is standard to use thevalue listed in Table T- 5.4.1 for the inertia coefficient CM. However, when estimating the water particleacceleration by means of an approximate equation, it is necessary to adjust the value of CM for the error in theestimate of water particle acceleration. The value of inertia coefficient shown here is mostly from the study byStelson and Mavis 40). According to the experiments of Hamada and et al., the inertia coefficient for a cube underwaves is in the range of 1.4 to 2.3.Table T- 5.4.1 Inertia Coefficient(8) Experimental Values for Drag Coefficient and Inertia Coefficient of Circular CylinderThere are many experimental values for the drag coefficient and inertia coefficient of a vertical circular cylinder;for example, those of Keulegan and Carpenter 41), Sarpkaya 42), 43), 44), Goda 45), Yamaguchi, Nakamura,Chakrabarti 46), 47), and Koderayama and Tashiro. There are much variations between these values. However,there is not sufficient data in the region of high Reynolds number, which is experienced in actual design. Odahas produced a summary of these researches which may be referred to.5.4.2 Wave Force on Large Isolated StructureThe wave force acting on a large isolated structure built in the sea shall be calculated using an appropriatenumerical calculation or hydraulic model experiments, considering the size of the structure and the cross-sectional form.[Commentary]The wave force acting on a large isolated structure whose dimensions are comparable to the wavelength can becalculated using the velocity potential, because it is generally possible to ignore the drag force. In particular, forstructures of a simple shape, analytical solutions obtained by means of diffraction theory are available. However, it isnecessary to calculate the breaking wave force by means of hydraulic model experiments if there is a possibility ofbreaking wave force exerted on structure.Circular cylinderSquare-basedprismCubeSphereFlat plateDDD DDDDDShape Reference volume Inertia coefficientπ4D 2.0 D2.19 D1.671.52π4D 2D 2D 3πD36,/ =1,/ =2,/ =0.610.851.0
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-122-[Technical Notes](1) Diffraction TheoryMacCamy and Fuchs 59) have determined the velocity potential of waves around an upright circular cylinder oflarge diameter using diffraction theory, and calculated the wave force from the water pressure distribution at thesurface of cylinder. Goda and Yoshimura 60) have applied diffraction theory to an upright elliptic cylinder, andpresented their results in terms of the inertia coefficient CM. Yamaguchi has investigated the effect of the wavenonlinearity on the wave force acting on an upright circular cylinder of large diameter by means of nonlineardiffraction theory, and pointed out that it is necessary to consider these effects when the water is shallow.(2) Isolated Structure of Arbitrary ShapeFor a structure that is complex in shape, it is difficult to obtain the wave force analytically, and so it is necessaryto carry out a numerical calculation. Various methods are available, such as integral equation methods.5.5 Wave Force Acting on Structure Located near the Still Water Level5.5.1 Uplift Acting on Horizontal Plate near the Still Water LevelFor a horizontal plate located near the still water level, an impact wave force may act on the bottom face ofthe plate (this wave force is hereafter referred to as the uplift), depending on the wave conditions and thestructural form of the plate. When there exists such a risk, the impulsive uplift shall be evaluated by meansof an appropriate method including hydraulic model experiments etc.[Technical Notes](1) Characteristics of Impulsive UpliftIf the bottom face of the plate is flat, the impulsive uplift acting on a horizontal plate near the still water levelvaries with the impact (uprising) velocity of the wave surface and the angle between the wave surface and theplate. As shown in Fig. T- 5.5.1 (a), when there is an angle between the wave surface and the plate, the wavesurface runs along the bottom face of the plate and the wave pressure distribution becomes as shown there. Thedistinct feature of the wave pressure in this case is its rapid rise in time. On the other hand, when the anglebetween the wave front and the plate is close to 0° as shown in Fig. T- 5.5.1 (b), a layer of air is trapped betweenthe wave surface and the plate, and compression of this layer of air results in the almost uniform wave pressuredistribution. The distinct feature of the wave pressure in this case is its oscillation in time with having a shortperiod and damping.Fig. T- 5.5.1 Impact between Wave Front and Horizontal PlateIn case of a pier with a deck plate supported by horizontal beams, the wave surface is disturbed by the beams,and the uplift becomes of complex nature. With beams, a layer of trapped air is often formed and this layer of airis compressed by the uprising wave surface. It is thus necessary to give consideration to the change in the upliftwith respect to the shape of the bottom face of the horizontal plate.The shape of the impacting wave surface varies greatly according to the condition whether the wave isprogressive or standing in nature. With standing waves, the shape of the impacting wave front varies with thePressure distributionPressure distributionWave impactWave impact(a)(b)
    • PART II DESIGN CONDITIONS-123-distance between the position of wave reflection and the horizontal plate. It is thus necessary to consider suchdifferences.(2) Uplift Acting on Horizontal Plate with Flat Bottom Face (with standing waves)Goda thought of the uplift acting on a horizontal plate as being the force arising from the sudden change in theupward momentum of wave surface by its collision with the plate. Using von Karman’s theory, he obtained thefollowing formulas for calculating the uplift from standing waves acting on a horizontal plate.(5.5.1)(5.5.2)whereP: total uplift (kN)z: correction factorr0: density of seawater (1.03 t/m3)g: gravitational acceleration (9.81 m/s2)H: wave height of progressive waves (m) (generally the highest wave height Hmax)L: wavelength of progressive waves (m)B: extension width of plate perpendicular to wave incidence (m)h: water depth (m)s: clearance of the plate above the still water level (m)s¢: clearance of the plate above the level corresponding to the middle of the wave crest and trough (m)One should take note of the fact that the uplift in the above equations does not depend on the length of thehorizontal plate.The impact force has the magnitude given by the above equations and takes the form of a pulse that lasts fora time t from the moment of the impact, that is given as follows:(5.5.3)where T is the wave period and l is the length of the horizontal plate. Provided the length of the horizontal plateis sufficiently small compared with the wavelength L and the bottom face of the horizontal plate is flat, equation(5.5.1) well represents the features of the uplift well (despite the fact that the equation is simple). Comparingcalculated values with z = 1.0 to experimental values, agreement is relatively good provided H/s¢ is no morethan 2.Tanimoto et al. 61) have proposed another method for calculating the uplift acting on horizontal plate basedon Wagner’s theory. With this calculation method, the angle of contact b between the wave surface and thehorizontal plate as well as the impact velocity Vn are given by Stokes’ third order wave theory, making itpossible to obtain the spatial distribution of the impact pressure and its change over time. Note however that theuse of Stokes’ third order wave theory makes the calculation rather complex. This calculation method isintended for use when the bottom face of the horizontal plate is flat. It cannot be applied directly to structures ofcomplicated shape such as an ordinary pier that have beams under the floor slab; the impact between the wavesurface and the floor slab is disturbed by the beams. In general, the presence of beams causes air to becometrapped in and the wave surface to be distorted, the result being that the impact force is less than for a horizontalplate with a flat surface. Accordingly, the value obtained from this calculation method may be thought of asbeing the upper limit of the uplift for an ordinary pier.(3) Uplift Acting on Open-type Wharf (with standing waves)Ito and Takeda 62) have conducted scale model tests of open piled marginal wharves (open-type wharves) toobtain the uplift acting on an access bridge, and its minimum weight to prevent moving and falling. Theexperimental conditions were the wave height up to 40 cm, a period of 1.0 s and 2.4 s, and a water depth of56 cm and 60 cm. According to the measurement records of wave pressure gauges attached to the access bridge,the peak value of the uplift varied considerably from wave to wave even under the same conditions.Nevertheless, the mean of these peak values is given approximately by the following equation:(5.5.4)wherep: mean peak value of the intensity of uplift (kN/m2)r0: density of seawater (1.03 t/m3)g: gravitational acceleration (9.81 m/s2)H: incident wave height (m) (Hmax)s: distance from the water level to the underside of access bridge (m)Note however that the peak value of the intensity of the uplift given by equation (5.5.4) acts only for anextremely short time, and that the phase of this uplift varies from place to place. This means that even if theintensity of the uplift p exceeds the deadweight q (specifically the weight per unit area (kN/m2)) of the accessP zr0g4--------HLB 2phL----------tanhHs¢----s¢H----–è øæ ö=s¢ s pH2L------ 2phL----------coth–=tpTl2L2------------s¢H2 s¢2–-----------------------=p r0g 8H 4.5s–( )=
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-124-bridge, the bridge will not necessarily move or fall down. Based on this perspective, Ito and Takeda haveobtained the threshold weight at which the access bridge starts to move and that at which the deck slab fallsdown. For waves of period 2.4 s, the relationship between the moving threshold weight per unit area q and thewave height H was as follows:(5.5.5)The moving threshold weight given by equation (5.5.5) is one fifth of the intensity of the uplift as given byequation (5.5.4). The falling threshold weight was found to be 1/2 to 1/3 of the moving threshold weight.In these access bridge experiments, Ito and Takeda also tested the access bridge with holes or slits of varioussizes, and investigated how the threshold weights changed when the void ratio was changed. In general, thechange in the moving threshold weight by the void ration is only slight. The falling threshold weight, on theother hand, drops noticeably when the void ratio exceeds 20%. Note that the bridge weight referred to here is theweight per unit area of the substantial part (i.e., the weight per unit area excluding the voids).Furthermore, Ito and Takeda 62) have attached a strain gauge to the deck slab of the model of open-type wharfand measured the stress. Based on their results, they proposed the following equation for the equivalent staticload (kN/m2) assumed to act with uniform distribution on the deck slab.(5.5.6)Note however that the value given by this equation corresponds to the upper limit of the experimental values andshould thus be thought of as corresponding to the case that the distance s from the water level to the underside ofthe is almost 0. The equivalent static load given by equation (5.5.6) is generally lower than the uplift acting on ahorizontal plate with a flat bottom face. It is thought that this is partly because the beams disturb the impactingwave front and cause air to become trapped in. It is also thought that because the uplift acts very locally and foran extremely short time, the equivalent static load becomes much smaller than the peak value of the uplift.Experimental research into the uplift acting on a pier has also been carried out by Murota and Furudoi, Nagaiand Kubo, Horikawa and Nakao, and Sawaragi and Nochino.(4) Uplift Acting on Horizontal Plate with Flat Bottom Face (with progressive waves)An impulsive uplift also acts when progressive waves act on a horizontal plate that is fixed near to the still waterlevel. Tanimoto et al. 63) have proposed a method for calculating this impulsive uplift, based on the same theoryby Wagner that was used for impulsive uplift by standing waves.(5) Uplift Acting on Superstructure of Detached Pier (with progressive waves)Ito and Takeda 62) have also carried out studies on the uplift from progressed waves acting on a detached pier.Specifically, they measured the stress occurring in the deck slabs of a detached pier model. Based on the upperlimits of their experimental results, they proposed the following equation for the uniformly distributedequivalent static load.(5.5.7)[References]1) Yoshiyuki ITO, Mutsumi Fujishima, Takao KITATANI: “On the stability of breakwaters”, Rept of PHRI, Vol. 5, No. 14,1966, 134p. (in Japanese).2) Yoshimi GODA: “A new method of wave pressure calculation for the design of composite breakwaters”, Rept of PHRI, Vol.12, No. 3, 1973, pp. 31-69 (in Japanese), also “New wave pressure formulae for composite breakwater” Proc. 14th Conf.Coastal Eng., ASCE, 1974, pp.1702-1720.3) Sainflou, G.: “Essai sur les diques maritimes verticales”, Annales des Ponts et Chaussées, Vol. 98, No. 1, 1928, pp. 5-48.4) Katsutoshi TANIMOTO, Katsutoshi KIMURA, Antonio Paulo dos Santos Pinto: “Random wave forces and design waveperiods of composite breakwaters under the action of double peaked spectral weves”, Rept of PHRI, Vol. 25, No. 2, 1986, pp.3-25 (in Japanese).5) Katsutoshi TANIMOTO, Katsutoshi KIMURA: “A hydraulic experimental study on trapezoidal caisson breakwaters”, Tech.Note of PHRI, No. 528, 1985 (in Japanese).6) Yoshimi GODA, Shusaku KAKIZAKI: “Study on finite amplitude standing waves and their pressures upon a vertical wall”,Rept of PHRI, Vol. 5, No. 10, 1966, pp. 1-57 (in Japanese).7) Katsutoshi TANIMOTO, Shigeo TAKAHASHI, Takao KITATANI: “Experimental study of impact breaking wave forces on avertical-wall caisson of composite breakwater”, Rept of PHRI, Vol. 20, No. 2, 1981, pp. 3-39 (in Japanese).8) Mitsuyasu, H.: “Experimental study on wave force against a wall”, Report of Trans. Tech. Res. Inst, No. 47, 1962, pp. 1-39.9) Michio MORIHIRA, Shusaku KAKIZAKI, Toru KIKUYA: “Experimental study on wave force damping effects due todeformed artificial blocks”, Rept of PHRI, Vol. 6, No. 4, 1967, pp. 3-31 (in Japanese).10) Yoshimi GODA, Suketo HARANAKA: “An experiment on the shock pressure of breaking waves”, Tech. Note of PHRI, No.32, 1967, pp. 1-18 (in Japanese).11) Shigeo TAKAHASHI, Katsutoshi TANIMOTO, Satoshi SUZUMURA: “Generation mechanism of impulsive pressure bybreaking wave on a vertical wall”, Rept of PHRI, Vol. 22, No. 4, 1983, pp. 3-31 (in Japanese).12) Yoshimi GODA: “Motion of composite breakwater on elastic foundation under the action of impulsive breaking wavepressure”, Rept of PHRI, Vol. 12, No. 3, 1973, pp. 3-29 (in Japanese).13) Katsutosi TANIMOTO, Shigeo TAKAHASHI, Kazuyuki MYOSE: “Experimental study of random wave forces on uprightsections of breakwaters”, Rept of PHRI, Vol. 23, No. 3, 1984, pp. 47-100 (in Japanese).q r0g 1.6H 0.9s–( )=p 4r0gH=p 2r0gH=
    • PART II DESIGN CONDITIONS-125-14) Shigeo TAKAHASHI, Katsutoshi TANIMOTO, Ken-ichirou SHIMOSAKO: “Wave and block forces on a caisson coveredwith wave dissipating blocks”, Rept of PHRI, Vol. 29, No. 1, 1990, pp. 54-75 (in Japanese).15) Katsutoshi TANIMOTO, Roshi OJIMA: “Experimental study of wave forces acting on a superstructure of slopingbreakwaters and on block type composite breakwaters”, Tech. Note of PHRI, No. 450, 1983 (in Japanese).16) Yoshiyuki ITO, Katsutoshi TANIMOTO: “Meandering damages of composite type breakwaters”, Tech. Note of PHRI,No.112, 1971 (in Japanese).17) Yoshimi GODA, Tomotsuka YOSHIMURA, Masahiko ITO: “Reflection and diffraction of water waves by an insularbreakwater”, Tech. Note of PHRI, 10, No. 2, 1971, pp. 3-52 (in Japanese).18) Yoshiyuki ITO, Katsutoshi TANIMOTO, Koji KOBUNE, Takao KITATANI, Masahiko TODOROKI: “An experimentalinvestigation of upright breakwaters at reefs”, Tech. Note of PHRI, No. 189, 1974 (in Japanese).19) Coastal Engineering Research Center: “Shore Protection Manual” Vol. II, US Army Corps of Engineers, 1984.20) Shigeo TAKAHASHI, Ken-ichirou SHIMOSAKO, Hitoshi SASAKI: “Experimental study on wave forces acting onperforated wall caisson breakwaters”, Rept of PHRI, Vol. 30, No. 4, 1991, pp. 3-34 (in Japanese).21) Katsutoshi TANIMOTO, Suketo HARANAKA, Eiji TOMIDA, Yoshikazu IZUMIDA, Satoshi SUZUMURA: “A hydraulicexperimental study on curved slit caisson breakwaters”, Rept of PHRI, Vol. 19, No. 4, 1980, pp. 3-53 (in Japanese).22) Katsutoshi TANIMOTO, Shigeo TAKAHASHI, Tsutomu MURANAGA “Uplift forces on a ceiling slab of wave dissipatingcaisson with a permeable front wall - analytical model for compression of an enclosed air layer -”, Rept of PHRI, Vol. 19,No. 1, 1980, pp. 3-31 (in Japanese).23) Sigeo TAKAHASHI, Katsutoshi TANIMOTO: “Uplift forces on a ceiling slab of wave dissipating caisson with a permeablefront wall (2nd Report) - field data analysis -”, Rept of PHRI, Vol.23, No.2, 1984, pp. 3-25 (in Japanese).24) Hudson, R. Y.: “Laboratory investigation of rubble-mound breakwater”, Proc. ASCE. Vol. 85, No. WW3., 1959, pp. 93-121.25) Van der Meer, J. W.: “Rock slopes and gravel beaches under wave attack”, Doctoral thesis, Delft Univ. of Tech., 1988, 152p.or Van der Meer, J. W.: “Stability of breakwater armour layer - Design equations”, Coastal Engineering, 11, 1987, pp. 219-239.26) Van der Meer, J. W.: “Stability of cubes, Tetrapods and Accropode”, Proc. of Breakwater 88, Eastbourne, UK., 1988, pp. 71-80.27) Burcharth, H. F. and Z. Liu: “Design of Dolos armour units”, Proc. 23rd Int. Conf. Coastal Eng., Venice, 1992, pp. 1053-1066.28) Katsutoshi TANIMOTO, Suketo HARANAKA, Kazuo YAMAZAKI: “Experimental study on the stability of wavedissipating concrete blocks against irregular waves”, Rept of PHRI, Vol. 24, No. 2, 1985, pp. 86-121 (in Japanese).29) Shigeo TAKAHASHI, Minoru HANZAWA, Hirokazu SATO, Michio GOMYO, Ken-ichiro SHIMOSAKO, KiyoshiTERAUCHI, Tomotsuka TAKAYAMA, Katsutoshi TANIMOTO: “Lifetime damage estimation with a new stability equationfor concrete blocks - study on wave-dissipating concrete blocks covering horizontally composite breakwaters, the first rept.-”, Rept of PHRI, Vol. 38, No. 1, 1998, pp. 3-28 (in Japanese).30) Van de Kreeke, J.: “Damage function of rubble mound breakwaters”, Jour. Waterway and Harbors Div., Vol. 95, No.WW3,ASCE., 1969, pp. 345-354.31) Christensen, F. T., P. C. Broberg, S. E. Sand, and P. Tryde: “Behavior of rubble-mound breakwater in directional and uni-directional waves”, Coastal Eng., Vol. 8, 1984, pp. 265-278.32) Brebner, A. and D. Donnelly: “Laboratory study of rubble foundations for vertical breakwaters”, Proc. 8th Conf. CoastalEng., New Mexico City, 1962, pp. 408-429.33) Katsutoshi TANIMOTO, Tadahiko YAGYU, Tsutomu MURANAGA, Kozo SHIBATA, Yoshimi GODA: “Stability of armorunits for foundation mounds of composite breakwater by irregular wave tests”, Rept of PHRI, Vol. 21, No. 3, 1982, pp. 3-42(in Japanese).34) Hirofumi INAGAKI, Takeo KATAYAMA: “Analysis of damage to armor stones of mounds in composite breakwaters”, Tech.Note of PHRI, No. 127, 1971, pp. 1-22 (in Japanese).35) Sigeo TAKAHASHI, Katsutoshi KIMURA, Katsutoshi TANIMOTO: “yStability of armour units of composite breakwatermound against oblique waves”, Rept of PHRI, Vol. 29, No. 2, 1990, pp. 3-36 (in Japanese).36) Morison, J. R., M. P. OBrien, J. W. Johonson, and S. A. Schaaf: “The force exerted by surface waves on piles”, PetroleumTrans., 189, TP2846, 1950, pp. 149-154.37) Yoshimi GODA, Suketo HARANAKA, Masaki KITAHARA: “Study of impulsive breaking wave forces on piles”, Rept ofPHRI, Vol. 5, No. 6, 1966, pp. 1-30 (in Japanese).38) Katsutoshi TANIMOTO, Shigeo TAKAHASHI, Tadao KANEKO, Keisuke SHIOTA, Koichiro OGURA: “Experimentalstudy on impulsive forces by breaking waves on circular cylinder”, Rept of PHRI, Vol. 25, No. 2, 1986, pp. 33-87 (inJapanese).39) Yoshiyuki ITO, Katsutoshi TANIMOTO, Koji KOBUNE: “Dynamic response of an offshore platform to random waves”,Rept of PHRI, Vol. 11, No. 3, 1972, pp. 59-86 (in Japanese).40) Stelson, T. E. and F. T. Mavis: “Virtual mass and acceleration in fluids”, Proc. ASCE., Vol. 81, Separate No. 670, 1955, pp.670-1 ~~~~ 670-9.41) Keulegan, G. H. and L. H. Carpenter: “Forces on cylinders and plates in an oscillating fluid”, Jour. National Bureau ofStandards, Vol. 60 No. 5, 1958, pp. 423-440.42) Sarpkaya, T.: “Forces on cylinders and spheres in a sinusoidally oscillating fluid”, Jour. Applied Mechanics, Trans. ASME,Vol. 42, No. 1, 1975, pp. 32-37.43) Sarpkaya, T.: “In-line and transverse forces on cylinders in oscillatory flow at high Reynolds number”, Prepr. 8th OffshoreTech. Conf., Vol. II, 1976, pp. 95-108.44) Sarpkaya, T., N. J. Collins, and S. R. Evans: “Wave forces on rough-walled cylinders at high Reynolds numbers”, Prepr. 9thOffshore Tech. Conf., Vol. III, No.2901, 1977, pp. 167-184.45) Goda, Y.: “Wave forces on a vertical circular cylinder: Experiments and proposed method of wave force computation”, Reportof P. H. T. R. I., No. 8, 1964, 74p.
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-126-46) Chakrabarti, S. K., A. L. Wollbert, and A. T. William: “Wave forces on vertical circular cylinder”, Jour. Waterways, Harborsand Coastal Eng. Div., Vol. 102, No. WW2, ASCE, 1976, pp. 203-221.47) Chakrabarti, S. K.: “Inline forces on fixed vertical cylinder in waves”, Jour. Waterway, Port, Coastal and Ocean Div., Vol.106, WW2, ASCE, 1980, pp. 145-155.48) Kim, Y. Y. and H. C. Hibbard: “Analysis of simultaneous wave force and water particle velocity measurements”, Prepr. 7thOTC, Vol. 1, No. 2192, 1975, pp. 461-469.49) Borgman, L. E.: “Spectral analysis of ocean wave forces on pilling”, Proc. ASCE, Vol. 93 No. WW2, 1967, pp. 129-156.50) Borgman, L. E.: “Ocean wave simulation for engineering design”, Proc. ASCE, Vol. 95 No. WW4, 1969, pp. 557-583.51) Hudspeth, R. T.: “Wave force prediction from non-linear random sea simulation”, Prepr. 7th OTC, No.2193, 1975, pp. 471-486.52) Sharma, J. and R. G. Dean: “Second-order directional seas and associated wave forces”, Prepr. 11th OTC, No.3645, 1979, pp.2505-2514.53) Tickell, R. G. and M. H. S. Elwany: “A probabilistic description of forces on a member in a short-crested random sea”,‘Mechanics of Wave-Induced Forces on Cylinders’, Pitman Pub. Ltd., London, 1979, pp. 561-576.54) Yoshimi GODA, Tatsuhiko IKEDA, Tadashi SASADA, Yasuharu KISHIRA: “Study on design wave forces on circularcylinders erected upon reefs”, Rept of PHRI, Vol. 11, No. 4, 1972, pp. 45-81 (in Japanese).55) Sarpkaya, T. and M. Isaacson: “Mechanics of Wave Forces on Offshore Structure”, Van Nostrand Reinhold Co., 1981, 651p.56) Yamamoto, T., and J. H. Nath: “Forccs on many cylinders near a plane boundary”, ASCE, National Water Resources andOcean Engineering Convention, Preprint No. 2633, 1976.57) Sarpkaya, T.: “In-line and transverse forces on cylinders near a wall in oscillatory flow at high Reynolds numbers”, Prepr. 9thOTC Paper No. 2898, 1977, pp. 161-166.58) Sarpkaya, T. and F. Rajabi.: “Hydrodynamic drag on bottom-mounted smooth and rough cylinders in periodic flow”,Prepr.12th OTC Paper No. 3761, 1980, pp. 219-226.59) MacCamy, R. C. and R. A. Fuchs: “Wave forces on piles, a diffraction theory”, U. S. Army Corps of Engineers, BeachErosion Board, Tech. Memo. No. 69, 1954, 17p.60) Yoshimi GODA, Tomotsuka YOSHIMURA: “Wave force computation for structures of large diameter, isolated in theoffshore”, Rept of PHRI, Vol. 10, No. 4, 1971, pp. 3-52 (in Japanese).61) Katsutoshi TANIMOTO, Shigeo TAKAHASHI, Yoshikazu IZUMIDA: “A calculation method of uplift force on a horizontalplatform”, Rept of PHRI, Vol. 17, No. 2, 1978, pp. 3-47 (in Japanese).62) Yoshiyuki ITO, Hideaki TAKEDA: “Uplift on pier deck due to wave motion”, Rept of PHRI, Vol. 6, No. 4, 1967, pp. 37-68(in Japanese).63) Katsutoshi TANIMOTO, Shigeo TAKAHASHI, Masahiko TODOROKI, Yoshikazu IZUMIDA: “Horizontal wave forces on arigid platform”, Rept of PHRI, Vol. 16, No. 3, 1977, pp. 39-68 (in Japanese).
    • PART II DESIGN CONDITIONS-127-Chapter 6 Tides and Abnormal Water Levels6.1 Design Water Level (Notification Article 6)The water level that is to be used for the structural design and stability analysis of port and harbor facilitiesshall be determined based on either the measured values or the hindcast values of astronomical tides andmeteorological tides, along with abnormal water levels caused by tsunamis and others. However, for portand harbor facilities on lakes or rivers for which the effects of tides are not large, the water level shall bedetermined appropriately based on the water level records or the like.[Commentary](1) Design water levelAs a general rule, the water level that is most dangerous to the safety of the structure in question is used as thedesign water level.(2) Simultaneous occurrence of storm surge, tsunamis, and seicheStorm surge and tsunamis both occur only very rarely, and so it may be assumed that they will not occur at thesame time. Seiche in the narrower sence occurs independently of storm surge or tsunami, and is treatedseparately.[Technical Notes](1) Rising of Mean Sea LevelApart from astronomical tides and storm surge, which are essential for the design water level, studies on thelong-term sea level rise are being carried out both in Japan and abroad. According to the Secondary EvaluationReport of the IPCC 1), it is estimated that the mean sea level will rise 15 cm to 95 cm between 1990 and 2100.Figure T- 6.1.2 shows the IPCC panel’s forecast for the mean sea level rise. Although it is known that the meansea level will rise in the future, it is hard to evaluate this rise quantitatively. The IPCC panel has thus producedthree estimates.Since the quantitative extent of the mean sea level rise is uncertain, in general it is hard to take account of itat the design stage. It is thus unavoidable that countermeasures in response to a rise in the mean sea level willhave to be carried out through maintenance work such as raising of the crests of structures. However, whendesigning important structures for which it is anticipated that subsequent repairs would be extremely difficult(for example, when designing the clearance of a bridge that will have to remain in service for a very long time orwhen designing the drainage outlets of reclaimed land), appropriate consideration should be given to the amountof mean sea level rise in the future.Note 1: The values 1.5, 2.5, and 4.5 shown in the three graphs represent the climate sensitivitiesfor the three scenarios, respectively.Note 2: The low, medium, and high represent the value of ice melting parameter for the threescenarios. The ice melting parameter represents the extent to which the ice at the poles,in Greenland, and in highland glaciers melts in response to a rise in air temperatures.Fig. T- 6.1.2 IPCC Panel’s Forecasts for Mean Sea Level Rise 1) (BaU Scenarios)Meansealevelriseoverthewholeworld(cm)IS 92 e/High/4.5IS 92 a/Medium/2.5IS 92 c/Low/1.5Year
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-128-6.2 Astronomical TideConsideration shall be given to the following astronomical tide parameters: the chart datum level, the meanwater level, the mean monthly-highest water level, and the mean monthly-lowest water level. As a generalrule, these parameters shall be determined from the tide observation records over one year or a longerperiod.[Commentary](1) DefinitionsThe definitions for the various types of water level are as follows:(a) Mean sea level (MSL)The average height of the sea level over a certain period is referred to as the mean water level for that period.For practical purposes, the mean water level is taken to be the average of the water level over one year.(b) Chat datum level (CDL)See PartⅠⅠⅠⅠ, Chapter 2 Datum Level for Construction Work.(c) Mean monthly-highest water level (HWL)The average of the monthly-highest water level, where the monthly-highest water level for a particular monthis defined as the highest water level occurring in the period from 2 days before the day of the lunar syzygy(new moon and full moon) to 4 days after the day of the lunar syzygy.(d) Mean monthly-lowest water level (LWL)The average of the monthly-lowest water level, where the monthly-lowest water level for a particular month isdefined as the lowest water level occurring in the period from 2 days before the day of the lunar syzygy to 4days after the day of the lunar syzygy.(e) Mean high water level (MHWL)The mean value of all of the high water levels, including the spring tide and the neap tide.(f) Mean low water level (MLWL)The mean value of all of the low water levels, including the spring tide and the neap tide.(g) Near highest high water level (NHHWL)The water level obtained by adding the sum of the amplitudes of the four principal tidal components (M2, S2,K1 and O1) to the mean sea level.[Technical Notes](1) In addition to the above definitions of water level, there are also the high water of ordinary spring tides(HWOST) and the low water of ordinary spring tides (LWOST). These refer respectively to the water levels atthe height h above and below the mean water level, where h is the sum of the amplitudes of the tidal componentsM2 and S2. The height of the HWOST as measured from the chart datum is known as the spring rise.Figure T- 6.2.1 shows an example of the relationship between these water levels, for the Tokyo TideObservation Station, along with the chart datum level (CDL), the mean sea level for Tokyo Bay (Tokyo Peil -TP), and other commonly used water levels.6.3 Storm SurgeThe storm surge parameters shall be determined by referring to the observed tide records collected over aslong a period as possible, inundation records for past disasters, and hindcast values for abnormalmeteorological conditions.[Commentary](1) Definition of Storm SurgeFluctuations in the sea level occur as the result of a combination of astronomical tide, meteorological tide, andseiche, along with the effects of factors such as ocean currents, the seawater temperature, seasonal fluctuationsin the atmospheric pressure, the water levels of rivers, and coastal waves. Out of these factors, the sea levelfluctuation due to meteorological factors, such as air pressure fluctuations caused by passing of high or lowpressure area and winds, are referred to as meteorological tides or deviations. The term “storm surge” refers to atype of meteorological tides, specifically an abnormal rise of the sea level that occurs when a typhoon passes by.The causes of storm surge are the depression of atmospheric pressure and the resultant rise of sea surface, thepropagation of elevated sea surface as long waves, the resonance of water in embayments, and the wind setup.The deviation of sea level from the astronomical tide during a storm surge is called the storm tide.
    • PART II DESIGN CONDITIONS-129-Fig. T- 6.2.1 Water Level Diagram for the Tokyo (Harumi) Tide Observation Station(2) Observation PeriodIt is desirable to study the storm surge records covering as long a period as possible; the minimum necessaryobservation period is considered to be 30 years. However, there are only a few tide observation stations that haveput together storm surge records covering several tens of years. In order to carry out a study of storm surgecovering the longest possible period, it is thus necessary to also carry out hindcasting from meteorologicalconditions, to study records from storm surge damage reports, newspapers and old documents, and to collectdata on past disasters.[Technical Notes](1) Meteorological Tide(a) GeneralMeteorological tide parameters to which consideration should be given include the storm tide and its duration.(b) Wind setupWhen a strong wind continues to blow for a prolonged time in a shallow bay, seawater is dragged by the wind.If the wind is onshore, seawater accumulates in the littoral zone, resulting in a rise in the sea level. If the anglebetween the wind direction and the line perpendicular to the shoreline is a, the sea level rise (cm) at theshoreline is given by the following equation:(6.3.1)whereF: fetch length (km)U: constant wind velocity (m/s)h: mean water depth (m)The term k is a coefficient that varies depending on the bay characteristics. Colding has obtained a value of k= 4.8 × 10-2 from the observation data in the Baltic Sea.(c) Static water level rise caused by depression in the atmosphericIf the atmospheric pressure drops slowly by (hPa), the water level in the sea area where the atmosphericpressure has dropped rises relative to the surrounding areas where the atmospheric pressure has not dropped,because of the pressure difference. The rise in water level z (cm) is given by the following equation:(6.3.2)Bench markHighest water level ever (Oct 19, 1979)(during the statistical period to obtain standard water level)Mean sea level for recent 5 year period* MSLMean monthly-highest water level* HWL HWOSTMean sea level forTokyo Bay (Tokyo Peil -TP)Edogawa construction work datum level (YP)Mean monthly-lowest water level* LWL LWOSTChart datum level (CDL) =Work datum level (WDL)Arakawa construction work datum level (Arakawa Peil -AP)Lowest water level ever recorded (Feb 13, 1953)Observation datum level (DL)Mean value over 1991~1995Highest water level ever recorded (Oct 1, 1917)(observed before the statistical period toobtain standard water levels)h0h0 kFh--- U acos( )2=DPz 0.99DP=
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-130-where: pressure difference (hPa): rise in water level (cm)(d) Estimation formula for storm tideFor places where numerical computation of storm surge have not been carried out, equation (6.3.3) may beused to estimate the maximum amount of storm tide. This equation incorporates the factors of suction causedby a depression in the atmospheric pressure and wind setup.(6.3.3)where: maximum amount of storm tide (cm)P: lowest atmosperic pressure (hPa)U: maximum wind velocity (m/s): angle between the predominant wind direction that causes the highest storm tide and the winddirection at the time of maximum wind speed U (º)The coefficients a, b, and c are determined by the relationship between the storm tide, the atmosphericpressure, and the wind data that have been observed at the place in question.(2) Numerical Computation of Storm SurgeIn order to analyze the phenomenon of storm surge in detail, numerical computations are carried out. With thismethod, the rise of sea surface caused by a depression in the atmospheric pressure (see (1)(c) above), along withthe tangential stress at the sea surface due to the wind and the tangential stress at the sea bottom due to viscosity,are given as external forces. The change in the water level and the flow velocity at each point is thenprogressively calculated for a series of time steps, by solving the equations of motions and continuity. Thetopography of the bay is approximated using a grid system (with adjacent mesh points separated by say a fewkilometers), with the average water depth at each mesh being inputted in advance. The atmospheric pressure andwind velocity within a typhoon is often calculated using Myers’ formula or a similar theoretical model.(3) Design Water Level for the Facilities for Protection against Storm SurgeThe following four methods exist for determing the design water level for storm surge protection facilities.(a) Use the highest water level observed in the past, or else this plus a little extra allowance.(b) Use the elevation above the mean-monthly highest water level by the amount of either the highest storm tideobserved in the past or the storm tide predicted for a model typhoon.(c) Obtain the occurrence probability curve for past storm surge levels, and then use the water level that isexpected to be exceeded only once within a certain return period (say 50 years or 100 years) (this water levelis obtained by extrapolating the probability curve).(d) Determine the design water level based on economic factors, considering the occurrence probability of variousstorm surge levels, and the damage to the hinterland for each water level, along with the cost of constructingstorm surge protection facilities.(4) Rise in Mean Water Level Due to Waves (Wave Setup)The rise in mean water level due to waves can be estimated using Fig. T- 4.7.1 and Fig. 4.7.2 in 4.7.1 WaveSetup. Near to the shoreline, this rise is 10% or more of the deepwater significant wave height, and thus itcannot be ignored when waves are high.6.4 TsunamiThe following tsunami parameters shall be considered: the highest water level, the lowest water level, thewater level deviation (rise of water level by tsunami above the astronomical tide), the tsunami wave height,and the tsunami period. These parameters shall be determined using an appropriate method, by referring tothe measured data (taken over as long a period as possible) and the heights of tsunami runup traces duringpast disasters.[Commentary](1) Tsunamis are waves with an extremely long period that mainly occur when the sea floor is raised and/or droppedby an earthquake in the sea. As a tsunami approaches the coast, the wave height rises rapidly owing to theshoaling and the concentration effect of the sea bottom topography, meaning that tsunami often causestremendous damage to coastal areas. It is important to investigate not only the possibility of flooding damage asa result of overflowing a tsunami barrier, but also the possibilities of losing small vessels that have been mooredin a harbor but are carried away by strong currents of tsunami, scouring of seabed at the openings ofbreakwaters, and sliding or overturning of breakwaters.DPzh0 a 1010 P–( ) bU2 qcos c+ +=h0q
    • PART II DESIGN CONDITIONS-131-(2) The wave height of a tsunami in the outer sea is generally extremely small, but it can nevertheless be detected bymeans of continuous observations recorded by a wave gauge out at sea. When a tsunami enters a bay, the waveheight increases greatly. Since the increase in wave height depends on the topography and natural periods of thebay, the tsunami parameters used in design are determined from the past tsunami records for the place inquestion or the values obtained from numerical computations for the place in question.[Technical Notes](1) Definitions of Tsunami-Related TermsThe definitions of various terms related to tsunamis are shown in Fig. T- 6.4.1.(a) Estimated tide levelThis is the tide level obtained by smoothing the tide level on a tide observation record by removing thecomponents that are thought to be of the tsunami and any oscillation component of shorter period by seiche.The estimated tide level is expressed as the elevation above the CDL (chart datum level). This estimated tidelevel may thus differ somewhat to the hindcasted tide level obtained from the tidal harmonic constants.(b) Runup height and tsunami trace heightThe elevation of the highest point to which a tsunami has runup the land or a structure is called the runupheight above the CDL (chart datum level). Note that the runup height of a tsunami is often determined basedon an investigation of tsunami traces left at the site in question. The elevation of a trace of a tsunami that hasrun up over the land or a structure above the CDL is called the tsunami trace height.(c) DeviationThe difference between the actual tide level and the estimated tide level described in (a). The maximum valueof the deviation when the actual tide level is higher than the estimated tide level is sometimes referred to as themaximum deviation or the tsunami height.(d) Highest water levelThe maximum value of the actual tide level above the CDL (chart datum level).(e) Tsunami wave heightAs with wind waves, the tsunami wave height may be analyzed using the zero-upcrossing method. In this case,the section between a point where the tsunami wave profile crosses over the estimated tide level from thenegative side to the positive side and the next such point is taken as one wave, and the difference between themaximum and minimum water levels within that section is taken as the tsunami wave height for that wave.The maximum tsunami wave height in a continuous tsunami wave record is defined as the highest tsunamiwave height.Fig. T- 6.4.1 Definitions of Tsunami-related Terms(f) Initial motionThis term refers to the instance at which a tsunami reaches the observation point and the water level first startsto deviate from the estimated tide level. If the first observed deviation of water level caused by the tsunami isa rise relative to the estimated tide level, the initial motion is referred to as the pushing initial motion. If it is afall relative to the estimated tide level, the initial motion is referred to as the drawing initial motion.(2) Tsunami PeriodThe period of tsunamis observed in a bay varies depending on the scale of the earthquake, the distance from theepicenter, and the resonance characteristics of the bay, and others. The wave height of a tsunami in a harbor isgreatly affected by the period of the tsunami. During a design process, it is thus desirable to carry outinvestigations on not only tsunamis having the periods that have actually been measured in the past, but alsotsunamis having the period same as the natural period of the bay or harbor in question.Estimated tide levelDeviationHighest water levelTsunami wave heightFirst arrival timeTime
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-132-(3) Transformation of Tsunami in a BayThe most important types of transformations that a tsunami undergoes in a bay are the increase in wave heightand flow velocity caused by the decrease in the cross-sectional area toward the end of bay, and the increase inwave height induced by seiche in the bay.Under the assumption of small amplitude waves, the influence of the change in cross-sectional area may becalculated approximately using Green’s equation (equation (6.4.1)).(6.4.1)whereH: height of long waves for a cross section with the width B and the water depth h (m)H0: height of long waves for a cross section with the width B0 and the water depth h0 (m)Note however that equation (6.4.1) is applicable under the conditions that the variations in both the width andthe water depth are very gentle and that no reflected waves moving offshore are generated. Moreover it does notconsider the energy loss due to friction. Accordingly, the equation cannot be applied to the area of shallow waternor the case when there are reflection effects at the end of the bay.(4) Tsunami on Tide Observation RecordsTide observation records provide an extremely useful source of tsunami data. However, when handling suchdata, it is necessary to take note of the fact 3) that if the tide observation station is within a harbor, there is a highpossibility of tsunami record being different from a tsunami just outside harbor because of the interferences ofstructures such as breakwaters etc. within the harbor.(5) Bore Type Tsunami 3)Notable features of the tsunami that accompanied the Nihonkai-Chubu Earthquake of 1983, along the northerncoast of Akita Prefecture where a coastline with a shallow bottom slope of about 1/200 continues for as much as30 km, were that the wave profile transformed markedly as the tsunami propagated, forming the shape ofmultiple bores, and there were rapid undulations of surface elevation with the period around 5 to 10 s. However,when this tsunami arrived at coastlines with a relatively steep bottom slope (around 1/50) such as the west coastof the Oga Peninsula, it did not produce multiple bores, but rather took the shape of standing waves. Eventhough the height of the incident tsunami was the same in both cases, there was a tendency for the bore typetsunami to have a higher runup than the standing wave type tsunami. A method for calculating the tsunami waveforce when a bore type tsunami acts on an upright wall has been presented based on experimental results 3).(6) Tsunami SimulationNumerical simulations of tsunamis correspond to the case where the meteorological disturbance term (whichrepresents a forcing external force) is removed from the numerical computation scheme for storm surge. Theincident wave profile is assigned in advance, or it is assumed that the initial variation in the water level is equalto the displacement of the sea floor in the earthquake fault model. The simulation makes it possible toinvestigate the effectiveness of breakwaters designed to protect harbors and coastal zones against tsunamis andthe effect of topographic changes (land reclamation etc.) on a tsunami 3), 4).In tsunami simulations that use hydraulic model experiments, a tsunami wave profile that has previouslybeen reproduced by a numerical simulation is generated at the model boundary to investigate the effectiveness ofbreakwaters and the effects of the topography of reclaimed land 5).The method of Iwasaki and Mano may be used to obtain the runup height over the land in a numericalcomputation of tsunami. When the water level exceeds the crown elevation of a breakwater or levee in thecalculation region, the quantity of overtopping per unit width may be calculated using Hom-ma’s formula.When estimating the effectiveness of tsunami mitigation facilities, the loss in tsunami momentum is animportant factor. With regard to the momentum loss that is proportional to the mean flow velocity, considerationis given to friction along the sea bottom, which may be evaluated using say Manning’s roughness formula, andthe aperture loss 6), which takes place when there is a sudden constriction or widening of the cross section at theopening between breakwaters.(7) Tsunami Wave ForceThe wave force of tsunami is given as the wave force of a long wave, and may be assumed to be as sketched inFig. T- 6.4.2. When h/L < 0.04 and there is no wave breaking, the wave force is assumed to be zero at a height h= 1.5H above the still water level and p (=1.1r0gH) at the still water level, and to have a linear distribution inbetween; it is assumed to have a constant intensity of p below the water surface.Correction for wave direction is not made, and the wave height H is that of progressive tsunami. Note,however, that if there is a breakwater, according to the results of numerical simulations, the tsunami wave heightin front of the breakwater becomes twice that for the case when there is no breakwater, owing to reflection. Inthis case the distance between the maximum water level in front of the breakwater and the still water level maybe used as the incident wave height. It is also acceptable to use one half of the standing wave height as theincident wave height.HH0------B0B------è øæ ö1 2¤ h0h-----è øæ ö1 4¤=
    • PART II DESIGN CONDITIONS-133-Fig. T- 6.4.2 Distribution of Wave Pressure by Tsunami6.5 SeicheFor harbors where the seiche motion is anticipated, the presence of seiche shall be considered as necessarywhen fixing the design water level or investigating the tranquility in mooring basins.[Commentary]Seiche is a phenomenon involving abnormal oscillations of the water level with a period of approximately a fewminutes to a few tens of minutes. It occurs when small fluctuations of the water level are generated by a microscalevariations of the atmospheric pressure by an air front or a low in the outer sea, and the components of theseoscillations whose period is the same as a natural period of the harbor are amplified through resonance. Depending onthe topography, the amplitude of these fluctuations may be anything from a few tens of centimeters up to around 2m.When seiche occurs in a harbor, even if the wave height is only a few tens of centimeters, the long wavelength resultsin a great deal of water movement in the horizontal direction, which can cause severe problems to moored vessels andcargo handling work. Seiche is particularly liable to occur in an artificially excavated harbor, which is long andnarrow in shape and surrounded by quaywalls. It is thus desirable to investigate the effects of seiche when drawing upa harbor plan. This can be done using say a numerical calculation 9), whereby incident waves with the period from afew minutes up to around one hour are inputted, and then the amplification factor for these waves in the harbor iscalculated. Small long waves in the outer sea may have an amplitude of the order of a few centimeters. It is desirableto avoid such the shape of a harbor that the amplitude of long waves may be amplified by ten times or more within theharbor.[Technical Notes](1) Natural PeriodsThe natural periods of a bay that has a long, narrow rectangular shape as shown in Fig. T- 6.5.1 (a) are givenapproximately as in the following equation:(6.5.1)whereT: natural period (s)l: length of bay (m)m: number of nodes in the bay (0, 1, 2,…)h: mean water depth in the bay (m)g: gravitational acceleration (m/s2) (= 9.81m/s2)In an actual bay, not only does the seawater within the bay oscillate in a periodic fashion, but the water of theopen sea around the bay entrance also oscillates somewhat. It is thus necessary to make a correction to thenatural period with equation (6.5.2) of the following:(6.5.2)whereh: mean water depth in the bay (m)a: bay entrance correction factor, as obtained from the following equation 10).(6.5.3)ll>>=Fig. T- 6.5.1 Bay Shape ModelsT4l2m 1+( ) gh--------------------------------=T a4lgh----------=a 12bpl------ 0.9228 lnpb4l------–è øæ ö+î þí ýì ü1 2¤=
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-134-wherel: length of bay (m)b: width of bay (m)Table T- 6.5.1 lists the values of the bay entrance correction factor a calculated for different values of b/l.Table T- 6.5.1 Bay Entrance Correction FactorThe natural periods of a rectangular harbor that has a narrow entrance as shown in Fig. T- 6.5.1 (b) may becalculated approximately with the following equation:(6.5.4)whereb: width of harbor (m)m: number of nodes in the harbor in the length direction (0, 1, 2, …)n: number of nodes in the harbor in the width direction (0, 1, 2, …)Note however that because of the effect of the harbor entrance, the natural periods of an actual harbor areslightly lower than those calculated using this equation.(2) AmplitudeThe magnitude of amplification factor for the resonant oscillations in a harbor by seiche is limited by the energycarried out by the disturbance waves that are radiated from the harbor entrance, and the energy lost through thevortices at the harbor entrance and the bottom friction within the harbor. Accordingly, even if the period of long-period waves arriving at the harbor coincide with one of the natural periods of the harbor, it is not the case thatthe amplitude of the oscillations in the harbor will rise to infinity. Note however that when there is very littleenergy loss by vortices and friction, it is necessary to take heed of the harbor paradox, which refers to aphenomenon whereby the narrowing of a harbor entrance results in the greater amplification within the harbor.The amplitude amplification factor R for the concave corners at the head of a rectangular-shaped harborwhen the entrance loss is ignored may be obtained as a function of the ratio of the harbor length to thewavelength using either Fig. T- 6.5.2 or Fig. T- 6.5.3. According to Fig. T- 6.5.2, in a harbor with a long,narrow rectangular shape, resonance occurs when the period is slightly longer than that corresponding to awavelength that satisfies the conventionally-cited resonance condition, namely the harbor length being oddquarters of the wavelength (1/4, 3/4, 5/4, etc.). According to Fig. T- 6.5.3, the resonance points for a harbor witha wide rectangular shape are more-or-less the same as those for a completely closed rectangular lake; in otherwords, they are given approximately by the following equation:: ,… (6.5.5)b/l 1 1/2 1/3 1/4 1/5 1/10 1/25a 1.320 1.261 1.217 1.187 1.163 1.106 1.064T2ghml----è øæ ö2mb----è øæ ö2+î þí ýì ü-------------------------------------------------=nlL--- m2 n22bl------è øæ ö2--------------+= m n, 0 1 2, ,=Fig. T- 6.5.2 Resonance Spectrum for a Harbor withLong, Narrow Rectangular Shape 11)Fig. T- 6.5.3 Resonance Spectrum for a Harbor withWide Rectangular Shape 11)AmplitudeamplificationfactorRRelative length of the portAmplitudeamplificationfactorRRelative length of the port
    • PART II DESIGN CONDITIONS-135-(3) Countermeasures against SeicheSeiche is the phenomenon whereby long-period waves penetrates into a harbor from the entrance, repeatesperfect reflection within the harbor, and increases its amplitude. In order to hold down the amplitude of seiche, itis thus necessary to make the reflection imperfect around the inner perimeter of the harbor, or increase theenergy loss within the harbor. For this reason, it is not advisable to build solid quaywalls around the wholeperimeter of a harbor. If a permeable rubble-mound breakwater with a gentle slope is used, wave reflection canbe reduced to some extent, and in addition one can expect a certain energy loss within the core of breakwater.Furthermore, by installing an inner breakwater close to the position of a node of the seiche in a harbor, theamplitude of the seiche can be somewhat reduced. Regarding the shape of the harbor, it is thought that anirregular shape is better than a geometrically regular shape.6.6 Groundwater Level and PermeationThe groundwater level in coastal aquifers of sandy beaches shall be examined when there is a risk ofarousing a problem by the change of the groundwater level.The flow velocity and rate of permeation through water-permeable ground or structures shall beexamined when there is a risk of arousing a problem by their changes.[Technical Notes](1) Groundwater Level in Coastal AquiferThe elevation of brackish groundwater intruding in acoastal aquifer may be estimated using the followingequation (see Fig. T- 6.6.1) 12):(6.6.1)where,h: depth below the sea surface of the interfacebetween fresh water and saltwater at the distancex (m)h0: depth below the sea surface of the interfacebetween fresh water and saltwater at x = 0 (m)hl: depth below the sea surface of the interfacebetween fresh water and saltwater at x = L (m): density of the fresh water (g/cm3): density of saltwater (g/cm3): elevation of fresh water above the sea surface at the coast (x = 0) (m): elevation of fresh water above the sea surface at x = L (m)L: distance from the coast (x = 0) to the reference point (m)x: landward distance from the coastline (m)Equation (6.6.1) cannot be applied if an impermeable layer exists close to the ground surface or in the aquifer:For the relationship between the rise of groundwater level due to wave runup and beach profile change, see in10.1 General [Technical Notes] (8).(2) Permeation into Foundation and Structures(a) Permeation through a sheet pile wallThe flow rate of permeation through a sheet pile wall is not determined purely by the permeability of the wall;rather, the permeability of the soil behind the wall has a dominating influence. Shoji et al. 13) examined thisproblem, and carried out comprehensive permeation experiments in which they not only varied the tension ofthe joints, but also added the cases with and without sand filling in the joint section. They concluded topropose the following experimental formula:(6.6.4)whereq: flow rate of permeation through a sheet pile joint per unit length in the vertical direction (cm3/s/cm)K: permeation coefficient for the joints (cm2-n/s)h: pressure head difference between the front and back of a joint (cm)n: coefficient depending on the state of the joints(n ≒ 0.5 when the joints are not filled with sand, and n ≒ 1.0 when the joints are filled with sand)When there was sand on both sides of the sheet pile and the joints were under tension, Shoji et al. obtained avalue of 7.0 × 10-4 cm/s for K in their experiments. However, they also pointed out that if the permeation flowSeaFresh water levelFresh waterSalt water levelSalt waterFig. T- 6.6.1 Schematic Drawing of Groundwaterat Coasth2h02hl2h02–( )xL---+=h0r1r2 r1–---------------z0= hlr1r2 r1–---------------zl=r1r2z0zlq Khn=
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-136-is estimated with this value, then the flow rate turns out to be as much as 30 times that observed in the field.For actual design, it is thus necessary to pay close attention to any difference between the state of the sheet pilewall used in the experiments and those used in the field.(b) Permeation through rubble moundThe flow rate of permeation through a rubble mound foundation of a gravity type structure may be estimatedusing the following equation:(6.6.5)whereq: flow rate of permeation per unit width (m3/s/m)U: mean permeation velocity for the whole cross section of rubble mound (m/s)H: height of the permeable layer (m)d: rubble stone size (m)g: gravitational acceleration (= 9.81 m/s2)DH/DS: hydraulic gradientz: resistance coefficientEquation (6.5.5) has been proposed based on the experimental results using eight different types of stones ofuniform size, with the diameter ranging from 5 mm to 100 mm. The virtual flow length DS may be taken to beas the total of the 70% to 80% of the permeable layer height and the width of the caisson base. The coefficientof resistance is shown in Fig. T- 6.6.3. When / , it is acceptable to take z ≒ 20.Fig. T- 6.6.3 Relationship between Resistance Coefficient and Reynolds Number[References]1) IPCC: “Climate Change 1995”, IPCC Second Assessment Report, The Science of Climate Change, 1995, 572p.2) Toshihiko NAGAI, Kazuteru SUGAHARA, Hiroshi WATANABE, Koji KAWAGUCHI: “Long team observation of the meantide level and lond waves at the Kurihama-Bay”, Rept of PHRI, Vol. 35, No. 4, 1996. (in Japanese).3) Katsutoshi TANIMOTO, Tomotsuka TAKAYAMA, Kazuo MURAKAMI, Shigeru MURATA, Hiroiti TSURUYA, ShigeoTAKAHASHI, Masayuki MORIKAWA, Yasutoshi YOSHIMOTO, Susumu NAKANO, Tetsuya HIRAISHI: “Field andlaboratory investigations of the tsunami caused by 1983 Nihonkai Chubu Earthquake”, Tech. Note of PHRI, No. 470, 1983,299p. (in Japanese).4) Chiaki GOTO, Kazuo SATO: “Development of tsunami numerical simulation system for Sanriku Coast in Japan”, Rept ofPHRI, Vol. 32, No. 2, 1995. (in Japanese).5) Tomotsuka TAKAYAMA, Tetsuya HIRAISHI: “Hydraulic model tests on tsunamis at Suzaki Port”, Tech. Note of PHRI, No.549, 1986, 131p. (in Japanese).6) Tomotsuka TAKAYAMA, Norihiro NAGAI, Tetsuya HIRAISHI: “The numerical calculation of tsunami in Tokyo Bay”,Tech. Note of PHRI, No. 454, 1986, 131p.(in Japanese).7) Toshihoko NAGAI, Noriaki HASHIMOTO, Tetsuya HIRAISHI, Katsuyoshi SHIMIZU: “Characteristics of the Hokkaido-East-off-Earthquake Tsunami”, Tech. Note of PHRI, No. 802, 1995, 97p. (in Japanese).8) Koji KOBUNE, Toshihiko NAGAI, Noriaki HASHIMOTO, Tetsuya HIRAISHI, Katsuyoshi SHIMIZU “Characteristics ofthe Irianjaya Earthquake Tsunami in 1996”, Tech. Note of PHRI, No. 842, 1996, 96p. (in Japanese).q UH=U2gdz---------DHDS--------×=678Re Ud=( n) 104>ReUdn-------=
    • PART II DESIGN CONDITIONS-137-9) Tomotsuka TAKAYAMA, Tetsuya HIRAISHI: “Amplification mechanism of harbor oscillation derived from fieldobservation and numerical simulation”, Tech. Note of PHRI, No. 636, 1988, 70p. (in Japanese).10) Honda, K., T. Terada, and D. Ishitani: “Secondary undulation of oceanic tides”, Philosophical Magazine, Vol.15,1908, pp.88-126.11) Ippen, A.T. and Y. Goda: “Wave-induced oscillations in harbors: the solution for a rectangular harbor connected to the opensea,” M.I.T. Hydrodynamics Lab. Report No.59, 1963, 90p.12) Todd, D. K.: “Groundwater Hydrology”, John Wiley & Sons, Inc., 1963.13) Yoshihiro SHOJI, Masaharu KUMEDA, Yukiharu TOMITA: “Experiments on seepage through interlocking joints of sheetpile”, Rept of PHRI, Vol. 21, No. 4, 1982, pp. 41-82 (in Japanese).
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-138-Chapter 7 Currents and Current Force7.1 General(1) The current parameters that shall be used in the design of port and harbor facilities are the velocityand the direction. The severest conditions shall be set, based on either the field measurements at theinstallation location of the facilities in question or the numerical estimation.(2) For the current force, consideration shall be given to the drag and lift, depending on the type of thefacilities in question and the structural form.[Commentary]For structures that are located in a place where there is strong currents such as a tidal currents or river flow, it isnecessary to carry out investigations on the forces produced by the currents with the largest velocity from the mostunfavorable direction. Depending on the type of structures or members, it may also be necessary to consider thevertical distribution of the current velocity. When waves coexist with currents, it is necessary to use the currentvelocity and direction in the state of coexistence. Types of currents in the sea area include ocean currents, tidalcurrents, and wind drift currents, which are described in the [Technical Notes] below, along with density currentscaused by the density differences due to salinity or water temperature. In addition, in the coastal area, there arelongshore currents and rip currents caused by waves.[Technical Notes](1) Ocean CurrentsOcean currents are the phenomenon involving the circulation of seawater around the ocean as a whole. They arethe result of a combination of the following currents: a) density currents that are based on local differences in thedensity of seawater, b) wind-driven drift currents that are caused by the wind, and c) gradient currents thataccompany spatial inequalities in the atmospheric pressure, along with d) compensation currents (upwellingcurrents and or sinking currents) that supplement the aforementioned currents. Ocean currents maintain thealmost steady direction and strength over prolonged periods of time.(2) Tidal Currents(a) The nature and strength of tidal currents vary with the geographical conditions of the sea area in question andthe celestial movements. In order to analyze the harmonic components of tidal currents, it is necessary to carryout continuous observation for at least 25 hours or advisably for full 15 days. In particular, if the topography ofa place is going to be changed considerably, for example when carrying out large-scale land reclamation inshallow coastal waters, it is desirable to examine the resultant changes in tidal currents at the planning stage.(b) The tidal currents are the flow of seawater in the horizontal direction that accompanies a tidal variation of sealevel. This variation consists of the tidal components (diurnal tide, semi-diurnal tide, etc.) of the water leveland is thus periodic.(3) Wind-Driven CurrentsWhen a wind blows over the sea surface, the friction on the boundary between the air and the sea surfaceproduces a shear stress that causes to induce a flow on the sea surface. As this flow develops, the turbulent eddyviscosity of the seawater causes the lower layers to start to be pulled along by the upper layers. If the windvelocity and direction remain constant for a prolonged period of time, a steady state of currents is eventuallyreached. Such the currents are referred to as the wind-driven currents.(4) Nearshore CurrentsIn the surf zone, there exist special currents called the nearshore currents induced by waves. Because thenearshore currents are induced within the surf zone, they transport suspended sediments and cause topographicalchange of beaches. Consequently, an understanding of the pattern of nearshore currents leads to a deeperperception of topographical change.7.2 Current Forces Acting on Submerged Members and Structures (Notification Article 7)It shall be standard to calculate the drag and lift forces caused by currents acting on a member or astructure that is submerged or near the water surface using the following equations:(1) Drag Force(7.2.1)FD12---CDr0AU2=
    • PART II DESIGN CONDITIONS-139-whereFD: drag force acting on the object in the direction of the current (kN)CD: drag coefficientr0: density of water (t/m3)A: projected area of the object in the direction of the current (m2)U: flow velocity (m/s)(2) Lift Force(7.2.2)whereFL: lift force acting on the object in the direction perpendicular to the current (kN)CL: lift coefficientAL: projected area of the object in the direction perpendicular to the current (m2)[Commentary]The fluid force due to the currents acting on members of a pile-supported structure such as a pier, a pipeline, or thearmor units of a mound is proportional to the square of the flow velocity. It may be divided into the drag force actingin the direction of the current and the lift force acting in the direction perpendicular to this. Note also that a thin, tube-like object in the water may be subject to vibrations excited by current-induced vortices.[Technical Notes](1) Drag CoefficientThe drag to a submerged object due to currents is expressed as the sum of the surface resistance due to frictionand the form drag due to pressure difference around the object. The drag coefficient varies according to theshape of the object, the roughness, the direction of the current, and the Reynolds number, and thus the valueappropriate to the conditions in question must be used.When the Reynolds number is greater than about 103, the values listed in Table T- 7.2.1 may be used asstandard values for the drag coefficient. Note that for a circular cylinder or sphere with a smooth surface, there isa phenomenon whereby the value of the drag coefficient drops suddenly when the Reynolds number is around105. However, for a circular cylinder with a rough surface, this drop in drag coefficient is not particularly large,and the drag coefficient settles down to a constant value that depends on the relative roughness.For the values of the drag coefficient when a prism or L-shaped member is oriented diagonally relative to thecurrent, search for references. The data for the cube have been obtained from wave force experiments carried outby Hamada, Mitsuyasu and Hase.Table T- 7.2.1 Drag CoefficientsFL12---CLr0ALU2=Flat plateCircular discRectangularprismCircular cylinder(rough surface) DBDbCubeD DSphere DDaShape Projected area Drag coefficientπ4D1.0 D2.0 B1.20.5 0.21.3 1.62D 2DBπ4D 2a b=/>= 1 1.12=/>= 2 1.15=/>= 4 1.19=/>= 10 1.29=/>= 18 1.40=/>= 2.01
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-140-(2) Lift CoefficientAs with the drag coefficient, the lift coefficient varies with the shape of the object, the direction of the current,and the Reynolds number. However, the lift coefficient is not well understood (see 5.4.1 Wave Force onSubmerged Members).(3) Current Force Acting on Submerged BreakwaterAs for the force acting on the coping of the submerged section at the opening of tsunami protection breakwater,Iwasaki et al. have measured the pressure on the coping due to the currents. They obtained the values of 0.94 forthe drag coefficient and 0.48 for the lift force coefficient. Tanimoto et al. have carried out similar measurements,obtaining the values 1.0 to 1.5 for the drag coefficient and 0.5 to 0.8 for the lift coefficient. They have alsopointed out, however, that when the flow velocity in the breakwater opening is large, the presence of the watersurface gradient causes the coefficient values to increase.7.3 Mass of Armor Stones and Concrete Blocks against Currents (Notification Article 48,Clause 6)It shall be standard to calculate the required mass for the armor units (rubble etc.) on a rubble mound to bestable against currents by means of either appropriate hydraulic model experiments or else the followingequation:(7.3.1)whereM: minimum mass of armor stones and blocks (t)rr: density of armor stones and blocks (t/m3)U: current velocity above armor stones and blocks (m/s)g: gravitational acceleration (= 9.81 m/s2)y: Isbash’s constant (1.20 for embedded stones; 0.86 for exposed stones)Sr: specific gravity of armor stones and blocks relative to waterq: slope angle in the axial direction of the channel bed (º)[Technical Notes](1) Isbash’s EquationWith regard to the mass of rubble stone that is stable against currents, the US Army Coastal EngineeringResearch Center (CERC) has presented equation (7.3.1) for the mass that a rubble stone must have in order toprevent scouring by tidal currents 8).(2) Isbash’s ConstantEquation (7.3.1) has been derived by considering the balance between the drag caused by a flow acting on aspherical object on a sloped surface and the frictional resistance of the object. The coefficient y is termedIsbash’s constant. It would appear that the values of 1.20 and 0.86 for embedded stones and exposed stones,respectively, were determined by Isbash, but the details were not documented. Since equation (7.3.1) has beenobtained by considering the balance of forces for steady flow, for places where it is anticipated that strongvortices will be generated, it is necessary to use rubble stones of larger mass.(3) Armor Units for the Mound at the Opening of Tsunami Protection BreakwatersIwasaki et al. have carried out two-dimensional steady flow experiments in which they used precast concreteblocks as the armor for the mound in the opening of breakwaters designed to protect harbors and coastal areaagainst tsunamis. They obtained a value of 1.08 for Isbash’s constant in equation (7.3.1). Tanimoto et al. havecarried out three-dimensional experiments on the opening of a tsunami breakwater. They clarified the structureof the three-dimensional flow near the opening, and revealed the relationship between the damage ratio andIsbashs constant when stones or precast concrete blocks were used as the covering material.[References]1) Kazuo MURAKAMI, Masayuki MORIKAWA, Tatsuya SAKAGUCHI: “Wind effect and water discharge effect on constantflow - discussion using observation data at off-Sennan (1978-1981) -”, Rept of PHRI, Vol. 21, No. 4, 1982, pp. 3-39 (inJapanese).2) Masch, F. D.: “Mixing and dispersion of wastes by wind and wave action”, ‘Advances in Water Pollution Research,’ Proc. Int.Conf., Vol. 3, 1962, pp. 145-168.3) Longuet-Higgins, M.S. and R.W. Stewart: “Radiation stress and mass transport in gravity waves, with application to ‘surfbeat’”, J. Fluid Mech., Vol. 13, 1962, pp. 481-504.4) Bowen, A. J., D. L. Inman, and V. P. Simons: “Wave ‘set-down’ and ‘set-up’”, J. Geophs. Res. Vol. 73, 1968, pp. 2569-2577.5) Kazumasa KATOH, Shin-ichi YANAGISHIMA, Tomoyoshi ISOGAMI, Hiroyuki MURAKAMI: “Wave set-up near theshoreline - field observation at HORF -”, Rept of PHRI, Vol. 28, No. 1, 1989, pp. 3-41 (in Japanese).MprrU648( )g3y6 Sr 1–( )3 qcos qsin–( )3--------------------------------------------------------------------------------=
    • PART II DESIGN CONDITIONS-141-6) Yoshimi GODA: “Deformation of irregular waves due to depth-controlled wave breaking”, Rept of PHRI, Vol. 14, No. 3,1975, pp. 59-106 (in Japanese), also “Irregular wave deformation in the surf zone”, Coastal Engineering in Japan, JSCE,Vol.18, 1975, pp.13-26.7) Katsutoshi TANIMOTO, Katsutoshi KIMURA, Keiji MIYAZAKI: “Study on stability of submerged disk at the openingsection of tsunami protection breakwaters”, Rept of PHRI, Vol. 27, No. 4, 1988, pp. 93-121 (in Japanese).8) Coastal Engineering Research Center: “Shore Protection Manual”, Vol. II, U.S. Army Corps of Engineering, 1977
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-142-Chapter 8 External Forces Acting on Floating Body and Its Motions8.1 GeneralThe motions of a floating body produced by external forces such as those due to winds, currents andwaves, along with the mooring force, shall be given due consideration in design of the floating body andrelated facilities.[Commentary](1) Floating BodyIn general, a floating body refers to a structure that is buoyant in water and its motions within a certain range ispermitted during use. When designing a floating body, it is necessary to investigate both its functions that aregoing to be demanded and its safety. In general, the design conditions for the investigation of its function differfrom those for the examination of its safety.(2) Mooring EquipmentMooring equipment comes in a whole variety of types and is generally composed of a combination of mooringlines, mooring anchors, sinkers, intermediate weights, intermediate buoys, mooring rods, connection joints, andfenders. The mooring equipment has a large influence on the motions of a floating body, and so it is important todesign this equipment safely and appropriately.[Technical Notes](1) Classification of Floating BodiesThe floating bodies used as port and harbor facilities can be divided into floating terminals, offshore petroleumstockpiling bases, floating breakwaters, mooring buoys, and floating bridges. Moreover, researches fordevelopment of extra large floating structures (mega-float) are being carried out.(2) Classification of Mooring Methods and Characteristic Features of Each MethodFloating bodies can also be classified by the type of mooring methods. As described below, mooring methodsinclude catenary mooring (slack mooring), taut mooring, and dolphin mooring.(a) Catenary mooring (Fig. T- 8.1.1(a))This is the most common mooring method. With this method, the chains or whatever used in the mooring aregiven sufficient lengths to make them slack. This means that the force restraining the motions of the floatingbody is small, but nevertheless the mooring system fulfills the function of keeping the floating body in more-or-less the same position. There are various types of catenary mooring, depending on factors like the materialof the mooring lines, the number of mooring lines, and the presence or absence of intermediate buoys andsinkers.(b) Taut mooring (Fig. T- 8.1.1(b))This is a mooring method that reduces the motions of the floating body greatly; a tension leg platform (TLP) isan example. With this method, the mooring lines are given a large initial tension so that they do not becomeslack even when the floating body moves. The advantages of this mooring method are that the floating bodydoes not move much, and only a small area is needed for installing the mooring lines. However, it is necessaryto take note of the fact that because a large tensile force is generated in the mooring lines, the design of thelines becomes the critical factor on the safety of the floating body.(c) Dolphin mooring (Fig. T- 8.1.1(c))With this method, mooring is maintained using either a pile-type dolphin or a gravity-type dolphin. In general,this method is suitable for restraining the motions of a floating body in the horizontal direction, but a largemooring force acts on the dolphin. This method has been used for mooring floating units of offshorepetroleum stockpiling bases.(d) Mooring method using a universal joint (Fig. T- 8.1.1(d))The mooring system shown in the figure is an example of a mooring method that can be used to moor a largeoffshore floating body. Examples of mooring systems that use a universal joint on the sea bottom include aSALM (Single Anchor Leg Mooring) type mooring buoy and a MAFCO (MAritime Facility of CylindricalcOnstruction) tower.
    • PART II DESIGN CONDITIONS-143-Fig. T- 8.1.1 Examples of Mooring Methods for Floating Body8.2 External Forces Acting on Floating Body (Notification Article 26, Clause 1)When a port or harbor facility is made of a floating structure, it shall be standard to take the followingforces in design calculation: wind drag force, current drag force, wave-exciting force, wave-drift force,wave-making resistance, restoring force, and mooring force. These forces shall be calculated by means ofan appropriate analytical method or hydraulic model experiments, in accordance with the mooring methodfor the floating body and the size of facility.[Technical Notes](1) Wind Drag ForceWith a structure for which a part of the floating body is above the sea surface, winds exert a force on thestructure. This force is called the wind drag force (or wind pressure), and is composed of a pressure drag and afriction drag. If the floating body is relatively small in size, the pressure drag is dominant. The pressure drag isproportional to the square of the wind velocity and is expressed as in the following equation:(8.2.1)whereFw: wind drag force (N)ra: density of air (1.23 kg/m3)AW: projected area of the part of the floating body above the sea surface as viewed from the direction inwhich the wind is blowing (m2)UW: wind velocity (m/s)CDW: wind drag coefficientThe wind drag coefficient is a proportionality constant and is also known as the wind pressure coefficient. It maybe determined by means of wind tunnel experiments or the like. However, it is also acceptable to use a value thathas been obtained in the past experiments for a structure with a shape similar to the structure under current study.Values such as those listed in Table T- 8.2.1 have been proposed as the wind drag coefficients of objects inthe uniform flow. As can be seen from this table, the wind drag coefficient varies with the shape of the floatingbody, but it is also affected by the wind direction and the Reynolds number. Note that it is considered that thewind pressure acts in the direction of the wind flow, with the point of application being the centroid of theprojection of the part of the floating body that is above the water surface. However, it is necessary to take heedof the fact that this may not necessarily be the case if the floating body is large. Moreover, the velocity of theactual wind is not uniform in the vertical direction, and so the value of the wind velocity UW used in the windpressure calculation is set as that at the elevation of 10 m above the sea surface.Mooring anchorChainDolphinFenderDamperUniversal joint(a) Catenary mooring (c) Dolphin mooring(b) Taut mooring (d) Mooring by universal jointFw12---raCDWAWU 2W=
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-144-Table T- 8.2.1 Wind Pressure Coefficient(2) Current Drag ForceWhen there is currents such as tidal currents, these currents will exert a force on the submerged part of thefloating body. This force is referred to as the flow pressure or the current drag force. Like the wind drag force, itis proportional to the square of the flow velocity. Note however that since the velocity of the current is generallysmall, the current drag force is actually expressed as being proportional to the square of the velocity of thecurrent relative to the velocity of motion of the floating body as in the following equation:| | (8.2.2)whereFC: current drag force (N)r0: density of fluid (for seawater, 1030 kg/m3)AC: projected area of the submerged part of the floating body as viewed from the direction of the currents(m2)UC: velocity of the currents (m/s)U: velocity of motion of the floating body (m/s)CDC: drag coefficient with respect to the currentsThe drag coefficient CDC is a function of the Reynolds number. When the Reynolds number is large, however,the values for steady flow in Table T- 7.2.1 in 7.2 Current Forces Acting on Submerged Members andStructures may be used. The drag coefficient for the currents varies with the shape of the floating body and thedirection of the currents. As with the wind pressure, the direction of the force exerted by the currents and thedirection of the currents itself are not necessarily the same. In general, the deeper the draft of the floating bodyrelative to the water depth, the larger the drag coefficient for the currents becomes. This is referred to as theshoaling effect, and the drag coefficient increases because the smaller the gap between the sea bottom and thebase of the floating body, the harder it is for water to flow through this gap.(3) Wave-Exciting ForceThe wave-exciting force is the force exerted by incident waves on the floating body when the floating body isconsidered to be fixed in the water. It is composed of a linear force that is proportional to the amplitude of theincident waves and a nonlinear force that is proportional to the square of the amplitude of the incident waves.The linear force is the force that the floating body receives from the incident waves as reaction when the floatingbody deforms the incident waves. The velocity potential for the deformed wave motion is obtained using wavediffraction theory. The nonlinear force, on the other hand, is composed of a force that accompanies the finiteamplitude nature of waves and a force that is proportional to the square of the flow velocity. The former forcedue to finite amplitude effect can be analyzed theoretically, but in practice it is often ignored. The latter forcethat is proportional to the square of the flow velocity becomes large, in particular when the diameter of thefloating body is small relative to the wavelength; it is necessary to determine this force experimentally.(4) Wave-Drift ForceWhen waves act on a floating body, the center of the floating body’s motion gradually shifts in the direction ofwave propagation. The force that causes this shift is called the wave-drift force. If it is assumed that the floatingbody is two-dimensional and the wave energy is not dissipated, then the wave-drift force is given by thefollowing equations:(8.2.3)2112Square cross-section 2.01.62.31.51.21.2Rectangular cross-section(ratio of side lengths = 1:2)(when one face is incontact with the ground)Circular cross-section(smooth surface)FC12---r0CDCAC= UC U– UC U–( )Fd18---r0gH2i R=
    • PART II DESIGN CONDITIONS-145-(8.2.4)wherer0: density of seawater (kg/m3)Fd: wave drift force per unit width (N/m)Hi: incident wave height (m)KR: reflection coefficientR: drift force coefficientIf the dimensions of the floating body are extremely small relative to the wavelength, the wave drift force maybe ignored as being much smaller than the wave-exciting force. However, as the floating body becomes larger,the wave drift force becomes dominant. When irregular waves act on a floating body moored at a system havingonly a small restraining force, such as a single point mooring buoy designed for use of supertankers, the wave-drift force becomes a dominant factor as it may give rise to slow drift motions.(5) Wave-Making ResistanceWhen a floating body moves in still water, the floating body exerts a force on the surrounding water, and thefloating body receives a corresponding reaction force from the water; this reaction force is called the wave-making resistance. This force may be determined by forcing the floating body to move through the still waterand measuring the force acting on the floating body. In general, however, an analytical method is used wherebyeach mode of the floating body motions is assumed to be realized separately, and the velocity potential, whichrepresents the motion of the fluid around the floating body, is obtained. Only the forces that are proportional tothe motion of the floating body may be determined analytically; the nonlinear forces that are proportional to thesquare of the motion cannot be determined analytically. Out of the linear forces (i.e., that proportional to themotion of the floating body), the term that is proportional to the acceleration of the floating body is called theadded mass term, while the term that is proportional to the velocity is called the wave damping term.(6) Restoring ForceThe static restoring force is the force that makes a floating body to return to its original position when thefloating body moves in still water. It is generated by buoyancy and gravity, when the floating body heaves, rollsor pitches. This force is generally treated as being proportional to the amplitude of the motion of the floatingbody, although this proportionality is lost if the amplitude becomes too large.(7) Mooring ForceThe mooring force (restraining force) is the force that is generated in order to restrain the motion of the floatingbody. The magintude of this force depends greatly on the displacement-restoration characteristics of the mooringsystem.(8) Solution Method for Wave-Exciting Force and Wave-Making Resistance Using Velocity PotentialThe method adopted for calculating the wave-exciting force and the wave-making resistance involvesderiviation of the velocity potential, which represents the motion of the fluid, and then calculating the wave-exciting force and the wave-making resistance from the potential. The analytical method with the velocitypotential is the same for both the wave-exciting force and the wave-making resistance, the only difference beingthe boundary conditions. The velocity potential may be obtained using any of a number of methods, such as aregion segmentation method, an integral equation method, a strip method, or a finite element method.(9) Wave Force Acting on Fixed Floating Body with Rectangular Cross SectionWhen a floating body is fixed in position, the velocity potential that satisfies the boundary conditions at the seabottom and around the floating body can yield the wave force. The wave force acting on a floating body with along rectangular cross section such as a floating breakwater can be determined using the approximation theoryof Ito and Chiba 2).(10) Materials for MooringFor the materials used in mooring and their characteristic features, search for appropriate references.(11) Forces Acting on an Extra Large Floating StructureFor an extra large floating structure (mega-float), the external forces described in (1) ~ (10) above are differentfrom those for a smaller floating body, because of its large size and elastic response characteristics of thefloating body structure. It is thus necessary to carry out sufficient investigations on the motions and elasticresponse characteristics of the floaty body structure.8.3 Motions of Floating Body and Mooring Force (Notification Article 26, Clause 2)The motions of a floating body and the mooring force shall be calculated by means of an appropriateanalytical method or hydraulic model experiments, in accordance with the shape of the floating body andthe characteristics of the external forces and the mooring system.R KR214ph L¤4ph L¤( )sinh--------------------------------+î þí ýì ü=
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-146-[Commentary]The motions of a floating body can be determined bysolving the dynamic equilibrium equation, with theexternal forces taken to be the forces due to winds andwaves, the restoring force of the floating body itself,and the reaction forces of the mooring lines andfenders. If the floating body is assumed to be a rigidbody, then its motions are comprised of the sixcomponents shown in Fig. T-8.3.1, namely surging,swaying, heaving, pitching, rolling and yawing. Out ofthese, the modes that represent motions within thehorizontal plane, namely surging, swaying and yawing,may show long-period oscillations with the period of afew minutes or more. Such long-period oscillationshave a large influence on the occupancy area of a vesselat a mooring buoy and the design of the mooring system. One may thus give separate consideration to the long-periodoscillations, taking only the wave-drift force and the long-period oscillation components of the winds and waves asthe external forces when doing analysis.If the floating body is very long, elastic deformation may accompany the motions of floaty body and this shouldbe investigated as necessary.[Technical Notes](1) Methods of Solving the Equations of Motions(a) Steady state solution method for nonlinear equations of motionThe equations of motions for a floating body are nonlinear, meaning that it is not easy to obtain solutions.Nevertheless, if it is assumed that the motion amplitudes are small and the equations of motion are linearizedby using linear approximations for the nonlinear terms, the solutions can be obtained relatively easily. Forexample, for a three-dimensional floating body, one ends up with a system of six simultaneous linearequations involving the amplitudes and phases of the six modes of motions. Note that if the floating body isassumed to be a rigid body and its motions are linear, then the motions are proportional to the external forces.In particular, if there are no currents or wind, then the motions are proportional to the wave height.(b) Numerical simulation of nonlinear motionsThe wind drag force and the current drag force are in general nonlinear, and moreover the restraining forces ofmooring equipment are also often nonlinear. In this case, an effective solution method is to use a numericalsimulation whereby the equations of motion are progressively solved for a series of time steps. Such numericalsimulation is commonplace nowadays. First, the time series data (which will be used as the external forces)are obtained for the wave-exciting force and the flow velocity due to the waves from the input of incidentwave spectrum, as well as the fluctuating wind speed from the wind spectrum. The external forces obtainedfrom these time series data are then put into the equations of motions for the floating body, and the time seriesdata for the motions of the floating body and the mooring force are calculated.Numerical simulations are used for analyzing the motions of all kinds of floating bodies. For example,Ueda and Shiraishi 3) have carried out numerical simulations on the motions of a moored vessel, and Suzukiand Moroishi 4) have analyzed the swinging motion of a vessel moored at a buoy.Note that the following is usually assumed as preconditions in a numerical simulation: ① the fluid is anideal fluid; ② the amplitudes of motions of the floating body are small; ③ the incident waves are linear andtheir superposition is allowed. If these assumptions cannot be held, it is necessary to carry out hydraulic modelexperiments.(2) Hydraulic Model ExperimentsHydraulic model experiments provide a powerful technique for determining the motions of a floating body andthe mooring force. Up to the present time, hydraulic model experiments have been carried out for all kinds offloating body. For examples, see references 5) and 6).(3) Law of Similarity for Mooring SystemsThe characteristics of the motions of a floating body vary greatly with the mooring method. When carrying outhydraulic model experiments on a floating body, it is thus particularly important to give appropriateconsideration to the laws of similarity for the displacement and reaction force characteristics of the mooringequipment. For example, with a mooring rope, if the material used in the hydraulic model experiments is keptthe same as that used in the field and the size is simply scaled down while maintaining the same shape, then thelaw of similarity will not hold; rather it is necessary to scale down the elastic modulus of the material used in themodels relative to that used in the prototype. In practice, however, it will probably be unable to find such amaterial, in which case various other contrivances must be used.Heaving Yawing RollingSurgingPitchingSwayingFig. T- 8.3.1 Components of Vessel’s Motion
    • PART II DESIGN CONDITIONS-147-[References]1) Tomotsuka TAKAYAMA, Tetsuya HIRAISHI, Masami FURUKAWA, Kunihisa SAO, Shin-ichiro TACHINO: “Feildobservation of motions of a SALM buoy and tensions of mooring hawsers”, Tech. Note of PHRI, No. 542, 1985, 38 p. (inJapanese).2) Yoshiyuki ITO, Shigeru CHIBA: “An approximate theory of floating breakwaters”, Rept of PHRI, Vol. 11, No. 2, 1972, pp.15-28 (in Japanese).3) Shigeru UEDA, Satoru SHIRAISHI: “Method and its evaluation for computation of moored ship’s motions”, Rept of PHRI,Vol. 22, No. 4, 1983, pp. 181-218 (in Japanese).4) Yasumasa SUZUKI, Kazuyuki MOROISHI: “On the motions of ships moored to single-point mooring systems”, Rept ofPHRI, Vol. 21, No. 2, 1982, pp. 107-150 (in Japanese).5) Yasumasa SUZUKI: “Study on the design of single point buoy mooring”, Tech. Note of PHRI, No. 829, 1996, 48 p. (inJapanese).6) Sigeru UEDA: “Analytical method of ship motions moored to quay walls and the aplications”, Tech. Note of PHRI, No. 504,1984, 372 p. (in Japanese).
    • TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN-148-Chapter 9 Estuarine Hydraulics9.1 General (Notification Article 8)In planning and designing port and harbor facilities in an estuary where a river flows into the sea, estuarinehydraulic phenomena such as the flow situation at the times of high water and low water in the river, thebedload, tidal changes and density currents, and the coexistence of waves and river flow shall be estimatedappropriately.[Commentary]In addition to the effect of outflow of fresh water during floods and droughts and the sediment transport from rivers,estuaries are also affected by the tide level changes, waves, tidal currents, longshore currents, and littoral drift. As aresult, several hydraulic phenomena occur such as the periodic changes in water level and current speed, theformation of density currents, and the settling and deposition of sediment. These phenomena have a large influenceon the flow regime in the estuary and the transport of sediment and others. It is thus necessary to give consideration toboth conditions of rivers and the sea when handling estuarine hydraulics.[Technical Notes](1) Tides in RiverThe surface water level in a river channel can be calculated using either equation (9.1.1) or equation (9.1.2).(a) When tides are negligible (see Fig. T- 9.1.1)(9.1.1)(b) When tides are consideredwhereDh: difference in water depth between two cross sections (m)h1: water depth at cross section 1 (m)h2: water depth at cross section 2 (m)z1: height of river bed above an arbitrary datum level at cross section 1 (m)z2: height of river bed above the arbitrary datum level at cross section 2 (m)z: height of river bed above the arbitrary datum level (m)a: velocity coefficient a ≒ 1.0Q: flow rate (m3/s)A: cross-sectional area (m2)K: flow carrying capacity of crosssection (m3/s), /R: hydraulic radius (m)n: Manning’s roughness coefficient (s/m1/3)Dx: distance between two cross sections(m)t: time (s)B: river width (m)H: water level from an arbitrary datumlevel (m), H = h + zi: channel bottom slopeg: gravitational acceleration (g = 9.81m/s2)Equation (9.1.1) is a modified form of the basic equation for non-uniform flow in a channel of arbitrary crosssection. Consequently, it cannot be applied to an estuary where there are strong tidal effects and a reverse,upstream flow occurs during a flood tide. However, it can be applied to an estuary where the tidal range issmall (less than 20 cm) and the tidal compartmut is not long (say up to about 3 to 4 km upstream). Even so, itshould only be used for the order estimate of hydraulic quantities during planning, because the calculation isonly an approximation while ignoring tides.Dh h1 h2 z2 z1–aQ22gs----------1A12--------1A22--------–è øç ÷æ ö Q22------1K12--------1K22--------+è øç ÷æ öDx––=–=1gA------¶Q¶t-------2QBgA2-----------¶H¶t-------Q2BgA3---------- i¶H¶x-------+è øæ ö––Q2gA3--------- H z–( )¶B¶x------–¶H¶x-------Q QK2----------- 0=+ +¶A¶t------¶Q¶x-------+ 0=Cross Section 2 Cross Section 1Fig. T- 9.1.1 Diagram Showing Water Level CurvesK2 A2R1 3/= n264748(9.1.2)
    • PART II DESIGN CONDITIONS-149-Equations (9.1.2) represents the equations of motions and continuity having been modified from the basicequations for unsteady flow in a river, where the flow rate and water level are the variables. In order toestimate the surface water level and flow rate due to the tidal action and propagation of tsunami into anestuary, simultaneous solutions can be obtained by equations (9.1.2) with appropriate boundary conditions.However, for a channel with a variable cross section, it is not so easy to solve equations (9.1.2) numerically.(2) Waves Entering an EstuaryUpon entering a river mouth, waves are deformed by the currents. In addition to refraction due to the waterdepth, refraction due to the difference in the directions between waves and currents causes the attenuation ofwave height. When the direction of waves is exactly opposite to that of river flow, however, wave height mayincrease through energy exchange through the river flow’s stopping action or radiation stress. When waves withan increased height run up the river channel, the wave height gradually decreases due to the effects of internaland external frictions, and turbulence of currents. These opposing effects are related to the properties of riverflow and waves, and the mechanism of wave height change is very complex.(a) Deformation of waves by currents (deepwater waves)As shown in Fig. T- 9.1.2, when waves propagates at anangle a across the straight boundary of discontinuitybetween the zone I where the water is still and the zone IIwhere the water is flowing with a uniform velocity,refraction occurs at the boundary, changing the wavecelerity and wavelength. If waves can be regarded asdeepwater waves (i.e., the water is sufficiently deeprelative to the wavelength in both the zones I and II), thewave celerity equation leads t