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STUDY OF RUBBLE MOUND AND CAISSON TYPE BREAKWATERS BY

EXPERIMENTAL AND NUMERICAL MODELLING UNDER EXTREME

WAVES

A THESIS SUBMITTED TO

THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES

OF

MIDDLE EAST TECHNICAL UNIVERSITY

BY

GÖZDE GÜNEY DOĞAN

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR

THE DEGREE OF MASTER OF SCIENCE

IN

CIVIL ENGINEERING

FEBRUARY 2016

Approval of the thesis:



WAVES

submitted by GÖZDE GÜNEY DOĞAN in partial fulfillment of the requirements

for the degree of Master of Science in Civil Engineering Department, Middle East

Technical University by,

Prof. Dr. Gülbin Dural Ünver

Dean, Graduate School of Natural and Applied Sciences _____________

Prof. Dr. İsmail Özgür Yaman

Head of Department, Civil Engineering _____________

Assist. Prof. Dr. Gülizar Özyurt Tarakcıoğlu

Supervisor, Civil Engineering Department, METU _____________

Examining Committee Members:

Prof. Dr. Ahmet Cevdet Yalçıner _____________

Civil Engineering Dept., METU

Assist. Prof. Dr. Gülizar Özyurt Tarakcıoğlu _____________


Prof. Dr. İsmail Aydın _____________


Assist. Prof. Dr. Talia Ekin Tokyay Sinha _____________


Assist. Prof. Dr. Aslı Numanoğlu Genç _____________

Civil Engineering Dept., Atılım University

Date: 05.02.2016

iv

I hereby declare that all information in this document has been obtained and

presented in accordance with academic rules and ethical conduct. I also declare

that, as required by these rules and conduct, I have fully cited and referenced all

material and results that are not original to this work.

Name, Last name : Gözde Güney Doğan

Signature :

v

ABSTRACT



WAVES

Doğan, Gözde Güney

M.S., Department of Civil Engineering

Supervisor: Asst. Prof. Dr. Gülizar Özyurt Tarakcıoğlu

February 2016, 144 pages

Many coastal structures are designed without considering loads of long waves or

extreme waves although they are constructed in areas prone to encounter these waves.

Performance of two different types of coastal structures, rubble mound and caisson

type breakwaters, is investigated under specified extreme wave conditions.

In the first part of the study, laboratory experiments are conducted to observe the

damage and failure phenomenon of the two types of breakwaters simultaneously which

were designed according to wind waves but tested under six different extreme wave

conditions. Pressure measurements along the front surface and bottom surface of the

vertical wall in caisson type breakwater are also carried out within the physical model

experiments for further investigation about the acting wave forces on the concrete

blocks of the caisson breakwater.

In the second part, the caisson type breakwater is modeled using a numerical software,

IH-2VOF, which is one of the RANS models that can be applied to simulate

hydrodynamic conditions around coastal structures. Two cases of the laboratory

vi

experiments are simulated by IH-2VOF model and pressure data is obtained from these

simulations.

Finally, the pressure measurements of laboratory experiments are compared with the

results obtained from the numerical model, IH-2VOF and presented for two wave

conditions along the front and bottom surfaces of vertical wall in caisson type

breakwater.

Keywords: rubble mound breakwaters, caisson type breakwaters, physical model

experiments, pressure measurements, numerical modelling, extreme waves

vii

ÖZ

TAŞ DOLGU VE KESON TIPI DALGAKIRANLARIN EKSTREM DALGALAR

ALTINDA DENEYSEL VE SAYISAL MODELLEME ILE ÇALIŞILMASI

Doğan, Gözde Güney

Yüksek Lisans, İnşaat Mühendisliği Bölümü

Tez Yöneticisi: Y. Doç. Dr. Gülizar Özyurt Tarakcıoğlu

Şubat 2016, 144 sayfa

Pek çok kıyı yapısı, uzun dalga ve ya ekstrem dalga koşullarına maruz kalma ihtimali

yüksek olan yerlerde inşa edildiği halde bu dalga koşulları dikkate alınmadan

tasarlanmaktadır. İki farklı temel kıyı yapısı olan taş dolgu ve keson tipi

dalgakıranların belirlenen ekstrem dalga koşulları altındaki performansları

araştırılmıştır.

Çalışmanın ilk kısmında, rüzgar dalgalarına göre tasarlanmış olan taş dolgu ve keson

tipi dalgakıran kesitlerinin ekstrem dalga koşulları altındaki hasar ve yıkılma

durumları gözlemlemek amacı ile fiziksel model deneyleri yapılmış ve bu kesitler altı

farklı ekstrem dalga koşulu için test edilmiştir. Buna ek olarak, keson tipi dalgakıran

kesitindeki beton bloklara etkiyen dalga yüklerini incelemek amacıyla deneylerde

blokların ön yüzeyi boyunca basınç ölçümleri alınmıştır.

İkinci kısımda, keson tipi dalgakıran kesiti ve deney düzeneği IH-2VOF isimli bir

program ile sayısal olarak modellenmiş ve deneylerden ikisinin simulasyonları

yapılmıştır. Keson tipi dalgakıran kesitindeki beton blokların ön yüzüne etkiyen yatay

viii

basınç değerleri ve alt yüzüne etkiyen kaldırma basıncı değerleri sayısal modelleme

yapılarak elde edilmiştir.

Son olarak, sayısal modelleme sonuçlarından elde edilen basınç değerleri ile

laboratuvar ölçümlerinden elde edilen basınç değerleri iki dalga koşulu için

karşılaştırılarak sunulmuştur.

Keywords: taş dolgu dalgakıran, keson tipi dalgakıran, fiziksel model deneyleri,

basınç ölçümü, sayısal modelleme, ekstrem dalgalar

ix

To my beloved family and

To my beloved ones...

x

ACKNOWLEDGEMENTS

First and foremost, I would like to thank Prof. Dr. Ahmet Cevdet Yalçıner for his

invaluable support at every step of not only my graduate studies but also my life. I am

so grateful to him that he has always listened to my problems patiently, most often

solved my problems heroically and motivated me continuously. He is one of the most

special persons in my life meaning much more than a university teacher. I will never

forget the moments of our conversations and his advices which enlighten my way

through life. I am really fascinated with not only his wide knowledge and experience

in technical issues but also in life, cultures and human relations. He is not only a great

academician but also a great people person. It is a great chance to meet him, to be a

student of him and to have a close relationship with him. I hope with all my heart that

this relationship will continue in the future.

I would also like to thank my supervisor, Assist. Prof. Dr. Gülizar Özyurt Tarakcıoğlu,

and co-supervisor, Dr. Cüneyt Baykal, for their support from the beginning of my

graduate study in METU Coastal and Ocean Engineering Laboratory. Dr. Tarakcıoğlu

encouraged me to work on the projects and told me her ideas about my thesis study

and helped me at each stage of my study. I have always admired her that she has a

great practical perspective. I am also thankfull to her for giving me a chance to

participate in the experimental work which was conducted at Technical University of

Braunschweig, for supporting me there and standing with me there, in my first

experience of living abroad. Dr. Cüneyt Baykal also helped me at each stage of my

experiments and numerical modelling. I was the one knocking on the door of him

during this study and he answered my questions with a great patience. He gave a lot

of importance to this study and always motivated me more than even myself. I hope I

have been a student worthy of his efforts.

xi

I would also like to express my sincere thanks to Prof. Dr. Ayşen Ergin who inspired

me in the way of being an academician. Her endless positive energy has always

stimulated me and given me a great motivation. Her unusual, enjoyful and rich content

lessons taught me looking things from different perspectives, most importantly from

the engineering point of view. She is the one I feel gratitude and made me choose

coastal engineering as my area of interest.

I feel also grateful to Dr. Işıkhan Güler for teaching me how to obtain any information

myself, how to search for the solution of a problem in a wide area and how to present

something effectively. Our long discussions about political issues are also so precious

that makes him meaning more than a teacher. I really appreciate his political standing

and participation and contribution to resistance movement. I hope we will always be

in communication.

I have always considered myself lucky to be a member of the family of Coastal and

Ocean Engineering Laboratory. Dr. Ayşen Ergin particularly creates this friendly and

beautiful atmosphere in the lab and makes us feel like at home but I would also like to

express my special thanks to our staff, Nuray Sefa, Yusuf Korkut and Arif Kayışlı for

their endless support in my work and contribution to this beautiful atmosphere.

I am deeply grateful to my lovely friends, Merih Himmetoğlu, Arın Özge Himmetoğlu,

Bircan Işık, Yağmur Öztürk and to my beloved one Burak Uçak for their full support,

encouragement and share of all the important moments with me while walking in this

way. Life would be meaningless without them.

I am so grateful to my lab friends, Ebru Demirci, Betül Aytöre, Gökhan Güler, Deniz

Velioğlu, Rozita Kian, Nilay Doğulu and Duha Metin for all the joyful moments that

we had together. I would also like to express my special thanks to Çağıl Kirezci for

being an excellent work partner. We have always been a ‘’last-minute’’ team with him

but succeded in the end. I will never forget our moments of Matlab coding.

xii

Finally, I would like to express my sincere thanks to my beloved family. My father,

Habib Doğan, has always provided me with unfailing support and continuous

encouragement since my childhood. He has always loved, protected and believed in

me and done his best as a father. I owe him most of the things I have. My mother,

Seval Doğan, also provided me unconditional love and I would never survive without

her support. She is the one that I can share everything in my life and the shoulder that

I can rest forever. I am also grateful to my brother, Ali Doğan that we had so much fun

together, laughed and made jokes during my thesis period. I am also deeply grateful to

my aunts, Nilgün Doğan Sarpkaya and Saniye Özkan for meaning much more than an

aunt in my life. Our long discussions about life and their advices enlighten me about

life. My sincere thanks are for my grandmother, Gülistan Doğan, who is the angel of

my life.

This thesis study is partly supported within the scope of RAPSODI (CONCERT_Dis-

021 and TUBİTAK-113M556) project in the framework of CONCERT-Japan Joint

Call and The Scientific and Technological Research Council of Turkey, and partly

supported within EC funded ASTARTE (Grant no: 603839) project. IH Cantabria is

also acknowledged for providing the numerical model, IH2VOF, which is used in this

thesis.

xiii

TABLE OF CONTENTS

ABSTRACT .............................................................................................................. v

ÖZ ............................................................................................................................ vii

ACKNOWLEDGEMENTS ...................................................................................... x

TABLE OF CONTENTS ......................................................................................... xiii

LIST OF TABLES ................................................................................................... xv

LIST OF FIGURES ................................................................................................ .xvi

CHAPTERS

1 INTRODUCTION .......................................................................................... 1

2 LITERATURE REVIEW ............................................................................... 5

2.1 Failure Mechanisms ............................................................................ 5

2.2 Forces and Pressures on Structures .................................................. 12

2.3 Numerical Modelling ........................................................................ 18

3 PHYSICAL MODEL EXPERIMENTS ....................................................... 21

3.1 General Description of Physical Model Experiments ...................... 21

3.2 Wave Flume ...................................................................................... 23

3.3 Model Scale ...................................................................................... 25

3.4 Laboratory and Scale Effects ............................................................ 29

3.5 Experimental Setup .......................................................................... 31

3.5.1 Rubble Mound Breakwater Cross-Section ...................................................... 33

3.5.2 Caisson Type Breakwater Cross-Section ........................................................ 35

3.6 Measuring Technique ....................................................................... 38

3.7 Wave Characteristics ........................................................................ 48

3.8 Summary of Physical Model Experiments ....................................... 55

4 NUMERICAL MODELLING ..................................................................... 57

4.1 Introduction to the Numerical Model, IH-2VOF ............................. 57

4.2 Theoretical Background of IH2VOF Model .................................... 59

xiv

4.3 Model Geometry and Mesh Generation ........................................... 66

4.4 Mesh Convergence Checks............................................................... 72

4.5 Hydraulic Conditions for the IH-2VOF Model ................................ 74

4.6 Summary of Numerical Modelling ................................................... 76

5 RESULTS AND DISCUSSION................................................................... 79

5.1 Physical Model Experiments ............................................................ 79

5.2 Numerical Modelling Results and Pressure Measurement

Comparison……………………………………………………………………….102

6 CONCLUSION AND FUTURE RECOMMENDATIONS ...................... 115

7 REFERENCES ........................................................................................... 119

8 APPENDICES ............................................................................................ 129

xv

LIST OF TABLES

Table 2.1: Failure Mode Matrix .............................................................................. 11

Table 3.1: Scaling factors using the similitude law of Froude ................................ 29

Table 3.2: Position of measuring devices in tests with respect to the initial position

of wave generator ............................................................................................. 42

Table 3.3: Wave characteristics before elimination ................................................ 51

Table 3.4: Wave characteristics before elimination, measured values ................... 51

Table 3.5: Characteristics of applied waves in model scale, caisson type breakwater

.......................................................................................................................... 52

Table 3.6: Characteristics of applied waves in model scale, rubble mound

breakwater ........................................................................................................ 52

Table 3.7: Ratio of measured wave heights to the design wave height in prototype53

Table 3.8: Summary of physical model experiments at METU .............................. 55

Table 4.1: Properties of the subzones in the mesh of caisson breakwater model ... 71

Table 5.1: Wave properties in model scale, caisson type breakwater ..................... 80

Table 5.2: Wave properties in model scale, rubble mound breakwater .................. 80

Table 5.3: Overview of detailed breakwater damage under related wave actions .. 97

Table 5.4: Observed properties of applied waves ................................................. 100

Table 8.1: Coordinates of Element Indices of Caisson Breakwater Model Geometry

in IH-2VOF .................................................................................................... 129

xvi

LIST OF FIGURES

Figure 2.1: Sketch of stages of sea dike failure a) Overflowing water, b) Creation of

scour-hole at leeward toe, c) Failure of leeward slope, d) Complete failure of

crest, leeward slope and toe (Jayaratne et al., 2013) .......................................... 7

Figure 2.2: Process of seawall overturning (Kato et al., 2012) ................................. 8

Figure 2.3: Overtopping of a composite breakwater by incoming tsunami wave (note

no armour damage) (Esteban, Miguel, et al., 2013) ........................................... 9

Figure 2.4: Overtopping of a composite breakwater by outgoing tsunami wave (note

the heavy damage) (Esteban, Miguel, et al., 2013) ............................................ 9

Figure 2.5: Comparison of various tsunami-bore velocities as a function of

inundation depth (Nouri et al., 2007) ............................................................... 14

Figure 2.6: Sketch showing some conceptual terms like tsunami height, inundation

depth and run-up height (Japan Weather Association materials,

http://www.japanecho.net/311-data/1205/ ) ..................................................... 15

Figure 2.7: Distribution of design wave pressure (Goda, 1974) ............................. 16

Figure 2.8: Vertical distribution of pressures for simple walls (Allsop, 1996) ....... 18

Figure 3.1: Flowchart of the model experiments .................................................... 23

Figure 3.2: The smaller basin and the wave flume ................................................. 24

Figure 3.3: a) Piston type wave maker b) Wave absorbers ..................................... 25

Figure 3.4: General layout of the basin (Top: top view, Bottom: Side view) ......... 25

Figure 3.5: View of horizontal platform in the wave flume ................................... 31

Figure 3.6: Caisson Type Breakwater ..................................................................... 32

Figure 3.7: Rubble Mound Breakwater ................................................................... 32

Figure 3.8: Cross-section of the caisson type breakwater with the horizontal

platform (Dimensions are in meters and the figure is not to scale.) ................. 33

Figure 3.9: Cross-section of the rubble mound breakwater with the horizontal

platform (Dimensions are in meters and the figure is not to scale.) ................. 33

xvii

Figure 3.10: Crown wall element used in rubble mound breakwater from different

perspectives (scale 1:50) .................................................................................. 34

Figure 3.11: Placement of the crown wall elements used in rubble mound

breakwater ........................................................................................................ 34

Figure 3.12: Geometric Details of Rubble Mound Cross-Section (Scale 1:50)...... 35

Figure 3.13: Layout of a concrete block used in caisson breakwater (scale 1:50) . 36

Figure 3.14: Placement of concrete blocks used in caisson type breakwater ......... 36

Figure 3.15: Geometric Details of the Caisson Cross-Section (Scale 1:50) ........... 37

Figure 3.16: Placement of the two cross-sections ................................................... 38

Figure 3.17: Wire type DHI-Wave Meter wave gauge ........................................... 39

Figure 3.18: a) Exemplary arrangement of overtopping wave gauge (WG2) in

caisson breakwater b) Exemplary arrangement of overtopping wave gauge

(WG2) in rubble mound breakwater ................................................................ 39

Figure 3.19: Example graph of calibration for WG3 .............................................. 40

Figure 3.20: Experimental setup including measuring instruments for caisson type

breakwater ........................................................................................................ 41

Figure 3.21: Experimental setup including measuring instruments for rubble mound

breakwater ........................................................................................................ 41

Figure 3.22: Profile measurement lines .................................................................. 43

Figure 3.23: Observation window and video recording system.............................. 43

Figure 3.24: Micro pressure transducer used in pressure measurements ................ 44

Figure 3.25: Pressure measurement points along the front surface of caisson

breakwater (Dimensions are in cm.) ................................................................ 45

Figure 3.26: Placement of two pressure transducers on the front surface of the

vertical wall element at still water level ........................................................... 45

Figure 3.27: Pressure measurement points along the bottom surface of caisson

breakwater (Dimensions are in cm.) ................................................................ 46

Figure 3.28: Results from 6 different static calibration pretests of the transducer 1 46

Figure 3.29: Results of 6 different static calibration pretests of transducer 2 ........ 47

Figure 3.30: Results of the dynamic water tank test of the transducers.................. 47

xviii

Figure 3.31: Frequencies and periods of the vertical motions of the ocean surface

(Holthuijsen, 2007) ........................................................................................... 48

Figure 3.32: Approximate regions of validity of analytical wave theories ............. 49

Figure 3.33: Biesel Transfer Function to obtain wave paddle displacement (Biesel,

1951) ................................................................................................................. 53

Figure 3.34: Sample surface profile ........................................................................ 54

Figure 4.1: Schematic diagram of main approaches in numerical modelling in

coastal and harbor engineering ......................................................................... 57

Figure 4.2: Sketch of volume averaging process for resolution of the porous flow

(IH-2VOF Course Lecture Notes, 2012) .......................................................... 62

Figure 4.3: Coral Interface, Zones .......................................................................... 67

Figure 4.4: Flowchart of generating a mesh in Coral ............................................. 68

Figure 4.5: Elements indices in defining geometry of caisson type breakwater (IH-

2VOF Course Lecture Notes, 2012) ................................................................. 70

Figure 4.6: Model geometry for caisson type breakwater ....................................... 70

Figure 4.7: Generated mesh with the subzones for caisson breakwater ................. 72

Figure 4.8: Quaility check for the generated mesh ................................................. 73

Figure 4.9: IH-2VOF GUI Preprocessing Main Menu ........................................... 74

Figure 4.10: Generation of new wave series ........................................................... 75

Figure 4.11: Setting wave gauge position ............................................................... 76

Figure 5.1: Stages of damage of caisson type breakwater for wave number 9 a)

start of damage b) major damage c) total failure ............................................. 81

Figure 5.2: Stages of damage of rubble mound breakwater for wave number 9

a) start of damage b) major damage c) total failure ......................................... 81

Figure 5.3: Wave Number 9 impact on the vertical wall of caisson type breakwater

.......................................................................................................................... 82

Figure 5.4: Wave Number 9 impact on the crown walls of rubble mound breakwater

.......................................................................................................................... 83

Figure 5.5: Breakwater profiles for caisson type breakwater, Wave number 9 Set 1

(wave approach is from left) ............................................................................ 84

xix


.......................................................................................................................... 85

Figure 5.7: Damage of caisson type breakwater (Top: Set 1, Bottom: Set 2) ........ 86

Figure 5.8: Breakwater profiles for rubble mound breakwater, Wave number 9 Set 1

.......................................................................................................................... 87


.......................................................................................................................... 88

Figure 5.10: Damage of rubble mound breakwater after wave number 9, Set 1 .... 89

Figure 5.11: Overflowing wave acting on the vertical walls of caisson type

breakwater ........................................................................................................ 90

Figure 5.12: Overflowing wave acting on the vertical walls of rubble mound

breakwater ........................................................................................................ 90

Figure 5.13: Breakwater profiles for caisson type breakwater, Wave number 10 Set

2 ........................................................................................................................ 91

Figure 5.14: Damage of caisson type breakwater after wave number 10 Set 2 ...... 92

Figure 5.15: Breakwater profiles for rubble mound breakwater, Wave number 10 Set

2 ........................................................................................................................ 93

Figure 5.16: Damage of rubble mound breakwater after wave number 10, Set 2 .. 93

Figure 5.17: Overturning of vertical walls under wave action ............................... 95

Figure 5.18: Sliding of the crown walls of the rubble mound breakwater under wave

action ................................................................................................................ 96

Figure 5.19: Water surface profiles for wave number 9, WG8............................. 104

Figure 5.20: Water surface profiles for wave number 9, WG2............................. 104

Figure 5.21: Water surface profiles for wave number 10, WG8........................... 105

Figure 5.22: Water surface profiles for wave number 10, WG2........................... 105

Figure 5.23: Wave loading identification, PROVERBS parameter map (Kortenhaus

et al., 1999) ..................................................................................................... 106

Figure 5.24: Example graph of measured pressure time series for wave number 9107

Figure 5.25: Definition sketch of an idealized impact wave pressure time history107


........................................................................................................................ 108

xx

Figure 5.27: Local maximum dynamic pressures (point data) and instantaneous

pressure distributions for wave number 9 ...................................................... 109

Figure 5.28: Local maximum quasi-static pressures (point data) and instantaneous


Figure 5.29: Local maximum uplift pressures (point data) and instantaneous uplift



pressure distributions for wave number 10 .................................................... 112


pressure distributions for wave number 10 .................................................... 113

Figure 8.1: Breakwater profile of caisson type breakwater – Line 1 .................... 130


Figure 8.3: Breakwater profile of rubble mound breakwater – Line 1 ................. 131


Figure 8.5: View of caisson type breakwater after Wave Number 12 .................. 132

Figure 8.6: View of rubble mound breakwater after Wave Number 12 ............... 132




Figure 8.10: Breakwater profile of rubble mound breakwater – Line 2 ............... 134

Figure 8.11: View of caisson type breakwater after Wave Number 15, Set-2 ...... 134

Figure 8.12: View of rubble mound breakwater after Wave Number 15, Set-2 ... 134

Figure 8.13: Breakwater profile of caisson type breakwater – Line 1 .................. 135




Figure 8.17: View of caisson type breakwater after Wave Number 17, Set-1 ...... 137





xxi


Figure 8.23: View of caisson type breakwater after Wave Number 17, Set-2 ..... 139














1

CHAPTER 1

1 INTRODUCTION

Tsunami is a typical long wave in the ocean, generated by seafloor or water surface

disturbances over a sufficiently large area (Wang, 2009). It has been observed and

recorded since ancient times, especially in Japan and the Mediterranean areas.

Tsunamis may attain large amplitudes in closed basins or shallow regions (Yalciner et

al. 2001; 2002; 2004; and 2005). The interest in tsunami research has increased in

recent years after the terrible consequences of the 2004 Indian Ocean tsunami and of

the 11th March 2011 tsunami in Japan.

2004 Indian Ocean tsunami was one of the deadliest and largest natural hazard all over

the world. ‘Tsunami risk reduction’ issue has come into prominence after this disaster

(Lovholt et al., 2014). Since 2004, six megathrust tsunamis happened in Indonesia,

Samoa, Chile and Japan in 2006, 2007, 2009, 2010 and 2011 (Lovholt et al., 2014).

An undersea earthquake with magnitude 9.0 occurred in Pacific coast of Tohoku, Japan

in 2011. The earthquake is named as "Great East Japan Earthquake" by being the most

powerful earthquake ever recorded in Japan and fifth most powerful earthquake in the

world since 1900 (RAPSODI Project Deliverable, D1). Transmission of the energy

caused giant tsunami waves that reached 40 meters in Miyako. The tsunami caused

nuclear explosions primarily in Fukushima Daiichi Nuclear Power Plant Complex

(RAPSODI Project Deliverable, D1, 2015). Overall world, tsunamis mostly occur in

Pacific Ocean. Despite tsunamis in oceans and open seas, there are great number of

tsunami records in the Mediterranean and Aegean Sea due to undersea earthquakes,

landslides and volcanic eruptions in this region as well. (RAPSODI Project

Deliverable, D1, 2015).

Tsunami history throughout the world indicates that the dense population, coastal

utilization and marine protected areas are vulnerable under tsunami motion. Ports,

2

harbors and marinas are some of the vulnerable places under tsunamis as well as

coastal ecosystems and aquaculture areas. However, all coastal facilities are critical

and must be resilient against natural hazards in order to facilitate recovery operations.

Therefore, it is important to develop a method for the design of coastal structures to

improve resilience against tsunami impacts.

One project focusing on this problem is Risk Assessment and design of Prevention

Structures fOr enhanced tsunami DIsaster resilience (RAPSODI) project. The

RAPSODI consortium consists of three European (NGI, METU, TUBS), and one

Japanese partner (PARI). The main research topics that the project deals with are

vulnerability assessment, the analysis of loads on structures and also numerical

tsunami modelling. The research has been done in three stages as the evaluation of

existing knowledge and comparisons of mitigation strategies (Stage 1), numerical and

experimental studies (Stage 2) and methodology for tsunami vulnerability assessment

and risk management (Stage 3). The first stage includes review and evaluation of tools

available for the numerical modelling, and the assessment of impact loads on

structures, failure modes, and vulnerability. A thorough investigation of the failure

mechanisms of coastal protection structures exposed to tsunamis is carried out in this

thesis within the scope of RAPSODI Project. A catalogue of failure modes of different

types of coastal structures based on observations of the 2011 Tohoku tsunami and

existing knowledge (RAPSODI Project Deliverable, D1, 2015) is prepared and

presented in Chapter 2. On the basis of this failure modes matrix, it is found out that

the existing research gaps and potential research areas are in the field of tsunami-

induced load and damage to coastal structures. Also, most of the missing information

in the literature is about performance of rubble mound breakwaters under tsunami

loads since these types of breakwaters are not common especially in Japan and are not

commonly observed in recent tsunami events. Therefore, laboratory experiments

within the RAPSODI Project were carried out in Technical University of

Braunschweig (TU-BS) hydraulic laboratory in collaboration with project partner

Middle East Technical University (METU) to investigate the damage and failure

mechanisms of rubble mound breakwaters with different configurations under solitary

3

waves and tsunami bores. In addition, it is found out that many coastal structures are

designed without considering loads of tsunami-like waves, long waves or extreme

waves although these structures can be exposed to these waves. Therefore, laboratory

experiments to understand the behavior of different types of coastal structures under

extreme waves are performed as a part of this thesis work to complement the

experimental study of RAPSODI Project. The hydraulic conditions in these

experiments are determined as extreme waves which defines the limitation of the

experimental work of this thesis as mentioned in Chapter 3.

The purpose of this thesis is to understand the damage and failure phenomenon of two

main types of coastal structures; rubble mound and caisson type breakwaters, under

extreme waves. Extreme waves are relatively large surface waves which are rare,

unpredictable, may occur without warning, and can impact with a huge force like

tsunami waves. The generation mechanism of extreme waves or the impact duration

to the structures are different from tsunami waves but large waves can cause flooding

and damage to coastal infrastructure and severe coastal disasters may occur due to

these extreme events. Therefore, it is necessary to consider the extreme wave

conditions in the design of coastal structures as in the case of tsunamis. These waves

are rare events but they occur in seas and oceans and a real danger to ships, platforms

and coastal structures as well as causing accidents resulting in human loss. Thus, 6

different extreme wave conditions are generated in laboratory and rubble mound and

caisson type breakwaters are examined under these wave actions in this thesis work.

Also, pressure measurements are carried out along the surface and bottom of the

concrete blocks of caisson type breakwater to investigate the forces acting on the

structure which cause the damage and failure of the structure.

Physical modelling is one of the classical methods for research in the field of coastal

engineering having some advantages. However, it has also some limitations and

deficiencies so does the other common method in coastal engineering, numerical

modelling. Therefore, coupling one method with the other one is an effective way to

minimize the limitations and deficiencies of each method. A numerical assessment is

4

also included in this study to make a comparison between the pressure measurements

and the numerical results in order to analyse the limitations of simulating the

experiments in the numerical environment. Many experimental tests are performed

with the aim of understanding damage behavior of breakwaters under extreme waves

and a caisson type breakwater is modeled by IH2VOF and the results are compared.

IH-2VOF is a numerical model which solves the two-dimensional (2D) wave flow

using the Reynolds Averaged Navier Stokes (RANS) equations at the fluid region and

Volume Averaged Reynolds Averaged Navier Stokes (VARANS) inside the porous

media (Hsu et al., 2002). The model is mainly used for the flow-structure interaction

especially in case of coastal structures like breakwaters and sea dikes. Detailed

information about the model is provided in Chapter 4.

In Chapter 2, a literature survey is presented including the basic research related to the

thesis topic to provide some background information. In Chapter 3, general description

of the physical model experiments is given including layout and properties of the wave

flume, the experimental setup, breakwater cross-sections, measuring equipment and

wave characteristics. Chapter 4 provides the description of the numerical model,

IH2VOF, theoretical background of the model, the convergence checks, model

geometry and the mesh generation. Chapter 5 includes the results of the experiments,

pressure measurements and numerical model analysis. The comparison experimental

and numerical model results is also discussed. Finally, in Chapter 6, conclusions and

future recommendations are presented.

5

CHAPTER 2

2 LITERATURE REVIEW

Tsunami – structure interaction and long wave – structure interaction research has

gained significant interest in recent years. Effects of these waves on coastal protection

structures, failure mechanisms of these structures or their damage behavior are

important subjects to be well understood in order to have coastal resilience. Many

studies can be reached through literature on these topics.

2.1 Failure Mechanisms

Field surveys carried out after the catastrophic events, 2011 The Great East Japan

Earthquake and Tsunami and 2004 Indian Ocean tsunami, form a great basis for

examining the failure mechanisms of coastal structures. A thorough literature survey

is performed through these survey reports from different authors. A failure modes

matrix is prepared using the reported failure mechanisms of coastal protection

structures in the above summarized reports to highlight the knowledge gaps so that

future studies can be planned.

For this review, overflow is defined as functional failure and it is observed for

seawalls and revetments, sea dikes and breakwaters in several places (Figure 2.1a).

One example is the coastal area in Otsuchi village which was completely destroyed as

the tsunami destroyed the breakwater and propagated inland along the Otsuchi and

Kotsuchi Rivers. Hydraulic control structures and seawalls were completely

overtopped during the inundation. (Mori et al., 2013)

6

Sliding was reported for revetments by Nagasawa and Tanaka (2012) who estimated

that the tsunami external force acted on the revetments seaward and the revetment fell

down seaward and destroyed.

Scour damage was seen on concrete seawalls. The example is two large scour profiles

observed at the leeward slope of the curved 2.5 m high concrete seawall in the east

side of Ishinomaki port extending about 60.0 m in length along the seawall. The

massive concrete platform placed at the toe of the leeward slope disappeared due to

the tsunami, leading to two scour holes being created according to Jayaratne et al.,

(2013). Scour was also reported by Yeh et al. (2012) for solid-concrete seawalls. They

conducted surveys along the Sanriku coast after 2011 event and stated that remarkable

destruction of upright solid-concrete type seawalls was closely related with the

tsunami induced scour. Also, the fast flow velocities with intense turbulence resulted

in severe undermining damage in the rear face of the mound-type seawall in

Kanahama, as well as formation of a large scour hole behind according to Yeh et al.,

(2012). Jayaratne et al. (2013) noticed severe damage to the leeward face and toe of

the sea dike at Soma city. Diverse failure patterns were observed from the north to the

south side, resulting in partial to total failure of the leeward face due to scour. Seaward

flow over the coastal dike may cause scouring at the seaward toe of the dike as also

pointed out in previous studies (e.g., Noguchi et al. 1997). Seaward flow during

tsunami drawdown caused scouring at the seaward toe of the coastal dike and

revetment. Scouring at the landward toe affected the stability of the seaward armor,

resulting in floating away of seaward armor and breaching of the dike. (Kato et al.,

2012) A simple sketch of creation of scour-hole causing complete failure of structure

toe and crest is provided in Figure 2.1b, 2.1c and 2.1d.

7

Figure 2.1: Sketch of stages of sea dike failure a) Overflowing water, b) Creation of

scour-hole at leeward toe, c) Failure of leeward slope, d) Complete failure of crest,

leeward slope and toe (Jayaratne et al., 2013)

Overturning was observed on concrete seawalls in some cases (Figure 2.2). The

concrete seawalls were overturned by return flow rather than by the incoming tsunami

as reported by Earthquake Engineering Research Institute, EERI (2011). Also,

overturning of a seawall which was observed on the Ryoishi Coast, Iwate Prefecture

induced by the Great East Japan Earthquake Tsunami may occur if the overturning

moment induced by the wave force on the seawall during tsunami runup or drawdown

is larger than the resistance moment due to the weight of the seawall reported by Kato

et al. (2012). Many tsunami gates designed to reduce flooding along rivers were also

overturned by the Great East Japan Earthquake and tsunami. (Sagara and Saito, 2013)

8

Figure 2.2: Process of seawall overturning (Kato et al., 2012)

Soil instability is another failure mechanism observed on seawalls and reported by

Yeh et al., (2012). Remarkable destruction of upright solid-concrete type seawalls was

closely related with also soil instability according to them. The rapid decrease in

inundation depth during the return-flow phase caused soil fluidization down to a

substantial depth and this mechanism explains severely undermined foundations

observed in the area along the Sanriku Coast of low flow velocities. They found that

soil instability played a major role in the failures. (Yeh et al., 2012)

In case of breakwaters; scouring, sliding, soil failure, seaward and leeward slope

failures and overturning are the failure mechanisms observed in field surveys.

Scouring, sliding and soil failure due to tsunami overflow was observed in Kamaishi

and Hachinohe Breakwaters. Both breakwaters were modelled in laboratory and

several experiments were performed by Arikawa and Shimosako (2013) to determine

factor of safety regarding sliding and overturning considering the scour at the leeward

(at the foundation level) as well as bearing capacity failure (soil failure). Jayaratne et

al. (2013) states that large concrete armour units had been placed in front of the

seaward slope of the breakwater at Ishinomaki Port. It was found that the primary

armour units on the seaward slope were displaced and scattered in front of the

9

breakwater, and some units were buried under tsunami deposits, though there was no

indication of damage to the front slope. Esteban et al., 2013 states that the exact failure

mechanism for each of the breakwater types is still unclear, and whether armour units

were displaced by the incoming or the outgoing wave could not be easily established

for any of the field failures recorded. Therefore, they carried out some preliminary

laboratory experiments which appear to indicate that although the incoming tsunami

wave can cause some movement to the caisson, the major failure mode of the armour

could occur as a result of the outgoing wave (Figure 2.3 and Figure 2.4). Also, in

Kamaishi City, the tsunami on March 11th overturned the north section (990 m in

length) of the newly completed offshore breakwater and although the south section

(670 m in length) survived mostly intact, it was left inclined as given in Fraser et al.

(2013) but explained in Yagyu (2011).

Figure 2.3: Overtopping of a composite breakwater by incoming tsunami wave (note

no armour damage) (Esteban et al., 2013)

Figure 2.4: Overtopping of a composite breakwater by outgoing tsunami wave (note

the heavy damage) (Esteban et al., 2013)

10

A failure modes matrix is prepared using the reported failure mechanisms of coastal

protection structures in the above summarized reports to highlight the knowledge gaps

so that future studies can be planned. The matrix is given in Table 2.1. In the matrix,

a tick marker represents the match of the structure with the observed failure

mechanism reported in the field surveys. The blanks mean that either a failure type is

not observed for a certain type of structure or there are no reports acquired or it can

not be decided which failure mechanism refer to the specified structure.

11

Table 2.1: Failure Mode Matrix

12

2.2 Forces and Pressures on Structures

As can be seen from Table 2.1 and examples of failures, breakwaters which are one of

the most important elements of coastal protection and exposed elements to tsunami

wave action should be a research topic necessary to observe their damage mechanisms

and collapse phenomenon experimentally, numerically and by field observations. Also

the acting forces on the structure under the wave attack is another point to consider

and investigate since these forces should be classified and identified for new design

considerations and to improve new methods for more resilient structures.

A comprehensive review of tsunami forces is presented by Nistor et al. (2009). He

states that three parameters are essential for defining the magnitude and application of

these forces: (1) inundation depth, (2) flow velocity, and (3) flow direction. The

parameters mainly depend on: (a) tsunami wave height and wave period; (b) coastal

topography; and (c) roughness of the coastal inland. Forces associated with tsunami

bores consist of: (1) hydrostatic force, (2) hydrodynamic (drag) force, (3) buoyant

force, (4) surge force and (5) impact of debris.

The hydrostatic force is generated by still or slow-moving water acting perpendicular

onto planar surfaces. The hydrostatic force per unit width, FHS, can be calculated using

the equation given below.

𝐹𝐻𝑆 = 1

2𝜌𝑔 (𝑑𝑠 +

𝑢𝑝2

2𝑔)2 [2.1]

Where ρ is the seawater density, g is the gravitational acceleration, ds is the inundation

depth and up is the normal component of flow velocity. Equation 2.1 is proposed by

the City and County of Honolulu Building Code (CCH, 2000) and accounts for the

velocity head. The point of application of the resultant hydrostatic force is located at

one third from the base of the triangular hydrostatic pressure distribution.

13

The buoyant force is the vertical force acting through the center of mass of a

submerged body. Its magnitude is equal to the weight of the volume of water displaced

by the submerged body as given in Equation 2.2. Buoyant forces can generate

significant damage to structural elements, and are calculated as follows:

𝐹𝐵 = 𝜌𝑔𝑉 [2.2]

where, V is the volume of water displaced by submerged structure (Nistor et al., 2009).

As the tsunami bore moves inland with moderate to high velocity, structures are

subjected to hydrodynamic forces caused by drag. Currently, there are differences

in estimating the magnitude of the hydrodynamic force. The general expression used

by existing codes is given below (Equation 2.3).

𝐹𝐷 = 𝜌 𝐶𝐷 𝐴 𝑢2

2 [2.3]

Where, FD is the drag force acting in the direction of flow and CD is the drag coefficient

that depends on the shape of the surface on which drag forces are applied (Nistor et

al., 2009). Drag coefficient values of 1.0 and 1.2 are recommended for circular piles

by CCH (2000) and FEMA 55 (2003) design codes, respectively. For the case of

rectangular piles, the drag coefficient recommended by the same two codes is 2.0.

Parameter A is the projected area of the body normal to the direction of flow. The flow

is assumed to be uniform, and therefore, the resultant force will act at the centroid of

the projected area A. The term u in Equation 2.3 is the tsunami bore velocity. The

hydrodynamic force is directly proportional to the square of the tsunami bore velocity

as indicated in Equation 2.3. Therefore, the estimation of the bore velocity remains to

be one of the critical elements on which there is significant disagreement in literature

(Nistor et al., 2009). Tsunami-bore velocity and direction can vary significantly during

a major tsunami inundation. The general form of the bore velocity is shown below

(Equation 2.4).

𝑢 = 𝐶 √𝑔𝑑𝑠 [2.4]

Where, C is a constant and ds is the inundation depth. Various formulations were

proposed by FEMA 55 (2003) based on Dames and Moore (1980), CCH (2000),

Kirkoz (1983), Murty (1997), Bryant (2001), and Camfield (1980) for estimating the

14

velocity of a tsunami bore in terms of inundation depth. The velocity inundation depth

relationships proposed are plotted in Figure 2.5.

Figure 2.5: Comparison of various tsunami-bore velocities as a function of

inundation depth (Nouri et al., 2007)

According to Nistor et al. (2009), the surge force is generated by the impact of the

forward-moving water of a tsunami bore on a structure. Due to lack of detailed

experimental research specifically applicable to tsunami bores running up the

shoreline, the calculation of the surge force exerted on a structure has considerable

uncertainty. Based on research conducted by Dames and Moore (1980), CCH (2000)

recommends Equation 2.5 for the surge force FS on walls with heights equal to or

greater than three times the surge height (3h).

𝐹𝑆 = 4.5𝜌𝑔ℎ2 [2.5]

Where, FS is the surge force per unit width of wall, and h is the surge height. The point

of application of the resultant surge force is located at a distance h above the base of

the wall.

15

A tsunami bore traveling towards the land carries debris such as floating automobiles,

floating pieces of buildings, drift wood, boats and ships. The impact of floating debris

can result in significant forces on a structure, leading to structural damage or collapse

(Saatcioglu et al. 2006a, 2006b). Both FEMA 55 (2003) and CCH (2000) codes

account for debris impact forces, using the same approach, and recommend using

Equation 2.6 for estimation of debris impact force.

𝐹𝑖 = 𝑚𝑏𝑑𝑢𝑏

𝑑𝑡= 𝑚

𝑢𝑖

∆𝑡 [2.6]

Where Fi is the impact force, mb is the mass of the body impacting the structure, ub is

the velocity of the impacting body (assumed equal to the flow velocity), ui is approach

velocity of the impacting body (assumed equal to the flow velocity) and Δt is the

impact duration taken equal to the time between the initial contact of the floating body

with the building and the instant of maximum impact force (Nistor et al., 2009).

According to FEMA 55 (2003), the impact force (a single concentrated load) acts

horizontally at the flow surface or at any point below it. Its magnitude is equal to the

force generated by 455 kg (1,000-pound) of debris traveling with the bore and acting

on a 0.092m2 (1 ft2) surface of the structural element. The impact force is to be applied

to the structural element at its most critical location, as determined by the structural

designer.

A sketch which conceptually shows some of the terms used in the force equations is

given in Figure 2.6.

Figure 2.6: Sketch showing some conceptual terms like tsunami height, inundation

depth and run-up height (Japan Weather Association materials,

http://www.japanecho.net/311-data/1205/ )

http://www.japanecho.net/311-data/1205/

16

In this study, it is aimed to understand the force-structure interaction through the

pressures acting on the structure since it is difficult to isolate separately these forces

mentioned above and to measure each parameter in the equations. The main focus of

this study is damage and failure mechanisms of the structures. Therefore, the basic

pressure formulas that can be used to obtain the forces on the structures are reviewed.

One of the most commonly used pressure formulas in the literature is given by Goda

(1974). He proposed a pressure formula for composite breakwaters which can be

applied for the whole ranges of wave action from nonbreaking to postbreaking waves.

Goda (1974) gives the distribution of design wave pressure as given in Figure 2.7.

Figure 2.7: Distribution of design wave pressure (Goda, 1974)

The intensities of wave pressures, p1, p2, and p3, are calculated with the following

formula:

𝑝1 = 𝑤𝑜𝐻𝐷(∝1+∝2 cos 2 𝛽) [2.7]

𝑝2 = 𝑝1

cosh(2𝜋ℎ𝐿⁄ ) [2.8]

𝑝3 = ∝3 𝑝1 [2.9]

Where

17

∝1= 0.6 + 1

2 (

4ℎ𝐿⁄

sinh4𝜋ℎ𝐿⁄) 2 [2.10]

∝2= min {ℎ𝑏−𝑑

3ℎ𝑏(𝐻𝐷

𝑑)2

,2𝑑

𝐻𝐷} [2.11]

∝3= 1 − ℎ′

ℎ [1 −

1

cosh2𝜋ℎ𝐿⁄] [2.12]

HD : design wave height (given in Equation 2.14)

wO : specific weight of sea water

L : wavelength of design wave

min{a,b}: smaller one of a or b

β : angle of wave approach

hb : water depth at which the breaker height is to be evaluated (given in Equation 2.16)

For the calculation of uplift pressure acting on the bottom of upright section, the

triangular distribution is assumed irrespective of wave overtopping (Goda, 1974). The

intensity of toe uplift is given by Equation 2.13.

𝑝𝑢 = ∝1∝3 𝑤𝑜𝐻𝐷 [2.13]

𝐻𝐷 = 𝐻𝑚𝑎𝑥 = min {1.8 𝐻13⁄, 𝐻𝑏} [2.14]

𝐻𝑏 = 0.17 𝐿0 {1 − 𝑒𝑥𝑝 [−1.5ℎ𝑏

𝐿0(1 + 15𝑡𝑎𝑛

43⁄ 𝜃)]} [2.15]

ℎ𝑏 = ℎ + 5𝐻13⁄𝑡𝑎𝑛𝜃 [2.16]

Where

L0 : deepwater wavelength calculated by 𝑔𝑇2/2𝜋

tanθ: mean gradient of sea bottom

Goda (1974) calibrated the other existing pressure formula of Hiroi (1920), Sainflou

(as cited in Goda, 1974), and Minikin (1950) with the cases of 21 slidings and 13

nonslidings of the upright sections of prototype breakwaters. He states that the

calibration shows that the new formulas are the most accurate ones. The Shore

18

Protection Manual (SPM) (1984) however states that Sainflou's method may

overestimate wave forces for short non-breaking waves. For long waves of low

steepness, the SPM recommends Sainflou's method (Allsop et al, 1996).

Allsop et al. (1996) also presents wave impacts on simple and composite vertical walls.

They conducted 2D hydraulic model tests to identify the wave pressures on these walls.

They aimed to develop a method to estimate wave forces under wave attack.

They give the vertical distribution of pressures on simple vertical walls as in Figure

2.8. They state that, for pulsating conditions Goda’s trapezoidal distribution of

pressure assumption is reasonably well-supported, but for impact conditions,

agreement is much less good.

Figure 2.8: Vertical distribution of pressures for simple walls (Allsop et al., 1996)

2.3 Numerical Modelling

Numerical modelling of hydraulic processes of wave-structure interaction is also an

essential part of research methods in coastal engineering due to the limitations of

physical modelling such as scale effects, long duration of experiments, laboratory

limitations and costly experiments. Although the numerical models need validation by

experiments or field measurements, they may provide at least successful preliminary

19

results in a shorter time period. There are number of models developed to investigate

the wave-structure interaction by means of solving wave reflection, wave

transmission, wave overtopping, wave diffraction and wave breaking.

IH2VOF is a numerical model that was developed by IH Cantabria. IH2VOF solves

the 2D Reynolds Averaged Navier–Stokes (RANS) equations at the clear fluid region

and the Volume-Averaged Reynolds Averaged Navier–Stokes (VARANS) equations

inside the porous media, based on the decomposition of the instantaneous velocity and

pressure fields into mean and turbulent components, and the κ-ε equations for the

turbulent kinetic energy κ, and its dissipation rate ε (IH2VOF website,

http://ih2vof.ihcantabria.com/). This permits the simulation of any kind of coastal

structure (e.g. rubble mound, vertical or mixed breakwaters). The free surface

movement is tracked by the volume of fluid (VOF) method for one phase only, water

and void (IH2VOF website, http://ih2vof.ihcantabria.com/). For the models based on

RANS equations, the most complete turbulence model is the Reynolds stress closure

model, which attempts to close the Reynolds stresses transport equation directly

(Launder and Spalding, 1974). The k-ε model is the most commonly used alternative

(Launder and Spalding, 1974; Rodi, 1980).

Liu et al. (1999) introduced a RANS model, namely COBRAS (Cornell Breaking

Waves and Structures) to simulate the overtopping phenomena of breaking waves on

a porous structure. The model solves the Reynolds averaged Navier–Stokes equations

to calculate the flow in the fluid region and the corresponding turbulence field is

modelled by an improved k–ɛ model. The flow in porous media was described by the

spatially averaged Navier–Stokes equations (Lara, 2005).

Hsu et al. (2002) introduced the Volume-Averaged/Reynolds Averaged Navier–Stokes

(VARANS) equations to improve the COBRAS model in order to define the surface

wave interaction with coastal structures. The volume-averaged Reynolds stress is

modelled by following the nonlinear eddy viscosity assumption in the VARANS

equations, and the volume averaged turbulent kinetic energy and its dissipation rate

http://ih2vof.ihcantabria.com/

http://ih2vof.ihcantabria.com/

20

are obtained by applying the volume-average of the standard k–ɛ equations. This

model has the advantage of introducing the small-scale turbulence effects as part of

the porous flow (Lara, 2005). Validation of the model is performed using the

experimental set in Liu et al. (1999). However, most of the validation focuses on

regular wave field in this validation study and it is also for a very small domain and

limited simulation time.

Lara (2005) presented an improved version of COBRAS, COBRASUC, developed by

University of Cantabria. The model is used to examine the interaction of random waves

with rubble mound breakwaters focusing on the overtopping phenomena. It is used to

simulate a large numerical wave flume including random waves and long simulation

times. The author states that these may help to reduce some uncertainties in using semi-

empirical formulae and give some statistical information on the overtopping process

(Lara, 2005).

21

CHAPTER 3

3 PHYSICAL MODEL EXPERIMENTS

3.1 General Description of Physical Model Experiments

Physical modelling is a process in which mainly the real-life problems are recreated

by a scale factor in laboratory conditions. Being one of the main techniques in coastal

engineering, physical modelling is used for observing the physical situation of the

hydraulic processes visually. Engineers may develop more creative and innovative

solutions with the help of these observations. It is not always possible to create the

exact environmental conditions of the natural system but an optimization can be made

to obtain reasonable results with reasonable simplifications in model experiments.

Most often, it is a cost and time efficient way compared to field observations and data

gathering in the field. Physical modelling has also an advantage of including the

turbulence effect which always exist in hydraulics.

On the other hand, there are also some disadvantages of laboratory experiments. Scale

effect is one of the major problems in reflection of the stresses and forces in the nature.

The scale effects and the deficiencies resulted from the inaccurately scaled parameters

like fluid density and viscosity may be minimized in large scale experiments but they

may be expensive and time consuming. Additionally, the ability of resources in the

laboratory to generate the necessary conditions could be limited. Thus, not every

condition pertinent to the problem can be observed.

As mentioned in Chapter 1, understanding the damage and failure behavior of coastal

structures is important to increase the coastal resilience. In Chapter 2, it is shown that

most of the missing information in the literature is about the performance of rubble

22

mound breakwaters under tsunami attack since rubble mound structures are not

common in Japan where the recent tsunami events provided much of the available

observations. Furthermore, many coastal structures are designed without considering

loads of tsunami-like waves, long waves or extreme waves although they are

constructed in areas prone to encounter these waves. Therefore, it is very important to

observe the damage behavior and failure mechanisms of rubble mound breakwaters

under different extreme wave conditions. In addition, comparison of the performance

of rubble mound and caisson type structures (which are more commonly observed

under tsunami attack) can provide additional insight to different failure mechanisms.

Observing two types of breakwaters in laboratory environment with accompanying

pressure measurements is the physical modelling part of this thesis. This chapter

presents the wave flume in which the tests are performed, the experimental setup, the

breakwater cross-sections, the measuring technique in the experiments and the

characteristics of the applied waves. The general process followed in this part of the

study is given in Figure 3.1.

23

Figure 3.1: Flowchart of the model experiments

3.2 Wave Flume

The experiments were performed in the wave flume constructed in one of the basins

(smaller basin) at METU Coastal and Ocean Engineering Laboratory. The basin has a

length of 26.8 meter and a width of 6.1 meter (Figure 3.2). The dimensions of the wave

flume which is located in the inner channel of this basin are 18m in length, 1.5m in

Identifying the aim of the study

Determining the procedure

- Physical Modelling

Model Setup

- Determining the model scale

- Design of the breakwaters

Wave Generation

- Determining the wave conditions

Data Collection

- Wave Gauge Measurements

- Profile Measurements

- Pressure Measurements

- Photo Collection and Video Recording

Data Analysis

24

width and 1.0 m in depth. The aim of constructing an inner flume is to reduce reflection

from the border walls of the basin which could distort the wave profile. This wave

flume has a horizontal bottom over the entire length.

Figure 3.2: The smaller basin and the wave flume

A piston type wave maker is placed at one end of the smaller basin which is capable

of generating regular and irregular waves and was used to generate the intended wave

conditions (Figure 3.3a). On the opposite end of the wave flume, there is a slope of

wave absorbers made of plastic wire scrubbers aiming to prevent reflection of the

Inner wave flume

Smaller Basin

25

waves from the end flume walls (Figure 3.3b). The layout of the wave basin is given

in Figure 3.4.

Figure 3.3: a) Piston type wave maker b) Wave absorbers

Figure 3.4: General layout of the basin (Top: top view, Bottom: Side view)

Dimensions are in cm and figure is not to scale.

3.3 Model Scale

Froude similitude law is applied in most of the model studies in the field of coastal

engineering because the effect of surface tension and elastic compression is rather

26

small and therefore can be neglected (Hughes, 1993). Gravity or viscous forces then

become the necessary parameters to define which take modellers to apply Froude

Theorem or Reynolds Theorem. One of these theorems together with the geometric

similarity would provide the appropriate conditions for the hydrodynamic similitude.

Frostick (2011) states that the main forces are gravity, friction and surface tension for

wave models. Therefore, it is suggested that Froude (Fr), Reynolds (Re) and Weber

(We) numbers must be the same in model and prototype for true dynamic similarity.

However, it is not possible to satisfy this condition. If Froude law is used in the model

(since the effects of gravity and inertia are dominant in the wave field) and the model

Reynolds number is in the same range as the prototype, then the Reynolds number

need not be exactly the same. Surface tension is generally negligible in prototype

waves. Therefore, if the model is not too small (wavelengths must be much greater

than 2 cm, wave periods >0.35 s, water depths >2 cm, Le Méhauté, 1976), Weber

similitude can be neglected (Frostick, 2011). In modelling flow through the structure

and forces on structures, if the Reynolds number is large enough and fully turbulent

flow conditions in the armour-/filter layers are maintained (ReD > 30000, e.g. Dai and

Kamel, 1969) the forces can be scaled by Froude. Viscous effects can be limited in the

model if diameters larger than 3–5 mm (in model scale) are used. The following model

boundary values can be derived regarding these conditions so that Froude similitude

law can be applied alone (Le Mehaute, 1976 and Hughes, 1993).

water depth: >5 cm (water depth=40cm in the experiments)

wave height >2–3 cm, design wave height: >5 cm (min wave height=9cm,

design wave height=10cm in the experiments)

wave period realistic wave steepness (steepness range = 0.018 – 0.036 in the

experiments)

rock diameter >3–5 mm (core layer rock diameter=12-21mm in the

experiments)

rock armour >25 mm (armor layer rock diameter=28-30mm in the

experiments)

27

For breaking waves, the Weber and Cauchy numbers may be important since they

determine the air intake, water turbulence and water compressibility. However, the

waves applied in the experiments are not breaking waves.

Since all these criteria are met in this model study, Froude similitude law was applied

the physical model experiments. Froude criterion is a parameter which expresses the

relative effect of inertial and gravity forces in a hydraulic flow (Hughes, 1993). It is

commonly expressed in the square of the number and given by Equation 3.1:

𝐹𝑟2 =

𝑢2

𝑔𝑑 [3.1]

Where u is the velocity of water particle, g is gravitational acceleration and d is the

water depth.

According to the similitude law, the Froude numbers in prototype ((Fr)p) and the model

((Fr)m must be equal to each other which implies Equation 3.2.

(𝐹𝑟) 𝑝 = (𝐹𝑟) 𝑚 [3.2]

The scale factor, λX, is the ratio of any parameter in the model to the parameter in the

prototype. To satisfy the geometric similitude, the length scale factor, λL, is the ratio

of dimensions (length parameters) of the model (Lm) to the dimensions of the prototype

(Lp) as given in Equation 3.3.

𝜆𝐿 =𝐿𝑚

𝐿𝑝 [3.3]

According to the square root of Equation 3.1., the Froude criterion is given by Equation

3.4.

𝜆𝑢 = √𝜆𝑔𝜆𝐿 [3.4]

28

Since velocity (u) is the ratio of length to time, the scale ratio for velocity is equal to

Equation 3.5.

𝜆𝑢 =𝜆𝐿

𝜆𝑇 [3.5]

The time scale then can be obtained from equations 3.4 and 3.5 as Equation 3.6 since

the gravitational scale is accepted as unity.

𝜆𝑇 = √𝜆𝐿 [3.6]

For the weight scaling of the armour units of the breakwaters, the stability numbers in

both the prototype and the model should be equal to each other according to CERC

(1984). From the equalization of the stability numbers, the weight scale (λw) can be

derived as Equation 3.7.

𝜆𝑊 = (𝜆𝐿3)

(𝛾𝑟) 𝑚

(𝛾𝑟) 𝑝[

(𝛾𝑟) 𝑝(𝛾𝑤) 𝑝

⁄ −1

(𝛾𝑟) 𝑚(𝛾𝑤) 𝑚

⁄ −1]

3

[3.7]

In Equation 3.7, (γr) m and (γr) p are unit weights of armour units that are used in model

and prototype, respectively, which were taken as 2.6 t/m3 and 2.7 t/m3. Also, (γw) m

and (γw) m are unit weight of water that is used in model and unit weight of sea water

in prototype. In the experiments, unit weight of water was taken as 1.0 t/m3 and the

unit weight of sea water (prototype) was taken as 1.025 t/m3.

The pressure scale, 𝜆𝑝,is obtained by Equation 3.8 which is used for the scaling of the

pressure values.

𝜆𝑝 =(𝜌𝑤)𝑝

(𝜌𝑤)𝑚𝜆𝐿 [3.8]

The scale factors to reproduce the basic physical parameters are given in Table 3.1.

29

Table 3.1: Scaling factors using the similitude law of Froude

Parameter Scale factor

λL

Conversion to model

scale

Model

Scale Unit

Length λL 1/λL 1/50 [m]

Volume (λL)3 1/(λL)3 1/125000 [m3]

Time √𝜆𝐿 1

√𝜆𝐿⁄ 1/7.07

[s]

Weight λw 1 / λw 1/163003.3 [kg]

Pressure λp 1/λp 1/51.25 [kg.m/s2/m2]

The model scale is chosen 1/50 as it was defined according to the laboratory

restrictions and considering the advantages and disadvantages of small scale and large

scale experiments. The water depths that can be obtained in the flume are from 0.3m

to 0.7m. Operation limits of the wave generator which is another restriction of the

laboratory are 0.05 Hz < Frequency < 2.0 Hz and -290 mm < piston amplitude < 290

mm.

3.4 Laboratory and Scale Effects

Hughes (1993) states that both refraction and diffraction in Froude-scaled long-wave

hydrodynamic physical models are correctly recreated for both geometrically

undistorted and distorted models. However, as mentioned in Section 3.1, scale effect

is a problem in laboratory experiments in coastal engineering in reproduction of the

stresses and forces in the nature.

Wave reflection problems are amplified in long-wave models since long waves reflect

more of their energy and it may be more difficult to operate wave absorption systems

in case of longer wavelengths. Accurate reproduction of bathymetry is also required

to obtain reliable results. Also, if the measured hydrodynamic parameters are small,

30

the possibility of measurement error and instrument intrusion are also laboratory

effects that the researchers should be aware of (Hughes, 1993). To minimize these

laboratory effects, a horizontal platform explained in detail in Section 3.5 was

constructed to recreate the bathymetry as much as possible. The surface of the platform

was covered with sand to prevent smoothness of the surface. The measurement

instruments were operated carefully and their calibration was performed by several

trials until obtaining reasonable results.

Scale effects are discussed under the titles of wave reflection, wave transmission,

surface tension and viscosity and friction in Hughes (1993). He stated that the most

important scale effect related with the physical modeling of rubble mound structures

is the viscous forces due to the flow through the underlayers and core of the structure.

It is not a primary issue for the armor layer of the breakwater since the Reynolds

number is sufficiently large based on the dimension of the armor unit to satisfy the

fully turbulent flow. In the underlayers and core of the breakwater on the model, it is

necessary to increase the size of the core and underlayer materials since scaling of

material sizes may cause viscous scale effects which the layers become less permeable

and may cause higher pressures from inside the structure (Hughes, 1993).

To determine the diameter of the material in the model, Dm, methods of Le Méhauté,

(1990) and Keulegan (1973) give a distortion factor, K, that is used in Equation 3.8.

𝐿𝑝

𝐿𝑚= 𝐾

𝐷𝑝

𝐷𝑚 or 𝜆𝐿 = 𝐾𝜆𝐷 [3.8]

Currently, as also suggested by Hudson et al. (1979), the K values obtained by Le

Méhauté (1990) and Keulegan (1973) methods can be averaged for application of long

wave physical models. Therefore, the diameters of the materials in the filter layer were

corrected by a factor of 1.1 and the diameters of the materials in the core layer were

corrected by a factor of 1.25 in the physical model experiments to minimize the effects

mentioned above.

31

In the physical model experiments, the effect of side walls of the wave flume was

eliminated by taking pressure measurements on the midline of the middle wall element

of the caisson type breakwater which was the most distant position to the side walls.

The boundary effect was also excluded in the damage analysis by observing the cases

which the vertical walls and the crown walls got stuck in the side walls of the flume

and taking into account these conditions in the damage behavior.

3.5 Experimental Setup

The experiments were carried out in the inner wave flume which was further divided

into two parallel sections (0.741 m wide each) by means of a vertical plywood plate to

be able to test the two breakwaters simultaneously. The bathymetry of the model

consisted of a plywood horizontal platform of slope 1:10, on which the breakwater

cross-sections were constructed (Figure 3.5). The platform height was 0.1 m for the

caisson type breakwater side and 0.2 m for the rubble mound breakwater. In order to

prevent the smooth surface of the platform and to reflect the roughness of the seabed

as much as possible, the surface of the platform was covered with aggregates.

Figure 3.5: View of horizontal platform in the wave flume

A caisson type (vertical wall) breakwater with a rubble foundation (Figure 3.6) was

constructed at one section and a rubble mound breakwater with a small berm (Figure

32

3.7) was placed at the other section. The cross-sections were designed according to the

design criteria which has a significant wave height of 5m and a significant wave period

of 9.5s. These cross-sections are generic ones which are widely observed in coastal

areas as vertical wall and rubble mound breakwaters.

Figure 3.6: Caisson Type Breakwater

Figure 3.7: Rubble Mound Breakwater

The caisson type breakwater cross-section is given in Figure 3.8. Both the seaside and

harbor side slopes of the rubble foundation in caisson type breakwater were 1:4. The

total length of the cross-section was 1.55m whereas the horizontal platform had a total

length of 3.63m. The crest elevation of the vertical wall is 0.08m above the still water

level.

The rubble mound breakwater cross-section is given in Figure 3.9. The seaside armor

slope in the rubble mound breakwater was 2:5 whereas the harbor side slope was 1:1.5.

The total length of the cross-section was 1.3m. The platform had a total length of 4.7

m. The crest elevation of the crown wall was 0.04m above the still water level.

33

Figure 3.8: Cross-section of the caisson type breakwater with the horizontal

platform (Dimensions are in meters and the figure is not to scale.)

Figure 3.9: Cross-section of the rubble mound breakwater with the horizontal

platform (Dimensions are in meters and the figure is not to scale.)

3.5.1 Rubble Mound Breakwater Cross-Section

The crown wall, used in the rubble mound breakwater consisted of three similar

concrete elements, which were 0.245 m wide (left element, element in the middle, and

the right element in respect to the direction of wave propagation), 0.09 m long, and

0.09 m high as presented in Figure 3.10 and Figure 3.11.

34

Figure 3.10: Crown wall element used in rubble mound breakwater from different

perspectives (scale 1:50)

Figure 3.11: Placement of the crown wall elements used in rubble mound

breakwater

The stones used for the construction of the rubble-mound breakwater were arranged

manually in three layers, separated by using different colors according to their mass

range:

• core layer (dark grey color): mass of stones between 5 and 25 g (0.4 – 2 t in

prototype),

35

• filter layer (white color): layer thickness of 0.06 m, mass of stones between

15 and 35 g (2 – 4 t in prototype),

• armour layer on the seaside (red color): layer thickness of 0.06 m, mass of

stones between 60 and 75 g (10 - 12 t in prototype),

• armour layer on the side of the port (white color): layer thickness of 0.06 m,

mass of stones between 15 and 35 g (2 - 4 t in prototype).

The arrangement of the layers in the investigated breakwater is shown in Figure 3.12.

Figure 3.12: Geometric Details of Rubble Mound Cross-Section (Scale 1:50)

3.5.2 Caisson Type Breakwater Cross-Section

The concrete blocks used in the vertical wall breakwater consisted of three similar

concrete elements, which were 0.245 m wide (left element, element in the middle, and

the right element in respect to the direction of wave propagation), 0.19 m long, and 0.3

m high as presented in Figure 3.13. The concrete blocks were produced as boxes to be

filled with sand. The blocks were soaked in water for about 24 hours to obtain fully

saturated conditions and then filled with sand by compressing (Figure 3.14).

36

Figure 3.13: Layout of a concrete block used in caisson breakwater (scale 1:50)

Figure 3.14: Placement of concrete blocks used in caisson type breakwater

37

The stones used for the construction of rubble foundation of the vertical wall

breakwater were arranged in two layers,

core layer (dark grey color): mass of stones between 5 and 25 g (0.4 – 2 t in

prototype),

armor layer (white color): layer thickness of 0.06 m, mass of stones between 15 and

35 g (2 – 4 t in prototype).

The arrangement of the layers in the investigated breakwaters is shown in Figure

3.15.

Figure 3.15: Geometric Details of the Caisson Cross-Section (Scale 1:50)

The placement of the two breakwater cross-sections in the flume can be seen in Figure

3.16

38

Figure 3.16: Placement of the two cross-sections

3.6 Measuring Technique

Eight wave gauges and two pressure sensors were used in the experiments to collect

data for each breakwater as shown in Figure 3.20 and 3.21 as well as in Table 3.2.

Wave Recording

Wave gauges (WG) were installed along the wave flume and over the breakwater

models to measure the water surface elevation (Figure 3.17). These wire type wave

gauges, (DHI (Danish Hydraulic Institute)-Wave Meter wave gauges) consist of two

parallel stainless steel electrodes which are conductive materials. The electrodes are

placed perpendicular to the wave direction. The bottom part of the wave gauges is the

recompensating electrodes which minimize the effect of salinity and temperature

effects.

39

Figure 3.17: Wire type DHI-Wave Meter wave gauge

Seven of the wave gauges were installed to measure the surface elevation (wave

height) and the wave period (WG1, WG3-WG8). One wave gauge (WG2) was used

for measuring overtopping and it was installed onto the front surface of the crown wall

in rubble mound breakwater and onto the front surface of the concrete block in caisson

type breakwater (Figure 3.18a and 3.18b). The wave gauges except (WG2) were

submerged up to half of the water depth of 0.4 m.

Figure 3.18: a) Exemplary arrangement of overtopping wave gauge (WG2) in

caisson breakwater b) Exemplary arrangement of overtopping wave gauge (WG2) in

rubble mound breakwater

40

For data from the wave gauges recording, an instrument system developed by Danish

Hydraulics Institute (DHI) was used. The wave gauges measure the voltage changes

in water and the system records the signal of these changes and transfers the record to

the computer. This voltage data is collected in the computer as .txt files by using a

software developed by TDG Data Concept Inc. The voltage data is then converted

into water surface elevation as the change of water surface elevation is proportional to

the change in voltage measured by the wave gauges.

The calibration of the recorded data is necessary to obtain this relationship between

recorded raw voltage data and the change of water surface elevation. Thus; the

following procedure was performed before each experiment:

- the still water level was lowered and raised after fixing the wave gauges at the

same level,

- the stillness of the water level was ensured

- the sensor data was recorded at desired water levels in unit volt and the

corresponding water level heights in unit lengths were used to plot calibration

lines.

In the model experiments, calibration was performed at the beginning of each

experiment by changing the water level at +5cm, 0cm and -5cm. The calibration

coefficients were obtained by using the MATLAB code written by Baykal (2009).

A graph showing an example of calibration is given in Figure 3.19.

Figure 3.19: Example graph of calibration for WG3

-0,4

-0,3

-0,2

-0,1

0

0,1

0,2

0,3

0,4

-6 -4 -2 0 2 4 6

Vo

ltag

e (V

)

Water Level (cm)

Calibration - WG3

41

Fig

ure

3.2

1:

Ex

per

imen

tal

setu

p i

ncl

udin

g m

easu

ring i

nst

rum

ents

for

cais

son t

ype

bre

akw

ater

Fig

ure

3.2

0:

Ex

per

imen

tal

setu

p i

ncl

udin

g m

easu

ring i

nst

rum

ents

for

rubb

le m

ound b

reak

wat

er

42

In summary, wave gauge WG1 is installed to measure the transmitted wave and WG2

is installed to measure the overtopping height whereas wave gauges WG3 – WG8 are

installed to measure the incident and reflected wave heights. The positions of the wave

gauges WG3 – WG4 and WG6 – WG7 are close to each other (20 cm distance) to

make the reflection analysis and obtain the reflected wave heights. The position of

measuring devices in tests with respect to the initial position of wave generator is given

in Table 3.2.

Table 3.2: Position of measuring devices in tests with respect to the initial position

of wave generator

(Caisson Type Breakwater) (Rubble Mound Breakwater)

Measuring

Device

Distance from the wave

maker

[m]

Measuring

Device

Distance from the wave

maker

[m]

WG1 17.669 WG1 18.947

WG2 17.550 WG2 18.842

WG3 16.870 WG3 18.100

WG4 16.670 WG4 17.900

WG5 16.540 WG5 15.600

WG6 7.800 WG6 7.800

WG7 7.600 WG7 7.600

WG8 0.000 WG8 0.000

Profile Measurement

Before and after each test, the profiles of the breakwaters were measured manually at

1cm intervals using a laser meter along two lines that are shown by the white rods in

Figure 3.22.

43

Figure 3.22: Profile measurement lines

Furthermore, photos of the breakwaters were taken before and after each test to record

and analyse the damage visually. Additionally, there were three video cameras

recording the tests from different angles: one was installed recording the caisson type

breakwater from the side view, one recorded the rubble mound breakwater from the

side view and a GoPro type camera was installed observing the rubble mound

breakwater from the top view.

Figure 3.23: Observation window and video recording system

Measurement Axis

Measurement Axis

44

Pressure Measurements

Pressure measurements were taken along the front surface and the bottom of the

caisson type breakwater and along the bottom of the breakwater by two micro pressure

transducers (Figure 3.24). The pressure transducer (model P310) is a disk type pressure

transducer developed by integrated SSK transducer technology and used for hydraulic

experiments as well as for other applications such as soil pressure measurements. The

features of the transducers can be listed as being micro type, low capacity, having high

sensitivity, high response frequency and a waterproof structure.

The transducers are 100 kPa sensors and their natural oscillation frequency is 9.1kHz.

The operating temperature range for the transducers is in between -100C and +550C.

Figure 3.24: Micro pressure transducer used in pressure measurements

Pressure measurements were taken from 2 different points above the still water level,

from 1 point on the still water level and 5 different points below the still water level

along the front surface of the vertical wall element of caisson type breakwater. These

points are shown in Figure 3.25.

45

Figure 3.25: Pressure measurement points along the front surface of caisson

breakwater (Dimensions are in cm.)

Figure 3.26: Placement of two pressure transducers on the front surface of the

vertical wall element at still water level

Pressure measurements were also taken from 6 different points along the bottom

surface of the middle vertical wall element in caisson type breakwater. These points

are shown in Figure 3.27.

46

Figure 3.27: Pressure measurement points along the bottom surface of caisson

breakwater (Dimensions are in cm.)

For the calibration of the data obtained from the transducers and for pretesting of the

transducers, 6 static calibration tests were performed by recording data by placing the

sensors at different water levels. The results obtained from these tests are given in

Figure 3.28 and Figure 3.29 for the two transducers.

Figure 3.28: Results from 6 different static calibration pretests of the transducer 1

-2

0

2

4

6

8

10

0 20 40 60 80 100

Pre

ssu

re (

kPa)

Sensor height (cm)

100 kPa - P310-1 Ser.12971

47

Figure 3.29: Results of 6 different static calibration pretests of transducer 2

As can be seen from the results, the transducers almost gave consistent results for the

hydrostatic pressure for different levels.

Also, a dynamic water tank test was performed for pretesting of the transducers by

submerging the sensors into a water tank in a periodic manner manually between -5

cm and -95 cm water levels. Results of the test are presented in Figure 3.30.

Figure 3.30: Results of the dynamic water tank test of the transducers

-2

0

2

4

6

8

10

0 20 40 60 80 100

Pre

ssu

re (

kPa)

Sensor height (cm)

100 kPa - P310-1 Ser.12972

0

0,2

0,4

0,6

0,8

1

1,2

0 10 20 30 40 50 60

Wat

er

Leve

l (m

)

Time (s)

P310-1 Ser.12971 P310-1 Ser.12972

48

The sampling interval was 5kHz in the experiments to keep the fine data to use it in

case of requirements. The calibration and other processes to analyze the data obtained

from the transducers, a Matlab code was executed. In the code, first the data record as

.txt files was transferred and the parameters like water depth, the sampling interval and

the depths of sensor positions were defined. Since it was difficult to analyze such fine

data, a smoothing process was included in the code. The code sorted the fine data by a

low pass filter process with a cut-off frequency of 20Hz. This process is presented in

the experimental study of Kısacık et al. (2012) on pressure measurements on a vertical

wall. The calibration coefficients were calculated according to the premeasured water

level records for calibration. After that, the mean water level correction was made.

Finally, the offset values resulting from the depths of sensor positions were obtained.

3.7 Wave Characteristics

Holthuijsen (2007) ordered the waves in terms of their period and wavelength as given

in Figure 3.31. Goda (2010) also stated that long-period waves are mainly referred to

the ones with periods of 30 to 300s.

Figure 3.31: Frequencies and periods of the vertical motions of the ocean surface

(Holthuijsen, 2007)

49

Hedges (1995) also suggests that since ocean waves propagate on water together with

currents driven by the wind, the tidal forces or gravity, it is more senseful to use the

wavelength instead of wave period in defining the limits to the validity of the various

analytical theories which exist for describing trains of regular waves. Therefore, he

suggests Ursell number (Equation 3.9) to use as the governing parameter in relatively

shallow water and the wave steepness (H/L) in deep water. The graph suggested

showing approximate regions of validity of analytical wave theories is given in Figure

3.32.

𝑈 =𝐻∗𝐿2

𝑑3 [3.9]

Where U is the Ursell number, H is wave height, L is wavelength and d is the water

depth.

Dean and Dalrymple (2000) also defines long wave limit according to wavelength and

the water depth and gives the following limitation:

2𝜋

𝐿𝑑 <

𝜋

10 [3.10]

Figure 3.32: Approximate regions of validity of analytical wave theories

(Hedges, 1995)

50

The wave characteristics for this study was initially determined by scanning a range of

different wave heights and periods, wave steepnesses, in the range of nonlinear

(cnoidal) waves. Therefore, 18 different waves have been defined at first as given in

Table 3.3. However, some of these waves (wave no: 7, 13 and 14) were eliminated

since they could not be generated due to the limited stroke length of the wave piston.

Waves with wave number 4, 5 and 6 were also eliminated as they were in the linear

region according to Hedges (1995) study. For the other waves, trial experiments were

carried out before the cross-sections were constructed in the flume and the wave

heights and periods were measured at the toe of the structures. According to these

measurements which are given in Table 3.4. wave heights of some of these waves were

very low since they were close to the long wave region (wave no: 1, 2, 3 and 8). These

waves were also not included in the study since the main focus of this study is to

observe the damage and failure mechanisms of the specified breakwaters.

51

Wav

e N

umbe

r1

23

45

68

910

1112

1415

1617

18

H (m

)0.

050.

050.

050.

050.

050.

050.

10.

10.

10.

10.

10.

150.

150.

150.

150.

15

H0/

L00.

001

0.00

20.

004

0.00

60.

010.

015

0.00

20.

004

0.00

60.

010.

015

0.00

20.

004

0.00

60.

010.

015

T (s

)5.

664.

002.

832.

311.

791.

465.

664.

003.

272.

532.

076.

934.

904.

003.

102.

53

L11

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7.79

5.42

4.35

3.25

2.53

11.1

27.

796.

314.

803.

8413

.65

9.60

7.79

5.97

4.80

kd0.

230.

320.

460.

580.

770.

990.

230.

320.

400.

520.

650.

180.

260.

320.

420.

52

d/L

0.04

0.05

0.07

0.09

0.12

0.16

0.04

0.05

0.06

0.08

0.10

0.03

0.04

0.05

0.07

0.08

H,p

roto

type

2.5

2.5

2.5

2.5

2.5

2.5

55

55

57.

57.

57.

57.

57.

5

T,pr

otot

ype

40.0

28.3

20.0

16.3

12.7

10.3

40.0

28.3

23.1

17.9

14.6

49.0

34.7

28.3

21.9

17.9

S0 (m

)0.

220.

160.

110.

090.

070.

050.

440.

310.

250.

190.

150.

810.

570.

470.

360.

29

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34

56

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1214

1516

1718

H,t

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M (

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40.

008

0.01

70.

036

0.04

50.

027

0.01

0.02

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047

0.09

90.

089

0.03

80.

059

0.05

40.

096

0.15

1

H,t

oe

-

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tica

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070.

065

0.03

90.

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057

0.08

0.11

30.

039

0.08

60.

119

0.09

50.

118

T (s

) 5.

24

2.8

2.2

1.75

1.5

5.5

4.5

3.2

2.5

2.1

6.8

4.95

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ow

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Tab

le 3

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teri

stic

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eli

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atio

n

52

Six different wave conditions with wave numbers 9, 10, 12, 15, 17 and 18 were applied

in the experiments at a water depth of 0.4m. The characteristics of these waves are

presented in Table 3.5 and Table 3.6. The characteristics are obtained from the

measurements of WG3 (at breakwater toes) in the flume before the construction of the

breakwater cross-sections. The studied waves are pointed in Figure 3.32 with red

points to illustrate the region where these waves correspond to. The region of the wave

periods of these waves is also illustrated by the red frame in Figure 3.31.

Table 3.5: Characteristics of applied waves in model scale, caisson type breakwater

Wave Number 9 10 12 15 17 18

Period (s) 4 3.2 2 4.95 3.1 2.5

Wave Height (m) 0.22 0.11 0.09 0.17 0.15 0.13

Steepness 0.028 0.018 0.024 0.018 0.026 0.025

Table 3.6: Characteristics of applied waves in model scale, rubble mound breakwater

Wave Number 9 10 12 15 17 18

Period (s) 4 3.2 2 4.95 3.1 2.5

Wave Height (m) 0.2 0.13 0.09 0.19 0.18 0.17

Steepness 0.026 0.021 0.024 0.02 0.03 0.036

As can be seen from Table 3.5 and 3.6, the wave heights are changing in a range of

0.09 – 0.22 m and wave periods are from 2s to 4.95s in model scale. The steepness

range is 0.018 – 0.036. The wave heights are in a range of 4.5m – 11m in prototype

and the wave periods correspond to a range of 14s – 35s in prototype.

Furthermore, the design wave parameters were specified as 5m of significant wave

height (Hs = 5m) and 9.5s of significant wave period (Ts = 9.5s). The cross-sections

were designed according to these wave characteristics but tested under the specified

nonlinear waves which represent the possible extreme wave conditions for such a

design case. The measured wave heights at the structure toe and the ratio of these

53

values to the design wave height (Htoe/Hdesign) in prototype is presented in Table

3.7.

Table 3.7: Ratio of measured wave heights to the design wave height in prototype

Wave No: 9 10 12 15 17 18

Htoe-measured 10.5 6 4.5 9 8.25 7.25

Htoe / Hdesign 2.1 1.2 0.9 1.8 1.65 1.45

To generate the applied waves in the laboratory, the amplitude of paddle displacement

and the frequency values were entered to the Moog device which was connected to the

piston. In order to obtain the paddle displacement (stroke length), Biesel transfer

functions (as cited in Hughes, 1993) which express the relation between wave

amplitude and wave paddle displacement are used. Biesel transfer function for piston

type paddle is given in Equation 3.11 and the graph of the equation is given in Figure

3.33.

𝐻

𝑆0=

2 sinh 2(𝑘ℎ)

sinh𝑘ℎ cosh𝑘ℎ+𝑘ℎ [3.11]

Where H is the wave height, S0 is the paddle displacement and h is the water depth.

Figure 3.33: Biesel Transfer Function to obtain wave paddle displacement (Hughes,

1993)

54

These cnoidal waves were generated as regular waves from the piston. To obtain the

paddle displacement values for the necessary wave parameters, series of trials were

performed by changing the paddle displacement and measuring the recorded data.

Finally, the results of these trials were fitted to a curve which give the wave height

over paddle displacement (H/S0) ratio.

For the analysis of the data obtained from wave gauge measurements, a simple matlab

code was used which execute the calibration and arithmetic correction processes. In

the calibration process, the voltage data was converted into the water level elevation

data. In the arithmetic correction process, mean of all data was subtracted from the

time series recorded to fit the arithmetic mean to zero. Thus, the raw data was

converted into distances from the mean water level. An example of the surface profile

is given in Figure 3.34. The second wave is taken as the representative wave of the

measurements and used for calculations.

Figure 3.34: Sample surface profile

All the experiments were repeated for 2 times to be able to make a comparison between

the repetitions and to obtain as accurate results as possible.

55

3.8 Summary of Physical Model Experiments

A summary of the experimental setup and programme for the tests performed at METU

is presented in Table 3.8.

Table 3.8: Summary of physical model experiments at METU

Experiments at METU

Facility Wave flume: 18×1.5×1.0 m, two parallel sections of width of

0.741 m for testing two breakwaters simultaneously

Model scale 1:50

Breakwaters

Caisson type breakwater with rubble foundation

Rubble mound breakwater with a crown wall unit and a small

berm

Breakwater

geometry

Caisson Type:

- Seaside and harbor slopes of rubble foundation 1:4

- Height: 0.38 m

- Caisson length: 0.19 m

- Breakwater basis length: 1.23 m

Rubble mound:

- Seaside slope 2:5

- Harbor slope 1:1.5

- Height: 0.3 m

- Crown length: 0.09 m

- Breakwater basis length: 1.29 m

Armour

layers

Core layer: 5 - 25 g

Filter layer: 0.07 m thick, 15 - 35 g

Armour layer on seaside: 0.09 m thick, 60 – 75 g

Armour layer on harbour side: 0.07 m thick, 15 - 35 g

56

Crown wall

units

Concrete

L-shape, all surfaces perpendicular

3 units: 0.245/0.245/0.245 m wide, 0.09 m long, 0.09 m high

Concrete

Block Units

Concrete boxes with full of compressed sand

L shape, all surfaces perpendicular

3 units: 0.245/0.245/0.245 m wide, 0.19 m long, 0.3 m high

Bathymetry

model

Caisson type breakwater:

Horizontal platform of height of 0.1 m with seaside slope 1:10

and harbour slope 2:5.2

Rubble mound breakwater:

Horizontal platform of height of 0.2 m with seaside slope 1:10

and harbour slope 2:4

Measuring

devices

8 wave gauges in each breakwater

2 pressure sensors

Flow regime

6 different cnoidal waves

Wave heights: 0.09 – 0.22m

Wave periods: 2s – 4.95s

Water depth: 0.40m

57

CHAPTER 4

4 NUMERICAL MODELLING

4.1 Introduction to the Numerical Model, IH-2VOF

Interest in numerical modelling of coastal structures has increased in recent years since

the computer resources have improved allowing larger storage capabilities, faster

central processing units (CPUs) and cheaper computers. The state-of-the-art numerical

models are also well calibrated and validated in terms of porous media flow,

overtopping phenomenon and pressure fields. Therefore, it can be said that numerical

modelling is now an available tool as complementing the physical modelling and for

design purposes.

As stated in Section 3.1, the classical approach in coastal engineering is physical model

testing. However, it has some handicaps and therefore, new methods to improve the

wave-structure interaction analysis are needed. At this point, integrating numerical

models can provide further insight. Main approaches in numerical modelling can be

schematized as given in Figure 4.1.

Figure 4.1: Schematic diagram of main approaches in numerical modelling in

coastal and harbor engineering

58

Non-linear shallow water equations and Bousinesq Equation models may be cheap

according to the computational cost, may be efficient and allow long simulations with

reliable statistics. On the other hand, wave breaking has to be triggered in the

computations and vertical structures can not be simulated. Also, overtopping can not

be calculated and pressure field is not provided.

SPH models have nonlinear interaction in the fluid and pressure field can be obtained.

It also has an advantage of modelling multi-connected free surfaces. However, these

models are subject to the ongoing research and the porous flow is not solved yet.

Pressure field also needs to be tailored and adapted.

Navier-Stokes models (RANS) solve the non-linear interaction in the fluid and the

pressure field is obtained. They allow modelling of multi-connected free surfaces,

porous media flow and turbulence is considered. The models may have high

computational time (process time) and their efficiency may be disputable. However,

the models are increasingly becoming a methodology of use in coastal engineering due

to several factors listed as the following:

- The number of underlying assumptions is quite low,

- Non-linear flow characteristics are considered,

- Wave dispersion is included,

- Breaking is not triggered artificially,

- Wave induced turbulence can be considered.

The IH-2VOF model solves the two-dimensional Reynolds Averaged Navier-Stokes

(RANS) equations, based on some assumptions. The model characterizes the flow

inside and outside of coastal structures which include permeable layers. It uses Navier-

Stokes model as an engineering tool. It includes mesh design as mesh dimension and

resolution, sea state definition, porous media parameters definition and post-process

and results management like run-up overtopping, loads and moments. Most

importantly for this study, the model allows modelling of both vertical breakwaters

59

and rubble mound breakwaters and has been validated by physical model experiments

and several studies as stated in Chapter 2.

The numerical model has been validated at laboratory scale for wave breaking over

porous and impermeable slopes, for submerged permeable sea dikes, for low crested

permeable sea dikes, for vertical breakwaters and for rubble mound breakwaters (Lara

et al., 2002; Garcia et al., 2004; Guanche et al., 2009). A prototype validation is also

necessary to obtain porous media friction coefficients for laboratory scale and to

overcome scale effects at laboratory scale. The model has been validated for vertical

breakwaters and rubble mound breakwaters in prototype by Guanche et al. (2009).

4.2 Theoretical Background of IH2VOF Model

Fluid domain governing equations: RANS Equations

In a turbulent flow, the instantaneous velocity field, ui, and pressure field, p, can be

split into two parts, the mean velocity and pressure components, �� 𝑖, and, ��, and the

turbulent velocity and pressure fluctuations, 𝑢𝑖′ and 𝑝′ as given in Equation 4.1.

𝑢𝑖 = �� 𝑖 + 𝑢𝑖′ and 𝑝 = �� + 𝑝′ [4.1]

Where i=1,2 for a bidimensional flow.

Applying the former decomposition to the Navier-Stokes equations, assuming

incompressible fluid and after time averaging, the continuity equation (Equation 4.2)

and the momentum equations (Equation 4.3) imply the following.

𝜕𝑢 𝑖

𝜕𝑥 𝑖= 0 [4.2]

𝜕𝑢 𝑖

𝜕𝑡+ �� 𝑗

𝜕𝑢 𝑖

𝜕𝑥 𝑗= −

1

𝜌

𝜕��

𝜕𝑥𝑖+

1

𝜌

𝜕�� 𝑖𝑗

𝜕𝑥𝑗−

𝜕𝑢𝑖′𝑢𝑗

′

𝜕𝑥𝑗+ 𝑔𝑖 [4.3]

60

𝜏𝑖𝑗 = 2𝜇𝑆𝑖𝑗 where [4.4]

𝑆𝑖𝑗 =1

2(

𝜕𝑢 𝑖

𝜕𝑥 𝑗+

𝜕𝑢 𝑗

𝜕𝑥 𝑖) [4.5]

In the momentum equation (Equation 4.3), the Reynolds stress tensor (𝜌𝑢𝑖′𝑢𝑗

′ )

represents the influence of the turbulence fluctuations on the mean flow field and

requires a closure hypothesis. Therefore, in the model, this term is closed with a second

order model. A summary of several closure models can be found in Jaw and Chen

(1998) including the one in the model. In IH-2VOF model, the Reynolds stress tensor

is assumed to be related to the strain rate of mean flow through the algebraic nonlinear

k-ε model as given in Equation 4.6 (Yang and Shih, 1993; Lin and Liu, 1999).

𝜌𝑢𝑖′𝑢𝑗

′ =2

3𝜌𝑘𝛿𝑖𝑗 − 𝐶𝑑𝜌

𝑘2

𝜀(

𝜕𝑢 𝑖

𝜕𝑥 𝑗+

𝜕𝑢 𝑗

𝜕𝑥 𝑖) −

𝜌𝑘3

𝜀2

[ 𝐶1 (

𝜕𝑢𝑖

𝜕𝑥𝑙

𝜕𝑢𝑙

𝜕𝑥𝑖+

𝜕𝑢𝑗

𝜕𝑥𝑙

𝜕𝑢𝑙

𝜕𝑥𝑖−

2

3

𝜕𝑢𝑙

𝜕𝑥𝑘

𝜕𝑢𝑘

𝜕𝑥𝑙𝛿𝑖𝑗) +

+𝐶2 (𝜕𝑢𝑖

𝜕𝑥𝑘

𝜕𝑢𝑗

𝜕𝑥𝑘−

1

3

𝜕𝑢𝑙

𝜕𝑥𝑘

𝜕𝑢𝑘

𝜕𝑥𝑙𝛿𝑖𝑗) + 𝐶3 (

𝜕𝑢𝑘

𝜕𝑥𝑖

𝜕𝑢𝑘

𝜕𝑥𝑗−

1

3

𝜕𝑢𝑙

𝜕𝑥𝑘

𝜕𝑢𝑙

𝜕𝑥𝑘𝛿𝑖𝑗)]

[4.6]

In which Cd, C1, C2 and C3 are empirical coefficients, 𝛿𝑖𝑗 is the Kronecker delta and k

is the turbulent kinetic energy defined as in Equation 4.7.

𝑘 =1

2(𝑢𝑖

′𝑢𝑖′ ) [4.7]

The dissipation rate of the turbulent kinetic energy is defined as in Equation 4.8.

휀 = 𝜗(𝜕𝑢𝑖

′

𝜕𝑥𝑗′⁄ ) 2

[4.8]

Where 𝜗 =𝜇

𝜌⁄ is the molecular kinematic viscosity.

61

It is important to note that the condition C1=C2=C3=0 in Equation 4.6 leads to the

conventional linear (isotropic) eddy viscosity model for the Reynolds stresses closure

giving Equation 4.9.

𝑢𝑖′𝑢𝑗

′ = −2𝜗𝑡𝜎𝑖𝑗 +2

3𝑘𝛿𝑖𝑗 [4.9]

Where 𝜗𝑡 is the eddy viscosity expressed as:

𝜗𝑡 = 𝐶𝑑(𝑘2

휀⁄ ) [4.10]

The values for the coefficients C2 and C3 are obtained from experimental results on

turbulent shear flow by Champagne et al. (1970). The C1 coefficient is deduced from

the assumption by Shih et al. (1996): C1 = 2C3. A value for Cd is finally proposed by

Rodi (1980). The values for the coefficients are summarized as the following:

Cd = 0.09, C1 = 0.0054, C2 = -0.0171, C3 = 0.0027 [4.11]

However, considering constant values for these coefficients may lead to inconsistent

physical situations in the momentum equation (Equation 4.3) under some extreme

circumstances such as negative turbulence energy or infinite nonlinear contributions.

Hence, modified expressions for the empirical coefficients have been implemented in

the IH-2VOF model:

𝐶𝑑 =2

3(

1

7.4+𝑆𝑚𝑎𝑥), 𝐶1 =

1

185.2+𝐷𝑚𝑎𝑥2 , 𝐶2 =

1

58.5+𝐷𝑚𝑎𝑥2 , 𝐶3 =

1

370.4+𝐷𝑚𝑎𝑥2 [4.12]

where;

𝑆𝑚𝑎𝑥 =𝑘

𝜀𝑚𝑎𝑥 [|

𝜕𝑢𝑖

𝜕𝑥��|] [4.13]

𝐷𝑚𝑎𝑥 =𝑘

𝜀𝑚𝑎𝑥 [|

𝜕𝑢𝑖

𝜕𝑥𝑗 |] [4.14]

62

It is important to note that all coefficients take their originally proposed values when

Smax and Dmax are zero. The governing equations for 𝑘 and 휀 are presented in Rodi

(1980) and Lin and Liu (1999).

Flow in porous media governing equations: Volume-Averaged RANS Equations

(VARANS)

The main assumption of the IH-2VOF model consist in considering that RANS

equations coupled with an appropriate turbulence model (𝑘 − 휀 model) can describe

the flow field in the porous media. To make the fluid/porous structure interaction

modelling easier, a volume-averaging process has been applied to the RANS and the

𝑘-휀 equations.

The flow in porous media is obtained in the IH-2VOF model through the resolution of

the Volume-Averaged Reynolds Averaged Navier-Stokes equations. The complete

mathematical formulation is presented in Hsu et al. (2002). These equations are

derived by integration of the RANS equations over a control volume. The size of the

averaging volume is chosen much larger than the characteristic pore size (microscopic

scale) but much smaller than the characteristic length scale of the flow, i.e. the scale

of the spatial variation of the physical variables in the fluid domain (macroscopic

scale). Schematic representation of the mathematical approach is given in Figure 4.2.

Figure 4.2: Sketch of volume averaging process for resolution of the porous flow

(IH-2VOF Course Lecture Notes, 2012)

63

The free surface movement is tracked by the volume of fluid (VOF) method, for only

one phase, water and void (http://ih2vof.ihcantabria.com/physics). In order to replicate

solid bodies immersed in the mesh, instead of treating them as sawtooth-shape, the

model uses a cutting cell method first which is given by Clarke et al. (1986). This

method uses orthogonal structured mesh in modelling to save computational time. In

this method, an openness function θ is defined to specify the fraction of volume of free

space in the cell. According to this fraction, if θ=0 it is defined as a ‘’solid cell’’

(entirely occupied by the solid), if θ=1 it is defined as a ‘’fluid cell’’ and if 0<θ<1 it is

defined as a ‘’partial cell’’. The original variables in the cell or on the cell faces are

multiplied by the openness coefficients to be redefined. To numerically carry out this

process, partial cell coefficients are specified at the cell centers and boundaries: θl, θr,

θt, θb which correspond to the openness at the left, right, top and bottom, respectively.

As a result, the redefined governing RANS equations are given as the following:

𝜕(𝜃𝑢𝑖)

𝜕𝑥𝑖= 0 [4.15]

𝜕(𝜃𝑢𝑖)

𝜕𝑡+ 𝜕𝑢𝑗

𝜕(𝜃𝑢𝑖)

𝜕𝑥𝑗= −

𝜃

𝜌

𝜕𝑝

𝜕𝑥𝑖+ 𝜌𝑔𝑖 +

𝜃

𝜌

𝜕(𝜏𝑖𝑗)

𝜕𝑥𝑗+ 𝑓𝑏 [4.16]

The last term in Equation 4.16 is a virtual force. It appears because the IH-2VOF model

considers two different numerical methods to simulate moving bodies within the

computational domain (Raosa, 2012). The first method is ‘’virtual force method’’

(Mittal and Iaccarino, 2005) and the second one is the ‘’direct forcing method’’

(Mohd-Yusof, 1997).

Initial Conditions and Boundary Conditions

The model considers zero velocities and hydrostatic pressure as the initial conditions

for the mean flow in the domain still water.

Regarding turbulence, the initial conditions can not be zero for the mean flow since

the turbulence generation represented by Reynolds stresses is proportional to the

http://ih2vof.ihcantabria.com/physics

64

turbulent kinetic energy 𝑘, as described in Equation 4.6. If the initial condition for 𝑘

is zero, no turbulence energy would be produced during the whole simulation and

mathematical singularities would occur in the equations. Therefore, the model uses an

initial value for the turbulence energy that produces a numerical disturbance given in

Equation 4.17.

𝑘 =1

2𝑢𝑡

2 [4.17]

With 𝑢𝑡 = 𝛿𝑐𝑖 where 𝑐𝑖 is the wave celerity in the generation zone and 𝛿 is a constant

equal to 0.0025 (Lin, 1998).

For the turbulent dissipation rate 휀, the model considers the expression given in

Equation 4.18.

휀 = 𝐶𝑑𝑘2

𝜗𝑡 [4.18]

Where 𝜗𝑡 = 𝜉𝜗 and ξ is a constant equal to 0.1 as given in Lin (1998).

Variation of the 𝛿 and ξ values were found to have a negligible effect on the final

results of the computations (Lin, 1998).

In the model, at solid boundaries, two types of conditions for the mean flow can be

considered as no slip and free slip. In the case of turbulent flows, the model considers

a log-law distribution for the mean tangential velocity in the turbulent boundary layer.

The application of an appropriate boundary condition at the mean free surface in

turbulent flows is quite complex as the mean free surface is not clearly defined

(Brocchini and Peregrine, 1996; Liu and Lin, 1997; Lin and Liu, 1999). In the IH-

2VOF model, the mean density fluctuations near the free surface due to mixing and air

intrusion are neglected and similarly to situations of laminar flow, the zero stress and

zero pressure conditions are imposed at the free surface.

65

The open boundary condition in the IH-2VOF model is expressed as the following

equation:

𝜕𝜙

𝜕𝑡+ 𝑐0

𝜕𝜙

𝜕𝑥= 0 [4.19]

Where ϕ represents the variable to be evaluated (��, 𝑣, 𝑘, 휀, etc.) and 𝑐0 the wave

celerity at the considered position expressed as:

𝑐0 = √𝑔(𝑑 + 𝑎) [4.20]

For long waves, and

𝑐0 = √𝑔𝜆

2𝜋tanh (

2𝜋

𝜆(𝑑 + 𝑎)) [4.21]

For short waves, where a is the wave amplitude, d is the water depth and λ is the wave

length for this depth. More details on the boundary conditions can be found in Rodi

(1980) and Liu and Lin (1997).

Wave Generation

Wave generation is a key factor for all the numerical models devoted to coastal

engineering as waves have to be generated to resemble those in the field or in the

experimental facility. Generated waves will not only cause incorrect results; they may

also cause the solution to be nonphysical.

The IH-2VOF model includes several procedures of wave generation: internal wave

maker, static wave paddle (Dirichlet boundary condition) and dynamic wave paddle

(moving boundary method). A more complete description can be found in Lara et al.

(2006) for internal wave maker, Torres et al. (2010) for static wave paddle method and

Lara et al. (2011) for dynamic wave paddle. In Dirichlet boundary condition, regular

66

waves (first order, second order, fifth order, cnoidal and solitary waves) and irregular

waves (first and second order) are implemented. In internal wave maker, wave

generation occurs in two directions; so there is a need to dissipate one of them.

Therefore, studies are combined with the sponge layer as an absorption method.

Moving boundary method replicates a piston type wave maker. It needs the paddle

position as input. Velocity is then calculated as a first order forward derivative of this

defined position.

Wave absorption boundary conditions are a key factor of IH-2VOF model. They allow

running simulations for a long time, avoiding most of the effects of reflected waves in

the flumes. Active and passive wave absorption methods are applied in the model, the

active wave absorption method can be applied to both static wave paddle and for

dynamic wave paddle. Active wave absorption is applied by following the

methodology developed by Schäffer and Klopman (2000) which is based on shallow

water linear theory. It identifies the waves that reach a boundary and then absorbs them

to prevent their reflection. Passive wave absorption is also provided in the model by a

sponge layer which is applied by following Israeli and Orszag (1981) formulation. The

method consists of a region in which a dissipation model is defined. The aim is to

prevent the reflections on the boundary, as waves generated travel in the two

directions, but it also absorbs any other incident waves from the zone of interest.

Perfect absorption is not realistic; so results up to 10% reflection considered as good.

4.3 Model Geometry and Mesh Generation

The IH-VOF model is operated by a Graphical User Interface (GUI), namely Coral,

developed to assist in generating the mesh. As preprocessing, different geometries can

be created and included within the mesh such as bottom profiles, obstacles

(breakwaters, caissons etc.) and porous media (rubble mounds, cores etc.). Once the

geometrical elements are introduced by the user, Coral creates a grid as output and this

can be read by the numerical model.

67

The Coral main window can be divided into 4 different areas as given in Figure 4.3.

- Zone 1: Graphical representation of the generated mesh and the geometry

- Zone 2: Controls for zooming, dynamic view, adjust view and view options

- Zone 3: Numerical domain and mesh resolution definition

- Zone 4: Obstacle and porous media definition

As can be seen from Figure 4.3, Zone 1 is a black window in which the numerical

domain is displayed in grey colour. Once objects are defined by the user, they appear

in different colours such as obstacles in yellow, porous bodies in red and water bodies

in cyan.

Zone 2 contains four controlling buttons as zoom allowing zoom in and zoom out, a

pan allowing a dynamic view of the mesh and an adjust view button adjusting mesh to

screen size capturing the whole domain. View options panel also displays different

view options for mesh cells depending on their properties.

Zone 3 allows the user to define the geometry on which the IH-2VOF model solves

the governing equations and provide the results. Zone 4 includes the introduction of

water and obstacles within the mesh defined in Zone 3.

Figure 4.3: Coral Interface, Zones

68

Figure 4.4: Flowchart of generating a mesh in Coral

Coral generate structured meshes with both uniform and non-uniform cell size. The

use of uniform (constant cell size) meshes is recommended (IH-2VOF Course Lecture

Notes, 2012) The computing mesh is constructed from a number of submeshes

(subzones) defined at each coordinate direction, X and Y. The origin of the coordinate

system in the mesh is in the upper left hand side of the domain, which implies a positive

Y direction pointing downwards. New subzones could be created in both directions

and then modified by choosing them in the subzone window. General flowchart of

generating a mesh in Coral is given in Figure 4.4.

Create a new project and save

Define the dimensions of the domain

- the width of the numerical flume

- the height of the numerical flume

Define the geometry

- obstacles

- porous media

- water bodies

Mesh Generation

- define cell sizes in X and Y direction

- use Generate! button

Mesh Quality Check

- ∆x, ∆y and the domain length

69

In the numerical modelling of the experiments, firstly, the domain was defined

according to the flume dimensions. Once the domain had been set, the next step was

to define the geometry to be simulated. Obstacles, porous media and water bodies were

defined using closed polygons. Each polygon was specified inserting the vertex

coordinates.

Obstacles are elements with zero porosity. Concrete elements such as caissons or

crown-walls can be defined as obstacles. The bottom bathymetry can also be defined

as impermeable using obstacles polygons.

Porous bodies are created following the same procedure as obstacles. In this case, the

porous media parameters must be introduced. These parameters are porosity, linear

friction coefficient, nonlinear friction coefficient, added mass coefficient and the

material diameter, D50. After introducing all of these parameters, the porous media

characteristics are stored.

Water bodies are introduced using the same method as the previous elements, but in

this case using the button ‘’Water’’.

To perform the model geometry definition for the caisson type breakwater, the

following geometrical features are defined (Figure 4.5).

- Two obstacles (the bathymetry and the caisson)

- Three porous media (two filter layers at the right hand side and the left hand

side, the core layer)

- Water

Figure 4.6 shows the obtained model geometry in the IH-2VOF model for the caisson

breakwater. The coordinates of the element indices which were introduced to the Coral

to obtain this geometry is provided in Appendix A.

70

Figure 4.5: Elements indices in defining geometry of caisson type breakwater (IH-

2VOF Course Lecture Notes, 2012)

Figure 4.6: Model geometry for caisson type breakwater

For the mesh generation for the model, a variable grid is chosen considering the total

number of cells allowing recreation of long domains with good discretization in the

areas of interest. The maximum resolution zone is placed around the breakwater where

a constant value of horizontal, ∆x, and vertical, ∆y, cell size is set. There are some

restrictions about setting the variable grid as the following (IH-2VOF Course Lecture

Notes, 2012):

- The spacing of adjacent cells should not differ by more than 10 – 20 %.

71

- Cell aspect ratios greater than 1 and less than 5 are more desirable. (1 < ∆x/∆y

< 5)

- Changes in the dimension of each cell have to be less than 5%. This criterion

is achieved ∆2x < 0.05 and ∆2y < 0.05.

- The horizontal discretization should be at least 70 - 100 cells per wave length

for nonbreaking waves and should be greater than 100 cells per wave length

for breaking waves.

- 7 – 10 cells per wave height are desirable in the vertical discretization.

- The domain length should be a distance equal to 1.5-2 wave length before an

obstacle or breakwater.

By following these requirements, the mesh properties defined for the mesh are given

in Table 4.1.

Table 4.1: Properties of the subzones in the mesh of caisson breakwater model

Subzone 1 Subzone 2 Subzone 3

Center 14.980 20.480 20.520

Division 0.000 15.000 20.500

Number Cells Left 599 274 1

Number Cells Right 1 1 44

Max. Sep. Center 0.020 0.020 0.020

X Direction

Subzone 1 Subzone 2 Subzone 3

Center 0.545 0.995 1.005

Division 0.000 0.550 1.000

Number Cells Left 49 89 1

Number Cells Right 1 1 29

Max. Sep. Center 0.005 0.005 0.005

Y Direction

72

3 subzones in mesh generation are defined in both X and Y directions regarding the

properties given above. The generated mesh with the subzones shown is given in

Figure 4.7.

Figure 4.7: Generated mesh with the subzones for caisson breakwater

4.4 Mesh Convergence Checks

It is important to check the quality of the generated mesh in the computational domain.

After the mesh is generated, by using the button ‘’Mesh quality’’, a new window

appears in the Coral showing two graphs (Figure 4.8). The upper graph on the window

shows the cell size as black line in X direction along the entire domain and the

derivative of that value as green line representing the variation in the cell size along

the domain. On that graph, X-axis displays the X-coordinate and the cell index

between brackets. Y-axis on the left hand side shows the cell size while Y-axis on the

right hand side shows the value of the derivative. The lower graph shows the same

aspects but for the Y-coordinate.

73

If the condition given in Section 4.3, ∆2x < 0.05 and ∆2y < 0.05, is not satisfied, the

green line on the graphs turns into red meaning that the absolute value of the derivative

curve has reached 0.05. This condition prevents variations in the cell size from being

too sharp. Therefore, if one of these green lines has turned into red, it means that it is

necessary to introduce more cells due to spacing between the adjacent cells.

In modelling of the breakwater, the convergence checks have been applied and the

following graphs (Figure 4.8) are obtained from the quality check.

Figure 4.8: Quaility check for the generated mesh

In order to ensure that the numerical model is able to simulate the regular wave

interaction with the breakwaters, the initial consideration regarding the dimensions of

the domain should also be satisfied. The domain is chosen according to the flume

dimensions given in Section 3.2. The domain length is taken as 22.3 m and the height

is taken as 1.2m. The maximum wave length of the applied waves is 9.7m. The domain

length condition is satisfied considering more than 1.2 wavelength (11.64m) in front

of the breakwaters. The reason behind choosing the domain height as 1.2m (rather than

1m which was the original dimension) is the consideration of possible overtopping

events.

74

4.5 Hydraulic Conditions for the IH-2VOF Model

In the IH-2VOF model, once the mesh generation is completed, the next step is to

establish the wave conditions. This process is carried out by IH-2VOF GUI. The main

menu of GUI is displayed in Figure 4.9.

Figure 4.9: IH-2VOF GUI Preprocessing Main Menu

There are three different possibilities in order to define the wave conditions in IH-

2VOF GUI. One of them is generating a new wave series with specified wave

characteristics such as wave height, wave period, wave series duration and sampling

frequency of the generated signal. Solitary, regular and irregular waves can be

generated by this option. Other option is to import a wave series which may be

generated before and to be used in the simulation in order to create the same conditions

obtained before. The last option is to reconstruct this wave series using a surface

record. A .dat file containing the free surface time series is needed in this option. The

file must include two columns as the time (in seconds) and the free surface elevation

75

(in meters). The wave conditions in the simulation of the two cases in this study were

defined by using the first option, creating new time series by defining the necessary

parameters. The waves were chosen as Cnoidal waves and the sampling frequency was

taken as 20Hz. The wave conditions are applied so that the free surface records at the

toe of the structures are almost the same as in the experiments. An example of defining

wave conditions is given in Figure 4.10.

Figure 4.10: Generation of new wave series

Once the wave series is established, then the wave paddle is generated in Section 3 of

the main preprocessing menu of GUI given in Figure 4.9. Static and dynamic wave

paddle options are provided. In case of dynamic paddle option, the initial position and

the maximum position of the wave paddle must be specified in order to define the

paddle stroke. In the simulations, dynamic paddle option is used since it represents a

piston type wave maker in wave generation in laboratory experiments.

Furthermore, Section 4 in the GUI menu (Figure 4.9) is to be filled in order to introduce

the simulation parameters such as the simulation time and the time step. Left and right

boundary absorption can also be selected in this section. Simulation can be carried out

considering a turbulence model or not. If the turbulence model is to be considered, the

76

parameters; turbulence seed parameter, the eddy viscosity and the parameter for

boundary layer turbulence resolution must be specified.

The properties to obtain and store in the whole domain can also be chosen in Section

4 as shown in Figure 4.10. VOF function, horizontal and vertical velocities, pressure

and turbulence fields can be saved for the entire domain at the specified sampling

frequency.

The GUI also allows locating wave gauges along the domain in order to obtain results

of free surface time history and energy spectra at those specific locations. Different

positions can be defined for these wave gauges by introducing their coordinates. Exact

locations are provided to the model as experiments.

The wave gauge locations are also defined as in the experiments. Sample sketch of

wave gauge places for caisson type breakwater is given in Figure 4.11.

Figure 4.11: Setting wave gauge position

4.6 Summary of Numerical Modelling

In summary, two cases of the physical model experiments (wave number 9 and wave

number 10) were simulated in the model, IH2VOF. The grid size in X direction (∆x)

was chosen 0.02m and in Y direction is 0.005m in the simulations. The initial time

step (dt) was defined as 0.05s in the simulations. The sampling frequency was defined

as 30Hz which corresponds to 0.033s of time step (∆t) but the ∆t values were changed

77

and adjusted around 0.03s by the model for each time step for convergence. The

simulation length was 35s which corresponds to a time duration of ten waves. The

results obtained from the simulations are discussed in Chapter 5.

79

CHAPTER 5

5 RESULTS AND DISCUSSION

5.1 Physical Model Experiments

In this section results of the physical model experiments are presented. First, the

analysis of the breakwater damage under the corresponding wave according to the

video recordings, profile measurements and photo documentation is presented. Then,

a summary of the results is provided in a table. Finally, a general discussion based on

these results is provided.

It is useful to give some important details about the laboratory experiments at this

point. There was no constant experiment duration in the physical model experiments

since the tests were finished after the observation of total failure of the breakwaters. In

case of no breakwater failure (wave number 12), the waves were applied as 500 waves,

1000 waves and 1000 waves cumulatively. After the experiments, profile

measurements were carried out via a laser distance meter in two lines on the

breakwaters with 1 cm intervals. The profile measurements obtained from each line on

the cross-sections for the two sets of each test are given in Appendix B. Photo

documentation was performed before and after each test as well as video recording

during the experiments. Surface profile measurements were analyzed by using a

Matlab code and the second wave in the surface profiles was taken as the determinative

wave of the characteristics of the measured waves. The surface profile of each wave

condition can be found in Appendix C. Wave reflection was eliminated by short

duration of the experiments and taking the second wave (it was the wave before the

start of reflection) as the representative wave for the pressure measurements. It may

be also useful to give the properties of the applied waves again which were already

80

given at Section 3.7. It is important to note that the characteristics given in Table 5.1

and Table 5.2 are the measured ones at breakwater toe while the flume was empty.

Table 5.1: Wave properties in model scale, caisson type breakwater

Wave Number 9 10 12 15 17 18

Period (s) 4 3.2 2 4.95 3.1 2.5

Wave Height (m) 0.22 0.11 0.09 0.17 0.15 0.13

Steepness 0.028 0.018 0.024 0.018 0.026 0.025

Table 5.2: Wave properties in model scale, rubble mound breakwater

Wave Number 9 10 12 15 17 18

Period (s) 4 3.2 2 4.95 3.1 2.5

Wave Height (m) 0.2 0.13 0.09 0.19 0.18 0.17

Steepness 0.026 0.021 0.024 0.02 0.03 0.036

The damage behavior of the structures under the applied waves are classified at three

stages as the start of damage, major damage and total failure for both breakwaters. The

descriptions of these stages are summarized as in the following:

Caisson type breakwater (Figure 5.1):

- Start of damage: Start of displacement of the vertical walls

- Major damage: Getting inclined and start of overturning of the vertical walls

- Total failure: Overturning and movement of the vertical walls together with

some damage on the slopes of the rubble foundation

Rubble mound breakwater (Figure 5.2):

- Start of damage: Start of displacement of crown walls and slope instability

- Major damage: Sliding and/or overturning of the crown walls and movement

of the stones together with the crown walls towards onshore

81

- Total failure: Movement of the crown walls towards onshore and total lose of

slope stability

Figure 5.1: Stages of damage of caisson type breakwater for wave number 9 a)

start of damage b) major damage c) total failure

Figure 5.2: Stages of damage of rubble mound breakwater for wave number 9

a) start of damage b) major damage c) total failure

a b

c

a b

c

82

Wave Number 9

Wave number 9 had a characteristic of an impact wave which directly hit on the

vertical walls of the caisson breakwater and the crown wall of the rubble mound

breakwater. The visual observation of an impact wave at the time of attack on the

structures is shown in Figure 5.3 and 5.4.

Figure 5.3: Wave Number 9 impact on the vertical wall of caisson type breakwater

83

Figure 5.4: Wave Number 9 impact on the crown walls of rubble mound breakwater

Both of the breakwaters were totally failed in the tests. The caisson type breakwater

started to be damaged at the 1st wave, had major damage by the 2nd wave and totally

failed by the 3rd wave in the tests.

The rubble mound breakwater started to get damage at the 2nd wave, had major damage

at the 5th wave and totally failed by the 7th wave, in the tests.

Sometimes, some difference between the two sets of the same experiment occurred

because the vertical walls and the crown walls got stuck in the side walls of the flume

in some of the tests. This fact was clearly observed from video recordings and was

taken into account in the analysis of the damage behavior.

The breakwater profiles of each set test for caisson type breakwater for Wave number

9 are given in Figure 5.5 and 5.6. The images of damaged breakwater are also given

in Figure 5.7.

84


(wave approach is from left)

The difference between the two lines of the profiles which are given in Figure 5.3 is

due to the fact that the three vertical wall elements were overturned and one element

was placed after another after the experiment (Figure 5.5).

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8

Y -

Ver

tica

l Dis

tan

ce (

m)

X -Horizontal Distance (m)

Line-1 Before After

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8

Y -

Ver

tica

l Dis

tan

ce (

m)

X - Horizontal Distance (m)

Line-2 Before After

85


In the second set, the vertical wall elements were overturned and washed away which

is clearly observed from profile measurements given in Figure 5.4. The elements were

placed side-by-side after the experiment which can be seen in Figure 5.5. Therefore,

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8

Y-

Ver

tica

l Dis

tan

ce (

m)


Line-1 Before After

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8

Y-

Ver

tica

l Dis

tan

ce (

m)


Line-2 Before After

86

there is almost no difference between the two lines of profile measurements of the

breakwater.

Figure 5.7: Damage of caisson type breakwater (Top: Set 1, Bottom: Set 2)

The breakwater profiles of each set test Wave number 9 for rubble mound breakwater

are given in Figure 5.8 and 5.9. The images of damaged breakwater are also given in

Figure 5.10.

87


0

0,1

0,2

0,3

0,4

0,5

0,6

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8

Y-

Ver

tica

l Dis

tan

ce (

m)


Line-1Before After

0

0,1

0,2

0,3

0,4

0,5

0,6

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6

Y -

Ver

tica

l Dis

tan

ce (

m)


Line-2 Before After

88


0

0,1

0,2

0,3

0,4

0,5

0,6

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8

Y-

Ver

tica

l Dis

tan

ce (

m)


Line-1 Before After

0

0,1

0,2

0,3

0,4

0,5

0,6

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6

Y-V

erti

cal D

ista

nce

(m

)


Line-2 Before After

89

Figure 5.10: Damage of rubble mound breakwater after wave number 9, Set 1

Wave Number 10

Wave number 10 had an overflow effect on the vertical walls of the caisson breakwater

and the crown walls of the rubble mound breakwater rather than hitting on these

structures. Therefore, Wave number 10 had a characteristic of overflowing wave

differing from Wave number 9. The visual observation of an overflow wave at the time

of acting on the structures is shown in Figure 5.11 and 5.12.

90

Figure 5.11: Overflowing wave acting on the vertical walls of caisson type

breakwater

Figure 5.12: Overflowing wave acting on the vertical walls of rubble mound

breakwater

Both of the breakwaters were totally failed in the two sets of Wave number 10

experiments. The caisson type breakwater started to be damaged at 7th wave, got major

damage at the 11th wave and totally failed by the 13th wave.

91

The rubble mound breakwater started to get damage at the 3rd wave, got major damage

at the 8th wave and totally failed by the 11th wave. The breakwater profiles for caisson

type breakwater are given in Figure 5.13. The images of damaged breakwater are also

given in Figure 5.14.

Figure 5.13: Breakwater profiles for caisson type breakwater, Wave number 10 Set

2

Although the caisson type breakwater is failed after wave number 10, it is not observed

in the two lines of the profile measurements (Figure 5.13) since the right and left

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8

Y-

Ver

tica

l Dis

tan

ce

X - Horizontal Distance

Line-1 Before After

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8

Y-

Ver

tica

l Dis

tan

ce (

m)


Line-2 Before After

92

vertical wall elements were stuck between the side walls of the wave flume and the

middle wall element (Figure 5.14).

Figure 5.14: Damage of caisson type breakwater after wave number 10 Set 2

The breakwater profiles of the first set for rubble mound breakwater are given in Figure

5.15. The images of damaged breakwater are also given in Figure 5.16.

0

0,1

0,2

0,3

0,4

0,5

0,6

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8

Y-

Ver

tica

l Dis

tan

ce (

m)


Line-1 Before After

93

Figure 5.15: Breakwater profiles for rubble mound breakwater, Wave number 10 Set

2

Figure 5.16: Damage of rubble mound breakwater after wave number 10, Set 2

Wave Number 12

Wave number 12 was applied in the tests as three sets of 500 waves, 1000 waves and

1000 waves again since the two of the breakwaters did not fail at the end of the sets.

Wave number 12 had a different characteristic behaving like an impact wave but on

the rubble mound breakwater but like an overflowing wave on the caisson type

breakwater. On the rubble mound breakwater, it hit on the stones of the armor layer

0

0,1

0,2

0,3

0,4

0,5

0,6

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8

Y-

Ver

tica

l Dis

tan

ce (

m)


Line-2 Before After

94

rather than the crown wall of rubble mound breakwater. Both of the structures had

minor damage after three sets which were applied cumulatively. Breakwater profiles

measured before and after each set and photos are given in Appendix C.

Wave Number 15

The wave number 15 had a characteristic of an impact wave hitting on the vertical

walls of caisson type breakwater and the crown walls of the rubble mound breakwater.

In the tests, both of the breakwaters were totally failed. The caisson type breakwater

started to be damaged at the first wave, had major damage at the 3rd wave and totally

failed by the 4th wave.

The rubble mound breakwater started to get damage at the second wave, had major

damage at the 6th wave and totally failed by the 11th wave. The breakwater profiles and

the images of damaged breakwaters are given in Appendix C.

Wave Number 17

The wave number 17 had a characteristic of an overflowing wave. In the tests, both of

the breakwaters were totally failed. The caisson type breakwater started to be damaged

at the 3rd wave, had major damage at the 10th wave and totally failed by the 11th wave.

The rubble mound breakwater started to get damage at the 4th wave, had major damage

at the 7th wave and totally failed by the 10th wave. The breakwater profiles and the

images of damaged breakwaters are given in Appendix C.

Wave Number 18

The wave number 18 had a characteristic of an impact wave hitting on the vertical

walls of caisson type breakwater but hitting on the stones of the armor layer of rubble

mound breakwater. In the tests, caisson type breakwater failed under the impact of the

wave but rubble mound breakwater did not fail.

Caisson type breakwater started to be damaged at the 4th wave, had major damage at

the 6th wave and totally failed by the 10th wave.

95

The rubble mound breakwater had some damage after many waves but remained

without failure after more than 100 waves. The breakwater profiles and the images of

damaged breakwaters are given in Appendix C.

Key findings on damage analysis

The relevant failure mode of caisson type breakwater in the cases which the breakwater

was failed under wave action was overturning of the vertical walls and movement of

the walls towards onshore. An example of this failure mode at the instant of

overturning of the vertical walls is given in Figure 5.17. The slopes of the rubble base

were stable in most of the experiments having minor damage unless the the vertical

walls move and wash away the stones.

Figure 5.17: Overturning of vertical walls under wave action

The major failure modes in rubble mound breakwater were overturning and sliding of

the crown walls. In case of impact waves, the crown walls were overturned and moved

towards the harbor slope leading the slope instability of the armor layers and total

failure of the structure. In case of overflowing waves, the crown walls slided

subsequently washing away the stones of the armor layer towards onshore. Then, the

slope stability was lost and the structure was totally failed. An example is given in

Figure 5.18.

96

Figure 5.18: Sliding of the crown walls of the rubble mound breakwater under wave

action

The seaside and harbor slopes of the rubble mound breakwater remained almost stable

unless the crown walls fail. However, the scour on the harbor slope which occurred

due to wave overtopping leaded the failure of the crown walls. In case of crown wall

failure, the upper part of the seaside armor layer stones washed away towards the

harbor slope together with the crown walls. Therefore, it can be concluded that the

crown wall stability plays a key role on slope stability and hence on the overall stability

of the breakwater but the armour layer at the harbour side of the breakwater is also

important for crown wall stability. Crown wall failure and slope instability are

interactive processes which one may cause the other subsequently.

A summary of detailed breakwater damage under related wave actions is provided in

Table 5.3.

97

Table 5.3: Overview of detailed breakwater damage under related wave actions

Test No Structure

Breakwater Damage

Seaside Slope Harbor slope Crown walls–

Vertical walls Damage

10-1

Rubble

mound

armor, filter and core

layer removed over

1/3 of slope length,

layers mixed

armour layer washed

away

Crown walls slided,

washed away

towards harbor slope

Total

failure

Caisson

Type

Few stones in filter

layer moved towards

onshore together with

concrete blocks

Some stones moved

towards onshore

together with

concrete blocks

Three elements of

concrete blocks were

overturned and

moved towards

onshore

Total

failure

10-2

Rubble

mound


layer removed over


layers mixed

armour layer washed

away

Crown walls slided,

washed away

towards harbor slope

Total

failure

Caisson

Type

Few stones in filter

layer moved towards

onshore together with

concrete blocks

Some stones moved

towards onshore

together with

concrete blocks

Middle element first

overturned and

prevented other two

concrete blocks from

overturning

Total

failure

Rubble

mound

Few stones of armor

layer moved within

seaside slope

Few stones in armor

layer moved within

slope downwards

Not moved Minor

damage

12-1 Caisson

Type

Few stones in first

layer moved within

slope

Few stones in first

layer moved within

slope

Not moved Minor

damage

12-2

Rubble

mound

Few stones of armor

layer moved within

seaside slope

Few stones in armor

layer moved within

slope downwards

Slightly moved in

flow direction

Minor

damage

Caisson

Type

Few stones in first

layer moved within

slope

Few stones in first

layer moved within

slope

Not moved Minor

damage

12-3

Rubble

mound

Few stones of armor

layer moved within

seaside slope

Few stones in armor

layer moved within

slope downwards

Slightly moved in

flow direction

Minor

damage

Caisson

Type

Few stones in first

layer moved within

slope

Few stones in first

layer moved within

slope

Not moved Minor

damage

17-1

Rubble

mound

Armor layer and

filter layer stones

moved towarsd

harbor slope

Armor layer washed

away together with

stones of seaside

slope and crown

walls

Crown walls slided

and washed away

Total

failure

Caisson

Type

Few stones in first

layer moved within

slope

Few stones in first

layer moved within

slope

Three concrete

elements overturned

and moved in flow

direction

Total

failure

17-2 Rubble

mound

Armor layer and

filter layer stones

Armor layer washed

away together with

stones of seaside

Crown walls slided

and washed away

Total

failure

98

Test No Structure

Breakwater Damage



moved towarsd

harbor slope

slope and crown

walls

Caisson

Type

Few stones in first

layer moved within

slope

Few stones in first

layer moved within

slope

Middle and left

concrete elements

overturned and

prevented right

element from

overturning

Total

failure

18-1

Rubble

mound

Some stones moved

upwards with the

slope and

accumulated in front

of the crown wall

Many stones in

armor layer moved

within slope and

accumulated at

harbor side toe

Middle element

slided other elements

slightly moved in

flow direction

Major

damage

Caisson

Type

Few stones in first

layer moved within

slope

Few stones moved

within slope

Middle and right

concrete blocks

overturned and

moved in flow

direction, left

element was stuck

Total

failure

18-2

Rubble

mound

Some stones moved

upwards with the

slope and


of the crown wall / 1

stone moved to habor

slope

Many stones in

armor layer moved

within slope and

accumulated at

harbor side toe

Crown walls slightly

moved in flow

direction and slightly

overturned

Major

Damage

Caisson

Type

Few stones in first

layer moved within

slope

Few stones moved

within slope

Middle and right

concrete blocks

overturned and

moved in flow

direction, left

element was stuck

Total

Failure

9-1

Rubble

mound


layer removed over


layers mixed

Armor layer washed

away together with

stones of seaside

slope and crown

walls

Crown walls

overturned and

moved towards

harbor slope

Total

Failure

Caisson

Type

Few stones in first

layer moved within

slope

Some stones in first

layer moved towards

onshore by concrete

blocks

All three elements

were overturned and

moved towards

onshore

Total

Failure

9-2

Rubble

mound


layer removed over


layers mixed

Armor layer washed

away together with

stones of seaside

slope and crown

walls

Crown walls

overturned and

moved towards

harbor slope

Total

Failure

Caisson

Type

Few stones in first

layer moved within

slope

Few stones in first

layer moved towards

onshore

All three elements

were overturned

Total

Failure

99

Test No Structure

Breakwater Damage



15-1

Rubble

mound


layer removed over


layers mixed

Armor layer washed

away together with

stones of seaside

slope and crown

walls / no slope left

Crown walls

overturned and

washed away

Total

Failure

Caisson

Type

Few stones in first

layer moved within

slope towards harbor

slope

Many stones in first

layer moved towards

onshore together

with moving

concrete blocks

Concrete blocks

were overturned and

washed away

Total

Failure

15-2

Rubble

mound

Some stones moved

upwards with the

slope and


of the crown wall /

slope unstable

Armor layer washed

away together with

stones of seaside

slope and crown

walls / no slope left

Crown walls

intended to overturn

and wash away but

were stuck between

side walls of the

flume

Total

Failure

Caisson

Type

Few stones in first

layer moved within

slope towards harbor

slope

Few stones in first

layer moved towards

onshore

All three elements

were overturned

Total

Failure

General Discussion

The damage behavior and failure of the two breakwaters are evaluated based on the

results presented above. Applied waves are classified according to five parameters for

an overall evaluation:

- Wave steepness (H/L)

- Ratio of wave height to water depth (H/d)

- Wave characteristics (impact wave or overflowing wave)

- Wave asymmetry and skewness

- Overtopping height

The properties of the applied waves in the experiments based on these parameters are

given in Table 5.4.

100

Wav

e N

oFa

il (X

)

Stee

pn

ess

(H/L

)H

/dA

SW

ave

Ch

arac

teri

stic

Ove

rto

p

97

0.02

580.

986

6Im

pact

to

cro

wn

wal

ls4

1012

0.02

140.

672

5O

verf

low

5

1299

90.

0238

0.47

32

Impa

ct t

o a

rmo

r st

one

s1

1513

0.01

970.

961

1Im

pact

to

cro

wn

wal

ls2

1710

0.02

950.

884

4O

verf

low

6

1899

90.

0363

0.86

53

Impa

ct t

o a

rmo

r st

one

s3

93

0.02

810.

736

6Im

pact

14

1013

0.01

780.

372

5O

verf

low

4

1299

90.

0244

0.30

32

Ove

rflo

w1

154

0.01

750.

571

1Im

pact

15

1711

0.02

570.

504

4O

verf

low

12

1810

0.02

640.

425

3Im

pact

13

A: S:

Fail

(X):

Stru

ctur

e fa

ilure

at

the

tim

e o

f Xt

h co

min

g w

ave

999:

Rel

ativ

e

Eval

uati

on

Mea

sure

m

ent

(cm

)

Rub

ble

Mo

und

Cai

sso

n

Asy

mm

etry

Skew

ness

No

fai

lure

Tab

le 5

.4:

Obse

rved

pro

per

ties

of

appli

ed w

aves

101

Based on the parameters given above and observed properties of the applied waves the

following discussions are carried out:

1) Caisson type vs. rubble mound breakwater comparison:

Two breakwaters were similar in cases of wave no 10, 12 and 17 whereas different in

cases of Wave no 9, 15 and 18 in terms of damage behavior (fail or not fail) and failure

times (at which wave the structure failed). In cases of wave 9, 15 and 18 which were

all impact waves, caisson type breakwater failed long before the rubble mound

breakwater. In cases of impact waves, the armor stones of the rubble mound

breakwater absorbed some of the wave energy but the vertical walls in caisson type

breakwater were directly exposed to the impact. Therefore, the caisson type

breakwater was much more unstable in these cases. Cases of wave no 10, 12 and 17

were overflowing waves and the breakwaters failed at similar times in these cases.

2) Rubble mound breakwater damage behavior

When the wave impact was to the armor stones rather than to the crown walls (cases

wave number 12 and 18), the rubble mound breakwater did not fail.

When wave impact was to the crown walls (cases wave number 9 and 15), the

breakwater failed at 7th and 13th waves respectively. This time difference is caused by

steepness and wave shape parameters since H/d and overtopping height are close to

each other in these two cases. It can be deduced that as the wave steepness increases

and wave shape gets non-sinusiodal, the breakwater gets more damage and fails earlier

in case of impact waves.

When wave characteristic was overflow (cases wave number 10 and 17), the

breakwater fails at 12th and 10th waves respectively. The difference arises from H/d

ratio.

102

3) Caisson type breakwater damage behavior

When wave impact occurred (in cases of wave number 9, 15 and 18), the breakwater

failed at 3rd, 4th, and 10th waves respectively. Failure time was similar in cases of wave

number 9 and 15 although the steepness, H/d ratios and wave shape parameters were

different in these two cases (Table 5.4). This is most probably due to the fact that the

wave impacted directly to the blocks and overflow heights were high and similar in

these cases. What makes the case of wave number 18 different from these two cases is

the H/d ratio which was less than the other two cases.

When overflow occurred (in cases of wave number 10, 12 and 17), the breakwater

failed at 13th wave, did not fail and failed at 11th waves respectively. The structure did

not fail in case of wave number 12 because the overtopping height and H/d ratio were

much less than the other two cases whereas the other parameters were similar and

although the steepness of wave number 12 was higher.

It can be concluded that the wave height and hence the overtopping height is a very

important parameter in caisson type breakwaters in both impact and overflowing

waves.

It should be noted that these overall discussios on the physical phenomenon of the

structures are carried out according to the measurements as well as the visual

observations during the experiments and from video recordings.

5.2 Numerical Modelling Results and Pressure Measurement

Comparison

Pressure measurements along the front and bottom surfaces of the vertical wall in

caisson type breakwater were carried out for two wave conditions, wave number 9 and

10. One impact wave and one overflowing wave characteristics were selected from the

applied waves. Pressure measurement experiments were repeated two times for each

case. The measurements correspond to pressure acting on the wall at the time of impact

103

of second wave on the wall. In other words, measured pressures are related to only the

second wave of the wave train.

On the other hand, the caisson type breakwater was modeled in IH2VOF and pressure

results were obtained from the numerical model. The initial time step (dt) was defined

as 0.05s in the simulations. The sampling frequency was defined as 30Hz which

corresponds to 0.033s of time step (∆t) but the ∆t values were changed and adjusted

around 0.03s by the model for each time step for convergence. The simulation length

was 35s.

The two wave conditions were applied in the computational tool, IH-2VOF, by using

the dynamic paddle option which represents a piston type wave maker in wave

generation in laboratory experiments. After the simulations were carried out, the

surface water profiles obtained from IH-2VOF and from the laboratory measurements

were overlapped for offshore (WG8) and overtopping gauges (WG2). The offshore

gauge is the wave gauge which was placed in front of the wave paddle and the

overtopping gauge is the one placed onto the front surface of the vertical walls (see

Figure 3.18 and 3.20). The results are given in Figure 5.19 and 5.20 for wave number

9 and in Figure 5.21 and 5.22 for wave number 10. These wave data are compared to

validate that the proper wave conditions were generated in the IH-2VOF model. After

the validation of the wave data, the obtained pressure data from IH-2VOF and from

the measurements were analysed.

104

Figure 5.19: Water surface profiles for wave number 9, WG8


105



106

Kortenhaus et al. (1999) presented a paremeter map including geometric and wave

parameters in combination to identify the wave impact loading which is given in

Figure 5.23. According to this parameter map, our structure stays on the ‘’composite

breakwater’’ classification and ‘’low-mound breakwater’’ side according to the ‘’hb*’’

definition which is 0.4 in our case. In this classification, our case wave number 9 is in

impact loads category and wave number 10 is in quasi-standing loading. This

classification is consistent with the pressure graphs obtained from analysis of our

measured data which are given in Figure 5.24 and 5.26.

Figure 5.23: Wave loading identification, PROVERBS parameter map (Kortenhaus

et al., 1999)

107


The dynamic and quasi-static parts of pressure time seri of wave number 9 is specified

according to the idealized time history of an impact pressure on vertical walls which

is given in Bullock et al. (2007). The definitional sketch of is given in Figure 5.25.

Figure 5.25: Definition sketch of an idealized impact wave pressure time history

108


In order to obtain the maximum dynamic pressures along the front and bottom surfaces

of the vertical walls of caisson type breakwater, the maximum pressure values of

second incident waves are obtained from the measurements. The same procedure is

also applied to the IH-2VOF pressure data.

Figure 5.27 presents the analysis results of pressure measurement data compared with

IH-2VOF simulation data and two prediction methods of Goda (1974) and Shore

Protection Manual (1984) based on Minikin (1963). In this graph, pointed data

represent the measured local maximum dynamic pressure values for wave number 9

which is classified as impact loading. Goda’s (1974) method is one of the most well-

accepted pressure formulas for vertical and composite walls but the pressure

measurements are slightly different from Goda’s distribution since it does not give

accurate estimates of wave pressures for impact wave loading which is our case in

wave number 9. Minikin’s (1963) method is one of the prediction methods which

account for impact waves however it has been cited erroneously in many publications

(Allsop et al., 1996). The Shore Protection Manual (1984) version of Minikin’s

approach is included in the graph (Figure 5.27) but it gives substantially greater

109

pressures as also quoted so in literature about prediction of impact forces (Allsop et

al., 1996).


pressure distributions for wave number 9

Figure 5.28 presents the dynamic pressure distributions obtained from IH-2VOF and

Goda’s (1974) prediction method with the quasi-static part of impact wave pressures

obtained from measurements for wave number 9. As can be seen from the graph, IH-

2VOF gives very close results with the measurements for the upper part of still water

level and gives similar results for the lower part. It is obvious that IH-2VOF is far from

being able to give compatible results with measurements in case of impact wave

pressures (Figure 5.28). However, the pressure distribution obtained fron IH-2VOF is

similar with pressure measurement data especially for the upper part of still water level

in case of quasi-static pressure.

-25

-20

-15

-10

-5

0

0,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0 8,0 9,0

Y -

Ver

tica

l Dis

tan

ce (

cm)

X - Maximum Dynamic Pressure (kPa)

Wave No 9Horizontal Pressure

IH2VOF

Goda (1974)

Measurement

Measurement-Trend

SPM (1984) - Minikin (1963)

110

Figure 5.28: Local maximum quasi-static pressures (point data) and instantaneous


Figure 5.29 presents the uplift pressures obtained from the measurements, IH-2VOF

simulation and Goda’s (1974) prediction method. The measurement data and Goda’s

formula seem consistent but IH-2VOF simulation results depart from these.

-25

-22,5

-20

-17,5

-15

-12,5

-10

-7,5

-5

-2,5

0

0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 2,2 2,4 2,6 2,8 3,0

Y -

Ver

tica

l Dis

tan

ce (

cm)



IH2VOF

Goda (1974)

Measurement

Measurement-Trend

111



Figure 5.30 presents the analysis results of pressure measurement data compared with

IH-2VOF simulation data and Goda’s (1974) prediction method. In the graph, full

point data represent the pressure measurements for wave number 10 which are taken

as the maximum values at the second incident wave. Wave number 10 is classified as

quasi-static loading and the results are almost consistent with Goda’s (1974) prediction

method which is more applicable for pressure estimation of quasi-standing waves. In

this case, there are some apocryphal data which are represented by empty points and

the trend line (pressure distribution) of the measured data is drawn without taking into

consideration of these data. These suspicious data on pressure measurements occurred

when the pressure transducers were placed 7cm above the still water level and, 3.5cm,

6.5cm and 9.5cm below the still water level. The further investigation of the suspicios

pressure measurement data shows that there may be some physical phenomenon for

this case which can not be explained with the measurements in this study. The data

show the same inconsistency when the pressure sensors were placed at the same levels

in both of the two repetition of the experiments. Therefore, this situation is most

0

0,5

1

1,5

2

2,5

3

0 0,05 0,1 0,15 0,2 0,25

Max

imu

m D

ynam

ic P

ress

ure

(kP

a)

X - Horizontal Distance Along Bottom Surface (m)

Measurement

Measurement-Trend

IH2VOF

Goda (1974)

112

probably related to a physical phenomenon occurring during the wave number 10

attack rather than an error of the transducers. One should note that it may be a further

study and discussion point.



Figure 5.31 presents the uplift pressures obtained from the measurements, IH-2VOF

simulation and Goda’s (1974) prediction method for wave number 10. The

measurement data and Goda’s formula seem consistent but IH-2VOF simulation

results again depart from these in terms of uplift pressure distribution in this case.

-25

-20

-15

-10

-5

0

0 0,5 1 1,5 2 2,5

Y -

Ver

tica

l Dis

tan

ce (

cm)



IH2VOF

Measurement

Measurement-Trend

Goda (1974)

113



0

0,5

1

1,5

2

2,5

0 0,05 0,1 0,15 0,2M

axim

um

Dyn

amic

Pre

ssu

re (

kPa)

X - Horizontal Distance Along Bottom Surface (m)

Measurement

Measurement-Trend

IH2VOF

Goda (1974)

115

CHAPTER 6

6 CONCLUSION AND FUTURE RECOMMENDATIONS

In this study, laboratory experiments on the performance of the rubble mound and

caisson type (vertical wall) breakwaters under extreme waves with the focus on

induced breakwater damage and failure phenomenon are performed. In addition, wave

pressure measurements acting on the vertical wall breakwater were carried out in the

experiments since damage and failure phenomenon are directly related with the forces

and pressures acting on the structures under wave action. Furthermore, the vertical

wall breakwater was modeled by a computational tool, IH-2VOF, to simulate two

cases of the experiments and obtain the pressure data from the software. Finally, the

pressure measurements are compared with the numerical model results and prediction

methods to explain the meaning of the results and to make an overall conclusion.

The conclusions of this study are summarized as the following:

- Physical model experiments are essential for investigation of wave induced

damage on coastal structures since it is not always feasible to observe the

structures in the field. Also, field observations are carried out mostly after the

damage occurs. However, like in the case of rubble mound breakwaters which

are observed in this study, one failure mode triggers another failure mode such

as sliding of the crown walls leads slope instability but also the scour in the

breakwater slope leads the crown wall movement. Therefore, the necessity of

the observation of damage and failure moments arise to investigate failure

mechanisms of the structures in detail.

116

- It is important to observe the wave behavior while acting on the structure

visually since it is not always possible to explain it by formulas and also it

provides a great perspective about the causing factor of the damage. In the

experiments, it is found out that two types of wave behavior which are

classified as impact wave and overflowing waves differ while acting on the

structure and this difference results in different damage behavior and different

times of failure of the structures.

- It is a complex process to evaluate the breakwater damage under different

waves since several wave parameters such as wave height, wave steepness,

overtopping height, wave asymmetry and skewness and wave behavior while

acting on the structure, should be taken into consideration. In general, it can be

concluded that in case of impact waves, the rubble mound breakwater was

more resilient since caisson type breakwater failed long before the rubble

mound breakwater in these cases. Also, wave height and hence the overtopping

height is a very important parameter in caisson type breakwaters in both impact

and overflowing waves.

- Profile measurements which are conducted before and after experiments to

record the breakwater damage need to be taken along more than two lines over

the cross-section in small-scale experiments. Because, as experienced in the

physical model experiments, two-lines profile measurement may not always

represent the overall breakwater damage like in case wave number 10. (See

Figure 5.11 and Figure 5.12). Therefore, as a further study, image processing,

which is a method of 3D modelling of an object in digital form, to obtain

breakwater damage will be applied to the physical model experiments and the

damage will also be analyzed by this method.

- Numerical model, IH-2VOF, give low pressure values for maximum dynamic

pressure on the front surface of the vertical wall breakwater compared to the

measurements and prediction methods for both two different wave conditions.

117

However, the model results depart from the measurements much more in case

of impact pressures. This is probably due to the fact that the model is not able

to resolve the physical phenomenon occurring at the insant of maximum impact

pressure acting on the structures. The mesh grid size is a critical factor on this

issue and therefore it may be a future study to increase the mesh fineness to

obtain more accurate results from the model.

- In order to increase the accuracy of numerical modelling part of this study,

some future studies need to be carried out for the sensitivity analysis of the

numerical model by simulations with different mesh size and time step values

especially in case of simulating impact wave loading conditions.

- For quasi-static wave condition, the vertical distribution of measured dynamic

pressures on the front surface of the caisson type breakwater conformed with

the simple distribution suggested by Goda but differed dramatically in case of

impact loading.

- Impact wave conditions result in very high pressures near to the still water

level, and these pressures can be very severe for vertical wall breakwaters.

Therefore, these conditions should definitely be taken into consideration in the

design of vertical wall breakwaters.

- Two types of breakwaters, rubble mound and caisson type breakwaters, were

designed according to wind waves but tested under extreme waves. Both of the

structures failed under most of the applied waves. Therefore, possible extreme

wave conditions should be considered in the design of breakwaters in order to

avoid any loss which may be caused by the possible extreme events.

119

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8 APPENDICES

A) IH2VOF Model Geometry - Coordinates of Element Indices

Table 8.1: Coordinates of Element Indices of Caisson Breakwater Model Geometry

in IH-2VOF

Element Vertices X Coordinate Y Coordinate

Bathymetry

1 17.103 -0.001

2 18.103 0.102

3 20.473 0.102

4 20.7362 -0.001

Caisson – Vert. Wall

1 19.283 0.182

2 19.283 0.482

3 19.313 0.482

4 19.313 0.442

5 19.473 0.442

6 19.473 0.182

Core Layer

1 18.763 0.102

2 19.083 0.182

3 19.673 0.182

4 19.993 0.102

Filter Layer-1

1 18.603 0.102

2 19.083 0.222

3 19.283 0.222

4 19.283 0.182

5 19.083 0.182

6 18.763 0.102

Filter Layer-2

1 19.473 0.182

2 19.473 0.222

3 19.673 0.222

4 20.153 0.102

5 19.993 0.102

6 19.673 0.182

Water

1 -0.005 -0.005

2 -0.005 0.402

3 22.305 0.402

4 22.305 -0.005

130

B) Breakwater Profile Measurements and Photos

Wave Number 12

Figure 8.1: Breakwater profile of caisson type breakwater – Line 1


0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8

Y -

Ver

tica

l Dis

tan

ce (

m)


Line 1Before

After first 500

After first 1000

After sec 1000

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8

Y=

Ver

tica

l Dis

tan

ce (

m)

X = Horizontal Distance (m)

Line 2Before

After first 500

After first 1000

After sec 1000

131

Figure 8.3: Breakwater profile of rubble mound breakwater – Line 1


0

0,1

0,2

0,3

0,4

0,5

0,6

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6

Y -

Ver

tica

l Dis

tan

ce (

m)


Line 1 Before

After first 500

After first 1000

After sec 1000

0

0,1

0,2

0,3

0,4

0,5

0,6

0 20 40 60 80 100 120 140 160

Y-

Ver

tica

l Dis

tan

ce (

m)


Line 2 Before

After first 500

After first 1000

After sec 1000

132

Figure 8.5: View of caisson type breakwater after Wave Number 12

Figure 8.6: View of rubble mound breakwater after Wave Number 12

Wave Number 15

Set-2


0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8

Y-

Ver

tica

l Dis

tan

ce (

m)


Line 1Before After

133



0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8

Y-

Ver

tica

l Dis

tan

ce (

m)


Line 2 Before After

0

0,1

0,2

0,3

0,4

0,5

0,6

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6

Y-

Ver

tica

l Dis

tan

ce (

m)


Line 1 Before After

134


Figure 8.11: View of caisson type breakwater after Wave Number 15, Set-2

Figure 8.12: View of rubble mound breakwater after Wave Number 15, Set-2

0

0,1

0,2

0,3

0,4

0,5

0,6

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6

Y-

Ver

tica

l Dis

tan

ce (

m)


Line 2 Before After

135

Wave Number 17

Set-1



0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8

Y-

Ver

tica

l Dis

tan

ce (

m)


Line 1 Before After

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8

Y-

Ver

tica

l Dis

tan

ce (

m)


Line 2 Before After

136



0

0,1

0,2

0,3

0,4

0,5

0,6

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8

Y-

Ver

tica

l DIs

tan

ce (

m)


Line 1Before After

0

0,1

0,2

0,3

0,4

0,5

0,6

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8

Y-

Ver

tica

l Dis

tan

ce (

m)


Line 2Before After

137



Set-2

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8

Y-

Ver

tica

l Dis

tan

ce (

m)


Line 1 Before After

138




0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8

Y-

Ver

tica

l Dis

tan

ce (

m)


Line 2 Before After

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8

Y-

Ver

tica

l Dis

tan

ce (

m)


Line 1 Before After

139




0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8

Y-

Ver

tica

l Dis

tan

ce (

m)


Line 2 Before After

140

Wave Number 18

Set-1



0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8

Y-

Ver

tica

l Dis

tan

ce (

m)


Line 1 Before After

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8

Y-

Ver

tica

l Dis

tan

ce (

m)


Line 2Before After

141



0

0,1

0,2

0,3

0,4

0,5

0,6

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6

Y-

Ver

tica

l Dis

tan

ce (

m)


Line 1Before After

0

0,1

0,2

0,3

0,4

0,5

0,6

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6

Y-

Ver

tica

l Dis

tan

ce (

m)


Line 2Before After

142



Set-2


0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8

Y-

Ver

tica

l Dis

tan

ce (

m)


Line 1Before After

143



0

0,05

0,1

0,15

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0,45

0,5

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8

Y-

Ver

tica

l Dis

tan

ce (

m)


Line 2 Before After

0

0,1

0,2

0,3

0,4

0,5

0,6

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6

Y-

Ver

tica

l Dis

tan

ce (

m)


Line 1Before After

144




0

0,1

0,2

0,3

0,4

0,5

0,6

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6

Y-

Ver

tica

l Dis

tan

ce (

m)


Line 2Before After

study of rubble mound and caisson type …etd.lib.metu.edu.tr/upload/12619827/index.pdf · ·...

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