Hydraulic stability of Cubipod armour units in Breaking conditions
Lien Vanhoutte
Promotor: Prof. Josep Medina (UPV Valencia) Co-Promotor: . Prof. dr. ir. Julien De Rouck
Masterthesis to obtain the degree: Master of Science in Civil Engineering
Laboratory of Ports and Coasts, Polytechnic University of Valencia Departement of Civil Engineering, Ghent University Academic year 2008-1009
i
Preface
I would like to thank my tutor of this project Prof. Medina for giving me the great opportu- nity to make my nal year project at the Laboratory for Ports and Coasts of the Polytechnic University of Valencia, and for his guidance throughout the project.
Special thanks also to Prof. De Rouck as my Erasmus-coordinator and co-tutor of this thesis for providing the possibility of this abroad experience.
Deep gratitude goes to Guille, for his guidance throughout the project, for sharing his ex- perience, for helping me with every single doubt, for encouraging me and helping me out in the stressful moments. A warm thanks as well to Jorge, Vicente, Kike, Mireille, Steven, César and Pepe, for providing a very nice working space in the laboratory.
Finally I want to thank my parents, my sisters, friends, and at mates in particular, for their support and many hours of listening during this thesis.
COPYRIGHTS
The author grants the permission for making this thesis available for consultation and for copying parts of this thesis for personal use. Any other use is subject to the limitations of the copyright, speci cally with regards to the obligation of referencing explicitly to this thesis when quoting obtained results.
1st of June 2009, Lien Vanhoutte ii
Overview
Hydraulic stability of Cubipod armour units in breaking conditions
Author: Lien Vanhoutte
Master thesis to obtain the degree of Master of Civil Engineering Academic year 2008-2009
Tutors: Prof. Josep R. Medina, Laboratory of Ports and Coasts, Polytechnic University of Valencia Prof. Julien De Rouck, Department of Civil Engineering, Ghent University
Summary In this report, the study of the new armour unit, Cubipod, designed by the Laboratory of Ports and Coastas of the Politecnic University of Valencia, is described. The general stability of mound breakwaters are discussed and an overview of dierent existing armour elements is given. Further, the wave height distribution in shallow water is analysed theoretically and compared with the obtained results. An experimental study of the Cubipod armour unit is carried out on a physical scaled mound breakwater model in breaking conditions. Results on re ection and damage progression are presented and compared with previous similar tests in deepwater conditions. A rst estimation of the hydraulic stability coe cient of the Cubipod in breaking conditions is proposed. The results show that the Cubipod has low re ection and high hydraulic stability.
Keywords: Cubipod - armour unit - mound breakwater - hydraulic stability - breaking conditions HYDRAULIC STABILITY OF CUBIPODARMOUR UNITSINBREAKINGCONDITIONS L. Vanhoutte1 Supervisor(s): J.R. Medina2, J. De Rouck3 1 Masterthesis student, Faculty of Engineering, Ghent University, Belgium 2 Professor, Lab. of Ports and Coasts, Polytechnic University of Valencia, Spain 3 Professor, Faculty of Engineering, Ghent University, Belgium
Abstract—In this Masterthesis an experimental study of the Cubipod ar- The Cubipod armour unit is designed to benefit from the ad- mour unit was carried out on a physical model breakwater in shallow water. vantages of the traditional cube, but to correct the drawbacks. The Cubipod is a new armour unit, designed by the Laboratory of Ports and Coasts of the Universidad Politcnica de Valencia. As the wave height is an Therefore, the design of the unit is based on the cube in order to important value when designing mound breakwaters, theories estimating obtain his robustness. The protuberances of the Cubipod avoid the maximum wave height in breaking conditions were studied and com- face-to-face settlement and increase the friction with the filter pared with the measured results in the Laboratory. Results on reflection layer as can be seen in figure 1. They avoid sliding of the ar- and damage progression were presented and compared with previous sim- ilar tests in deepwater conditions. An estimation of the hydraulic stability mour elements and thus, Heterogeneous Packing and loss of el- KD coefficient of the Cubipod in breaking conditions was proposed using ements above the still water level is reduced. All this indicates a the Virtual Net Method[2]. The results show that the Cubipod has low re- higher hydraulic stability of Cubipods in comparison with cube flection and a high hydraulic stability. elements, which was proved in earlier executed tests [3]. Keywords—Cubipod - armour unit - mound breakwater - hydraulic sta- bility - breaking conditions
I.INTRODUCTION Mound breakwaters play an important role in the protection of harbours. They have many failure modes, but the most im- portant one is the loss of hydraulic stability of the armour layer under wave attack. This can be caused by direct extraction of armour units, or by excessive settlement causing Heterogeneous Packing of the armour layer as described by Gomez-Marton & Medina [2]. Generally, mound breakwaters are placed in shallow water Fig. 1. The new armour unit: the Cubipod and thus subjected to breaking conditions. An important fac- tor influencing the hydraulic stability is the maximum incident III.EXPERIMENTS wave height. Hydraulic stability of armour layers has been in- tensively studied in literature and several formulae have been Regular experiments on five different physical model break- proposed for predicting armour damage. The first models were waters were carried out in the 2D wave flume of the laboratory only valid for stationary conditions. In 1988, Van der Meer [8] of Ports and Coasts in the Polytechnic University of Valencia. A proposed a first formula for irregular waves. Medina [7] pro- section with a double layer of Cubipods, one with a single layer posed a method applicable to nonstationary conditions, based of Cubipods, each with and without toe berm were considered. on an exponential model for individual waves of the storm. The Finally, experiments were carried out on a section consisting of most frequently cited armour stability formula was published by a cube layer covered by a Cubipod layer. Hudson in 1959[4] for regular waves, and later popularized for The unit weight of the Cubipods is 128g, and they have a 3 irregular waves by SPM using the equivalences H1/3 and H1/10 density of 2300kg/m . The water depth changes from 30cm to as representative of the wave height. 42 cm near the model. For every water depth different periods were considered, lancing waves with increasing wave height for II.ARMOURUNITS every period. The wave height was increased until breaking oc- Originally, harbours were built with wooden or stone con- cured. Registered wave heights were separated in incident and structions. The continuous growing of the harbours meant a reflected waves with the LASA V-method (Figueres & Medina need for higher stones and design of artificial concrete armour [1]), and the reflection coefficient was obtained as CR [%] = units was forced. Many different breakwater armour units ex- Hr/Hi. Damage progression was analysed visually, establish- ist, each with their own advantages and disadvantages. Their ing the damage levels Initiation of Damage, Iribarren Damage characteristics have an important influence on the hydraulic sta- and Destruction, as well as quantitatively, using the Virtual Net bility of the mound breakwater and explains why improvement Method proposed by Gmez-Martn & Medina [2], which allows and development of armour units is still an important subject of to measure also the failure mode of Heterogeneous Packing, and research. not only extraction of armour units. IV. RESULTS for a double layer of Cubipods with toe berm and KD=23 for a single layer were found. K =18 was found for a combined A. Breaking wave height D armour layer with cubes and Cubipods. Comparison between The incident wave height is an important factor influencing the damage progression in deepwater conditions and in shallow the design of coastal structures. An overly conservative estima- water shows us that KD in shallow water is less than in deepwa- tion of this value can greatly increase costs and make projects ter conditions. Waves with higher energy reach the breakwater, uneconomical, whereas underestimation could result in struc- which means that the damage will initiate earlier than in deep- tural failure or significant maintenance costs. A short study con- water conditions. In Fig. 3, the damage progression for the dif- cerning the maximum wave height in breaking conditions was ferent breakwater sections are shown, with D0,2 the linearized executed. dimensionless damage proposed by Medina [6] and indication Different theories exist to estimate this maximum value. of the Initiation of damage and Initiation of Iribarren damage. Many theories however, overestimate this value. Further, they suppose mostly that the energy from the broken waves is con- centrated in the breaking wave height, which means that all the broken waves have the breaking wave height in the surfing zone. This statement however didn’t correspond with the reality. The energy from the broken waves was distributed back over the smaller wave heights in the distribution. In Fig. 2 is the theory of Le Roux (2007) [6] shown to estimate the real wave heights. The estimation is similar to the measured values, however, he underestimates the breaking wave height and supposes a con- stant wave height after breaking, independent of the wave pe- riod.
Fig. 3. Linearised dimensionless equivalent damage as a function of dimension- less wave height for the different studied breakwater sections
V. CONCLUSION Calculating a mound breakwater in breaking conditions, spe- cial attention has to paid to the maximum wave height. Many existing theories overestimate this wave height, which can re- sult in uneconomical results. According to the executed tests, the Cubipod proves to have a high hydraulic stability in break- ing conditions and shows to be a very promising armour unit, with a simple and robust shape, an easy placement pattern and a high hydraulic stability compared with other armour units, also in breaking conditions.
VI.BIBLIOGRAPHY (1) Figueres, M. & Medina, J.R.: Estimation of incident and reflected waves Fig. 2. Graphic showing the theory of Le Roux (2007) [5] to estimate the wave using a fully nonlinear wave model. Proc. of the 29th Coast. Eng. Conf., pp. height, compared with the measured results in the Laboratory 594-603, 2004. (2) Gomez-Martin, M.E. & Medina, J.R.: Analisis de averas de diques en talud B. Hydraulic stability con manto principal formado por bloques de hormigon. VIII Jorn. Espaolas de Ing. de Costas y Puertos, 2005. The reflection coefficient differs between 10% and 30% for (3) Gomez-Martin, M.E. & Medina, J.R.: Cubipod concrete armour unit and Heterogeneous Packing. Proc of Coast. Structures, ASCE, 2007. kh > 1, 5 and increases until 50% for small kh values. For high (4) Hudson: Laboratory investigation of rubble mound breakwaters. J. Wtrwy., kh values, the type of armour layer has a big influence on the Port, Coast. and Oc. Division, 85(3):93-121, 1959. reflection coefficient and a single layer reflects less energy than (5) Le Roux, L.: A simple method to determine breaker height and depth for a double layer. For small values of kh, however this influence different deepwater height/length ratios and sea floor slopes. Coastal Engr. 54, 271-277, 2007. decreases and becomes nil. Reflections coefficients in shallow (6) Medina, J.R., Hudspeth, R.T. and Fassardi, C.: Breakwater armor damage water is lower than in deepwater conditions because the crest due to wave groups. J. Wtrwy., Port, Coast. and Oc. Engrg., ASCE, 120(2),pp. breaks and a lot of energy is dissipated which means less reflec- 179-198, 1994. (7) Medina, J.R.: Wave climate simulation and breakwater stability. Proc. of the tion. 25th Coast. Eng. Conf., ASCE, pp. 1789-1802, 1996. Damage analysis resulted in a higher hydraulic stability for (8) Van der Meer, J.W.: Suitable wave-height parameter for characterizing sections with toe berm, because there is no increase of porosity breakwater stability. J. of Waterw., Port, Coast. and Oc. Eng., ASCE, 114(1):66- at the bottom of the breakwater. Those are the common built 80, 1988. breakwater sections. Hydraulic stability coefficients of KD=28 Contents
Extended abstract ii
List of Figures ix
List of Tables xiii
1 Introduction 1
2 Stability of Mound Breakwaters 4
2.1 Introduction ...... 4
2.2 A Short History ...... 5
2.3 Analysis of the stability of a mound breakwater ...... 9
2.3.1 General stability of a mound breakwater ...... 9
2.3.2 Heterogeneous packing ...... 12
2.3.2.1 Introduction ...... 12
2.3.2.2 Heterogeneous packing ...... 12
2.3.3 Damage criteria ...... 14
2.4 Quantization of the stability ...... 16
2.4.1 Formula to calculate the stability of a mound breakwater ...... 16
v Contents vi
3 Armour Units 18
3.1 Introduction ...... 18
3.2 History: the armour units since the 50's ...... 19
3.3 Classi cation of armour units ...... 24
3.4 A new armour unit: The Cubipod ...... 28
3.4.1 Introduction ...... 28
3.4.2 Idea ...... 28
3.4.3 Concept ...... 29
4 Wave height in breaking conditions 33
4.1 Introduction ...... 33
4.2 The surf zone ...... 34
4.3 Types of breaking waves ...... 34
4.4 Models to estimate the wave height distribution ...... 36
4.5 Maximum wave height in breaking conditions ...... 38
5 Experimental setup 43
5.1 Introduction ...... 43
5.2 The Test Equipment ...... 43
5.2.1 2D Wave Flume ...... 44
5.2.2 Wave Generation System ...... 44
5.2.3 Wave Measurement ...... 47
5.2.4 Energy dissipation system ...... 48
5.2.5 Data Processing ...... 49
5.3 Calibration of the wave ume ...... 50
5.4 Experimental Design ...... 50 Contents vii
5.4.1 Physical characteristics of the studied model ...... 50
5.4.2 Construction of the physical model ...... 54
5.4.2.1 Preparation ...... 54
5.4.2.2 Control of the material characteristics ...... 56
5.4.2.3 Construction of the model ...... 59
5.4.2.4 Reconstruction of the model ...... 61
5.4.2.5 Placement of the sensors ...... 63
5.4.3 Experiments ...... 64
5.4.3.1 Realized experiments ...... 64
5.4.3.2 Experimental procedure ...... 65
5.4.4 Procedure to analyse the data ...... 66
5.4.4.1 Separating the incident and re ected waves: LASA V . . . . . 66
5.4.4.2 Analysis of the waves: LPCLAB 1.0...... 67
5.4.4.3 Analysis of the re ection coe cient ...... 69
5.4.4.4 Analysis of the damage progression ...... 70
6 Results 77
6.1 Introduction ...... 77
6.2 Calibration of the wave ume ...... 78
6.3 Interpretation of the theories calculating the maximum wave height ...... 80
6.4 Hydraulic stability of the mound breakwater ...... 85
6.4.1 Wave re ection ...... 85
6.4.1.1 The re ection coe cient in function of kh ...... 85
6.4.1.2 The re ection coe cient in function of Ir ...... 87
6.4.1.3 Comparing with the re ection coe cient in deepwater . . . . . 88 Contents viii
6.4.2 Damage analysis on the armour layer ...... 93
6.4.2.1 Introduction ...... 93
6.4.2.2 Qualitative analysis ...... 93
6.4.2.3 Quantitative analysis ...... 96
7 Conclusions 102
A Terminology of the experiments 104
B Wave ume 106
C Working of the AWACS 108
D Seperation of incident and re ected waves 113
E Calculation of the initial porosity 115
F Example of a test report 116
G Test results 119
Bibliography 130 List of Figures
2.1 Mound Breakwater failure modes de ned by Bruun ...... 10
2.2 The two most important failure modes by mound breakwaters: extraction of armour elements and heterogeneous packing. The classical view vs. the hetero- geneous packing view ...... 14
3.1 Face to face tting by cubes reducing the friction with the lter layer ...... 19
3.2 A selection of the existing concrete armour units ...... 23
3.3 A new armour element: the Cubipod ...... 28
3.4 Drop test results of Cubipods compared with cubes showing the lost weight . . 30
3.5 Penetration of the Cubipods in the armour layer ...... 30
3.6 The separating eect of the protuberances avoiding the face-to-face arrangement 31
3.7 Example of placement in a depository of Cubipods ...... 32
3.8 The casting system designed by SATO and the tongs for movement and man- ufacture ...... 32
4.1 Types of breaking waves ...... 36
4.2 Distribution of the wave heights by breaking, concerning that all the broken wave heights will have the breaking wave height in the sur ng zone ...... 37
4.3 Distribution of the breaking wave heights over the distribution of the unbroken waves (Goda [46]) ...... 42
ix List of Figures x
5.1 Longitudinal section of the 2D wave- ume ...... 44
5.2 Wave generation system in the LPC wave ume and setup of active wave ab- sorption system ...... 46
5.3 Wave gauges for wave measurement and Step-Gauge Run-up Measurement Sys- tem (S-GRMS) constructed by University of Ghent ...... 48
5.4 Wave energy dissipation system in the LPC wave ume ...... 49
5.5 Cross section of the studied models: 2 layers of Cubipods (C2), 1 layer of Cubipods (C1), 1 layer of cubes covered by one layer of Cubipods (CB) . . . . 52
5.6 Cross section of the studied models: 2 layers of Cubipods with toe berm (C2B), 1 layer of Cubipods with toe berm (C1B) ...... 53
5.7 Draw the cross section of the mound breakwater on the wall of the canal . . . . 55
5.8 The concrete grout to provide a rough surface for the model ...... 55
5.9 Grading curve for the core material ...... 57
5.10 Grading curve for the lter material ...... 58
5.11 Construction of the model: the core and the lter ...... 59
5.12 Construction proses of the armour layer ...... 62
5.13 Construction of the lter on the inner slope and a crest on the top of the mound breakwater after destruction of the core and the lter layer ...... 63
5.14 Parameter window of the LASA-V software ...... 67
5.15 Example of the separation of incident and re ected wave trains by LASA V . . 68
5.16 Parameter window of the LPCLab software ...... 69
5.17 Virtual net to measure the equivalent damage analysis and counting the units in AutoCAD for damage calculation ...... 73
5.18 Above: foto with the real net and the designed net in Photoshop (start of the tests with h=38). Under: foto without the real net and the pasted virtual net in Photoshop (end of the tests with h=38) ...... 74
5.19 Damage levels in the armour layer ...... 76 List of Figures xi
6.1 Results of the calibration of the wave ume ...... 79
6.2 Theoretical models to estimate the breaking wave height in function of the water depth, compared with the maximum measured wave height: Keulegan and Patterson (K&P), Collins for dierent slopes, SPM for dierent slopes and Weggel for a horizontal bottom ...... 82
6.3 Theoretical models to estimate the relation Hb/H0 in function of H0/L0, com- pared with the measured results: Komar and Gaughan (K&G), Sakai and Bat- tjes (S&B) ...... 83
6.4 Theorecal model of Le Roux to estimate the real water wave height for h=30cm, compared with the measured results ...... 84
6.5 The re ection coe cient (CR) in function of the dimensionless relative wave depth (kh) ...... 89
6.6 The re ection coe cient in function of the dimensionless relative water depth (kh): comparing single and double layers of Cubipods ...... 90
6.7 The re ection coe cient in function of the dimensionless relative water depth (kh): comparing a combined cube-cubipod layer with a double layer of Cubipods and a single layer of Cubipods ...... 91
6.8 The re ection coe cient (CR) in function of the number of Iribarren ...... 92
6.9 In uence of the presence of a toe berm on the hydraulic stability of a mound breakwater ...... 99
6.10 The linearised dimensionless damage as a function of a dimensionless height.
Above: the qualitative calculated KD's. Under: the quantitative calculated KD 100
6.11 Comparison a double Cubipod layer in breaking with non-breaking conditions, and with Quarrystone in breaking conditions. Dimensionless damage as a func- tion of dimensionless wave height ...... 101
B.1 Cross section of the 2D wave- ume of the Laboratory of Ports and Coasts of the Politecnic University of Valencia ...... 107
C.1 A detailed scheme of the working of the AWACS ...... 110 List of Figures xii
C.2 The steps to activate the control system ...... 110
C.3 Software to manage the AWACS. Above: the startscreen Under: the calibration of the AWACS ...... 111
C.4 Windows to realize the wave generation ...... 112
C.5 The program Multicard, for the aquisition of the datas ...... 112
E.1 Calculation of the initial porosity ...... 115
F.1 Example of a test report ...... 117
F.2 Example of a test report ...... 118 List of Tables
2.1 Hydraulic stability criteria for the armour layer of a mound breakwater as cited in[1] ...... 9
3.1 Classi cation of breakwater armour units by shape [34] ...... 24
3.2 Classi cation of armour units by shape, placement and stability factor...... 26
3.3 Classi cation of armour units by placement method and structural strength (Mijlemans, 2006) ...... 27
4.1 Type of breaking in function of the number of Iribarren ...... 35
5.1 Calculating the theoretic equivalent cube size and the theoretic volume of the Cubipods ...... 51
5.2 Theoretic characteristics of the used materials ...... 51
5.3 Grading characteristics of the core material ...... 57
5.4 Grading characteristics of the lter material ...... 58
5.5 Theoretical and measured characteristics of the Cubipods ...... 59
5.6 The real initial porosity in the dierent models [%] ...... 61
5.7 Position of the wave gauges and distance between them in the canal ...... 64
6.1 Incident wave heights producing the levels of damage: IDa and IIDa ...... 94
xiii Chapter 1
Introduction
Breakwaters are arti cial structures with the principal function of protecting a coastal area from excessive wave action, as there are ports, port facilities, coastal areas and coastal instal- lations. They reduce the transmitted energy by forcing the waves to break and re ect when hitting the breakwater.
Very often, an original harbour is protected in a natural area. As the economy keeps growing, the importance and application of the ports increase and a continuous port expansion is necessary. Growing ship draughts also oblige to expand the existing ports. Due to this facts, the natural protection can no longer resist the wave action and ports grow through sea side. Breakwaters start to play an important role.
Generally, breakwaters are divided in two dierent types: mound breakwaters and vertical breakwaters. The mound breakwaters are sloped structures, constructed with a low permeable core, covered by one or two lter layers and an armour layer. The dissipation of wave energy is mainly through absorbtion, but also re ection plays an important role. A principal design objective is to determine the size and layout of the components of the cross-section. Designing and constructing a stable structure with acceptable energy absorbing characteristics continues to rely heavily on past experience and physical modelling. Vertical breakwaters function mainly in re ecting the incident waves and consist of a vertical wall, resting on a rubble mound foundation.
1 Introduction 2
In the beginning of the mound breakwater use, they consisted typically of quarrystone, sta- bilised by their own weight. As ports kept growing, the mound breakwaters had to resist higher wave action. This was no longer possible with quarrystone, as their size is limited. Concrete units were used. First, the elements were simple cubes, but soon, problems concerning those elements were discovered. Later on, dierent shapes were developed, each with their own advantages and disadvantages. They dier in placement pattern, risk of progressive failure, number of layers, structural strength and hydraulic stability. Failures in the 70's, however, showed that slender units, designed for maximum interlocking, provide insu cient structural stability, which may cause progressive failure. This event set an end to the rapid development of elements with high hydraulic stability and reduced weight. The 80's meant a decade of big changes: not only the hydraulic stability and interlocking, but also the structural strength and robustness of the elements has been recognized.
The aim of this project is to study the characteristics of the Cubipod in breaking conditions. The Cubipod is a new armour element, invented by the Laboratory of Ports and Coasts in the Polytecnic University of Valencia. In recent history, stability studies in deepwater conditions showed successful results for this element and also overtopping performance seemed to be smaller in comparison with cubes. Now, an experimental study of the hydraulic stability of the Cubipod armour unit has been carried out on a physical scale model in 2D, in shallow water. Dierent models are obtained: a model with a double armour layer, with a single armour layer and with a combined layer of cubes covered by a Cubipod layer. The main objective is determining the hydraulic stability in breaking conditions and to compare those results for the dierent sections. The results also will be compared with the earlier obtained results in the deepwater tests.
In Chapter 2, as theoretical background on breakwater design, the stability of a mound break- water is discussed. First a historical resume is given, starting by the rst published formula to calculate the weight of rock materials of a mound breakwaters until the last developments. This is followed by an overview of the dierent failure modes and the quantization of the stability.
Chapter 3 provides an overview of the dierent existing armour units. A historical overview Introduction 3 since the 50's is given, followed by dierent systems to classify the existing armour units. Further, the new armour unit, the Cubipod, is presented, given its idea and concept including the dierent advantages of the element.
In Chapter 4, the maximum existing wave height in shallow waters is brie y discussed. Dier- ent types of wave breaking are mentioned and models to estimate the wave height distribution are discussed followed by theories to estimate the maximum wave height in breaking condi- tions.
In Chapter 5, the experimental setup is described, including the test equipment and the experimental design. Here the physical characteristics of the studied model are given, the construction of the model is described and the experimental procedure and the entire procedure to analyse the data are given.
Chapter 6 gives the results of the realised tests. The theories estimating the maximum wave height in breaking conditions are compared with the measured results in the Laboratory. The re ection results, damage progression and estimation of the hydraulic stability coe cient KD for the dierent sections are discussed. Those results are compared to previously executed test in deepwater conditions.
Finally, Chapter 7, presents the conclusions of the realized work. Chapter 2
Stability of Mound Breakwaters
2.1 Introduction
Mound breakwaters are the most commonly used breakwaters in Europe because of their easy construction and reparation process, high capacity to disperse the incoming energy and resist big storms. Design of mound breakwaters, however is a complex theme and has been studied across the world. An important evolution is made from elementary studies, considering only stationary regular waves to more complicated models, able to predict breakwater stability due to non-linear wave action in non-stationary conditions.
The most important parts of a traditional mound breakwater are the core, lter layers, the armour layer, the toe and the crest. The bulk of the cross-section comprises a relatively dense rock ll core, forming the base of the mound breakwater. This core should form a good foundation for the lter layers which avoid the small particles of the core to escape and has to be relative impermeable to avoid transmission of energy through the mound breakwater. The armour layer, founded on the lter layer(s) consists of rock or concrete blocks and should be permeable and robust to protect the mound breakwater against excessive wave action. The dissipation of wave energy occurs rather through absorption than re ection. Incident wave energy is dissipated primarily through turbulent run-up within and over the armour layer. If the wave is steep or the seaward slope of the breakwater is relatively at then the wave will overturn and plunge onto the slope, dissipating further energy. Sometimes a screen wall
4 Stability of Mound Breakwaters 5 is placed above the crest of the mound breakwater to avoid overtopping and improve the conditions during construction.
In this chapter, a brief historical background concerning the most important evolutions in the studies of mound breakwaters is given. Further a study of the analysis of their stability is described, including the description of a new failure mode called heterogeneous packing, followed by the way to quantify the stability of an armour layer.
2.2 A Short History
Breakwater design depends on many variables as there are: wave height, water density, armour density, armour slope, core permeability, wave period, storm duration, wave grouping, etc. This makes clear why during many years authors proposed dierent formulae to estimate damage on the armour layer due to wave attack. An overview of the most important formulae can be found in table 2.1.
Until 1933 there didn't exist any method to calculate mound breakwaters. They were con- structed based on experiences giving us qualitative criteria about the in uence of the wave- height, the angle of the slope, the weight of the armour elements, etc. Castro (1933) [1] published the rst formula to calculate the weight of rock materials of a mound breakwater.
In 1938, Iribarren [2] developed a theoretical model for the stability of armour units on a slope under wave attack. Since his work, many studies about mound breakwater stability were developed, showing dierent formulae to predict damage in the armour layer due to wave attack. The majority of those formulae assume a constant incident wave and initial damage zero. The reality, however, shows that wave conditions are not stationary. That's why new methods should be developed applying to no stationary processes. Many formulae, similar to the formula of Iribarren, were developed (F.C. Tyrrel (1949), Mathews (1951) and Rodolf (1951)) and in 1950 Iribarren and Nogales [3] generalized the formula by introducing the eect of the depth and the period, using a modi cation in the wave-height. Two years later Larras (1952) [4] presented another formula taking into account the depth and the length of the wave. Stability of Mound Breakwaters 6
Hedar (1953) marks up that it's necessary to consider two possible states to lose stability: when the wave climbs on the slope before breaking and when the broken wave descends from the mound breakwater.
The most frequently cited armour stability formula was published by Hudson (1959) [5] based on the pioneering work of Iribarren. Hudson's formula was originally proposed for regular waves, yet SPM (1973) and SPM (1984) [6] popularized the formula as well for irregular waves using the equivalences H1/3 and H1/10 respectively as representative of the wave height of irregular waves. Core permeability, wave period, storm duration, random waves, wave grouping were not considered. Iribarren (1965) presented in the Navigation Conference the relation of the friction coe cient with the number of elements on the slope. He also limited in this year the use of his formula by introducing, in an indirect way, the eect of the period in the stability.
Carstens et al.(1966) [7] present the rst results of tests on rock mound breakwaters with irregular waves. Font (1968) veri es empirically the in uence of the storm duration on the stability of mound breakwaters.
Battjes (1974) [8] introduces for the rst time the parameter of Iribarren in the study of characteristics of the ow on smooth and impermeable slopes. Other experimental works in the same line were done by Ahrens and McCartney (1975), Bruun and Johannesson (1976), Bruun and Bünbak (1976).
An extensive investigation was performed by Thompson and Shuttler (1975) on the stability of rubble mound revetments under random waves. One of their main conclusions was that, within the scatter of the results, the erosion damage showed a clear dependence on the wave period. The work of Thompson and Shuttler has therefore been used, as a starting point for an extensive model research program. Analysis of the results from all of these tests has resulted in two practical design formulae that describe the in uence of wave period, storm duration, armor grading, spectrum shape, grouping of waves, and the permeability of the core.
In 1976, PIANC [9], presented the most important used formulae and calculations of break- waters until this time, showing the big dierence in results between the dierent methods. Stability of Mound Breakwaters 7
The occured damages in the breakwaters in Bilbao (1976), Sines (1978) and San Siprian (1979) showed the importance of the calculation of a mound breakwater and of the methods to calculate the incident waves.
Whillock and Price (1976) [10] showed by interlocking elements, that the security margin be- tween initiation of damage and destruction of the armour layer is very low, introducing for the rst time the concept "fragility" of the slope. Magoon and Baird (1977) [11] accentuated the importance of the movements of the armour elements due to wave attack when the ar- mour elements break, especially by the most slender elements with the highest interlocking development.
Losada and Giménez-Curto (1979,a) [12] use the concept of interacting curves to analyze the stability using the wave-height and the period and recognize the intrinsic arbitrariness of the response of rock mound breakwaters. Losada and Giménez-Curto (1981) [13] use for the rst time the hypothesis of equivalence in the study of probability of failure and analyse the in uence of the duration in the probability of failure. In 1982 Losada and Giménez-Curto [14] present a hypothesis to calculate the stability of quarrystone mound breakwaters with non-perpendicular incident wave.
Lorenzo and Losada (1984) show, using results of eld tests, laboratory tests and numerical modelling, the fragility of the slopes with dolosse with big size, because of their structural weakness. Those results can be generalized for slender elements showing interlocking.
Desiré (1985) [15] and Desiré and Losada (1985) study the stability of mound breakwaters with paralelipepidic armour elements by doing many experiments with regular waves, observing a big deviation in the results. They concluded that the results of the tests should be seen like a statistic problem caused by the random nature of the variables (characteristics of the ow, resistance of the elements).
Van der Meer (1988) [16] proposed formulae including wave period, permeability and storm duration. The cumulative eects of previous storms however were not included. Vidal et al.
(1995) [17] introduced a new wave height parameter Hn (The average of the n highest waves Stability of Mound Breakwaters 8 in a sea state), to characterize breakwater stability under irregular waves and Jensen et al.
(1996) indicated that H250 is a suitable wave height parameter for irregular waves.
Medina (1996) [18] developed an exponential model applicable to individual waves of the storm, including the non-stationary conditions of waves. Melby and Kobayashi (1998) [19] charac- terized relationships for predicting temporal variations of mean damage with wave height and period varying with time for breaking wave conditions.
Vandenbosch et al. (2002) [20] analyzed the in uence of placement density on the stability of a mound breakwater with two layers of concrete cube armour units. He showed that increase of placement density not always means an increase of stability. An armour layer with a high density can cause other failure modes, as there are displacement of the armour layer or the lifting up of elements because of suppression.
Medina et al. designed in 2003 a Neural Network model applicable to non-stationary condi- tions. Accordingly, new methods to be applied in non-stationary conditions are required to avoid simplifying the concept of 'design sea state', which implies stationary conditions. Also the project CLASH (2002-2004) was focussed in obtaining a neural network model to predict overtopping on coastal structures (De Rouck et al.) [21].
Vidal et al. (2004) [22], showed that the H50 parameter, de ned as the average of the 50 highest waves in the structures lifetime, can be used to describe the evolution of damage in rubble mound breakwaters attacked by sea states of any duration and wave height distribution.
Gómez-Martín and Medina (2004-2006) [23] adjusted the wave-to-wave exponential model to estimate the n50% parameter for rubble mound breakwaters, in case of rock slopes or slopes with cubes. The model is also applicable in non-stationary conditions. In 2005 Gómez-Martín and Medina [24] de ned a new failure mode of mound breakwaters, named 'Heterogeneous Packing', the most important failure mode in case of armour layers formed by cubes or concrete elements. It is characterized by a decrease of porosity of the armour layer on some places and increase on others, without extracting armour units. They also described a new methodology 'Virtual Net Method' to provide damage measurement, considering the dierence in porosity compared to the initial porosity of each of the zones of the armour layer. Stability of Mound Breakwaters 9
3 Castro 1933 0√,704 H γr W = 2 · 3 (cotθ+1) cotθ−2/γr (γr/γw−1) 3 Iribarren 1938 K H γr W = 3 · 3 (cosθ−sinθ) (γr/γw−1) 2 Tyrrel 1949 K H T γr W = 3 · 3 (µ−tanθ) (γr/γw−1) 3 Matthews 1951 0,0149 H γr W = 2 3 (µcotθ−0,75sinθ) (γr/γw−1) 2 Rodolf 1951 0,0162 H T γr W = 3 3 tan (45−θ/2) (γr/γw−1) 2πH 3 K· L sinh 4πz 3 Larras 1952 L γrH W = 3 3 (cotθ−sinθ) (γr/γw−1) 3 Hedar: climbing waves 1953 K0 H γr W = 3 3 (µcosθ+sinθ) (γr/γw−1) 3 Hedar: descending waves 1953 K H γr W = 3 3 (µcosθ−sinθ) (γr/γw−1) 3 Hudson 1959 1 H γr W = 3 KDcotθ (γr/γw−1)
Table 2.1: Hydraulic stability criteria for the armour layer of a mound breakwater as cited in[1]
2.3 Analysis of the stability of a mound breakwater
2.3.1 General stability of a mound breakwater
To understand the structural stability of mound breakwaters, in the rst place, the dierent reasons for loss of stability should be understood, and thus the dierent failure modes have to be de ned.
Bruun (1979) [25] speci ed eleven dierent principal failure modes demonstrated in gure 2.1.
1. Loss of armour units (increasing porosity).
2. Rocking of the armour units; breaking is due to fatigue.
3. Damage of the inner slope by wave overtopping.
4. Sliding of the armour layer due to a lack of friction with the layers below.
5. Lack of compactness in the underlying layers, causing excessive transmission of energy to the interior of the breakwater; this might lift the breakwater cap and the interior layers. Stability of Mound Breakwaters 10
Figure 2.1: Mound Breakwater failure modes de ned by Bruun
6. Undermining of the crone wall.
7. Breaking of the armour units caused by impact, simply by exceeding its structural resistance or by slamming into other units.
8. Settlement or collapsing of the subsoil.
9. Erosion of the breakwater toe or the breakwater interior.
10. Loss of the mechanical characteristics of the materials.
11. Construction errors.
Those failure modes can be rearranged into ve families of failure (Gómez-Martín, 2002) [26]:
I Unit stability: the capacity of each piece to resist the movement caused by wave action (1, 2, 3).
II Global stability: the stability of the entire breakwater, or more speci c, of the entire armour layer, acting as one piece. It includes the movement of the armour layer or the movement of big parts (4, 5, 6).
III Structural stability: resistance of the elements or their material. This includes the ability of the elements of resisting the tensions caused by transport, construction, wave action, the used granular and the movements caused by currents (7, 2). Stability of Mound Breakwaters 11
IV Geotechnical stability: the resistance of the underground or the sensitivity to erosion of the breakwater toe (8, 9).
V Errors in the construction (10, 11).
The relative importance of every failure mechanism depends on dierent factors, as there are: intensity of the waves, depth of the mound breakwater, type of the ground, type of construction materials, etc. Loss of stability of the armour layer, being extraction of armour units out of the armour layer or breaking of individual armour units by exceeding their structural strength and crest overtopping of the breakwater are considered to be the most important failure modes of a mound breakwater. Those failure modes have been intensively studied and play a dominant roll in the design of a breakwater.
In this report, only the hydraulic stability of the armour units will be studied, more speci cally the loss of armour elements in certain zones of the breakwater slope, which is usually considered as the main mode of failure and is classi ed into the failure family of 'Unit Stability' in the classi cation of Gómez-Martín. This failure mode can be caused by two dierent reasons: the simple extraction of the armour units under wave attack, or their excessive settlement, causing a heterogeneous packing. This last failure mode is proposed by Gómez-Martín and Medina [24] and will be commented later in this chapter.
Once de ned the dierent types of damage, there's a need to specify the moment when a mound breakwater is considered as damaged. Therefore, four damage levels will be distinguished, de ned by Losada et al. in 1986 [27], and completed by Vidal et al in 1991 [28] with the level of Initiation of destruction (this is commented later in this Masterthesis in 6.4.2.2):
Initiation of Damage (IDa)
Initiation of Iribarren Damage (IIDa)
Initiation of Destruction (IDe)
Destruction (De) Stability of Mound Breakwaters 12
2.3.2 Heterogeneous packing
2.3.2.1 Introduction
This project works with armour layers consisting of cubes or Cubipod elements. Those are robust armour elements which means that in the rst place the hydraulic stability, the capacity of the elements to resist against movement due to wave attack supposing that they don't break, will be studied. Their structural stability, however, may not be forgotten. The monolithic and robust elements probably won't reach such a tensional situation able to break them, but the elements can break partially, due to slamming between each other, decreasing their weight, and thus decreasing their structural stability. An element in the armour layer can move in three dierent ways:
I: Pitching in their position in the armour layer. This is important when the structural stability can be the origin of additional tensions on the elements.
II: Displacement by extraction out of the armour layer. The extraction of elements out of their original position was during many years considered as the principal indicator of the stability of an armour layer under wave attack and the stability calculations were based on this failure mode (Fig. 2.2).
III: Packing of the elements as a result of small unit movements and frequent face-to-face arrangements. This new failure mode is de ned by Gómez-Martín and Medina [24] and is called 'Heterogeneous Packing' also shown in gure 2.2.
2.3.2.2 Heterogeneous packing
Heterogeneous packing is the most important failure mode in case of armour layers formed by cubes or concrete elements and is characterized by a decrease of porosity of the armour layer on some places and increase on others, without extracting armour units, but only by moving them within the armour layer. In tests, they observed that this failure mode tends to increase the packing density below the still water level, which is balanced by a corresponding reduction in packing density above and Stability of Mound Breakwaters 13 near the still water level. Heterogeneous Packing occurs always, but the intensity and the relative importance of this failure mode depends on four main factors:
Type of armour unit
Dierence between the initial porosity and minimum porosity
Slope of the armour layer
Friction coe cient between the armour layer and the lter layer
The Heterogeneous Packing has an eect similar to the erosion caused by extracting armour units, because the reduction of the packing density near the mean water level can facilitate the extraction of units from the inner layers. Thus, the armour layer is damaged by two dierent failure mechanisms: armour unit extraction and Heterogeneous Packing. In both cases, the result is similar: a decrease in the number of armour units near the mean water level. Studying the stability of the armour layer by wave attack, it's very important to take this failure mode into account together with the extraction of elements.
To have extraction of an armour element out of the armour layer, the wave has to overcome the friction and the interlocking between the elements in the armour layer and their own weight. Friction is a microscopic type of resistance between dierent elements; interlocking refers to a macroscopic type of resistance, formed by the contact between the protuberances of the elements. If the height of the wave exceeds a critical point, extraction of elements or heterogeneous packing of armour elements starts, and only their own weight oer resistance to displacement. Those extractions or Heterogeneous Packing stop when the wave decreases. The mound break- water obtains a stable situation, called 'Partial Stability', which depends on the number of displaced elements, the wave attack and his duration. The moved elements are in an unfavourable situation. Their probability to displacement is high. When the wave exceeds a certain value, the armour layer won't obtain a stable situation, but develop until complete destruction occurs. It's important to know that during this process, Heterogeneous Packing of the elements can Stability of Mound Breakwaters 14
Figure 2.2: The two most important failure modes by mound breakwaters: extraction of armour elements and heterogeneous packing. The classical view vs. the heterogeneous packing view increase the capacity of the armour layer in some places, but can also lead to important disintegrations, causing damage.
2.3.3 Damage criteria
The classic de nition declares damage of an armour layer as the percentage of displaced units compared to the total number of units used to construct the slope. The classic failure criteria are directly (extraction of armour units) or indirectly (changing in pro le of the armour layer) connected to lose or extract armour units due to wave attack as shown in the left side of picture 2.2. This classic de nition, however, doesn't allow generalizing the result, because damage depends on the size of the armour layer.
A better de nition was given by Van de Kreeke [29] and Oullet [30]. This de nition consists in comparing the displaced elements with the initial number of elements in a determined zone of the breakwater slope near the mean water level.
Iribarren (1965) [31] proposed a clear damage de nition for mound breakwaters. A mound breakwater reaches his failure level when the rst armour layer has been displaced in an area su ciently large to expose at least one armour unit of the layer below. If the breakwater reaches this state, it is considered as seriously damaged, because wave action can damage the second armour layer, and the underlayer will be in danger as well and total destruction of the breakwater is impending. Stability of Mound Breakwaters 15
In 1980 Paape and Ligteringen [32] mentioned that measuring the number or percentage of blocks removed and displaced to the toe of the structure, is only valid for small damages which is evenly distributed over the slope. With appreciable damage, it is important to observe whether concentrations of block removal occur, which consequently aect the basic idea of a two-layer armour cover and eventually even lead to exposure of the second layer and core. Therefore, they proposed a damage classi cation in function of the percentage of displaced blocks and the eect of such removal on the armour layer. It is obvious that such a classi cation is subjective.
In general, two dierent systems exist to quantify the damage:
Quantitative criteria's: the number or percentage of displaced armour units is compared to the initial ones.
Qualitative criteria's: important changes in the morphology of the armour layer are concerned.
A disadvantage of quantitative citeria's is that they don't give information about Hetero- geneous Packing, which can be very important in situations with Cubipod elements in the armour layer. The second method provides qualitative information about the damage level, but has a principal disadvantage to be subjective. Concerning this facts, a new method for damage estimation, taking into account the number of displaced elements and the changes in porosity of the armour layer by Heterogeneous Packing, is necessary. Gómez-Martín and Medina (2006) [24] present a new method for damage estimation: the Virtual Net Method. An equivalent dimensionless damage measurement is used to take into account the dierence in porosity, in each zone of the armour layer, compared to their initial porosity. This method is explained in 6.4.2.3. The method is complemented using qualitative criteria's considering dierent levels of damage: Initiation of damage, Initiation of Iribarren damage, Initiation of destruccion and Destruccion. Those are explained further in 6.4.2.2. Stability of Mound Breakwaters 16
2.4 Quantization of the stability
2.4.1 Formula to calculate the stability of a mound breakwater
As described in the short history, during the years, many formulae to calculate the stability of a mound breakwater have been developed. The Shore Protection Manual (1984) [6], based on the works of Hudson (1959) [5], proposes the next formulae to calculate the stability of a mound breakwater:
3 1 H γr (2.1) W = 3 kD (Sr − 1) cotα s Hs 1/3 3 W Ns = = (KDcotα) ; ∆ = Sr − 1 and Dn50 = (2.2) ∆Dn50 γr
With: W the weight of on individual element of the armour layer, in N
γr is the unit weight of the armour elements, in N/m3 H is the incident wave-height, in m
Sr is the speci c gravity of the armour units, relative to the water at the structure α is the angle of the structure slope, respective to the horizontal, in degrees H is the design wave height at the structure, in meter
Ns the hydraulic stability coe cient
KD is the hydraulic stability coe cient, depending on many characteristics:
Form of the element of the armour layer
Number of layers of the armour layer
Way of collocating the elements
Roughness of the elements
Interlocking between the elements
Water depth near the structure (breaking or non-breaking) Stability of Mound Breakwaters 17
Part of the mound breakwater (head or body of the mound breakwater)
Angle of the incident wave
Porosity of the core
Size of the core
Width of the crest
Other geometrical characteristics of the section
The values of KD need to be obtained experimentally, determining the wave-height that pro- duces initiation of damage. The value KD takes into account many variables, where the most important one is the used armour unit. Therefore, KD is an important characteristic for ev- ery armour unit, as well to be able to use the Hudson design formula, as to provide a unit characteristic that allows comparison with other units. SPM [6] resumed recommended KD values in a table. They give the hydraulic stability factor in function of the type of the armour unit, the number of armour layers, the way of collocation (uniform or random), the part of the mound breakwater (head or body) and the water depth (breaking or non-breaking).
This method to obtain the KD values experimentally however, shows some shortcomings. KD doesn't depend on the period, storm duration, wave grouping, etc. The prototype can be dierent from the real construction: the real construction method is not the same as in the laboratory and the used materials can be very dierent. Further, The wave-height for irregular wave was not de ned, SPM recomended H=H1/3 and later H=H1/10. Chapter 3
Armour Units
3.1 Introduction
Originaly, harbours were built with wooden or stone constructions. The continuous increase of the economy, however, meant the necessity of bigger harbours. Therefore, the harbours were built more into sea, which led to an increase of the height of the attacking waves. The design of the harbour evolved to constructions with a heavy rock outer layer. The continuous increase of the attacking waves meant always a need for larger stones to guarantee the stability of the construction. The size of natural stones has their limits, and design of arti cial concrete armour units was forced. The rst elements were simple cubes, but soon, problems concerning those elements were discovered. Nowadays, many dierent breakwater armour units exist, each with their own advantages and disadvantages.
The characteristics of the concrete armour elements have an important in uence on the hy- draulic stability of the mound breakwater. Further, the cost of the armour layer is an im- portant part of the total cost of the breakwater. Those facts explain why improvement and development of armour units is still an important subject of research.
In this chapter a historical overview of the development of the armour units for breakwaters during the last 50 years is given. Further, dierent ways to classify the existing elements are discussed and lastly the new armour unit, the Cubipod, is introduced. The motivation and concept of the design, with his advantages are explained.
18 Armour Units 19
Figure 3.1: Face to face tting by cubes reducing the friction with the lter layer
3.2 History: the armour units since the 50's
In the past 50 years a large variety of concrete breakwater armour units has been developed. Today design engineers have the choice between many dierent breakwater armour concepts. However, in many cases standard type solutions are applied and possible alternative concepts are not seriously considered. The most important and mentioned armour units in this part are resumed in the table 3.2.
Until World War II breakwater armouring was typically either made of rock or of parallelepi- pedic concrete units (cubes). The placement was either random or uniform. Breakwaters were mostly designed with gentle slopes and relatively large armour units that were mainly stabilised by their own weight. Those units have numerous advantages: a high structural strength, cheap and easy to fabricate, store and put into place; furthermore the elements have a low risk to progressive failure. But these units do have certain drawbacks that must be taken into consideration. They have a low hydraulic stability (KD=6) and tend to settle to a regular pattern. The layer becomes an almost solid layer which can lead to excess pore pressure and lifting of the blocks. This also means an important loss of friction with the underlying layer and can cause a sliding of the armour units. Another important disadvantage to mention is the phenomenon of Heterogeneous Packing. This failure mode, without extraction of units, tends to reduce the packing density of the armour layer near the still water level without extracting armour units, but only by moving the units within the armour layer, caused by unit movements and face-to-face tting (Fig 3.1).
From the 50's the economical development and the increase of the dimensions of the tankers, Armour Units 20 obliged us to realize depth mound breakwaters. Many laboratories in the world tried to develop and patent new types of arti cial breakwater armour units. The main objective was to design elements with a high stability coe cient to reduce the weight of the mantel elements and thus the total cost of the structure.
In 1950 The Laboratoir Dauphinois d'Hydraulique in Grenoble introduced the Tetrapod, a four-legged concrete structure and the rst interlocking armour unit. The tetrapod is the rst of the "engineered" precast concrete armour units widely used all over the world produced by many contractors and no longer protected by a patent. His main advantages are a slightly improved interlocking compared to a cube element and a larger porosity of the armour layer, which causes wave energy dissipation and reduces the wave run-up.
The tetrapod inspired similar concrete structures for use in breakwaters, including the modi ed Cube (US, 1959), the Stabit (U.K., 1961), the Akmon (Netherlands, 1962), the Dolos (South Africa, 1963), the Seabee (Australia, 1978), the Accropode (France, 1981), the Hollow Cube (Germany, 1991), the A-jack (U.S., 1998), and the Xbloc (Netherlands, 2001), among others.
A large variety of concrete armour units has been developed in the period 1950 - 1970. How- ever, most of the blocks from those days have been applied only for a very limited number of projects. These armour units are typically either randomly or uniform placed in double layers. The governing stability factors are the units' own weight and their interlocking.
The Dolos was developed in the 60´s for rehabilitating the damaged breakwater at the Port of East London in South Africa. Dolosse are armour units with a slender shape, a relatively slender central section and long legs will face high stresses in the central part of the armour block. These blocks have a high risk of breaking in the central part and broken armour units have little residual stability and reinforcement should uneconomical.
The failure of the Sines breakwater (Portugal, 1978) who was constructed with dolosse in- dicated that slender armour units, designed for maximum interlocking, provide insu cient structural stability and breakage of armour units may cause progressive failure. This event set an end to the rapid development of elements with high stability coe cient and reduced weight. Armour Units 21
More failures in the last two decades meant the end of the general con dence and the optimism in the classical techniques to design. The 80's meant a decade of big changes. The reasons of failure were analysed and new methods of calculation and design were searched.
Single layer randomly placed armour units have been applied since 1980. The Accropode (France, 1980) was the rst block of this new generation of armour units and became the leading armour unit worldwide for the next 20 years. The Accropode is a compact shape and the basic concept of the unit was a balance between interlocking and structural stability. The blocks are placed in a single layer on a prede ned grid. The orientation of the block has to vary; therefore Sogreah recommends various techniques for placement. However, sling techniques and grid placing do not guarantee a perfect interlocking of the individual armour units. Therefore relatively conservative KD values are recommended for design. Unfortunately, Sogreah did not succeed to overcome these di culties by developing a more reliable placement procedure.
CoreLoc and A-Jack are further examples of this type of single layer randomly placed armour units that have been developed subsequently. Hence, these blocks are more economical than traditional double armour layers. The CoreLoc, developed by the US Army of Engineers in 1994, appeared to be more slender then the Accropode and to have a higher hydraulic stability. After drop tests, it was found that the structural stability of the CoreLoc was signi cantly better than for dolos units because of his more compact central section. However he showed with respect to structural stability, residual stability after breaking as well as ease of casting and placement.
The A-Jack, introduced by Armortec (1997) consists of three long cement stakes joined at the middle, forming six legs. It is a high interlocking armour unit that has been applied up to know only for revetments and not for breakwater armouring. The elements are very slender and the structural stability might be very critical if the blocks exceed a great size (1-2m3), however the large KD value limits the block size and thus A-Jacks can be cost-e cient for temporary structures and moderate wave conditions.
The parallel development of a completely dierent type of armour concept started in the late 60th. The armour layer consists of hollow blocks that are placed orderly in one layer. Each Armour Units 22 block is tied to its position by the neighbouring blocks. Their hydraulic stability is not based on weight or interlocking, but is extremely high as it is based on friction between the block and the blocks around. The friction between uniformly placed blocks varies signi cantly less than interlocking between randomly placed blocks. Therefore a friction type armour layer is more homogeneous than interlocking armour and very stable. The wave energy is dissipated in the proper elements, in the internal voids of the blocks. These elements provide a erce reduction of the weight and a relatively high porosity of the armour layer, but on the other hand some of the sections have to be reinforced due to their slenderness. As placement of these elements is very di cult under water, they are normally only applied in circumstances where construction can be done above low water. Typical examples of these elements are Cob, Shed and Seabee.
Another possible discussion concerning armour elements is reinforcement of slender units. Treadwell and Wagoon (2006) [33] are of opinion that concrete armour units for coastal struc- tures need reinforcement. Concrete armour units are believed to be one of the very few coastal concrete structures that generally do not contain reinforcement. Concrete is a very strong ma- terial in compression, but with very little strength in tension, especially during impact events. The main bene ts of reinforcement of concrete armour units are added strength during casting, curing, moving, placing, and during all service loading conditions (including violent rocking during severe storms) and avoidance of rapid failure, if indeed failure occurs at all. Given the maintance problems and catastrophic failures that have been experienced by concrete armour unit installations, it is clear that the added cost of reinforcement would be more than oset by reduced costs of maintance and repair and evaluations and the avoidance of the negative economic impacts to revenue streams when coastal protection systems suer severe damage. Armour Units 23
Figure 3.2: A selection of the existing concrete armour units Armour Units 24
3.3 Classi cation of armour units
As there are over a hundred dierent armour units, a manner to classify them is needed. There are many criteria; armour units can be classi ed according their shape, their placement pattern, the risk of progressive failure, the number of layers, their structural strength and the way they resist wave action. Each of those classi cationsystems are described. All the mentioned armour units can be seen in the table 3.2.
A rst way to classifying armour units is by their shape as shown in table 3.1. This classi cation was made by Muttray, Reedijk, and Klabbers (2004) [34].
Shape Armour blocks
Cubical Cube, Antifer cube, Modi ed cube, Grabbelar, Cob, Shed Double anchor Dolos, Akmon, Toskane Thetraeder Tetrapod, Tethrahedron, Tripod Combined bars 2D: Accropod, Gassho, Core-Loc 3D: Hexapod, Hexaleg, A-Jack L-shaped blocks Bipod Slab type (various shapes) Tribar, Trilong, N-shaped block, Hollow square Others Stabit, Seabee
Table 3.1: Classi cation of breakwater armour units by shape [34]
The placement pattern of armour elements can be uniform or randomly. In case of robust elements, random placement is suggested to guarantee the porosity of the armour layers and to avoid the excess pore pressure inside the breakwater which may lift the blocks. If the placement of the elements is random and there's no request concerning the orientation of the individual elements to obtain a good disposition, the construction is much easier then in case of uniform placement.
Concerning the risk of progressive failure, armour units can be classi ed in slender blocks and compact blocks. In case of slender armour units, the stability is mainly due to interlocking and the average Armour Units 25 hydraulic stability is large. However, the variation in hydraulic resistance is also relatively large and the structural stability is low. Therefore slender blocks shall be considered as a series system with a large risk of progressive failure, because if they break in parts, the hydraulic stability sharply decreases causing simultaneous loss of weight and interlocking. The stability of compact blocks is mainly due to the own weight. The structural stability is high and the variation in hydraulic stability is relatively low. Thus, the armour layer can be considered as a parallel system with a low risk of progressive failure.
The elemens can be placed in one or two layers. Single armour layer is more cost e cient due to the reduced number of armour blocks. It means saving concrete and lower costs for fabrication and placement of blocks. Single layer placement also has technical advantages, there is less rocking then in double armour layer and therefore a lower risk of impact loads and breakage . Double armour layers do not provide additional safety against failure -except for compact armour units with large structural stability and limited interlocking- because the second layer tends to create breaking and is sensitive to rocking, thus the structural integrity of the armour units is jeopardized. The placement in two layers on at slopes is an uneconomical solution.
Armour elements can resist wave action by their own weight, by interlocking or by friction. In case of slender armour units, the stability is mainly due to interlocking and the average hydraulic stability is large, however, the structural stability is low. The stability of compact blocks is mainly due to the own weight. The average hydraulic stability is low. However, the structural stability is high. Hollow elements will resist wave action mainly by friction.
A more general overview, combining dierent classi cation criteria, is proposed by Bakker et al. (2003) [35] and is shown in table 3.2. He includes criteria for placement pattern (random or uniform), number of layers (single or double layer), shape (simple and complex) and domimant method of hydraulic stability (resisting wave action by own weight, interlocking or friction). Armour Units 26
Placement Number Shape Stability factor pattern of layers Own weight Interlocking Friction
Cube double layer simple Antifer cube Modi ed cube complex Tetrapod, Akmon, Tribar, Tripod Random Stabit, Dolos A-Jack single layer simple Cube Accropode Core-Loc complex accropode
Seabee, Hollow Uniform single layer simple Cube, Diahitis complex Cob, Shed
Table 3.2: Classi cation of armour units by shape, placement and stability factor.
A common problem in the design of armour units is the need to choose between higher hy- draulic stability and higher structural strength. Armour units can increase their hydraulic stability by increasing their own weight, interlocking and higher friction with the inner layer. Interlocking and a higher friction usually mean a signi cant reduction in structural strength.
As a general rule, the stability coe cient, KD increases from the massive to the slender cate- gory; however this means a decrease of the structural strength.
A classi cation by structural strength of the units is done by Mijlemans in 2006 [36]. Elements can be subdivided in three groups: robust units that dispose of a very high structural strength, fragile armour units with low structural resistance and an intermediate group that provides a reasonably high structural stability. The classi cation of Mijlemans (2006) is also based on the placement method (number of layers and placement pattern) and creates in this way ten families of arti cial concrete armour emelents as shown in table 3.3.
The robust units have a massive form that provides a high structural strength. The large and Armour Units 27 compact cross-sections cause small tensile stresses which decreases the risk of unit breaking. They resist wave attack mainly by their own weight and the average hydraulic stability can be considered rather low. Because of their high structural stability and their low variation in hydraulic stability, they present a low risk of progressive failure.
Fragile units have a very low structural stability because of their limited cross-sectional areas. The most important stability factor is interlocking which provides them with a high average hydraulic stability. Their variation in hydraulic stability however is quite high and together with the low structural stability, the risk of progressive failure is high. Fragile elements can be subdivided into hollow units, where the interlocking is provided by their reciprocal friction, and slender solid units where the slender members interlace with one another.
The intermediate group is originated to combine the high structural stability of robust ar- mour units with the interlocking characteristics of the fragile elements. Their form provides an amount of resistance by interlocking, but avoids also too slender cross-sectional areas to maintain a high structural strength. They have a rather massive form, therefore their dom- inant hydraulic stability factors are their own weight and interlocking. They provide a high hydraulic stability and an intermediate structural resistance which decreases their risk of pro- gressive failure in comparison with the fragile units above.
Structural resistance Placement method Robust Intermediate Fragil
group 3 Random multiple layers group 1 group 2 group 4 one layer group 5
Uniform multiple layers group 6 group 7 group 8 group 11 one layer group 9 group 10 group 12
Table 3.3: Classi cation of armour units by placement method and structural strength (Mijlemans, 2006) Armour Units 28
3.4 A new armour unit: The Cubipod
3.4.1 Introduction
The Cubipod is a new armour unit for the protection of maritime structures invented by Josep R. Medina and M. Esther Gómez-Martín, patented in 2005 by the Laboratory of Ports and Coasts of the UPV (Patent number: P200501750) and licensed by SATO.
Figure 3.3: A new armour element: the Cubipod
3.4.2 Idea
Numerous armour units have shown high hydraulic stability such as Tetrapods, Dolos, Ac- cropodes, Core-locs, X-blocks, etc. which permit a reduction in the concrete armour unit weight, however they have a low structural strength. The collapse in Sines (Portugal) and the severe damage in San Ciprián (Spain) showed us that the structural strength is an important parameter in the choice of the armour element.
Randomly placed massive units with a simple shape like cubes or parallellepipedics are widely used because of their numerous advantages: structurally robust, cheap and easy to fabricate, manufacture, store and put into place; furthermore there is a low risk to progressive failure. Nevertheless, these units do have certain drawbacks that must be taken into consideration. Armour Units 29
They have a low hydraulic stability (KD=6 for cubes) and a high Heterogeneous Packing failure mode.
3.4.3 Concept
The Cubipod is designed to form the protective layer of mound breakwaters, seawalls and piers in order to protect coasts, hydraulic or maritime constructions or in general to resist wave breaking. The aim of the new armour unit is to bene t from the advantages of the traditional cubic block, like the high structural strength and easy placement, but to correct the drawbacks by preventing self packing and increasing the friction with the lter layer. The new element is a massive cubic element with equal protuberances on every side which have the form of truncated pyramids with a square section. Preferably the size of the protuberances had to be small in comparison with the cube or parallelepiped. Its principal function should be to avoid settlement while the structural strength and hydraulic stability of a cube is maintained. Therefore, the total volume of the protuberances should be an order of magnitude lower than the volume of the basic element; e.g. not exceed 15% of the volume of the basic element without protuberances. The nal result is shown in gure 3.3.
Robustness and high structural strength The design of the unit is based on the cube in order to obtain his robustness. The cross-sectional areas are large and not slender, that's why the Cubipod has a high individual structural strength. In order to assess the structural strength of this new armor unit, overturning, free fall and extreme free fall tests have been carried out. The Cubipod armour units were able to withstand higher drops than did the conventional cubic blocks [37].
High friction with the lter layer Cubic elements tend to place their sides parallel to their underlying layer, which means a decrease of the friction between the armour layer and the lter layer. In case of Cubipods, the protuberances penetrate in the lter layer and provide an important increase of the friction with this layer.
Face-to-face tting The protuberances avoid sliding of the armour elements. Due to this, fact face-to-face tting and the loss of elements above the still water level is reduced. This Armour Units 30
Figure 3.4: Drop test results of Cubipods compared with cubes showing the lost weight
Figure 3.5: Penetration of the Cubipods in the armour layer Armour Units 31
Figure 3.6: The separating eect of the protuberances avoiding the face-to-face arrangement means that Cubipods reduce the Heterogeneous Packing failure mode of the armour layer compared with the former used cube elements. The separating eect of the protuberances avoiding this face-to-face arrangement is showed is gure 3.6.
Hydraulic stability The hydraulic stability of Cubipods is higher than of cube elements thanks to higher friction with the lter layer and reduce of the Heterogeneous Packing as explained above. This is proved in earlier tests in deepwater conditions [38]. This means a reduction of the loss of elements above the upper parts and a lower run-up and overtopping. Armour Units 32
Figure 3.7: Example of placement in a depository of Cubipods
Figure 3.8: The casting system designed by SATO and the tongs for movement and manufacture
Easy casting, e cient storage and handling The Spanish construction company SATO has designed a casting system and specially adapted tongs for the e cient movement and manufacture of Cubipods (Fig 3.8). Thanks to this system the fabrication can be done easy and fast [?]. Thanks to their form, the storage can be done e ciently, using little space (Fig 3.7). As the placement of the Cubipods is random and there's no request concerning the orientation of the individual elements to obtain a good random disposition, the placement of the elements is much easier then in case of uniform placement. Chapter 4
Wave height in breaking conditions
4.1 Introduction
As the majority of mound breakwaters are built in shallow waters, a study of the behaviour of waves in breaking conditions may be important knowing that those dier a lot from the conditions in deepwater. The height of waves is an important factor in uencing the design of coastal constructions. An overly conservative estimation can greatly increase costs and make projects uneconomical, whereas underestimation could result in structural failure or signi cant maintenance costs.
In this chapter, rst, general information will be given about breaking waves: the dierent types are shortly discussed. Some existing theories are presented to estimate the wave height distribution in shallow waters followed by formulae to calculate the maximum wave height in breaking conditions. In the next chapter, showing the results, a short comparison between the obtained maximum wave height in the executed experiments and the existing theories is done. The goal of this chapter is not to propose new formulae to calculate breaking characteristics, but to give an overview of existing models and to compare dierent theories with the measured results in the laboratory experiments.
33 Wave height in breaking conditions 34
4.2 The surf zone
As waves enter shallow water, they slow down, grow taller and change shape. At a depth of half its wave length, the rounded waves start to rise and their crests become shorter while their troughs lengthen. Although their period stays the same, their overall wave length short- ens. The 'bumps' gradually steepen and nally break in the surf. There is a distinct dierence between the oscillatory wave motion before breaking and the turbulent waves with air entrain- ment after breaking. In case of actual sea waves, some waves break far from the shore, some at an intermediate distance and others approach quite near the shoreline before breaking. In coastal waters therefore, wave breaking takes place in a relatively wide zone of variable water depth, which is called the wave breaking zone or the surf zone.
4.3 Types of breaking waves
There are four types of breakers in the surf zone (Fig 4.1); spilling, plunging, collapsing and surging. The slope of the beach and the types of waves approaching the surf zone determine which type of breaker is going to be predominant.
Spilling In this type of wave, the crest undergoes deformation and destabilizes, resulting in it spilling over the front of the wave. Only the top portion of the wave curls over. Light foam tends to appear up the shore. It occurs most often on gentle beaches and is usually the most observed type of wave.
In a spilling breaker, the energy which the wave has transported over many miles of sea is released gradually over a considerable distance. The wave peaks up until it is very steep but not vertical. Only the topmost portion of the wave curls over and descends on the forward slope of the wave, where it then slides down into the trough. This explains why these waves may look like an advancing line of foam.
Plunging The wave peaks up until it is an advancing vertical wall of water. The crest of the wave advances faster than the base of the breaker, curls over and crashes into the base of the wave, creating a sizable splash. It tends to happen most often when the gradient of the Wave height in breaking conditions 35 sea oor is medium to steep or from a sudden change in depth (a rock ledge or reef). It is also a feature of breaking waves in oshore conditions. These type of waves arise when the steep gradient of the sea oor or ledge is angular to the approaching swell direction.
In a plunging breaker, the energy is released suddenly into a downwardly directed mass of water. A considerable amount of air is trapped when this happens and this air escapes explosively behind the wave, throwing water high above the surface. The plunging breaker is characterized by a loud explosive sound.
Collapsing Collapsing waves are a cross between plunging and surging, in which the crest never fully breaks, yet the bottom face of the wave gets steeper and collapses, resulting in foam.
Surging On steeper beaches, a wave might advance up without breaking at all. It deforms and attens from the bottom. The front of the wave advances up towards the crest, creating re ection.
Iribarren's number The deepwater Iribarren number (Iribarren and Nogales, 1949) Ir = p tan(α)/ H/L0, also called the breaker parameter describes a certain type of wave breaking
and contains a combination of structure slope and wave steepness: s0 = H/L0 (table 4.1). For the executed tests we nd numbers of Iribarren with values between 2 and 5. This is because the slope is the mound breakwater is rather high (compared to the slope of a beach). Breaking due to the mound breakwater will happen by collapsing or surging. As we are in shallow waters with a horizontal bottom, the wave breaking taking place before the breakwater will happen as spilling or plunging.
Breaking type spilling plunging collapsing surging
Ir Ir < 0, 5 0, 5 < Ir < 2, 5 2, 5 < Ir < 3 Ir > 3
Table 4.1: Type of breaking in function of the number of Iribarren Wave height in breaking conditions 36
Figure 4.1: Types of breaking waves
4.4 Models to estimate the wave height distribution
In deep water, the approximately linear behaviour of the waves allows for a theoretically sound statistical description of the wave characteristics, based on a Gaussian distribution of instan- taneous values of surface evaluation, resulting in a Rayleigh distribution of wave heights. In shallow water, the wave behaviour is more complicated and the knowledge of the statistical description of wave eld characteristics is more limited. The distribution before wave break- ing can be approximated as being Rayleighan, which means that a group of random waves entering the surf zone is assumed to have a Rayleigh distribution. Among the waves obeying that distribution, those with height exceeding the breaking limit will break and cannot occupy their original position in the wave height distribution. Breaking causes a truncation of the waveheight distribution.
Several authors have developed wave height distributions that modify the Rayleigh distri- bution of deepwater waves to take into account wave shoaling and breaking. Two dierent kind of models can be distinguished to account for the portion of energy retained by the broken waves:
The rst type supposes that the energy from the broken waves is concentrated in the breaking wave height. All the broken waves will have the breaking wave height in the sur ng zone (Fig ??). Wave height in breaking conditions 37
Figure 4.2: Distribution of the wave heights by breaking, concerning that all the broken wave heights will have the breaking wave height in the sur ng zone
The second type presents truncated wave height distributions that distribute the energy from the broken waves back over the smaller wave heights in the distribution.
Collins (1970), Mase and Iwagaki (1982) and Dally and Dean (1986) presented a method to calculate the distribution of the heights of breaking waves in shallow water. Given a sequence of wave heights and periods and direction at some oshore location, or a joint probability distribution of those variables, they apply a monochromatic wave model for shoaling and breaking to calculate the onshore transformation of that monochromatic wave class. These methods, however, are algorithmic and do not result in explicit expressions for further analyses or extrapolation to low probabilities of exceedance.
Another approach consists of making empirical adaptations to the Rayleigh distribution of the wave heights to allow for the eects of shallow water and breaking, resulting in explicit ana- lytical expressions. Glukhovskiy (1966) proposed a distribution for shallow waters by maken the exponent an increasing function of the wave-height-to-depth ratio. For su ciently low wave height-to-water depth ratio, the distribution becomes a Rayleigh distribution. Tayfun (1981) presented a theoretical model for the distribution of wave heights, including the eect of wave breaking, based on a narrow-banded random phase model with a nite number of spectral components. The distributions given by Glukhovskiy an Tayfun are both point models, yielding a local wave height distribution for given local depth and wave parameters (lowest two spectral moments). The Rayleigh distribution gives a poor description of the measured wave height distribution. It underestimates the lower wave heights and overestimates the higher ones. The Glukho- Wave height in breaking conditions 38 viskiy distribution yields a better approximation, however, in general, this distribution still overestimates the extreme wave heights and underestimates the lower wave heights on shallow foreshores.
Battjes and Groenendijk (2000) [39] proposed a composite Weibull wave height distribution to give a better description of the measured wave height distributions in shallow waters. The wave height distributions on shallow foreshores show a transition between a linear trend for lower heights and a downward relation for the higher waves. This abrupt transition does not lend itself to a distribution with one single expression and one shape parameter. Therefore a combination of two Weibull-distributions was assumed, each having a dierent exponent, matched at the transition height Htr. The model predicts the local wave height distribution in shallow foreshores for a given local water depth, bottom slope and total wave energy with signi cantly accuracy than existing models.
4.5 Maximum wave height in breaking conditions
As the wave height is one of the most important factors in uencing the design of a mound breakwater, over the years, many equations have been proposed to express the breaker height/breaker depth ratio as a function of other variables. Those models however, do not employ all the variables aecting the breaker height and depth, with the result that they apply only to limi- ted conditions. Here, some models are explained, mentioning that this list is not complete at all as there exist many formulae to calculate breaking characteristics.
Keulegan and Patterson (1940) [40] noted that the Hb/db ratio is related to wave breaking which they considered to take place at values between 0,71 and 0,78. This gives us a simple formula to calculate the breaking height, because it does not take into account the bottom
slope α, neither the wave period T.
Collins (1970) [41] was among the rst to consider the eect of the bottom slope on wave breaking, but did not take other variables into account. His equation which yields a ratio of 0,72 over a horizontal bed, increases to 1,21 for a 5O slope. Wave height in breaking conditions 39
H b = 0, 72 + 5, 6tanα (4.1) db
Weggel (1972) [42] published one of the most useful equations. He considered the eect of the sea oor slope α in addition to the gravity constant g and wave period T. We can see however, that the function becomes independent of the period T if the sea bottom is horizontal (E2=0).
His equation is valid for tanα ≤ 1.
Hb E2Hb (4.2) = E1 − 2 db gTw 1, 56 E = 1 1 + e−19,5tanα 43, 75 E = 2 1 + e−19tanα
Komar and Gaughan (1973) [43] derived a semi-empirical relationship from linear wave theory, where the subscript 0 denotes deepwater conditions (Fig 6.3). This equation takes into account the wave period T, using the formula of Airy for L0, but does not take the bottom slope into account, neither the water depth in shallow water.
H H −1/5 b = 0, 56 0 (4.3) H0 L0
Sakai and Battjes (1980) [44] plotted a curve of the wave breaking limit as function of Hb/H0 against H0/L0 (Fig 6.3). They also only take into account the wave period T, but do not take into account the bottom slope neither the water depth in shallow water. This curve is described by the following equations:
" −0,3118# H0 H0 Hb = H0 0, 3839 when < 0, 0208 L0 L0 " −0,1686# H0 H0 Hb = H0 0, 6683 when 0, 0208 ≤ < 0, 1 (4.4) L0 L0
H0 Hb = H0 when 0, 1 ≤ L0 Wave height in breaking conditions 40
Komar (1998) proposed two seperated equations for Hb and db, where S is the sea oor gradient.
0,2 20,4 Hb = 0, 39g TH0 (4.5a) 0,27 S (4.5b) db = Hb 1, 2 0,5 Hb L0
Experimental work (Shore Protection Manual, 1984 [6]; Demirbilek and Vincent, 2002) for waves breaking over dierent bottom slopes with wave periods between 0s - 6s resulted in a formula showing the dependance of the water depth and bottom slope:
2 Hb = db −0, 0036α + 0, 0843α + 0, 835 (4.6)
Le Roux (2006) [45] presents approximations providing a very simple method to estimate wave parameters and using the wave period as fundamental parameter because it is assumed to be constant in all water depths. The expressions apply to smooth bottom pro les without ridge and runnel systems and assuming an absence of marine currents. As a wave begins to shoal under these conditions, its height decreases initially and then increases shortly before breaking whereas the wavelength decreases up to breaking. The wave height Hw in any water depth changes in accordance with the deepwater wave height H0, wavelength L0 and water depth d:
H0 Hw = H0 A exp B (4.7) L0 where
d −0,18 d A = 0.5878 when ≤ 0, 0844 (4.8) L0 L0 d 2 d d A = 0.9672 − 0.5013 + 0, 9521 when 0, 0844 ≤ ≤ 06 (4.9) L0 L0 L0 d A = 1 when > 06 (4.10) L0 d −2,3211 B = 0, 0042 (4.11) L0 Wave height in breaking conditions 41
By replacing Hb with Hw and db with d in equation 4.6 and using speci c of H0 and L0, changing the waterdepths simultaneously in equations 4.7 and 4.6 until the breaker height Hw coincides, the breaker height and depth for both developing and Airy waves over any bottom slope can be calculated.
Examining Hb for dierent wave periods shows that:
2 L gTw H = b = (4.12) b 16 48π
Among Goda [46], however, the breaking limit for random sea waves should be allowed a range of variation because even a regular wave train exhibits some uctuation in breaker height and a train of random sea waves would show a greater uctuation owing the variation of individual wave periods and other characteristics. Therefore wave breaking is assumed to take place in the range of relative wave height from x2 to x1 with a probability of occurrence which varies linearly between the two boundaries. With this assumption, the portion of waves which is removed from the original distribution due to the process of breaking is represented by the zone of slashed lines shown in gure 4.3 The heights of individual random waves after breaking are assumed to be distributed in the range of nondimensional wave heights between 0 and x1 with a probability proportional to the distribution of unbroken waves. Wave height in breaking conditions 42
Figure 4.3: Distribution of the breaking wave heights over the distribution of the unbroken waves (Goda [46]) Chapter 5
Experimental setup
5.1 Introduction
In this chapter, the experimental setup of the hydraulic model tests will be discussed. First of all, the test equipment will be presented, including the wave ume, the system used to generate the waves, the dierent measurement sensors and the data processing system. Next the calibration of the wave generator and the experimental design of the models will be set out, starting with the theoretical characteristics of the model. As the theoretical values are not the real values for the model, the practical design values of the model will presented, together with the construction method and the position of the wave gauges. This experimental design is concluded with the realized experiments, the characteristics of the experiments and the methodology used for the tests. To end the chapter, the method used to analyse the data is set out.
5.2 The Test Equipment
The experiments are performed in het Laboratory of Port and Coastal Engineering to inves- tigate the hydraulic stability of Cubipods in breaking conditions. This laboratory disposes of a 2D wind and wave ume with sensors gauging the position to control the exact parameters of the experiments.
43 Experimental setup 44
Figure 5.1: Longitudinal section of the 2D wave- ume
5.2.1 2D Wave Flume
The 2D wave ume has a square cross-section of 1.2m x 1.2m and is 30 m long. In the centre
of the wave ume, the bottom shows a gentle upward slope (4%; tanα = 1/25) over 6,15m, hence the water depth near the model is 25 cm less than the water depth near the wavemaker. On the raised oor the model is put. A detailed plot of the total test setup within the wave ume is shown in Appendix B.
The slope and the foreshore are intended to stabilize the return ow during the tests and if not present, the translational movements of the water volumes would result in an elevation of the water level on one side of the canal. This slope and platform assure the recirculation of the water in the ume. Another important advantage from the upward slope of the canal oor is that it permits the wave generation to occur at a higher water depth than the water depth near the model, and thus attack the model with higher waves, without the limitation of wave breaking at the wavemaker that occurs in umes with a uniform oor.
The water depth used for the experiments is between 55 cm and 65 cm near the wave generator and between 30 cm and 40 cm near the model. The model is placed at a distance of . . . m from the wave generator slab (measured at the toe of the breakwater) and is built on a scale of 1/50.
5.2.2 Wave Generation System
On one of the ends of the ume, a wave generating system is constructed. It consists of a metal slab that moves horizontally by aid of a electronic piston. This movement is transmitted Experimental setup 45 on the water.
The piston is attached to the upper part of the paddle which means that a strong momentum is introduced in the vertical slab when moving the water mass. However, a rigid steel frame forces the paddle to move equally in a horizontal way on bronze rolls sliding on steel rail tracks. The hydraulic compressor provides oil under pressure to a piston that moves the metal slab which transmits its movements on the water. The movement of the piston is controlled by a valve, which is guided by a position gauge communicating with the central electronic-informatics system and transmitting the necessary corrections to obtain the correct movement.
Hydraulic model testing of wave impact on structures is often hampered by wave re ection from the test structure, here a mound breakwater. The wavegenerator has a theoretical movement to generate a certain wave. As the re ected waves return to the wavemaker, they are usually re-re ected, which results in an uncontrollable, most undesirable nonlinear distortion of the desired waves impinging on the test structure, because the wavegenerator keeps having the same movement.
Therefore, the wave generator is provided with an Active Wave Absorption Control System (AWACS). AWACS is a digital control system, which enables wavemakers to generate the desired waves and, at the same time, absorb spurious re ected waves. The system provides superior wave generation accuracy in hydraulic umes. The used system in the laboratory is DHI AWACS2, from Denmark.
The principle of the AWACS is to measure the surface elevation (waves) by two installed wave gauges integrated in the paddle front. The measured waves are the superposition of the desired waves and the re ected waves returning to the wavemaker. The measured waves are compared with the speci ed, desired waves. By use of the digital recursive lter of the AWACS the re ected waves are identi ed and absorbed by the wavemaker. Hereby, spurious re-re ection from the wave paddle is eliminated.
Photos of the wave generation system are shown in gure 5.2. The detailed working of the soft- ware to manage the AWACS and to generate the waves in the ume is explained in Appendix C. Experimental setup 46
Figure 5.2: Wave generation system in the LPC wave ume and setup of active wave absorption system Experimental setup 47
5.2.3 Wave Measurement
The measuring system consists out of wave gauges, run-up sensors and a measurement system for the erosion of the armour layer.
Wave Height The wave height is measured by wave gauges(Fig 5.3). They consist of two vertical parallel conductors that work as a dielectric. The conductors dip into the water. The current that ows between the wires is proportional to the depth of immersion. The current is noticed by an electronic circuit providing an output voltage. This output is proportional to the instantaneous depth of immersion, the wave height in cm above the mean water level. This type of gauges is very reliable in calibration and linear in the transformation of the data.
The output voltage can be calibrated in terms of the wave height by varying the depth of immersion of the probe in still water by a measured amount and noting the change in output signal.
The gauges have to be calibrated every day before starting the experiments, to intercept the changes in water level in the ume caused by leaks and the climatically changes being change in temperature or humidity. These changes can aect on the working of the gauges signi cantly. To allow this calibration, the gauges are connected with the electronic equipment. The measured data are sent to the computer which translates the signals in wave heights in relation to the average water level. The sending of the data happens at a sampling frequency of 20Hz.
Run-up A Step-Gauge Run-up System constructed by the University of Ghent is used to measure the run-up (Fig 5.3). The electrodes of dierent length are placed one behind the other, in this way they follow the pro le of the breakwater. The distance between the armour units and the gauge can be set to less than 2mm, without touching the Cubipods. The working of a step-gauge is very simple. Each electrode is connected to a circuit which detects if the electrode is dry or wet. There are two analogue outputs: the rst gives a voltage which corresponds to the position of the highest electrode that still makes contact with the water, the second gives a voltage that corresponds to the number of electrodes that are wet. The measured results of the Steup-Gauge Run-up System are not used in this Masterthesis. Experimental setup 48
Figure 5.3: Wave gauges for wave measurement and Step-Gauge Run-up Measurement System (S- GRMS) constructed by University of Ghent
Above this Step-gauge System, visual support is given by a person and a camera next to the canal. Accomplishing every test, there's a person looking to perceive the run-up with help of the measuring rod on the wall and there's a camera next to the canal lming the right side of the model through the glass wall.
Erosion of the armour layer Measuring of the erosion of the armour layer is done as described in (Gómez-Martín and Medina) [24] and is based on the method of the virtual mesh. After every test, pictures are made of the armour layer with a camera that is placed on a standard over the wave ume. Those pictures are used to measure the erosion of the armour layer as explained in 5.4.4.4.
5.2.4 Energy dissipation system
On the other side of the canal there is an energy dissipation system. This system consists of ve groups of three grooved metal frameworks, and a plastic perforated plate. The metal frameworks have three dierent porosities: 70%, 50% and 30%, with the highest porosity starting at the side where the wave approaches. A rst group of three frameworks with 70% porosity is followed by two groups with a porosity of 50%. The rst of these two groups has many and thin bars, the second has the same porosity but less bars, and thus the bars and voids are wider. The fourth and fth group have a porosity of 30% and again, the rst is ner Experimental setup 49
Figure 5.4: Wave energy dissipation system in the LPC wave ume than the secons one. The voids between the three frameworks of this group have been lled with quarrystone.
5.2.5 Data Processing
In the central computer situated in the o ce area of the laboratory, the correct data is inputted. This data is sent to the wave generator to generate the correct wave. Afterwards the measured data by the wave gauges and the Step-Gauge Run-up System, are sent to the same central computer to analyse these results. This is explained more in detail in Appendix C. Experimental setup 50
5.3 Calibration of the wave ume
Before starting the experiments on the breakwater model, it is important to know if the wave generation in the laboratory is representative for those that really need to be generated. If the required conditions are not represented accurately, this will aect the results of the experiments. The factor that needs to be veri ed to calibrate and control these conditions is the wave generation. Calibration experiments in the wave ume were carried out to examine these eects before starting the actual model experiments. The energy absorption system AWACS in the wavemaker guarantees a constant wave generation.
To control the operation of wavemaker, the theoretical dates (wave height and wave period) of the lanced wave have to be compared with the measured wave height and wave period near the wavemaker.
5.4 Experimental Design
5.4.1 Physical characteristics of the studied model
The used model is a mound breakwater with an inner slope of 4:3 and an outer slope of 3:2. Although no speci c prototype breakwater is considered, reference is made to prototype values. A basic scale factor of 1:50 is considered, which corresponds with real Cubipods of 16ton and standard Mediteranean dimensions. The mound breakwater consists of three parts. The core of ne gravel (type G2) forming the base of the mound breakwater, a lter layer (type G1) forming the underground for the main armour units and the armour layer existing of the Cubipods (or cubes). The armour units reach until the toe of the structure. The Cubipods are made of resin and have a density of 2,30t/m3, they weight 128g and have a theoretic equivalent cube size of 3,82cm. The cubes, also made of resin, weight 147,2g each and have a cube size of 4,00cm, slightly bigger than the size of the Cubipods. The calculation of the theoretic equivalent cube size and theoretic volume using the known dimensions of the Cubipods is shown in table 5.1. The theoretical characteristics of all the used materials are shown in table 5.2. The proposed porosity of the armour layer is 41%. Experimental setup 51
cubes Cubipods
L cube [cm] 4 3,575 h pyramid trunc [cm] 0 0,894 V cube [cm3] 64 45,691 V pyramid trunc [cm3] 0 1,666 V total [cm3] 64 55,686
D50 [cm] 4 3,819
Table 5.1: Calculating the theoretic equivalent cube size and the theoretic volume of the Cubipods
Model of the cubes Model of the Cubipods
3 3 D50 [cm] density [t/m ] weight [g] D50 [cm] density [t/m ] weight [g] Armour layer 4,00 2,3 147,2 3,82 2,30 128 Filter (G1) 1,80 2,70 16 1,80 2,70 16 Core (G2) 0,70 2,70 0,90 0,70 2,70 0,90
Table 5.2: Theoretic characteristics of the used materials
The considered water depths vary between 30cm and 42cm near the model. The crest is supposed to be high enough so that overtopping is not considered. Only tests in breaking wave conditions were carried out: the breakwater is assumed to be in shallow water.
Five dierent models, each with the same core- and lterconstruction, will be considered (Fig 5.5 and Fig 5.6):
double layer of Cubipods: C2
single layer of Cubipods: C1
single layer of cubes covered by a single layer of Cubipods: CB
double layer of Cubipods with toe berm: C2B
single layer of Cubipods with toe berm: C1B Experimental setup 52
Figure 5.5: Cross section of the studied models: 2 layers of Cubipods (C2), 1 layer of Cubipods (C1), 1 layer of cubes covered by one layer of Cubipods (CB) Experimental setup 53
Figure 5.6: Cross section of the studied models: 2 layers of Cubipods with toe berm (C2B), 1 layer of Cubipods with toe berm (C1B) Experimental setup 54
First the tests C2 will be considered. Afterwards, the second layer is removed and the rst layer of C2 will be used to execute the experiments C1. To realize the tests CB, in the beginning only the layer of cubes will be placed. Waves will be lanced to stabilize this layer before collocating the second layer of Cubipods. Afterwards the tests C2B and C1B with a toe were executed. The toe berm is placed to sustain the bottom rows without making this too rigid. To execute those two series of experiments (C2B and C1B), all the elements are removed of the model, the toe berm is constructed, and the double layer of Cubipods is placed. For the experiments with a single layer of Cubipods, the section C2B is removed and a new layer with Cubipods is placed, and thus not the rst layer of the former experiments, as done in the tests without toe berm.
The two types of experiments without toe berm C2 and C1 are executed rst because those are the standard sections of the 'Ports of the State'. The models C2B and C1B with toe berm however, are more realistic sections. In breaking conditions a lot of turbulence near the bottom takes place, which can cause fast erosion of the lower part of the breakwater. Placing a toe berm is therefore common.
The armour units in the model setup are painted in dierent colours to easily recognize unit movements during the experiments. The lower layer is completely white, while the upper layer is painted in dierently coloured strips. Also the cubes are painted in two dierent colors: white and blue.
5.4.2 Construction of the physical model
5.4.2.1 Preparation
First the wave ume is cleaned and its interior is repainted with anti-oxidant paint. The real cross section of the model breakwater is plotted and is attached to the inner side of the wave ume. Signi cant points, indicated by a small gap, are marked correctly to the ume wall and the cross section can be drawn correctly (Fig 5.7). The cross section is also painted at the other side of the wave ume by perpendicular projection. The oor of the canal is cleaned and a concrete grout is poured in the wave ume on the place where the breakwater will come, which provides a rough surface for the model (Fig 5.8). Experimental setup 55
Figure 5.7: Draw the cross section of the mound breakwater on the wall of the canal
Figure 5.8: The concrete grout to provide a rough surface for the model Experimental setup 56
5.4.2.2 Control of the material characteristics
The received materials for the core and the lter layer show a great dispersion of particle size. Therefore we make a granulomatric separation of the received materials and compare this with the theoretical values. The used terms D15,D50 and D85 are the corresponding diameters of the sieves where respectively 15%, 50% or 85% of the materials can pass. Also the Cubipods need to have the correct theoretical weight and density, to afterwards be able to make right conclusions concerning the stability of those elements. For a part of the Cubipods the practical values are measured and controlled with the theoretical ones.
The core (G2) The proposed particle size of the core material for the mound breakwater is D50=7mm and D85/D15=2. After the sieving, the granulometric distribution is controlled and the material is washed. The results can be seen in table 5.3 and in gure 5.9. There can be concluded that the theoretic and the real values dier very little, which means that the theoretic values are accepted.
The lter layer (G1) The proposed particle size of the core material for the mound break- water is D50=17mm and D85/D15=1.5. After sieving, the granulometric distribution is also controlled and the materials of the lter layer are also washed. The results can be seen in table 5.4 and in gure 5.10. There can be concluded that the theoretic and the real values of the lter material dier very little, which means that the theoretic values are accepted.
The armour layer (G0) The Cubipod model units are fabricated by a private enterprise, and are supposed to be delivered in the requested size and weight. To verify this, a part of the Cubipods (5%) are weighted to know their real average weight and the standard deviation. Obtaining the results in table 5.5 , the proposed theoretical values are considered satisfactory and thus accepted. Experimental setup 57
theoretic design values measured values
Sample weight [g] 3000 3001,5
D85 [mm] 9,25 8,55
D50 [mm] 7,00 6,75
D15 [mm] 5,50 5,20
D85/D15 1,68 1,64
W85 [g] 2,14 1,69
W50 [g] 0,93 0,83
W15 [g] 0,45 0,38
Table 5.3: Grading characteristics of the core material
Figure 5.9: Grading curve for the core material Experimental setup 58
theoretic design values measured values
Sample weight [g] 3000 3001
D85 [mm] 21,00 20,59
D50 [mm] 17,50 17,82
D15 [mm] 14,00 15,24
D85/D15 1,50 1,35
W85 [g] 25,00 23,55
W50 [g] 14,00 15,27
W15 [g] 7,41 9,55
Table 5.4: Grading characteristics of the lter material
Figure 5.10: Grading curve for the lter material Experimental setup 59
3 3 weight [g] density [g/cm ] volume [cm ] D50 [cm] Theoretical values 128 2,30 55,65 3,82 Measured average dry 128 2,29 55,86 3,823 Measured standard deviation dry 2,37 0,008 Measured average saturated 129,2 2,29 56,44 3,84 Measured standard deviation saturated 2,36 0,011 Percentage measured 5% 5%
Table 5.5: Theoretical and measured characteristics of the Cubipods
Figure 5.11: Construction of the model: the core and the lter
5.4.2.3 Construction of the model
First, the core material is put in place according to the indicated lines on the ume walls. A perfect placement of the core is very important because it has to support the other layers: the lter and the armour layer. Afterwards, the lter is constructed with a thickness of 6,67cm only on the outer slope, making sure that the slope is constant over the whole width of the breakwater. On the inner slope no lter material is placed (Fig 5.11).
Finally the armour units are collocated. The theoretic thickness of the layer is the equivalent cube size of the Cubipod, being 3,82cm. The number of collocated units depends on the proposed theoretical porosity. In collocation tests with a crane, they have seen that the porosity of Cubipods placed in a 'blind' way can vary between 36% and 50%. For this reason, Experimental setup 60 in those experiments will be worked with a proposed porosity of 41%, which is comparable to earlier tests. The theoretic number of the units per area and per row to collocate to reach a porosity of 41% can be calculated with the formulae 5.1 and 5.2, a number of 19 elements per row is found. The way of collocating the units, however, is done randomly, as is also done in real life. They let the elements fall without determining a certain position before. This means that the number of elements sometimes can dier from the theoretic calculated number. If there was no place left for 19 elements, 18 units were collocated. In the reverse case, if there was place left, an extra Cubipod was placed. This caused a little dierence in porosity. In table 5.6 can be seen that the initial porosities of each Cubipod strip are between 36% and 50% which are acceptable values. Only the porosity of the cube layer is lower than 36%. Before placing the Cubipods, tests on the cube layer were executed and this provocated face to face tting of the cubes. Therefore the porosity of this layer is lower than 36%. Details of this calculation can be seen in Appendix E.
(1 − P ) Vt (5.1) Ntheor = 3 D50
number (1 − P ) b = (5.2) row D50 With
P the porosity of the armour layer
3 Vt the theoretic volume of the determined elements in m
D50 the size of the equivalent cube
b the width of the canal being 1,22m
In gure 5.12, the construction proses of the armour layer for a double layer of Cubipods C2 is shown step by step. First the under layer of white Cubipods is collocated, afterwards the second layer with the dierent colours covers this under layer. It is clear that the elements are placed randomly and are not following an exact line, which is also in reality. Experimental setup 61
Color Preal C2 Preal C2B Preal C1B Preal CB white 41 42 - 24 cyan 41 42 39 37 yellow 41 38 41 35 red 41 36 38 35 grey 41 42 39 35 blue 41 39 38 38 green 41 39 39 36 magenta 41 38 38 38 yellow 41 39 39 39 cyan 39 39 39 39
Table 5.6: The real initial porosity in the dierent models [%]
For the other models C2B, C1B and CB, the way of construction is the same. For the combined layer CB, rst some waves are lanced to stabilize this cube layer, before collocating the Cubipods. The single layer of Cubipods (C1) is formed by removing the second layer of Cubipods of B2 and thus is formed by the same number of Cubipods as the rst layer of C2.
5.4.2.4 Reconstruction of the model
After the rst experiments however, the core and the lter are destroyed partially. To guaran- tee their stability, a change is executed in the construction of the core and lter structure. As the lter was only constructed on the outer slope, now also a lter layer is placed on the inner slope to guarantee a higher stability. Further, on the top of the breakwater, a little crest with lter material is built on the inner side of the mound breakwater, to sustain the Cubipods placed over there. This change can be seen in gure 5.13 and in the sections in gure 5.5 and 5.6. For the further experiments, this construction is always used, which means that the experiments are not done with the real section of 'The ports of the State', but with a little change to guarantee the stability in the following experiments. Experimental setup 62
Figure 5.12: Construction proses of the armour layer Experimental setup 63
Figure 5.13: Construction of the lter on the inner slope and a crest on the top of the mound breakwater after destruction of the core and the lter layer
5.4.2.5 Placement of the sensors
The wave gauges are placed in the main line of the canal between the wave generator and the breakwater model in two dierent groups, one group of four wave gauges near the wave generator and another group of four wave gauges near the model. Furthermore, a ninth wave gauge is place on the breakwater model to measure the run-up. Those nine wave gauges will permit us to obtain the incident and re ected wave in the canal. The most important group of wave gauges is the one near the model, the measured values will be used to calculate the stability of the mound breakwater. The other group near the wavemaker is rather to know if the wave generation is representative for those that really need to be generated. The distance between the wave gauges of the same group are determined according to the criteria proposed by Mansard and Funke, based on the used wave periods and lengths. They propose three wave gauges per group and recommend the following distances, relative to the used wave length:
L d1 ≈ 10
L L 6 < d1 + d2 < 3
L d1 + d2 = 5
3L d1 + d2 =6 10 Experimental setup 64
Position in the canal [cm] Wave gauge 1 Wave gauge 2 Wave gauge 3 Wave gauge 4 Near wave generator 340 360 410 440 Near model 1446 1476 1526 1546
Distance [cm] d1 d2 d3 Near wave generator 20 50 30 Near model 30 50 20
Table 5.7: Position of the wave gauges and distance between them in the canal
In the present experiments the four wave gauges in each group are separated according to these recommendations. The eventually lack of one of the equations, however, is not a big problem because we have four wave gauges in every group. Anyhow, the wave gauges are placed in a way that all occurring waves and wave lengths can be registered accurately, and the gauges can be kept xed for all wave periods to avoid loss of time.
Another restriction to the positioning and separation of the gauges is that they should be at least one meter away from the bottom slope in the centre of the ume, to keep the gauge registering away from being in uenced by a change in water depth. This results in the dis- tances between the wave gauges shown in Table 5.7.
5.4.3 Experiments
5.4.3.1 Realized experiments
To study the hydraulic stability of the Cubipod armour units, both, regular and irregular wave tests are considered. However, in this project only the regular waves will be studied because, before they experienced that irregular waves do not damage more than regular waves.
In regular wave tests, the wave in every experiment is characterized by his wave height and pe- riod. The representative wave height is the average wave height (Hm). Increasing water depths are considered (h=30cm, h=35 cm, h=38 cm, h=40 cm). For each of those water depths; a series of increasing periods (T(s)=0.85s, T(s)=1.28s, T(s)=1.70s, T(s)=2.13s, T(s)=2.55s) is considered, while for every period, a series waves with increasing design wave height (step of Experimental setup 65
1cm) is lanced.
Starting with wave heights that don't produce damage, the heights are increased until the waves break (this is the maximum wave height compatible with the water depth) in the model. In practice wave trains of 100 waves were executed.
5.4.3.2 Experimental procedure
Every day, before starting the experiments, rst the water level is controlled. The loss of water had to be compensated and during the tests, the depth was automatically and continuously measured and compensated when necessary.
Having the correct water level, the manual calibration of the wave gauges can be done. This is done by moving them up and down over a range of 15cm (10cm for the wave gauge on the mound breakwater) while a second person adjusts the measurements in the data acquisition system. After the calibration, a wave is lanced and the data registered by the wave gauges is reviewed to make sure that all of the wave gauges continue to measure correctly. This is done by opening the measured data in an Excel le and plotting them. If one of the sensors doesn't work correctly, calibration of this sensor has to be repeated.
Before starting the tests, a photograph of the armour layer is taken. One with and one without the virtual framework, which is used to de ne the nine strips that divide the slope for damage analysis.
Every test set with a certain water depth, is started with a wave height that for sure will not produce any damage to the armour layer. Before starting a new test, the water in the canal has to be still, to make sure that all in uence of earlier introduced waves was excluded and could not in uence.
During each test, the breakwater slope is guarded by a camera so the damage progression can be looked after.
After every test, a photograph is taken with a xed camera perpendicular to the slope. Those are used afterwards to analyse the damage progression using the virtual net method. Experimental setup 66
After every test, the wave height is increased by one centimeter until breaking of the waves occurs. Some (two or three) waves with higher wave height are lanced to be sure that the maximum wave height will be reached. Then, waves with a higher period (and again a low wave height) are lanced. After the complete test set of the ve dierent periods, the water depth is changed.
The registered data by the wave gauges are rst analysed by the software LASA-V. This programme separates incident and re ected wave trains. Afterwards those results are examined by the software LPCLAB. This software generates a report that represents all the requested and useful information about the waves.
The pictures made by the camera, are loaded in Photoshop to draw a virtual framework on it. Afterwards this photograph is loaded in AutoCAD to indicate the Cubipod by points and to calculate the damage progression using the Virtual Net Method.
5.4.4 Procedure to analyse the data
5.4.4.1 Separating the incident and re ected waves: LASA V
The response of maritime structures depends on the incident wave eld, however in laboratory model tests as well as in prototype only the incident wave added to its re ection can be measured. This makes it necessary to distinguish the incident wave train seperated from the re ected wave train to study and predict response of maritime structures both in model tests and in prototype.
Various methods for wave separation have been developed, a short resume can be found in Appendix D. In this project, the separation of the waves is done using the LASA-V method, proposed by Figueres and Medina [55]. This method is an optimization of the 'LASA local wave model' method developed by Medina [54], based on linear and Stokes-II nonlinear com- ponents and a simulated annealing algorithm to optimize the parameters of the wave model in each small local time-segment of the measured record. To obtain the water surface eleva- tion corresponding to the incident and re ected wave trains at any point of the record, the results of the optimization in each time window overlap. The optimized model that is used in Experimental setup 67
Figure 5.14: Parameter window of the LASA-V software this Masterthesis uses an approximate Stokes-V wave model. This model is able to analyse experiments with highly nonlinear waves, as in intermediate depth conditions.
The seven parameters controlling the simulated annealing process are: cost function, gener- ation mechanism, initial solution, initial control parameter, reduction of control parameter, length of markov chains and stop criterion. Those have to be implemented in the program, also the number of linear wave components, number of nonlinear Stokes V wave components and the duration of the time window which is xed to 2∆t = 2T0 (Fig. 5.14). The program LASA-V is applied to the four sensors near the model and near the slab. These results are referred to the central sensors (here S3 and S7).
5.4.4.2 Analysis of the waves: LPCLAB 1.0.
After separating the incident and re ected waves by LASA-V, the waves are analysed by a sofware, developed by the laboratory of Ports and Coasts in Valencia, LPCLAB 1.0. This software analyses the wave data in time- and frequency domain, generating a report in Excel Experimental setup 68
Figure 5.15: Example of the separation of incident and re ected wave trains by LASA V with all the relevant wave parameters, as well as some graphics. An example of such a report is represented in Appendix ??.
In the beginning the register of the sensors is not regular due to transition. From the slab without movement to movement you need time to generate the correct height. At the end, the same phenomenon occurs, the slap can't stop immediately. To analyse the dates with LPCLab 1.0, we select the central part of the register, ignoring the transitions in the beginning and at the end as shown in gure 5.16.
The most important parameters for further research are the wave re ection coe cient, the
Iribarren number and the measured wave heights. We will use the average wave heights Hm and
H1/10 for further calculations. Those real wave characteristics dier from the theoretic values, depending on various parameters like the wave generation, propagation and re ection. For a correct analysis of the breakwater behaviour, it is critical that the real wave characteristics are taken into account correctly.
There are four graphics generated. Two concerning the measurements near the slab, and the two others concerning the measurements near the model. The rst always shows the measured wave together with the sum of the calculated separated waves. The second graphic shows the calculated incident and re ected waves separated. Further, there are two more graphics showing the wave spectrum. Experimental setup 69
Figure 5.16: Parameter window of the LPCLab software
After utilizing the programs LASA-V and LPCLAB 1.0. we know the next wave heights:
Htotal registered in the sensors: Ht
Hre ected by separating the wave: Hr
Hincident by separating the wave: Hi
Hregenerated, total by counting up the incident and the re ected wave: Hrt
Hrt should x with Ht to consider that the separation was done correctly.
5.4.4.3 Analysis of the re ection coe cient
The re ection coe cient is the ratio of the re ected wave height to the incident wave height, and is calculated by the program LPCLAB 1.0. This value indicates how much energy is dissipated by the mound breakwater and how much energy is re ected. Experimental setup 70
Hr CR = . (5.3) Hi
The wave height used to establish this re ection coe cient is the average wave height in regular wave tests (Hm). The re ection coe cient depends on the characteristics of the wave (wave length, wave period, water depth) and on the type of construction. To show the in uence of those wave characteristics; the re ection coe cient will be described in function of two dierent values: the Iribarren number or the dimensionless relative water depth kh:
tan (α) Ir = (5.4) q H L0
d kh = 2π (5.5) L
The re ection coe cient mainly depends on the wave length. Therefore, a good way to show the results will be in function of the dimensionless relative water depth, knowing that this parameter only shows the in uence of the wave lengths. The number of Iribarren shows the in uence of both wave height en wave length, and thus seems not ideal to represent the re ection coe cient results. The number of Iribarren however, also called the breaker parameter, describes a certain type of wave breaking (Table 4.1). The relative amount of wave energy that can be re ected o a slope depends intimately on the breaking processes . Because of this, it is natural to try to relate the re ection coe cient to Ir. The graphics showing the re ection coe cient in function of the Iribarren number will give us information about the relation between the re ection on the mound breakwater and the type of wave breaking.
Both representations, the re ection coe cient in function of the dimensionless relative water depth and in function of the number of Iribarren, will be accomplished for the executed tests.
5.4.4.4 Analysis of the damage progression
In all the executed tests, the damage progression of the breakwater armour layer was analysed both quantitatively with the Virtual Net Method and qualitatively through visual analysis Experimental setup 71 of photos after each test. Important to mention is that this analysis is done after seperating incident and re ected wave, and thus calculating with only the incident wave height.
Quantitative analysis Conventional analysis of mound breakwater takes into account only the armour unit extraction failure mode; therefore, traditional methods, as there is the visual counting method considers only the extraction of armour units assuming constant porosity to measure damage of the armour layer.
The visual counting method de nes the eroded area by:
3 3 NeDn NeDn A = 50 = 50 (5.6) b (1 − p) bφ
And the dimensionless damage by:
A (5.7) S = 2 Dn50
In which Ne is the number of eroded armour units, Dn50 is the equivalent cube size or nominal diameter, p and φ = 1 − p are the constant porosity and packing density coe cient of the armour layer and b is the observed cross section width.
When Heterogeneous Packing takes place, the porosity of the armour layer changes over time, and the equivalent dimensionless armour damage should be measured taking into account the changes in porosity for each area of the armour layer in regard to initial porosity. Gómez- Martín and Medina (2006) described the Virtual Net Method to measure the equivalent di- mensionless armour damage. This method involves projecting a virtual net over the armour layer dividing it into nine strips, each of which is n times the width of the equivalent cube
Dn50 (Fig 5.17). The dimensionless damage in each strip can be calculated using the equation:
φi 1 − pi Di = n 1 − = n 1 − (5.8) φ0i 1 − p0 Experimental setup 72
In which p0 and φ0i are the initial porosity and packing density coe cient, respectively. pi
and φi are the porosity and packing density coe cient after the wave attack. Pi takes into account the number of elements in every strip, using the following equation:
2 NiDn50 pi = 1 − = 1 − φi (5.9) ab
Ni is the number of armour units in strip i (upper layer), the dimensions of each strip are the strip height 'a', being n times the equivalent cube size, and the strip width 'b', here 75cm. Not the whole width of the mound breakwater is considered, but only the central part. The extreme parts are not taken into account to avoid calculating with parts in uenced by of the ume wall.
Counting up the armour damages in each strip over the slope, the equivalent damage De can be obtained using the following equation:
X De = Di (5.10) where only the damages higher than zero are taken into account. A damage higher than zero, means loss of packing density (higher porosity). A negative value of the damage stands for a higher packing density, which means higher stability and thus not considered as damage. Only the positive values of the calculated damages in the dierent strips are counted up to receive the total damage.
The most important advantage is that this method takes into account the change of porosity in the armour layer, caused by Heterogeneous Packing or unit extraction.
After every test, a photograph perpendicular on the mound breakwater is taken using a camera that is placed on a standard over the wave ume. Every photo corresponds with a certain water depth, wave-height and period. A real metal net that can be placed on the top of the armour layer is used to divide the armour layer in nine strips. Only the rst and last photo of the day could be taken with this real metal net, because of the presence of the Step Gauge above the model during the tests. Therefore, an equal virtual net is drawn with the graphical Experimental setup 73 computer program 'Photoshop' on the photos without the real net. It's important that the camera doesn't move, to make sure that this virtual net is placed equal as the real net (Fig 5.18).
Using the technical drawing program AutoCAD, every Cubipod is marked with a point, using dierent layers for the dierent strips of the armour layer (Fig 5.17). With the command PRICAPAXYZ, developed by LPC, the Cubipods in every layer can be counted easily. With this result, the porosity of every strip and thus the damage can be calculated with the former equations.
As we are interested in the behaviour of the mound breakwater after a series of waves, and not after every wave, we calculate the dimensionless damage only after a series of tests. At the end of a sequence of tests with a constant water depth (h=30cm, h=35cm, h=38cm, h=40cm, h=42cm), the dimensionless damage will be measured.
Figure 5.17: Virtual net to measure the equivalent damage analysis and counting the units in Au- toCAD for damage calculation Experimental setup 74
Figure 5.18: Above: foto with the real net and the designed net in Photoshop (start of the tests with h=38). Under: foto without the real net and the pasted virtual net in Photoshop (end of the tests with h=38) Experimental setup 75
Qualitative analysis To verify qualitatively the failure modes, it's necessary to de ne a method to validate the level of damage. To de ne this level, there are dierent classi cations: Losada et al. (1986) [27] proposed the following three damage levels: Initiation of Damage (IDa), Initiation of Iribarren Damage (IIDa), and Destruction (De). In order to me more precise, another stage of damage is included by Vidal et al.(1991) [28] called Initiation of Destruction (IDe). They are de ned through a visual analysis of photos after every test. Those four damage levels were de ned based on experimental information and provide an internationally known basis for comparison with other results. A representation of the four damage levels is given in gure 5.19.
Initiation of damage (Ida) This level of damage de nes the condition attained when a certain number of armour units are displaced from their original position to a new one at a distance equal to or larger than a unit length. Holes larger than average porous size are clearly appreciable. In this research we adopted for this number a value of 2% of the displaced units required to achieve Iribarren's damage.
Initiation of Iribarren damage (IIDa) This damage occurs when the extension of the failure area on the main layer is so large that the wave action may extract armor units placed on the lower armour layer.
Initiation of Destruction (IDe) A small number of units, two or three, in the lower armour layer are forced out and the waves work directly on pieces of the secondary layer.
Destruction (De) Pieces of the secondary layer are removed. If the wave height does not change the mound will de nitely be destroyed and it will cease to give the level of service de ned in the design.
The wave height corresponding to the three signi cant damage levels (IDa, IIDa and IDe) is obtained out of the visual qualitative analysis and in each case the corresponding dimensionless armour damage will be calculated. The wave height corresponding to the initiation of damage
will be used to calculate a rst estimation of the hydraulic stability factor KD. Experimental setup 76
Figure 5.19: Damage levels in the armour layer Chapter 6
Results
6.1 Introduction
In this chapter, the results of the executed experiments are discussed and is subdivided in three parts. In the rst part the results of the ume calibration are presented, which have an important in uence on the physical model tests. A good working of the wavemaker is necessary to be able to interpret the obtained results afterwards. In the second part, the discussed theories to calculate the maximum wave height in breaking conditions are compared with the measured results in the laboratory. Further, in the last section, the results of the experiments on the mound breakwater model of Cubipods are commented. Both results on wave re ection and on damage progression of the armour layer are presented. The damage is studied qualitatively and quantitatively. A rst indication of the value of the hydraulic stability coe cient is calculated for the dierent mound breakwater sections in shallow water.
All the results of the dierent studied sections rst will be described, then explained and nally compared with the obtained results of the other sections. Graphics are used to illustrate the results in a clear way. A comparison with earlier executed tests in deepwater conditions is also done.
An overview of the executed tests and the most important results can be found in Appendix G, while the complete results of the LPCLab test reports can be found on the available cd-rom. A short explanation of the used terminology is resumed in Appendix A.
77 Results 78
6.2 Calibration of the wave ume
As mentioned in Chapter 5, before starting the experiments, the calibration of the wavemaker is executed. This calibration has been carried out with the following characteristics:
The generated wave is irregular with a JONSWAP spectrum (γ = 3, 3)
The considered water depths are 40cm, 45cm, 50cm and 55cm (near the wavemaker)
Wave periods of 1s, 1,5s, 2s, 2,5s and 3s are used
Wave heights between 2cm and 30cm are lanced
The energy dissipation system that will be used during the model experiments has been put in place
The AWACS active energy absorption system in the wavemaker is put in place to guar- antee a constant wave generation
The measurement of the generated wave height is registered simultaneously, and is mea- sured by a sampling frequency of 20Hz
To control the operation of wavemaker, the theoretical dates (wave height and wave period) of the lanced wave are compared with the measured wave height and wave period in the sensor near the wavemaker, being sensor 3. Those results are represented graphically in gure 6.1.
We see that the real average wave height near the wavemaker is less than the theoretical value, a dierence that increases with increasing wave height and decreasing period. This dierence is due to the loss of energy in the wave ume. This energy loss increases with increasing wave height and decreasing period. Larger the wave height and smaller the period, larger the loss of energy, and larger the dierence between theoretical and measured value. In the graphic of the period can be seen that the real period and the theoretical period correspond very well. Concerning those graphics, we can decide that the wavemaker realizes the waves with the asked characteristics. Results 79
Figure 6.1: Results of the calibration of the wave ume Results 80
6.3 Interpretation of the theories calculating the maximum wave height
The theoretical breaker height and breaker depth are presented in dierent graphics using the presented models in Chapter 4 to calculate the characteristics of breaking waves. Further, those results are compared with the measured results in the laboratory.
The following characteristics are taken into account:
As the tests are done with a horizontal bottom, the slope α in the executed tests is zero.
The water depth in shallow water is the water depth near the model, being 25cm less than the water depth near the wavemaker.
The measured wave heights used to compare with the dierent theories are the incident wave heights (after separating the total heights by the software LASA-V). This means that the in uence of the present mound breakwater, being the in uence of the re ected wave on the total wave height, is eliminated.
As the breaking wave height Hb, the highest value of the maximum wave heights near the model is taken.
gT 2 To calculate the wavelength L0 in deepwater, the Airy formula (1845) is used: L0 = 2π
As measured wave height in deepwater H0, the measured wave height near the wavemaker is used. This is not totally correct, because the the situation near the wavemaker is
in intermedias water depths. The measured wave lengths will not reach L0 and the
measured wave heights will be higher than H0.
The models proposed by Keulegan and Patterson, Collins, SPM and Demirbilek and Vincent depend only of the breaking depth and the bottom slope. Those can be visualized in a graphic showing the breaking wave height in function of the water depth. For the formula of Collins and of SPM and Demirbilek and Vincent, three curves are drawn with three dierent bottom slopes: a horizontal bottom (as in the executed tests), a smooth slope of 3O and a steeper slope of 10O (Fig 6.2). Results 81
All the theories give a linear link between the two variables. As the water depth increases, the breaking wave height also increases with a certain factor. We see that the lower boundary of the theory of Keulegan and Patterson and the model of Collins for horizontal slopes give us the smallest values of breaking height. Little higher values are given by the upper boundary of Keulegan and Petterson together with the model of Weggel for a horizontal slope. The values concerning the theory of Collins, change a lot in function of the bottom slope. The highest wave on a water depth of 30cm is 21,6cm for a horizontal bottom, while this is 30,40cm for a bottom slope of 3O and increases until 51,22cm if the slope becomes 10O. The model of SPM and Demirbilek and Vincent also shows the in uence of the bottom slope, but the in uence of the slope is rather small. The highest wave that can exist in a water depth of 30cm changes from 25,05cm to 25,18cm until 25,49cm when the bottom slope changes from horizontal to 3O until 10O. This dierence is very small. For a horizontal bottom the model of SPM and Demirbilek and Vincent gives higher values than Collins, but for higher bottom slopes, the values of Collins are clearly higher.
Comparing those results with the results measured during the experiments, we see that the lower boundary of Keulegan and Patterson and the model of Collins (horizontal bottom) estimates the breaking wave height very well. The upper boundary of Keulegan and Patterson and the theory of Weggel overstimate the breaking wave height a bit, and SPM and Demirbilek and Vincent give us an overly conservative estimation which can increase the cost of a project. The lower measured breaking wave height for depth 40cm than for depth 38cm, is not possible, and the reason has to be searched in the measurement system of the wave heights or the analyses afterwards.
Concerning the formulae given by Komar and Gaughan and Sakai and Battjes, the relation
Hb/H0 can be described in function of H0/L0 (Fig 6.3). The values Hb,H0 and L0 of the executed tests are de ned as described above. The two theoretical curves have the same form as the curve of the measured values. For
increasing H0/L0, which means decreasing wave period, the breaker wave height decreases.
For the same characteristics in deepwater conditions (means also for the same peiod), the Results 82
Figure 6.2: Theoretical models to estimate the breaking wave height in function of the water depth, compared with the maximum measured wave height: Keulegan and Patterson (K&P), Collins for dierent slopes, SPM for dierent slopes and Weggel for a horizontal bottom Results 83
Figure 6.3: Theoretical models to estimate the relation Hb/H0 in function of H0/L0, compared with the measured results: Komar and Gaughan (K&G), Sakai and Battjes (S&B)
model of Sakai and Battjes gives higher values for Hb/H0 than the theory of Komar and
Gaughan. The measured values Hb/H0 however, are higher than both. This means that both theories tends to underestimate the maximum wave height which could result in structural failure or signi cant maintenance costs.
The results of Le Roux are shown in a graphic giving the deepwater wave height H0, calculated with the formula of Airy, in function of Hw, being the wave height in any water depth (Fig 6.4). To compare this theory with the measured results, we will x a certain water depth, being h=30cm. The same can be done for the other water depths. Concerning the iterative method of Le Roux to calculate the characteristics, the breaker height is given by the formula proposed by SPM concerning a horizontal bottom. This is in the graphics a horizontal line
given by: H = 0, 835 · 30cm = 25, 05cm, because we x a water depth of 30cm.
Concerning the theory, we see that for increasing period, and a xed deepwater wave height, the real wave height increases. Also can be seen that the waves with a dierent period have the same breaking wave height, the wave height given by the formula of SPM and Demirbilek Results 84
Figure 6.4: Theorecal model of Le Roux to estimate the real water wave height for h=30cm, com- pared with the measured results and Vincent, as explained in the theory of Le Roux. Ones reached the breaking wave height, concerning Le Roux, all the waves with a higher deepwater wave height, will have an equal maximum wave height in shallow waters. Comparing those results with the measured ones, we see that for increasing period and a xed deepwater wave height, the real wave height also increases, however, we see also clearly that the measured results are a little higher than the calculated values, which means that the real wave heights are underestimated by the theory of Le Roux. Another dierence is that the breaking wave height changes with the period, higher the period, higher the breaking wave height. Further, we see that ones reached the maximum wave height, for higher deepwater wave heights, the maximum wave height in shallow waters decreases, it doesn't reach anymore the breaking wave height Hb. The reason therefore can be found in the fact that how higher the deepwater wave height, how stronger the breaking will be, saying that the loss of energy by breaking will be higher, which will result in a lower wave height, as can be seen in the curves of the measured results. This fact, however is not seen in the theoretical model of Le Roux. Results 85
6.4 Hydraulic stability of the mound breakwater
6.4.1 Wave re ection
As mentioned in 5.4.4.3, the re ection coe cient will be represented in function of the dimen- sionless relative water depth rst, and secondly in function of the number of Iribarren. Here we don't make a dierence between the models with or without toe berm, because this has no in uence on the re ection coe cient. The results in the dierent sections are explained, and further, the obtained results are compared with the results in deepwater conditions [36].
d kh = 2π (6.1) L
tan (α) Ir = (6.2) q H L
6.4.1.1 The re ection coe cient in function of kh
In the three cases (double cubipod layer, single cubipod layer, and the combination of a cube with a cubipod layer) the same tradition can be seen in the graphics showing the re ection coe cient in function of kh (Fig 6.5). First of all, we see that the executed tests can be divided in groups with a constant value of dimensionless relative water depth. For a certain water depth and period, dierent waves with increasing wave height were lanced. This wave height, however, does not in uence on the wave length, so does not in uence on kh. This means that the dierent experiments with the same water depth and the same period (but dierent wave height) have a constant value of kh, which explains the separated groups of points in the graphics. Further can be seen that the wave length and wave period will play an important role. For
kh > 1, 5 the re ection coe cient is rather small, while for smaller kh values the re ection coe cient increases, rising more steeply for kh approximately 0,50.
We conclude that there is a correlation between the wave re ection and the parameter kh. Small numbers of kh, and thus large wave lengths and small wave periods, coincide with higher Results 86 re ection coe cients. The crest does not break on the slope but only runs up and down on it. Few energy is being dissipated, which leaves room for signi cant re ection.
Double Cubipod layer - Single Cubipod layer Comparing the re ection coe cient in case of two layers of Cubipods with a single layered mound breakwater, there can be easily seen that for high values of kh, the re ection coe cient is clearly higher for a double layer of Cubipods (15% - 25%) than for a single layer (7% - 15%). This dierence however decreases when kh decreases. For kh approximately one, the situation is opposite; the double layer reaches values of 10% - 20% while the single layer reaches higher values from 15% to 25%. For small values of kh the dierence can be supposed as nil, for both sections, the CR varies between 30% and 50%. (Fig 6.6).
Waves with small wave lengths will dissipate more energy on a one layered mound breakwater than in case of a double layer. This dierence for high values of kh is due to the higher porosity in case of one armour layer, and thus easier access to the core to dissipate a lot of energy. Two layers of armour elements decrease the access to the core and less energy will be dissipated, thus a higher re ection coe cient will occur. Decreasing kh, however, means that the crest does not break on the slope but runs up and down on it and the type of armour layer will in uence the re ection coe cient. A double armour layer can dissipate more energy than a single one, which explains less re ection in case of a double layered armour layer compared with a single layer. Further increasing of the wave lengths, means less in uence of the number of armour layers on the re ection coe cient as can be seen in the graphics. The dierence in the coe cient of re ection is negligible for small kh, which means that a single layer of Cubipods and a double layer of Cubipods dissipate the same energy in case of waves with high wave lengths.
Double Cubipod layer - Combined layer A comparison of a mound breakwater consist- ing of a cube-cubipod combined layer with a double layer of Cubipods is shown in gure 6.7. The results are very similar but for high values of kh, a double layered mound breakwater of Cubipods re ects a little less energy than in case of the combined cube-cubipod layer.
This is due to the fact that cube elements tend to re-organize its units to an almost solid Results 87 plate where all the cubes have the same orientation and with a very low porosity. Therefore, less energy can be dissipated and more re ection occurs. As this cube layer is covered by a cubipod layer, this re-organization will only take place partially, which means that the porosity in the upper layer will be similar in both cases. This explains the little dierence in re ection coe cient between both.
Single Cubipod layer - Combined layer Also the comparison of a combined cube- cubipod layer is made with a single cubipod layer (Fig 6.7). For high values of kh, the re ection coe cient of the mound breakwater with one cubipod layer is less than in case of the combined layer. Thus, for waves with small wave lengths, a mound breakwater with one layer of Cubipods dissipates more energy than in case of the combined layer. Decreasing the kh coe cient, however, the re ection coe cient of the one layered cubipod armour layer becomes a little higher then in the combined case.
The reason is the same as explained above in the comparison between the single and double layer with only Cubipods. The higher porosity in case of one armour layer compared to two armour layers, causes a lower re ection of energy. As the double layered armour layer now also has a cube layer, the dierence is bigger, because those Cubipods tend to re-organize to an almost solid plate with a very low porosity, which means that less energy can be dissipated. As the wave length increases, the dierence in re ection coe cient decreases and the importance of the type of armour layer seems less important.
6.4.1.2 The re ection coe cient in function of Ir
The graphics showing the re ection coe cient in function of the number of Iribarren are also enclosed (Fig 6.8). A clear dierence can be seen between the re ection coe cient for waves
with Ir > 3 and Ir < 3. Small numbers of Iribarren coincide with little re ection, while waves with high numbers of Iribarren have a high re ection coe cient.
Experiments with small Iribarren numbers, where short wave lengths and thus small periods
occur, coincide with plunging breaking (0, 5 < Ir < 2, 5) and collapsing (2, 5 < Ir < 3). A lot of energy is dissipated which means little re ection. Results 88
A high theoretical Iribarren's number, on the other hand, means large wave lengths and thus large periods occur. High Iribarren numbers coincide with surging wave breaking. The crest does not break on the slope but only runs up and down on it. Few energy is dissipated, which leaves room for re ection. This correlation between wave re ection, number of Iribarren and type of wave breaking is also shown in Battjes [8].
6.4.1.3 Comparing with the re ection coe cient in deepwater
Earlier tests were executed in deepwater on mound breakwaters with an armour layer existing of a double layer of Cubipods. Those results can be compared with our tests. In deepwater conditions, the re ection coe cient varies between 15% and 60%, and in shallow water between 10% and 50%.
As waves enter shallow water, their overall wave length shortens, the crest will break and thus a lot of energy is dissipated which means little re ection. Results 89
Figure 6.5: The re ection coe cient (CR) in function of the dimensionless relative wave depth (kh) Results 90
Figure 6.6: The re ection coe cient in function of the dimensionless relative water depth (kh): comparing single and double layers of Cubipods Results 91
Figure 6.7: The re ection coe cient in function of the dimensionless relative water depth (kh): comparing a combined cube-cubipod layer with a double layer of Cubipods and a single layer of Cubipods Results 92
Figure 6.8: The re ection coe cient (CR) in function of the number of Iribarren Results 93
6.4.2 Damage analysis on the armour layer
6.4.2.1 Introduction
To make a rst estimation of the hydraulic stability coe cient for the considered breakwater sections in breaking conditions, damage analysis is executed using the qualitative method, based on the photos made after every experiment. Further, to receive more exact results, the damage progression is studied using a quantitative method, the Virtual Net Method described by Gómez-Martín & Medina [24], taking into account the heterogeneous packing. A more correct result is obtained. Here can be mentioned that during the experiments could be seen clearly that heterogeneous packing took place before extraction of armour units.
6.4.2.2 Qualitative analysis
To make a rst estimation of the hydraulic stability coe cient, the damage is analysed quali- tatively, using the photos made after every experiment. The aim is to obtain the value of the incident wave height corresponding with Initiation of damage (IDa), Initiation of damage of Iribarren (IIDa) and Initiation of destruction (IDe) using the de nitions explained in 5.4.4.4 and to compare those results for the dierent breakwater sections. Those values of incident wave height will be used later on to estimate the hydraulic stability coe cient, using the Hudson [5] formula proposed by SPM[6]. As the tests were always stopped before IDe, only the rst two levels will be considered here. Concerning the de nitions of the damage levels, for a single layer of Cubipods, there is no dierence between IDa and IIDa, thus only one level is obtained. The results can be seen in 6.1. The corresponding incident wave height producing those levels of damage, is taken as the maximum of the signi cant incident wave heights H1/10 of all the earlier lanced waves by this type of armour layer.
The dimensionless damage corresponding to those two damage levels is calculated. They dier a little between the dierent types of armour layers but the average values can be given as:
De=1,2 for IDa and De=3 for IIDa. Results 94
IA IAI
De H1/10 [cm] De H1/10 [cm] Double layer Cubipods without toe berm: C2 1,20 16,5 2,96 23,4 Single layer Cubipods without toe berm: C1 1,26 19,8 Double layer Cubipods with toe berm: C2B 1,32 19,7 2,97 23,6 Single layer Cubipods with toe berm: C1B 1,10 18,4 Combined layer: CB 1,37 16,9 3,15 23,6
Table 6.1: Incident wave heights producing the levels of damage: IDa and IIDa
For the double armour layer, the breakwater section with toe berm can resist a higher wave height until IDa or IIDa occurs than in the situation without toe berm. The elements move more downwards if there is no toe berm, thus damage will occur earlier.
For the single armour layer, the situation seems to be opposite. The reason therefore, however, has nothing to do with the presence or absence of a toe berm. The executed tests on the section without toe berm are formed by the rst layer of B2, taking o the coloured elements of the upper layer. The elements of the under layer were already stabilized during the tests on the double layered section and thus have a higher friction with the lter, which means that they can resist a higher wave height before reaching a damage level. The dierence for the higher wave height in case of a single layer B1 compared with the double layered breakwater B2, can be explained in the same way.
The wave height corresponding with IDa for the double layered breakwater with toe berm C2B is higher than for the single layered, which indicates a higher hydraulic stability of the section C2B than of the section C1B.
For the combined section CB, no explicit conclusion can be made concerning the hydraulic stability in comparison with the other sections. More tests are necessary to exclude the right solution.
The formula of Hudson, proposed by SPM, to calculate the number of stability Ns is used to Results 95 estimate the hydraulic stability coe cient and is de ned as:
H1/10 1 NS = = (KDcotα) 3 (6.3) ∆Dn 3 NS KD = (6.4) cotα
The incident wave height is de ned as the signi cant wave height H1/10 causing IDa, as proposed by SPM [6]. Also here, the maximum signi cant incident wave height of all the earlier tests is taken as corresponding wave height. Knowing the breakwater slope (1:1,5), the dimensions of the armour units (Dn=3,82cm for Cubipods and Dn=4,00cm for cubes), their 3 density (2,30t/m ) and the wave height producing IDa, the value of KD can be calculated. For the combined layer CB, the calculation is done with the dimensions of the cubes, because this results in a lower value of stability than when it should be calculated with the lower cubipod dimensions.
KD=43 was found for double layer of Cubipods, KD=35 for a single layer of Cubipods and
KD=23 for a combined armour layer with cubes and Cubipods, knowing that this lower value is also due to the calculation with the cube dimensions. Important to know is that those values are valid for shallow water (breaking conditions), in the structure head of a mound breakwater and random collocation of the Cubipods. Those values, however, are just a rst estimation. More experiments need to be carried out to optimize this parameter.
Important to mention is the high value of hydraulic stability coe cient of Cubipods, compared with other armour units. Some of them are published in SPM (1984) [6], those can be seen in table ??.
Also necessary to mention is that the calculation of the hydraulic stability coe cient here is based on results of damage tests assuming damage by Heterogeneous Packing. Knowing that this failure mode occurs almost always before extracting of armour units, the received results here probably will be more exact than those received by the traditional methods. Results 96
6.4.2.3 Quantitative analysis
The qualitative analysis gave us a rst estimation of the stability of the dierent armour breakwaters. To obtain a more correct restult, however, a quantitative analysis is necessary. The quantitative analysis of the damage is done using the Virtual Net Method, that compares the porosity in every zone of the armour layer to the initial porosity and results in the equiv- alent dimensionless damage, as explained in section 5.4.4.4. This can be transformed to the linearized dimensionless damage by elevating it to the power 0,2 (Eq. 6.5). In a graphical presentation this ultimate value provides a clearly understandable image.
D∗ = D0,2 (6.5)
After every series of tests with a constant water depth, the dimensionless damage De is calcu- lated, and this for the dierent studied models. Here, the same remark as in the qualitative analysis about the wave height can be made. As corresponding wave height, the maximum measured incident average wave height Hm during the series of tests with the concerned water depth is taken.
If the linearized dimensionless damage D* values are represented simply as a function of the corresponding scaled wave heights, it is rather di cult to interpret them and to compare them with other test results, especially because low density concrete is used. To provide a more accurate representation and especially to be able to compare the obtained results with the results of the earlier cubipod model tests in non-breaking conditions in deepwater [38], the average incident wave height is divided by the wave height that causes IDa (HD=0) for an equivalent cube with the density and weight of the used Cubipods, but KD of a regular cube. Using the Hudson formula, this results in HD=0(KD=6)=10,03 cm. Thus, the linearized dimensionless damage of the wave tests are presented with respect to a dimensionless wave height: . With this conversion, the comparison with the former results can H1/10/HD=0,KD=6 be done eectively.
The results are also compared with the equation proposed by Medina et al. [47], based on the test results for quarrystone in SPM [6]. Based on this equation, a general equation for each type of armour unit can be deduced, where Hm is the average incident wave height: Results 97
0,2 H1/10 D = (6.6) HD=0 1, 6 1/3 4 Hm D∗ = D0,2 = 1, 60,2 (6.7) KD HD=0
First, we study the in uence of the presence of a toe berm by comparing both: the double ar- mour layer with and without toe berm and the single armour layer with and without toe berm.
In the graphics (Fig 6.9) showing the results of the double armour layer is it clear that the hydraulic stability is lower if there is no toe berm. After a series of experiments however can be seen that this dierence becomes nil. In case of a toe berm the armour elements at the bottom of the mound breakwater can't remove, and thus increase of porosity will only occur at the top of the breakwater. For the elements near the bottom, the porosity decreases because the elements from above push them down. When this toe berm is not present, however, the elements near the bottom can remove and also here the porosity will increase, thus higher damage occurs in the beginning. After a series of experiments, the removed elements are collected at the bottom and form a massive entity, working like a toe berm, which explains the small dierence at the end.
The graphics showing the results of the single armour layer, however, show the opposite. The mound breakwater without toe berm seems to have a higher hydraulic stability. The reason therefore, however, has nothing to do with the presence or absence of a toe berm. The executed tests on the section without toe berm is formed by the rst layer of B2, taking o the elements of the upper layer. The elements were already stabilized during the tests on the double layered section and thus have a higher friction with the lter layer. In the results of the section without toe berm can be seen that at the top of the breakwater, little damage takes place, the majority of the damage is due to the layers at the bottom, and thus due to the absence of a toe berm. In the experiments with toe berm, there is no damage at the bottom near the toe berm, but the damage is only due to removing units at the top of the breakwater. In this case, an explicit conclusion can't be made. Results 98
As mound breakwaters with toe berm are the common built breakwaters in breaking condi- tions, the further hydraulic stability analysis will only be executed with this types of break- water.
The graphics with the calculated dimensionless damage results (the isolated points in Fig 6.10) show a dierence between the three breakwater sections. The double layer gives more stable results than the single layer of Cubipods, while the combined layer of cubes and Cubipods gives the lowest results.
Changing KD by a certain hydraulic stability coe cient in the equation 6.7, the equivalent line for every armour unit can be drawn in the graphic showing D* in function of Hm/HD=0. We can draw the lines with KD=43, KD=35 and KD=23, corresponding with the double Cubipod layer, the single Cubipod layer and the combined layer of Cubipods and cubes, in the graphics. Also the lines indicating IDa and IIDa are drawn. The result can be seen above in the gure 6.10.
For the dierent breakwater sections, the results of the dimensionless damage (the isolated points) seem to be higher than the equations, using the qualitative calculated stability coef-
cient predict, which means that the qualitative manner to calculate KD overestimates the stability coe cient. Better adjustment would be obtained with the line KD=28 for double layer of Cubipods, KD=23 for a single layer of Cubipods and KD=18 for the combined layer as we prefer to place the line on the safe side. This is shown in the second graphic of gure 6.10.
Further, comparing the results with the executed tests in deepwater for a double layered breakwater, there can be seen that the results in breaking conditions are less stable than in non-breaking conditions. For the same incident wave height a higher dimensionless damage is occurred in case of breaking conditions than in case of a non-breaking situation. On the other hand, to receive a certain level of dimensionless damage, in non-breaking conditions a higher incident wave height is needed than in breaking conditions. This is normal because in breaking conditions, waves with higher energy reach the breakwater, which means that the damage will initiate earlier than in deepwater conditions. Results 99
Figure 6.9: In uence of the presence of a toe berm on the hydraulic stability of a mound breakwater Results 100
Figure 6.10: The linearised dimensionless damage as a function of a dimensionless height. Above:
the qualitative calculated KD's. Under: the quantitative calculated KD Results 101
Figure 6.11: Comparison a double Cubipod layer in breaking with non-breaking conditions, and with Quarrystone in breaking conditions. Dimensionless damage as a function of dimension- less wave height Chapter 7
Conclusions
The stability of the armour layer of a mound breakwater depends on many factors, but in this project only the hydraulic stability of the armour units is studied, more speci cally the loss of armour elements in certain zones of the breakwater slope which can be caused by two reasons: simple extraction of the armour units under wave attack or their excessive settlement causing Heterogeneous Packing. The hydraulic stability in breaking conditions of the recently invented Cubipod is studied.
The goal of the Cubipod unit is to bene t from the advantages of the traditional cube, but to correct the drawbacks. Therefore, the design of the unit is based on the cube in order to obtain his robustness. The protuberances of the Cubipod avoid face-to-face settlement and increase the friction with the lter layer. They avoid sliding of the armour elements. Due to this, Heterogeneous Packing and loss of elements above the still water level is reduced. All this indicates a higher hydraulic stability of Cubipods in comparison with cube elements. Furthermore, easy casting, e cient storage and handling are other advantages.
As the incident wave height is an important factor in uencing the design of coastal structures, a short study is done concerning the maximum wave height in breaking conditions. Dierent existing theories were commented and compared with the measured values. In general can be concluded that the theories overestimate the maximum wave height. Further, many theories suppose that the energy from the broken waves is concentrated in the breaking wave height,
102 Conclusions 103 which meant that all the broken waves would have the breaking wave height in the sur ng zone. This statement however doesn't correspond with the measured results. The energy from the broken waves is distributed back over the smaller wave heights in the distribution.
The aim of this nal project was the experimental study of the behaviour of Cubipod breakwa- ters under wave attack in breaking conditions. The most important results were the re ection coe cient and the hydraulic stability coe cient of the armour layer. The obtained results were compared to the similar previous tests on Cubipod breakwaters in deepwater condi- tions. The re ection coe cient of the Cubipod armour layer diers between 10% and 30% for kh > 1, 5 and increases until 50% for small kh values. For high kh values, the type of armour layer has a big in uence on the re ection coe cient. For small values of kh, however this in uence decreases and becomes nil. Re ections coe cients in shallow water is lower than in deepwater conditions because the crest breaks and a lot of energy is dissipated which means less re ection.
All tests proved that the Cubipod has a high hydraulic stability in breaking conditions, com- pared with all other published armour unit values. Stability factors of KD=28 and KD=23 were obtained for respectively a double layer and a single layer of Cubipods. For a combined layer with Cubipods above cubes, a stability factor KD=18 was obtained. Comparison be- tween the damage progression in deepwater conditions and in shallow water shows us that the hydraulic stability coe cient in shallow water is less than in deepwater conditions. Waves with higher energy reach the breakwater, which means that the damage will initiate earlier than in deepwater conditions.
Finally, the Cubipod shows to be a very promising armour unit, with a simple and robust shape, an easy placement pattern and a high hydraulic stability, also in breaking conditions. It can certainly be a very good alternative for regular cubes, and when more experiments will be carried out, probably as well for many other armour units. Appendix A
Terminology of the experiments
Every experiment has a code: VBWX_YZAC, e.g. VB01_3216 or VB04_5117. The termi- nology of the experiments is the following:
The rst two letters VB stand for the laboratory where the tests have been carried out (V=Polytechnic University of Valencia) and for the conditions of the executed tests (tests in breaking conditions).
The next number (W) refers to the wave type. As we only consider regular waves, is this number always 0.
Further, the type of armour layer is de ned by the following de nitions:
1: double armour layer
2: single armour layer
3: double armour layer with toe berm
4: single armour layer with toe berm
5: cubipods above cubes
The number 'Y' stands for the water depth in the model. The following values are considered:
1: hmodel = 20 cm
104 Terminology of the experiments 105
2: hmodel = 25 cm
3: hmodel = 30 cm
4: hmodel = 35 cm
5: hmodel = 38 cm
6: hmodel = 40 cm
7: hmodel = 42 cm
The next value represents the period of the lanced wave in model being:
1: T = 0.85 s
2: T = 1.28 s
3: T = 1.70 s
4: T = 2.13 s
5: T = 2.55 s
The last two numbers describe the wave height in model. A wave height of 6 cm in model, results in 'AC'=06, a wave height of 12 cm in model results in 'AC'=12. Appendix B
Wave ume
A detailed plot of the total test setup within the wave ume is shown on the next page. From left to right one can see: the wavemaker, a rst group of four wave gauges, the transition slope, the second group of wave gauges, the breakwater model, an extra wave gauge to measure the run-up together with the Step-Gauge system and nally in the right end the energy dissipator.
106 Wave ume 107
Figure B.1: Cross section of the 2D wave- ume of the Laboratory of Ports and Coasts of the Po- litecnic University of Valencia Appendix C
Working of the AWACS
Many authors and laboratories resolved the re-re ection problem by placing an active re ection absorption system in the wave generator. Schäer and Klopman (2000) [48] review various types of those techniques. However, most of the wave absorption methods have not been published and some doubts still remain regarding the true eectiveness of methods based on sophisticated lters and black boxes. The wavegenerator in the laboratory is provided with an Active Wave Absorption Control System AWACS. A more detailed scheme of the working of the AWACS, provided by DHI AWACS2, is given in gure C.1.
Before starting any other software, the next steps in the central control unit behind the wavemaker, have to be followed. First, the principal button, feeding the other two, has to be swithed on. Than, the second button, providing 24V has to be swithed on, and last, the third button that provides 220V. Now the control unit receives alimentation.
Afterwards the converter is activated to change analogical signals from the computer in optical signals going to the control system of the AWACS. Then the software 'DHI Wave Synthesizer' can be started (Fig C.3). Here, an important option is 'Active Absorption'. The AWACS only will work if this option is activated, if not, the wavemaker will not take into account possible re-re ections.
Every day before starting the experiments, the two wave gauges should be calibrated. DHI AWACS2 features self-calibration of the paddle-mounted wave gauges. This is done by putting
108 Working of the AWACS 109 the button DSC in the starting window of the program. First 'oset scan' is done, this comment is used to put the present water level of the wavemaker on zero. The number of columns depends on the number of wave gauges, in our case two (called A & B). The standard deviation in calm water is supposed to be more or les 0,002V. If the values of the standard deviations are less than 0,005V, it is accepted. If not, the button 'skipp all' is pushed and the oset scan is executed a second time.
Afterwards the calibration is done. The program starts to work and the information on the screen is actualizing continual. At the end, the old and new values have to be controlled and should be similar.
Now the waves to generate can be de ned. In the window 'wave parameter' we de ne 'regular waves' and further 'Stokes 1st order'. In this window the wave height in meters, the period in seconds and the water depth in meters have to be introduced. All those values are in prototype and without taking into account any scale.
In the next window 'wave generation' (Fig C.4), the scale of the used model has to be de ned, and should be higher than 1. The duration of the test is obtained by multiplying the theoretical period of the experiment by the number of desired waves. The program calculates the amplitud and the velocity of the wavemaker. It's important to check if the utilization of the wavemaker is less than 100%.
Before putting the start button, the software 'Multicard' for the aquisition of the datas has to be activated (Fig C.5). Here the water depth near the wavemaker has to be given, and in the window 'toma los datos' the duration of the test has to be de ned. This duration will be little higher than the duration given in 'DHI Synthesizer' to be able to also have datas after the wavegenerator stopped moving. After putting 'realizar ensayo' the wave height in cm and the period in seconds of the model are asked.
Now the experiment can be started. When nished, the datas has to be saved and the next experiment can be started. Working of the AWACS 110
Figure C.1: A detailed scheme of the working of the AWACS
Figure C.2: The steps to activate the control system Working of the AWACS 111
Figure C.3: Software to manage the AWACS. Above: the startscreen Under: the calibration of the AWACS Working of the AWACS 112
Figure C.4: Windows to realize the wave generation
Figure C.5: The program Multicard, for the aquisition of the datas Appendix D
Seperation of incident and re ected waves
The response of maritime structures depends on the incident wave eld, however in laboratory model tests as well as in prototype only the incident wave added to its re ection can be measured. This makes it necessary to distinguish the incident wave train seperated from the re ected wave train to study and predict response of maritime structures both in model tests and in prototype.
Various methods for wave separation have been developed but those, however can only separate the incident wave from its direct re ection on the breakwater, which means that they don't take into account multire ections in the wave ume. Therefore, the wave ume in the laboratory is provided with an AWACS.
The basic method on which most existing techniques for separating incident and re ected waves in laboratory are founded is the two-point method. This method is popularized by Goda and Suzuki (1976) [49] and is based on linear dispersion and wave superposition. This method, however is only usefull in numerical and noise free simulations, but not when using real measurements in wave umes. Some methods like the three-point least squares method of Mansard and Funke (1981) [50] may reduce the instability and sensitivity to noise, but stationarity and linearity still remain
113 Seperation of incident and re ected waves 114 as two fundamental principles of the frequency-domain techniques used by most laboratories for separating incident and re ected waves. One of their main disadvantages is the inconsistency produced by the fact that future measured data are needed to estimate earlier analysed data. Time-domain methods like those proposed by Kimura (1985) [51] and further developed by Frigaard and Brorsen (1994) [52] or Schäer and Hyllested (1999) [53] resolve this problem but still assume linear models.
The LASA method (Local Approximation using Simulated Annealing) developed by Medina [54] for the analysis of incident and re ected waves in the time-domain, is based on a local approximation model considering linear and Stokes-II nonlinear components, and a simulated annealing algorithm to optimize the parameters of the wave model in each small local time- segment of the measured record. To obtain the water surface elevation corresponding to the incident and re ected wave trains at any point of the record, the results of the optimization in each time window overlap. The method can be used for nonstationary and nonlinear waves.
The LASA method has been compared with the 2-point method from Goda and Suzuki and the method developed by Kimura and resulted very robust in numeric experiments and very consistent in physical experiments with both regular and irregular waves. The method can directly be applied to regular and irregular two-dimensional waves without excessive steepness, using whatever number of measuring gauges. This implies a huge advantage for the use in both prototype and laboratory model tests with irregular and nonstationary waves, considering the fact that up till this time, no other methods were available to analyse adequately the wave separation of this very common and necessary experiment type.
Figueres and Medina [55] optimized the 'LASA local wave model' method, based on linear and Stokes-II nonlinear components to the 'LASA-V wave model' using an approximate Stokes-V wave model. This model is able to analyse experiments with highly nonlinear waves as in intermediate depth conditions. Appendix E
Calculation of the initial porosity
Figure E.1: Calculation of the initial porosity
115 Appendix F
Example of a test report
An example of the report le for the results near the wavemaker generated by the software tool LPCLab is presented here. The reports of all the executed tests can be found on the included cd-rom.
116 Example of a test report 117
Figure F.1: Example of a test report Example of a test report 118
Figure F.2: Example of a test report Appendix G
Test results
An overview of the executed tests and the most important results are given. The used ter- minology of the experiments can be found in Appendix A and all the complete LPCLab test reports can be found on the available cd-rom.
119 Test results 120 Test results 121 Test results 122 Test results 123 Test results 124 Test results 125 Test results 126 Test results 127 Test results 128 Test results 129 Bibliography
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