study of prefabricated re-usable breakwaters for shore

Laboratory of Ports and Coasts, Polytechnic University ValenciaDepartment of Civil Engineering, Ghent university

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Study of prefabricated re-usable breakwatersfor shore protection

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Jonas Maertens

Tutors:Prof. Josep R. MEDINAProf. Julien DE ROUCK

Masterthesis to obtain the title Master of Science in EngineeringAcademic year 2006–2007

A word of thanks

Firstly I would like to show my appreciation to prof. Medina for giving me the opportunityto make my final year project at the Port and Coastal Engineering Laboratory, and for hisguidance as my tutor throughout the project.

Deep gratitude goes to Joaquin and Esther for there guidance throughout this project andsharing there experiences. Further I wish to thank Ben and John for carrying out the manytests with me, Ana and Modest for there efforts in analysing the data in the LASA andLPCLAB program. Also a word of thank goes to Luis, Olaya, Fede and Pepe who made it areally pleasant stay at the laboratory.

Special thanks go to prof. De Rouck for coordinating the Erasmus project at Ghent Universityand of course my parents, who gave me the opportunity to have this wonderful experienceabroad.

CopyrightThe author gives the permission to make this project available for consultation and to copyparts from it for personal use. Any other use is submitted to the restrictions of copyright,with in particular the obligation to mention explicitly the source when quoting results of thisproject.

Jonas Maertens

June 2007

i

Overview

“Study of prefabricated re-usable breakwaters for shore protection”

by Jonas Maertens1

Masterthesis to obtain the title Master of Science in EngineeringAcademic year 2006 - 2007

Tutors:Prof. Josep R. MEDINA2

Prof. Julien DE ROUCK3

This Master thesis was made in cooperation with the European Erasmus project:

• Receiving University:“Universidad Politecnica de Valencia”(Laboratorio de Puertos y Costas)

• Sending University:“Universiteit Gent”(Department of Coastal Engineering)

1Masterthesis student, Faculty of Engineering, Ghent University, Belgium2Professor, Lab. of Ports and Coasts, Polytechnic University of Valencia, Spain3Professor, Faculty of Engineering, Ghent University, Belgium

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Summary

In this project the behaviour of prefabricated re-usable breakwaters is studied. This re-usableprefabricated modular based breakwater is intended for shore protection, and was patentedby Medina and Rodrıguez (2003) in the LPC4 of the Polytechnic University of Valencia.

The inventive breakwater is based on a reduced number of different prismatic, tubular modulesincluding one quadrangular-section module, two triangular-section modules and a straighttrapezoidal-section module, such that it is possible to produce a breakwater of any width,height and section. In the MODUMAR-project, which is subject of this master thesis, only1 quadrangular and 1 triangular module was used. Moreover, the modules have a thicknessof the order of 2.5 metres, a similar height and a length of 6 to 12 metres. In this way, thedimensions of the modules are suitable for the standard containers that are used to transportgoods by road, ship and train. This will lower the cost to transport the breakwater tohis location and will it make easier to re-use the breakwater at another location then firstinstalled.

Tests were carried out at the laboratory of Port and Coastal Engineering (LPC) of the Po-litechnic University of Valencia (UPV) to examine the transmission coefficient and the waveabsorption by the modular breakwater. The results of the tests are compared to those ob-tained for typical low-crested structures (LCS) for shore protection. To improve the predictivecapacity of the modular breakwater a Neural Network (NN) model, optimized by evolution-ary strategy, is proposed to describe the reflection and transmission performance of modularbreakwaters.

Keywords: Wave transmission – Detached breakwater – Prefabricated modules – Coastprotection – Neural Network model

4Laboratory of Ports and Coast

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STUDY OF PREFABRICATED RE-USABLE BREAKWATERS FOR SHORE PROTECTION

[EXTENDED ABSTRACT]

Author: Jonas MAERTENS 1

Tutors: Josep Ramon MEDINA2

Julien DE ROUCK3

ABSTRACT The study object of this Master thesis is the prefabricated modular breakwater for shore protection that was patented by Medina and Rodríguez (2003) in the Laboratory of Ports and Coast (LPC) of the Polytechnic University of Valencia. Wave transmission is a leading parameter determing the response of the shoreline to a detached breakwater. Therefore the modular breakwater was tested during 3 months (March to May 2007) in the 2D wave flume of the LPC, to estimate the transmission of seawaves over the breakwater, and this for different regular and irregular wave trains. After a short introduction to coastal engineering, the results of the transmission tests are exposed. The results are compared to those obtained for typical lowcrested structures (LCS) for shore protection. To improve the predictive capacity of the modular breakwater a Neural Network (NN) model, optimized by evolutionary strategy, is proposed to describe the reflection and transmission performance of modular breakwaters. Keywords: Wave transmission – Detached breakwater – Prefabricated modules – Coast protection – Neural Network model

1. INTRODUCTION Beach erosion and the corresponding shoreline retreat cause unacceptable economic and environmental risks in numerous coastal areas. Shore protection structures as groins and detached breakwaters, beach nourishment or a combination of structures and sediment addition are the most common response to the risk caused by persistent beach erosion. Low crested and submerged structures (LCS) such as detached breakwaters and artificial reefs are becoming very common coastal protection systems. Their purpose is to reduce the hydraulic loading to a required level that maintains the dynamic equilibrium of the shoreline. To obtain this goal, they are designed to allow the transmission of a certain amount of wave energy over the structure by overtopping and also some transmission through the porous structure (exposed breakwaters) or wave breaking and energy dissipation on shallow crest (submerged structures).

2. MODULAR BREAKWATER Prefabricated concrete submerged structures appear to be reasonable alternatives to conventional LCS in environmentally sensitive areas. The dust, noise and turbidity associated to the use of quarry stones, the materials supply problems (materials footprint) and the difficult reversibility of dumping quarry stones on sandy beaches. Medina and Rodríguez (2003) proposed the use of a new proprietary modular breakwater concept for shore protection in environmentally sensitive areas. Using 2 types of prefabricated concrete modules, a variety of coastal structures for shore protection can be constructed.

1Masterthesis student, Faculty of Engineering, Ghent University, BELGIUM 2Professor, Lab. of Ports and Coasts, ETSI Caminos, Universidad Politcnica de Valencia, SPAIN 3Professor, Faculty of Engineering, Ghent University, BELGIUM

The modules were designed to solve the logistics of storage and transportation as conventional containers (2.5 m high, 2.5 m wide and 6 or 12 meters long) in the multimodal transportation network. The elements of the modular breakwater are re-usable and have clear advantages in environmentally sensitive areas and in cases of urgent shore protection. We decided to test 5 different configurations made out of the 2 elements discussed before.

3. EXPERIMENTS The experiments were conducted in the wave flume of the Laboratory of Port and Coastal Engineering (LPC) of the Polytechnic University of Valencia (UPV). The 2D wave flume has a square cross-section (1.2 m x 1.2 m) and is 30 m long. The waves in the wave flume are generated by a metallic slab that is located at on one of the ends of the flume. In order to register the height, capacity wave gauges are used. Use was made of the LASA method proposed by Medina (2001) to separate reflected and incident waves from the registry. We tested in total 5 different configurations. Each configuration was tested with 4 different freeboards. For every freedboard there were 8 experiments: 4 with regular (10 waves) and 4 with irregular (1000 waves) waves. The irregular wave experiments were adjusted to the JONSWAP spectrum, with a peak-enhancement factor γ of 3.3.

4. RESULTS The most important result of the analysis of the recorded data is the transmission coefficient Kt. This transmission coefficient is calculated as: With Ht the significant transmitted wave height and Hi the significant incident wave height. The results of the experiments are compared to different studies of typical low-crested rubble mound structures (LCS) for shore protection. Equation 2 shows the formula for conventional quarry stone LCS proposed by Briganti et al. (2003) for the European DELOS project on LCS. Remarkable was the comparison between the results and the formula proposed by Ahrens (1987). With a root mean square error (RMSE) of 4.3% the formula (Eq: 3) predicts the wave transmission of the modular breakwater adequately.

5. NEURAL NETWORK MODEL

To improve the predictive capacity of the modular breakwater a Neural Netwerk (NN) model, optimized by evolutionary strategy, is proposed to describe the reflection and transmission performance of modular breakwaters. The following input parameters were used to make the NN for wave transmission: freeboard divided by waterdepth (F/d), freeboard divided by incident waveheight (F/Hi), waterdepth divided by wavelength (d/L) and crest width divided by wave length (B/L). The NN was trained with 70% of the experimental results and verified with the remaining 30%. A second Neural Network was proposed to predict the wave reflection. The input parameters of this NN are structure height divided by waterdepth (h/d), wave number multiplied by waterdepth (kd) and freeboard divided by incident wave height (F/Hi). With the use of both NNs, design graphs can be made with the proportional transmitted, reflected and dissipated energy.

REFERENCES Ahrens J. (1987), “Characteristics of reef breakwaters,”

Tech. Rep. CERC-87-17, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS

Briganti R., van der Meer J.W., Buccino M. and

Calíbrese M. (2003), “Wave Transmission behind Low-Crested Structures,” Proc. Coastal Structures 2003, ASCE, pp:580-592

Medina J.R (2001), “Estimation of incident and reflected

waves using simulated annealing,” Journal of Waterway, port, coastal and ocean engineering, 4(127), pp:231-221

Medina J.R. and Rodríguez J. (2003), “Dique modular para

la proteccin de costas” Patente de invención, UPV

List of Symbols

Symbol Definition Unit

α Spectral wave parameter [-]αs Structure slope [o]A Cross sectional area of the breakwater [m]B Crest width (horizontal) [m]d Water depht [s]Dn50 Nominal diameter, (M/ρ)1/3 [m]ξ Surf similarity parameter, (tanα/s0.5

0 ) [-]f Frequency [Hz]F Crest freeboard of the structure (=Rc) [m]Fr Froude Number [-]γ Peak-enhancement factor [-]g Gravitaional acceleration (= 9.81) [m/s2]G Gap width between breakwaters [m]h Structure height [m]H0 Deep water wave height [m]Hi Incident wave height [m]Hmo Significant wave height based on wave energy spectrum (m0)1/2 [m]Hs Significant wave height, average of highest 1/3 of all waves [m]Ht Transmitted wave height [m]k Wave number (=2π

L ) [m−1]Kr Reflection coefficient [-]Kt Transmission coefficient [-]λg Geometric scale [-]λt Time scale [-]L0 Deep water wave lenght [m]Li Incident water wave lenght [m]Ls Length of a detached breakwater [m]µ Dynamic viscosity [Pa · s]

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Symbol Definition Unit

mn Moment of spectral density of the nth ord [m2/sn]ν Kinematic viscosity [m2/s]N Numbre of incident waves [-]NN’s Neural Networks [-]ω Angular frequency [rad/s]ωp Angular peak frequency [rad/s]Rc Crest freeboard of the structure (=F) [m]Re Reynoulds Number [-]σ Spectral width parameter [-]σt Surface tension [N/m]s0 Wave steepness =(H0/L0) [-]S(f) The spectral wave density [m2s]T Wave period [s]Tp Peak period of Wave spectrum [s]U10 Wind speed at 10m height [m/s]v Velocity [-]We Weber Number [-]X The distance to the shoreline [m]

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Contents

A word of thanks i

Overview ii

Summary iii

List of Symbols vi

1 Introduction 1

1.1 Coastal erosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Classification of coastal structures . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Hard defences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.2 Soft defences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.2.3 Retreat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Detached low-crested breakwaters for shore protection 8

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Types of low-crested structures . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.1 Rubble mound with a trapezoidal cross section . . . . . . . . . . . . . 9

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2.2.2 Flexible-membrane units . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.3 Prefabricated modular units . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 State of the art of Prefabricated modular breakwaters . . . . . . . . . . . . . 11

2.3.1 P.E.P. Reef Unit(Prefabricated Erosion Prevention breakwater) . . . . 11

2.3.2 Beachsaver reef unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3.3 Device for preventing beach erosion . . . . . . . . . . . . . . . . . . . 13

2.3.4 Double-T Sill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3.5 Reef Balls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3.6 Beach Prisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.4 MODUMAR project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3 Theoretical model 20

3.1 The wave transmission phenomenon . . . . . . . . . . . . . . . . . . . . . . . 21

3.2 Parameters influencing wave transmission . . . . . . . . . . . . . . . . . . . . 22

3.2.1 Hydraulic Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.2.2 Geometric parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.3 Relevant studies on wave transmission . . . . . . . . . . . . . . . . . . . . . . 24

3.3.1 Dattatri et al. (1978) . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.3.2 Shore Protection Manual, U.S. Army Corps of Engineers (1984) . . . . 26

3.3.3 Ahrens (1987) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.3.4 D’Angremond et al. (1996) . . . . . . . . . . . . . . . . . . . . . . . . 28

3.3.5 Seabrook and Hall (1998) . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.3.6 Briganti et al. (2003) . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

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3.3.7 Comparison of predictive equations for wave transmission . . . . . . . 30

4 Experiments 31

4.1 Test equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.1.1 2D Wave Flume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.1.2 Wave generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.1.3 Energy Dissipation System . . . . . . . . . . . . . . . . . . . . . . . . 36

4.1.4 Wave gauges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.2 Analysis of the wave recordings . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.2.1 Separating the incident and reflected waves . . . . . . . . . . . . . . . 39

4.2.2 Analysis of the data produced by the LASA program . . . . . . . . . . 40

4.2.3 Model scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.3 Design of the modular breakwater . . . . . . . . . . . . . . . . . . . . . . . . 42

4.3.1 The geometric characteristics of the different modules . . . . . . . . . 42

4.3.2 The different compositions tested in the MODUMAR project . . . . . 44

4.3.3 Construction and positioning of the different modules . . . . . . . . . 46

4.4 Overview of the executed tests . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.4.1 Regular wave experiments . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.4.2 Irregular wave experiments . . . . . . . . . . . . . . . . . . . . . . . . 49

5 Results 51

5.1 Results of the experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.1.1 Influence of the crest freeboard on wave transmission . . . . . . . . . . 54

5.1.2 Influence of the crest width . . . . . . . . . . . . . . . . . . . . . . . . 55

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5.1.3 Energy proportions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

5.2 Comparison of the results with different theories of LCS . . . . . . . . . . . . 57

5.3 Comparison with the results of the REFLOTA project . . . . . . . . . . . . . 62

5.4 Neural Network Model to estimate wave transmission . . . . . . . . . . . . . 63

5.4.1 Background of Neural Networks . . . . . . . . . . . . . . . . . . . . . 63

5.4.2 Neuroport 2.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.4.3 Neural Network simulation . . . . . . . . . . . . . . . . . . . . . . . . 66

5.5 Neural Network Model to estimate wave reflection . . . . . . . . . . . . . . . 69

6 Conclusions 71

A Report File LPCLap 3.6 73

B Nomenclature of the experiments 76

C Calibration of the wave gauges 78

D Tables with the results 79

References 85

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Chapter 1

Introduction

This chapter gives you an introduction in the science of coastal engineering. After a briefexplanation of the coastal erosion problem, there is a classification of the different types ofcoastal protection structures.

1

Chapter 1: Introduction 2

1.1 Coastal erosion

The coastal zone all around the world is a dynamic area. It is the area in which the majorityof a water body’s kinetic energy is dissipated through wave breaking, runup and bed friction.The most significant result of these processes is the erosion and subsequent transport of theshore and beach materials. This littoral zone is very important to the public for economic andsocial reasons and to wildlife for habitat and food supply purposes. Moreover, the beachesat the Mediterranean coast of Spain are the most determining factor for the tourist industryin Spain and erosion of those beaches can have serious economical, social and environmentalconsequences. It is therefore very important that the coastal zone is protected and maintainedso that these considerations are addressed in a compatible and effective way. It’s the task offthe coastal engineer to protect the coast against the impact off the sea.

The shoreline is a dynamic system where stability is maintained despite the continued move-ment of waves, tides, wind and sediment. The present configuration of the shoreline is nowcontrolled by the various coastal defences, which mankind has put in place over the last 100- 200 years. These have stopped or slowed down the transport of sediments and reduced theability of the shoreline to respond to natural forcing factors.

There can be several causes of coastal erosion, including natural processes and sediment deficitdue to human impact.

• Natural erosion:Erosion caused by the action of waves, tides, currents, sea level rise,... The beachwill erode if there is less new sand entering a coastal system than is leaving it. Sandaccumulates or gets trapped in shoals and on the beach ”updrift” of the inlet, while thebeach ”downdrift” of the inlet erodes.

• Human impact erosion:Erosion caused by coastal engineering works (harbours, coast protection systems,... ),who change wave climate and currents to nearby located coasts.

The fight against coastal erosion is necessary along nearly the hole length of the Mediterraneancoast of Spain. Various coastal structures can be applied to solve, or at least, to reducethese problems. They can provide direct protection (breakwaters, seawalls, dikes) or indirectprotection (offshore breakwaters of various designs). The coastal engineer has to be alert thatthose construction don’t produce a chain effect, in eroding the coast elsewhere.


1.2 Classification of coastal structures

The main purpose of this chapter is to summarize alternatives and their functional designfor shore protection. Coastal defence and stabilization works are used to retain or rebuildnatural systems (cliffs, dunes, wetlands, and beaches) or to protect mans artifacts (buildings,infrastructure, etc.) landward of the shoreline. Coastal defence constructions can generallybe divided into two categories, hard and soft defences.

1.2.1 Hard defences

Groynes

Groynes are wooden, concrete and/or rock barriers at right angles to the sea. Groynes actas a barrier to physically stop sediment transport in the direction of littoral drift throughthe system. This causes a build-up of the beach on the groyne’s updrift side. The down-drift side of the groyne will be starved of material, and can cause another erosion problem.Consequently, a groin system results in a saw-tooth shaped shoreline within the groin fieldand a differential in beach level on either side of the groin (Fig. 1.1).Groins are usually designed in conjunction with beach nourishment activities and are intendedto lengthen the design life of a nourishment project by maintaining the beach design profilein areas of accelerated erosion (i.e., erosion hotspots). The strategy employed in these casesis to maintain the minimum beach profile in these hotspots while allowing some sedimenttransport to continue over and around the structures toward downdrift beaches.At one time groynes were invariably the chosen solution to a beach erosion problem wherenowadays the coastal engineer has many alternatives.


Figure 1.1: Groynes

Sea walls

Seawalls are built parallel to the shoreline as a reinforcement of a part of the coastal profile.Quite often seawalls are used to protect promenades, roads, and houses placed seaward of thecrest edge of the natural beach profile. The walls can be sloping, vertical or curved to reflectwave power. Erosion of the beach profile landward of a seawall might be stopped or at leastreduced. However, erosion of the seabed immediately in front of the structure will in mostcases be enhanced due to increased wave reflection caused by the seawall.


Figure 1.2: Vertical sea wall

Revetments

Revetments are onshore structures with the principal function of protecting the shoreline fromerosion. Revetment structures typically consist of a cladding of stone, concrete, or asphaltto armour sloping natural shoreline profiles. In the technical literature there is often nodistinction between seawalls and revetments.

Detached breakwaters

A submerged or emerged detached breakwater is placed parallel to the coastline to create azone of reduced wave energy in the lee of the structure and reducing shore erosion. Beachmaterial transported along the beach moves into the sheltered area behind the breakwaterwhere it is deposited in the lower wave energy region. The nearshore wave pattern, whichis strongly influenced by diffraction at the heads of the structures, will cause salient’s1 andsometimes tombolos2. That makes the coastline similar to a series of pocket beaches (Fig.1.3).

Detached or offshore breakwaters have been used extensively for coast protection, particularlyon coastlines where the tidal range is negligible or small.

1Triangular landforms in the sheltered area of a detached breakwater2When the landform is joined to the obstacle


Figure 1.3: Detached nearshore breakwaters

The examples of simple geometrical empirical criteria for the lay-out and shoreline responseof the detached, exposed (emerged) breakwaters are given below Harris and Herbich (1986):

- for tombolo formation:Ls/X > (1.0 to 1.5) (1.1)

- for salient formation:Ls/X = (0.5 to 1.0) (1.2)

- for salients where there are multiple breakwaters:

G ·X/L2s > 0.5 (1.3)

Where Ls is the length of a breakwater and X is the distance to the shore, G is the gap width(Fig. 1.3).

1.2.2 Soft defences

Mobile/ responsive defence measures which seek to work with nature rather than control it.Such structures may consist of sand or shingle beaches and dunes or banks which may be


natural or constructed.

Beach nourishment

Beach nourishment or replenishment is one of the most popular soft coastal defence engineer-ing techniques. This involves importing alien sand off the beach and piling it on top of theexisting sand. The imported sand must be of a similar quality to the existing beach materialso it can integrate with the natural processes occurring there. The source off the sand caneither be onshore or offshore.

Dune construction

Dune construction is the piling up of beach quality sand to form protective dune fields toreplace those washed away during severe storms. An essential component of dune reconstruc-tion is planting of dune vegetation and placement of netting or snow fencing to help retainwind-blown sand normally trapped by mature dune vegetation.

Beach Dewatering

Beach dewatering systems are part of an experimental erosion-control strategy by which wateris removed from the beach face to promote accretion of actively-moving sediment in the swashzone. The theory behind the concept is based on the supposition that draining water fromthe beach face can reduce the local groundwater table, thereby stabilizing the existing beachby reducing the buoyancy forces and lubrication between individual grains of sand on theexisting beach.

1.2.3 Retreat

In areas where dense coastal development has not already occurred, retreat can be the mosteconomic solution. Otherwise in areas of dense coastal development, retreat is the finaladaptation option. Relocation here also considers abandonment and demolition. If space isavailable, threatened structures may be moved landward in response to a retreating shoreline.To some, retreat is the only option. But practically, all constraints (economic, environmental,social, legal, etc.) must be evaluated for this alternative as well as for all others as previouslydiscussed.

Chapter 2

Detached low-crested breakwatersfor shore protection

After a short introduction of low-crested detached breakwaters, we will discus the differenttypes of low-crested structures.

1. Rubble mound with a trapezoidal cross section of rock or concrete

2. Flexible-membrane units constructed of concrete-, sand- or water-filled containers

3. Prefabricated modular units constructed of concrete, timber or other materials

Further one we will give a short ‘state of the art’ of the prefabricated modular breakwaters.We will end this chapter with the description of the modular breakwater which is the subjectof this thesis and was patented in the LPC of the UPV by Medina and Rodrıguez (2003).

8

Chapter 2: Detached low-crested breakwaters for shore protection 9

2.1 Introduction

Low crested and submerged structures (LCS) such as detached breakwaters and artificial reefs1

are becoming very common coastal protection systems (used alone or in combination withsand nourishment or groynes). Their purpose is to reduce the hydraulic loading to a requiredlevel that maintains the dynamic equilibrium of the shoreline. To obtain this goal, they aredesigned to allow the transmission of a certain amount of wave energy over the structure byovertopping and also some transmission through the porous structure (exposed breakwaters)or wave breaking and energy dissipation on shallow crest (submerged structures), Pilarczyk(2003).Continued research, especially on submerged breakwaters, should further explore improvedtechniques to predict shore response and methods to optimize breakwater design. A goodstep in this direction was made in the European Project DELOS (Environmental Design ofLow Crested Coastal Defence Structures, 1998-2003) (http://www.delos.unibo.it).

2.2 Types of low-crested structures

2.2.1 Rubble mound with a trapezoidal cross section

The most common type of a detached breakwater in use today is the shore-parallel rubblemound structure. These types of structures were usually emergent, constructed out of nat-ural rock material or concrete units, and placed some distance seaward of the shoreline. Astatically stable breakwater is a structure where the weight of the elements in the armourlayer is sufficient to withstand wave forces.Usually rubble mound offshore breakwaters, and especially the low-crested submerged struc-tures, provide environmentally friendly coastal solutions. However, high construction costand the difficulty of predicting the response of the beach are the two main disadvantages thatinhibit use of rubble mound breakwaters.

In its most simple shape a rubble mound breakwater is a mound of stones. However, ahomogeneous structure of stones large enough to resist displacements due to wave forces isvery permeable and might cause too much penetration not only of waves, but also of sedimentsif present in the area. Moreover, large stones are expensive because most quarries yieldmainly finer material (quarry run) and only relatively few large stones. As a consequence theconventional rubble-mound structures consist of a core of finer material covered by big blocksforming the so-called armour layer. To prevent finer material being washed out through thearmour layer, filter layers must be provided. The filter layer just beneath the armour layer isalso called the underlayer. Structures consisting of armour layer, filter layer(s), and core arereferred as multilayer structures. Concrete armour units are used as armour blocks in areaswith rough wave climates or at sites where a sufficient amount of large quarry stones is notavailable.

1Submerged breakwaters with broad crest


2.2.2 Flexible-membrane units

Flexible-membrane units or commonly called geosynthetic containers, Pilarczyk (2000), canbe manufactured according to any need and in a wide range of sizes ranging from very small(liters) to very big (200 m3 and more).. The number of applications is rapidly growing.One group of geosynthetic containers is that of mattresses, which may come in many kinds.They include containers of limited thickness covering a large area. They can be placedendlessly: the base and top sheet of prefabricated mattresses are sewn together as neededand only then the assembled mattress is filled.Another group of elements that can also be manufactured endlessly are geosynthetic tubes(Fig. 2.1). They are found in flood and erosion protection, as structural elements, or ascasings to be filled with sludge or slurry. Tubes made of strong impermeable material areused as storage tanks for liquids or can be used as a special application as rubber weirs.

Figure 2.1: Breakwater using geotubes

2.2.3 Prefabricated modular units

Prefabricated concrete submerged structures appear to be reasonable alternatives to rub-ble mound structures in environmentally sensitive areas. The use of prefabricated concreteelements has some advantages compared to rubble mound structures. First of all, the elimi-nation of the dust, noise and turbidity associated to the use of quarry stones. Prefabricatedconcrete structures generate most of the environmental impact in an industrialized area, faraway from the environmentally sensitive coastal area. Secondly, the difficult reversibility ofdumping quarry stones on sandy beaches can give problems when the breakwater is no longerneeded, prefabricated units can easily be removed and reused elsewhere.


2.3 State of the art of Prefabricated modular breakwaters

In this paragraph we will give a state of the art in the development of different types ofprefabricated modular breakwaters. The last type of prefabricated units in the list below(page 17) is the one that is invented and patented in the laboratory of Ports and Coast ofValencia, and also subject of this Master thesis.

2.3.1 P.E.P. Reef Unit(Prefabricated Erosion Prevention breakwater)

The first type of unit is called P.E.P. Reef unit short for Prefabricated Erosion Preventionconcrete breakwater American Coastal Engineering (1993), it was patented by Rauch (1992),which was installed in two separate experimental projects in Palm Beach County, FL at theDupont property and at Midtown Palm Beach from 1988 through 1995. The third installationwas in Indian River County, FL at Vero Beach in 1996.

Figure 2.2: P.E.P. Reef Unit

The general triangular shape units have three openings just below the crest, and the flattersloping face was oriented seaward. The design purpose of the P.E.P. Reef was to a) reduce waveheight, b) stabilize the shoreline position, c) limit sediment volume changes in the vicinity ofthe breakwater, and d) lower wave energy landward of the breakwater during storms. ThePrefabricate Erosion Prevention breakwater units are made of reinforced concrete and castoffsite in a mold. They are then transported by barge and placed by crane in the nearshoreadjacent to the beach. The individual units are locked together, and placed parallel to shorein segments of various lengths and configurations, depending on the project location. Theinstalled P.E.P. units at Vero Beach are 1.83 m high, 4.57 m wide, 3.66 m long and weighing23 tons. These reinforced steel concrete structures were installed directly on the sandy floorwithout the use of geotextiles.


2.3.2 Beachsaver reef unit

A second design, called the Beachsaver breakwater unit was designed by Breakwaters Inter-national, Creter et al. (1994) and was installed in three project locations in New Jersey totest different configurations and site conditions. The first installation of this type of breakwa-ter was in Long Island Sound at Oakwood, New York, in 1984. A shifting problem resultedin a redesign of the units. As part of the US Army Corps of Engineers National Shore-line Erosion Control Development and Demonstration Program, a demonstration project hasbeen installed at Cape May Point, New Jersey, Stauble and Giovannozzi (2003) to evalu-ate prototype-scale innovative or non-traditional methods of shoreline erosion control. Theproject consists of placing a redesigned Beachsaver Reef and a linear prefabricated concretesill called the Double-T (Paragraph: 2.3.4) across the seaward end of two adjacent groin com-partments, in order to assess the effectiveness of these structures in retaining sand within thegroin compartments and to reduce shoreline erosion. Placement was in August and September2002, by a barge-mounted crane. The project was monitored by Stauble and Tabar (2003).

An important patented design, Creter (1993), feature of the Beachsaver reef is the backwashflume (circled in the Fig. 2.3). The flume consists of three slotted openings which are wideron the curved beachward face and become narrower as they arc upward to the top of thestructure. As a storm wave recedes, the flume projects a high velocity curtain of water andsuspended sand upward off the reef so that the next incoming wave cycles the sand backtowards the beach. This inhibition of the offshore movement of sand is key in erosion controlduring storm events.

Figure 2.3: Beachsaver Reef

The triangular shape Beachsaver Reef. is a narrow-crested prefabricated concrete breakwaterstructure that is 3.05 m long, 4.75 m wide and 1.83 m high, weighing 19.1 metric tons (Fig.2.4). The units have a narrow crest width of 0.46 m. Individual units were locked together bya built-in hook and eye configuration to make a long submerged continuous reef structure atthe seaward end of the groins. The units were placed on a on the seaward side of a geotextilemat with the use of the crane. Divers were used to align the individual units and insure thatthe interlocking was accomplished.


Figure 2.4: Dimension of the Beachsaver Reef

In Spain, a Beachsaver submerged structure was constructed at the El Campello beach (Ali-cante) in 2003.

2.3.3 Device for preventing beach erosion

This prefabricated module was patented by Schaaf and Schaaf (1983), it is an off-shore reef-like structure for preventing beach erosion. The structure comprises a string of prism-shapedmodules placed in side-by-side relation. Each module has oppositely inclined front and rearwalls adapted to face seaward and landward, respectively (Fig. 2.5). At least one flow controlpassage extends through the module so as to converge from its front to rear wall openings.Incoming waves flow through the passage in a manner dissipating the wave energy whileminimizing the wave impact forces tending to move the module. An opening is provided inthe module bottom wall in communication with a through conduit enabling the module tofixedly seat or interlock itself in either sandy or coral-like shoreline areas. The module isuniquely designed to provide a minimal air lifting load for helicopter installation.


Figure 2.5: Device for preventing beach erosion, Cecil y Craig Schaaf (1983)

2.3.4 Double-T Sill

A prefabricated concrete Double-T structure was placed together with the Beachsaver unitat Cape May Point, New Jersey ,Stauble and Giovannozzi (2003). It is expected to act as asill across the seaward end of that cell to create a perched beach. The name comes from theshape of the prefabricated concrete units with two vertical legs on a flat base when viewedon its end looks like two Ts. The Double-T units are 9.14 m long and 4.57 m wide, they areplaced end to end in an inverted position with the flat surface on the sand bed (Fig. 2.6).The vertical legs extend 0.86 m in the water column and a single unit has a weight of 17.3tons. An extension of the legs on one end of each unit allowed an interlocking effect betweenthe units, designed to maintaining a linear orientation of the sill.

Figure 2.6: Dimension of Double-T sill


2.3.5 Reef Balls

Reef Balls can be used as submerged breakwaters to protect a beach from erosion or even tobuild up a beach that has already eroded, Barber (1999). They can also be used in a varietyof erosion control applications such as creating a wave fence for marinas or as red mangrovepots for shoreline stabilization. Shorelines can also be stabilized using Reef Balls as a nearshore breakwater or to grow oysters to create a protective near shore oyster bar. However, allthese applications for Reef Balls require specific engineering because erosion control requiresdetailed, site specific planning, to avoid unexpected results.

Figure 2.7: Reef Ball

Reef Balls are a modular system and it is possible to move or remove them in case that isneeded, but because a living reef system will develop on the Reef Balls one should considerReef Balls as a permanent feature.

2.3.6 Beach Prisms

Beach Prisms were created in the late 80’s as a means to protect shorelines from erosion. Theproduct consists of prefabricated concrete prisms, measuring 3 to 4 feet in height and 10 feetin length. Its triangular slotted design creates stability and durability, that has been provento withstand hurricanes (Hurricane Isabel specifically). Beach Prisms are permitted by stateand federal agencies, including the Department of Natural Resources and the Army Corpsof Engineers. Beach Prisms have been installed on over 20 sites around the Chesapeake Bayand the Potomac River (Fig. 2.8). (www.beachprisms.com)


Figure 2.8: Beach Prisms installed in Chesapeake Bay


2.4 MODUMAR project

To keep some of the advantages of the prefabricated structures described above and to avoidsome of the disadvantages, Rodrıguez (2003) proposed the use of a new proprietary modularbreakwater concept for shore protection in environmentally sensitive areas. Using severaltypes of prefabricated concrete modules, a variety of coastal structures for shore protectioncan be constructed. The modules were designed to solve the logistics of storage and trans-portation (Fig. 2.9) as conventional containers (2.5 m high and 2.5 m wide) in the multimodaltransportation network.

Figure 2.9: Transportation as a conventional container

The elements of the modular breakwater are re-usable and have clear advantages in envi-ronmentally sensitive areas and in cases of urgent shore protection. Prefabricated modulardetached breakwaters were expected to show a performance similar to conventional rubblemound LCS with the same cross section, the hydraulic response was analyzed with 2D physicalexperiments described in chapter 4 of this master thesis.

The group GADEA BROTHERS, specialist in prefabricated concrete, signed an agreementof collaboration with the Polytechnical University of Valencia (UPV) in November of 2003.By means of this agreement, the Valencian company was committed to make the prototypes(Fig. 2.10) of the modular breakwater for the protection of coasts patented by the Laboratoryof Ports and Coasts of the UPV.


Figure 2.10: Prototype of the square module (C-88)

The positioning of the different modules on the sea floor was already subject of research inthe Laboratory of Porst and Coast, Medina and Rodrıguez (2003). The proposed solutionfor the installation of the breakwater included the use of floting elements (Fig. 2.11). Withthose elements a fast and precise positioning is possible.


Figure 2.11: Positioning of the modular breakwater using floating elements

In order to analyze the response of modular breakwaters to scour and liquefaction problems,an experimental installation of three short segment of the TCT configuration have been placedin the Spanish Santa Ma del Mar beach (Cadiz). Medina et al. (2006) described in detail theexperimental installation in November 2005, a rapid settlement was observed during the firstweeks after installation and then the settling process stabilized.

Chapter 3

Theoretical model

Many studies have been performed in the past to get better insight in wave transmission. Therecent MODUMAR project focused on wave transmission of the modular breakwater patentedin the LPC of the UPV. This chapter offers a brief review on wave transmission. Secondly,the most relevant studies on wave transmission, close related to the MODUMAR project, aretreated. Later on (Chapter 5) we will compare the results of the experiments done in theMODUMAR project with the different theories. With the help of a neural netwerk, we willtry to adapt the theory to this specific type of low-crested breakwater.

20

Chapter 3: Theoretical model 21

3.1 The wave transmission phenomenon

Breakwaters are applied worldwide to create sheltered areas for commercial, recreational,environmental or protective reasons. When incident waves are blocked by a high-crestedbreakwater structure, most of the wave energy will be dissipated and there will appear somereflection. Energy dissipation can be clearly visual in the form of spectacular wave attackscausing severe wave overtopping, expressed in a discharge or in a percentage of the totalincident waves. As the name already implies, low-crested structures have relative small crestfreeboards compared to the incident waves, and are frequently or always overtopped. In thiscase, one speaks of wave transmission instead of wave overtopping, expressed as ratio of thetransmitted wave height over the incident wave height.

Kt =Ht

Hi(3.1)

The reflection that appears in front of the breakwater is expressed as the ratio of the reflectedwave height over the incident wave height.

Kr =Hr

Hi(3.2)

The wave gauges in the wave flume in front of the breakwater will give us data of the sum ofthe reflected and the incident wave. Here in the LPC-UPV a software packet LASA, Medina(2001), was developed to seperate those two waves. And to estimate the reflection coefficient.The energy absorbated bij the structure can be calculated as the difference of the incidentwave energy and the sum of the transmitted and reflected energy.

Etransmited + Ereflected + Eabsorbed = 100% = Eincident (3.3)


3.2 Parameters influencing wave transmission

To obtain a valid and useful prediction model it is important to have pre-knowledge of theparameters influencing wave transmission. A division is made in hydraulic and structuralparameters, influencing wave transmission, van Oosten and Marco (2005).

3.2.1 Hydraulic Parameters

• Incident wave height (Hi)

The most important hydraulic parameter involved in wave transmission, is the incident waveheight. In case of irregular waves, this parameter is commonly expressed like the significantwave height, which is the average of highest 1/3 of all waves. The incident wave height isdirectly present in the definition of the wave transmission coefficient Kt (Eq: 3.1).

• Incident wave period (Ti)

For the incident wave period can be stated, that a longer wave period means lower wavesteepness for a constant wave height. A lower wave steepness will increase the wave run-upand from this it results in more wave transmission. The experiments were carried out with 2different incident wave heights (10 cm and 20 cm). For each incident wave height we tested2 different incident wave periods (1.5 s en 2.5 s for regular waves and 2 s and 3 s for irregularwaves).

3.2.2 Geometric parameters

• Crest freeboard (Rc)

The structure crest freeboard, symbolized as Rc, is the distance between sea water level andthe crest of the breakwater structure. In every study the crest freeboard is found to be one ofthe most important structural parameters for wave transmission. For emerged impermeablestructures, a decreasing relative crest freeboard leads to more overtopping. Therefore, thetransmission coefficient Kt will increase. In general, a higher relative freeboard gives a lowertransmission coefficient. When a structure is submerged and the crest is situated well belowthe water level, the influence of the crest freeboard will disappear.

• Crest width (B)


A wider crest will reduce wave transmission, Briganti et al. (2003). At low-crested structures,a larger relative crest width will lead to a longer way for the waves to overtop the structureand therefore more wave energy dissipation is present. Van der Meer and Daemen (1994)summarized the influence of the relative crest width for submerged structures. An increasingrelative crest width will force the waves to break and therefore more energy is dissipated onthe crest, resulting in a lower transmission coefficient. A small relative crest width has noinfluence on wave transmission at all.

• Structure slopes (α)

For emerged structures, the seaside slope influences wave run-up and therefore wave over-topping, hence wave transmission. On the gentler slope more energy will be dissipated andless transmission occurs. The seaside slope is included in the surf similarity parameter, alsoknown as the Iribarren number1 (ξ), describing the type of wave breaking on the slope itself,and has its influence on wave transmission. For submerged breakwaters the seaside slopeseems to be of minor importance, because wave run-up is not present.

Figure 3.1: TCT2 composition with different parameters

1The Irribarren Number, also known as the surf similarity parameter, is a dimensionless parameter that isused to describe the characteristics of ocean wave phenomena. It is defined as ξ == tanα√

HmoLmo

= tanα√2πHgT2


3.3 Relevant studies on wave transmission

3.3.1 Dattatri et al. (1978)

Dattatri et al. (1978) published one of the first works related to the dissipation of energy dueto the installation of submerged breakwaters. The authors offered in this article the resultsof a series of tests (Fig. 3.2) made in laboratory with submerged elements, of different forms,permeable and impermeable.

Figure 3.2: Overview of the test executed by Dattatri et al. (1978)

The values of the transmission coefficients shown in the graphs below, were a first approachof Kt, made from the datasets of the different experiments. It is possible to observe that thevalues of Kt fluctuate between 0.1 and 0.9, depending on the following parameters:

• Freeboard (Rc, in the graphs ds was used)

• Initial wave height (Hi)

• Water depth (d)

• Crest width (B)

• Wave period (T)


Figure 3.3: Kt by Dattatri et al. (1978) for impermeable breakwaters

Figure 3.4: Kt by Dattatri et al. (1978) for permeable breakwaters


3.3.2 Shore Protection Manual, U.S. Army Corps of Engineers (1984)

For submerged breakwaters and artificial reefs, the greater the submergence, the less thewave energy will impact the structure, and the less effective the structure will be for waveattenuation. The Shore Protection Manual U.S. Army Corps of Engineers (1984) presentsnumerous graphs of empirical data from wave tank tests that can be used to determine wavetransmission coefficients.

Figure 3.5: Kt by Shore Protection Manual (1984)

The proposed formula for wave transmission is:

Kt = −0.4Rc

Hi+ 0.8

(B

Hi

)−0.31 (1− e−0.5ξ

)(3.4)


3.3.3 Ahrens (1987)

Ahrens (1987) presents an empirical formula for sub aerial breakwaters, where the crest ofthe structure is above the still water level and the ratio of freeboard to the incident waveheight is greater than one (Rc/H > 1.0) as follows:

Kt =1.0

1.0 +(

HALDn50

)0.592 (3.5)

where H is the incident wave height, A is the cross sectional area of the breakwater, L is thewavelength, d the water depth and Dn50 is the nominal armor unit diameter of the mediansize (50%) armor unit given by:

Dn50 =(

Ma50

ρa

)1/3

(3.6)

where Ma50 is the mass of the median size armor unit and ρa is the mass density of the armormaterial.

Ahrens (1987) also presents an empirical formula for reef breakwaters where the ratio of thefreeboard to the incident wave height is less than one (Rc/H < 1.0), as

Kt =1.0

1.0 + C1 ·C2 ·C3(3.7)

Where:

C1 =(

h

d

)1.188

(3.8a)

C2 =(

A

d ·L

)0.261

(3.8b)

C3 = exp

(0.529 ·

(F

H

)+ 0.00551 ·C4

)(3.8c)

C4 =A3/2

D2n50 ·L

(3.8d)


3.3.4 D’Angremond et al. (1996)

D’Angremond et al. (1996) (often referred to De Jong) proposed another transmission formulafor mound structures. The formula was derived, based on available data on rubble moundbreakwaters and breakwaters with an armour layer of Tetrapods. An extensive investigationon the influences of crest width and surf similarity parameter was carried out in this research.

For mound structures:

Kt = −0.4Rc

Hsi+ 0.64

(B

Hsi

)−0.65 (1− e−0.5ξ

)(3.9)

Having a lower boundary of: Ktl = 0.075 and having a upper boundary of: Ktu = 0.8

For smooth structures:

Kt = −0.4Rc

Hsi+ 0.80

(B

Hsi

)−0.65 (1− e−0.5ξ

)(3.10)

Having a lower boundary of: Ktl = 0.075 and having a upper boundary of: Ktu = 0.8

3.3.5 Seabrook and Hall (1998)

Seabrook and Hall (1998) performed extensive physical modeling tests of submerged break-waters, using various depths of submergence, crest widths, water depths, and incident waveconditions. From that data he developed the following design equation for wave transmissionat submerged rubble mound breakwaters:

Kt = 1.0− (D1 + D2 + D3) (3.11)

Where:D1 = e0.65(F/H)−1.09(H/B) (3.12a)

D2 = −0.047(

BF

LDn50

)(3.12b)

D3 = 0.067(

FH

BDn50

)(3.12c)

When using the equations of Ahrens (1987) and Seabrook and Hall (1998), the terms con-taining the nominal armor unit diameter, Dn50 are often found to be negligible compared tothe other terms.


3.3.6 Briganti et al. (2003)

Briganti et al. (2003) analyzed the extensive database produced by the EU founded projectDELOS and used the 2D random wave datasets to improve the prediction of the transmissioncoefficient starting with the formula of d’Angremond et al. (1996). The same set of parameterswas used as the governing ones for wave transmission in the aforementioned papers. Theoutcome of this analysis is the calibration of two design formulae based on the d’Angremond etal. (1996) relationship. The analysis highlighted the need of a supplementary formula allowinga reliable estimate of the transmission coefficient at wide crested breakwater (B/Hi > 10).

The formula for mound structures with B/Hi > 10:

Kt = −0.35Rc

Hsi+ 0.51

(B

Hsi

)−0.65 (1− e−0.41ξ

)(3.13)

Having a lower boundary of: Ktl = 0.05 and having a upper boundary of: Ktu = −0.006WcHi

+0.93

The formula for mound structures with B/Hi < 10: (same as 3.9)

Kt = −0.4Rc

Hsi+ 0.64

(B

Hsi

)−0.65 (1− e−0.5ξ

)(3.14)

Having a lower boundary of: Ktl = 0.075 and having an upper boundary of: Ktu = 0.8

For the range 8 < Wc/Hi < 10 an interpolation should be made between the two differentformulae.


3.3.7 Comparison of predictive equations for wave transmission

The equations of D’Angremond et al. (1996) and Briganti et al. (2003) are linear, if plottedKt versus Rc/Hi. The test to obtain the formula of Seabrook and Hall (1998) dealt only withsubmerged structures and the equation is not applicable to surface-piercing structures. TheAhrens (1987) equations produce an S-curve (Fig. 3.6).

Figure 3.6: Transmission coefficient versus relative submergence

Chapter 4

Experiments

In this chapter the experimental setup of the MODUMAR project is explained. First, theused test equipment is commented briefly. In a second part the analysis of the data isexplained. Further, the design of different types of the modular breakwaters is described andthe preparation and construction of the physical model is commented and illustrated. Finally,an overview of the different executed tests is given.

31

Chapter 4: Experiments 32

4.1 Test equipment

The experiments were conducted in the wave flume of the Laboratory of Port and CoastalEngineering (LPC) of the Polytechnic University of Valencia (UPV).

4.1.1 2D Wave Flume

The 2D wave flume has a square cross-section (1.2 m x 1.2 m) and is 30 m long. In the centerof the wavenflume, the bottom shows a gentle upward slope (4%), hence the water depth nearthe model is 25 cm less than the water depth near the wavemaker. This change in waterdepth makes it possible to generate waves of higher wave height, without breaking the wavesat the generator. After the slope of 4%, which has a length of 6.25 m, we colocated a gravelslope of 3% over a length of 3 meter. From this point on an 9 cm thick horizontal layer ofgravel was colocated (Fig. 4.2). The gravel used for the slope and layer was W50 ≈ 50gr.The different models are placed at a distance of 15.72 m from the wave generator slab,measured from the middle of the model. The water depth used for the experiments changedwith the different freeboards (Rc) that were tested.Besides the layer of gravel (Fig. 4.1), there was another adaptation of he wave flume necessaryto execute the test. The prefabricated modules have an length of 60 cm, and for a 2D waveexperiment we needed to narrow the wave flume to this width. We narrowed the wave flumewith the use of meth-acrylate panels of a length of 2 m. And this over a total length of 6 m.The use of these panels gives us the possibility to observe the model during the experiments(Fig. 4.19).

Figure 4.1: Collocating the gravel layer at both sides of the panels


Figure 4.2: 2D Wave Flume


4.1.2 Wave generation

The waves in the wave flume are generated by a metallic slab that is located at on one of theends of the flume. The metallic slab is moved by a hydraulic piston, which has a maximumdisplacement of 80 cm. The metallic slab moves horizontally on bronze rolls sliding on steelrail tracks and supported by a very rigid metal frame (Fig. 4.3). In front of the paddle twoperforated metal plates are located to absorb the transversal waves generated by the paddle.

Figure 4.3: The paddle and the transversal wave absorbing plates

The piston is attached to the upper part of the paddle which means that a strong momentumis introduced in the vertical slab when moving the water mass. The rigid metal frame forcesthe paddle to move equally in a horizontal way. The movement of the piston is steered by avalve which displacements are controlled by a position sensor. This valve allows the injectionof the fluid at both sides of the piston and with variable discharge (Fig. 4.4).


Figure 4.4: The hydraulic piston

The computer program takes the data from the prepared theoretical sequence, the data aretranslated in movements of the piston, that are communicated to the hydraulic system ofgeneration through electrical impulses (Fig. 4.5). The computer program used for the wavegenerating was developed in the LPC and is called “Modelizacion Fisica de Oleaje v3.2”.The same program was also used to calibrate the wave gauges every morning before theexperiments (Appendix: C).

Figure 4.5: Control room


Figure 4.6: Energy dissipation system

4.1.3 Energy Dissipation System

At the end of the flume opposite to the wave generator, there is an energy dissipation system,which absorbs the transmitted waves. The reflection coefficient of the wave energy dissipationsystem is inferior to 0.15, or it absorbs more than 95% of the energy. In the experiments whowere carried out, we assumed a perfect absorption of the energy.The absorption system consists of five groups of three grooved metal frameworks, and a plasticperforated plate. The metal frameworks have three different porosities: 70%, 50% and 30%,with the highest porosity starting at the side where the wave approaches. A first group ofthree frameworks with 70% porosity is followed by two groups with a porosity of 50%. Thefirst of these two groups has many and thin bars, the second has the same porosity but lessbars, and thus the bars and voids are wider. The fourth and fifth group have a porosity of30% and again, the first is finer than the second one. The voids between the three frameworksof this group have been filled with quarrystone (Fig. 4.6).

4.1.4 Wave gauges

In order to register the height, capacity wave gauges are used. The gauges consist of twovertical parallel conductors that use the water in between as a dielectric. This way theymeasure variations in water level as variations in capacity. The gauges are connected withan electronic equipment (Fig. 4.5) that makes it possible to calibrate them and to transferthe data to the computer, which translates the signals in wave heights in cm respected to themean level of the channel. The sending of the data happens at a sampling frequency of 20


Hz. The duration of each test included the duration of the wave generation, followed by 50sec of recording data from the wave gauges.In the MODUMAR project 9 wave gauges were used. A first group of 3 wave gauges (S1 toS3) were placed in front of the model, 2 wave gauges (S4 to S5) were placed at both sides ofthe model, and a last group of 3 (S6 to S8) wave gauges were place behind the model. Thelast wave gauge (S9) was attached to the paddle, as a control for the generated wave height(Fig. 4.7 and 4.8).

The exact positions are given in Table 4.1 and refer to the distance (in cm) from the neutralpoint of the paddle.

S1 S2 S3 S4 S5 S6 S7 S8 S9Position 1379.5 1409.5 1459.5 1572 1572 1659.5 1709.5 1739.5 0

Table 4.1: Distance of the wave gauges to the paddle (cm)

The cross-sectional of the structure is 60 cm. (6 m in the prototype), that corresponds tothe length of a module. In order to delimit the refraction, meth-acrylate plates are placed,considering that the wave gauges located before and after the model are inside and wavegauges S4 en S5 are outside the new created channel (Fig. 4.9).

Figure 4.7: Location of the wave gauges


Figure 4.8: General view of the wave gauges

Figure 4.9: Transversal view


4.2 Analysis of the wave recordings

4.2.1 Separating the incident and reflected waves

The different wave gauges in the 2D wave flume are measuring the fluctuating water level.This fluctuation of the water level is a superposition of incident and reflected waves. Theseparation of incident and reflected waves is a complex problem, that has great influenceon the results of physical laboratory experiments. In the previous chapter we said that theincident wave height Hi is together with the freeboard Rc the most important parameter forwave transmission. This makes it necessary to separate incident and reflected wave trains inorder to adequately study and to predict the response of our model. Nevertheless we assumeda perfect absorption of the wave dissipating system (Paragraph: 4.1.3), this makes thatonly wave gauges S1, S2 and S3 (wave gauges in front of the model) will register significantreflection waves. The separating of the incident and reflected waves will only be carried outon these wave gauges.

In the Port and Coastal Laboratory (LPC), use was made of the LASA method proposedby Medina (2001) to separate reflected and incident waves from the registry. Method LASA(Local Approximation using Simulated Annealing) allows the analysis of the incident andreflected surge in the dominion of the time, unlike previous methods like 2-point of Godaand Suzuki (1977) that makes the analysis in the dominion of the frequency. The generalprocedure of local approach to make a separation of incident and reflected surges can settledown in three stages:

• Elimination of the noise:Wave records should be cleared of low- and high frequency noise.

• Time windows and overlapping:Splitting the input data in small segments in which an approximation will be soughtwith a reasonable overlapping system.

• Local approximation:A local approximation model for estimating its parameters is required.

The LASA-method is based on the use of triangular windows with linear superposition with a50% overlap. Use was made of a the most recent version : LASA V 2.0, which considers linearand non-linear Stokes V waves in the time domain and which has a Local Approximation usingSimulated Annealing. The parameter window of the LASA program (Fig. 4.10) shows theimplemented parameters in the method:


Figure 4.10: Parameter window of LASA V 2.0

In the figure 4.11 below, an example is shown of the separation by LASA of incident andreflected waves out of the registered wave.

Figure 4.11: Registered, incident and reflected wave height (Exp: 1M02 1520)

4.2.2 Analysis of the data produced by the LASA program

After the separation of the wave recordings into incident and reflected waves by means of theprogram LASA V2.0, the recorded wave heights and their respective incident and reflectedpart were analyzed by a software tool, named LPCLAB 3.6, developed at the LPC. Thisprogram analyses the data both in frequency and time domain, and generates a report withthe wave parameters. An example of such a report file can be found in appendix A.


4.2.3 Model scaling

In order for a model to accurately represent the prototype situation, the relative effect ofvarious forces and interactions must be the same in the model as in the prototype. Thiscondition is achieved by ensuring dynamic similarity between the model and the prototypeand is best described through dimensional analysis.

Defining the scale of the model as the ratio of the physical length of an object in the proto-type to the physical length of the same object in the model, the scale of any parameter orphenomenon in the mode1 can be simply defined as:

λa =am

ap(4.1)

where λa represents the scale of a parameter a. The subscripts m and p represent prototypeand model respectively. In order for a model and a prototype to be dynamically similar, thescale of all dimensionless parameters must be unity. Dimensionless parameters are importantas they describe the relative forces. Typically, there are three dimensionless parameters whichdescribe the dynamics of a hydraulic model.

Froude Number(Fr) : Fr =v√gd

(4.2a)

Reynoulds Number(Re) : Re =ρvl

µ(4.2b)

Weber NumberWe : We =v2

(σt/ρl)1/2(4.2c)

The Froude number represents the ratio of inertial forces to gravitational forces, the Reynoldsnumber the inertial forces to viscous forces and the Weber number inertial forces to surfacetension forces.

Where the effects of friction are small relative to gravitational forces and the Reynolds num-ber for the model can be maintained within a similar range as that in the prototype, thusmaintaining similar drag coefficients, Reynolds number similarity is not as important, Dal-rymple (1985).Modeling effects due to incorrect Weber number similarity are typically insignificant whenthe wavelengths are much greater than 2 cm, Dalrymple (1985).It is therefore expected that the model results can adequately represent the transmissioncharacteristics resulting from Froude scale phenomena.

The geometric scale in the experiments is λg = 1/10, and concerning the froude similaritythe time scale is λt = 1/

√10.


4.3 Design of the modular breakwater

The original idea for the modules, consisted of making an easy to transport breakwater. Themodules were designed to solve the logistics of storage and transportation as conventionalcontainers (2.5 m high and 2.5 m wide) in the multimodal transportation network. The ele-ments of the modular breakwater are re-usable and have clear advantages in environmentallysensitive areas and in cases of urgent shore protection.

4.3.1 The geometric characteristics of the different modules

There are four different modules who were patented by Medina and Rodrıguez (2003). In theexperiments done in the laboratory only two of the four modules have been used: C-88 andT-70, these two modules made 5 different compositions.

• Triangular module T-70

The grooves located in the surface of the frontal panel of the triangular module (Fig. 4.12)favour the dissipation of energy, and as additional advantage a certain facility to reach thesuperior base by a person during the installation of floaters, storage or any other operation.This design of the triangular modules allows us to make a composition of two triangular mod-ules, which has the same dimensions of the quadrangular module (Fig. 4.13). By consequencetwo triangular T-70 modules can be transported in one container.

Figure 4.12: Side view of the triangular module


Figure 4.13: Composition of 2 triangular modules

The frontal holes that can be observed in the T-70 module, allow the installation of thefloaters. Once the module is installed, these holes will be closed by the ecosystem that developsinside the modules. Because of this, there is decided to study the hydraulic behaviour in thelaboratory without these holes.

• Square module C-88

In this module it is necessary to emphasize the design of the superior panel (Fig. 4.15). Theridges located on top of the superior panel facilitate the interconnection between heights, offerdrag of the waves of the sea that cross their freeboard and are creating the correspondingturbulences. Three superior holes are constructed to allow the ballasting of the structurethrough them and in addition they make it possible to evacuate the gases that generates thefuture biomass that settles inside the modules.


Figure 4.14: Side view of the Square module

Figure 4.15: Superior panel of the C-88 module

Both modules have also holes at the sides to connect the different modules of the same layerto each other.

4.3.2 The different compositions tested in the MODUMAR project

We decided to test 5 different compositions made out of the 2 elements discussed before. Thenomenclature of the different compositions depends on the modules used to make the toplayer of the composition, and the number of layers.


(C = Square module and T = Triangular module).

1

TCT

2

TT

3

T3CT

4

TCT2

5

TT2

Table 4.2: Different configurations


4.3.3 Construction and positioning of the different modules

The different modules were made in the lab with a scale 1/10.

Figure 4.16: Construction of the modules

After the construction of the different modules, the different compositions had to be made.To interconnect the different modules, bolts were used (Fig. 4.17).

Figure 4.17: Connection of TCT configuration

The last construction phase was the collocation of the breakwater in the wave flume. To makea precise collocation, we used the crane (Fig. 4.18).


Figure 4.18: Collocation of the T3CT configuration

Figure 4.19: Observing the model during experiment


4.4 Overview of the executed tests

We tested in total 5 different configurations (Table: 4.2). Every configuration was testedwith 4 different freeboards. For every freedboard there were 8 experiments: 4 Regular and 4Irregular wave trains.

The nomenclature of the experiments is: xMyz aabb (Explanation in App: B).

4.4.1 Regular wave experiments

In case of regular waves, it was not necessary to use any kind of extra software. The waveheight and wave period were directly entered in the central computer. For each regular wavetrain the number of waves was 10. Each series begins with three transition waves to give thepaddle the time to start from still water to the complete wave movement. Then ten waveswith the desired wave height and period are generated. And at the end comes another set ofthree waves to stop the moving of the paddle (Fig. 4.20).

Figure 4.20: Regular wave train consisting 16 waves (Exp: 1M03 2520)

The following regular wave experiments for every freeboard were launched:

Experiment Period HeightxM0z 1510 1.5 s 10 mxM0z 1520 1.5 s 20 mxM0z 2510 2.5 s 10 mxM0z 2520 2.5 s 20 m


4.4.2 Irregular wave experiments

The more important irregular wave experiments were adjusted to the Jonswap spectrum.Jonswap is an acronym for JOint North Sea WAve Project. The expression of this wave spec-trum was proposed by Hasselmann et al. (1973), obtained from measurements in the NorthSea. It is basically the wave energy spectrum of Pierson and Moskowitz (1964), multiplied byan extra peak enhancement factor and fetch-dependent scale parameters. The first factor inthe expression is similar to the Pierson-Moskowitz spectrum and the second factor expressesthe weight of γ.

S(ω) =αg2

ω5exp

[−5

4

(ωp

ω

)4]

γr (4.3a)

r = exp

[−(ω − ωp)

2

2σ2ω2p

](4.3b)

Wave data collected during the JONSWAP experiment were used to determine the values forthe constants in equation: 4.3a:

α = 0.076(

U210

Fg

)0.22

(4.4a)

ωp = 22(

g2

U10F

)1/3

(4.4b)

γ = 3.3 (4.4c)

σ =

{0.07ω ≤ ωp

0.09ω > ωp

(4.4d)

The Jonswap spectrum is similar to the Pierson-Moskowitz spectrum, the peak in the spec-trum is more pronounced, as specified by the peak-enhancement factor γ, a narrower morepeaked spectra (Fig. 4.21) is a more typical form of growing wind seas in deep water. Thespectra is characterized by the significant wave height Hs and the wave peak period Tp. Werethe significant wave height is defined as the average of highest 1/3 of all waves.

To generate the sequence of movements that conduct the wavemaker producing irregularwaves, use was made of a software tool developed in the laboratory LPC, called GeneradorOleaje (Fig. 4.22). It randomly generates an amount of scaled waves for the wave flumeaccording to the chosen spectrum. In this case the sequence was generated according to theJonswap spectrum, and for each irregular wave test a number of 1000 waves was generated.


Figure 4.21: The Pierson-Moskowitz spectrum and the standard JONSWAP spectrum

Figure 4.22: Generador Oleaje

Following irregular wave experiments for every freeboard were launched:

Experiment Peak Period (Tp) Significant wave Height (Hs)xM1z 2010 2.0 s 10 mxM1z 2020 2.0 s 20 mxM1z 3010 3.0 s 10 mxM1z 3020 3.0 s 20 m

Chapter 5

Results

In this chapter, the results of the experiments carried out in the laboratoy of Ports and Coastof the UPV are presented, and the influence of the different parameters will be discussed. Inthe second paragraph, the transmission coefficients obtained by the different experiments arecompared with the theoretical models that are presented in chapter 3. In paragraph 5.4 and5.5 we will analyse the data of the experiments with the use of a neural network, to predictthe wave transmission and the wave reflection of the prefabricated modular breakwater.

51

Chapter 5: Results 52

5.1 Results of the experiments

The most important result of the analysis of the recorded data (see chapter 4) is the trans-mission coefficient Kt. This transmission coefficient is calculated as:

Kt =Ht

Hi(5.1)

In case of an irregular experiment, Ht is the significant transmited wave height and Hi thesignificant incident wave height. The incident wave height is calculated in two different ways:

• The experimental method: Hi was calculated as the average of the significant waveheights, measured by the wave gauges S4 and S5.

• The estimated method: Hi was calculated as the average of the significant wave heightsof the output wave, generated by the LASA program, for wave gauges S1, S2 and S3.

Where the transmitted wave height was calculated as the average of the significant waveheights measured by the wave gauges S6, S7 and S8.The significant wave height is defined as the mean value of the 1/3-highest wave heights. Thisfraction of the waves can be identified in the Rayleigh distribution (Fig. 5.1), so that thesignificant wave height can be determined from this distribution.

Figure 5.1: The significant wave height in the Rayleigh probability density function


The square root of the variance of the surface, is the standard deviation of the surface. Thestandard deviation is a common measure for the variations about the mean and is thus areasonable scale for the surface height variations. For historical reasons it has become astandard to denote four times the standard deviation as the significant wave height.

Hs = 4×√

variance = 4

√∫ ∞0

Sη(f)df (5.2)

Related to the spectrum, a series of characteristic numbers are called the spectral moments.These numbers, denoted mk, k = 0, 1, ... are defined as

mk =∫ ∞

0fkSη(f)df (5.3)

The spectral moment m0 is just the variance of the surface. If the significant wave height isestimated from the total wave energy, the notation Hm0 is suggested instead of H1/3 or Hs

and hence

Hm0 = 4√

m0 = 4

√∫ ∞0

f0Sη(f)df = Hs (5.4)

For regular wave tests, the considered wavelength is the mean wavelength Lm. In case ofirregular wave tests, the mean wave length is L01, which is the wavelength associated withthe mean wave period T01 = 2π

√m0m1

,where m0 and m1 are the moments of the incident wave

spectrum, of the zeroth and 1st order, respectively.

Figure 5.2: Wave spectrum of wave gauge 3 (registrated, incident and reflected) and gauge 6


5.1.1 Influence of the crest freeboard on wave transmission

The most determing parameter for wave transmission is the crest freeboard (Rc or F). In figure5.3, the influence of the crest freeboard is shown. If the crest of the modular breakwater issituated more than 1 wave height below the still water surface, we can see that the wavesare almost totally transmitted over the structure. For relative freeboards between -1 and+1 we have a clear linear relationship between the relative freeboard and the transmissioncoefficient. This linear relationship has already been noted by U.S. Army Corps of Engineers(1984) and D’Angremond et al. (1996). They concluded that: Kt ≈ −0.4Rc

Hi, where Briganti

et al. (2003) proposed Kt ≈ −0.35RcHi

(Paragraph: 3.3).

Figure 5.3: Influence of the crest freeboard

The transmission coefficient for the modular breakwater, if the crest height is equal to theStill Water Level (SWL), varies between 50% and 70%. This means that more than half ofthe wave energy was reflected or dissipated by the breakwater.


5.1.2 Influence of the crest width

In the executed experiments 5 different configurations were tested, with three different crestwidths. The TCT and the TCT2 configurations have a crest width (B) of 2.5 m, the TTand TT2 configurations have a crest width of 0.8 m and the T3CT configuration has a crestwidth of 7.5 m. The graph below (Fig: 5.4) shows the different transmitted energies for thedifferent configurations of the same crest width.

Figure 5.4: Influence of the crest width

We can conclude that an increasing crest width gives a descending transmitted energy, thisobservation is more pronounced for an emerged breakwater. This trend is logical, as a biggercrest width will dissipate more energy of the transmitted wave. This relationship was alreadyfound by Dattatri et al. (1978), and was shown in figures 3.3 and 3.4.


5.1.3 Energy proportions

The estimation of Kt and Kr can be considered to estimate the proportion of energy transmit-ted, reflected and dissipated which can be calculated as

{Kt

2},{Kr

2}, and

{1−Kt

2 −Kr2}

respectively (Formula: 3.3).

Figure 5.5 shows the percentage of energy transmitted, reflected and dissipated, for differentvalues of crest freeboard over depth (F/d) parameter.

Figure 5.5: % energy transmitted, dissipated and reflected

For a submerged modular breakwater with a F/d value smaller than -0.6, the energy is almosttotally transmitted, and less than 10% is reflected. For crest freeboards bigger than -0.6 thewaves will be partialy reflected, and there will occur an increasing dissipation of the waveenergy. For a crest freeboard of 0 m, the following proportions of the incident wave energywere measured:

Transmitted energy 25% to 45%Dissipated energy 35% to 55%Reflected energy 10% to 25%

Table 5.1: Energy proportions


5.2 Comparison of the results with different theories of LCS

In chapter 3 different theories of low crested structures were presented. Those theories werebased on experiments with rubble mound breakwaters. In this paragraph we will comparethose theories with the experiments of the modular breakwater, carried out with the 2D waveflume of the LPC.

• DELOS

Figure 5.6: Comparison with the formula of Briganti et al. (2003)

In figure 5.6 the formula obtained by the DELOS project is shown for 3 different crest widthstogether with the results of the MODUMAR project. We can conclude that this formula isacceptable for the configurations with a crest width of 0.8 m. For the configurations witha crest width more than 0.8 m the DELOS formula gives us transmission coefficients whichare lower than the coefficients obtained in the experiments with the modular breakwater.The crest width of the modular breakwater is a parameter that has an influence on thetransmission but less influence than there was proposed by Briganti et al. (2003) for rubblemound structures.


• Ahrens

Figure 5.7: Comparison with the formula of Ahrens (1987)

The formula proposed by Ahrens (1987), seems to give a really good approximation of the dataobtained in the MODUMAR project. The influence of the crest width in the formula of Ahrensis less important, it only appears in the term with the cross sectional area of the breakwater(A). Later on Wamsley and Ahrens (2003) redefined the formula with a transmission coefficientassociated with overtopping or transmission over the crest and a transmission coefficientassociated with wave energy transmitted through the structure. Nevertheless, this redefinitionof the formula is not necessary for the prefabricated modular breakwater. It seems that theold formula of Ahrens gives us a very good tool to calculate the wave transmission of themodular breakwater, with only a root mean square error (RMSE) of 4.3%.


• D’Angremond

Figure 5.8: Comparison with the formula of D’Angremond et al. (1996)

The formula proposed by D’Angremond et al. (1996), give transmission coefficients which areapproximately 20% lower than the transmission coefficients obtained with the experiments.This difference of 20% is the same for the 3 different crest widths (Fig. 5.8), and gets a littlesmaller for bigger transmission coefficients.


• Seabrook and Hall (1998)

Figure 5.9: Comparison with the formula of Seabrook and Hall (1998)

The formulation proposed by Seabrook and Hall (1998) was based only on tests with sub-merged structures, the difference between the calculated values with the formula and thevalues of the experiments is significant. The structures with a small crest have a higher trans-mission coefficient and the structures with a wide crest have a lower transmission coefficientthan that obtained by the experiments (Fig. 5.9).


• SPM

Figure 5.10: Comparison with formula of the Shore Protection Manual

The formula proposed by U.S. Army Corps of Engineers (1984) only give transmission coeffi-cients in a small range of values, and the difference between the experiments and the formulais significant.


5.3 Comparison with the results of the REFLOTA project

The modular breakwater patented by Medina and Rodrıguez (2003) was already tested in thelaboratory of Ports and Coast of the UPV, in the year 2004. The 36 irregular wave trainswhich were launched in 2004 during the experiments of the REFLOTA project are comparedwith the 84 irregular wave trains executed in the MODUMAR project (March-May 2007).

Figure 5.11: Comparison with experiments in the year 2004

The results of both projects are similar, although some results of the REFLOTA projectare anomaly. The dispersion of the data obtained in the MODUMAR project are less thanthe dispersion of the data in the REFLOTA project. This indicates that the test of theMODUMAR project were carried out with more precision.


5.4 Neural Network Model to estimate wave transmission

Computational prediction models, called ’artificial neural networks’ (hereafter NNs), haveproven to be useful in many fields of technology. Thanks to these tools it is possible to solvecomplicated problems where many relations are involved, van Oosten and Marco (2005). Oneof the main goals of this study is to use a NN to solve the wave transmission phenomenon,trying to improve the results compared to previous prediction formulae.

5.4.1 Background of Neural Networks

• Neural network structure

A NN obtains information from Ii input parameters (placed in the so-called input layer) andthis information is managed by Hn neurons (placed in the so-called hidden layer) to finallydeliver Oj output parameters (output layer). A NN is therefore represented by means ofa IiHnOj - structure, where i is the number of inputs parameters, n the number of hiddenneurons and j is the number of output parameters. Although there is always one input layerand one output layer present, it is possible to have more than one hidden layer. It is clearthat in this study the output is restricted to only one parameter: the wave transmissioncoefficient Kt. The number of neurons in the hidden layer is determined by the amount ofdates available, to train the NN. Graphically the neural network is schematized in figure 5.12.

Figure 5.12: Neural Network schematization


All input parameters are connected to every neuron in the hidden layer. The strength ofthe relationship between an input parameter and a certain neuron in the hidden layer isrepresented by a set weight ( Wni ). On the other hand, every neuron (in the hidden layer aswell in the output layer) also has two parameters (αj and βj) to adjust the calculation workof the neuron itself.

• Neural network learning

A basic aspect of NNs is the learning process. Learning is basically the process that determinesthe value of weights and biases. Starting with small random initialization values of weightsand biases, the network processes the inputs. The resulting output of a network generallydeviates from the desired output. The goal of the learning process is to adapt the weights andbiases in such a way, that the difference between the desired and calculated output becomessmaller.The transmission data set was divided into two groups. A first group consisting of 70% ofavailable data, to train the NN and a second group with the remaining 30% of the availabledata to verify the NN afterwards.A common problem with neural networks is overfitting. The error on the training data setis small, but when new data are introduced the network error is large. Overfitting indicatesthat the network has memorized the training data but has not learned to generalize newsituations. Figure 5.13 shows the result of an overfitted network. To improve generalizations,the transmission network was created with a method called early stopping.

Figure 5.13: Example of overfitting


5.4.2 Neuroport 2.0

In this paper, NN models are optimized using evolutionary strategies, Medina and Yepes(1999), to eliminate the experimental noise and to select the most significant explicativevariables. From an initial population of fully-connected NN, mutation algorithms affectingboth NN parameters and topology lead to an optimized pruned NN scheme in which someparameters and sometimes input variables and neurons are eliminated during the evolutionary.Simulating annealing (SA) was used to create initial population and the predicted meansquared error (PSE) given by Moody (1992) (Eq: 5.5) was taken as the cost function for theevolutionary optimization.

PSE = MSE

[1 +

2P

(N − P )

](5.5)

in which MSE is the mean squared error, P is the number of free parameters and N is thenumber of input-output cases used for training.The optimized computer program NEUROPORT 2.0, developed in the LPC, was used tomake the different NNs for wave transmission.

• Evolutionary Strategy (200+200)-ES

The (200+200)-ES algorithm used in this paper is similar to that proposed by Medina (1999).The (200+200)-ES means that the training of the neural network is done using 200 parentsand 200 offspring, and using sufficient generations to decrease the error, without howeverpassing the level of overfitting.

• Sigmoidal and lineal neurons

The NEUROPORT 2.0 program uses 2 different types of neurons in the hidden layer(s).Sometimes it is advisable to replace a sigmoidal neuron by a lineal one to lower the amountof parameters in the NN. If xij is the signal sent from neuron i to neuron j then the outputof neuron j can be calculated as follows,

Sigmoidal neuron:

xj =1

1 + exp

[(1 + βj)

(αj −

i=Nk∑i=1

Wijxij

)] (5.6)

Lineal neuron:

xj = αj +i=Nk∑i=1

Wijxij (5.7)


• Input parameters

The output of the NN model is the wave transmission, less obvious is the input parameters.Too many input parameters will make the NN too complex, and there will be too little datato obtain a small PSE. Too few input parameters can give an oversimplified NN. We chose totrain the Neural Network with the following input parameters:

Input parameters :

F/d

F/H

d/L

B/L

(5.8)

5.4.3 Neural Network simulation

With the input characteristics specified before, the neural network was trained. The trainingresults in the configuration are shown in figure 5.14. One of the input variables was deactivatedcompletely (d/L), and the two non-linear neurons in the hidden layer deactivated one of itsparameters (β). To assure a good functioning of the network, the used number of parametershas to be much smaller than the number of training data. The resulting number of parametersis 15, while 59 training data are provided. This ratio (N/P) 3.93 is not very high and theresults should be interpreted with care, but it is sufficient for the first approximation presentedhere.

Figure 5.14: Configuration of the used Neural Network for wave transmission

We only used 59 of the 84 available data obtained by the experiments in the wave flume totrain the NN. The other 25 data are used to verify the NN. This verification shows us if theNN is overfitted or not. The verification is shown in figure 5.15, where the measured value ofthe transmission coefficient is plotted against the calculated value of the NN.


Figure 5.15: Verification of the NN for wave transmission

The RMSE of the training data is 2.78% and the RMSE of the test data is 3.46%. Theseerrors are very low, which makes this NN reliable when predicting the wave transmission ifnew input data is entered. Once the NN model has learned the behaviour of the phenomenonto be reproduced, a virtual laboratory is available. 3000 virtual simulations were executed,600 for every configuration. An overview of the executed virtual tests is shown in table 5.2

Table 5.2: Overview of virtual tests


The results of the wave transmission for a given wave period T01 of 5 s and a given significantwave height Hs of 1 m are shown in figure 5.16.

Figure 5.16: Wave transmission for random freeboards (T01 = 5 s and Hs = 1 m)


5.5 Neural Network Model to estimate wave reflection

Another NN was used to predict the wave reflection of the modular breakwater. The sameNN which was used for wave transmission gave an error of the test data above 15%. Otherinput parameters were used to describe the reflection phenomenon.

Input parameters :

h/d

kd

F/H

(5.9)

The training of the NN with 59 input data of the irregular wave experiments results in theconfiguration shown in figure 5.17.

Figure 5.17: Configuration of the used Neural Network for wave reflection

The RMSE of the training data is 4.3% and the RMSE of the test data is 5.4%. These errorsare accepatble to predict reliable the wave reflection if new input data will be entered. Now wecan predict the reflection and transmission coefficients with the help of the 2 NNs. Further-more, it is possible to estimate the proportion of energy transmitted, reflected and dissipated.This can be calculated as

{Kt

2},{Kr

2}, and

{1−Kt

2 −Kr2}

respectively (Formula: 3.3).

Figure 5.18 shows the percentage of transmitted, reflected and dissipated energy, for differentvalues of crest freeboard over depth (F / d), for configurations of one level. In figure 5.19 thepercentage of energy is shown for configurations of 2 levels.


Figure 5.18: % energy transmitted, dissipated and reflected for 1 layer congigurations

Figure 5.19: % energy transmitted, dissipated and reflected for 2 layer configurations

Chapter 6

Conclusions

Wave transmission is a leading parameter determing the response of the shoreline to a de-tached breakwater. Wave transmission can vary significantly depending on the structureconfiguration and the incident wave conditions. Therefore, it is important to test the wavetransmission of the modular breakwater that was patented by Medina and Rodrıguez (2003).2D physical experiments were conducted at the LPC-UPV wave flume to analyze the hy-draulic performance. From March to May 2007 5 different configurations were tested (TCT,TT, T3CT ,TCT2 and TT2) under different wave conditions and different relative submer-gence.

For the irregular tests described in this study, the transmission performance of modularbreakwaters was similar to that corresponding to conventional quarry stone LCS with thesame cross section. Therefore, it is reasonable to expect functional performance of the mod-ular breakwater similar to conventional LCS. Several published empirical formulae for wavetransmission coefficient were compared with the results of the experiments on the modularbreakwater.

Remarkable was the comparison between the results and the formula proposed by Ahrens(1987) (See page 27). With a root mean square error (RMSE) of 4.3% the formula predictsthe wave transmission of the modular breakwater adequately. Other formulae gave a RMSEabove 10%, and can give a wrong prediction of the wave transmission over the modularbreakwater.

71

Chapter 6: Conclusions 72

The application of an artificial neural network as a generalized wave transmission predictionmethod was also evaluated. After a internal discussion the next significant input parameterswere used to make the NN for wave transmission: freeboard divided by waterdepth (F/d),freeboard divided by incident waveheight (F/Hi), waterdepth divided by wavelength (d/L)and crest width divided by wave length (B/L). The NN was trained with 70% of the exper-imental results and verified with the remaining 30%. The root mean square errors for thetraining and test data were respectivly 2.78% and 3.46%.

A second Neural Network was proposed to predict the wave reflection. The input parametersof this NN are structure height divided by waterdepth (h/d), wave number multiplied bywaterdepth (kd) and freeboard divided by incident wave height (F/Hi). The root meansquare errors for the training and test data were respectively 4.3% and 5.4%.

With the use of both NNs, design graphs can be made with the proportional transmitted,reflected and dissipated energy (Fig. 6.1).

Figure 6.1: % energy transmitted, dissipated and reflected

Appendix A

Report File LPCLap 3.6

An example of the report file generated by the software tool LPCLab is presented here.Experiment: 1M13 2020

73

Appendix A: Report File LPCLap 3.6 74

Appendix A: Report File LPCLap 3.6 75

Appendix B

Nomenclature of the experiments

The nomenclature of the different experiments can be interpretated as follow:

xMyz aabb

Where:x = Configuration number:

Configuration1 TCT2 TT3 T3CT4 TCT25 TT2

y = Type of waves

0 = Regular waves1 = Irreguler waves

z = Freeboard number

1M, 2M and 3M 4M and 5M1 0 cm -10 cm2 10 cm -5 cm3 20 cm 0 cm4 30 cm 5 cm

76

Appendix B: Nomenclature of the experiments 77

aa = Period

Regular Irregular1.5 s 2 s2.5 s 3 s

bb = Wave height

Regular Irregular10 cm 10 cm20 cm 20 cm

Appendix C

Calibration of the wave gauges

Calibration of the gauges had to be repeated daily, before starting the tests, given the fact thatclimatically changes (temperature, humidity) and changes in the water level affect the mea-suring sensibility of the gauges. The capacity gauges are widely used in maritime engineeringlaboratories because of their reliability of calibration and linearity in the transformation data.The gauges are connected with an electronic equipment that makes it possible to calibratethem, the computer program used to calibrate the gauges is “Modelizacion Fisica de Oleajev3.2” (Fig. C.1).

Figure C.1: Computer program to calibrate the wave gauges

78

Appendix D

Tables with the results

In this appendix all the results of the different experiments are given in Excel tables. Thenomenclature of the different experiments can be found in appendix B and the list of symbols(Page vi) explains all parameters used in the tables below.

79

Appendix D: Tables with the results 80

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study of prefabricated re-usable breakwaters for shore

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