Introduction to Coastal Dynamics and Shoreline Protection

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Introduction to Coastal Dynamics and Shoreline Protection

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Introduction to Coastal Dynamics and Shoreline Protection G. Benassai University of Naples Parthenope, Italy

Introduction to Coastal Dynamics and Shoreline Protection G. Benassai University of Naples Parthenope, Italy

Published by WIT Press Ashurst Lodge, Ashurst, Southampton, SO40 7AA, UK Tel: 44 (0) 238 029 3223; Fax: 44 (0) 238 029 2853 E-Mail: [email protected] http://www.witpress.com For USA, Canada and Mexico WIT Press 25 Bridge Street, Billerica, MA 01821, USA Tel: 978 667 5841; Fax: 978 667 7582 E-Mail: [email protected] http://www.witpress.com British Library Cataloguing-in-Publication Data A Catalogue record for this book is available from the British Library ISBN: 1-84564-054-3 No responsibility is assumed by the Publisher, the Editors and Authors for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. © WIT Press 2006 Printed in Great Britain by Lightning Source UK Ltd., Milton Keynes All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the Publisher.

Contents

Preface

xi

CHAPTER 1 Integrated approach to coastal dynamics 1. Coastal dynamics basic approach 2. Coastal erosion and remediation study 2.1 Data acquisition 2.2 Critical erosion evaluation 2.3 Planning analysis 3. Causes of coastal erosion 4. Space and time scales 5. Meteomarine factors 5.1 Wind 5.2 Waves 5.3 Currents 5.4 Sea level variations 6. Sediment transport and coastal structures 6.1 Modes of sediment movement and their appearance region 6.2 Coastal structures and sediment transport 7. Elements of coastal management

1 1 3 4 6 7 7 8 9 10 10 14 16 17 17 19 21

CHAPTER 2 Beach morphology and sediment analysis 1. Introduction 2. Beach classification 3. Beach morphology and sediment transport 4. Seasonal profiles, bars and berms 5. Equilibrium beach profile 6. Sediment analysis 6.1 Bathymetric and geophysical surveys 6.2 Physical and chemical analysis

27 27 27 30 33 33 35 35 37

6.3 Sediment size classification 7. Case study

39 42

CHAPTER 3 Linear wave analysis 1. Introduction to linear wave theory 1.1 Governing equations 1.2 Boundary conditions 1.3 Linearized boundary conditions 2. Results of the linear theory 2.1 Wave profile, length and celerity 2.2 Group celerity 2.3 Velocity components 2.4 Particle displacements 2.5 Wave pressure 3. Case study

45 45 45 49 50 51 51 54 56 58 60 62

CHAPTER 4 Sea level variability 1. Introduction 2. Astronomical tide 3. Long waves (tsunami and seiches) 4. Wave set-up and set-down 4.1 Radiation stress 4.2 Water level fluctuations due to radiation stress 5. Storm surge 6. Case study

67 67 67 71 73 74 76 77 85

CHAPTER 5 Random wave measurement and analysis 1. Wave measurements 1.1 Ultrasonic and pressure gauges 1.2 Wave buoys 1.3 Italian Sea Wave measurement Network 1.4 Satellite remote sensing 1.4.1 Radar altimeter 1.4.2 Synthetic Aperture Radars 2. Statistical properties of random waves 2.1 Data sampling 2.2 Data processing 2.2.1 Time domain analysis 2.2.2 Directional wave spectra 2.2.3 Pierson – Moskowitz and Jonswap spectrum 3. Statistical representation of wave climate 4. Case study

87 87 87 88 89 90 90 92 93 93 95 95 99 100 102 103

CHAPTER 6 Short term wave prediction 1. Introduction 2. Elements of wind measurement analysis 2.1 Wind information needed for wave hindcasting 2.2 Geostrophic and low-height winds 3. Wave prediction on deep water 3.1 Fetch and duration limited growth 3.2 Significant wave (SMB) model 3.2.1 Case study 3.3 Spectral wave models 3.3.1 First, second and third generation models 3.3.2 Third generation models 3.3.3 WaveWatch III 3.3.4 Case study (WWIII application for the Gulf of Naples)

107 107 108 109 110 111 112 114 116 117 118 119 122 124

CHAPTER 7 Long term wave statistics 1. Introduction 1.1 Wave data 1.2 Data selection 1.3 Extreme value probability distribution 2. Data fitting to the probability distribution 2.1 Normal Probability Distribution 2.2 Log-Normal Distribution 2.3 Gumbel distribution 2.4 Weibull distribution 3. Parameter calculation 3.1 Statistical tests of fit 3.2 Confidence intervals 3.3 Statistics of offshore extreme waves 3.4 Wave height persistence 3.5 Case study

127 127 128 129 129 129 130 131 131 132 133 133 134 135 137 138

CHAPTER 8 Wave transformation in the coastal zone 1. Wave energy and energy flux 1.1 Potential Energy 1.2 Kinetic Energy 1.3 Energy Flux 2. Refraction and shoaling 2.4 Discussion on Kr and Ks 3. Total reflection 4. Wave diffraction 5. Numerical models for wave propagation 5.1 Phase-averaged model 6. Finite depth spectral wave models 6.1 Other finite depth spectral wave models

143 143 143 144 145 146 150 152 155 156 158 159 161

6.2 Phase-resolving models 6.2.1 Boundary Integral Models 6.2.1.1 Mild Slope Equation Models 6.2.1.2 Boussinesq equation model 6.2.2 Lagrangian models – Ray method for wave transformation 6.2.3 Eulerian models 6.3 Grid models 7. Wave breaking

161 163 163 165 166 169 169 172

CHAPTER 7 Sediment transport 1. Introduction 2. Basic concepts of sediment transport 2.1 Critical bed shear stress 2.2 The Shields parameter and modified Shields diagram 2.3 Sediment fall velocity 2.4 Bed load and suspended load 2.4.1 Bed-load and shear stress 2.4.2 Steady bed load in sheet flow transport 2.4.3 Basics of suspended load transport formulation 2.5 The bottom boundary layer and the bed roughness 2.6 Bed load and suspended load: a simple parametrical model 2.7 Case study 3. Basic shore processes 3.1 Nearshore circulation 3.2 Wave run-up in the swash zone 3.3 Bar formation by cross-zone flow mechanisms

175 175 176 176 177 179 180 181 182 183 185 187 189 194 194 198 199

CHAPTER 10 Beach profile modeling 1. Cross-shore transport 2. Cross-shore sediment transport and equilibrium beach profile 3. Dean’s model for equilibrium beach profile 3.1 Equilibrium parameter A 4. Processes of accretion and erosion 4.1 Surf zone 4.2 Swash zone 5. Erosion/accretion parameters 5.1 Case study 6. Analytical profile modelling 6.1 Case study 7. Numerical beach profile modeling 7.1 Example of numerical model: SBEACH

201 201 203 204 207 208 208 208 209 213 214 219 220 222

CHAPTER 11 Shoreline modeling 1. Introduction

227 227

2. Longshore transport 2.1 Case study 3. Numerical shoreline modeling 3.1 GENESIS 3.1.1 Governing equations 3.1.2 Model parameters 3.1.3 Model implementation 3.1.4 Model calibration

228 230 231 234 234 236 239 241

CHAPTER 12 Comparison and choice among alternative protection systems 1. Introduction 2. Insertion of protection systems on the coastline 3. Shoreline protection systems 4. Hard measures 4.1 Detached emerged breakwaters 4.2 Detached submerged breakwaters 4.3 Emerged or semi-submerged groins 4.4 “T”-shaped emerged of semi-submerged groins 4.5 Adherent breakwaters 4.6 Seawalls 5. Soft measures 5.1 Artificial nourishment 5.2 Dune restoration 6. Schematic indications for the choice 7. Mechanisms of protection 7.1 Efficiency 7.2 Induced efforts

245 245 245 246 248 248 249 250 252 252 254 254 254 256 258 260 260 261

CHAPTER 13 Hydraulic design 1. Dimensional analysis 2. Wave run-up Ru and run-down Rd 3. Overtopping discharge 4. Transmission coefficient 5. Reflections 6. Case study

263 263 265 268 270 271 273

CHAPTER 14 Structural design 1. Introduction 2. Structural stability 2.1 Hudson formulation 2.2 Van der Meer Formulation 2.3 Comparison of Hudson and new formulae 3. Armour layers with concrete units

275 275 277 279 280 283 283

4. Low-crested structures 5. Reef breakwaters 6. Statically stable low-crested breakwater 7. Submerged breakwaters 8. Filter and core characteristics 9. Toe stability and protection 10. Breakwater head stability 11. Fundamentals of probabilistic design 12. Deterministic design – case study

285 286 286 287 287 288 289 289 291

CHAPTER 15 Beach fills 1. Introduction 2. Beach fill profile 3. Volume computation 4. Beach planform evolution 5. Longevity of beach fills 6. Effect of fill length and of wave climate 6.1 Case study 7. Compatibility of the borrow material 7.1 Case study 8. Sediment sources 9. Monitoring

293 293 296 298 298 301 303 305 306 308 309 310

References

313

Preface This book was developed from lecture notes for a course on Coastal Dynamics and Shoreline Protection addressed to students of Environmental Sciences. This is the reason why it is organized to introduce the reader to the fundamental principles of the topics treated in each chapter. It can be used as a training aid both for students and for practicing engineers, as almost every topic is developed with case studies. The book, which deals primarily with sandy coastlines, is divided into three parts. In the first part, which is limited to Chapter 1 – Integrated approach to coastal dynamics, the reader is introduced to the approach of a coastal erosion and remediation study and to coastal management. In the second part, the meteomarine factors cited in Chapter 1 are dealt with in some detail, together with the mechanisms of sediment transport. The topics addressed are, amongst others, linear and higher order waves, random waves and spectra, wave transformation in the coastal zone, water levels, short-term and longterm wave prediction, sediment transport, shoreline and beach profile modeling. The third part deals with the choice between various protection systems and tries to give the reader some basic elements of hydraulic and structural design for both rigid structures and beach fills. Acknowledgements have to be addressed to all the people who inspired me, in particular my father Edoardo for the first approach to the maritime structures, Giulio Scarsi and Laura Rebaudengo of Genoa University for their rigorous analytical approach to the maritime hydraulics. Many thanks have to be addressed to all the students to whom I had the privilege of teaching the concepts reported in this book for more than 14 years, and to the University Parthenope of Naples where I currently teach the course on coastal dynamics and shoreline protection. Additional thanks have to be addressed to the people who typed the manuscript for their patience and their contributions, especially Dr I. Ascione and Dr. E. Chianese. Finally, particular thanks is due to my wife Maria Pia and my sons Edoardo Maria and Rossella who have given me total support and encouragement, and to whom this book is dedicated. G. Benassai Naples, 2006.

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Chapter 1 Integrated approach to coastal dynamics 1 Coastal dynamics basic approach The littoral area is a system in unstable dynamic equilibrium: storms create short term erosional events, natural recovery after the storm and seasonal fluctuations may not be in balance to produce long term erosion. Shore protection projects moderate the long term average erosion rate and reduce damage caused by flooding and wave attack. The coastal environment constitutes a fragile, little known and complex ecosystem that is an important resource for most nations. The high economic interest relative to environmental resources and man’s extensive and growing use of the coastal zone drives the need for the optimization and the mitigation actions. In order to reach a satisfactory design, we must understand each element and its interactions, the inputs and the outputs, and how they affect the system and neighboring systems. In fact, any kind of protection scheme interfering with the littoral transport (groynes, breakwaters etc.) modifies this equilibrium. The relative consequences cannot be estimated without the analysis of the physical phenomena and the simultaneous consideration of the local process and their interaction with adjacent systems. In the past, mistakes were made by not considering the proper system boundaries or by not considering a super-system, when necessary. This restricted vision produced huge damages for the neighboring beaches, with catastrophic environmental, economic and social consequences. For this reason, an integrated approach to the coastal zone has to be done with a preliminary identification of all systems that influence the design and that are affected by it. The monitoring of the systems must be done on both a short and long time scale and has to be extended to the entire “physiographic unit”. This is characterized by the circumstance that the coastal sediments move inside it without external influences. The identification can be based on the study of the

2

INTRODUCTION TO COASTAL DYNAMICS AND SHORELINE PROTECTION

natural factors (wind, currents, human impact), or on the consequences of these factors: erosion and accretion. The identification requires the knowledge of the dynamic conditions and of the interaction with the littoral evolution. The limits of the area involved can be variable in time in relation to the events (natural or anthropic), which modify the coastal dynamics. The analysis of the wave conditions and in particular the interaction between the waves and the sediment plays a relevant role for understanding the physical processes. This analysis, then, has to be focused on the monitoring of the wave climate and on the statistical analysis of its spatial and temporal characteristics (wave height, direction and period). A statistically valid analysis can be obtained through the monitoring of the waves for a period of 10 years or more. When the waves approach the shoreline, they are modified by the seabed through processes such as refraction, shoaling, bottom friction and diffraction (if waves interact with structures). The waves, then, change in height and direction. This feature plays a relevant role in the littoral transport process. A numerical model is then required in order to consider the role of the bottom in changing the wave characteristics, due to lack of field local data regarding the littoral transport. This interaction between the waves and the bottom is due primarily to second order shallow water phenomena, such as the wave drift (which is responsible for mass transport) and the radiation stress, which is associated with the longshore current for obliquely incoming waves. The wave drift is directed normal to the shoreline, transporting the water particles near the surface in the direction of wave propagation. The shore-parallel component of the radiation stress generates the longshore current, which carries sediments along the shoreline (the so-called littoral drift). Other significant interactions can occur between waves and currents. Wavecurrent interaction may affect the development of rip currents. In fact the weak currents generated by a gentle alongshore variation in the wave field can cause significant refractive effect on the waves so as to change the structure of the forcing which drives the currents. This can cause the development of instabilities of the cellular circulation and can influence the rip channels spacing and depth. From the literature it is assumed that the longshore sediment transport is more relevant than the cross-shore one. The latter process, although significant during storms, gives little final influence on the sediment dispersion along the coastline. The littoral transport on a long time scale is directly connected with the longshore component of the energy transmitted during the breaking phenomena. This parameter can be computed on the basis of both the offshore wave climate (frequency of events classified by period, direction and wave height) and the propagation features of the waves. So a statistical analysis has to be carried out through all the possible combinations of wave height, period and direction, statistically computed from field measurements. The sum of these contributions, related to the breaking wave energy flux, allows to compute the

INTEGRATED APPROACH TO COASTAL DYNAMICS

3

longshore transport on several time scales. The applicability of the results depends on the analysis of the effective sediment transport, which means to put in the numerical model more information, such as grain size in relation to the depth and the breaking wave type (the most important parameters during the sediment suspension). The results obtained have to correspond with an independent assessment about the beach morphology and the influence of existing structures. The complexity of environmental phenomena makes the design process extremely complex. Even if the more sophisticated methods are used (backanalysis of a finite number of real cases, or the results of the close reproduction of phenomena), it is possible to make large errors in relation to the techniques and materials used and the boundary conditions imposed. This is the reason why the design is done by trial and error. This approach is obviously unacceptable in the prototype, but it is possible, however, in numerical models. These numerical models are used to verify the impact of structure in several environmental conditions, optimizing the localization, typology and the dimension of protection systems. In this phase a quantitative evaluation is carried out by numerical simulation of the coastline evolution in order to identify the potential environmental impact of the project. This prognostic step of the design process requires the definition of boundaries and the identification of the coastal dynamics through the analysis of available data. The impact assessment of the sediment budget supplied by the rivers, the analysis of available maps and aerial photographs and the study of the impact of existing structures define the boundaries of the physiographic unit. The numerical simulation in the final phase allows the quantification of the specific environmental impact, the time scale and the significant trend of the coastline modifications resulting from the interaction between the new structure and the mean wave climate.

2 Coastal erosion and remediation study The fundamental criteria of a coastal dynamics study are based on an accurate evaluation of the environmental, economic and social aspects of the area of interest on a spatial scale of the physiographic unit. In fact, the key concept in coastal design is the integration, that is the awareness that nothing should be done within a littoral cell without thinking about how it affects the rest of the cell, which by definition is part of the same system. The main goals of the coastal dynamics study are the assimilation and collection of a huge quantity of experiences, actually distributed among several private companies and government agencies, in order to reach a complete vision of the existing knowledge and in order to plan the coastal protection in the best way. In fact, a deep knowledge of the integrated physical processes can avoid unwise and dangerous actions and plays a substantial role in minimizing possible local negative consequences.

4


With these premises, the main technical steps of a coastal dynamics study are the following: • • •

Data acquisition Critical erosion evaluation Planning analysis

A typical scheme of a coastal dynamics study is given in figure 1.1. Offshore Waves and Winds

Tides and Currents

Offshore Wave Climate

Hydrodynamics

DATA ACQUISITION

Coastal Morphology

PLANNING ANALYSIS

CRITICAL EROSION EVALUATION

Bathimetry

Coastal Dynamics Analysis

Inshore Wave Climate

Sediment Transport Analysis

Littoral Transport Analysis

Sediment Transport Evolution Satellite and Aerial Maps Bathimetry Dispersion of Sediments Effects of Structures

Numerical Model Shoreline Evolution

Wave-Current Interactions

Sediment Budget Physiographic Unit Significant Parameters

Trial-Error Design

Shoreline Simulations

Figure 1.1- The main steps of an integrated approach to coastal design. 2.1 Data acquisition The first phase of the study will involve the identification and acquisition of available data. Coastal data are usually acquired through field observation and may be divided into the following categories:


5

• •

Field data (bathymetric and topographic surveys, sedimentology); Office data provided by: interpretation of historical maps, aerial photographs, etc; numerical simulations of the coastline, laboratory and office data analyses. Data are provided by various sources, such as: • Literature sources (University Departments, Journals and conference proceedings, reports of research projects); • Local sources, which provide detailed and sometimes unique data pertinent to the site (reports of local newspapers, interviews with fishermen, etc.); • Government agencies, which provide data archives and studies with relevant coastal information; • Private companies, such as oil, gas and construction companies. Some of these data are in the public domain and include also environmental impact reports containing extensive coastal process data; • Computerized literature databases containing information that may be acquired by key terms, subjects, titles and author names, available to major Universities and Government agency libraries. Data requested to characterize the significant coastal processes and to analyze the characteristics of severe storms include the following: Wave data, which include wave height, period, steepness and direction and breaker type. These data may be available through various techniques: recorded wave data, obtained using buoys and other recording instruments located offshore (piers or other coastal structures near the study site); hindcast data obtained from numerical prediction models and used to estimate wave statistics. Water level data are provided using tide gauges deployed near the study site. The water level is commonly measured through three types of instruments: pressure transducers, floating gauges and staff gauges. Typically, water level measurements are related to a given datum; daily records are usually published in reports, while predicted water levels and tidal current information for each day can be obtained from the annual Tide Tables. Geologic and sediment data include geologic maps and data collected during bathymetric surveys. These data are important to characterize the response of the coastline to severe storm events. Aerial photographs are useful for studies over long time scales to understand shoreline change assessments and to get information about coastal landforms and materials, behavior of engineering structures, location of rip currents, storm effects on the coastline, etc. Satellite data, like aerial photographs, are useful for assessing large-scale changes of the coastal zone. Finally, remote sensing allow to define spatial patterns of suspended sediments in shallow waters and freshwater discharges near estuaries.

6


2.2 Critical erosion evaluation The most part of defense actions in the past were done in emergency conditions and economic constraints. Usually the actions were focused on the restoration of the previous conditions without paying attention to the causes of erosion. Besides, the actions were not focused on the efficiency, on the past experiences and, above all, on the need to reduce the environmental impact. For this reason, the first step of the critical erosion evaluation is the analysis of the existent structures, which means: • Impact analysis of the structures on the coastline evolution and on the local bathymetry; • Localization, time and costs evaluation for dredging operations and maintenance of ports and waterways; • Evaluation of the amount of volume for artificial nourishment; • Sustainability of the project location at all the technical and administrative levels. The basic critical shoreline changes can be summarized in three types: • Natural shoreline accretion • Shoreline erosion • Interactions between coastal structures and littoral processes The fundamental criteria to detect these critical situations are the following: • Physiographic unit • Littoral transport intensity • Coastline evolution • Sediment loss • Human impact Coastal erosion studies involve part of the following phenomena: • Erosion processes caused by natural or human impact • Sediment supply by rivers or dunes • Conflicting demands on the coastal area After the data acquisition and analysis, a hypothesis of critical area localization on provincial or regional scale has to be defined in order to focus the areas with the greater erosion problems. All the coastal area characterized by different erosion levels has to be detected and classified, in order to identify the urgency level and the correct strategy. The classification of the critical areas starts from the following identification of the damaged areas: • Areas with high erosion level: they need huge restoring activity of the littoral transport and/or beach nourishment • Areas with medium erosion level: they need a beach stabilization but specific restoring actions are not required. • Areas with low erosion level: they only need maintenance of existing equilibrium.


7

2.3 Planning analysis The planning analysis requires: • • • • •

Analysis of the environmental local risks (erosion processes; loss of sediment; human impact, etc); Analysis of the existing negative responses; Final setting of physiographic unit limits; Classification of critical zones according to priority criteria; Checklist of possible alternatives to shore protection (retreat, do nothing);

In relation to the erosion level found out in the physiographic unit, the following options can be chosen: • • •

Passive hard structures: revetments, bulkheads, sea walls; Active hard structures: groins, detached breakwaters (emerged or submerged); Soft structures: artificial nourishment alone or protected with submerged structures, sand bypass.

The choice among alternative solutions is based on extensive coastal knowledge, which is the combination of theory and experience. Some of these solutions will be illustrated in chapter 12.

3 Causes of coastal erosion The main causes of coastal erosion can be divided into natural and human. Nevertheless, it has to be observed that the latter causes are indirectly related to the most part of the “natural” erosion processes. Natural causes The main natural cause of erosion is the imbalance between the loss of sediment due to offshore transport and the decrease of the longshore transport, which results in a negative sediment budget. The global climatic change emphasizes this problem and affect the sediment transport; the decrease of run off is also responsible for loss of littoral transport. The forces acting on littoral sediments are related to wave conditions. The strong dissipative processes associated to breaking events generate alongshore currents responsible for the littoral sediment transport between the breaker zone and the swash zone, which are responsible for spatial change. During severe meteomarine events, the sediment near the coastline is transported offshore and deposited in a bar far away from the shoreline by the steeper waves. During the following calm periods, the smaller waves tend to move the sand from the bar location toward the beach, even if part of the sediment is lost in the open sea. Other factors affecting the sediment transport are density currents and tidal currents which may change the wave circulation pattern. Another natural cause

8


of erosion is the mean sea level and the direct sediment transport by the wind, which results in the dunes formation. Human impact Human causes depend on the interaction between coastal structures and littoral transport, because they can modify the natural equilibrium through the imbalance of longshore sediment budget. Dams and other flood prevention structures reduces sedimentation in rivers and accelerates erosion processes. Besides, urbanization of coastal areas decreases the longshore sediment transport causing the erosion of some areas and the silting up of others. Localized structures like emerged and submerged breakwaters, groins and their combinations reduce the damages, although they need a focus study on sediment dynamics in the interested area and on the total extension of physiographic unit. This analysis has to be carried out to avoid additional damage both on the shoreline evolution and on the quality of the coastal environment.

4 Space and time scales Before the examination of the physical phenomena directly responsible for coastal processes, a first fundamental issue concerns the spatial and temporal scale on which processes take place. In this context the processes developing in relatively shallow water will be considered, that is between the coast line and the breaker zone where the interaction between the water forces and the bottom is particularly relevant. The usual approach when hydrodynamics (turbulence, waves, tides, stormsurges, currents, etc.) and morphodynamics (ripple formation, bar formation, cross-shore transport, longshore transport, etc.) are involved is the division of processes in relation to the spatial and temporal scale of observation (see figure 1.2). The processes involved can be distinguished in relation to the spatial/temporal scale of observation: • • •

Small scale (0.1mm – 10m, 0.1sec – 1 day) Intermediate scale (1m – 10km, 1sec – 1 year) Large scale (1 km – 100km, 1month – ten-years periods)

Different processes are connected to each other: in fact, the large scale processes modify boundary conditions for the processes on the intermediate scale, which, in turn, influence the processes on smaller scales. Some interesting questions about the influence of resolution on the correct description of the phenomena may be raised: the relationships between spatial resolution and predictability show that while increasing resolution provides more descriptive information about the patterns in data, it also increases the difficulty of accurate modeling.


9

Figure 1.2 - Space-time scales relationships, (modified from De Vriend, H.J., 1991). Processes on small scale Small scale processes involve interactions between bottom currents and sediments, which generate the sediments transport. Several bed forms are shaped by wave action (ripples and dunes). The bottom morphology and the bottom boundary layer dynamics are crucial at this scale to define the processes involved in the sediment transport. Processes on intermediate scale Intermediate scale processes involve the wave dynamics, the littoral wave circulation and the evolution of the bottom morphology due to sediment transport. Processes of wave dynamics include refraction and shoaling (caused by the depth decrease) diffraction, reflection (in presence of sheltering structures), breaking and dissipation. The circulation in the surf zone has to be evaluated in order to compute the sediment transport. The next step is to consider bathymetry evolution, which, in turn, modifies the circulation. The processes go on till an equilibrium is reached. Processes on large scale Large scale processes involve the behavior of wide coastal areas on long times, which is known in literature as LSCB (Large Scale Coastal Behavior). Large scale models are developed integrating the ones on small and intermediate scale. The starting input is a known morphology, then the forcing (waves, currents, river inlets, structures, etc) have to be imposed to find out a new configuration. The large scale observation is important from an economic and social point of view, and it represents an efficient tool for the correct coastal zone management.

5 Meteomarine factors Meteomarine factors are directly associated with climate, such as winds and atmospheric pressure variation, waves, currents, tides and storm surge, which affect coastal morphology.

10


5.1 Wind Wind is caused by pressure gradients between adjacent areas. Pressure variations are generally the result of temperature differences due to disomogeneous insulation of adjacent zones reached by solar radiation (e.g. between lands and oceans). Wind fields vary in a wide range of spatial and temporal scales, from large-scale (permanent winds) to local (short winds). Hydrodynamics is strongly influenced by wind action, which is responsible for wave generation, wind setup, surge and surface currents. Wind forces directly modify coastal morphology through transport and deposition of sediments on the beach and the dunes, while they indirectly modify coastal morphology generating waves responsible for sediment transport. Wind action has a substantial role in some phenomena such as sea breezes, water level fluctuations and seiches. Sea breezes occur in a coastal area, especially in summer, and are generated by pressure gradients between water and coast: during the day, the warm air over the land becomes lighter and rises, thus forming an area of low pressure, resulting in a landward-directed breeze. During the night, the cooling of land is faster than water, which results in a seawarddirected breeze. Breezes don’t play a significant role in shaping the coastal morphology and give little contribution in sediment transport. Rapid changes in atmospheric pressure and directional shifts of strong winds on small seas and confined water bodies, cause periodic water level oscillations called seiches. 5.2 Waves Waves are the main factor in determining the shape and morphology of beaches and significantly influence the planning and design of harbours and coastal structures. The wave crest is the high water level reached by the free surface, whereas the wave trough is the low water level. The wave height (H) is defined as the vertical distance between the crest and the trough. The wave length (L) is the distance over which the wave pattern repeats itself. The wave speed (C) is the velocity of a single wave, while the wave period T is the time required for a wave to pass a particular location. The inverse of the period is the wave frequency f. When waves become large or travel toward shore into shallow water, higherorder wave theories are often required to describe wave phenomena. These theories represent nonlinear waves, while the linear theory is valid when waves are small and travel on deep water (but it still provides some insight for finiteamplitude periodic waves). However, the linear theory cannot account for the fact that wave crests are higher above the mean water line than the troughs are below the mean water line (U.S. Army Corps of Engineers - Coastal Engineering Research Center, 2001). Waves are strongly related to wind action on surface water, which provides a source of energy for wave formation. Waves propagate energy supplied by the


11

wind at air-sea interface, contribute to longshore transport and move bottom materials onshore and offshore. The mechanical characteristics of waves are important factors in planning and design of coastal structures because they interact with obstacles (breakwaters and coastal protection works), changing their characteristics until breaking occurs. Waves are divided in two main groups: short waves (period lower than 20s) and long waves, also called long-period oscillations (period between 30s and 40min). Water-level oscillations with a period longer than 1 hour (called astronomical currents and storms surge) are related to water-level variations. Short waves include wind waves and swell, whereas long waves can be divided into surf-beats, harbour resonance, seiche and tsunamis. Wave Classification A typical classification based on the frequency representation of all oceanic waves is given in Kinsman, B., 1965 (figure 1.3). A wave field is formed by many individual wave components, each characterized by a wave height, a wave period and a direction. Wave fields with many different wave periods and heights are called irregular, whereas wave fields with many wave directions are called directional. A wave field can be more or less irregular and more or less directional. Gravity waves are one of the most important factors acting on coastal morphology. Wave conditions vary extensively from one site to another, and depend on the wind climate and on the fetch extension, that is the water distance covered by wind without obstructions. Short waves are divided in two groups: •

•

Wind waves (also called sea waves), are generated by the local wind field. They are generally steep (high and short), irregular and directional waves. Their directionality makes difficult to recognize defined wave fronts, so they are also named short-crested waves. Swell are waves that traveled long distances away from their generation area and are more regular and unidirectional than wind waves. A portion of wave energy is lost during the propagation in deep water due to dissipation phenomena, which results in long period waves.

Wave Generation Wind waves are generated as a result of the action of the winds on the sea surface. Wave properties (height, period, direction) at a site depend on the following factors: • The wind field (speed, direction and duration); • The fetch of the wind field (meteorological fetch) or of the water area (geographical fetch); • The water depth in the wave generation area.

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Figure 1.3-Waves classification by frequency (after Kinsman, B.,1965). Wave height and period are closely related to wind conditions, from which they are estimated. The analysis of historical measured wind records is useful to reconstruct wave climate at a site. Such a computation is known as wave hindcasting. Forecast wind conditions are used to perform the wave forecasting. Wave transformation When waves approach a shoreline, they are affected by the seabed through refraction, shoaling, bottom friction and wave-breaking. Wave-breaking can also occur at deep water when the waves are getting too steep. The following transformations may occur: • Shoaling is the wave deformation, starting when water depth becomes less than about half the wavelength. This process causes a reduction in the wave propagation velocity and a shortening of the waves. • Refraction is caused by the fact that waves propagate more slowly in shallow than in deep water. When the wave front travels at an angle with the bathymetry, a change in direction of wave propagation occurs. An example of refraction phenomenon due to the bottom interaction is given in figure 1.4. • Diffraction is caused by sheltering structures such as breakwaters. This is the process by which the waves propagate into the lee zone behind the structures by energy transmittance laterally along the wave crests. • Bottom friction causes energy dissipation and thereby wave height reduction as the water depth becomes shallower. Friction is of special importance over large shallow water areas.


13

Figure 1.4 – Waves usually do not approach the shoreline parallel to the coast, but interact with bottom, resulting in wave refraction (after Thurman, H.V., 1985). • Depth-induced wave breaking happens when the wave height becomes greater than a certain fraction of the water depth. The wave height of an individual wave at breaking is often said to be around 80% of the water depth, but this is an approximate number, depending on breaking type and beach slope. • Wave-current interactions occur in the presence of a large scale current field (like a river mouth) and in the presence of rip currents. They influence the associated sediment transport and the subsequent shoreline evolution. • Wave-wave interactions result from nonlinear coupling of wave components and result in energy transfer from some wave component to other ones. Statistical description of wave parameters A statistical description of waves is necessary in order to make a correct analysis of the wave climate and of the littoral transport. This statistical description is based on the directional distribution of the following wave characteristics: • The significant wave height Hs, which is defined as the mean of the highest third of the waves in a time-series of waves representing a certain sea state (Hs computed on the basis of a spectrum is referred to as Hm0). • The mean wave period Tm, which is defined as the mean of all wave periods in a time-series representing a certain sea state. • The peak wave period Tp, which is the wave period with the highest energy. The analysis of the distribution of the wave energy as a function of wave frequency for a time-series of individual waves is referred to as a spectral analysis. The peak wave period is extracted from the spectra. • The mean wave direction θm, which is defined as the mean of all the individual wave directions in a time-series representing a certain sea state.

14


These parameters are often calculated from a time-series of the surface elevations once every three hours. The time-series is thereafter statistically analyzed to arrive at a synthetic description of the wave conditions in order to reach two main goals: •

•

Identify the occurrence probability of the extreme wave events for the design of maritime structures; this is often done through the percentage of exceedance of the wave height Hs; Identify the wave climate for the computation of coastal dynamics processes; this is often done through a directional distribution of the wave heights, often presented in the form of a wave rose or scatter diagram of Tp, versus Hs.

5.3 Currents Currents occur within the deep ocean, over the continental shelf and within the offshore and nearshore zones. They may be quasi-steady and persist for several hours to several weeks (ocean and shelf currents), or they may be oscillatory with periods of seconds (currents under waves). Currents may be limited to the surface or to the seabed, or they may extend over the full depth of water. Surface currents can have a different direction to those at the seabed. A partial currents classification based on the water depth divides the currents into the ocean, shelf and nearshore currents. The largest currents are those of the open ocean (ocean currents), which are driven by global scale interactions between the atmosphere and the sea. The continental shelf can extend between 1 and several kilometers from the coast. Continental shelf currents, are a complex mix of several components, among which there are internal waves, coastal trapped waves, tides and local wind induced currents. Shelf and ocean currents are generally of little significance within the shallower waters of the nearshore zone. This area is the preserve of wave induced currents which include: • • • •

oscillatory currents at the seabed prior to wavebreaking; mass transport of water shoreward as waves break; rip currents; longshore currents.

Currents are also an important aspect of many designs, particularly those involving the environment, water quality and habitat. Ocean currents are driven by the circulation of winds above the surface water, but coastal design needs the analysis of the wave-induced currents rather than the ocean currents. Wave-induced currents Nearshore currents are mainly caused by surface waves breaking on a beach. In fact, when surface waves break on a beach, wave energy is lost to turbulence generated in the process of breaking, and wave momentum is transferred into the


15

water column generating nearshore currents. There are two current systems whose flow structures are predominantly horizontal, alongshore currents caused by obliquely incident waves and cell-like circulations, which can occur when waves are nearly at normal incidence. The scheme of a nearshore current system is indicated in figure 1.5. Cross shore currents It is known that the propagation of surface waves produces a mass transport in the direction of wave propagation, which is a second-order correction to the linear wave theory. This mass transport is called the wave drift and is directed toward the coast. When the waves are breaking, water is also transported in surface rollers towards the coast. These two contributions are concentrated near the surface. As the net flow must be zero, they are compensated by a return flow in the offshore direction, which is concentrated near the bed (undertow). Long shore currents The longshore current is generated by the shore-parallel component of the stress associated with the breaking process for obliquely incoming waves, the socalled radiation stresses. This current, which is parallel to the shoreline, carries the sediments alongshore and it is approximately proportional to the square root of the wave height and to sin(2αb), where 2αb is the wave incidence angle at breaking.

UNIT CELL

RIP HEAD

MASS TRANSPORT

WAVE BREAKING

RIP CURRENT

LONGSHORE CURRENT

SURF ZONE

SHORELINE

Figure 1.5 – Nearshore current system. Rip currents Rip currents have been defined as currents in the offshoreward direction which return the sea water transported shoreward by wave action. These currents,

16


which are concentrated within the surface layer, are part of the cellular circulations, depicted in figure 1.5, ‘‘fed’’ by the converging alongshore flows close to the shoreline. Rip currents cause a seaward transport of beach sand, hence have direct impacts on beach morphology. Recent studies (Yu, J. & D.N. Slinn, 2003) show that the offshore directed rip currents interact with the incident waves to produce a negative feedback on the wave forcing, reducing the strength and offshore extent of the currents. 5.4 Sea level variations Water-level variations are important because they lead to identification of the swash zone and the fluctuations of the coastline. The extreme water levels are associated to flooding events. Water-level variations can be divided in two types: • Regularly oscillating variations with periods from half day up to one year (astronomical tides); • Non regular variations with recurrence periods from days up to several years, mainly caused by meteorological conditions. Astronomical tide The astronomical tide consists of the periodic rise and fall of water level generated by gravitational interaction among the earth, moon and sun. These factors determine the tide at a given location, mainly generated in the deep oceans from which travels into the coastal waters. The tidal wave height in deep water is normally less than 0.5m, whereas in shallow water it is modified by shoaling and friction; at specific locations the tide can be up to 15m high. The tidal conditions at a specific location vary according to semi-diurnal and diurnal tidal constituents and are published in Tidal Tables. If the semi-diurnal constituents determine the tide at a given location, the tide is called semi-diurnal, and if the diurnal constituents dominate it is called diurnal tide. A semi-diurnal tide has two high waters and two low waters every day, whereas diurnal tides have only one of each every day. In addition to these diurnal and semidiurnal variations the contribution of the fortnightly variations must be added, that cause the tide to be higher than normal at full moon and at new moon (spring tide), and lower than the normal at the quarters (neap tide). Meteorological water-level variations The water level also varies as a function of the wind impact and atmospheric pressure variations on the water surface: • Wind action drives onshore and offshore the surface waters and is responsible for the water-level rise (wind set-up) in restricted areas subject to wind stress: when wind drives water offshore, deep waters move onshore, and vice versa. • Weather disturbances cause water level variations called barometric surge and storm surge. High onshore wind over the shallow water surface associated with low barometric pressure causes a temporary


17

sea level rise, which results in flooding and coastal damage. The storm surge is the result of the combined impact of the wind stress on the water surface, and the atmospheric pressure reduction. The storm surge does not include the effect of the astronomical tide. The combined effect of astronomical and meteorological surges is often referred to as a tidal-wave. Barometric surges are often associated to storm surge and are generated by the inverse relationship between sea level and barometric pressure: water surface level rises as atmospheric pressure decreases of about 0.1 m for each kPa of pressure difference. In figure 1.6 an example of barometric surge superimposed on astronomical tide is given.

6 Sediment transport and coastal structures 6.1 Modes of sediment movement and their appearance region

Mean sea level (m)

The inshore sediment movement is usually divided into bed load, suspended load and sheet flow, as shown in the scheme of Figure 1.7. On deep water, waves have only a minor influence on sediment transport. As a wave enters shallow water, it begins to “feel” the bottom, its profile deviating from the linear one. In

Time (Days) Figure 1.6 - Example of barometric surge superimposed on astronomical tide (G. Benassai, 2002). fact, linear wave theory predicts that the crest and trough heights of the wave are equal (see Figure 1.8), that is, the wave is evenly distributed about the still water level. In contrast, finite amplitude wave theories predict waves with peaked crests and flat troughs. The crests are further above the still water level than the troughs are below this level (Young, I.R., 1999). When a resisting force of the

18


sand particle on the bottom becomes smaller than a wave force on it, the sand begins to move. The depth of this point on the beach is called a critical depth for sediment movement and the critical velocity is defined as the water particle velocity at this depth. When a shearing force larger than the critical condition for sediment movement acts on the sea bed a sediment movement of traction mode (bed load transport) takes place. As the shear stress increases further, sand ripples are formed on the bed. Suspended sediment occurs by the advection of the trapped sediment in the vortex formed periodically around the sand ripple (Sawaragi, T., 1995). When the bottom shear stress increases beyond a certain limit, ripples disappear and the so-called sheet flow in which sediment in high concentration is transported within a thin layer appears. Because a great deal of the sand particles are transported in the thin layer in this range, fluid turbulence near the bottom is repressed and any systematic turbulence (such as vortex on the ripple), does not occur there. In the shallow water region where incident waves break, a great deal of sediment is brought into suspension by the turbulence caused by breaking waves. Breaking waves of the plunging type suspend more sediment than breaking waves of the spilling type. In fact in the plunging breakers the crest becomes faster than the trough, curls and violently collapses. swash zone

breaker zone

breaking point

Disapperance of ripples Initial motion Generation of ripples

Bed load transport

Figure 1.7- Sediment movement and mode of sediment transport on the beach. A considerable amount of energy is released into a downwardly directed mass of water and the turbulence reaches the area beyond the breaking zone. Sediment materials are suspended and transported offshore by undertow currents. A large trough is formed and becomes deeper until the energy is completely exhausted. Offshore a bar is formed, localized between the breaking point and the deepest zone reached by vorticity. In the swash zone, fluid motions become entirely different from that in the shallow water region and sand movement also differs from the other part of the


19

beach. In fact, the swash zone is characterized by a fluctuation of coastline associated with sediment transport which occurs when the energy of the waves advancing up the beach is not completely exhausted. Swash dynamics depend on the wave frequency oscillations: at low frequencies, if the beach is permeable and the sand is not saturated, the water percolates through the substrate and the backrush decreases. An amount of sediment is accumulated on the beach in the swash zone and the beach slope increases. The result is a convex beach profile. At high frequencies (storm waves), if the substrate is saturated, the water cannot percolate through the sand and the backrush current cannot decrease. In this case the sediment transport associated with backrush is greater than uprush, which results in a concave beach profile. 6.2 Coastal structures and sediment transport Coastal structures interfering with littoral transport are the most common causes of coastline modification. The principal structures that may cause erosion are: • • • •

Groynes or similar shore normal structures Ports Inlet jetties at river mouths Detached breakwaters (a)

(b)

(c)

Figure 1.8 – Wave profiles: sinusoidal (a), cnoidal (b) and solitary (c). The accumulation and erosion pattern adjacent to coastal structures depend on the type of coastline, (the wave orientation of the shoreline) and on the extent and the shape of coastal structures. The typical impact of the coastal processes and the related erosion problems for different types of structures will be briefly discussed in the following.

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Groynes Groynes are normally built perpendicular to the shoreline with the purpose of protecting a section of the shoreline by blocking (part) of the littoral transport, whereby sand is accumulated on the upstream side of the groyne. However, the trapping of the sand causes a deficit in the littoral drift budget, and the coastal protection is always associated with a corresponding erosion on the lee side of the structure. In other words, a groyne just shifts the erosion problem to the downstream area. This is the reason why groynes are often built in long series along the shoreline, a so-called groyne field. Ports The primary purpose of a port is to provide safe mooring and navigation for vessels but when built on the shoreline it interferes with littoral drift budget and the results are sedimentation and shoreline impact. Like a groyne, the port acts as a blockage of the littoral transport, whereby it causes trapping of the sand on the upstream side in the form of an accumulating sand filet, and the possible bypass causes sedimentation in the entrance. The sedimentation requires maintenance dredging and deposition of the dredged sand. The result is a deficit in the littoral drift budget which causes lee side erosion on the adjacent shoreline. A port must consequently minimize sedimentation and coastal impact. These requirements have not always been given adequate attention. The result is that many ports trap large amounts of sand and suffer from severe sedimentation. Inlet jetties at river mouths River mouths are often by nature shallow and variable in location, which makes them unsuitable for navigation. In order to improve navigation conditions (and to some extent flushing conditions), many river inlets have regulated mouths. The regulation may consist of jetties, possibly combined with maintenance dredging programs. For the above reasons, regulated inlets are normally obstructions to the littoral transport which means upstream sand accumulation along the upstream jetty, loss of sand due to sedimentation in the deepened channel and the associated maintenance dredging. Detached breakwaters Detached breakwaters are used as shore and coast protection measures. In general terms, a detached breakwater is a coast-parallel structure located inside or close to the surf-zone. Breakwater schemes have many variables, depending on the distance from shoreline and location relative to the surf-zone, length and orientation crest height, (emerged or submerged). The breakwater shelters the coast partly from the waves, however as the waves diffract into the sheltered area, a complete shelter cannot be obtained. Submerged breakwaters have a lower visual impact, but provide less shelter. The longshore current is partially blocked by the circulation currents which cause some of the longshore current to be diverted outside the breakwater. So the littoral transport in lee of the


21

breakwater is decreased due the attenuated wave and longshore currents in the area sheltered by the breakwater. This causes trapping of sand behind the breakwater dependent on the length and shoreline distance, until a tombolo is eventually formed. For shorter or submerged breakwaters, only a salient in the shoreline will develop. In case of trapping of sand, a tombolo will be developed, which causes lee side erosion downstream of the breakwater very similar to what is developed for groynes.

7 Elements of coastal management The coastal system is comprised of a complex, dynamic web of interrelationships among human activities, societal demands, natural resources, and external natural and human inputs. The system is driven by human activities in terms of societal demands for use of the natural resources of the coastal area to produce desired products and services, e.g., seafood, marine transportation, recreation etc. Societal demands for outputs from a coastal area usually exceed the capacity of the area to meet all the demands simultaneously. Coastal resources, e.g., fish and recreations, are often “common property resources” with “open” or “free” access to users. Free access often leads to excessive use of the resource, e.g. degradation or exhaustion of the resource, coastal pollution and habitat degradation. The Integrated Coastal Management (ICM) is the process used to decide what mix of outputs will be produced. Integrated coastal management can be defined as “a continuous and dynamic process by which decisions are taken for the sustainable use, development, and protection of coastal and marine areas and resources. ICM acknowledges the interrelationships that exist among coastal and ocean uses and the environments potentially affected, and is designed to overcome the fragmentation inherent in the sectorial management approach. ICM is multi-purpose oriented, it analyzes and addresses implications of development, conflicting uses, and interrelationships between physical processes and human activities, and it promotes linkages and harmonization among sectorial coastal and ocean activities” (Cicin-Sain, B. & R.W. Knecht, 1998; Pernetta, J. & D. Elder, 1993). Pressures The coastal areas, which accommodate one of the more fragile and precious habitats of the world, are under pressure from economic causes, because recent large migrations have resulted in coastal stress and overloads (Kamphuis, J.W., 2000). The following pressures on the coastal zone are indicated: •

Population density: According to the 1994 distribution of population in relation to the distance from the nearest coastline, 20.6 percent of the world’s population lives within 30 km of the coast, and 37 percent within 100 km (Gommes R., J. Du Guerny, F. Nachtergaele & R. Brinkman, 1997). The coastal regions of

22


•

•

•

European countries are subject to constant pressures due to population density: half of European population lives in a narrow strip about 50 kilometres far away from the sea. The resources of the coastal zones produce a great part of the economic wealth. Population density has a substantial influence: on the equilibrium of natural ecosystems, as a result of human activities; on the quality and the amount of the natural resources (forests, grounds, waters, fishing zones, shores, etc.) as result of activity and population concentration. In turn, these factors increase the demand for use and exploitation of resources and require waste disposal; on the natural landscape, modified as a consequence of the human activities, the dimension and the scale of the relative structures and associated impact; Migration: as a result of migration to coastal areas, the coastal population is growing at a faster rate than the world population. Probably within the next 20 to 30 years, the coastal population will almost double; Tourism generates large fluxes of people who take vacations in far away coastal areas. The Mediterranean is one of the main tourist destinations of the world, giving accommodation to 30% of the international tourists: a third part of introits comes from the international tourism. Tourism usually has a seasonal frequency and increases in years. Probably the pressures on the littoral zones will continue to grow in future, with a doubling of tourism in the Mediterranean in the next 20 years. Tourism interacts with coastal environment in terms of land use and water resources consumption; Erosion caused by natural and human factors increase resources exhaustion, pollution and habitat degradation: these factors emphasize the fragility of coastal areas and push priority on protecting and upgrading the coastal system. Erosion of the habitat takes place mainly for the competitive use of the coastal zone. The analysis of erosion data (Table 1.1) shows that in the European coastal zones 1500 km are artificial coasts (Balearic islands, Gulf of the Lion, Sardinia, Adriatic, Ionian and Aegean), occupied by harbours (1250 km) (Corine, 1998). According to the data collected by Corine, approximately 25% of the Italian Adriatic coast and 7.4% of the Aegean coast shows an evolutionary tendency to erosion, whereas approximately 50% of the Euro-Mediterranean coastal zone is considered stable.

Conflicts The analysis of conflicts takes into account the interactions among natural resources and different economic, political and environmental factors. Conflicts among user groups and current social, economic and environmental conditions


23

represent a problem that often requires an immediate solution. The challenge in this context is to combine the following interests: • •

Public interests: shore protection, resource preservation, development of infrastructure and public utilities, etc.; Private interests: development of projects and coastal protection, industrial development, navigation, etc.

There are often inherent conflicts of interests in such projects, both with respect to the objectives and with respect to costs sharing. Resolving these planning matters is often as difficult as it is to find a suitable technical solution. However, the dissemination of the planning concepts, of the principles of sustainable development and environmental protection as well as of the physical mechanisms in the coastal zone, are all important for the success of the entire planning and design process. Table 1.1 - Evolutionary trends of some coasts of the European part of the Mediterranean Sea for both rocky coasts and beaches as % of coasts (Corine, 1998). MARITIME REGION Balearic Islands Gulf of Lion Sardinia

Adriatic Sea Ionian Sea Aegean Sea

Total coastline (km)

Stability

Erosion

Sedimentation

No information

Not applicable

2861

68.8%

19.6%

2.4%

0.5%

8.7%

1366

46.0%

14.4%

7.8%

4.1%

27.8%

5521

57.0%

18.4%

3.6%

16.0%

5.0%

970

51.7%

25.6%

7.6%

3.9%

11.1%

3890

52.3%

22.5%

1.2%

19.7%

4.3%

3408

49.5%

7.4%

2.9%

37.5%

2.6%

Coastal management In the European coastal regions local administrations have the best knowledge of the real problems. They interact with citizens, private companies and non governing organizations. Regional agencies give the guidelines and principles to coordinate the local initiatives, whereas political and national programs facilitate the participations on regional and local level. In many cases the cooperation between States is also necessary: as an example, it would be better that countries

24


joining the same sea try to coordinate their own initiatives, rather than propose different and contrasting political actions. The strategy of coastal zone integrated management (figure 1.9) encourages this transnational approach in the countries joining the “regional seas” like the Mediterranean or the Baltic Sea. Another aim is to prevent political strategies that damage the coast. In the case of the agricultural pollution, the integrated coastal management will give to the PAC (Common Agricultural Policy) the measures to decrease the impact of fertilizers on coastal waters.

Figure 1.9 -Coastal management strategy (after Townend, I.H., 1994). Coastal management Objectives and Activities Chapter 17 of Agenda 21 so describes the objectives and processes of Integrated Coastal Management programs: Coastal States commit themselves to integrated management and sustainable development of coastal areas and the marine environment under their national jurisdiction. To this end, it is necessary to, inter alia: • • • •

Provide for an integrated policy and decision-making process, including all involved sectors, to promote compatibility and a balance of uses; Identify existing and projected uses of coastal areas and their interactions; Concentrate on well-defined issues concerning coastal management; Apply preventive and precautionary approaches in project planning and implementation, including prior assessment and systematic observation of the impacts of major projects;


•

•

25

Promote the application of methods, such as environmental accounting, that reflect changes in value resulting from uses of coastal and marine areas, including pollution, marine erosion, loss of resources and habitat destruction; Provide access, as far as possible, for concerned individuals, groups and organizations to relevant information and opportunities for consultation and participation in planning and decision-making at appropriate levels.

The activities associated with the coastal management concern: •

•

•

Coordinating mechanisms (such as a high-level policy planning body) for integrated management and sustainable development of coastal and marine areas and their resources, at both the local and national levels. Such mechanisms should include consultation, as appropriate, with the academic and private sectors, nongovernmental organizations, resource user groups, and local communities; Data and Information: Coastal States, where necessary, should improve their capacity to collect, analyze, assess and use information for sustainable use of resources, including environmental impacts of activities affecting the coastal and marine areas. Information for management purposes should receive priority support in view of the intensity and magnitude of the changes occurring in the coastal and marine areas; International and regional cooperation and coordination: The role of international cooperation and coordination on a bilateral basis and, where applicable, within a sub-regional, interregional, regional or global framework, is to support and supplement national efforts of coastal States to promote integrated management and sustainable development of coastal and marine areas.

Planning and management of the coastal zones must necessarily be founded on the so-called “principle of precaution”: responsible subjects must try to preview the possible damages for the coastal zone and identify the more appropriate interventions. According to this principle, if they are not sure that some participation can take negative repercussions for a coastal zone, they must address their action with maximum caution. This approach assumes particular importance in vulnerable zones that could have negative consequences as a result of urbanization or tourism. In the past, many attempts to preserve the coastal regions failed, in spite of the good intentions, because they were addressed to sectorial aspects. As an example, the tourism in the coastal zones cannot be treated without paying attention to other concurrent factors, such as water supply, regional planning, impact of tourism on the existing natural habitats. The Integrated Coastal

26


Management has the objective to facilitate contacts between local, regional and national administrations in order to allow the responsible subjects to obtain a precise picture of the real necessities involved. The interested local subjects and organisms must be involved in planning and management of the coastal zones: without the contribution of companies and citizens who live and work in the coastal zones, the ICM will not be able to work successfully.

Chapter 2 Beach morphology and sediment analysis 1 Introduction A beach is an accumulation of loose material around the limit of wave action. According to King (1972) the beach may be taken to extend from the extreme upper limit of wave action to the zone where the waves, approaching from deep water, first cause appreciable movement of beach material. According to the nature of the beach material, we can define gravely, sandy and silty beaches. Beaches have variable planar shapes (eg. tongues, tombolos, cuspids) and their classification depends on sediment characteristics (mineral and granular properties) obtained by topographic and bathymetric surveys, as described in the following sections. The beach profiles show a typical morphology extending between the low tide level and the first major change in topography (e.g. a dune), and covering also the submerged profile. The coastline is subject to cyclical changes on different temporal scales (a few seconds to geological ages). This variability provides great interest for researchers in the field of geology, sedimentology and coastal engineering.

2 Beach classification Geologists describe beach classification using different criteria: according to grain size criteria we distinguish gravely, sandy and silty beaches. Some criteria are based on lithology: marine processes modify chemical and physical properties of a rock (erosion and dissolution); strong temperature changes, crystallisation and weathering processes cause physical alteration of rocks (mechanical disintegration); chemical processes like oxidation, reduction and biochemical reactions cause decomposition of rocks. Coasts consisting of firm material are defined as consolidated coasts, whereas unconsolidated coasts are subject to vigorous erosive processes. Volcanic coasts are residues of calderas originated by volcanic explosion and are characterised by circular physiognomy (convex or concave) and deposits of volcanic material.

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Early classifications, based on a genetic approach, distinguish coast affected by rising sea level (submergence), coasts affected by falling sea level (emergence), or compound coasts, affected by both phenomena (Davis, R.A., Jr., & Hayes, M. O. 1984; Johnson, D. 1919). Later classifications are based on onshore and shoreline morphology as those of Cotton (1952) and Shepard (1937). Inman and Nordstrom (1971) classification includes conditions of the offshore bottom. The most widely used coastal classification was introduced by Shepard in 1937, who distinguishes primary coasts - formed mostly by non-marine agents and secondary coasts – shaped primarily by marine processes or by marine organisms. As described in Shepard (1973), primary and secondary coasts include many groups and subgroups, so that Shepard’s classification is more detailed than others and includes all the existing world’s coasts. According to Shepard’s classification, primary coasts include: 1.

Land erosion coasts - shaped by subaerial erosion and partly drowned by postglacial rise of sea level (with or without crustal sinking) or inundated by melting of an ice mass from a coastal valley;

2.

Subaerial deposition coasts – for example, coasts originated by rivers, glacial and wind deposition;

3.

Volcanic coasts – originated by lava flows, fragmental volcanic products, volcanic collapse or explosion;

4.

Coasts shaped by diastrophic movements;

5.

Ice coasts – formed by various types of glaciers.

Primary coasts morphology reflects either tectonic or terrestrial or land-based processes. Generally they are coarse and irregular, because they have not been straightened out by currents and waves. Secondary coasts include: 1. 2. 3.

Wave erosion coasts – coasts eroded by wave action Marine deposition coasts - prograded by waves and currents Coasts built by organisms - formed by the growth of animals and/or plants.

Major features of secondary coasts are sea cliffs and wave-cut platforms; secondary coasts are affected by shoreline straightening over time. frequently they are characterised by the formation of beaches, sand spits, bars, and barrier islands. Longshore drift (the movement of sand along the shoreline in the direction of the waves) is one of the most important processes affecting secondary coasts. Energy-based classification Tides and waves are dominant forces driving littoral processes on open coasts because they sort the sediment and move it alongshore. Davies (1964) applied an energy-based classification to coastal morphology by dividing the world’s shores

BEACH MORPHOLOGY AND SEDIMENT ANALYSIS

29

according to tide range. Hayes (1979) expanded this classification, defining five tidal coastlines categories: 1. 2. 3. 4. 5.

microtidal 5 m

The Hayes (1979) classification (see Figure 2.1) was primarily based on shores with low to moderate wave power and was intended to be applied to trailing edge, depositional coasts. In the attempt to incorporate wave energy as a significant factor modifying shoreline morphology, five shoreline categories were identified based on the relative influence of tide range versus mean wave height (Hayes, M. O. 1979; Nummedal, D. & Fischer, I. A. 1978). 1. 2. 3. 4. 5.

Tide-dominated (high) Tide-dominated (low) Mixed-energy (tide-dominated) Mixed energy (wave-dominated) Wave-dominated.

The relative effects of these processes are significant, not the absolute values. Also, at the lower end of the energy scales, there is a delicate balance between the forces;

Mean tidal range

Tide dominated

Wave dominated Mean wave height Figure 2.1 - Energy-based classification of shorelines.

tide-dominated, wave-dominated, or mixed-energy morphologies may develop with very little difference in wave or tide parameters (U.S. Army Corps of Engineers - Coastal Engineering Research Center, 1995).

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3 Beach morphology and sediment transport In Italy the total development of shoreline amounts approximately to 7500 km, of which 55% are rocky coasts and 45% are beaches (most of them are sandy beaches). In northern Adriatic there are mild sloped sandy beaches, while steep shores are typical of Liguria, Calabria, Sicily and Sardinia, where little beaches (pocket beaches) are confined between adjacent capes. In Italy there are few silty beaches: actually they have an ecological importance because they are related to the so-called humid areas (areas covered by vegetation used by migratory birds). 32% of the Italian beach is subject to erosion, only 5% is in advance and 63% is stable; protection systems defend 15% (500 km) of beaches A general compendium (approximately 2000 km) of the morphology of Italian beaches is described in 60 maps (scale 1:100000) of CNR Italian Beach Atlas (Fierro G., AA. VV., 1999). Coastal zone definition is not simple because temporal and spatial variations modify boundaries and features. Besides, different definitions are used by researchers to describe elements and characteristics of a coast. Because of this, the following basic classification (U.S. Army Corps of Engineers - Coastal Engineering Research Center, 1995) presents a general definition of coastal zone, (based on geological criteria) which defines four subzones: • • • •

Coast Shore Shoreface Continental Shelf

A coast is a transitional zone between land and water extending from the maximum reach of storm waves to the first major change in topography. The coastline is defined by the presence of cliff formed by wave erosion, dune or permanent vegetation. In some areas tide action obscures the landward limit of the coast (large deltas like Mississippi). The shore zone (Figure 2.2) is a sloping area where unconsolidated sediments are subject to wave action. The term ‘backshore’ is used for the zone above the limit of the swash of normal high spring tide, and is, therefore, only exceptionally under the direct influence of the waves. On a rocky coast it includes the cliffs, while a low coast may consist of sand dunes or mature salt marsh. The ‘foreshore’ zone is a sloping portion of the beach including all that part of the beach which is regularly covered and uncovered by the tide. On a tideless beach this zone will be narrow, only covering the distance between the limit of the swash and backwash of the larger waves. The foreshore zone includes the surf zone (a zone traversed by breaking waves extending between the wave breakpoint and the maximum run-up of the swash) and a swash zone, where wave swash (uprush of water) and backwash (back rush of water) foreshore.


31

The ‘berm’ is a terrace formed in the backshore zone above the limit of the swash at high tide to form a flat terrace, or a ridge with a reverse slope. Below low water the positive features on the sandy floor in the offshore zone are called ‘submarine bars’. The hollows found on the landward side of the submarine bars of sandy beaches are termed ‘troughs’. Another feature of coastal zones is the shoreface, a narrow sloping zone between the continental shelf and the low water limit, where unconsolidated sediments are subject to vigorous transport. Continental shelf is a slightly sloping zone of submerged continental margin extending from the offshore limit of shoreface to the slope of shelf break. Researchers divide continental shelf in a inner part, a middle part and a outer part.

Figure 2.2 Beach profile Sediment budget in the littoral zone is related to movements of materials between offshore and onshore zones. Sediments are mainly supplied by rivers, channels, beaches and dunes erosion. Secondary sources are artificial replenishment, industrial refuse materials, civil works, etc. In shallow water bottom materials are influenced by wave action, whereas in deep water currents action on bottom material is the main cause of sediment transport. In the littoral zone, sediment patterns and composition depend on the beach slope, characteristics of the area, external and internal sources of materials. Analysis of sediment characteristics, illustrated in the following subsection, plays a significant role in the study of littoral transport and sources of bottom materials. Offshore zone In deep water, waves have only a little influence on sediment transport. As a wave enters in shallow water, it begins to drag the bottom; wave length and speed increase, whereas the period remains constant. The wave energy increases with the wave height. In this phenomena, wave-bottom interactions produce some bed forms depending on the bottom contours and wave strength:

32


• • • •

Moderate waves produce vortices of suspended particles, and generate some bed forms such as ripples. Strong wave action produces flat bottom and sediments are transported by sheet flows. When swell waves interact with bottom materials, ripples dimension depend on fluid particles excursion. In case of high wave speed, even if sheet flows occur, flat bottoms are not observed. Sea waves produce small ripples. Near the breaking zone, fluid motion becomes turbulent and many particles are suspended.

Surf zone and breaking zone: In this area breaking processes cause energy dissipation and produce vortices and turbulence phenomena. Breaking mechanisms are usually divided into two groups: spilling and plunging. •

•

Spilling occurs when steep waves advance up a gentle beach: when the wave breaks, the energy is gradually released over a considerable distance, and wave deformations are smaller than in plunging breakers. Suspended sediments are transported offshore by undertow currents or superficial currents associated with breaking. Breaking mechanisms continue their action with less intensity in the part of the surf zone nearest to the offshore zone, where the waves which generate the breaking process are recomposed. Plunging usually occurs on slightly steeper beaches: the crest becomes faster than the wave base, curls and violently descends into the wave trough. A considerable amount of energy is released into a downwardly directed mass of water and the turbulence reaches the area beyond the breaking zone. Bottom materials are suspended and transported offshore by undertow currents. A large bore is formed and becomes deeper and deeper until the energy is completely exausted. Ahead of the bore, a sediment accumulation is formed, localized between the breaking point and the deepest zone reached by vorticity.

Swash zone The swash is a fluctuation of coastline associated with sediment transport which occurs when the energy of the waves advancing up the beach is not completely exhausted. Swash dynamics depend on the frequency oscillations. At low frequencies, if the beach is permeable and the sand is not saturated, the water percolates through the substrate and the backrush decreases. An amount of sediment is accumulated on the beach in the swash zone and the beach slope increases. The result is a convex beach profile; At high frequencies (storm waves), if the substrate is saturated, the water cannot percolate through the sand and the backrush current does not decrease. In this case the sediment transport associated with backrush is greater than uprush, which results in a concave beach profile.


33

4 Seasonal profiles, bars and berms The beach slope is related to grain size: larger grain sizes generate steeper beaches as shown, for example in CERC (1984). During the winter storm waves move sand offshore, while the summer waves move sand onto the beach. Kamphuis (2000) shows that beach slopes are a function of the ratio (H/D) which represents the ratio of disturbing wave forces to restoring particle forces. On this basis, several qualitative accretion/erosion criteria were conceived (see Chapter 9). The interface where the sea surface meets the shoreline moves up and down the beach in a small area called swash zone. Even in case of low flow velocity, the small flow depth makes the shear stress extremely large. As a result, even coarse material can be mobilized by slow-moving swash. During the action of larger waves the beach material is redistributed offshore to become a longshore bar or sandbar, generally visible at low tide. The bars are an accumulation of material near the point of breaking waves and are considered offshore features of a beach (Kamphuis, J.W., 2000). Bars are formed near the breaking point (sometimes seaward of a trough) because the breaking waves set up a shoreward current with a compensating counter-current along the bottom. Sand carried by the offshore moving bottom current is deposited where the current reaches the wave break (Kamphuis, J.W., 2000). Berms form as a result of preferential shoreward transport within the swash. They are generally preserved (left behind) after a highwater event (stormy high tide, etc.). The berm is periodically overtopped during storms or extreme high tides. On sandy and shingle beaches berms build seaward through the multiple accretion of bars to the beach face. Vertical accretion to the berm is accomplished by swash, which is influenced by wave height. A beach may have more than one berm or none at all (e.g. an eroded beach backed by a seawall). Some beaches, particularly mesotidal gravel beaches, may exhibit multiple berms (e.g. LHT berm, HHT berm, summer berm, winter berm, storm berm, etc). High-water berms are formed during storm surges or spring tides (HHT berm).

5 Equilibrium beach profile The equilibrium beach profile results from steady wave forcing during the seasonal cycle. As described above, summer wave conditions move sand onto the beach, while winter storm waves move sand offshore. Beach profiles fluctuate with the seasonal cycle of wave energy: storms cause larger and more energetic waves in winter than in summer. As a result, the winter profile is characterized by the presence of a bar or by a berm on the foreshore (Figure 2.3). Dean (1983), conceived an equilibrium profile on the basis of constant energy dissipation.

34


Summer shoreline

Summer profile

Winter shoreline

berm

m.s.l.

cliff trough

bar Winter profile

bar

Figure 2.3 - Winter and summer beach profiles. The equilibrium profile is expressed in equation 2.1.

1 dF = De h dx

(2.1)

where: h is the water depth at distance x from the coast line F is the wave energy flux in shallow water; De is the dissipation coefficient of energy. Wave energy flux in shallow water is expressed as follows (see chapter 3): ρgH b2 ( gd )1 / 2 8 Hb is the breaking wave height, given by: F=

H b = d bγ

(2.2)

(2.3)

where γ is the breaker index (0.78 ↔1) and hb is the breaking depth. We define the equilibrium parameter A as: d = Ax 2 3

(2.4)

substituting this definition in (2.2) we obtain: F = (1 / 8) ρg 3 / 2γd 5 / 2 = (1 / 8) ρg 3 / 2γ 2 A5 / 2 x 5 / 3

(2.5)

With a little algebra we have: De =

1 dF 1 ρg 3 / 2γ 2 5 5 / 2 2 / 3 A x = d dx d 8 3

(2.6)


35

Finally, A can be expressed as a function of De according to the following expression:  24 1   A =  De 3/ 2 2  ρ g γ  5 

2/3

(2.7)

Dissipation of energy due to breaking waves destabilize sediment particles. When destabilizing forces are balanced by restoring forces, dynamical equilibrium occurs. The profile parameter A depends on grain size and fall velocity of particles. According to Moore (1982) and Dean (1983), it is possible to define relationships over ranges of grain sizes. For example: A = ( 1.04 + 0.086 ln( D )) 2

for 0.1×10 −3 ≤ D ≤ 1.0 ×10 −3 m

for 0.1×10−3 m ≤ D ≤ 0.2 ×10−3 m

A = 20 ⋅ D0.63

(2.8) (2.9)

Where D is the grain diameter. Dean (1983) also proposed a simple relationship between A and fall velocity: A = 0.50 ⋅w f 0.44

(2.10)

where wf is the fall velocity in m/s.

6 Sediment analysis 6.1 Bathymetric and geophysical surveys Temporal and spatial scales are important to define the zone of shoreline object of surveys as the time interval between two successive samplings. With regard to the spatial scale, it is necessary to survey the whole physiographic unit. From the engineer’s point of view, a physiographic unit covers the zone where any coastal change in plan or profile influences the adjacent coastline. In other words, it is a confined area where sediments move and the exchanges with the adjacent beaches are limited or negligible. The definition of a physiographic unit is important to define the limits of the area (generally variable) where the studies of the effects of coastal dynamics are necessary. With regard to the temporal scale, the study of the short term coastal dynamics requires a short time interval (analysis of the daily phenomena covering the observed period). In order to study long term phenomena, a long time interval is needed (seasonal phenomena require at least a time step of ten years). A preliminary characterization of physiographic units is carried out by analysis of coastal morphology. The first step is the comparison between historical charts and the definition of the area limits; the following step is the

36


analysis of photographs and maps obtained by aero-photographic and topographic surveys. Then, the inspection of the coastline variations allows to examine the following characteristics: • • • •

the coastline cyclical fluctuations; evolution of river mouth as flèches (one-direction oriented flows) or cuspids (divergence of the flow); concave coastline (to which center sediment flow gradually converges); deposits and erosions of buildings near coastal structures.

Topographic surveys The topographic surveys are integrated with bathymetric surveys and coastal profiles. The analysis of the maps concurs to estimate the type of coastal morphology (emerged and submerged coast) and allows to characterize the elements of short-long term equilibrium. The topographic surveys are then related with the sediment characteristics, which pattern gives an alternate characterization of the physiographic unit. The topographic characteristics of the emerged and submerged beach are needed to verify the morphological evolution and they should be measured in the same period of the year, in order to avoid influence of the seasonal variability of the equilibrium profile. The ‘dry’ topographic survey is performed along transects (50 meters width or more) or from the coastline until buildings or any human infrastructure is reached; Bathymetric surveys are normally carried out using transects spaced by 50-100 meters or more until the 10-meters bathymetric line is reached. When steep zones are found, a more fine spacing and orthogonal sections are then needed. Bathymetric surveys Bathymetric surveys can be carried out until 1.5 meters depth, using an accurate echo sounder with an emission cone not wider than 10°. The depth measured has to be corrected in order to account for the tide excursions. The submerge profile for depths lower than 1.5 meters is generally measured with a graduated stick. Finally, the survey is plotted on scales 1:1000 or higher, interpolating the bathymetric lines every 0.5 or 1 meter. In transparent and shallow waters (10 meters depth) the surveys can also be integrated by aero photographic survey techniques. Sampling sediments The distribution of sediments and their selection can be studied through an accurate sampling strategy. The sampling site must be selected according to beach morphology and site variability: for example, trough, bar and foreshore regions are more variable than the nearshore and dune zones. Typically, grain size distributions are better sorted in the summer than in the winter. Finally, shoreline seasonal changes and engineering structures should be considered in selecting sampling points. Number of samples collected depends on research objectives:


• •

•

37

If the intent is to grossly characterize the sediments of a beach, usually only a few samples are needed; If the objective is to characterize the site as a whole, a set of samples needs to be collected. According to Hobson (1977), combining samples from different transects across the beach can reduce the high variability in spatial grain size distribution; If the intent of the study is to analyze the differences among the portions of the same beach, many more samples are needed.

In the third case, the first step of the survey is the development of a sampling project to define all the sampling locations. In the cross shore, according to Stauble and Hoel (1986), sampling points along the profile have to be located at all major changes in morphology: dune base, mid berm, mean high water, mid-tide, mid berm, mean high water and then at 3-m intervals until the depth of closure. In the longshore direction, sediment sampling should coincide with survey profile lines so that the samples can be spatially located and related to morphology and hydrodynamic zones (U.S. Army Corps of Engineers - Coastal Engineering Research Center, 1995). 6.2 Physical and chemical analysis The most important sediment characteristic is the particle grain size (the measure of grain dimensions and their statistical distribution). Other interesting parameters are colour, texture, surface morphology (aspect and structure), shape and degree of rounding. The definition of sediment morphology and texture gives some indications of their origin and evolution; the analysis of petrography is useful to define the origin of sediment matrix. Grain size can be defined by direct measurement of particle diameters or, indirectly, by determination of their ‘hydraulic equivalents’ based on settling velocities of quartz spheres. The analysis is carried out using samples of 50 grams collected on the beach. The containers are opportunely labelled using a resistant plastic support where are signed place, date and hour of sampling. The oldest method of grain size determination uses a set of nested sieves with different mesh size. Each sieve is formed by woven stainless or brass steel wires. An amount of sediments pass through a set of nested sieves in which the size is gradually smaller down the stack. Grains are trapped on a sieve if their size is smaller than mesh openings. The sieves are agitated by hand (or mechanically) to make the selection more efficient (without forcing grains through the mesh). The weight of each size class is expressed as a percent of the total sample weight. The sieve analysis is a widely accepted method of grain-size determination because it is relatively easy and quick, but it can be a deadly process if the number of samples is too high. The amount of grains can affect the accuracy of the analysis: when the sample is too little, small errors can be more significant; if too much sand is used, one of the sieves in the stuck may become overloaded. Besides, grains can stick together or tend to get stuck in the mesh.

38


Figure 2.4 - Sampling points along the beach profile (U.S. Army Corps of Engineers - Coastal Engineering Research Center, 1995). Analysis of muddy sediments is commonly carried out by pipette analysis. The sample of sediments is put in a one litre graduated cylinder containing distilled water. An amount of dispersing agent is added to avoid particle flocculation. After agitation, 20 ml aliquots of mixture are taken using a pipette. The water in each aliquot is evaporated and the sediment amount is determined measuring weights of containers with and without sediments. In some cases, the presence of contaminants can have a significant influence on the accuracy of measurements. Pipette analysis is often a tedious process and requires great accuracy. Rapid Sediment Analyzer (RSA) is a method faster than the ones described above. RSA is a long cylinder containing distilled water, where an amount of sediment is introduced and allowed to settle. Particles are collected on a pan connected with a balance recording sediments weight. Some RSA have a computerized system to record weight data over time. The method is based on the principle that the falling velocity of grains in water varies with the diameter, shape and specific weight of particles. The system measures indirectly the grain size, on the base of settling and hydraulic behavior of particles. Measured velocities are compared with known settling rates and the distribution of particles is expressed as “equivalent diameters”. Some disadvantages are that RSA are calibrated with quartz spheres, whereas particles analyzed can have various shape and nature; finally, walls of the container can interfere with natural falling down of sediments.


39

6.3 Sediment size classification Sediments occur in a wide range of sizes, between micrometers and centimetres. The range of grain sizes of practical interest to coastal engineers is enormous, covering about seven orders of magnitude, from clay particles to large breakwater armour stone blocks. Diameter is the most important property; morphological parameters are defined by several geometric indices of rounding. Sediment size classification is usually performed with the assumption that particles are roughly circular and the grain size can be expressed as a projected cross section. Most common classifications are based on Wentworth scale (1922) and Krumbein scale (1936). Wentworth divides grains into four size classes based on particle diameter: mud (less than 0.06 mm) sand (between 0.05 and 2 mm) gravel (between 2 and 64 mm), cobble/boulder (larger than 64 mm). Statistical analysis of sediments demonstrates that size distribution of particles has a logarithmic distribution, so Krumbein (1936) proposes an alternate system called ‘phi scale’, in which grain diameter is expressed as:

ϕ = − log 2 ( D)

(2.11)

where d is the particle diameter in mm. Phi diameters are indicated by writing ϕ after the numerical value. For example, a 2.0 ϕ sand grain has a diameter of 0.25 mm. To convert from phi units to millimeters, the inverse equation is used: D = 2 −ϕ

(2.12)

The benefits of the phi unit include: 1) it has whole numbers at the limits of sediment classes in the Wentworth scale 2) it allows comparison of different size distributions because it is dimensionless. Disadvantages of this phi unit are: (a) As grain size get coarser, phi size gets smaller, which is both counterintuitive and ambiguous; (b) it is difficult to physically interpret size in phi units without considerable experience; (c) phi doesn’t represent a unit of length because it is a dimensionless unit (U.S. Army Corps of Engineers - Coastal Engineering Research Center, 1995). After the sieve analysis, the weights of the sediment trapped on each sieve are tabulated and divided by the total weight of the sample in order to calculate weight percent. The cumulative frequency for each size is calculated summing up the weights for sediment trapped on that sieve and all those higher in the stack. Sediment character is described by a histogram that graphically shows the relative abundance of each size class. Poorly sorted samples can have multiple modes, whereas better-sorted samples will have a single mode (a single peak). Table 2.1 compares Wentworth and Krumbein scales. Method of moments Mathematical determination of grain size utilizes a statistical measure called the “method of moments”.

40


Table 2.1 - Wentworth and Krumbein scales

Gravel

Sand

Mud

Size categories

Millimetres

phi

Cobble/Boulder

>64

0.63, fw=0.30. The bed roughness is usually defined as: (Nielsen, 1992): ks=30z0

(9.50)

Hence, the rougher the bed the steeper the velocity gradients and the more stress exerted by the fluid motion. However, in sediment transport modeling, the specification of ks remains a problem. When waves and currents coexist, the bed roughness is mainly linked to the wave motion. Total bed roughness is composed of the grain roughness (roughness due to the individual particles on the bed kd), roughness exerted by bedforms (form drag roughness, kr) and due to sediment movement (km). The latter two terms are called moveable bed roughness. Thus: ks=kd+kr+km

(9.51)

190

AN INTRODUCTION TO COASTAL DYNAMICS AND SHORELINE PROTECTION

For a flat fixed bed, ks=kd=2.5D50 (where D50 is the mean grain size). However, in the surf zone the bed is rarely immobile and for a moveable bed under waves, Nielsen (1992) proposed ks =

8η r2

λr

+ 170 D50 (θ '−0.05)1 / 2

(9.52)

where ηr is the bedform height, λr is the bedform wavelength and θ′ is the skin friction Shields parameter. 2.6 Bed load and suspended load: a simple parametrical model

Bed load Bagnold (1966) pointed out one of the shortcomings in Einstein’s formulation by stating the following paradox. Consider the ideal case of fluid flow over a bed of uniform, perfectly piled spheres in a plane bed, so that all particles are equally exposed. Statistical variations due to turbulence are neglected. When the tractive stress exceeds the critical value, all particles in the upper layer are peeled off simultaneously and are dispersed. Hence the next layer of particles is exposed to the flow and should consequently also be peeled off. The result is that all the subsequent underlying layers are also eroded, so that a stable bed could not exist at all when the shear stress exceeds the critical value. Bagnold explained the paradox by assuming that in a water-sediment mixture the total shear stress τ′ would be separated in two parts:

τ′ =τF+τG

(9.53) where τF is the shear stress transmitted by the intergranular fluid, while τG is the shear stress transmitted because of the interchange of momentum caused by the encounters of solid particles, i.e. a tangential dispersive stress. The existence of such dispersive stresses was confirmed by his experiments. Bagnold argues that when a layer of spheres is peeled off, some of the spheres may go into suspension, while others will be transported as bed load. Thus a dispersive pressure on the next layer of spheres will develop and act as a stabilizing agency. Hence, a certain part of the total bed shear stress is transmitted as a grain shear stress τG, and a correspondingly minor part as fluid stress τ′ =τF+τG. Continuing this argument, it is understood that exactly so many layers of spheres will be eroded that the residual fluid stress τF on the first immovable layer is equal to (or smaller than) the critical tractive stress τG . The mechanism in transmission of a tractive shear stress τ greater than the critical is then the following: τc is transferred directly from the fluid to the immovable bed, while the residual stress τ′ -τc is transferred to the moving particles and further from these to the fixed bed as a dispersive stress. The effective bottom shear stress ( τ c' ) is given by:

τ c' =

⎞ 2 1 ⎛ 0.06 ⎟U ρ⎜ 2 ⎜⎝ (log(12d 2.5 D50 )) ⎟⎠

(9.54)

SEDIMENT TRANSPORT

191

Bijker (1986) presented a method for the calculation of sediment transport in combined wave and current motion. The mean bed shear stress ( τ wc ) by Bijker (1986) in this situation is given by:

1 (9.55) 2 τc is the bed shear stress by current alone, and τw,max is the maximum bed shear stress by wave alone:

τ wc = τ c + τ w, max

τc =

⎞ 2 1 1 ⎛ 0.06 ⎟U ρU 2 = ρ ⎜⎜ 2 2 ⎝ (log(12d k s )) ⎟⎠

τ w, max =

1 ρf cU m2 2

⎛ ⎛ k ⎞0.2 ⎞ f w = exp⎜ 5.5⎜⎜ s ⎟⎟ − 6.3 ⎟ ⎜ ⎝ Aw ⎠ ⎟ ⎝ ⎠

(9.56) (9.57) (9.58)

where: d=water depth [m]; ks=bed roughness [m]; U=average velocity of current [m/s]; Aw=amplitude of the water particle on the bottom [m]; Um=maximum horizontal velocity of the water particle on the bottom [m/s]. The bed load transport is given by:

⎛ − 0.27( s − 1) D50 ρg ⎞ τ ⎟⎟ qB = 2 D50 c exp⎜⎜ ρ µrτ wc ⎝

⎠ transporting

(9.59)

stirring up

3

where: qB= bed load transport [m /m×s]; D50=median sediment grain size [m]; g=acceleration of gravity [m/s2]; µr=ripple factor=τ’c/τwc [-]; 0.27=experimental coefficient. Suspended load The suspended load is defined as the part of the total load which is moving without continuous contact with the bed as the result of the agitation of the fluid turbulence. The appearance of ripples will increase the bed shear stress (flow resistance). On the other hand, more grains will be suspended due to the flow separation on the lee side of the ripples, thus the suspended load is related to the total bed shear stress. Einstein-Bijker formula for suspended sediment transport is: ⎛ ⎞ ⎛ d ⎞ ⎟⎟ + I 2 ⎟ qS = 1.83qB ⎜⎜ I1 ln⎜⎜ ⎟ ⎝ 0.033k s ⎠ ⎝ ⎠

where I1 and I2 are the Einsten integrals given by:

(9.60)

192


I1 = 0.216

I 2 = 0.216

A(z* −1)

1⎛ 1 −

(1 − A) z*

∫

A(z* −1)

1⎛ 1− B ⎞

(1 − A) z*

z

B⎞ * ⎜ ⎟ dB A⎝ B ⎠

∫A ⎜⎝

⎟ B ⎠

(9.61)

z*

lnBdB

(9.62)

where A=ks /d; B=z/d; z*=wf /(κu*,C); u *,c = τ c / ρ = friction velocity. κ is the Von Karman constant (κ=0.40, dimensionless) and qB is the bed load transport under combined wave and current [m3/m×s]. The values of Integrals I1 and I2 can be used to calculate the Einstein Total Integral Q as follows:

Q = [ I1 ln(d / 0.033k s ) + I 2 ]

(9.63)

For given values ks, d and z* , the Einstein Total Integral Q can be also calculated using the table 9.1 or figure 9.5, which gives the representation of 1.83Q (= qS /qB) versus A(=ks//h). The suspended load qS is a function of the bed load transport and the Einstein Total Integral: q S = 1.83Qq B

(9.64)

This indicates that the suspended load transport is directly and linearly proportional to the bed load. The total transport QT can now be written as: QT = q B + q S = q B (1 + 1.83Q)

(9.65)

2.7 Case study Example 1

Calculate the sediment fall velocity in sea water (ρ=1,025 Kg/m3 ; ν=10-6 m2/s) for a quartz sediment sand (ρs =2,650 Kg/m3) with diameter D=0.15 mm. Solution: The sediment fall velocity can be calculated using the sediment fluid-parameter S* : s=ρs/ρ=2.59 g=acceleration due to gravity=9.8 m/s; D=0.15mm=1.5⋅10-4m. D 1.5 ⋅ 10 −4 ( s − 1) gD = ( 2.59 − 1) ⋅ 9.8 ⋅ 1.5 ⋅ 10 − 4 = 1.81 4v 4 ⋅ 10 − 6 The figure 9.5 in correspondence of S*=1.81 the dimensionless fall velocity can be calculated by the following expression: S* =

SEDIMENT TRANSPORT

wf ( s − 1) gD

= S * ≈ 0.3

so we have: w f = S * ( s − 1) gD = 0.0145m / s = 1.45cm / s

Example 2

In a coastal region, (sea water density ρ=1025 kg/m3; kinematic viscosity v=10-6 m2/s) the flow speed is U=1 m/s at 2 m water depth; Wave parameters are: H=0.5 m and T=8 s (L=35 m); the sediment density is 2650 kg/m3 and D50=0.15 mm. The bed roughness is ks=2 cm. Calculate the sediment transport under current and under combined wave and current. Solution: The effective bottom shear stress is given by:

1 ⎛

0.06

⎞

⎟U 2 = 1.33N / m 2 τ c' = ρ ⎜⎜ 2 ⎝ (log(12d 2.5 D50 ))2 ⎟⎠ The total bottom shear stress is:

τc =

⎞ 2 1 ⎛⎜ 0.06 ⎟U = 3.24 N / m 2 ρ⎜ 2 ⎟ 2 ⎝ (log(12d k s )) ⎠

The ripple factor is:

µr =

τ c' 0.41 = τc

The bed load transport is: q B = 2 D50

⎛ − 0.27( s − 1) D50 ρg ⎞ τc m3 ⎟⎟ = 1.0395×10-5 exp⎜⎜ ρ µ rτ wc m× s ⎝ ⎠

The relative density of the sediment is: s = ρ s / ρ = 2.59

The fall velocity is:

wf =

⎛ 36ν ⎜ ⎜D ⎝ 50

The friction velocity is:

2

⎞ 36ν ⎟ + 7.5( s − 1) D50 − ⎟ D50 ⎠ = 0.012 m/s 2.8

193

194


u *,c = τ c / ρ = 0.056 m/s the Q values can be calculated by numerical integration or using figure 9.5 or using table 9.1. By numerical integration: A ( z* −1) I 1 = 0.216 (1 − A) z* I 2 = 0.216

A ( z* −1) (1 − A) z*

z*

⎛1− B ⎞ ∫A ⎜⎝ B ⎟⎠ dB = 2.62 1

z*

⎛1− B ⎞ ∫A ⎜⎝ B ⎟⎠ ln BdB = -4.83 1

The suspended sediment transport is: ⎛ ⎛ h q S = 1.83q B Q = 1.83q B ⎜ I 1 ln⎜⎜ ⎜ 0 . 033 ks ⎝ ⎝

⎞ ⎞ m3 ⎟⎟ + I 2 ⎟ = 3.0755×10-4 ⎟ m× s ⎠ ⎠

Figure 9.5 - Suspended sediment transport parameters.

SEDIMENT TRANSPORT

195

The total sediment transport is: QT = q B + q S = 3.1795×10-4

m3 m× s

If we consider the combined wave and current, by linear wave theory the amplitude of water particle on the bottom is: Aw =

H 1 = 0.68 2 sinh(2πh / L)

the maximum horizontal velocity of water particle on the bottom is: 2π = 0.53 m/s T

U m = Aw ω = Aw

the wave friction coefficient is: ⎞ − 6.3 ⎟ = 0.028 ⎟ ⎠ the maximum bottom shear stress by wave is: ⎛ ⎛k f w = exp⎜ 5.5⎜⎜ s ⎜ ⎝ Aw ⎝

⎞ ⎟⎟ ⎠

0 .2

1 ρf cU m2 =4.07 N/m2 2 The mean bottom stress under combined wave and current is:

τ w, max =

1 2

τ wc = τ c + τ w, max =5.28 N/m2 the bed load transport is: q B = 2 D50

⎛ − 0.27( s − 1) D50 ρg ⎞ τc m3 ⎟⎟ = 1.2532×10-5 exp⎜⎜ ρ µ rτ wc m× s ⎝ ⎠

the friction velocity is: u *,WC =

τ Wc =0.072 m/s ρ

The suspended sediment transport parameters are: A=ks /d =0.01 z*=wf /(κu*,wC)=0.42 the Q values can be calculated by numerical integration or using figure 9.5 or using table 9.1 . By numerical integration: I 1 = 0.216

A ( z* −1) (1 − A) z*

z*

⎛1− B ⎞ ∫A ⎜⎝ B ⎟⎠ dB = 3.8 1

196


I 2 = 0.216

A ( z* −1) (1 − A) z*

z*

⎛1− B ⎞ ∫A ⎜⎝ B ⎟⎠ ln BdB = -6.3 1

. ks/h

z*=0.00

Table 9.1- Einstein Integral factor Q.

z* =3.00 0.432 0.432 0.432 0.432 0.431 0.431 0.430 0.428 0.424 0.417 0.404 0.374 0.339 0.317

z* =4.00 0.276 0.276 0.276 0.276 0.275 0.275 0.275 0.274 0.273 0.270 0.264 0.249 0.236

SEDIMENT TRANSPORT

0.00001 303000 0.00002 144000 0.00005 53600 0.0001 25300 0.0002 11900 0.0005 4360 0.001 2030 0.002 940 0.005 336 0.01 153 0.02 68.9 0.05 23.2 0.1 9.8 0.2 3.9 0.5 0.8 1 0

z* =0.20 32800 17900 7980 4320 2330 1020 545 289 123 63.9 32.8 13.1 6.3 2.8 0.7 0

EINSTEIN INTEGRAL FACTOR Q z* 0.40 z* z* z* z* z* =0.60 =0.80 =1.00 =1.50 =2.00 3880 527 88 20.0 2.33 0.973 2430 377 71.6 17.9 2.31 0.973 1300 239 53.6 14.4 2.28 0.967 803 169 42.7 13.6 2.25 0.967 496 119 33.9 11.9 2.21 0.967 260 74.3 24.6 9.8 2.13 0.962 158 51.2 19.1 8.4 2.05 0.951 95.6 35.1 14.6 7.0 1.96 0.940 48.5 20.8 10.0 5.4 1.78 0.907 28.6 13.8 7.3 4.3 1.62 0.869 16.5 8.9 5.2 3.3 1.42 0.809 7.7 4.8 3.1 2.2 1.10 0.694 4.1 2.8 2.0 1.5 0.84 0.568 2.0 1.5 1.2 0.9 0.55 0.414 0.6 0.5 0.4 0.3 0.17 0 0 0 0 0

197

198


The suspended sediment transport is: 3 ⎛ ⎞ 5.6481×10-4 m ⎛ d ⎞ ⎟⎟ + I 2 ⎟ = qS = 1.83qB Q = 1.83qB ⎜⎜ I1 ln⎜⎜ m× s ⎟ ⎝ 0.033k s ⎠ ⎝ ⎠

The total sediment transport is: QT = q B + q S = 5.7734×10-4

m3 m× s

3 Basic shore processes When waves approach a sloping beach and break, nearshore currents are generated, which action depends on the beach characteristics and the wave conditions. Beach morphology is strongly controlled by nearshore currents because of sediment movements; water fluxes between the coast and the offshore zone contribute to renew the coastal waters. Nearshore current patterns are a combination of longshore currents, rip currents and undertow. For large incident wave angle, alongshore momentum generated by the wave breaking process sets up strong longshore currents. The forward flow of the water particles in the breaking process sets up longshore currents. Smaller incident wave angle generate weaker longshore currents. The forward flow of the water particles in the breaking waves also “pumps” water across the breaking zone, increasing the water level there. The onshore momentum of the waves holds some of this water close to shore, causing a shoreward elevated water level (wave set-up). This phenomenon can be explained by the concept of radiation stress, introduced by Longuet-Higgins and Stewart (1964) and described in chapter 3. 3.1 Nearshore circulation

The explaination for the generation of the cell circulation was developed following the introduction of the concept of radiation stress by Longuet-Higgins and Stewart (1964), defined as the excess of flow of momentum due to the presence of waves. The shoreward component of the radiation stress produces a set-down immediately offshore of the breakers and a set-up within the surf zone. In a two-dimensional case, the wave crests are always parallel to the shoreline. Averaging over one wave period, continuity of mass must be satisfied at every cross section. This necessitates a vertical distribution of mass transport velocity: forward flow at the surface and near the bottom, return flow near middepth (Ippen, 1966). The forward flow at the surface transports the water in surface rollers toward the coast,and the wave drift is also directed toward the coast. These contributions are concentrated near the surface. As the net flow must be zero, they are compensated by a return flow in the offshore direction, which is concentrated near the bed (undertow).

SEDIMENT TRANSPORT

199

In a three-dimensional case, a cellular circulation takes place, which is constituted by longshore currents and rip currents.

Figure 9.6-Nearshore circulation pattern. Two dimensional case (after Ippen, 1966). The longshore current is generated by the shore-parallel component of the radiation stress associated with the breaking process for obliquely incoming waves. This current, which is parallel to the shoreline, carries the sediments alongshore and it is approximately proportional to the square root of the wave height and to sin(2αb), where αb is the wave incidence angle at breaking. The movement of beach sediment along the coast is referred to as littoral transport or longshore sediment transport, whereas the actual volumes of sand involved in the transport are termed the littoral drift. This longshore movement of beach sediments is of particular importance because the transport can either be interrupted by the construction of jetties and breakwaters (structures which block all or a portion of the longshore sediment transport), or can be captured by inlets and submarine canyons. In the case of a jetty, the result is a buildup of the beach along the updrift side of the structure and an erosion of the beach downdrift of the structure (CEM, 2001). The rip currents are part of cellular circulations fed by longshore currents within the surf zone that increase from zero at a point between two neighboring rips, reaching a maximum just before turning seaward to form the rip (see figure 9.6). The longshore currents are in turn fed by the slow shoreward transport of water into the surf zone from breaking waves. A nearshore circulation cell thus consists of longshore currents feeding the rips, the seaward flowing rip currents that extend through the breaking zone and spread out into rip heads, and a return onshore flow to replace the water moving offshore through rips. (Shepard and Inman, 1950). The cell circulation results from alongshore variation in wave heights, which in turn produce a longshore variation in set-up elevations. The set-up results from the Sxx onshore component of the radiation stress being balanced by the pressure gradient of the seaward-sloping water surface in the nearshore. Balancing those forces yields:

⎛ ∂η 8 ⎞ ∂d = −⎜⎜1 + 2 ⎟⎟ ∂x 3 γ ⎝ ⎠ ∂x

(9.66)

200


For the cross-shore slope of the set-up denoted by η . There is a direct proportionality with the beach slope S 0 = ∂d / ∂x , but not a direct dependence on the

Figure 9.7 - The nearshore cell circulation consists of (1) feeder longshore currents, (2) seaward-flowing rip currents, and (3) a return flow of water from the offshore zone into the surf zone (after Komar, 1988). wave height. However, the larger waves break in deeper water than smaller waves, and the set up therefore begins farther seaward at longshore locations where the larger waves occur. Inside the surf zone, the mean water level is higher shoreward of the larger breakers than it is shoreward of the small waves. A longshore pressure gradient therefore exists, which will drive a longshore current from positions of high waves and set-up to adjacent position of low-waves. In addition of the Sxx component of the radiation stress, there is a Syy component, a moment flux acting parallel to the wave crest, in this case parallel to the shoreline. This component is given by:

⎡ ⎤ kd 1 S yy = ρgH 2 ⎢ ⎥ 8 ⎣ sinh(2kd ) ⎦

(9.67)

since the wave height varies alongshore, Syy will similarly vary and there will exist a longshore gradient:

∂S yy ∂y

=

⎡ ⎤ ∂H 1 kd ρgH ⎢ ⎥ 4 ⎣ sinh(2kd ) ⎦ ∂y

(9.68)

This longshore gradient produces a flow of water away from the regions of high waves and toward position of low waves. The flow then turns seaward as a rip current where the waves and the set-up are lowest and the longshore currents converge.

SEDIMENT TRANSPORT

201

The cell circulation therefore depends on the existence of variations in wave heights along the shore. The most obvious way to produce this variation is by wave refraction, which can concentrate the wave rays in one area of a beach, causing high waves, and at the same time spread the rays in the adjacent area of the beach and then produce low waves. The position of rip currents and the overall cell circulation will then be governed by wave reflection and hence by the offshore topography. Headlands, breakwaters and jetties can affect the incident waves by the partial sheltering of the shore and thereby produce significant longshore variations in wave height and set-up. Wave reflection and diffraction produce alongshore gradients with lower waves and set-up in the lee of the headland or breakwater, which in turn generate longshore currents flowing inward toward the sheltered region. In some situations this process can account for the development of strong rip currents adjacent to jetties and breakwaters. An example of rip current acting on bottom topography is the phenomenon of rip channels. On a barred profile the wave breaking on the bar will induce a wave set-up, causing an increase of water level inshore of the bar. A bar will be in many cases interrupted by holes (rip channels) found at more or less regular intervals. The wave breaking is less intensive in the rip-channels due to the larger depth and because the wave refraction may concentrate the wave energy on the bars at the sides of the channel. Wave-current interaction may affect the development of rip-currents. In fact, the weak currents generated by a gentle alongshore variation of the wave field can cause significant refractive effect on the waves as to change the structure of the forcing which drives the currents and the instability of the cellular circulation. When currents are weak compared to the wave group velocity, their effects on waves are small, but such effects are sometimes not negligible. This is the case of rip currents produced by alongshore topographic variations on otherwise alongshore uniform beaches. These alongshore variations in the topography, like gentle rip channels, produce longshore variations in the radiation stress and provides the source of vorticity and of horizontal circulations, which interact with the waves, so wave radiation stress will be modified. Such changes of course are small relative to the effect due to wave breaking, but can be comparable to the variations caused by the topography. When this is the case, the circulations of interest can be significantly affected by the wave-current interaction. The interaction of the narrow offshore directed rip currents and incident waves produces a forcing effect opposite to that due to topography, hence it reduces the strength of the currents and restricts their offshore extent. The two physical processes due to refraction by currents, behind the wave rays and changes in the wave energy, both contribute to this negative feedback, on the wave forcing (Yu and Slinn, 2003).

202


Figure 9.8 - The circulation current generated by normally incident waves on a barred coast with rip-channels (after Fredsøe and Deigaard, 1992). 3.2 Wave run-up in the swash zone

The wave run-up is defined as the maximum elevation of the wave uprush above the mean sea level. The uprush is given by the sum of two components: the positive elevation of the mean water level caused by wave action and the fluctuations above the mean water level (swash). The concept of wave run-up is frequently used to describe the beach profile processes. The wave run-up parameter calculation depends on the processes of wave transformation, such as the wave reflection, the interaction between the bottom and the waves and the sediments properties (e.g. porosity and permeability). Actually, some formulations of wave run-up are based on the empirical studies carried out by Hunt (1979) for regular waves and for irregular waves. Regular waves For regular breaking waves, the run-up is a function of the beach slope, incident wave height and wave steepness. According the Hunt (1979) formulation: R = ξ 0 for 0.1 L0 bgT

offshore motion

(10.20)

The condition expressing onshore motion signifies a summer or accretionary beach profile, and the condition expressing offshore motion signifies a winter or erosional beach profile. By replacing Hb by H0 and examining small-scale largetank data of Saville, Dean (1973) obtained the criterion:

πw f H0 = 1.7 L0 gT

(small scale)

(10.21)

From Dean’s results, it is clear that the sand size (through the fall velocity) plays a major role in the formation of the different seasonal profiles as does the wave period. Beaches with finer sand (and smaller fall velocities) require a smaller value of wave steepness for the formation of a storm profile. Some studies demonstrated that criteria based on two parameters were more predictive than criteria based on a single parameter. Sunamura and Horikawa (1974) introduced also the dependence on the beach slope and the sand diameter : H 0 L0

C* = tan( β )

− 0.27 

D  L  0

   

0.67

(10.22)

where H0 and L0 are the offshore wave height and wave length, D is the sand grain diameter, and β is the beach slope. • • •

C*>8 C* 0 safe 

where R (resistance) and S (load or surcharge) are functions of many stochastic variables x1 , x 2 , … , x n , we obtain: G = K D1 / 3

ADn ∆(cot gα )1 / 3 R ( x1 , x2 , x3 , x4 )

−

Hs S ( x5 )

where: KD = deterministic damage coefficient, A = normal distributed variable with mean µA = 1 (if no bias) and a standard deviation, (σA = 0.18 for Hudson’s formula) signifying the uncertainty of the formulae.

STRUCTURAL DESIGN

295

Dn, ∆ and cotgα are assumed normal distributed with variational coefficients estimated to be in the order of 6%, 4% and 5%, respectively. Hs is given by a long–term extreme value distribution (e.g. a Weibull or Gumbel distribution). FORM analysis makes it possible to calculate the relative influence of the uncertain parameters on the failure probability, and to quantify the benefit by reducing the uncertainties of the design formulae.

12 Deterministic design - case study Calculate the design armour weight for a structure built in natural rocks elements using the following input parameters: N=3000; S=2; p=0.4; Hs=3 m; cotgα=2; γs=2600 kg/m3; γ0=1030 kg/m3; Tm=8 sec; KD =2 (structure trunk); KD=1.6 (structure head). Hudson formula:

γ s 2600(kg / m 3 ) = − 1 = 1.52 γ 0 1030(kg / m 3 )

∆=

W50 =

γs ⋅ H 3

1 =4997 kg =5.0 ton ⋅ K D ⋅ (∆ − 1)3 cot g α

Calculation of ξm and ξmc leads to: sm =

2πH s gT

2

=

2π ⋅ 3 9.81 ⋅ 8

2

= 0.03

[

ξm =

ξ mc = 6.2 p 0.31 tan α

tgα

]

sm

1 /( p + 0.5)

=

0.5 0.03

= 2.89

=3.72

ξm

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