• TABLE OF CONTENTS
HIDE
 Half Title
 Title Page
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 Abstract
 Introduction
 Review of literature and potential...
 Description of the Delray Beach...
 Delray Beach Nourishment Project...
 Application and modeling resul...
 Summary, conclusions, and...
 Model for beach planform evolu...
 Program listing and sample input...
 Reference
 Biographical sketch














Group Title: UFLCOEL-99014
Title: Erosional hot spots at Delray Beach, Florida
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Permanent Link: http://ufdc.ufl.edu/UF00091062/00001
 Material Information
Title: Erosional hot spots at Delray Beach, Florida mechanics and probable causes
Series Title: UFLCOEL-99014
Physical Description: ix, 109 p. : ill., maps ; 28 cm.
Language: English
Creator: Fernández, Guillermo José Simón
University of Florida -- Coastal and Oceanographic Engineering Dept
Publisher: Coastal & Oceanographic Engineering Dept., University of Florida
Place of Publication: Gainesville Fla
Publication Date: 1999
 Subjects
Subject: Beach erosion -- Florida -- Delray Beach   ( lcsh )
Beach nourishment -- Florida -- Delray Beach   ( lcsh )
Coast changes -- Mathematical models -- Florida -- Delray Beach   ( lcsh )
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis (M.S.)--University of Florida, 1999.
Bibliography: Includes bibliographical references (p. 108-109).
Statement of Responsibility: by Guillermo José Simón Fernández.
 Record Information
Bibliographic ID: UF00091062
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 43305680

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Table of Contents
    Half Title
        Half Title
    Title Page
        Page i
    Acknowledgement
        Page ii
        Page iii
    Table of Contents
        Page iv
        Page v
    List of Tables
        Page vi
    List of Figures
        Page vii
        Page viii
        Page ix
    Abstract
        Page x
        Page xi
    Introduction
        Page 1
        Page 2
        Page 3
    Review of literature and potential causes for erosional hot spots
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
    Description of the Delray Beach Nourishment Project and compilation of data
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
    Delray Beach Nourishment Project performance
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
    Application and modeling results
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
        Page 60
        Page 61
        Page 62
        Page 63
        Page 64
        Page 65
        Page 66
        Page 67
        Page 68
        Page 69
        Page 70
        Page 71
        Page 72
        Page 73
        Page 74
        Page 75
        Page 76
        Page 77
        Page 78
        Page 79
        Page 80
    Summary, conclusions, and recommendations
        Page 81
        Page 82
        Page 83
        Page 84
    Model for beach planform evolution
        Page 85
        Page 86
        Page 87
        Page 88
        Page 89
    Program listing and sample input and output
        Page 90
        Page 91
        Page 92
        Page 93
        Page 94
        Page 95
        Page 96
        Page 97
        Page 98
        Page 99
        Page 100
        Page 101
        Page 102
        Page 103
        Page 104
    Reference
        Page 105
        Page 106
        Page 107
        Page 108
    Biographical sketch
        Page 109
Full Text




UFL/COEL-99/014


EROSIONAL HOT SPOTS AT DELRAY BEACH, FLORIDA:
MECHANISMS AND PROBABLE CAUSES



by



Guillermo Jose Sim6n Fernandez




Thesis


1999
















EROSIONAL HOT SPOTS AT DELRAY BEACH, FLORIDA:
MECHANISMS AND PROBABLE CAUSES
















By

GUILLERMO JOSE SIMON FERNANDEZ


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


1999
















ACKNOWLEDGEMENT


I would like to express my sincere appreciation to my supervisory committee chairman

Dr. Robert G. Dean. His support and advice made this experience an irreplaceable one. I also

would like to express appreciation to Dr. Ashish J. Mehta who always showed concern for my

development and to Dr. Daniel M. Hanes for their excellent lectures and for serving in my

supervisory committee.

I extend my acknowledgement to all other faculty members, including Dr. Michel Ochi,

Dr. Robert J. Thieke, and Dr. Hsiang Wang, whose lectures helped me fulfill my coastal

engineering interests. Special thanks go to Helen Twedell for her assistance in the archives and

her affection, Becky Hudson for her friendship, and to Subara Malakar for his computer aid.

I would like to express my special gratitude to Dr. Bruce Taylor from Taylor Engineering

and to Miguel A. Yafiez from Consultoria Yafiez-Taylor, who have encouraged and supported

me, ever since I decided to come to the University of Florida to complete my academic and

professional skills, and my personal interests.

My friends at the Coastal and Oceanographic Engineering Department made my

experience in Gainesville unforgettable. I would like to thank Nicholas Grunnet, Erica Carr,

Roberto Liotta, Kevin Barry, Edward Albada, Hugo Rodriguez, Kerry Anne Donohue, Joel

Melanson, Al Browder, and Jamie MacMahan, with whom I shared wonderful moments.

Finally, I would like to thank my wonderful mother and father from whom I learned to

reach all my goals. The support received from Marcela Ballina is also greatly appreciated.









This work is dedicated to my extraordinary wife and son, whose presence,

companionship, and love throughout times of joys and hardships have been an invaluable source

of inspiration. Thanks Lulu and Rodrigo for your support in all my endeavors.
















TABLE OF CONTENTS



A C K N O W L E D G E M EN T ........ ................................................................................................ ii

LIST O F TA B LE S........................................................ ........... ....................... ................. vi

L IST O F FIG U R E S ........................................................ ..... .......................... ........... .... vii

A B S T R A C T ............................................................................................................... ......... ...... x

CHAPTERS

1 IN T R O D U C T IO N .......................... .. .. ............................ ...... ................... ..... ..... ... 1

1.1 P rob lem Statem ent ...................................................................... ........................ ....... 1
1.2 O objectives and Scope ....................................................................................... ........... 3

2 REVIEW OF LITERATURE AND POTENTIAL CAUSES FOR EROSIONAL
H O T SP O T S ................................................................. ........... ...... 4

2 .1 Introduction ....................... ........... ... .. .............. .. ............ ................ . .......... 4
2.2 Possible Mechanisms for Creating Erosional Hot Spots.................................................. 5
2.2.1 R fraction ...................... .. ..................... ............................ ................................. 6
2.2.2 B reaks in B ars (D iffraction) ................................................................ ... 12
2.2.3 Use of Different Sediment Sizes Along the Nourished Beach............................. 13
2.2.4 Use of Different Sand Placement Techniques .................................................. 15
2.2.5 Presence of Coastal Structures............................................................. ................ 16

3 DESCRIPTION OF THE DELRAY BEACH NOURISHMENT PROJECT AND
CO M PILA TION O F D A TA .................................................................... ... .......................... 19

3.1 Data Sources ..... ............................................. 19
3.2 Site D description ........................................ .................. .................... 20
3.2.1 H historical Evolution .................. ..................................................................... 20
3.2.2 Delray Beach Nourishment Project Desciption............................................. 23
3.2.3 H ydrodynam ic Conditions ............................................. ........................... 27
3 .2 .4 L ittoral T ran sport.......... ................................................................ .... ............... 2 8
3.2.5 B each Profiles ............ ............................ .......... ..................... .. ................ 29

4 DELRAY BEACH NOURISHMENT PROJECT PERFORMANCE................................. 30

4.1 Previous Studies at D elray B each, FL ............................................................................ 30
4 .1.1 Sh o relin e C h an g es ................................................................................................ 3 1


iv










4.1.2 Volumetric Profile Changes........ ............................ ..... ................. 35
4.1.3 Conclusions from the Previous Studies ............................................... ......... 36
4.2 Analysis of the Field Data............. ......................... .... ....... .......... 36
4.2.1 Distribution of Fill Volumes Along the Project ................................................ 37
4.2.2 Sedim ent Size A nalysis.......................................................................... ............. 37
4 .2 .3 Shoreline C changes .......................................... ................................................ 42
4.2.4 V olum etric Profile Changes .................................... .......................... ............... 45
4 .2 .5 Sum m ary . ........ ........... ..................................... ... ............... ........ .. ... .............. 4 9

5 APPLICATION AND MODELING RESULTS ................................................ ........... 51

5.1 Numerical Model for Beach Planform Evolution............................ ........ ............... 51
5.1.1 Application of Delray Beach Data for Planform Performance Predictions.......... 52
5.1.2 Predicted Shoreline and Volumetric Profile Changes ....................................... 55
5.1.3 Influnce of the Sediment Transport Parameter ............ .................................. 59
5.2 Comparison Between Measured and Predicted Changes..................... ... ............. 61
5 .2 .1 Shoreline C changes ........................................ .................................................. 62
5.2.2 Volumetric Profile Changes...... ........................... ..... .................. 65
5.2.3 Standard D aviation A nalysis...................................................... .... .. ............... 67
5.3 Hot Spot Identification and Mitigation Measures..................................................... 74
5.3.1 H historical Shoreline Position ............................................... ............... ... 75
5.3.2 Sediment Size Distribution Along the Project.......................................... 75
5.3.3 Standard Deviation Reference Value................. ................ ............... 76
5 .3 .4 Sum m ary . ........ ........... ....................................... ... .............. ...... .. .... .......... 80

6 SUMMARY, CONCLUSIONS AND RECOMMENDATIONS........................................ 81

6 .1 S u m m a ry ......................................................................................................................... 8 1
6.2 C conclusions ............... .... ............... .... ............................ ... ............... ............. 82
6.1 R ecom m endations ......................... ................................................. ........................... 84


APPENDICES

A MODEL FOR BEACH PLANFORM EVOLUTION. ................................................ 85

B PROGRAM LISTING AND SAMPLE INPUT AND OUTPUT................ ................ 90

R E F E R E N C E S ... ........... ........................................ ..................... ............... .. 105

B IO G RA PH ICA L SK ETCH .................................................................................................. 109
















LIST OF TABLES


Table page

3.1 Volume of sand placed in the Delray Beach Nourishment Project................................... 23

3.2 Delray Beach renourishment project, forty-eight month monitoring study. History of Dune
Accretion from DNR monument R-177 to R-182 ....................................................... 27

3.3 Predicted tidal datums (NGVD) for Delray Beach, Florida................ .... ............... 28

3.4 Available profile data for Delray Beach, FL from the Bureau of Beaches and Coastal
Sy stem s ........................................................... ........ ......... ....... 2 9

5.1 Approximate corresponding values of the sediment transport parameter to selected sediment
sizes (from D ean, 1989).................... ............................................... ....................... ...... 55

5.2 Standard deviations computed for the 1975-1990 span............................................ 74
















LIST OF FIGURES


Figure page

2.1 Post-nourishment irregular bathymetry due to mechanic and hydraulic placement .............. 7

2.2 Irregular bathymetry due to dredge spoil placement ....................................................... 8

2.3 Beach planshape due to refraction over a 2 m deep hole, 1220 m offshore, from Motyka and
W illis (1974) .................. .... ...................... ... ............................ ................. . ..... ........... 9

2.4 Shoreline position showing the shoreline displacement after 2 hours, from Horikawa et al.
(1977) ...................................................................................... ........................... .. ... 10

2.5 Contours of diffraction coefficients for single pit with a/L=1.0, b/L=0.5, d/h=3, K/h=0.167,
and 0=00, from McDougal et al. (1995). Waves propagate from left to right................... 10

2.6 Wave refraction behind a dredged hole or borrow pit and associated longshore sediment
transport .................................................................................................................................... 12

2.7 Influence of borrow pits at Grand Isle, Louisiana, on the shoreline configuration (Date of
the Photography: M ay of 1998) ........... .............................. ................................ ..... 13

2.8 Effect of nourishment scale parameter, AF, on width of resulting dry beach. Four examples
of decreasing AF, with same added volume per unit beach length (Dean, 1991) ............... 14

2.9 Low ering of the profile at seaw alls ............... ............................................................. 17

2.10 Change in bathymetry due to background erosion under influence of a groin (adapted from
B ridges, 1995).. ................. ............................................ ........................ ................... 18

3.1 Location m ap for D elray Beach, Florida............................................................................ 21

3.2 Historical shoreline position from DNR monuments at Delray Beach, FL........................ 22

3.3 Placement of sand for the different maintenance fills .................................... ......... 24

3.4 Location of the borrow area with respect of the fill area ............................................... 26

4.1 Mean high water shoreline changes computed by Beachler (1993)................................... 33
a) Between 1974 to 1990, and
b) Between 1973 and 1990










4.2 Comparison between mean high water shoreline changes from 1974 to 1990 and mean high
water shoreline changes from 1974 to 1995 (Beachler and Mann, 1996).......................... 34

4.3 Measured mean high water shoreline changes between January, 1987 and October, 1992
(from Gravens,1997) ............................. ............................................ ........... 34

4.4 Volume changes computed by Beachler (1993) between 1974 and 1990.......................... 35

4.5 Volumes of sand placed along the project for each of the nourishments........................... 38

4.6 Cumulative volume of sand placed along the project................................ ..................... 39

4.7 Longshore distribution of the sediment size.......................... ............. ............ ..... 40
a) After second renourishment, and
b) After third renourishment

4.8 Sedim ent size variation w ith tim e ..................................................................................... 41
a) After second renourishment, and
b) After third renourishment

4.9 Shoreline changes from 1975 to 1990 ........................................... ........................... 43

4.10 Shoreline changes from 1975 to 1998 ........................................... ........................... 44

4.11 Comparison between the 1/15/75 and 8/1/90 profiles at R-188 ....................................... 46

4.12 V olum etric profile changes from 1975 to 1990............................................... ............... 47

4.13 V olum etric profile changes from 1975 to 1998............................................... ............... 48

5.1 Computational scheme used in computational method ................................................. 53

5.2 Predicted volume and NGVD shoreline changes from 1975 to 1990 with ...................... 57
a) Incoming deep water waves perpendicular to the shoreline, and
b) Incoming deep water waves 200 north from perpendicular to the shoreline

5.3 Predicted volume and NGVD shoreline changes from 1975 to 1998 with ...................... 58
a) Incoming deep water waves perpendicular to the shoreline, and
b) Incoming deep water waves 200 north from perpendicular to the shoreline

5.4 Variation of sediment transport with different sediment sizes................. ......... ....... 61

5.5 Comparison between the predicted and the measured NGVD shoreline changes from 1975
to 1990 .. ......................... .............. .. .......... . 63

5.6 Comparison between the predicted and the measured NGVD shoreline changes from 1975
to 1998 .. ......................... .............. .. .......... . 64

5.7 Comparison between the predicted and the measured volumetric profile changes from 1975
to 1990 .. ......................... .............. .. .......... . 66










5.8 Comparison between the predicted and the measured volumetric profile changes from 1975
to 1998 .. .................. ..................... .. .......... . 66

5.9 Values of ~p,/,p computed for the fill area for 1975-1998, with ................................... 69
a) Incoming deep water waves perpendicular to the shoreline, and
b) Incoming deep water waves 200 north from perpendicular to the shoreline

5.10 Values of opm/m, computed for the fill area for 1975-1998, with...................................... 70
a) Incoming deep water waves perpendicular to the shoreline, and
b) Incoming deep water waves 200 north from perpendicular to the shoreline

5.11 Values of opm computed for the fill area for 1975-1998, with........................................... 71
a) Incoming deep water waves perpendicular to the shoreline, and
b) Incoming deep water waves 20 north from perpendicular to the shoreline

5.12 Values of 1p computed for the fill area for 1975-1998, with ............................................ 72
a) Incoming deep water waves perpendicular to the shoreline, and
b) Incoming deep water waves 200 north from perpendicular to the shoreline

5.13 Location of erosional hot spots and cold spots for 1975 to 1990, using .............................. 78
a) Shoreline changes differences, and
b) Volume changes differences.
The area shown encompasses the project limits

5.14 Location of erosional hot spots and cold spots for 1975 to 1998, using .............................. 79
a) Shoreline changes differences, and
b) Volume changes differences.
The area shown encompasses the project limits
















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science


EROSIONAL HOT SPOTS AT DELRAY BEACH, FLORIDA:
MECHANISMS AND PROBABLE CAUSES

By

Guillermo Jose Sim6n Fernandez

August, 1999


Chairman: Dr. Robert G. Dean
Major Department: Coastal and Oceanographic Engineering

The Delray Beach restoration project has been nourished four times since 1973. The

monitoring of the project, as well as other studies, has demonstrated that the beach fill has

performed atypically in some areas along the project, showing higher erosion rates than the

project's average.

Being a matter of recent concern, erosional hot spots lack established criteria that would

allow them to be clearly identified. An erosional hot spot is an area of the shoreline that is

receding faster than the rest of the project and that is not predicted directly from applying

available theory. On the other hand, erosional cold spots are areas which accrete considerably

faster or erode more slowly than the rest of the fill and are not predicted by available theory.

A detailed analysis of the behavior of the beach fills is performed, based on shoreline and

volumetric profile changes. In order to predict the shoreline position after the initial nourishment,

a one-dimensional numerical model for beach planform evolution is applied. The model considers

a simplified refraction and shoaling of the wave field by assuming straight and parallel contours,

and considers that the active profile is displaced seaward or landward without change of form.










The model can include the presence of shore-parallel structures and background erosion;

however, the case of Delray Beach is that of an uninterrupted beach.

Erosional hot spots have been identified within the area encompassed by the Delray

Beach project as a result of a standard deviation analysis of the shoreline and volume changes.

Additionally, the value of the sediment transport parameter is analyzed in detail, and compared to

the statistical difference between measured and predicted changes. Measured shoreline and

volume changes were also compared to predictions with different incoming deep water wave

angle conditions.

The one-line model applied proved to be accurate when predicting shoreline and volume

changes. However, in order to achieve higher precision on prediction values, a model is needed

that not only accounts for the three-dimensional character of the nearshore processes, but also

includes more data such as different sediment characteristics along the project.

The Delray Beach restoration project has been renourished three times since 1973, when

the initial nourishment took place. Monitoring of the project has been performed on a yearly

basis, providing a rich data set that allowed analysis of its morphological behavior in detail. A

total of 3.7 million cubic meters have been placed over a distance of 4.3 kilometers, from a

borrow area around 800 meters seaward of Delray Beach. Although an overall successful project,

its behavior has been atypical in some areas.

Compilation of data and other studies on Delray Beach, FL, are also included. Even

though these contributions are not focused on the location of erosional hot spots, their results

have been compared showing a reasonable agreement. The collected data were analyzed and

correlated with the results computed from the measured and predicted conditions.
















CHAPTER 1
INTRODUCTION



1.1 Problem Statement

Beach erosion is one of the most important issues and concerns in the coastal

environment. As the sea encroaches upon the coast and anthropogenic activities increase along

many beaches of the world, the natural response of the environment oftentimes is for the

shoreline to retreat in order to reach a new equilibrium, always governed by waves, currents,

tides, and wind. The consequences of not preserving this environment could be costly, as a beach-

dune system provides storm protection to coastal properties, such as homes, hotels, and roads,

provides recreational and tourist areas, and environmental benefits, such as turtle nesting and

wildlife refuges.

The most "natural" solution to this problem is the placement of additional sand to restore

(or to build) a beach. This process is called beach nourishment and unlike other solutions such as

groin fields, headlands, and seawalls, there is no negative impact to the downdrift beaches.

Another solution that has proven to produce minimal environmental alteration, is nearshore

nourishment, which is the placement of sand on the nearshore to build a berm, and it is applied

under different physical settings than beach nourishment.

Beach nourishment projects require periodic maintenance according to the observed

behavior. As will be shown in this thesis, at Delray Beach, FL, for example, this periodic

maintenance has been accomplished according to its performance at the time. In order to design

an economical project, the lifetime of a beach nourishment should be estimated. If the project's

sand is lost rapidly, then the project can be regarded as a failure, even if this is produced locally.










When a project experiences localized erosion, which is larger than the rest of the project

and that has not been predicted by diffusion theory, this is interpreted as an erosional hot spot in

that area. An erosional hot spot is a limited area, although at times hard to identify, characterized

by a narrower beach and/or loss of sand from the cross-shore section greater than the rest of the

project. They can last months or they can be permanent, or until a new fill is built to renourish the

area. Furthermore, an erosional hot spot has the characteristic that cannot be predicted directly

from applying the diffusion theory, first introduced by Pelnard-Considere (1956) or other

available theories. The concept of erosional hot spot and cold spot, does not apply for other

coastal features such as beach cusps or perhaps daily events. The time scale associated with this

analysis is important, as an erosional hot spot could be overlooked if different time spans are

considered. Nevertheless, since this thesis is intended to analyze the overall performance of the

project, by looking at its localized performance, the time spans consider the first survey and the

most recent ones. In addition, long time scale erosion is not considered as responsible for

erosional hot spots, since it is considered as its natural behavior, and therefore, can be accounted

for through background erosion.

Erosional hot spots are of recent concern, therefore, the related literature is sparse and

mostly related to a case-by-case analyses. Most of the research performed to understand localized

erosion of the shoreline is focused on the effects that borrow sites have on the wave field.

When a nourished area presents localized erosion, the storm protection, recreational

areas, and environmental benefits could be jeopardized. Thus, the entire nourishment can be

regarded by some as a failure, even if it has proven to perform as predicted for the rest of project.

It is thus necessary to investigate the potential causes leading to erosional hot spots in order to

avoid them in future projects and to provide solutions to restore the desired conditions of a

nourishment with erosional hot spots. The avoidance of hot spots would lead to more economic

projects and to better distribution of the economic resources derived from taxpayers.










1.2 Objectives and Scope

In 1973 the City Council of Delray Beach decided to restore the city's shoreline using

beach nourishment, a technique that started to achieve popularity in Florida during this decade. In

order to estimate the lifetime of the beach fill, the Coastal and Oceanographic Engineering

Laboratory (1973), provided performance predictions of the beach restoration project for five

years, when the first periodic maintenance took place. Although inaccurate, this theory indicated

that renourishment should take place after approximately five years of construction.

At present, improved theories and numerical methods are able to predict the performance

of a beach fill better than in the 1970s. These predictions become important in order to determine

the lifetime of a beach nourishment project and thus allow better allocation of economic

resources. However, erosional hot spots can significantly diminish the lifetime of a project. The

main objective of this thesis is to identify any highly erosive areas that occur as hot spots and to

detect potential causes, at the Delray Beach restoration project. Methods and criteria are also

developed and applied to identify those areas that have evolved atypically.

The procedure used to identify erosional hot spots is based on shoreline and volumetric

profile changes, which can describe the overall and local performance of the beach fill. This

procedure not only will be an aid to identify hot spots, but it will also help describe the behavior

of the shoreline of the entire project. The predictive capability of the numerical model of

planform evolution applied here, can also be evaluated in terms of agreement between the

measured and simulated shoreline positions.

Reviews of the potential causes of hot spots and the available literature are also included.

Previous studies and contributions that suggest the presence of erosional hot spots in the

nourishment project were evaluated, and compared to the results presented here. Finally,

conclusions towards the application of the numerical model DNRBSM, as well as its capabilities

and limitations, are drawn.
















CHAPTER 2
REVIEW OF LITERATURE AND POTENTIAL CAUSES FOR EROSIONAL HOT SPOTS



2.1 Introduction

Beach restoration programs through nourishments have been ongoing as an alternative

measure to restore Florida's beaches since the 1970s. As a recent concept, the effectiveness of

beach fill projects has been questioned, especially given the fact that, economic resources derive

from taxpayers and therefore may become a major public concern.

Erosional hot spots can prevent a beach nourishment project to be considered as

successful, even though this problem can be regarded as local. Dean and Dalrymple (1999)

mention that all nourished beaches have erosional hot spots to some extent, thus, becoming

important to analyze and, if possible, to prevent.

Some researchers have proposed different methods of predicting the overall performance

of beach fills. Some of these methods include those from Krumbein and James (1965), James

(1974), Dean (1974), and Pilarczyk and van Overeem (1987); other approaches like those

presented by Dean and Grant (1989), and Hanson and Kraus (1989) consider many more

important parameters yielding a more accurate approximation to the shoreline response

prediction. These methods allow, to different degrees of detail, the prediction of the planform

evolution of a beach fill with time, however, they do not predict the presence of erosional hot

spots since, as defined earlier, they are a consequence of some irregularity in the coastal zone that

is not accounted for in those methodologies.

Numerical and physical modeling has been carried out by a number of investigators,

though not necessarily directed to erosional hot spots. Motyka and Willis (1974) obtained some










preliminary results from the study of beach erosion caused by wave refraction over offshore

dredged holes with the aid of mathematical modeling. Horikawa et al. (1977) studied

mathematical and laboratory models to examine the effects on shoreline shape due to exploitation

of submarine deposits of sand and shingle, using an idealized sandy beach and hindcast waves

typical of those on the eastern coast of Japan. These experiments provided a good qualitative

agreement with the mathematical and the laboratory tests. A more recent study is that of

McDougal et al. (1996), who used linearized shallow-water wave theory to investigate the

interaction of surface waves with multiple rectangular submarine pits in water of otherwise

uniform depth. The application that McDougal and his coworkers gave to this type of breakwater

was on navigation channels, never mentioning the possible relationship with beaches. However,

their method provides a good tool to understand the wave diffraction patterns due to propagation

over these holes.



2.2 Possible Mechanisms for Creating Erosional Hot Spots

The analysis of erosional hot spots requires a case-by-case analysis. While some research

has been carried out on the direct effects of dredged holes, no detailed work has been performed

to study the effects of placing sand of different sizes along the beach, or the long term effects of

mechanically versus hydraulically placed sand on a beach, for example.

A closer examination of the erosional hot spots, was made by Bridges (1995), with

particular interest in the effects of residual bathymetry as a probable cause to erosional hot spots,

where numerical and physical modeling were utilized. The following mechanisms were identified

as potential developers of erosional hot spots:

refraction due to offshore bathymetry and borrow pits,

breaks in bars,

sediment size differentials along the nourished area,










use of different sand placement techniques, and

presence of coastal structures.

A brief review of these mechanisms is presented below with a broader explanation of the

refraction process, which is the one that has received more attention among researchers. The

motivation for presenting these mechanisms is not to give a full understanding of the processes

creating hot spots, but to be able to make an intuitive approach to the understanding of a

particular case. Headland effects are considered to be mechanisms predictable by the diffusion

theory, thus not considered as a potential cause for erosional hot spots.



2.2.1 Refraction

Refraction is clearly a major mechanism that shapes the shoreline. Therefore, after large

amounts of sand are placed on the beach, the newly-created bathymetry will play a significant

role in the planform evolution.

There are two identified situations that can be regarded as the probable responsible for

changing the refraction pattern. Firstly, an irregular offshore bathymetry or what Dean and Yoo

(1992) called "residual" contours, and secondly, the location of the fill's borrow sites.

2.2.1.1 Residual Bathvmetry

This man-made irregular bathymetry is believed to be the consequence of different

volumes of sand placed along the nourished area. Then "residual" contours are formed beyond

the depth of limiting motion resulting in refraction and shoaling changes. It is important to

mention that this sand that has been placed to a depth where waves cannot transport it, is of more

concern than that placed shallower since the latter will be "spread out" by the longshore transport.

Therefore, while the deep contours will continue to alter the wave field, the shallower contours

ones will have no long lasting effect on the wave field nor the beach. Dean and Yoo (1992)

suggested an equation to compute the displacement of the shoreline about its mean alignment Ays,










caused from an offshore contour with a displacement about the mean contour alignment AyR. This

is


Ays = 1 ,AyR (2.1)



in which C1 and C, are the wave celebrities at the "residual" contour and at the depth of limiting

motion, respectively. Several mechanisms can be the reason of residual bathymetry, for example,

irregular beach fill placement and dredge spoil placement. The first one results from sand that is

placed both hydraulically and mechanically. As it will be discussed later, when placed

mechanically, the outcome is a beach profile with a steeper slope, thus yielding an uneven

bathymetry. Figure 2.1 shows these contours.

Points of discharge
from pipeline

Low tide datum



..---..... . ''.......
-h
.......... ............
Depth of Irregular
closure contours
(exaggerated)

Figure 2.1 Post-nourishment irregular bathymetry due to mechanical and hydraulic placement.




Further description of the process used to build the beach fill is shown in Section 2.2.4.

Another common practice that can lead to an irregular bathymetry is dredge spoil. This

would be the case of a beach confined by to inlets. When the navigation channels are dredged,

and the sand is placed on the adjacent beach, it can result in a major alteration of the bathymetry,

especially due to the fact that the channels are often dredged periodically. It ought to be

mentioned that the dredged sand is not distributed evenly on longer segments of the beach for

economic and technology reasons. The newly formed refraction pattern will produce waves to










bend in such a manner that sand can be transported away from the center of the fill area creating

an erosional hot spot. This phenomenon is depicted in Figure 2.2.

Sediment
Original shoreline transport
position.
. I transport


Z ,This area will erode due to the
I M / new refraction pattern originated '
> I / offshore
z / Dredge
spoil
I I I

Offshore bathymetry starts to
build up concave contours


Figure 2.2 Irregular bathymetry due to dredge spoil placement.




In order to test this residual bathymetry theory, Bridges (1995) developed a numerical

sediment transport model as well as a physical model. The results found from this modeling are

limited, yet encouraging. They are limited due to discrepancies between the numerical and the

physical model, since it was difficult to determine which one is more accurate. However, the

quantitative results should encourage further research, since it was found that in fact there is a

shoreline change as a consequence of residual bathymetry. In addition, the results confirmed that

there is a relationship between the shoreline change and the wave celerity ratio as suggested by

Dean and Yoo in Equation 2.1.

2.2.1.2 Borrow Pit Location

The influence of dredged holes on the shoreline is a subject that has been studied by

several authors with numerical and analytical modeling. This is another case where refraction

plays a major role in shaping the beach with an erosional hot spot. A borrow pit is formed when

mined for sand, most of the times, for the nourishment project itself. Different authors have found

apparently opposite results when analyzing the effects of dredged holes on the shoreline. Motyka

and Willis (1974) used a mathematical model to investigate the effect of dredged holes on the

coasts of England. Although they consider their conclusions "conservative", they found that there











is retreat in the shoreline due to refraction over the modeled holes. Figure 2.3 shows some of their

results.


POSITION OF
r0 EDGED
0 AFTER Ib DAYS HOLE
WAVE Ht 2m
o WAVE ANGLE 10

0 ____ ._ -i /\
WAVE PERIOD.8s


AFTER 3 MTHS
-40 -20 WAVE Ht i041m
S WAVE ANGLE 20
0 .
WAVE PERIOD = 5s
AFTER 6 MHS I
WAVE HI 036m
WAVE ANGLE 10
WMVE PERIOD Ss
.20 .20 AFTER 9 MTHS
MWVE HI 035m
WAVE ANGLE- tO10
WAVE PERIOD 5s
40 10
AFTER 9 HTHS I1 DAYS
20 WAVE HI 179m
WAVE ANGLE 10. /

WAVE PERIOD 8s'. \ .
2 AFTER 12 MTHS

-40 -20 AVE Ht m047m
WAVE ANGLE 100
WAVE PERIOD .5s I /
I ... "1
-20




DISTANCE ALONG SHORE -m


Figure 2.3 Beach planshape due to refraction over a 2 m deep hole, 1220 m offshore, from
Motyka and Willis (1974).




Horikawa et al. (1977) presented more results from numerical and physical modeling on


the same topic. Using data typical from the Eastern coast of Japan, their results are exactly the

opposite to those presented above by Motyka and Willis. Instead of erosion, the dredged holes

produce beach accretion, and the reason is argued to be refraction as well. The results are shown

in Figure 2.4 where the numerical and physical results are compared.










McDougal et al. (1995) developed a theoretical model using linearized shallow-water

wave theory and a two dimensional Green's function. In this study, the pits have the function of a

breakwater, and it is suggested that this mechanism could be applied to protect navigation

channels. Figure 2.5 presents an example of their computation results and it shows some

interesting results. It can be seen that seaward of the pit a partial standing wave system develops,

while in the lee of the pit a shadow zone exists in which wave heights are reduced up to 60%.

Even though there is no further comment on the possible effects on the beach due to the alteration

of the wave field, their results can be conclusive when trying to understand the refraction

mechanism behind a hole.


HOLE
2 125
4 Observed



S-2



of dredged hole (cm )

Figure 2.4 Shoreline position showing the shoreline displacement after 2 hours, from Horikawa et
al. (1977).

/ -----
S- .. ...

















Figure 2.5 Contours of Diffraction Coefficients for Single Pit with a/L=1.0, b/L=0.5, d/h=3,
/h=10.167, and 0=00 from McDougal et al. (1995) Waves Propagate from Left to Right.
..% -:- --------- -3--



v ,. :l o/ -, "~-, "---- ---_ -"







K/h=0. 167, and 80=0, from McDougal et al. (1995). Waves Propagate from Left to Right.










Another study on the impact of dredged holes on the shoreline was conducted by Kojima

et al. (1986), studying the case of Kyushu Island, Japan. Kojima and his coworkers are skeptical

when affirming that the dredge holes are the reason of the erosion of the beach at Kyushu Island.

However, they suggest a mechanism different than refraction or diffraction that may cause the

beach to erode. They suggest that the dredged holes at the study site, are gradually refilled with

sand coming from the landward side of the hole. This will cause the beach profile to steepen and

eventually to lose sand from the beach, creating what we call an erosional hot spot.

It has been shown that there are different theories on how a dredged hole influences the

shoreline. The mechanisms that can make a beach erode or accrete because of the presence of a

dredged hole are explained below.

There are two phenomena that change the sediment movement alongshore in the presence

of dredged holes or borrow pits, related to refraction: "bending" of the wave rays and water level

differentials. This refraction can be viewed as an anti-shoal process. When travelling over the

hole, the wave celerity will increase, causing the wave rays to bend away from its lee. When

arriving at the beach, wave orthogonals will have an angle that will transport the sand in opposite

directions as shown in Figure 2.6. In addition, an area of lower wave heights (and less energy) is

created behind the borrow pit causing a wave set-up differential. The difference in water

elevations will generate longshore currents towards the region behind the borrow pit, thus

transporting sand that can form a salient. This is also illustrated in Figure 2.6.

Whether the planform will become a salient or an erosional hot spot, depends on a

number of variables. Whichever process is stronger and more able to move sand in or out of the

sheltered area, will determine the outcome. The fact that borrow pits could have an important

impact on the shoreline is well known. However, the how that impact is uncertain, and in order to

carry out predictions, it is necessary to bring into account sediment characteristics, wave

characteristics, detailed bathymetry, and detailed configuration as well as location of the borrow

pit. Then, refraction and diffraction should be accounted for in order to determine the











hydrodynamics produced by the holes. Another example of salients due to dredged holes is one

located at Grand Isle, Louisiana, where two borrow pits produced two salients behind them. The

negative impact of this case is that the beach becomes narrower in between the salients, since it

lost sand to feed them. Therefore, this area can be identified as an erosional hot spot. An aerial

photo of Grand Isle is presented in Figure 2.7.



Sediment transport in opposite directions
: 4 due to the wave angle at breaking \
_____ Original shoreline
Sediment transport
towards the region \ Sediment transport
behind the borrow pit \ towards the region
due to the difference in Area of lower set-up due to the behind the borrow pit
set-up srea of the wave's energy due to the difference in
*\ \spreading of the wave's energy/ /
(lower wave heights) s
Area of Area of
higher set-up higher set-up


... .... ....... .......... ..... ....................... ... .............
.. ... ..... ......... ..................................... ... 8 Borrow pit, waves are
... \ / 10 refracted by its
...... .. ........... .... m bathym etry
v .......................... ................. ............... ................ ...............................

Wave rays


Figure 2.6 Wave refraction behind a dredged hole or borrow pit and associated longshore
sediment transport.




2.2.2 Breaks in Bars (Diffraction)

This mechanism consists in the diffraction of waves when travelling over discontinuous

nearshore bars or, in other words, when bars act as submerged breakwaters. Once diffracted as

described, waves will move sediment in opposite directions creating areas of intensified erosion

of the subaerial beach. However, these features are associated with relative short term processes,

such as storms, and therefore they may last only for a few months, and the erosional effect can

eventually disappear. This phenomenon is not exclusive of bars. Any other feature acting as an

underwater breakwater with a gap or break can actually produce the discussed diffraction with the

associated beach erosion.






























0' '.5Mi
01 '1Km

Figure 2.7 Influence of borrow pits at Grand Isle, Louisiana, on the shoreline configuration (Date
of the Photography: May of 1998).


2.2.3 Use of Different Sediment Sizes along the Nourished Beach

This mechanism is much less studied than refraction and diffraction from dredged holes

and submerged berms and bars. It consists in the non-uniform placement of sand along the beach.

The consequence has to be regarded as a local effect, in some cases, as erosional hot spots. When

sand is placed along the beach with uniform characteristics it would be expected from theory that

the beach will perform without great differences, or at least, to remain within the average

performance of the project. When there is an area with higher erosion rates than the rest of the

project it could mean that the beach is formed of finer sand in that area. The reason is that profiles

with finer sand will move faster to equilibration and have less additional dry beach width per

volume placed, resulting in larger shoreline erosion rates. In other words, according to Dean

(1991), the dry beach width corresponding to a finer sediment is narrower than that of a coarser

beach. Figure 2.8 shows the difference in profile equilibration between different sand sizes. This

Figure shows that for a finer sand the slope of the beach is milder, and the dry beach narrower










than the one with coarser material. AF and AN are the scale parameters for the fill and for the

native conditions, respectively; likewise, DF and DN, are the fill and the native sediment sizes,

respectively.





Al IiFi((inqS Pioliw
J Prj98.lm ^ ah mDl AL Oldn'I
04 0,m O3 10w 75 _mn
45 3M



h.=6mr

D a. Oe a17 onm
15 9M








5 Eh,=6m






Offshore OIstance (ml
Figure 2.8 Effect of nourishment scale parameter, AF, on width of resulting dry beach.
four examples of decreasing AF, with same added volume per unit beach length (Dean, 1991).


One reason that there may be a longshore vaiability in sediment sizes, is economy in the

dredging operations. Fine sand is easier to pump than coarse sand, therefore, it requires less fuel.

When the borrow site contains different sediment sizes, the contractor can decide to place finer

sand at the most distant point of the project, and coarser sand at the closest location from the

borrow area, in order to make the overall operation less costly. This process is called dredge

selectivity. A typical scenario for dredge selectivity is when an inlet's ebb tidal shoal is selected










for the borrow site. An inlet's shoal is a mixture of sand from the inlet and sand carried along the

coast that encounters the beach. Therefore, there can be a vast variety of sediment sizes in an ebb

tidal shoal. For example, during ebb conditions, currents will carry sediments out of the inlet

depositing on the ebb shoal. However, this deposition is not uniform if we consider the

hydrodynamic characteristics of the grains. Assuming that a fine grain will have a smaller fall

velocity than a coarse grain, it will be transported for a greater distance, thus, being deposited

further away. A coarser grain would be deposited closer to the entrance of the inlet. The dredging

contractor can take advantage of this situation to minimize costs recognizing that is cheaper to

pump finer sediment.



2.2.4 Use of Different Sand Placement Techniques

This concept was briefly introduced in Section 2.2.1.1, when the concept of residual

bathymetry was explained. There are two ways of placing sand on the beach: mechanical and

hydraulically. Sand is placed hydraulically when a dredge pumps a mixture of sand and water.

When the sand is first pumped into the beach, it is placed in specific points, and then spread out

by bulldozers. Mechanically placed sand is transported dry from the borrow sites using trucks and

common earth moving equipment, and then dumped on the beach. Then again, bulldozers will

complete the process of filling the design template. Another possibility for mechanically placed

sand is the use of barges to transport the sand and then place it in the nearshore. Once sand is in

place, the contractor is required to achieve the design template with a specific initial beach slope.

Moving large volumes of sand into the beach with trucks can be costly. For this reason,

the sand is placed hydraulically in 98% of the beach nourishment projects in the United States

(Dean and Dalrymple, 1999).

The most important influence on the performance of the project from the two placement

methods, is the angle of repose of the material. Bagnold (1963) showed that a mixture of sand and

water has different mobility characteristics than sand alone. In addition, when placed










mechanically, the earth moving equipment cannot reach underwater fill areas. These factors

become important when the contractor is filling a design template. Oftentimes, the construction

slope is different from the design template, impeding the contractor to achieve the requested

profile. In order to remedy this problem, more sand is placed on the beach to achieve the desired

profile. This overfill practice is common due to the high costs of returning to fill again the same

spot. Therefore, when contractors decide to overfill using different placement methods, different

volumes will be placed in each section. According to Dean (1991) the dry beach width varies

directly with volume per unit width of beach. Thus, when different volumes are placed along the

beach, there is the possibility of having different dry beach widths and therefore, the potential for

hot spots. In order to achieve the design template with hydraulic fills it is not uncommon to have

volumetric overfills of 25%.



2.2.5 Presence of Coastal Structures

Because beach nourishment projects are usually built as a consequence of ongoing

erosion, previous remedial measures include structures such as seawalls and groin fields. These

two features can have negative impacts on a beach nourishment project.

2.2.5.1 Lowering of the Profile at Seawalls

Seawalls are shore-parallel structures that provide protection from encroachment of the

sea and wave attack. Beaches in front of seawalls are often more eroded than those without

protection due to lowering of the profile. This mechanism is shown in Figure 2.9 and explained

below.

The post-nourishment profile has its design dry beach width seaward of the structure.

Due to the trend of the background erosion, this dry beach width will get narrower until it reaches

the incipient beach profile, and further back. This means that the "origin" of the beach profile

(intersection between the sea level and the beach profile, or in other words the shoreline) will










move landward of the seawall. Then it is called a "virtual origin." Dean (1991) states that the

beach profile seaward of the structure will keep the same position as if the seawall were not there.

As it is depicted in Figure 2.9, the presence of the seawall will result in a greater water

depth at the toe of the structure. Should it be necessary to nourish this area, the truncation of the

upper part of the equilibrium beach profile will be a main factor in reestablishing an incipient

beach. For example, in order to renourish this area with the incipient beach, the required volume

will be that between the existing profile seaward of the seawall and the incipient beach profile.

This means that, in order for the beach to achieve the desired equilibrium profile, a volume must

be added to achieve an incipient dry beach and then a second volume to advance the beach to the

desired width. The associated erosion of not considering this volume required to achieve an

incipient dry beach can lead to an erosional hot spot.

Shore-parallel
structure

Virtual origin


Design beach
This volume must be / profile
added to achieve the
incipient dry beach


Background
erosion

Figure 2.9 Lowering of the profile at seawalls.




2.2.5.2 Residual Structure-Induced Slope

Other structures used to control ongoing erosion are groins. If a nourishment project takes

places where groins previously existed, the volume of sand held by the groins can play a

significant role in the development of the beach. Oftentimes, the groins are removed as part of the

nourishment construction after the new sand is placed. Then, the remnant bathymetry will act

together with the new fill bathymetry to form a highly erosive area as explained below and shown

in Figure 2.10.











Groins are built in erosive beaches to store sand from the longshore transport, resulting in

an altered bathymetry. However, it is clear that the groin can only stabilize the beach that is

within its reach, thus allowing the rest of the profile to continue its eroding tendency (excluding

inlets, there is no need to build groins on a beach that is not eroding).

Once the structures are removed, the segment of the profile that was under control of it

will recede faster than the normal erosion rates of background erosion and spreading out losses.

The reason is that the beach profile is no longer under the equilibrium achieved with the

structures in place (milder slope within the structure's reach, and steeper further away), and will

go faster to achieve the equilibrium profile characteristic of an uninterrupted beach. This

phenomenon is shown in Figure 2.10.








5 -----6-5
S-- Original Contour
-------4
----Contour influenced by
3 _background erosion
2 Contours, in meters


Groin to be
removed after
sand is placed

Figure 2.10 Change in bathymetry due to background erosion under influence of a groin (adapted
from Bridges, 1995).




Another mechanism causing erosional hot spots associated with groins, is that due rip

currents. These currents might be strong enough to mobilize large amounts of sand and create

highly erosive areas. However, it is difficult to make further statements towards this process since

there is no research providing useful information on this topic, nor surveys to determine volumes

of sand deposited in the head of a "rip" current.
















CHAPTER 3
DESCRIPTION OF THE DELRAY BEACH NOURISHMENT PROJECT AND
COMPILATION OF DATA



3.1 Data Sources

The Delray Beach Nourishment Project is the consequence of severe erosion during the

1960s. As it will be shown later, during this decade the erosion trend demanded further action to

protect the city's public and private properties. The City Council of Delray Beach, FL, authorized

Arthur V. Strock & Associates, Inc. in the early 70's to conduct the necessary studies to design

the Beach Restoration Project for the city's beach and its corresponding monitoring. The first

available reports from the Delray Beach area are from Arthur V. Strock & Associates, Inc., which

basically include monitoring studies on the performance of the project; after 1985, this company

was replaced by Coastal Planning and Engineering, to make the necessary monitoring analyses,

providing a valuable source of information. The most important information acquired from these

reports are the sediment information, fill volumes, and overall description of the project's

performance.

The modem era provides a reliable high quality data base of shoreline positions and

profiles. The Bureau of Beaches and Coastal Systems of the Florida Department of

Environmental Protection, devoted to preserve Florida's coastal resources, developed an internet

website which contains, among other data, historical shoreline trends, nearshore and offshore

bathymetry, profile information, general coastal regulations, and description of projects in

Florida. In the case of the Delray Beach project, this website contains considerable profile

information, which proved to be very accurate when comparing results with other authors, such as

Beachler (1993), Beachler and Mann (1996), and Coastal Planning and Engineering (1997).










Additional information was obtained from other reports, papers, and studies performed at the site

of interest.



3.2 Site Description

The city of Delray Beach is located in the middle southern portion of Palm Beach County

in the southeast coast of Florida (Figure 3.1). The beach is located on approximately 4.8 km of

the barrier island delimited by South Lake Worth Inlet on the north and Boca Raton Inlet on the

south. The beach restoration project occupies approximately 4.3 km of the total beach length and

is bounded by the Department of Natural Resources (DNR) monuments R-175 and R-189.



3.2.1 Historical Evolution

Located on the east coast of Florida, Delray Beach had been identified by a highly

erosive area for the past decades. This area is also affected by a system of littoral barriers and

inlets all along the coast, from Georgia to the Florida Keys. Most of these inlets are influenced by

littoral drift, making them very unstable. As population continued to establish along this coast,

the necessity to create stable entrances became imperative. Dean (1988) explains that the

shoreline erosion on the east coast of Florida is due dominantly to the management of the inlets.

While the efforts to make these entrances stable, mainly for navigational purposes have worked,

the shoreline has been influenced negatively, retreating substantially.

The database available from the Bureau of Beaches and Coastal Systems includes

historical Mean High Water (MHW) shoreline positions for Delray Beach. These historical

positions are displayed in Figure 3.2 for each of the monuments within the project area. The

earliest shoreline position for this area dates from 1884. Since then, a slow retreat is recorded in

most of the project length except for the northern-third of the project, until the 1920's. The

shoreline then recovered faster than it was receding, until the 1940's when it continued accreting

slowly. It is from 1962 to 1970 when a fast erosion of the shoreline was noticed, and up to 3.7









m/year of shoreline retreat at R-176 were found. As a result of hard coastal structures, the

shoreline position remained more or less in the same location until the nourishment program was

started in 1973. This nourishment project helped stop the erosional trend that started in the

1960s.


Sf'.JA!COSNWILLE









STIN L. BEACH H
'A.UW'S'E













R O CDRLNTAr --rL '



Srr T PonM



., |A






NTS I -
L' -x... L H
e'RW R ONr ( / .11|
riT S jJ L ;i


Figure 3.1 Location map for Delray Beach, Florida.





















140 -
R-1 5 ushme
120 ----R-1 7F
R-1 7

100 R-- -R-1 87
S-R-19
100
. . .. R-1 79 |,m

80


60





20 ___



1870 1880 1 90 1E00 1 10 1920 1930 1E40 1E50 1 60 1970 1980 190 2(00 2C

-20

Year






140 ----------------------
R -1 I
-- R-10 N shm nt
120 -i -- 1
R-i

100 R 4
10 . ..... R -164





4o _-_ tit
60 __


40






l 0 180 180 190 0 1910 1920 1 930 1940 1950 1950 1970 190 19 0 200 2

-20 --

Year






140 -I I

-- R-185 N, Eishnm nt ""
120 ....--- r |-186--
--T-187
100.. R-188


80 it









'0. . . . . .I I .. ....



1 70 1180 1190 1100 1110 1120 1E30 1140 1150 160 170 1 0 190 2(00 2

-20

Year


Figure 3.2 Historical shoreline position from DNR monuments at Delray Beach, FL.










3.2.2 Delray Beach Nourishment Project Description

The erosion control project was planned to be carried out on a periodic basis, as is

necessary in this type of project. After the project's almost 26 years of life, sand was placed non-

uniformly (Figure 3.3). The initial nourishment, in 1973, placed approximately 1.25 million cubic

meters on the 4.3 km project. Five years later, in 1978, 536,000 cubic meters was placed over two

separate segments. The second and the third renourishments placed 994,000 and 780,000 cubic

meters respectively, as shown in Figure 3.3. A summary of the volumes of sand distributed along

Delray Beach as part of this restoration program, is shown in Table 3.1.



Table 3.1 Volume of sand placed in the Delray Beach Nourishment Project

Period of Construction Length Volume Placed Cumulative Volume
Encompassed [ x 103 m3 ] [ x 103 m3]
[ km]
July -August, 1973 4.27 1250 1250
February May, 1978 1.98 (north section) 404 1654
0.91 (south section) 132 1786
September- October, 1984 4.27 994 2780
November -December, 1992 3.14 780 3560
Source: Coastal Planning and Engineering, 1997.

In addition, the fourth renourishment has been proposed to take place in 1999/2000.

As it can be noticed from Table 3.1, the time span between every nourishment has been gradually

growing from 5 to 8 years. This is a natural, positive influence of the project on the adjacent

beaches. The reason can be thought as if we were building a longer project, which can be

explained from the diffusion theory from Pelnard-Consid6re (1956).

The native sediment on this area has been reported to have a mean grain size of 0.46 mm,

however, this sand barely formed a dry beach prior to the year of 1973 when the project took

place. Further analysis of the sediment size distribution and its evolution due to the project, will

be completed later in this thesis since it might be a potential cause for erosional hot spots, and

therefore, has to be examined in detail.























1500 0 1500

GRAPHIC SCALE IN FEET

Al



































LEGEND :
A FOEP SURVEY
MONUMENT


Figure 3.3 Placement of sand for the different maintenance fills.










In addition, it should be mentioned that the project is located where no other coastal

project will impact directly in a short term. Both South Lake Worth Inlet (updrift), and Boca

Raton Inlet (downdrift), are located sufficiently away so that inlet stabilization and/or dredging

operations would not affect the project performance predictions. On the other hand, other

nourishment projects located on the same barrier island will not influence the project's

performance either, since they are sufficiently distant.

3.2.2.1 Borrow Area

The designated borrow area is shown in Figure 3.4. It is located more or less directly

seaward of the restoration area, approximately 760 meters offshore. It includes a no-dredging

zone 300 meters wide to protect a sewage outfall. This outfall is located almost directly seaward

of Atlantic Avenue, at DNR monument R-180. The offshore borrow site is approximately 300

meters wide, 2740 meters long, and before being dredged it was located a depth of 16 m.

Very long profiles were available for the entire project area for the year of 1990 (reaching

a depth of -30 meters), from the Florida Department of Environmental Protection internet

website. However, no further data was available for the borrow pit. Thus it was not possible to

make any further comparisons for volumes removed from or filling of the borrow pit.

Bathymetric contours in the borrow area were more or less straight before dredging

occurred, and after this dredging, the nearshore contours remained practically straight and

parallel.

The available material, as analyzed before the initial nourishment, is a fine to medium

gray quartz sand, is well sorted, and its diameter is smaller than that of the beach material. As

noted, the beach sand was determined to have a 0.46 mm mean diameter, while the borrow

material was calculated to have a mean diameter of 0.20 mm (Arthur V. Strock & Associates, Inc,

1973). Therefore, similar to many nourishment projects, this is a case where finer sand is placed

on the beach to restore it.
















-..-NORTH CONSTRUCTION LIMIT
Mw7R PRUJECr LMIT


'No dredging
zone








*BORROW AREA


SOUTH COWTMSr CTR LIMIT


I1ray Beach SOUTH miePCT
'of Highinadl BI


Figure 3.4 Location of the borrow area with respect of the fill area.










3.2.2.2 Dune Restoration

To avoid sand being blown out of the project dunes, in 1974 dune vegetation was planted.

In 1979, a program to evaluate the accretion of the dune in the vicinity of the public beach (see

Figure 3.3) was initiated. A sand fence and additional dune vegetation was placed in this area in

1980. Since then the dune has continued to expand in elevation as well as width (Coastal

Planning and Engineering, Inc., 1997). Table 3.2 shows a summary of the history of dune

accretion at the public beach.



Table 3.2 Delray Beach renourishment project, forty-eight month monitoring study. History of
Dune Accretion from DNR monument R-177 to R-182

Date Accretion Comments
[m' ]
July 1973 Original restoration project
May 1979 55,000 First renourishment project
July 1980 Sand fence installation along public beach
October 1984 5,160 Immediately after second renourishment project
November 1985 8,250 First year after second renourishment project
December 1986 1,600 Second year after second renourishment project
March 1988 4,400 Third year after second renourishment project
January 1989 385 Fourth year after second renourishment project
March 1990 3,070 Fifth year after second renourishment project
December 1992 9,600 Immediately after third renourishment project
December 1993 3,840 First year after third renourishment project
December 1994 2,790 Second year after third renourishment project
December 1995 3,950 Third year after third renourishment project
January 1997 5,000 Fourth year after third renourishment project
103,045 Total volume of sand accreated on the public
beaches dunes since project inception in 1973.
Source: Coastal Planning and Engineering, Inc., 1997.

Table 3.2 shows a total accreated volume of 103,045 m3. Thus for the public beach

(encompassing approximately 1.98 km), the dune growth has been 2.3 m3/m/year.



3.2.3 Hydrodynamic Conditions

For the entire monitoring area, the dominant deep water wave direction is 200 north from

the perpendicular to the shoreline and will be considered constant for most of the year. For










modeling purposes, the wave height has been defined in terms of its representative characteristics

This means that it will be considered in terms of the effective value of time-varying wave height

and period according to the Ralyleigh distribution. Dean and Grant (1989) include a series of

plots for the state of Florida in which wave height, period, depth of limiting motion, and the

coefficient of diffusivity, are defined upon the location on the Florida coast. The effective deep

water wave height and period for Delray Beach is 0.43 meters (1.4 ft) and 6.5 seconds,

respectively. In addition, the depth of limiting motion and berm height, (d.+B), is 7.16 meters

(23.5 ft).

The tidal planes are also defined for this area. Table 3.3 shows these values with

reference on the National Geodetic Vertical Datum (NGVD).


DNR
Monument
R-175
R-176
R-177
R-178
R-179
R-180
R-181
R-182
T-183
R-184
R-185
R-186
T-187
R-188
R-189
Source: Balsil


Table 3.3 Predicted tidal datums

MHHW MHW
[m] [m]
0.591 0.570
0.591 0.570
0.591 0.570
0.591 0.570
0.591 0.570
0.591 0.570
0.591 0.570
0.588 0.570
0.588 0.570
0.588 0.570
0.588 0.570
0.588 0.570
0.588 0.570
0.588 0.570
0.588 0.567


(NGVD) for Delray Beach, Florida.

MTL MLW
[m] [m]
0.128 -0.283
0.128 -0.280
0.128 -0.280
0.128 -0.280
0.128 -0.280
0.128 -0.280
0.128 -0.280
0.128 -0.280
0.128 -0.280
0.128 -0.280
0.128 -0.280
0.128 -0.277
0.128 -0.277
0.128 -0.277
0.128 -0.277


lie, 1987.


3.2.4 Littoral Transport

Several authors, including Dombrowski and Mehta (1993) have noted that the longshore

sediment transport on the east coast of Florida is towards the south. According to their study,


MLLW
[m]
-0.335
-0.335
-0.332
-0.332
-0.332
-0.332
-0.332
-0.332
-0.332
-0.332
-0.332
-0.332
-0.332
-0.329
-0.329










123,000 m3/year of sand leave South Lake Worth Inlet, north of Delray Beach, and 93,000

m3/year of sand arrive at Boca Raton Inlet, just south of Delray Beach. Assuming a linear

distribution of the longshore sediment transport in this area, Delray Beach would have a

longshore sediment transport of 108,000 m3/year.



3.2.5 Beach Profiles

Cross-shore sections are vital to analyze the local behavior of the project. Beach profile

availability is summarized in Table 3.4. These data are available from the Bureau of Beaches and

Coastal Systems.



Table 3.4 Available profile data for Delray Beach, FL from the Bureau of Beaches and Coastal
Systems.

Approximate Date of Profiles Available Comments
Survey
1/14/75 R-175 through R-189 Approx. 1000 m long (-15 m deep)
8/1/90 R-175 through R-189 Approx. 1600 m long (-28 m deep)
10/92 (Prenourishment) R-175 through R-189 Approx. 600 m long (-8 m deep)
12/92 (Postnourishment) R-175 through R-189 Approx. 600 m long (-8 m deep)
12/93 R-175 through R-189 Approx. 600 m long (-8 m deep)
12/94 R-175 through R-189 Approx. 600 m long (-8 m deep)
12/95 R-175 through R-189 Approx. 600 m long (-8 m deep)
1/97 R-175 through R-189 Approx. 600 m long (-8 m deep)
1/15/98 R-175 through R-189 Approx. 450 m long (-7 m deep)
















CHAPTER 4
DELRAY BEACH NOURISHMENT PROJECT PERFORMANCE



The City of Delray Beach, Florida, has arranged for the monitoring of the nourishment

project since 1973. The project was planned, since its conception, as a beach restoration program

which would eventually require periodic maintenance, just as any beach nourishment project

should be planned. In order to schedule these periodic maintenance, it is necessary to make a

first approximation of the overall performance and life of the project.

However, these predictions are difficult to achieve in fine detail, at least at present. The

evolution of the project depends upon a set of factors that act together to shape the beach, in both

longshore and cross-shore directions. Moreover, the coastal environment is subject to sudden and

strong changes that can determine the evolution of the beach, especially during storms.

The fact that it is still difficult to predict the detailed evolution of a beach nourishment

project, leads to the necessity to monitor these type of projects, and even to be subject to further

research, like the one performed in this thesis.

There are two main tools that will be used to anlayze the evolution of the project locally:

shoreline changes and volumetric profile changes.



4.1 Previous Studies of the Delray Beach Nourishment Project

The Delray Beach Nourishment Project has been part of several studies in which the

shoreline and volume changes have been modeled and/or measured. There are three main efforts

that contributed to available results for this project. The first is formed by the set of monitoring

studies performed initially by Arthur V. Strock & Associates, Inc., and later by Coastal Planning










and Engineering, Inc. These reports are focused on annual observations of the project. Beach

samples, beach profiles, and high water level position are measured, to then compute shoreline

and volume changes, and sediment size analyses. Therefore, these reports do not carry on

performance predictions of any kind, but they do constitute a rich set of data.

The second contribution used in this thesis, is the one presented by Beachler (1993) and

Beachler and Mann (1996), where the purpose is to show that much of the sand which moves out

of the project can actually be accounted for and benefits the neighboring beaches. In this way, the

authors extend the study area about 3 kilometers north and south of the project, to analyze the

benefits of the Delray Beach Nourishment Project to the adjacent areas.

Finally, the third contribution which includes results on shoreline response at the Delray

Beach area, is that presented by Gravens (1997). This paper concerns evaluation of the relative

influence of various procedures for developing input wave conditions for use in numerical models

of shoreline change. His modeling was performed using GENESIS, a program developed by the

U.S Army Corps of Engineers. Gravens selected the Delray Beach site because the physical

setting and evolution of the shoreline are expected to conform to the assumptions imposed by

one-line theory, or in other words, that the nearshore bathymetry can be regarded as straight and

parallel; in addition, this site was chosen because of the nourishment program that has been

ongoing since 1973, which provides the necessary data.



4.1.1 Shoreline Changes

Coastal Planning and Engineering (1997), summarizes the Mean High Water (MHW)

changes since the last nourishment as follows. The shoreline within the project area advanced 66

m on average, with the largest advance at monuments R-186 and T-187, where it reached 82 m

and 83 m respectively. After forty-eight months, the MHW shoreline retreat is 40.5 m on average,

with 65 m and 72 m at DNR monuments R-186 and T-187, respectively, as the largest recessions.

This large retreat is attributed to the largest shoreline advance during the project construction and










also because it is near the end of the fill area, where losses are expected to be larger. In addition,

the majority of the MHW shoreline retreat is due to equilibration after the construction profile

(Coastal Planning and Engineering, 1997).

Arthur V. Strock & Associates, Inc. (1984) mentions in regard to the shoreline changes at

the earlier stages, that prior to the second renourishment, in 1983, the shoreline retreat rates were

larger from DNR monument R-180 to the south with the highest shoreline retreat rate at R-186

(7.3 m/year). In fact, at the first three monuments of study (from R-175 to R-177), the shoreline

advanced. It is important to point out that these results were obtained after the first

renourishment, in 1978, where sand was placed nonuniformly over two separate areas (see Figure

3.3).

Beachler (1993) focused on the shoreline changes from the years of 1973 and 1974 to the

year 1990. Figure 4.1 shows the MHW shoreline changes computed by Beachler (1993). In this

figure, a minimum value within the fill area is reached at R-186. In addition, this figure shows

positive shoreline changes from R-165 to R-201, which is explained to be due to the spreading

out of the Delray Beach project sand. Figure 4. lb includes the effects of the initial nourishment,

thus a wider dry beach width is computed. It is noticeable, however, that around R-186 an area

with higher erosive rates prevails. Beachler and Mann (1996) extended Beachler's previous work

to analyze the changes to 1995 which now include the effects of the 1992 renourishment where

sand was placed as previously shown in Figure 3.3. Their results are shown in Figure 4.2. In this

graph it is possible to see that the shoreline changes reach a minimum at the first monuments,

where no sand was placed in 1992, and another minimum at R-186.

The study performed by Gravens (1997) is aimed at analyzing the influence of different

wave conditions on predictions of the shoreline changes. The modeling starts in January 1987 and

predicts shoreline positions for October 1992, immediately before the third renourishment. Figure

4.3 depicts an example of his modeling, where only the measured conditions are of interest. The

figure is bounded by the limits of the project. Gravens (1997) mentions that a comparatively










higher erosion rate of almost 2.0 m/yr occurs around 2000 m from the origin. The first 2500 m of

the project average 1.6 m/yr of erosion and the remainder of the modeled reach, only 0.8 m/yr.

Even though this paper is not directed to identifying erosional hot spots, it does refer to the

mentioned area with 2.0 m/yr of recession, as an erosional hot spot. This highly erosive area

corresponds to the location of an opening in an offshore reef and to a 300-m-wide no-dredging

zone where an outfall pipeline lies.

1974 1990 SHORELINE CHANGES


;a) FILL -SEA =>
15IG

t o ,A







4Iea R*i Ails Rm1 mIsI Al IIS0 To R"t
ONR fONIWJMFNT


1973 1990 SHORELINE CHANGES
IAVERiAG)
S IORELIME CAME IFEETI
o b) FILL AREA "

















a) Between 1974 to 1990, and
91 R b) Between 197 3 and 1990. 1
DNR WOYIENT

Figure 4.1 Mean high water shoreline changes computed by Beachler (1993)
a) Between 1974 to 1990, and
b) Between 1973 and 1990.









8W

4.3
a::
2J


I 20
4i


iIU
i I ""!


165 157 In 1i'1 173 175 177 179 1B'1 113 I 187 189 191 1 1'05 117 1 201
It 1 8 17 172 17< 176 178 180 182 b14 186 IB BS 'B2 i 4 19i 190 201
EEP MONLUMENT
pr1974 TO 1a 1974TO195
ri.. AR=A I1 FROCW MHIONIMENt 17f -" MDONiIETI 1-'

Figure 4.2 Comparison between mean high water shoreline changes from 1974 to 1990 and mean
high water shoreline changes from 1974 to 1995 (Beachler and Mann, 1996).


0 51" Lo000 MI 7OW 15 3000
DiuauCJ EraM Q0doi j]


300 404 400 300


Figure 4.3 Measured mean high water shoreline changes between January, 1987 and October,
1992 (from Gravens,1997).


~I


I










4.1.2 Volumetric Profile Changes

The latest monitoring report from Coastal Planning and Engineering, Inc. corresponds to

the 48-month monitoring after the third renourishment. Volume changes are computed in this

report from the monument (onshore) to the -24 foot contour (-7.3 m). Even though these changes

are not analyzed locally, it has been calculated that, the area with the highest erosion trends is that

encompassed by monuments R-186 and T-187. Their results also show that outside the 1992

project limits, there has been a positive impact after sand has spread out. Again, there has been a

larger volume of sand placed towards the southern limits of the project (T-187).

The results from Beachler (1993) also show a highly erosive trend at approximately R-

186, with respect to its surroundings. This is depicted in Figure 4.4, where volume changes were

computed to the -18 foot contour (-5.5 m). From this figure, it becomes somewhat obvious that

at R-186 an erosional hot spot exists; however, further research is necessary to try to predict or

explain the potential causes behind this phenomenon.




VCLUMe CHANGE A CUBIC 'ARDS54Thou-*NaI
100-
sb* 'FL FILL AREA
80 ... ..







-20-





ITM A170 M 17S ATIM ldl R1 o RI15%1 01
ONA MONUMENT


Figure 4.4 Volume changes computed by Beachler (1993) between 1974 and 1990.










One more study that analyzes data from the Delray Beach Nourishment Project was

carried out by Dean and Abramian (1991). This report studies techniques for evaluating potential

sands for beach nourishment projects and is another source of data for grain sand distribution.



4.1.3 Conclusions from the Previous Studies

It is important to mention that none of the previous studies was focused on the

identification and analysis of erosional hot spots, except for the monitoring studies which should

be able to detect such a problem if it happened to exist; however, none of the monitoring reports

mention the presence of erosional hot spots at all. Only the study by Gravens (1997) has included

some comments in what he considers the presence of an erosional hot spot. This erosional hot

spot is said to be found around DNR monument R-180, landward of the reef opening, and where

a no-dredge zone is located; nevertheless, he considers a somewhat different time span for

modeling, as he studies shoreline positions from January of 1987 through October of 1992, and

the other two studies consider the changes between 1973 and 1990, and 1992 to 1997. It is

possible then that, for some reason, only during this lapse a higher erosive trend was acting in this

area.

Further analysis of the results presented by Beachler (1993), Beachler and Mann (1996),

and Coastal Planning and Engineering, Inc. (1997), suggest that it is possible to determine the

areas with larger erosion trends. Both set of reports coincide that the erosion rates are larger at R-

186 and T-187, between 1974 and 1990, and between 1974 and 1995. Of course, this does not

necessarily mean that there is an erosional hot spot in this area.



4.2 Analysis of the Field Data

From the profile data it is possible to study the behavior of the beach locally through

shoreline and volume changes. Shoreline changes are important to be analyzed because they are

the most visible factors in evaluating beach profile fluctuations, and because the beach width










provides natural protection from storms absorbing the energy of the waves. In addition, the beach

width represents available recreational area for beach goers. Volumetric profile changes are here

referred to as the change in volume per unit width at a location. The importance of volumetric

profile changes is that they account for most of the profile equilibration as it moves offshore to

form the bar system. Volume changes are important to compute since it is necessary to study the

amount of sand that remains within the project after construction completion.



4.2.1 Distribution of Nourishment Volumes Along the Project

Every nourishment has been designed different, according to the observed need prior to

each nourishment. This is why, only the initial nourishment and the second renourishment,

encompassed the entire study limits, from R-175 to R-189. Likewise, sand has not been placed

uniformly every time a nourishment takes place. The outcome is an irregular placement of sand

that may help explain why some areas have higher erosion rates than others.

According to the monitoring reports, Figure 4.5 depicts the longshore distribution of sand

placement for each of the nourishments. Figure 4.6 shows the total volume per unit width placed

in the Delray Beach Nourishment Project. This information was obtained from the monitoring

and construction reports from Arthur V. Strock & Associates, Inc. and from Coastal Planning and

Engineering, Inc. Except for the second renourishment in 1984, where no detailed information

was available, the volume of sand per unit length placed is significantly non-uniform along the

project length (see Figures 4.5 and 4.6).



4.2.2 Sediment Size Distribution Along the Project

The monitoring reports provide results of sediment collection and analysis. However,

data are relatively complete after the second renourishment. Composite analyses of sand samples

were considered to study the sediment size distribution. Figure 4.7 portrays the mean grain size

distribution along the project since October of 1984, when the second renourisment took place.











The same data is plotted showing the mean grain size evolution over time in Figure 4.8. Sand

samples were collected at DNR monuments R-177, R-180, R-184, and T-187, starting form the

top of dune to the -20 foot contour (-6.1 m), covering the beach and nearshore zones.



-- 1973 ---1978
1984 1992

450














-250 -200 -150 -100 -050 000 050 1-00 150 200 250
= --- --- T -- -- -- I I

I \ I I

___ -__ _/ __ I I
I I I
-- -- -----J---t- 4 -






is clear, when the mean grain size ranges from 000 050 100 150 200 250months
Longshore Distance [k]

Figure 4.5 Volumes of sand placed along the project for each of the nourishment.







Figure 4.7a shows the variation of the sediment size along the project after the second

renourishment. Even though there is no information available for the first month at DNR

monument T-187 for the second renourishment, the influence of the fill material in the first month

is clear, when the mean grain size ranges from 0.21 to 0.29 mm approximately. After 15 months

there is a large increase in the mean grain size over the entire project where the sediment size

ranges from 0.38 to 0.39 mm. From the 27th month to the 52nd, the mean grain size has less

variation, with an average around 0.35 mm. It is possible to argue that, for the first month, coarser

sand was found on the updrift side of the project, however, these differences disappear after the








39


first year and these fluctuations have become more stable. Figure 4.8a depicts the convergence of

the mean grain size to a value around 0.35 mm.


-Volume Placed se 140
-Volume Placed since 1973
Volume Placed since 1974
S 0 12009






800









S200




-250 -200 -1 50 -1 00 -050 000 050 1 00 1 50 200 250
Longshore Distance [km]

Figure 4.6 Cumulative volume of sand placed along the project.




The sediment size variation along the project after the third renourishment is shown in

Figure 4.7b, where after one year the project has the finer sand, ranging from 0.24 to 0.33 mm.

After two years, the sand reaches its larger mean diameter and ranges from 0.38 mm on the

updrift side to 0.28 mm on the downdrift side. From the mean grain size evolution depicted in

Figure 4.8b it is remarkable that at T-187 the mean grain size has the finer sand with respect to

the rest of the project.

Therefore, these two figures describe the manner in which the mean grain size has

evolved since 1984 within the entire project. Since the native mean grain size in 1973 was 0.46
------ f ----------------------------- 3 8 8 -------------------------------- -----o n t h
























mm and the fill mean grain size is around 0.20 mm, there is a tendency to reach an equilibrium, as

shown in the figures; however, it is noticeable how the interaction of the fill sand, the native sand,









40



and the longshore sediment transport interact together to yield a nonuniform sediment size along


the beach, thus, causing the beach to evolve differently from one location to the other.






Sediment Size Variation along Delray Beach Project
2nd Renourishment (October, 1984)


--^^-4- --7 - -- --- --
...... .. . ...... .......-..... ...........
--- ~--..---.....KI-- j--

0 3520


0 300
-- 0276





0 200-



R-17 R-18 R- 84 T-187
2 -1 75 -1 5 -1 25 -1 -0 75 -0 5 -0 25 0 025 05 075 1 1 25 15 1 75 2
Longshore Distance [km]




Sediment Size Variation along Delray Beach Project
3rd Renourishment (December, 1992)


b)

-)400

S-... --- 375






-7 --------- -L--_ -- -
) 2750 --.. ---







--- -17- -1 -)R-175 ---
A A I A
R-171 R-18 R 184 T-187


--1 month
--*-- 15months
- 27 months
41 months
- 52 months































12 months
- --- 24 months
- 36 months
49 months


-2 -1 75 -15 -1 25 -1 -075 -0 5 -025 0 025 05 075 1 125 15 175 2
Longshore Distance, [km]

Figure 4.7 Longshore distribution of the sediment size
a) After second renourishment, and
b) After third renourishment.










41








Mean Grain Size Evolution (1984 Renourishment)


a)
0425 a)-

0400 -" "











03275
0350-- --""-------"--------



0325 ----- - -

0 300 --

0275 ----

0250

0225

0200

0175

0150
0 6 12 18 24 30 36 42 48 54 6
Months after Nourishment




Mean Grain Size Evolution (1992 Renounrishment)


0450

0425 b)

0400

0375

0350 -',

0325-

0300 ---

0275- -' "

0250

0225

0200

n 17 -


--R-177
--,-- R-180
--R-184
T-187


- R-177
----R-180
- R-184
T-187


0 6 12 18 24 30 36 42 48 54 60
Months after Nourishment


Figure 4.8 Sediment size variation with time

a) After second renourishment, and

b) After third renourishment.


E
E


a)
c
(0

I5


E
E


(0
(5
c,
0)


0










4.2.3 Shoreline Changes

As explained before, shoreline changes are important because the dry beach width

provides protection from storms to the coastal region, it is the most visible factor to analyze the

changes of the shoreline, and provides recreational area. Instead of shoreline positions, shoreline

changes are presented here in order to identify the areas with the largest deviation, and therefore

to identify possible erosional hot spots and cold spots.

Based on the profiles provided by the Bureau of Beaches and Coastal Systems of the

State of Florida through their internet website, it was possible to calculate the shoreline changes

of the beach throughout the life span of the project. Changes within two periods of time are

presented here: from January 14, 1975, to August 1st, 1990, and from January 15, 1975, to

January 15, 1998.

These shoreline changes are shown in Figure 4.9 and 4.10. In order to study the beach

response in the vicinity of the project, shoreline changes between 1975 and 1990 are shown from

monument R-165 through monument R-201, this is, about 3 kilometers north and 3 kilometers

south of the project limits. Shoreline changes between 1975 and 1998 encompass the project

length only, since no more data were available.

From 1975 to 1990 the measured values of the shoreline change show that there is a large

fluctuation along the study area. During this period, the project area has been renourished twice,

in 1978 and in 1984 as shown in Figure 3.3. The middle part of the project (approximately from

R-178 to R-185) has advanced around 30 m, which is the projected dry beach width to maintain

through the beach nourishments. The areas outside of updrift and downdrift sides of the project

show an advance of approximately 15 m. In addition, Figure 4.9 shows that there are two minima

at R-177 and at R-186 of 10 m. The fact that the ends of the project have more erosion than the

middle area, can be explained from the diffusion theory first introduced by Pelnard-Considere

(1956). Therefore, the shoreline (and volume) changes in these areas should be predictable.

















Fill area












20










.0 -6.0 -5.0 -4.0 -3.0 -2.0 -1.0 00 1 0 20 30 40 50 6 7


10




A AA A AA A A A A A A-- AAAA &AA A A A AA AAA A
10 (0 N C 0) N T 1 N ^ 0 CO C ^10 ( N 0 -0 CO 1M 0O M M 0 N M 0)0
2 E &1 & n2 ____2 0 0


Longshore Distance [km]


Figure 4.9 Shoreline changes from 1975 to 1990.















-- Fill area -










35


30


25


20


15


10
A A0 A A 0A A A A A I A A A r A AO
0. CD O O C C CD CO CO

-------- -------- '---- o------ ---- O---------------------
n, n, n, ,, 5 ,, ,,n, n, n, ,

pY _


Longshore Distance [km]


Figure 4.10 Shoreline changes from 1975 to 1998.










After fifteen years, the updrift area of the project has accreted, although large differences

within short distances are present. Same differences are present on the downdrift side, however,

much less shoreline advancement is computed.

For the period 1975 to 1998, where only the project area is analyzed (Figure 4.10), it can

be seen that from monument R-175 to R-180, the shoreline increases its width from 15 to 50 m; at

R-186, the shoreline advanced only 15 m, while at the previous and at the next survey lines the

advancements are 43 and 30 m, respectively. Finally, at the middle portion of the project, the

shoreline advanced between 36 and 50 meters.



4.2.4 Volume Changes

Volume changes represent the sand remaining within the project. These volumes are

computed per unit width of beach. Because some of the profiles consist of very long surveys

(reaching -28 m), it is necessary to establish a datum plane of reference, to which volumes are to

be computed. This is very important in order to exclude negative volume changes associated with

the borrow areas. As an example, Figure 4.11 shows the survey lines at R-188 in 1975 and 1990.

The depression shown in this figure from -15 m to -20 m represents the borrow pit as surveyed in

1990, which means that the third renourishment in 1992 is not accounted for.

This borrow pit is bounded seaward by the aforementioned shore-parallel reef. Whether

some influence exists from the borrow pit or not, is difficult to establish; however, Figure 4.11

shows that, from -8 m to -15 m, the profile has steepened probably due to sand lost to the borrow

pit. This process can be regarded as a natural tendency of the profile to compensate for the sand

lost in the dredging operation. Therefore, if this volume is accounted for in the volumetric profile

changes, there will be an error, given that this material is not the consequence of wave and

current action. In fact, some authors such as Kojima et al. (1986), have noted the possibility that

this steepening of the profile due to replenishment of the borrow pit, can reach the shoreline if the












hole is located close enough to the beach (thus becoming another potential cause for erosional hot


spots).





10





Cross-shor Distance [m
0 __---------------------------------------------
20 400 600 800 1000 1200 1400 1600 100





-10
-5 --_ __-- \



S--1/15/75
R -ef
5 8/1/90
z -15 -----


-20 -
Borrow pit

-25 ------


-30-


-35

Figure 4.11 Comparison between the 1/15/75 and 8/1/90 profiles at R-188.




In this context, volumetric profile changes were computed out to different depths. Figure


4.12 shows the volume changes between 1975 and 1990, and Figure 4.13 between 1975 and


1998. From both plots it is noted that the values converge around -7 m. Note in Figure 4.12 that


volume changes indicate large loss of volume for depths greater than 9 m in the fill area.


Computations for volume changes will then be computed from the monument to the -7 m datum


plane.


Figure 4.12 shows that updrift of the project, despite large fluctuations, there is a volume


accumulation after 15 years, while downdrift of the project area, there are large fluctuations


showing both loss and gain of volume. Throughout the project area, there is an approximate
















Fill area
600


400 _






.0 -6.0 -5.0 -4.0 -3..0\ -20 .'0 l n 0 1 I C C 0 140 V5 0~ 7














I'
1000







Longshore Distance [km]

--5 m - x- --6 m -7 m -9 m -- -12.5 m --- 17.5 m -20 m - -22.5 m


Figure 4.12 Volumetric Profile Changes from 1975 to 1990.


T -7
E

0)


E
-Z
>,















Fill area



















150 .




100







a0 _
LO QO O r- 0' 0"N (0 O O r- 00 0
" 00 : 00 00 00 00 00 00 00 00
0: FL "F "7 "--"-- "7-"79"--"7-"-------" ----


Longshore Distance [km]


- -----5 m -6 m -r -6.5 m -7 m -7 -7.3 m


Figure 4.13 Volumetric profile changes from 1975 to 1998.










average increase of 150 m3/m except around monument R-186 where the volume changes are

close to zero, indicating that all the sand placed in this area has been lost. This result is consistent

to that computed by Beachler (1993), shown in Figure 4.4. From T-187 to R-189 the volume

increase is on the order of 100 m3/m.

For the other period of time, that is, 1975 to 1998, Figure 4.13 shows large fluctuations as

well. The largest difference is present, again, at R-186, where the volume gained after three

renourishments is 90 m3/m, while an approximate average for the volume change in the rest of the

project is around 250 m3/m. Also, for the updrift side of the project, there is a small gain of

volume compared to the rest of the project, which is due to the third renourishment which was

placed between R-180 and R-188.



4.2.5 Summary

The analysis of the field data yields information on grain size, shoreline and volume

changes, profile information, and description of the volumes placed throughout the life of the

project. Previous contributions describe the effects that different wave conditions have on the

shoreline response, and the positive influence of Delray Beach nourishment on adjacent beaches.

The distribution of volumes along the project has been shown to be irregular, that is, the

volume of sand per unit width of beach placed varies along the project. In addition, every

nourishment has had different limits.

The mean sediment size is also analyzed here. Perhaps, as a consequence of the

irregularity of the volumes placed along the beach, the mean grain size proved to be also

irregular. Two patterns have been identified: coarser sand is located on the updrift part of the

project, and the slow natural tendency of the project to reach an equilibrium of the mean grain

size.

Volumetric and shoreline changes show large fluctuations. A highly erosive zone has

been identified around monument R-186, which is also consistent with the previous studies







50


performed at Delray Beach. Whether this area corresponds to an erosional hot spot can only be

determined after performance predictions are applied, in this case through the one-line numerical

model DNRBSM.
















CHAPTER 5
APPLICATION AND MODELING RESULTS



5.1 Numerical Model for Beach Planform Evolution

Dean and Grant (1989) developed a one-line model for calculating the shoreline response

in the vicinity of beach nourishment projects. The original purpose of the model was to establish

thirty-year shoreline position predictions for a beach nourishment project. The original

numerical procedure did not consider the fact that most nourishment projects are periodically

maintained according to the observed losses. A new version of this methodology is applied in

this thesis, and it is able to compute the shoreline response over a period of time, including

renourishments, if any. Additonally, Appendix A contains the description of the theory and

governing equations used to develop the model and, since no written literature that accounted for

the modifications performed to Dean and Grant (1989) methodology exist, Appendix B contains

the program listing and a sample input and output. However, this thesis is exclusively directed to

the analysis of the performance of the Delray Beach Nourishment Project, and therefore, the

development of the latest version of the program is not included.

This methodology was developed in Fortran language. The name of the program is

DNRBSM and stands for Department of Natural Resources, Beaches and Shores, which is the

entity that first sponsored the development of this methodology. The letter 'm' was later added

to stand for multiple nourishments. For further detail in the development of the program and its

applications, including description of variables, numerical procedure and detailed capabilities of

the model, the reader is referred to Dean and Grant (1989).










5.1.1 Application of the Delray Beach Data for Planform Performance Predictions

Prior to using the program, certain data are required. These data include mean grain

size, volume of sand placed along the project per unit width, wave characteristics, background

erosion, location of coastal structures, boundaries of the project, etc. The compilation of these

data was mostly taken from the monitoring reports from Arthur V. Strock & Associates, Inc., and

later Coastal Planning and Engineering, Inc.

5.1.1.1 Sediment Size

From several sand samples collected throughout the life span of the project, it has been

seen that the mean sediment size varies both with time and location along the project. This is due

to the large difference between the fill grain size and the native grain size. The variation of the

mean grain size with time along the project has been previously described in Figures 4.7 and 4.8.

Given the importance that the sediment size has in the sediment transport equation

(through the sediment transport parameter, K), it was necessary to determine a sediment size

representative of the actual conditions. However, the large fluctuations along the project show

that there is no apparent representative mean grain size, and even an average is probably

unrealistic. To account for this situation, several runs varying the mean sediment size were

performed. These results will be shown later in this chapter.

It seems, however, that the tendency of the mean grain size is to reach an "equilibrium"

around 0.3 to 0.35 mm. From the information compiled, a mean grain size of 0.32 mm was used

to compute shoreline and volumetric changes. According to Dean (1989) the sediment transport

parameter, K, corresponding to this diameter is approximately 1.10.

5.1.1.2 Wave Characteristics

The effective deep water wave height of 0.43 meters (1.4 ft), and a period of 6.5 seconds

is used. The dominant deep water wave direction adopted in the model is 200 north from the

perpendicular to the beach, and is assumed to be constant throughout the entire year. These










characteristics were previously discussed in Section 3.2.3. In addition, the sum of the depth of

limiting motion and berm height (h,+B) has been set to 7.16 meters (23.5 ft) as mentioned before.



5.1.1.3 Model Set-up

The numerical solution applied here is based on an explicit scheme in which the

equations for sediment transport and continuity are solved sequentially. The one-line numerical

method uses a grid or computational scheme as depicted in Figure 5.1, where the shoreline

positions are held constant for a time step, At, while the sediment transport is computed. After

this computation, the sediment transport is held constant and the shoreline positions are updated.

This process is then repeated until the time of desired modeling has been accomplished. The

DNRBSM model assumes straight and parallel contours seaward of h., and contours parallel to

the nourished shoreline landward of h.. The project length encompasses 56 cells, 76.2 meters

(250 ft) wide each, for a total of 4270 meters. The total modeled length was 200 cells or 15240

meters (50000 ft).





QI1
Q = sediment transport
y = shoreline position
i = time step
SAx = cell width = 76.2 m


Figure 5.1 Computational scheme used in computational method.









The grid system applied in this case requires definition of the boundary conditions at both

ends in order to solve the continuity and sediment transport equations. The case of Delray Beach

is that of an uninterrupted shoreline, which means that the shoreline position is specified at both

ends of the computational domain for all times, and the initial shoreline is also specified.

The stability criterion for this numerical procedure is given by

1 Ax2
(At) (5.1)
2 G

in which G is the "alongshore diffusivity" coefficient in the so-called diffusion or heat conduction

equation. The same graphical procedure used to estimate the effective deep water wave height

and period, and the depth of limiting motion discussed in Section 3.2.3, is available for the

coefficient of alongshore diffusivity, from Dean and Grant (1989). According to the location of

the project, this coefficient is approximately 4.18x10- m2/s (0.045 ft2/s). Therefore, a time step

of 86400 seconds (1 day), which is a reasonable value for this type of modeling, meets the

criterion established for numerical stability. Additionally, it has been found that the area

encompassed by Delray Beach does not show background erosion (Dean et al. 1998).

The initial conditions are specified from the volume per unit width placed in the first

nourishment. These volumes are input for each one of the nourishments at the corresponding

time step. In order to account for shoreline changes, the nourished profile is assumed to be of the

same form as the pre-nourished form, but displaced seaward. Once the volume change, depth of

limiting motion and berm height are known, the shoreline change is computed using the

following expression,


Ay = (5.2)
h +B

in which, Ay indicates the shoreline change, and AV the volume change per unit beach length.

Notice from Equation 5.2, that a constant profile is assumed, thus not accounting for the profile

equilibration immediately after sand has been placed.










5.1.2 Predicted Shoreline and Volumetric Profile Changes

Shoreline changes are calculated here using the National Geodetic Vertical Datum

(NGVD) as reference. The predicted shoreline and volume changes between 1975 and 1990, are

shown in Figure 5.2. Because predicted shoreline and volume changes are proportional to

(h,+B) (see Equation 5.2), they can be plotted in the same figure. Additionally, these changes

show the influence that the sediment transport parameter, K, has for modifying the shoreline

displacements. According to Dean (1989), the sediment diameter, D, is related to the sediment

transport parameter, K, as shown in Table 5.1. This table, includes selected grain sizes that will

be used later in this thesis.



Table 5.1 Approximate corresponding values of the sediment transport parameter to selected
sediment sizes (from Dean, 1989).

Sediment Diameter, Sediment Transport Parameter,
D [mm] K
0.40 0.95
0.35 1.04
0.33 1.10
0.29 1.18
0.27 1.24
0.24 1.30
0.22 1.36
0.20 1.41
0.18 1.45
0.17 1.50
0.15 1.55


Even though it is known from refraction theory that waves "wrap" around a beach

nourishment project, thus spreading out sand almost independently from the wave angle,

conditions with normal and oblique waves were tested.

5.1.2.1 Changes from 1975 to 1990

Figure 5.2 shows the predicted shoreline and volume changes at the Delray Beach

Nourishment Project. It can be seen from these figures that, regardless of the sediment transport










parameter, these changes are characterized by three maxima and two minima. The maxima

correspond to the center part of the project which is the area that erodes least compared to the

limits of the project. The two other maxima, together with the minima, are the consequence of a

rapid erosion at the project ends. While the sharp gradients at the ends of the fill planform

experiment high sediment transport rates, the areas immediately outside of the project rapidly

accrete.

The importance of the sediment transport parameter, K, will be examined later in Section

5.1.3, since the variation of this value can highly alter the results.

Finally, this model predicts that there are more shoreline and volume changes from using

an incoming wave angle of 200 in the area encompassed by the project. On the other hand, in the

adjacent beaches to the project, the shoreline has less changes with the incoming angle of 20.

This could possibly be regarded as if the project was acting as an erodible barrier to the longshore

transport, and therefore, sand is stored within the project limits; however, this mechanism is

discarded given the dimensions of the project, which makes it a small perturbation compared to

the length of the spreading out limits. It is important to mention that, even though spreading out

losses change with oblique waves, this change is relatively small.

5.1.2.2 Changes from 1975 to 1998

Shoreline and volumetric profile changes for this period are shown in Figure 5.3. This

figure describes the predicted changes for different sediment transport parameters and wave

angles. The difference between these changes and those from 1975 to 1990 is mainly given by

the 1992 nourishment which took place from approximately R-180 to R-188. Even though it had

been mentioned before that this period would be analyzed only within the project limits due to

lack of data outside the limits, a broader analysis of the theoretical predictions may help

understand the general performance of the project.

On the updrift side of the project, the greater erosion due to large spreading out losses, as

well as the accretion immediately updrift from it, still remain similar to those seen for the period









57



of 1974 to 1990. On the downdrift side of the project, although this same pattern is not clearly


observed, it is possible to notice that it is starting to develop.


-60 -50 -40 -30 -20 -10 00 10
Longshore Distance [km]
-- K=095 ----- K=1 10


-60 -50 -40 -30 -20 -10 00 1 0
Longshore Distance [km]


20 30 40 50 60


K=1 30


300

275

250

225

200

175

150

125 3

100

75

50

25


20 30 40 50 60


K=095----- K=1 10 K=1 30

Figure 5.2 Predicted volume and NGVD shoreline changes from 1975 to 1990 with
a) Incoming deep water waves perpendicular to the shoreline, and
b) Incoming deep water waves 200 north from perpendicular to the shoreline.


















70 500

65

60 a) 450



50 --- 350


-,300 o
40-- _

35 -, 250

30
25 .-200 3
25--- 3
20 / + 150
20 -_- -- -_ _
15Fill area
100


50


0 0
-60 -50 -40 -30 -20 -10 00 10 20 30 40 50 60
Longshore Distance [km]
-- K=0 95 ----- K= 10 K=1 30


70 500

65

60 ___b) _____450

55 ________ ___ _____
5--- --400

50 350

45-- <
-300
40-- 3
9
35 -_ 250

30 ---

25 _3
20 ___ 150

Fill area
15.*/ _____ __
100

10-
--50


0 0
0" -------- --fi-- ------ ------- ------ ------- ? ---fi-- ........-- ----------- ------- -------- ------- o


-60 -50 -40 -30 -20 -10 00 10 20 30 40 50 60
Longshore Distance [km]
-- K=0 95 ----- K= 10 K=1 30



Figure 5.3 Predicted volume and NGVD shoreline changes from 1975 to 1998 with
a) Incoming deep water waves perpendicular to the shoreline, and
b) Incoming deep water waves 200 north from perpendicular to the shoreline.









It is interesting that the maxima achieved immediately outside of the project ends due to

large accretion, have almost the same value regardless of the values of K and wave angle, for both

periods. These results can be regarded as if the beach had a maximum natural capacity to accrete,

after which sand is more readily transported away from the project.

In addition, the largest changes are seen at the middle of the 1992 renourishment, that is,

around monument R-184, which is the area that erodes slower compared to the rest of the project.

In Figure 4.5, where the volumes of sand placed for each nourishment are shown, it can be seen

that the fluctuations in volumes placed alongshore as a result of the construction procedures, are

not as important as the project's sharp ends, and according to theory, they are smoothed out

faster.



5.1.3 Influence and Importance of the Sediment Transport Parameter

The equation of longshore sediment transport used in this model, which is also widely

applied, is developed in terms of the energy available in the waves arriving at the beach. This

relationship has been developed by Inman and Bagnold (1963) as

KP
Q = (5.3)
(P, P)g(O- P)

where Q is the longshore sediment transport, ps and p are the density of the sand and water,

respectively, g is the acceleration of gravity, and p the porosity. P1 is the alongshore energy flux

per unit of beach width, and K a dimensionless parameter later adopted as the sediment transport

parameter. Therefore, the longshore sediment transport is directly proportional to the constant K

for the same beach geometry. The correct value of this parameter is particularly important in

beach nourishment projects since the larger the parameter, the larger the longshore sediment

transport, and thus the smaller the life of the project.

Komar and Inman (1970) introduced a K value of 0.77. Other studies such as those from

Kraus et al. (1982), Dean et al. (1982) and Caldwell (1956) have found that K has the value of










0.2, 1.23, and 2.2, respectively. There is still no general consensus as to what the value of K is,

or as to whether it is constant or possibly varies with other parameters, such as diameter, fall

velocity, beach profile, or angle of incidence of waves. From several field experiments, Dean

(1989) suggested that the sediment transport parameter depends on the grain size. This

dependency shows that larger sediment sizes are associated with lower values of K, which is

expected from intuition as coarser sand is less transportable. The corresponding values of K to

selected grain sizes are shown in Table 5.1.

It has been mentioned that the Delray Beach Nourishment Project has a somewhat large

variation in the sediment size, both alongshore and with time. Therefore, it is of great

importance that a representative sand diameter is chosen. To study the effects that modeling

with finer or coarser sand would have on the predictions, Figure 5.4 describes how these changes

would be if only longshore sand transport is considered.

It is clear, as illustrated in Figure 5.4, that there is more sediment transport expected from

considering finer sand, and less from coarser. The ends of the project are the areas where more

differences are expected from modeling with different grain sizes than the actual conditions.

This analysis shows that a different grain size could alter the predictions not only by using one

sediment size along the entire project, but also in a particular location, what could develop into an

erosional hot spot. Therefore, these theoretical assumptions must be considered when the

measured and predicted conditions are compared.

The effects of the sediment transport parameter on the performance predictions from

Figures 5.2 and 5.3, are more important within the project limits. However, when changing the

grain size from 0.40 to 0.24 mm, the shoreline retreated only about 7 and 10 meters more in the

center of the project for 1990 and for 1998, respectively. Adjacent to the beach nourishment

project, the difference between changes with different sediment transport parameters are minimal,

however, from conservation of sand, they extend over a longer distance.













Incoming
waves





---->


1F >Finer sand

__ Sand used in
model
---> Coarser sand


Note: the size of the arrow indicates
the amount of sand transport.



Beach Fill


--- >


Original
shoreline


- Finer sand

Sand used in
model
--------- Coarser sand


U


av _aQ
at ax


A Vpredicted-A measured





Figure 5.4 Variation of sediment transport with different sediment sizes.




5.2 Comparison Between Measured and Predicted Changes

The comparisons presented below are divided into shoreline changes and volumetric

profile changes, which have been the tools used throughout this thesis to analyze the beach

evolution.

This analysis, however, will not compare the curves previously shown for predicted and

measured changes directly. In order to be able to recognize the "natural" erosion of the


- - - - - --- - - - - - - - - - -
---k.


// __ __ 1,


- -----










shoreline, the volumes placed or added beach widths, will be substracted from the volumetric and

shoreline changes, respectively. The volumes substracted are those presented in Chapter 4 in

Figure 4.5 which were added in between the periods analyzed.

The same two periods considered before are examined here. However, for the 1975-

1998 period, only the area encompassed by the project is studied, since no data were available for

the vicinity of the project.



5.2.1 Shoreline Changes

5.2.1.1 Changes from 1975 to 1990

Over this period, two renourishments have been carried out to maintain Delray Beach: the

first in 1978, and the second in 1984, which encompassed two separate areas as described before.

Although it is difficult to specify one sediment diameter representative for the entire

project, it is possible to perform a first approach. From the analysis of the grain size distribution

along the project in Section 4.2.2, it has been determined that the average mean grain size is 0.33

mm. Coincidentally, the average between the native and the fill mean grain sizes (0.46 and 0.20

mm, respectively), is also 0.33 mm, which corresponds to a sediment transport parameter of

K=1.10. Additionally, grain sizes tend to range between 0.30 and 0.35 mm. Even though other

sediment sizes will be accounted for later in this thesis, the comparisons between measured and

shoreline changes are based on K=1.10.

The predicted and measured shoreline changes, including the subtraction of the added

beach width, are portrayed in Figure 5.5. This figure shows that the predicted quantities are in

good agreement with the measured values within the project limits. On the updrift side, there

appears to be an overprediction of the shoreline changes, while, on the downdrift side, despite the

large fluctuations of the measured values, it seems to be underpredicted. Overprediction as used

here refers to the predicted changes being smaller than those found in the field, and by

underprediction, the opposite.











Shoreline changes "without" added beach width
between 1/14/75 and 1/15/90



Fill area



1~~~~~ ~ ~ ---I^_ ^ -- -- ^ __--- ---- -----------
T .. .. -









I --- ---- --- ---- --- ^ \ -- ---- --- --------S
I100
'-
---- ------_ ------_ ------_ ---- 4- 0 ---- --_f _-------- --- ---








Longshore distance [km]
-- Predicted Measured ------ Difference [p-m]

Figure 5.5 Comparison between the predicted and the measured NGVD shoreline changes from
1975 to 1990.




Analyzing closer the area encompassed by the project, the differences between predicted

and measured values are less than 10 meters except for three areas around monuments R-178, R-

184, and R-186. The first two are overpredicted while the other one is underpredicted. Although

the presence of these three peaks may suggest the presence of cold or hot spots, it is necessary to

establish a criterion to determine such behavior. This will be examined in Section 5.3.

A standard deviation analysis is also presented later in this thesis (see Section 5.2.3),

which will be an indicator of the overall performance of the nourishment, and will be an aid for

locating erosional hot spots (and eventually cold spots).

5.2.1.2 Changes from 1975 to 1998

This period considers one more nourishment, as in October of 1992, sand was placed

over the southern part of the project, roughly, from R-180 to R-188. Shoreline changes between










January 1975 and January 1998 are illustrated in Figure 5.6. The results shown in this figure

have the same degree of agreement between predicted and measured conditions as those from

Figure 5.5, and they can also be regarded as a good approximation. In this case, shoreline

positions were predicted within a 10-meter "error" for almost the entire project, except for the

downdrift side where, at R-186, the shoreline was underpredicted almost 40 meters, and at T-187

about 20 meters.

It can also be noted that from the updrift end to R-180, the shoreline changes were

overpredicted, while for the rest of the project, they were underpredicted. The area that is

presented here as underpredicted coincides with the area where the 1992 renourishment took

place. Therefore, it can be said that it eroded faster than predicted, however, only the downdrift

end proved to be poorly approximated, since up to 37 meters were underpredicted.




Shoreline changes "without" added beach width
between 1/14/75 and 1/15/98


*-4Fill area


20

















Longshore distance [km]
_- Predicted Measu red- - Difference [p m]


Figure 5.6 Comparison between the predicted and the measured NGVD shoreline changes from
1975 to 1998.










Comparing Figures 5.5 and 5.6 some similarities can be found within the project limits,

where the effects of the last renourishment are readily seen. Quantitatively, both comparisons

predict shoreline changes within 10 meters approximately, except for the aforementioned areas.

Qualitatively, both predictions were best at the middle of the project, and found largest

differences at R-178 and at R-186.



5.2.2 Volumetric Profile Changes

5.2.2.1 Changes from 1975 to 1990

Volumetric profile changes over this period are portrayed in Figure 5.7. This prediction

proved to be less accurate than that for shoreline changes. The entire project length was

predicted within approximately 150 m3/m of "error". The largest differences were around R-181

and R-186, where 140 and 160 m3/m were underpredicted, and around R-178, where 120 m3/m

were overpredicted.

On the updrift vicinity of the fill area predictions were very close to the actual measured

values, except around R-170, where a cold spot might be present. On the downdrift side there is

a large fluctuation in the volume changes so that it is not possible to predict accurately such

changes with this model. However, the prediction in this area agreed on average with the

measured conditions. Therefore, differences presented in Figure 5.7 can also be regarded as

relatively small and as a good performance prediction.

5.2.2.2 Changes from 1975 to 1998

The analysis of the volumetric changes for this interval, which includes the presence of

one more nourishment than the previous case, is shown in Figure 5.8. It can be noted from this

figure, that volumetric changes for this period were predicted more accurately than for the 1975-

1990 span. The entire project area is predicted within nearly 100 m3/m, with the exception of the

downdrift side, where a large underprediction of 275 m3/m was found. At R-178 where 120 m3/m

were found for the 1975-1990 term, an overprediction is again found, this time of 140 m3/m.












Volume changes "without" volume placed
between 1/14/75 and 1/15/90


A A A A A A A A A AA A A A A A AI A A A A A A A A A


Longshore distance [km]
-- Predicted Measured ------ Difference

Figure 5.7 Comparison between the predicted and the measured volumetric profile changes from
1975 to 1990.


Volume changes "without" volume placed
between 1/14/75 and 1/15/98


Longshore distance [km]
Predicted Measured ------ Difference

Figure 5.8 Comparison between the predicted and the measured volumetric profile changes from
1975 to 1998.


Fill area


2


J'


/ \.


I-;


I-n










It is also remarkable that comparing Figures 5.6 and 5.8, which correspond to shoreline

and volume changes for the 1975-1998 span, respectively, the predictions are very similar. In

other words, both plots show under and overpredictions at approximately over the same locations.

Particularly, at R-186 where the largest differences were found, these differences follow the

Equation 5.2 almost exactly. The implication is that the nourished profiles were displaced

approximately with the same form as the pre-nourished profile.



5.2.3 Standard Deviation Analysis

In order to describe whether predictions agree or disagree with field measurements, the

standard deviation is computed here for both, shoreline and volumetric changes. Given also the

importance and uncertainty of the sediment transport parameter, several grain sizes were

modeled, as well as different wave conditions. Only the area encompassed by the project is

accounted for, since the purpose of this thesis is to identify erosional hot spots.

The standard deviation is given by

1
S= Ay2 (5.4)


where N is the number of points and Ay the shoreline changes. Obviously, the same expression is

applicable to any other data types such as volume changes. Equation 5.4 provides the root mean

square (rms) deviation of the data from the origin, while Equation 5.5, shown below, provides the

rms deviation from a reference value, in this case, the measured changes,


a pm( (5.5)


where p denotes the predicted data, and m the measured data.

After several runs of the DNRBSM model, varying the sediment transport parameter and

incoming deep water wave direction, a set of plots was obtained to summarize these results. Of

particular interest is the relationship qm/pO, which means that, when this expression approaches










zero, a good overall planform performance prediction has been made. In general, it can be said

that if opm/,l is smaller than 0.4 to 0.45 a good prediction has been achieved. Likewise, opm/ m,

upm, and Op were computed and summarized in graphic forms. Figure 5.9 shows computed

values of upm/,l, Figure 5.10 the values of opm/m, and Figures 5.11 and 5.12 show upm and Op

values, respectively. These data represent computations only for the period of 1975-1998, since

these are the actual conditions of the project, and because predictions proved to be less accurate

for this interval. However, for K=1.10, the standard deviation is computed for the 1975-1990

span.

Figures 5.9 and 5.10 describe the overall performance of the project based on the

standard deviations computed from the differences between measured and predicted values for

1975-1998. The results illustrated in Figure 5.9a show that, for an increasing K, there is

apparently better agreement between predicted and measured values. However, this does not

mean that the actual value of K should be larger than the one previously considered of 1.10. The

curves appear to converge to a value around 0.22 and 0.26 for shoreline and volume changes,

respectively, when K=2.0, whose corresponding diameter is not determined by Dean (1989).

According to the sediment size analysis, and considering the relationship between the sediment

size and the sediment transport parameter given in Table 5.1, if it is assumed that K=1.10 as the

representative conditions for this project, it is then found that Upm/ap = 0.3 for the shoreline

changes, and 0.33 for the volume changes. Therefore the project has a good overall performance.

For an incoming deep water wave angle of 200, Figure 5.9b shows that Upm/ap values also

decrease with larger K, not showing, however, convergence to any specific value. For a value of

K=1.10, which was assigned for Delray Beach, it has been found that upm/p = 0.44 for shoreline

changes, and upm/p = 0.46 for volumetric changes. These values are considered fairly good for

performance predictions.









69







Values of opm / Op (deep water incident wave angle = 0)


045



04





03 M





025



02



015
..^---------------------------









Sediment Transport Parameter, K

--Shoreline Changes -U-Volume Changes




Values of opm / Op (deep water incident wave angle = 20 deg)


055 -

05

045

04

035

03

025

02

015

01

0


b)ediment Transport Parameter, K


Sediment Transport Parameter, K


-*-Shoreline Changes -*-Volume Changes





Figure 5.9 Values of pm/qp computed for the fill area for 1975-1998, with
a) Incoming deep water waves perpendicular to the shoreline, and
b) Incoming deep water waves 200 north from perpendicular to the shoreline.









70







Values of opm / Gm (deep water incident wave angle = 0)


E
0 3 -- -- -- ; -- -- -- ------ -- --.-.-.-.-

0 19 B". -- -- -- -- -- -- --- --- --- .--- -- -- -- -- -- -- -
025

023

021

019

017
a)
015


Sediment Transport Parameter, K

---Shoreline Changes -U-Volume Changes



Values of Gpm / Gm (deep water incident wave angle = 20 deg)


IC m-shoreli e = 52. m

T raCnp-vOlumE = 71.9 m3 m

















b)


Sediment Transport Parameter, K


-.--Shoreline Changes -1 Volume Changes



Figure 5.10 Values of pm/,, computed for the fill area for 1975-1998, with
a) Incoming deep water waves perpendicular to the shoreline, and
b) Incoming deep water waves 200 north from perpendicular to the shoreline.


04



035



03

E
025
E


02



0 15



01








71






Values of opm (deep water incident wave angle = 0)


O t- t- t- t- t- t- t- t- t- t- t- t- t-
Sediment Transport Parameter, K

-*-Shoreline Changes ---Volume Changes


Values of opm (deep water incident wave angle = 20 deg)


0 o (0 (-
Sediment Transport Parameter, K

-*-Shoreline Changes ---Volume Changes


Figure 5.11 Values of pm, computed for the fill area for 1975-1998, with
a) Incoming deep water waves perpendicular to the shoreline, and
b) Incoming deep water waves 200 north from perpendicular to the shoreline.










72









Values of Op (deep water incident wave angle = 0)


55




50




Co
S45




40




35














60



55



650
0)
350)

3 45
0)







35



30


430

410


--- 3907

370

350


_330

310

290

O -sho enllnd = 52. m 270
270

a) O -vol me = 3 '1.9 m 2
250
o---o-------------------------------- 5

Sediment Transport Parameter, K

-*-Shoreline Changes -U-Volume Changes




Values of opm (deep water incident wave angle = 20 deg)







SU--- 350



330
__-- - - - - - _^ - - 330



310



290



S270
Offshorelln, = 52.. m

b) -O-voilme =371. m3
250


Sediment Transport Parameter, K

-*-Shoreline Changes ---Volume Changes



Figure 5.12 Values of p computed for the fill area for 1975-1998, with

a) Incoming deep water waves perpendicular to the shoreline, and

b) Incoming deep water waves 200 north from perpendicular to the shoreline.


.Q
C)
CD
0
2
(D


CD
4
CD


'3
















ci














3
2
J


CD
=
C)
I
fD


3
60
2










From Figure 5.9, it is clear that the overall performance of the project has been

apparently better predicted for perpendicular incoming waves. The reason is that when

considering an incoming wave angle different than zero, a longshore sediment transport is

induced in the vicinity of the project, thus interacting with the beach fill. These conditions can

also be modeled, however, it is necessary to establish a different sediment transport parameter for

the vicinity of the project. At present, DNRBSM is only configured to manage one sediment size

for the entire area, therefore, the results in which spreading out effects are investigated alone

(perpendicular waves), are assumed to be more accurate.

Unlike op,/ap, the values of opm/,m are referred to the measured standard deviation,

which is a constant. Therefore, this parameter can also be considered as an overall indicator of

the project performance, as shown in Figure 5.10. In Figure 5.10a, a minimum appears to be

achieved around K=1.50 with (pm/(p=0.21, and (,m/(m=0.25 for shoreline and volumetric

changes, respectively. Thus, the values of qpm/m are closer to zero than those illustrated in

Figure 5.9 for opm/ap, as they range from about 0.30 to 0.21. Furthermore, the same differences

of modeling with two different wave angles found before, are found here. In general, there is a

better prediction using those values calculated from a perpendicular wave angle.

The other two figures, 5.11 and 5.12, show the values used to plot Figures 5.9 and 5.10,

and therefore, they have the same characteristics and differences among them. The standard

deviation of the measured values is 52.6 m and 371.9 m3/m, for shoreline and volume changes,

respectively.

In conclusion, it has been found that the project has a good overall performance. This

allows to identify any highly erosive areas, as it is expected that most of the project do not have a

large deviation from the predicted values. In addition, it has been shown that the value of Opm/ap

becomes smaller with larger sediment transport parameters, and with waves perpendicular to the

original shoreline.










Although not illustrated in a graphic form, the standard deviations for the 1975-1990

period, were computed for only three different sediment transport parameters, since they

predictions proved to be very similar to the measured conditions (see Table 5.2).



Table 5.2 Standard deviations computed for the 1975-1990 span.

Data Shoreline Changes Volume Changes
K a Op Upm Upm/lp Up!mU p U pmlp apml
[m] [m] [m3/m] [ /m]
0.95 00 58.7 7.3 0.124 0.120 420.5 88.6 0.211 0.183
0.95 200 55.6 8.2 0.148 0.135 398.5 106.5 0.267 0.220

1.10 00 60.3 7.5 0.125 0.123 432.0 81.4 0.188 0.170
1.10 200 57.0 7.6 0.133 0.124 408.5 97.7 0.239 0.202

1.30 00 62.2 8.3 0.134 0.136 445.8 75.1 0.169 0.155
1.30 200 58.8 7.3 0.124 0.119 420.8 88.3 0.210 0.182
Note: a is the deep water wave angle of approach; Um-shorehne = 61.0 m; Um-volume = 484.7 m3/m.

For the 1975-1990 period we have that, for shoreline changes, opm/,p = 0.125 when K =

1.10 and waves perpendicular to the beach, and for volume changes, opm/Up = 0.188. Therefore,

these changes have been better predicted than those for the 1975-1998 period, and the overall

performance of the project can be considered as very good, from 1975 through 1990.



5.3 Hot Spot Identification and Mitigation Measures

As it has been defined herein, an erosional hot spot has the characteristic that can not be

predicted directly from applying diffusion theory. Based on this, three criteria will be considered

in order to identify erosional hot spots, and eventually cold spots: historical shoreline changes, the

sediment size distribution, and the standard deviation reference value. Although these tools are

used to identify and locate erosional hot spots, they do not exclude other techniques that may be

more suitable for other situations, such as wave refraction and diffraction analyses. The method

of study will depend upon the potential causes of the erosional hot spots.










5.3.1 Historical Shoreline Positions

This criterion is aimed at identifying the areas that historically present more erosion than

others. To achieve this, the erosive trend of the shoreline encompassed between DNR

monuments R-175 and R-189 has been previously described in Section 3.2.1.

Throughout the project area, an overall advance of the shoreline has been identified since

1884 until the early 1960's. It is during this decade when a large erosive trend has affected

Delray Beach, mainly as a result of inlet management on the east coast of Florida (Dean, 1988).

From 1962 to 1970, the beach had an average shoreline change of 1.86 m/year. After this year

the shoreline was stabilized by hard coastal structures, which were still not enough to withstand

the encroaching sea. From R-175 to R-180 the erosive rates were larger than the average,

including the worst case at R-176 with 3.7 m/year. From R-181 through the downdrift end of the

project, the shoreline retreat was below the average with the lowest shoreline retreat at R-186

(0.65 m/year).

From the historical shoreline positions, it can be observed that, should any erosional hot

spot existed at Delray Beach prior to the nourishments, that would be within the first third of the

project, where the largest erosion rates were found. However, it is only during an eight-year

interval, when the erosive trend is found, and it has been identified as a natural adjustment due to

inlet management Prior to this decade, it is an accreting process which dominates the shoreline

changes. It is concluded, therefore, that there is no evident highly erosive trend, within the

project area that would lead to an erosional hot spot.



5.3.2 Sediment Size Distribution Along the Project

As described in the literature review, having different sediment sizes along the project,

causes the beach to equilibrate differently. For the second renourishment, there is a larger mean

grain size on the updrift side, however, the rest of the project suggest a fairly even distribution of

the grain size, thus, not suggesting any large fluctuations that may cause large differences in the










shoreline changes. At R-177, on the updrift side of the project, a larger sediment size was found

compared to the rest of the project. This may be an indicator of why the beach presented a

higher erosion rate between R-180 and R-188, causing the authorities to decide to restore only

this segment in the third renourishment. The sediment size variation is depicted in Figures 4.7

and 4.8.

The last renourishment took place only from R-180 to R-188. Since 1992, the mean

grain size has proven to be finer at the downdrift side of the project, which is a potential factor

that may cause an erosional hot spot, due to the narrower beach width associated with finer grain

sizes. In order to determine the existence of an erosional hot spot, it is necessary to apply the

performance predictions included in this chapter.



5.3.3 Standard Deviation Reference Value

To establish a criterion to determine the presence of an erosional hot spot, the standard

deviation is used. The method considers that those areas with higher deviations from the

standard are erosional hot spots or cold spots.

However, this method will always include areas with larger deviations than the standard,

even if the predictions are within an allowable range. For example, if the difference between

predicted and measured changes followed the normal probability distribution, only 68.3% of the

points are considered to be within one standard deviation, leading to a 31.7% of the remaining

area, as erosional hot spots and cold spots, even if the project had performed well.

To account for this, an erosional hot spot will be considered where an area with larger

deviations than the standard exists over a substantial longshore length, and it will not be

considered a hot spot, where only a spike or peak exceeds the standard deviation.

Since an erosional hot spot has been defined as an area that does not perform as predicted

by theory, the standard deviation to be considered must be that of the differences between

measured and predicted quantities.










The differences between predicted and measured changes with K = 1.10 and deep water

waves perpendicular to the shoreline, are depicted in Figures 5.13 and 5.14. On these figures,

erosional hot spots and cold spots have also been identified. In order to identify these spots it is

necessary to correlate shoreline and volumetric profile changes, as both are indicators of the

performance of the beach.

Figure 5.13 depicts the differences previously shown between predicted and measured

quantities for the 1975-1990 period. The shoreline change differences shown in Figure 5.13a

portray two cold spots and one erosional hot spot. The hot spot found around R-186, has the

same location as one of the hot spots identified from the volume differences (Figure 5.13b). The

other hot spot identified by the volumetric changes, encompasses monuments R-180 and R-181,

but there is no evidence whatsoever, that an erosional hot spot can be identified at the same

location using shoreline changes (Figure 5.13a). It is at this location where Gravens (1997) has

identified the presence of an erosional hot spot, probably due to a sewage outfall and a 300-m-

wide no-dredging zone. However, the time span used by Gravens is from 1987 to 1992. Both

shoreline and volume changes identify an erosional cold spot at R-178.

The 1975-1998 span is illustrated in Figure 5.14. Both plots included in this figure,

clearly locate an erosional hot spot at the downdrift end of the project. It is remarkable that, for

the shoreline changes, the entire project has a deviation smaller than one standard deviation,

except for what has been identified as an erosional hot spot. Additionally, both shoreline and

volume change differences, have more or less the same areas with accretion or erosion, that is,

both plots identify overprediction within the first third, underprediction within the middle third,

and another underprediction over the last third, the last one, leading to an erosional hot spot.

Finally, the comparison between the two intervals of time, shows that differences in the

1975-1998 are much larger than the other. The hot spots found for the 1975-1990 span, reach up

to 2a, while for 1975-1998, the hot spot at R-186 almost extents to 3a.








78




Erosional hot spot identification (1975-1990)


Longshore Distance [km]


Erosional hot spot identification (1975-1990)


Longshore Distance [km]


Figure 5.13 Location of erosional hot spots and cold spots for 1975 to 1990, using
a) Shoreline changes differences, and
b) Volume changes differences.
The area shown encompasses the project limits.








79




Erosional hot spot identification (1975-1998)


Longshore Distance [km]


Erosional hot spot identification (1975-1998)


b)


HtR1t




1--1--- -------- ---- -- --.--- 103 16\





-2 5 -2.0 -1 5 -1_0 -C5 00 005 5 20 2
l ^----/ ^-G O -




-103 16 ... .. --- ... .-- .-mf -103 16

A- & -- --- A -- & -- A --- -- 150 ---A -A -- A A --- A -- A ---- A -- A -


Longshore Distance [km]


Figure 5.14 Location of erosional hot spots and cold spots for 1975 to 1998, using
a) Shoreline changes differences, and
b) Volume changes differences.
The area shown encompasses the project limits.










5.3.4 Summary

Figures 5.13 and 5.14 are consistent in identifying the presence of erosional hot spots at

the downdrift end. The potential cause of this highly erosive zone is attributed to the finer sand

located in this area. It is also consistent that the updrift third of the project, where the coarser

sediment was found, presents slower erosive rates than the rest of the fill. It has been mentioned

also, that the nourishment project possibly may act as a natural barrier to the longshore sediment

transport, situation that was not accounted for in the final results. However, this mechanism was

discarded given the relative dimensions of the project, which tends to smooth out with time, and

represents only a short distance seaward compared to a few kilometers over which the project is

extended. The finer sand located in the vicinity of monument T-187, is believed to cause the

erosional hot spot located in this area. Moreover, the location of this hot spot is the same as that

identified from Beachler (1993).

No other large systems of hot spots or cold spots were found. The hot spot described by

Gravens (1997), which is located around R-180 may have disappeared after the 1992

renourishment. The reason is that the location of the hot spot was immediately downdrift of the

fill, where large accretion rates are expected.

Hot spots created by sediment size differentials along the coast, could be the result of

dredge selectivity, as explained in Chapter 2. Stricter controls in dredge operations are suggested

in order to achieve a more uniform grain size along the project. Likewise, another remedial

measure is simply to place enough fill to achieve the equilibrium design, which gives the

contractor more freedom as to where to mine. Therefore, different template sections can be

considered along the project as a function of the grain size. Both remedial measures are likely to

increase the cost of the dredging operation, and therefore, the cost of the beach nourishment;

however, every project should be analyzed carefully to consider the options. Borrow sites where

large variation in the grain size is found, are more likely to produce erosional hot spots due to

dredge selectivity.
















CHAPTER 6
SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS



6.1 Summary

A numerical model for beach planform evolution was used to compute shoreline changes

and volumetric profile changes. This methodology is similar to a one-dimensional model based

on the linearization of the equations of sediment transport and continuity, first introduced by

Pelnard-Considere (1956). The result is transformed into the heat-conduction equation (see

Appendix A). In addition, the model accounts for renourishments throughout the life of the

project.

The hydrodynamic conditions were represented by effective parameters. Initial volumes

were considered distributed along the project in accordance with their actual placement, and the

sediment size representative of the project was taken as the mean grain size. This mean sediment

size proved to be converging to a value near the average between the borrow zone and the native

beach, and was taken as 0.33 mm, although, given the variability of this parameter, other

diameters were evaluated. This experimentation allowed conclusions to be developed towards this

essential characteristic of the beach. According to Dean et al. (1998) this area presents negligible

background erosion.

Two time intervals were considered, the first being from 1975 to 1990, and the second

from 1975 to 1998. This permitted separation of the effects of the last renourishment to analyze

the behavior of the fill prior to this nourishment. Shoreline and volumetric profile changes were

computed and compared to the actual measured conditions. Finally, a criterion based on the










standard deviation of the difference between measured and predicted conditions was established

to identify areas with accentuated erosion or accretion.



6.2 Conclusions

Erosional hot spots and cold spots were identified within the Delray Beach limits, with

different degrees of erosion or accretion according to the time spans examined. Even though the

1975-1990 time span proved to be better simulated with the numerical modeling, it shows at least

three areas in which the actual trends present large deviation from the predicted values. The

standard deviation computed from the differences between measured and predicted values, was

smaller in the case of 1975-1990, which means better prediction, thus better performance of the

project. For this interval, the shoreline changes identify two cold spots and one hot spot, while

volume changes identify two hot spots and one cold spot. The location of the updrift cold spot

and the downdrift hot spot coincide in the locations obtained from both analyses. Moreover, the

location of this hot spot, agrees with the results provided by Beachler (1993), around DNR

monument No. R-186. The hot spot identified around R-181, does not show any signs of

reappearance after the 1992 renourishment, perhaps, because high accretion rates are expected in

this region (immediately outside of the fill).

From the 1975-1998 analysis, both shoreline and volume changes were predicted with

good accuracy from R-175 through R-185. Almost all the points exceeding the value of the

standard deviation occupy the area from R-186 to the downdrift end of the project. This has been

identified as an erosional hot spot, given the fact that it has been repeatedly found as such in

several analyses and other studies, and has not been mitigated. The reason, although not obvious,

appears to be the smaller sediment size found within these limits. Since DNRBSM does not

account for sediment size differentials along the beach, any area with a large variation of the

sediment size would not be predicted accurately.










Therefore, two time spans have been examined. Nonetheless, further considerations

towards the time scales can be determined as needed, since they could become a factor in

identifying highly erosive areas. For instance, in his study, Gravens (1997) used a different period

than those analyzed herein, and found an erosional hot spot in the middle portion of the project.

Other coastal features such as beach cusps are not considered as erosional hot spots.

The DNRBSM model, however, has been applied successfully in the prediction of the

shoreline positions. It is also important to mention that shoreline retreat due to equilibration of the

cross-shore section is not accounted for. The reliability of this program can be increased if

different sediment sizes can be represented. Nonetheless, the model has proved successful in

predicting both shoreline and volumetric changes with acceptable accuracy. A numerical model

that could account for cross-shore changes at the same time, can also increase its accuracy. It is

still shown that shoreline and volume changes are difficult to predict in fine detail, thus additional

criteria have to be applied to interpret the results.

The influence of the sediment transport parameter is readily observed from the analysis

performed in Chapter 5. Varying the sediment transport parameter for different sizes, predictions

appeared to be better. This could mean that even though the diameter of the sediment is 0.33 mm,

the actual sediment transport parameter could differ from 1.10, the value that corresponds to the

relationship proposed by Dean (1989). However, it is suggested that consideration of the

sediment size (and the sediment transport parameter) should be computed differently than the

simple average of the mean grain sizes found. It would be necessary then to apply some statistical

method to account for more representative conditions. The overall performance of the project has

been described as upm/,p = 0.3 for shoreline changes and pm/qp = 0.33 for volume changes,

which are reasonable values. Likewise, the values of opm/m for shoreline and volumetric profile

changes were 0.25 and 0.28, respectively, with K = 1.10 and a perpendicular incoming waves.










6.3 Recommendations

Improvements to the numerical model can be performed to achieve a finer detail of

prediction. Sand variability is among the most important parameters that are needed in order to

better predict shoreline and volume changes, according to the results obtained from this thesis.

Cross-shore motion of sediments is also important in order to account for equilibration after

project completion. In order to predict erosional hot spots, it would be necessary to develop a

large and rich set of data, and perhaps a somewhat complex model, able to put together all the

variables that will define the shoreline performance. All these requirements imply a much more

expensive approach to the project, but a much precise one. DNRBSM provides with a reasonable

level of accuracy.

Further research is also necessary in order to understand the potential causes creating hot

(and cold) spots, including the consequences of different placement techniques, and sediment size

variations along the beach. Application of refraction and diffraction models are also suggested for

the case of Delray Beach.
















APPENDIX A
MODEL FOR BEACH PLANFORM EVOLUTION



Introduction

A beach nourishment project represents an alongshore and cross-shore perturbation,

which is equilibrated by waves and currents. While the shoreline retreats due to equilibration of

the profile and the possible formation of a bar system, sand is also eroded away from the fill area

"flattening out" this anomaly due to longshore sediment transport. Realistic prediction of the

shoreline evolution should include longshore and cross-shore transport, however, cross-shore

motion is still less predictable and, oftentimes, considered the less dominant from the two

transport directions. (Such assumptions are applied in this thesis for the analysis of the

performance of the Delray Beach restoration project.) Therefore, it is valid to apply numerical

methods to predict only the spreading out losses of beach nourishment projects, thereby providing

a valuable estimate of the overall performance.



Background

The numerical procedure applied throughout this thesis was developed by Dean and

Grant (1989) and is called DNRBS. The version applied in this thesis accounts for multiple

nourishments, and was named DNRBSM. It consists of a one-dimensional model in which the

shoreline position is computed. This type of model is the simplest approach to describe a beach

nourishment planform evolution, and requires that the profile form is unchanged as the spreading

out losses occur. A three-dimensional model would be required to account for profile changes to

cross-shore transport.









Governing Equations

The bases for predicting beach nourishment project changes are the equations of

longshore sediment transport and continuity. The three-dimension continuity equation is

ah aq, aq,
= (A-l)
at ax ay

in which h is the water depth relative to a fixed datum, t is time, and qx and qy are the sediment

transport components in the longshore and cross-shore directions, respectively. Since the

proposed method calculates only transport in the longshore direction, qy = 0. The integration of

Equation A-i with respect to y, yields

-- Yhdy= y qdy (A-2)
at JYl ax JfY

in which y, and Y2 are a landward location and a seaward location, respectively, in which the

cross-shore transport is zero. These locations are considered to be the top of dune of height B,

and the depth of limiting motion, h.. In addition, volumes are computed per unit width of beach.

The integral on the left hand side of the equation represents the total volume in the system, V, or

volume of the water column. Therefore, -a V/lt can be regarded as the time rate of change of

volume of sand instead of water. The integral on the right hand side is the total longshore

sediment transport Q. The continuity or conservation of sand equation then becomes

+ = 0 (A-3)
at ax

It has been noted that the beach profile is considered constant with respect with time,

assuming that a seaward or landward displacement is associated with accretion or erosion,

respectively. This shoreline displacement, Ay, associated with a volume change, AVis

1
Ay =- AV (A-4)
h.+B









Substituting Equation A-4 into A-3 yields the one-dimensional equation for conservation

of sand

ay 1 aQ
+ = 0 (A-5)
at h. +B ax

The longshore sediment transport equation is an empirically based energy flux model.

The final form of this equation is

KH/2 / sin(1 -aj )cos(3 -ab (
Q = S--1 (A-6)
8(s 1X p)

in which K is the longshore sediment transport parameter, Hb is the wave height, g is time, K is

the ratio of breaking wave height to water depth (usually assumed as 0.78), P is the azimuth of the

outward normal to the shoreline, ab is the azimuth of the direction from which the breaking

waves originate, s is the specific gravity of the sediment (approximately 2.65), and p is the

porosity of the sand (usually taken as 0.35). (P-ab) is the angle between the wave crest and the

shoreline at breaking conditions.

The longshore sediment transport equation (A-6) can be linearized and then combined

with the one-dimensional conservation of sand equation (A-5), to yield the classical heat-

conduction equation proposed by Pelnard-Considere (1956)


= G (A-7)
at ax2

in which G is the longshore diffusivity coefficient, and is defined as

KH/ 2g/K
G = b-(A-8)
8(s-1X1-pXh. +B)

Equation A-7 describes the planform evolution of a beach nourishment and different

boundary conditions, like those for uninterrupted shorelines or littoral barriers, can be simulated.

In order to predict with good accuracy the shoreline position it is necessary to include

long-term background erosion, ayB/lt. To incorporate this into the numerical solution,









background erosion rates are translated into background transport rates, as shown by the

following equation


QB(x) =QB(xo)-(h. + B)f dx (A-9)
o dt

in which xo is a reference shoreline location at which a reference transport QB(xo) is specified.

QB(x), is the total sediment transport along the beach including the associated background

erosion.

If the bathymetric contours are regarded as straight and parallel, it is possibly to apply

simplified wave refraction and shoaling to express the transport in terms of deep water

conditions. Applying Snell's Law and foregoing the algebra, the sediment transport is computed

by

KH24 06 02 COS 2 S
Q g co=s sin 0 (A-10)
8(S --1X --)214 04 2K4

in which the subscript 'o' denotes deep water conditions. If Equation A-10 is also linearized in

the form of Equation A-7, the appropriate value of the longshore diffusivity coefficient, G,

defined in deep water wave conditions is

KH4T 02g06 I s12 (o -ao)cos2( o -a.)
8(s -1-pv)214 0204 (h. +B) cos(o -a (.)

in which the subscript '.' denotes conditions at the depth of limiting motion.

The finite-difference solution applied here, requires the following relationship to be

achieved, which, if exceeded, will cause numerical instability


Atm =- (A-12)
2 G

in which Ax is the alongshore grid spacing. This expression shows that the smaller the grid

spacing and the larger the wave height, the smaller the allowable time step.




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