• TABLE OF CONTENTS
HIDE
 Front Cover
 Title Page
 Table of Contents
 List of Figures
 List of Tables
 Introduction
 Objectives
 Analysis and results
 Summary and interpretation
 Conclusions and recommendation...
 References
 Appendix A






Group Title: UFL/COEL (University of Florida. Coastal and Oceanographic Engineering Laboratory) ; 94/013
Title: Equilibrium beach profiles
CITATION THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00085004/00001
 Material Information
Title: Equilibrium beach profiles concepts and evaluation
Series Title: UFLCOEL-94013
Physical Description: v, 22, 14 leaves : ill. ; 28 cm.
Language: English
Creator: Dean, Robert G ( Robert George ), 1930-
Charles, Lynda L., 1962-
Florida Sea Grant College
University of Florida -- Coastal and Oceanographic Engineering Dept
Publisher: Dept. of Coastal and Oceanographic Engineering, University of Florida
Place of Publication: Gainesville Fla
Publication Date: 1994
 Subjects
Subject: Coast changes -- Mathematical models   ( lcsh )
Beach erosion -- Mathematical models   ( lcsh )
Beach nourishment -- Mathematical models   ( lcsh )
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Bibliography: Includes bibliographical references (leaves 20-22).
Statement of Responsibility: prepared for Florida Sea Grant College Program, University of Florida ; prepared by Robert G. Dean, Lynda Charles.
General Note: "August 30, 1994."
Funding: This publication is being made available as part of the report series written by the faculty, staff, and students of the Coastal and Oceanographic Program of the Department of Civil and Coastal Engineering.
 Record Information
Bibliographic ID: UF00085004
Volume ID: VID00001
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 31795612

Table of Contents
    Front Cover
        Front Cover
    Title Page
        Page i
    Table of Contents
        Page ii
    List of Figures
        Page iii
        Page iv
    List of Tables
        Page v
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
    Objectives
        Page 7
        Page 6
    Analysis and results
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
    Summary and interpretation
        Page 18
        Page 19
        Page 17
    Conclusions and recommendations
        Page 20
        Page 19
    References
        Page 20
        Page 21
        Page 22
    Appendix A
        Appendix A
        A - 1
        A - 2
        A - 3
        A - 4
        A - 5
        A - 6
        A - 7
        A - 8
        A - 9
        A - 10
        A - 11
        A - 12
        A - 13
        A - 14
Full Text



UFL/COEL-94/013


EQUILIBRIUM BEACH PROFILES:
CONCEPTS AND EVALUATION





by




Robert G. Dean
Lynda Charles


August 30, 1994



Prepared for:
Florida Sea Grant College Program
University of Florida
Gainesville, FL 32611









UFL/COEL-94/013


EQUILIBRIUM BEACH PROFILES:
CONCEPTS AND EVALUATION








August 30, 1994





Prepared for:

Florida Sea Grant College Program
University of Florida
Gainesville, Florida








Prepared by:

Robert G. Dean
Lynda Charles









Department of Coastal and Oceanographic Engineering
University of Florida
Gainesville, Florida











TABLE OF CONTENTS


LIST OF FIGURES . . ... . ..

LIST OF TABLES . . .

INTRODUCTION . . ... . .

BACKGROUND . . .

OBJECTIVES . . . .

FIELD PROCEDURES . ... . .

ANALYSIS AND RESULTS . . .

Variation of Beach Slope With Sediment Size .

Comparisons of Measured and Predicted Profiles

SUMMARY AND INTERPRETATION . . ....

CONCLUSIONS AND RECOMMENDATIONS . . .

ACKNOWLEDGEMENTS . .. . .

REFERENCES . . . .


..... 1 iii




* . 1

* . 1

* . 7





. . 7

. . 11



* 17
. . 19
......7 20

.....7




17

. . 17

20


. 20


APPENDIX


GRAPHICAL PRESENTATIONS OF FLORIDA EAST COAST AND
COUNTY BY COUNTY CROSS-SHORE DISTRIBUTIONS OF
SEDIMENT AND PROFILE CHARACTERISTICS .. A-1


* .









LIST OF FIGURES


FIGURE PAGE

1 Variation of Sediment Scale Parameter, A, With Sediment
Size, D, and Fall Velocity, wf. From Dean (1987) . 4

2 Numbers of DNR Monuments Along Florida's Predominantly
Sandy Shoreline Counties . . ... . ... 8

3 Variation of Average Profile Slope with Average
Median Diameter, Both to Approximately 2 m Depth.
Comparison of County Averages (Points) and Equilibrium
Beach Profile Theory (Line) . . . .. 10

4 Blindfolded Comparison of Average Measured and Predicted
Profiles. Based on Moore's Relationship. All Twelve
Florida East Coast Counties . . .. 12

5 Blindfolded Comparison of Average and Predicted Profiles.
Based on Kriebel et al. (1991) Relationship. All Twelve
Florida East Coast Counties . . ... .15

6 Comparison of Average Measured and Computed Profiles.
Based on A = 0.1 m1/3. All Twelve Florida East Coast
Counties . . . . ... ... 16

A-i All Counties. a) Cross-Shore Distribution of Average
Median Sediment Size. b) Blindfolded Comparison of
Average Calculated and Measured Beach Profiles. Values
in Parentheses in Upper Panel Denote Number of Profiles
Contributing to Average . . . A-2

A-2 Nassau County. a) Cross-Shore Distribution of Average
Median Sediment Size. b) Blindfolded Comparison of
Average Calculated and Measured Beach Profiles. Values
in Parentheses in Upper Panel Denote Number of Profiles
Contributing to Average . . .... .. A-3

A-3 Duval County. a) Cross-Shore Distribution of Average
Median Sediment Size. b) Blindfolded Comparison of
Average Calculated and Measured Beach Profiles. Values
in Parentheses in Upper Panel Denote Number of Profiles
Contributing to Average . . . . A-4

A-4 St. Johns County. a) Cross-Shore Distribution of Average
Median Sediment Size. b) Blindfolded Comparison of
Average Calculated and Measured Beach Profiles. Values
in Parentheses in Upper Panel Denote Number of Profiles
Contributing to Average . . . A-5


iii









A-5 Flagler County. a) Cross-Shore Distribution of Average
Median Sediment Size. b) Blindfolded Comparison of
Average Calculated and Measured Beach Profiles. Values
in Parentheses in Upper Panel Denote Number of Profiles
Contributing to Average . . . . A-6

A-6 Volusia County. a) Cross-Shore Distribution of Average
Median Sediment Size. b) Blindfolded Comparison of
Average Calculated and Measured Beach Profiles. Values
in Parentheses in Upper Panel Denote Number of Profiles
Contributing to Average . . .. .. A-7

A-7 Brevard County. a) Cross-Shore Distribution of Average
Median Sediment Size. b) Blindfolded Comparison of
Average Calculated and Measured Beach Profiles. Values
in Parentheses in Upper Panel Denote Number of Profiles
Contributing to Average . . . ... .A-8

A-8 Indian River County. a) Cross-Shore Distribution of
Average Median Sediment Size. b) Blindfolded Comparison
of Average Calculated and Measured Beach Profiles.
Values in Parentheses in Upper Panel Denote Number of
Profiles Contributing to Average . . ... A-9

A-9 St. Lucie County. a) Cross-Shore Distribution of
Average Median Sediment Size. b) Blindfolded Comparison
of Average Calculated and Measured Beach Profiles.
Values in Parentheses in Upper Panel Denote Number of
Profiles Contributing to Average . . ... A-10

A-10 Martin County. a) Cross-Shore Distribution of Average
Median Sediment Size. b) Blindfolded Comparison of
Average Calculated and Measured Beach Profiles. Values
in Parentheses in Upper Panel Denote Number of Profiles
Contributing to Average . . ... A-11

A-11 Palm Beach County. a) Cross-Shore Distribution of
Average Median Sediment Size. b) Blindfolded Comparison
of Average Calculated and Measured Beach Profiles.
Values in Parentheses in Upper Panel Denote Number of
Profiles Contributing to Average . . A-12

A-12 Broward County. a) Cross-Shore Distribution of Average
Median Sediment Size. b) Blindfolded Comparison of
Average Calculated and Measured Beach Profiles. Values
in Parentheses in Upper Panel Denote Number of Profiles
Contributing to Average .. . . .. A-13

A-13 Dade County. a) Cross-Shore Distribution of Average
Median Sediment Size. b) Blindfolded Comparison of
Average Calculated and Measured Beach Profiles. Values
in Parentheses in Upper Panel Denote Number of Profiles
Contributing to Average . . .. A-14









LIST OF TABLES


TABLE PAGE

1 Summary of Recommended Sediment Scale Parameter (A)
Values (From Dean, 1994) . . . . 5

2 Summary of Data Characteristics . . . 9

3 Comparison of Measured and Computed Depths . .. 14

4 Standard Deviations for Various Depths and Sediment
Scale Parameter, A, Relationships . ... .18









EQUILIBRIUM BEACH PROFILES:
CONCEPTS AND EVALUATION

INTRODUCTION

Equilibrium beach profile (EBP) methodology is useful for a
variety of engineering applications, including beach nourishment
with materials different than the native and incorporation as an
element of some cross-shore sediment transport models. EBP's are
also an essential stepping stone to the understanding of the
behavior of profile dynamics. Sediment particles forming all
profiles are acted on by a number of forces, some of which act
seaward and others act landward. By definition, for EBP's, these
forces are in balance. An equilibrium beach profile might be
considered as one which would occur if the forcing (dominantly
waves and water levels) were held constant for a sufficiently long
time for the sediment transport resulting from the force imbalance
to mold the profile to one in which the forces are in balance. In
nature, profiles may never achieve equilibrium under the constantly
changing tides and waves, a complicating factor in studies of this
type. In some locations, the average seasonal shoreline
fluctuations may amount to more than 30 meters, however, in
Florida, these fluctuations are generally less than 10 m. The time
scales associated with the equilibration process vary with water
depth, being shorter in the more dynamic environment of the shallow
nearshore waters and much longer where waves may break on the order
of once annually or so. These characteristics raise questions as to
whether or not studies of natural profiles can contribute to the
understanding of the subject of equilibrium beach profiles.
Attempts to predict the quantitative characteristics of equilibrium
beach profiles based on sediment characteristics are fairly recent
and there have been no comprehensive studies to evaluate existing
methodology and, if necessary, to carry out the necessary
refinements. This study was conducted to address this question.

BACKGROUND

EBP's have been a subject of considerable interest to Coastal
Engineers and Marine Geologists for many years. Several features of
EBP's are known based on observations: (1) They tend to be concave
upward, (2) Their slopes are greater for coarser materials, and (3)
Higher waves result in milder slopes.

Keulegan and Krumbein (1919) investigated the characteristics
of mild bottom slopes such that the waves never break but rather
are continually dissipated by energy loss due to bottom friction.
Bruun (1954) examined a number of beach profiles from the Danish
North Sea and Monterey Bay, California and concluded that they
could be represented reasonably well by the simple relationship









h=Ay2/3 (1)

in which h is the depth at a distance y from the shoreline, and A
is a sediment scale parameter. Eagleson, Glenne and Dracup (1963)
developed a complex characterization of the wave and gravity forces
acting on a particle located outside the zone of "appreciable
breaker influence" and developed expressions for the seaward limit
of motion and for the beach slope for which a sand particle would
be in equilibrium.

Swart (1974) carried out a series of wave tank tests and
developed empirical relationships relating profile geometry and
transport characteristics to the wave and sediment conditions. The
active profile was considered as four zones and empirical
expressions were developed for each zone. Vellinga (1983)
investigated dune erosion using wave tank tests and developed the
following "erosion profile" which included the effect of deep water
significant wave height, Hos, and sediment fall velocity, wf,

( 6) h=0.47 [( .6)1.28 ( f )0.56y+18]0.5-2.0 (2)
H 0, H,, 0.0268


in which all of the values are expressed in the metric system. It
can be shown that Eqs. (1) and (2) are in reasonable agreement for
wave heights on the order of 1 m; however, for large wave heights,
increased slopes are predicted by Eq. (2) for water depths inside
the breaking zone which is contrary to nature.

Two of the disadvantages of Eq. (1) are that the slope of the
profile at the shoreline is infinite and the scale parameter, A, is
not non-dimensional but rather has dimensions of length to the one-
third power. Dean (1977) considered EBP's to be the result of
(unknown) constructive forces and several candidate destructive
forces: (1) Wave energy dissipation per unit volume, (2) Wave
energy dissipation per unit surface area and (3) Uniform bottom
shear stress due to oblique waves. It was found that for all three
destructive forces, the EBP could be represented by an equation of
the form
h=Aym (3)

in which the exponent m was found to be 2/3 for the case of wave
energy dissipation per unit volume and 2/5 for the other two
destructive forces. Dean (1977) examined over 500 profiles
collected by Hayden et al. (1975) extending from the eastern end of
Long Island, NY south around the Florida peninsula to the
Texas/Mexico Border. Best least squares fits were carried out for
these profiles for the scale parameter, A, and the exponent, m. A
histogram of the 500+ m values showed a reasonably wide range with
a clear peak at a value of 2/3, In an attempt to provide a basis
for extending Eq. (1) in a prognostic manner, Moore (1982) examined








a number of beach profiles from nature and laboratory conditions
and expressed the values of the sediment scale parameter, A, as a
function of sediment size, D. This is shown in a slightly modified
form (by Dean, 1987) in Figure 1. Dean has shown that if the A
versus D relationship is transformed to an A versus fall velocity
relationship, the result is
A=0.067wf44 (4)

thereby potentially allowing calculation of profiles composed of
other shapes than are typical for sands, for example, shell.
Because the material comprising most beaches lies within a fairly
narrow size range, say 0.1 mm to 1.0 mm, and because of the
difficulty of reading this range from Figure 1, Dean (1994) has
developed the tabulation presented in Table 1 which ranges from a
sediment size, D, of 0.1 mm to 1.09 mm. As noted in the footnote to
the table, although the tabulated values are presented to four
significant figures in some cases, this does not imply that the
values are known to this accuracy, but merely ensures that two
individuals carrying out calculations involving EBP's would obtain
the same results. Figure 1 will be referred to as "Moore's curve".

To remove the infinite slope at the shoreline inherent in
Eq. (1), Dean (1991) has shown that consideration of gravity as a
destructive force yields

y h +h (5)
m A312

which can be shown to approximate a linear slope, m, in shallow
water and Eq. (1) in deep water. Larson (1988) and Larson and Kraus
(1989,1990) have shown that Eq. (5) can also be obtained
alternatively by considering the more complete breaking wave model
of Dally et al. (1985). Exponential EBP's having the following form
have been proposed by Bodge (1992) and Komar and McDougal (1993).
h = ho(l-e-ky) (6)

Neither Bodge nor Komar and McDougal present a basis for applying
their EBP's in design.

Inman et al. (1993) analyzed 23 historical profiles from the
San Diego region and have recommended a form for equilibrium beach
profiles that consists of two independent segments (for the inner
and outer portions of the profile), each fit by the form of Eq.
(3), generalized as
h-ho = A(y-yo)m (7)

The inner segment is allowed a vertical offset relative to mean sea
level (thus avoiding the infinite slope at the waterline) and the
outer segment is allowed a horizontal offset. Fits to each profile
required determination of 7 parameters. It was found that this














SEDIMENT FALL VELOCITY, wf (cm/s)

1.0 10.0


Suggested Empirica
Relationship A vs D
From Hughes'
Field Results
From Individual Field
Profiles where a Range of
Sand Sizes was Given
I S v/}


From Swar's
Laboratory Results


1.r0









0.10


I I_


31


(Moore)
(Moore)


.7


Based on Transforming
A vs D Curve using
Fall Velocity Relationship


10.0


100.0


A = 0.067 w10.44


100.0


SEDIMENT SIZE D (mm)


Figure 1. Variation of Sediment Scale Parameter, A, With Sediment Size, D, and Fall velocity, w,. From Dean (1987).


1


0


0.01
0.i


-


I


t















Table 1
Summary of Recommended Sediment Scale Parameter (A) Values
(From Dean, 1994)


D(mm) 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.1 0.063 0.0672 0.0714 0.0756 0.0798 0.084 0.0872 0.0904 0.0936 0.0968

0.2 0.100 0.103 0.106 0.109 0.112 0.115 0.117 0.119 0.121 0.123
0.3 0.125 0.127 0.129 0.131 0.133 0.135 0.137 0.139 0.141 0.143
0.4 0.145 0.1466 0.1482 0.1498 0.1514 0.153 0.1546 0.1562 0.1578 0.1594
0.5 0.161 0.1622 0.1634 0.1646 0.1658 0.167 0.1682 0.1694 0.1706 0.1718

0.6 0.173 0.1742 0.1754 0.1766 0.1778 0.179 0.1802 0.1814 0.1826 0.1838

0.7 0.185 0.1859 0.1868 0.1877 0.1886 0.1895 0.1904 0.1913 0.1922 0.1931

0.8 0.194 0.1948 0.1956 0.1964 0.1972 0.198 0.1988 0.1996 0.2004 0.2012
0.9 0.202 0.2028 0.2036 0.2044 0.2052 0.206 0.2068 0.2076 0.2084 0.2092
1.0 0.210 0.2108 0.2116 0.2124 0.2132 0.2140 0.2148 0.2156 0.2164 0.2172

Notes:
(1) The A values above, some to four places, are not intended to suggest that they are known to that accuracy, but rather are presented for consistency
and sensitivity tests of the effects of variation in grain size.
(2) As an example of use of the values in the table, the A value for a median sand size of 0.24 mm is: A = 0.112 ml3. To convert A values to feet
units, multiply by 1.5.









method provided a significantly improved fit over the EBP form
being tested here in which only one free parameter existed. No
basis was presented for applying this method to engineering
problems or to test it in a "blindfolded" manner.

Most applications and evaluations of the EBP concepts have
been conducted considering a single sediment size across the
profile. Exceptions include Larson (1991), Work and Dean (1991) and
Dean, et al (1993) who carried out evaluations of the equilibrium
beach profile theory considering variations of sediment size over
the profile. Larson, noting the sediment sorting that occurs over
most profiles, developed an analytical form of the wave energy
dissipation per unit volume that varied exponentially across the
profile. Additionally, he fit a form of the profile with a uniform
A value and allowed for a shift in the shoreline position. It was
found, based on fits to profiles at three locations, that the
exponential relationship provided the best fit. Although these
evaluations were based on best fit approaches rather than
blindfolded, Larson did comment on the relationship between the
best fit values and those based on the Moore relationship. It was
found in two cases that the agreement was reasonable and that
significant differences existed in the third case. Work and Dean
(1991) carried out both blindfolded and best fit tests for profiles
at four locations. It was found that the blindfolded tests agreed
reasonably well with the measured profiles out to depths of
approximately 1.5 to 6 m in three of the cases, but underpredicted
the depth by a factor of approximately two in the fourth case. Dean
et al. (1993) carried out blindfolded comparisons for ten profiles
on the north island of New Zealand. In this study, the A vs D
relationship of Moore (1982) was used with the EBP form that
includes a finite slope at the water line (Eq. 5). Thus, although
these comparisons were not entirely consistent as the Moore
relationship was determined based on the EBP relationship without
the slope term, it was found that reasonably good agreement was
obtained in nine of the ten cases for which blindfolded comparisons
were carried out. It was shown that the blindfolded profiles agreed
better with the measured profiles than the average of the measured
profiles.

Finally, EBP approaches presented and evaluated here are not
meant to apply to three dimensional situations or extraneous
influences such as near inlets where other agents are operative or
where rock outcrops and reefs are present.

OBJECTIVES

The general objectives of the present study were, through
comprehensive field data collection and analysis efforts, to
evaluate existing EBP methodology and, as appropriate, to develop
improvements. Specifically, the intent was to compare some of the
basic tenets of the EBP theory, one of which is that the beach
profile slope depends on the sediment size. Secondly, calculated
profiles based on the cross-shore distribution of sediment sizes








and existing EBP theory (Eq. 1 and Moore's curve) will be compared
with the measured and the applicability of the theory will be
evaluated. Based on the results of this comparison, the theory may
be modified as appropriate. Finally, potentially productive
approaches for future efforts will be identified.

FIELD PROCEDURES

The field data utilized here were collected along the twelve
sandy beach counties of the east coast of Florida ranging from
Nassau County on the north through Dade County to the south. The
data were collected along selected Department of Natural Resources
(DNR), now the Department of Environmental Protection (DEP) profile
lines which are spaced nominally at 1000 feet (approximately 328
meters). DNR surveyed every third profile to a nominal depth of 30
feet (9 meters) whereas the intermediate profiles were measured to
wading depths (less than 2 meters). Figure 2 presents the twenty
four CCCL Counties, twelve along each of the east and west coast
counties. The numbers adjacent to each county indicates the number
of profiles within that county. Our sediment and other data were
collected along the "long" DNR lines and where possible, at every
ninth profile resulting in an approximate spacing of 9000 feet (2.7
km). In some counties this objective was not achieved due to
restricted beach access or other reasons. An attempt was made to
collect 10 sediment samples across the profile at the following
nominal depths: 1 m, 2 m, 4 m, 6 m, 8 m and 9 m depths.

In total, data from 165 profiles and 986 sediment samples were
collected and will form the basis of the analysis to be presented
in this report. The numbers of profiles and sediment samples for
each east coast county are presented in Table 2.

ANALYSIS AND RESULTS

Variation of Beach Slope With Sediment Size

One of the basic tenets of EBP methodology is that the
equilibrium beach slope increases with sediment size as reflected
in Figure 1 and Table 1. To evaluate this concept, the average
profiles for each county were averaged and the average slope out to
the approximate 2 m contour was calculated and compared with the
average sediment size out to the same contour. The points,
representing county averages in Figure 3 show a clear but somewhat
scattered relationship between average beach slope and average
sediment size.

Based on Figure 3, it is concluded that there is a correlation
between sediment size and profile slope. To test the relationships
in Figure 1 and Table 1, the average slope associated with a
particular sediment size, D (or equivalently A), was determined
from Eq. 1 as









method provided a significantly improved fit over the EBP form
being tested here in which only one free parameter existed. No
basis was presented for applying this method to engineering
problems or to test it in a "blindfolded" manner.

Most applications and evaluations of the EBP concepts have
been conducted considering a single sediment size across the
profile. Exceptions include Larson (1991), Work and Dean (1991) and
Dean, et al (1993) who carried out evaluations of the equilibrium
beach profile theory considering variations of sediment size over
the profile. Larson, noting the sediment sorting that occurs over
most profiles, developed an analytical form of the wave energy
dissipation per unit volume that varied exponentially across the
profile. Additionally, he fit a form of the profile with a uniform
A value and allowed for a shift in the shoreline position. It was
found, based on fits to profiles at three locations, that the
exponential relationship provided the best fit. Although these
evaluations were based on best fit approaches rather than
blindfolded, Larson did comment on the relationship between the
best fit values and those based on the Moore relationship. It was
found in two cases that the agreement was reasonable and that
significant differences existed in the third case. Work and Dean
(1991) carried out both blindfolded and best fit tests for profiles
at four locations. It was found that the blindfolded tests agreed
reasonably well with the measured profiles out to depths of
approximately 1.5 to 6 m in three of the cases, but underpredicted
the depth by a factor of approximately two in the fourth case. Dean
et al. (1993) carried out blindfolded comparisons for ten profiles
on the north island of New Zealand. In this study, the A vs D
relationship of Moore (1982) was used with the EBP form that
includes a finite slope at the water line (Eq. 5). Thus, although
these comparisons were not entirely consistent as the Moore
relationship was determined based on the EBP relationship without
the slope term, it was found that reasonably good agreement was
obtained in nine of the ten cases for which blindfolded comparisons
were carried out. It was shown that the blindfolded profiles agreed
better with the measured profiles than the average of the measured
profiles.

Finally, EBP approaches presented and evaluated here are not
meant to apply to three dimensional situations or extraneous
influences such as near inlets where other agents are operative or
where rock outcrops and reefs are present.

OBJECTIVES

The general objectives of the present study were, through
comprehensive field data collection and analysis efforts, to
evaluate existing EBP methodology and, as appropriate, to develop
improvements. Specifically, the intent was to compare some of the
basic tenets of the EBP theory, one of which is that the beach
profile slope depends on the sediment size. Secondly, calculated
profiles based on the cross-shore distribution of sediment sizes








and existing EBP theory (Eq. 1 and Moore's curve) will be compared
with the measured and the applicability of the theory will be
evaluated. Based on the results of this comparison, the theory may
be modified as appropriate. Finally, potentially productive
approaches for future efforts will be identified.

FIELD PROCEDURES

The field data utilized here were collected along the twelve
sandy beach counties of the east coast of Florida ranging from
Nassau County on the north through Dade County to the south. The
data were collected along selected Department of Natural Resources
(DNR), now the Department of Environmental Protection (DEP) profile
lines which are spaced nominally at 1000 feet (approximately 328
meters). DNR surveyed every third profile to a nominal depth of 30
feet (9 meters) whereas the intermediate profiles were measured to
wading depths (less than 2 meters). Figure 2 presents the twenty
four CCCL Counties, twelve along each of the east and west coast
counties. The numbers adjacent to each county indicates the number
of profiles within that county. Our sediment and other data were
collected along the "long" DNR lines and where possible, at every
ninth profile resulting in an approximate spacing of 9000 feet (2.7
km). In some counties this objective was not achieved due to
restricted beach access or other reasons. An attempt was made to
collect 10 sediment samples across the profile at the following
nominal depths: 1 m, 2 m, 4 m, 6 m, 8 m and 9 m depths.

In total, data from 165 profiles and 986 sediment samples were
collected and will form the basis of the analysis to be presented
in this report. The numbers of profiles and sediment samples for
each east coast county are presented in Table 2.

ANALYSIS AND RESULTS

Variation of Beach Slope With Sediment Size

One of the basic tenets of EBP methodology is that the
equilibrium beach slope increases with sediment size as reflected
in Figure 1 and Table 1. To evaluate this concept, the average
profiles for each county were averaged and the average slope out to
the approximate 2 m contour was calculated and compared with the
average sediment size out to the same contour. The points,
representing county averages in Figure 3 show a clear but somewhat
scattered relationship between average beach slope and average
sediment size.

Based on Figure 3, it is concluded that there is a correlation
between sediment size and profile slope. To test the relationships
in Figure 1 and Table 1, the average slope associated with a
particular sediment size, D (or equivalently A), was determined
from Eq. 1 as





















Nassau
\ (82)
Duval
. (80)
St. Johns
(209)
SRagler
(100)
Volusla
N (234)


Franklin
(239)


Brevard
(219)
Indian River


Pinellas
(193)


(67) %. -
Sarasota V- VS(ln
(183) (1
Charlotte Palm Beach
(68) L (227)
(239) Broward
Co (128)
(148) 6.b
Dade
N 0 (113)

















Figure 2. Numbers of DNR Monuments Along Florida's Predominantly Sandy Shoreline
Counties.











TABLE 2

SUMMARY OF DATA CHARACTERISTICS

County Number of Number of
Profiles Sediment Samples

Nassau 7 31
Duval 8 44
St Johns 22 138
Flagler 11 75
Volusia 23 153
Brevard 23 143
Indian River 12 66
St Lucie 13 68
Martin 2 12
Palm Beach 23 159
Broward 13 60
Dade 8 37

Totals 165 986





















0.05




00.04




10.03



.0 1
0.02




0.01




0.00
0.


---- ------ ---- --- ---- -------






------------- ---i
............ ............ .. .. .... .... R e...


.............. ... .. ......... ........... ... .. .. ... .. O..y
............. ............ ............ .-"^ ... ..... ........... ............


............ ............ ....... ....... A )- : ... .. ...... .... .. .........
........ ... ....... .. .......... .. .... .............. .------
............. ............ ......... .... ........ ..... .......... _





................... -- A vs D Relationsp.........
........ ..... ... ... D ata.. O .y ........... ..
........ .... .. ... -.^..,... .. ..... ............ .. . ..


i ... ... ... .......... i

. . . . . .
. . . . . . . . . . . . . . . .


0


0.1 0.2 0.3 0.4 0.5
Average Median Diameter, Dso%, (mm)


0.6


Figure 3. Variation of Average Profile Slope with Average Median Diameter, Both to
Approximately 2 m Depth. Comparison of County Averages (Points) and
Equilibrium Beach Profile Theory (Line).












h A3/2
= (8)
y hu/2

The solid line in Figure 3 presents the results of Eq. (8). It is
seen that the relationship correctly portrays the trend, but may be
somewhat high.

Comparisons of Measured and Predicted Profiles

The most basic evaluation of the existing EBP theory is
founded on a blindfolded comparison of measured and predicted
profiles. The "blindfolded" profiles are those based entirely on
existing relationships and do not entail any curve fitting or any
other subjective elements. For this purpose, the sediment scale
parameter, A, was determined from Table 1 based on the median
sediment size and it was assumed that the A value varied linearly
between adjacent sampling locations. This allowed establishment of
the equilibrium profile between the two points at offshore
distances, y(n) and y(n+l) in accordance with the following
relationship

h(n+l) =[h(n)3/2+ 2 (A(n+1)5/2-A(n)5/2)]2/3 (9)
5BB

in which BB is the slope of the A vs y relationship between the two
points of interest, ie

BB= A(n+l) -A(n) (10)
y(n+l) -y(n)

This process was repeated to the last point in the profile and
various comparisons were carried out between predicted and measured
profiles.

The comparison to be presented first is the average of the 165
measured and predicted profiles as shown in Figure 4. The upper
panel in this figure presents the distribution of the average grain
size across the profile and the numbers in parentheses indicate the
number of profiles that contributed to the sediment size at that
location. The lower panel presents a comparison between the average
measured and calculated profiles. It is emphasized that the
calculated profiles were determined in a "blindfolded" manner, that
is they are based only on knowledge of the measured grain size
distribution across the profile and the EBP methods described
earlier. It is seen from the lower panel of Figure 3 that the
average profiles agree quite well for water depths out to 4 meters,
then deviate for greater depths with the measured depths being
progressively greater than the calculated. The reason/
interpretation for this deviation will be explored later.

The same type of comparisons as presented in Figure 3 was
carried out for the twelve individual counties on the east coat of


















0 100 200 300 400 500 600 700
Offshore Distance (m)

a) Measured Sediment Sizes, D50%, (mm)
Averages for 165 Florida East Coast Profiles







........ i Mar......... ........... .
.........i.---

.......... .......... ....................... .. .... : ....... .. ........ .

-........ M measured ................. ...................
---A.. Calculated


I -I -- I-


0 100


200 300 400 500 600
Offshore Distance (m)


700


b) Comparison of Measured and Predicted Profiles
Averages for 165 Florida East Coast Profiles


Figure 4. Blindfolded Comparison of Average Measured and Predicted Profiles. Based on
Moore's Relationship. All Twelve Florida East Coast Counties.


0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0


I I I I I I
_ :.. .. .. .....: i .. .. ....: : : : : .. : : : : : : :... .... .... : .. .. : ... ...... ... .. .. .. ... ....
. ......... ........: ........... ............. .......... .........
.. .... ..... ...... .-) I .. .. .. .. ...... .
-.. 6 .... ........... ... ... .... ....... ... D 5 0 % .so (M M ) -
i............ .i.. mm (79).

-. 5 .
.61......(165) ...(47).......1.. 8). ... ..


I I I I i .


0






-5






-10









Florida: these comparisons along with a repeat presentation of the
results in Figure 4 are presented in Appendix A as Figures A-1 A-
13 and are discussed as follows. A general result supported by the
comparisons was that the county wide average measured and
calculated profiles agreed reasonably well out to 3 or 4 meters and
then deviated in the manner shown in Figure 4. This finding is
similar to that for the aggregate of all 165 profiles. Table 3
summarizes the average deviation for the twelve counties at
approximate depths of 2 and 4 meters.

A second blindfolded test was carried using a sediment scale
parameter, A, representation proposed by Kriebel, et al (1991)
2
A=2.25( w )1/3 (1)


in which the fall velocity is in m/s and g is the gravitational
constant. This form has the advantage of dimensional consistency.
To apply Eq.(11), the sediment sizes were converted to fall
velocities using a standard empirical relationship (Rouse, 1937)
considering a water temperature of 200 Centigrade. The comparison
between the same 165 measured profile averages with those computed
based on Eq. (11) is presented in Figure 5. It is seen that this
representation fits reasonably well in water depths less than 2 m,
but does not fit as well as Moore's relationship as shown in Figure
4.

An additional evaluation was carried out to determine whether
the "A" value versus D representation should differ from that shown
in Figure 1. Some results from Hughes (1978) suggest that perhaps
the A value is independent of grain size whereas other results from
this author suggest that data from the Brevard County area, vary in
a manner qualitatively consistent with Figure 1. Several tests were
carried out to address this question. The first was to determine
whether a single value of the A parameter could provide as good a
fit as that based on the measured grain sizes. First, the standard
deviations at the various depths were calculated for the
blindfolded calculations. Secondly, the standard deviations were
calculated for various constant values of the A parameters. It was
found that an A value of 0.1 m13 yielded a particularly good fit,
in fact better than that for the blindfolded test (Figure 4)
especially in water depths greater than 4 m. The comparison between
the measured and calculated profiles for the entire Florida east
coast is shown in Figure 6 for a fixed value A = 0.1 mn3.

Based on the results shown in Figures 4 and 6, an attempt was
made to determine whether altered values of the A vs D relationship
would yield an improved blindfolded test. Since a constant A value
of 0.1 m'~ had yielded a high quality fit, several tests with the
values of A were conducted












TABLE 3


COMPARISON OF MEASURED AND COMPUTED DEPTHS

Nominal Depth Nominal Depth
of 2 to 3 meters of 3 to 4 meters
County
Average Average Average Average
Measured Calculated Measured Calculated
Depth (m) Depth (m) Depth (m) Depth (m)

Nassau 2.61 2.83 4.57 3.68
Duval 1.83 1.94 3.66 3.55
St Johns 1.91 2.02 3.74 3.61
Flagler 1.83 1.64 3.66 3.07
Volusia 2.15 2.42 3.98 3.97
Brevard 2.63 2.50 4.46 3.43
Indian River 1.83 2.00 3.99 5.00
St Lucie 1.83 1.42 4.65 4.76
Martin 1.83 1.94 3.66 3.72
Palm Beach 1.83 1.94 3.66 3.74
Broward 1.83 1.49 3.99 3.69
Dade 1.83 2.12 3.66 2.74

Overall 2.03 2.05 3.99 3.76
Average _






0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0


200 300 400
Offshore Distance (r


500 600 700


a) Measured Sediment Sizes, D50%, (mm)
Averages for 165 Florida East Coast Profiles


0 100


200 300 400 500 600
Offshore Distance (m)


b) Comparison of Measured and Predicted Profiles
Averages for 165 Florida East Coast Profiles

Figure 5. Blindfolded Comparison of Average and Predicted Profiles. Based on
Kriebel, et al (1991) Relationship. All Twelve Florida East Coast Counties.


0 100


I I I I I I

........... . ..... . .... ... . . .. .. .


S-( 1 :65) ....... ..... -- .-

....... .(I65) 1- 6J3 ......- ....(147)....... -(118) ..-..
-*--.1.65 61)*-* --- *- -- -.................-.7 (8)


I I I I I


0






-5







-10


0
0


"

4-41
a.)


........... Kriebels.Method.For. determining. A..


.. .............-

.. ..... .... .... ... --- ... -......
......... .......... ........... .......... .-.. .... .-. .. .. ........ ..........
-....I Measured ........
*-A Calculated

... ... .....i... .... .............
.. .. .. .. .. .. .. .. .. .


700






0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0


.. ..... .......... Constant A.Value.





-5........
-5 -- -----------------.........






-10
0 100 200 300 400
Offshore Distance


500
(m)


600 700


b) Comparison of Measured and Predicted Profiles
Averages for 165 Florida East Coast Profiles
Figure 6. Comparison of Average Measured and Computed Profiles. Based on A = 0.1 m13.
All Twelve Florida East Coast Counties.


I I I I I I

..... ...... ........... ..........
.. .I 6 ........ -........... .... ....... D 50%, (m m ) --
." . : . ". . 1 . .4 -) ( ..
(1 6 5 ) **--* -- -- *- .- -I...... ...
....... ,, -- ... .. .. *:* .......... ". ".. ... .....
... .61) (6 -- (147)... ... 18).....
........ .......... .................... ....... ... .........


) 100 200 300 400 500 600 700
Offshore Distance (m)

a) Measured Sediment Sizes, D50%, (mm)
Averages for 165 Florida East Coast Profiles










AN=0.1+F (Aoo-0 .1) (12)

such that if the factor, F, is unity, the value of the new A is the
same as that from Moore's curve (Figure 1 and Table 1) and if the
factor, F, is zero, the value of the new A is always 0.1 m1/3. The
standard deviations for these tests are presented in Table 4 for F
values of 0, 0.1, 0.2, ...... 1.0. In general, it is seen that for
the shallower depths, the standard deviations are smallest for a F
value of approximately 0.5 whereas for greater depths, a F value of
zero, corresponding to a constant A value of 0.1 m 13 yields the
smallest standard deviation. These results will be interpreted in
the following section.


SUMMARY AND INTERPRETATION

In summary, although it is not known whether the profiles
being examined are in equilibrium, because of the shorter response
times, it is reasonable to consider the shallower portions of the
profiles to be in equilibrium, at least on the average. Although
there are considerable differences between the county wide measured
and calculated profile averages, for depths less than 4 m, these
differences appear to be unbiased (Table 2) based on Moore's
relationship.

Comparisons were carried out to determine whether there was a
clear dependency of the beach slope with grain size. For this
purpose, the data were organized by county and the average profile
slope to the nominal 2 meter depth was compared with the average
grain size to this depth. The results are presented in Figure 3
where it is shown that, indeed there is a correlation between grain
size and average slope.

It was found, based on blindfolded comparisons of profiles
that, particularly in those depths greater than 4 meters, a
constant value of A = 0.1 m1/3 yields a somewhat improved fit over
that based on Moore's curve. In interpreting these results, it is
important to consider that the shallower and deeper portions of the
profile experience different forces. Inside the breaking zone the
effects of breaking waves are to cause an additional destructive
force acting on the bottom and thus a milder beach slope. Of
course, at any point along the east coast of Florida, there is a
range of wave heights affecting the profile. The percentage of time
that waves are breaking decreases from approximately 100% at the
shoreline to a very small percentage for water depths greater than
3 to 4 meters. Thus, at any given water depth, the profile slope
reflects the percentages of times that waves are breaking versus
not breaking. Since the form of the EBP being evaluated herein is









TABLE 4


STANDARD DEVIATIONS FOR VARIOUS DEPTHS AND
SEDIMENT SCALE PARAMETER, A, RELATIONSHIPS


Standard Deviations Between Measured and Calculated Depths (m)
Factor For the Following Measured Water Depths (m)
F
F 0.94 2.03 3.99 5.85 7.60 9.14

0.0 0.39 0.60 1.06 1.23 1.47 1.90
0.1 0.38 0.57 1.04 1.24 1.53 2.00
0.2 0.38 0.56 1.08 1.26 1.61 2.11
0.3 0.37 0.55 1.03 1.30 1.71 2.24
0.4 0.37 0.54 1.05 1.36 1.83 2.37
0.5 0.37 0.55 1.07 1.44 1.95 2.52
0.6 0.37 0.56 1.11 1.53 2.08 2.67
0.7 0.38 0.58 1.16 1.63 2.22 2.82
0.8 0.39 0.60 1.21 1.74 2.37 2.98
0.9 0.40 0.63 1.27 1.86 2.51 3.14
1.0 0.41 0.66 1.34 1.98 2.67 3.30








based on a breaking wave regime, it may be appropriate to limit the
comparison to water depths of 2 to 3 meters.

It is of interest to note that a depth of about 4 m
corresponding to the approximate depth to which the profiles agreed
using Moore's relationship is also a reasonable depth to which the
sand is activated by breaking waves along the Florida east coast.
Dean and Grant (1989) have estimated that the so-called "depth of
closure" ranges from approximately 5.8 m at the north end of
Nassau County to 4.3 m at the south end of Dade County. The
findings that the profile shapes differ within and outside the zone
of reasonably active breaking are consist with our understanding of
the forces forming EBP's and provide the basis for the following
interpretation. Within the generally active surf zone, there are
both constructive an destructive forces acting. Seaward of this
region, one of the destructive forces, the equivalent offshore
bottom shear stress drive by the gradient of the momentum flux is
not active. This changes the force balance, with the onshore bottom
forces larger that the offshore forces relative to the breaking
zone. This, in turn results in a steeper beach profile.

CONCLUSIONS AND RECOMMENDATIONS

The following conclusions are based on the evaluation of
equilibrium beach profile methodology using an extensive data set
from the east coast of Florida which encompasses approximately 600
kilometers.

It is concluded that there are two distinct zones operative
that govern the shape of the beach profiles. The inner zone is
subjected to and shaped by the action of breaking waves on a
somewhat regular basis. As is well known, the breaking waves cause
destructive forces to be exerted on the beach profile and result in
a characteristic shape that has been found to be well represented
by a simple equation of the form of Equation (1). For data from the
east coast of Florida, the depth which separates these two zones is
approximately 3 to 4 meters. In the outer zone, the destructive
forces due to breaking waves are present only rarely and there is
a relative predominance of constructive forces resulting in a
steeper equilibrium slope for the same sediment size.

For the inner zone (3 to 4 meters), it was found, based on
"blindfolded" tests, that the existing equilibrium beach profile
methods provide reasonably good agreement with the measured profile
characteristics. For the outer zone, an A value of 0.1 m1/3 provided
an improved fit to the average data. Slightly improved
representations within the breaking zone could be provided by
decreasing slightly the variation of the sediment scale parameter,
A, with sediment size, D.It is recommended that the A values in
Table 1 be modified in accordance with Eq. (12) with a
proportionality factor, F, of 0.5 over the range of sediment sizes
encompassed in this study, ie approximately 0.1 mm < D < 0.6 mm.










AN=0.1+F (Aoo-0 .1) (12)

such that if the factor, F, is unity, the value of the new A is the
same as that from Moore's curve (Figure 1 and Table 1) and if the
factor, F, is zero, the value of the new A is always 0.1 m1/3. The
standard deviations for these tests are presented in Table 4 for F
values of 0, 0.1, 0.2, ...... 1.0. In general, it is seen that for
the shallower depths, the standard deviations are smallest for a F
value of approximately 0.5 whereas for greater depths, a F value of
zero, corresponding to a constant A value of 0.1 m 13 yields the
smallest standard deviation. These results will be interpreted in
the following section.


SUMMARY AND INTERPRETATION

In summary, although it is not known whether the profiles
being examined are in equilibrium, because of the shorter response
times, it is reasonable to consider the shallower portions of the
profiles to be in equilibrium, at least on the average. Although
there are considerable differences between the county wide measured
and calculated profile averages, for depths less than 4 m, these
differences appear to be unbiased (Table 2) based on Moore's
relationship.

Comparisons were carried out to determine whether there was a
clear dependency of the beach slope with grain size. For this
purpose, the data were organized by county and the average profile
slope to the nominal 2 meter depth was compared with the average
grain size to this depth. The results are presented in Figure 3
where it is shown that, indeed there is a correlation between grain
size and average slope.

It was found, based on blindfolded comparisons of profiles
that, particularly in those depths greater than 4 meters, a
constant value of A = 0.1 m1/3 yields a somewhat improved fit over
that based on Moore's curve. In interpreting these results, it is
important to consider that the shallower and deeper portions of the
profile experience different forces. Inside the breaking zone the
effects of breaking waves are to cause an additional destructive
force acting on the bottom and thus a milder beach slope. Of
course, at any point along the east coast of Florida, there is a
range of wave heights affecting the profile. The percentage of time
that waves are breaking decreases from approximately 100% at the
shoreline to a very small percentage for water depths greater than
3 to 4 meters. Thus, at any given water depth, the profile slope
reflects the percentages of times that waves are breaking versus
not breaking. Since the form of the EBP being evaluated herein is









Several potentially rewarding areas for future research were
identified in this study. It would appear that considerable
opportunity exists for investigating the profiles of equilibrium
for waters in the seaward zone that are not affected predominantly
by breaking. Secondly, the differences between the profiles of the
inner and outer zones contain quantitative information concerning
the relative magnitudes of the constructive and destructive forces
and could contribute to an improved understanding of the dynamics
of the profile system.

It is hoped that this report will stimulate other comparisons
with extensive data sets and will provide direction for future
research.

ACKNOWLEDGEMENTS

Support for this study was provided by the Florida Sea Grant
Program under Contract No. R/C-S-31 and matching funds were
provided by the Department of Coastal and Oceanographic
Engineering. Funding for this effort by these two entities is
hereby gratefully acknowledged.

REFERENCES

Bodge, K.R. 1992. "Representing equilibrium beach profiles with an
exponential expression," Journal of Coastal Research, Vol 8, No. 1,
pp 47-55.

Bruun, P. 1954. "Coast erosion and the development of beach
profiles," U. S. Army Beach Erosion Board Technical Memorandum No.
44.

Dally, W.R., R.G. Dean and R.A. Dalrymple, 1985. "Wave height
variation across beaches of arbitrary profile," Journal of
Geophysical Research, Vol. 90, No. C6, pp.11917-11927.

Dean, R.G. 1977. "Equilibrium beach profiles: U. S. Atlantic and
Gulf coasts," Department of Civil Engineering, Ocean Engineering
Report No. 12, University of Delaware, Newark, Delaware.

Dean, R.G. 1987. "Coastal sediment processes: Toward engineering
solutions," Coastal Sediments '87, Specialty Conference on Advances
in Understanding of Coastal Sediment Processes, ASCE, Vol. 1, New
Orleans, Louisiana, pp 1-24.

Dean, R.G. 1991. "Equilibrium beach profiles: Characteristics and
applications," Journal of Coastal Research, Vol 7, No. 1, pp 53-84.

Dean, R.G. 1994. "Cross-shore sediment transport processes," (in
Draft Form), Prepared for the Coastal Engineering Research Center
as a Chapter in the Forthcoming Coastal Engineering Manual.








based on a breaking wave regime, it may be appropriate to limit the
comparison to water depths of 2 to 3 meters.

It is of interest to note that a depth of about 4 m
corresponding to the approximate depth to which the profiles agreed
using Moore's relationship is also a reasonable depth to which the
sand is activated by breaking waves along the Florida east coast.
Dean and Grant (1989) have estimated that the so-called "depth of
closure" ranges from approximately 5.8 m at the north end of
Nassau County to 4.3 m at the south end of Dade County. The
findings that the profile shapes differ within and outside the zone
of reasonably active breaking are consist with our understanding of
the forces forming EBP's and provide the basis for the following
interpretation. Within the generally active surf zone, there are
both constructive an destructive forces acting. Seaward of this
region, one of the destructive forces, the equivalent offshore
bottom shear stress drive by the gradient of the momentum flux is
not active. This changes the force balance, with the onshore bottom
forces larger that the offshore forces relative to the breaking
zone. This, in turn results in a steeper beach profile.

CONCLUSIONS AND RECOMMENDATIONS

The following conclusions are based on the evaluation of
equilibrium beach profile methodology using an extensive data set
from the east coast of Florida which encompasses approximately 600
kilometers.

It is concluded that there are two distinct zones operative
that govern the shape of the beach profiles. The inner zone is
subjected to and shaped by the action of breaking waves on a
somewhat regular basis. As is well known, the breaking waves cause
destructive forces to be exerted on the beach profile and result in
a characteristic shape that has been found to be well represented
by a simple equation of the form of Equation (1). For data from the
east coast of Florida, the depth which separates these two zones is
approximately 3 to 4 meters. In the outer zone, the destructive
forces due to breaking waves are present only rarely and there is
a relative predominance of constructive forces resulting in a
steeper equilibrium slope for the same sediment size.

For the inner zone (3 to 4 meters), it was found, based on
"blindfolded" tests, that the existing equilibrium beach profile
methods provide reasonably good agreement with the measured profile
characteristics. For the outer zone, an A value of 0.1 m1/3 provided
an improved fit to the average data. Slightly improved
representations within the breaking zone could be provided by
decreasing slightly the variation of the sediment scale parameter,
A, with sediment size, D.It is recommended that the A values in
Table 1 be modified in accordance with Eq. (12) with a
proportionality factor, F, of 0.5 over the range of sediment sizes
encompassed in this study, ie approximately 0.1 mm < D < 0.6 mm.









Several potentially rewarding areas for future research were
identified in this study. It would appear that considerable
opportunity exists for investigating the profiles of equilibrium
for waters in the seaward zone that are not affected predominantly
by breaking. Secondly, the differences between the profiles of the
inner and outer zones contain quantitative information concerning
the relative magnitudes of the constructive and destructive forces
and could contribute to an improved understanding of the dynamics
of the profile system.

It is hoped that this report will stimulate other comparisons
with extensive data sets and will provide direction for future
research.

ACKNOWLEDGEMENTS

Support for this study was provided by the Florida Sea Grant
Program under Contract No. R/C-S-31 and matching funds were
provided by the Department of Coastal and Oceanographic
Engineering. Funding for this effort by these two entities is
hereby gratefully acknowledged.

REFERENCES

Bodge, K.R. 1992. "Representing equilibrium beach profiles with an
exponential expression," Journal of Coastal Research, Vol 8, No. 1,
pp 47-55.

Bruun, P. 1954. "Coast erosion and the development of beach
profiles," U. S. Army Beach Erosion Board Technical Memorandum No.
44.

Dally, W.R., R.G. Dean and R.A. Dalrymple, 1985. "Wave height
variation across beaches of arbitrary profile," Journal of
Geophysical Research, Vol. 90, No. C6, pp.11917-11927.

Dean, R.G. 1977. "Equilibrium beach profiles: U. S. Atlantic and
Gulf coasts," Department of Civil Engineering, Ocean Engineering
Report No. 12, University of Delaware, Newark, Delaware.

Dean, R.G. 1987. "Coastal sediment processes: Toward engineering
solutions," Coastal Sediments '87, Specialty Conference on Advances
in Understanding of Coastal Sediment Processes, ASCE, Vol. 1, New
Orleans, Louisiana, pp 1-24.

Dean, R.G. 1991. "Equilibrium beach profiles: Characteristics and
applications," Journal of Coastal Research, Vol 7, No. 1, pp 53-84.

Dean, R.G. 1994. "Cross-shore sediment transport processes," (in
Draft Form), Prepared for the Coastal Engineering Research Center
as a Chapter in the Forthcoming Coastal Engineering Manual.









Dean, R.G. and J. Grant, 1989. Development of methodology for
thirty-year shoreline projections in the vicinity of beach
nourishment projects," Department of Coastal and Oceanographic
Engineering Report No. UFL/COEL-89/026, University of Florida,
Gainesville, FL.

Dean, R.G., T. Healy and A. Dommerholt, 1993. "A Blind-folded test
of equilibrium beach profile concepts with New Zealand data,"
Marine Geology, Vol. 109, pp. 253-266.

Eagleson, P.S, B. Glenne and J.A. Dracup, 1963. "Equilibrium
characteristics of sand beaches," Journal of Hydraulics Division,
American Society of Civil Engineers, Vol. 89, No. 1, pp. 35-57.

Hayden, B., W. Felder, J. Fisher, D. Resio, L. Vincent, and R.
Dolan, 1975. "Systematic variations in inshore bathymetry," Report
No. 10, Department of Environmental Sciences, University of
Virginia, Charlottesville, VA

Hughes, S.A. 1978. "The variation of beach profiles when
approximated by a theoretical curve," Masters Thesis, Department of
Coastal and Oceanographic Engineering, University of Florida,
Gainesville, FL.

Inman, D.L., M.H.S. Elwany and S.A. Jenkins, 1993. "Shorerise and
Bar-Berm Profiles on Ocean Beaches", Journal of Geophysical
Research, Vol. 98, No. C10, pp. 18,181 18,199.

Keulegan, G.H. and W.C. Krumbein, 1919. "Stable configuration of
bottom slope in a shallow sea and its bearing on geological
processes,"Transactions, American Geophysical Union, Vol. 30, No.
6, pp. 855-861.

Komar, P.D., and McDougal, W.G., 1993. "The analysis of exponential
beach profiles", Journal of Coastal Research, Vol. 10, No. 1, pp.
59-69.

Kriebel, D.L., N.C. Kraus and M. Larson, 1991. "Engineering methods
for predicting beach profile response," Proceedings, ASCE
Conference on Coastal Sediments '91, pp. 557-571.

Larson, M., 1988. "Quantification of beach profile change", Report
No. 1008, Department of Water Resources and Engineering, University
of Lund, Lund, Sweden.

Larson, M., 1991. "Equilibrium profile of a beach with varying
grain size," Proceedings, ASCE Conference on Coastal Sediments '91,
pp. 905-919.

Larson, M., and N.C. Kraus, 1989. "SBEACH: Numerical model for
simulating storm-induced beach change, Report 1: Empirical
foundation and model development," Technical Report CERC-89-9 U.S.









Army Coastal Engineering Research Center, U.S. Army Waterways
Experiment Station.

Larson, M., and N.C. Kraus, 1990. "SBEACH: Numerical model for
simulating storm-induced beach change, Report 2: Numerical
formulation and model tests," Technical Report CERC-89-9, U.S. Army
Coastal Engineering Research Center, Waterways Experiment Station.

Moore, B.D. 1982. "Beach profile evolution in response to changes
in water level and wave height," Masters Thesis, Department of
Civil Engineering, University of Delaware, Newark, DE.

Rouse, H. 1937. "Nomogram for the settling velocity of spheres,"
Division of Geology and Geography Exhibit D, Report of the
Commission on Sedimentation, 1936-1937, National Research Council,
Washington, D. C., pp. 57-64.

Swart, D.H. 1974. A schematization of onshore-offshore
transport," Proceedings, Fourteenth International Conference on
Coastal Engineering, ASCE, pp. 884-890.

Vellinga, P. 1983. "Predictive computational model for beach and
dune erosion during storm surges," Proceedings, ASCE Specialty
Conference on Coastal Structures '83, pp. 806-819.

Work, P.A. and R.G. Dean, 1991. "Effect of varying grain size on
equilibrium beach profiles," Proceedings, ASCE Conference on
Coastal Sediments '91, pp. 890-904.


___ _











APPENDIX A

GRAPHICAL PRESENTATIONS OF
FLORIDA EAST COAST AND COUNTY BY COUNTY
CROSS-SHORE DISTRIBUTIONS OF
SEDIMENT AND PROFILE CHARACTERISTICS








INTRODUCTION


The graphs on the following pages present the cross-shore distributions of median
sediment size (Upper Panel) and a blindfolded comparison of the average calculated and
measured beach profiles (Lower Panel). The calculated beach profiles are based solely on the
measured sediment size distributions and Moore's relationship (Figure 1 and Table 1) and not
on any curve fitting to obtain a best-fit, ie the calculated profiles are obtained in a blindfolded
manner. The values in parentheses in the upper panel represent the number of profiles for which
data were available and contributed to the average at this particular cross-shore location.

Figure A-1 presents the averages for the entire east coast of Florida and is based on 165
profiles and 986 sediment samples and is a representation of Figure 3 for sake of completeness.
Figures A-2 through A-13 present the same type of information commencing with Nassau
County on Florida's east coast to Dade County at the south.

















0 100 200 300 400 5
Offshore Distance (m)


0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0


700


a) Measured Sediment Sizes, D50%, (mm)
Averages for 165 Florida East Coast Profiles









. .........- .......... ........... ....."..... ........ ..........
........ Measured ............. .... .......... -
...A.- Calculated


.. .


0 100


200 300 400 5
Offshore Distance (m)


)0 600


700


b) Comparison of Measured and Predicted Profiles
Averages for 165 Florida East Coast Profiles


Figure A-1.


All Counties. a) Cross-Shore Distribution of Average Median Sediment Size.
b) Blindfolded Comparison of Average Calculated and Measured Beach Profiles.
Values in Parentheses in Upper Panel Denote Number of Profiles Contributing
to Average.


A-2


I I I I I I


-:' ii --*- D50%, (mm) -


---...-(165) 6. (147) ....... (I 8)
-1 I ............ .... .......... .. ... .i

,.I 1 I I I


)0 600


0






-5






-10

















0 100 200 300 400 5
Offshore Distance (m)


0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0


700


a) Measured Sediment Sizes, D50%, (mm)
Averages for 7 Nassau County Profiles




....... ... ...... : ........... ................






A--- Calculated


0 100


200 300 400 5
Offshore Distance (m)


)0 600 700


b) Comparison of Measured and Predicted Profiles
Averages for 7 Nassau County Profiles


Figure A-2.


Nassau County. a) Cross-Shore Distribution of Average Median Sediment Size.
b) Blindfolded Comparison of Average Calculated and Measured Beach Profiles.
Values in Parentheses in Upper Panel Denote Number of Profiles Contributing
to Average.


A-3


I I I I4



;.. . : .. .-.:( 4 ) : .:

... .- -- .......... ........... ....... ..
II---- -- --I ^:I- -I
-7 .......... .-- --- ---

.. ... .
... ... .. .. .. ... .. .. ... .. .. ... ..


O0 600


0






-5






-10





S0.7 I I I
0 .46 '...- .... ..... ........ : ........... : ........... .......... ..........
S 0.5 -.. D (m m ) ........ ... .........................
0.4 .


2 0.2 ) (8)
CO 0 .1 .... .. .. .......... ........ ........... ....... .. .... .
C 0.1 -
0.0
0 100 200 300 400 500 600 700
Offshore Distance (m)

a) Measured Sediment Sizes, D50%, (mm)
Averages for 8 Duval County Profiles
0



S- ---------- assured .........-------- ----
...... .A ; :: .... .... ............ ........... ........... %......................

Z . . . . . .. . .. . . . .. . . . . ..

.5 ......... ,........... ........ ..... ............. ..: ...... .........
-5 .. .. ...... ............

........ -- M easured............... ................
o .**A-- Calculated

.. .. .......... ..... ... ....... .. .
10 :
0 100 200 300 400 500 600 700
Offshore Distance (m)

b) Comparison of Measured and Predicted Profiles
Averages for 8 Duval County Profiles


Figure A-3. Duval County. a) Cross-Shore Distribution of Average Median Sediment Size.
b) Blindfolded Comparison of Average Calculated and Measured Beach Profiles.
Values in Parentheses in Upper Panel Denote Number of Profiles Contributing
to Average.


A-4





0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0


0







-5






-1 n


-J-. J


0 100 200 300 400 500
Offshore Distance (m)


600


700


a) Measured Sediment Sizes, Do0%, (mm)
Averages for 22 St Johns County Profiles



.. ........ ............ ........... ........... ...... .

. ..... .
........... ........... ........... ...................... ..... .


................................



---A-- Calculated


I I i I i i


0 100 200 300 400 5(
Offshore Distance (m)


)0 600


700


Comparison of Measured and Predicted Profiles
Averages for 22 St Johns County Profiles


Figure A-4. St. Johns County. a) Cross-Shore Distribution of Average Median Sediment Size.
b) Blindfolded Comparison of Average Calculated and Measured Beach Profiles.
Values in Parentheses in Upper Panel Denote Number of Profiles Contributing
to Average.

A-5


I I I I I I
------ 1 --- -- ) --- j -- ) --

....... -*- D 50 (m m ) ....... ......... .......... .........



...(-22).(22)- .. ..... .. ....... --i .......... ......;..... 8) ...i........
. .......... .......... ........... ........... ........... ........... ..........
S(22 2(11)





0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
(


200 300 400 5
Offshore Distance (m)


)0 600


700


a) Measured Sediment Sizes, D50%, (mm)
Averages for 11 Flagler County Profiles















I I I I I I
........ ..........--- ......... ........... -4- ...- --.......-...........





A-- Calculated : :
........iii ... ... ... ... .. ... ... .. .. ... ..



. . . . . .. .


0 100


200 300 400 500 600
Offshore Distance (m)


700


b) Comparison of Measured and Predicted Profiles
Averages for 11 Flagler County Profiles


Figure A-5. Flagler County. a) Cross-Shore Distribution of Average Median Sediment Size.
b) Blindfolded Comparison of Average Calculated and Measured Beach Profiles.
Values in Parentheses in Upper Panel Denote Number of Profiles Contributing
to Average.


A-6


I I I I I
...........................................

S...... D50%, (....................


.........................
.... . . .... ( 1 . .. .: . . . .
I- I I I
_ 0 .. .. . .. . .. . . .
... ... ... ... .... ... ... ....... ... .. ... .... .. ... ...
..( .. .. .. .. .. .. .. .


)
3


100


0






-5






-10


I I i




0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0


200 300 400 500 600
Offshore Distance (m)


700


a) Measured Sediment Sizes, D50%, (mm)
Averages for 23 Volusia County Profiles
SI I I



- - - - : .- -




Measured .......................
S**-A- Calculated


...i... ... ... ........ .i


0 100


200 300 400 5
Offshore Distance (m)


600


700


Comparison of Measured and Predicted Profiles
Averages for 23 Volusia County Profiles


Figure A-6.


Volusia County. a) Cross-Shore Distribution of Average Median Sediment Size.
b) Blindfolded Comparison of Average Calculated and Measured Beach Profiles.
Values in Parentheses in Upper Panel Denote Number of Profiles Contributing
to Average.


A-7


I I I I I I

..... ...- D 50 .... % ,(m m ).. ........ ....... .. .......





-i -


0 100


0






-5






-10


00

















0 100 200 300 400 500
Offshore Distance (m)


600


700


a) Measured Sediment Sizes, D50%, (mm)
Averages for 23 Brevard County Profiles



............ ...................... ........... ...................... .... ........
......... ........ ... .... .... ......... .. ........... ..... ..... .. ... .....






....... Measured ........ ......-.........* ---
-A-- -- Calculated


i i i I i


0 100 200 300 400 500
Offshore Distance (m)


600


700


b) Comparison of Measured and Predicted Profiles
Averages for 23 Brevard County Profiles


Figure A-7.


Brevard County. a) Cross-Shore Distribution of Average Median Sediment Size.
b) Blindfolded Comparison of Average Calculated and Measured Beach Profiles.
Values in Parentheses in Upper Panel Denote Number of Profiles Contributing
to Average.


A-8


0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0


I I I I I I
........... .......... ........... ---------------

S- Dso%, (m m ) ....... ......... ........ ...


. .::: . ..:: :::::: j;;::::: : :::.. ........... ............ .. ...
-...... .. .. ........... ........... ........... .......... ..........


S. (23)


0






-5






-10




0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0


200 300 400 500
Offshore Distance (m)


600


a) Measured Sediment Sizes, D50%, (mm)
Averages for 12 Indian River County Profiles











........ --- M measured ...- --..:...- .- -
----- Calculated


..1 .


0 100


200 300 400 5
Offshore Distance (m)


30 600


b) Comparison of Measured and Predicted Profiles
Averages for 12 Indian River County Profiles


Figure A-8.


Indian River County. a) Cross-Shore Distribution of Average Median Sediment
Size. b) Blindfolded Comparison of Average Calculated and Measured Beach
Profiles. Values in Parentheses in Upper Panel Denote Number of Profiles
Contributing to Average.


A-9


I I I I I I


(2). *-- D 50%, (m m ) ....... .......... ........... ......

z 02(11 1 (1O7 n-

.......... .. %..... ...-----
.. . .. . 1) .. .. .( Y . .


0 100


0






-5






-10


700


700





- -~~-- --~- -~- ~ -- -





0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0


200 300 400 5
Offshore Distance (m)


)0 600


700


a) Measured Sediment Sizes, D5o%, (mm)
Averages for 13 St Lucie County Profiles











... M measured ... ..................... ........
-.*A-- Calculated

... ....................................


0 100 200 300 400 500
Offshore Distance (m)


600


700


b) Comparison of Measured and Predicted Profiles
Averages for 13 St Lucie County Profiles


Figure A-9. St. Lucie County. a) Cross-Shore Distribution of Average Median Sediment Size.
b) Blindfolded Comparison of Average Calculated and Measured Beach Profiles.
Values in Parentheses in Upper Panel Denote Number of Profiles Contributing
to Average.

A-10


I I I I I I

.. D5 %, (m m ) ... ....... ( .......... 6)-

r ( I3)::: :::::::: .:;; :(1 )




- .1...... .. .... ...................
.. .. .. .. .. .. .. .. .. .


0 100


0







-5






_1 n


-J vJ





-





0.7 1 1 1 1
0.6 ......
S. : : : : ........ .. ... ... .......... :::::::::::::::: ......................: :
S 0.5 .. D 50%, (m m ) .......... ................................



0.0
0 .5. :....... :D,. D:, (m m ): .. .......... ........... : ...........

S 0 .3 2 ) ....... ........... ........... ........... ........... ...... ... ...... ......
I 0.2 ........l
0 .1 .... .... .... ..... .. -
0.0 I I
S 0 100 200 300 400 500 600 700
Offshore Distance (m)

a) Measured Sediment Sizes, D50%, (mm)
Averages for 2 Martin County Profiles
0



Z ............. ... ..... .... .... ................ ..... ................ ...........
0
o3 .

S............. .Calculat ..ed.


o .-- Calculated
S.. ........... ....... .... ................. ...........

-10 200i i 4 00
0 -A.. Calculated -------

0 100 200 300 400 500 600 700
Offshore Distance (m)

b) Comparison of Measured and Predicted Profiles
Averages for 2 Martin County Profiles


Figure A-10. Martin County. a) Cross-Shore Distribution of Average Median Sediment Size.
b) Blindfolded Comparison of Average Calculated and Measured Beach Profiles.
Values in Parentheses in Upper Panel Denote Number of Profiles Contributing
to Average.


A-11
















0 100 200 300 400 5
Offshore Distance (m)


0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0


a) Measured Sediment Sizes, D50%, (mm)
Averages for 23 Palm Beach County Profiles







................ .......... .........-. ........


........ -- Measured .....
A--- Calculated


SI I


0 100


200 300 400 5
Offshore Distance (m)


30 600


700


b) Comparison of Measured and Predicted Profiles
Averages for 23 Palm Beach County Profiles


Figure A-11. Palm Beach County. a) Cross-Shore Distribution of Average Median Sediment
Size. b) Blindfolded Comparison of Average Calculated and Measured Beach
Profiles. Values in Parentheses in Upper Panel Denote Number of Profiles
Contributing to Average.
A-12


. .. D., ( m m ) ......... ....... ........ .........
....
D 5o%, (m m ) ......................................

(3 i I I I.t I II_::_ :
.(2 ........... ........... .... ...... .:............ .......... .........
(2 3)..) .... . .



. .. . .. . . . . . . .


600 700


0






-5






-10


)0




0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0


200 300 400 5
Offshore Distance (m)


)0 600 700


0






-5






-1 n


a) Measured Sediment Sizes, D50%, (mm)
Averages for 13 Broward County Profiles



. ...* ....... ........... ,............ ......................... ... ..



........ -.. M measured ........... .............. ......... .....
..... -.. 0 M measured .. ...... -. .. ..................... .........-

..A.-- Calculated

.. . . . . .. . . . .


0 100 200 300 400 500
Offshore Distance (m)


600


700


b) Comparison of Measured and Predicted Profiles
Averages for 13 Broward County Profiles


Figure A-12. Broward County. a) Cross-Shore Distribution of Average Median Sediment Size.
b) Blindfolded Comparison of Average Calculated and Measured Beach Profiles.
Values in Parentheses in Upper Panel Denote Number of Profiles Contributing
to Average.
A-13


0 100


I iI I

. ...... ... : ........... : ........... ... .. .. ..... .: ........... . . .
.(3)..... ......... --- --- .. .......... ...........
:(!L) ..' ^ ^^(4).. . .




3) ................................- D 5 %, (m m )
I I-. I I I_--_---__---
...... ..... .....


,J V,





0.7



.. 0.4 ... .
0 ... ....... ...................... ...........------- --







0.0 ..
S 0 100 200 300 400 500 600 700
Offshore Distance (m)
a) Measured Sediment Sizes, D50%, (mm)







Averages for 8 Dade County Profiles
'0 .. .... .......... ....... .. ........... ............ I .......... ........ ..








0 .3 :..... ..:: .. .. .i.:: ::::::::.: ..::::: ..:::::.:::; : i .::::: ::.






0 1
m -10 I i i










S 0 100 200 300 400 500 600 700
Offshore Distance (m)

b) Comparison of Measured Sedimentand Predicted Profiles(mm)
Averages for 8 Dade County Profiles













Figure A-13. Dade County. a) Cross-Shore Distribution of Average Median Sediment Size.
b) Blindfolded Comparison of Average Calculated and Measured Beach Profiles.
Values in Parentheses in Upper Panel Denote Number of Profiles Contributing
to Average.
A-14
.. .. .

.............. ............... .................... ...... ......
.- M measured ..........................................
o 0 A- Calculated


101--------
0 100 200 300 400 500 600 700
Offshore Distance (m)

b) Comparison of Measured and Predicted Profiles
Averages for 8 Dade County Profiles


Figure A-13. Dade County. a) Cross-Shore Distribution of Average Median Sediment Size.
b) Blindfolded Comparison of Average Calculated and Measured Beach Profiles.
Values in Parentheses in Upper Panel Denote Number of Profiles Contributing
to Average.
A-14




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