• TABLE OF CONTENTS
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 Front Cover
 Report documentation page
 Title Page
 Table of Contents
 Introduction
 Background
 Methodology based on equilibrium...
 Laboratory studies
 Field data
 Summary, conclusions and recommendation...
 References
 Appendix A: Listing of program...
 Appendix B: Detailed description...
 Appendix C: Additional data for...






Group Title: UFL/COEL (University of Florida. Coastal and Oceanographic Engineering Laboratory) ; 91/016
Title: Rational techniques for evaluating potential sands for beach nourishment
CITATION THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00078628/00001
 Material Information
Title: Rational techniques for evaluating potential sands for beach nourishment
Series Title: UFLCOEL-91016
Physical Description: 1 v. in various pagings : ill. ; 28 cm.
Language: English
Creator: Dean, Robert G ( Robert George ), 1930-
Abramian, Jorge Emilio, 1958-
University of Florida -- Coastal and Oceanographic Engineering Dept
Coastal Engineering Research Center (U.S.)
Publisher: Coastal and Oceanographic Engineering Dept., University of Florida
Place of Publication: Gainesville Florida
Publication Date: 1991
 Subjects
Subject: Shore protection   ( lcsh )
Sand -- Research   ( lcsh )
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Bibliography: Includes bibliographical references.
Statement of Responsibility: by Robert G. Dean and Jorge Abramian.
General Note: "November, 1991."
General Note: Sponsored by: Coastal Engineering Research Center.
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: UF00078628
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 - 26104282

Table of Contents
    Front Cover
        Front Cover
    Report documentation page
        Unnumbered ( 2 )
    Title Page
        Page 1
    Table of Contents
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
    Introduction
        Page 7
        Page 8
        Page 9
    Background
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
    Methodology based on equilibrium beach profiles
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
    Laboratory studies
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
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        Page 45
        Page 46
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        Page 65
        Page 66
        Page 67
        Page 68
        Page 69
        Page 70
        Page 71
    Field data
        Page 72
        Page 73
        Page 74
        Page 75
        Page 76
        Page 77
        Page 78
        Page 79
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        Page 91
        Page 92
        Page 93
        Page 94
        Page 95
        Page 96
        Page 97
    Summary, conclusions and recommendation for further research
        Page 98
        Page 99
        Page 100
    References
        Page 102
        Page 103
    Appendix A: Listing of program eqpr. for and input and output files for examples 1 and 4
        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
        A-15
        A-16
        A-17
        A-18
        A-19
        A-20
        A-21
        A-22
        A-23
        A-24
        A-25
        A-26
        A-27
        A-28
        A-29
        A-30
        A-31
        A-32
        A-33
        A-34
        A-35
        A-36
        A-37
        A-38
        A-39
        A-40
        A-41
        A-42
        A-43
        A-44
        A-45
        A-46
        A-47
        A-48
    Appendix B: Detailed description of program eqpr. for and input and output files
        B-1
        B-2
        B-3
        B-4
        B-5
        B-6
        B-7
        B-8
        B-9
    Appendix C: Additional data for Delray Beach, Florida
        C-1
        C-2
        C-3
        C-4
        C-5
        C-6
        C-7
        C-8
        C-9
        C-10
        C-11
        C-12
        C-13
        C-14
        C-15
        C-16
Full Text



UFL/COEL-91/016


RATIONAL TECHNIQUES FOR EVALUATING
POTENTIAL SANDS FOR BEACH NOURISHMENT





by


Robert G. Dean
and
Jorge Abramian


November, 1991



Sponsor:

Coastal Engineering Research Center
U.S. Army Engineer
Waterways Experiment Station
3909 Halls Ferry Road
Vicksburg, MS 39180-6199






REPORT DOCUMENTATION PAGE
1. Rport Do. 2. 3. Raeipintt 'A acesaloe o.


4. Titla and Subtitle 3. sport Dat
RATIONAL TECHNIQUES FOR EVALUATING POTENTIAL SANDS November, 1991
FOR BEACH NOURISHMENT 6.

7. Auhor(.) Robert G. Dean 8. Pe rfmis, Oraniatim Report No.
and UFL/COEL-91/016
Jorge Abramian
9. Pertfo mi Organiatlion rae Addre n 10. Projec/Tlak/ork nit no.
Coastal and Oceanographic Engineering Department
University of Florida 11. coract or grnt no.
336 Weil Hall DACW39-89-K-0025
Gainesville, FL 32611 13. Typ of aRort
12. Sponsorina OrganluhtoM ma aOd Addn Final
Coastal Engineering Research Center
U.S. Army Engineer Waterways Experiment Station
3909 Halls Ferry Road
Vicksburg, Mississippi 39180-6199 14.

15. Supplentary Motes



16. Abstract


The rational design of beach nourishment projects requires the ability to
calculate the geometry of the added sand volume, both as a function of space and
time. This capability is essential for quantitative evaluation of the relative
merits of various borrow areas and in benefit/cost analysis of such projects
including the volumes and timing of renourishments. In many cases the material
may be a by-product of a dredging project carried out for other purposes.
Particular design aspects of significance include the equilibrated beach profile,
especially the additional dry beach width and the longevity of the project.
Traditionally, attempts to quantify benefits of beach nourishment have utilized
"compatibility" and "overfill" factors which relate the sand sizes of borrow and
native material. This report presents, for two-dimensional conditions, procedures
for predicting the equilibrium beach profile resulting from placement of an
arbitrary volume of material with an arbitrary grain size distribution on a
profile of arbitrary shape. The procedures have been developed into a computer
program which has been proven effective for a wide range of sediment and profile
characteristics. The method provides, for the first time, a rational basis for
assessing the relative merits of various nourishment materials in providing
equilibrated additional dry beach widths.



17. Originator's Uly words 18. Availability Stateat
Beaches
Nourishment
Profiles
Sediment
Compatibility
19. U. S. Security ClIassf. of the Report 20. U. S. Security Classif. of This Page 21. No. of ?age. 22. Price

Unclassified Unclassified 175













RATIONAL TECHNIQUES FOR
EVALUATING POTENTIAL SANDS FOR BEACH NOURISHMENT






Prepared by:


Robert G. Dean
and
Jorge Abramian


Sponsored by:


Coastal Engineering Research Center
U.S. Army Engineer Waterways Experiment Station
3909 Halls Ferry Road
Vicksburg, Mississippi 39180-6199









Coastal and Oceanographic Engineering Department
University of Florida
Gainesville, FL 32611


November, 1991











CONTENTS


PREFACE . . . . . . .. . . 1


LIST OF TABLES . . . .

LIST OF FIGURES . . . . . . .

PART I: INTRODUCTION . . . .

PART II: BACKGROUND . . . .


PART III: METHODOLOGY BASED ON EQUILIBRIUM BEACH PROFILES .


Examples . . .
Summary and Conclusions for Methodology Presented . .

PART IV: LABORATORY STUDIES . . . .


Introduction and Description of Facilities . .
Objectives . . . . .
Experimental Procedures . . . . .
Test Results . . . . .
Comparison of Laboratory Data with Predictions . .
Comparison Based on Parameterized Fit to the Actual A Values
Comparison Based on Localized A Values . . .

PART V: FIELD DATA . . . .


Delray Beach, Florida . . . . ..
Jupiter Island, Florida . . . . .
Conclusions Based on Field Data . . . .

PART VI: SUMMARY, CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER R

Summary . . . . . . ..
Conclusions . . . . . ..
Recommendations for Further Research . . .

PART VII: REFERENCES . . . . . .

APPENDIX A: LISTING OF PROGRAM EQPR.FOR AND INPUT AND OUTPUT FILES
EXAMPLES 1 AND 4 . . . .

APPENDIX B: DETAILED DESCRIPTION OF PROGRAM EQPR.FOR AND INPUT AND
FILES . . . . . .


Introduction . . .
Description of FORTRAN Program and Inp


3

7

. 10

. 21


. 26
. 32

. 35

. 35
. 35
. 37
. 37
. 61
61
. 69

. 72

. 72
. 83
. 93

RESEARCH 98

. . 98
. . 99
. . 99

. 101


FOR



OUTPUT


ut Files .
ut Files . . .


APPENDIX C: ADDITIONAL DATA FOR DELRAY BEACH, FLORIDA


. . Cl









LIST OF TABLES


No. page


1 Experimental Conditions, Wave Tank Tests . . .... 35
2 Results of the Tracer Analysis . . . .... 59
3 Summary of Nourishment History (Post 1973) at Jupiter Island . 83


LIST OF FIGURES

No Pa


1 Sand transport losses and beach profiles associated with a beach
nourishment project. . . . ... .. . 8
2 Variation of sediment scale parameter, A, with sediment size and
fall velocity. (Dean 1987) . . . . .. 12
3 Three generic types of nourished profiles. (a) intersecting
profile, (b) non-intersecting profile and (c) submerged profile. .13
4 Effect of nourishment material scale parameter, AF, on width of
resulting dry beach. Four examples of decreasing AF with same
added volume per unit beach length. . . . ... 15
5 Effect of increasing volume of sand added on resulting beach
profile. AF = 0.1 mi13, AN = 0.2 m1/3, h. = 6.0 m, B = 1.5 m. .. .... 16
6 Illustration of effect of volume added, V, and fill sediment scale
parameter, AF, on additional dry beach width, Ay, Example
conditions: B = 1.5 m, h. = 6 m, AN = 0.1 1/3. . . .. 17
7 Variation of non-dimensional shoreline advancement Ay/W., with A'
and V. Results shown for h,/B = 2.0. . . . ... 19
8 Variation of non-dimensional shoreline advancement Ay/W*, with A'
and V. Results shown for h./B = 4.0. . . . ... 20
9 Definition sketch. . . . ... . 22
10 Flow diagram for problem solution. . . . ... 24
11 Method of determining grain size, D., for computation of current
increment of equilibrium profile. . . . .... 25
12 Cumulative grain size distribution, Examples 1 through 4. . ... 27
13 Example 1. Original, placed and equilibrium profiles. Case of
non-intersecting profiles. Idealized grain size distribution. ... 29
14 Example 2. Original, placed and equilibrium profiles. Case of
intersecting profiles. Idealized grain size distribution. ... .30
15 Example 3. Original, placed and equilibrium profiles. Case of
non-intersecting profiles. Idealized grain size distribution
smaller than native. Incipient submerged profile. . . ... 31
16 Example 4. Original, placed and equilibrium profiles. Case of
non-intersecting profiles for user-specified original profile and
nourishment material grain size distribution. . . ... 33
17 Additional dry beach width, Ay, versus nourishment volume per
unit beach length, V. Three nourishment materials. . ... 34
18 Schematic of laboratory facilities. . . . .... 36
19 Experiment 1. Measured profiles at various times. . ... 38









20 Variation of mean sediment size with time at several locations
across beach. All six experiments. Sediment diameter in
millimeters. ........ . .. . . . 39
21 Experiment 1. Initial and final profiles and initial and final
grain size distributions. . ... . . . 40
22 Experiment 1. Grain size distributions at six locations across
the profile after 24 hours of testing. . . . ... 41
23 Experiment 2. Measured profiles at various times. . ... 43
24 Experiment 2. Initial and final profiles and initial and final
grain size distributions. . . . . . 44
25 Experiment 2. Grain Size distributions at six locations across
the profile after 24 hours of testing. . . .. .. .45
26 Experiment 3. Measured profiles at various times. . ... 46
27 Experiment 3. Initial and final profiles and initial and final
grain size distributions. . .... . . . 47
28 Experiment 3. Grain size distributions at six locations across
the profile after 24 hours of testing. . . . ... 48
29 Experiment 4. Measured profiles at various times. . ... 49
30 Experiment 4. Initial and final profiles and initial and final
grain size distributions. . .. . . . 51
31 Experiment 4. Grain size distributions at six locations across
the profile after 24 hours. . . . . .. 52
32 Experiment 5. Measured profiles at various times. . ... 53
33 Experiment 5. Initial and final profiles and initial and final
grain size distributions. . ... . . . 54
34 Experiment 5. Grain size distributions at six locations across
the profile after 24 hours. . . . . . 55
35 Experiment 6. Measured profiles at various times. . ... 56
36 Experiment 6. Initial and final profiles and initial and final
grain size distributions. . .. . . . 57
37 Experiment 6. Grain size distributions at six locations across
the profile after 24 hours. . . . . . 60
38 Experiment 1. Equilibrium beach profiles. Top: exponential
variation of A. Middle: linear variation of A. Bottom:
average A .............. ..... . . . . 63
39 Experiment 2. Equilibrium beach profiles. Top: exponential
variation of A. Middle: linear variation of A. Bottom:
average A. . . ..... .. . . . 64
40 Experiment 3. Equilibrium beach profiles. Top: exponential
variation of A. Middle: linear variation of A. Bottom:
average A. . ... . . . . . 65
41 Experiment 4. Equilibrium beach profiles. Top: exponential
variation of A. Middle: linear variation of A. Bottom:
average A ........... . . . . 66
42 Experiment 5. Equilibrium beach profiles. Top: exponential
variation of A. Middle: linear variation of A. Bottom:
average A. . . . . . . .67
43 Experiment 6. Equilibrium beach profiles. Top: exponential
variation of A. Middle: linear variation of A. Bottom:
average A ............. . . . .68
44 Experiments 1, 2 and 3. Comparison of predicted and measured
profiles for exponential fit to A values as determined from
measured mean sediment sizes. . . . . 70









45 Experiments 1, 2 and 3. Comparison of predicted and measured
profiles for local A values as determined from measured mean
sediment sizes. . ..... .. . . . 71
46 Nourishment events at Delray Beach, Florida and subsequent
volume changes (Coastal Planning and Engineering, Inc.). . ... 73
47 Location map of Delray Beach, Florida nourishment project
(Coastal Planning and Engineering, Inc.) . . . .. 74
48 Average grain size variation across profile 180.88 Delray Beach,
Florida, 1988. . . ..... . . 75
49 Exponential fit to A parameter distribution across profile 180.88
Delray Beach, Florida, 1988. ........... . 76
50 Average grain size variation across profile 184.88 Delray Beach,
Florida, 1988. ... ... ...... .. . . 77
51 Exponential fit to A parameter distribution across profile 184.88
Delray Beach, Florida, 1988. ... . . . 78
52 Average grain size variation across profile 187.88 Delray Beach,
Florida, 1988. . . .. . . . .. 79
53 Exponential fit to A parameter distribution across profile 187.88
Delray Beach, Florida, 1988. . . ... . 80
54 "Blind folded" comparison of computed and measured profiles,
Delray Beach, Florida, 1988. Computed profiles based on A
parameter fit to measured sediment size. . . . ... 81
55 Comparison of computed and measured profiles, Delray Beach,
Florida, 1988. Computed profiles are best fit based on
exponential A parameter. . ... .. . . 82
56 Project limits and profile designations Jupiter Island project
(Arthur V. Strock and Associates, Inc.). . ... . .84
57 Comparison of computed and measured profiles, Jupiter Island,
Florida, 1987. Computed profiles are best fit based on
exponential A parameter distribution. . . . ... 85
58 Comparison of computed and measured profiles, Jupiter Island,
Florida, 1987. Computed profiles are best fit based on
exponential A parameter distribution. . . . ... 86
59 Comparison of computed and measured profiles, Jupiter Island,
Florida, 1987. Computed profiles are best fit based on
exponential A parameter distribution. . ... . 87
60 Comparison of computed and measured profiles, Jupiter Island,
Florida, 1987. Computed profiles are best fit based on
exponential A parameter distribution. . . . ... 88
61 Longshore variations of A values at shoreline, end of line and
average, 1973. A values based on exponential fit to A parameter
distribution. Jupiter Island, Florida. . . ... 90
62 Longshore variations of A values at shoreline, end of line and
average, 1981. A values based on exponential fit to A parameter
distribution. Jupiter Island, Florida. . . . ... 91
63 Longshore variations of A values at shoreline, end of line and
average, 1987. A values based on exponential fit to A parameter
distribution. Jupiter Island, Florida. . . . ... 92
64 Longshore variations of A values based on slopes, volumes and
the average of the two. Jupiter Island, Florida, 1973. . .. .94
65 Longshore variations of A values based on slopes, volumes and
the average of the two. Jupiter Island, Florida, 1981. . .. .95









66 Longshore variations of A values based on slopes, volumes and
the average of the two. Jupiter Island, Florida, 1987. . .. .96
A-i Listing for program EQPR.FOR ........ . . A3
A-2 Listing of input file EQPR.INP for example 1 . . A14
A-3 Listing of output file EQPR.OUT for example 1 . . A16
A-4 Listing of input file EQPR.INP for example 4 . . .. A32
A-5 Listing of output file EQPR.OUT for example 4 . . .. A34
B-1 Flow diagram for problem solution. . . ... .. .. B3
B-2 Three regions considered in computational process . ... B7
C-1 Average grain size distribution across Delray Beach, Florida,
1976 . . ....... . . . . C3
C-2 Grain size distributions at various locations across the profile.
Delray Beach, Florida, 1976. . . ... . C4
C-3 Beach profiles at R177 for 1973, 1983 and 1988. Delray Beach,
Florida. . . ... . . . . C5
C-4 Beach profiles at R180 for 1973, 1983 and 1988. Delray Beach,
Florida. . . ... . . . . C6
C-5 Beach profiles at R184 for 1973, 1983 and 1988. Delray Beach,
Florida. . . ... . . . . C7
C-6 Beach profiles at R187 for 1973, 1983 and 1988. Delray Beach,
Florida. . . . ... . . . .. C8
C-7 Grain size distributions at various locations across profile R177.
Delray Beach, Florida, 1988. Grain diameter in millimeters. . C9
C-8 Grain size distributions at various locations across profile R180.
Delray Beach, Florida, 1988. Grain diameter in millimeters. C10
C-9 Grain size distributions at various locations across profile R184.
Delray Beach, Florida, 1988. Grain diameter in millimeters. C11
C-10 Grain size distributions at various locations across profile R187.
Delray Beach, Florida, 1988. Grain diameter in millimeters. ... C12
C-ll Beach profile at station R177 in 1988 at Delray Beach, Florida
and associated grain size distributions. Grain diameter in
millimeters. .. .. .... .... . . . .. C13
C-12 Beach profile at station R180 in 1980 at Delray Beach, Florida
and associated grain size distributions. Grain diameter in
millimeters. . . ... .. . . . C14
C-13 Beach profile at station R184 in 1988 at Delray Beach, Florida
and associated grain size distributions. Grain diameter in
millimeters. ..... . . . . . C15
C-14 Beach profile at station R187 in 1988 at Delray Beach, Florida
and associated grain size distributions. Grain diameter in
millimeters. . . ... .. . . . C16









RATIONAL TECHNIQUES FOR EVALUATING POTENTIAL
SANDS FOR BEACH NOURISHMENT


PART I: INTRODUCTION


1. The rational design of beach nourishment projects requires the
ability to calculate the geometry of the added sand volume, both as a function
of space and time. This capability is essential for quantitative evaluation
of the relative merits of various borrow areas and in benefit/cost analysis of
such projects including the volumes and timing of renourishments. In many
cases the material may be a by-product of a dredging project carried out for
other purposes. Particular design aspects of significance include the
equilibrated beach profile, especially the additional dry beach width and the
longevity of the project. Traditionally, attempts to quantify benefits of
beach nourishment have utilized "compatibility" and "overfill" factors which
relate the sand sizes of borrow and native material.
2. In a general sense, the problem of the evolution of beach
nourishment projects can be considered as occurring over two more or less
distinct time scales, see Figure 1. The beach profile which is usually placed
at a relatively steep slope equilibrates over a fairly short time scale,
perhaps with a "folding time" on the order of several years. The time scale
associated with the planform evolution depends primarily on the length of the
project and the wave climate; for longer projects (say greater than several
kilometers), the time scale is on the order of decades. Regardless of whether
these two time scales are distinct or not, it is useful to consider the
equilibrium beach profile associated with the volume and texture (i.e. grain
size distribution) of the nourishment material.
3. This paper presents, for two-dimensional conditions, procedures for
predicting the equilibrium beach profile resulting from placement of an
arbitrary volume of material with an arbitrary grain size distribution on a
profile of arbitrary shape.
4. This report is organized as follows: Part II reviews the background
relative to efforts to quantify the suitability and/or effectiveness of
materials for beach nourishment. Additionally, characteristics of equilibrium
beach profiles relevant to beach nourishment are presented. These latter
results pertain for perfectly sorted sediments. Part III describes and









Original Shoreline


t~"Spreading Out" Losses





Sand Moves Offshore to
Equilibrate Profile



Nourished Shoreline


Sp "Spreading Out" Losses

a) Plan View Showing "Spreading Out" Losses
and Sand Moving Offshore to Equilibrate Profile


Dry Beach Widt
(Fine Sand)


Dry Beach Width (Coarse Sand)

Initial Placed Profile

_ Equilibrated Profile (Coarse Sand)
Sea Level


Original Profile


Equilibrated Profile (Fine Sand)


b) Elevation View Showing Original Profile, Initial Placed Profile
and Adjusted Profiles That Would Result by Nourishment
with Coarse and Fine Sands

Figure 1. Sand transport losses and beach profiles associated with a beach
nourishment project.









illustrates with examples the methodology developed in the present study for
calculating equilibrium profiles for sediments of arbitrary sorting. A
computer program developed for this purpose is described in terms of the
general algorithms employed. Part IV presents the results of a limited set of
laboratory studies carried out in conjunction with this study. Part V
describes relevant field data from Delray Beach, FL and Jupiter Island, FL.
Both areas have experienced multiple beach nourishment programs. Part VI
provides the summary, conclusions and recommendations for further research.
Part VII is a list of references. Appendix A is a list of the computer
program provided to carry out calculations of equilibrium profiles for
sediments of arbitrary sorting. Additionally, listings are provided of the
input and output files for two of the examples presented in this report.
Appendix B provides a detailed discussion of the computer program. Appendix C
contains additional data for the Delray Beach, FL nourishment project.









PART II. BACKGROUND


5. Various investigators have proposed procedures for relating the
overall qualities of borrow and native sediments. As a rule of thumb, an
attempt is made to locate borrow material with granulometric characteristics
similar to those of the native material. Generally, the available procedures
focus on comparing the grain size characteristics rather than on their
response to a wave and tide regime. Thus these methods must be considered as
ad hoc and not truly representative of the performance of a beach nourishment
material. Moreover these procedures do not address the additional dry beach
width, a factor of primary concern to the designer and funding entities. A
brief review of the various available methods follows.
6. Krumbein and James (1965) proposed a method which considered the
grain size distributions, f(o), of the borrow and native materials to be each
represented by log-normal distributions as proposed earlier by Krumbein (1967)

f($) 1e- /2o2 (1)


in which 0 is the sediment diameter expressed in phi units, defined as

*=-log2 (D(mm)) (2)

where, as indicated, D is the sediment diameter in millimeters and p and a are
the sample mean and standard deviation in phi units. This method defined
compatibility of the borrow material on the basis of the proportion of borrow
material distribution which was common with the native sand size distribution.
This approach appears somewhat reasonable in discounting the finer fraction of
the borrow material, but less reasonable in discounting similarly the
proportion of coarse material which is in excess relative to the native sand.
7. James (1974) developed a complex method addressing the relative
renourishment frequency for different sand characteristics; however, this
procedure only considered longshore sediment transport and considered the
nourishment project to be located in an area where the ambient longshore
sediment transport had been interrupted completely.
8. Dean (1974) presented a method which attempted to address the
deficiency noted above of the earlier Krumbein and James method. The borrow
material was only discounted for the excessive proportion of fines present;
excessive proportions of coarser material were included in the compatible









fraction. However, it was considered that all the fine fraction smaller than
a critical value was lost. This method resulted in a considerably higher
compatibility than that of Krumbein and James (1965).
9. James (1975) developed a renourishment factor based on the relative
characteristics of the borrow and native sand characteristics. Similar to
earlier methods, this procedure was based on the size distributions rather
than their associated equilibrium profiles. Compared to the method by Dean
(1974), the primary difference is the retention of a portion of the fine
fraction in the compatibility considerations.
10. At present, the methods of James discussed in 7 and 9 above are
those recommended in the Shore Protection Manual (1984).
11. Companion to the problem of defining borrow material compatibility
is that of sampling across the pre-nourishment profile to establish the
"native" sand characteristics. This problem has been addressed by several
investigators.
12. Although the primary focus of the present paper is the equilibrium
beach profile for sand of arbitrary distribution, it is useful to consider,
for background purposes, profiles which result for the idealized case of
uniform borrow and native sediment sizes.
13. Dean (1991) has considered equilibrium beach profiles represented
by h(y) Ay213 first proposed by Bruun (1954) and found later by Dean (1977)
in an analysis of more than 500 profiles extending from the eastern end of
Long Island around Florida to the Gulf of Mexico border. Moore (1982)
investigated the relationship between the sediment scale parameter, A, and the
sand diameter, D, and established the results shown by the curved line in
Figure 2. Later Dean (1987) simply transformed this A vs D relationship to A
vs w where w is the fall velocity and found the result to be well approximated
by the straight line in Figure 2.
14. It has been shown that three types of profiles could occur
depending on the relative sizes of the borrow and native sands. These are
termed "intersecting", "non-intersecting", and "submerged" profiles and are
illustrated in Figure 3. The reader is referred to the paper (Dean, 1991) for
the criteria separating the three profile types and the volumes required to
achieve, for example, a desired additional dry beach width of the nourished
profile (for intersecting and non-intersecting profiles).















SEDIMENT FALL VELOCITY, w (cm/s)


LU
I-







LU


0
0=
C.


1.0





Fn

of
0.10







0.01 -
0.01


0.1 1.0 10.0 100.0
SEDIMENT SIZE, D (mm)


Figure 2.


Variation of sediment scale
(Dean, 1987).


parameter, A, with sediment size and fall velocity.













<~------_


Added Sand :


a) Intersecting Profile ApAN


Added Sand --':


b) Non-Intersecting Profile


Ay<0


Virtual Origin of
Nourished Profile


c) Submerged Profile Ap

Figure 3. Three generic types of nourished profiles. (a) intersecting
profile, (b) non-intersecting profile and (c) submerged profile.









15. The significance of these three profile types can be seen by
referring to Figures 4, 5 and 6. Figure 4 shows the effect on additional dry
beach width of placing the same volume (340 m3/m) of sand of four different
sizes. In the upper panel, the sediment is coarser than the native and the
profiles intersect with an additional dry beach width of 92.4 m. Panel b
shows the effect of using sand of the same size as the native resulting in a
dry beach width of 45.3 m. Panels c and d present the results for decreasing
sediment size; in Panel d, the dry beach width is zero.
16. Figure 5 shows the effect of nourishing with various quantities bf
a sediment which is smaller than the native. With the same sediment size, the
volumes of sediment increase from Panels a to d. With increasing volume, the-
landward and seaward extents of the nourished regions increase and in Panel d,
sufficient volume has been added to achieve a transition between submerged and
non-intersecting profiles.
17. These types of results can also be presented as shown in Figure 6
for an example which is in a form more representative of beach nourishment
concerns. This figure shows the relationship of additional dry beach width Ay
versus volume added, V, for three values of nourishment sediment scale
parameter, AF. Other variables common to the three cases are: berm height, B
2.0 m, depth of effective motion, h, = 8.0 m, and native sediment scale
parameter, AN = 0.1 m113. Of interest is that for AF = 0.12 > AN, the profiles
are initially intersecting and the additional dry beach width increases
relatively rapidly. However, with increasing volume, the profile becomes
non-intersecting and the slope d(Ay)/dV is approximately the same as that for
AF AN which is almost a constant. For AF = 0.08 m113 < AN, for small volumes
of sediment, there is no additional beach width, i.e. the profile is
submerged. However, with increasing volumes, there is a critical volume at
which the landward end of the submerged profile just reaches the shoreline;
for still greater volumes, the profile becomes a non-intersecting profile and
remains so for increasing volumes. For this case, the slope, d(Ay)/dv, is
essentially constant and parallel to the case of AF = AN. It is stressed that
all of these results apply for equilibrium profiles and that the equilibration
process may take several years to complete. In most nourishment projects, the
sand is placed steeper than equilibrium and will provide greater additional
dry beach width than equilibrium during the equilibration process.










S92.4m


H-


a) Intersecting Profiles,
AN= 0.1ml/AF = 0.14mI/3


b) Non-Intersecting Profiles
AN= AF= 0.1m1/3


c) Non-Intersecting Profiles -' .,._
AN = 0.1m1 3,AF = 0.09m1 /3


SL d) Limiting Case
Non-Intersecting


of Nourishment Advancement,
Profiles, AN= 0.1mIlAF = 0.09m1/3


6m


















= 6m





600
600


OFFSHORE DISTANCE (m)


Effect of nourishment material scale parameter, AF,
resulting dry beach. Four examples of decreasing AF
volume per unit beach length.


on width of
with same added


Figure 4.


15.9m
-I I--









OFFSHORE DISTANCE (m)


+ 4

O


L 10
-L
LU


J B = 1.5m

") Ad Vuh= 6m



a) Added Volume = 120 m3 /m


c) Added Volume = 900 m3 /m


d) Added Volume = 1660 m3/m .m
Case of Incipient Dry Beach


Figure 5. Effect of increasing volume of sand added on resulting beach
profile. AF = 0.1 m1/3, AN = 0.2 m1/3, h* = 6.0 m, B = 1.5 m.


















200 -

E/

I I /


o / o















Figure 6. Illustration of effect of volume added, V, and fill sediment scale
4 / 4
Wu 100 /
0
0/


z / I\




0 1000 2000
VOLUME ADDED PER UNIT BEACH LENGTH, VL(m3/m)


Figure 6. Illustration of effect of volume added, V, and fill sediment scale
parameter, AF, on additional dry beach width, Ay, Example
conditions: B = 1.5 m, h. = 6 m, AN = 0.1 m1/3.









18. In general it can be shown (Dean, 1991) that the non-dimensional
additional beach width, Ay/W*, is related to the non-dimensional volume added,
V/BW*, non-dimensional berm height, B/h., and ratio of fill to nourishment
sediment scale factors, AF/A1, i.e.



Ay B A,) (3)
BWf h. AJ


where h* and W* are the depth of limiting motion and width of the active
profile for the initial native profile. Figures 7 and 8 present this
relationship for B/h* = 1/2 and 1/4, respectively. Several features of these
figures are of interest. First, for AF/A^ > 1.2 (approximately), there is
little additional dry beach width gained for coarser (greater AF/AN) material
used. Secondly for AF/AN < 1, and a fixed volume, there is a rapidly
decreasing dry beach width with decreasing AF/AN. Finally the transition from
intersecting to non-intersecting profiles is indicated by the bold line in
Figures 7 and 8 and the transition from non-intersecting profiles to submerged
profiles occurs at the vertical asymptotic lines at the left end of each of
the curves.













10.0


_A = AWBW. = 10.0



1.0 I'ec I




S/ o ,\de
"O- iVl --- =0.2
/ /| -.p- -- -I- ^-i ...
0.10 V = 0.1

I! 1V' = 0.05

-Asymptotes = 0.02
for Ay = 0 I ,, ..-_ --7 ------
0.01 = 0.01
"-iW.- '' ---o
S --- V = 0 .0 0 5
^ ^--- {- -^" ~ ^ -- "
B- ---- ,-------------....----

A V = V/BW. =0.002

0.001 -Definition Sketch
0 1.0 2.0 2.8
A' = AF/AN

Figure 7. Variation of non-dimensional shoreline advancement Ay/W., with A'
and V. Results shown for h*/B = 2.0.






















0.1

I I 3' 0.1


S Asymptotes v
for Ay = 0

V' = 0.02




I i '
0.01 =


= 0.0051

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







Definition Sketch


--- L; I AF V
W. B AN BW

0.0001 ---
0 1.0 2.0 2.8
A' = A /A

Figure 8. Variation of non-dimensional shoreline advancement Ay/W., with A'
and V. Results shown for h2/B = 4.0.









PART III: METHODOLOGY BASED ON EQUILIBRIUM BEACH PROFILES


19. The method developed herein is based on an equilibrium profile for
a sediment volume with a distribution of sediment sizes. The following
assumptions/considerations are made: (1) A volume of sand, V, per unit beach
length is placed at a slope steeper than equilibrium in conjunction with a
beach nourishment project, (2) The sand is well-mixed at the time of
placement, (3) This sand will be reworked such that the volume removed from
the placement cross-section is sufficient to extend the nourished equilibrium
profile out to a specified depth, h*, of limiting motion (see Figure 9) or to
intersection with the initial profile, (4) Within the zone of sediment removal
from the placement cross-section, sorting occurs down to a specified
thickness, Ahmi, (5) The available sediment is sorted across the profile with
the coarser fraction remaining in the berm and shallower water region and the
finer sediment distributed offshore, and (6) the volumes of sediment removed
and deposited are equal, i.e. volume is conserved.
20. With the above basis, the procedure can be considered as one of
locally establishing segments of an equilibrium profile consistent with the
local A value and of balancing sediment volumes. Because the equilibrium beach
profile form h = Ay2/3 yields an unrealistic infinite slope at y = 0, the
modified form was used which recognizes the effect of gravity for the larger
slopes

h + /2(4)
s A3/2

as initially proposed by Dean (1983) and later shown by Larson (1988) and
Larson and Kraus (1989) to be derivable from the breaking wave model of Dally,
et al. (1985) under the consideration of uniform wave energy dissipation per
unit volume. In Equation 4, s is the beachface slope. It can be shown easily
that in shallow water

(5)
h = sy

i.e. the beach is planar consistent with measurements in nature. In deeper
water Equation 4 approximates h Ay2/3.
21. Because the A value is now local, the depth at a location y + dy is
referenced to the depth at y based on Equation 4,

















Placed Profile


Figure 9. Definition sketch.










h(y+dy) h(y) + dy (6)
(ay/ah)

where


= 13 hhO (7)
s 2 A/2h(y)


and the dy values are maintained reasonably small, on the order of 1-2 m.
22. A step-by-step discussion of the procedure is as follows and is
illustrated in the program flow chart, Figure 10.
a. With specified initial profile, ho(y), added volume, V, berm
height, B, and placement slope, Sp, the placed profile h1(y) is
determined by iteration such that the volume out to the location
where hp(y) ho(y) is the volume placed. This procedure also
determines the berm advancement, Ay,.
b. A trial value of the volume sorted, VGEN, and equilibrated berm
advancement DYEQ are assumed (refer to Figure 9 for definition of
variables). For each pair of these quantities, the equilibrium
profile is advanced from y to y + dy, where dy is constant, say 1-2
meters. This advancement is in accord with Equations 6 and 7. The
local A is that associated with the diameter for the coarser
fraction of the sediments that has not been deposited up to y in the
equilibration process (see Figure 11). This step-by-step
advancement is continued until the depth equals the specified
terminal depth, h. or until the equilibrium profile intersects with
the initial profile. At that stage, the volume actually generated
through erosion of the placed profile is substituted for the volume
available and the equilibrated berm advancement, DYEQ, is held fixed
in this inner loop and the process repeated. This inner loop (with
DYEQ) fixed is repeated until VGEN values in two successive
iterations agree within an acceptable limit.
c. The value of DYEQ is changed to attempt to ensure that the
associated value of h = h, or profile intersection will be achieved
coincident with the deposition of VGEN for that value of DYEQ. The
DYEQ at the k+l iteration is based on the following simple algorithm





































Outer
Loop
Establish Improved
Estimate of DYEQ


Outer Loop o,
Completed ?


Yes


Program Completed


Figure 10. Flow diagram for problem solution.











VGEN = Horizontal + Inclined Hatched Volumes
VUSED = Vertical + Inclined Hatched Voumes
R = 1 USED
VGEN
Placed Profile



Yc ---


Equilibrium
Profile


h,


Carried Out to
Here in this
Illustration


DIAMETER


(b) Cumulative Grain Size Distribution


(a) Original, Placed and Equilibrium Profiles,
The Latter Carried Out to ye


Figure 11. Method of determining grain size, Dc, for computation of current increment of
equilibrium profile.


z 0.5
o
I-
O R

a.O











DYEQ* = DYEQk + Fk+ (ADYEQ)


in which ADYEQ is specified as some reasonable value, say 2 or 5
meters and F1 = +1, F2 = +1 for k=2 and the positive and negative
signs apply depending on whether VEN > VUSED (F2 = +1) or VEN < VUSED
(F2 = -1). In subsequent iterations (k>2), Fk" = Fk if the sign of
VGEN VusED did not change in the preceding iteration and
F+1 = -0.5 Fk if a sign change did occur.
23. It is noted that the solution procedure structure is identical for
both idealized and arbitrary grain size distributions. In this context,
idealized refers to grain size distributions given by Equation 1.
Additionally, the method can be applied for arbitrary initial profiles.


Examples


24. Methods developed in the earlier sections of this paper will be
illustrated with examples.
Example 1 -- Idealized initial profile and log-normal size distribution, non-
intersecting profile
25. In this example, the initial profile was specified as characterized
by the following:
Uniform Sand Size: A = 0.1 m1/3 (D = 0.20 mm)
Berm Height: B = 1.5 m
Beach Face Slope: so = 1:10
The characteristics of the nourishment material are as follows:
Volume Added: 140.0 m3/m
Log-normal Sand Size: p = 1.60 (D = 0.33 mm), a = 0.400
Berm Height: B = 1.5 m
Placed Slope : sp = 1:10
Equilibrium Beach Face Slope: sE = 1:20
Mixed Depth: Ahmix = 0.2 m
Depth of Active Motion: h. = 6 m
Figure 12 presents the size distribution of the sediment. The volume and
slope above yielded a placed shoreline advancement Ay. = 58.2 m.








































DIAMETER (mm)



Figure 12. Cumulative grain size distribution, Examples 1 through 4.









26. Figure 13 shows the initial placed and equilibrium beach profiles.
It is seen that for this case the equilibrated shoreline advancement is
20.3 m. The volume eroded for this case is 66.8 m3 and, of course, the volume
eroded is equal to the volume deposited. For this example, the equilibrium
profile extends to an offshore distance of 550 m where it reaches the
specified depth of 6 m.
Example 2 Idealized initial profile and log-normal size distribution.
intersecting profiles
27. The characteristics of this example are the same as for Example 1
except the sorting coefficient, a, of the placed sand is 0.10 rather than
0.40. The cumulative sediment size distribution is shown in Figure 12. For
this case the equilibrium and original profiles intersect at a depth of 4.69 m
which is located at a distance of 425 m offshore. The initial, placed and
equilibrium profiles are presented in Figure 14.
Example 3 Sand smaller than native, near-zero shoreline advancement
28. The initial profile was specified as follows:
Uniform Sand Size: AN = 0.1 mi/3 (D = 0.2 mm)
Berm Height: B = 1.5 m
Beach Face Slope: so = 1:10
The characteristics of the nourished profile are:
Volume Added: 240 m3/m
Log-Normal Sand Size: p = 2.640 (D = 0.16 mm), a = 0.100 (See Figure
12)
Berm Height: B = 1.5 m
Placed Slope: sp 1:10
Equilibrium Beach Face Slope: sEQ = 1:10
Mixed Depth: Ahmix = 0.2 m
Depth of Active Motion: h* = 6 m
29. This example, presented in Figure 15, illustrates conditions near a
transition to a submerged profile.
Example 4 User-specified initial beach profile and sediment characteristics
30. In this example, the initial beach profile was specified by nine
points. Between these points, the profile is considered as a series of
straight line segments. The sediment size distribution is specified as linear
as shown in Figure 12. A sediment volume of 600 m3/m has been added. Other
variables are similar to those specified in Example 3 and are shown along with

















-j
\ -\M.Placed OFFSHORE DISTANCE (m)
E 0 200 300 400 500 600

O -

> Equilibrium

"" jOriginal h*= 6m
;:' ...;.,


W Volume Added = 140.0m3/m~ -
0 5.0 -Ao= 0.1m/3 4= 1.6
So= 0.10 a= 0.4 '':-
p= 0.10 =1.50m
B = 1.5m :
SEQ= 0.05 h = 6.0m ="

Figure 13. Example 1. Original, placed and equilibrium profiles. Case of non-
intersecting profiles. Idealized grain size distribution.















-UTU = il.3am
-\ -Placed OFFSHORE DISTANCE (m)
S \ 200 300 400 500 600
S0 I
O-

> Equilibrium
S hi = 4.69 m (Intersection Depth)
' UJ Original

I-
SVolume Added 140.0m
a 5.0 -Ao= 0.1m3 ga = 1.6V
s= 0.10
-s= 0.10 0(= 0.1
P 00 B =1.5m
s= 0.05
EQ h.= 6.0m

Figure 14. Example 2. Original, placed and equilibrium profiles. Case of intersecting
profiles. Idealized grain size distribution.



















E
-j
C,

0
I-
I-






0.
W 5.0







Figure 15.


Example 3. Original, placed and equilibrium profiles. Case of non-
intersecting profiles. Idealized grain size distribution smaller than native.
Incipient submerged profile.









the initial, placed and equilibrium profiles in Figure 16. The equilibrium
profile is of the non-intersecting type; however, intersection nearly occurs.
Other characteristics are similar to those in the three previous examples.
Additional example of variation of additional dry beach width vs volume added
31. Figure 17 presents the variation of additional dry beach width
versus nourishment sand volume added for three different grain sizes. The
common characteristics are:

Ao = 0.10 m1/3
so =s sEQ = 1:10
Ahlix = 0.2 m
B 1.5 m
h- 6 m
32. These results are in the form of Figure 6 which was based on
perfectly sorted sediment. For the upper curve in Figure 17, which applies for
sediment coarser than the native, there is a transition from intersecting to
non-intersecting profiles at an added volume of 600 m3/m. For the other two
sediments, all equilibrium profiles are non-intersecting.


Summary and Conclusions for Methodology Presented


33. Based on earlier work, three distinct types of equilibrium profiles
can exist: non-intersecting, intersecting and submerged.
34. Methods have been developed and illustrated with examples to
calculate the non-intersecting and intersecting equilibrium beach profiles
resulting from beach nourishment. With sand of different characteristics, the
method can accommodate varying ranges of realism, from idealized initial
profile and grain size distribution nourished profiles represented by
analytical forms, to the most realistic case in which the initial profile and
nourishment grain size distribution are arbitrary and are user-specified. The
equilibrium nourished profile is based locally on the differential equation
for equilibrium for a distribution of sizes. Examples are presented
illustrating the influence of various parameters.















S. . -. Placed
g OFFSHORE DISTANCE (m)
-J
o 0 20 300 400 500 600
O
(0
:-



Equilibrium
S:"* h.= 6m
S Original



S 5.0 -
50 so= 0.1 Volume Added = 600.0m /m "
a-0.
SS p= 0.1 B = 1.5m
EQ 01 h, = 6.0m



Figure 16. Example 4. Original, placed and equilibrium profiles. Case of non-
intersecting profiles for user-specified original profile and nourishment
material grain size distribution.












200-
INTERSECTING NON-INTERSECTING
E PROFILES PROFILES






I-






0



00
0 200 400 600 800 1000 1200

VOLUME ADDED PER UNIT BEACH LENGTH,'V-(m3/m)


Figure 17. Additional dry beach width, Ay, versus nourishment volume per unit beach
length, V. Three nourishment materials.
length, V. Three nourishment materials.









PART IV: LABORATORY STUDIES


Introduction and Descrintion of Facilities


35. An exploratory series of laboratory studies was conducted to
investigate profile response to waves of different characteristics for the
case of a poorly sorted sediment. A total of six experiments was conducted
using the same sand but different initial beach slopes and wave conditions.
36. The test conditions for the laboratory experiments are presented in
Table 1 and a schematic of the facilities is shown in Figure 18.


Experimental


Table 1
Conditions_ Wave


Tank Tests


Run Wave Period Wave Height Water Depth Initial
No. T(sec) H(cm) h(cm) Slope


1 1.25 9.0 22.5 1:10.85

2 1.25 9.0 22.0 1:5.74

3 1.25 11.0 22.5 1:9.93

4 1.25 11.0 21.0 1:13.94

5 1.25 8.5 20.0 1:24.27

6 1.25 9.0 21.0 1:14.33



Objectives


37. The general objectives of the laboratory studies are:
a. To document the evolution and sorting with time of initially
planar beach profiles and poorly sorted sediments, and
b. To compare experimental profiles and sediment size distributions
with predicted values based on techniques developed in this study.



































" I.STEEL FRRME

2.ENGINE AND CONTROLS
3.WRTER INLET
i.SANO BEACH
SUPPORT BEAM
6.PISTON
7.SUPPORTS
8.MOVING CART
9.POINTER GAGE









Figure 18. Schematic of laboratory facilities.









Experimental Procedures


38. The six tests commenced with the initially planar beach slopes
presented in Table 1. Prior to establishing the initial profile, the sand from
across the profile was mixed to approximate uniformity. After establishing the
uniform slope, sand samples at 4 or 5 different locations across the profile
were collected for later analysis.
39. The desired wave conditions were established and the profile
documented and sand sampling repeated at 1, 5, 10 and 24 hours (Experiments 1-
3) and 1, 6, 12 and 24 hours (Experiments 4-6). The wave heights were measured
visually and the location and height of the breaking waves were documented
several times during the test.


Test Results


40. The results of the test program are described below for each of the
experiments.
Experiment 1.
41. The profile evolution from a planar slope of 1:10.85 is presented
in Figure 19 for the initial profile and profiles at 1, 5, 10 and 24 hours of
testing. It is seen that only minor changes occurred between 10 and 24 hours
indicating that the system had approached equilibrium. The general
characteristics of the final profile relative to the initial include a concave
upward profile with most of the sand transported seaward and only a minor
amount transported landward to form a berm feature. Figure 20 presents the
variation with time of mean grain diameter for four locations across the beach
for all six experiments at 0, 10 and 24 hours. For Experiment 1 (Figure 20a),
it is clear that the initial mean grain size was reasonably uniform across the
beach and that, with progressing time, the coarser sediments were transported
shoreward and the finer sediments seaward. Figure 21 presents the initial and
final profiles and the grain size distributions at each of three locations
across the profile, and the initial grain size distribution. Figure 22 shows
the grain size distribution at 24 hours at six locations across the profile.
For this experiment, a substantial cross-profile sorting is evident with the
coarser sediment concentrated near the water line.












0.3
_ORIGINAL
.. ................ I H

--- -- -- 10H
S24H
0.2






0. I





SHE.



10.85

-.1.00




\ -



-0.2






-0 .3 i l-IIll- I -
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0

DISTANCE (m)


Figure 19. Experiment 1. Measured profiles at various times.






















a) EXPERIMENT t I
S At 1.3 I
......... ~T 1.7 H
-.-. AT 2.1 N
---- Ar 3.0 N






.-a.-- ---------
-- ...__. _.-----



0 6 i2 18 a
TIME








d) EXPERIMENT 4 q
AT 1.7 M
--...... Rft 2.7 N
.-.. AT 3.2 2
---- AT 4.2 H


IB 24


6 12
TIME


i8 24 0


b) EXPERIMENT a 2
AT 1.2 H
--.. .. AT 1.6
RT 2.0 M
A--- T 2.5 M






/ .'*^ --- ------------



0 6 12 18 2
TIME








e) EXPERIMENT 5
AT 2.7 M
--.--. T q.0 H
AT 5.0 N
AT 0.5 H1





.,.*---"I,'-

w" ^;'


6 12
TI ME


s18 2


Figure 20.


Variation of mean sediment size with time at several locations across beach.
All six experiments. Sediment diameter in millimeters.


c) EXPERIMENT 3
AT 1.6 H
........ T 2. L
Ar.-. T 2.8
---.. AT 3.1 H






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



0 6 12 B1 2'
TIME








f) EXPERIMENT A 6
Ar 2.0 H
..... AT 3.0 M
.. lT 3.5 N
_... AT 1.5 5






..--i


6 12
TIME












-I ORIGORIGINAL


-.....-.. 24 H


G.S.0. AT 1.3H


20 10\ G.5.D. AT 2.41M

0. .o o 80
S GRAIN DIhMETER 60.

.40.
20.

'.^V of.0. o. o .4 6.6 o0. .b
GRAIN 0DAMETER
10.85

'1\.00 o.S.O. RAT

_\ 'Jo0
f / 80.
1 .-. 60.



20 02 o 0.6

\ ,GRAIN OIANME


INITIAL DISTRIBUTION
100

80

60 .



20

0
0.0 0.2 60. 6.6 6.
GRAIN OIRMETER


3.4M








TER


I I I I 2I I I I I I I I I I55 9
1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 8.0 6.5 7.0 7.5 0.0 8.5 9.0 9.5


10.0


DISTANCE (m)

Figure 21. Experiment 1. Initial and final profiles and initial and final grain size
distributions.


I


















G.S.D. AT 1.3 H


Aso
wO
30

20
140
0.0 0.1 0.2 0.3 O. 0.5 0.8 0.7 0.8 0.9 1.0
GRAIN OIflHETER







G.S.D. AT 2.4 H
S00
90
60
70

\so

30

10

0.0 O 0. 0. 0.62 007 .. 0.6 1.0
GRAIN D(IAETER


G.S.D. AT 1.8 H


0.0 0.1 0.2 0.3 0.1 0.5 0.6 0.7 0.8 0.9 I.
GRAIN OlAIETER







G.S.D. AT 3.0 H














0.0 0.1 0.2 0.3 0.1 0.5 0.6 0.7 0.8 0.9 1
GRAIN DIAMETER


G.S.D. AT 2.1 H














0.0 0.1 .2 0.30. 0.5 0. 0.7 0.0 0.9 1.0
GRAIN DIAfETER







G.5.0. AT 3.4 H














.0 0.1 0.2 0.3 0.4 0.5 0.5 0.7 0.9 1.0
GRAIN OGIAETER


Figure 22. Experiment 1. Grain size distributions at six locations across the profile
after 24 hours of testing.









Experiment 2.
42. The evolution of this profile is presented in Figure 23 for times
of 0, 1, 5, 10 and 24 hours. This profile commenced with a relatively steep
uniform slope (1:5.74) and practically all of the sediment transport was
seaward. The variation with time of mean diameter at four locations across the
profile have been presented in Figure 20b. There is substantially less
pattern to the mean size distributions compared to Experiment. 1. There has
been some reduction in mean grain size in the seaward portion of the profile
and some size increases toward shore with very little change at the most
shoreward location sampled. The initial and final profiles and the final grain
size distributions at three locations across the profile are presented in
Figure 24 along with the initial grain size distribution. Figure 25 presents
the grain size distribution at six locations across the profile after 24 hours
of testing.
Experiment 3.
43. Figure 26 presents the profile evolution for Experiment 3 at 0, 1,
5, 10 and 24 hours. This result is of interest in that wave and initial slope
conditions are nearly the same as presented in Experiment 1, except that most
of the sediment transport was shoreward in Experiment 3. The variation with
time of mean grain sizes at four locations across the beach at 0, 5, 10 and 24
hours have been presented in Figure 20c. Figure 27 presents the initial and
final profiles and the grain size distributions at three locations across the
profile. Grain size distributions at six locations across the profile at the
final (24 hour) survey are presented in Figure 28. In general, sorting across
the profile has occurred.
Experiment 4.
44. Some improvements to the set-up were made before running this
experiment, including water level control and recording of the waves. The
conditions involved a slope of 1:13.94 which is milder than in the previous
experiments. The other variables were kept in the same range. As in the
former experiment irregular waves occurred.
45. Inspection of Figure 29 shows that a berm and a bar were formed as
in the first experiment. The volumes do not match as well as in previous
cases, which is due to lack of lateral symmetry and the substantial
consolidation observed at the very beginning of the experiment. Nevertheless
erosion at the offshore end of the beach was observed. Figure 29 shows the












0.3
_ORIGINAL
.. ............... IH

-- IOH
- 24H
0.2






0. 1


\\ 5.7q


1.00 SL




cm










-0.2 I






-0.3
1.0 1.5 2.0 2.5 3.0 3.5 4.0 .5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0

DISTANCE (m)


Figure 23. Experiment 2. Measured profiles at various times.































-P 0


DISTANCE (m)


Figure 24.


Experiment 2. Initial and final profiles and initial and final grain size
distributions.




















G.S.D. AT 1.2 H













0.0 0.1 0.2 0.3 O.4 0.5 0.6 0.7 0.8 0.9 1
GRIN DIfRETER







G.S.D. AT 2.3 M


.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
GRAIN DIAMETER


G.S.D. AT 1.6 H













0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
GRAIN DIAMETER







G.S.D. AT 2.5 M













0.0 0.1 0.2 0.3 0. 0.5 0.6 0.7 0.0 0.9 1
GRAIN OIARETER


G.5.D. AT 2.0 M


0.0 0.1 0.2 0.3 0.U 0.5 0.6 0.7 0. 0.9 1.0
GRAIN 0ARHETER







G.S.D. AT 3.2 H













0.0 0.1 0.2 0.3 O. 0.5 0. 0. 0. 0.9 1.0
GRAIN DIAMETER


Figure 25. Experiment 2. Grain Size distributions at six locations across the profile
after 24 hours of testing.













ORIGINAL
.................. IH

10H
24qH
0.2






0. 1




X




r- Qa
V,


-0.1


9.93

1.00
-0.2 /:

/m/imrmwmmmmDRnimnmz3THrmnmintmmimrnjn;tnni7 mtnmmmimummmfmnmnwm mn mimmnminim mwmr




-0 .3 I I I I I I I iI
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0

DISTANCE (m)


Figure 26. Experiment 3. Measured profiles at various times.













ORIGINAL
. .. .. 24 H


G.S.D. AT 1.3M

80.
-60.
z

40.
SG.5.. AT 2.:
20, 1 0
20. .0 800
Z 'C\ GRAIN DIAMETER a60O


20.

\" i.0 020.4 0,60.
GRAIN DIAMETER








9.93
"'" ---


;-*,\ t 'oo


INITIAL DISTRIBUTION


0
0



0-





.0 6.2 6.4 o.s 6.8
GRAIN DIAMETER


3M







7 .0


G.3.D. AT 3.1M
1


S60.


20

0 .;0
GRAIN DIAMETER


I I I I I I I I I I I I f I I I
1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5


10.0


DISTANCE (m)


Figure 27. Experiment 3.
distributions.


Initial and final profiles and initial and final grain size


SHL







































4-c
co

G.S.D. AT 2.6 H G.5.O. AT 3.1 M G.S.O. AT 4.6 H
too 100 100
90 90 90
80 o0 80
70 70 70
.SO SO w0
so ; Uso U so
.S0 .40 50

30 30 30
20 20 20
10 10 10
a o L. a k P w- 0. .
0.0 0.1 0.2 0.3 0.4 0.S 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 o. 0.5 0.8 0.7 0.8 0.9 1.0
GRIN DIAMETER GRAIN DIARETER GRAIN DIAMETER








Figure 28. Experiment 3. Grain size distributions at six locations across the profile
after 24 hours of testing.












0.3
_ORIGINAL
........- ... ....... 1 H
.- .. .. -- 6H
12H
24H
0.2






0.1 A





0.0 S--L






1.00
-0.2 -






-0.2 "mm m""" .






-0.3
1.0 L.5 2.0 2.5 3.0 3.5 41.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 LO.0

DISTANCE (m)


Figure 29. Experiment 4. Measured profiles at various times.









profiles for 0, 1, 6, 12 and 24 hours. The grain sizes variations are shown
in Figure 30. The variations with time of mean grain sizes at four locations
across the profile are presented in Figure 20d. Figure 31 provides the grain
size distributions at six locations across the profile at the final (24 hour)
survey.
46. Although a clear trend in grain sizes is not evident, it can be
seen that the most seaward sample has about the same distribution as the
original and that this time a sorting to finer sizes has been achieved at the
berm.
Experiment 5.
47. This experiment included the mildest initial slope of all six
tests. A berm trapping a lagoon was formed with the sand apparently
originating from both onshore and offshore sides of the beach. Also an
offshore bar was formed clearly with sand provided by the zone in between.
The evolution of the beach is shown in Figure 32 for 0, 1, 6, 12 and 24 hours.
The initially mild slope became even milder on the average below the still
water level. From Figure 33 which shows the grain size distributions for the
initial and final, it can be concluded that the concentration of fine grain
sizes offshore is greater. The variation with time of mean grain sizes at
four locations across the profile are presented as Figure 20e. Figure 34
provides the grain size distributions at six locations across the profile at
the final (24 hour) survey.
Experiment 6.
48. This was the most sophisticated experiment because of the sand
tracers which were used. The evolution of the beach is shown in Figure 35.
As in Experiment 1, a berm was formed but most of the sand was transported
offshore where it formed a bar feature.
49. The sand size distributions for the initial and final profiles are
shown in Figure 36. It is clear that far offshore the sand is finer even
though from this figure the location of the coarsest sand is not so evident.
Some shift to coarser sizes from the initial occurs at the berm and at 3.0 m.
50. The tracers were followed as carefully as possible, but this was
not always an easy task.
51. The initial tracer seive sizes and distributions were as follows:
a. Blue: #100 at 4.5 m.
b. Orange: #100 at shoreline.











0.3
_ORIGINAL
2.... _24 H INITIAL DISTRIBUTION
100
6.5.0. RT 1.7M
S80
0.2 80
5 Z 60
60. 0
0 040
01 lt DG.S.D. AT 2.7MM a


0 0 0.6 .0 .0 2 .0
8o .0.( 6.2 6.4 2.60.8 .0
0.20 GRAIN DIAMETER
0 0 .8 .L
~ '0 --o .2 .0. 6.: 'a4 .0
S', \ GRAIN DIAMETER S3L


P ,,;.5.0. AT 3.7M
-nn I C





-0.2 -2
\ 13. 94 / ^^-
A.\ -0 0.2 0.To.6 A.a U.0
".' \ GRAIN DIflHETER

-0.2 "k_






-0.3 I I I I I I I I I I
1.0 1.5 2.0 2.5 3.0 3.5 41.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 1 .0

DISTANCE (m)


Figure 30. Experiment 4. Initial and final profiles and initial and final grain size


distributions.





















G.S.D. AT 2.2 H


0.0 0.1 0.2 0.3 O.' 0.5 0.6 0.7 0.0 O.9 1
GRAIN OIAHETER







G.S.D. AT 3.2 H














0.0 0.I 0.2 0.3 O.i 0.5 0.5 0.7 0.9 .
GRAIN DIAMETER


0.0 0.1


0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.9
GRAIN ODIAETER


G.S.D. AT 3.7 H
too
100

80
70



40
60



30
20

0
0.0 0.1 0.2 0.3 0.l 0.5 0.6 0.7 0,8 0.9 I
GRAIN DIAMETER


G.S.D. RT 2.7 H














0.0 0. 0.2 0.3 0.3 O. 5 .0. 0.6 0. 0. I
GRAIN DIAMETER


G.S.D. RT 4.2 H














0.0 0.1 0.2 0.3 O. 0.5 0.6 0.7 0.8 0.5 1.0
GRAIN DIAMETER


Figure 31. Experiment 4. Grain size distributions at six locations across the profile
after 24 hours.


G.S.D. AT 1.7 M












0.3
_ORIGINAL
.................... IH
-.. - 6H
12H
24H
0.2






0.1






0. -


2t. 27

,1.00

-0. I






-0.2 'nnm'mrnmom2.mimn7mmnmmmmmmimnmmmmmwm rmmmi nmmmmmimmhmrmmimmmn nnrnnflli#mnnnm.mn






-0.3 I I I
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 1 .0

DISTANCE (m)


Figure 32. Experiment 5. Measured profiles at various times.



































-0. 1





-0.2





-0.3




Figure 33


DISTANCE (m)


Experiment 5.
distributions.


Initial and final profiles and initial and final grain size




















G.S.D. AT 2.8 H
,------------------. 00
90
so
80
70



40

t-
30


0.0 0.1 0.2 00.3 O.S O. 0.7 0.8 0.9 1.0
GRAIN DOIAETER







G.S.O. AT 5.5 M
Inn


.O0 0.1 0.2 0. 0.4 0.5 0.6 0.7 0.9 1.0
GRAIN ODIfETER


G.S.D. AT 3.5 H














.o 0.1 6.3R O.i .n 0.6 0.s o.. 0.9 1
GRAIN DIAMETER


G.S.O. AT 6.5 H














0.0 0.1 0.2 0.3 0.4 0.5 0.8 0.7 0.8 0.9 I.
GRIN OIARETER


G.S.D. AT 4.5 H














0.0 O.1 0.2 0.3 0.4 .s 06.7 0.1 0.e9
GRAIN DIAMETER







G.S.D. AT 8.0 H














0.0 0.1 02 0.3 0.4 0.5 0.6 0.7 0.0.0 9 .
GRAIN DIRMETER


Figure 34. Experiment 5. Grain size distributions at six locations across the profile
after 24 hours.













ORIGINAL
.................... H
._._._._- 6H
2H
S2411H


SML
..... ... .. ...... ...... ....... ---- -- ... --- .- ............ .. .
swt.




\, 14.33

1.00






*^\\ -


I I I I I I I I 1
2.0 2.5 3.0 3.5 4.O 4.5 5.0 5.5 6.0 6.5

DISTANCE (m)


.0 7.5 I I.
7.0 7.5 8.0 8.5


9.0 9.5 10.0


Experiment 6. Measured profiles at various times.


m 0.0
C-

R


I I
1.0 L.5


Figure 35.




































-0.





-0.2





-0.3
I.



Figure 36.


Experiment 6.
distributions.


.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0

DISTANCE (m)

Initial and final profiles and initial and final grain size









E. Magenta: #70 at 4.5 m.
d. Green #70 at shoreline.
e. Yellow: #50 at 4.5 m.
f. Red: #50 at shoreline.
52. The results of the tracer investigation are summarized in Table 2.
The following can be concluded from the analysis:
a. The red tracers were the most readily tracked.

b. The blue tracer was lost completely. This was probably due to the
small size of these grains (#100) and that they were initially
located in relatively deep water. The interpretation is that when
the action of the waves began they were suspended and spread over a
large area with a very low concentration making it difficult to
follow their path or even to find them in a later examination of
the sand.

c. Similar problems to the blue tracer could have occurred with the
orange; however, as the placement of the orange was closer to the
shoreline, the area over which it was spread was smaller and the
concentration higher. This allowed these particles to be
identified upon the conclusion of the experiment.

d. The tracers which were initially located at the shoreline were
transported and sorted on the beach face during the first hour of
wave action. They remained there until the end of the experiment.
At that time they were located 4 cm below the surface corresponding
to the profile during the first hour.

e. The orange tracer was found at the top of the berm while the red,
not so evenly spread, was found at the low part of the beach face.
Recall that the orange tracer was the finest and that the red was
the coarsest.

f. At the bottom of the profile, just before the offshore bar, tracers
of different colors were found, indicating that transport has
occurred in both directions--seaward and landward--of this point.

g. No other evidence has been found indicating major patterns in the
sediment transport.

53. Other results concerning all experiments are presented below and
will be used later to develop additional conclusions.
54. Figures 20f and 37 present the remaining grain size information for
Experiment 6.
55. By comparison, the profiles equilibrated after 12 hours of wave
action and then, only approximately. However, the main features of the final
profile were established very fast, that is the beach face slope, the sand bar










Table 2

Results of the Tracer Analysis


Type of
Time Observation


Orange


Green


Red Yellow Magenta


Visual
At 1.5 m
At 1.6-1.7 m
At 1.7-2.0 m

Sample tubes
At 1.5 m
At 1.7 m

Accumulation
tube
At 1.9 m

At 2.5 m
At 3.0 m
At 3.5 m
At 4.0 m

At 5.0 m


Dyed zone





On the top


Few grains


Many

Some


Slightly
dyed


Visual


Accumulation
tube
At 2.0 m
At 2.5 m
At 2.9 m
At 3.1 m
At 3.2 m


24 HR Sample tubes
At 1.95 m

At 2.30 m

At 2.50 m

At 2.80 m
At 3.00 m
At 3.50 m
At 3.80 m
At 4.20 m
At 4.60 m
At 5.10 m


Layer at 4 cm
below top
Few at 1-5
cms from top
Layer at 1.5
cm below top


Few top


Few top
3 Grains


Few
Few
Layer at
3.5 cm
below ton


1 HR


Dyed zone


Spots


Slightly
dyed
Some


Slightly
dyed


6 HR


Layers by
the glass


Few















































Figure 37. Experiment 6. Grain size distributions at six locations across the profile
after 24 hours.










and the berm were formed in the first six hours and after that they only
migrated or modified their volumes slightly. Layers of sand were added or
removed from the existing features, but the slopes which dominate the main
characteristics of the beach remained almost constant. The tracers
(Experiment 6) only confirmed the way in which the main beach features
developed. At the very beginning of the experiment the waves carried the
finest tracers up the beach face. Furthermore, the coarsest tracer type was
spread over a larger area. After some hours a berm had been formed and the
beach face became steeper. The sediments were no longer able to be
transported up the beach as far as before so the orange tracers which were
transported to the farthest onshore location remained uncovered until the end
of the experiment. On the other hand, the other tracers were covered by
successive layers being found after 24 hours at some depths below the surface.


Comparison of Laboratory Data with Predictions


56. In this section, the six "final" (i.e. 24 hours) profiles obtained
in the laboratory experiments were compared with computed profiles based on
the cross-shore varying mean grain sizes as documented in the laboratory. It
is stressed that the comparisons to be presented are "blind folded" in the
sense that they do not incorporate any calibrations or adjustments to improve
the fit. Rather, the computed profiles are based on the empirical relationship
between the sediment scale parameter, A, and the sediment size, D, presented
in Figure 2. Comparisons are presented for: (a) profiles for parameterized
fits to the actual A vs y distributions, and (2) profiles for the local A
values.


Comparison Based on Parameterized Fit
to the Actual A Values


57. The method will first be described, then the results of the
comparison presented.
58. The procedure considers cross-shore variations of A of the forms

A(y) = A e-~ (9)









A(y) = Ao + my (10)


in which y is the offshore distance from the still water line, k and m are
empirical constants describing the best-fit variation in the cross-shore
direction and A. is the (idealized) sediment scale parameter evaluated at the
shoreline.
59. The general expression for equilibrium beach profiles is


h823 =A3/2 (11)
ay

in which A is the local value of the sediment scale parameter. Substituting
Equation 9 into Equation 11 and integrating


h(y) =A (1-3/2 2/3 (12)


and considering the variation given by Equation 10


h(y) = {-- [(A, + my)2.s-A' ] 2/3 (13)


60. The method described above was applied as follows. The distribution
of the A parameter across the profile was determined for each of the final
sediment samples based on the mean diameter and transforming to A via
Figure 2. Next the best least-squares representations of these data by
Equations 9 and 10 were established. Finally, the calculated profiles were
based on Equations 12 and 13. Figures 38-43 present a comparison of the
calculated and measured profiles for the six experiments. These results are
discussed briefly below.
61. For Experiments 1, 5 and 6 the predicted profile is somewhat
steeper than the measured whereas for Experiments 2 and 3, the measured is
steeper than the predicted and for Experiment 4, there is reasonable
agreement.












0.00


Figure 38.


Experiment 1. Equilibrium beach profiles. Top:
Middle: linear variation of A. Bottom: average


exponential variation of A.
A.


CALCULATED PROFILE
............... ....... MEASURED PROFILE O=o.i 33
RO=0. IM '
--.---- .. K=0.26






100 200 300 400 500 600 700 800 90












0 100 200 300 400 500 600 700 800 90
DISTANCE (m)
CALCULATED PROFILE
...................... MEASURED PROFILE o 33
RAO=0. 14M
---------.. M= -0.03













0 100 200 300 400 500 600 700 800 90







DISTANCE (m)
-






DISTANCE (m)


E
m
C4
LO C
w


0.20


0.30


0. 10













-.. CALCULATED PROFILE
\ ..................-.. MEASURED PROFILE 11 Mo.33
A O=O. 1M
K= 0.08






0 100 200 300 400 500 600 700 90
DISTANCE (m)
-, ___CALCULATED PROFILE
R\ ............. ....... MEASURED PROFILE o. 33
S.P0=0.11 M
M= -0.01






100 200 300 900 o00 600 700 800 9C
DISTANCE (m)
____CALCULATED PROFILE
-----------..................... MEASURED PROFILE








0 100 200 300 400 500 600 700 800 90
DISTANCE (m)


Figure 39.


Experiment 2. Equilibrium beach profiles.
Middle: linear variation of A. Bottom: av


Top: exponential variation of A.
erage A.


S


4
a '
p. 0


0.30


10












10












0.00


Figure 40.


Experiment


3. Equilibrium beach profiles.


Middle: linear variation of A. Bottom: average A.


Top: exponential variation of A.


CALCULATED PROFILE
-..................- MEASURED PROFILE 0.33

PAO=0.11 M






0 t00 200 300 400 500 600 700 800 91
DISTANCE (m)
CALCULATED PROFILE
-- .- ..........-... MEASURED PROFILE
-'" ~ AO0= 0. 1I M
M= -0.04






0 t00 200 300 400 500 600 700 800 900






DISTANCE (m)
CALCULATED PROFILE









0 100 200 300 900 500 600 700 800 910
DISTANCE (m)


E
C' fz
U-'


0.30












0.00


400 500
DISTANCE (m)


Figure 41.


Experiment 4. Equilibrium beach profiles. Top: exponential variation of A.
Middle: linear variation of A. Bottom: average A.


---. CALCULATED PROFILE
-..-- --............... MEASUREO PROFILE 0. 33
SAO= 0=. 11 M







0 100 200 300 O0 50oo G 00 700 800 901
DISTANCE (m)

.. CALCULATED PROFILE
- ..MEASURED PROFILE 0- -
A 0=0.11 M
M= 0.00









...LCULATED PROFILE
-. .. ;............... M U ED PR F IE







I I1 I1II1I1


E-

nr


0.30


900











0.00


Figure 42.


Experiment 5. Equilibrium beach profiles. Top:
Middle: linear variation of A. Bottom: average


exponential
A.


variation of A.


CALCULATED PROFILE
:::........':::J.ERASURED PROFILE .33
F10=0. 13 M
K=0.09






S100 200 300 00 500 700 800 901
DISTANCE (m)
CALCULATED PROFILE
-.. .--.-.-- ::.-- .-------.-.1IJERSURED PROFILE o.3
AO=0. 12 M
M= -0.01





S100 200 300 400 500oo 700 800 90(
DISTANCE (m)
CALCULATED PROFILE
::..------.....-------E---ASURED PROFILE








So00 200 300 400 500 600 700 800 900
DISTANCE (m)


-4


0.30











0.00


Figure 43.


Experiment 6. Equilibrium beach profiles. Top: exponential variation of A.
Middle: linear variation of A. Bottom: average A.


-CALCULATED PROFILE
...................... MEASURED PROFILE
.. O=0.14 M
-K=0.25






0 to1 200 300 400 S0 600 700 800 901
DISTANCE (m)
CA. LCULTED PROFILE
...---.... ............ MEASURED PROFILE
lO= 0. 14 M
M= -0. 03






0 100 200 300 400 500 600 700 800 901
DISTANCE (m)
., CALCULATED PROFILE
---------- -----------MEASURED PROFILE
^^ ^ .................... ME. SURED PROFILE







0 100 200 300 400 o00 800 700 800 90
DISTANCE (m)


0.30









Comparisons Based on Localized A Values


62. In this comparison which was only applied to Experiments 1, 2 and
3, the calculated profile was based on the local A(y) value as given by


h (y+dy) =[h3/2 (y) +A3/2 (y) dy]2/3 (14)


which follows directly from the differential form (Equation 11). The results
of applying Equation 14 to calculate profiles are presented in Figures 44 and
45. The results are somewhat similar to those presented and described for the
other method and will not be discussed further.










0.00


300.0
DISTANCE (m)

EXPERIMENT u 3


I
300.0
DISTANCE (m)


Figure 44.


Experiments
exponential


1, 2 and 3. Comparison of predicted and measured profiles for
fit to A values as determined from measured mean sediment sizes.


EXPERIMENT a 1

CA...LCULATED PROFILE
.................... MEASURED PR.OFILE







0.0 100.0 200.0 300.0 400.0 500.0 6
DISTANCE (m)

EXPERIMENT # 2

Ir .......... ........ MEASURED PRO0FILE


0.30


0.30


0.0


CALCULATED PROFILE
.................... HEASUREO PROFILE



j...... ............. .......











0.00


DISTANCE (m)

EXPERIMENT 4 3


300.0
DISTANCE (m)


Figure 45


Experiments 1, 2 and 3. Comparison of predicted and measured profiles for
local A values as determined from measured mean sediment sizes.


EXPERIMENT a 1


.................... MERSUREO PROFILE













CALCULATED PROFILE
--- -------------MEASURED PROFILE
."" ..................... ..MEASURE PROFILE








nn -on n no n ^ -


0.30


0.00


-0.30


bt-0U.0


600.0


CALCULATED PROFILE
--................ .. HEASURE0 PROFILE





----,~"









PART V: FIELD DATA


63. Two sets of field data were located which provided a basis for
comparison with and evaluation using the general methodology presented. These
were Delray Beach, Florida and Jupiter Island, Florida; both sites have
experienced multiple renourishment events. As with most field results, the
data sets are not as complete as desired. However, even though incomplete and
complex, field data are valuable as they contain no scale effects. The
following sections present field data from these two sites and utilize the
available data to evaluate the general methodology presented here.


Delrav Beach. Florida


64. As shown in Figure 46, Delray Beach was nourished in 1973, 1978 and
1984. Figure 47 presents the northerly and southerly limits of the 1984
nourishment. The mean diameter of this nourishment material is reported to be
0.16 mm whereas that of the native is 0.22 mm.
65. Figure 48 portrays, for Station 180.88, the 1988 distribution of
mean sediment size across the beach profile and Figure 49 presents the
associated A parameter with an exponential fit. The same information is
presented in Figures 50 and 51 for Station 184.88 and Figures 52 and 53 for
Station 187.88. Additional profile and sediment size information for Delray
Beach is contained in Appendix C. Two types of profile comparisons were
carried out as described below.
66. The first type of profile comparison is "blind-folded" in the sense
that only the best-fit exponential A relationships (Figures 49, 51 and 53)
were used with Equation 12 for the calculated profiles. These comparisons are
presented in Figure 54. In general, the comparisons are considered to be
quite good with the deviations for depths greater than 4 to 5 m believed to be
due to nourishment material not equilibrating to greater depths.
67. The second type of profile comparison is also based on exponential
distributions of A values using best least squares fit to the measured profile
data. These result are presented in Figure 55 and again the agreement is
generally good.















































Figure 46.


Nourishment events at Delray Beach,
(Coastal Planning and Engineering,


Florida and subsequent volume changes
Inc.).



































































Figure 47. Location map of Delray Beach, Florida nourishment project (Coastal
Planning and Engineering, Inc.).

74












08 180.88


0 1 0 1 2 2 3 3 4 4 5 5 6 I I I I I I I 1
SO 100 150 200 250 300 350 4 00 q50 500 550 600 650 700 750 800 850 900 950 1000 1050 1100


DISTANCE (m)
Figure 48. Average grain size variation across profile 180.88 Delray Beach, Florida,
1988.


1.000


*1
1:1



N


U. IU -

0.100

0.050 -

0.000


I























T-

E 0.150
UJ
I-


I 0.100


4.


-DB 180.88


SI I


200.0


LENGTH (m)
Figure 49. Exponential fit to A parameter distribution across profile 180.88 Delray
Beach, Florida, 1988.


250.0


0.200


I


r1-


0.050 1


0.000 L
10(


0.0


300.0


400.0











DB 184.88


I I I I I I I I I I I I I I I I I I I I I
0 50 100 150 200 250 300 350 400 450 0 50 550 600 650 700 750 800 850 900 950 1000 1050 1100

DISTANCE (m)
50. Average grain size variation across profile 184.88 Delray Beach, Florida,
1988.


I:




n

U


Figure















DB 184.88









,-
-_'r


200.0


300.0


400.0


LENGTH (m)

Figure 51. Exponential fit to A parameter distribution across profile 184.88 Delray
Beach, Florida, 1988.


250.0




0.200


0.150




0.100


0.050 1-


0.000 LI
100.0












08 187.88


I I IO I I I I I I I I I6 I 0 00 1 1050 1
so t00 ISO 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 1050 1100


DISTANCE (m)
Figure 52. Average grain size variation across profile 187.88 Delray Beach, Florida,
1988.


1.000


P4
H


H
W
EA


0.000













250.0




0.200



E
S0.150

0.100
LU
w
S 0.100

0-
4


- DB 187.88


0.050 t-


0.000 L
100.0


200.0


300.0


400.0


LENGTH (m)
Figure 53. Exponential fit to A parameter distribution across profile 187.88 Delray
Beach, Florida, 1988.











0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00




0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00


0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00


Figure 54.


PROFILE n DB180.88

CALCULATED PROFILE









0.0 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 q50.0 500.0 550.0 6,
DISTANCE (m)

PROFILE s DB184.88

-CRLCULRTED PROFILE
S" .. ...... ... ..... MEASURED PRO FILE


I I I I I I
50.0 100.0 [50.0 200.0 250.0 300.0


DISTANCE (m)

PROFILE a 08187.88
_- --__---_ __ CALCULATED PROFILE
~_ ..^.. ...............ME.S.U.B PROFILE


.0 50.0 100.0 150.0 I I I
0.0 50.0 100.0 150.0 200.0 250.0 300.0 350.0


"Blind folded"
Florida, 1988.
sediment size.


I 3 I I I
350.0 400.0 450.0 500.0 550.0


00.0


00.0 I 50.0
400.0 450.0 500.0 550.0 600.0


DISTANCE (m)

comparison of computed and measured profiles, Delray Beach,
Computed profiles based on A parameter fit to measured











PROFILE n DB180.88
0.00
1.00 -
2.00 ...----.--
3.00 -
4.00 -O-.
m 5.00
P 6.00 CALCULATED PROFILE
w 7.00 ...................... MEASURED PROFILE --
Q 8.00
9.00
10.00 I
00. 0 0.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0
DISTANCE (m)

PROFILE t DB184.88

i.oo

0.00
1.00
2.00 -
3.00 ......


6.00 CALCULATED PROFILE
7.00 ..................... MEASURED PROFILE ... -
f 8.00 .
9.00
10.00I
0.0 50.0 100.0 150.0 200.0 250.0 300.0 350.0 q00.0 450.0
DISTANCE (m)

PROFILE n 08187.88
0.00
1.00 --- ..... .
2.00 -
3.00 -...... .....
4.00
5.00
P 6.00 CALCULATED PROFILE
7 7.00 .................... MEASURED PROFILE
n 8.00 ""-
9.00
10.00 I I I I
00.0 .0 100.0 150.0 200.0 250.0. 000.0 330.0 400.0 450.0
DISTANCE (m)

Figure 55. Comparison of computed and measured profiles, Delray Beach, Florida, 1988.
Computed profiles are best fit based on exponential A parameter.









Jupiter Island. Florida


68. This site has been nourished five times with the first nourishment
also occurring in 1973. The nourishment history is summarized in Table 3.
Because no information is available describing the grain size distribution
across the beach, comparisons are limited to information available in
profiles, both pre- and post-nourishment. The nourished area and the profile
designation are shown in Figure 56. The mean diameter of the nourishment
material is reported to be 0.12 mm compared to the native of 0.20 mm.


Table 3
Summary of Nourishment History (Post 1973) at Jupiter Island



Segment Volume
Year Seement Length m Cubic Meters

1973 1 5,120 1,850,000
1974 1 2,800 750,000

1977 1 790 200,000
1977 2 1,100 163,000
1978 1 2,330 650,000

1983 1 1,780 454,000
1983 2 960 311,000

1987 1 950 287,000
1987 2 3,300 1,067,000
1987 3 1,080 353,000

Total 6,085.000 cubic meters



69. Figures 57, 58, 59 and 60 present best least squares fits to the 12
available 1987 measured profiles in which an exponential variation of A with
offshore distance has been utilized. The general fit to the measured profiles
is considered good, although at some profiles there is a nearshore rock reef
(e.g. profile J13.87, Figure 58) which protrudes above the sand surface.
70. The second type of analysis presented compares the effective A
parameter in the shallower and deeper portions of the profiles before
nourishment (1973) and after nourishment (1981 and 1987). Based on the



































































Figure 56.


Project limits and profile designations Jupiter Island project
(Arthur V. Strock and Associates, Inc.).

84










PROFILE


# J5.87


DISTANCE (m)


PROFILE


t J6.87


E
a
m fa
?
1^1 *-1


0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00


Figure 57.


DISTANCE (m)

PROFILE J7.87





-- CALCULATED PROFILE
.................... MEASURED PROFILE



0.0 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0
DISTANCE (m)
Comparison of computed and measured profiles, Jupiter Island, Florida, 1987.
Computed profiles are best fit based on exponential A parameter distribution.


CALCULATED PROFILE
................ -MEASURED PROFILE


I I Ii .-











0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00


Figure 58.


200.0
DISTANCE


250.0
(m)


450.0


Comparison of computed and measured profiles, Jupiter Island, Florida, 1987.
Computed profiles are best fit based on exponential A parameter distribution.


PROFILE t J11.87





CALCULATED PROFILE
-..................... MEASURED PROFILE



0.0 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 4!
DISTANCE (m)

PROFILE J12.87





CALCULATED PROFILE
...................... MEASURED PROFILE



0.0 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 45
DISTANCE (m)

PROFILE # J13.87





--- CALCULATED PROFILE
.--.....-..............MEASURED PROFILE
-


0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00


0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00












0.00
1 .00
2.00
3.00
9.00
5.00
6.00
7.00
8.00
9.00
10.00




0.00
1.00
2.00
3.00
. 00
5.00
6.00
7.00
8.00
9.00
10.00




0.00
1 .00
2.00
3.00
14.00
5.00
6.00
7.00
8.00
9.00
10.00


I I
200.0 2!
DISTANCE )
DISTANCE (m)


PROFILE # J19.87





--- CALCULATED PROFILE
......................MEASURED PROFILE


I I
200.0 25
DISTANCE (m)


450.0


Figure 59.


Comparison of computed and measured profiles, Jupiter Island, Florida, 1987.
Computed profiles are best fit based on exponential A parameter distribution.


PROFILE # J17.87





CALCULATED PROFILE
.................... MEASURED PROFILE


I I I I I I I
0.0 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 4
DISTANCE (m)

PROFILE # J18.87






-- CALCULATED PROFILE
................... ME SURED PROFILE











PROFILE


t J20.87


DISTANCE (m)


m a
00


0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00


PROFILE


# J21.87


DISTANCE (m)


PROFILE


t J22.87


DISTANCE (m)


Figure 60.


Comparison of computed and measured profiles, Jupiter Island, Florida, 1987.
Computed profiles are best fit based on exponential A parameter distribution.


0.00
1.00
2.00
3.00
q. 00
5.00
6.00
7.00
8.00
9.00
10.00


___CALCULATED PROFILE
...................... MEASURED PROFILE


0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00


___CALCULATED PROFILE
............... ......MEASURED PROFILE









exponential distribution which resulted in the profile fits in Figures 57, 58,
59 and 60, the A values near the shore (Ao), at the end of the profile lines
and the average of these two are compared for 1983, 1981 and 1987, in
Figures 61, 62 and 63, respectively. In those plots, north is to the right.
It is noted that for pre-nourishment conditions (1973), there was a
substantial difference between the shallow water and end-of-line A values. In
1981 (Figure 62), after nourishment, the range had decreased some; however,
the mean was about the same. This is interpreted as due to the beach berm
being displaced by the relatively finer nourishment sand into deeper water,
such that the nearshore and end-of-line A values were more nearly the same.
Finally in 1987, (Figure 63) the A values at the shoreline and end-of-line are
nearly the same. This is interpreted as the nourished sediment being
transported over the entire profile such that the A parameter is approximately
uniform across the profile.
71. A simpler but similar type of analysis to that presented in the
preceding paragraph was carried out based on the overall characteristic of the
profile. In particular, if h = Ay213 is appropriate, then the average slope,
s, to the end of line where the water depth is h', at an offshore distance,
y', is

A 3/2 (15)
(h') 1/2


Hence the A value based on overall slope, Ak, is

A, = [(h) 1/2/3 (16)

72. Similarly, it can be shown readily that the volume per unit length,
V, to the end of the line is

V= 3A,(y) /3 = 3 (h')5/2 (17)
5 5 (Ay) 3/2

Thus the A value based on volume, A,, is



3 (h') 5/2 2/3 (18)
Av -



In interpreting the differences between As and Ay, it is noted that if the
sediment is coarser nearshore and thus the values of A greater than offshore,



































981836 986836


South
(Downdrift)


ALONGSHORE DISTANCE


Figure 61. Longshore variations of A values at shoreline, end of line and average, 1973.
A values based on exponential fit to A parameter distribution. Jupiter
Island, Florida.


0.04 -


0.00 -
971836


976836


991836


996836



































976836


South
(Downdrift)


981836 986836 991836
ALONGSHORE DISTANCE


Figure 62. Longshore variations of A values at shoreline, end of line and average, 1981.
A values based on exponential fit to A parameter distribution. Jupiter
Island, Florida.


0.04 -


0.00 -
971836


996836
















A AT SHORELINE
----- A AT END OF LINE
--- AVERAGE


['A -


7.
7Wzz-


- "i~ ,

*.. .Al


976836
South
(Downdrift)


981836 986836 991836
ALONGSHORE DISTANCE


996836


Figure 63. Longshore variations of A values at shoreline, end of line and average, 1987.
A values based on exponential fit to A parameter distribution. Jupiter
Island, Florida.


nnn


97183
971836









then it is to be expected that A, > A, as will be seen. Figures 64, 65 and 66
each present the A values based on slopes and volumes and the average of the
two for 1973, 1981 and 1987, respectively. The results and interpretation are
generally similar to those presented for Figures 61, 62 and 63. Prior to
nourishment (Figure 64), the A values based on volumes were somewhat greater
than those based on slopes and the average A value was approximately 0.10
m1/3. Following nourishment, the relative difference between the two A values
is approximately the same, except the average A has decreased somewhat.
Finally in 1987, after further nourishment, the A value had decreased further
to less than 0.08 m1/3 and the A values based on area and volume are nearly
the same.


Conclusions Based on Field Data


73. Based on analysis of available field data from two nourishment
sites at Delray Beach, Florida and Jupiter Island, Florida, the following are
concluded. A "blindfolded" comparison of predicted and measured (1988)
profiles for Delray Beach shows good agreement (Figure 54). The computed
profiles in this comparison are based on an exponential fit to the A values
associated with the mean grain sizes. Differences exist primarily for depths
greater than 4 to 5 m and may be attributed to the nourished profile
equilibrating only to these depths. Additionally, by allowing the parameters
in the exponential A representation to be free, a good fit is obtained across
the entire profile (Figure 55). At Jupiter Island, since there are no cross-
shore sediment size data, the analysis concentrated on the variation of A
values in the nearshore and near the end-of-line. Two methods were employed
and although the general results of the two methods were similar, the
quantitative results differed. Based on an exponential A fit, prior to
nourishment the shoreline A value was substantially greater than that at the
end-of-line. By 1987, these two values were nearly the same and the mean
value had not changed appreciably from the pre-nourished values. A second
approach to examining the A values nearshore and near end-of-line is based on
the average slopes and volumes of the measured profiles. Again, prior to
nourishment, the two A values differed whereas in 1987, they were virtually
identical. A result which differed by this method compared to that based on



































976836


South
(Downdrift)


981836 986836 991836
ALONGSHORE DISTANCE


Figure 64. Longshore variations of A values based on slopes, volumes and the average of
the two. Jupiter Island, Florida, 1973.


0.00 L
971836


996836

















0.12




A..- **V9 -
0.08





0.04 --AC
--- AC
AVE


0.00 I
971836 976836
Downuth
(Downdrift)


981836 986836


991836


ALONGSHORE DISTANCE


Figure 65. Longshore variations of A values based on slopes, volumes and the average of
the two. Jupiter Island, Florida, 1981.


996836



































981836 986836


South
(Downdrift)


ALONGSHORE DISTANCE


Figure 66. Longshore variations of A values based on slopes, volumes and the average of
the two. Jupiter Island, Florida, 1987.


0.00 '-
971836


976836


991836


996836









the exponential A fit is that the post-nourishment average A value decreased
to approximately 0.08 m1/3 from the pre-nourishment value of 0.10 m1/3. This
result is qualitatively consistent with the use of sediment for nourishment
which is finer than the native.









PART VI: SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS
FOR FURTHER RESEARCH


Summary


74. A method has been developed and illustrated by application for the
prediction of the two-dimensional profile equilibrium resulting from the
placement of a specified volume of a well-mixed sand of arbitrary size
distribution. It is shown that upon placement of a given volume of material,
three types of profiles can result depending on the material size,
characteristics, the volume, berm height and closure depth. These are: (1)
intersecting, (2) non-intersecting, and (3) submerged profiles. The method is
applicable to the first two types. The method assumes that locally, the
profile is in equilibrium with the profile scale characteristics consistent
with a relationship developed by Moore. An iterative method is employed which
ensures that the volume eroded from the placed profile is equal to that
deposited seaward.
75. Applications provided to illustrate the method have included
idealized grain size distributions and profiles, a specified grain size
distribution and profile and a range of various mean grain sizes and sorting.
76. Limited small scale wave tank tests were conducted to investigate
sediment sorting occurring due to profile evolution from an initially planar
slope. Profiles and surface sand samples were taken across the profile at
approximately 0, 1, 5, 10 and 24 hours after commencement of testing. The
sand samples were later analyzed for grain size distribution. Although the
results were not completely consistent, it was found that in all six cases,
the mean sediment size decreased with seaward distance from the equilibrium
shoreline.
77. The concepts of the method were compared where possible with field
data from Delray Beach, FL and Jupiter Island, FL, both of which have been
nourished on multiple occasions. It was found that the profiles could be
predicted reasonably well using the methods employed here. Additionally, the
effects of nourishment at Jupiter Island caused changes in profile shape
consistent with concepts employed.




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