Citation
Rational techniques for evaluating potential sands for beach nourishment

Material Information

Title:
Rational techniques for evaluating potential sands for beach nourishment
Series Title:
UFLCOEL-91016
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.)
Place of Publication:
Gainesville Florida
Publisher:
Coastal and Oceanographic Engineering Dept., University of Florida
Publication Date:
Language:
English
Physical Description:
1 v. in various pagings : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Shore protection ( lcsh )
Sand -- Research ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Bibliography:
Includes bibliographical references.
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.
Statement of Responsibility:
by Robert G. Dean and Jorge Abramian.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
26104282 ( OCLC )

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. .3. Recipient's AMtesaoe no.


4. Titn. and Subtitle 5. sport Dat .
RATIONAL TECHNIQUES FOR EVALUATING POTENTIAL SANDS November, 1991
FOR BEACH NOURISHMENT 6.

7. Author(.) Robert G. Dean S. PerfoinSg Oransization Report No.
and UFL/COEL-91/016
Jorge .Abramian
9. Performing organization "ae and Mdreas 10. Project/lak/ork Unit no.
Coastal and Oceanographic Engineering Department
University of Florida 11. contract or grant no.
336 Weil Hall DACW39-89-K-0025
Gainesville, FL 32611 13. Type of Report 12. Sponsoring organization sae ad aseaf Final
Coastal Engineering Research Center
U.S. Army Engineer Waterways Experiment Station
3909 Halls Ferry Road
Vicksburg, Mississippi 39180-6199 14.

15. Suppiemotary Notes



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 may words. 18. Availability Stateaet
Beaches
Nourishment
Profiles Sediment
Compatibility
19. U. S. Security Classif. of the Report 20. U. S. Security Clasaif. of This Page 21. No. of Page, 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


Page
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 ESEARCH 98 . . 98 . . 99 . . 99 . . 101


FOR OUTPUT


. . . . . . . .
ut Files . . . . .


APPENDIX C: ADDITIONAL DATA FOR DELRAY BEACH, FLORIDA


Al


Bl

B Bl


. . . Cl


2










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 Pave


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, A7, 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 m1/3, AN 0.2 M/3, h. 6.0 m, B = 1.5 m. . . 16
6 Illustration of effect of volume added, V, and fill sediment scale
parameter, A7, on additional dry beach width, Ay, Example
conditions: B = 1.5 m, h. = 6 m, AN = 0.1 i1/3............ 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


3









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


4









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


5










66 Longshore variations of A values based on slopes, volumes and
the average of the two. Jupiter Island, Florida, 1987. . . . 96 A-1 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. . Cli C-10 Grain size distributions at various locations across profile R187.
Delray Beach, Florida, 1988. Grain diameter in millimeters. C12 C-11 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


6










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


7









Original Shoreline


V -"Spreading Out" Losses






Sand Moves Offshore to
-.- Equilibrate Profile
p..

Nourished Shoreline


"Spreading Out" Losses


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


Dry Beach Width (Coarse Sand)

Dry Beach Width Initial Placed Profile
(Fine Sand)
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.


8









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.


9









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($) = 1 2/2y2 (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


10










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).


11
















0.
1.01


Lu I
LLI




LU
-j

(I)


0
0=


0.10


0.1


From Individual Field Profiles Where a Rang of Sand Sizes was Giv


7

/


0.01 1
0.


SEDIMENT FALL VELOCITY, w (cm/s)
1.0 10.0


Suggested EmpiricalRelationship A vs. D (Moore)

From Hughes' Field Results

m






-From Swarts Laboratory Results


- Based on u
A vs. D Cu Fall Veloc


f~0


ransforming ye Using y Relationship


100.0


A 0 A = 0.067 wO.4


I I I I


0.1


1.0


10.0


100.0


SEDIMENT SIZE, D (mm)


Figure 2.


Variation of sediment scale parameter, A, with sediment size and fall velocity. (Dean, 1987) .


100.0


01


01









W.

-eAy

B



Added Sand a) Intersecting Profile AF.AN R1W2

B



Added Sand I b) Non-intersecting Profile


Ay

-B



h Virtual Origin of '
Nourished Profile


Added Sand c) Submerged Profile AF

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


13









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 of 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, thelandward 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 mi/3. 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 i1/3 < 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.


14











92.4 m



h,= 6m


a) Intersecting Profiles, AN= 0.Am1/AF 0.14m1/3


45.3m
_-i -


V


h= 6


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


15.9m


h.

c) Non-inteirsecting Profiles AN = 0.1 m1/",AF= 1.91/3--


q V


d) Limiting Case of Nourishment Advancement


Non-Intersecting


100


Proflies, AN= 0-1/3,AF = 0-09M13


200


300


400


500


0


OFFSHORE DISTANCE (m)


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


M










6m h*= 6m


I
E.

IJJ
a


4

6

8


Figure 4.


-j
600


=


I


0










OFFSHORE DISTANCE (m)
0 100 200 300 400 500
S .I I I
E
+4 B=1.5m

0
h.= 6m

LL, 10
LI a) Added Volume = 120 m3/m





0 0

b) Added Volume = 490 m3/m

C\7



LUd /m











profi c).Added VolumeA = 900 m13,Jm-60mB=15m
0



U. 0
0t
d)AddVlme016 3/



Figur 5. Efec ofdnceasn Volume of o san adeInrsutnMec
prfie A0-01r'3 ~=02i11,h n n


16



















200





/ \ L100


-
z


I It,
0



0





0 1000 2000
VOLUME ADDED PER UNIT BEACH LENGTH, V(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 m/3.


17









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/A, i.e.


AY =f (V B~(3)
W, BW, h, Av


where hi and W1 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.


18















10.0








1.0


1.0


2.0


2.8


A'= AF/AN


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


19


AW= AM/BW. = 10.0






4 _- fj



= 0.2

tV = 0.1

V' =0.05


Asymptote W' 0.02 for Ay = 0 "
Y,= 0.01

Y= 0.005 AFr = V/BW, = 0.002


- Definition Sketch _


0.10 0.01 0.001


0


Figure 7.











1.0 0.1




,





0.01 0.001


w.

i ~




Dr
-Definition Sketchi


1


ii
I


i-i = 0.0051-


0.002 FI;w


I'


1.0


- 0.001


K~ Ii; AF V


wy h; AF V
W B AN 'BW,


2.0


2.8


A'=AF/AN

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

20


Non-intersecting '
Profiles ---------= /BW = 5.0


Intersecting
2 I Profiles
11



S__0.1


Asymptotes ,=On for Ay =0




IE


0.0001


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, Ah,, (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 Ay213 yields an unrealistic infinite slope at y = 0, the modified form was used which recognizes the effect of gravity for the larger slopes

y = + h3/2 (4)


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,


21
















Placed Profile


s sEQ \ s .. h h)
\ (y) iEQ ibhOriglqProil -1


EqurIllbri --,rofile .i.


Figure 9. Definition sketch.










h(y+dy) = h(y) + dy (6)
(Oy/ah)

where


ay 3,h<01 (7) jh I + 3b h>o
2 A3/2(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, s., the placed profile h,(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


23









Input: Volume Initial Profile
Sediment Characteristics, HSTAR


Establish Initial
Profile Hp(I)


Establish Placed
Profile, HP(I)


Trial DYEQ,
VGEN


Generate EquilIne
Profile HEQ(I) Loop VGEN,LVUSED


inner Loop Hold DYEQ Completed ? No Fixed Set
FVAVAIL =VGEN


Outer
Loop
Establish Improved Estimate of DYEQCompleted ?


Yes


Program Compee


Figure 10. Flow diagram for problem solution.


24











VGEN = Horizontal + Inclined Hatched Volumes


BJ


0 Dc 0.5
DIAMETER


VUSED = Ve

AYEO Placed Profile



Yso EQE Sp C


rtical + Inclined Hatched Voumes

R = 1 VUSED
VGEN


ri na - -1


Profhn -.. -- -,W$2I





Computations-Carried Out to Here in this 1.0 illustration
(mm)


(b) Cumulative Grain Size Distribution


Figure 11.


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


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


Lfl


;


z
I
-.
4.


1.0


0.5

R

0


- -

V










(8)
DYEQk* = DYEQk + kfl (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 VGEN > VUSED (F2 = +1) or VGEN USED (F2 = -1). In subsequent iterations (k>2), Fk+l Fk if the sign of
VGEN VUSE did not change in the preceding iteration and
Fk+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, nonintersecting profile
25. In this example, the initial profile was specified as characterized by the following:
Uniform Sand Size: A = 0.1 M13 (D = 0.20 mm)
Berm Height: B 1.5 m
Beach Face Slope: s. 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 : s, = 1:10
Equilibrium Beach Face Slope: sE = 1:20
Mixed Depth: Ahbi = 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.


26

















1.0









0.5



Z



0


0 -


0.5


1.0


DIAMETER (mm)



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


27


I I,/


Example 1 PCI' Example 4
- I !
I /

- /

Example 2


// Example 3

- I '









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 lop-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: s. = 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: Ahi 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


28



















-j

0


w
'C cc



a


0 5.0


DY0 58.3

DYEQ = 20.3 m
Placed OFFSHORE DISTANCE (m)
200 300 400 500 600

%

Equilibrium

_-Original h*= 6m



1Volume Added =140.0m3/m:*.
-Ao= 0.1M3 go= 1.6 so= 0.10 cg= 0.4 ;
-S00.10 a0=O
s=0.10 B =1.5m SEQ= 0.05 h. =6.Om


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














DY0 5
2 -- DYEQ = 19.3m

-,Placed OFFSHORE DISTANCE (m)

0 \ 200 300 400 500 600
0

> 'tEquilibrum
h= 4.69 m (Intersection Depth) j --Original


I
O5.0 A= 0.1m f Volume Added = 140.0m3/n :
se 0.10
-sp=0*10 B7=1.5m
-s = 0.05
EQ h.= 6.Om

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


acting














DYo =89.0 m
-2.0
DYEQ =1.50 m
Placed OFFSHORE DISTANCE (m)

C 200 300 400 500 600

0
I- Equilibrium
>
Original
h.= 6m



A0= 0.1 m1/ Volume Added = 240.0 i
L5.0 -so= 0.1 g= 2.64
sp= 0.1 o=0.10 SEQ =0.1 B = 1.5m
h.,= 6.Om .



Figure 15. Example 3. Original, placed and equilibrium profiles. Case of nonintersecting 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:

A. = 0.10 Mi1/3
so = s, sEQ = 1:10
Ahmi. 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.


32













---DY0 = 187.1 m

-2.0 -DYEQ = 139.7 m1
E .. Placed
OFFSHORE DISTANCE (i)
co 2yb0 300 400 500 600
S0



p- Equilibrium
-i .- h.= 6m LU Original



S5.0
se 0.1 Volume Added =600.0M3/M
P.,= 0.1 B =1.5m.S E 0.1 h*= 6.Om ;.




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












200 -
INTERSECTING NON-INTERSECTING E PROFILES PROFILES


3f










2w 4 1000010012
U.V,





z0
0

0

0 200 400 600 800 1000 1200

VOLUME ADDED PER UNIT BEACH LENGTH,t(m3/m)


Figure 17. Additional dry beach width, Ay, versus nourishment volume per unit beach
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.


35
















2 3


A _______1A


I-i


I -A ,I


I


B


[1
I,


5


7


I.STEEL FRAME
2.ENGINE AND CONTROLS
3.WRTER INLET 4.SAND BEACH S.SUPPORT BEAM
6. PISTON
7. SUPPORTS
8.MOVING CART 9.POINTER GAGE


Figure 18. Schematic of laboratory facilities.


4~* 444 It
II *~


Ivy-


wJ ON


9


I


f-


T,










Exnerimental 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 13) 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.


37











0.3 --OR IGINAL 1K

10H
-- 24H
0.2





0. 1





(44
SHE

10.85

1.00







-0.2 NA






-0.3 J .O 2. 0 2'.5 3'.0 3 1.5 4 1.0 4 1.5 5 1.0 5.1 6. a 6.5 7.0 7 .5 8.1 8 1.5 9. 0 9. 5 10

DISTANCE (m)


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





















a) EXPERIMENT I
A t1.3 HI
-... ...At 1...
At 2 .- n A t 3.0


1.0 0.9 0.8
0. 7 0.6
0.5
0.4 c-0.3
0.2 0.1 0.0










1.0
0.9
a.8 0.7
W0.6 O.5 0.4
r0.



0.1
0.0


6 i2
TIME


a: Iii
LU
S
IS
C
2 IS at
S


4


10.0 0.9
0.8.
0.7
0.6
0.5

0.3.
0.21
0.1
fin


1.0 0.9

0. 7 a.: S0.7




0.1.
0.0


18 24 I


b) EXPERIMENT a 2
AT 1.2 II
.... .. AT 1.6 M
.. AT 2.0 M
- -...AT 2.5 M





----_-_-


TIME








e) EXPERIMENT a 5


6 i2
TIME


10.0


0.8.
,a W 0. 7.




0.3
0.2j
00


1.0 0.9
0.8

0.6 30.5 0.3



0.1 0.0


IS 24 0


c) EXPERIMENT 3
AT 1. 1 AT 2.8 K AT 3.1 A






.- .


0 6 12 18 1
TIME







f) EXPERIMENT # 6


-- 12
TIME


is 24


Figure 20.


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


U, '-0


i 12 18 2
T I ME







d) EXPERIMENT a 4


AT 1.7 M At 2.7 At '.2 '


ST 2.7 K
-1 q.0 AT 5.0 N AT 0.5 H


0


At 2.0 I .At 3.0 H f 3.5 I A- '.


I


-


.


.


24













-I OR IGINRI.


I1.0


.. .. 24 H


80


0.3






0.2






0.1


M 60


0

200-


INITIAL DISTRIBUTION


0.0


6.2 6.4 6. 6.
GRAIN OIAMETER


SWL


G.S. AT 1.3N 30
80
60
0-i
20 1 G.S.. AT 2.4N
0. .80.
GRAIN DIAMETER 60


20
-........................... -.-- ..a
100 u.lfl.2 0. 6.8 .5..
-' GRAIN DIAMETER

10.85

1.00 10, G.S.O. AT


. ~60


20
... 0.
GRAIN DIANE


I I I I I I 4I I I I I .
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


DISTANCE (m) Figure 21. Experiment 1. Initial and final profiles and initial and final grain size
distributions.


3.14M rER


0.0


HZ
r.


C


-0. I






-0.2






-0.3


.0


10.0





















G.S.D. AT 2.1 H


100 90
80
70 ,60

u0


30
2a
10
0

















300
90 80 a0
80


0
38 20 I0
0


100 90 80
70 60
U50


30 20
10


.8


108 90 80
70 60
u58
40 30
20



8.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 .8 0.9 .0
GRAIN DIAmETER


;-- -- -,
.8 0.! 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
GRAIN DIRHETER









G.S.D. AT 3.0 H


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 .
GRAIN DIAnETER


too
- 00 90 80 7C 60
'54 40


20 : 0
0


180



70 60
050 LUs
w .0
30 20


0
.0


GRAIN DiMETER G.S.D. AT 3.4 H


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 .
GRAIN GIAKETER


.0


Figure 22. Experiment 1. Grain size distributions at six locations across the profile

after 24 hours of testing.


H


s::-: -. -.-. .
0.0 0.1 0.2 0.3 0.4 0.5 0.8 0.7 0.8 0.9 I
GRAIN WAIVETER









G.S.D. AT 2.4 H


G.S.D. AT 1.3 H


G.S.D. AT 1.8 M




-


.


///4,


0









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


42












0.3
ORIGINAL
---- --- --- ---- Il-H

11H
-. ----- -------- I OH
- 24H
0.2






0. 1














-0.






-0.2






-0.3 I I I I I
1.0 1.5 2.0 2.5 3.0 3.5 4.0 q.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.











0.3
ORIGINAL
24 H INITIAL DISTRIBUTION !00

G.S.D. AT 1.2M 80
10(
.0 Z 60

60.0

20 20 20 ~G.S.D. AT 2.OM 2
0. 1 -.0 t
GARIN DIAMETER 10. .0 6.2 6.4 6.6 .8 .0
5. 74 60. GRAIN DIAMETER 20
0.0 ..............A 201 2
r\ RI DIAMETER00. 6. .a .s .a 0


0 .0 -- ---- - - -- - ------ --0 0. 0. 0. 0.6 0. 6 '
GRAIN DIAMETER



lt G.S.O. AT 2.511
120




-0.1 -80.
600
W40
20
.S.---AT----0.2 -GRAIN DIAMETER






-0 3 1.0 1 1.5 2 1.0 2 1.5 3 1.0 3. 1 q1.0 4.5 5.so S.S 61.0 61.5 71.0 71.S 81.0 81.5 91.0 9 1.5 10.0


DISTANCE (m)


Figure 24. Experiment 2. Initial and final profiles and initial and final grain size
distributions.
























G.S.D. AT 1.2 M
















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









G.S.D. AT 2.3 M


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


t00
90 80 70

(40

0 30
20
1 0
0


G.S.D. AT 1.6 M
















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









G.S.D. AT 2.5 M


t00
90 00
70
60



30
20
[a
0













90 .0
700 90
050



40 30
20 10
0
.0


G.5.0. AT 2.0 M


100 90
00
70
50
,so U50 wq .0.
30
20 t0
0
.0












90
00 70 G-o jSO
w .40

a
30 20 10
0
.0


.
GRAIN DIAMETER


.0


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


Ln'


-.




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


400


90
0 70


'U:O

(40
30 20 10
0


0.0 0.1 0.2 0.3 G.M 0.5 0.6 0.7 0.0 0.9 .
GRAON 0A METER









G.S.D. AT 3.2 M
















0.0 0.1 0.2 0.3 O.Y 0.5 0.5 0.7 0.8 0.9 1


.











0.3
ORIGINAL




0.2






0 1





SUL

E





-0.1 -9.93

1.00
-0.2

/Thrm/mrnn/Th'm#Dnmz'Thmhmmm ,mrpnrmtzmarm/mmmmmmmminrnrmmmmimnr~nnnrnnmmrnminninnnnrnnzmrnm





[.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.












0.3
ORIGINAL
. 24 H INITIAL DISTRIBUTION 100

80
0.2 G.S.D. AT I.3M
lot _ __ __ Z 60
80.c
(4 a.

0. 20

0.1 20 Io G..0. AT 2.314
.00 0 ~
0.1, 2 0 1. _._ _._ _._.0 .0 6.2 6.4 6 6.8 .o
GRAIN OIANETER U GRAIN DIAMETER





GRAIN DIAMETER



G.5.0. AT 3.111
-001
-0.2 -IGRNDMT


-0.3 80.

200

-0.2 - -GRAIN D[AMETER






-0.3
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 27. Experiment 3. Initial and final profiles and initial and final grain size
distributions.























100 too
90

70

USo 40 30
20
to
0


G.S.D. AT 1.8 M
100 90 00 70
~60 Uo
w .s40
0 30
20
to
0 i .0 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 1.3 H
















0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.9 0.9 .
GRAIN DIAMETER









G.S.D. AT 2.6 M
















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


G.S.U. AT 2.1 M
100 to
00 70 6o oSO
05 30




.0 0.0 0.1 0.2 0.3 0.4 0.5 0.8 0.7 0.0 0.9 1.0
GRAIN DIAMETER


400 too 90 80 70
-so oSO
w

30
20 10
0
.0


G.5.0. AT 4.6 M


.0 0.1 0.2 0.3 0.q 0.5 0.8 0.7 0.8 0.9 1
GRAIN DIAMETER


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


G.S.O. AT 3.1 M
100 90
80 70
-60


0 30
20 10

.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
GRAIN DIAMETER


100
90 00 70
-60 uSO
w .0.
30 20 10
a


00


.0












0.3
OR[GINAL
-H
6H 12H
- - -.24H1
0.2






0.1





sV.
00 ... ...------+- - _- :
P441


-0. 1





13.94

1.00
-0.2 /-0.3 7I 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 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.


50












0.3
ORIGINAL
..... ..24 H INITIAL DISTRIBUTION 100

G.S.6. AT 1.7M
lot __________ 80
0.2 80
w Z 60.
'U
4 0
G.S.D. AT 2.78 a.

0. 20
0.1 GRAIN DIAMETER U
-' a
-.0 6.2 6.4 6.6 6.s .0 20. GRAIN DIAMETER

'0. . .
11, GRAIN DIAMETER SWL RAI OqA4

04 G.5.0. AT 3.7M


60.
-0.1 -020.N
1 3 .94
0 -.2 0 w-. -r. .0 GRAIN DIAMETER

-0.2
rmwrrMSr11flMt7A7MsACmsmhSMq17 gmmmaq ..wsmaernwzcrnmeaqmaznomawassmea-0.3II I III I
1.0 1.5 2.0 2.5 3.0 3.5 4.0 41.5 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 30. Experiment 4. Initial and final profiles and initial and final grain size
distributions.






















G.S.0. AT 1.7 H


too
90
00 70 60Z
w
Uii u50

0.
30
20







l0
0 140






too


70

=


0.
so
20 l0
0


100 90
00 70
60
Z ,50
0 30



20 .
.8 0.0 0.!


- I
z
'Li,
(4
C
'"I
a.





.0


G.S.D. AT 2.2 H


0.2 6.3 0.4 0.5 0.8 0.7 0.0 0.9
GRAIN DIAMETER


G.S.D. AT 3.7 H


soe
90 80 70
60 50


30
20


0.0 0. 0.2 0.3 0. 0.5 0.8 0.7 0.8 0.9 I
GRAIN DIAMETER


.







-


G.S.D. RT 2.7 H















0.0 0.1 0.2 0.3 0.4 .5 0.6 0.7 0.0 0.5 1
GAIN DIAMETER


.0


.


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


Lfl


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0. 0.9 1
GRAIN DIAMETER








G.S.D. AT 3.2 H















0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.9 a
GRAIN DIAMETER


100 so
0 70 60
50

0
30




40










0.
I0
0
700




to
0
750



30


20


G.S.). AT 4.2 H















0.0 0.1 0.2 0.3 0. 4 0.5 0.6 0.7 0.8 0.9 1.0
GRAIN DIAMETER


I












0.3
ORIGINAL
---- --- --- -- - I H
- - - - 6H
12H
-24H
0.2






0.1





SkL
5141

6 24.27 100
-0.1






-0.1







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 32. Experiment 5. Measured profiles at various times.













ORIGINAL


- - -- 24 H


G.S.0. AT 3.3M
10'


C 60


20 0.







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


100



Z 60
w 40


G.S.D. AT 4.5M


u 60.c ,...0..


20
0.
ORRIN D-TM-EE- .0
GRAIN' OfflMTER -


INITIAL DISTRIBUTION


..2 6.4 6.6 6.8 .0
GRAIN DIAMETER


SWL
--- ;D- A T- 8;OM


24 27 '80.
2 Io

.00 40
20
J 0. .
7 j2 \GRtA IN DIAMETER


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


DISTANCE (m)


Figure 33


Experiment 5. distributions.


Initial and final profiles and initial and final grain size


0.2






0.1


0.0


-


(-ii


-0. 1






-0.2






-0.3


[.0


10.0


20





















G.S.D. AT 2.8 H
100 so
00 70
,60
~~50
w 40 30
20 I0

0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.7 0.0 0.9 1.0
GRAIN DIAMETER








G.S.0. AT 5.5 8
Inn


too 90
00 70
'60


40
30 20 10





too
0










100 90 I0
70 60 ~so ,SO
W40




I 0
0


0.2 0.3 0.4 0.5 0.6 0.7 0.1 0.9 k
GRAIN DIAMETER


90 00 70
~60 00

30
20
10
0 .0


G.S.D. AT 3.5 H














3.0 0.1 6.2 6.3 d.q d.s 6.0.7 0. 0.9


GRAIN OAMETER


G.5.0. AT 6.5 H


-0 - -*
0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.7 0.8 0.9 .
GRAIN DIAMETER


100
90
0 70
-60 ,50 qa ad
30 20 10

.0









too
90 00 70 so USO


30 20 1to
0
.0


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


U, U,


.0 k I


G.S.D. AT 4.5 H














0.0 0.1 0.2 0.3 0.4 0.5 0.6 6.7 6.1 .i
GARIN DIAMETER








G.S.D. AT 8.0 H














0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.9 .
GRAIN DIAMETER


,
i












0.3
-ORIGINAL
--- --- --- --- --- I H
- - - - 6H
- - - -. 6H
S---24
0.2






0.1





SMLl




U' ~' 14.33

1.00



-0.2I






-0.3 N




1.0 L.5 2.0 2.5 3.0 3.5 4.0 41.5 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 35. Experiment 6. Measured profiles at various times.












ORIGINAL
...... .-..24 H INITIAL DISTRIBUTION I00
G.5.D. AT 2.OM

Z, so
0.2 0 60.
Sqo.
20 lot 6.5.0. AT 3.0M
20 10s
0. .20 . .0 80. 20
a:0
0G0 GRAIN DIAMETER


001 GRAIN DI METEE
A
fr~GAI DIA20GRANEIAMTE
0.0 ........ ....... ....... 00S


G.S.0. AT 4.5H f. 14.33 I0
U,80
1.00 60
-0.1
20
0

GRAIN DIAMETER

-0.2







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 36. Experiment 6. Initial and final profiles and initial and final grain size
distributions.










c. 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.

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


58










Table 2

Results of the Tracer Analysis


Type of Time Observation


Oranie


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


Few Few Some Few Few


Few



Few


Few


Few top
3 Grains


Few


Few Few
Layer at 3.5 cm below ton


59


1 HR


Dyed zone


Spots


Slightly
dyed Some


Slightly dyed


Many Some Some Many


6 HR


Few


Many


Layers by the glass

























100 seo so
80 70
60
5i0


30
20
to
0











100 90
80 70



40
I-so



30
20


10
0


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 .
GARIN DIAMETER









G.S.D. AT 4.0 M
















0.8 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 t
GRAIN fERIETER


G.S.D. AT 2.0 M


100 90
80 70
60 ,iSo 'i40 30
20
10

0











100 90
80 70 80

W10 30
20 10
0


.0


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


M~
0


G.S.D. AT 2.8 M
















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









G.S.D. AT t.5 M















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


.0


too 90
80 70

Us
I-SO
w


30 20

10





too
0
.0










100 90 80 70
~60



30 20
10
0
.0


G.S.D. AT 3.5 M


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









G.S.D. AT 5.3 M















0:0
0.0 Q.i 0.2 0.3 0.4 0.5 0.6 0.7 0.0 4.9 .


GRAIN DIAMETER


.0


.
.
.
.
.






-











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

Ay) =A. e-J' (9)


61










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


ah123/ 2 (11)


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



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


and considering the variation given by Equation 10



h(y) = 1-- [(A, + my)2.s-S ] 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.


62












0.00 0.10


0.20


0.30 0.00 0.10


0.20


0.30 0.00


1 UU


300


'lul
DISTANCE


Soo
(m)


600


700


800


r4


CALCULATED PROFILE
...............--------MEASURED PROFILE nO=o.14 0.33
----. .. K= 0. 26






a to 200 300 400 So0 So0 700 800 90 DISTANCE (m)

CALCULATED PROFILE

----- ----------------------MEASURED PROFILE 0 .33
--------- M= -0. 03






0 too 200 300 1100 Soo 600 700 auu U0 DISTANCE (m)

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


901


Figure 38.


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


exponential variation of A. A.


0


0.20


0.30


0


A4


H
04


0


0. 10


200



















P24


too


200


300


q00
DISTANCE


Stoo
(m)


600


700


Boo


0.00 0. 10


0.20


0.30 0.00 0. 10


0.20


0.30 0.00


900


Figure 39.


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


Top: exponential variation of A. erage A.


CALCULATED PROFILE MEASURED PROFILE 0.3
,s A0=0.11 K= 0.08






0 too 200 300 400 Soo 600 70 DISTANCE (m)
CALCULATED PROFILE MEASURED PROFILE M0.33
,. AP0=0.11l M= -0.01






100 200 300 400 Soo 600 700 V00 9C DISTANCE (m)
CALCULATED PROFILE MEASURED PROFILE




-


. 04


i


0


0. 10


0.20


0.30


a

















i4


200


300


400
DISTANCE


500
(m)


600


700


800


900


Figure 40.


Experiment


3. Equilibrium beach profiles.


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


Top: exponential variation of A.


0.00 0.10


0.20


0.30 0.00 0.10


0.20


0.30 0.00


EH


I



P.4


0 t00 200 300 400 500 600 700 800 90( DISTANCE (n

CALCULATED PROFILE
.MEASURED PROFILE M0.33
AP0=0. 11 H






M= -0. 04






0 00 200 300 400 500 600 700 800 90
DISTANCE (m)

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

I I I I
n ,nn 2- 00506070 0 0


0.10


0.20


0.30


0


100
















I


EA
P4


too


200


300


4L0 500 DISTANCE (m)


600


Figure 41.


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


0.00 0.10


0.20 0.30


0.00 0.10


0.20


0.30 0.00 0. 10


0.20


0.30


E H4


H em


CALCULATED PROFILE
---- .........MEASURED PROFILE 0.33
A = 0. 1 1 M K= 0.01




0

0 too 200 300 400 Soo 600 700 800 901
DISTANCE (m) CALCULATED PROFILE MEASURED PROFILE 0.33
-0=0. 11 M M= 0.00




0

0 too 200 300 400 500 Soo 700 800 90( DISTANCE (m) CALCULATED PROFILE
- .MEASURED PROFILE




-


0


700


Soo


900


















E


400
DISTANCE


Soo
(M)


Soo


700


800


900


Figure 42.


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


exponential variation of A. A.


0.00 0.10


0.20


0.30 0.00 0. to


0.20


0.30


0.00 0. 10


0.20


0.30


CALCULATED PROFILE
--- ::- J: ENSURED PROFILE
-10= 0. 13 M K= 0.09






100o 200 300 q00 goo 700 Soo 901 DISTANCE (m)
CALCULATED PROFILE
-- -- ---------1EASURED PROFILE
0=0.12 M M= -0.01






100 200 300 400 TA0 700 800 90(
DISTANCE (mn)
CALCULATED PROFILE ........--- .~JIEASURED PROFILE








n too0 200 300


Li PA
-4 C


PA



















4


D
DISTANCE


Atn


Soo
(m)


700


800


goo


Figure 43.


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


0.00 0.10


0.20



0.30 0.00


CALCULATED PROFILE ....................MEASURED PROFILE
-..,. A0=0. 14 M K= 0.25






0 too 200 300 4o Soo 600 700 S00 901 DISTANCE (m)
CALCULATED PROFILE .......-------------MEASURED PROFILE
-,0=0. 14 M
.M= -0. 03






0 too 200 300 400 500 600 700 60 901 DISTANCE (m)

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




-- -n n n -f . . . . ...



Stood 200 300 gi 0


0. 10


0.20


0.30 0.00 0. 10


0.20


0.30


a'


P4


F'
PA
N
C


0









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.


69











EXPERIMENT # I CALCULATED PROFILE ...MEASURED PROFILE


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




0.0 100.0 200.0 300.0 400.0 500.0 6 DISTANCE (m) EXPERIMENT # 2
F1


100.0


200.0



100.0


200.0


300.0
DISTANCE (m)

EXPERIMENT u 3


300.0
DISTANCE (W)


400.0


400.0


500.0


6


500.0


0.10


-0. 20


-0.30




0.00 0.10


0.20


600.0


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.


0.00


H
N
a


30.0 30.0


E


p4
N
a


-J
0


0.0


0.30


0.00


P4


CALCULATED PRFILE
-s................... MEnAS UR E P ROF ILtE

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


0.10


0.20


0. 30


0.0


CALCULATED PROFILE ,r....... .....NEASURED PROFILE












0.00


100.0


200.0


DISTANCE W

EXPERIMENT 4 3


300.0
DISTANCE (m)W


400.0


500.0


400.0


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 # 1 CALCULATED PROFILE ---------MEASURED PROFILE














nfl in.....n.....
0.0 100.0 200.0 D T300.0


EXPERIMENT # 2 ........ .. CALCULATED PROFILE
-', ... ...... ....MEASURED PROFILE








0 10 100 0 2 100 03


P4


-4
H


P4


0.10


0.20


0.30




0.00


*0.10


0.20


0.30


0.00 0.10


0.20


-0.30


p4
0


0.0


0.0


600.0


's CALCULATED PROFILE
.....------ --MEASURED PROFILE

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


30.0


.


.


.










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.


Delray 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.


72


















2.8 2.6



2.4 2.2.


2.O


1.8


1.6.


I


0


4--.


rn 0*
0


z


4.4*


4-- 0
-4


a


0


/


8/7A 3/74 10/74 8/75


6/76 677


7)76 7179 7/80 7/81


1/83'7/83 7/84 8i/84


MONTH/YEAR


------AVERAGE VOLUME CHANGE


Figure 46.


Nourishment events at Delray Beach,


(Coastal Planning and Engineering, Inc.).


Florida and subsequent volume changes


z
9
r


-h
0

'0 Iz


0
r
C
r
~1
-n
0
C
z
0

0
0
0
0
0
0
(A
C)
P
-C
a 30


-J
U)


N
N


0
N


0 "


1.2.


1.01


N*


3/88


1i86


1/87


...,e














4

0


NORTH


/


I


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


74


CITYLIMIT -NORTH LIMIT
1984 CONST --R-17


-17s

R-177 R-178
ATLANTIC AVE. -79 R-80

CITY OF R-181




00
a-182
DELRAY BEACH U -e








R-18


OUTH LIMIT 1984 CONST. 1 SOTHR-8

7--90












1.000 0.950 0.900 0.850 0.800

0.750 0.700 0.650 0.600 0.550 0.500

0.450 0.400


0.350 0.300 0.250 0.200 0.150 0.100

0.050 0.000
0


08 180.88


s o


Figure 48.


I I I I I I I I I I


100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 1050 1100 DISTANCE (m)


Average grain size variation across profile 180.88 Delray Beach, Florida, 1988.


*1

1:11

N

H
0 [:1
a


icC













250.0


0.200 I


C2

E0.150




S0.100 .4


I


DB 180.88







-1


r-


0.050 -


0.000 1
10


0.0


200.0


300.0


400.0


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


C-'


I I


I


i











1.000 0.950

0.900 0.850 0.800

0.750 0.700 0.650 0.600 0.550

0.500

0.450 0.400

0.350 0.300

0.250

0.200

0.150 0.100 0.050 0.000


I I I I I I I I I I I I I I I I I I I I I I
0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 1050 1100

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


I4



Hn Ua


_DB 184.88


Figure













250.0 0.200


I Ii


DB 184.88


0.150


0.100


0.050 -


0.000 L
100.0


200.0


300.0


400.0


LENGTH (m)

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


I


I


I


I


I


I












08 187.88


1.000 0.950

0.900 0.850

0.800 0.750

0.700 0.650 0.600

0.550

0.500 0.450 0.400

0.350 0.300

0.250 0.200

0.150

0.100

0.050

0.000


I I I I I I I I I I I I I 1 0 100 I 50 100 1 1 I1 too ISO 2oo 250 300 350 400 450 500 550 600 650 700 750 80 85 90 950 1000 1050 1100


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


P4

H

W


L 19-a


0


50













250.0




0.200. CE

0.150
M
I


0.100
4.


DB 187.88


0.050 t-


0.000 I.
100.0


200.0


1
400.0


300.0


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


00
0


I


I


I


I















R

H
04
r14


H
04
0


N


0.00 4.00
2.00
3.00 4.00
5.00 6.00 7.00 8.00 9.00 10.00




0.00 7.00
2.00
3.00 4.00
5.00 6.00

8.00 9.00 10.00


0.00 1.00
2.00
3.00
4.00 S. 00
6.00 7.00 8.00 9.00 10.00


Figure 54.


PROFILE n DB180.88 CALCULATED PROFILE
n..,.ME ASURED PROFILE








0.0 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0 550.0 6,
DISTANCE (m)

PROFILE s DB184.88

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

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


0.0


II I I I
50.0 100.0 [50.0 200.0 250.0 300.0


DISTANCE (m) PROFILE # 08187.88

-- --____-___CALCULRTEO PROFILE
.-..MEAS.BFO PIl0F ILE




-.


. 2 .I I I
0 1.0 5 10.0 1100. 0 150. 0 200. 0 250.0 300.0 350.0


"Blind folded" Florida, 1988. sediment size.


350.0 400.0 450.0 500.0 550.0


D0.0


600.0


4 I I I 400. 0 450.0 500. 0 550.0 600.0


DISTANCE (n)

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


00
H











PROFILE # 0B180.88
0.00
1.00 2.00 3.00 4.00
5.00
P 6.00 CALCULATED PROFILE
7.00 ............. ...MEASURED PROFILE
8.00
9.00 10.00
0.0 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 DISTANCE (M)

PROFILE # 0B184.88
0.00 .
1.00
2.00
3.00 ......
H 00
5.00 .,
6.00 CALCULATED PROFILE
Pq .0 ... .......---...MEASURED P80F ILE
fl 8.00
9.00
10.00
0.0 50.0 100.0 150.0 200.0 250.0 300.0 350.0 q0o.o 450.0 DISTANCE (i)

PROFILE # 0B187.88
0.00
1.00 -
2.00
3.00 --......... ....- .
4.00 5.00
E 6.00 CALCULATED PROFILE
7.00 ..-..-----.-.........MEASURED PROFILE
f 8.00 -.. -. .
9.00
10.00 . 1 1 0
0.0 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0
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


83














N. Project Limit


000.000


- J5 Y =990,000













y 980,000


9000


Scale In Feet 0 3000 6000


Y = 970,000


-North Construction Limit
- Y = 997,032


N


Y = 991,820










Y = 983,671 '51. 5J18 End 1973
Construction



0 South Construction
1-0 Limit



.4







S. Project
Limit


Figure 56.


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


84


Y =1



















04


H
04
a


E-.
P4


0.00 1.00
2.00
3.00 L.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 57.


PROFILE


4 J5.87


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 t J6.87


I-f I I I f I
0.0 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 4 DISTANCE (W)

PROFILE # J7.87


0.0


50. a


to0. 0


150.0


200.0


250.0


300.0


350.0


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


30.0 0.0















0.0


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


00


--..,..... -- --- -- - - - - - - -

CALCULATED PROFILE .--...E.---- EASURED PROFILE


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


-I I


4


3


a


400.0











PROFILE # J11.87






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


-


100.0


150.0


200.0 25
DISTANCE (m)


0.0


300.0


PROFILE J12.87






CALCULATED PROFILE
--.......--............MEASURED PROF ILE


100. 0


150.0


200.0 250.0
DISTANCE (iv)


300.0


0


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


Figure 58.


PROFILE # J13.87






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


0.0


50.0


100.0


150.0


200.0
DISTANCE


250.0
(M)


300.0


350.0


400.0


450.0


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
4.00
5.00 6.00 7.00 8.00
9.00 10.00


0


0.0


50.0


0.00 .00
2.00
3.00 4.00 S. 00
6.00 7.00 8.00 9.00 10.00


00


ES
P4


350.0


400.0


450.0


0.0


50.0


350.0


400.0


450.0



















W
Q


0.00 1 00
2.00
3.00

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 I .00
2.00
3.00
11.00 S. 00
6.00 7.00 8.00 9.00 10.00


100.0


150.0


1 1
200.0 250.0
DISTANCE (m)


300.0


350.0


400.0


PROFILE # J17.87






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 # J18.87






CALCULATED PROFILE
..MEASREDPROFILE


450.0


PROFILE # J19.87






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


50.0


100.0


150.0


1 1
200.0 250.0
DISTANCE (M)


300.0


350.0


400.0


4


30.0


Figure 59.


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


50.0


50.0


00


z
H
p.'
N
0


0.0


S

H p.'
N
0


0.0











PROFILE


# J20.87


CALCULATED PROFILE
~...................... M E ASU RE D PROGF IL E



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

PROFILE # J21.87


P4
0


0.00 1.00
2.00
3.00 4.00
5.00 6 .00 7.00
8.00 9.00 10.00




0.00 S.00
2.00
3.00
4.00 5.00
6.00 7.00 8.00 9.00 10.00




0. 00 S. 00
2. 00
3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00


0.0


50.0


100.0


150.0


200.0


250.0


300.0


DISTANCE (m)


350.0


400.0


Figure 60.


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


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

PROFILE # J22.87






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


-t


00


04
C1


CALCULATED PROFILE
-.-.-..MEASURED PROFILE


0
M


50.0 50. 0 50.0


4









exponential distribution which resulted in the profile fits in Figures 57, 58,
59 and 60, the A values near the shore (A.), 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

A3/2 (15)
(h') 1/2


Hence the A value based on overall slope, A, is A, = [s (h') 1/2]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)S/3 = 3 (h')5/2 (17)
5 V (AV)3

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



3 (hl) s/2 2/3 (18)



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


89













0.24
A2AT SHORELINE
--- ---A AT END OF LINE
0.20 - AVERAGE



v 0.16

LI

0.12



0.08


0.04



0.00
971836 976836 981836 986836 991836 996836 South ALONGSHORE DISTANCE (Downdrift) 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.













0.24
A AT SHORELINE
-----A AT END OF LINE
0.20 - AVERAGE



0.16

I-
cc
0.12






0.04


0.00
971836 976836 981836 986836 991836 996836 South ALONGSHORE DISTANCE (Downdrift)

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.















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


['A -


7.
7Wzz


~ Al





I I I I I I I I I


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.


0.24



0.20


Ma



w
I-




.4


'0
M


0.16



0.12 0.08


0.04


no nf


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 mi/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 Mi/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 crossshore 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


93














A CONSIDERING SLOPES
--- -------A CONSIDERING VOLUMES
- - AVERAGE


H


971836


I I I


976836


South (Downdrift)


981836


986836


991836


996836


ALONGSHORE DISTANCE


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


0.12


'0


C.,
r

Ir
w I
w
4
4 0.
IC


0.08





0.04


f ff


I I I I I I I I I I

















0.12
-!




L 0.08





0.04 A CONSIDERING SLOPES
--- A CONSIDERING VOLUMES
AVERAGE


0.00
971836 976836 981836 986836 991836 996836 nuth ALONGSHORE DISTANCE (Downdrift)
Figure 65. Longshore variations of A values based on slopes, volumes and the average of
the two. Jupiter Island, Florida, 1981.














A CONSIDERING SLOPES
------A CONSIDERING VOLUMES
AVERAGE


4,7


I I I I I I I I I I


976836


981836


986836


991836


996836


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.


0.12


'C a-'


C,


0.08





0.04


0.00
971836









the exponential A fit is that the post-nourishment average A value decreased to approximately 0.08 mi13 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.


97










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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