Citation
Experimental study of sediment sorting across the beach and its influence on the equilibrium profile

Material Information

Title:
Experimental study of sediment sorting across the beach and its influence on the equilibrium profile
Series Title:
UFLCOEL
Creator:
Abramian, Jorge Emilio, 1958- ( Author, Primary )
Dean, Robert G. ( Thesis advisor )
United States -- National Oceanic and Atmospheric AdministrationUnited States -- National Oceanic and Atmospheric Administration
University of Florida -- Coastal and Oceanographic Engineering Dept
Place of Publication:
Gainesville, Fla.
Publisher:
Coastal & Oceanographic Engineering Dept., University of Florida
Publication Date:
Copyright Date:
1990
Language:
English
Physical Description:
x, 105 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Sedimentation and deposition ( lcsh )
Beach erosion ( lcsh )
Coastal and Oceanographic Engineering thesis M. Eng ( local )
Dissertations, Academic -- Coastal and Oceanographic Engineering -- UF ( local )
Genre:
bibliography ( marcgt )
technical report ( marcgt )
non-fiction ( marcgt )

Notes

Abstract:
Improved procedures for predicting beach response to wave action are needed to optimize nourishment projects, reduce the volume of sand required and estimate performance. To date, no model has been able to satisfactorily represent the evolution and final profile of the beaches of well-graded sand, nor have experiments addressed the non-idealized case of sediment sorting across a beach composes of well graded sand. Therefore, no reliable and proven method exists to predict the dry width of a beach with multiple grain sizes. The equilibrium beach profile equation developed by Robert G. Dean is widely used but should be treated like an idealized beach representing a kind of “average” beach. Its limitation to beaches with a unique grain size has been demonstrated several times. New forms of the equation regarding varying sediment sizes have been tested with differing results. Due to the lack of studies about the subject, theses attempts considered arbitrary variations of the grain sizes with offshore distance. To address the deficiency in information related to well-graded sediments, an experimental program has been carried out. This thesis describes the set of experiments performed in the laboratory using a wave tank in which a well-graded sand beach was simulated. Data collected and analyzed included sand samples, beach profiles, and wave characteristics. The sand samples were taken from different locations at different intervals within the 24 hours duration of each experiment. With these results and use of the Dally wave transformation model, an analysis of the dissipation of energy per unit water volume across the beach is presented. The dissipation of energy per unit volume was the original concept associated with the equilibrium beach profile in which a single value is associated with each diameter. However, results obtained herein support a relationship of the dissipation with the particle Reynold Number. A new approach to the problem based on this result is also presented.
Bibliography:
Includes bibliography.
General Note:
"UFL/COEL-91/010"
General Note:
A thesis presented to the graduate school of the University of Florida.
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 Jorge Emilio 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:
26058628 ( OCLC )

Full Text
UFL/COEL-91/010

EXPERIMENTAL STUDY OF SEDIMENT SORTING ACROSS THE BEACH AND ITS INFLUENCE ON THE EQUILIBRIUM PROFILE
by
Jorge Emilio Abramian
Thesis

1991

I




EXPERIMENTAL STUDY OF SEDIMENT SORTING ACROSS THE BEACH AND
ITS INFLUENCE ON THE EQUILIBRIUM PROFILE
By
JORGE EMILIO ABRAMIAN

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

1991




ACKNOWLEDGEMENTS

I consider my experience at the University of Florida one of the best I have ever had. Many factors have contributed to this fact. First of all is the support of my parents who did whatever they could to offer me a good education, even when they were not always in the best situation to do so. Secondly, my wife and my daughter who accompanied me, all the time hearing and sharing my problems. Of course the persons who decided to accept and support me at the school have contributed too, beginning whith the first person that I met in the department, Dr. M. Sheppard, who encouraged me with his words and his politeness, and Dr. H. Wang, who leads the school. But this experience would not have been so great if it were not for the smiles (and doughnuts) shared by the people of the coastal engineering department: professors, staff members and students. Among them I have to mention my dear friend Chulhee Yoo, who offered me his friendship from the very beginning, and of course Dr. Robert G. Dean, my advisor. From Dr. Dean I not only learned a lot of technical things, I also learned how to love the physics, the work and the nature. I appreciate very much his example, which was the most encouraging help. I will never forget these years. Finally, appreciation for the financial support provided by the Coastal Engineering Research Center is gratefully acknowledged.

ii




TABLE OF CONTENTS
ACKNOWLEDGEMENTS ................................ 11
LIST OF TABLES .................................... v
LIST OF FIGURES .................................... vi
ABSTRACT ........................................ ix
CHAPTERS
1 INTRODUCTION .................................. 1
1.1 Description of the Problem .......................... .. 1
1.2 Scope . . . . . . . . . . . . . . . . . . . .. 2
2 BACKGROUND AND THEORY .......................... 4
2.1 Relation Between Grain Sizes Distributions of Borrow and Native Sand . 4 2.2 Equilibrium Beach Profiles .................................. 5
2.3 Sediment Sorting ........ ................................. 6
2.4 Evolution of Beach Profiles and Sand Bar Formation ................ 10
3 LABORATORY STUDIES .............................. 12
3.1, Introduction and Description of Facilities .................. 12
3.2 Objectives . . .. .. . .. . . .. .. .. . . . . . 12
3.3 Experimental Procedures ................................... 14
3.4 Main Characterists of the Tests ............................... 15
3.5 Description of the Results ....... ............................ 16
3.5.1 Experiment 1 ............................... 16
3.5.2 Experiment 2 16
3.5.3 Experiment 3 16

iii




3.5.4 Experiment 4 . . . . . . . . . . . . . . . .
3.5.5 Experiment 5 . . . . . . . . . . . . . . . .
3.5.6 Experiment 6 . . . . . . . . . . . . . . . .
4 ANALYSIS OF RESULTS . . . . . . . . . . . . . .
4.1 Grain Size Distribution . . . . . . . . . . . . . . .
4.2 Sediment Sorting and Beach Profile Formation Processes . . . . . .

4.3 Beach Profiles . . . . . . . . . . . . .
4.4 Energy Considerations . . . . . . . . . . .
5 WAVE TRANSFORMATION MODEL . . . . . . . .
6 DIMENSIONAL ANALYSIS .....................
7 CONCLUSIONS AND RECOMMENDATIONS ..........
7.1 Conclusions ................................
7.2 Recommendations ............................
BIBLIOGRAPHY .............................
APPENDICES

A
B

COMPUTER PROGRAM DEVELOPED FOR THE THESIS ....... EQUILIBRIUM BEACH EQUATIONS ...................

B.1 CASE OF EXPONENTIAL VARIATION OF THE A PARAMETER B.2 CASE OF LINEAR VARIATION OF THE A PARAMETER ..... C EXPERIMENTAL BEACH FACE SLOPES AND BASCOM'S RESULTS BIOGRAPHICAL SKETCH ............................

iv

22 26 26
46 46 46

. . . . 55
. 70 . . . . 71
. 82 . . . . 87
. . . . 87
. . . . 89
. . . . 91

94 101

101 101 103 105




LIST OF TABLES
3.1 EXPERIMENTAL CONDITIONS, WAVE TANK TESTS ....... ..14 3.2 MAIN CHARACTERISTICS OF THE EXPERIMENTS ........ 15 3.3 RESULTS OF THE TRACER ANALYSIS ................ 45
4.1 LOCATION OF BREAKING AND MAXIMUM SORTING ...... 54 5.1 RANGE OF DISSIPATION OF ENERGY ................ 81

V




LIST OF FIGURES

2.1 Relationship Between A Parameter and Grain Diameter . . . . 6 2.2 Three Types of Nourished Beach Profiles . . . . . . . . 7
3.1 Wave Tank Schematic . . . . . . . . . . . . . . 13
3.2 EXPERIMENT 1. Measured Profiles at Various Times. T=1.25 sec;
Hb= 7.0 cms; d= 22.5 cms . . . . . . . . . . . . 17
3.3 EXPERIMENT 1. Initial and Final Conditions. T= 1.25 sec; Hb= 7.0
cms; d= 22.5 cms; Xb= 2.5 m . . . . . . . . . . . . 18
3.4 EXPERIMENT 2. Measured Profiles at Various Times. T=1.25 sec;
Hb= 8.0 cms; d= 22.0 cms . . . . . . . . . . . . 19
3.5 EXPERIMENT 2. Initial and Final Conditions. T= 1.25 sec; Hb= 8.0
cms; d= 22.0 cms; Xb= 2.1 m . . . . . . . . . . . . 20
3.6 EXPERIMENT 3. Measured Profiles at Various Times. T=1.25 sec;
Hb= 12.0 cms; d= 22.5 cms . . . . . . . . . . . . 21
3.7 EXPERIMENT 3. Initial and Final Conditions. T= 1.25 sec; Hb= 12.0
cms; d= 22.5 cms; Xb= 2.7 m . . . . . . . . . . . . 23
3.8 EXPERIMENT 4. Measured Profiles at Various Times. T=1.25 sec;
Hb= 11.0 cms; d= 21.0 cms . . . . . . . . . . . . 24
3.9- EXPERIMENT 4. Initial and Final Conditions. T= 1.25 sec; Hb= 11.0
cms; d= 21.0 cms; Xb= 3.8 m . . . . . . . . . . . . 25
3.10 EXPERIMENT 5. Measured Profiles at Various Times. T=1.25 sec;
Hb= 10.0 cms; d= 20.0 cms . . . . . . . . . . . . 27
3.11 EXPERIMENT 5. Initial and Final Conditions. T= 1.25 sec; Hb= 10.0
cms; d= 20.0 cms; Xb= 7.5 m . . . . . . . . . . . . 28
3.12 EXPERIMENT 6. Measured Profiles at Various Times. T=1.25 sec;
Hb=-9.0 cms; d= 21.0 cms . . . . . . . . . . . . 29
3.13 EXPERIMENT 6. Initial and Final Conditions. T= 1.25 sec; Hb= 9.0
cms; d= 21.0 cms; Xb= 4.6 m . . . . . . . . . . . . 30

vi




3.14 EXPERIMENT 1. Grain Size Distributions at Six Locations after 24
Hours . ... .. ..... .. .....................
3.15 EXPERIMENT 2. Grain Size Distributions at Six Locations after 24
Hours .. .... .. . . ... .................
3.16 EXPERIMENT 3. Grain Size Distributions at Six Locations after 24
Hours . .-........ .. -... ..................
3.17 EXPERIMENT 4. Grain Size Distributions at Six Locations after 24
Hours ........ .............. .....................
3.18 EXPERIMENT 5. Grain Size Distributions at Six Locations after 24
Hours ........ ....................................
3.19 EXPERIMENT 6. Grain Size Distributions at Six Locations after 24
Hours ........ ....................................
3.20 EXPERIMENT 1. Mean Diameter Variation across the Beach . . 3.21 EXPERIMENT 2. Mean Diameter Variation across the Beach . . 3.22 EXPERIMENT 3. Mean Diameter Variation across the Beach . . 3.23 EXPERIMENT 4. Mean Diameter Variation across the Beach . . 3.24 EXPERIMENT 5. Mean Diameter Variation across the Beach . . 3.25 EXPERIMENT 6. Mean Diameter Variation across the Beach . . 4.1 EXPERIMENT 1. Sorting Variation across the Beach . . . . .
4.2 EXPERIMENT 2. Sorting Variation across the Beach . . . . .
4.3 EXPERIMENT 3. Sorting Variation across the Beach . . . . .
4.4 EXPERIMENT 4. Sorting Variation across the Beach . . . . .
4.5. EXPERIMENT 5. Sorting Variation across the Beach . . . . .

4.6 EXPERIMENT 6. Sorting Variation across the Beach . . . . .
4.7 Mean Diameter Versus Time at Several Locations. All Experiments . 4.8 EXPERIMENT 1. Profile and Mean Diameter and Sorting Variation
across the Beach .
4.9 EXPERIMENT 2. Profile and Mean Diameter and Sorting Variation
across the Beach ... .
4.10 EXPERIMENT 3. Profile and Mean Diameter and Sorting Variation
across the Beach .

vii

32 33 34 35 36 37 39
40 41 42 43 44 47 48 49 50 51

52 53 56 57 58




4.11 EXPERIMENT 4. Profile and Mean Diameter and Sorting Variation
across the Beach 59
4.12 EXPERIMENT 5. Profile and Mean Diameter and Sorting Variation
across the Beach 60
4.13 EXPERIMENT 6. Profile and Mean Diameter and Sorting Variation
across the Beach 61
4.14 EXPERIMENT 1. Equilibrium Beach Profiles. Top: Exponential Variation of A. Middle: Linear Variation of A. Bottom: Average A . . 64
4.15 EXPERIMENT 2. Equilibrium Beach Profiles. Top: Exponential Variation of A. Middle: Linear Variation of A. Bottom: Average A . . 65
4.16 EXPERIMENT 3. Equilibrium Beach Profiles. Top: Exponential Variation of A. Middle: Linear Variation of A. Bottom: Average A . . 66
4.17 EXPERIMENT 4. Equilibrium Beach Profiles. Top: Exponential Variation of A. Middle: Linear Variation of A. Bottom: Average A . . 67
4.18 EXPERIMENT 5. Equilibrium Beach Profiles. Top: Exponential Variation of A. Middle: Linear Variation of A. Bottom: Average A . . 68
4.19 EXPERIMENT 6. Equilibrium Beach Profiles. Top: Exponential Variation of A. Middle: Linear Variation of A. Bottom: Average A . . 69
5.1 EXPERIMENT 1. Top: Dissipation Versus Distance. Bottom: Dissipation Versus Distance and Mean Diameter Versus Distance . . . . 73
5.2 EXPERIMENT 2. Top: Dissipation Versus Distance. Bottom: Dissipation Versus Distance and Mean Diameter Versus Distance . . . . 74
5.3 EXPERIMENT 3. Top: Dissipation Versus Distance. Bottom: Dissipation Versus Distance and Mean Diameter Versus Distance . . . . 75
5.4 EXPERIMENT 4. Top: Dissipation Versus Distance. Bottom: Dissipation Versus Distance and Mean Diameter Versus Distance . . . . 76
5.5 EXPERIMENT 5. Top: Dissipation Versus Distance. Bottom: Dissipation Versus Distance and Mean Diameter Versus Distance . . . . 77
5.6 EXPERIMENT 6. Top: Dissipation Versus Distance. Bottom: Dissipation Versus Distance and Mean Diameter Versus Distance . . . . 78 5.7 Lag Versus Distance. All Experiments . . . . . . . . . 80
6.1 Dissipation of Energy Per Unit Volume Versus Fall Velocity . . . 83 6.2 Dissipation Of Energy Per Unit Volume Versus Reynolds Number . 85 C.1 Size-Slope Relationship at the Beach Reference Point . . . . . 104

viii




Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering EXPERIMENTAL STUDY OF SEDIMENT SORTING ACROSS THE BEACH AND
ITS INFLUENCE ON THE EQUILIBRIUM PROFILE By
JORGE EMILIO ABRAMIAN
August 1991
Chairman: Dr. Robert G. Dean
Major Department: Coastal and Oceanographic Engineering
Improved procedures for predicting beach response to wave action are needed to optimize nourishment projects, reduce the volume of sand required and estimate performance. To date, no model has been able to satisfactorily represent the evolution and final profile of the beaches of well-graded sand, nor have experiments addressed the non-idealized case of sediment sorting across a beach composed of well-graded sand. Therefore, no reliable and proven method exists to predict the dry width of a beach with multiple grain sizes. The equilibrium beach profile equation developed by Robert G. Dean is widely used but should be treated like an idealized beach representing a kind of "average" beach. Its limitation to beaches with a unique grain size has been demonstrated several times. New forms of the equation regarding varying sediment sizes have been tested with differing results. Due to the lack of studies about the subject, these attempts considered arbitrary variations of the grain sizes with offshore distance. To address the deficiency in information related to well-graded sediments, an experimental program has been carried out. This thesis describes the set of experiments performed in the laboratory using a wave tank in which a well-graded sand beach was simulated. Data collected and analyzed included sand samples, beach profiles and wave characteristics. The sand samples were taken from different locations at different

ix




intervals within the 24 hours duration of each experiment. With these results and use of the Dally wave transformation model, an analysis of the dissipation of energy per unit water volume across the beach is presented. The dissipation of energy per unit volume was the original concept associated with the equilibrium beach profile in which a single value is associated with each diameter. However, results obtained herein support a relationship of the dissipation with the particle Reynold Number. A new approach to the problem based on this result is also presented.

x

.lie i mi im




CHAPTER 1
INTRODUCTION
1.1 Description of the Problem
Beach profiles have been studied for many years, however; the most important advances were achieved relatively recently. Concern over prevention of impacts due to hurricanes, other storms and sea level rise has encouraged the investigation of the nature of beach changes and new concepts of shore protection have been developed and applied. Among these concepts is that of beach nourishment. The nourishment of beaches provides recreational benefits and enhancement of a natural habitat for nesting sea turtles. Nourishment projects have been constructed at many locations in the United States as well as in many other countries, even though all aspects of this process are not well understood.
As usual, when initiating the study of complex phenomena, in order to render the problem of profile response tractable, it has been necessary to approximate the mechanisms by several simpler methods. Because of this, the concept of an equilibrium beach profile of monotonic form has proven to be very helpful. Even though this idealized beach may not be truly representative of natural conditions, the concept is very useful and has been widely employed. Bruun (1954) first proposed the following simple algebraic form for equilibrium beach profiles: h = Ay2/3 in which h is the water depth at a distance y offshore and A is a scale parameter. Later, working with a large number of profiles, Dean (1977) confirmed this interesting result and interpreted the form of this profile as related to uniform wave energy dissipation per unit water volume. Although this concept for a single grain size is useful in analysis, an extension to include the effect of different grain sizes present on the beaches in nature is necessary today to better predict response to beach nourishment.

1




2
An accurate prediction of the optimum performance of nourishment projects is posed specifically as the calculation of the designed new dry beach width with the minimum volume of filling material. For this reason several attempts have been made to apply the equilibrium profile equation making the A parameter variable with distance offshore. One attempt considers a linear variation of 'A' while the second attempt considers an exponential variation. It was found that in some cases the linear variation fitted the actual profiles better and sometimes the exponential form provided the better fit. An alternative is to conduct a simple numerical integration for the actual variation of the A parameter based on the available sediment information.
To study the post-nourishment equilibrium profiles with well graded (poorly sorted) material, several experiments were performed in a wave tank in conjuction with a research project sponsored by the Coastal Engineering Research Center (CERC). The objectives of these experiments were to determine the applicability of the theories employed and to compare the results with field data and from the numerical model under development.
These experiments raised a number of questions which required review of the basic concepts and common assumptions. Additionally the experiments showed different distributions of sand sizes across the beach, i.e. the A parameter variation across the beach did not follow a consistent pattern.
The cause of the different behavior and identification of the most important factors governing the phenomenon will be the primary subjects of this thesis. A summary of the available knowledge will be presented as well as a description of the experiments performed. A comparison of the results of the experiments will be provided and conclusions presented. During this study including the experimental phase a number of interesting phenomena were observed, but they are only mentioned here as they are beyond the scope of this thesis.
1.2 Scope
The comments above set the main and primary purpose of this thesis which is the study of the distribution of sand grain sizes across the beach and their relationship with




3
the beach profile. The wave action causes the sediment to be sorted accordingly to the available amount of energy at each location and the fall velocity of the particle. A simple demonstration of this fact is that, in general the finer sediment will be transported offshore where the wave disturbance on the bottom is sufficiently small that the particles can settle and remain in equilibrium.
Even though this concept is very clear, in reality the behavior is not always so simple, nor readily predictable. In the landward direction starting from the breaker zone contradictory results have been found: sometimes the particle sizes increase in that direction while an opposite trend is observed on other occasions. Even in the seaward direction, where the trend seems to be more predictible, occasionaly larger grains than expected were found. An experiment which emulates a real beach with well graded sand was used for the investigation. From these experiments, data related with the facts identified in the first paragraph of this section and others related to the nature of the beach development were obtained.
Hopefully those experiments and this presentation will contribute to a better understanding of the evolution of beaches and nourishment projects, which is the general purpose of the thesis.




CHAPTER 2
BACKGROUND AND THEORY
Various investigators have proposed procedures for relating the overall qualities of borrow and native sediments, and some research has been conducted to study the sorting of sediments both alongshore and across-shore. Beach profiles have been studied by several investigators, but to date, the profiles resulting from the action of waves and tides on well graded sand beaches is a poorly understood and almost unexplored issue. A brief review of the available knowledge follows.
2.1 Relation Between Grain Sizes Distributions of Borrow and Native Sand
Krumbein and James (1965) proposed a method which considered the grain size distributions f(P), of the borrow and native materials to be each represented by log-normal distributions as proposed earlier by Krumbein (1957)
f(b) e (2.1) in which D is the sediment diameter expressed in phi units, defined as
= -log2(D(mm)) (2.2) where, D is the sediment diameter in milimeters and ys 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. James (1974)

4




5
developed a complex method addressing the relative renourishment frequency for different sand characteristics; however, this procedure addressed longshore sediment transport and considered the nourishment project to be located in an area where the ambient longshore sediment transport had been interrupted completely.
Dean (1974) presented a method which attempted to address the deficiency noted above of the earlier Krumbein and James method. The borrow material was only discounted for the excessive proportion of fines present; excessive proportions of coarser material were included in the compatible fraction. However, it was considered that all the fine fraction smaller than a critical value was lost. This method resulted in a considerably higher compatibility than that of Krumbein and James (1965).
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 proportion of the fine fraction in the compatibility considerations.
The method of James (1974) is the recommended in the Shore Protection Manual (1984).
2.2 Equilibrium Beach Profiles
Considering first the idealized case of uniform borrow and native sediment sizes, Dean (1991) has considered equilibrium beach profiles represented by h = Ay (2.3) first proposed by Bruun (1954) and later confirmed by Dean (1977) in an anlysis 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 2.1.




6

1.0 ..
Suggested Empirical Relationship
From Hughes' Field Reseuls n Fild Results From Individual Fild Profiles Where a Range of Sand Sizes Was Given
0.10 --Z From Swart's Laboratory Results
0.011_

Cl) U.1

0.1

1.0 10.0
SEDIMENT SIZE, D (mm)

100.0

Figure 2.1: Relationship Between A Parameter and Grain Diameter
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 the essentially straight line in the same figure. It has been shown that for nourished beaches, three types of profiles can occur depending on the relative sizes of the borrow and native sands. These are termed intersecting, nonintersecting, and submerged profiles and are illustrated in Figure 2.2. The reader is referred to 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.)
2.3 Sediment Sorting
Inman (1949) investigated the relationships between the threshold velocity and the mean diameters as well as the sorting. Inman defined the threshold shear velocity, u., velocity as:

0.01




7

W.
Added Sand h
a) Intersecting Profile AFpAN
h.
Added Sand b) Non-Intersecting Profile
AY<0
.
-B
' 7
h
Virtual Origin of '.. Nourished Profile Added Sand c) Submerged Profile Ac Figure 2.2: Three Types of Nourished Beach Profiles

*




8

-, (2.4)
where r = critical shear stress and found that the threshold velocity was minimum for a mean diameter of 0.18 mm. Inman also pointed out the unique characteristics of the grain sizes of 0.18 mm:
(1) They are moved by weaker currents than grains smaller or larger than themselves; (2) once moved they do not have as great a tendency to go into suspension as do smaller grains; and (3) they are more readily carried into suspension than larger material. ...Since both coarse and fine materials are more difficult to move and since very fine material is readily carried into suspension, bottom sediment in the process of transportation tends to become progressively better
sorted as its median diameter nears 0.18 mm.
Cornaglia (1891) proposed that the unbalanced velocities of crest and trough due to nonlinear waves in shallow water will cause the sediments to move in the same direction as the waves while the influence of gravity will pull the sediment downslope in the seaward direction. Cornaglia then stated that there would be a point where both forces have to be in equilibrium resulting in a null sediment transport at that location.
Ippen and Eagleson (1955) concluded after a series of experiments using an artificially roughened fixed plane beach, that the hydrodynamic drag forces and sediment particle weight were the primary forces involved in the net sediment motion for their test conditions. They also confirmed the existence of the Cornaglia "neutral line" where a zero net sediment particle velocity is achieved at a particular depth for each sediment size on the given beach under a particular wave. They found that for the beach under study and a range of wave steepnesses of 0.01 to 0.08 the "null point" was independent of the sediment diameter to roughness diameter ratio and boundary layer effects.




9
The following formula was proposed for the planar beach of 1:15 slope:
(H/d)2(L/H)(C/w) = 11.6 (2.5) Miller and Ziegler (1958) pointed out that two models could be applied. They comment regarding the first model where no seaward motion under gravity is considered: Our expectation under this model is that the median sediment size will increase regularly toward the shore and, at a given null point, will be greater than, or equal to that null point value. The sorting will become better by regular degrees toward the shore ... where the curve drops to zero, the accumulated mass of sediment in transport is abruptly deposited to be once again put into motion in
a different manner in zone B. The sorting at this point should be poor. ...
In the second model both landward and seaward motion due to gravity were considered. Under this assumption they expected perfect sorting, increasing grain sizes toward shoreline and an offshore accumulation of poorly sorted coarse sand. Finally Miller and Ziegler found that field experiments agreed better with the first model and that the expectations regarding increasing sizes from the top of the foreshore down to the breaker line were satisfied.
Bascom (1959) studied west coast beaches finding that the largest sand particles were located at the plunge point and became smaller in the seaward direction. Based on results by Johnson (1959), Bascom concluded that the ratio Ho/Lo could probably control the beach face slope. Bascom also developed a curve which relates the grain size to the beach face slope.
Blackley and Heathershaw (1982) mentioned the result obtained by Evans (1939) about coarse to fine grading in an onshore direction landward of the breaker zone due to reduced velocities at the top of the swash zone. They reached the same conclusion after carrying out fluorescent tracer studies on wide surf-zone beaches.
Murray (1967) discussed the limitations of the 'null point' concept noting that it only considers one of the many mechanisms involved in sediment transport processes. He recog-

1




10
nized the tendency of the finer grains to move offshore not only as a result of bed load but of suspended load as well.
2.4 Evolution of Beach Profiles and Sand Bar Formation
Several attemps have been made to develop a transport model and to predict the formation of offshore bars, berms or erosion, but to date a complete realistic and physics based model, which takes into consideration the wave conditions, the original bottom shape as well as non-uniform grain size distributions has not been developed.
Dean (1973) developed a method to predict conditions under which bars would formed. The wave characteristics and the fall velocity of the sediment were correlated with barred profiles with good results, although the method does not describe the profile evolution.
Wang, Dalrymple and Shiau (1975) developed a model superimposing the mean flow profile and an exponential sediment concentration profile obtaining good results far outside the breaker zone and not generating any sand bar. Dally (1980) proposed a model for beach profile evolution using a breaking wave model and a suspended sediment transport model (assuming an exponential variation of the sediment concentration). The results are in good qualitative agreement with large wave tank results, but fail to predict bar recovery and do not provide good quantitative agreement, even though the breaking wave model used agreed well with the data.
Bailard and Inman (1981) review the work by Bagnold (1963)-who found the transport rate to be proportional to the dissipation of energy in unidirectional steady flows-and improved it by accounting for the time dependence of the dissipation of energy and of the proportionality factor which also depends on the friction angle and the slope of the bed. Limitations are pointed out by the authors in the sense that it can only be applied in bed transport dominated cases and plane bottoms. Also the drag coefficient was considered constant in the calculation of the shear stress, which the authors recognize as a limitation.
Later, Bailard (1982) compared an extended version of the model described above using experimental data to calculate volume changes. The results were not very encouraging and




11
Bailard attributed the differences to inadequate experimental determinations. The sand used in the experiment was well sorted with a median diameter approximately 0.17 mm.
Trowbridge and Young (1989) formulated a detailed model to be applied seaward of the breaker. The objective was the estimation of the sand transport and associated morphological changes. Four parts are included in the model: An empirical sediment transport relationship, a theoretical based expression for the mean bottom shear stress, a shoaling model and the equation of sediment mass conservation. The model considers a gently sloping beach, straight and parallel bottom contours, random and normally incident waves, a turbulent boundary layer and sediment transport as sheet flow. They concluded that the Bailard model was not applicable for a sediment transport relationship. The predictions were in good agreement with the measured migration of the offshore bar. Other constraints are that the model only predicted onshore transport and thus applies to situations far from and only on one side of equilibrium.
Roelvink and Stive (1989) performed an experimental investigation to judge the importance of the different mechanisms influencing the bar formation process. They empirically found that all of the three contributions-undertow, asymmetry of the orbital velocity, short wave and long wave interaction-were of the same order of magnitude.
Larson and Kraus (1989) developed a numerical model discriminating four zones, each with different transport characteristics: they are the offshore, breaker, broken and swash zones. This model was calibrated using the large wave tank data of Saville (1957) and good agreement was found. Two sets of experiments were conducted, one with a uniform sand size of 0.22 mm and one with a uniform sand size of 0.4 mm.




CHAPTER 3
LABORATORY STUDIES
3.1 Introduction and Description of Facilities A series of laboratory studies was conducted in the Coastal and Oceanographic Engineering Laboratory to investigate the response of beach profiles to wave action. Cases studied included well graded sand and planar initial forms with varying slopes and wave conditions. A total of 6 experiments has been conducted, each with conditions selected accordingly to the results developed by preceding tests.
The major facility was a wave tank equipped with a piston type wavemaker which oscillated periodically with a stroke which could be controlled manually. The period range for testing is between 1.25 seconds to approximately 5 seconds, but was set constant at 1.25 seconds.
A "scoop" was used to collect shallow samples from the surface of the beaches. To measure the profiles a point gage mounted on a moving carriage was used. In the last 3 experiments a wave gage and a strip chart recorder were used to analyze the wave data.
In the sixth experiment, fluorescent tracers and a camcorder were used to provide additional documentation of the experiments. Scales, chronometer, test tubes and tapes also have been used to obtain the experimental results.
The test conditions are presented in Table 3.1 and a schematic of the facilities is shown in Figure 3.1.
3.2 Objectives
The objectives of the experiments were:

12




9,

6

A5
7
I.STEEL FRAME
2.ENGINE AND CONTROLS
3.HATER INLET 4.SAND BEACH S.SUPPORT BEAM
6.PISTON
7.SUPPORTS
B.NOVING CARRIAGE
9.POINT GAGE

Figure 3.1: Wave Tank Schematic

A---

I __ ____

I-.

q-

I

I




14

Table 3.1: EXPERIMENTAL CONDITIONS, WAVE TANK TESTS
Run Wave Period Wave Height' Depth Initial Slope (sec) (cms) (cms)
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
'In horizontal portion of the tank
* To document the evolution and sorting with time for initially planar beach profiles
and poorly sorted sediments.
* To compare the experimental profiles and sediment size distributions with predicted
values based on current knowledge and background.
* To investigate details of the sediment sorting mechanisms.
3.3 Experimental Procedures
The tests commenced with initial planar beach slopes, obtained by marking guide elevations on the tank wall. Prior to establishing the profile, the sand was mixed to approximate uniform sediment size. The desired wave conditions were established, the initial beach profile was documented and sediment samples were collected from different locations along the profile.
Each run was conducted for 24 hours after which it was expected that additional changes would be minimal. During each run the profiles were measured several times and coincidently sand samples were taken from different positions. The profiles were measured only along the centerline of the tank. This fact could be partially responsible for the differences between the eroded and accreted volumes as sometimes non-symmetric (across the tank) profiles were observed. The number of samples collected depended on the length of the




15

Table 3.2: MAIN CHARACTERISTICS OF THE EXPERIMENTS
No Slope d hb Hb Xb d/Lo H/Ho Ho L Hb/d Notes cm cm cm m m m
1 1:10.85 22.5 10 7 2.5 .041 1.059 6.61 1.18 0.70 2 1:5.74 22.0 5 8 2.1 .020 1.226 6.52 1.21 0.62
3 1:9.93 22.5 8.4 12 2.7 .034 1.098 10.91 1.10 0.70 irregular 4 1:13.94 21.0 9.0 11 3.8 .037 1.000 11.00 1.12 0.81 irregular 5 1:24.27 20.0 12.8 10 7.5 .052 1.016 9.75 1.33 1.28 1st brk 5.8 7 4.7 .023 .857 8.00 0.93 0.82 2nd brk 6 1:14.33 21.0 10.4 9 4.6 .043 1.055 9.50 1.21 1.15 1st brk 8.2 6 3.1 .033 1.104 5.43 1.09 0.73 2nd brk
T = 1.25 sec; Lo = 2.43 m
beach. For each run the sampling density for the final profile was greater than that for profiles at intermediate times. The location and the height of the breaking wave were documented several times during each test. Each run differed by only a few parameters to make the analysis simpler. The depth was approximately the same for all tests. The desired wave height was obtained by adjusting the wavemaker stroke.
The tracers used in Experiment 6 were of 6 different colors. Each tracer was made with dyed sand and screened to obtain a very narrow range of sizes (corresponding to Sieve Nos: 50, 70 and 100 -2 colors each). The tracers were placed at two different sites along the beach and their displacement was followed visually and with a video camera. After the experiment they were tracked by examining the samples during sieve analysis in the visual accumulation tube. Also small cores were obtained with test tubes and were examined to further establish the transport of the tracers.
3.4 Main Characterists of the Tests
Each test differed from the others even when the test parameters were sometimes quite small. The set up of the experiments was designed to cover a wide range of conditions. For this purpose, tests with very steep and very mild slopes were performed. The wave height was also varied. The main characteristics of each test are summarized on Table 3.2.




16
3.5 Description of the Results
3.5.1 Experiment 1
The profile evolution from a planar slope of 1:10.85 is shown in Figure 3.2, including the initial condition and at 1, 5, 10 and 24 hours. 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 3.3 presents both the initial and final profiles and the grain size distributions at different locations at 24 hours. In the top left corner the initial grain size distribution is shown. For Experiment 1, 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. The final volumes above and below the initial profile seem to match reasonably well, even though a small loss of sand is perceptible.
3.5.2 Experiment 2
With the exception of a much steeper initial beach slope, (1:5.74 vs 1:10.85), conditions of this experiment differed only slightly from Experiment 1.
The evolution of this profile is presented in Figure 3.4 for times of 0, 1, 5, 10 and 24 hours. The initial profile resulted in practically only seaward sediment transport and an associated bar was built very quickly and increased in volume until the end of the experiment.
Figure 3.5 presents the grain size distributions and it is seen that the sorting of sediment is not very evident. Coarse material is present near the seaward portion of the profile.
Like in the first experiment, erosion was found at the shoreline, but this time no berm feature was formed.
3.5.3 Experiment 3
Figure 3.6 presents the profile results for Experiment 3 at 0, 1, 5, 10 and 24 hours. The initial slope was very similar to that of the first experiment; however, the piston stroke




ORIGINAL
------------------- I
------ -.-------...- lol
-- -- - 51H
- .. ... .... 1. 11

_r 0.0
-
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..... ..........
10.85
1.00

I I I I I I I ~ I I
-4

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5
DISTANCE (M)

7.0 7.5 8.0 8.5

9.0 9.5 10.0

Figure 3.2: EXPERIMENT 1. Measured Profiles at Various Times. T=1.25 sec; IIb= 7.0 cnis; d1= 22.5 cmis

0.3
0.2

0.1 -

-0.3

1.0

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

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INITIAL DISTRIBUTION

0.2
0.1
0.0
c
(L
-0.1
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101
80 u 60 a40

G.S.0. AT 1.3M1

00 z 60 u40
a.

20

20 10\ G.S.D. AT 2.41
. . / 0 -.
GRAIN DIAMETER 060 u 0
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.............GRAI ............ .. ................................... .
--------' -------- -n -----------------0 k0 0. 4 0.6 5 .9 W4 .
GRAIN DIAMETER'
80.
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c:
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0. .RO.I N.4 0.6 .8 .0 GRA1N DIAMETER

0. 4 .6 .8
GRAIN DIAMETER

SWL

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 3.3: EXPERIMENT 1. Initial and Final Conditions. T= 1.25 see; lIb= 7.0 cms; d=
22.5 cms; Xb= 2.5 in

0.3

ORIGINAL .. .. .....24 H

.0

-0.3

Co

-I

1.0

10.0

lunimananmanammmmarmimanmmmmarnanmmann>nsnm010izinunnminanannamnmmamnmanmnannnnmnnmammannnmanmaannmunamamman




0.3
ORIGINAL
--- I H
- -- ---. 5H
- 10H
0.2
0. 1
5. 74
-1 .00 W
0 0 -- - - ~ -- ...-..... ....... ............ ......- ......... ..... ...... ............. ..........
'-N
-0.1
-0.2
-0.3
1.0 1.5 2.0 2.5 3.0 3.5 1.0 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 3.4: EXPERIMENT 2. Measured Profiles at Various Times. T= 1.25 sec;
IIb= 8.0 cns; d= 22.0 cns




ORIGINAL ...... .... 24 H

G.S.D. 4T. 1.21
y 804 u 60. .40.
20.

z Li
.

INITIAL DISTRIBUTION

INI TIAL DISTRIBUTION 80 60
40
2N

0.2
0.1

i-i

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SWL

0e

I I I. I I I [ I I I I I
1.5 2.0 2.5 3.0 3.5 q.0 q. 5 5.0 5.5 6.0 6.5 7.0 7.5

I .
8.0 8.5 9.0

DISTANCE (M)
Figure 3.5: EXPERIMENT 2. litial and Final Conditions. T= 1.25 sec; IIb= 8.0 cins; d= 22.0 cns; Xb= 2.1 in

0.3

0. Ir .F0608.0 1 G.S.D. AT 2.0H
z- 0 -* -9 2- I .-& -. 0
GRAIN DIAMETER 00
5.74 G 60 GRAIN DIAMETER
1.00 20
GRAIN DIAMETER
G. S.LD. AT 2. 51H 10(i
80
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cc
' 40
0
GRAIN DIAMETER

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Lu

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-0.2

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. 1
9.5 10.0

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0.3
ORIGINAL
- III
0 0 ---- ,~~- --- -------- --------- -- --i- --n- - - -- 1
1.0"
.2411
0.2
0.1
F-
-0.1
9.93
1.00
-0.2
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 3.6: EXPERIMENT 3. Measured Profiles at Various Times. T=--1.25 sec; lIb=h 12.0 cims; (1-= 22.5 cmns




22
was changed to obtain larger waves which also became irregular. The final profile shape obtained includes a relatively large berm feature, a small inshore bar that cause breaking of the waves, an erosion zone and finally a second offshore bar.
Figure 3.7 presents information concerning the variations of grain sizes. Even though the patterns are not very definite, it is seen that the distribution at 1.3 m has coarser components than that at 3.1 m seaward of the berm and at the same time the maximum percent at the first is about 40 and corresponds to 1.8 mm while at the offshore location the maximum percent is about 60 and corresponds to a finer diameter that is 0.9 mm. From this latter fact it can be concluded that a degree of sorting had occurred although is not very distinct.
3.5.4 Experiment 4
Some improvements were made to the set-up 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 used before. The other variables were kept in the same range. As in the former experiment irregular waves occurred.
Inspection of Figure 3.8 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 can be explained by the lateral lack of symmetry, the strong consolidation observed at the very beginning of the experiment and by the fact that after 24 hours small ripple features were observed all over the tank. Nevertheless erosion at the offshore end of the beach was observed. On Figure 3.8 the profiles for 0, 1, 6, 12 and 24 hours are shown. The grain sizes variations are shown in Figure 3.9.
Although a clear trend 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.




ORIGINAL

- ---- ------ 24 if

INITIAL DISTRIBUTION
100.

0

G.S.D. AT 1.314 101
80.
u 60.
qG.S
20 0O .
0 0 0. 2 0
GRAIN DIAMETER u60
40.
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---- --- --- ~ --- ---- --- ---- --- --- .0 0 .2.
GRAIN
. 9.93
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1. AT 2. 3H .2 0.'1 GRAIN 0
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D I lETER

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GfiAIN DIAMETER

INNNENIENIIM/NNNNNIN INN/NIN I/ENM/MNJA/01M I/$NNNI/flDMI/NNNA E/ MiMG G MN AM RA MEWA

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 3.7: EXPERIMENT 3. Initial and Final Conditions. T= 1.25 sec; lIb= 12.0 cls; d= 22.5 cmns; Xb= 2.7 in

0.3

0.2
0.1 -

0.0

LLU
D~

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ORIGINAL
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0 2 ...2'4I
0.2
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I
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1.00
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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 3.8: EXPERIMENT 4. Measured Profiles at Various Times. T=1.25 c; III)= 11.0 cois; d= 21.0 c is




ORIGINAL . ... . .. 24 H

INITIAL DISTRIBUTION

0.3
0.2
0.1

I I I I I I I I I I I I I I 1.5 2.0 2.5 3.0 3.5 q.0 4. 5 5 .0 5.5 6.0 6.5 7.0 7.5 8.0

in
G.S.0. AT 1.70
80.
U z60
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40 .0 .2 .4 2 GRAIN
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G.5.0. AT 3.7
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20
13.914 0.
.u 0.2 U. 4 U.6 0.a .0
1.0 GRAIN DIAME fER

I I I 8.5 9.0 9.5

DISTANCE (M)
Figure 3.9: EXPERIMENT 4. Initial and Final Conditions. T= 1.25 sec; IIb= 11.0 cmis; d= 21.0 cins; Xb= 3.8 in

6.6 6. DIAMETER
SWL
-. -. -. -. -. I -. -

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-0.2

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26

3.5.5 Experiment 5
This experiment included the mildest initial slope of all the 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 3.10 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 3.11, which shows the grain size distributions, it can be concluded that the concentration of finer grain sizes offshore is greater.
3.5.6 Experiment 6
This was the most sophisticated experiment because of the sand tracers which were used. The evolution of the beach is shown in Figure 3.12. As in Experiment 1, a berm was formed but most of the sand was transported offshore where it formed a bar feature.
The sand distributions are shown in Figure 3.13. 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.
The tracers were followed as carefully as possible, but this was not always an easy task.
The initial tracer sizes and distributions were as follows:
" Blue : #100 at 4.5 m.
" Orange: #100 at shoreline.
" Magenta: # 70 at 4.5 m.
" Green: # 70 at shoreline.
" Yellow: # 50 at 4.5 m.
" Red: # 50 at shoreline.
The results of the tracer investigation are summarized in Table 3.3. The following can be concluded from the analysis:




0.3
ORIGINAL .111
-- -- -- 6H
S-12H
.24H
0.2
0.1
5WL
0
CD
-0.1I
-0.22.
-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 3.10: EXPERIMENT 5. Measured Profiles at Various Times. T= 1.25 sec;
IIb= 10.0 cmns; d= 20.0 cuis




ORIGINAL
----------- 24 H INIT[AL DISTRIBUTION
too
G.S.D. AT 3.3M
10r1 80
0.2 80
u- Z 60.
uj 60. ui
w Li
a 40.a
4i 40
20 CI
0.. G.S.D. AT 4.5H 20
0.1 -GRAIN DIAMETER '-o Z 0
60 .0 6.2 0-4 3.6 6.8 .o GRAIN OIAMETER
ISU
0. -------- --- ------ ------------ .- ----. ..TRHETER.. ..--... .. G. S. A T 8.01
.20
-7j.0. -~ 20604 W '80.
-0.) 20
1.0 1.5 2.0 2.5 3.0 3.5 41.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 1.0
DISTRiNCE (M)
Figure 3.11: EXPERIMENT 5. Initial and Final Conditions. T= 1.25 sec; lIh= 1(.) cis;
d=. 20.0 c2s Xb= 7.5 m

I

0.3




0.3
ORIGINAL
- IlH
- -- - - 61
2411
0.2
0.1
. -. - .- - -S...
\ 4.33
1.00
-0.2
-0.23\\ N
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 3.12: EXPERIMENT 6. Measured Profiles at Various Tiies. T= 1.25 bec; III)= 9.0 cmis; d= 21.0 cms

. |




ORIGINAL
- .-. --.. ..24 H1 INITIAL DISTRIBUTION
G.5.0. AT 2.Ot
10( -80
0.2 -80.
I 60
Ui 60.4U
c U
2 40 C 0
l20.i O 1 G.S.D. AT 3.01 a0. 20
0.1 GRAIN DIAMETER 60
c: 0 40 '.0 6.2 o.q 6.6 6.8 .0
2 I0 GRAIN DIAMETER 00
.0 0.2 0.4 0.6 0.8 .0
GRAIN DIAMETER SWL 0 0 --------. ------.. ------.--.--------.. . . . . ...... .-.--.. .. . . . .... ......... ........ .. . . . . .......... .. .. ....... . .
CL G.S.D. AT 4.5
-- 14.33 109
C) ~-80. C:
1.00 L)60.
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\0. 01. Y40608t
GRAIN DIAMETER
-0.2
-0.3 I I I
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0
DISTANCE (M)
Figure 3.13: EXPERIMENT 6. Initial and Final Conditions. T= 1.25 sec; III= 9.0 cmsib;
d= 21.0 cms; Xb= 4.6 in

I.

0.3




31
1. The red tracers were the most readily tracked.
2. 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.
3. 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.
4. 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 surface during the first hour.
5. 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. It is good to recall at this point
that the orange tracer was the finest and that the red was the coarsest.
6. 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.
7. No other evidence has been found indicating major patterns in the sediment transport.
Other results concerning all experiments are presented below and will be used later to develop additional conclusions.
Figures 3.14 through 3.19 show the grain size distributions obtained at six different locations after 24 hours of wave action for each experiment.




G.S.D. AT 1.3 H

0.3 0.4 0.5 0.6 0.7 0.0 0.9 GRAIN DIAMETER

t00
90 80 70 60 U50
30 20
10
0
500 90 80
70 60
L s0
2: 30 20
0

0.3 O.4 0.5 0.6 O.7 4.8 0.9 GRAIN DIAMETER

100 90 "0
70
60 I050 Lu40
d.
30 20
10 0
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00
90 60 70 60 LUS L40
30 20 10
0

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

G.S.D. AT 3.0 H

0.0 0.5

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
GRAIN DIAETER

t00 90 80 70 60 U50
LU40 30
20
t0 0
5.0

z
L .0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
GRAIN DIAhETER

G.S.D. AT 3.4 H 100 90
70
60
50
110 30
20
o0
0n 0 A~ 0 A. 1n a a a5a

. . . . .

Figure 3.14: EXPERIMENT 1. Grain Size Distributions at Six Locations after 21 lmlurs

0.0 0.5 0.2

G.S.0. AT 2.4 H

.0

C.)

0.0 0.1 0.2

G. S.D. A T 2. 1 H

G.S.O. AT 1.8 M

z

0

P\,-




G.S.D. AT 1.2 H

90 B0 70
60
50 40 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 DIfRETER

G.S.D. AT 1.6 H
100 ,

90
80 70 S60 U50 UJ40
30
20 10 0
.0

G.S.O. AT 2.3 H

a.
90
10
~60
S40
A.
30
20
0
0

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GRAIN ODAiETER

'U,
u
.i

1.. U
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 2.5 H

z
U
a
1.0

luu
300
70 60 10
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 OANETER

G.S.D. AT 2.0 H
100 90
60 70
60
50 110
30 20 10
0

.AA

z .U
(L
.0

. . . .
GRAIN DIAMETER
G.S.D. AT 3.2 H

90 so
50
40 30
20
0
0 4.1 0.2 0.3 0.4 0.5 0.6 0.7 0.6 0.9
GRAIN DIAMETER

.0

Figure 3.15: EXPERIMENT 2. Grain Size Distributions at Six Locations after 2-1 lusrs

u 9L

00

0




G.S.D. AT 1.3 H 100
90 60
70 60 50 MO 30
20
0.0 0.1 0.2 0.3 0.1 0.5 0.6 0.7 0.0 0.9 1
GRAIN DIAMETER
G.S.D. AT 2.6 H
800 90
0 70
60 50
30
20
10
0. 0 0.1 0.2 0. 3 0.M 0.5 0.6 0.7 0.8 0.9 1.
GRAIN DIAHETER

G.S.D. AT 1.8 H
100

90 0 70
g60 U50
aL.
30
20
.0
0 .0

0.0 0.1 0.2 0.3 0.4 O.S 0.6 6.7 6.8 0.9
GRAIN DIRMETER
G.S.D. AT 3.1 H

0.0 0.1 0.2 0.3 0.M 0.5 0.6 0.7 0.8 0.9
GRAIN DIRHETER

,u.. *-

90
60
410 70 60 US0
30
20 10
0

100
90 80 70
60 us0 dM 30
20
0.1 . . . .

.0

Id CL
.0

G.S.D. AT 2.1 H

0.0 0.1 0.2 0.3 0.4 O.S 0.6 0.7 0.0 0.9 1.0
GRAIN DIMETER
G.S.D. AT 4.6 H

90
0 10 50 40
30
20
10
0 .0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.1 0.6 1.0
GRAIN DIAhEIER

Figure 3.16: EXPERIMENT 3. Grain Size Distributions at Six Locations after 2.1 ours

LU IL

c
CL.

100




G.S.D. AT 1.7 H

6wu 100
90 90
60 00 70 70
60 60 50 050
Ala 'I 40 30 30
20 20
*0 to 0 0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.9 .0
GRAIN DIAMETER
G.S.D. AT 3.2 H
too. 100

gUo SAO
30
0
20
10 40

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

90 00
70 S60
Z
'a U50
c U40
I.
30
20
1 0 .0

G.S.D. AT 2.2 H

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.9
GRAIN DIRNETER
G.S.D. AT 3.7 H
Ii

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

9L

G.S.D. AT 2.7 H 100 90
80 70 60
50
30
20
0

100 90 go
70
50 W40
C.
30
.0
10
1 0
.0

. . . . .
GRAIN DIMAETER
G.S.D. AT 4.2 H

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

.0

Figure 3.17: EXPERIMENT 4. Grain Size Distributions at Six Locations after 2-1 Hours

z
w
Li
C
uj a.

w~

0




G.S.D. AT 2.8 M
t00 100
90 90
60 0 70 70 60 60 50 L5U 0 9"40 30 30
20 20
10 10
0 0
.0 0.1 0.2 0.3 0. 4 0.S 0.6 0.7 0. 0.9 1.0
GRAIN DIAPETER
G.S.D. AT 5.5 M
100 100

W&
0. .2 0.3 i.1* 0.5 0.6 0.7 d0 0.9 1.0
GRAIN DIAMETER

G.S.D. AT 3.5 H
0.0 0.1 0.2 0.3 0. q 0.5 0.6 0.7 0.0 0.9 1

GRAIN DIAIETER
G.S.D. AT 6.5 H

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

100
60 10
~60 L50
30
20

.0

zl WI
CC~ Cj
a.
1.0

G.S.D. AT 4.5 H
0.0 0.1 0.2 0.3 0. 4 0.5 0.6 0. 0.8 0.1 1

.0
GRAIN D(RhETER

G.S.D. AT 8.0 H 100
7:
*0
*0 I0 20 30
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.1 0.9 1.0
GRAIN DIAMETER

Figure 3.18: EXPERIMENT 5. Grain Size Distributions at Six Locations after 2-1 Hours

w
u
9L

70
u 0 CL
10
50
30 20
*0
0

0o>

,

.0




G.S.D. AT 2.0 H
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
GRAIN DIAMETER
G.S.0. AT 4.0 H

O.0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.a 9
GRAIN DIAMETER

G.S.D. AT 2.8 H
100 ,

I00
90
so 70 60
W50
U4
0
30 20 10
0
800
so
60 70 60 L)50 W40
30 20 10
0

0. 0 . . . .

0.0 0.1 0.2 6.3 6.4 6.5 6.6 6.7 6.4 6.9
GRAIN DIAMETER
G.S.D. AT 4.5 H

100
90 60
70
160
$50
UJ4O cc 30
20
10
8.0

G.S.D. AT 3.5 H

0.0 O.1 0.2 0.3 0.4 0.5 0.6 0.7 0.6 0. 3
GRAIN DIAMETER

90
60
70
60 ,50
30
20
10
0
.0
t00 90
60 70
-60
Z
LJ50 U 40
30
20 t0 0
.0

-I
LUj 0.

90
60 s0
60
50 40
30
20
10

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.9 1.0
GRAIN DIAMETER

0.0

0.1 o. 0.2 0 0.0. 0.6 0.7 0. 0.1 1.0
GRAIN DfIAMETER

Figure 3.19: EXPERIMENT 6. Grain Size Distributions at Six Locations after 2-1 IHours

G.S.O. AT 5.3 H

.0

-

I








-

-

L




38
In the next plots (Figures 3.20 through 3.25) the mean diameter of the samples are plotted versus distance for several times. The mean diameter is measured in milimeters but was actually calculated in Phi units using the following formula:
mean = ( so + 16 + D (3.1)
3
and then transformed to milimeters.




-1 -

1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30
0.25
0.20 0.15 0.10 0.05 0.00

0.5 1.0 1.5 2.

0.0

INITIAL
-------.-- 10 H S
- 24 HRS
INITIAL WATER LINE

I I I I I I I I I I I I I I ~
-4

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 3.20: EXPERIMENT 1. Mean Diameter Variation across the leach

LbJ
x
Lu

FINAL
WATER LINE
t2




0.0

1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40
0.35 0.30 0.25
0.20
0.15 0.10 0.05 0.00

LiLi
CD al:
cc
uLJ
al:

I I I I I I I I I I I I I I I I
I I I I

0.5 1.0 1.5 2.

INITIAL .--... -------....--.a 5 HiRS
-- ------ ao 10 HAS
a 24 HRS

INITIAL WATER LINE
- - ---

I I I I I I I I I I I I I I 1 ~ -~1
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 3.21: EXPERIMENT 2. Mean Diameter Variation across the Beach

FINAL 4ATER LINE
4,

-U-




INITIAL
-- --- ... 0 5 HIRS
- .. ---. ..... 10 fIRS
... a 24 MRS

1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50
0.45 0.40 0.35 0.30 0.25
0.20
0.15 0.10 0.05 0.00

INITIAL WATER LINE
E

FINAL
WATER LIN
T
NK

*

I I I i I I I I I I I I I I I I I

0.5 1.0 1.5 2.0 2.5 3.0 3.5 '.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5
DISTANCE (M)
Figure 3.22: EXPERIMENT 3. Mean Diameter Variation across the Ileaci

.p..
I-.

I -1
9.0 9.5 10.0

Lt.J LLJ LLJ M
cE
M
Lui
CE
Luj 07:

--

0.0

-




INITIAL
- -. H RS
- ----..- --- 0 4 HRS

1.00
0.95 0.90 0.85 0.80 0.75 0.70 0.65
0.60 0.55 0.50
0.45 0.40 0.35 0.30 0.25
0.20
0.15 0.10 0.05 0.00

I I I

0.5 1.0 1.5 2.

FINAL
WATER LINE

INITIAL WATER LINE
A A.

I 1 I
9.0 9.5 10.0

I I I I

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
DISTANCE (M)
Figure 3.23: EXPERIMENT 4. Mean Diameter Variation across the Beach

cc
F
LLJ
Li
37
Cc
LL a:

*0'
/
/ / .)

0.0




INITIAL
...---...-........... 0 6 HRS
--- - ---.-..o 12 HRS
--- 24 HRS
FINAL
WATER LINE

1.00 0.95 0.90
0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50
0.40 0.35 0.30 0.25
0.20
0.15 0.10 0.05 0.00

~V.j.A..
,/q\4
,4~ ~/~\/\
..,
.s~.
'S - -

0.0 0.5 1.0 1.5 2.0 2.5

. .
3.0 3.5

I I I I I

4.0 4.5 5.0 5.5 6.0 6.5 DISTANCE (M)

I I I I I 1
7.0 7. 5 8. 0 8. 5 9. 0 9. 5 10.0

Figure 3.24: EXPERIMENT 5. Mean Diameter Variation across the leach

rc
LU
CE
LD
Cc

INITIAL WATER LINE




tITIAL
- 6 HRS
----------------- JO 12 HRS
-- -- -. ..-- 24 HHS

1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 0.45
0.40 0.35 0.30
0.25 0.20
0.15
0.10 0.05 0.00

INITIAL WATER LINE

57
bJ LUJ CE
U
CE
LUJ CE

I I I I I I I I I I I I I ~ 1
~1 .

0.5 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 3.25: EXPERIMENT 6. Mean Diameter Variation across the heach

-
' -- .

FINAL
WATER LINE

0.0




45
Table 3.3: RESULTS OF THE TRACER ANALYSIS

Time Type of Observation Orange Green Red Yellow Magenta
1 HR Visual
At 1.5 m Dyed zone
At 1.6-1.7 m Dyed zone
At 1.7-2.0 m Spots
Sample tubes
At 1.5 m On the top
At 1.7 m Few grains
Accumulation tube
At 1.9 m Many Slightly Many dyed
At 2.5 m Some Some Some
At 3.0 m
At 3.5 m Some At 4.0 m Slightly Slightly Many Dyed Dyed
At 5.0 m Few Many
6 HR Visual Layers by the
_________ _____ glass Accumulation tube
At 2.0 m Few At 2.5 m Few At 2.9 m Some
At 3.1 m Few Few
At 3.2 m Few 24 HR Sample tubes
At 1.95 m Layer at 4 cm Few below top
At 2.30 m Few at 1-5 cms from top
At 2.50 m Layer at 1.5 Few cm below top
At 2.80 m Few top Few top At 3.00 m 3 Grains
At 3.50 m Few Few
At 3.80 m
At 4.20 m Few At 4.60 m Few
At 5.10 m Layer at 3.5 cm below top




CHAPTER 4
ANALYSIS OF RESULTS
4.1 Grain Size Distribution
The initial grain size distribution used in the experiments included sizes ranging between 0.08 mm to 0.8 mm. Even though the distribution could be considered as well graded, a concentration of sizes around 0.1 mm was present.
The wave action modified that initial distribution (almost uniform over the beach) making the distributions narrower or wider depending on the location and concentrating grain sizes around different mean values depending on the case. Naturally, perfect sorting was never achieved. Figures 4.1-4.6 summarize the characteristics of the resulting distributions.
The most well sorted sample among all cases (all locations, all experiments) is o = 0.31 obtained in Experiment 1 where the finally state showed that 69 % of the grains were of about 0.15 mm from an initially distribution characterized by 0' = 0.64 and 40 % of the grains of 0.1 mm. It appears that there is a capability of a particular sand composition being sorted up to a certain point independent of the waves and the beach slope.
A comparison between the breaking point distance and the maximum sorting locations is presented in Table 4.1.
4.2 Sediment Sorting and Beach Profile Formation Processes
Figure 4.7 shows the grain sizes versus time for each experiment. This figure demonstrates the relative rapidity of the sediment sorting process. In most cases the sediment distribution has been established after only six hours. In the sixth experiment the process was delayed a little because of the formation of a second breaker offshore.

46




FINAL
-.1

1.50 1.45 1.40 1.35 1.30 1.25
1.20
1.15 1.10 1.05 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50
0.45 0.40 0.35 0.30 0.25
0.20
0.15 0.10 0.05 0.00

0.5 1.0 1.5 2.0 2.5

0.0

0

FINAL
WATER LINE

i .
3.0 3.5

I I I I I
-r

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 4.1: EXPERIMENT 1. Sorting Variation across the Heach

CD (ID

A

INITIAL
---.--------0 5 HRS
- -.. .. a 10 HHS
0 24 HiS
INITIAL WATER LINE




INITIAL
S-------------. O 5 HARS
- ---. o 10 HRS
S4 - 0 24 HRS

1.50
1.45 1 .40
1.35 1.30 1.25
1.20
1.15 1.10 1.05 1.00
0.95 0.90 0.85 0.80 0.75 0.70
0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.25
0.20
0.15 0.10 0.05 0.00

I I I I I
~1 *

0.0

0.5

I'

INIT IAL HFATER LINE
\ I
-1 -

I I I
1.0 1.5 2.0

2.5 3.0 3.5

4.0 4.5 5.0 5.5 6.0 6.5 DISTANCE (M)

7.0 7.5 8.0 8.5 9.0

Figure 4.2: EXPERIMENT 2. Sorting Variation across the leach

CD
(r)

FINRL
4ATER LINE
le

00

. 1
9.5 10.0

I




INITIAL
---------- -- -.. 0 5 H RS
- ------ -4 ---- o HHRS
- ~-~~ ~ --a 24 HR5

1.50 1.4q5
I LI 1.35
1.30 1.25
1.20
1.15 1.10 1.05 1.00
0.95 0.90 0.85 0.80
0.75 0.70 0.65 0.60 0.55 0.50 0.45
0.40 0.35 0.30 0.25
0.20
0.15 0.10 0.05 0.00

4\ .
\ I. 1~

/ /
/
/
/

/
/

/

I I I I I I I I I I I

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
DI

4.5 5.0 5.5 6.0 STANCE (M)

. .
6.5 7.0

(L0

.5 8.0 8.5 9.0 9.5 10.0

Figure 4.3: EXPERIMENT 3. Sorting Variation across the Beach

C-

FINAL INITIAL WATER LINE WATER LINE

0.0




INITIAL
---------------. .o HRS
- .~.-.-. .-.~.-. .. 10 IH S

1. 50 1.45
1.40 1.35 1.30
1.25 1.20
1.15 1.10 1.05 1.00
0.95 0.90 0.85 0.80
0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40
0.35 0.30 0.25
0.20
0.15 0.10 0.05 0.00

A.

INITIAL WATER LINE
---

I I I I I I I I I-

0.5 1.0 1.5 2.0 2.5 3.0 3.5 41.0 4.5 5.0 5.5 6.0
DISTANCE (M)

I I I I .
6.5 7.0 7.5 8.0 8.5 9.0

Figure 4.4: EXPERIMENT 4. Sorting Variation across the lieach

CD
CD)
ZO

FINAL
WATER LINE
.X
---

0.0

C" 0)

. 1
9.5 10.0




INITIAL
-------------------- .0 5 HRS
.-.-.-. ... 10 IIHRS
--0- : 24 HRS
FINAL
WATER LINE

1.50
1.45 1.40 1. 35 1.30 1.25
1.20
1.15 1.10 1.05 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50
0.45 0.40 0.35 0.30 0.25
0.20
0.15 0.10 0.05 0.00

0.5 1.0 1.5 2.0 2.5 3.0 3.5 '4.0 '4.5 5.0 5.5 6.0
DISTANCE (M)

INITIAL WATER LINE
*'

V-' ~
*. ...............................
V
- o

I 6 5 I I I
6.5 7.0 7.5 8.0 8.5 9.0 9.5

Figure 4.5: EXPERIMENT 5. Sorting Variation across the Beach

I :1

CD
H
CD UCO

I I I I I I I~--]-----------1------------1-------------*~--*****-*-~-**-*-I-******-

0.0

10.0

-~




IN ITIRL
- ------------------.. H Z)
- -- --- - 0 HRS
- ~~~~~ ~- ~a 24 iiRS

1.50 1.45 1.40 1.35 1.30 1 .25
1 .20
1.15 1.10 1.05 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50
0.415 0.110 0.35 0.30 0.25
0.20
0.15 0.10 0.05 0.00

1.5 2.0 2.5

INITIAL WA ER LINE
p
-4
AL A E
/N \ /

I I I I I 1~ I
-t

3.0 3.5 41.0
DI

.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0
STANCE (M)

Figure 4.6: EXPEllMENT 6. Sorting Variation across the Ieach

C)i
cc)

FINAL
WATER LINE
I ~

ca"

0.0

0.5 1.0




EXPERIMENT x 2

B i2
TIME

18

i.0 0.9
0.8
c
0. 7
L0. 6
0.5
0.4 c 0.3
0.2
0.0 24 0

S 12 TIME

is 24

I.0 0.9 0.8
c'
0. 7 L0. 6 S0.5
z
c 0.3 X: 0.2 0.1
n n

EXPERIMENT a 3
_____AT 1.6 N ...- --..- - 2.3 I N
-- --. Al 2.6 N
Al_ 0 .1 N
--~ .

0

6 i2
TIME

EXPERIMENT a 4

i 2 TIME

18

Laj
z LU

EXPERIMENT a 5

AT 2.7 II 0.9 ......... AT q.o N
0.8 ---. AT 5.0
0.7 0.6 0.5 0.4
0.3 ..-w ---------- ....

0.1

6 12
TIME

i.0
0.9.
0.8 0. 7.
A0. 6 S0.5
0.4
z
cc 0.3j Li
2:0.2;
0.1
0.0

is 24

EXPERIMENT a 6

6 IM
TIME

Figure 4.7: Mean Diameter Versus Time at Several Locations. All Experiients

1.0
0.9.
0.8.
0. 7.
110.6. 0.5
C0.4 c:0.3.
20.2 0.1.
0.0

. I 1.j N
-----. AT 1.8 H
NT 2.' N
-- I 0t .0 N
.-......._...
.,:1we .-.. .. - - -

-AT 1.2 H ......... IA 1.6 "
A T 2.0 N AT 2.5 "
. .... ...... ....... .. . .

0

1.0 0.9 0.8 0. 7 0.6
0.5 00.4 0.3
2:0.2 0.1
0.0
0

NT 1.7 N
- -- 0t.2 N

Cit

_---_--_ NI 2.0 N
. . o .0 N
-- --.. NI 3.5 N
NI 1.011

i8 24

EXPERIMENT a I

.

I

-

i




54

Table 4.1: LOCATION OF BREAKING AND MAXIMUM SORTING
Experiment # Location of Breaking Observations
best sorting (m) location (m)
1 2.5 2.5
2 1.3 Corresponds to top of berm
2.0 2.1
2.5-3.1 Corresp. to end of profile 3 1.6 Corresp. to top of berm
3.1 2.7
4 1.7 Corresp. to top of berm
3.3 3.8
5 3.5 4.0 2nd breaking 5.0 7.0 1st breaking
8.0
6 1.9 Corresp. to top of berm
2.3 4.6 2nd breaking 3.5 3.1 1st breaking

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 and the berm were formed in the first six hours and after that they only migrated or modified their volumes. 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 run 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 succesive layers being found after 24 hours at some depths below the surface.




55
For purposes of interpretation the final profile and the distribution of the mean diameter accross the beach as well as the sorting were plotted in a single plot for each experiment in Figures 4.8-4.13.
4.3 Beach Profiles
Among the resulting profiles similarities and differences were observed and can be characterized as described in the following paragraphs.
The observation of the profiles showed that they were active over their entire length, that is, the profiles experienced changes from above the water level to the bottom of the channel. Moreover, particles over the entire length of the beaches were mobilized oscillating back and forward and never they remained static in their possitions. A careful examination of the final beach faces shows that the slope of the beach face was almost exactly the same in all 6 experiments, regardless of the initial beach slope or the wave characteristics. While the initial planar slopes ranged between 1:5.74 and 1:24.27, the final beach face slopes ranged between 1:6.04 and 1:7.05.
Bascom (1959) defined a reference point for the beaches in nature which was subject to wave action at the mid-tide elevation to somewhat above the mean water level. He assumed that the characteristics of the sand were the same in that zone that could be 'fairly wide'. Due to the scale, that reference point was very difficult to identify in the experiments conducted here. However it was noted that the grain size and the sorting varied somewhat over the length of the beach face, Bascom neglected variations of sediments characteristics assuming they were not important. The final beach face slopes were almost the same whereas the grain diameters found on the beach faces of each experiment varied substantially. The grains on the beach faces of the experiments ranged from a minimum mean diameter of 0.14 mm (Experiment 3) to a maximum of 0.55 mm (Experiment 1). Suggested variations with Ho/Lo were not confirmed either, but considering that all the experiments had the same period there is a possibility that the period could affect the beach face. Considering that the main features of the beach are formed in the first stage of the




56-

INITIAL
-24 H1
---------------....2
-- -r -1.0 1.5 2.0 2.5 3. 0 3.5 4.0 4.5 5.0 5.5 6.0 S.5 7.0 7.5 8.0 8.5 9.0 9.5 1

0.3
0.2
0.1 0.0
-0. 1
-0.2
-0.3
0.7 0.6 0.5 0.4
0.3
0.2

1.0 1.5 2.0 2.5 3.0 3.5 4.0 1.5 5.0 5.5 1.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5
DISTANCE (M) SORTING
INITIAL
.................. 5 H
10 H
..-----24 H
*
.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
DISTANCE (M)

0.0

10.0 10.0

Figure 4.8: EXPERIMENT 1. Profile and Mean Diameter and Sorting Variation across the Beach

=
I
uJ

DISTANCE (M) MEAN DIAMETER

u-I
z

INITIAL
.................. 5 H
.. .-. ----.... 10 H
------24 H

IV.

0.1
0.0

Z zn

1.5
L.4 1.3
1.2
1.1 1.0 0.9 0.8 0.7 0.6
0.5 0.4 0.3
0.2 0.1
0.0




57

0.3
0.2 0.1 0.0
-0.1
-0.2
-0.3

Figure 4.9: EXPERIMENT 2. Profile and Mean Diameter and Sorting Variation across the Beach

I

INITIAL
--------..--.-- 24 H
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 S.0 5.5 6.0 S.S 7.0 7.5 8.0 8.5 9.0 9.5 1
DISTANCE (M)
MERN DIAMETER
INITIAL
.................. 5 H
. .. . ..... 10 H
------- 24 H
- - - 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.S 8.0 8.5 9.0 9.5 1
OISTRNCE (M) SORTING
INITIAL
.................. S H
-...- _ - 10 H
----.-- 24 H
1.0 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 8.0 8.5 9.0 9.5 1
DISTANCE (M)

0.7 0.6 0.5 0.4 0.3
0.2 0.1
0.0

Q
z
C
Ln

0.0 0.0 0.0

1.5
1.4 1.3
1.2 1.1
1.0
0.9 0.8 0.7 0.S
0.5 0.4 0.3 0.2 0.1 0.0




58-

0.3
0.2
0.1 0.0
-0.1
-0.2
-0.3
0.7

(
LuJ

0.6
0.5
0.4
0.3
0.2
0.1
0.0
1.5
1.4
1.3
1.2 1.1
1.0 0.9
0.8 0.7
0.6 0.5
0.4
0.3
0.2 0.1
0.0

DISTANCE (M)
Figure 4.10: EXPERIMENT 3. Profile and Mean Diameter and Sorting Variation across the Beach

[NIT IAL
----------- 24 H
po p va a -- --- - -- -- - - -
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
DISTANCE (M) MEAN DIAMETER
INITIAL
.................. S H
... .. .. ..10 H
----------- 24 H
1.0 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 8.0 8.5 9.0 9.5 1
DISTANCE (M) SORTING
INITIAL
.................. S H
-- -- -- 10 H
----------24 H
\ j
1 1 2 2.S 3. 3. Q S S - - - 7.
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 5.0 6.S 7.0 7.5 .0 k.5 9. 9. 1

0.0

0.0
0.0

LU LUi
z c
z




59.

INITIAL
---------- 24 H
-. -. -- -.W
I I I I I I I\

0.3
0.2 0. 1 0.0
-0. 1
-0.2
-0.3

Figure 4.11: EXPERIMENT 4. Profile and Mean Diameter and Sorting Variation across the Beach

t.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 .0 8.5 7.0 7.5 8.0 8.5 9.0 9.5
DISTANCE (M)
MEAN DIAMETER
INITIAL
.................. 6 H
. - --- 12 H
-------24 H
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 8.5 7.0 7.5 8.0 8.5 9.0 9.5
DISTANCE (M SORTING
INITIAL
.................. 6 H
... .- ... ..,.. 12 H
---..-- --24 H
----

. . I. I T
.0 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 8.0 S.5 9.0 9.5 1
DISTANCE (M)

LU

0.7

LUJ I-
LUJ
z
z
cc 0f

0.6 0.5
0.4 0.3

0.1 0.0

1.5
1.4 1.3
* 1.2
1.1 1.0 0.9 0.8 0.7 0.5 0.5
0.4 0.3
0.2 0.1 0.0

t0.0

10.0 0.0




60

0.3
0.2 0.1
0.0
-0.1
-0.2
-0.3
0.7

DISTANCE (M) MEAN DIAMETER

INITIAL
.................. 6 H
. 12 H
--------24 H
.................6.
--
1.0 1.5 2.0 2.5 3.0 3.5 41.0 '1.5 5.0 5.5 6.0 8.5 7.0 7.5 8.0 8.5 9.0 9.5
DISTANCE (M) SOR TING
[NIT [AL
..................6H
..__ .- ...12 H
.........--- 24 H
)A

0.6
0.5
0.4
0.3
0.2
0.1
0.0
1.5 1.4
1.3
1.2 1. 1 1.0 0.9 0.8 0.7 0.6 0.5 0.' -l 0.3
0.2 0.1 0.0

Figure 4.12: the Beach

EXPERIMENT 5. Profile and Mean Diameter and Sorting Variation across

INITIAL
---------- 24 H
1. - 3 -- --
t.0 1.5 2.0 2.5 3.0 3.5 14.0 4.S S.0 5.5 6.0 S.5 '7.0 '7.S 8.0 8.5 9.0 '9.S

.0 1.5 2.0 2.5 3.0 3.5 4.0 '.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5
DISTANCE (M)

0aLu

z
C
I
0
z
CD
I-

10.0

10.0
10.0

I




61

0.3
0.2 0. 1
0.0
-0. 1
-0.2
-0.3
0.7 0.6 0.5 0.4 0.3
0.2

OISTRNCE (M)
MERN DIAMETER
INITIAL
.................. 6 H
. .. .. ...... 12 H
----- 24 H
X *

INI TRIAL
----------- 24 H
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 5.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 I

1.0 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 8.0 8.5 9.0 9.5 10.0
DISTANCE (M)
SORTING

1.5 1.4
1.3
1.2
1. 1
1.0 0.9 0.8 0.7
0.6
0.5 0. 4
0.3
0.2 0.1
0.0

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 '.5 7.0 7.5 8.0 8.5 9.0 9.5
DISTANCE (M)

Figure 4.13: EXPERIMENT 6. Profile and Mean Diameter and Sorting Variation across the Beach

.0.0

CL LU

LU LUJ
z CE

0.1 0.0

z
(
(n

INITIAL
................... 8 H
.. . .....- 12 H
-.---.---- 24 H

.0.0

'. arge----




62
process, the original mean diameter could play an important role. That is coincident with the Bascom observations on Halfmoon Bay where, because of longshore sediment sorting, different grain sizes and corresponding different beach face slopes were observed.' Further investigation about the influence of the initial grain size distribution on the beach face slope is considered worthwhile.
A sand bar was not always formed; however some of the sand bar shapes were similar. In the first experiment no sand bar was present, in the third a system of two bars was observed. In the remaining experiments only one offshore bar was present.
Superimposing final profiles from Experiments 1 and 6 reveals an amazing agreement in the zone extending from the top of the beach face through the base of the bar on Experiment 6. The initial slope was steeper in the first profile, but the waves were smaller. The mean diameter variation across the beach followed a more or less similar pattern in both cases. This seems to indicate that the beach equilibrium equation works if somehow the diameters are arrayed in the same way.
Experiments 2 and 5 are also surprisingly of almost the same profile between the top of the beach face and a location just seaward of the breaker zone. The offshore end of both profiles are coincident too. In this case the main difference in the final profiles is the middle part. In the second experiment the initial slope was very steep (1:5.74) while in the fifth it was the mildest (1:24.27). Since the wave heights were within one centimeter, this difference probably did not play an important role. Obviously, even when the results show similarities, the final profiles will never be exactly equal. Nevertheless, if the concept of depth of closure is considered and set equal to the depth at the seaward base of the bar, the equilibrium beach formula will still be satisfactorily similar. Again the variation of mean diameters across the beach are somewhat equivalent.
The equilibrium beach equation could be applied to the pairs of profiles 1-6 and 2-5 by adjusting the values of A or m, but what is more difficult to explain using the equilibrium
'See Appendix C for further analysis of the final beach face slope.




63
profile is the reason for the differences between those pairs. These observations raise doubts about the concept of a unique equilibrium profile. Experiments 3 and 4 are peculiar in the sense that they do not resemble any other experiments. Coincidingly they were developed in the most irregular wave fields.
Some analyses using the sand data and the equilibrium beach equation have been made. The equilibrium profile (Equation 2.3) using the average A values obtained in each experiment have been plotted in Figures 4.14 to 4.19. In the application here, the equilibrium profile were based on the assumption of an exponential variation of the A parameter. This time the different values of the mean diameter across the beach obtained in each experiment have been transformed into A values (Figure 2.1) and then fitted with an exponential curve defined by the parameters k and AO (considering only the submerged part of the profiles). These values were replaced in the corresponding equilibrium beach profile2 which is now of the form:
h = Ao( (1 e-l5y)) 2/34.1) The resulting beach profiles were plotted and compared with the actual profiles on the same figures as before.
Finally the same procedure was applied except using a linear variation of the A parameter defined by the m and AO values and the associated equation-for equilibrium beach profile valid for this case,3 that is:
2 2/3
h = (- ((Ao + my)2. A.5)) (4.2) The results are shown in the same figures.
The different fits show different tendencies, which confirms that depending on the case one formula is more suitable than the other.
To some extent the original equation h = Ay2/3 fits better than the others, even though the concurrence is limited to only the first parts of the profiles.
2See Appendix B.
'See Appendix B.




0.00
CALCULATED PROFILE ..0...................MEASURED PROFILE 0.33
E -o.10 -'-,.A = .1
---..---- ..--- .K= 0 26
-0.20
-0.30 1
0 too 200 300 400 Soo 600 700 Soo 9oo
0.00 LENGTH (M)
- CALCULATED PROFILE
-0 10. ..............MEASURED PROF IL E AO .1 .33
-.. '. AM 0. 03
M -0.20U-1
-0.30
0 100 200 300 400 Soo 600 700 800 900
0.00 LENGTH (M) CALCULATED PROFILE ..........................MEASURED PROFILE
-0.10
I-i
-0.30
0 too 200 300 400 Soo 600 700 800 900 LENGTH (M)
Figure 4.14: EXPERIMENT 1. Equilibrium Beach Profiles. Top: Exponential Variation of A. Middle: Linear Variation of A. Bottom: Average A




0.00
-0.10
0- -0.20
-0.30
0.00

200

300

400
LENGTH (M)

5oo

600

700

800

900

Figure 4.15: EXPERIMENT 2. Equilibrium Beach Profiles. Top: Exponential Variation of A. Middle: Linear Variation of A. Bottom: Average A

-----__CALCULATED PROFILE
.... ...................MEASURED PROFILE AO= 0.11 M0
K= 0. 08
-0-0
0 too 200 300 400 Soo 600 7008 90C LENGTH (M)
-----___ CALCULATED PROFILE
- I= I
M= -0. 010 too 200 300 400 Soo 600 700 Soo 900 LENGTH (M)
... CALCULATED PROFILE
.................MEASURED PROFILE

-0.10
-0.20

a1i~j C)

-0.30
0.00
- -0 1

tii
w

-0.20
-0.30

Mi

o

100

0




C: U-1
0

100

200

300

400
LENGTH (M)

500

600

700

800

Figure 4.16: EXPERIMENT 3. Equilibrium Beach Profiles. Top: Exponential Variation of A. Middle: Linear Variation of A. Bottom: Average A

0.00
-0. 10
-0.20
-0.30

CALCULA TED PROF ILE
ENSUREDD PROF ILE 0.33
---,AO= 0. 1 1 M K= 0.49
0 to 200 300 400 500 600 700 800 9o LENGTH (M)
CALCULATED PROFILE
-EASURED PROFILE O.33
- --. P0= 0.11l M= -0. 04
---------.-----------0 t00 200 300 400 500 600 700 800 go LENGTH (M)
CALCULA TED PROF ILE ............... EASURED PROF ILE

0.00
_ -0. 10

I
a
MJ

-0.20
-0.30

0.00
- 0 .10

IL
to Mi

-0.20
-0.30

0

900




0.00 S-0. 10

300

300

L400
LENGTH

400
LENGTH

(HM) 50 600

600

500
Iii)

700

700

800

--___..__CALCULATED PROFILE
-. MEASURED PROFILE 0.33 A0= 0. 11 M
K= 0.01
- -.......
0100 200 300 400 500 6 00 700 800 90
100 20 300LENGTH
----.. CALCUL A TED PROF IL E
.. ......................MEASURED PROFILE
-0=0. 11 M
M= 0.00
-.........

900

86o

900

Figure 4.17: EXPERIMENT 4. Equilibrium Beach Profiles. Top: Exponential Variation of A. Middle: Linear Variation of A. Bottom: Average A

0

1
0

UJ m-

-0.20
-0.30
0.00
-0. 10
-0.20
-0.30

0.00
--0. 10

100

200

CL
11C)

-0.20
-0.30

--.._______CALCULATED PROFILE
-M .EASURED PROFILE
-

100

200

0

a




0.00

3uu

400
LENGTH

So)

600

700

800

900

Figure 4.18: EXPERIMENT 5. Equilibrium Beach Profiles. Top: Exponential Variation of A. Middle: Linear Variation of A. Bottom: Average A

-0. 10 Q- -0.20
-0.30
0.00
-0. 10
L -0.20 I-j
-0.30
0.00
-0.10

CALCULATED PROFILE M. MEASURED D PROFILE 3 .33 A0=0.13 M K= 0.09
-I
0 too 200 300 o00 So 700 Soo 90( LENGTH (M)
CALCULATED PROFILE
- MEASURED D PROFILE 033 A0= 0. 12 M M= -0. 01
0 too 200 300 400 500 e 700 800 90 LENGTH (M)
CALCULATED PROFILE
-----.:::,ESURED PROFILE
-

CL u-I
co

-0.20
-0.30

0

t

2c0




0

200

300

400
LENGTH (M)

Soo

600

Figure 4.19: 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
-0. 10
-0.20

I
U-i 03

-. CALCULATED PROFILE
-. ....... MEASURED PROFILE RO=0. 114 M0.33
- ----~...--- --....=...4.
K= 0.25
0 100 200 300 400 500 600 700 800 90 LENGTH (M)
CALCULATED PROFILE ........... ......... MEASURED PROFILE 0.33
-,- -.. AR = 0. 114 M
-..... -M= -0.03
0 100 200 300 400 500 600 700 800 90 LENGTH (M)
.,__CALCULATED PROFILE
............... .......- MEASURED PROFILE
-.--- -. .

-0.30
0.00 S-0. 10

uLJ C)

-0.20
-0.30

0

100

m0

0

700

800

90




70
Another aspect to mention is the apparently agreement between some of the experiments and the second model proposed by Miller and Ziegler. An accumulation of coarser sand at the bottom was observed in Experiments 3, 4, 5.
4.4 Energy Considerations
The experiments have established several details of the beach evolution process. The sorting process has been shown to be irregular; the grain sizes do not vary consistently in the cross-shore direction and the sorting of the samples at each location do not follow a consistent pattern. The equilibrium beach profiles were different using the same sand indicating that they depend on more than one parameter. The slope of the initial profile seems to play an important role in relation to the final equilibrium profile. This would seem to imply the existence of more than one equilibrium beach profile, at least under laboratory conditions.
To continue the investigation, the origin of the equilibrium beach equation based on uniform wave energy dissipation per unit volume is reviewed. The derivation of wave energy dissipation follows from the expression for flux of wave energy as given by: Flux of Energy = gpgH2C (4.3) where
1 2kh
C = -C(l+ ) (4.4)
2 sinh(2kh)
C = wave celerity
k = wave number
h = water depth
This requires the calculation of the wave height at each point. For this purpose, Dally's (1980) wave transformation model was employed. As described in the following chapter, the application of the model provides the wave heights across the final profile of each experiment and allows calculation of the dissipation of wave energy per unit volume across the beach.




CHAPTER 5
WAVE TRANSFORMATION MODEL
Dally, Dean and Dalrymple (1985) developed a wave transformation model applicable in the surf zone. The model is very general in the sense that it includes shoaling, breaking, wave set-up and bottom friction. Additionally, the model can be applied across a profile of arbitrary form. The model introduces a coefficient F which relates the stable height after initial breaking to the water depth, and a coefficient K that is a dimensionless decay coefficient.
The model solution requires an iterative procedure. The input values are: reference offshore wave height and its location, bottom profile, ratio of wave height to breaking depth, the bottom friction factor, and the coefficients K and F.
The basic equation used for the dissipation of wave energy is: d(H2h'/2) K 2
= -(H2 h1/2 r2h5/2) (5.1) dx h
Which can be interpreted as the rate of energy dissipation is equal to the excess wave energy flux relative to the equilibrium value. Should be noted that for convenience and consistency with the Dally's paper, the x axis is chosen perpendicular to the wave crest and directed onshore. The wave set-up can be expressed as:
7 3 1 8(H2) (5.2) ax 16 (h'+ 7) ax
where the total water depth, h, is the sum of the still water level and the gradient of wave set-up, 77, can be expressed as:
h = h'+ 77 (5.3)

71




72
and wave energy dissipation due to bottom friction is: ELB = pf H3 g 3/2 () 127r
in which f is the Darcy-Weisbach function factor with an approximate range 0.01-0.2. The model was calibrated using the laboratory data collected by Horikawa and Kuo (1966) and the conclusion was that the model describes the transformation of the waves very well.
In applying the model, the coefficients K and I' were set to the values found in the calibration by Dally, Dean and Dalrymple, i.e. 0.17 and 0.4 respectively. Because of the lack of other sources and a particular calibration, the friction factor was set to 0.1. The model was extended seaward of the breaking zone using the traditional linear theory, but considering a decay due to bottom friction. Following calculation of the wave transformation across the beach, the distribution of the dissipation of energy per unit volume was established. The computer program is presented in Appendix A.
After applying the model to the conditions of the six experiments, the dissipation of wave energy was plotted versus distance offshore. These results are shown in Figures 5.1-5.6. In the same figures (upper panels) two straight horizontal lines show the range corresponding to the dissipation per unit volume when it is calculated as a function of the A parameter based on Dean's approach. The equation' used for the calculation is:
D. = 2 A3/2 (5.5) In the calculations the higher limit was obtained replacing the value of A by that that corresponds to a grain size which is only smaller than 15 % of all grains of a sample representative of the initial beach. Correspondingly, the lower limit was deduced from the size of the grain which is only smaller than 85 % of the sample. The results are shown in the Table 5.1.
The figures mentioned above show that in those cases in which two breakpoints occurred, the first did not cause large dissipation, therefore these were weak events and thus probably
'The reader is referred to Dean (1991) for details.




73-

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)

500
400
350 300
250 200
ISO
10 500
0
500 450
400
350 300
250 200
150 100 50
0

.7
.6
.5

z

.4 ILL
LU
.3 Z
.2 C

.

IU.U
10.0

Figure 5.1: EXPERIMENT 1. Top: Dissipation Versus Distance. Bottom: Dissipation Versus Distance and Mean Diameter Versus Distance

.0 1.5 2.0 '2.5 '3.0 3.5 14.0 4.5 5.0 5.5 6.0 8.5 7.0 7.5 8.0 8.5 9.0 9.5
DISTANCE (M)

0ISSIP./VOL.
..... MEAN DIAMETER
0
0




74

L.0 1.5 2.0 2.5 3.0 3.5 14.0 4.5 5.0 5.5 8.0 8.5 7.0 7.5 8.0 8.5 9.0 9.5
DISTANCE (M)

500 'Sao
t450 400 350 300
250 200 150 100
50
0
500 '150
400
350 300 250
200 ISO
100
50
0

I I I I 1 1 1 1 1 | |
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 8.5 7.0 7.5 8.0 8.5 9.0 9.5
DISTANCE (M)

Figure 5.2: EXPERIMENT 2. Top: Dissipation Versus Distance. Bottom: Dissipation Versus Distance and Mean Diameter Versus Distance

0ISSIP./VOL. MEAN DIAMETER
'"----

10.0

0.7
0.8
0.5 4 LULU 0.3 Z 0.2 3
0.1
0.0 10.0




75

I I I
-.0 1.5 2.0 2.5

7- - -- -I I------F F W ~ F FF-

I T
3.0 3.5 4.0 4.5 5.0 5.5 6.0 8.5 7.0 7.5 8.0 8.5 9.0 9.5
DISTANCE (M)

500 450
400 350
300
250 200 150 100 50
0
500
450 400
350
300
250
200 150
100
0

.0 1.5 2.0 2.5 3.0 3.5 1.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5
DISTANCE (M)

10.0
0.7
0.5
0.5
0.4 0I 0.3 = 0.2 C
0.1
10.0

Figure 5.3: EXPERIMENT 3. Top: Dissipation Versus Distance. Bottom: Dissipation Versus Distance and Mean Diameter Versus Distance

0ISSIP./VOL. MEAN DIAMETER
I I I I I~~. I [ 1 I --I

-




76

i i i....

500
450 400
350 300
250 200
150 so
0
500 450 400 350 300
250 200
150 t00 50
0

I I I I I I I I I I

i.0 1.5 2.0 2.5 3.0 3.5 4.0 '4.5 5.0 5.5 6.0 .5 .7.0 .5 8.0 8.5 9.0 9.5
DISTANCE (M)

0.0

0.7 0.6 0.5
'.4 LU

LUJ 0.3 Z 0.2 C:
'0.0 10.0

Figure 5.4: EXPERIMENT 4. Top: Dissipation Versus Distance. Bottom: Dissipation Versus Distance and Mean Diameter Versus Distance

1.0 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 8.0 8.5 9.0 9.5 I
DISTANCE (M)

DISSIP./VOL. MEAN DIAMETER

U-.-.-




77

500 450
400 350 300
250 200 150 100
50
0

500 450 400 350 300
250 200 150 00
50

--'--- --- --- - -- ~ -.. ~. .
1.0 1.5 2.0 2.5 3.0 3.5 14.0 '4.5 5.0 5.5 8.0 5.5 7.0 7.5 8.0 8.5 9.0 9.5
DISTANCE (M)

OISSIP./VOL. MEAN DIAMETER
.- ---

-

Ln
CD
z
C I
C
If)
-LO
(n

0.7 0.6
0.5
0.4 U-i
U-i 0.3 z
0.2 O
0.1

,_ I I F -- i rorwo
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
OISTRNCE (M)
Figure 5.5: EXPERIMENT 5. Top: Dissipation Versus Distance. Bottom: Dissipation Versus Distance and Mean Diameter Versus Distance

10.0

>O
z
N
U)
-j
z
c
CL f-li f.$i




78-

1.0 1.5 2.0 2.5 3.0 3.5 4.0 L4.5 5.0 5.5 .0 6.5 7.0 7.5 8.0 8.5 9.0 9.5
DISTANCE (M)

.0 1.5 2.0 2.5 3.0

U.7
0.8 0.5
0.4 bJ
ULJ .3 X 0.2 0
0. 1

I ~ ~ 11v111rrro

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 5.6: EXPERIMENT 6. Top: Dissipation Versus Distance. Bottom: Dissipation Versus Distance and Mean Diameter Versus Distance

(n
x
Zc 0
C3
-n
N.

500
450 400 350 300
250 200 150 100 50

10.0

0
(n
N.
z
c
(I,
LO

500
450
400
350
300
250
200 ISO
100 50
0

DISSIP./VOL. MEAN DIAMETER

V

'I ...




79
did not influence the distribution of the grain sizes greatly. The shape of the curves resemble the shape of the corresponding curves of the mean diameters across the beach, but a shift between them is noticed. These shifts can be interpreted as a delay in the grain sizes to respond to the turbulence and is likely to be a function of the mean diameter, the profile slope, the water depth and the wave height and period. The shifts are not regular across the same profile and of course each experiment showed different shifs between the dissipation and the mean diameter. The approximate shifts to align the maximum dissipation with the maximum mean diameter are listed below, where "seaward" shift denotes a seaward shift of the dissipation peak to align it with the sediment peak and "landward" means the opposite. The shifts of the maximum peaks in the first, third and sixth experiments are very clear. In the second, fourth and fifth experiments the intensities and directions of the shifts are not so clear and the values shown below should be considered as approximations to which could be the real values.
" Experiment 1: 0.02 m landward
" Experiment 2: 0.20 m seaward
" Experiment 3: 0.50 m landward
" Experiment 4: 0.45 m seaward
" Experiment 5: 0.57 m landward Experiment 6: 0.20 m landward
If the minor peaks are considered too, a variation of the shifts across the beach can be noted and the lags measured. Including these minor peaks the results shown in Figure 5.7 were developed. Again these values of the lags cannot be considered as exact values, but only as one of the multiple possibilities. Similarities related to the shape of the curves are observed between Experiments 1-6 and 2-5. Also it can be seen that there is a dominant




80

1.0 0.9
K EXPERIMENT I 0.8 N EXPERIMENT 2 0.7 > EXPERIMENT 3 X EXPERIMENT 14 0.6 1 EXPERIMENT O.5 NEXPSIMENT
0.'4 0.3
0.2 0.1 C) 0.0
-J -0.1
-0.2
-0.3 \ \
-0.s1
-0.5
-0.6
-0.7
-0.8
-0.9
-1.0 1 I I I
0.0 0.5 1.0 1.5 2.0 2.5 3.0 .3.5 14.0 '.5 5.0
DISTANCE (M)

Figure 5.7: Lag Versus Distance. All Experiments




81

Table 5.1: RANGE OF DISSIPATION OF ENERGY
Experiment D15 D85 A15 A85 D-15 D.85
mm mm m1/3 M113 kg/ms3 kg/ms"/3
1 0.34 0.14 0.128 0.076 457 209 2 0.38 0.14 0.136 0.076 500 209 3 0.39 0.13 0.138 0.076 511 209 4 0.38 0.14 0.136 0.076 500 209 5 0.31 0.13 0.122 0.073 425 196 6 0.42 0.09 0.144 0.057 545 135

slope lag-distance for all experiments and that in general the lags decrease or even reverse direction in the seaward direction.
To qualify these results the following should be pointed out:
" The dissipation was calculated with a wave transformation model which has its limitations. No direct measurements of dissipation were possible, therefore, there is some
uncertainty of the dissipation curve.
" The lags are calculated based on the results with some subjective interpretation. The
available data were not sufficient to develop definitive conclusions.
* The results are based on experiments and the relevance of them to nature should be
questioned.




CHAPTER 6
DIMENSIONAL ANALYSIS
The development of the equilibrium beach profile equation considered the dissipation per unit volume only as a function of the sediment diameter. As a result the next set of equations could be derived: D. 1 9(ECg) (6.1) h 9y
or
D. = 1pg3/2,(Hh) (6.2)
8 hOy
Assuming
H = ,h (6.3) if D. depends only on grain size, and the grain size is uniform, direct integration of the equation will lead to the familiar: h = A($)y2/3 (6.4) If instead, the dissipation is thought to have a more complex dependence on, for example the fall velocity, bottom stress, density and the gravity as well as the mean diameter, dimensional analysis will show that indeed, the dissipation depends on two non-dimensional numbers, one of them, the Reynolds number defined as R = U(6.5)
V
where D = Diameter in metric units.
Several attemps were made to develop graphical correlations between the parameters involved, but encouraging results were not achieved until the dissipation was related to the

82




83

500 450
400 350 300
250 200 ISO
100 50
0

,.0 6.0

7.0

3.0

(M /s)

Figure 6.1: Dissipation of Energy Per Unit Volume Versus Fall Velocity

600
550

V)
0..
(n

3.0 4.0

EXPERIMENT 2 EXPERIMENT 3 EXPERIMENT ti EXPERIMENT 5 W EXPERIMENT
N
K N

,.0 2.0

FRLL VELOCITT




84
mean diameter corresponding to the shifted location. The first curve of some interest is shown in Figure 6.1 where the dissipation per unit volume is plotted versus fall velocity. Many points are arrayed in a curve on the upper portion of this plot. This curve may represent a kind of limit curve. A certain diameter could be encountered at a certain turbulent limit or below, but if the turbulence is greater the particle will be transported. Some points are arrayed in a second line below the upper curve, that can be explained as before, some particles are found in a place where they still have a capacity to withstand more energy. There could be another explanation if the tendency to a second arrangement is verified.
Using the same technique, the points in a plot 'Dissipation versus Reynolds Number' (Figure 6.2) also show a nice grouping. A least square fit with a logarithmic function appears reasonable. If the variation of the lags with distance is considered, more points can be taken into account (because more samples will then correspond to the non-zero dissipation zone) and a grouping of a different kind.
A correlation coefficient was calculated in the latter case for both linear and logarithmic fittings obtained by the Least Squares Method. The correlation in the first case is p = 0.89 while in the second is p = 0.61. Hence it may be reasonable to consider
__2_(____/2 UbD
- =3120(H2h/2) a(-) + b (6.6)
8 hOy V
From 6.6 assuming H = nh it follows that:
1 3/2 2,(h5/2) UbD
-pg /2 h = a(- )+ b (6.7)
8 hay V
Considering
11gk
Ub = --tanh(kh) (6.8)
2 o
Which for simplicity, using the breaking model, H = nh, for shallow water results in,
Ub = rv-,/gh (6.9)
2




85

600
550
500
450 400 350 300
250 200 150 100
0

REYNOLDS NUMBER

Figure 6.2: Dissipation Of Energy Per Unit Volume Versus Reynolds Number

cn
z
(Lf~
C

25.0 50.0 75.0 100.0 125.0 150.0 175.0

EXPERIMENT I N EXPERIMENT 2
EXPERIMENT XPERIMENT 4
* EXPERIMENT 5
EXPERIMENT 6
L.3. FIT: LINE
>
~K

200.0




86

To finally give replacing in 6.7
1 pg3/22 a(h/2) r h + b (6.10)
8 a hay 2 h/2D+(
or
A(h) h'/2D+B (6.11) hay
It should be remarked that A and B depend on the constants obtained from the 'DissipationReynolds' linear fit and D is variable with distance.
The Equation 6.11 involves only the experimental data used, which raises questions regarding application to prototype profiles. Attempts to apply the equation to real beaches were found discouraging yielding unreasonable slopes. As noted before, other variables including the initial slope could probably have an important influence in the development of a new relationship for the equilibrium beach profiles. At present, it can only be said that in the experiments, the Reynolds Number and the Dissipation of Energy per Unit Volume were correlated which demonstrates that the dissipation and the mean grain sizes are closely related.




CHAPTER 7
CONCLUSIONS AND RECOMMENDATIONS
7.1 Conclusions
The objective of this study was to identify and establish the significance of the variables that govern beach profile formation and sediment sorting across the beach. Even though the state of knowledge at this time does not allow achieving quantitative results, some interesting qualitative relationsips were determined. The final conclusions and considerations are listed below. It is emphasized that these conclusions are based on laboratory tests and may require modifications when addressing conditions in nature.
1. The sediment sorting process as well as the formation of the principal features on the
beaches is a relatively rapid process that define the future conditions of the beach.
These results could be of some value in future model development.
2. The beach face slopes appear to be related to the original grain size distribution rather
than the offshore wave height, energy or final grain sizes at the beach face, even though
a relation with the wave period was not studied and is thus not discarded.
3. The grain size distributions across the beach do not follow a consistent law in the
sense of monotonically increasing or decreasing. However, a reasonably relationship
between wave energy dissipation and mean grain diameter was confirmed.
4. The concept of a unique equilibrium beach profile is doubted and new approaches
to the equilibrium beach equation considering the dissipation related not only to the diameter but to other variables as well is considered worthwhile. An influence of the
initial slope on the final equilibrium profile is likely to be important.

87




88

5. A shift exists between the locations of the maximum dissipation and the maximum
mean diameter, indicating a delay of the particles to respond to the dissipation of the
energy, however, in some cases the shift was in the opposite direction.
6. A relationship between the Reynolds number to the particle diameter and the dissipation of energy per unit volume was found, however, more study is required to quantify
this relationship its significance and applicability.
7. A maximum sorting capability of a sand under waves action is suspected.
The experimental conditions probably resulted in dominant bedload transport, but whith some suspended transport present. The transport was over a non-planar bed most of the time. Under this premise, beach formation is dominated by the dissipation per unit volume where it is large enough to be transferred to the bottom. Beyond that point, the beach seems to be influenced by the sediment characteristics (fall velocity), the initial slope and the dissipation. In the turbulent environment of breaking waves, and landward of that location that is the part of the beach mainly dominated by the dissipation it seems reasonable to assume that each particle found at the bottom is the smallest particle that is stable on the particular equilibrium profile. Smaller grains are either dragged from the location or moved into the water column' or even buried (in the case of larger grains). This totally agrees with the extended concept of the "null point". When the dissipation starts to be weaker, grains of different characteristics settle and remain steady at the bottom.2 In the "Dissipation- Reynolds Number"curve (Figure 6.2) it is clearly seen that most of the points are consistent with the above description. Points with greater dissipation are aligned in a sort of limiting curve, implying that the constituents of the samples taken from the bottom were not able to be moved by the present level of energy. Larger grains would be buried or carried down and smaller grains would be put in suspension. Many samples with many different Reynolds Numbers are found when the dissipation is close to zero. The
'Note that only one Reynolds number could be present in those conditions.
2In this case many Reynolds Numbers are compatible.




89
conclusion that the Reynolds Number and the dissipation per unit volume are correlated is even easier to believe if only samples from places where the dissipation is above a minimum value are considered or what in this case will be equivalent, a limiting distance seaward of the breaking is chosen. Discarding all samples beyond that point the correlation coefficient will be closer to one. The proposed Equation 6.6 could represent the phenomena involved up to that location where the dissipation of energy is irrelevant, however, one should recall the limitations of this thesis and of the experimental method. The applicability of the "Dissipation-Reynolds" curve in nature was not verified, but preliminary attempts to do so did not satisfy the expectations.
7.2 Recommendations
The set of experiments described above was not designed in anticipation of some specific questions which arose during the program. A set of experiments which allows detailed study of several phenomena is recommended.
The setup of these experiments should include instrumentation devices to measure the wave height at different locations in order to calibrate a wave transformation model, over a movable bed. Different periods should be included as well as different initial grain size distributions.
To satisfactorily correlate the dissipation per unit volume with the mean grain diameter, the sampling should be very intensive and the position of the samples should be taken with care. Measurements of the bottom velocity would be very helpful. Furthermore, comparison with field data will give a more accurate perspective of the value of the concepts involved. New specific tests to verify the relationship between the beach face slope and the other variables will be helpful also to better understand the beach evolution.
Colored sand tracers allow easy visualization of the sediment cross-shore transport which could be helpful to fully understand the beach formation process.
This set of experiments seems to be the first of its kind. Although the resources to perform them were limited, the results proved to be very helpful and at least no contradictory