UFL/COEL89/015
EFFECTS OF SEAWALLS ON THE ADJACENT BEACH
by
Takao Toue
and
Hsiang Wang
Sea Grant Project No. R/CS26
Grant No. NA86AADSG068
1989
UFL/COEL89/015
EFFECTS OF SEAWALLS ON THE
ADJACENT BEACH
Takao Toue
and
Hsiang Wang
Coastal and
Oceanographic Engineering Department
College of Engineering
University of Florida
Gainesville, Florida 32611
Sea Grant Project No. R/CS26
Grant No. NA86AADSG068
1989
TABLE OF CONTENTS
ACKNOWLEDGEMENTS
LIST OF FIGURES ....................
LIST OF TABLES ....................
ABSTRACT ........................
CHAPTERS
1 INTRODUCTION ...................
1.1 Statement of the Problem ............
1.2 Effects of Seawalls Literature Review .....
1.2.1 Model Test ................
1.2.2 Field Survey ...............
1.2.3 Numerical Simulation ..........
1.3 Possible Mechanisms of Seawall's Effects ...
1.4 Objectives and Procedure ............
2 MODEL TEST APPARATUS, PROCEDURE AND
2.1 Model Test Apparatus ..............
2.1.1 Wave Basin ................
2.1.2 The Beach and Seawall Model .....
2.1.3 Measurement Apparatus .........
2.2 Experimental Procedures ..... ......
2.3 Test Condition ..................
3 EXPERIMENTAL RESULTS AND DISCUSSION .
3.1 Evaluation of Model Test ...........
........
........
,. . .
CONDITION
........
........
. .
. . o
. . .
..e.....
. .
. .
. . ii
3.1.1 Design of Model Beach ...................... 18
3.1.2 Assessment of Equilibrium Beach Profile . .... 21
3.1.3 Assessment of Normal and Storm Profiles Classification 21
3.1.4 Flow Regime and Mode of Sediment Transport . ... 27
3.2 M odeling Law ................... ........... 30
3.2.1 Modelling Requirement from Dean's Equilibrium Profile 32
3.2.2 Hughes' Modeling Law ...................... 33
3.2.3 Wang's Modeling Law Revised . . . .... 34
3.2.4 Noda's Modeling Law ...................... 40
3.2.5 Summary ............................. 42
3.3 Comparison to 2D and 3D Model Test Results . . .... 42
3.3.1 Beach Profile Comparison ... ....... .... .. 43
3.3.2 Offshore Breaking Bars ..................... 45
3.3.3 Reflection Bars .......................... 48
3.3.4 Scour .. .. ... . .. .. .. .. .. .. 50
4 VOLUME CHANGE ANLYSIS ....................... 56
4.1 Definition of Volumetric Changes . . . .. .. 56
4.2 Results and Discussion ......................... 59
5 SHORELINE AND HYDROGRAPHIC CHANGES ............ 71
5.1 Empirical Eigenfunction (EEF) Analysis . . . ... 71
5.1.1 Literature Review ....................... .. .. 71
5.1.2 Basic Concept on Empirical Eigenfunction Analysis . 78
5.1.3 Formulation and Procedure of EEF for Contour Lines .. 81
5.1.4 Results and Discussion ...................... 82
5.2 Shoreline Changes Based on OneLine Theory ........... ..92
5.3 Correlation Between Shoreline Changes and Volumetric Changes 96
6 PROTOTYPE APPLICATION ....................... 99
1!
7 CONCLUDING REMARKS ......................... 101
7.1 Important Findings ................... ....... 101
7.2 Recommendation for Future Study . . . ... 103
APPENDICES
A CONTOUR MAPS ................... ........... 104
B RESULTS OF EMPIRICAL EIGENFUNCTION ANALYSIS ....... 114
BIBLIOGRAPHY .......................... ....... 126
BIOGRAPHICAL SKETCH ................... ....... 130
LIST OF FIGURES
1.1 Erosion Mechanisms in the Presence of Seawall . . 7
2.1 Beach and Seawall System in the Experiment . . 9
2.2 Geometry of the Initial Profile in the Model Test . ... 10
2.3 General View of the Beach Profile Measurement System (after
Bodge, 1986) ............................. 12
2.4 Assembly of Beach Profile Measurement System . ... 13
2.5 Locations of the Wave and Current Measurement Points . 14
3.1 Correlation of Equilibrium Beach Profile Scale Parameter, A,
with Combined Sediment Wave Parameter, Hb/TW ...... ..20
3.2 Comparison of Equilibrium Beach Profile to the Final Beach
Profile in the Model Test ...................... 22
3.3 Comparison of Equilibrium Beach Profile to the Beach Profile
in the Model Test for each elapsed time (Case 1) . ... 23
3.4 Comparison of Equilibrium Beach Profile to the Beach Profile
in the Model Test for each elapsed time (Case 3) . ... 24
3.5 Comparison of Equilibrium Beach Profile to the Beach Profile
in the Model Test for recovery condition (Case 1) . . 25
3.6 Criterion of Normal and Storm Profile (after Kriebel at al., 1986) 26
3.7 Criterion of Normal and Storm Profile (after Sunamura and
Horikawa, 1974) ........................... 27
3.8 Criterion of Normal and Storm Profile (after Hattori and Kawa
m ata, 1980) .............................. 28
3.9 Criterion of Normal and Storm Profile (after Wang, 1985) 28
3.10 Jonsson's Flow Regime ....................... 29
3.11 Classification of Sediment Transport Model (after Shibayama
and Horikawa 1980) ......................... 31
3.12 Reduction of Settling Velocity in the Oscillatory Flow (after
Hwang 1985) ............................. 39
3.13 Moore's Diagram for Scale Parameter A . . .. 41
3.14 Comparison of Initial Beach Profiles between 2D and 3D Model
Test . . . . . . . . 46
3.15 Comparison of Beach Profiles after 4 Hours Duration between
2D and 3D Model Test ....................... 47
3.16 Relation between HB and ht adopted by Horikawa(1988) .. 48
3.17 Breaking Wave Index adopted by Horikawa (1987) . ... 49
3.18 Relation ht and he .................. ....... 49
3.19 Definition of Scour Depth and Other Parameters . ... 51
3.20 Relation of SI and ho ........................ 53
3.21 Relation between St/Ho to ho x tan/Lo . . ... 54
4.1 Sketch of Coordinate System . . . .. .. 57
4.2 Definition of Three types Volumetric Changes . ... 58
4.3 Rate of Volumetric Change along a Profile, p . ... 61
4.4 Cumulative Rate of Volumetric Change Referenced to Down
wave Boundary, i6r ......................... 62
4.5 Rate of Volumetric Change in a Local Control Area, i; . 63
4.6 Ratio of the Rate of Volumetric Changes with and without Sea
w all . . . . . . . .. 67
4.7 Ratio of Volumetric Changes with and without Seawall for 4
Hours Duration ............................ 68
4.8 Sketch of 12 Sections Surrounding Seawall . . .... 69
4.9 Volumetric Changes in Sections for 4 hours Duration . 70
5.1 Contour Maps for Four Hours Elapsed Time . .... 72
5.2 Schematic of Seasonal Sand Volume Changes at Torry Pine Beach
California, based of a Dual Pivotal Points (after Aubrey 1979) 74
5.3 Spatial Eigenfunction in Birkemeier's Study . . ... 75
5.4 Definition of d" ........................... 83
5.5
5.6
5.7
5.8
5.9
5.10
5.11
5.12
5.13
A.1
A.2
A.3
A.4
A.5
A.6
A.7
A.8
A.9
B.1
B.2
B.3
B.4
Contour Map for Erosive condition t=0 hour .
Contour Map for
Contour Map for
Contour Map for
Contour Map for
Contour Map for
Contour Map for
Contour Map for
Contour Map for
Eigenfunction for
Eigenfunction for
Eigenfunction for
Eigenfunction for
......... 105
Erosive condition t=1 hour . . ... 106
Erosive condition t=2 hour . . ... 107
Erosive condition t=4 hour . . ... 108
Recovery condition t=1 hour . ... 109
Recovery condition t=2 hour . ... 110
Recovery condition t=4 hour . ... 111
Recovery condition t=8 hour . ... 112
Recovery condition t=12 hour . ... 113
Case 1 ...................... 115
Case 2 ...................... 116
Case 3 ...................... 117
Case 4 ...................... 118
Real Shoreline Changes, Net Shoreline Changes and Results of
EEF (Case 1) .............................
Real Shoreline Changes, Net Shoreline Changes and Results of
EEF (Case 2) .............................
Real Shoreline Changes, Net Shoreline Changes and Results of
EEF (Case 3) .............................
Real Shoreline Changes, Net Shoreline Changes and Results of
EEF (Case 4) .............................
Real Shoreline Changes, Net Shoreline Changes and Results of
EEF (Case 5) .............................
Real Shoreline Changes, Net Shoreline Changes and Results of
EEF (Case 6) .............................
Schematic Concept of OneLine Theory . . . .
Ratios of Ultimate Mean Shoreline Position with and without
Seaw all . . . . . . . .
Compariosn of Shoreline Change between Measured and Calcu
lated . . . . . . . . .
B.5 Eigenfunction for Case 5 ...................... 119
B.6 Eigenfunction for Case 6 ................... .. .. 120
B.7 Eigenfunction for Case 1 (recovery) . ..... . .. 121
B.8 Eigenfunction for Case 2 (recovery) . .... .. 122
B.9 Eigenfunction for Case 3 (recovery) . . ..... 123
B.10 Eigenfunction for Case 4 (recovery) . ..... . .. 124
B.11 Eigenfunction for Case 6 (recovery) . ... .. 125
LIST OF TABLES
2.1 Physical Parameters of the Model . . . .... 11
2.2 Test Condition ................... ......... 16
3.1 2D Model Test Condition (Barnett 1987) . . .... 43
3.2 Comparison of Scale Parameter "A" in 2D and 3D Model Test 55
4.1 On/Offshore and Longshore Transport Rate for Natural Beach 64
4.2 On/Offshore and Longshore Transport Rate for Seawall Backed
Beach .. . . . . .. . . 64
5.1 Contribution of Each EEF .............. ....... 85
5.2 Estimated Values of e, C1, C2, k and 6 . . .... 96
6.1 Example of Prototype Quantities Based upon Laboratory Re
sults ................... ................100
EFFECTS OF SEAWALLS ON THE ADJACENT BEACH
by
TAKAO TOUE and HSIANG WANG
Abstract
This study was carried out to examine the effects of seawalls on the adjacent
beach by three dimensional model test. The results obtained from model test were
analyzed in terms of volumetric changes and shoreline and hydrographic change to
quantify the effects of seawalls.
The experiments were carried out in the wave basin of Coastal and Oceano
graphic Engineering department, University of Florida. A model seawall was in
stalled on the test beach (19mxl4m) which was initially molded into equilibrium
shapes. During the test, hydrographic surveys were conducted at regular time in
tervals. The main variable in the experiment is the wave angle. Cases both with
and without seawall were tested.
Before examining the effects of seawalls, the problems inherent to model test
were examined. First, assessment of equilibrium beach profile concept, flow regime
and modes of sediment transport were examined. The experimental set up is found
to be reasonably representative of prototype phenomena, for the erosive conditions
but not for the recovery conditions. Second, using equilibrium beach profile as a
prototype template, several modeling laws were examined. Again, it was found
that modeling law for erosion is far more firmly established than for that of accre
tion. From this analysis, it was also confirmed that the physical meanings of scale
parameter "A" of the equilibrium profile is the settling velocity scale parameter.
The effects of seawalls were examined in terms of volumetric changes and shore
line changes. In the volumetric change analysis, three types of volumetric changes
were defined and examined. Especially, the volume change in a control area sur
rounding seawall showed that the erosion rate in front of and adjacent the seawall
was larger than that without seawall for oblique incident waves, but is smaller for
normal incident waves. Although the rate of erosion was larger with seawall, the
analysis also showed that the influence of seawall was localized.
In the shoreline and hydrographic change analysis, first of all, the dominant
modes of shoreline movement were examined using empirical eigenfunction. The
dominant mode of eigenfunction of shoreline was represented by the simple retreat
mode and the rhythmic feature mode. These dominant modes did not differ between
cases with and without seawall. Moreover, the temporal eigenfunction without
seawall is very similar to that with seawall. The most obvious effect of seawall which
appeared in the first spatial eigenfunction mode was the groin effect at the downdrift
side. The hydrographic change analysis revealed that the first spatial eigenfunction
was much more irregular and the contribution of the first eigenfunction was smaller
than that of the shoreline.
Based on the empirical solution of oneline theory, alongshore diffusivity was
calculated. The calculated value was compared with the existing formula and was
found to be reasonable for natural beach.
xii
CHAPTER 1
INTRODUCTION
1.1 Statement of the Problem
Beach erosion is found along many portions of the coast of the world. The
causes of the erosion could be sea level rise, reduction in sediment supply, interrup
tion of the littoral drift by structures. There are several conventional engineering
solutions to combat such erosion. Those are (1) coastal structures such as groins,
seawalls, breakwaters and coastal dikes, and (2) nonstructural solutions, such as
beach nourishments. Among them, seawalls might be the most efficient and direct
method to protect the upland property provided that they are designed adequately.
Recently, the adverse effects of seawalls on their fronting and adjacent beaches
have gained great attention and raised criticism about the use of seawalls in the
coastal area. The most often alleged effects are (1) offshore profile slope steepening,
(2) intensified local scour, (3) transport of sand to a substantial distance offshore,
(4) adverse down drift erosion and (5) delay poststorm recovery (Dean, 1986).
Although numerous example can be found from articles in newspaper or popular
magazine reporting the adverse effects of seawalls, reliable and scientific based doc
ument is actually scarce. Moreover, the conclusion derived from the few technical
reports on the adverse effects of seawalls remain controversial. Considering the
merits of seawall as the reliable structure to protect upland erosion,abandoning or
prohibiting seawalls altogether as means of coastal protection without firmly estab
lishing their effects might be irrational. Therefore, there is a need to examine the
effects of seawalls carefully and to quantify them if possible. Also, to examine the
causes and effects of seawalls might lead to more rational design in the future.
2
1.2 Effects of Seawalls Literature Review
A summary of an evaluation on the coastal armoring effects was given by Dean
(1986). Subsequently, Kraus (1987) also presented a general review. Although
Kraus titled his paper as the review of effects of seawall, the subject was extended
to revetments, breakwaters and dikes. In the present study, the terminology of
seawall is defined as the vertical structure with backfills and is normally located
onshore from the shoreline. Based on this definition, the literatures concerning
effects of seawalls are reviewed.
1.2.1 Model Test
There were many two dimensional model tests related to seawall, but most
studies paid attention to the local scour and the stability of seawall. Hattori and
Kawamata's (1977) and Barnett's (1987) two dimensional wave tank studies were
the few dealing with beach evolution in front of seawalls. Hattori and Kawamata
concluded that except in the immediate vicinity of seawall, the erosional and recov
ery process of beaches with or without the presence of seawall was similar. Barnett
(1987) also carried out two dimensional model test, and concluded that the ma
jor transport process was not significantly influenced by the presence of seawall.
Furthermore, he examined the volume change of beach profile, and found that the
volume of sand retained upland of the structure which would be eroded under iden
tical wave condition without seawall was found to be greater than the additional
volume eroded at the toe of the structures The ratio of sand volume saved versus
additional volume eroded was found to be approximately 2 to 1.
Three dimensional experiment for seawall effects was carried out by McDougal,
Sturtevant and Kommer (1987) in a relatively small basin (7m x 7m). Only flanking
effects were examined. Combining with field survey results, they established an
empirical relation between flanking and the length of seawall as
s = 0.101 x L,
I
(1.1)
3
where s is the flanking erosion, and L, is the length of the seawall.
Equation (1.1) does not include the forcing factor such as the wave height, period
and so on. Besides, the data, upon which the equation was based, was considerably
scattered.
1.2.2 Field Survey
Field observations of beach changes under the influence of seawall were con
ducted by only a few. Based on aerialphotograph, Birkemeier (1980) estimated the
bluff and shore erosion along a stretch of beach in the southeastern section of Lake
Michigan from 1970 to 1974. To compare erosion rate of both protected and unpro
tected shorelines, he selected five reaches along the beach, each approximately 1.6
km long and each with different characteristics; one of which contained a section of
seawall 579 meter long. Erosion due to flanking at both downdrift and updrift of the
seawall were evident. These erosions appeared to be localized as all the five reaches
sustained approximately the same rate of shoreline and bluff recession. Since his
study is based on interpretation of aerialphotos the beach changes in front of a
seawall cannot be evaluated.
Berigan's (1985) study was based on beach surveys from the water line to the
seawall front. The Traval Seawall is located in San Francisco. It was built to protect
a 220m long badly eroding beach front. The toe of structure is above the highest
astronomical tide. By analyzing beach profiles taken over a seven year period and
relation of beach changes to wave energy, Berigan found that: low wave energy
has little effect; intermediate wave energy built up the beach and high wave energy
removed sand in front of seawall. He also concluded that while beach rebuilding
is a slow process, the existence of the seawall accelerated the rebuilding process
considerably compared with a beach with no seawall, which is quite contrary to
common belief.
Kana and Svetichny (1982) monitored the beach profile change in South Car
4
olina coast where the beach nourishment projects were carried out. They compared
the sculptured beach to the seawall backed beach, and concluded the seawall backed
beach results the more significant erosion than the sculptured beach but flawed.
Kriebel, Dally and Dean (1986) also monitored the beach profile at Clearwater
in Florida after hurricane Elena. They examined the recovery process at downdrift
side of seawall, in front of seawall and the updrift side of seawall. After comparing
the profiles, they made the general remark that the toe scouring at the base of a
seawall associated with a storm event was clearly evident but also suggested that
the presence of seawall did not considerably alter the beach recovery. The same
amount of sand that would have supplied to beach through upland was probably
deprived from the beach in the form toe scouring.
Walton and Sensabaugh (1985) investigated the flanking effects in Florida coast,
and suggested the suitable return wall length.
Dette and Gartner (1987) presented the time history of the island of Sylt/North
Sea and also by examining the changes in the beach topography which were mea
sured in 1869, 1953 and 1967; the long term resonance of the coastal structures on
the foreshore bed features were estimated. They obtained the following conclusion:
(1) The characteristic feature of the foreshore consisting of longshore bars and
troughs has not been "destroyed" due to the presence of coastal structures.
(2) In the vicinity of the coastal structures, it is obvious that the trough has deep
ened with time and also seems to be shifted landward.
(3) With respect to a final judgement about the interaction of structure and fore
shore topography probably the considered time space is not yet sufficient.
1.2.3 Numerical Simulation
The models developed by Ozasa and Brampton (1980) and Hanson and Kraus
(1980) have been applied on seawallbacked beaches. The authors made the sim
plified assumption in their model that the beach profile simply moves seaward or
shoreward in parallel to itself without changing form. Hanson and Kraus (1986)
in their shoreline evolution model incorporated a seawall as a solid boundary to
compute plan form changes. Local effects such as sea bottom scouring and flanking
were not modeled. As Kraus (1987) observed, the simulation does not follow the
real sediment transport.
Kraus and Larson (1988) and Larson (1988) incorporated in their beach profile
model a two dimensional longshore bar configuration and allowed the bar to move
and to change shape and volume based on wave properties. A seawall is permitted
in the model as a solid boundary. Again, similar to Hanson and Kraus's approach,
local scour and wave reflection effects are not modelled.
1.3 Possible Mechanisms of Seawall's Effects
The effects of seawall are not well understood, but several possible mechanisms
can be deduced from our general knowledge in coastal engineering. These are illus
trated in Fig. 1.1 and are also described below:
(1) flanking effects: Flanking due to wave refraction and diffraction is expected to
occur on the corners of the seawall to cause local erosion.
(2) cross wave effects: During storm surge period, the water depth in front of sea
wall is likely to be larger than that along the beach and wave reflection will occur
as shown in Fig. 1.1 b. Consequently, the longshore current together with more
reflected wave energy trapped in the trough will remove sand in front of seawall and
transport them to down drift location.
(3) groin effects: If the shoreline retreats due to littoral drift, the seawall will even
tually protrude seaward and act like a groin. Although this groin effect does not
remove sand from the system it increases downdrift erosion pressure.
(4) sand supply cut off: Seawall prevents sand from being added to the littoral
system, which again adds erosional stress downdrift and could result in lower bar
profile in front of seawall during the storm surge period.
1.4 Objectives and Procedure
The main objective of the present study was to attempt to quantify the three di
mensional effects of seawall on beach changes described in previous section. In order
to gain a fundamental understanding it was decided to conduct three dimensional
model tests in the laboratory environment. In analyzing the model test results, the
following problems have been addressed.
(1) Effects of seawall on the volumetric changes in the system
(2) Effects of seawall on the shoreline and hydrography
Furthermore, the inherent problems associated with model testing such as scale
effects, modeling law and so on are also examined to insure the adequacy of the
model test results.
This report consists of seven chapters. After introduction, model test proce
dure is described in chapter 2. In chapter 3, the problem inherently related to the
model test is examined carefully including modeling laws. The effects of seawall on
volumetric changes and shoreline changes are examined in chapter 4 and 5, respec
tively. In analyzing the shoreline changes, both empirical eigenfunction analysis and
a oneline concept are employed. Then, in chapter 6, based on the modeling law
established in the present study, model test results are translated into prototype.
Finally, in chapter 7, conclusions and recommendations for future studies are given.
ErodinK Shoreline
with Flanking
b) Cross Wove Effect
Seowall
Storm Profile
without Seawoll
in
'... Normal Profile
/Storm Profile
with Seawall
d) Sand Supply Cut Off (Shaded Area
indicates Sand denied to the System)
Figure 1.1: Erosion Mechanisms in the Presence of Seawall
Waves
a) Flanking
Shoreline
Seowall
A
I
g r
CHAPTER 2
MODEL TEST APPARATUS, PROCEDURE AND CONDITION
2.1 Model Test Apparatus
2.1.1 Wave Basin
The model test is carried out in the wave basin of the Coastal and Oceanographic
Engineering Department, University of Florida. The dimension of the basin is
approximately 28 m x 28 m and 1 meter deep. It is equipped with a snaketype
wave maker which consists of 88 paddles of 24 cm width each. By adjusting the
phase of each individual paddle, waves of various oblique angles can be generated.
The wave maker is capable of generating waves of wave heights ranging from 1 cm
to 12 cm and wave periods from 0.89 to 1.89 sec.
2.1.2 The Beach and Seawall Model
The beach and seawall system used in the experiments is shown in Fig.2.1 The
beach is composed of 125 tons of well sorted fine quartz sand. The total length of
the beach is about 19 m and the distance from the back shore to the toe of the
beach is 14 m. The orientation of the shoreline is 10 degree to the wave maker. The
back shore of the beach is supported by a block wall of 81 cm high.
Both sides of the beach are constrained by wooden templates cut into a design
beach profile shape. This design allows wave induced longshore current to circulate
unimpeded through the backside of the beach.
The beach profile is shaped in accordance with the concept of equilibrium beach
profile (Dean, 1977). Based upon a fall velocity of Ws = 1.7 cm/sec, which corre
sponds to the median size of the beach sand used in the model, the geometry of the
r1rF
05
Figure 2.1: Beach and Seawall System in the Experiment
STILL WATER 0 I I\
Y(m)
0.2 h(Y)= 0.089Y
0.4
Figure 2.2: Geometry of the Initial Profile in the Model Test
profile is given by
0.152y 2.50m < y < 1.22m
0.135y 1.22m < y < 0.61m (2.1)
0.130y 0.61m < y < 0.095m
0.089y2/3 0.095m < y
Figure 2.2 shows the geometry of the profile according the above equation. The
details concerning the model beach design and the physical parameters involved can
be found in Bodge (1986). Table 2.1 summarizes the physical parameters related
to model design.
The model seawall is made of sheet metal. It is installed parallel to the beach
near its center. The length of the seawall is 3.0 m and with 1.0 m return walls on
each side to prevent flanking. The height of the seawall is 45 cm which is sufficient
to prevent wave over toppings. The toe of the seawall is located at 45 cm above the
basin bottom which corresponds to the mean water level of storm conditions in the
present test configurations. Details of test conditions will be discussed later.
Table 2.1: Physical Parameters of the Model
Median Sediment Size Dso = 0.16 mm
Sorting Coefficient So = 1.27
Median Fall Velocity W, = 1.7 cm/sec
Shoreline Length 19 m
Backshore to Toe Length 14 m
Time Scale Nt w 6
Vertical Length Scale N,v 9
Horizontal Length Scale Nh = 18
Distortion (N, : Nh) 2 : 1
Design Water depth 45 cm and 35 cm
Design Submerged Profile h(x) = A x2/3
Design A Parameter A = 0.089 m1/3
2.1.3 Measurement Apparatus
There are three basic quantities to be measured: the beach profile and hydro
graphic changes, the input wave conditions and the near shore current.
The measurement of beach profile and nearshore contour was carried out by
means of an automated profile measurement system designed by the Coastal and
Oceanographic Engineering Laboratory (COEL). The assembly, as shown in Fig.
2.3, consists of four major components: the supporting platform, the wheeled truss,
the profiler carriage and the profiler.
The supporting platform is a rectangular steel frame spans the entire area to
be surveyed. The wheeled truss, as the name implies, is a steel truss structure
with guided wheels.The truss is placed on the pair of shoreparallel rails of the
supporting platform and is free to traverse from one end of the beach to the other.
The crossshore movement is facilitated by the motorized profiler carriage mounted
on the truss. The profiler, which is the heart of the system, is a pivoting arm
mounted on the carriage. At the lower end of the arm, a freely rotating PVC wheel
is attached. As the carriage moves forward, the profiling arm swings behind and
below the carriage following the beach face as the bottom wheel rolls along the
irting
Figure 2.3: General View of the Beach Profile Measurement System ( after Bodge,
1986)
Figure 2.4: Assembly of Beach Profile Measurement System
bed. This assembly is shown in Fig. 2.4. The horizontal position is determined
by the voltage change across a potentiometer on the carriage as it is at different
locations on the truss. The vertical position is determined by the voltage change
across a potentiometer owing to the change of angle of the arm. This angle is then
converted into vertical distance. All the signals were collected and stored in the
COEL computer system and also recorded on strip charts.
Waves were measured by two capacitancetype wave gauges. One is located
in the offshore region between the wavemaker and the toe of the beach and the
other one is mounted on the carriage. The offshore gauge monitors the incident
wave conditions and the carriage gauge provides the local wave conditions, usually
in the breaking zone. Near shore currents were also measured using an electric
magnetic current meter. Video and still photographs were also employed to estimate
wave direction and current patterns. Rhodamine dye was used for flow pattern
Y *
(m)I
8
6
4  
3 6 9 12 15 X(m)
current& wav wave UrEn
Figure 2.5: Locations of the Wave and Current Measurement Points
visualization.
The locations where wave and current measurements were performed are given
in Fig. 2.5 together with beach profile measurement lines.
2.2 Experimental Procedures
The experiments were carried out following the steps outlined here:
Step 1 The initial beach profile was molded in the equilibrium shape according to
Eq.2.1 for every test case. First, wooden templates cut into the initial profile
were inserted into and across the beach at a spacing of about 3.6 m. The beach
between the templates was then molded in shape by a wooden bar along the
templates. After completion of one section, the templates were removed and
reinserted into the next section and so on until the complete beach was molded
into equilibrium profile.
15
Step 2 The basin was filled to the required water depth and the wave generat
ing machine was adjusted to produce the test wave condition including wave
height, wave period and wave incident angle.
Step 3 The initial beach profiles were surveyed after the beach attended certain
degree of saturation. A total of 21 profiles were surveyed at equal spacing of
75 cm. The grid system was as shown in Fig. 2.5 with the origin at the left
lower corner, the xaxis parallel to shore and yaxis perpendicular to shore.
Step 4 The beach was then subject to the test wave conditions for a designated
duration. Each test usually began with waves of erosional nature for about 4
hrs or until the beach reached a state while the erosional process became very
slow. The wave condition was then changed to affect beach recovery. The
recovery process was much slower and usually took 12 hrs to reach a state of
Squasiequilibrium. During this test period, profile measurements were carried
out at regular intervals. In the erosional phase, surveys were conducted at 0,
1, 2, and 4 hrs whereas in the recovery phase, the intervals were 1, 2, 3, 8 and
12 hrs.
2.3 Test Condition
A total of six tests were conducted. Table 2.2 summarizes the test conditions.
In all tests, the wave height was set at 11cm and the wave period at 1.74 sec during
the erosion phase; the wave height was changed to 3.0 cm while keeping the period
the same at 1.74 sec during the recovery phase. The corresponding water depths
were 45 cm for erosional phase and 35 cm for recovery phase. One of the main
parameters was the wave incident angle which was changed from 0 degree to 5
degrees and, finally, to 10 degrees. Of the six tests, three were with seawall and
three without so that the effects of seawall can be examined in reference to cases
without seawall.
Table 2.2: Test Condition
Case wave wave water wave seawall elapsed
height period depth angle time
(cm) (sec) (cm) (o) (hour)
Casel 11.0 1.74 45.0 0 no 4.0
Casel[R] 3.0 1.74 35.0 0 no 12.0
Case2 11.0 1.74 45.0 0 yes 4.0
Case2[R] 3.0 1.74 35.0 0 yes 12.0
Case3 11.0 1.74 45.0 5 no 4.0
Case3[R] 3.0 1.74 35.0 5 no 12.0
Case4 11.0 1.74 45.0 5 yes 4.0
Case4[R] 3.0 1.74 35.0 10 yes 12.0
Case5 11.0 1.74 45.0 10 no 12.0
Case6 11.0 1.74 45.0 10 yes 5.0
Case6[R] 3.0 1.74 35.0 10 yes 12.0
CHAPTER 3
EXPERIMENTAL RESULTS AND DISCUSSION
3.1 Evaluation of Model Test
Laboratory experiments serve two basic purposes:
1. To discover and understand the fundamental underlying principle of a physical
phenomenon or process such that knowledge gained from the experiments can be
applied to prototype project.
2. To faithfully portray the prototype condition so that the laboratory results can
be extrapolated to prototype application.
To achieve the first purpose, laboratory experiments are often designed in such
a way that the pertinent factors affecting the process are isolated. Experiments
are then carried out to establish the relationship between these factors and their
corresponding effects. The physical rules derived from the experiments are then
applied to the actual engineering works. The difficulty with this approach lies in
the fact that we must identify the most pertinent factors which is not always an
easy task for a complicated system as the coastal beach. Furthermore, to study
the effect of an isolated factor gives no assurance or information on the interactions
among the factors.
The second approach does not make an explicit attempt to isolate the factors.
Rather, its attempts to duplicate the prototype process as faithfully as possible
so that the experimental results can be directly applied to the prototype. The
difficulty with this approach is the degree of success of faithfully reproducing the
natural system at a reduced scale.
18
The approach of the present experiments lies in between the above two in that
the experiment is designed to portray the prototype condition as closely as possi
ble. However, owing to the inherent difficulty that will be discussed later complete
similarity can not be achieved between the model and the prototype. We must
supplement our approach by attempting to identify the most pertinent factors in
the process and to establish their roles in the whole process. Again owing to the
complexity of the phenomenon these factors and their interactions can not always
be easily sorted out. Therefore, before the results are presented, it is instructive
to first examine here the relevance of the experiment to the prototype process it
attempts to replicate.
3.1.1 Design of Model Beach
The experiment is not intended to model a specific prototype condition. How
ever, the model beach must fulfill two basic requirements: it represents initially an
equilibrium condition and it realistically portrays a plausible prototype condition.
To fulfill these requirements, the original design by Bodge (1987) was closely fol
lowed. Bodge's laboratory experiments were designed to model a stretch of sandy
beach along Atlanticcoast near Duck North Carolina where he conducted field tests
on shortterm impoundment tests of longshore sediment transport. Hughes' (1983)
moveablebed modeling law was utilized to scale the model beach based upon typi
cal profiles measured in the field. In Hughes' modelling law, there are two criteria
that involve four scale parameters:
Tn = /2 (3.1)
52/3
A = (3.2)
Wn
19
where A, 6, Tn, and W., are the ratios of prototype to model of the horizontal
length, the vertical length, the time scale and the sediment particle fall velocity,
respectively. Bodge established W, = 1.47 and selected Tn = 6. Thus, based
upon the above criteria, he arrived at A = 9 and 6 = 18, and therefore a
2:1 horizontal/vertical distortion. The details of the model design parameters are
given in Table 2.2. The time scale was so chosen that the corresponding vertical
and horizontal length scales, when applied to the field profiles, produced a model
geometry which closely resembled an equilibrium profile for the median grain size.
Therefore, the two basic requirements stated above are fulfilled. Specifically, the
submerged portion of the beach profile follows:
h(y) = Ay2/3 (3.3)
where h(y) is the water depth at y, y is the distance from the shoreline and A is
the scale parameter.
The scale parameter "A" is shown to be a function of grain size diameter (Moore,
1982), or more appropriately, a function of fall velocity. Based upon Moore's dia
gram, A = 0.078 m for the model sand. The best fit of the field profiles obtained by
Bodge yielded a value of A = 0.13 m. This, when scaled to the model, would give
a value of A = 0.098 m. Bodge compromised the selection by choosing A to be the
average of the two values, or A = 0.089 m. He also observed that the profile was
fairly stable for all experiment waves, of which wave heights were 0.03 m to 0.1 m,
and wave periods were 0.85 to 0.19 sec. In the present model design, there appears
to be no reason to change the value A as suggested by Bodge; the value of A =
0.089 m is used. Dean (1986) replotted the value of A as a function of fall velocity
as shown in Fig.3.1. Thus, for the test range of Hb/TW from 1.93 to 7.23, the value
of "A" is no longer a constant but varies from 0.15 to 0.06. Consequently, there is
no tangible advantage to select one value over the other as long as the A value falls
in the mid range of the extremes.
,Normal Profile I Storm Profile
.v I I 1 I
0.5 
Hb= Breaking Wave
Height
T =Wave Period
Sw =Sediment Fall
Velocity
0.10
0.05
h(x)=AxK3
1.
.01
I I 11
(No Bar) I
I I I I I III
Bar Present
1 I I 1 I I 1 I.
 Recommended
Relationship
From Hughes'
Field Results
From Swart's N
Laboratory Results
I I I I iii
I I I I I i l l
FALL VELOCITY/ WAVE CHARACTERISTICS
(Hb / wT)
PARAMETER,
;ri 
Figure 3.1: Correlation of Equilibrium Beach Profile Scale Parameter, A, with
Combined Sediment Wave Parameter, Hb/TW
1
  (No Bar) II
' '""' ~L `'~~II
i
21
3.1.2 Assessment of Equilibrium Beach Profile
To assess the applicability of equilibrium beach profile at this laboratory scale,
profiles measured at the center of the test section (x = 7.5 m) without seawall were
used.
For the erosive wave condition, the fall velocity parameter assumes the value:
Hb 0.13
= 4.39 (3.4)
TW 1.74 x 0.017 = 4)
According to Fig. 3.1, the value of "A" is 0.09. Under this condition, it is found
that:
a. The over all submerged profiles at the final stage of the tests match well with
the equilibrium profile for all wave angles tested 0 5 and 100. Fig. 3.2 shows
the comparisons of the experimental results and the theoretical profile.
b. Moreover, the equilibrium profile also represents the model beach profiles
well during the transient stages. Figs.3.3 and 3.4 shows the comparisons for elapsed
time of 1 hr., 2 hrs., and 4 hrs. respectively.
For the recovery wave condition, the fall velocity parameter assumes the value
of 1.01 and the corresponding "A" value is 0.24. As can be seen in Fig.3.5 the
comparison is poor.
3.1.3 Assessment of Normal and Storm Profiles Classification
The classification of normal and storm beach profiles is a tool used by many in
vestigators to determine whether a beach is undergoing or will undergo an erosional
or accretional process. The topic has been quite extensively researched since the
first attempt by Johnson (1952). A literature review is given recently by Kriebel
et al. (1986). Four criteria purposed by four different authorsDean (1973, 1977),
Sunamura (1974), Hattori and Kawamata (1980) and Wang (1985)are tested here.
Common to all the four criteria are two parameters, the wave steepness, Ho/L,,
for the wave condition and the sediment fall velocity, W, or sediment particle size,
0C0
po
(O
o
w 0
o
C
0
O
0
1"
0
CD
en
0
M,
Equilibrium Beach Profile
 0.
m
0.I
0.0
0.i
Equilibrium Beach Profile
( RA=0.09 m'
I 1s
0 O
or
CD0
CD
CD
0
CD
C+
r
(D
0
t = 1 hour
n t
0 (q
oDM
0
EL
C,,
0
0
CD
0,
0
(C
r
el
t = 4 hour
Equilibrium Beach Profile
; 0,09 m"'' )
0.0
0./
0./
/.0 2.0 3.0 4.0 5.0 6.0
m
Equilibrium Beach Profile
t 2 hu( A = 0.09 m" )
t = 2 hour
I I I i I I I  1 I
1.0 2.0 3.0 4.0 5.0 6.0
Equilibrium Beach Profile
INITIAL PROFILE
FINAL PROFILE
EQUILIBRIUM PROFILE
EQUILIBRIUM PROFILE
X=9.0 m
(m)
X=8.25 m
(m)
X=7.50 m
(m)
X=6.75 m
X=5.25 m
(m)
X=4.50 m
h =Ay
(A=0.24)
Figure 3.5: Comparison of Equilibrium Beach Profile to the Beach Profile in the
Model Test for recovery condition (Case 1)
Iwagaki and Noda,1963 o
 Saville, 1957 A A
Rector, 1954 a
a
"0 I AUTHOR
EROSIVE
SACCRETIVE
oooo, __I fC.I1 ', U3
0.001 0.010 0.100
Ir W
Figure 3.6: Criterion of Normal and Storm Profile (after Kriebel at al., 1986)
D, for sediment characteristics. With the exception of Dean, the other three authors
all included an additional parameter of beach slope, tanf, but for different reasons.
Sunamura included tan# as the effect of initial condition. Wang and Hattori and
Kawamata, on the other hand, utilize this parameter to account for wave breaking
forms in the surf zone. Dean (as modified by Kriebel et al.) and Sunamura have
different values for laboratory and field data whereas Hattori and Wang have one
condition for all the data (Wang, however, used the same data set as Dean's).
In the present comparison, the profiles at x = 7.5 m(at the center of test beach)
are used. The results are shown in Figs.3.6 to 3.9. All the four criteria past the test
for erosional condition as the data point falls well within the zone of erosive profile.
For the accretive profile, Hattori and Kawamata's, and Sunamura's criterion passed
the test but both Dean's and Wang's failed.
Figure 3.7: Criterion of Normal and Storm Profile (after Sunamura and Horikawa,
1974)
3.1.4 Flow Regime and Mode of Sediment Transport
It was remarked by Wang (1985) that practically all the proposed beach classi
fication criteria were based upon the premise that in the surf zone the suspended
sediment transport mode dominates as signified by the presence of the fall velocity
parameter. The equilibrium beach profile is also based upon the same concept.
This, while well may be the situation under prototype condition, may or may not
be true at the laboratory scale. In fact, the results presented above seem to sug
gest otherwise. To examine the flow regime of the experiment, Jonsson's(1966) flow
regime chart is used. His diagram as shown in Fig.3.10 consists of three regimes and
three transition zones. The position is determined by two parameters; a roughness
parameter defined as
am/ko
(3.5)
ws / gT
Erosive Profile ..
 ,r1/1
A/ Pr
4 1/
,,/  Accretive Profile
.LE. Lucaion
mbhaOT. 0 o MaiLCAS (JAAN)
/ A TO IT .. A A KlluA CoaSt (JPaM)
t tACT .. KASIMa COAST (JAN)
MWCT AL. 44 AlITA COAST (JPAu)
SoOu ao KAu Iko (U.S.A)
OQuA 0a HlDuA CoAST J*A) I
CAwstVT L. TuLIM COAsT (TAIAMS)
SSUnwAmAsAU ** SurmTHA. SAc. (INOIA)I
, ,1 1 ( 1 ,
+ ACCRETIVE
102
3.8: Criterion of Normal and Storm Profile (after Hattori and Kawamata,
r' (W/T)
Ho/qTZ
Figure 3.9: Criterion of Normal and Storm Profile (after Wang, 1985)
AUTHOR
+ EROSIVE
105
1
Figure
1980)
04
10' Laminar __ _Z
Sio *
0/ *
10 Transition
Si/ Rough turbulent
10'
10 2 5 10'2 5 10' 2 5 10' 2 5 10' 2 5 10'
R. AUTHOR
SEROSIVE
SACCRETIVE;
Figure 3.10: Jonsson's Flow Regime
and a Reynolds number given by
R = am (3.6)
where ub is the amplitude of the fluid particle velocity near the bed,am is the am
plitude of the fluid particle displacement, k, is the roughness length and v is the
kinematic viscosity. Assuming k, = D N 1.5D and using linear wave theory, the
flow status at wave breaking point was decided and plotted in Fig.3.10. Therefore,
for erosional tests, the flow is in the transition zone between rough turbulent to
smooth turbulent and, for accretional tests, the flow is in the transition zone be
tween smooth turbulent to laminar. Since in all likelihood, the field flow condition
would be in rough turbulent regime, the results in the recovery tests might not have
practical value.
Now we turn our attention to the mode of sediment transport. Shibayama and
Horikawa (1980) proposed to use two parameters to classify mode of transport.
30
These parameters are relative fall velocity and the Shields parameter; they are
defined as follows:
Ub/W (3.7)
Tm = (3.8)
2sgD
where ,m, is the Shields parameter ,f, is the Jonsson's friction coefficient,
s is the sediment specific gravity in the fluid and g is the gravity acceleration.
Again, using linear wave theory, we obtain:
Xm = 0.828 for the storm condition
and
1m = 0.315 for the recovery condition.
The positions of these conditions are plotted in Fig.3.11. It is shown that for the
storm condition the mode of sediment transport is in the transition zone of bed
load and suspended load whereas for the recovery condition the mode is bed load.
This result further reinforces the observation that the recovery tests should be
viewed with caution to extract any qualitative or quantitative conclusions for field
applications. The laboratory results for the storm wave condition, on the other
hand, are more realistic and their application to prototype is possible provided
proper scaling laws can be established.
3.2 Modeling Law
Modelling law for beach evolution process has been studied by many investi
gators, notably, Noda (1972), Kamphuis (1975), Hughes (1983), Dean (1983) and
Wang (1985). Yet, a completely correct modelling law is still not available. The
fundamental difficulty is that the basic mechanism of coastal sediment transport is
not well understood. In addition, practical considerations severely limit the choice
of material that can be used in the laboratory. Consequently, the scaling of sed
iment size, specific weight and viscosity are all very limited. Finally, there lacks
0 No movement
I Bed load (BL)
2 Bed loadSuspended load intermediate iBSI) Transition 4
3 Suspended load (SL) 4
4 Sheet flow (SF) 4
0 Field data
S Honkawa et al. (1982) 3 3
.1 33 SF(Sheet flow)
S8 2 2 12 3
:a 0 12 2 ', SL(Suspended load)
2 22 .2 2
4 2 22
I 2
2 i 2
o 'BL
No movement' BL BSI
i i i i Ii i r II ___
0.02 0.04 0.06 0.08 0.1 0.2 0.4 0.6 0.81.0
Shields parameter 7,.
Figure 3.11: Classification of Sediment Transport Model (after Shibayama and
Horikawa 1980)
quality prototype data for verification purposes.
In the present study, the initial profile of the model is approximately scaled in
accordance with Bodge's field profile (1987) with the assumption that equilibrium
is attained at both laboratory and field conditions. There is, however, no field infor
mation on beach evolution to compare with the laboratory results. An alternative
approach is taken here. Since Dean's (1977) equilibrium profile is derived from an
assemblage of field data, it can be treated as a prototype template of some sort. If
the beach response is slow, the equilibrium profile should at least match with the
final profile. If the beach response is fast, the equilibrium profile should also repre
sent well the transient profiles (the entire profiles as well as the origin could move
as a function of time). Based upon this approach, a number of proposed modelling
laws are examined here.
32
3.2.1 Modelling Requirement from Dean's Equilibrium Profile
Let Pp and P, denote, respectively, the prototype and model values of a physical
quantity ,P, and let P, = Pp/Pm be the scale ratio. We further define A and 6 as
the horizontal length scale and vertical length scale of the geometry, respectively.
Then, if the equilibrium profile applies equally well to the prototype and the
model, we should have the following scale relationship for the factor "A":
An = h = 23 (3.9)
In addition, A should be a function of fall velocity, following the empirical rela
tionship as given by Fig.3.1 or,
f(HbI/TW)
An = (3.10)
fm((Hb/TW)
Therefore, we have two constraints among six physical properties two geometrical
properties ,A and 6 two flow properties,H and T, one sediment property, W, and
one scale coefficient, A. If H is the same as the geometrical vertical scale, the
actual variables reduced to five. The dynamic behavior in a gravitational flow field
is usually simulated by preserving the Froude number between prototype and model.
This scaling law yields for the time variable:
T 1/2 (3.11)
Therefore, we arrived at a system with two degrees of freedom provided the wave
period can be treated as time scale in the Froude similitude.
In the present experiments, if we select Wn = 1.47 and A = 18 to be consistent
with Bodge's values, the following scale ratios are then obtained from the above
three equations:
An = 1.29
6 = 8.88 (3.12)
T, = 6.04
33
These are very close to the actual values used by Bodge and the initial condition
in the present experiments. Therefore, the initial beach profile conforms with the
empirical modeling law as it should.
For the erosive wave conditions tested, the nondimensional fall velocity is equal
to 4.39 and the corresponding Am value is 0.09. In the previous Section, it was
shown that the equilibrium profile represents well the model beach profiles for the
final stage as well as for the intermediate stages. This implies that the underlying
mechanism of sediment transport is properly modeled under the erosive wave condi
tion. The fact that intermediate stages are also well represented by the equilibrium
profile seems to suggest that the morphological time scale is of the same order as
the wave time scale, a phenomenon which is often observed in the field under storm
wave conditions.
For the recovery wave conditions, on the other hand, the fall velocity parameter
becomes 1.01 and the corresponding value of Am should be 0.24. Neither the shape
of the equilibrium profile (controlled by the 2/3 power law) nor the scale of it
(controlled by the factor A) appears to compare well with the experiments. A value
of Am = 0.1 would be the best choice under this circumstance. Again, as observed in
the previous Section, under recovery wave condition, the flow regime is most likely
turbulent at field scale but is in a transition regime between laminar and smooth
turbulent in the laboratory. Thus, the sediment transport mechanism appears to
be not properly modeled in this case.
3.2.2 Hughes' Modeling Law
The Hughes' modeling law which the present model design is partially based
upon is examined here. The criteria as specified in Eqs.(3.1) and (3.2) are repeated
here:
T. = 1 (3.1)
63/2
A = (3.2)
W.
Equation (3.1) is essentially a statement of Froude similarity between prototype
and model. Equation (3.2) is the preservation of nondimensional fall velocity pa
rameter, used by Dean in his empirical formula to determine "A". This can be seen
by letting wave height H follow the vertical scale and wave period T follow the time
scale. Eliminating A from Eqs. (3.1) and (3.2) we have
( )P ( ) (3.13)
TW TW
This is a more restrictive condition than the Dean's empirical relation given by Eq.
(3.10) which only requires An to obey the empirical functional relationship. The
Hughes' law also has two degrees of freedom and is equivalent to Dean's empirical
relationship.
3.2.3 Wang's Modeling Law Revised
Based on the argument that the beach elevation changes must be constrained
by the sediment conservation law, Wang (1985) proposed a different set of Modeling
Law. A revised version of the Wang's law is discussed here.
The sediment conservation equation states that
+ K = 0 (3.14)
at ay
where z is the change of bottom elevation, q. is the sediment transport rate in the
direction of x, and K is the coefficient related to the porosity and is usually taken
as unity.
A set of nondimensional variables are introduced here.
t z z x
r=; z= = ; x = (3.15)
tb b qb Xb
Here the reference values are selected at breaking point signified by the subscript
b. Other reference values, of course, can be used as long as they are consistent
35
and represent the characteristics of the phenomenon. Now, substituting these non
dimensional variables into Eq. (3.14), we arrived at the nondimensional transport
equation in surf zone
9Z _= (t q (3.16)
8t h b as t
To maintain similitude between model and prototype requires
qbtb qbti
(hOb)m ) (3.17)
hbxa hbxb
or
q 1 (3.18)
hnXn
where h, and x, are the geometrical scales of 6 and A, respectively, t, is a morpho
logical time scale and q, is the sediment transport scale.
Since the mechanisms of bed load transport and suspended load transport are
quite different, Wang argued that the Modeling criteria are also different depending
upon which mode of transport dominant. Here only the suspended load dominant
case is discussed.
Wang proposed that the suspended load transport rate can be expressed by
depth averaged properties:
q, = hVC (3.19)
Here h=depth; V= mean transport velocity and C = mean sediment concentration.
Following Hattori and Kawamata's approach, it is assumed that the suspended sed
iment concentration is directly proportional to the stirring power due to turbulence,
Pt, and inversely proportional to the settling power due to gravity, Pr. The stirring
power per unit volume can be expressed as
Pt = pgu' (3.20)
where u' is the turbulent velocity The resisting power is
Pr = (Ps p)gW
(3.21)
36
with W being the settling velocity. Therefore, we have
C oc (3.22)
1'W
where
A = ( 1) (3.23)
Based on field measurement of kinetic energy and momentum flux in surf zone,
Thornton (1978) suggested that the ratio of turbulent velocity intensity and the
waveinduced velocity intensity is a function of surf zone parameter, i.e.,
= f/() (3.24)
Olu
where a' and a are the standard deviations of the turbulent and waveinduced
velocities, respectively, and e = tan/3//Ho/Lo. Thus, substituting Eq. (3.24) into
Eq. (3.22) and absorbing the proportionally constant into f(e), we arrived at
= f(w) (3.25)
7'W
For steep waves u can be assumed to be proportional to H/T the above equation
can, therefore, be expressed as
C= f(7) (3.26)
Physically, this equation states that the suspended sediment concentration in surf
zone is proportional to a function of surf zone parameter (or the breaker type),
and is inversely proportional to the specific gravity and the relative fall velocity.
Substituting Eq. (3.26) into Eq. (3.19), results in
S=hVf () (3.27)
Substituting Eq. (3.27) into Eq. (3.18) gives
V fA( )tn
n/ = 1 (3.28)
A number of assumptions are made here
37
a. The wave height is proportional to water depth, thus, can be treated as a ver
tical scale, or, H, = 6.
b. The morphological scale is the same as the wave period scale, or, t, = T,. This
is justified in that during erosional process the rate of erosion is proportional
to the number of waves propagated in the duration.
c. V oc 61/2. This is based upon the results by Wang, et. al. (1982). That the net
transport velocity is found to be
V o c2'/gh (3.29)
where x is the wave height to water depth ratio.
d. ep = ,m. It is a more restrictive but sufficient condition to guarantee fp() =
fm(C). In fact, if ~p = em, we have f,,() = 1 and this parameter can be
eliminated from Eq. (3.28). However, for ep = em requires
(tan/3/H/L)p = (tanf3/VH,/Lo)m (3.30)
Since L, = gT2 and (tan),n = 6/A, Eq. (3.30) is equivalent to
Tn= 1/ (3.31)
which is the Froude similarity between prototype and model.
Now substituting the above four condition into Eq. (3.28), we arrive at the
following modeling criterion
6 = (,Y1W,)2/3A2/3
(3.32)
If we define A, as
A, = a('YW)2/3 (3.33)
with a a proportional constant, Eq. (3.32) can be written as
6 = (A,)A,2/3 (3.34)
This equation is almost the same as Dean's equilibrium profile equation, the dif
ference being the functional dependency of the scale parameter, A. Based upon
empirical evidence, Dean and Moore suggested A to be a function of sediment par
ticle size, D, or nondimensional fall velocity, Hb/TW. Based upon sediment mass
conservation equation, the correct form of A is suggested here to be (see Eq. (3.28))
A, = (Y )2/3 (3.35)
Wang paid special attention to the scaling of settling velocity in a wave field as
the magnitude of the velocity is affected by the nature of the oscillatory flow field
(Fig.3.12). Hwang (1985) suggested that
W Vt V
W= f.( R, ) (3.36)
where
Wo is the terminal velocity in calm water,
Vf and V, are the amplitude of fluid and particle oscillations, respectively and
R is the particle Reynolds number.
Proper modeling requires
W, = (Wo)n[f,( R )] (3.37)
This is difficult to fulfill. At present, W is treated as equal to Wo. Thus,
W. = (Wo), (3.38)
It is further observed here that for small Reynolds number, WD/v < 1.0,
W oc D2
(3.39)
Fall Velocity (w)
HO'S Dotg(1964)
Reo pS
S2700 776
v 800 7.90
a 230 2.65
o 28 7.76
o 1.1 7.76
Vf /wo
W A? v D vs
= f ( ._.O__ ; o( ) IR = .Wo Vs
Wo Wo Vf
Figure 3.12: Reduction of Settling Velocity in the Oscillatory Flow (after Hwang
1985)
40
for higher Reynolds number but less than 103,
W, oc D (3.40)
and finally for high Reynolds number,
Wo oc D1/2 (3.41)
The corresponding slope of A, in these ranges are D1'ss, D0.67 and D'.33, respec
tively. They are consistent with the data compiled by Moore (Fig.3.13) in which
the slope of curve A decreases with increasing D.
For erosive wave condition, this model law is applied to the test results. For
horizontal scale A = 18 and W, = (Wo), = 1.47, the vertical scale should be
6 = (1.47)2/3 x 182/3 = 8.88 (3.42)
which is very close to the value of 9 used in model design. The corresponding
An = (W,)2/3 = 1.29. This is very close to the ratio determined from the empirical
diagram of Moore's, which gives a ratio of 1.31.
3.2.4 Noda's Modeling Law
Noda gave a set of empirical modeling law as follows:
Dn. (.)1.8 = (6)0.55 (3.43)
A = () 1.32 ()0.386 (3.44)
This set of equation has two degrees of freedom. Eliminating from the above
equations, we have
6 = D~0.17X08S (3.45)
The shape factor 0.83 is in the same magnitude as in the previous model laws. The
scale factor, on the other hand, has a quite different functional dependency on D
E
U
Lii
V)
I.0
0.10
0.01
0.01
0.1 1.0 10.0 100.0
SEDIMENT SIZE, D(mm).
r
42
given by Moore (1982). If we further let D, = 1.21, the value used in the present
experiments, Eq. (3.43) yields
6 = 1.41 (3.46)
This is a very restrictive criterion and is quite different from the value used here.
3.2.5 Summary
For the verification of the modeling laws, we have assumed that the equilibrium
beach profile can be treated as a prototype template for the model results to be
compared to. Four different modeling laws are examinedHughes, Wang's, Noda's
and an empirical law derived from Dean's equilibrium profile concept.
The experimental results show that the model tests were carried out under
different flow regime, thus, required different scaling laws for the recovery conditions
and for the erosive conditions. Of the four modeling laws, only Wang's can address
the problem of different modeling laws for different sediment transport modes. For
comparison purposes, only results from the erosive wave conditions are tested.
Noda's model is definitely inadequate. Hughes' model, Dean's equilibrium con
cept and Wang's model are consistent, although they are derived from significantly
different argument. All of them give reasonable results. Finally, Wang's model
provides a rational explanation of the scale parameter "A" as well as its functional
dependency and how it should be scaled without resorting to empirical graphs.
It also addresses bed load dominated case and transient profile modeling that, in
principle, can not be addressed by the equilibrium concept.
3.3 Comparison to 2D and 3D Model Test Results
Barnett (1987) conducted two dimensional (2D) model tests of a vertical seawall
on beach in a wave tank in the same laboratory here in the Department of Coastal
and Oceanographic Engineering, University of Florida. His results are compared
with the results of the present study which are from three dimensional (3D) con
ducted in a wave basin.
3.3.1 Beach Profile Comparison
The 2D and 3D experiments were conducted under rather close but not iden
tical conditions. To facilitate comparison, certain adjustment has to be made first.
The test conditions of 2D experiment are given in Table 3.1. By comparing with
the test conditions of the 3D model given in Table 2.2, a selected sets of data with
similar test conditionsCases 1A and 9C are used for the natural beach without
seawall and Cases 3A and 12C are used for beaches with seawall.
Table 3.1: 2D Model Test Condition (Barnett 1987)
Wave Condition
Wave Height(cm) 11.75 8.80 4.00
Wave Periods(s) 1.81 1.30 1.81
Sediment Condition
Diameter(mm) dso = 0.15
Settling Velocity(cm/s) W = 0.017
Water Depth(cm) 46.0 and 56.0
Seawall Location shoreline and 0.3m from the shoreline
Initial Profile A = 0.075m1/3
Case 1A and 3A are based upon an equilibrium beach profile with scale factor "A"
equal to 0.075. Cases 9C and 12C have the same initial profile as Case 1A but
with the water level raised by 10cm to represent storm surge condition. Therefore,
strictly speaking, the initial condition of Case 9C and 12C is not an equilibrium
profile. If it were to be treated as an equilibrium profile, the "A" value has to be
adjusted according to
Ac = AA(y/yA)(XA/C) 2/3 (3.47)
where subscripts A and C denote Case 1A or 3A and Case 9C or 12C, respectively.
If AA = 0.075, yA = 46cm, yc = 56cm and the x scales are the same then an
equivalent A is obtained as equal to 0.091. Table 3.2 summarized the condition of
these cases.
As can be seen from Table 3.2, the initial profiles of the cases to be compared
are usually not the same because of the slightly different test conditions. Therefore,
one can not be assured that the subsequent comparison of profile evolution are
meaningful. The first step is to attempt to establish the profile relationship between
2D and 3D test so that meaningful comparisons can be made. This is handled by
treating the 2D experiment as a distorted model of 3D case, or vice versa.
Based on the modeling requirement from Dean's equilibrium beach profile, we
have
Y2 = A h32/2 (3.48)
and
y 3 = A/2 (3.49)
where subscript 2 and 3 refer to 2D and 3D cases respectively.
Dividing Eq.(3.48) by Eq.(3.49) gives
2_ = (A2s /h2 )S/ (3.50)
Y3 A3 h3
This is the basic equation used for profile adjustment. All the scale adjustment were
made by using 3D case as reference. Since the vertical scale (the water depth) and
the "A" values are known, the most convenient adjustment is the horizontal scale,
or
A = Y( h2)3/2 (3.51)
Figure 3.14 compares the initial conditions of 3D and 2D cases with and with
out profile adjustment. Figure 3.15 compares profile 4 hrs after the test for cases
with and without seawall. For the cases without seawall, the agreement is very good
within the surf zone. The 2D tests generally produced bottom undulation due to
wave reflections confined in the channel. For cases with seawall, the comparison is
45
less satisfying. The most significant difference between them is the bar formation.
Prominent multiple reflection bars appeared in all the 2D tests, whereas in 3D
test, no reflection bar were formed in case 2 and 6 and only small ones appeared in
case 4.
3.3.2 Offshore Breaking Bars
There are a few studies which examine the relation between the scale of the
breaking bar such as the bar height or width and the other property such as wave
height or sediment. Keulegan (1948) found in a laboratory experiment that the
ratio of the water depth of the bar trough, ht, to the depth of the bar crest, he, has
an average value of 1.69, i.e.,
ht = 1.69he (3.52)
Sunamura (1985) mentioned that the relation given by Eq. (3.52) was supported by
Kajima's large model test, and also suggested the simple relation between ht and
the breaking wave height HB as
ht = HB (3.53)
Combining Eq. (3.52) and Eq. (3.53), we have
he = 0.59HB = 0.59ht (3.54)
It is not always easy to examine the relationship between he and ht, because
the breaking point bar is not always stable; the breaking bar formed rapidly then
disappeared, ht sometimes is also unrecognizable. Selecting the maximum bar height
in the test, the relation given by Eq. (3.53) are examined by both test results as
shown in Fig3.16. Since the breaking wave height in 2D model test is not available,
the breaking wave height were estimated by using the breaking wave index shown
in Fig.3.17.
The data are scattered but the relation given by Eq. (3.53) agreed with model
test results reasonably well. The difference between 2D and 3D, however, is not
46
COMPARISON OF BEACH PROFILE BETWEEN 20 RND 30 MODEL TEST
IOO DISTORTED ACCORDING TO THE RELATION OF A VALUE
........... 20 TEST S
20.00
60.On
"*"i ~~~~~~~  ,,,
^\ 1
No.0 .. ....
So.
tfl. OO   .__________________________" ~ : ::: > ^ ^ ___
1.00 *3.00 2.00 *I.00
0 1.00
2.00 3.00 4.00 5.00 8.00
DISTANCE FROM THE BRSE LINE I1I
7.00 8.O0 9.00
10.00
COMHPRISON OF BEACH PROFILE BETWEEN 20 AND 30 MODEL TEST
DISTlNCE FROM THE !ASE LINE I()
Figure 3.14: Comparison of Initial Beach Profiles between 2D and 3D Model Test
47
COMPARISON OF BEACH PROFILE BETWEEN 20 AND 3D MODEL TEST
DISTORTED ACCORDING TO THE RELATION OF A VALUE
........... 20 TEST 9
 20 TEST I
30 CASE I

00.0
Y.000
4.00 3.00 2.00 1.00 0.00
1.00 2.00 3.00 4.00 S.00 6.00
DISTANCE FROM THE 8RSE LINE IN)
7.00 8.00 9.00
COMPARISON OF BEACH PROFILE BETWEEN 2D AND 3D MODEL TEST
DISTORTED ACCORDING TO THE RELATION CF A VALUE
.......... 20 ES It
120.00  0 TEST 2
 0 CASE 2
20.00
0.00
SO. O
. Ol.80
4.00 3.00 2.00 1.00 0.00
1.00 2.00 3.00 4.00 S.00
DISTANCE FROM THE SASE LINE IN)
6.00 7.00
.0 .00 1.00
Figure 3.15: Comparison of Beach Profiles after 4 Hours Duration between 2D and
3D Model Test
20.00
60.00
Prototype exp.
S i Shimizu et a. (1985)
inner bar
./* athor
E*0 .
:: 1 o*o 3 D
2D
O
E 0.1. /
S v v
Smallscale exp.
S / Watanabe et al. (1980)
v Yokotsuka (1985)
0.01 ,,
0.01 0.1 1 10
Breaker height, HB, m
Figure 3.16: Relation between HB and ht adopted by Horikawa(1988)
found. The relation between he and ht is also examined in Fig. 3.18. The data are
scattered again, but the dashed line in Fig. 3.18 calculated by using least square
sense is given by
h, = 0.6ht (3.55)
This coefficient is very close to the value proposed by Keulegan. The scatter of
the data points does not permit us to establish the difference between 2D and 3D
cases.
3.3.3 Reflection Bars
The reflection bars and the offshore bars (or breaking bars) are formed by
different mechanisms. The offshore bar is formed by breaking waves while the
reflection bars result from the standing waves due to reflection. The location of
latter usually coincide with nodes and antinodes of the standing wave system.
Xie (1981) found that there are two types of reflection bar, that is, for fine
sediment the bar forms at antinode, but for coarse sediment the bar forms at the
node. Irie et al. (1984) also came to the same conclusion and they noted that the
criterion of these two formations is a function of Ursell number and the ratio of
.s .. Beach slope
1/10
1 /20 Goda
f 1/30 (1970a)
*So ',_ ^1/50 or less
1.0
S Suna mura(1983)
C1/10 5
0.5 1/20 Ostendorf and Madsen
4 05 \1/30 (1979)
C
nr "1/50 \
0
I 0.001 0.01 0.1 1.0
Relative water depth at breaking h./L,
Figure 3.17: Breaking Wave Index adopted by Horikawa (1987)
10 20
ht (cm)
Figure 3.18: Relation ht and he
he
(cm)
50
the fluid velocity at the bottom to sediment settling velocity. Both studies are two
dimensional. Irie et al. (1984) and Silvester (1987) also conducted three dimensional
tests on breakwaters and seawalls. Their results also showed similar reflection bar
pattern. Hsu and Silvester (1989) demonstrated that with angled waves bar and
trough occurrence also dependant upon the obliquity. These are determined in
fractions of the distance of island crests, formed at wave interactions, termed the
crest length. Katsui and Toue (1988) examined the bathymetric change around a
large offshore structure by 3D model test and found that well defined reflection
bars formed in front of the structures. It should be noted here that all the studies
cited above were carried out at nonbreaking waves.
In the present study, reflection bars in 2D test are prominent even within
breaking zone. In 3D tests, the reflection bar is far more difficult to maintain; it
appears and then disappears. This is probably because the energy flux reflected
from seawall tends to propagate along the wave crest (a diffraction phenomenon)
and the fact that the wave induced current is less organized to sustain stable bar
formation.
3.3.4 Scour
The scour depth and the other quantity are defined in Fig.3.19. Two scour
depths, SI and S,, are defined. SI is the depth from the elevation of the nearest bar
crest to the elevation of the scoured bed at the toe of the seawall, and Sg is the
depth from the initial bed to the bar crest. The reason for defining two scour depths
is that S1 and S, might be caused by the different mechanisms. As can be seen in
Fig.3.15, the beach is eroded from the entire region in front of seawall in Test 2A,
while the erosion occurred only in the vicinity of the seawall in Test 12C and Case
2. In other word, SI is caused by strong vortices due to interaction of wave and
structure, while S, is caused by the sediment depletion to form offshore bar. As to
the parameter s which is relevant to the scouring, (1) incident wave height,Ho, (2)
Figure 3.19: Definition of Scour Depth and Other Parameters
52
wave period, T, (3) initial water depth at the seawall, h, and (4) distance from the
seawall to the nearest bar, yfb are considered. After several attempts to examine
their relation, the clear relation between SI and h, was found in Fig.3.20. The
following observation based on physical reasoning are made:
(1) The scour depth might be directly related to the wave height.
(2) For the case that the elevation of the toe is above the still water level, if the
elevation of the toe is so high that the wave can not reach the seawall, the scouring
does not occur. Thus, some variables which define the relation of ho to the wave
run up height must be included, and the wave run up is related to the beach slope
and the wave steepness.
(3) The waves which reach the seawall must be influenced by the breaking wave
condition.
Consequently, based on the relation obtained in Fig.3.20 and the physical reasoning
above, the scour depth, S, is given as a function of Ho, Lo, h0 and the surf similarity
parameter based on the tanfb (Figure 3.21).
20.0
I
C
SI 10.0
(cm)
0.0
8.0
0.0 10.0
ho(cm)
Figure 3.20: Relation of SL and h,
L
i I i
0.0 1.0 2.0 3.0 4.0 5.0
o Tan Pb
Lo
Figure 3.21: Relation between SI/Ho to ho x tanib/Lo
Ho
0.0 L
0.5
Table 3.2: Comparison of Scale Parameter "A" in 2D and 3D Model Test
3D model test Cases 1A and 3A Cases 9C and 12C
water depth 45cm 46cm 56cm
wave height 11.75cm 11.0cm 11.0cm
wave period 1.73sec. 1.7sec 1.7sec
scale parameter 0.09m1/3 0.075m1/3 0.089m1/3
CHAPTER 4
VOLUME CHANGE ANALYSIS
The effects of seawall on beach changes are evaluated using two major indices
the effects on volumetric changes of beach material and the effects on shoreline and
contourline changes in foreshore and backshore region. The effects on volumetric
changes is addressed here first.
4.1 Definition of Volumetric Changes
The basic equation used to compute the sediment volumetric changes is the
sediment mass conservation equation given by
az aq.q aq
= ( + + ) (4.1)
9t x By
Referring to Fig.4.1, the terms in Eq. (4.1) are defines as
x=shoreparallel axis, y=shoreperpendicular axis; z=profile elevation;
The origin is set at the undisturbed still water level at the down wave boundary
of the test region 7.5 m from the center of the seawall. Three different types of
volumetric changes are computed; their definitions are shown in Fig.4.2.
(1) Rate of Volumetric Changes along a Profile, ip(x, t)
The volume change along a profile can be obtained simply by integrating Eq.
(4.1) along a profile from y = 0 to y = yo
p(x,) = o iz
= {q(yo) q (0) + xdy} (4.2)
where y, is the offshore boundary. Since q,(0) = 0, the above equation becomes
iP(x,t) = qy(yo) f dy (4.3)
Jo ax
Xo X N
Figure 4.1: Sketch of Coordinate System
The units of Vp(x, t) are volume per unit length per unit time.
(2) Cumulative Rate of Volumetric Changes Referenced to DownWave Boundary,
If Eq. (4.3) is integrated along shore from x = 0 to a = zo, we have
Vc(xo,t) = / ( qUyo)dx {q,(xo) q(x0)}dy (4.4)
0 0y
This represents the cumulative rate of volumetric changes in a control area bounded
along shore from x = 0 to x = xo
(3) Rate of Volumetric Changes in a Local Control Area Centered around the Sea
wall, 6 (t)
In this case, the integration of Eq. (4.3) is carried out from W/2 to W/2,
where W/2 is the long shore distance measured from the centerline of the seawall
location, i.e.,
= ze+W/2
i(t) zw/ i, p(x,t)dx
JfcW/2
58
z
Z
Y
VP
xo x
Vc
C(seawall)
I
r X
Figure 4.2: Definition of Three types Volumetric Changes
zX+W/2
= Q.(x2 + W/2,t) Qx( W/2,t) + 2Iqy (o)dx (4.5)
JzeW/2
where
Q, is the longshore transport rate, xz is the location of center of seawall and
W/2 and W/2 are the variable downdrift and the updrift boundary of the local
control area respectively.
4.2 Results and Discussion
Based on Eqs. (4.3), (4.4) and (4.5), p and vi are calculated. The integra
tion are carried out by the following discrete formulas
( =_ (zk z,) (4.6)
i=l
J
(po)e = E(pAp):Ax (4.7)
i=j
) = ( ( "(4.8)
where
i,j and k denote y, x and t respectively,
Ay = 0.05m, Ax = 0.75m At = 3600s, 7200s, and 14400s,
I is the integer so that IAy = 7.0m
J is the integer so that JAx = 15.5m
ji and j2 are the integer so that jlAx = x W/2 and j2Ax = xz +W/2 respectively.
The results are presented in Figs. 4.3, 4.4 and 4.5. In the case of ii and Oe, the
abscissa is the longshore distance measured from origin. In the case of i), the
abscissa is the width of the local control areas nondimensionalized with respect to
the seawall length, or W/L, where W is the width of the control area and L, is
length of the seawall. The ordinate of all three cases represents the rate of volume
change per hour. All the computations are carried out to a total of four hours
duration even though some of the experimental runs were carried out to a much
60
longer duration. Since the topographic changes were measured at 1 hour, 2 hours
and 4 hours after the test began, the computed points denoted as t=4 hours in the
graphs actually represent the average values from t=2 hours to t=4 hours.
The rate of volumetric change along individual profile is examined first. In
Fig. 4.3, the seawall is located at x = 6m to 9m, and the wave incident angle is
defined as shown. Therefore, the updrift boundary is at the right hand side for all
the cases shown. Under normally incident waves, the rate of erosion in the center
portion of the test region is almost uniform with or without the seawall. Also, in
this center region, the rate of volumetric erosion is seen to be smaller on profiles
fronting the seawall than that of natural beach. This is similar to the 2D results
by Barnett. Towards the two sides of the test region, the volumetric rate of change
along individual profile becomes erratic, perhaps owing to boundary effects.
For the cases of oblique wave of 50 and 100 incident wave angles, Erosional rate
along individual profile becomes more irregular due to the three dimensional flow
pattern in the near shore zone. For natural beach, there is a definite appearance
of rhythmic feature. For beach with seawall, the rate of changes along individual
profiles are very irregular. However, if a line is drawn across the region to represent
the averaged rate, one clearly sees trend of increasing erosion forward the downdrift
side. And, the slope of the line also appears to increase with increasing wave angle,
which means the difference of the averaged rate of erosion between the updrift and
downdrift sides becomes larger as the incident wave angle becomes larger.
In the next case, the cumulative volumetric change with reference to a fixed
downwave boundary is given in Fig.4.4. For the case of normal incident waves,
the slopes of the cumulative curves are almost uniform, an additional indication
of uniform erosional rate. For cases with oblique waves angles on natural beaches,
the cumulative curves reveal an undulation superimposed upon uniform erosion. If
mean straight lines are fitted on the curves, the effects on wave angle in rate of
. 000
. 0.000
 0.000 oo I
0.000 o10.000
1.000
 0.000
WAVE ANGLE 5 DEGREE.NATURAL BEACH
11.000 .00I II
0.000 10.000 ;
'1.000
UI0.0
HAVE ANGLE 0 DEGREE.NRTURAL BEACH
 " TOTAL
1.000 '
0.000
10.000
Longshore distance (m)
'1.000
U~ 000
HAVE ANGLE 10 DECREE. SEAWALL BACKED BEACH
I /w ve I
  / .
HOUR
HOUR
WflMn ILL.Z.2~rL....L L
I.000 0
1.000
0.000
q.o000
1 1.00 0
4.000
0.000
1 .o00oo
20.000 0.000
seawall /
HAVE ANGLE 5 DEGREE.SEAWALL BACKED BEACH
Longshoe distance (m)
HAVE ANGLE 10 DEGREENATURAL BEACH
_ TO/w ave ~
=^^^"l ITOTL
__"__ _____ * a HOUR
 I I& I HOUR
M e  HOUR
G , 2l HOUR
 IHOUR
S^^S^Sa o "'ou8
3^^t=^^^^.I
 HOUR
a I HOUR
I Ig( N
 I
0, '1 W ,S%
U
.
ooo
W I
cet
0
('0
(0
s:::
1.000
10.000
1o.000
o.ooo
0.o
.000
0.000
T
ToDOD
x
u
4.000 Ii 0.000 10.000 I
O.000 0.000 10.000
1.000
0 0
II .
0
0
0
D
q.00oo
0.000
a,0
..000
.000 0.1
0D0
distance from downwave boundary. (m)
HAVE ANGLE 0 DECREE.SEAMALL BACKED BEACH
10.000
distance from down.wave boundary (m)
HAVE ANGLE 5 DECREE.NATURAL BEACH
1 1 1 1 1 1 1 1
10.000
q.000
1.000
0.1
OTM.
4 1
 
   .
  i
000
HAVE ANGLE 5 DECREE. SEAALL BACKED BEACH
 TOTAL
"q HOUR
 2 HOUR
 I HOUR
Z 'TWrr+SbII z I
 TOTn
 q HOUR
6 i HOUR
 I HOUR
I II I I I
20.000
~J~E~E~I~
10.000 2
XIOTH OF C.R. I N )
WAVE ANGLE 0 DECREE.NATURAL BEACH
11 T. TI
1.000
r
P
o
n
1 0.000
s
q.000 '
.000 0.000
1.000
D0.000
. 1.000
20.000 0.I
 * TO TM.
     
10.000
MIDTH OF C.n. I H I
HAVE ANGLE 0 DECREE.SERHALL BACKED BEACH
00 10 20 000
10.000
NIDTH OF C.A. ( H )
10.000
WIDTH OF C.A. I H I
HAVE ANGLE 5 DECREENATURAL BEACH
 TBITM.
   I _ ___  I 8U
SHOU
000
4.000
S0.000
0.
0.000
0.000
u:
$000
_)ao
1.o000
0.
HOUR
 ... a OU
 0 HO
OTM.
HItm
HOUR
I non
20.000
 TOTAi
11 HOUR
 a ROUR
   B
i 1 1 1 1 ::J a ,
I I I I I I I
II I ill I
HAVE ANCLE 5 DECREE.SEAARLL B
KICKED BEACH
,
oo00
000
20.000
Table 4.1: On/Offshore and Longshore Transport Rate for Natural Beach
wave angle (deg.) on/offshore transport rate gradient of longshore transport rate
m3/m/s x 106
0 8.18 0.
5 8.18 0.54
10 8.18 1.68
Table 4.2: On/Offshore and Longshore Transport Rate for Seawall Backed Beach
wave angle (deg.) on/offshore transport rate gradient of longshore transport rate
m3/m/s x 106
updrift downdrift updrift downdrift
0 9.75 9.58 0.0 0.0
5 9.75 9.58 3.31 3.55
10 9.75 9.58 4.49 5.1
erosion is clearly revealed. If we further assume that under normal wave incident
wave angle, the spatially averaged transport is in the on/offshore direction only,
the longshore and on/offshore component of transport rate can be separated by the
following equation
bT(a) = 'o + 6i(a) (4.9)
where OT(a) is rate of the gradient of the transport; V, is the on/offshore compo
nent assumed here to be independent of wave angle, a, and Oz(a) is the longshore
component. Based upon this equation, the longshore and on/offshore component
for the three cases of the natural beach are given in Table 4.1. Now, for the cases
with seawall, the slope on the down drift and on the updrift are different. Com
paring with the case of 00, the slope are steeper in the downdrift side but milder in
the updrift side. By using Eq. (4.9), the on/offshore component and the longshore
component are established separately for the downdrift and the updrift sections.
These results are also given in Table 4.2. The negative longshore components in the
updrift side are the consequence of groin effects.
65
We now turn the attention to examine the extent of seawall on the rate of volu
metric change within a control region centered around the seawall. The results are
plotted in Fig.4.5 with various width of the control region. Using the same data
set, the ratio of volumetric change, with(6,) and without(6,,), is plotted against the
nondimensional control width (W/L,)(Fig.4.6). If the ratio is larger than 1.0, the
rate of erosion is larger with seawall than without seawall and vice versa. From this
Figure, a number of observations can be made.
(a) For normal incident waves, the rate of erosion in the vicinity of seawall in
cluding the fronting beach is generally smaller for the case of seawall than without.
This is particular apparent for beaches fronting the seawall (or when W/L, < 1)
(b) Under oblique wave condition, the rate of erosion is considerably faster for sea
walled beach than natural beach in the early stage of wave attack, but this trend is
reversed as time progresses. In the final stage of reaching a new equilibrium con
dition, this ratio is either less than 1 or approach 1 as the control width increases.
Thus, the effects of seawall in volumetric erosion appears to be localized.
Considering the final total volume change, the results are given in Fig.4.7. In
Fig.4.7a, the ratio of total volume change with(v,) and without (v,) seawall is plotted
for the updrift and downdrift region separately. In the updrift region, v,/v, is always
less than 1 irrespective the width of the control region and the wave angles. Thus,
in the case of normal incident wave, this value less than one because more sand is
retained by the seawall in the backshore than the additional material being eroded
in front of the seawall, when compared with the natural beach case. For cases with
oblique waves, on the other hand, sand is retained in the updrift due to groin effect;
they also makes this ratio less than unity. On the downdrift side, the situation is
different. As expected, under normal incident waves,v,/v, is less than onemuch the
same as the updrift side. Under oblique waves, v,/v,, is less than 1 when W/L, = 0.5,
66
or when the control region coincides with the seawall length. Apparently, even
under oblique wave, the material retained from the scouring trough in front of the
seawall. However, when W/L, becomes larger than 0.5, v,/v, also becomes larger
than 1. The presence of seawall now interrupt the normal longshore transport and
causes downdrift erosion to be greater than the natural beach condition. Finally, in
Fig.4.7b, the ratio of total volumetric changes including both updrift and downdrift
region are given. It can be seen that when W/L, < 1.25, v,/v, < 1.25. When
W/L, > 1, the ratio of v,/v, quickly becomes constant and approaches 1 as it
should when W/L, becomes large. Therefore, the effects of seawall appears to be
quite localized, certainly within 3 to 4 seawall length for the cases tested.
To examine the volume change in more detail, we divide the region surrounding
the seawall into 12 sections as shown in Fig.4.8. The seawall is located at the center
section C1; Sections L1, C1 and R1 are on the beach and the rest sections are in
offshore. The total volume changes after four hours duration within each sections
are then computed and the results expressed in percentages of change are presented
in Fig.4.9. From this Figure, it can be seen that for the case of zero incident wave
angle, flanking effects and toe scouring are evident. Material lost from flanking and
toe scouring are deposited offshore to form offshore bars. Since the material saved
on backshore is more than offset the increased material loss to the offshore owing
to the presence of the seawall the total volume loss in the control area is generally
less for the case with seawall than without seawall. However, as the control area
becomes large, this difference of losses becomes small. For the case of oblique waves,
the scouring hole in front of the seawall remains prominent. The decrease in updrift
erosion and increase in downdrift erosion, mainly in the beach sections (L1,R1) are
also evident.
WRYE RNCLE 10 DECREE
2.00 
....oo.....
0.00
TO OF NIOTH OF CONTROL AREA TO SEARALL LENGTH (W/Ls)
RAVE ANCLE 5 DECREE
. ...... ".......... ...
. ...........
o
 , " .... ..... F... . D 
 g :
 0.0
HRI0N OF NIOIH OF CONTROL. ARA TO SMALL LENGTH WILs)
MRVE RNCLE 0 DECREE
0.00 I 1
 .. _____ L _____ U L _____ 0.......... U
ITIO r it oS CO2.0L RE T SE H (W
ARTIM oF WIDTH OF CONTROL AE(A TO SEAW0.LL LENGTH (WILs)
  it NOU
... r A IwU
I
S.00
* Ir HOU
SIT I 0l0
Q ir I MM
s.00
Figure 4.6: Ratio of the Rate of Volumetric Changes with and without Seawall
On
*^
  a HOUR
C
.I.0o
0.,"
o
0>
^~O
0.00
. ........ .. 
..__ * r^ ....... .... . .... ....
_ i 
**" .P ^ ^ B "S * r   
(a) UpDrift and DownDrift Separately
 ..... .... E .8 
.00
RuAI OF NIOH OF CONTROL M REA TO S AArLL LENGTH(W/Ls)
(b) Total Region
  0 00tCRE
. 0 DE0Rti
60 0 DEGREE
Figure 4.7: Ratio of Volumetric Changes with and without Seawall for 4 Hours
Duration
1.00
6.00
__
OO0
0
So00
6.75
2.25 2.25 2.25
L4 C4 R4
L3 C3 R3
L2 C2 R2
LI C1 RI
unit: m
.
x
Figure 4.8: Sketch of 12 Sections Surrounding Seawall
NATURAL BEACH,
2.0 + 0.2 1.U
1 12.4 8.9 0.9
11.0 6.0 14.5
13.1 13.2 16 6
(H) CRSE 1 00O
+ 1.5 1.2 5.3
4.9 + 1.3 2.9
8.2 8.7 18.0
6.1 18.8 28.7
(C) CRSE 3 5u
2.4 + 2.0 2.0
11.3 9.5 8.1
15.3 11.9 6,4
11.0 10.8 13.0
(E) CASE lO 
SEAWALL BACKED BEACH ,
L C R
+6.5 +7.1 1.1
13.9 4.7 + 8.5
10.8 19.0 27.2
18.2 SEAHALL 27.1
(B) CSE 00o
+ 0.5 +0.6 +3.8
5.3 0.5 5.9
15.8 20.5 27.8
20.41 SEAWALL 20.4
(D CRSE 1 50
0.5 + 4.3 + 1.8
4.9 7.8 + 2.5
24.1 21.2 10.5
28.1 SEAWALL 8.5
(F) CRSE b 10o
Figure 4.9: Volumetric Changes in Sections for 4 hours Duration
CHAPTER 5
SHORELINE AND HYDROGRAPHIC CHANGES
As stated in Chapter 2, hydrographic surveys were carried out at regular time
intervals. In the erosional phase, surveys were conducted at 0, 1, 2, and 4 hours
whereas in the recovery phase, the intervals were 1, 2, 3, 8 and 12 hours. The
timeelapsed contour plots are illustrated in Fig. 5.1. The complete data sets are
presented in Appendix A. In this Chapter, the three dimensional shoreline and
hydrographic changes are examined by means of Empirical Eigenfunction (EEF)
analysis and OneLine Model (OLM) analysis.
5.1 Empirical Eigenfunction (EEF) Analysis
5.1.1 Literature Review
Since Winant et al. (1975) showed the usefulness of empirical eigenfunction
(EEF) analysis or empirical orthogonal function (EOF) analysis, many investiga
tors have utilized EEF to examine beach profile changes. In applying EEF to the
bathymetric data, the solution is usually not unique, thus several EEFs for the
bathymetric changes can be defined and examined their physical meanings.
Winant et al. (1975) applied EEF to data set obtained from two years monthly
surveys at Torrey Pine Beach, California. The analysis separates the temporal and
spatial dependance of data, i.e.
h(x,t) = em(x)c,,(t) (5.1)
where
e,(x) is the spatial eigenfunction and cm(t) is the temporal eigenfunction.
They found that only first three eigen vectors explain the original data well. They
(a) CASE 1
(b) CASE 2
(d) CASE 4
.(e) ICASE 5
01
I
o
0
0
0
ct
o
(o) CASE 3
(f) CASE 6
73
named the first, second and third spatial EEF as mean function, barberm function
and terrace function respectively. The physical meanings of these three function are
described below:
(1) mean function. Mean beach function is the arithmetic mean profile of the data.
If the beach is stable, it has a constant time dependance.
(2) barberm function. This is the seasonal eigenfunction, characterized by a strong
seasonal temporal dependance.
(3) terrace function. This function has a broad maximum near the position of the
lowtide terrace with complicated time dependance.
Aubrey (1979) applied EEF to beach profile changes. He found two pivotal
points where beach profile does not change seasonally. The pivotal points are defined
as the zero crossing points of the second spatial eigenfunction. Based on a dual
pivotal points, he calculated seasonal volume change or sediment movement at Torry
Pine Beach California as shown in Fig. 5.2
Hashimoto and Uda (1982) investigated the response of beach profiles to incident
waves at Ajigaura beach, Japan. Defining the original data set as the difference
from the mean value, they examined the relation between the eigenfunction and
wave characteristics. They found that the time derivatives of the first temporal
eigenfunction has clear relation to the wave angle given by
dC1
= 0.42 + 0.0670(t 12) (5.2)
dt
where 0 is the wave angles anddenotes the average over five weeks. For the second
temporal function, they found the following relation to wave characteristics
d Q2
dt = 1.13 0.53H ,,,,,, (5.3)
where Hmean,maz is the weekly mean value of the daily maximum significant wave
height.
WINTER (BAR) PROFILE
SUUMER BERMM) PROFILE
 . SEASONAL VOLUME EXCHANGES
62
4
____________________ " MSL 
S ..... PIVOTAL POINTS
eO
S_ 10
500 400 300 200 100
D/STANCE OFFSHORE, meters
Figure 5.2: Schematic of Seasonal Sand Volume Changes at Torry Pine Beach Cal
ifornia, based of a Dual Pivotal Points (after Aubrey 1979)
These two studies showed how to utilize EEF analysis to quantify or predict
beach profile changes.
Similar analysis to Winant et al. were carried out also by Birkemeier (1984),
Wright et al. (1984) and Kriebel et al. (1986). In Birkemeier's study, the original
data set is the same as that of Hashimoto and Uda. From the shape of the first eigen
function shown in Fig. 5.3, he concluded that the first eigenfunction describes the
changes of the profile from a single bar configuration to a double bar shape, and the
first and second eigenfunction appear to result from two unique sequence of storm
recovery activities, rather than being controlled seasonally. Moreover, although the
third eigenfunction accounted for 1/2 of the variance of the second eigenfunction,
its weightings (temporal vectors) have the most welldefined annual cycle.
Wright et al. conducted two types of eigenfunction analysis. The first type used
the same method as Winant's, and the second is called "floating datum" analysis. He
0.6
 IST 37.6 X
.. 2ND 27.2 '.
c 3\  3RD 13.3 X
3 0.4 37 SPACE PTS.
115 TIME PTS.
t
N 0.0

: 0.2
C)
z
0.4
0 100 200 300 400 500 600 700
DISTANCE, M
Figure 5.3: Spatial Eigenfunction in Birkemeier's Study
mentioned "floating datum" analysis best express profile changes and can be related
to beach profile. In the "floating datum" analysis, the variability is referenced to
the instantaneous positions of the shoreline and is independent of absolute degree
of accretion or erosion.
Kriebel et al used EEF to examine the beach recovery process at Clearwater,
Florida. They compared eigenfunctions of seawallbacked beach and natural beach,
and found the eigenfunction has no significant difference between them except in
the vicinity of seawall.
Barnett (1987) used EEF in his two dimensional laboratory experiment, and
examined EEF characteristics for the seawallbacked beach. The original data set
is defined as the difference from the initial beach profile. He found the first eigen
function describes the bar trough features and the second describes the reflection
bars.
76
The method mentioned above is basically based on the same idea as Winant et
al. As the usefulness or powerfulness of EEF analysis to beach profile changes has
been demonstrated, different versions were developed.
Uda and Hashimoto (1982) and Dick and Dalrymple (1984) calculated the two
spatial eigenfunction in the direction of crossshore and longshore at a certain
time. Uda and Hashimoto examined the beach profile changes at Misawa fishery
port where 180 m long break water is constructed. They assumed the beach profile
data is represented by
h(x, y, to) = ek(y, t)c k(, to) (5.4)
k
where
ek(y,to) is the spatial eigenfunction in the direction of crossshore.
Ck(x, to) is the spatial eigenfunction in the direction of longshore.
They found all ek and cl are independent of time, and c2 and c3 are time dependant,
and have clear correlation to the shoreline changes. They described the character
istics of the eigenfunction, as follows:
The first eigenfunction el corresponded to a mean profile. The second
eigenfunction e2 turned out to correspond to profile changes due to long
shore sand transport, because its value was positive over a broad region
of the shore, and the second time function c2 corresponding to it, which
gave longshore change of the beach profile, was correlated with shoreline
position, y,. The third eigenfunction es corresponded to profile changes
due to the influence of the breakwater, because e3 took positive values
near the shoreline and negative value in the offshore zone, and function
c3 was correlated with the offshore distance y" of the four meter depth
line from the shore. (Uda and Hashimoto, 1982, p. 1414).
Then, combining one line theory, they developed the prediction model of beach
profile changes. The results obtained from their model explained the field data
well.
Dick and Dalrymple calculated three types of EEF to examine the beach profile
changes at Berthany Beach, Delaware. The first type is the same as the Winant et
al. and called the "temporal analysis"; the second is the same as the Uda et al. and
named the "spatial analysis," and the third is very similar to the second, but the
original data sets are defined as the difference between two surveys, called "difference
spatial analysis." In their spatial analysis, the second spatial eigenfunction in the
direction of longshore was named the "rotation function" which explain the beach
rotation. They also examined the sensitivity of EEF. The seasonal movement of
beach can be determined by the "spatial analysis" from two surveys, one taken from
the summer profile and other from the winter, instead of using repeated surveys that
are necessary for the "temporal analysis."
Garrow (1984) applied EEF to examine the rhythmic feature of shore line and
contour lines in the field. First he examined the EEF calculated based on the hypo
thetical data matrices representative of ideal beach topography. He found that if the
sinusoidal pattern remained stable but varied in amplitudes, the analysis produces
a sinusoidal mean and a single sinusoidal eigen vectors 180 degree out of phase with
the mean. From the analysis of the field data, three important morphologic compo
nents are found, those are, overall accretion/erosion of the shoreline, configuration
of 800850m wavelength beach rhythmic topography, and longshore profile or phase
of rhythmic features. But they could not be easily separated.
The same type of EEF analysis sometimes produced different results. For ex
ample, the second eigenfunction obtained by Birkemeier explained the movement
of the single bar to the double bars or vise versa, while the function from Winant
et al. or Aubrey is defined as the barberm function. The spatial eigenfunction
in the direction of cross shore calculated by Uda and Hashimoto is independent
to time, while the function calculated by Dick and Dalrymple is time dependant.
The main cause of these difference might be the differences of time scale, survey
intervals (sampling time) and local geographic characteristics.
Some comments on EEF by several examiner are summarized here.
78
Birkemeier: EEF has a number of significant limitations. First, the eigen vectors do
not necessarily have any physical significance. Secondly, the analysis assumes
that every survey is equally spaced in time and that all cases are equally
weighted, an assumption that is not usually the case with field data. Finally,
when analyzing data from a single profile line, the EEF analysis does not
separate crossshore effects from long shore effects
Dick and Dalrymple: The EEF method is an efficient way to describe beach profile
changes, however, it should be emphasized that it is a descriptive process and
therefore does not reveal any information regarding the governing process.
Garrow: This mathematical technique has two main goals. One goal is to deter
mine a new set of variables which are independent each others. The second
goal is to define the fewest new variables possible that can completely describe
the original data.
EEF analysis, of course, is not used only in beach profile but other natural
phenomena such as wave spectrum parametric study (Vincent and Resio, 1977)
edge wave analysis (Kato 1984). In meteorology and geology, EEF analysis has
often been conducted to quantify stochastic data (Kutzbach 1967).
5.1.2 Basic Concept on Empirical Eigenfunction Analysis
The usefulness of EEF analysis is to reduce the number of data from original
data sets. In the present study, the data are the hydrographic survey, and since the
measurement is carried out four times at 21 x 140 points, the number of variables
would exceed 4 x 21 x 140 = 11760. If Uda and Hashimoto's representation (Eq.
5.4) is possible and the first three EEF can represent most of the original data, the
number of data needed would reduce to 4 x (3 x (21 +140)) = 1932. The EEF that
will be presented here, reduces the number of necessary data to 384. Furthermore,
In EEF analysis, since the two eigenfunction is assumed to be independent to each
79
other, the new set of variables can be examined independently. Hereinafter, the
basic concepts of EEF is described.
Suppose, for example, we have some survey data at M points, and N times
surveys are carried out. Thus, the number of data is MxN, this would compose M
by N matrix, say, F. F can be represented as
f1l f12 fiN
f21 f2N
F = (5.5)
fM1 fM2 fMN
In the analysis of bathymetric changes, the variables fnm would be the water
depth at a point of space and time. Defining a vector f, as
f2i
f = i (5.6)
then we have
F =[fif2... fN] (5.7)
One wants to determine which vector e has the highest resemblance to all the obser
vation vectors f, simultaneously, where resemblance is measured with the squared
and normalized inner product between a vector f and e. This is the equivalent to
maximizing
etRe (5.8)
subject to the condition
e'e = 1 (5.9)
where R is an M x M symmetric matrix whose element, rij is given by
N
rai = N1 E finfi, (5.10)
n=1
or
R = N(FFt) (5.11)
This problem yields to eigen value problem, i. e.
Re = eA (5.12)
In fact, one obtains not just one eigenvector, but series el, i = 1, 2....M associated
with M eigen values of R. It can be shown that e, are orthogonal and that A, are
real and positive. Thus, writing eq. (5.12) for all eigen vectors
RE = EL (5.13)
where E is an M by M orthogonal matrix whose column are eigen vectors, ei,....eiM.
Note that
EE = I (5.14)
and L is an M by M diagonal matrix whose ith diagonal element A, is the eigenvalue
associated with ei. Combining eqs. (5.11) and (5.12)
N1FFtE = EL
FFtE = ELN
EtFFtE = EtELN
= LN (5.15)
Defining
C = EtF (5.16)
where C is M by N matrix
it follows that
F = EC (5.17)
From eq. (5.17), it is clear that the observation vector f,, representing the nth
observation of the M variables, can be expressed as a linear combination of the M
81
eigenvectors. The cith element of C will be referred to as the coefficient associated
with the ith eigenvector for the nth observation. From Eq. (5.16), it can be shown
that ci, play the same role in Eq. (5.17) as the coefficients in, for example, a Fourier
series representation. The N observations refer to N different time and, therefore,
the elements in the ith row of C represent time variations of the coefficient associated
with the ith eigenvector. Different representations are possible, the basic concept is
the same as presented.
5.1.3 Formulation and Procedure of EEF for Contour Lines
In essence, EEF analysis is similar to harmonic analysis with the exception
that the functional form is not determined a priori but is part of the solution.
For a multivariate function such as the three dimensional contour line represented
by h(x, y, t) there are several possible combinations of eigenfunction representation
such as
h(x,y,t) = wmc,(t)em(x)f,(y) (5.18)
h(x,y,t) = WmCm(t)em(X, y) (5.19)
h(x, y, t) = E WmCm(, to)em(Yto) (5.20)
These combinations are, however, not independent of each other. The hope is to
have the right choice such that most the variance in the data set will be accounted
for in fewest terms. Unfortunately, at present, there is no criterion for making such
a choice and one has to rely on intuition and trial and error. After a number of pre
liminary tests, it is decided to use the distance from a baseline to particular contours
as the dependent variable. Thus, we assume that this distance can be represented
by the linear sum of spatial eigenfunctions, S,(x), and temporal eigenfunctions,
Tt(t), of the following form
o00
d"(x,t) = E tvS,(x)T (t) (5.21)
n=l
where w' is the weighting function, m is the mode and n denotes nth contour line.
But, if we apply EEF analysis based of Eq. (5.21), the influence of the initial profile
dominates the other modes. Since in the laboratory the initial profile is the same, it
is logical to eliminate this effect in the EEF analysis and to use the following form
D"(x,t) = dn(x,t) d(x, to) (5.22)
00
= E wnS(x)T (t) (5.23)
m=l
or, in the discrete form neglecting superscripts m for brevity
Dij = E wmSmTmi (5.24)
m=l
where i and j denote x and t respectively.
In applying the procedure outlined here to the present experiment data set, a num
ber of problems are identified that require special attention:
(1) Owing to the existence of offshore shoals and bars, the dm(y, t) has, at times,
multivalues as illustrated in Fig. 5.4. Care must be exercised to select the depth
contour that is physically meaningful. (2) In EEF analysis, the contour lines are
assumed to be continuous. But, in the case of seawall, the contour lines near it are
clearly not continuous. In such case, the contour lines are divided into segmented
continuous lines and EEF analysis is performed to each line individually. (3) In
the recovery process, the final profile in the stormy wave condition is taken as the
initial profile and is eliminated in the EEF analysis.
5.1.4 Results and Discussion
EEf analysis is performed for eight contour lines for each test case, they are
0.5, 0.0, 5.0, 7.5, 10.0, 12.5, 15.0, and 20.0 cm respectively. They are measured
with respect to the still water level in the erosional wave condition. Thus, 0.0
corresponds to shoreline in the erosional cases and 10.0 corresponds to shoreline in
the recovery cases. The results are presented in Figs. A.1 to A.9 in the appendix.
In these results, with the exception of Case 5, all the case have both erosional and
dn
...... ... Y
Figure 5.4: Definition of d"
recovery phases. The recovery processes are identified with a "R" following the
caption. Case 5 has erosional phase only. Also, duration of test is 12 hours in Case
5, 5 hours in Case 6 and 4 hours for the rest. In the spatial eigenfunctions, the
ordinate represents the eigenvectors multiplied by the associated weighting value.
It should be noted here that if the spatial and temporal eigenfunction are of same
sign the contour line progresses whereas if they are of opposite sign the contour line
regresses.
Figures 5.5 to 5.10 compare the real shoreline changes and shapes of eigenfunc
tions for each tested. In the figures, the top graph gives the real shoreline changes
at different elapsed times as measured, the middle graph provides the net change of
measured profile at different time from the initial profile. The bottom graph plots
the first two spatial eigenvectors.
Table 5.1 summarized the contribution of each eigenvector (mode) to the total
84
variance. Based upon these results, a number of qualitative observations are made.
Shoreline Changes
Shoreline change is the primary signature of beach erosion and accretion. For
all the cases tested, the first eigenvector appears to account for more than 90%
of the variance. Therefore, there is no surprising that the real shoreline change is
similar to the first spatial eigenvector. For cases of erosional waves with normal
incident angle, ideally the shoreline would recede uniformly as there should be no
longshore component of sediment transport. By examining Fig. 5.5 for the case of
no seawall, the first spatial eigenvector is almost a parallel line with the exception
near the edges where the three dimensional effect comes into play. For the case with
seawall (Fig. 5.6), the first spatial eigenvector is also almost a parallel line. The
flanking effects, if any, is not visible. The temporal vectors are almost identical for
both cases.
Under oblique waves, for the case of no seawall, the first spatial eigenvector
exhibits a rhythmic feature in addition to a uniform recession (Fig 5.7). The first
temporal vector appears to be similar to the case of normal incident waves. With
the presence of seawall, the rhythmic feature on the updrift sides becomes more pro
nounced. Again, the temporal vectors possess similar characteristics as the previous
cases. Now, as the wave angle increases (to 10 degrees), this rhythmic features di
minishes in amplitude. The groin effect becomes more evident that results in severe
down drift erosion immediately in the shadow of the seawall.
It is not clear at this moment whether this rhythmic feature is both induced and
controlled by the basin characteristics alone or it is induced by the basin charac
teristics but eventually controlled by the nearshore topography. Since the rhythmic
feature is an often observed phenomenon, particularly immediately after storm at
tack, there is a strong possibility that it is controlled by the nearshore topography.
Table 5.1: Contribution of Each EEF
case modes Water depth of Contour Lines(cm)
5 0 5 7.5 10 12.5 15 20
Erosive Condition [D]:downdrift [U]:updrift
case 1 1 st 92.1 94.5 93.1 79.7 72.7 64.7 80.5 85.4
2 nd 5.9 4.7 5.6 18.7 18.7 23.2 17.7 10.9
case 2 1 st 95.4 96.3 90.4 89.2 88.2 87.5 83.1 70.9
[D] 2 nd 3.4 3.6 9.4 6.2 8.3 8.0 10.8 18.5
case 2 1 st 94.2 98.0 96.3 ** ** ** ** **
[U] 2 nd 4.3 1.4 2.1 ** ** *
case 3 1 st 95.8 97.8 95.8 83.7 86.5 85.7 86.3 76.9
2 nd 3.4 1.7 3.1 13.0 11.2 11.8 8.5 17.6
case 4 1 st 98.3 99.3 95.6 86.7 88.9 88.2 91.2 84.0
[D] 2 nd 1.5 0.5 3.5 10.5 7.1 8.3 5.8 11.8
case 4 1 st 97.3 98.4 96.7 ** ** ** ** **
[U] 2 nd 1.9 1.3 2.7 ** ** ** ** *
case 5 1 st 97.1 98.7 92.8 94.8 95.0 97.3 98.4 92.6
2 nd 7.0 9.0 7.1 5.2 5.0 2.7 1.6 7.4
case 6 1 st 98.6 99.7 96.3 92.8 92.0 93.7 91.2 92.8
[D] 2 nd 0.9 0.2 3.0 5.1 5.9 3.7 5.6 4.3
case 6 1 st 91.5 97.1 90.3 ** ** ** ** **
[U] 2 nd 3.9 2.3 6.2 ** **
Recovery Condition
case 1[R] 1 st ** ** ** 85.7 90.3 91.6 85.8 84.9
2 nd ** ** ** 9.9 7.3 6.2 7.2 9.1
case 2[R] 1 st ** ** ** 83.5 86.1 86.6 90.4 79.7
2 nd ** ** 11.9 10.3 10.5 7.3 9.7
case 3[R] 1 st ** ** ** 92.0 94.5 83.6 84.5 91.4
2 nd ** ** 6.1 4.4 12.8 10.1 5.7
case 4[R] 1 st ** ** ** 92.1 91.7 90.0 84.5 94.5
2 nd ** ** 5.7 6.2 8.4 8.4 4.8
case 6[R] 1 st ** ** ** 82.0 81.3 78.2 85.8 88.0
2 nd 11.1 12.4 18.3 9.1 7.0
8.25
DISTANCE ( Y ) H
^o
Ip
ai2
0
i.,
c0
0
':
em
S0.00
2.00
8.25
DISTANCE ( Y ) M
S0.00
DIFFERENCE FROM INITIAL PROFILE
....... ...... i HOUR
 2 HOUR
IS I HOUR
. A.. ...... .. .........
0.75S
15.7S
EAL00 REnL SHORELINE CHANGE
^ i 
0.00
^ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~  '"~ Ts '**7
0.7S 8.2s 15.75
DISTANCE IY ) N
o
CD .00 DIFFERENCE FROH INITIAL PROFILE. ......... Nun
*.......A ...... 1 HOUR
S.... 2 HOUR
 I HOUR
0
"... .. ... ... ... ... .. . ........ ............. ..
.......... .... ..
'. O. u". t***
C+
0 .9 U e.e .
0 2.001
0.5S .25 15.75
DISTANCE ( Y)
o
10 SPRC1IL EIGEN FUNCTION
w
0 0 x ....... ... ... ....... .......
0 1." 1 =:::&=
C .25 25.75
W DISTANCE C 3 N
0
REAL SHORELINE CHANGE
8.2S
DISTANCE ( Y ) H
DIFFERENCE FROM INITIAL PROFILE
8.2S
DISTANCE (I ) N
5P~C IRE &ZLEN.~&INCT1ON
n 3 ****~*** ~ A
. 8.25
8.25
DISTANCE ( Y ) H
WTI
O2 
'Cl'
1,00
0.00
E .1)1
2 nn.
S75
*0.
2.00
z 0.00
........ ...... .. HOUR
2 HOUI
E HOUR
.., ... .. . . U'... '
.1. f('
1.00
3 0.00
1S. 7
 ...T. .. i i7
"""n *~r
15.75
. .
0.75
