HYDRODYNAMICS AND SEDIMENT TRANSPORT
IN THE VICINITY OF SUBMERGED BREAKWATERS
Michael Jonathan Bootcheck
HYDRODYNAMICS AND SEDIMENT TRANSPORT
IN THE VICINITY OF SUBMERGED BREAKWATERS
MICHAEL JONATHAN BOOTCHECK
A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF ENGINEERING
UNIVERSITY OF FLORIDA
I want to express my sincere thanks to Dr. Robert G. Dean, my committee
chairman, for his support and guidance. Not only has Professor Dean led me in my
endeavors at the University of Florida, but has provided guidance and lessons that will aid
me for the rest of my career. Considerable thanks go to Dr. Robert J. Thieke, not only for
serving on my committee, but for expanding my interest in the considerable expanse that
is Fluid Dynamics. Thanks also go to Dr. Hsiang Wang for serving on my thesis
Thanks also go to Viktor Adams, George Chappell, Sidney Schofield, and Sonya
Brooks for their assistance in planning and executing the 30 + "field trips" to West Palm
Beach, Perdido Key, Miami, etc... although sometimes they seemed more like work than
leisure. The encounters of sharks, barracuda, stingrays, jellyfish and triggerfish will
always be some of my fondest memories of my stay in the coastal department.
Grateful thanks also go to the staff of Coastal Engineering, Becky Hudson, Sandra
Bivins, and Lucy Hamm. The numerous consultations between Becky and myself
probably had to do as much with life in general as they did with coastal, but I think that
they taught me some valuable lessons about people and the politics associated with them.
Finally, I would like to thank my parents for instilling in me the drive to do well
in school even when it is difficult to see the light at the end of the tunnel. Without their
assistance, I do not think I would have made it out of Purdue in the first place.
This thesis is dedicated to my family; it never could have come to fruition without their
help and support. I will always treasure the 25 years that I was able to spend with Bernard and
Frances Bootcheck. I would like to express my sincere appreciation for the time I have been able
to spend with Harold and Leona Moats, and look forward to many more. Last, but certainly not
least, I would like to dedicate this thesis to my mother, Marilynne, for her countless words of
encouragement and strive to the goal. Brian, Timothy and Ronald deserve much thanks for
bringing outside angles and insights to the forefront.
TABLE OF CONTENTS
ACKNOWLEDGMENTS ............................................... iii
LIST OF FIGURES ............................................... ...... vi
LIST OF SYMBOLS .................................................. viii
ABSTRACT ......................................................... xii
1 INTRODUCTION ......................................... .... .. 1
1.1 Objectives and Rationale ................ ....................... 1
1.2 Report Organization ............................................ 2
2 EROSION CONTROL ALTERNATIVES ................................ 3
2.1 Overview ................................................... 3
2.2 Construction Alternatives ................ ...................... 4
2.2.1 Traditional Solutions ............... .................. 6
220.127.116.11 Beach nourishment .............................. 6
18.104.22.168 Attached structures ............................... 8
22.214.171.124 Detached emergent breakwater .................... 10
2.2.2 Innovative Approaches ................................. 11
126.96.36.199 Beach dewatering .............................. 12
188.8.131.52 Artificial seaweed ............................. 16
184.108.40.206 Submerged breakwaters .........................21
3 OBJECTIVES OF SUBMERGED BREAKWATERS ........................ 23
3.1 Reduction of Wave Height ..................................... 23
3.2 Increase of the Sediment Retention Time.in the Vicinity ............... 24
3.3 Trapping Sediments Up/Downdrift............................... 25
4 EFFECTS OF SUBMERGED BREAKWATERS ..........................27
4.1 Hydraulics/Hydrodynamics ..................................... 27
4.2 Sediment Transport ........................................... 31
5 LITERATURE REVIEW .............................................. 34
5.1 W ave Transmission/Reflection Studies ............................. 35
5.2 Sediment Transport and Current Velocity Studies .................... 49
6 METHODOLOGY: FORMULATION ...................................51
6.1 Hydrodynamics and Hydraulics ................................ 51
6.1.1 Analytical Model ................ .................... 52
6.1.2 Numerical Model ................... ................ 55
6.2 Sediment Transport ............................................ 59
6.2.1 Suspended Load ....................................... 60
6.2.2 Bed Load ............................................ 61
7 RESULTS AND COMPARISONS ....................................... 63
7.1 Hydrodynamic Results of Submerged Breakwaters ................... 63
7.1.1 Studies of W ave Attenuation ............................. 63
7.1.2 Studies of Ponding Elevation ............................. 67
7.2 Studies of Sediment Transport ................ .................. 69
8 SUMMARY, CONCLUSIONS AND RECOMMENDATIONS ................ 74
8.1 Summary and Conclusions ...................................... 74
8.2 Recommendations ........................................... 75
REFERENCES ................................. ....................... 76
APPENDIX ............................... ............................ 83
BIOGRAPHICAL SKETCH .............................................. 95
LIST OF FIGURES
4.1 Sketch of Elevation and Plan View of Nearshore Zone with Submerged Segmented
Breakwater or Natural Bar ............................................ 29
4.2 Scour Locations, Cross-Sectional View ................................. 30
4.3 Definition Sketch for Cross-Shore and Longshore Sediment Transport .......... 32
5.1 Graph of Transmission and Reflection Coefficients (Goda, 1969) .............. 39
5.2 Plot of Experimental Data Set for Goda's Energy Equation ................... 40
5.3 Ponding Level as a Function of R/Ho, Diskin, et al. (1970) ................... 42
5.4 Ponding Level as a Function of Incoming Deep Water Wave Height ............ 43
5.5 Plot of Transmission Coefficients for Tanaka Study (1976) ................... 47
5.6 Plot of Values for Averin and Sidorchuk .................................48
6.1 Definition Sketch Including Coordinate Frame ............................. 51
6.2 Plot of Normalized Values for Analytical Model ........................... 55
6.3 Definition Sketch of Various Flow Possibilities ............................ 58
7.1 Comparison of Goda (1967) Laboratory Data and Model Results .............. 64
7.2 Comparison of Conserved Energy Measurements by Goda with Predictions by
Numerical Model ..................... ........................... 65
7.3 Comparison of Model and Averin and Sidorchuk (1967) ..................... 66
7.4 Comparison Between Numerical Model and Tanaka (1976) ................... 67
7.5 Comparison of Model Values with Diskin, et al. (1970) ...................... 68
7.6 Plot of Longshore Average Profile Changes for July 1992 to June 1995 for Palm
Beach, Fl, PEP Reef Installation ........................................ 70
7.7 Diagram of Zones in Vicinity of Breakwater ............................... 71
7.8 Numerical Model Sediment Erosion Volume Estimates for P.E.P. Reef ......... 71
7.9 Numerical Model Estimation of Ponding Elevation for P.E.P. Reef ............. 72
7.10 Normalized Plot of Sediment Transport and Ponding Elevations for P.E.P. Reef
Simulations ...................................................... 73
LIST OF SYMBOLS
a, Goda's coefficient for eta values due to cos (ot)
Ac Seelig's cross-sectional flow area
Ace Seelig's cross-sectional flow area between the
breakwater & shoreline at the end of the system
B Seelig's breakwater gap width
bo2 Goda coefficient for nonlinear terms
b22 Goda coefficient for nonlinear terms
By elevation of bottom of vent
C Wave Celerity
Cd Seelig's discharge coefficient
C1,2.3,4 coefficients, Ahrens (1987)
dso median stone size diameter
DEP height of breakwater vent
e base of natural logarithms
E wave energy per unit surface area ( -pgH2)
f Darcy-Weisbach friction coefficient (0.16)
-7 wave energy flux
g acceleration due to gravity
h total water depth
he critical depth over weir
h, Depth of water at structure including ponding effects
(Numerical Model Variable)
H Wave height
Ho Deep water wave height
HIR,T wave height (incident, reflected, transmitted)
Hmo deepwater significant wave height
Hmax maximum wave height (Goda)
Hmin minimum wave height (occurs at the nodes at x=1/4,31/4)
IMAX number of units in breakwater
k wave number, 2xt/L
Lo deep water wave length
N Number of breakwaters
P.E.P. Prefabricated Erosion Prevention
Qsand volume of sediment moved
Q,,, volume of suspended load sediment transport
Qbed volume of bedload sediment transport
Qx water transport rate alongshore
qy water transport rate cross-shore
qyc water transport rate cross-shore over crest
qyv water transport rate cross-shore through vents
R freeboard(distance from water surface to top of breakwater)
Re Reynold's number
RUp vertical height of runup on the structure if the breakwater
were high enough that no overtopping occurred
T wave period
Tv elevation of top of vent
W Diskin's height of breakwater
WBZ width of the breaking zone
X breakwater length
XLV percentage of length of breakwater vented
YMio ratio of waveheight to depth
ZC Diskin's distance from top of breakwater to ponding
a Goda's empirical parametric approximations
P Goda's empirical parametric approximations
At incremental time unit
Ax length of individual units
AY distance from shoreline to breakwater
li free surface elevation of incoming wave
illmax maximum level of free surface seaward of reef
1llmin minimum level of free surface seaward of reef
Tl2max maximum level of free surface landward of reef
rl2min minimum level of free surface landward of reef
Tr surface elevation
Tr ponding elevation
KT transmission coefficient
KR reflection coefficient
v kinematic viscosity
p density (0.35)
o wave angular frequency, phase angle (=2x/T)
Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Engineering
HYDRODYNAMICS AND SEDIMENT TRANSPORT
IN THE VICINITY OF SUBMERGED BREAKWATERS
Michael Jonathan Bootcheck
Chairperson: Dr. Robert G. Dean
Major Department: Coastal & Oceanographic Engineering
As coastal erosion currently affects many of the world's shorelines, there is great
demand for stabilization methods. One area of continued interest is the use of submerged
breakwaters to attenuate incoming waves in order to reduce the sediment transport in its
A submerged breakwater is a structure placed below the surface of the water,
which will still have an impact on the approaching waves. When waves interact with a
submerged breakwater, wave energy is dissipated, reflected back offshore, and
transmitted toward the beach. These actions lead to the three central characteristics of
submerged breakwaters: 1) wave height reduction which leads to reduced sediment
transport (sediment transport potential is proportional to an exponent of the square of the
incoming wave height); 2) wave height diffraction which results in transport behind and
deposition near the breakwater end; and 3) ponding between the breakwater and the
shoreline, resulting from the waves passing over the structure. This ponding induces a
longshore flow behind the breakwater and therefore, sediment transport.
To assess the effect of a submerged breakwater, an analytical and a numerical
model were created to simulate both field and laboratory experiments. The purpose of
these models was to verify and quantify the wave attenuation characteristics, as well as
the ponding associated with submerged breakwaters.
The analytical model was based on simple linear wave theory and linearized flow
equations which relate the incoming wave characteristics to ponding elevation, as well as
the cross-shore and longshore transport attributed to the breakwater. The numerical
model uses standard hydraulic weir equations and simple linear wave theory to model
breakwater configurations and physical conditions to those of available field and
laboratory conditions. An additional feature of the numerical model was the addition of
vents in the breakwater.
The numerical models wave attenuation results are compared with published data
from several sources and authors. There is reasonable correlation with all three studies,
except for the crest elevations upper limit imposed by linear theory. The model estimates
for ponding are also compared with a laboratory study.
Given the nature of the models presented, the results clearly indicate that ponding
impacts for submerged breakwaters can be significant, and in some cases may outweigh
the benefits due to wave height reduction. Therefore, careful planning and analysis
should be exercised in the design of submerged breakwaters as coastal erosion
Recent trends in the coastal areas of the world have created a desire for long-term
solutions to beach erosion. In many cases, unfortunately, the solutions have proven to be
either ineffective or costly to maintain.
1.1 Objectives and Rationale
The purpose of this thesis is to present two models for wave transmission over a
submerged breakwater and to compare model results with data from other researchers.
For clarification, submerged breakwaters will be defined as rubble-mound (permeable) or
solid (impermeable) structures whose crest is at or below the Mean Water Level (MWL)
and are usually placed parallel to shore. These structures are used to provide partial
protection against incident wave attack, primarily for large storm waves.
The two models presented here will be compared and contrasted to other models
associated with the performance of submerged breakwaters. The results will also be
compared with field data from an installation at Palm Beach, Florida, conducted by the
University of Florida Coastal and Oceanographic Engineering Laboratory. The data that
will be compared include wave height measurements, current measurements, and
sediment transport quantities. Comparisons will also be made with several researcher's
estimates of ponding elevation and the free-surface elevation of the water above MWL,
located landward of the breakwater (discussed in depth in Chapter 4).
1.2 Report Organization
This report is arranged in the following manner. An overview of coastal erosion
countermeasures follows this chapter and will detail such solutions as beach nourishment,
groins, beach dewatering and artificial seaweed. Chapter 3 discusses the objectives
associated with submerged breakwaters and Chapter 4 follows with some of the
interactions that they can have on the environment in the vicinity of the structure. A
literature review of relevant works will be presented in Chapter 5 chronicling some of the
major contributions by authors such as Goda, Takeda, and Moriya(1967), Diskin, Vajda,
and Amir(1970), Seelig and Walton(1980) and Dalrymple(1978). These demonstrate
some of the attempts to estimate wave height transmission and reflection, as well as
current velocity estimates and ponding elevations. Chapter 6 presents the development of
an analytical model that describes the hydrodynamic interaction of a submerged
breakwater with the incident waves and the resulting ponding and currents. It also
describes a numerical model that was developed to estimate current velocities and
sediment transport volumes, as well as wave height transmission and reflection estimates.
Chapter 7 presents results and comparisons with other studies of transmission and
reflection coefficients, as well as sediment transport quantities obtained from a field study
conducted in Palm Beach, Florida. Chapter 8 contains the summary and conclusions.
EROSION CONTROL ALTERNATIVES
Most coastlines at least occasionally experience erosional tendencies that could
lead to the destruction of life and property. The costs associated with protecting the areas
behind the shoreline must be compared with the associated benefits. Some of the
purposes for coastal development include protection of multi-million dollar
condominiums and public infrastructure, recreational/tourist beach areas (often supplying
tremendous income to the local economy), shoaling of harbors, and navigational
channels. Another popular reason for preserving, or armoring, the coastlines is to protect
existing roads and highways, including evacuation routes. In some cases, the costs of a
beach protection system are small compared to the value of an existing highway or other
structures. Other times, it may be more cost effective to let nature act and to relocate the
thoroughfare, for example. Several approaches have been utilized in the ongoing battle
with mother nature, including permeable/impermeable breakwaters, seawalls, beach
nourishments, etc. Many innovative methods have either been tried or suggested for
future efforts, including artificial seaweed, beach dewatering, as well as numerous
methods of "wave energy absorbers." The following sections describe some of the more
widely accepted methods of shoreline protection, as well as presenting some of the more
2.2 Construction Alternatives
When building in a coastal setting, physical parameters can be limiting when
choosing a construction method. The local wave climate, including wave heights and
directions, as well as frequency of occurrence and period, weigh heavily in evaluating the
local impacts. Some structures, such as submerged or emergent breakwaters and jetties,
have a significant impact on the hydrodynamics of the nearshore area, while others, such
as beach nourishment projects, primarily augment the sediment budget with a minimal
effect on hydraulics. A second factor that can affect the selection of design alternatives is
the visual appeal of the countermeasure. For example, a submerged breakwater or beach
nourishment will be less intrusive to the natural beauty of the surroundings, compared to
an emergent quarry-stone or concrete structure. However, there could be detrimental
impacts associated with these choices; for example, a submerged structure will allow
higher transmitted waves than an emergent structure, and, therefore, potential for
increased shoreline erosion. Some cost/benefit analyses of the desired effects of the
structure must be established before any design can take place. Some of the criteria
include: the financial resources available for the project, the time frame desired before a
future project should begin (how long do you want it to last, ie., if beach nourishment is
the selected construction technique, how long before re-nourishment), what impacts will
the various methods have on local boat traffic, as well as human traffic (high current
velocities must be avoided to prevent formation of rip currents). An assessment of the
sediment impacts of the available structures as well as the hydraulic/hydrodynamic effects
will help in deciding which method to choose. A table presented by Sawaragi(1995)
describes the functions of various coastal structures.
Table 2.1 Hydraulic function of various coastal structures (Sawaragi, 1995)
Structures Hydraulic Function Function to Control Results
Groins Spur Dike for Direct Trapping of Saw-tooth Shape
Longshore Current Longshore Current Shoreline
Offshore Detached Reduction and Control Control of Longshore Concave-Convex
Breakwaters of Wave Height and and Cross-Shore Shoreline, Obstacle
Direction by Sediment Transport to Natural Coastal
Headland Control of Wave Re-distribution of
Height and Direction Incident Wave
by Diffraction and Energy Evenly
Artificial Beach Reduction of Wave Control of Longshore
Energy by Breaking and Cross-Shore
and Energy Loss in Sediment Transport
Sea Dike Control of Landward Prevention of Local Scouring, Loss
Limit of Wave Shoreline to Retreat, of Foreshore Due to
Penetration Control of Longshore Return Flow or
Sediment Transport Reflected Waves
As any device placed in the nearshore system will interact with the longshore
current and sediment systems, the following discussions will present some of the effects
of the different options available.
2.2.1 Traditional Solutions
Some of the more traditional structures placed in the nearshore zone, each with
different characteristics and traits, are breakwaters, groins and beach nourishment. Since
each coastal method will be accompanied by particular time and spatial scales, it is
important to the success of a project, that it be coupled with appropriate understanding
and planning. The following sections will discuss the merits and drawbacks of the more
common traditional beach erosion technologies.
220.127.116.11 Beach nourishment
This method involves the placement of sand on the existing beach, or in the
location desired, with the understanding that it is only a temporary solution. There are
two main types of beach nourishment to be considered: dynamic and static (Sawaragi p.
295). A dynamic nourishment project is one that is designed such that the sand is placed
upstream from an erosional area so that the sand placed will be carried by natural currents
to supply the area desired. Such projects are sometimes referred to as "feeder beaches."
A static nourishment is one in which the sand is placed directly in the erosional location.
These somewhat unique countermeasures can be quite effective in providing a beach,
although much time and effort must be put into its design as would any other coastal
engineering project. Dean (1995) and Bruun (1989), among others have established
simple methods in order to provide competent design with little background in coastal
engineering. Some important variables must be studied in order to effectively design
such a nourishment.
When considering beach nourishment as a possible solution to an eroding beach,
it is important to obtain accurate estimates for relevant environmental factors, ie.
incoming wave heights and directions, variability of wave heights and storm frequencies.
Other parameters vital to the success of a nourishment are: 1) determining the sediment
sizes on the native beach, 2) determining the proximity to hard structures or relevant
geologic influences (hard bottom, submarine canyons, presence of submerged obstacles,
etc.), and 3) estimating the impacts on the surrounding areas. Also, since beach
nourishment success rates are dependent on such a large variety of independent variables,
it will probably be best if a background search is done to identify previous attempts for
similar conditions (ie., if a project is to be conducted on Lake Michigan, it would be
relevant to study other nourishment projects in comparable conditions such as Wood
(1984), whereas a nourishment in Florida could be compared to numerous projects
completed in virtually every area of the state, as described by Dean (1994)). Insight
gained from previous projects will far outweigh the minimal effort spent in locating such
articles and could provide additional insight into some of the intricacies of design. An
additional characteristic of beach nourishments is that since they are "temporary"
solutions, there can be no guarantees as to project longevity. The process of sea level rise
is an example of environmental forcing that can be predicted, but only the future will
reveal the extent, therefore, if additional rise occurs it will provide an increased adverse
impact and reduce the project longevity. Changing wave conditions and frequencies can
also influence the longevity (although all effort should be put into finding the conditions
that can be expected and then aligning a risk analysis procedure for a margin of safety).
It is also important to note that the lifespan of a beach nourishment can often be
significantly extended when used in conjunction with one of the other techniques, such as
stabilization structures. Results of two studies, Imperial Beach, California (Curren and
Chatham (1977)), and West Palm Beach, Florida, will be discussed in Chapter 7-Results
18.104.22.168 Attached structures
The choices involved in shore-perpendicular structures include jetties and groins.
The jetties associated with navigational channels are at one extreme in the attached
breakwater spectrum, while groins are at the other. Jetties are structures extending into
the water to direct and confine tidal or river flow into a channel and to prevent, or
minimize, the shoaling of the channel by littoral material. A jetty or breakwater can be
effective in dissipating much of the incident wave energy, and is therefore useful in
protecting harbors and marinas from high storm waves. One side effect that a jetty can
have is the reduction or interference with the longshore transport so that areas downdrift
will encounter increased erosion rates. Therefore, this option would not be suitable in
areas where this effect is to be avoided (in areas where there are long stretches of beach
front and no rivers to supply new sand, or areas with large littoral transport rates. This
impact can be offset through the use of sand bypassing plants (which can pump sand from
the updrift side to the downdrift) so that the littoral transport may be continued. This
benefit can be two-fold: (1) nourishment of the downdrift beach and (2) reduction of the
shoaling of the entrance channel (U.S. Army Corps of Engineers (1984)).
A groin is a structure constructed in the coastal area, connected to and usually
perpendicular to the shore and extending into the littoral zone, designed to accumulate or
retain sand by limiting the longshore transport. Groins are usually placed in areas where
a retreat of the coastline has been noted, indicating a longshore gradient of the total
longshore sediment transport. The gradient may be due to a structure interfering with the
sediment transport, or a net loss of sand due to natural physical conditions. By
constructing a series of groins, arrayed in a "field," the longshore gradient of the total
longshore transport may be reduced. However, the groin field does not "produce sand," it
only delays its journey in the longshore transport system. Multiple groins may be
arranged in order to increase the longevity of a beach nourishment project, via a decrease
in the local transport rates, while leaving the overall sediment balance unaffected. The
groin field will initially act as a "sand trap" (it will retain sediments). Eventually,
however, the holding capacity of the groin field will be met, and then the longshore
sediment transport system will approach its original characteristics. The action of the
groin field initially capturing sediments will adversely impact areas downstream of the
groin field, therefore, it is advised that construction of a groin field be coupled with a
beach nourishment project to minimize these effects, (Silvester(1990)). There are two
potential sedimentary impacts of groins, (a) trapping of sand -accretional, or (b) loss of
sand -erosional. Of course the nourishment should be designed such that the volume is
at least equal to the holding capacity of the groin field, in most cases a minimum volume
of remaining sediment is allotted and when this volume is reached, a re-nourishment is
constructed to "reset" the system to the same circumstances as the post construction. This
system of nourishment/groin construction can help to lessen the impact to the downdrift
Another option in groin construction is the use of T-type or L-type groins, so
named to reflect the shape of the groin. This design alternative is not intended to affect
the longshore transport as much as to control the sediment transport in the cross-shore
direction, which is not impacted by shore-normal groins. The longshore transport rates
will be affected by the design variables associated with the groins, such as length of
structure, height, depth, distance between groins, as well as the physical conditions, such
as incoming wave direction, wave climate, and perhaps most directly the net and gross
longshore transport rates.
Groins with crest elevations designed to provide a template to the beach profile
allow both fluid and sedimentary longshore flow over the crest, and result in less of a
disturbance to the beach because they do not force an abrupt end to longshore transport,
(although the impact may still be significant). However, groins provide little protection
from high energy storm waves. Future research involving coupling of submerged
breakwaters and groins could lead to dramatic improvements, as noted for the previously
mentioned experiments related to Imperial Beach, California, and West Palm Beach,
22.214.171.124 Detached emergent breakwater
These structures may be used to protect navigation channels, or other coastal
areas. As they may be considered unsightly, they would not be a first choice for
construction in front of a natural recreational beach. Also, it is usually not necessary to
prevent all wave energy from reaching the shore, as this could have detrimental effects on
the longshore transport in the vicinity. This interruption could adversely impact
downstream beaches and therefore must be accounted for. Chapters 6, 7, and 8, of the
U.S. Army Corps. of Engineers Shore Protection Manual (1984), present a set of design
criteria for these structures and should be consulted when designing such structures.
Some of the drawbacks to detached emergent structures are that: (1) they present a
strong effect on longshore currents, allowing for the formation of tombolos and
decreasing the sediment supply downstream, (2) there is no cross-shore transport (without
overtopping) and therefore water may stagnate in it's lee, and, perhaps most importantly,
(3) they are costly to construct.
2.2.2 Innovative Approaches
Some coastal erosion settings require solutions that must not affect the shoreline
in the manners previously discussed. Frequently, a new methodology will be developed
that will decrease the wave or current forcing in a particular area, while still allowing
longshore transport to remain continuous. Some of the more popular approaches that
have been gaining acclaim are beach dewatering, use of artificial seaweed, and
submerged breakwaters. All three of these countermeasures have shown promise in
reducing the amount of erosion at the shoreline for a given set of wave conditions. The
impact of beach dewatering is mostly in the foreshore zone in that its impact is to
decrease the water table to increase the stability of the shoreline. The uses of artificial
seaweed and submerged breakwaters have also been popular research topics and their
impacts are discussed in the following sections.
126.96.36.199 Beach dewatering
A beach dewatering system involves pumping water from within the beach in
order to provide sufficient forcing (lowering the water table under the beach) to result in
increasing the volume of sediment above the mean lower water level. This method has
been employed in several countries with varying degrees of success. The first known
field installation took place in Denmark in 1981 (Lenz (1994)), although it's impact had
not been expected. (The drainage system had been installed as a means to supply water
for a beach front aquarium.) Several questions must be considered for coastal
countermeasure: is protection from storm surge desired, what will be the downstream
impact, how high and extensive can maintenance run and will effectiveness significantly
decrease with time, and are certain options more economically favorable than others (ie
is one much cheaper and therefore attractive) (beach nourishment, submerged
breakwaters, groins, etc...)? Some of the attractions of beach dewatering are that: (1) it is
invisible, that is, the piping and pumps (if necessary) are below ground and therefore
aesthetically pleasing (the water removed may be routed to an existing storm water
system, offshore, or to a filtration system); (2) it should not have any significant negative
impacts on upstream/downstream beaches; and (3) laboratory studies have shown
promise in profile recovery time after storms, although only field installations can
demonstrate whether or not they can significantly impact the shoreline position. Some of
the questions regarding beach dewatering are as follows: (1) can the initial and
maintenance costs be controlled ( it has been estimated by Bruun (1989) that initial
construction costs can reach, and exceed, $250 / foot of shoreline), (2) what is the
efficiency of the pumping mechanism (both mechanically and due to corrosion/clogging),
(3) what is the accessibility to piping (it can be hard to maintain something that is buried
in the sand if fouling occurs, and (4) what are the possible impacts on animals that nest on
the beach (does the increased percolation affect the reproductive success of sea turtles?).
Several hypothesis have been proposed to explain the effect of beach dewatering
on a beach profile, for example: 1) increasing the sediment deposition rates on the shore
face by lowering the water table, creating a larger volume of uprush than downrush, 2)
creating an increase in the sediment fall velocity due to the net addition of a vertical
component in the velocity field, and 3) increasing the effective sand size through an
increase in the local pressure gradient (Dean and Dalrymple(1994)). Any of the
mechanisms may prove to be the theory that holds for all cases; however, it is more likely
that a combination of the proposed theories will explain the phenomenon most
adequately. Laboratory and construction projects have clearly shown that dewatering soil
can lead to a dramatic increase in stability, and therefore an equilibrium associated with
an increased angle of repose. The author has witnessed construction projects in sand that
demonstrated the value of dewatering in order to prevent slumping of the soil, therefore
allowing construction projects to be completed. It is, therefore, logical to assume that if a
watertable can be lowered near the beachface, that a higher angle of repose will result.
This has been shown in laboratory studies. For example, a set of experiments was
conducted at the Stevens Institute of Technology. The conclusion was that "In general, it
can be stated that a beach stabilized with a Stabeach erosion control system will undergo
significantly less transformation over time." (Lenz, 1994, p. 36). As of this writing the
author is unaware of field verification that firmly establishes the impacts and extent that
beach drains have even for simple installations (ie. plane and parallel bathymetry along
straight shorelines). Due to the variability in the coastal zone, it can be difficult to
separate effects due to natural fluctuations and those due to nearshore construction
modifications (Bruun 1989). Several field studies have been constructed in the U.S. and
two of these will be discussed in the following paragraphs.
Sailfish Point, Stuart, Florida, was the location of a beach dewatering system,
installed in the spring of 1988. The project location is situated at the southern end of
Hutchinson Island on the East Coast of Florida, about one mile north of the Saint Lucie
Inlet and immediately south of Martin County's Bathtub Reef Park. Even though there is
a natural reef -400 feet seaward of the beach, which dissipates some of the incoming
wave energy, the beach had been experiencing an average yearly erosion rate of
approximately 15 feet over a 10 year period, although several of the encompassed years
actually resulted in accretion (Lenz 1994). It was determined by Coastal Stabilization,
Inc. and the developer of Sailfish Point, Inc., that the conditions would be appropriate for
construction of a beach dewatering system (Lenz 1994). A dewatering system 600 feet
long was installed and through the subsequent 10 months, accretion was noted on the
shoreline. However, the same region had experienced accretion immediately before the
project. This is accepted and undisputed; however, it does not follow that accretion
occurred only because of the installation of the dewatering. This presents something of a
quandary: if the results are known, how do we determine the impact that the construction
actually had? One approach is a study of the beach profiles in the project location, as
well as several lines used as "controls" and located considerably up and downstream of
the project area. In this case, it appeared that accretion had occurred in locations other
than the area influenced by the dewatering, (Lenz 1994), therefore it is clear that not all
accretion can be credited to the system. The most direct way to assess the impact of the
dewatering is to evaluate the implications of the new gradient. The effect will be limited
by several characteristics, related to the designed piping/pumping systems along with the
sediment characteristics (the soil porosity will limit the flow rates), and the locations of
sources of fluid pollution (ie. are there aquifers or other sources of water in the area that
could inadvertently be pumped). The following list could help in assessing the value of a
beach dewatering system.
1. Conduct porosity tests, and collect sediment samples in the area of interest,
including boring and pumping tests
Is the soil suitable for draining? (A granular soil will be much better suited that of
clay or clayey soil mixtures)
2. How much money is to be invested in the pumping and piping mechanisms?
Clearly a larger pump should pull more waterthrough the soil and, therefore,
result in more accretion than a smaller pump. But, as the beach widens the impact of the
dewatering will be diminished, it is therefore suggested that the pumping and piping be
sized to result in the largest beach width desired.
3. Is this option really cheaper, in the long-term, than other countermeasures?
In addition to Sailfish Point, a second installation was installed at Englewood
Public Beach, Florida, in the Fall of 1993, although quantitative data has not been
published and the installation has been removed. Several other projects were planned
including four installations totaling 5800 lineal feet on Nantucket Island, Massachusetts,
with others in North Carolina (1,000 feet and in the proposal stage), Fort Pierce, Florida
(permitting has been approved and waiting on funding), as well as Longboat Key, Florida
(in the investigation phase) (Lenz 1994).
Until the results of field installations have been analyzed, and a significant
number studied, it will continue to be difficult, or impossible, to estimate the impacts of
this type of countermeasure.
188.8.131.52 Artificial seaweed
According to Rogers (1987), the earliest known field installations of artificial
seaweed for erosion control took place in Denmark in 1963 on the North Sea. This
solution involves the placement of polypropylene "plants" or other energy absorbing
elements attached to the sea floor with an objective of dissipating some of the energy of
incoming waves, and a desired result of lengthening the lifespan of the beach.
Specifically, the plastic plants are theorized to reduce the sediment transport by
"absorbing part of the turbulent shear stress with the fronds (Rogers p. 21). A reduced
bedload would then follow from the reduced shear stress transferred to the bottom
sediments. A similar reduction would be expected for the suspended sediment transport
due to a reduction in vertical mixing within the boundary layer established by the
seaweed, Rogers (1987).
One installation was conducted with the New Jersey Department of Conservation
and Economic Development off the Atlantic Shoreline near Ocean City, NJ. The project
consisted of dense bundles of artificial seaweed placed in 15 feet of water, and
approximately 800 feet from the shoreline. The project was 900 feet long in the
alongshore dimension, 90 feet wide and constructed in rows oriented parallel to the
shoreline. A rope was used to attach the "fronds," a collection of the polypropylene
strips, to the sea floor. Each frond was attached to a rope grid, with each individual being
anchored with weights and concrete anchors. The original design called for 3,000 feet of
the shoreline to be monitored to note any shoreline changes. It was reported by Wicker
(1966), that the anchoring system failed just months after installation and therefore its
effectiveness can not be determined. It is not known whether the anchorage was cut by
commercial fishing gear or was lost due to natural causes.
A second U.S. installation took place along Wallops Island, VA. The length of
the fronds, as well as the depth of water, were approximately the same as the Ocean City
project. One major difference was that at this installation the anchoring was done with
steel frames, although it was still destroyed. For this project, however, the means of
destruction is known to have been northeast storms that impacted the area. The project
came to an end after only a few months. After these two failed attempts, there were no
more field projects in U.S. waters for the next decade, although research continued in
The main emphasis for the European interest in artificial seaweed centered around
two erosional conditions: excessive tidal scour in secondary inlet channels and localized
scour around man-made offshore structures (Angus 1982), which is significantly different
than the two early U.S. tests that were geared toward reducing shoreline erosion. Since
these early experiments, studies have been conducted in the Netherlands, Denmark,
England, Norway, etc. However, each countries studies were often intended to affect
only specific conditions. For example, in the Netherlands, research on artificial seaweeds
concentrated on the use of seaweed as a "low-cost alternative to rock mattress" to control
tidal scour in secondary channels of tidal inlets (Bakkerl972). A major development in
the construction of polypropylene came about in 1964 by Shell Plastics Laboratory,
Nicolon and the Dutch Ministry of Transport and Waterways. A method was developed
in which the plastic could be injected with air to significantly increase the buoyancy of
the seaweed. It allowed the specific gravity to be lowered from 0.9 to 0.2. The added air
allows the fronds to remain buoyant with a larger amount of fouling than previously
available. Fouling takes place when marine organisms and debris attach to the
Two problems can be associated with the documentation of artificial seaweed
projects. The first problem in analyzing the efficiency and effectiveness of artificial
seaweed as a means of erosion control is the lack of significant numbers of field profiles
over long periods. Most of the field studies involve little, or no beach profiles, Rogers
(1987). It is very difficult to assess the impact of an erosion control measure if no control
is available. A second problem associated with these projects is a lack of data
quantifying wave attenuation and wave-induced currents for field projects, whereas these
quantities can be readily measured in laboratory tests. As wave height reduction is
supposed to be a major benefit ofartificial seaweed, it is important to establish a database
of field measurements in order to better design future projects.
There have, however, been a few field projects that have been well monitored,
including relatively detailed survey information. One such case occurred at the Cape
Hatteras Lighthouse in North Carolina. The shoreline erosion had previously been
documented as averaging 20 to 24 feet per year since 1823 (Rogers 1987). In order to
protect a U.S. Navy facility, a set of three groins was constructed in 1969 to stabilize the
shoreline. The project was successful in anchoring the shoreline position at the facility,
however, significant erosional increases were encountered downstream. This is due, at
least in part, to the net longshore transport rate of 1.5 million cubic yards per year (U.S.
Army Corps of Engineers 1984b). In the ensuing decades, numerous repairs were made
to the groins, and several beach nourishment projects took place to counteract the
erosional trends. In May of 1981, a manufacturer of artificial seaweed, Seascape, donated
and placed 500 units of the polypropylene fronds. These were placed in five parallel
rows, each 350 feet in length, and placed in 4 to 7 feet of water with fronds four feet in
length. It is noted by Terchunian (1981) that a profile taken August 1981 showed that an
offshore bar had moved shoreward and deposited up to 6 feet of sand in the area of the
artificial seaweed. This was accompanied by accretion at the beach as well, the mean
high water line had migrated 190 feet seaward of the preconstruction position. As it
appeared that the project was responsible for the dramatic changes in the coastal
configuration, a larger installation was designed. In November of 1984, five rows of
plants were placed 10 feet apart (length measured perpendicular to the shoreline), and
placed in 6 to 10 feet of water and extending for 5,000 feet. The initial distance from the
shoreline to the seaweed was roughly 500 feet. In is also important to note that this
project was constructed south of the most southerly groin, and that the net transport is to
the south. The project was also done in conjunction with a beach nourishment project.
After placement, the shoreline position was measured to be 245 feet seaward of its initial
position. The logical question to ask is "why did the shoreline position change?" Was it,
as the manufacturer claims, a result of the artificial seaweed placement, or was it due to
natural cyclic accretion patterns and the nourishment project. The manufacturer based his
claims on pre-construction and post-construction photographs showing the seaward
A group of scientists, including S. Rogers, studied the area and found that, upon
reviewing long-term shoreline position, through the use of aerial photographs, although
the average annual shoreline change may be 20 feet erosionall), there were wide ranging
results that could yield a large erosional trend, of many years, only to be followed by large
accretional trends. On the basis of this information, they concluded that it was possible
that this was due to natural shoreline fluctuations, although still not ruling out the
possible influences of the seaweed. As evidence, the researchers noted that the area north
of the groin (just north of the project), also encountered substantial accretion, and this
area could not have been influenced by the seaweed.
In addition to the pre/post comparisons, the National Park Service requested that
the area be monitored by the U.S. Army Corps of Engineers to determine the
effectiveness of the seaweed. It is important to note that these surveys did not begin until
the project had been installed and therefore no pre-construction survey was conducted.
The Army concluded that "the deposition behind the seaweed was part of a general
accretion" and "could not, in any way, be attributed to the seaweed" (Rogers p. 24).
There have been several other artificial seaweed projects in the U.S., but none
have been clearly and conclusively shown to be an effective means of stabilizing a
shoreline. In addition to the anchoring problems associated with this method, several
other problems require consideration when constructing an artificial seaweed bed: what
will the environmental impact be to the flora and fauna, will the introduction of
submerged "structures" be a hazard to beach users, and will the beach likely evolve in the
It is the author's opinion that there is insufficient data that conclusively
demonstrates the effectiveness of artificial seaweed as a means to control coastal erosion.
This could be due in part to a lack of field data, but I think that the reviewed projects
more likely demonstrate an ineffectiveness in this type of countermeasure. However, I do
feel that it could be effective as a countermeasure to scour in the vicinity of other
structures, via the effect of lowering the velocity near the bed.
184.108.40.206 Submerged breakwaters
This has been an area of continuing interest to the coastal engineering community
for decades, however, only recently has the database of field surveys, wave heights,
current speeds, and bathymetry become large enough to cover a wide range of conditions
in order to test numerical and analytical models, although the addition of future surveys
and field experiments will only help to yield a more reliable base to begin competent
design of structures in the coastal environment. As it is visually appealing, while still
able to decrease the incoming wave energy, it can be a very attractive countermeasure to
beach erosion. However, there are several adverse impacts that must be considered in the
design: how to deal with the ponding of water, impacts on the currents in the vicinity,
scour, etc. The remainder of this thesis will be dedicated to the impacts and design
considerations associated with submerged breakwaters.
OBJECTIVES OF SUBMERGED BREAKWATERS
3.1 Reduction of Wave Height
A primary design objective of a submerged breakwater is to provide protection
from damage due to waves, while at the same time leaving the aesthetics of the areas
undisturbed. If serenity of surroundings is of no concern, an emergent structure, at a
significantly increased cost due to magnitude, will usually provide a greater degree of
protection for given wave characteristics and parameters.
Incoming wave energy is split into three components at a submerged breakwater:
a reflected wave, a transmitted wave and dissipated energy. The efficiency of a
submerged breakwater is measured by its ability to dissipate energy and reduce the size of
the transmitted wave. The wave height attenuation will be primarily dependent on the
freeboard and the incoming wave height (Goda 1969, Browder 1994, Seelig 1980), with
an apparent limit of 35 percent for submerged breakwaters, Browder (1994).
Wave attenuation will also vary with the porosity and wave length. Numerous
authors have published results describing wave transmission through a variety of rubble-
mound configurations, Shore Protection Manual (1984), and broad crested structures are
also well documented, Diskin (1970). However, little research has been collected on
wave attenuation for thin-walled vertical breakwaters. Some of the more prevalent
studies of transmitted wave heights have been conducted by: Goda, Seelig, Dean, etc.,
each will be discussed in detail in Chapter 5 (Literature Review).
3.2 Increase of the Sediment Retention Time in the Vicinity of Submerged Breakwaters
Due to the wave attenuation characteristic of submerged breakwaters, less energy
will be available, as transmitted waves, to move sediment in the breakwater lee.
Therefore, an increase in the amount of time that it takes for sediment to move in its
vicinity should result from a submerged breakwater. A second characteristic of
breakwaters that increases the retention time is the diffraction of waves around the ends
of the breakwater. Diffracted waves will act to transport sediment toward the breakwater
centerline, and therefore, impede sediment transport from behind the breakwater.
An additional factor that may contribute to an increase in the retention time is the
use of accessory structures, as demonstrated in studies conducted at the Hydraulics
Laboratory of the U.S. Army Engineer Waterways Experiment Station. The change in the
sediment transport characteristics for multiple structure configurations has been studied,
at least qualitatively, by Markle (1977) and Curren (1977), who discussed some
interactions of submerged breakwaters and groins.
Due to the conservation of mass, an increase in the retention time will be greatest
during the initial profile equilibration, from the "pre-structure" to the "post-construction"
conditions. The construction of groins, as discussed in Chapter 2, will induce a gradient
in the sediment transport rate, and this could lead to a decrease in the sediment erosion
rate, at least locally and initially. This is due to the fact that sediment transport volume
change is proportional to the gradient of sediment transport, and not the magnitude.
However, once equilibrium is reached, a conservation of mass will ultimately be
reached. In this respect, an increase in retention time, while still very useful, must be
termed a "temporary" impact, although it could be a cyclic occurrence due to the nature of
longshore currents and influences of updrift areas (ie. sand waves passing down the beach
or future construction). The use of groins is well documented in the literature for their
ability to anchor beaches and to keep them from eroding, and coupling this with a
structure that can reduce the height of incoming waves, as submerged breakwaters do,
may provide dramatic benefits for shoreline protection. Only future studies will
determine whether these benefits outweigh the detrimental aspects of submerged
breakwaters, such as ponding and it's impact on sediment transport, as will be discussed
in the following chapters.
3.3 Trapping Sediments Up/Downdrift
The trapping ability of submerged breakwaters can be related to the increased
sediment retention time, as discussed above. A submerged breakwater study discussed by
Dean and Chen (1996), presents information on the trapping characteristics of a
The submerged breakwater installation at Palm Beach, Florida, (Dean and Chen
1996), was studied in order to assess the impact it had on sediment transport, as well as
the existing conditions in the vicinity. Initially, the project experienced a large movement
of sand from behind the breakwater to the downstream area. The movement of this large
quantity did not continue immediately downstream, as might be expected. The bulk of
the sediment seemed to stay at the southern extreme of the breakwater, as if trapped by
the breakwater. This impact may be attributed to the diffraction of waves at the ends of
the breakwater, and possibly to a gradient in the sediment transport rate initiated by a
strong seaward flow at the ends, similar to a rip current located at the end of a sandbar,
causing a gradient in a natural setting (Dalrymple 1978).
As this impact of a submerged breakwater will depend on many local variables, ie.
sediment size, pre-construction beach profiles, wave attenuation characteristics, etc., at
this time it is impossible to predict, with any degree of certainty, the trapping
characteristics of submerged breakwaters.
EFFECTS OF SUBMERGED BREAKWATERS
The most obvious method to evaluate the effects of submerged breakwaters is to
compare a beach with a submerged breakwater to a beach without. In a beach without a
breakwater the oncoming waves will transport water towards the shore, and from there it
will move in two directions. Some of the mass transport, transport by waves = ,
will return to the offshore zone directly, while the other will travel along the shoreline in
a narrow zone. When this flow turns offshore, it may create a rip current as pictured in
The percentage of water that moves in either direction will depend primarily on
two factors, the incoming wave energy (E=-pgH2), and the bottom bathymetry. For
normally incident waves and beaches in which the offshore bathymetry is "uniformly
planar with straight and parallel bottom contours (having no longshore variability)," most
of the mass transport will be in the onshore-offshore direction, with little being
transported along the shoreline (Dalrymple, 1978, p. 1415). On beaches with sand bars
however, much like a submerged breakwater, a higher percentage of the water may be
transported along the shoreline before it's return trip offshore, Dalrymple (1978). In this
case, the obstruction created in the water column by the sand bar has changed the
hydraulic balance of the "bar-less" beach.
Many models and theories exist to explain the generation of rip currents, for both
structurally induced, and for the plane parallel beach (wave interaction induced). Some of
the studies pertaining to the wave interaction models include: Bowen (1969), Bowen and
Inman (1969), Sasaki (1975), and Dalrymple (1975). Bowen (1969) and Noda (1974)
discuss the generation of rip currents due to bottom topography, and Dalrymple, Dean, and
Ster (1975) discuss the impact of barred shorelines on wave-induced currents. A model
from Liu and Mei (1976) pertains to the current generation from structural interaction, which
would be most applicable to a study of rip current generation in the vicinity of a submerged
breakwater. A brief discussion of current generation, and the associated velocities, will be
discussed in Chapter 7.
A second effect of the structure will be a set-up of water, ponding, inside of the
breakwater, in order to create the necessary head (volume of water necessary to drive a
flow), to reach equilibrium with the incoming transport.
The head will be a function of the incoming wave height, presence of other
currents, freeboard, etc. For submerged breakwaters and sand bars, however, the height
of ponding will be substantially larger due to the partial obstruction of the water column.
When studying submerged breakwaters, the height of ponding becomes an important
consideration because it can lead to substantial sediment erosion and may cause rip
currents, Figure 4.1. A detailed discussion of structure induced ponding will be presented
in Chapter 5.
Coast Bar/ < Hi
os / /
SX \- _-
Figure 4.1 Sketch of Elevation and Plan View of Nearshore
Zone with Submerged Segmented Breakwater or Natural Bar
Ponding has not been well documented in the past in terms of field verification,
but several theories and estimates have been proposed as to the magnitude of this
phenomenon. Discussions of ponding may be found in Longuet-Higgins (1967), Diskin
et al. (1970), Gourlay (1971), Dalrymple and Dean (1971), Dalrymple (1978), among
A third impact of a submerged breakwater is the scour that may be induced
through the modification of the bottom shear stress. Scouring occurs in regions where the
flow velocities create a shear force on sediment particles that is sufficient to result in
movement of sediment. In the case of submerged breakwaters, a high velocity along the
structure/sediment line can result in particle motion at the base of the structure, and thus
undermine the breakwater. The local scour that results may affect the structural integrity,
and this can be vitally important in the placement and design of submerged breakwaters,
as they are heavily dependent on the freeboard for wave attenuation.
The structure induced scour can occur in three locations: seaward, shoreward, and
at the ends of the breakwater. The seaward side of the breakwater will be directly
impacted by the actions of the breaking waves (1), as indicated in Figure 4.2, cross-shore
LWave Induced Scour Locations
Figure 4.2 Scour Locations, Cross-Sectional View
currents (2), and any longshore-offshore currents (3).
The resulting flow-field becomes very complex, even for the simplest of
structures. Analytical results are not available for most cases, therefore empirical
equations are utilized for cases of even the basic cylindrical pile arrangement. Due to the
intricacies of a submerged breakwater, possibly further complicated by the presence of
vents, an analytic solution relating structure height, water depth (thereby yielding the
freeboard), vent size (if applicable), current patterns, wave field, as well as sediment
characteristics is not in sight. Even an empirical relationship would require numerous
controlled laboratory and field experiments to derive, and would still only be applicable
for specific parameters and flow fields. Therefore, the alternatives must be followed at
this time, namely to rely on basic local scour equations for simple shapes (ie. Cylindrical
piles), and modified to model that of a simple breakwater (Sheppard 1990). It is
important to note that this methodology is only intended to give gross estimates of local
scour. Although scour is very important for the longevity of a submerged breakwater, for
the purposes of this thesis, it is assumed that a breakwater elevation is constant.
4.2 Sediment Transport
When building in a coastal setting, the sediment transport, both cross-shore and
longshore will be impacted by a submerged breakwater. This section will discuss briefly
the impact of a submerged breakwater on the resulting transport rate. The cross-shore
transport shall be delimited as the flow normal to the shoreline (and breakwater), for
definitional purposes, whereas the longshore transport is shore parallel. Figure 4.3 shows
the components of sediment transport in relation to the breakwater and beach.
As the incoming waves are transmitted over the breakwater, part of the wave
energy is dissipated by the breakwater and part is reflected back offshore. Thus, the wave
energy impacting the area landward of the breakwater is decreased. As a result, the
offshore sediment transport rate will be attenuated due to the presence of the structure.
Also, a breakwater acts as a barrier to cross-shore sand transport in the bottom of the
water column. Under storm wave conditions, this will prevent sand on the beach from
being transported to the seaward side of the breakwater, and during mild wave conditions,
the breakwater also blocks onshore directed movement of sediment from the seaward
Longshore Transport I
Figure 4.3 Definition Sketch for Cross-Shore and Longshore Sediment
According to the continuity equation, the sediment volume change at a particular
position is determined by the gradients in sediment transport, rather than the transport
itself. Since the cross-shore sediment transport rate is almost zero at the breakwater
position, the gradient of transport becomes very significant. During erosive wave
conditions, this discontinuity of the transport rate will cause scour on the seaward side of
the breakwater, while under milder waves, scour may occur on the shoreward side of the
Due to the existence of the breakwater, there is a water set-up inside of the
structure. The water ponding inside induces flow in the longshore direction toward the
ends of the structure and may cause rip currents to offshore (as shown in Figure 4.1). As
a result, sediment inside the breakwater is carried by longshore currents to the ends of the
structure and may be transported offshore, or continue downstream. Although the cross-
shore transport might be somewhat restricted at the breakwater, the longshore sediment
transport due to ponding induced currents could be quite significant, which can lead to
substantial sediment erosion landward of the breakwater.
This chapter summarizes some of the major hydrodynamic studies of submerged
breakwaters. A brief summary is presented in Table 5.1, where KT and KR are the wave
height transmission and reflection coefficients, respectively. Among the previous studies,
Curren and Chatham (1977), Dean, Browder, Goodrich, and Donaldson (1994), and Dean
and Chen (1996) pertain to current characteristics and sediment transport in the vicinity of
Table 5.1 Summary of Relevant Literature
Year Type of Study Sediment Ponding KT KR
Adams & Sonu 1986 Review of Tanaka _
Ahrens 1987 Laboratory Study
Baba 1986 Review of Averin /
Curren & Chatham 1977 Model Study /
(Imperial Beach, CA)
Dattatri, Raman, & 1978 Labor y
Funke Laboratory Study
Dean, Browder, 1994 Lab y
Goodrich & Laboratory Study
GDonaldson (Vero Beach, FL)
Dean & Chen 1996 Field Study (Palm / / /
Table 5.1 Continued
Year Type of Study Sediment Ponding KT KR
Diskin, Vajda, & 1970 Structure Induced /
Goda 1967 Laboratory Study / /
Hall 1939 Laboratory Study / /
Johnson, Fuchs, & 1951 Analytical Flux /
Seelig & Walton 1980 / /
Van Der Meer & 1992 Review at Delft /
5.1 Wave Transmission/Reflection Studies
Utilizing artificial submerged breakwaters as shoreline protection was described
in the literature as early as 1939. Hall (1939) described a low artificial reef of precast
concrete, situated parallel to shore, in shallow water. The breakwater was intended to
cause sediment accretion for the beach near Hollywood, Florida, Hall (1939). Laboratory
experiments were conducted in conjunction with the design process to study the
breakwater impact on wave transmission of monochromatic waves of varying heights and
for various freeboard values (where freeboard is the depth from the top of the structure to
the water surface). The experiment led Hall to conclude that submerged breakwaters
placed parallel to the shore in shallow water could reduce the rate of littoral drift in the
lee of the breakwater. Hall also determined that vertical walled structures provided the
most effective means for attenuating wave height and that for protection from storm
waves, the structure height should be at least 80 percent of the water depth.
Johnson, Fuchs, and Morison (1951) applied an energy flux approach to evaluate
the transmission coefficient (KT, ratio of transmitted wave height to incident wave height).
Equation 5.1 represents the calculation of average energy flux above a submerged barrier
with crest at z=-R,
1 rT po 2 cosh2k(h +z) (5.1)
._ r- on2 dzdt (5.1)
T J -R cosh(kh)sinh(kh)
A transmission coefficient may be obtained by redistributing this portion of the
flux over the entire water column on the lee side of the breakwater, (Equation 5.2).
KT=1 sinh(2k(h+R)) +2k(h+R)
K = 1 (5.2)
such that KT depends on the freeboard, R.
Goda (1969) and Goda, Takeda, and Moriya (1967) present laboratory
measurements of wave transmission over submerged and emergent breakwaters. The
relevant tests were first published in 1968, with a re-analysis in 1969. The tests were
conducted with a breakwater 50 cm high and waves of eight second period, with wave
steepness H/L=0.14. The incident wave height (H,) and freeboard (R) were varied in the
tests. One last note on the parameters of Goda's laboratory measurements is that his tests
were conducted with a minimum breakwater thickness of 0.9 cm, (0.03 feet), the closest
case to a "thin walled vertical breakwater." Goda applies Healy's method for separating
incident and reflected wave components, as described in the following paragraphs.
Healy represents the total wave system as the sum of incident and reflected
-T =aicos(kx-ot)+KRaicos(kx+ot) (5.3)
whereHmlxa=2ai(1 +KR) and Hn =2ai(l -KR). Therefore, KR may be defined as:
The amplitude, IllI may be expressed as a function of distance, x.
Ill=a/((1 +KR)2+2KRcos(2kx)) (5.5)
It should be noted that Healy's method provides only an approximation of the
wave heights due to it's basis in linear wave theory. Healy's method assumes a
sinusoidal wave profile, whereas the actual wave profile contains many higher order
harmonics and associated non-linear effects, Dean (1991). This is noted by Goda and
therefore gives rise to the correction factors that he applies to "adjust for nonlinearities."
The paper published by Goda (1969), "Re-analysis of Laboratory Data on Wave
Transmission over Breakwaters," adds non-linear terms in an attempt to correct Healy's
method for Goda's experimental data set. According to Goda, the result of applying
Healy's method is that the incident wave height tends to be overestimated and the
reflected wave height underestimated. Based on his reanalysis, Goda presented the
following empirical formula for transmission coefficient, KT
fr R R
K =0.5 1 -sin- p--) for a-P-RP-a (5.6)
HI 2a H, H,
where a=2.0 and
0.1 for high mound breakwaters,
P =0.3 for medium mound breakwaters
The wave amplitude was expressed as 0.5 for low mound breakwaters
1 2 1 2
Ti=H, coskxcosot+-b22kH2 cos2kxcos2at+-b02kH2 cos2kx (5.7)
b02 =(cothkh +tanhkh) (5.8)
b 22=(3coth3kh -cothkh) (5.9)
The maximum and minimum wave heights were given by
Hm =2H, Hii=b 2kH2
Hi=-(Hmax +Hin) =H(1 +-b22kH,) (5.10)
HR =-(Hmx -Hmin) =H,(1 --b22kH,) (5.11)
where,H, and HR designate apparent incident wave height and apparent reflected wave
height, respectively. Therefore, KR was determined by the ratio of HR' to H,'. Figure 5.1
illustrates the influence of freeboard on both KT and KR, according to Equation 5.6 from
Upper Limit of
V + / -
S*Upp Lower Limit of
-2.5 -1.5 -0.5 0.5 1.5
Transmission Coeff. + Reflection Coeff.
Figure 5.1 Graph of Transmission and Reflection Coefficients (Goda 1969)
Also of relevance in Goda's article is his use of the following wave energy
where KE represents the proportion of the incident wave energy contained in the reflected
and transmitted waves. Figure 5.2 demonstrates the energy dependence on freeboard,
(Goda's Equation 5.12).
Figure 5.2 Plot of Experimental Data Set for Goda's Energy Equation
Goda (1969) also suggests that the following formula be utilized for the
calculation of the transmission coefficients of composite breakwaters, "based on the
principle of summation of the wave energies due to overtopping of the crest and passing
through the rubble mound:"
P R d2
0.25[1 -sint(P 1R2+0.1(1- R)
HT- a H, h
T I 0.1(1--)
for a->- R>-a
* = ~ -
II I U
____ U __ _U _
-2 -1.5 -1 -0.5 0 0.5
Another related study was conducted by Diskin, Vajda, and Amir (1970). It
focused on the ponding effect associated with the presence of low or submerged
breakwaters. According to Diskin, the main advantage of such structures is the low cost.
Two problems associated with this design: the efficiency of the breakwater in wave
height attenuation, and the "piling-up of water inside the protected area," Diskin, et al.
(1970). The article further states that much attention has surrounded the reduction in
wave height, whereas little is known about the piling-up phenomenon.
As Diskin noted, ponding appears to be dependent on the wave climate and also
on the local bathymetry (including breakwaters or other obstructions). Two instances
where ponding will be most noticeable are locations in which restrictions are placed on
longshore and/or crosshore flows, such as areas completely enclosed by breakwaters, for
example protected swimming areas, and locations where a breakwater of sufficient length
exists such that conditions at the center may be considered as two dimensional, as
modeled in this thesis.
According to Diskin, the piling-up phenomenon is an expression of the quasi-
equilibrium reached between the mean rate of water flowing into the protected zone by
waves breaking over the low or submerged breakwater, and that of water flowing out of
the protected zone as a result of the difference in mean water levels inside and outside.
The two flows are unsteady and periodic, having a period, T, equal to that of the wave
Also, note that Diskin's study was for permeable breakwaters. Diskin
approximated his results by the curve plotted in Figure 5.3, which defines a bell shaped
curve being symmetrical about the maximum ordinate at R/Ho=-0.7.
S0.5 --- -/ ---- ----
-2.5 -2 -1.5 -1 -0.5 0 0.5 1
Figure 5.3 Ponding Level as a Function of R/Ho, Diskin, et al. (1970)
Therefore, by fitting a Gaussian-type equation to the data points, the following
relationship was formulated:
l=0.6e -(0.7R H which is valid for the range -2.0 < < +1.5 (5.14)
Figure 5.4, on the next page, represents several values for ponding as estimated
with Equation 5.14.
The variance associated with the tests was reported to be in the range of 4% to
28%, with a "mean error of 10%," depending on magnitudes of the experimental
0 ....................... .... ..
0 0.5 1 1.5 2
R=0.0 R=0.5 R=1.0 R=2.0
Figure 5.4 Ponding Level as a Function of Incoming Deep Water Wave Height
variables, Diskin (1970). After trying to determine the influence of various parameters,
including deep water wave steepness (H0/Lo), non-dimensional depth (h/Ho), etc., it was
concluded that "none of these parameters had a significant effect in reducing the scatter of
values of the relative height of piling-up." In fact they concluded that the term (Ho/h),
only became relevant when larger than 1.0. The relative depth of the experimental data
was: 0.10 < -H < 0.83
One significant difference between the experimental set-up for the laboratory
experiments was that it was 2-dimensional, limiting flow to above and through the
breakwater. Chapter 7, the results section of this thesis will elaborate on this subject.
Diskin concludes that maximum piling-up will occur when significant overtopping takes
place such that flow fails to return seaward over the breakwater and only flows through
Dattatri, Raman, and Funke (1978) conducted experiments over a range of
breakwater configurations and freeboard values to determine transmission coefficients.
The conclusion of the authors was that the relative depth of submergence was the most
important parameter in the performance of submerged breakwaters. Quantitative data for
the experiments involving thin-walled barrier tests were not presented for analysis.
Seelig and Walton (1980), present a method for estimating the hydrodynamics in
the vicinity of offshore segmented breakwaters, including the seaward flow through the
gaps. Factors investigated which affect the flow rate include: breakwater freeboard, wave
height and period, breakwater length and spacing, number of breakwaters, distance
offshore, water depth, and shore attachment.
Volumetric rate of overtopping for an impermeable breakwater is given as:
qg"- H3) (p a (5.15)
R -R a
where Ho is the deep water wave height, Rup is the vertical height of run up on the
structure if the breakwater were high enough that no overtopping occurred, and Qo* and a
are empirical coefficients found in the Shore Protection Manual (U.S. Army, Corps of
Engineers, Coastal Engineering Research Center, 1977, Ch. 7).
Due to the buildup of water landward of the breakwater, additional return flow
will occur through the gap openings. The method presented by Seelig and Walton
represents the exit flow rate through the breakwater gaps via "a combined continuity-
energy equation for discharge."
Q=VAc=Cd,2ghb A, (5.16)
whereV is the average velocity, A, is the cross-sectional flow area, hb is the wave
breaking depth, Cd is an empirical coefficient that is influenced by many factors (a value
of 0.8 is suggested when analyzing the flow through the gaps).
At equilibrium, for existing wave conditions, and assuming incoming waves
orthogonal to the shoreline, the resulting condition is:
q 1- h N 2= (CdBds(N-1)+2CdAce) (5.17)
where N is the number of breakwaters, Ace is the cross-sectional flow area between the
breakwaters and shoreline at the end of the system, and B is the gap width between
Equation 5.17 can be represented in dimensionless form as:
It is also noted that values of V should be kept below 0.5 ft/sec for "extreme
design conditions," as higher values could transport significant amounts of sediment out
of the breakwater system, could also cause scour around the structure and be hazardous to
swimmers. This preceding methodology was intended as a "first approximation" of the
water velocity and flow rate through the breakwater gaps caused by overtopping, Seelig
and Walton (1980).
The study of wave transmission values for a submerged breakwater were analyzed
and presented by Adams and Sonu (1986) for a model study of an existing structure at
Santa Monica, California. A model study was conducted to assess the design
applicability of the Tanaka (1976), method for predicting transmission coefficients as a
function of freeboard and deep water wave height. The Adams-Sonu article presents a
three-dimensional model study that was used to establish transmission coefficients,
Adams & Sonu (1986).
The Santa Monica breakwater is approximately 610 meters long and positioned
approximately 610 meters from the shoreline, as of 1983 (considered as appropriate at the
time of the measurements and model study). The freeboard was estimated to be 1.6
meters below mean lower low water (MLLW) with a crest width of 13.4 meters. These
conditions vary considerably from the initial construction of the breakwater due to the
impact of many decades of attack from incoming waves, tides, storms, etc..., in which the
structure was transformed from an emergent structure with an elevation of 3 meters above
MLLW. The slope of the breakwater has also been accordingly altered, from initial
conditions of side slopes 1.25:1 to an "equilibrium" side slope of 2 horizontal to 1
The hydraulic model study, conducted by Offshore Technology Corporation, was
three-dimensional and designed to test various breakwater configurations. The freeboard
in the study was varied from 1.8 meters to an emergent extreme of -1.8 meters (recall that
freeboard is positive if the structure is submerged), with significant wave heights varying
from 1.9 meters to 4.1 meters.
The following figure demonstrates the impact of freeboard on KT for Tanaka's
study. Tanaka (1976) determined that the wave transmission was most dependent on the
depth of submergence, freeboard, and the breakwater crest width (Figure 5.5).
-- B/Lo=0.025 - B/Lo=0.050 - B/Lo=0.075 ---- B/Lo=0.100
Figure 5.5 Plot of Transmission Coefficients for Tanaka Study (1976)
Baba (1986) reviewed results of Averin and Sidorchuk (1967). Figure 5.6
displays the effect of freeboard to incident wave height ratio on the transmission
-2 -1.5 -1 -0.5 0
0.5 1 1.5 2 2.5
Figure 5.6 Plot of Values for Averin and Sidorchuk
Over 200 laboratory test were conducted by Ahrens (1987) in order to establish
stability, damage, and wave attenuation characteristics for various submerged rubble-
mound breakwater configurations. The following expression for wave height
transmission was based on an analysis of the wave data:
K1T( A 3/2
1.0+ h exp[C3 (_p R )C4( At ) (5.19)
h h Lmo d520 p
where C1=1.19, C2=0.26, C3=0.53, C4=0.0051, h=total water depth, h. =critical depth over
structure, At =cross sectional area, L, = wavelength of incident wave, dso = median stone
diameter, Hmo=deep water significant wave height, and R/Hmo = freeboard ratio (where
Van Der Meer and d'Angremond (1992) reviewed numerous studies of rubble
mound submerged breakwaters, and several experiments conducted at Delft Hydraulics in
the Netherlands. The barrier freeboard is cited as the dominant design parameter for
0 0.4 0.8 1.2 1.6 2 2.4 2.8
submerged structures. A counter-intuitive result proposed by Van Der Meer and
d'Angremond is that KT remains constant for 1.0 < < 2.0. As the structure height
decreases, and therefore R/Hi increases, it is expected that the transmission coefficient
would approach unity. Therefore, an asymptotic behavior of KT is expected as the relative
freeboard increases, (as R/Hi --, KT -1.0). Van Der Meer and d'Angremond presented
results for tests of both emergent and submerged breakwaters, but did not present findings
for the range of submerged breakwaters noted above, ie. where ,. is constant.
Most of the literature surveyed indicated that the amount of freeboard over the
structure was the most important variable in the performance of a submerged breakwater.
In most cases it is compared with the incident wave height, thereby defining the "relative
freeboard." The comparisons of the present model with the aforementioned authors are
presented in Chapter 7.
5.2 Sediment Transport and Current Velocity Studies
As discussed in Chapter 3, Curren and Chatham (1977) conducted literally
hundreds of tests comprising a model study for Imperial Beach, California. The study
was site specific in Southern California, but also extended to studies of multiple
breakwater configurations, groin fields and numerous other combinations of coastal
erosion countermeasures. However, only qualitative results were published for the
studies of single breakwater configurations.
Dean, Browder, Goodrich, and Donaldson (1994) conducted a model study of
various submerged breakwater configurations pertaining to a P.E.P. Reef installation at
Vero Beach, Florida. The model tests demonstrated significant current velocities in the
vicinity of a submerged breakwater. Breakwater configuration was also studied and
documented in this study, with the conclusion that breakwaters should be segmented, as
long uninterrupted breakwaters can lead to production of substantial longshore currents.
Dean and Chen (1996) summarize a 36 month field study of a submerged
breakwater installation of a P.E.P. Reef installation at Palm Beach, Florida. The study is
very thorough and presents data on wave heights in the vicinity of the breakwater, as well
as bathymetric changes in the vicinity of the structure. Chapter 7 will compare the results
of this study with a numerical model, developed in the following chapter.
6.1 Hydrodynamics and Hydraulics
This chapter will present the simple linear theory representing the interaction of
an incident wave train with a submerged breakwater system, including the ponding and
longshore flows that result from the structure. The adopted coordinate system is
described in Figure 6.1, where the y-axis is directed seaward, and the x-axis alongshore.
S x Shoreline
Figure 6.1 Definition Sketch Including
6.1.1 Analytical Model
As this thesis is concerned only with normally incident waves, the incoming,
landward directed mass transport will cause return flow over and around the breakwater.
Both of these variables will be expressed as a function of the wave setup, or ponding
elevation, landward of the breakwater, Ti. From linear wave theory we can determine that
the landward volumetric transport, qy, by the waves will be:
y -- (6.1)
where p is the density of water, C is the wave celerity, and E the wave energy density. As
demonstrated in Figure 6.1, due to the coordinate system, q, will be negative, ie., toward
the shore. Also, due to the ponding phenomenon, a wave setup will result. The net
seaward flow at the breakwater is expressed in linearized form as:
p =- + (6.2)
In this case, R, is considered a constant.
The total longshore flow, Qx, over the cross-section area inside of the breakwater
can be linearized as a function of the water surface elevation, rl, in the x-direction:
Qx- A (6.3)
in which, Rx, similar to Ry, is considered a constant associated with the shore-parallel
flow, and AY is the distance from the shoreline to the breakwater. Considering mass
conservation and combining Equations 6.2 and 6.3, we arrive at a linear second order
inhomogeneous partial differential equation:
R. ax (__ E =o (6.4)
ax pC Ry
Which can be simplified to yield:
a2- Rx ERx
ax2 AY R pC AY(6.5)
where the right hand term is equivalent to the forcing term.
The boundary conditions associated with this model are:(1) rj = 0 at the
breakwater ends and (2) n is symmetric about the breakwater centerline.
The solution of this equation is
1r =-- +a cosh k(x-Xo) (6.6)
in which k= Rx According to the two boundary conditions listed above, a E ,
A\ Ayy pC
and xo=0. Therefore,
S=- [ C- (6.7)
pC cosh kX/2
ER AY sinhkx
p C sinh( X) (6.8)
E pC cosh kX/2
pC Ry (6.9)
pCE cosh kX/2.
Equations 6.7, 6.8, and 6.9 may be normalized as:
-/= cosh kx
S_ cosh kx
ch X (6.11)
Qx_ sinh kx
sinh X (6.12)
Figure 6.2 illustrates the levels for ponding, qy, and Qx, as a function of position
along the breakwater. The breakwater is symmetric, so the total length would be 1000. It
is also important to note that rI is a maximum at the breakwater centerline, and that this
0.5 ................... ............................-.....
-1 I I II II
0 100 200 300 400 500
x, Position Along Breakwater
-Eta qy Qx
Figure 6.2 Plot of Normalized Values for Analytical Model
corresponds with zero longshore flow, Qx. Also, q, is negative due to the orientation of
the coordinate frame, but, note that the net flow increases (Iql),with increasing distance
from the centerline due to the associated reduced set-up.
6.1.2 Numerical Model
The numerical model utilizes standard hydraulic expressions for the weir
equations and simple linear wave theory to model breakwater configurations and physical
conditions to that of field and laboratory installations. The following section will
describe some features of the numerical model.
-1 --II---I----------- I --- 1 -- I --- 1 --
describe some features of the numerical model.
The form of the incoming wave form is:
rl,=- 2cos(ot+ky) (6.13)
The instantaneous flow over the crest of a fully submerged impermeable
breakwater may be represented by the following weir equation
(Z1 u+Z2 u) 2glZu-Z2u sign (6.14)
where, g = acceleration due to gravity, and
Z ,=I +R- (6.15)
where rll=surface elevation seaward of breakwater
where rl2=surface elevation landward of breakwater
and qnew is a function of the previous estimate of q and the present iteration. Therefore,
the longshore transport of water may be represented by equation 6.18.
g(ht)(AY)(At)Tr(1) -T(I-1) Q,(I)(qy(1) +qy(I-1))At
x( ) IQx()I 2(h)( (6.18)
which must be solved explicitly through the following system, and where AY= cross-
shore distance from the coast to the breakwater, At = time increment, r(I) is the ponding
value,fis the Darcy-Weisbach friction factor, and h, = total depth including ponding
landward of the breakwater.
The flow over the crest, in addition to any flow through the vents, is calculated for
1/100 of a wave cycle, and this value is then transferred into a ponding elevation for each
segment of the breakwater, and this in turn will then be subjected to the long wave
equation where Qx will result.
For cases in which the flow over the crest is critical, ie. the breakwater is
emergent for some portions of the wave cycle, and submerged for others, the flow over
the crest of the breakwater will be:
qyc=0.5484 n12 sign (6.19)
where rl, is the free surface elevation, varying with the wave profile.
One significant feature of the numerical model is the ability to include vents into
the breakwater configuration, modeling the P.E.P. Reef installation in Palm Beach, FL.
The vents introduce a supplemental flow that must be considered in the continuity
condition. Therefore, it is useful to consider the four possible flow regimes: 1) Flow over
the crest of the breakwater, such that the breakwater is submerged for all portions of the
wave cycle, 2) critical flow over the structure, ie. the breakwater alternates between
emergent and submergent, 3) full flow through the vents, ie. the vents are submerged for
all portions of the wave cycle, and 4) critical flow through the vents. These four flows
must then be combined to yield net cross-shore flow, and therefore yield six possible
q =0 __
S =0 -
Figure 6.3 Definition Sketch of Various Flow Possibilities
~T q 2
combinations, as shown in Figure 6.3, where qi is flow over the crest of the breakwater
and q2 is flow through the vents.
For the case of complete submergence for the entire wave profile, the flow
through the vents is expressed as:
q v() =(XL,)(Dc)(DE)F/ (sign) (6.20)
where XLv = the longshore proportion of the structure occupied by the vents, Dc= a
constant, and DEp=height of vent, and ZZ is a function of the incoming
wave profile and the present free surface elevation.
For critical flow through the vents, the unit discharge is:
where rc is the water surface elevation above the vent sill.
Therefore, the flow rates for the six combinations may be summarized as
described in Table 6.1
6.2 Sediment Transport
In order to estimate the additional sediment transport resulting from the ponding,
two simplified sediment models were developed to quantify the effects of the submerged
breakwater on the sediment budget. The following sections present a bedload transport
model and a suspended sediment transport model.
Table 6.1 Summary of Various Flow Rates
Flow q, q2 Total q,
A (6.14) (6.20) (Zu+Z2u) 2glZ -| Z2ulsign
+ XLVCDEp 2g Zsign
B (6.19) (6.20) 3
0.5484g1 sign + XLvDDEPZ2g ign
C 0 (6.20) XLvDcD sign
D 0 (6.21) 3
g(r c2 )XLvsign
E 0 (6.14) XLV(Zlu+Z2u) 2glZlu-Z2uign
F 0 (6.19) 3
*Note: ric, above, is the water elevation above the vent sill.
6.2.1 Suspended Load
Transport via suspended load mechanics encompasses sediment flow throughout
the water column. This model assumes that the suspended sediment concentration within
the surf zone will be unchanged from the case of a beach without a breakwater, and
therefore the additional sediment transport will be in accordance with the increase in the
water transport over that which would occur with normally oblique waves. The
additional sediment transport is defined as:
Qsus(i)=2Qx(Ima)K Y, t
where Qx (I,) is the flow rate at the end of the breakwater, Kpp is:
K =3KK- f- (6.23)
p 20(s -1)(I -p) r
where, K=0.8, K=0.77, f-Darcy Weisbach friction factor (=0.16), s=2.65, p=density of
sediment (=0.35), and Yr,, is a term relating the existing beach profile to an equilibrium
S A(0.78) (6.24)
where, H, = incoming wave height, A=Moore's sediment parameter, and AY=cross-shore
6.2.2 Bed Load
This bed load model takes into account the additional transport which is
considered proportional to the additional bed shear stress resulting form the wave
ponding behind the breakwater.
The average wave introduced shear stress inside the breakwater is:
The shear stress resulting from current is:
I,=K" c AY=K" pfQ
8 (AY)2 (h 2)
And since It=p g(s-1)(1 -p)Qbed' we can write an expression for the sediment transport
Qbed save- x Q max 2K "
K"=2.63 f Bz
where WBZ is the width of the wave breaking zone, and
RESULTS AND COMPARISONS
The numerical model presented in Chapter 6 may be adapted to simulate
laboratory and field conditions, and, therefore its results may be compared with those of
other researchers. This chapter will compare and contrast published field, laboratory, and
empirical relationships with data generated from the model.
7.1 Hydrodynamic Results of Submerged Breakwaters
7.1.1 Studies of Wave Attenuation
The wave attenuation due to a submerged breakwater depends primarily on the
freeboard and the incoming wave height. As Figure 7.1 illustrates, there is a reasonable
correlation between both the estimate of KT and KR for the model and the values of Goda
(1969). The model data follow the lower limit as established in Equation 5.6, for which
a=2.2 and P=0.8. The model results in Figure 7.1 are for the same conditions as the study
of Goda, Takeda, and Moriya (1967), ie. freeboard elevation (R), water depth (h), and
incoming wave height (Hi), were all consistent. It is also important to note that for a case
with R=-Hi, (an emergent breakwater with an elevation equal to the incoming wave
height), there will be no transmitted wave, due to the model basis on simple linear wave
theory, and therefore iC must be zero. The lab study of Goda, et al., includes the higher
order harmonics and non-linear effects of real waves, and therefore cannot be duplicated
with the model in its present form (a possible future advancement is the addition of non-
linear terms to the model to account for nonlinear effects).
Transmission Coeff. + Reflection Coeff. X Model kt A Model kr
Figure 7.1 Comparison of Goda (1967) Laboratory Data and Model Results
Figure 7.2 compares the conserved wave energy, KE (Equation 5.12), for Goda
experimental values, and predicted model estimates. .Note that for a breakwater elevation
equal to the incoming wave height (R=-Hi), the reflected wave height will be equal to the
incoming wave height and therefore,
KE=K +KR=02+1l =
-1.5 -0.5 0.5 1.5
-1.5 -1 -0.5 0 0.5
A Goda Value
* Model Predictioni
Figure 7.2 Comparison of Conserved Energy Measurements by Goda with Predictions by
Similar results for wave attenuation were found when model output was
compared with published data from Averin and Sidorchuk (1967), as well as Tanaka
(1976), as shown in Figure 7.3 and 7.4, respectively.
The comparison of model predictions with the nomograph of Averin and
Sidorchuk correlate fairly well for the more submerged breakwaters, but diverge in
_ ---- -- _---_-_-- -------------------
A A A A
-0.6 -0.2 0.2 0.6 1 1.4 1.8 2.2 2.6
Averin & Sidorchuk--Model
Figure 7.3 Comparison of Model and Averin and Sidorchuk (1967)
estimates when the breakwater becomes subaerial. For emergent breakwaters, Averin and
Sidorchuk predict KT to stabilize at approximately 20% of the incoming wave height,
whereas the model predicts K,= 0, for R < Hi. As both methods are applied to
impermeable breakwaters, the numerical model predictions would seem more realistic for
The study conducted by Tanaka was for wide crested breakwaters, and therefore,
in addition to R/Ho, the transmission coefficient is defined in terms of the breakwater
crest width, B, to deep water wave length, Lo, ratio (B/Lo). Therefore, the case of B/Lo =
0.025 is the most applicable to the assumption of the numerical model, ie. a relatively
narrow crested breakwater. Therefore, it is clear that due to the aforementioned
Figure 7.4 Comparison Between Numerical Model and Tanaka (1976)
contribution of crest width to reduced transmission, the numerical model should tend to
overestimate the transmission coefficient for the entire range of freeboard to wave height
values, which is not represented in the results. It is also important to note that for
emergent breakwaters with a surface elevation larger than the incoming wave height,
Tanaka predicts a slight rise in rr as the breakwater becomes more emergent. This result
is not expected, even for permeable structures in which transmission through the structure
may be the primary mode of wave transmission.
7.1.2 Studies of Ponding Elevation
Ponding elevation estimates are compared with those of Diskin, et al. (1970), as
shown in Figure 7.5. Because this study was conducted on rubble-mound (permeable)
structures, there will be a finite level of ponding/wave set-up associated with emergent
breakwaters that exceed the incoming wave height. It is also important to note that the
tests were conducted on breakwaters of trapezoidal cross-section, compared with the
computer simulation, where a finite crested impermeable vertical breakwater is modeled
(Diskin points out that the breakwater "acted as a broad crested weir," which clearly does
not equate with the numerical model being based in part on a sharp crested weir).
The numerical model results show only qualitative agreement with the
experimental results of Diskin, et al.. A major difference is that for the impermeable
barrier considered in the numerical model, the non-dimensional set-up rises to unity at
R/H and then is zero for smaller values of R/Hi. By contrast, for values of R/Hi smaller
than -1, wave induced set-up occurs through the permeable breakwater. As shown in
-2.5 -2 -1.5 -1 -0.5 0 0.5 1
R/HI (R/Ho, Diskin)
Figure 7.5 Comparison of Model Values with Diskin, et al. (1970)
Figure 7.5, Diskin, et al. estimate the maximum ponding to be 60 % of the incoming
wave height. This maximum occurs for R/Hi = 0.7. Since the numerical model is based
on an impermeable structure, and simulated as 2-dimensional, the predicted ponding
elevation will be greater than freeboard for emergent structures, where the incoming wave
height is larger than the top of the breakwater.
It is also important to note that no data of ponding elevations are known for any
field installations of breakwaters, so it is impossible to verify the model with full-scale
7.2 Studies of Sediment Transport
The introduction of a submerged breakwater may lead to an erosional tendency as
noted previously in this thesis. A study of a submerged breakwater installation at Palm
Beach, Florida, measured beach profiles and shoreline positions for a period of 35 months
(Dean and Chen 1996).
Evidence of the impact of the breakwater can be found in Figure 7.6, which
illustrates the average change in water depth for the regions near the submerged
breakwater, as shown in Figure 7.7. Dean and Chen (1996) noted that the net longshore
transport in the vicinity is north to south. The area north of the breakwater, Zone 1 and
Zone 2, encountered very little erosion, whereas the area influenced by the breakwater
0 60 120 180 240 300 360 420 480
Distance From Shoreline (feet)
North of Reef -*- Within Reef -. South of Reef
Figure 7.6 Plot of Longshore Average Profile Changes for July 1992 to June 1995 for
Palm Beach, Fl, PEP Reef Installation
was accompanied with severe erosion. The area landward of the breakwater, Zone 3,
experienced an average erosion of approximately 3.2 feet in depth. The region south of
the breakwater also experienced substantial erosion and this is attributed to the
interference of the longshore transport by the breakwater. It is equally important to note
that in the region seaward of the breakwater, zones 2 and 4 specifically, no erosion was
found, these patterns strongly suggest that the reef adversely impacted the shoreline.
The numerical hydrodynamic and sediment transport models were used to
simulate these conditions, and estimates of erosional volumes made. The actual erosion
rates were measured as -40,000 yd3/yr, Dean and Chen (1996), and the model estimates
Zone 1 Zone 2
Figure 7.7 Diagram of Zones in Vicinity of Breakwater
were for ~ 160,000 yd3/yr via the bedload transport model, 3,100 yd3/yr via suspended
load, and 100,000 yd3/yr for a factor known as Qsand (Qsand ccx, where C, is a constant).
S500000 - - -
0 100 200 300
Cross-Shore Distance (meters)
Figure 7.8 Numerical Model Sediment Erosion Volume
Estimates for P.E.P. Reef
It is important to note that the cross-shore distance is an important parameter in
estimating the sediment erosion volume, as shown in Figure 7.8. The figure demonstrates
that a relatively small change in cross-shore distance can result in dramatically different
estimates of erosion volumes. It is also important to note that the numerical model
includes no calibration factors, that the model estimate is within an order of magnitude of
the actual erosion, and that this erosion is a result of ponding landward of the submerged
breakwater. Figure 7.9 and 7.10 demonstrate the dependence of ponding elevation and
normalized model estimates of ponding elevation and sediment transport, respectively, as
a function of cross-shore distance, while maintaining constant values for all other
Figure 7.9 Numerical Model Estimation of Ponding Elevation for P.E.P. Reef
Figure 7.10 Normalized Plot of Sediment Transport and Ponding Elevations for
P.E.P. Reef Simulations
A final note relating the numerical simulations of the P.E.P. Reef is the estimate
of ponding elevations. Although no field data are available to compare, the estimate of
-2.2 millimeters seems reasonable. In summary, although the gross estimates of erosion
volumes are significantly different than documented in the field experiment, the
additional erosion due to the presence of the structure is supported.
100 200 300
Cross-Shore Distance (meters)
-w- Sediment Transport I
. . . . - . - -..
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
8.1 Summary and Conclusions
As many of the world's coastlines are currently experiencing shoreline erosion,
researchers have been seeking better ways to protect the beaches. Some of the more
innovative research efforts have been directed toward use of artificial seaweed, beach
dewatering, and submerged breakwaters.
With the goal of modeling hydrodynamics and sediment transport near a
submerged breakwater, analytical and numerical models were developed and compared to
published data. The numerical model presents estimates for wave attenuation, ponding
elevations and sediment transport in response to interactions of submerged breakwaters
The numerical model yields reasonable correlation with published empirical
wave height data from Goda (1969), Averin and Sidorchuk (1967), and Tanaka (1976).
Differences in the results are primarily attributed to the model being based on linear wave
theory. One drawback of linear wave theory is that for the case of an emergent
breakwater with crest at the same elevation as the incoming wave height, the transmission
coefficient must be zero.
The comparison of model data for ponding elevations is in qualitative agreement
with the laboratory investigation of Diskin, Vajda, and Amir (1970), for R/Hi > 0.5. For
emergent structures, (R/Hi < 0), calculated ponding elevations will be somewhat higher
than the breakwater crest.
The sediment transport estimates are only within an order of magnitude and
require the most improvement. The numerical model overestimates the erosion. In the
future, the use of a calibration coefficient, or an improved model for bedload/suspended
load transport may lead to better estimations.
The numerical model's results indicate that certain aspects of the model may
benefit from future effort. Removal of the linear wave restriction would improve
transmission coefficient and ponding elevations, especially for R < 0.
A second area that should be addressed is breakwater induced sediment transport.
The model developed here was based on preliminary concepts and could be improved
possibly by use of more complex relationships. Additionally, availability of more field
data would be useful.
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The author was born in Michigan City, Indiana, on February 10, 1971.
Michigan City was a small rural community located at the intersection of Lake Michigan,
the Wolverine State and the Boilermaker State. Upon graduation from Michigan City
Rogers, he took his studies to Purdue University, where he spent three years studying
aero/astro engineering. Upon further reflection, he discovered that after growing up on
the water, he spent many weekends and most afternoons either fishing on Lake Michigan,
or on the creek behind his home, he would have to find a career involving coastal fluids,
rather than the gaseous variety associated with airfoils. In fact most of his childhood
activities revolved around the water, either fishing, waterskiing, swimming, or snorkeling,
and eventually scuba diving.
Therefore, in the fall of 1993, and under the tutelage of Professor William L.
Wood, he entered the School of Civil Engineering at Purdue. He earned a Bachelor of
Science in Civil Engineering in 1994, studying hydraulics and environmental engineering.
Upon graduation, he took his studies to the Department of Coastal and Oceanographic
Engineering at the University of Florida, under the guidance of Professor Robert G. Dean.
Upon graduation in August of 1996, he planned to enter law school and then enter
the fields of patent, coastal and environmental law, as long as he could be guaranteed
frequent trips to the Florida Keys to scuba dive.