Citation
Hydrodynamics and sediment transport in the vicinity of submerged breakwaters

Material Information

Title:
Hydrodynamics and sediment transport in the vicinity of submerged breakwaters
Series Title:
UFLCOEL-96012
Creator:
Bootcheck, Michael Jonathan, 1971-
University of Florida -- Coastal and Oceanographic Engineering Dept
Place of Publication:
Gainesville Fla
Publisher:
Coastal & Oceanographic Engineering Dept., University of Florida
Publication Date:
Language:
English
Physical Description:
xiii, 95 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Breakwaters ( lcsh )
Sediment transport ( lcsh )
Beach nourishment ( lcsh )
Shore protection ( lcsh )
Hydrodynamics ( lcsh )
Coastal and Oceanographic Engineering thesis, M.S ( lcsh )
Dissertations, Academic -- Coastal and Oceanographic Engineering -- UF ( lcsh )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (M.E.)--University of Florida, 1996.
Bibliography:
Includes bibliographical references (leaves 76-82).
Statement of Responsibility:
by Michael Jonathan Bootcheck.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
36800141 ( OCLC )

Full Text



UFLICOEL-96/012


HYDRODYNAMICS AND SEDIMENT TRANSPORT IN THE VICINITY OF SUBMERGED BREAKWATERS by



Michael Jonathan Bootcheck Thesis


1996













HYDRODYNAMICS AND SEDIMENT TRANSPORT IN THE VICINITY OF SUBMERGED BREAKWATERS













By

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 1996












ACKNOWLEDGMENTS


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 committee.

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.

iii
























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 ...................................................... xi


CHAPTERS
1 INTRODUCTION .................................................1I
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
2.2.1.1 Beach nourishment............................ 6
2.2.1.2 Attached structures............................. 8
2.2.1.3 Detached emergent breakwater ...................10
2.2.2 Innovative Approaches............................... 11
2.2.2.1 Beach dewatering............................ 12
2.2.2.2 Artificial seaweed............................ 16
2.2.2.3 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


iv







4.2 Sediment Transport......................................... 31

5 LITERATURE REVIEW............................................ 34
5.1 Wave 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 Wave 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


v













LIST OF FIGURES


Figure Page

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 RIHo, 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


vi







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


vii







LIST OF SYMBOLS


a, Goda' s coefficient for eta values due to cos (at)

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

b02 Goda coefficient for nonlinear terms b22 Goda coefficient for nonlinear terms

Bv elevation of bottom of vent C Wave Celerity Cd Seelig's discharge coefficient C1,2.3,4 coefficients, Ahrens (1987)

d~o median stone size diameter Dc constant DEP height of breakwater vent e base of natural logarithms E wave energy per unit surface area (JpgH 2)
8
f Darcy-Weisbach friction coefficient (0. 16)

.7 ~ wave energy flux I

g acceleration due to gravity h total water depth


viii







hc critical depth over weir

ht Depth of water at structure including ponding effects

(Numerical Model Variable) H Wave height Ho Deep water wave height HI.RT 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, 2itJL K 0.77

K" coefficient

KPP coefficient L wavelength

I-10 deep water wave length N Number of breakwaters P.E.P. Prefabricated Erosion Prevention Qsand volume of sediment moved

QSUS volume of suspended load sediment transport Qbed volume of bedload sediment transport

Q. water transport rate alongshore


ix







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 s 2.65

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 Y~fi ratio of waveheight to depth

ZC Diskin' s distance from top of breakwater to ponding

elevation



ac Goda' s empirical parametric approximations

Goda' s empirical parametric approximations At incremental time unit AX length of individual units


x







AY distance from shoreline to breakwater Il free surface elevation of incoming wave 1max maximum level of free surface seaward of reef 11lmin minimum level of free surface seaward of reef Tl2max maximum level of free surface landward of reef 112min minimum level of free surface landward of reef 11 surface elevation

TI ponding elevation K 0.8

KT transmission coefficient KR reflection coefficient V kinematic viscosity 7C pi

p density (0.35) a wave angular frequency, phase angle ( =27r/T)


xi













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 By

Michael Jonathan Bootcheck

August 1996


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 lee.

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


xii







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 countermeasures.


xiii












CHAPTER 1
INTRODUCTION


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


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.












CHAPTER 2
EROSION CONTROL ALTERNATIVES



2.1 Overview



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


3






4


widely accepted methods of shoreline protection, as well as presenting some of the more novel approaches.


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







5


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 Sediment Movement

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 Diffraction View Headland Control of Wave Re-distribution of Height and Direction Incident Wave by Diffraction and Energy Evenly Reflection

Artificial Beach Reduction of Wave Control of Longshore Energy by Breaking and Cross-Shore and Energy Loss in Sediment Transport Permeable Layer

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.







6


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.

2.2.1.1 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.







7


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).







8


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 and Comparisons.

2.2.1.2 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)).







9


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







10


system of nourishment/groin construction can help to lessen the impact to the downdrift areas.

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, Florida.

2.2.1.3 Detached emergzent 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







I1I

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







12


seaweed and submerged breakwaters have also been popular research topics and their impacts are discussed in the following sections.



2.2.2.1 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







13


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 accessability 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







14

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







15

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.






16


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.

2.2.2.2 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).







17

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 Europe.

The main emphasis for the European interest in artificial seaweed centered around two erosional conditions: excessive tidal scour in secondary inlet channels and localized







18

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 polypropylene strands.

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







19

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 198 1, 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 (198 1) 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







20

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 movement.

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 (erosional), 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 Ojust 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







21


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 prescribed manner?

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.

2.2.2.3 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







22

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.













CHAPTER 3
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 rubblemound configurations, Shore Protection Manual (1984), and broad crested structures are also well documented, Diskin (1970). However, little research has been collected on


23







24


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







25


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 submerged breakwater.







26


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.













CHAPTER 4
EFFECTS OF SUBMERGED BREAKWATERS




4.1 Hydraulics/Hydrodynamics




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 EC) 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 Figure 4. 1.

The percentage of water that moves in either direction will depend primarily on two factors, the incoming wave energy (E=-IpgH 2), and the bottom bathymetry. For
8
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


27







28

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 Stern (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.







29


Coast Trough Breakwater 7





Elevation











x


Plan

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 (197 1), Dalrymple and Dean (197 1), Dalrymple (197 8), among others.

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







30

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


Sea Floor



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







31

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







32


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 side.













Cross-Shore Transport





q C
xI
Longshore Transporti


Figure 4.3 Definition Sketch for Cross-Shore and Longshore Sediment
Transport




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







33


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 structure.

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 crossshore 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.















CHAPTER 5
LITERATURE REVIEW


This chapter summarizes some of the major hydrodynamic studies of submerged breakwaters. A brief summary is presented in Table 5. 1, where 1KT 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 submerged breakwaters. Table 5.1 Summary of Relevant Literature Year Type of Study Sediment Ponding KT K, Transport/
Current
Velocities

Adams & Sonu 1986 Review of Tanaka V________Ahrens 1987 Laboratory Study _____Baba 1986 Review of Averin and Sidorchuk

Curren & Chatham 1977 Model Study
____(Imperial Beach, CA)_____Dattatri, Raman, & 1978 Laboratory Study Funke

Dean, Browder, 1994 Laboratory Study Goodrich & (Vero Beach, FL) DonaldsonI

Dean & Chen 1996 Field Study (Palm// /
__________________ ____ I Beach, FL)______ _____


34








35


Table 5.1 Continued_______Year Type of Study Sediment Ponding KCT K, Transport/
Current
Velocities

Diskin, Vajda, & 1970 Structure Induced V Amidr Ponding ____Goda 1967 Laboratory Study V (Empirical)______Hall 1939 Laboratory Study V V Johnson, Fuchs, & 1951 Analytical Flux V Morison Approach ____Seelig & Walton 1980 V V Van Der Meer & 1992 Review at Delft V d'Angremond Netherlands



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







36


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 stormn waves, the structure height should be at least 80 percent of the water depth.

Johnson, Fuchs, and Morison (195 1) 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,


=I [TfO G2 COsh 2k(h +z) ddt (5.1) TJ0O-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).



K T=j 1 sinh(2k(h +R)) +2k(h +R) (5.2) N sinh(2kh) +2kh


such that 1T 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=0O. 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







37

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 components.


-q =aicos(kx-jt) +YRaicos(kx+at) (5.3)



wherel~ma,=2ai(l -sKR) and H =2a1( i-KR). Therefore, KR may be defined as:


K-R = mxmn(5.4) Hfmax +H.i



The amplitude, hl I may be expressed as a function of distance, x.

hi =a1( +K)2 +2KRcos(2hx)) (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







38


reflected wave height underestimated. Based on his reanalysis, Goda presented the following empirical formula for transmission coefficient, KT


Kt= 0.51 -sn 7 R o ra~p2 R P-cc(5.6) H, sin2a H-~) H,




where ax=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 21 2 Ti=H, coskxcosojt+ b22kH; cos 2kxcos 2ut+-b2kH; cos 2kx (5.7)
2 4



b02 -(cothkh +tanhkh) (5.8)
2



b 22=-(3coth 3kh -cothkh) (5.9)
4



The maximum and minimum wave heights were given by

Hm. =2H1 H=b 2H


H= 1-(H~a +H.,i) =HI( 1 +b22kH,) (5.10)
2 mx2



HR I (Hmax -Hmin) =HI( 1 1-b22kH,) (5.11)
2 2


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








39


illustrates the influence of freeboard on both KT and KR, according to Equation 5.6 from Goda (1969).


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 conservation relationship:


2 +K2
KE-KR+KT


(5.12)


where 1'zE 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).


1 +

~0.g +
0.)6
+ +r
1 01

0.4

0.2 Limitt 0

-20.2 -15-. .
HJ~




STransmission Coeff. + Reflection Coeff.







40


I R
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:"


0.25[1 -i- R
HT= ja H, h T H{ 0.1(1_d)
h


for a->R >
H,

fo r 13-a
H,


W 0.6 Ca



~0.4 a) 0.2
cc


* = ~U


U..
U
____ U ____ U ___~- -~
U U U U


n


1.5 2


-2 -1.5 -1 -0.5 0 0.5


-2.5


(5.13)







41


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 quasiequilibrium 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 train.

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 RIH0=-0.7.








0.8 0.7 0.6 0.5

0.4 0.3

0.2 0.1

0
r1-


0 0.5


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:


a=06e (0.7+R IH,)2 which is valid for the range -2.0 < R~ < +1.5 (5.14)
HO H0


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


42


[Emnrgn S ubmeraed~


0



0


-2 -1.5 -1 -0.5
R/Ho


1


.5







43


-J
w




z

0
0 .. ............

0 0.5 1 1.5 2 Ho (meters)



-R=0.0- -R=0.5.. R=1.0,,- R=2.I

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 (H01L0), non-dimensional depth (h/H0l), 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
h
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







44


place such that flow fails to return seaward over the breakwater and oniy flows through the breakwater.

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:



q =g(?". H0)y) 112( 0' 108 (5.15)




where HO is the deep water wave height, R. is the vertical height of run up on the structure if the breakwater were high enough that no overtopping occurred, and Q.* 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






45


represents the exit flow rate through the breakwater gaps via "a combined continuityenergy equation for discharge.


Q=VAC=CdV/~ghib A, (5.16)



where V 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:


1, (I-L) N=2Zh(CdlBd(N-1)+2CdeAc) (5.171)
"1


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 breakwaters.

Equation 5.17 can be represented in dimensionless form as:


V
V= (5.18)




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







46


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-S onu 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 vertical (2: 1).

The hydraulic model study, conducted by Offshore Technology Corporation, was three-dimensional and designed to test various breakwater configurations. The freeboard







47

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 rT 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).


U
0 4
U
0
C-)
0 (i2


I
H


1

0.9 0.8 0.7 0.6 0.5

0.4 0.3

0.2 0.1

0


-0.5 0
R/Ho


0.5


I- BILo=0.025 -BILo=0.050 --- B/Lo=O.075


1 1.5 2 2.5


---I- B/Lo=O. 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 coefficient.


-2


-1.5 -1


OOF


Z.5







48


1 -.
a)
0
0)0. 6



co0.2 -0
-0.4 0 0.4 0.8 1.2 1.6 2 2.4 2.8 R/Hi


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 rubblemound breakwater configurations. The following expression for wave height transmission was based on an analysis of the wave data:



K T ho+ ( ) '2)1 e c 3 ( R ) C ( A t 3/2 ( 5 .1 9 )




where C 1=1.19, C2=0.26, C3=0.53, C4=0.0051, h=total water depth, h. =critical depth over structure, At =cross sectional area, LP = wavelength of incident wave, d~o= median stone diameter, Hmo=deep water significant wave height, and RIHm. = freeboard ratio (where RIH,0 <1.0).

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







49


submerged structures. A counter-intuitive result proposed by Van Der Meer and d'Angremond is that CT remains constant for 1.0 < R!~ < 2.0. As the structure height decreases, and therefore RIH1 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/H1 --a, 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 ic., 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.






50


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.












CHAPTER 6
METHODOLOGY: FORMULATION



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.


Breakwater











x Shoreline

Figure 6.1 Definition Sketch Including Coordinate Frame


51







52


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, i. From linear wave theory we can determine that the landward volumetric transport, qY, by the waves will be:


qy=- -(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, qY 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:



qy CR (6.2)




In this case, RY is considered a constant.

The total longshore flow, Q,. over the cross-section area inside of the breakwater can be linearized as a function of the water surface elevation, 11, in the x-direction: Q"=- AYarj (6.3) RX ax



in which, R,,, similar to RY, is considered a constant associated with the shore-parallel







53


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: a('&YaL)
R., ax +( E =0 (6.4)





Which can be simplified to yield:


a2ij R x ERX
1=-(65 aX2 AYRY PCAY(65


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) Tj is symmetric about the breakwater centerline.

The solution of this equation is

ER= L- +a cosh k(x-x0)(6)





in which k= Rx.According to the two boundary conditions listed above, a= -fER,
SAY yP pC
and x0=0. Therefore,
Ey,_coshk1
= [ (6.7) p C cosh kX/21







54


ER AY sinhkx
QXP CRX in~ X) (6.8)

2


ERY[i coshkx] q =-E~ +pC Lcosh kX2~ PC R Y (6.9) E coshkx]
P C cosh kX/2J



Equations 6.7, 6.8, and 6.9 may be normalized as:


-= cosh kx T1 cosh k X (6.10)
2



q_ -cosh kx cohkX (6.11)
2




QFl sinh kx sinh kX(6.12)
2





Figure 6.2 illustrates the levels for ponding, qY, and Q, 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 il is a maximum at the breakwater centerline, and that this







55


0.




0.






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, Q.* Also, qY is negative due to the orientation of the coordinate frame, but, note that the net flow increases (Iqyl),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.







56


The form of the incoming wave form is: H.
I"1=-2i cos(oit+ky) (6.13)




The instantaneous flow over the crest of a fully submerged impermeable breakwater may be represented by the following weir equation qy()=(Z1 +Z2 u) V2gIZ1u-Z2uI sign (6.14)
2


where, g =acceleration due to gravity, and z iI R-qNEW (6.15)


where Tj I=sur face elevation seaward of breakwater


Z~=1++qNEW (6.16) where T12=surface elevation landward of breakwater



Sign. IU-Z2 (6.17)
Iu Z2u




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.







57


QI- g(ht)(AY)(At)rI(J) -T(I- 1) Q,,(I)(q,(1) +q,(I- 1))At Q Q((') Ax 1 IfA Q.,(1)I 2(ht)(A) (6.18) 1fA)8h 2 AY



which must be solved explicitly through the following system, and where AY= crossshore distance from the coast to the breakwater, At = time increment, 11(I) is the ponding valueJf is the Darcy-Weisbach friction factor, and ht = 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=0.5484Vg- 13/ sign (6.19)


where il 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








58


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


(A):










:q 1=0 .






(C)


(E)


* q









(B) q1O
q







* (D)





1 7 O




H


(F)


Figure 6.3 Definition Sketch of Various Flow Possibilities







59


combinations, as shown in Figure 6.3, where q, 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:





where XLv = the longshore proportion of the structure occupied by the vents, Dc= a constant, and D~p=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:


3




where m~c 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.







60


Table 6.1 Summary of Various Flow Rates
Flow q, q2 Total q
Geometry ____ ________________________________A (6.14) (6.20) (Z+Z)2gZ ZIsn



B (6.19) (6.20) 3
0.5484 1 Csign + X~~DP g~g C 0 1(6.20) X~DDp2-g~g D 0 (6.21) 3 E 0 (6.14) Xl(Z+Z)2gZ-ZIsn

2

F 0 (6.19) 3

0. 5 484XL Vg-l 2Sign



*Note: il., 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:


Q~(i)=2Qx(IjKpt (6.22


(6.22)







61

where Q., (I) is the flow rate at the end of the breakwater, KPP is.


K =3r, fK (6.23)




where, K~=0.8, K=0.77, ftDarcy Weisbach friction factor (=0. 16), s=2.65, p--density of sediment (=0.35), and Y,,,, is a term relating the existing beach profile to an equilibrium profile:



A__0.78_1 (6.24) ra t (AY)



where, H, = incoming wave height, A=Moore's sediment parameter, and AY=cross-shore distance.


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:


-1
AY (6.25)


The shear stress resulting from current is:







62


=L 2
8


(6.26)


Waves


(6.27)


Current


I,=K"-rAY=K" pfQ~Ww
8 (A]0)2 (h 2)


(6.28)


And since I1=P g(S-1)(1 -P)Qbed' we can write an expression for the sediment transport as:


(6.29)


Qbed('ave )= x (Imax )2K //


where,

K"=2.63 f. BZ 8(s -1)(1 -p)g(AY*h)

where WBZ is the width of the wave breaking zone, and


WBZ=(Yrat(AY)(.1


(6.30)


(6.31)













CHAPTER 7
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


63







64

theory, and therefore CT 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 nonlinear terms to the model to account for nonlinear effects).





AAL

0.87
~ 0.8

-.A "
00.6- Ar4) pper iLiiht of / A
TLransimsillf
ct Coetfficienit XX

0.40


~0.2-S Loweriit of Transmission

0
-2.5 -1.5 -0.5 0.5 1.5
RIHi

*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,


K =K 2 +K =0+2= (71


(7.1)


















w



03.8





oO.4



0
o


-2.5 -2


-1.5 -1 -0.5 0 0.5
R


IA Goda Value


1


e Model Predictionj


Figure 7.2 Comparison of Conserved Energy Measurements by Goda with Predictions by Numerical Model


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


65


A 1


A~ AA A

A ~~ AA A


U


1.5 2







66


-0.6 -0.2 0.2 0.6 1 1.4 1.8 2.2 2.6
R/Hi

Averin & Sidorchuk- ModelI

Figure 7.3 Comparison of Model and Averin and Sidorchuk (1967)


estimates when the breakwater becomes subaerial. For emergent breakwaters, Averin and Sidorchuk predict iC,. to stabilize at approximately 20% of the incoming wave height, whereas the model predicts lCT= 0, for R <5 H_. As both methods are applied to impermeable breakwaters, the numerical model predictions would seem more realistic for this range.

The study conducted by Tanaka was for wide crested breakwaters, and therefore, in addition to WIHO, 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


Z0.8

0
0
C
0
*c5 0.4


CZ,


A


0000OF 'OOK
0000000,

loo,
/010 oool







67


0.9- _ __ - -_
0.8


U


0.37
0.2
0.1 -.... .7 . _. .0

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
R/Ho


F BJTo=0.025 BILo=0.050 - BILo=0.075 BILo=0. 100 Model

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 ir 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)







68


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/H1. By contrast, for values of R/H1 smaller than -1, wave induced set-up occurs through the permeable breakwater. As shown in








0.8


0

II
S0.6
0~
CL 0.4
0*


-2.5 -2 -1.5 -1 -0.5 0 0.5 1 R/HI (R/Ho, Diskin)
.MODEL- Diskin

Figure 7.5 Comparison of Model Values with Diskin, et al. (1970)







69


Figure 7.5, Diskin, et al. estimate the maximum ponding to be 60 % of the incoming wave height. This maximum occurs for R/H1 = 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 installation elevations.


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 I and Zone 2, encountered very little erosion, whereas the area influenced by the breakwater







70


0 60 120 180 240 300 360 420 480 Distance From Shoreline (feet)


j.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


2
.4-


0) c:0 -6
C

cD -8


Er9ef








71


Notth
Zone 1 Zone 2


Breakwater


a~Zone 3








Zone 5

So~


Zone 4







Zone 6

h


2, 000' 4,000' 2,000'


240' 240'
Figure 7.7 Diagram of Zones in Vicinity of Breakwater



were for 160,000 yd3/yr via the bedload transport model, 3, 100 yd 3/yr via suspended load, and 100,000 yd 3/yr for a factor known as Qand ( QsanP = x I where C, is a constant).


100 200 300
Cross-Shore Distance (meters)


400 500


2000000


E 1500000E
0 o0 1000000.



0
0)


. ~ ~ ~ ~ ~ ~ ~ ~ cap .rs~ .A .... .... ....


Figure 7.8 Numerical Model Sediment Erosion Volume Estimates for P.E.P. Reef







72


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 parameters.



0.0035S 0.003 .. . . . . . . . . .


0)0.0025 .. . . . . . . . .

0
I






0.001 I
0 100 200 300 400 500 Cross-Shore Distance (meters)



Figure 7.9 Numerical Model Estimation of Ponding Elevation for P.E.P. Reef







73


1


0.8


S0.6






0.


.. . . . . . .

.. . . . . . .

---------


100 200 300
Cross-Shore Distance (meters)


-w- Sediment TransportI


I -w Ponding


0


I I1
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.


'~rn i2 I
400 500


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


I
400


500













CHAPTER 8
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 and waves.

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.


74







75

The comparison of model data for ponding elevations is in qualitative agreement with the laboratory investigation of Diskin, Vajda, and Amir (1970), for R/H1 > 0.5. For emergent structures, (R/T1 < 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.


8.2 Recommendations



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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Pages 83-94
missing fro m original













BIOGRAPHICAL SKETCH


The author was born in Michigan City, Indiana, on February 10, 197 1.

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.


95